News <2008>

December 2008

Dec 29, 2008

Factor tables of this page will be updated in mid-January. Until then, contributions are kept on the web server. You can reserve numbers as usual. If you forgot your reservation keys, tell so by email.

My Pentium 4 processor could not withstand demanding programs and broke down. Take care for your CPU!

Dec 26, 2008

I'm afraid that I can't update this page for several days or a week because my computer crashed yesterday.

Dec 25, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(38·10¹⁴⁵+61)/9 = 4(2)₁₄₄9_<146> = 7 · 89 · 4211 · 240030140333_<12> · 6318701319397581967_<19> · C110

C110 = P42 · P68

P42 = 959520805192593881541714464704553517162347_<42>

P68 = 11059100304528524565462268921955338143239467920276603381903889550329_<68>

Number: n
N=10611436828906870090522936495968919633890384936146829850407470739275500463086914188108300526561796213920262163
  ( 110 digits)
SNFS difficulty: 146 digits.
Divisors found:

Thu Dec 25 11:57:28 2008  prp42 factor: 959520805192593881541714464704553517162347
Thu Dec 25 11:57:28 2008  prp68 factor: 11059100304528524565462268921955338143239467920276603381903889550329
Thu Dec 25 11:57:28 2008  elapsed time 00:35:41 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.47 hours.
Scaled time: 13.66 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_4_2_144_9
n: 10611436828906870090522936495968919633890384936146829850407470739275500463086914188108300526561796213920262163
type: snfs
skew: 1.10
deg: 5
c5: 38
c0: 61
m: 100000000000000000000000000000
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 1870001)
Primes: RFBsize:114155, AFBsize:114048, largePrimes:12063139 encountered
Relations: rels:11157151, finalFF:260073
Max relations in full relation-set: 28
Initial matrix: 228269 x 260073 with sparse part having weight 43425032.
Pruned matrix : 222316 x 223521 with weight 33941924.

Msieve: found 1169180 hash collisions in 12167702 relations
Msieve: matrix is 285178 x 285426 (74.7 MB)

Total sieving time: 7.09 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,56,56,2.5,2.5,100000
total time: 7.47 hours.
 --------- CPU info (if available) ----------

(8·10¹⁸⁸+1)/9 = (8)₁₈₇9_<188> = 10867 · C184

C184 = P72 · P113

P72 = 200566861506992331136426364484679792245665453316940240273757774540395067_<72>

P113 = 40782949523419614037769977548545749947635754809093559084419918633991991426423339650836469118542851487206338102201_<113>

Number: n
N=8179708188910360622884778585523961432675889287649663098268969254521844933182008731838491661809964929501140046828829381511814566015357402124679202069466171794321237589848982137562242467
  ( 184 digits)
SNFS difficulty: 190 digits.
Divisors found:

Thu Dec 25 21:52:08 2008  prp72 factor: 200566861506992331136426364484679792245665453316940240273757774540395067
Thu Dec 25 21:52:08 2008  prp113 factor: 40782949523419614037769977548545749947635754809093559084419918633991991426423339650836469118542851487206338102201
Thu Dec 25 21:52:08 2008  elapsed time 04:14:57 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20050930-k8
Total time: 69.18 hours.
Scaled time: 139.12 units (timescale=2.011).
Factorization parameters were as follows:
name: KA_8_187_9
n: 8179708188910360622884778585523961432675889287649663098268969254521844933182008731838491661809964929501140046828829381511814566015357402124679202069466171794321237589848982137562242467
type: snfs
skew: 1.66
deg: 5
c5: 2
c0: 25
m: 100000000000000000000000000000000000000
rlim: 9000000
alim: 9000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 8600001)
Primes: RFBsize:602489, AFBsize:602100, largePrimes:34905775 encountered
Relations: rels:31238877, finalFF:727045
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 3975978 hash collisions in 36541534 relations
Msieve: matrix is 1696807 x 1697055 (460.7 MB)

Total sieving time: 68.38 hours.
Total relation processing time: 0.80 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,9000000,9000000,29,29,58,58,2.5,2.5,100000
total time: 69.18 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830490)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830462)
Total of 4 processors activated (22643.71 BogoMIPS).

Dec 25, 2008 (2nd)

By Sinkiti Sibata / Msieve

(38·10¹⁴³+61)/9 = 4(2)₁₄₂9_<144> = 3² · 23 · 8898879841_<10> · 576568337208290100918143_<24> · C108

C108 = P51 · P58

P51 = 247067337455777187755752491982412454361833257217269_<51>

P58 = 1609049019393037299239339702182176490310075105569308816401_<58>

Number: 42229_143
N=397543457057266918884845579618051966809384919381927176588582112286687485108113865531283414443127005287628869
  ( 108 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=247067337455777187755752491982412454361833257217269
 r2=1609049019393037299239339702182176490310075105569308816401
Version: 
Total time: 9.34 hours.
Scaled time: 18.43 units (timescale=1.972).
Factorization parameters were as follows:
name: 42229_143
n: 397543457057266918884845579618051966809384919381927176588582112286687485108113865531283414443127005287628869
m: 50000000000000000000000000000
deg: 5
c5: 304
c0: 1525
skew: 1.38
type: snfs
lss: 1
rlim: 1900000
alim: 1900000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1900000/1900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [950000, 1850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 262775 x 263023
Total sieving time: 9.34 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000
total time: 9.34 hours.
 --------- CPU info (if available) ----------

(38·10¹⁴⁷+61)/9 = 4(2)₁₄₆9_<148> = 167 · 2369773339_<10> · 294392469467_<12> · C125

C125 = P39 · P86

P39 = 390767166238674756702854534057738664529_<39>

P86 = 92741271271455106967496554922563178454113145520981313433082313450604481966509315597931_<86>

Number: 42229_147
N=36240243768118729202943463309695426736944896402283016562377648348010345900851403545823189583259160747606835955616325055489499
  ( 125 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=390767166238674756702854534057738664529
 r2=92741271271455106967496554922563178454113145520981313433082313450604481966509315597931
Version: 
Total time: 11.97 hours.
Scaled time: 30.70 units (timescale=2.564).
Factorization parameters were as follows:
name: 42229_147
n: 36240243768118729202943463309695426736944896402283016562377648348010345900851403545823189583259160747606835955616325055489499
m: 200000000000000000000000000000
deg: 5
c5: 475
c0: 244
skew: 0.88
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 2550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 357888 x 358136
Total sieving time: 11.97 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 11.97 hours.
 --------- CPU info (if available) ----------

(13·10¹⁴⁹-7)/3 = 4(3)₁₄₈1_<150> = 137 · 23119651 · C141

C141 = P57 · P84

P57 = 188970213715321747672299761534754833377917059582227123669_<57>

P84 = 723980555610444002576019194415271366760489277242380215274116190741913804171160915877_<84>

Number: 43331_149
N=136810760319442984511388306121793604504251223416095814639746515650962970987884593570645608634044828921380847408566690807883000354617384592713
  ( 141 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=188970213715321747672299761534754833377917059582227123669
 r2=723980555610444002576019194415271366760489277242380215274116190741913804171160915877
Version: 
Total time: 17.52 hours.
Scaled time: 36.01 units (timescale=2.055).
Factorization parameters were as follows:
name: 43331_149
n: 136810760319442984511388306121793604504251223416095814639746515650962970987884593570645608634044828921380847408566690807883000354617384592713
m: 1000000000000000000000000000000
deg: 5
c5: 13
c0: -70
skew: 1.40
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 449125 x 449373
Total sieving time: 17.52 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 17.52 hours.
 --------- CPU info (if available) ----------

Dec 25, 2008

By Serge Batalov / Msieve-1.39

(13·10¹⁵⁷-7)/3 = 4(3)₁₅₆1_<158> = 17³ · 67 · 137 · 769 · C148

C148 = P45 · P104

P45 = 123302230368263597667057025479304489207485833_<45>

P104 = 10134041800873407971458001266515153364324752965728397706141656301510332896590942027080433617388959869489_<104>

SNFS difficulty: 159 digits.
Divisors found:
 r1=123302230368263597667057025479304489207485833 (pp45)
 r2=10134041800873407971458001266515153364324752965728397706141656301510332896590942027080433617388959869489 (pp104)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.525).
Factorization parameters were as follows:
n: 1249549956692905843078530648495289271477668421273383397930121240701021840408969782908108656684854663018608144097023393943249861817083459645496449337
m: 20000000000000000000000000000000
deg: 5
c5: 325
c0: -56
skew: 0.70
type: snfs
lss: 1
rlim: 3100000
alim: 3100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3100000/3100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1550000, 2950001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 577511 x 577759
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,52,52,2.4,2.4,100000
total time: 20.00 hours.

(38·10¹⁷³-11)/9 = 4(2)₁₇₂1_<174> = 383 · C172

C172 = P77 · P95

P77 = 21373934917885229960501801036667767687297501292726057634758836826598560231947_<77>

P95 = 51577208181595520712952190859726794005821242274496299179553509825685887968828943498649093422521_<95>

SNFS difficulty: 175 digits.
Divisors found:
 r1=21373934917885229960501801036667767687297501292726057634758836826598560231947 (pp77)
 r2=51577208181595520712952190859726794005821242274496299179553509825685887968828943498649093422521 (pp95)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 1102407890919640266898752538439222512329561937917029300841311285175514940527995358282564548883086742094574992747316507107629823034522773426167682042355671598491441833478387
m: 50000000000000000000000000000000000
deg: 5
c5: 304
c0: -275
skew: 0.98
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 8200001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1149407 x 1149655
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.5,2.5,200000
total time: 70.00 hours.

(38·10¹⁶³+43)/9 = 4(2)₁₆₂7_<164> = 1409 · C161

C161 = P52 · P109

P52 = 4810957160735656694134600221951725247720036705800339_<52>

P109 = 6228717072530466781791563604942513648430182164800452761903679474999292240561911205887774266569403833476578177_<109>

SNFS difficulty: 165 digits.
Divisors found:
 r1=4810957160735656694134600221951725247720036705800339 (pp52)
 r2=6228717072530466781791563604942513648430182164800452761903679474999292240561911205887774266569403833476578177 (pp109)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.316).
Factorization parameters were as follows:
n: 29966091002286885892279788660200299660910022868858922797886602002996609100228688589227978866020029966091002286885892279788660200299660910022868858922797886602003
m: 500000000000000000000000000000000
deg: 5
c5: 304
c0: 1075
skew: 1.29
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2050000, 4650001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 813692 x 813940
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,52,52,2.4,2.4,100000
total time: 56.00 hours.

(13·10¹⁶⁵-7)/3 = 4(3)₁₆₄1_<166> = 137 · C164

C164 = P79 · P85

P79 = 6085843468199487275442039551130758294656791892404326335166720315393967284370157_<79>

P85 = 5197335501903661657599518956480061122136436218334285817046668712234291023306740922759_<85>

SNFS difficulty: 166 digits.
Divisors found:
 r1=6085843468199487275442039551130758294656791892404326335166720315393967284370157 (pp79)
 r2=5197335501903661657599518956480061122136436218334285817046668712234291023306740922759 (pp85)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 31630170316301703163017031630170316301703163017031630170316301703163017031630170316301703163017031630170316301703163017031630170316301703163017031630170316301703163
m: 1000000000000000000000000000000000
deg: 5
c5: 13
c0: -7
skew: 0.88
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2050000, 4050001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 746923 x 747171
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,52,52,2.4,2.4,200000
total time: 36.00 hours.

Dec 24, 2008 (5th)

By Jo Yeong Uk / GGNFS / Msieve v1.39

(13·10¹²⁹-7)/3 = 4(3)₁₂₈1_<130> = 103993 · 9537211 · 799114214868023969_<18> · C100

C100 = P39 · P62

P39 = 346643489439315219050321521524858945557_<39>

P62 = 15772651068440529298755132621651886781971748870337901617836909_<62>

Number: 43331_129
N=5467486804072968524263441446230274033369319439416686948461744728066650046424741948248473440936163313
  ( 100 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=346643489439315219050321521524858945557
 r2=15772651068440529298755132621651886781971748870337901617836909
Version: 
Total time: 1.74 hours.
Scaled time: 4.16 units (timescale=2.391).
Factorization parameters were as follows:
n: 5467486804072968524263441446230274033369319439416686948461744728066650046424741948248473440936163313
m: 100000000000000000000000000
deg: 5
c5: 13
c0: -70
skew: 1.40
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [500000, 1000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 2953047
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 157950 x 158195
Total sieving time: 1.54 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000
total time: 1.74 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Dec 24, 2008 (4th)

By Sinkiti Sibata / Msieve

(13·10¹⁵⁴-7)/3 = 4(3)₁₅₃1_<155> = 4299968837_<10> · 5420661282707945028204253_<25> · 4248099842885959289351740481_<28> · C93

C93 = P43 · P50

P43 = 6196057801656421501364047194416498849394697_<43>

P50 = 70630835377785084555386441008655114290296665265803_<50>

Tue Dec 23 22:52:12 2008  Msieve v. 1.39
Tue Dec 23 22:52:12 2008  random seeds: 4415d7f4 e16d18f3
Tue Dec 23 22:52:12 2008  factoring 437632738580035654262129319099138766292963493690866696448476387894541006903564451451163646691 (93 digits)
Tue Dec 23 22:52:13 2008  searching for 15-digit factors
Tue Dec 23 22:52:14 2008  commencing quadratic sieve (93-digit input)
Tue Dec 23 22:52:14 2008  using multiplier of 19
Tue Dec 23 22:52:14 2008  using 32kb Intel Core sieve core
Tue Dec 23 22:52:14 2008  sieve interval: 36 blocks of size 32768
Tue Dec 23 22:52:14 2008  processing polynomials in batches of 6
Tue Dec 23 22:52:14 2008  using a sieve bound of 1923137 (71699 primes)
Tue Dec 23 22:52:14 2008  using large prime bound of 232699577 (27 bits)
Tue Dec 23 22:52:14 2008  using double large prime bound of 1148767303677169 (42-51 bits)
Tue Dec 23 22:52:14 2008  using trial factoring cutoff of 51 bits
Tue Dec 23 22:52:14 2008  polynomial 'A' values have 12 factors
Wed Dec 24 01:24:11 2008  71822 relations (18303 full + 53519 combined from 959170 partial), need 71795
Wed Dec 24 01:24:12 2008  begin with 977473 relations
Wed Dec 24 01:24:13 2008  reduce to 182815 relations in 10 passes
Wed Dec 24 01:24:13 2008  attempting to read 182815 relations
Wed Dec 24 01:24:15 2008  recovered 182815 relations
Wed Dec 24 01:24:15 2008  recovered 165366 polynomials
Wed Dec 24 01:24:15 2008  attempting to build 71822 cycles
Wed Dec 24 01:24:15 2008  found 71822 cycles in 5 passes
Wed Dec 24 01:24:15 2008  distribution of cycle lengths:
Wed Dec 24 01:24:15 2008     length 1 : 18303
Wed Dec 24 01:24:15 2008     length 2 : 13016
Wed Dec 24 01:24:15 2008     length 3 : 12483
Wed Dec 24 01:24:15 2008     length 4 : 9444
Wed Dec 24 01:24:15 2008     length 5 : 7095
Wed Dec 24 01:24:15 2008     length 6 : 4692
Wed Dec 24 01:24:15 2008     length 7 : 2928
Wed Dec 24 01:24:15 2008     length 9+: 3861
Wed Dec 24 01:24:15 2008  largest cycle: 22 relations
Wed Dec 24 01:24:16 2008  matrix is 71699 x 71822 (18.6 MB) with weight 4599586 (64.04/col)
Wed Dec 24 01:24:16 2008  sparse part has weight 4599586 (64.04/col)
Wed Dec 24 01:24:17 2008  filtering completed in 3 passes
Wed Dec 24 01:24:17 2008  matrix is 67741 x 67805 (17.7 MB) with weight 4379423 (64.59/col)
Wed Dec 24 01:24:17 2008  sparse part has weight 4379423 (64.59/col)
Wed Dec 24 01:24:17 2008  saving the first 48 matrix rows for later
Wed Dec 24 01:24:17 2008  matrix is 67693 x 67805 (11.6 MB) with weight 3510908 (51.78/col)
Wed Dec 24 01:24:17 2008  sparse part has weight 2623737 (38.70/col)
Wed Dec 24 01:24:17 2008  matrix includes 64 packed rows
Wed Dec 24 01:24:17 2008  using block size 27122 for processor cache size 1024 kB
Wed Dec 24 01:24:18 2008  commencing Lanczos iteration
Wed Dec 24 01:24:18 2008  memory use: 10.9 MB
Wed Dec 24 01:24:47 2008  lanczos halted after 1071 iterations (dim = 67691)
Wed Dec 24 01:24:47 2008  recovered 16 nontrivial dependencies
Wed Dec 24 01:24:48 2008  prp43 factor: 6196057801656421501364047194416498849394697
Wed Dec 24 01:24:48 2008  prp50 factor: 70630835377785084555386441008655114290296665265803
Wed Dec 24 01:24:48 2008  elapsed time 02:32:36

(38·10¹³⁶+61)/9 = 4(2)₁₃₅9_<137> = 11² · 507571 · 990643 · C123

C123 = P32 · P46 · P47

P32 = 12994371931234232563572230204953_<32>

P46 = 2821341889370461231082316680328888029873454389_<46>

P47 = 18929133352137533796090816854860634959299355049_<47>

Number: 42229_136
N=693971668979787672360221564933897224316140193326896041334006376981172056648340109892525747331357177578992585148159179582133
  ( 123 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=12994371931234232563572230204953
 r2=2821341889370461231082316680328888029873454389
 r3=18929133352137533796090816854860634959299355049
Version: 
Total time: 6.24 hours.
Scaled time: 12.28 units (timescale=1.967).
Factorization parameters were as follows:
name: 42229_136
n: 693971668979787672360221564933897224316140193326896041334006376981172056648340109892525747331357177578992585148159179582133
m: 1000000000000000000000000000
deg: 5
c5: 380
c0: 61
skew: 0.69
type: snfs
lss: 1
rlim: 1370000
alim: 1370000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1370000/1370000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [685000, 1360001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 193020 x 193268
Total sieving time: 6.24 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1370000,1370000,26,26,48,48,2.3,2.3,75000
total time: 6.24 hours.
 --------- CPU info (if available) ----------

(38·10¹³⁷+61)/9 = 4(2)₁₃₆9_<138> = 3 · 127 · 151 · C133

C133 = P37 · P47 · P50

P37 = 6456539318974069952317840383913635547_<37>

P47 = 84353085074939403498494219218028513808174498829_<47>

P50 = 13475298467557402274192836515690867490289089049393_<50>

Number: 42229_137
N=7339038470080864615984812053018758968594709325793436968281834527858410634653008329808663541781339142761680176291429354995084775550959
  ( 133 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=6456539318974069952317840383913635547
 r2=84353085074939403498494219218028513808174498829
 r3=13475298467557402274192836515690867490289089049393
Version: 
Total time: 5.42 hours.
Scaled time: 13.96 units (timescale=2.575).
Factorization parameters were as follows:
name: 42229_137
n: 7339038470080864615984812053018758968594709325793436968281834527858410634653008329808663541781339142761680176291429354995084775550959
m: 2000000000000000000000000000
deg: 5
c5: 475
c0: 244
skew: 0.88
type: snfs
lss: 1
rlim: 1460000
alim: 1460000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1460000/1460000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [730000, 1480001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 206320 x 206568
Total sieving time: 5.42 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1460000,1460000,26,26,48,48,2.3,2.3,75000
total time: 5.42 hours.
 --------- CPU info (if available) ----------

(38·10¹³²+61)/9 = 4(2)₁₃₁9_<133> = 11 · 776001532639_<12> · C120

C120 = P49 · P72

P49 = 2969872220720596372610570814567592219469836109293_<49>

P72 = 166551312272968076499268266318802432077753188457365327152386424859382757_<72>

Number: 42229_132
N=494636115644049218819442914466771717713015102938955522069569580741406160381239875380518653429265348791970272174371660801
  ( 120 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=2969872220720596372610570814567592219469836109293
 r2=166551312272968076499268266318802432077753188457365327152386424859382757
Version: 
Total time: 4.08 hours.
Scaled time: 9.61 units (timescale=2.357).
Factorization parameters were as follows:
name: 42229_132
n: 494636115644049218819442914466771717713015102938955522069569580741406160381239875380518653429265348791970272174371660801
m: 200000000000000000000000000
deg: 5
c5: 475
c0: 244
skew: 0.88
type: snfs
lss: 1
rlim: 1210000
alim: 1210000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1210000/1210000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [605000, 1130001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 162582 x 162827
Total sieving time: 4.08 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1210000,1210000,26,26,47,47,2.3,2.3,75000
total time: 4.08 hours.
 --------- CPU info (if available) ----------

(38·10¹³³+61)/9 = 4(2)₁₃₂9_<134> = 7 · 17 · 31 · 7446191 · 92316751817_<11> · C113

C113 = P52 · P61

P52 = 3454354056951432918786575190491331483927052530924391_<52>

P61 = 4820042812404022801199777592890218362440628066520836743662493_<61>

Number: 42229_133
N=16650134443707430675722745496325348238405457625575494554061037823950827364147409161145258157135657400068205566763
  ( 113 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=3454354056951432918786575190491331483927052530924391
 r2=4820042812404022801199777592890218362440628066520836743662493
Version: 
Total time: 4.36 hours.
Scaled time: 8.73 units (timescale=2.003).
Factorization parameters were as follows:
name: 42229_133
n: 16650134443707430675722745496325348238405457625575494554061037823950827364147409161145258157135657400068205566763
m: 500000000000000000000000000
deg: 5
c5: 304
c0: 1525
skew: 1.38
type: snfs
lss: 1
rlim: 1290000
alim: 1290000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1290000/1290000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [645000, 1095001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 149895 x 150143
Total sieving time: 4.36 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1290000,1290000,26,26,47,47,2.3,2.3,75000
total time: 4.36 hours.
 --------- CPU info (if available) ----------

(13·10¹³⁸-7)/3 = 4(3)₁₃₇1_<139> = 1003753 · 217066632061_<12> · C122

C122 = P57 · P65

P57 = 272710477884165309368820146712980890078113632640440282561_<57>

P65 = 72929015177053713033881917987365982816088025384408340890063152887_<65>

Number: 43331_138
N=19888506580555862802074130987443151078615717105176811792365248436258887922009032248563497555435293494812111456084822903607
  ( 122 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=272710477884165309368820146712980890078113632640440282561
 r2=72929015177053713033881917987365982816088025384408340890063152887
Version: 
Total time: 4.53 hours.
Scaled time: 11.65 units (timescale=2.575).
Factorization parameters were as follows:
name: 43331_138
n: 19888506580555862802074130987443151078615717105176811792365248436258887922009032248563497555435293494812111456084822903607
m: 5000000000000000000000000000
deg: 5
c5: 104
c0: -175
skew: 1.11
type: snfs
lss: 1
rlim: 1540000
alim: 1540000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1540000/1540000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [770000, 1370001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 229684 x 229931
Total sieving time: 4.53 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1540000,1540000,26,26,48,48,2.3,2.3,100000
total time: 4.53 hours.
 --------- CPU info (if available) ----------

(13·10¹²⁶-7)/3 = 4(3)₁₂₅1_<127> = 41 · 113 · 612958849049_<12> · 3602570233447_<13> · C99

C99 = P32 · P68

P32 = 30490364046617984017424864824609_<32>

P68 = 13891636547419071980552984173367140215460386040448597016954924515941_<68>

Wed Dec 24 06:14:06 2008  Msieve v. 1.39
Wed Dec 24 06:14:06 2008  random seeds: 638a2880 0697d978
Wed Dec 24 06:14:06 2008  factoring 423561055534110855772718836647845940152748087470775841943157918715306066768867674318721107189592069 (99 digits)
Wed Dec 24 06:14:07 2008  searching for 15-digit factors
Wed Dec 24 06:14:09 2008  commencing quadratic sieve (99-digit input)
Wed Dec 24 06:14:09 2008  using multiplier of 1
Wed Dec 24 06:14:09 2008  using 32kb Intel Core sieve core
Wed Dec 24 06:14:09 2008  sieve interval: 36 blocks of size 32768
Wed Dec 24 06:14:09 2008  processing polynomials in batches of 6
Wed Dec 24 06:14:09 2008  using a sieve bound of 2612251 (95257 primes)
Wed Dec 24 06:14:09 2008  using large prime bound of 391837650 (28 bits)
Wed Dec 24 06:14:09 2008  using double large prime bound of 2934884765895450 (43-52 bits)
Wed Dec 24 06:14:09 2008  using trial factoring cutoff of 52 bits
Wed Dec 24 06:14:09 2008  polynomial 'A' values have 13 factors
Wed Dec 24 14:57:37 2008  95665 relations (22800 full + 72865 combined from 1444038 partial), need 95353
Wed Dec 24 14:57:39 2008  begin with 1466838 relations
Wed Dec 24 14:57:40 2008  reduce to 252523 relations in 11 passes
Wed Dec 24 14:57:40 2008  attempting to read 252523 relations
Wed Dec 24 14:57:45 2008  recovered 252523 relations
Wed Dec 24 14:57:45 2008  recovered 241794 polynomials
Wed Dec 24 14:57:45 2008  attempting to build 95665 cycles
Wed Dec 24 14:57:45 2008  found 95665 cycles in 6 passes
Wed Dec 24 14:57:45 2008  distribution of cycle lengths:
Wed Dec 24 14:57:45 2008     length 1 : 22800
Wed Dec 24 14:57:45 2008     length 2 : 16294
Wed Dec 24 14:57:45 2008     length 3 : 15927
Wed Dec 24 14:57:45 2008     length 4 : 13040
Wed Dec 24 14:57:45 2008     length 5 : 10046
Wed Dec 24 14:57:45 2008     length 6 : 6811
Wed Dec 24 14:57:45 2008     length 7 : 4397
Wed Dec 24 14:57:45 2008     length 9+: 6350
Wed Dec 24 14:57:45 2008  largest cycle: 23 relations
Wed Dec 24 14:57:45 2008  matrix is 95257 x 95665 (25.5 MB) with weight 6314404 (66.01/col)
Wed Dec 24 14:57:45 2008  sparse part has weight 6314404 (66.01/col)
Wed Dec 24 14:57:47 2008  filtering completed in 3 passes
Wed Dec 24 14:57:47 2008  matrix is 91395 x 91459 (24.5 MB) with weight 6046936 (66.12/col)
Wed Dec 24 14:57:47 2008  sparse part has weight 6046936 (66.12/col)
Wed Dec 24 14:57:47 2008  saving the first 48 matrix rows for later
Wed Dec 24 14:57:47 2008  matrix is 91347 x 91459 (14.3 MB) with weight 4688883 (51.27/col)
Wed Dec 24 14:57:47 2008  sparse part has weight 3211621 (35.12/col)
Wed Dec 24 14:57:47 2008  matrix includes 64 packed rows
Wed Dec 24 14:57:47 2008  using block size 36583 for processor cache size 1024 kB
Wed Dec 24 14:57:48 2008  commencing Lanczos iteration
Wed Dec 24 14:57:48 2008  memory use: 14.5 MB
Wed Dec 24 14:58:43 2008  lanczos halted after 1447 iterations (dim = 91341)
Wed Dec 24 14:58:43 2008  recovered 13 nontrivial dependencies
Wed Dec 24 14:58:44 2008  prp32 factor: 30490364046617984017424864824609
Wed Dec 24 14:58:44 2008  prp68 factor: 13891636547419071980552984173367140215460386040448597016954924515941
Wed Dec 24 14:58:44 2008  elapsed time 08:44:38

(38·10¹³⁹+61)/9 = 4(2)₁₃₈9_<140> = 7 · 43 · 79 · 118751 · 13963483 · C124

C124 = P41 · P83

P41 = 40995216861330514782493424946046859932427_<41>

P83 = 26120607663077197279728695742834580519372241488994079940765343709210850548980030161_<83>

Number: 42229_139
N=1070819975697581372026915209957136700305843805306366832768537504626396109208627745838362563415637931633490196373116881930747
  ( 124 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=40995216861330514782493424946046859932427
 r2=26120607663077197279728695742834580519372241488994079940765343709210850548980030161
Version: 
Total time: 6.97 hours.
Scaled time: 14.00 units (timescale=2.010).
Factorization parameters were as follows:
name: 42229_139
n: 1070819975697581372026915209957136700305843805306366832768537504626396109208627745838362563415637931633490196373116881930747
m: 10000000000000000000000000000
deg: 5
c5: 19
c0: 305
skew: 1.74
type: snfs
lss: 1
rlim: 1580000
alim: 1580000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1580000/1580000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [790000, 1490001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 208332 x 208580
Total sieving time: 6.97 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000
total time: 6.97 hours.
 --------- CPU info (if available) ----------

(13·10¹³⁹-7)/3 = 4(3)₁₃₈1_<140> = 35561357833129779817_<20> · 339685932960896082541_<21> · C100

C100 = P42 · P58

P42 = 580227981425170480885365056415884167587353_<42>

P58 = 6182548491273330202741775652459471890874048806489022017791_<58>

Number: 43331_139
N=3587287631154757617814951158449886668895226167431297560934889849904751035171338016447415764312597223
  ( 100 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=580227981425170480885365056415884167587353
 r2=6182548491273330202741775652459471890874048806489022017791
Version: 
Total time: 7.16 hours.
Scaled time: 18.36 units (timescale=2.564).
Factorization parameters were as follows:
name: 43331_139
n: 3587287631154757617814951158449886668895226167431297560934889849904751035171338016447415764312597223
m: 10000000000000000000000000000
deg: 5
c5: 13
c0: -70
skew: 1.40
type: snfs
lss: 1
rlim: 1570000
alim: 1570000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1570000/1570000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [785000, 1785001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 267552 x 267800
Total sieving time: 7.16 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000
total time: 7.16 hours.
 --------- CPU info (if available) ----------

(13·10¹³⁶-7)/3 = 4(3)₁₃₅1_<137> = 41 · 461 · 1097 · 1144019 · 6912769 · C117

C117 = P39 · P79

P39 = 153868017024233492936781291144992798777_<39>

P79 = 1717501200001193868071551512936241855900994787663081370386972669289649929323709_<79>

Number: 43331_136
N=264268503880925151311871568681403279980594971164576904562485281555967178805595058087289716052263653659523810732303893
  ( 117 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=153868017024233492936781291144992798777
 r2=1717501200001193868071551512936241855900994787663081370386972669289649929323709
Version: 
Total time: 4.87 hours.
Scaled time: 12.50 units (timescale=2.564).
Factorization parameters were as follows:
name: 43331_136
n: 264268503880925151311871568681403279980594971164576904562485281555967178805595058087289716052263653659523810732303893
m: 2000000000000000000000000000
deg: 5
c5: 65
c0: -112
skew: 1.11
type: snfs
lss: 1
rlim: 1410000
alim: 1410000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1410000/1410000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [705000, 1380001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 194934 x 195182
Total sieving time: 4.87 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1410000,1410000,26,26,48,48,2.3,2.3,75000
total time: 4.87 hours.
 --------- CPU info (if available) ----------

(38·10¹⁴⁰+61)/9 = 4(2)₁₃₉9_<141> = 3 · 11 · 13² · 409 · 66376463 · C127

C127 = P61 · P66

P61 = 4363189719756629305373249732984127052389932144242640081636599_<61>

P66 = 639144315774237606362299455808713290546585132219180798704818559069_<66>

Number: 42229_140
N=2788707908027038368820676356991699645995675322839068899344297739110534039864931465687628595805788445793745961473494234473766331
  ( 127 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=4363189719756629305373249732984127052389932144242640081636599
 r2=639144315774237606362299455808713290546585132219180798704818559069
Version: 
Total time: 6.86 hours.
Scaled time: 13.78 units (timescale=2.010).
Factorization parameters were as follows:
name: 42227_140
n: 2788707908027038368820676356991699645995675322839068899344297739110534039864931465687628595805788445793745961473494234473766331
m: 10000000000000000000000000000
deg: 5
c5: 38
c0: 61
skew: 1.10
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [800000, 1500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 249081 x 249329
Total sieving time: 6.86 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000
total time: 6.86 hours.
 --------- CPU info (if available) ----------

Dec 24, 2008 (3rd)

By Robert Backstrom / GGNFS, GMP-ECM, Msieve

(13·10¹²⁴-7)/3 = 4(3)₁₂₃1_<125> = 67 · 1697 · 60793 · C115

C115 = P43 · P73

P43 = 1498047185326462845874791264840983789868623_<43>

P73 = 4184912521601170246850918800640022065043403650310690001096570127074950871_<73>

Number: n
N=6269196423822103232539740936099023112203802212838271361405353100480408276012089605380855071374200647972655269420633
  ( 115 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=1498047185326462845874791264840983789868623 (pp43)
 r2=4184912521601170246850918800640022065043403650310690001096570127074950871 (pp73)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.99 hours.
Scaled time: 3.64 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_4_3_123_1
n: 6269196423822103232539740936099023112203802212838271361405353100480408276012089605380855071374200647972655269420633
type: snfs
skew: 1.40
deg: 5
c5: 13
c0: -70
m: 10000000000000000000000000
rlim: 650000
alim: 650000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 650000/650000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [325000, 605001)
Primes: RFBsize:52831, AFBsize:53207, largePrimes:6633415 encountered
Relations: rels:5890129, finalFF:152374
Max relations in full relation-set: 48
Initial matrix: 106103 x 152374 with sparse part having weight 24339461.
Pruned matrix : 100481 x 101075 with weight 12235988.
Total sieving time: 1.78 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.08 hours.
Total square root time: 0.04 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,650000,650000,28,28,56,56,2.5,2.5,50000
total time: 1.99 hours.
 --------- CPU info (if available) ----------

(13·10¹³⁵-7)/3 = 4(3)₁₃₄1_<136> = 21521 · 376824788300183_<15> · C117

C117 = P46 · P71

P46 = 7462194341926544919338500194924283255312005077_<46>

P71 = 71606695242654519563333342916952318853502485124430637614152778256430721_<71>

Number: n
N=534343076083794997371281760082808935626601181033359381519995052241174855210527261550171279430169719357538447850770517
  ( 117 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=7462194341926544919338500194924283255312005077 (pp46)
 r2=71606695242654519563333342916952318853502485124430637614152778256430721 (pp71)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.56 hours.
Scaled time: 6.51 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_4_3_134_1
n: 534343076083794997371281760082808935626601181033359381519995052241174855210527261550171279430169719357538447850770517
type: snfs
skew: 0.88
deg: 5
c5: 13
c0: -7
m: 1000000000000000000000000000
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [500000, 1020001)
Primes: RFBsize:78498, AFBsize:78306, largePrimes:9031572 encountered
Relations: rels:8076284, finalFF:178919
Max relations in full relation-set: 48
Initial matrix: 156869 x 178919 with sparse part having weight 27811347.
Pruned matrix : 154011 x 154859 with weight 21176060.
Total sieving time: 3.13 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.26 hours.
Total square root time: 0.03 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,56,56,2.5,2.5,75000
total time: 3.56 hours.
 --------- CPU info (if available) ----------

(34·10¹⁸⁵+11)/9 = 3(7)₁₈₄9_<186> = 1039 · C183

C183 = P36 · P56 · P91

P36 = 553108953256060747840665463564358923_<36>

P56 = 84899358098754026519470500100735842692276241566795948069_<56>

P91 = 7742937698796390773077022171625908268690825320600198553953076059596260413718230752249653803_<91>

GMP-ECM 6.0.1 [powered by GMP 4.1.4] [ECM]
Input number is 363597476205753395358785156667736071008448294300074858303924713934338573414608063308737033472355897764944925676398246176879478130681210565714896802481018072933376109507004598438669661 (183 digits)
Using B1=1830000, B2=1986068894, polynomial Dickson(6), sigma=2182743119
Step 1 took 41688ms
Step 2 took 20734ms
********** Factor found in step 2: 553108953256060747840665463564358923
Found probable prime factor of 36 digits: 553108953256060747840665463564358923
Composite cofactor 657370440426457224196909528676015642805819843550172264758862997221749950147843630565666366392439605388006719253164554952138526942848104848416356407 has 147 digits

Number: n
N=657370440426457224196909528676015642805819843550172264758862997221749950147843630565666366392439605388006719253164554952138526942848104848416356407
  ( 147 digits)
SNFS difficulty: 186 digits.
Divisors found:

Wed Dec 24 13:32:23 2008  prp56 factor: 84899358098754026519470500100735842692276241566795948069
Wed Dec 24 13:32:23 2008  prp91 factor: 7742937698796390773077022171625908268690825320600198553953076059596260413718230752249653803
Wed Dec 24 13:32:23 2008  elapsed time 20:34:53 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 70.68 hours.
Scaled time: 46.58 units (timescale=0.659).
Factorization parameters were as follows:
name: KA_3_7_184_9
n: 657370440426457224196909528676015642805819843550172264758862997221749950147843630565666366392439605388006719253164554952138526942848104848416356407
type: snfs
skew: 0.80
deg: 5
c5: 34
c0: 11
m: 10000000000000000000000000000000000000
rlim: 8500000
alim: 8500000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 8500000/8500000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 3150001)
Primes: RFBsize:571119, AFBsize:571308, largePrimes:32711526 encountered
Relations: rels:29594547, finalFF:1086092
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 4539192 hash collisions in 33167915 relations
Msieve: matrix is 1455727 x 1455975 (395.1 MB)

Total sieving time: 68.38 hours.
Total relation processing time: 2.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,8500000,8500000,29,29,58,58,2.5,2.5,100000
total time: 70.68 hours.
 --------- CPU info (if available) ----------

Dec 24, 2008 (2nd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39, Msieve-1.39+pol51 gnfs

(38·10¹⁴⁴+61)/9 = 4(2)₁₄₃9_<145> = 11 · 503 · 919 · 16719328669_<11> · 5872408641739_<13> · C115

C115 = P33 · P39 · P45

P33 = 185958730996919530697610925218379_<33>

P39 = 435936853888932377299397412491753686571_<39>

P45 = 104325299889160694313575763049847352543268633_<45>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1036791296
Step 1 took 8186ms
Step 2 took 9254ms
********** Factor found in step 2: 185958730996919530697610925218379
Found probable prime factor of 33 digits: 185958730996919530697610925218379
Composite cofactor has 83 digits

Tue Dec 23 05:15:51 2008
Tue Dec 23 05:15:51 2008  Msieve v. 1.39
Tue Dec 23 05:15:51 2008  random seeds: 90094d45 a7ce150a
Tue Dec 23 05:15:51 2008  factoring 45479243014700098733299390696402372968311259821857132401813685792934459068137627443 (83 digits)
Tue Dec 23 05:15:52 2008  searching for 15-digit factors
Tue Dec 23 05:15:52 2008  commencing quadratic sieve (83-digit input)
Tue Dec 23 05:15:52 2008  using multiplier of 3
Tue Dec 23 05:15:52 2008  using 64kb Opteron sieve core
Tue Dec 23 05:15:52 2008  sieve interval: 6 blocks of size 65536
Tue Dec 23 05:15:52 2008  processing polynomials in batches of 17
Tue Dec 23 05:15:52 2008  using a sieve bound of 1368329 (52647 primes)
Tue Dec 23 05:15:52 2008  using large prime bound of 121781281 (26 bits)
Tue Dec 23 05:15:52 2008  using trial factoring cutoff of 27 bits
Tue Dec 23 05:15:52 2008  polynomial 'A' values have 11 factors
Tue Dec 23 05:38:35 2008  52767 relations (26541 full + 26226 combined from 280810 partial), need 52743
Tue Dec 23 05:38:35 2008  begin with 307351 relations
Tue Dec 23 05:38:35 2008  reduce to 75673 relations in 2 passes
Tue Dec 23 05:38:35 2008  attempting to read 75673 relations
Tue Dec 23 05:38:36 2008  recovered 75673 relations
Tue Dec 23 05:38:36 2008  recovered 69585 polynomials
Tue Dec 23 05:38:36 2008  attempting to build 52767 cycles
Tue Dec 23 05:38:36 2008  found 52767 cycles in 1 passes
Tue Dec 23 05:38:36 2008  distribution of cycle lengths:
Tue Dec 23 05:38:36 2008     length 1 : 26541
Tue Dec 23 05:38:36 2008     length 2 : 26226
Tue Dec 23 05:38:36 2008  largest cycle: 2 relations
Tue Dec 23 05:38:36 2008  matrix is 52647 x 52767 (8.0 MB) with weight 1682549 (31.89/col)
Tue Dec 23 05:38:36 2008  sparse part has weight 1682549 (31.89/col)
Tue Dec 23 05:38:37 2008  filtering completed in 3 passes
Tue Dec 23 05:38:37 2008  matrix is 38828 x 38887 (6.4 MB) with weight 1373197 (35.31/col)
Tue Dec 23 05:38:37 2008  sparse part has weight 1373197 (35.31/col)
Tue Dec 23 05:38:37 2008  saving the first 48 matrix rows for later
Tue Dec 23 05:38:37 2008  matrix is 38780 x 38887 (4.3 MB) with weight 1039749 (26.74/col)
Tue Dec 23 05:38:37 2008  sparse part has weight 747149 (19.21/col)
Tue Dec 23 05:38:37 2008  matrix includes 64 packed rows
Tue Dec 23 05:38:37 2008  using block size 15554 for processor cache size 1024 kB
Tue Dec 23 05:38:37 2008  commencing Lanczos iteration
Tue Dec 23 05:38:37 2008  memory use: 4.3 MB
Tue Dec 23 05:38:42 2008  lanczos halted after 615 iterations (dim = 38778)
Tue Dec 23 05:38:42 2008  recovered 17 nontrivial dependencies
Tue Dec 23 05:38:42 2008  prp39 factor: 435936853888932377299397412491753686571
Tue Dec 23 05:38:42 2008  prp45 factor: 104325299889160694313575763049847352543268633
Tue Dec 23 05:38:42 2008  elapsed time 00:22:51

(38·10¹⁴⁵+43)/9 = 4(2)₁₄₄7_<146> = 1663 · 1723 · C140

C140 = P48 · P93

P48 = 143361658105740544577121897169041849714893542691_<48>

P93 = 102785190506482758977581155294308544825255338892896261035565418692162299061389923861016260253_<93>

SNFS difficulty: 146 digits.
Divisors found:
 r1=143361658105740544577121897169041849714893542691 (pp48)
 r2=102785190506482758977581155294308544825255338892896261035565418692162299061389923861016260253 (pp93)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.286).
Factorization parameters were as follows:
n: 14735455339723790094059125859440585500133569147151785776260491207954850254618973891914116647648234899910001267636934356764995196823221960823
m: 100000000000000000000000000000
deg: 5
c5: 38
c0: 43
skew: 1.03
type: snfs
lss: 1
rlim: 1940000
alim: 1940000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1940000/1940000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [970000, 2570001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 336574 x 336822
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1940000,1940000,26,26,49,49,2.3,2.3,100000
total time: 11.00 hours.

(38·10¹⁵³+43)/9 = 4(2)₁₅₂7_<154> = 3² · C153

C153 = P69 · P85

P69 = 429658841311150490118038632706779529774463197589532158877111287918973_<69>

P85 = 1091879783126345287514741812724212614608670024173592287059530931202710184194869602711_<85>

SNFS difficulty: 155 digits.
Divisors found:
 r1=429658841311150490118038632706779529774463197589532158877111287918973 (pp69)
 r2=1091879783126345287514741812724212614608670024173592287059530931202710184194869602711 (pp85)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.314).
Factorization parameters were as follows:
n: 469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135803
m: 5000000000000000000000000000000
deg: 5
c5: 304
c0: 1075
skew: 1.29
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1400000, 2600001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 565118 x 565366
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,52,52,2.4,2.4,100000
total time: 12.00 hours.

(38·10¹⁴⁶+61)/9 = 4(2)₁₄₅9_<147> = 3 · 11 · 13 · 743 · C142

C142 = P35 · P107

P35 = 29371295975761612541641795908618293_<35>

P107 = 45099515002463330270041583910624200505787042854484125648106218811048271349055997284919050293096397504594099_<107>

SNFS difficulty: 147 digits.
Divisors found:
 r1=29371295975761612541641795908618293 (pp35)
 r2=45099515002463330270041583910624200505787042854484125648106218811048271349055997284919050293096397504594099 (pp107)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 1324631203500651683693406439032280216667834433648700135914133222343181966331360678601593810207538336744258682347511418843854913841454891253007
m: 100000000000000000000000000000
deg: 5
c5: 380
c0: 61
skew: 0.69
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 2400001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 294682 x 294930
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,49,49,2.3,2.3,200000
total time: 6.00 hours.

(13·10¹⁴⁵-7)/3 = 4(3)₁₄₄1_<146> = 3709 · 3847 · 2170109 · 39052045075867533488696837658421_<32> · C101

C101 = P35 · P66

P35 = 78208945654866767181969270770471203_<35>

P66 = 458206575016335709488301915918886731111651833495759452288453585491_<66>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3061227314
Step 1 took 8259ms
Step 2 took 8999ms
********** Factor found in step 2: 78208945654866767181969270770471203
Found probable prime factor of 35 digits: 78208945654866767181969270770471203
Probable prime cofactor 458206575016335709488301915918886731111651833495759452288453585491 has 66 digits

(13·10¹⁶²-7)/3 = 4(3)₁₆₁1_<163> = 97 · 4001 · 239027 · 365699 · 179076571 · 30747058603981_<14> · C125

C125 = P32 · P93

P32 = 35369121000324091221140788630633_<32>

P93 = 655910323226196685402316639620192425902591627772168768126116843748558306589316695535468462797_<93>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3840470679
Step 1 took 9843ms
Step 2 took 10386ms
********** Factor found in step 2: 35369121000324091221140788630633
Found probable prime factor of 32 digits: 35369121000324091221140788630633
Probable prime cofactor 655910323226196685402316639620192425902591627772168768126116843748558306589316695535468462797 has 93 digits

(13·10¹⁴⁰-7)/3 = 4(3)₁₃₉1_<141> = 4152577859_<10> · C132

C132 = P46 · P86

P46 = 1618888627972634184177225680705039794519589281_<46>

P86 = 64459560671406830134081826137348849162306203510285790506146547055011181477654430473489_<86>

SNFS difficulty: 141 digits.
Divisors found:
 r1=1618888627972634184177225680705039794519589281 (pp46)
 r2=64459560671406830134081826137348849162306203510285790506146547055011181477654430473489 (pp86)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.673).
Factorization parameters were as follows:
n: 104352849735052573600242117298572566832474972586259539976354079321149059118299684921894039635232118915300832492670990117450639071409
m: 10000000000000000000000000000
deg: 5
c5: 13
c0: -7
skew: 0.88
type: snfs
lss: 1
rlim: 1570000
alim: 1570000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1570000/1570000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [785000, 1585001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 261172 x 261420
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,49,49,2.3,2.3,100000
total time: 3.90 hours.

(38·10¹⁵⁴+61)/9 = 4(2)₁₅₃9_<155> = 11 · 3598943 · C148

C148 = P56 · P92

P56 = 15141979967594079491718919468985969669399230154355609013_<56>

P92 = 70435364495469228989127803857011940423160477324626942530227526262722573852534558759089710621_<92>

SNFS difficulty: 156 digits.
Divisors found:
 r1=15141979967594079491718919468985969669399230154355609013 (pp56)
 r2=70435364495469228989127803857011940423160477324626942530227526262722573852534558759089710621 (pp92)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.307).
Factorization parameters were as follows:
n: 1066530878200582333156814053010519584177460948501779101207877934822484930669472630820726636637030327622259753443826100714526010508747662406389427073
m: 10000000000000000000000000000000
deg: 5
c5: 19
c0: 305
skew: 1.74
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1400000, 2200001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 470528 x 470776
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,52,52,2.4,2.4,100000
total time: 17.00 hours.

(13·10¹⁹⁴-7)/3 = 4(3)₁₉₃1_<195> = 3881 · 4040009 · 12429749 · 4005775577929_<13> · 66007507859850270736596089399561_<32> · C133

C133 = P31 · P103

P31 = 4448855391179499901841920088701_<31>

P103 = 1890190271245129714956635517993862966113876278013600663354393732491301918077570212567736137795152565619_<103>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1699384495
Step 1 took 9871ms
Step 2 took 10861ms
********** Factor found in step 2: 4448855391179499901841920088701
Found probable prime factor of 31 digits: 4448855391179499901841920088701
Probable prime cofactor has 103 digits

(38·10¹⁷⁴+61)/9 = 4(2)₁₇₃9_<175> = 11 · 557 · 23333 · 59218732301_<11> · C156

C156 = P42 · C115

P42 = 262088313569048659823633945899080702035203_<42>

C115 = [1902899549437374369035951375932780225773552267114939321874434723505133347794160411662937567103887497100312817310473_<115>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=113264461
Step 1 took 13984ms
Step 2 took 13062ms
********** Factor found in step 2: 262088313569048659823633945899080702035203
Found probable prime factor of 42 digits: 262088313569048659823633945899080702035203
Composite cofactor has 115 digits

(13·10²⁰³-7)/3 = 4(3)₂₀₂1_<204> = 127 · 259042595353901_<15> · C188

C188 = P38 · P150

P38 = 63444856538474819856481993655770160539_<38>

P150 = 207611197901601014143416821146774403219826219131558291970037945989725439970919940184172631734257013957795695677276118342125803124864277075013790561427_<150>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3263277877
Step 1 took 12681ms
Step 2 took 11857ms
********** Factor found in step 2: 63444856538474819856481993655770160539
Found probable prime factor of 38 digits: 63444856538474819856481993655770160539
Probable prime cofactor has 150 digits

(13·10¹⁵²-7)/3 = 4(3)₁₅₁1_<153> = 233 · 40277009 · C143

C143 = P41 · P103

P41 = 20031893966274074423596077442708505693053_<41>

P103 = 2305085038050452143230599323022197163476467261349173660893918734016736964140945346920717888247983995591_<103>

SNFS difficulty: 154 digits.
Divisors found:
 r1=20031893966274074423596077442708505693053 (pp41)
 r2=2305085038050452143230599323022197163476467261349173660893918734016736964140945346920717888247983995591 (pp103)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.689).
Factorization parameters were as follows:
n: 46175219065471497544696430236163828161418409151702714305658788678833996656676372801075680683544452514045855985835996777599255062948253551329323
m: 2000000000000000000000000000000
deg: 5
c5: 325
c0: -56
skew: 0.70
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1300000, 2300001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 503364 x 503612
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,52,52,2.4,2.4,100000
total time: 14.00 hours.

(16·10²²⁰-61)/9 = 1(7)₂₁₉1_<221> = 13 · 353 · 1877 · 16492937 · 1805034167_<10> · 937019983238111_<15> · 55949358235598934650206505967480781_<35> · C148

C148 = P63 · P85

P63 = 502302273034882362079860646223768728379203876736278008316737227_<63>

P85 = 2632707497199637986790781217412309087011431749152792902304523313521897147926180843269_<85>

Number: 17771_220
N=1322414960079354351709834861520621170706984511895469829631709464819715591749118547779968053941698236864151284187903149814300379387206849149544675063
  ( 148 digits)
Divisors found:
 r1=502302273034882362079860646223768728379203876736278008316737227 (pp63)
 r2=2632707497199637986790781217412309087011431749152792902304523313521897147926180843269 (pp85)
Version: Msieve-1.39
Total time: 1400.00 hours.
Scaled time: 3830.40 units (timescale=2.736).
Factorization parameters were as follows:
name: 17771_220
n: 1322414960079354351709834861520621170706984511895469829631709464819715591749118547779968053941698236864151284187903149814300379387206849149544675063
skew: 190966.40
c5: 24166860
c4: -17657193107092
c3: -2881381445141050978
c2: 749005469110315625842208
c1: -28000830886921387321901315893
c0: 8308569654994887332138921957235
Y1: 253242919256012579
Y0: -8864032069059734770877792666
# norm 2.53e+20
# alpha -5.85
# Murphy_E 7.15e-12
type: gnfs
rlim: 36000000
alim: 36000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 36000000/36000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved algebraic special-q in [18000000, 19000001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 3086519 x 3086767
Total sieving time: 1280.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 30.00 hours (4 cpu)
Time per square root: 1.50 hours.
Prototype def-par.txt line would be:
gnfs,147,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,36000000,36000000,29,29,58,58,2.6,2.6,100000
total time: 1400.00 hours.

C148 is the largest number which was factored by GNFS in our tables so far. Congratulations!

Dec 24, 2008

By Serge Batalov / GMP-ECM 6.2.1

(38·10²⁰⁵+61)/9 = 4(2)₂₀₄9_<206> = 7 · 996172031694311_<15> · C190

C190 = P39 · C152

P39 = 604708101318908926128095438473785832727_<39>

C152 = [10012970019827499748751154328820037782074317676296066223065340785954584373285105326974194401949500349014357279371189711576864463523554910181915957776451_<152>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3954599440
Step 1 took 16015ms
Step 2 took 15053ms
********** Factor found in step 2: 604708101318908926128095438473785832727
Found probable prime factor of 39 digits: 604708101318908926128095438473785832727
Composite cofactor has 152 digits

Dec 23, 2008 (8th)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39

(38·10¹²⁹+61)/9 = 4(2)₁₂₈9_<130> = 113 · 212476189 · 206782920150614243_<18> · C102

C102 = P31 · P72

P31 = 6877800995261078438976596986477_<31>

P72 = 123648287482431227866137204018035742921025020239320352409776567579513327_<72>

Factor found in step 1: 6877800995261078438976596986477

(38·10¹⁵¹+61)/9 = 4(2)₁₅₀9_<152> = 7 · 1117 · 20743 · 192637 · 82137278791_<11> · C128

C128 = P29 · P99

P29 = 56185303161233834414804494597_<29>

P99 = 292829995865447732444269891383468434429946313251210428873631095088198685156325342448697256025078463_<99>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3917450993
Step 1 took 9731ms
Step 2 took 10584ms
********** Factor found in step 2: 56185303161233834414804494597
Found probable prime factor of 29 digits: 56185303161233834414804494597
Probable prime cofactor 292829995865447732444269891383468434429946313251210428873631095088198685156325342448697256025078463 has 99 digits

(13·10¹⁴⁵-7)/3 = 4(3)₁₄₄1_<146> = 3709 · 3847 · 2170109 · C133

C133 = P32 · C101

P32 = 39052045075867533488696837658421_<32>

C101 = [35835853124155232087376837262708155018312446867976450226551174108265579054212486580985798592914115673_<101>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2266195174
Step 1 took 9764ms
Step 2 took 10698ms
********** Factor found in step 2: 39052045075867533488696837658421
Found probable prime factor of 32 digits: 39052045075867533488696837658421
Composite cofactor has 101 digits

(13·10¹⁸⁶-7)/3 = 4(3)₁₈₅1_<187> = 29 · 41 · 1723 · 2881969280353873_<16> · C165

C165 = P34 · C132

P34 = 2267180036234447141280701752917889_<34>

C132 = [323727512032728409566065549304498685213258027853771402670265835962965506247762803100126933161757433369766377101984695411470824717509_<132>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=980914334
Step 1 took 13664ms
Step 2 took 13602ms
********** Factor found in step 2: 2267180036234447141280701752917889
Found probable prime factor of 34 digits: 2267180036234447141280701752917889
Composite cofactor has 132 digits

(13·10¹⁹⁴-7)/3 = 4(3)₁₉₃1_<195> = 3881 · 4040009 · 12429749 · 4005775577929_<13> · C165

C165 = P32 · C133

P32 = 66007507859850270736596089399561_<32>

C133 = [8409183178583936583030174346844415915814492342050749419119294169308338808320971385476178209350780286513505479940764510332776202970919_<133>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=230614363
Step 1 took 13630ms
Step 2 took 13457ms
********** Factor found in step 2: 66007507859850270736596089399561
Found probable prime factor of 32 digits: 66007507859850270736596089399561
Composite cofactor 8409183178583936583030174346844415915814492342050749419119294169308338808320971385476178209350780286513505479940764510332776202970919 has 133 digits

(38·10¹⁸⁰+61)/9 = 4(2)₁₇₉9_<181> = 11² · 193 · 2125621 · 9206214079_<10> · 61673945456472526189_<20> · C141

C141 = P32 · P109

P32 = 37615930741760579786512667771617_<32>

P109 = 3982519964961393426250352239850021980260372565021485335616685544317069003492639457212340339450474841652800179_<109>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1328187747
Step 1 took 11835ms
Step 2 took 11587ms
********** Factor found in step 2: 37615930741760579786512667771617
Found probable prime factor of 32 digits: 37615930741760579786512667771617
Probable prime cofactor 3982519964961393426250352239850021980260372565021485335616685544317069003492639457212340339450474841652800179 has 109 digits

(38·10¹⁷⁵+61)/9 = 4(2)₁₇₄9_<176> = 7 · 48661 · C171

C171 = P31 · C140

P31 = 1740394642983557583386337035393_<31>

C140 = [71222018811833964655417651567953033432448526235056638873220031832622185237876237006720634532335848847765089902608605674576837157124980845239_<140>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=205899236
Step 1 took 13705ms
********** Factor found in step 1: 1740394642983557583386337035393
Found probable prime factor of 31 digits: 1740394642983557583386337035393
Composite cofactor has 140 digits

(13·10²⁰⁴-7)/3 = 4(3)₂₀₃1_<205> = 119179 · 279991 · 11574691 · 21512664293_<11> · C177

C177 = P32 · P146

P32 = 26308325916731982485427287860457_<32>

P146 = 19823551780928035006602671905281634246612561791914656475871110593336489297213306083897826212562111916418038463405766923512493202714696938292099769_<146>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1594125605
Step 1 took 16110ms
Step 2 took 14725ms
********** Factor found in step 2: 26308325916731982485427287860457
Found probable prime factor of 32 digits: 26308325916731982485427287860457
Probable prime cofactor has 146 digits

(13·10¹⁹³-7)/3 = 4(3)₁₉₂1_<194> = 151 · 10209190744703_<14> · C179

C179 = P31 · C148

P31 = 7709568588244219307028066227297_<31>

C148 = [3646059534317701069724515171275791765391252664992167269599666190068435969269326867841860958544963686066522189227458537555849678015726858695874479291_<148>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2528423854
Step 1 took 15951ms
Step 2 took 14697ms
********** Factor found in step 2: 7709568588244219307028066227297
Found probable prime factor of 31 digits: 7709568588244219307028066227297
Composite cofactor has 148 digits

(13·10¹²⁵-7)/3 = 4(3)₁₂₄1_<126> = 17 · 19 · 137 · 3943 · 80849611 · C110

C110 = P39 · P71

P39 = 756960282992795240590601586497232434921_<39>

P71 = 40580855963552503455078830310304821124582047703016518551277824518526757_<71>

SNFS difficulty: 126 digits.
Divisors found:
 r1=756960282992795240590601586497232434921 (pp39)
 r2=40580855963552503455078830310304821124582047703016518551277824518526757 (pp71)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 30718096214260565396870102557694086018037165181434351721059131933001350211212314245444509148935415858799681197
m: 10000000000000000000000000
deg: 5
c5: 13
c0: -7
skew: 0.88
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [445000, 695001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 125763 x 125999
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,49,49,2.3,2.3,50000
total time: 1.30 hours.

Dec 23, 2008 (7th)

By Sinkiti Sibata / Msieve

(38·10¹⁵⁵+43)/9 = 4(2)₁₅₄7_<156> = 13 · 648404825447551_<15> · C140

C140 = P62 · P78

P62 = 68502326768501726934975760518634987979255867421670311224348881_<62>

P78 = 731216821236048149998573343592774757206363666972266538567208965878323259710609_<78>

Number: 42227_155
N=50090053626936883206705630949905665484857244831913664200001658149686866574332055065172584204637245327813337676459217261678272501746512978529
  ( 140 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=68502326768501726934975760518634987979255867421670311224348881
 r2=731216821236048149998573343592774757206363666972266538567208965878323259710609
Version: 
Total time: 32.15 hours.
Scaled time: 82.43 units (timescale=2.564).
Factorization parameters were as follows:
name: 42227_155
n: 50090053626936883206705630949905665484857244831913664200001658149686866574332055065172584204637245327813337676459217261678272501746512978529
m: 10000000000000000000000000000000
deg: 5
c5: 38
c0: 43
skew: 1.03
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 560105 x 560353
Total sieving time: 32.15 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 32.15 hours.
 --------- CPU info (if available) ----------

(37·10¹⁵⁶+17)/9 = 4(1)₁₅₅3_<157> = 3³ · 29 · 10189769 · 13778351 · 2556268457_<10> · C131

C131 = P34 · P97

P34 = 3797525954125859456188033584306947_<34>

P97 = 3852375905322761719761070474805539193083531228124173816698883017752530486655049572263981171562611_<97>

Number: 42227_156
N=14629497485512292314226146150939449758591397444048985543210067506643763064342654028641902815319618485210777765254764855395452758617
  ( 131 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=3797525954125859456188033584306947
 r2=3852375905322761719761070474805539193083531228124173816698883017752530486655049572263981171562611
Version: 
Total time: 30.38 hours.
Scaled time: 60.50 units (timescale=1.991).
Factorization parameters were as follows:
name: 42227_156
n: 14629497485512292314226146150939449758591397444048985543210067506643763064342654028641902815319618485210777765254764855395452758617
m: 20000000000000000000000000000000
deg: 5
c5: 185
c0: 272
skew: 1.08
type: snfs
lss: 1
rlim: 3100000
alim: 3100000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3100000/3100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1550000, 2650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 579590 x 579838
Total sieving time: 30.38 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,50,50,2.4,2.4,100000
total time: 30.38 hours.
 --------- CPU info (if available) ----------

(38·10¹¹¹+61)/9 = 4(2)₁₁₀9_<112> = 11339154493_<11> · 7499477233123_<13> · C89

C89 = P37 · P52

P37 = 7397064209141958485367330886373433809_<37>

P52 = 6712279544020820708812321814113647261175372549034179_<52>

Tue Dec 23 17:27:13 2008  Msieve v. 1.39
Tue Dec 23 17:27:13 2008  random seeds: 7cbef738 6f66a5b2
Tue Dec 23 17:27:13 2008  factoring 49651162776832117853392950700141070758766904970016036759288163519498755604332466735157811 (89 digits)
Tue Dec 23 17:27:14 2008  searching for 15-digit factors
Tue Dec 23 17:27:16 2008  commencing quadratic sieve (89-digit input)
Tue Dec 23 17:27:16 2008  using multiplier of 11
Tue Dec 23 17:27:16 2008  using 32kb Intel Core sieve core
Tue Dec 23 17:27:16 2008  sieve interval: 32 blocks of size 32768
Tue Dec 23 17:27:16 2008  processing polynomials in batches of 7
Tue Dec 23 17:27:16 2008  using a sieve bound of 1556189 (58842 primes)
Tue Dec 23 17:27:16 2008  using large prime bound of 124495120 (26 bits)
Tue Dec 23 17:27:16 2008  using double large prime bound of 372626841652480 (42-49 bits)
Tue Dec 23 17:27:16 2008  using trial factoring cutoff of 49 bits
Tue Dec 23 17:27:16 2008  polynomial 'A' values have 11 factors
Tue Dec 23 18:38:03 2008  59083 relations (15371 full + 43712 combined from 629948 partial), need 58938
Tue Dec 23 18:38:04 2008  begin with 645319 relations
Tue Dec 23 18:38:04 2008  reduce to 144756 relations in 9 passes
Tue Dec 23 18:38:04 2008  attempting to read 144756 relations
Tue Dec 23 18:38:06 2008  recovered 144756 relations
Tue Dec 23 18:38:06 2008  recovered 124039 polynomials
Tue Dec 23 18:38:06 2008  attempting to build 59083 cycles
Tue Dec 23 18:38:06 2008  found 59083 cycles in 5 passes
Tue Dec 23 18:38:06 2008  distribution of cycle lengths:
Tue Dec 23 18:38:06 2008     length 1 : 15371
Tue Dec 23 18:38:06 2008     length 2 : 11272
Tue Dec 23 18:38:06 2008     length 3 : 10572
Tue Dec 23 18:38:06 2008     length 4 : 7903
Tue Dec 23 18:38:06 2008     length 5 : 5658
Tue Dec 23 18:38:06 2008     length 6 : 3490
Tue Dec 23 18:38:06 2008     length 7 : 2178
Tue Dec 23 18:38:06 2008     length 9+: 2639
Tue Dec 23 18:38:06 2008  largest cycle: 20 relations
Tue Dec 23 18:38:07 2008  matrix is 58842 x 59083 (14.7 MB) with weight 3621608 (61.30/col)
Tue Dec 23 18:38:07 2008  sparse part has weight 3621608 (61.30/col)
Tue Dec 23 18:38:07 2008  filtering completed in 3 passes
Tue Dec 23 18:38:07 2008  matrix is 55011 x 55075 (13.8 MB) with weight 3403270 (61.79/col)
Tue Dec 23 18:38:07 2008  sparse part has weight 3403270 (61.79/col)
Tue Dec 23 18:38:08 2008  saving the first 48 matrix rows for later
Tue Dec 23 18:38:08 2008  matrix is 54963 x 55075 (10.5 MB) with weight 2875828 (52.22/col)
Tue Dec 23 18:38:08 2008  sparse part has weight 2420144 (43.94/col)
Tue Dec 23 18:38:08 2008  matrix includes 64 packed rows
Tue Dec 23 18:38:08 2008  using block size 22030 for processor cache size 1024 kB
Tue Dec 23 18:38:08 2008  commencing Lanczos iteration
Tue Dec 23 18:38:08 2008  memory use: 9.3 MB
Tue Dec 23 18:38:29 2008  lanczos halted after 871 iterations (dim = 54961)
Tue Dec 23 18:38:29 2008  recovered 17 nontrivial dependencies
Tue Dec 23 18:38:29 2008  prp37 factor: 7397064209141958485367330886373433809
Tue Dec 23 18:38:29 2008  prp52 factor: 6712279544020820708812321814113647261175372549034179
Tue Dec 23 18:38:29 2008  elapsed time 01:11:16

(38·10¹⁵⁷+43)/9 = 4(2)₁₅₆7_<158> = 3833 · 5659 · C151

C151 = P59 · P92

P59 = 91465142275684836616097261496147067070594607462692509039543_<59>

P92 = 21281731504266448543814676309892699432806272010865082270499088002856980384586766615972344087_<92>

Number: 42227_157
N=1946536599910654994557048257147197041338131628011548883606705701794496211816949357822976664975587383170602105211092084740339931779936681520738685232241
  ( 151 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=91465142275684836616097261496147067070594607462692509039543
 r2=21281731504266448543814676309892699432806272010865082270499088002856980384586766615972344087
Version: 
Total time: 34.06 hours.
Scaled time: 85.63 units (timescale=2.514).
Factorization parameters were as follows:
name:42227_157
n: 1946536599910654994557048257147197041338131628011548883606705701794496211816949357822976664975587383170602105211092084740339931779936681520738685232241
m: 20000000000000000000000000000000
deg: 5
c5: 475
c0: 172
skew: 0.82
type: snfs
lss: 1
rlim: 3100000
alim: 3100000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3100000/3100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1550000, 2850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 522055 x 522303
Total sieving time: 34.06 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,50,50,2.4,2.4,100000
total time: 34.06 hours.
 --------- CPU info (if available) ----------

(13·10¹¹⁶-7)/3 = 4(3)₁₁₅1_<117> = 41 · 105225587 · C108

C108 = P47 · P61

P47 = 20912340313401736804695249831314117167056127139_<47>

P61 = 4803018351672359716761183080233491333287524164537900935628787_<61>

Number: 43331_116
N=100442354301686248318155650268889154362152020216994424474504576240621884645894815542260238572668695980350393
  ( 108 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=20912340313401736804695249831314117167056127139
 r2=4803018351672359716761183080233491333287524164537900935628787
Version: 
Total time: 1.52 hours.
Scaled time: 3.02 units (timescale=1.991).
Factorization parameters were as follows:
name: 43331_116
n: 100442354301686248318155650268889154362152020216994424474504576240621884645894815542260238572668695980350393
m: 200000000000000000000000
deg: 5
c5: 65
c0: -112
skew: 1.11
type: snfs
lss: 1
rlim: 660000
alim: 660000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 660000/660000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [330000, 530001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 68965 x 69199
Total sieving time: 1.52 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,118,5,0,0,0,0,0,0,0,0,660000,660000,25,25,45,45,2.2,2.2,50000
total time: 1.52 hours.
 --------- CPU info (if available) ----------

(38·10¹²²+61)/9 = 4(2)₁₂₁9_<123> = 3 · 11 · 13 · 1447 · 8190245732611_<13> · 42734715820119503_<17> · C88

C88 = P38 · P51

P38 = 17894098175364997990374216358774504223_<38>

P51 = 108599467479248166102092723780312641021472824805237_<51>

Tue Dec 23 18:47:15 2008  Msieve v. 1.39
Tue Dec 23 18:47:15 2008  random seeds: 160947d4 cef27f46
Tue Dec 23 18:47:15 2008  factoring 1943289532866025046805189916901455945080339390486360112365850271499631585958241209015851 (88 digits)
Tue Dec 23 18:47:16 2008  searching for 15-digit factors
Tue Dec 23 18:47:17 2008  commencing quadratic sieve (88-digit input)
Tue Dec 23 18:47:17 2008  using multiplier of 19
Tue Dec 23 18:47:17 2008  using 32kb Intel Core sieve core
Tue Dec 23 18:47:17 2008  sieve interval: 24 blocks of size 32768
Tue Dec 23 18:47:17 2008  processing polynomials in batches of 9
Tue Dec 23 18:47:17 2008  using a sieve bound of 1506511 (57333 primes)
Tue Dec 23 18:47:17 2008  using large prime bound of 120520880 (26 bits)
Tue Dec 23 18:47:17 2008  using double large prime bound of 351489263807840 (42-49 bits)
Tue Dec 23 18:47:17 2008  using trial factoring cutoff of 49 bits
Tue Dec 23 18:47:17 2008  polynomial 'A' values have 11 factors
Tue Dec 23 19:37:18 2008  57729 relations (16066 full + 41663 combined from 603363 partial), need 57429
Tue Dec 23 19:37:19 2008  begin with 619429 relations
Tue Dec 23 19:37:19 2008  reduce to 138258 relations in 10 passes
Tue Dec 23 19:37:19 2008  attempting to read 138258 relations
Tue Dec 23 19:37:21 2008  recovered 138258 relations
Tue Dec 23 19:37:21 2008  recovered 115980 polynomials
Tue Dec 23 19:37:21 2008  attempting to build 57729 cycles
Tue Dec 23 19:37:21 2008  found 57729 cycles in 5 passes
Tue Dec 23 19:37:21 2008  distribution of cycle lengths:
Tue Dec 23 19:37:21 2008     length 1 : 16066
Tue Dec 23 19:37:21 2008     length 2 : 11406
Tue Dec 23 19:37:21 2008     length 3 : 10192
Tue Dec 23 19:37:21 2008     length 4 : 7446
Tue Dec 23 19:37:21 2008     length 5 : 5239
Tue Dec 23 19:37:21 2008     length 6 : 3296
Tue Dec 23 19:37:21 2008     length 7 : 1905
Tue Dec 23 19:37:21 2008     length 9+: 2179
Tue Dec 23 19:37:21 2008  largest cycle: 19 relations
Tue Dec 23 19:37:21 2008  matrix is 57333 x 57729 (13.8 MB) with weight 3385288 (58.64/col)
Tue Dec 23 19:37:21 2008  sparse part has weight 3385288 (58.64/col)
Tue Dec 23 19:37:22 2008  filtering completed in 3 passes
Tue Dec 23 19:37:22 2008  matrix is 52973 x 53036 (12.7 MB) with weight 3125748 (58.94/col)
Tue Dec 23 19:37:22 2008  sparse part has weight 3125748 (58.94/col)
Tue Dec 23 19:37:22 2008  saving the first 48 matrix rows for later
Tue Dec 23 19:37:22 2008  matrix is 52925 x 53036 (9.3 MB) with weight 2584488 (48.73/col)
Tue Dec 23 19:37:22 2008  sparse part has weight 2112719 (39.84/col)
Tue Dec 23 19:37:22 2008  matrix includes 64 packed rows
Tue Dec 23 19:37:22 2008  using block size 21214 for processor cache size 1024 kB
Tue Dec 23 19:37:23 2008  commencing Lanczos iteration
Tue Dec 23 19:37:23 2008  memory use: 8.5 MB
Tue Dec 23 19:37:40 2008  lanczos halted after 838 iterations (dim = 52924)
Tue Dec 23 19:37:41 2008  recovered 17 nontrivial dependencies
Tue Dec 23 19:37:42 2008  prp38 factor: 17894098175364997990374216358774504223
Tue Dec 23 19:37:42 2008  prp51 factor: 108599467479248166102092723780312641021472824805237
Tue Dec 23 19:37:42 2008  elapsed time 00:50:27

(13·10¹¹⁹-7)/3 = 4(3)₁₁₈1_<120> = 23 · 127 · C117

C117 = P48 · P70

P48 = 113514518603811468544415778265029062834435682901_<48>

P70 = 1306890282973394626750519136011642653347252960413338529753654668995311_<70>

Number: 43331_119
N=148351021339723838867967591007645783407508844003195252767317128837156225037087755334930959716991897751911445851877211
  ( 117 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=113514518603811468544415778265029062834435682901
 r2=1306890282973394626750519136011642653347252960413338529753654668995311
Version: 
Total time: 2.19 hours.
Scaled time: 4.38 units (timescale=1.997).
Factorization parameters were as follows:
name: 43331_119
n: 148351021339723838867967591007645783407508844003195252767317128837156225037087755334930959716991897751911445851877211
m: 1000000000000000000000000
deg: 5
c5: 13
c0: -70
skew: 1.40
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 665001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 87580 x 87818
Total sieving time: 2.19 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 2.19 hours.
 --------- CPU info (if available) ----------

(38·10¹²⁴+61)/9 = 4(2)₁₂₃9_<125> = 11 · 47² · 383 · 170711 · 1500390189343255882395007_<25> · C89

C89 = P41 · P48

P41 = 63555308651323802072448928885255075100069_<41>

P48 = 278699608001282959114888883431789684547614379749_<48>

Tue Dec 23 20:12:21 2008  Msieve v. 1.39
Tue Dec 23 20:12:21 2008  random seeds: 7df503ec db120c14
Tue Dec 23 20:12:21 2008  factoring 17712839607524491181194896261236888181051603158412905861666362722760429830774699542102681 (89 digits)
Tue Dec 23 20:12:22 2008  searching for 15-digit factors
Tue Dec 23 20:12:24 2008  commencing quadratic sieve (89-digit input)
Tue Dec 23 20:12:24 2008  using multiplier of 1
Tue Dec 23 20:12:24 2008  using 32kb Intel Core sieve core
Tue Dec 23 20:12:24 2008  sieve interval: 30 blocks of size 32768
Tue Dec 23 20:12:24 2008  processing polynomials in batches of 7
Tue Dec 23 20:12:24 2008  using a sieve bound of 1546837 (58547 primes)
Tue Dec 23 20:12:24 2008  using large prime bound of 123746960 (26 bits)
Tue Dec 23 20:12:24 2008  using double large prime bound of 368605688486800 (42-49 bits)
Tue Dec 23 20:12:24 2008  using trial factoring cutoff of 49 bits
Tue Dec 23 20:12:24 2008  polynomial 'A' values have 11 factors
Tue Dec 23 21:02:17 2008  58671 relations (16518 full + 42153 combined from 614508 partial), need 58643
Tue Dec 23 21:02:18 2008  begin with 631026 relations
Tue Dec 23 21:02:19 2008  reduce to 139761 relations in 11 passes
Tue Dec 23 21:02:19 2008  attempting to read 139761 relations
Tue Dec 23 21:02:20 2008  recovered 139761 relations
Tue Dec 23 21:02:20 2008  recovered 112916 polynomials
Tue Dec 23 21:02:20 2008  attempting to build 58671 cycles
Tue Dec 23 21:02:21 2008  found 58671 cycles in 6 passes
Tue Dec 23 21:02:21 2008  distribution of cycle lengths:
Tue Dec 23 21:02:21 2008     length 1 : 16518
Tue Dec 23 21:02:21 2008     length 2 : 11650
Tue Dec 23 21:02:21 2008     length 3 : 10419
Tue Dec 23 21:02:21 2008     length 4 : 7564
Tue Dec 23 21:02:21 2008     length 5 : 5203
Tue Dec 23 21:02:21 2008     length 6 : 3267
Tue Dec 23 21:02:21 2008     length 7 : 1916
Tue Dec 23 21:02:21 2008     length 9+: 2134
Tue Dec 23 21:02:21 2008  largest cycle: 19 relations
Tue Dec 23 21:02:21 2008  matrix is 58547 x 58671 (13.9 MB) with weight 3403013 (58.00/col)
Tue Dec 23 21:02:21 2008  sparse part has weight 3403013 (58.00/col)
Tue Dec 23 21:02:21 2008  filtering completed in 3 passes
Tue Dec 23 21:02:21 2008  matrix is 53864 x 53928 (12.9 MB) with weight 3170121 (58.78/col)
Tue Dec 23 21:02:21 2008  sparse part has weight 3170121 (58.78/col)
Tue Dec 23 21:02:22 2008  saving the first 48 matrix rows for later
Tue Dec 23 21:02:22 2008  matrix is 53816 x 53928 (9.1 MB) with weight 2584186 (47.92/col)
Tue Dec 23 21:02:22 2008  sparse part has weight 2066484 (38.32/col)
Tue Dec 23 21:02:22 2008  matrix includes 64 packed rows
Tue Dec 23 21:02:22 2008  using block size 21571 for processor cache size 1024 kB
Tue Dec 23 21:02:22 2008  commencing Lanczos iteration
Tue Dec 23 21:02:22 2008  memory use: 8.4 MB
Tue Dec 23 21:02:40 2008  lanczos halted after 853 iterations (dim = 53814)
Tue Dec 23 21:02:40 2008  recovered 16 nontrivial dependencies
Tue Dec 23 21:02:41 2008  prp41 factor: 63555308651323802072448928885255075100069
Tue Dec 23 21:02:41 2008  prp48 factor: 278699608001282959114888883431789684547614379749
Tue Dec 23 21:02:41 2008  elapsed time 00:50:20

(38·10¹²³+61)/9 = 4(2)₁₂₂9_<124> = 59 · 29050033885209937_<17> · C106

C106 = P38 · P68

P38 = 90758930904109184231531507553783048527_<38>

P68 = 27142700885477796848302781645863411898017548539507764956042342567569_<68>

Number: 42229_123
N=2463442514215982536119131591935078249728878201624727560526653267928776465809352361520806512445821303420863
  ( 106 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=90758930904109184231531507553783048527
 r2=27142700885477796848302781645863411898017548539507764956042342567569
Version: 
Total time: 1.88 hours.
Scaled time: 4.84 units (timescale=2.575).
Factorization parameters were as follows:
name: 42229_123
n: 2463442514215982536119131591935078249728878201624727560526653267928776465809352361520806512445821303420863
m: 5000000000000000000000000
deg: 5
c5: 304
c0: 1525
skew: 1.38
type: snfs
lss: 1
rlim: 880000
alim: 880000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 880000/880000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [440000, 640001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 111021 x 111261
Total sieving time: 1.88 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000
total time: 1.88 hours.
 --------- CPU info (if available) ----------

(38·10¹³¹+61)/9 = 4(2)₁₃₀9_<132> = 3 · 661 · C129

C129 = P62 · P68

P62 = 18931593415430636447428825920870807172531523070990639092291417_<62>

P68 = 11246857801195903571673445644347018389968064581167169333729364888739_<68>

Number: 42229_131
N=212920939093405054070712164509441362694010197792346052557852860424721241665265871014736370258306718215946657701574494312769653163
  ( 129 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=18931593415430636447428825920870807172531523070990639092291417
 r2=11246857801195903571673445644347018389968064581167169333729364888739
Version: 
Total time: 3.43 hours.
Scaled time: 7.84 units (timescale=2.282).
Factorization parameters were as follows:
name: 42229_131
n: 212920939093405054070712164509441362694010197792346052557852860424721241665265871014736370258306718215946657701574494312769653163
m: 100000000000000000000000000
deg: 5
c5: 380
c0: 61
skew: 0.69
type: snfs
lss: 1
rlim: 1130000
alim: 1130000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1130000/1130000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [565000, 1015001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 159415 x 159663
Total sieving time: 3.43 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1130000,1130000,26,26,47,47,2.3,2.3,50000
total time: 3.43 hours.
 --------- CPU info (if available) ----------

(38·10¹²⁵+61)/9 = 4(2)₁₂₄9_<126> = 3⁴ · 23789 · C120

C120 = P48 · P72

P48 = 375555149263134842089555204601763364829365781719_<48>

P72 = 583453381194914039518484879886709379205169265358315351203669660340202799_<72>

Number: 42229_125
N=219118921662736653480897241240879679435937152310888693873048609053267290890344184505974190904823332197951341875626831481
  ( 120 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=375555149263134842089555204601763364829365781719
 r2=583453381194914039518484879886709379205169265358315351203669660340202799
Version: 
Total time: 2.23 hours.
Scaled time: 4.43 units (timescale=1.991).
Factorization parameters were as follows:
name: 42229_125
n: 219118921662736653480897241240879679435937152310888693873048609053267290890344184505974190904823332197951341875626831481
m: 10000000000000000000000000
deg: 5
c5: 38
c0: 61
skew: 1.10
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 123791 x 124029
Total sieving time: 2.23 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 2.23 hours.
 --------- CPU info (if available) ----------

(13·10¹⁷⁴-7)/3 = 4(3)₁₇₃1_<175> = 2661733 · 2981915448269_<13> · 57373034177700817_<17> · 210183647146556081_<18> · 1886441303582244311116568671646101_<34> · C89

C89 = P37 · P53

P37 = 1154850117862112282943626662349224241_<37>

P53 = 20781965619296732780146962236360397468436031673870679_<53>

ue Dec 23 21:17:52 2008  Msieve v. 1.39
Tue Dec 23 21:17:52 2008  random seeds: 9d7994a0 f4a4cbfc
Tue Dec 23 21:17:52 2008  factoring 24000055444851197132978321002485393490269394924989129370986539182893234062802945405929639 (89 digits)
Tue Dec 23 21:17:53 2008  searching for 15-digit factors
Tue Dec 23 21:17:54 2008  commencing quadratic sieve (89-digit input)
Tue Dec 23 21:17:54 2008  using multiplier of 39
Tue Dec 23 21:17:54 2008  using 32kb Intel Core sieve core
Tue Dec 23 21:17:54 2008  sieve interval: 30 blocks of size 32768
Tue Dec 23 21:17:54 2008  processing polynomials in batches of 7
Tue Dec 23 21:17:54 2008  using a sieve bound of 1545007 (58667 primes)
Tue Dec 23 21:17:54 2008  using large prime bound of 123600560 (26 bits)
Tue Dec 23 21:17:54 2008  using double large prime bound of 367821176096160 (42-49 bits)
Tue Dec 23 21:17:54 2008  using trial factoring cutoff of 49 bits
Tue Dec 23 21:17:54 2008  polynomial 'A' values have 12 factors
Tue Dec 23 22:28:02 2008  58882 relations (15618 full + 43264 combined from 622557 partial), need 58763
Tue Dec 23 22:28:03 2008  begin with 638175 relations
Tue Dec 23 22:28:03 2008  reduce to 143131 relations in 9 passes
Tue Dec 23 22:28:03 2008  attempting to read 143131 relations
Tue Dec 23 22:28:05 2008  recovered 143131 relations
Tue Dec 23 22:28:05 2008  recovered 124085 polynomials
Tue Dec 23 22:28:05 2008  attempting to build 58882 cycles
Tue Dec 23 22:28:05 2008  found 58881 cycles in 5 passes
Tue Dec 23 22:28:05 2008  distribution of cycle lengths:
Tue Dec 23 22:28:05 2008     length 1 : 15618
Tue Dec 23 22:28:05 2008     length 2 : 11396
Tue Dec 23 22:28:05 2008     length 3 : 10604
Tue Dec 23 22:28:05 2008     length 4 : 7945
Tue Dec 23 22:28:05 2008     length 5 : 5461
Tue Dec 23 22:28:05 2008     length 6 : 3495
Tue Dec 23 22:28:05 2008     length 7 : 2019
Tue Dec 23 22:28:05 2008     length 9+: 2343
Tue Dec 23 22:28:05 2008  largest cycle: 17 relations
Tue Dec 23 22:28:06 2008  matrix is 58667 x 58881 (14.2 MB) with weight 3480054 (59.10/col)
Tue Dec 23 22:28:06 2008  sparse part has weight 3480054 (59.10/col)
Tue Dec 23 22:28:06 2008  filtering completed in 3 passes
Tue Dec 23 22:28:06 2008  matrix is 54828 x 54892 (13.3 MB) with weight 3262907 (59.44/col)
Tue Dec 23 22:28:06 2008  sparse part has weight 3262907 (59.44/col)
Tue Dec 23 22:28:06 2008  saving the first 48 matrix rows for later
Tue Dec 23 22:28:06 2008  matrix is 54780 x 54892 (8.1 MB) with weight 2523354 (45.97/col)
Tue Dec 23 22:28:06 2008  sparse part has weight 1787841 (32.57/col)
Tue Dec 23 22:28:06 2008  matrix includes 64 packed rows
Tue Dec 23 22:28:06 2008  using block size 21956 for processor cache size 1024 kB
Tue Dec 23 22:28:07 2008  commencing Lanczos iteration
Tue Dec 23 22:28:07 2008  memory use: 8.0 MB
Tue Dec 23 22:28:24 2008  lanczos halted after 868 iterations (dim = 54778)
Tue Dec 23 22:28:24 2008  recovered 17 nontrivial dependencies
Tue Dec 23 22:28:24 2008  prp37 factor: 1154850117862112282943626662349224241
Tue Dec 23 22:28:24 2008  prp53 factor: 20781965619296732780146962236360397468436031673870679
Tue Dec 23 22:28:24 2008  elapsed time 01:10:32

Dec 23, 2008 (6th)

By Jo Yeong Uk / GGNFS / Msieve v1.39

(38·10¹⁵⁸+7)/9 = 4(2)₁₅₇3_<159> = 3 · 41 · 227 · 457 · 719 · 11692937714243057_<17> · C133

C133 = P60 · P74

P60 = 261684502017364426401172993314582377543873715761538550838501_<60>

P74 = 15040538615515346545319103996178595611693408558594037216409591162891195973_<74>

I've used Greg Childer's x64 binaries that is about 30% faster.

Number: 42223_158
N=3935875857674073259892366744726611131660458011927081245662043080032693008432327787653104908465235028172227775906183483719689864556473
  ( 133 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=261684502017364426401172993314582377543873715761538550838501
 r2=15040538615515346545319103996178595611693408558594037216409591162891195973
Version: 
Total time: 16.42 hours.
Scaled time: 39.20 units (timescale=2.387).
Factorization parameters were as follows:
n: 3935875857674073259892366744726611131660458011927081245662043080032693008432327787653104908465235028172227775906183483719689864556473
m: 100000000000000000000000000000000
deg: 5
c5: 19
c0: 350
skew: 1.79
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9164673
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 657541 x 657789
Total sieving time: 14.77 hours.
Total relation processing time: 0.62 hours.
Matrix solve time: 0.95 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 16.42 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(13·10¹⁶³-7)/3 = 4(3)₁₆₂1_<164> = 23 · 181 · 201977806379599_<15> · 256380435467453624357_<21> · 3848836599303511776161_<22> · C104

C104 = P40 · P65

P40 = 2484322471920498002597770188046418572961_<40>

P65 = 21022759073577810522071683163551125750312379421937000260369560979_<65>

Number: 43331_163
N=52227312788259904783285448177771151215979194504591185340103120146351292794322523024425734515127250088819
  ( 104 digits)
Divisors found:
 r1=2484322471920498002597770188046418572961
 r2=21022759073577810522071683163551125750312379421937000260369560979
Version: 
Total time: 3.98 hours.
Scaled time: 9.53 units (timescale=2.391).
Factorization parameters were as follows:
name: 43331_163
n: 52227312788259904783285448177771151215979194504591185340103120146351292794322523024425734515127250088819
skew: 22078.67
# norm 5.99e+14
c5: 21240
c4: -1497386772
c3: -38425098620186
c2: 845882405351926079
c1: 8026727642520429063354
c0: 1072508182475386490862336
# alpha -6.69
Y1: 84046748929
Y0: -75536254703912113145
# Murphy_E 2.05e-09
# M 14288233827694019863237397998856850064401035115600452898033582468342007884707128037624699464864009909031
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved algebraic special-q in [750000, 1500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 5069392
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 241075 x 241323
Total sieving time: 3.46 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000
total time: 3.98 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Dec 23, 2008 (5th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(13·10¹⁰⁶-7)/3 = 4(3)₁₀₅1_<107> = 41 · 13774823 · 49522433 · C91

C91 = P32 · P59

P32 = 57847164065344667246749592041001_<32>

P59 = 26783551748975471064496580057189581449979924547068814782949_<59>

Number: n
N=1549352512275633183368088459353775952136320751322520942606357553923121412953602781723691949
  ( 91 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=57847164065344667246749592041001 (pp32)
 r2=26783551748975471064496580057189581449979924547068814782949 (pp59)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.65 hours.
Scaled time: 1.18 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_4_3_105_1
n: 1549352512275633183368088459353775952136320751322520942606357553923121412953602781723691949
type: snfs
skew: 0.56
deg: 5
c5: 130
c0: -7
m: 1000000000000000000000
rlim: 450000
alim: 450000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 2000
Factor base limits: 450000/450000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [225000, 271001)
Primes: RFBsize:37706, AFBsize:37704, largePrimes:4143192 encountered
Relations: rels:3498691, finalFF:97136
Max relations in full relation-set: 48
Initial matrix: 75477 x 97136 with sparse part having weight 10956977.
Pruned matrix : 70519 x 70960 with weight 5601496.
Total sieving time: 0.56 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.02 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,107,5,0,0,0,0,0,0,0,0,450000,450000,28,28,56,56,2.5,2.5,50000
total time: 0.65 hours.
 --------- CPU info (if available) ----------

(38·10¹¹⁶+61)/9 = 4(2)₁₁₅9_<117> = 3² · 11 · 13 · 6271 · 7643257 · 44775959 · 883573237 · C87

C87 = P40 · P47

P40 = 4242755187407345742527427668930198334521_<40>

P47 = 40776679208206304454293512576431198414080057327_<47>

Tue Dec 23 18:19:00 2008  
Tue Dec 23 18:19:00 2008  
Tue Dec 23 18:19:00 2008  Msieve v. 1.39
Tue Dec 23 18:19:00 2008  random seeds: 96cc2620 f2dff84d
Tue Dec 23 18:19:00 2008  factoring 173005467235862557859424523342614033694193668612191137256544163118007289277935603085367 (87 digits)
Tue Dec 23 18:19:01 2008  searching for 15-digit factors
Tue Dec 23 18:19:02 2008  commencing quadratic sieve (87-digit input)
Tue Dec 23 18:19:02 2008  using multiplier of 7
Tue Dec 23 18:19:02 2008  using 64kb Opteron sieve core
Tue Dec 23 18:19:02 2008  sieve interval: 10 blocks of size 65536
Tue Dec 23 18:19:02 2008  processing polynomials in batches of 11
Tue Dec 23 18:19:02 2008  using a sieve bound of 1480243 (56254 primes)
Tue Dec 23 18:19:02 2008  using large prime bound of 118419440 (26 bits)
Tue Dec 23 18:19:02 2008  using double large prime bound of 340534638927600 (41-49 bits)
Tue Dec 23 18:19:02 2008  using trial factoring cutoff of 49 bits
Tue Dec 23 18:19:02 2008  polynomial 'A' values have 11 factors
Tue Dec 23 18:48:34 2008  56642 relations (16217 full + 40425 combined from 588342 partial), need 56350
Tue Dec 23 18:48:34 2008  begin with 604559 relations
Tue Dec 23 18:48:34 2008  reduce to 134247 relations in 11 passes
Tue Dec 23 18:48:34 2008  attempting to read 134247 relations
Tue Dec 23 18:48:35 2008  recovered 134247 relations
Tue Dec 23 18:48:35 2008  recovered 109821 polynomials
Tue Dec 23 18:48:35 2008  attempting to build 56642 cycles
Tue Dec 23 18:48:36 2008  found 56642 cycles in 5 passes
Tue Dec 23 18:48:36 2008  distribution of cycle lengths:
Tue Dec 23 18:48:36 2008     length 1 : 16217
Tue Dec 23 18:48:36 2008     length 2 : 11293
Tue Dec 23 18:48:36 2008     length 3 : 10010
Tue Dec 23 18:48:36 2008     length 4 : 7280
Tue Dec 23 18:48:36 2008     length 5 : 5006
Tue Dec 23 18:48:36 2008     length 6 : 3000
Tue Dec 23 18:48:36 2008     length 7 : 1762
Tue Dec 23 18:48:36 2008     length 9+: 2074
Tue Dec 23 18:48:36 2008  largest cycle: 17 relations
Tue Dec 23 18:48:36 2008  matrix is 56254 x 56642 (12.9 MB) with weight 3166386 (55.90/col)
Tue Dec 23 18:48:36 2008  sparse part has weight 3166386 (55.90/col)
Tue Dec 23 18:48:37 2008  filtering completed in 3 passes
Tue Dec 23 18:48:37 2008  matrix is 51309 x 51373 (11.8 MB) with weight 2892193 (56.30/col)
Tue Dec 23 18:48:37 2008  sparse part has weight 2892193 (56.30/col)
Tue Dec 23 18:48:37 2008  saving the first 48 matrix rows for later
Tue Dec 23 18:48:37 2008  matrix is 51261 x 51373 (7.7 MB) with weight 2276433 (44.31/col)
Tue Dec 23 18:48:37 2008  sparse part has weight 1699820 (33.09/col)
Tue Dec 23 18:48:37 2008  matrix includes 64 packed rows
Tue Dec 23 18:48:37 2008  using block size 20549 for processor cache size 1024 kB
Tue Dec 23 18:48:37 2008  commencing Lanczos iteration
Tue Dec 23 18:48:37 2008  memory use: 7.5 MB
Tue Dec 23 18:48:51 2008  lanczos halted after 812 iterations (dim = 51259)
Tue Dec 23 18:48:51 2008  recovered 16 nontrivial dependencies
Tue Dec 23 18:48:52 2008  prp40 factor: 4242755187407345742527427668930198334521
Tue Dec 23 18:48:52 2008  prp47 factor: 40776679208206304454293512576431198414080057327
Tue Dec 23 18:48:52 2008  elapsed time 00:29:52

(13·10¹³⁴-7)/3 = 4(3)₁₃₃1_<135> = 8849 · 48271117 · 8224435209442541_<16> · 423468662193971749903_<21> · C87

C87 = P32 · P55

P32 = 69478828398569728593459721798867_<32>

P55 = 4192380641004827675507764758323249935285647811508989127_<55>

Tue Dec 23 19:41:18 2008  
Tue Dec 23 19:41:18 2008  
Tue Dec 23 19:41:18 2008  Msieve v. 1.39
Tue Dec 23 19:41:18 2008  random seeds: baed84ac 587f7957
Tue Dec 23 19:41:18 2008  factoring 291281695137860183482012662507685449765126395405237570140944533477572342538205183919109 (87 digits)
Tue Dec 23 19:41:18 2008  searching for 15-digit factors
Tue Dec 23 19:41:19 2008  commencing quadratic sieve (87-digit input)
Tue Dec 23 19:41:19 2008  using multiplier of 29
Tue Dec 23 19:41:19 2008  using 64kb Opteron sieve core
Tue Dec 23 19:41:19 2008  sieve interval: 10 blocks of size 65536
Tue Dec 23 19:41:19 2008  processing polynomials in batches of 11
Tue Dec 23 19:41:19 2008  using a sieve bound of 1489667 (56642 primes)
Tue Dec 23 19:41:19 2008  using large prime bound of 119173360 (26 bits)
Tue Dec 23 19:41:19 2008  using double large prime bound of 344447000754720 (42-49 bits)
Tue Dec 23 19:41:19 2008  using trial factoring cutoff of 49 bits
Tue Dec 23 19:41:19 2008  polynomial 'A' values have 11 factors
Tue Dec 23 20:13:40 2008  56750 relations (16023 full + 40727 combined from 592860 partial), need 56738
Tue Dec 23 20:13:40 2008  begin with 608883 relations
Tue Dec 23 20:13:41 2008  reduce to 135001 relations in 8 passes
Tue Dec 23 20:13:41 2008  attempting to read 135001 relations
Tue Dec 23 20:13:42 2008  recovered 135001 relations
Tue Dec 23 20:13:42 2008  recovered 113426 polynomials
Tue Dec 23 20:13:42 2008  attempting to build 56750 cycles
Tue Dec 23 20:13:42 2008  found 56750 cycles in 6 passes
Tue Dec 23 20:13:42 2008  distribution of cycle lengths:
Tue Dec 23 20:13:42 2008     length 1 : 16023
Tue Dec 23 20:13:42 2008     length 2 : 11360
Tue Dec 23 20:13:42 2008     length 3 : 9954
Tue Dec 23 20:13:42 2008     length 4 : 7463
Tue Dec 23 20:13:42 2008     length 5 : 5058
Tue Dec 23 20:13:42 2008     length 6 : 3100
Tue Dec 23 20:13:42 2008     length 7 : 1796
Tue Dec 23 20:13:42 2008     length 9+: 1996
Tue Dec 23 20:13:42 2008  largest cycle: 19 relations
Tue Dec 23 20:13:42 2008  matrix is 56642 x 56750 (13.3 MB) with weight 3250880 (57.28/col)
Tue Dec 23 20:13:42 2008  sparse part has weight 3250880 (57.28/col)
Tue Dec 23 20:13:43 2008  filtering completed in 3 passes
Tue Dec 23 20:13:43 2008  matrix is 52021 x 52085 (12.3 MB) with weight 3026197 (58.10/col)
Tue Dec 23 20:13:43 2008  sparse part has weight 3026197 (58.10/col)
Tue Dec 23 20:13:43 2008  saving the first 48 matrix rows for later
Tue Dec 23 20:13:43 2008  matrix is 51973 x 52085 (8.6 MB) with weight 2442834 (46.90/col)
Tue Dec 23 20:13:43 2008  sparse part has weight 1949032 (37.42/col)
Tue Dec 23 20:13:43 2008  matrix includes 64 packed rows
Tue Dec 23 20:13:43 2008  using block size 20834 for processor cache size 1024 kB
Tue Dec 23 20:13:44 2008  commencing Lanczos iteration
Tue Dec 23 20:13:44 2008  memory use: 8.0 MB
Tue Dec 23 20:13:59 2008  lanczos halted after 823 iterations (dim = 51967)
Tue Dec 23 20:13:59 2008  recovered 13 nontrivial dependencies
Tue Dec 23 20:14:00 2008  prp32 factor: 69478828398569728593459721798867
Tue Dec 23 20:14:00 2008  prp55 factor: 4192380641004827675507764758323249935285647811508989127
Tue Dec 23 20:14:00 2008  elapsed time 00:32:42

(13·10¹⁰⁹-7)/3 = 4(3)₁₀₈1_<110> = 17 · 137 · 977 · C104

C104 = P31 · P73

P31 = 3407814690944317539762588740159_<31>

P73 = 5588330392801960092177439750747650769278886747644606354321657148324217573_<73>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 19043994410441148270827281371648092179964575240551285550193450360143908141146468972425614524063478614107 (104 digits)
Using B1=714000, B2=696728352, polynomial Dickson(3), sigma=1623556616
Step 1 took 4969ms
Step 2 took 2609ms
********** Factor found in step 2: 3407814690944317539762588740159
Found probable prime factor of 31 digits: 3407814690944317539762588740159
Probable prime cofactor 5588330392801960092177439750747650769278886747644606354321657148324217573 has 73 digits

(38·10¹⁰⁹+61)/9 = 4(2)₁₀₈9_<110> = 7 · 199 · 881 · 580373 · C98

C98 = P44 · P55

P44 = 26751738096440014307990911916120465357207011_<44>

P55 = 2215923985067384009560418171449180919028006614390617771_<55>

Number: n
N=59279818090142310194468555816137740448324236376809698473858515326593093225915093020485675422392481
  ( 98 digits)
SNFS difficulty: 111 digits.
Divisors found:

Wed Dec 24 00:30:23 2008  prp44 factor: 26751738096440014307990911916120465357207011
Wed Dec 24 00:30:23 2008  prp55 factor: 2215923985067384009560418171449180919028006614390617771
Wed Dec 24 00:30:23 2008  elapsed time 00:05:05 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.65 hours.
Scaled time: 1.20 units (timescale=1.828).
Factorization parameters were as follows:
name: KA_4_2_108_9
n: 59279818090142310194468555816137740448324236376809698473858515326593093225915093020485675422392481
type: snfs
skew: 1.74
deg: 5
c5: 19
c0: 305
m: 10000000000000000000000
rlim: 450000
alim: 450000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 5000
Factor base limits: 450000/450000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 275001)
Primes: RFBsize:37706, AFBsize:37830, largePrimes:4770991 encountered
Relations: rels:3870829, finalFF:81071
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 105623 hash collisions in 3950766 relations
Msieve: matrix is 89786 x 90033 (23.6 MB)

Total sieving time: 0.60 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,450000,450000,29,29,58,58,2.5,2.5,50000
total time: 0.65 hours.
 --------- CPU info (if available) ----------

Dec 23, 2008 (4th)

By Sinkiti Sibata / Msieve

(38·10¹⁴⁹+43)/9 = 4(2)₁₄₈7_<150> = 13 · 113453640491_<12> · C138

C138 = P39 · P47 · P53

P39 = 123132274553465756860058461410327710779_<39>

P47 = 27267256871151239064440712042018508774862667557_<47>

P53 = 85264047995684401299884905037961478641338880822995323_<53>

Number: 42227_149
N=286272281242565584871308935586551398963328947291933211769489506901789407053841847782020315712273819190869798534111037762948452697250984669
  ( 138 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=123132274553465756860058461410327710779
 r2=27267256871151239064440712042018508774862667557
 r3=85264047995684401299884905037961478641338880822995323
Version: 
Total time: 17.03 hours.
Scaled time: 33.49 units (timescale=1.967).
Factorization parameters were as follows:
name: 42227_149
n: 286272281242565584871308935586551398963328947291933211769489506901789407053841847782020315712273819190869798534111037762948452697250984669
m: 1000000000000000000000000000000
deg: 5
c5: 19
c0: 215
skew: 1.62
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 326210 x 326458
Total sieving time: 17.03 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 17.03 hours.
 --------- CPU info (if available) ----------

Dec 23, 2008 (3rd)

By Serge Batalov / GMP-ECM 6.2.1

(38·10¹⁷⁹+43)/9 = 4(2)₁₇₈7_<180> = 13 · 190548791 · C171

C171 = P32 · C139

P32 = 83693711822605989870189783269927_<32>

C139 = [2036567026754301909068906536670007279613488322697273803941595712633680899678332169392476463478230146670448373216770032371376154711024549247_<139>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=28284232
Step 1 took 50467ms
Step 2 took 24270ms
********** Factor found in step 2: 83693711822605989870189783269927
Found probable prime factor of 32 digits: 83693711822605989870189783269927
Composite cofactor has 139 digits

(38·10¹⁹⁵+43)/9 = 4(2)₁₉₄7_<196> = 3 · 1409 · 36583 · 2631581 · C182

C182 = P37 · P145

P37 = 1110098676846052025875562910419707159_<37>

P145 = 9346547020444687949473270005207416033036409081717352834060726263287081343511433873690747964630107753834169432220989123151666306482271859585653093_<145>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=3282926492
Step 1 took 58616ms
Step 2 took 26203ms
********** Factor found in step 2: 1110098676846052025875562910419707159
Found probable prime factor of 37 digits: 1110098676846052025875562910419707159
Probable prime cofactor has 145 digits

Dec 23, 2008 (2nd)

By Robert Backstrom / GMP-ECM

(11·10¹⁶⁶-17)/3 = 3(6)₁₆₅1_<167> = 31 · 9645541 · C159

C159 = P40 · P120

P40 = 1116427148631667120168455525371131408601_<40>

P120 = 109838035390645973298719203114797829250387790912028941879398460215801086922957023513075842014334465944683742916668887991_<120>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 122626164662483025347743472836949508140489448044728201240835654816634849691809178531191224129656978175172463918374192254346624590463586353818380837812123010591 (159 digits)
Using B1=2860000, B2=4281671950, polynomial Dickson(6), sigma=2445717877
Step 1 took 37615ms
Step 2 took 13651ms
********** Factor found in step 2: 1116427148631667120168455525371131408601
Found probable prime factor of 40 digits: 1116427148631667120168455525371131408601
Probable prime cofactor 109838035390645973298719203114797829250387790912028941879398460215801086922957023513075842014334465944683742916668887991 has 120 digits

Dec 23, 2008

Factorizations of 422...229 and Factorizations of 433...331 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Dec 22, 2008 (5th)

By Jo Yeong Uk / GMP-ECM, Msieve

(37·10¹⁹⁰+53)/9 = 4(1)₁₈₉7_<191> = 59 · 33366083669_<11> · 1038688946123696607997710239_<28> · 228822554008790119385212155709949_<33> · C119

C119 = P37 · P41 · P42

P37 = 6700559039122072293901319740648826129_<37>

P41 = 94122795556702802098640504555138641771009_<41>

P42 = 139319457310594504389225773069331905769337_<42>

GMP-ECM 6.2.1 [powered by GMP 4.2.3] [ECM]
Input number is 87865347299839227077677777536365983116150872999131750437968032584396075641901842890425376739301590272179304048017141257 (119 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2495475907
Step 1 took 13322ms
Step 2 took 9282ms
********** Factor found in step 2: 6700559039122072293901319740648826129
Found probable prime factor of 37 digits: 6700559039122072293901319740648826129
Composite cofactor 13113136797515870136423584090069674988260781902340888649157796440990324986327751033 has 83 digits

Mon Dec 22 22:59:56 2008  
Mon Dec 22 22:59:56 2008  
Mon Dec 22 22:59:56 2008  Msieve v. 1.39
Mon Dec 22 22:59:56 2008  random seeds: 5344db90 d0343cf0
Mon Dec 22 22:59:56 2008  factoring 13113136797515870136423584090069674988260781902340888649157796440990324986327751033 (83 digits)
Mon Dec 22 22:59:57 2008  searching for 15-digit factors
Mon Dec 22 22:59:58 2008  commencing quadratic sieve (83-digit input)
Mon Dec 22 22:59:58 2008  using multiplier of 1
Mon Dec 22 22:59:58 2008  using VC8 32kb sieve core
Mon Dec 22 22:59:58 2008  sieve interval: 12 blocks of size 32768
Mon Dec 22 22:59:58 2008  processing polynomials in batches of 17
Mon Dec 22 22:59:58 2008  using a sieve bound of 1357919 (52059 primes)
Mon Dec 22 22:59:58 2008  using large prime bound of 124928548 (26 bits)
Mon Dec 22 22:59:58 2008  using trial factoring cutoff of 27 bits
Mon Dec 22 22:59:58 2008  polynomial 'A' values have 10 factors
Mon Dec 22 23:15:29 2008  52266 relations (26562 full + 25704 combined from 277983 partial), need 52155
Mon Dec 22 23:15:29 2008  begin with 304545 relations
Mon Dec 22 23:15:29 2008  reduce to 74683 relations in 2 passes
Mon Dec 22 23:15:29 2008  attempting to read 74683 relations
Mon Dec 22 23:15:30 2008  recovered 74683 relations
Mon Dec 22 23:15:30 2008  recovered 66029 polynomials
Mon Dec 22 23:15:30 2008  attempting to build 52266 cycles
Mon Dec 22 23:15:30 2008  found 52266 cycles in 1 passes
Mon Dec 22 23:15:30 2008  distribution of cycle lengths:
Mon Dec 22 23:15:30 2008     length 1 : 26562
Mon Dec 22 23:15:30 2008     length 2 : 25704
Mon Dec 22 23:15:30 2008  largest cycle: 2 relations
Mon Dec 22 23:15:30 2008  matrix is 52059 x 52266 (7.7 MB) with weight 1591401 (30.45/col)
Mon Dec 22 23:15:30 2008  sparse part has weight 1591401 (30.45/col)
Mon Dec 22 23:15:30 2008  filtering completed in 3 passes
Mon Dec 22 23:15:30 2008  matrix is 37218 x 37282 (6.0 MB) with weight 1276780 (34.25/col)
Mon Dec 22 23:15:30 2008  sparse part has weight 1276780 (34.25/col)
Mon Dec 22 23:15:30 2008  saving the first 48 matrix rows for later
Mon Dec 22 23:15:30 2008  matrix is 37170 x 37282 (4.8 MB) with weight 1060890 (28.46/col)
Mon Dec 22 23:15:30 2008  sparse part has weight 894883 (24.00/col)
Mon Dec 22 23:15:30 2008  matrix includes 64 packed rows
Mon Dec 22 23:15:30 2008  using block size 14912 for processor cache size 4096 kB
Mon Dec 22 23:15:30 2008  commencing Lanczos iteration
Mon Dec 22 23:15:30 2008  memory use: 4.5 MB
Mon Dec 22 23:15:35 2008  lanczos halted after 589 iterations (dim = 37168)
Mon Dec 22 23:15:35 2008  recovered 15 nontrivial dependencies
Mon Dec 22 23:15:35 2008  prp41 factor: 94122795556702802098640504555138641771009
Mon Dec 22 23:15:35 2008  prp42 factor: 139319457310594504389225773069331905769337
Mon Dec 22 23:15:35 2008  elapsed time 00:15:39

Dec 22, 2008 (4th)

By Serge Batalov / GMP-ECM 6.2.1

(38·10¹⁷⁶+43)/9 = 4(2)₁₇₅7_<177> = 7 · 953 · 18013 · 276447312401475563_<18> · C152

C152 = P36 · C116

P36 = 178756426448137413914826142437964919_<36>

C116 = [71103349768243348700450905945142994417179643820598258646824953982535526988209326934630523825762360058327976339721717_<116>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1342266695
Step 1 took 43401ms
Step 2 took 21416ms
********** Factor found in step 2: 178756426448137413914826142437964919
Found probable prime factor of 36 digits: 178756426448137413914826142437964919
Composite cofactor has 116 digits

Dec 22, 2008 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, Msieve v1.39

(38·10¹⁵⁶+7)/9 = 4(2)₁₅₅3_<157> = 1571 · 20627 · 161999 · 31370407 · C137

C137 = P40 · P97

P40 = 3151311867708119352908892784260206809733_<40>

P97 = 8135888003589561713984004929583919997606982433878122227315798705604256568191678963555861658276451_<97>

Number: 42223_156
N=25638720420055904175047718597666401571261026682120717702745767511977789529191792514452212244210202584659272309033290926661594350071497583
  ( 137 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=3151311867708119352908892784260206809733
 r2=8135888003589561713984004929583919997606982433878122227315798705604256568191678963555861658276451
Version: 
Total time: 17.75 hours.
Scaled time: 42.36 units (timescale=2.387).
Factorization parameters were as follows:
n: 25638720420055904175047718597666401571261026682120717702745767511977789529191792514452212244210202584659272309033290926661594350071497583
m: 10000000000000000000000000000000
deg: 5
c5: 380
c0: 7
skew: 0.45
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1500000, 2600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8115178
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 565574 x 565822
Total sieving time: 16.58 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 0.68 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000
total time: 17.75 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(35·10¹⁸⁶-17)/9 = 3(8)₁₈₅7_<187> = 157 · 24359 · 61381 · 8547631 · 741825421 · 12281370259_<11> · 1354976246545216979406271187005039_<34> · C117

C117 = P43 · P74

P43 = 5120353883635458429190544130895666258719013_<43>

P74 = 30662425523328166855980476520758336325858134810791000702868819091594477883_<74>

Number: 38887_186
N=157002469610056383002517699709502160585077480848188350871607152214104956824868980051866840757039680270434992140089479
  ( 117 digits)
Divisors found:
 r1=5120353883635458429190544130895666258719013
 r2=30662425523328166855980476520758336325858134810791000702868819091594477883
Version: 
Total time: 22.72 hours.
Scaled time: 54.15 units (timescale=2.384).
Factorization parameters were as follows:
name: 38887_186
n: 157002469610056383002517699709502160585077480848188350871607152214104956824868980051866840757039680270434992140089479
skew: 90503.15
# norm 3.19e+16
c5: 7200
c4: -1050000632
c3: 784336535541926
c2: 6556944883925153517
c1: -2168736184919240296891976
c0: 307461253102532191921522760
# alpha -7.15
Y1: 2113994864537
Y0: -29357272872032918557839
# Murphy_E 4.67e-10
# M 22297279247945908317688117096806927032070203219509894621581388695827552723266532914832455914310598281190746054030867
type: gnfs
rlim: 3300000
alim: 3300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3300000/3300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [1650000, 2925001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9009334
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 505641 x 505889
Polynomial selection time: 1.73 hours.
Total sieving time: 19.51 hours.
Total relation processing time: 0.70 hours.
Matrix solve time: 0.67 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3300000,3300000,27,27,52,52,2.4,2.4,75000
total time: 22.72 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Dec 22, 2008 (2nd)

By Sinkiti Sibata / GGNFS, Msieve

(38·10¹⁵⁰+43)/9 = 4(2)₁₄₉7_<151> = 3 · 5404033 · 1315507653822793_<16> · 1793543806775351758201343_<25> · C105

C105 = P46 · P59

P46 = 1474436240860335083889521243713798444857541487_<46>

P59 = 74863559958939232893634955690188665701792653148056199268121_<59>

Number: 42227_150
N=110381545923280664073717632487428289003590698192574383665984937129689496720053069202801052883676794035927
  ( 105 digits)
Divisors found:
 r1=1474436240860335083889521243713798444857541487 (pp46)
 r2=74863559958939232893634955690188665701792653148056199268121 (pp59)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 15.61 hours.
Scaled time: 7.37 units (timescale=0.472).
Factorization parameters were as follows:
name: 42227_150
n: 110381545923280664073717632487428289003590698192574383665984937129689496720053069202801052883676794035927
skew: 13420.60
# norm 9.52e+14
c5: 107460
c4: -360905256
c3: -62359547385495
c2: -486725426096074673
c1: 4105199284466708023171
c0: -86832314907525862615335
# alpha -6.88
Y1: 67446069691
Y0: -63435188891743035196
# Murphy_E 1.97e-09
# M 69240885770336502168462731026371669070686911436648784413026709589522938575061457362992740606116577231612
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2150001)
Primes: RFBsize:183072, AFBsize:182694, largePrimes:4397803 encountered
Relations: rels:4492136, finalFF:486116
Max relations in full relation-set: 28
Initial matrix: 365843 x 486116 with sparse part having weight 33668090.
Pruned matrix : 267920 x 269813 with weight 16505009.
Total sieving time: 13.47 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 1.68 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 15.61 hours.
 --------- CPU info (if available) ----------

(38·10¹⁴⁰+43)/9 = 4(2)₁₃₉7_<141> = 7 · 2039 · 16902410577105783452297695849_<29> · C109

C109 = P44 · P66

P44 = 12699265945218353733988416402502984096925867_<44>

P66 = 137815655861186307456994950037515633314473360940130795156807220753_<66>

Number: 42227_140
N=1750157665195895484648268135865022403532332639214085226117860426329641105594587945290563927802167775344917851
  ( 109 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=12699265945218353733988416402502984096925867
 r2=137815655861186307456994950037515633314473360940130795156807220753
Version: 
Total time: 10.29 hours.
Scaled time: 20.61 units (timescale=2.003).
Factorization parameters were as follows:
name: 42227_140
n: 1750157665195895484648268135865022403532332639214085226117860426329641105594587945290563927802167775344917851
m: 10000000000000000000000000000
deg: 5
c5: 38
c0: 43
skew: 1.03
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [800000, 1900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 255864 x 256112
Total sieving time: 10.29 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000
total time: 10.29 hours.
 --------- CPU info (if available) ----------

(38·10¹⁴⁴+43)/9 = 4(2)₁₄₃7_<145> = 3³ · 31 · 1606157397847_<13> · C130

C130 = P59 · P71

P59 = 43754364299985865542408997922500687052406885856436424436163_<59>

P71 = 71780445327028706891060593598257035580865296056623661966850183987404811_<71>

Number: 42227_144
N=3140707754454032100209047495164969064451607130248949747422702757390517541777485585989335253410516591681046770886049171734308580193
  ( 130 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=43754364299985865542408997922500687052406885856436424436163
 r2=71780445327028706891060593598257035580865296056623661966850183987404811
Version: 
Total time: 10.43 hours.
Scaled time: 20.90 units (timescale=2.003).
Factorization parameters were as follows:
name: 42227_144
n: 3140707754454032100209047495164969064451607130248949747422702757390517541777485585989335253410516591681046770886049171734308580193
m: 100000000000000000000000000000
deg: 5
c5: 19
c0: 215
skew: 1.62
type: snfs
lss: 1
rlim: 1920000
alim: 1920000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1920000/1920000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [960000, 1960001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 262590 x 262838
Total sieving time: 10.43 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1920000,1920000,26,26,49,49,2.3,2.3,100000
total time: 10.43 hours.
 --------- CPU info (if available) ----------

(38·10¹⁴⁶+43)/9 = 4(2)₁₄₅7_<147> = 7² · 9222235349_<10> · 81823735257070026169067_<23> · C113

C113 = P54 · P59

P54 = 324669516616670697087399863175104643086264125364574157_<54>

P59 = 35171265133319275701635037151479684144701079965460533176633_<59>

Number: 42227_146
N=11419037649631533302730167351422803394561213724399974201383070218486899102995497193219122768932079190766508073381
  ( 113 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=324669516616670697087399863175104643086264125364574157
 r2=35171265133319275701635037151479684144701079965460533176633
Version: 
Total time: 13.24 hours.
Scaled time: 31.31 units (timescale=2.366).
Factorization parameters were as follows:
name: 42227_146
n: 11419037649631533302730167351422803394561213724399974201383070218486899102995497193219122768932079190766508073381
m: 200000000000000000000000000000
deg: 5
c5: 95
c0: 344
skew: 1.29
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 2750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 362115 x 362360
Total sieving time: 13.24 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 13.24 hours.
 --------- CPU info (if available) ----------

Dec 22, 2008

By Robert Backstrom / GGNFS, Msieve

(37·10¹⁸⁶+71)/9 = 4(1)₁₈₅9_<187> = 3² · 59² · C183

C183 = P47 · P136

P47 = 55044224415250538928921553264661339723266003429_<47>

P136 = 2383970764021785908203194996945240916853952320935449385966474798602815965953926289351897727903544055041607935420772339895475891591817859_<136>

Number: n
N=131223821734211468962019570082387280510425200648316611162536662871815605704334996683938558878710176230045999269402506020336145779026177379141086887902936930994002716687768875837438511
  ( 183 digits)
SNFS difficulty: 187 digits.
Divisors found:

Mon Dec 22 05:04:18 2008  prp47 factor: 55044224415250538928921553264661339723266003429
Mon Dec 22 05:04:18 2008  prp136 factor: 2383970764021785908203194996945240916853952320935449385966474798602815965953926289351897727903544055041607935420772339895475891591817859
Mon Dec 22 05:04:19 2008  elapsed time 06:55:19 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 93.76 hours.
Scaled time: 192.30 units (timescale=2.051).
Factorization parameters were as follows:
name: KA_4_1_185_9
n: 131223821734211468962019570082387280510425200648316611162536662871815605704334996683938558878710176230045999269402506020336145779026177379141086887902936930994002716687768875837438511
type: snfs
skew: 0.72
deg: 5
c5: 370
c0: 71
m: 10000000000000000000000000000000000000
rlim: 8800000
alim: 8800000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8800000/8800000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 5700001)
Primes: RFBsize:590006, AFBsize:589651, largePrimes:33470457 encountered
Relations: rels:31004910, finalFF:1017105
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 7398741 hash collisions in 38005293 relations
Msieve: matrix is 1645242 x 1645490 (446.2 MB)

Total sieving time: 91.92 hours.
Total relation processing time: 1.84 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,8800000,8800000,29,29,58,58,2.5,2.5,100000
total time: 93.76 hours.
 --------- CPU info (if available) ----------

(2·10¹⁸⁶+7)/9 = (2)₁₈₅3_<186> = 61 · 7247 · C180

C180 = P64 · P117

P64 = 1000296869048935293617966311639974939939901074399500816397239041_<64>

P117 = 502539820663756223904404112395960972646821102101410044844975062438931281776309797410654017639319069448362694337047509_<117>

Number: n
N=502689009182368786229739433665535365051501745713256638071202379327618261987938982602687425711989861768062809986319318615101833482757641312792455040123379990413720594892227246598869
  ( 180 digits)
SNFS difficulty: 186 digits.
Divisors found:

Mon Dec 22 17:13:51 2008  prp64 factor: 1000296869048935293617966311639974939939901074399500816397239041
Mon Dec 22 17:13:51 2008  prp117 factor: 502539820663756223904404112395960972646821102101410044844975062438931281776309797410654017639319069448362694337047509
Mon Dec 22 17:13:51 2008  elapsed time 03:54:27 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 45.86 hours.
Scaled time: 92.19 units (timescale=2.010).
Factorization parameters were as follows:
name: KA_2_185_3
n: 502689009182368786229739433665535365051501745713256638071202379327618261987938982602687425711989861768062809986319318615101833482757641312792455040123379990413720594892227246598869
type: snfs
skew: 0.81
deg: 5
c5: 20
c0: 7
m: 10000000000000000000000000000000000000
rlim: 8500000
alim: 8500000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8500000/8500000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 6750001)
Primes: RFBsize:571119, AFBsize:570202, largePrimes:34438043 encountered
Relations: rels:31297614, finalFF:904990
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 3087212 hash collisions in 32883378 relations
Msieve: matrix is 1657566 x 1657814 (456.2 MB)

Total sieving time: 45.11 hours.
Total relation processing time: 0.76 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,8500000,8500000,29,29,58,58,2.5,2.5,100000
total time: 45.86 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830490)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830462)
Total of 4 processors activated (22643.71 BogoMIPS).

Dec 21, 2008 (5th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(38·10¹⁵⁴-11)/9 = 4(2)₁₅₃1_<155> = 277 · 719 · 6091 · 33053 · 207502704317_<12> · 237956979619_<12> · C119

C119 = P59 · P60

P59 = 51587834613479025493547275460082123019777651055195321608609_<59>

P60 = 413393303095561319836967443404945417817696145003663940983647_<60>

Number: n
N=21326065350413624233193962291332887661551544452586939041686174287451002112206135225323163185190177586449359373803417023
  ( 119 digits)
SNFS difficulty: 156 digits.
Divisors found:

Sun Dec 21 11:31:14 2008  prp59 factor: 51587834613479025493547275460082123019777651055195321608609
Sun Dec 21 11:31:14 2008  prp60 factor: 413393303095561319836967443404945417817696145003663940983647
Sun Dec 21 11:31:14 2008  elapsed time 01:19:32 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 20.64 hours.
Scaled time: 37.54 units (timescale=1.819).
Factorization parameters were as follows:
name: KA_4_2_153_1
n: 21326065350413624233193962291332887661551544452586939041686174287451002112206135225323163185190177586449359373803417023
type: snfs
skew: 1.23
deg: 5
c5: 19
c0: -55
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 2550001)
Primes: RFBsize:216816, AFBsize:216782, largePrimes:16418732 encountered
Relations: rels:15539332, finalFF:525467
Max relations in full relation-set: 28
Initial matrix: 433663 x 525467 with sparse part having weight 80415786.
Pruned matrix : 404065 x 406297 with weight 54293410.

Msieve: found 1223712 hash collisions in 16391218 relations
Msieve: matrix is 523190 x 523438 (139.4 MB)

Total sieving time: 20.24 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,56,56,2.5,2.5,100000
total time: 20.64 hours.
 --------- CPU info (if available) ----------

(38·10¹⁴¹+43)/9 = 4(2)₁₄₀7_<142> = 3 · 173 · 21157 · 180243689 · 173456622431_<12> · C116

C116 = P40 · P76

P40 = 1755675497577629798819125718774504104057_<40>

P76 = 7005262960181509629676894759365346286335418889322710401815129565027157909263_<76>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 12298968533278811763657986664253858669350572760397013486487978589390414885086829887869288821107164783220801116179991 (116 digits)
Using B1=2986000, B2=5706890290, polynomial Dickson(6), sigma=3859119621
Step 1 took 23235ms
Step 2 took 10750ms
********** Factor found in step 2: 1755675497577629798819125718774504104057
Found probable prime factor of 40 digits: 1755675497577629798819125718774504104057
Probable prime cofactor 7005262960181509629676894759365346286335418889322710401815129565027157909263 has 76 digits

Dec 21, 2008 (4th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / Msieve v1.39

(38·10¹⁵⁵-11)/9 = 4(2)₁₅₄1_<156> = 103 · 2111 · 58267513 · 7551094801_<10> · C133

C133 = P58 · P75

P58 = 8170250646439144324324539951122523668008977214876413918613_<58>

P75 = 540186647223365813208039585829871641900469751792558202249175396131868628473_<75>

Number: 42221_155
N=4413460303674498541861344363652947120119783104812592625476960256960945509230348423050843447267531724857326155033566161392143756467949
  ( 133 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=8170250646439144324324539951122523668008977214876413918613
 r2=540186647223365813208039585829871641900469751792558202249175396131868628473
Version: 
Total time: 13.44 hours.
Scaled time: 32.11 units (timescale=2.389).
Factorization parameters were as follows:
n: 4413460303674498541861344363652947120119783104812592625476960256960945509230348423050843447267531724857326155033566161392143756467949
m: 10000000000000000000000000000000
deg: 5
c5: 38
c0: -11
skew: 0.78
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7818933
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 471139 x 471387
Total sieving time: 12.38 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.51 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 13.44 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(37·10¹⁷³+17)/9 = 4(1)₁₇₂3_<174> = C174

C174 = P82 · P93

P82 = 2309642251320926628434349570227406190719013760451867200648957231633000117723292239_<82>

P93 = 177997744402185728430025384772804913156559791188015710518448917566430790426321615278811044967_<93>

Number: 41113_173
N=411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113
  ( 174 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=2309642251320926628434349570227406190719013760451867200648957231633000117723292239 (pp82)
 r2=177997744402185728430025384772804913156559791188015710518448917566430790426321615278811044967 (pp93)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 135.17 hours.
Scaled time: 322.66 units (timescale=2.387).
Factorization parameters were as follows:
n: 411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113
m: 100000000000000000000000000000000000
deg: 5
c5: 37
c0: 1700
skew: 2.15
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [2800000, 5400001)
Primes: RFBsize:387202, AFBsize:386654, largePrimes:16029251 encountered
Relations: rels:16426603, finalFF:927524
Max relations in full relation-set: 28
Initial matrix: 773923 x 927524 with sparse part having weight 115621215.
Pruned matrix : 697149 x 701082 with weight 92001068.
Total sieving time: 129.09 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 5.71 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,5600000,5600000,28,28,52,52,2.5,2.5,100000
total time: 135.17 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Dec 21, 2008 (3rd)

By Sinkiti Sibata / Msieve

(38·10¹¹⁶+43)/9 = 4(2)₁₁₅7_<117> = 7 · C116

C116 = P49 · P68

P49 = 1259410019485966740729222522666084595106750113901_<49>

P68 = 47893425797961438500296126851957768875428420854455429268527512319561_<68>

Number: 42227_116
N=60317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317461
  ( 116 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=1259410019485966740729222522666084595106750113901
 r2=47893425797961438500296126851957768875428420854455429268527512319561
Version: 
Total time: 1.82 hours.
Scaled time: 3.62 units (timescale=1.985).
Factorization parameters were as follows:
name: 42227_116
n: 60317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317461
m: 200000000000000000000000
deg: 5
c5: 95
c0: 344
skew: 1.29
type: snfs
lss: 1
rlim: 660000
alim: 660000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 660000/660000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [330000, 580001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 77068 x 77307
Total sieving time: 1.82 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,118,5,0,0,0,0,0,0,0,0,660000,660000,25,25,45,45,2.2,2.2,50000
total time: 1.82 hours.
 --------- CPU info (if available) ----------

(38·10¹²²+43)/9 = 4(2)₁₂₁7_<123> = 7 · 17 · 61 · 149 · C117

C117 = P57 · P60

P57 = 421173275667591299966378819510053262339263564370298327557_<57>

P60 = 926866564584146824501549658874176921660428292030357582201921_<60>

Number: 42227_122
N=390371427112672185902270102305050820709697309077296521718673900043752418633496601046257062255716090668489495772636997
  ( 117 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=421173275667591299966378819510053262339263564370298327557
 r2=926866564584146824501549658874176921660428292030357582201921
Version: 
Total time: 2.34 hours.
Scaled time: 4.65 units (timescale=1.985).
Factorization parameters were as follows:
name: 42227_122
n: 390371427112672185902270102305050820709697309077296521718673900043752418633496601046257062255716090668489495772636997
m: 2000000000000000000000000
deg: 5
c5: 475
c0: 172
skew: 0.82
type: snfs
lss: 1
rlim: 820000
alim: 820000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 820000/820000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [410000, 710001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 91077 x 91317
Total sieving time: 2.34 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,820000,820000,25,25,46,46,2.2,2.2,50000
total time: 2.34 hours.
 --------- CPU info (if available) ----------

(38·10¹⁰¹+43)/9 = 4(2)₁₀₀7_<102> = 13 · 115879 · C96

C96 = P36 · P61

P36 = 149610333136568974573076601882886309_<36>

P61 = 1873403840352829086869098148580338599604466026363314354447189_<61>

Sun Dec 21 06:00:54 2008  Msieve v. 1.39
Sun Dec 21 06:00:54 2008  random seeds: 2932d9f0 724ffcd1
Sun Dec 21 06:00:54 2008  factoring 280280572654514438616821274593606077308905258749492821240074840813542390186993609529185431635401 (96 digits)
Sun Dec 21 06:00:55 2008  searching for 15-digit factors
Sun Dec 21 06:00:56 2008  commencing quadratic sieve (96-digit input)
Sun Dec 21 06:00:57 2008  using multiplier of 1
Sun Dec 21 06:00:57 2008  using 32kb Intel Core sieve core
Sun Dec 21 06:00:57 2008  sieve interval: 36 blocks of size 32768
Sun Dec 21 06:00:57 2008  processing polynomials in batches of 6
Sun Dec 21 06:00:57 2008  using a sieve bound of 2245951 (83529 primes)
Sun Dec 21 06:00:57 2008  using large prime bound of 336892650 (28 bits)
Sun Dec 21 06:00:57 2008  using double large prime bound of 2236066681946550 (43-51 bits)
Sun Dec 21 06:00:57 2008  using trial factoring cutoff of 51 bits
Sun Dec 21 06:00:57 2008  polynomial 'A' values have 12 factors
Sun Dec 21 10:26:20 2008  83888 relations (20624 full + 63264 combined from 1250885 partial), need 83625
Sun Dec 21 10:26:21 2008  begin with 1271509 relations
Sun Dec 21 10:26:23 2008  reduce to 219257 relations in 14 passes
Sun Dec 21 10:26:23 2008  attempting to read 219257 relations
Sun Dec 21 10:26:26 2008  recovered 219257 relations
Sun Dec 21 10:26:26 2008  recovered 203786 polynomials
Sun Dec 21 10:26:26 2008  attempting to build 83888 cycles
Sun Dec 21 10:26:26 2008  found 83888 cycles in 5 passes
Sun Dec 21 10:26:26 2008  distribution of cycle lengths:
Sun Dec 21 10:26:26 2008     length 1 : 20624
Sun Dec 21 10:26:26 2008     length 2 : 14487
Sun Dec 21 10:26:26 2008     length 3 : 14122
Sun Dec 21 10:26:26 2008     length 4 : 11284
Sun Dec 21 10:26:26 2008     length 5 : 8549
Sun Dec 21 10:26:26 2008     length 6 : 5869
Sun Dec 21 10:26:26 2008     length 7 : 3664
Sun Dec 21 10:26:26 2008     length 9+: 5289
Sun Dec 21 10:26:26 2008  largest cycle: 18 relations
Sun Dec 21 10:26:27 2008  matrix is 83529 x 83888 (22.8 MB) with weight 5628323 (67.09/col)
Sun Dec 21 10:26:27 2008  sparse part has weight 5628323 (67.09/col)
Sun Dec 21 10:26:28 2008  filtering completed in 3 passes
Sun Dec 21 10:26:28 2008  matrix is 79673 x 79736 (21.7 MB) with weight 5371984 (67.37/col)
Sun Dec 21 10:26:28 2008  sparse part has weight 5371984 (67.37/col)
Sun Dec 21 10:26:28 2008  saving the first 48 matrix rows for later
Sun Dec 21 10:26:28 2008  matrix is 79625 x 79736 (15.2 MB) with weight 4447552 (55.78/col)
Sun Dec 21 10:26:28 2008  sparse part has weight 3513534 (44.06/col)
Sun Dec 21 10:26:28 2008  matrix includes 64 packed rows
Sun Dec 21 10:26:28 2008  using block size 31894 for processor cache size 1024 kB
Sun Dec 21 10:26:29 2008  commencing Lanczos iteration
Sun Dec 21 10:26:29 2008  memory use: 13.8 MB
Sun Dec 21 10:27:14 2008  lanczos halted after 1261 iterations (dim = 79624)
Sun Dec 21 10:27:14 2008  recovered 16 nontrivial dependencies
Sun Dec 21 10:27:15 2008  prp36 factor: 149610333136568974573076601882886309
Sun Dec 21 10:27:15 2008  prp61 factor: 1873403840352829086869098148580338599604466026363314354447189
Sun Dec 21 10:27:15 2008  elapsed time 04:26:21

(38·10¹²⁹+43)/9 = 4(2)₁₂₈7_<130> = 3 · 31 · 58189 · C123

C123 = P37 · P87

P37 = 1232507627891317146613035330415084249_<37>

P87 = 633034863906915936488414072851613985408624063435282028990273697724896163138531480627299_<87>

Number: 42227_129
N=780220298486415738373901401055962471239385898458475638842840492193351812645781852909460998563306448789737672072710454313451
  ( 123 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=1232507627891317146613035330415084249
 r2=633034863906915936488414072851613985408624063435282028990273697724896163138531480627299
Version: 
Total time: 2.82 hours.
Scaled time: 5.67 units (timescale=2.010).
Factorization parameters were as follows:
name: 42227_129
n: 780220298486415738373901401055962471239385898458475638842840492193351812645781852909460998563306448789737672072710454313451
m: 100000000000000000000000000
deg: 5
c5: 19
c0: 215
skew: 1.62
type: snfs
lss: 1
rlim: 1080000
alim: 1080000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1080000/1080000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [540000, 840001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 148817 x 149065
Total sieving time: 2.82 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1080000,1080000,26,26,47,47,2.3,2.3,50000
total time: 2.82 hours.
 --------- CPU info (if available) ----------

(38·10¹³⁴+43)/9 = 4(2)₁₃₃7_<135> = 7 · 179 · 199 · C130

C130 = P36 · P40 · P54

P36 = 976249081765964679035742823768959109_<36>

P40 = 2341296925239378772934166687655885634501_<40>

P54 = 740832125045200102183124573455647869445175399351741849_<54>

Number: 42227_134
N=1693311819361059977550250142260473245004841534978252083330548280998857905738678316651983870759312212387645418722592299976427317041
  ( 130 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=976249081765964679035742823768959109
 r2=2341296925239378772934166687655885634501
 r3=740832125045200102183124573455647869445175399351741849
Version: 
Total time: 4.33 hours.
Scaled time: 8.49 units (timescale=1.960).
Factorization parameters were as follows:
name: 42227_134
n: 1693311819361059977550250142260473245004841534978252083330548280998857905738678316651983870759312212387645418722592299976427317041
m: 1000000000000000000000000000
deg: 5
c5: 19
c0: 215
skew: 1.62
type: snfs
lss: 1
rlim: 1310000
alim: 1310000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1310000/1310000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [655000, 1105001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 170006 x 170254
Total sieving time: 4.33 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1310000,1310000,26,26,48,48,2.3,2.3,75000
total time: 4.33 hours.
 --------- CPU info (if available) ----------

(38·10¹⁵⁴+7)/9 = 4(2)₁₅₃3_<155> = 109 · 21407 · 153487 · 1581644833984969930562339_<25> · C119

C119 = P57 · P63

P57 = 321166027817848058882563135857714158627714576218012383011_<57>

P63 = 232085824426105456188431120454237300232428792761128210394472227_<63>

Number: 42223_154
N=74538082343762785448110691159984807842440835697113941110272639034909759506082539134491568195318220352077422549926135497
  ( 119 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=321166027817848058882563135857714158627714576218012383011
 r2=232085824426105456188431120454237300232428792761128210394472227
Version: 
Total time: 21.67 hours.
Scaled time: 55.56 units (timescale=2.564).
Factorization parameters were as follows:
name: 42223_154
n: 74538082343762785448110691159984807842440835697113941110272639034909759506082539134491568195318220352077422549926135497
m: 10000000000000000000000000000000
deg: 5
c5: 19
c0: 35
skew: 1.13
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 460519 x 460767
Total sieving time: 21.67 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 21.67 hours.
 --------- CPU info (if available) ----------

(38·10¹¹⁴+43)/9 = 4(2)₁₁₃7_<115> = 3 · 31 · 270737 · 5986022611_<10> · C98

C98 = P40 · P58

P40 = 8392236225335848609185007290798128808749_<40>

P58 = 3338062573732403028949060455916560045484897247255070478873_<58>

Sun Dec 21 14:24:23 2008  Msieve v. 1.39
Sun Dec 21 14:24:23 2008  random seeds: 4496b508 55cd2144
Sun Dec 21 14:24:23 2008  factoring 28013809653714889828606582246638760452158805911349423981945536736639371761734654695622944462059877 (98 digits)
Sun Dec 21 14:24:24 2008  searching for 15-digit factors
Sun Dec 21 14:24:26 2008  commencing quadratic sieve (98-digit input)
Sun Dec 21 14:24:26 2008  using multiplier of 13
Sun Dec 21 14:24:26 2008  using 32kb Intel Core sieve core
Sun Dec 21 14:24:26 2008  sieve interval: 36 blocks of size 32768
Sun Dec 21 14:24:26 2008  processing polynomials in batches of 6
Sun Dec 21 14:24:26 2008  using a sieve bound of 2472797 (90588 primes)
Sun Dec 21 14:24:26 2008  using large prime bound of 370919550 (28 bits)
Sun Dec 21 14:24:26 2008  using double large prime bound of 2658908975208750 (43-52 bits)
Sun Dec 21 14:24:26 2008  using trial factoring cutoff of 52 bits
Sun Dec 21 14:24:26 2008  polynomial 'A' values have 13 factors
Sun Dec 21 21:45:00 2008  90841 relations (22207 full + 68634 combined from 1358298 partial), need 90684
Sun Dec 21 21:45:01 2008  begin with 1380505 relations
Sun Dec 21 21:45:03 2008  reduce to 237264 relations in 13 passes
Sun Dec 21 21:45:03 2008  attempting to read 237264 relations
Sun Dec 21 21:45:07 2008  recovered 237264 relations
Sun Dec 21 21:45:07 2008  recovered 225925 polynomials
Sun Dec 21 21:45:07 2008  attempting to build 90841 cycles
Sun Dec 21 21:45:07 2008  found 90841 cycles in 6 passes
Sun Dec 21 21:45:07 2008  distribution of cycle lengths:
Sun Dec 21 21:45:07 2008     length 1 : 22207
Sun Dec 21 21:45:07 2008     length 2 : 16089
Sun Dec 21 21:45:07 2008     length 3 : 15123
Sun Dec 21 21:45:07 2008     length 4 : 12342
Sun Dec 21 21:45:07 2008     length 5 : 9156
Sun Dec 21 21:45:07 2008     length 6 : 6348
Sun Dec 21 21:45:07 2008     length 7 : 4061
Sun Dec 21 21:45:07 2008     length 9+: 5515
Sun Dec 21 21:45:07 2008  largest cycle: 24 relations
Sun Dec 21 21:45:08 2008  matrix is 90588 x 90841 (24.3 MB) with weight 6018077 (66.25/col)
Sun Dec 21 21:45:08 2008  sparse part has weight 6018077 (66.25/col)
Sun Dec 21 21:45:09 2008  filtering completed in 3 passes
Sun Dec 21 21:45:09 2008  matrix is 86557 x 86621 (23.3 MB) with weight 5762657 (66.53/col)
Sun Dec 21 21:45:09 2008  sparse part has weight 5762657 (66.53/col)
Sun Dec 21 21:45:09 2008  saving the first 48 matrix rows for later
Sun Dec 21 21:45:09 2008  matrix is 86509 x 86621 (14.0 MB) with weight 4514781 (52.12/col)
Sun Dec 21 21:45:09 2008  sparse part has weight 3151662 (36.38/col)
Sun Dec 21 21:45:09 2008  matrix includes 64 packed rows
Sun Dec 21 21:45:09 2008  using block size 34648 for processor cache size 1024 kB
Sun Dec 21 21:45:10 2008  commencing Lanczos iteration
Sun Dec 21 21:45:10 2008  memory use: 13.8 MB
Sun Dec 21 21:45:59 2008  lanczos halted after 1370 iterations (dim = 86505)
Sun Dec 21 21:45:59 2008  recovered 16 nontrivial dependencies
Sun Dec 21 21:46:00 2008  prp40 factor: 8392236225335848609185007290798128808749
Sun Dec 21 21:46:00 2008  prp58 factor: 3338062573732403028949060455916560045484897247255070478873
Sun Dec 21 21:46:00 2008  elapsed time 07:21:37

(38·10¹³⁹+43)/9 = 4(2)₁₃₈7_<140> = 23 · 47 · 157 · 1091 · 490913 · 95099288952186151_<17> · C109

C109 = P34 · P76

P34 = 1393980093270082701445581996312139_<34>

P76 = 3503907362859903751937502287009860162839613179165479888499563514926963907713_<76>

Number: 42227_139
N=4884377112489178144273156295792950485073388003515582263988391522853491148860966070259939401017505922337628107
  ( 109 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=1393980093270082701445581996312139
 r2=3503907362859903751937502287009860162839613179165479888499563514926963907713
Version: 
Total time: 6.96 hours.
Scaled time: 13.90 units (timescale=1.997).
Factorization parameters were as follows:
name: 42227_139
n: 4884377112489178144273156295792950485073388003515582263988391522853491148860966070259939401017505922337628107
m: 10000000000000000000000000000
deg: 5
c5: 19
c0: 215
skew: 1.62
type: snfs
lss: 1
rlim: 1580000
alim: 1580000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1580000/1580000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [790000, 1490001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 200308 x 200556
Total sieving time: 6.96 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000
total time: 6.96 hours.
 --------- CPU info (if available) ----------

Dec 21, 2008 (2nd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39

(38·10¹²³+43)/9 = 4(2)₁₂₂7_<124> = 3 · 523 · 4981091 · 595375639 · C105

C105 = P37 · P69

P37 = 6625236622908351129130519627635150409_<37>

P69 = 136962354440508632796329576785523794043541101927468396673154669332863_<69>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2291580702
Step 1 took 8167ms
Step 2 took 5212ms
********** Factor found in step 2: 6625236622908351129130519627635150409
Found probable prime factor of 37 digits: 6625236622908351129130519627635150409
Probable prime cofactor 136962354440508632796329576785523794043541101927468396673154669332863 has 69 digits

(38·10¹⁰²+43)/9 = 4(2)₁₀₁7_<103> = 3 · 283 · C100

C100 = P46 · P55

P46 = 2339819275170388413017198578896211823485991939_<46>

P55 = 2125450928489942711483795575495927297447161644376716257_<55>

SNFS difficulty: 103 digits.
Divisors found:
 r1=2339819275170388413017198578896211823485991939 (pp46)
 r2=2125450928489942711483795575495927297447161644376716257 (pp55)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.732).
Factorization parameters were as follows:
n: 4973171050909566810626881298259390132181651616280591545609213453736421934301792959036775291192252323
m: 20000000000000000000000000
deg: 4
c4: 475
c0: 86
skew: 0.65
type: snfs
lss: 1
rlim: 380000
alim: 380000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 380000/380000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [190000, 250001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 37602 x 37840
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,103,4,0,0,0,0,0,0,0,0,380000,380000,25,25,44,44,2.2,2.2,20000
total time: 0.30 hours.

(38·10¹⁵²+43)/9 = 4(2)₁₅₁7_<153> = 7 · 113 · 140869 · 549053809 · 611191649 · C128

C128 = P34 · P94

P34 = 3311927853322341988197805383433981_<34>

P94 = 3409384512902395854395804534112932958824831083076127506595975133098149114787081693316069646053_<94>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=965743905
Step 1 took 9800ms
Step 2 took 5995ms
********** Factor found in step 2: 3311927853322341988197805383433981
Found probable prime factor of 34 digits: 3311927853322341988197805383433981
Probable prime cofactor 3409384512902395854395804534112932958824831083076127506595975133098149114787081693316069646053 has 94 digits

(38·10¹⁶⁹+43)/9 = 4(2)₁₆₈7_<170> = 59 · 337 · 977 · 39198743 · 227965993 · C147

C147 = P28 · P119

P28 = 2655820141606970410062410591_<28>

P119 = 91584872364486444849043172878832212662987223413797999591678382550522470542734022451786510752287876994744879249741744633_<119>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3830038547
Step 1 took 11702ms
Step 2 took 6882ms
********** Factor found in step 2: 2655820141606970410062410591
Found probable prime factor of 28 digits: 2655820141606970410062410591
Probable prime cofactor 91584872364486444849043172878832212662987223413797999591678382550522470542734022451786510752287876994744879249741744633 has 119 digits

(38·10¹¹³+43)/9 = 4(2)₁₁₂7_<114> = 13 · 25237 · 1575809689_<10> · C99

C99 = P41 · P59

P41 = 49735454513288675927478118921779346906991_<41>

P59 = 16420642634281376632440806439033280504579372286731350984533_<59>

SNFS difficulty: 115 digits.
Divisors found:
 r1=49735454513288675927478118921779346906991 (pp41)
 r2=16420642634281376632440806439033280504579372286731350984533 (pp59)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.727).
Factorization parameters were as follows:
n: 816688124816270146188018767143009804753821509031817108709323199602796756189812586828039616230570203
m: 50000000000000000000000
deg: 5
c5: 304
c0: 1075
skew: 1.29
type: snfs
lss: 1
rlim: 600000
alim: 600000
lpbr: 25
lpba: 25
mfbr: 47
mfba: 47
rlambda: 2.2
alambda: 2.2
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved rational special-q in [300000, 550001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 69513 x 69761
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,600000,25,25,47,47,2.2,2.2,50000
total time: 0.90 hours.

(38·10²⁰⁵+43)/9 = 4(2)₂₀₄7_<206> = 23 · 39769717773101_<14> · 8283027066071539_<16> · C175

C175 = P37 · P138

P37 = 7446927812275566885066367640755661501_<37>

P138 = 748332346108083517204496076352281303579644183334234639264171266650967495931706368107585190904256579382948621638256477256434360566405057791_<138>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2569832959
Step 1 took 16203ms
Step 2 took 8239ms
********** Factor found in step 2: 7446927812275566885066367640755661501
Found probable prime factor of 37 digits: 7446927812275566885066367640755661501
Probable prime cofactor has 138 digits

(38·10¹⁹¹+43)/9 = 4(2)₁₉₀7_<192> = 13 · 717303940796383_<15> · C176

C176 = P35 · C142

P35 = 12195699723660604747700062962777713_<35>

C142 = [3712682365398479438282243464664815196302016944064203440914178876499906302165494535438255401453384930597328776467752153773796030078075034987601_<142>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2348945104
Step 1 took 16054ms
Step 2 took 8272ms
********** Factor found in step 2: 12195699723660604747700062962777713
Found probable prime factor of 35 digits: 12195699723660604747700062962777713
Composite cofactor has 142 digits

(38·10¹⁷²+43)/9 = 4(2)₁₇₁7_<173> = 78904708409084059771_<20> · C153

C153 = P33 · C121

P33 = 203557052143526710221580765970953_<33>

C121 = [2628766520436983600848734312946145497452786791325720620424489826049404434795255603834058064887550987569889245091927009729_<121>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1531914312
Step 1 took 11706ms
Step 2 took 6748ms
********** Factor found in step 2: 203557052143526710221580765970953
Found probable prime factor of 33 digits: 203557052143526710221580765970953
Composite cofactor has 121 digits

Dec 21, 2008

Factorizations of 422...227 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Dec 20, 2008 (5th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / Msieve v1.39

(37·10¹⁸⁶+53)/9 = 4(1)₁₈₅7_<187> = 139 · 2017 · 109199 · 4908232860071_<13> · 704264442759638437_<18> · 10378488878367712824242152948117_<32> · C115

C115 = P49 · P67

P49 = 2689929817698759709554943418445374763129549819167_<49>

P67 = 1391502082959891862381969553973756799821963452576981458534155488297_<67>

Number: 41117_186
N=3743042944343746327051073365541314201342334703437542556352179663331113160500440981418270935251237401012936934788599
  ( 115 digits)
Divisors found:
 r1=2689929817698759709554943418445374763129549819167
 r2=1391502082959891862381969553973756799821963452576981458534155488297
Version: 
Total time: 23.49 hours.
Scaled time: 56.17 units (timescale=2.391).
Factorization parameters were as follows:
name: 41117_186
n: 3743042944343746327051073365541314201342334703437542556352179663331113160500440981418270935251237401012936934788599
skew: 19576.61
# norm 1.71e+15
c5: 71040
c4: 5792275644
c3: -75240063274582
c2: -1887877505352075585
c1: 13052664014638656996786
c0: 93295585212988908690842265
# alpha -4.74
Y1: 612224461663
Y0: -8797188109558810865144
# Murphy_E 5.31e-10
# M 2485795306113775412739937617463062509924090181073194909416249828870954543475074827476885729509114857968585428779381
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [1400000, 2730001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9452756
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 554579 x 554827
Polynomial selection time: 1.33 hours.
Total sieving time: 20.54 hours.
Total relation processing time: 0.81 hours.
Matrix solve time: 0.69 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,52,52,2.6,2.6,70000
total time: 23.49 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Dec 20, 2008 (4th)

By Erik Branger / GGNFS, Msieve

(37·10¹⁵⁵+53)/9 = 4(1)₁₅₄7_<156> = 3 · 7² · 6133 · 5060729981_<10> · C140

C140 = P66 · P75

P66 = 269367314763042914282201634549081377562001210180121850198455089769_<66>

P75 = 334511345691997716865981461494206580384756565786245263349384660653593436903_<75>

Number: 41117_155
N=90106422946825408363604857144748861894415378687351286417994381988145740514085075549840680353930716088170577060545290073747118283014102345407
  ( 140 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=269367314763042914282201634549081377562001210180121850198455089769
 r2=334511345691997716865981461494206580384756565786245263349384660653593436903
Version: 
Total time: 23.50 hours.
Scaled time: 50.72 units (timescale=2.158).
Factorization parameters were as follows:
n: 90106422946825408363604857144748861894415378687351286417994381988145740514085075549840680353930716088170577060545290073747118283014102345407
m: 10000000000000000000000000000000
deg: 5
c5: 37
c0: 53
skew: 1.07
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 464074 x 464322
Total sieving time: 23.50 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 23.50 hours.
 --------- CPU info (if available) ----------

Dec 20, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(29·10¹⁸⁴+43)/9 = 3(2)₁₈₃7_<185> = 13 · 37 · C182

C182 = P84 · P99

P84 = 111279443625051066686752583950724085052587338038048389915997789891205474859639594563_<84>

P99 = 601998579502120043908560040845175574623627224208589111827646965534334972535100226307763607247653009_<99>

Number: n
N=66990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990067
  ( 182 digits)
SNFS difficulty: 186 digits.
Divisors found:

Sat Dec 20 12:36:23 2008  prp84 factor: 111279443625051066686752583950724085052587338038048389915997789891205474859639594563
Sat Dec 20 12:36:23 2008  prp99 factor: 601998579502120043908560040845175574623627224208589111827646965534334972535100226307763607247653009
Sat Dec 20 12:36:23 2008  elapsed time 02:46:43 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 75.44 hours.
Scaled time: 151.78 units (timescale=2.012).
Factorization parameters were as follows:
name: KA_3_2_183_7
n: 66990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990067
type: snfs
skew: 1.71
deg: 5
c5: 29
c0: 430
m: 10000000000000000000000000000000000000
rlim: 8500000
alim: 8500000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8500000/8500000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 5000001)
Primes: RFBsize:571119, AFBsize:570987, largePrimes:30886821 encountered
Relations: rels:27632037, finalFF:860192
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 7185617 hash collisions in 37455763 relations
Msieve: matrix is 1392558 x 1392806 (375.4 MB)

Total sieving time: 74.58 hours.
Total relation processing time: 0.85 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,8500000,8500000,29,29,58,58,2.5,2.5,100000
total time: 75.44 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830490)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830462)
Total of 4 processors activated (22643.71 BogoMIPS).

Dec 20, 2008 (2nd)

By Sinkiti Sibata / GGNFS, Msieve

(38·10¹⁴⁹+7)/9 = 4(2)₁₄₈3_<150> = 3 · 942700533825610283281_<21> · 20730491537768293860737_<23> · C106

C106 = P52 · P54

P52 = 9200186247536074110725736408181370462425062932285921_<52>

P54 = 782780251568680203916999787491470260852006980070718293_<54>

Number: 42223_149
N=7201724105325000015271685446739135051345465751365130548241989191456787699852270086959653138717414921052853
  ( 106 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=9200186247536074110725736408181370462425062932285921 (pp52)
 r2=782780251568680203916999787491470260852006980070718293 (pp54)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 32.37 hours.
Scaled time: 15.28 units (timescale=0.472).
Factorization parameters were as follows:
name: 42223_149
n: 7201724105325000015271685446739135051345465751365130548241989191456787699852270086959653138717414921052853
m: 1000000000000000000000000000000
deg: 5
c5: 19
c0: 35
skew: 1.13
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1950001)
Primes: RFBsize:169511, AFBsize:169171, largePrimes:7064924 encountered
Relations: rels:7144749, finalFF:554927
Max relations in full relation-set: 28
Initial matrix: 338747 x 554927 with sparse part having weight 60132314.
Pruned matrix : 271443 x 273200 with weight 27469857.
Total sieving time: 29.50 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 2.48 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 32.37 hours.
 --------- CPU info (if available) ----------

(38·10¹⁵⁰+7)/9 = 4(2)₁₄₉3_<151> = 863 · 354115717612803949610519013179_<30> · C119

C119 = P44 · P75

P44 = 15431000559815206035395680817815150310335313_<44>

P75 = 895346212652991183542440571902343530844413019287198941007927920963839486323_<75>

Number: 42223_150
N=13816087908676731462588855160525165982813315669594685075162160784517590741668791402353425690447665556919582119807424099
  ( 119 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=15431000559815206035395680817815150310335313
 r2=895346212652991183542440571902343530844413019287198941007927920963839486323
Version: 
Total time: 14.72 hours.
Scaled time: 37.91 units (timescale=2.575).
Factorization parameters were as follows:
name: 42223_150
n: 13816087908676731462588855160525165982813315669594685075162160784517590741668791402353425690447665556919582119807424099
m: 1000000000000000000000000000000
deg: 5
c5: 38
c0: 7
skew: 0.71
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 1900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 390910 x 391158
Total sieving time: 14.72 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 14.72 hours.
 --------- CPU info (if available) ----------

Dec 20, 2008

By Serge Batalov / Msieve-1.39

(38·10¹⁷⁰+7)/9 = 4(2)₁₆₉3_<171> = 3 · 157 · 2753 · 196771 · C160

C160 = P42 · P55 · P64

P42 = 153476075151060773153342076445236124223591_<42>

P55 = 1917702948548351014972144075788906674953668710503672193_<55>

P64 = 5622518013204771026946571224850334036846250412736550122129247077_<64>

SNFS difficulty: 171 digits.
Divisors found:
 r1=153476075151060773153342076445236124223591 (pp42)
 r2=1917702948548351014972144075788906674953668710503672193 (pp55)
 r3=5622518013204771026946571224850334036846250412736550122129247077 (pp64)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 1654828058268818266826261750512835223969607670110340280285501032823035481764827422126230743258275115337701206453136677726673505147628725557203557147602078050851
m: 10000000000000000000000000000000000
deg: 5
c5: 38
c0: 7
skew: 0.71
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 5550001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 874715 x 874963
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,200000
total time: 55.00 hours.

(37·10¹⁶⁶+53)/9 = 4(1)₁₆₅7_<167> = 173898349349_<12> · C156

C156 = P69 · P87

P69 = 538011999070133912246986997440759766268356209654134229710176541138511_<69>

P87 = 439411878873081543610582036653852567797126398884022586714170752552913700796583215412903_<87>

SNFS difficulty: 167 digits.
Divisors found:
 r1=538011999070133912246986997440759766268356209654134229710176541138511 (pp69)
 r2=439411878873081543610582036653852567797126398884022586714170752552913700796583215412903 (pp87)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.309).
Factorization parameters were as follows:
n: 236408863367670142721103299844704445499417936577501671655105982078525215703490151195127495684341517913294975327058250115806342823270262708415877058579607433
m: 1000000000000000000000000000000000
deg: 5
c5: 370
c0: 53
skew: 0.68
type: snfs
lss: 1
rlim: 4300000
alim: 4300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4300000/4300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2150000, 5650001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 954792 x 955039
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,4300000,4300000,27,27,52,52,2.4,2.4,100000
total time: 45.00 hours.

Dec 19, 2008 (4th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / Msieve v1.39

(37·10¹⁷⁵+71)/9 = 4(1)₁₇₄9_<176> = 7 · 1277 · 131517606982631_<15> · 705741823656784897_<18> · 4900621212089152019167274959_<28> · C113

C113 = P47 · P66

P47 = 27453836811193533274952439583072078790856233791_<47>

P66 = 368286958765672743643689545618535973113755495971514753154648801787_<66>

Number: 41119_175
N=10110890065643541273876685037705613811147665442907802879999742534726910408194518400360771008434790950557690584517
  ( 113 digits)
Divisors found:
 r1=27453836811193533274952439583072078790856233791
 r2=368286958765672743643689545618535973113755495971514753154648801787
Version: 
Total time: 17.05 hours.
Scaled time: 40.67 units (timescale=2.385).
Factorization parameters were as follows:
name: 41119_175
n: 10110890065643541273876685037705613811147665442907802879999742534726910408194518400360771008434790950557690584517
skew: 31984.13
# norm 1.63e+15
c5: 30360
c4: 1656856535
c3: -70094780515248
c2: -2243626268782858410
c1: 50520317420498134325496
c0: -50669818649517852164082573
# alpha -5.19
Y1: 1865253410543
Y0: -3195175792034622680434
# Murphy_E 7.24e-10
# M 5786324711396589223504645891167661672681231097769903942441373431869606174401351108406813980815335802242941075202
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1200000, 2160001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8619601
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 412092 x 412340
Polynomial selection time: 1.04 hours.
Total sieving time: 14.87 hours.
Total relation processing time: 0.63 hours.
Matrix solve time: 0.36 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,51,51,2.6,2.6,60000
total time: 17.05 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Dec 19, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(38·10¹⁶⁵-11)/9 = 4(2)₁₆₄1_<166> = 3² · 7 · 29 · 433 · 14103704127121829141_<20> · 512830241895585414353418585991_<30> · C111

C111 = P46 · P66

P46 = 2929181820706174355164874093534364725713662073_<46>

P66 = 251919332497036727931045115049442101193333340434130266632902737037_<66>

Number: n
N=737917529034754159507563986949881633271119592299813842582578872003532723125311534918896755506803917146199297701
  ( 111 digits)
Divisors found:

Fri Dec 19 10:35:19 2008  prp46 factor: 2929181820706174355164874093534364725713662073
Fri Dec 19 10:35:19 2008  prp66 factor: 251919332497036727931045115049442101193333340434130266632902737037
Fri Dec 19 10:35:19 2008  elapsed time 01:12:51 (Msieve 1.39 - dependency 5)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 14.05 hours.
Scaled time: 25.30 units (timescale=1.801).
Factorization parameters were as follows:
n: 737917529034754159507563986949881633271119592299813842582578872003532723125311534918896755506803917146199297701
Y0: -2383114440365214673050
Y1:  666243497711
c0: -312209647156954433244650149
c1:  14556975766321877839966
c2:  843009328727785431
c3: -27567575689852
c4:  956954044
c5:  9600
skew: 23510.92
name: KA_4_2_164_1
type: gnfs
rlim: 3400000
alim: 3400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 2300001)
Primes: RFBsize:243539, AFBsize:244085, largePrimes:15000202 encountered
Relations: rels:13799352, finalFF:770852
Max relations in full relation-set: 28
Initial matrix: 487700 x 770852 with sparse part having weight 92119394.
Pruned matrix : 

Msieve: found 810713 hash collisions in 14297157 relations
Msieve: matrix is 402030 x 402276 (111.7 MB)

Total sieving time: 13.69 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3400000,3400000,28,28,56,56,2.5,2.5,100000
total time: 14.05 hours.
 --------- CPU info (if available) ----------

Dec 19, 2008 (2nd)

By Sinkiti Sibata / Msieve

(38·10¹³⁶+7)/9 = 4(2)₁₃₅3_<137> = 409 · 6361 · C131

C131 = P49 · P82

P49 = 8594000668119493432759132571049781552594004445247_<49>

P82 = 1888413082581267978490482365718941523363737007376231943020350468156526437976112641_<82>

Number: 42223_136
N=16229023293389009133139106090876295081397306947333103820777599984556803097659300782781313782997714996228246862748288574754789067327
  ( 131 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=8594000668119493432759132571049781552594004445247
 r2=1888413082581267978490482365718941523363737007376231943020350468156526437976112641
Version: 
Total time: 4.82 hours.
Scaled time: 12.40 units (timescale=2.575).
Factorization parameters were as follows:
name: 42223_136
n: 16229023293389009133139106090876295081397306947333103820777599984556803097659300782781313782997714996228246862748288574754789067327
m: 2000000000000000000000000000
deg: 5
c5: 95
c0: 56
skew: 0.90
type: snfs
lss: 1
rlim: 1420000
alim: 1420000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1420000/1420000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [710000, 1385001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 222874 x 223122
Total sieving time: 4.82 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1420000,1420000,26,26,48,48,2.3,2.3,75000
total time: 4.82 hours.
 --------- CPU info (if available) ----------

(38·10¹⁴⁶+7)/9 = 4(2)₁₄₅3_<147> = 3² · 96157 · 541469 · 22900003348416823_<17> · C119

C119 = P53 · P67

P53 = 13474293956396481663403791718049203306600304054932849_<53>

P67 = 2920132186621567969038207626747820838665582277038474633583932183017_<67>

Number: 42223_146
N=39346719474073836211165386970759767038358231641254866087382141856300037559614084744521490143159896516392312603913225433
  ( 119 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=13474293956396481663403791718049203306600304054932849
 r2=2920132186621567969038207626747820838665582277038474633583932183017
Version: 
Total time: 11.92 hours.
Scaled time: 30.69 units (timescale=2.575).
Factorization parameters were as follows:
42223_146
n: 39346719474073836211165386970759767038358231641254866087382141856300037559614084744521490143159896516392312603913225433
m: 200000000000000000000000000000
deg: 5
c5: 95
c0: 56
skew: 0.90
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 2550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 332704 x 332952
Total sieving time: 11.92 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 11.92 hours.
 --------- CPU info (if available) ----------

(38·10¹²⁰+7)/9 = 4(2)₁₁₉3_<121> = 29 · 4924903 · 245566854496031743_<18> · C96

C96 = P41 · P55

P41 = 19955093527642430225778981756086814003767_<41>

P55 = 6032841192967150543154636232473256336681085904002749509_<55>

Fri Dec 19 07:35:03 2008  Msieve v. 1.39
Fri Dec 19 07:35:03 2008  random seeds: 6b80e7dc 791eff7b
Fri Dec 19 07:35:03 2008  factoring 120385910243073423257026243810404870767812331654226840017936550483511807178296703100252683400403 (96 digits)
Fri Dec 19 07:35:04 2008  searching for 15-digit factors
Fri Dec 19 07:35:05 2008  commencing quadratic sieve (96-digit input)
Fri Dec 19 07:35:05 2008  using multiplier of 37
Fri Dec 19 07:35:05 2008  using 32kb Intel Core sieve core
Fri Dec 19 07:35:05 2008  sieve interval: 36 blocks of size 32768
Fri Dec 19 07:35:05 2008  processing polynomials in batches of 6
Fri Dec 19 07:35:06 2008  using a sieve bound of 2192963 (81176 primes)
Fri Dec 19 07:35:06 2008  using large prime bound of 328944450 (28 bits)
Fri Dec 19 07:35:06 2008  using double large prime bound of 2142005338065300 (43-51 bits)
Fri Dec 19 07:35:06 2008  using trial factoring cutoff of 51 bits
Fri Dec 19 07:35:06 2008  polynomial 'A' values have 12 factors
Fri Dec 19 07:35:06 2008  restarting with 1596 full and 94647 partial relations
Fri Dec 19 11:27:17 2008  81338 relations (20175 full + 61163 combined from 1215310 partial), need 81272
Fri Dec 19 11:27:18 2008  begin with 1235485 relations
Fri Dec 19 11:27:20 2008  reduce to 211262 relations in 11 passes
Fri Dec 19 11:27:20 2008  attempting to read 211262 relations
Fri Dec 19 11:27:23 2008  recovered 211262 relations
Fri Dec 19 11:27:23 2008  recovered 196167 polynomials
Fri Dec 19 11:27:23 2008  attempting to build 81338 cycles
Fri Dec 19 11:27:23 2008  found 81338 cycles in 5 passes
Fri Dec 19 11:27:23 2008  distribution of cycle lengths:
Fri Dec 19 11:27:23 2008     length 1 : 20175
Fri Dec 19 11:27:23 2008     length 2 : 14340
Fri Dec 19 11:27:23 2008     length 3 : 13606
Fri Dec 19 11:27:23 2008     length 4 : 10935
Fri Dec 19 11:27:23 2008     length 5 : 8292
Fri Dec 19 11:27:23 2008     length 6 : 5597
Fri Dec 19 11:27:23 2008     length 7 : 3511
Fri Dec 19 11:27:23 2008     length 9+: 4882
Fri Dec 19 11:27:23 2008  largest cycle: 19 relations
Fri Dec 19 11:27:24 2008  matrix is 81176 x 81338 (22.8 MB) with weight 5643868 (69.39/col)
Fri Dec 19 11:27:24 2008  sparse part has weight 5643868 (69.39/col)
Fri Dec 19 11:27:25 2008  filtering completed in 3 passes
Fri Dec 19 11:27:25 2008  matrix is 77244 x 77308 (21.8 MB) with weight 5404103 (69.90/col)
Fri Dec 19 11:27:25 2008  sparse part has weight 5404103 (69.90/col)
Fri Dec 19 11:27:25 2008  saving the first 48 matrix rows for later
Fri Dec 19 11:27:25 2008  matrix is 77196 x 77308 (16.0 MB) with weight 4523024 (58.51/col)
Fri Dec 19 11:27:25 2008  sparse part has weight 3722876 (48.16/col)
Fri Dec 19 11:27:25 2008  matrix includes 64 packed rows
Fri Dec 19 11:27:25 2008  using block size 30923 for processor cache size 1024 kB
Fri Dec 19 11:27:26 2008  commencing Lanczos iteration
Fri Dec 19 11:27:26 2008  memory use: 14.0 MB
Fri Dec 19 11:28:10 2008  lanczos halted after 1222 iterations (dim = 77195)
Fri Dec 19 11:28:11 2008  recovered 18 nontrivial dependencies
Fri Dec 19 11:28:12 2008  prp41 factor: 19955093527642430225778981756086814003767
Fri Dec 19 11:28:12 2008  prp55 factor: 6032841192967150543154636232473256336681085904002749509
Fri Dec 19 11:28:12 2008  elapsed time 03:53:09

(38·10¹⁵¹+7)/9 = 4(2)₁₅₀3_<152> = 23 · 1176371562578041651_<19> · C133

C133 = P63 · P70

P63 = 485460562826957331754454944330962706119706627186220853762299653_<63>

P70 = 3214509981924084416777889458865269747634632549732810562486889213808567_<70>

Number: 42223_151
N=1560517825037738459854438489255803864062404112623963858125778119538120217593954522496759798220909008287552424483930190183364432527251
  ( 133 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=485460562826957331754454944330962706119706627186220853762299653
 r2=3214509981924084416777889458865269747634632549732810562486889213808567
Version: 
Total time: 22.29 hours.
Scaled time: 43.45 units (timescale=1.949).
Factorization parameters were as follows:
name: 42223_151
n: 1560517825037738459854438489255803864062404112623963858125778119538120217593954522496759798220909008287552424483930190183364432527251
m: 2000000000000000000000000000000
deg: 5
c5: 95
c0: 56
skew: 0.90
type: snfs
lss: 1
rlim: 2500000
alim: 2500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1250000, 2050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 438175 x 438423
Total sieving time: 22.29 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2500000,2500000,27,27,50,50,2.4,2.4,100000
total time: 22.29 hours.
 --------- CPU info (if available) ----------

Dec 19, 2008

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39

(38·10¹⁶²+7)/9 = 4(2)₁₆₁3_<163> = 22666112659648690795351599407939_<32> · C132

C132 = P34 · P98

P34 = 5160396681170916091071232604105399_<34>

P98 = 36097818491499062140649356899516517790791368456473008648453082759802006328144553713905393610559843_<98>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1554662117
Step 1 took 9808ms
Step 2 took 5990ms
********** Factor found in step 2: 5160396681170916091071232604105399
Found probable prime factor of 34 digits: 5160396681170916091071232604105399
Probable prime cofactor 36097818491499062140649356899516517790791368456473008648453082759802006328144553713905393610559843 has 98 digits

(38·10¹⁹¹-11)/9 = 4(2)₁₉₀1_<192> = 41 · 2687 · 774334507 · 375832150285823251963801943606447_<33> · C146

C146 = P39 · P107

P39 = 956276603516830937978406238709621853569_<39>

P107 = 13771571192961589841833862853688482747346196734485423041265570383728431701766189556898870971868907507954463_<107>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2975364834
Step 1 took 11760ms
Step 2 took 6495ms
********** Factor found in step 2: 956276603516830937978406238709621853569
Found probable prime factor of 39 digits: 956276603516830937978406238709621853569
Probable prime cofactor 13771571192961589841833862853688482747346196734485423041265570383728431701766189556898870971868907507954463 has 107 digits

(38·10¹⁵⁷+7)/9 = 4(2)₁₅₆3_<158> = 17 · 937 · C154

C154 = P48 · P107

P48 = 174202237292790959315768467382894756765173949951_<48>

P107 = 15215942083033820802184377816467863773879005591771502744651031164528244378458407456255021493967981424428537_<107>

SNFS difficulty: 159 digits.
Divisors found:
 r1=174202237292790959315768467382894756765173949951 (pp48)
 r2=15215942083033820802184377816467863773879005591771502744651031164528244378458407456255021493967981424428537 (pp107)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.293).
Factorization parameters were as follows:
n: 2650651153382021609782297835534071330417617064613109562572805714245854869873954562258912814503247047662892976471983314848529237379761580904151059214151687
m: 20000000000000000000000000000000
deg: 5
c5: 475
c0: 28
skew: 0.57
type: snfs
lss: 1
rlim: 3100000
alim: 3100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3100000/3100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1550000, 2850001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 616516 x 616764
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,52,52,2.4,2.4,100000
total time: 20.00 hours.

Dec 18, 2008 (9th)

By Jo Yeong Uk / GGNFS

(35·10¹⁸⁹+1)/9 = 3(8)₁₈₈9_<190> = C190

C190 = P56 · P135

P56 = 20293470058904574878183102843477356409653799265487560509_<56>

P135 = 191632524038562972599764005358059709580489479276799676408280772785787623231363395916154199246135197563472355670762941811936146063579821_<135>

Number: 38889_189
N=3888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889
  ( 190 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=20293470058904574878183102843477356409653799265487560509 (pp56)
 r2=191632524038562972599764005358059709580489479276799676408280772785787623231363395916154199246135197563472355670762941811936146063579821 (pp135)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 242.97 hours.
Scaled time: 568.30 units (timescale=2.339).
Factorization parameters were as follows:
n: 3888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889
m: 100000000000000000000000000000000000000
deg: 5
c5: 7
c0: 2
skew: 0.78
type: snfs
lss: 1
rlim: 11000000
alim: 11000000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 11000000/11000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5500000, 9600001)
Primes: RFBsize:726517, AFBsize:725838, largePrimes:19522578 encountered
Relations: rels:20498731, finalFF:1670579
Max relations in full relation-set: 28
Initial matrix: 1452420 x 1670579 with sparse part having weight 185962661.
Pruned matrix : 1271563 x 1278889 with weight 148415716.
Total sieving time: 220.23 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 22.12 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,11000000,11000000,28,28,54,54,2.5,2.5,100000
total time: 242.97 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Dec 18, 2008 (8th)

By Sinkiti Sibata / Msieve

(38·10¹⁰⁴+7)/9 = 4(2)₁₀₃3_<105> = 3 · 61 · 236169149 · C94

C94 = P41 · P54

P41 = 43086254634327649365606923085903856891003_<41>

P54 = 226739972183122477267800170574550311949755005078106823_<54>

Thu Dec 18 13:46:28 2008  Msieve v. 1.39
Thu Dec 18 13:46:28 2008  random seeds: a062d230 7342cb8e
Thu Dec 18 13:46:28 2008  factoring 9769376177262383140812846225412865846706679693162836475583025059828022012012145065217901613469 (94 digits)
Thu Dec 18 13:46:29 2008  searching for 15-digit factors
Thu Dec 18 13:46:31 2008  commencing quadratic sieve (94-digit input)
Thu Dec 18 13:46:31 2008  using multiplier of 1
Thu Dec 18 13:46:31 2008  using 32kb Intel Core sieve core
Thu Dec 18 13:46:31 2008  sieve interval: 36 blocks of size 32768
Thu Dec 18 13:46:31 2008  processing polynomials in batches of 6
Thu Dec 18 13:46:31 2008  using a sieve bound of 2090227 (77647 primes)
Thu Dec 18 13:46:31 2008  using large prime bound of 296812234 (28 bits)
Thu Dec 18 13:46:31 2008  using double large prime bound of 1780193407171906 (42-51 bits)
Thu Dec 18 13:46:31 2008  using trial factoring cutoff of 51 bits
Thu Dec 18 13:46:31 2008  polynomial 'A' values have 12 factors
Thu Dec 18 14:13:12 2008  2642 relations (2371 full + 271 combined from 141243 partial), need 77743
Thu Dec 18 14:13:12 2008  elapsed time 00:26:44
Thu Dec 18 14:32:42 2008  
Thu Dec 18 14:32:42 2008  
Thu Dec 18 14:32:42 2008  Msieve v. 1.39
Thu Dec 18 14:32:42 2008  random seeds: fba8aee8 1a77b463
Thu Dec 18 14:32:42 2008  factoring 9769376177262383140812846225412865846706679693162836475583025059828022012012145065217901613469 (94 digits)
Thu Dec 18 14:32:43 2008  searching for 15-digit factors
Thu Dec 18 14:32:44 2008  commencing quadratic sieve (94-digit input)
Thu Dec 18 14:32:44 2008  using multiplier of 1
Thu Dec 18 14:32:44 2008  using 32kb Intel Core sieve core
Thu Dec 18 14:32:44 2008  sieve interval: 36 blocks of size 32768
Thu Dec 18 14:32:44 2008  processing polynomials in batches of 6
Thu Dec 18 14:32:44 2008  using a sieve bound of 2090227 (77647 primes)
Thu Dec 18 14:32:44 2008  using large prime bound of 296812234 (28 bits)
Thu Dec 18 14:32:44 2008  using double large prime bound of 1780193407171906 (42-51 bits)
Thu Dec 18 14:32:44 2008  using trial factoring cutoff of 51 bits
Thu Dec 18 14:32:44 2008  polynomial 'A' values have 12 factors
Thu Dec 18 14:32:45 2008  restarting with 2371 full and 141243 partial relations
Thu Dec 18 17:41:26 2008  77942 relations (18849 full + 59093 combined from 1146357 partial), need 77743
Thu Dec 18 17:41:27 2008  begin with 1165206 relations
Thu Dec 18 17:41:29 2008  reduce to 204517 relations in 12 passes
Thu Dec 18 17:41:29 2008  attempting to read 204517 relations
Thu Dec 18 17:41:32 2008  recovered 204517 relations
Thu Dec 18 17:41:32 2008  recovered 188574 polynomials
Thu Dec 18 17:41:32 2008  attempting to build 77942 cycles
Thu Dec 18 17:41:32 2008  found 77942 cycles in 5 passes
Thu Dec 18 17:41:32 2008  distribution of cycle lengths:
Thu Dec 18 17:41:32 2008     length 1 : 18849
Thu Dec 18 17:41:32 2008     length 2 : 13493
Thu Dec 18 17:41:32 2008     length 3 : 13130
Thu Dec 18 17:41:32 2008     length 4 : 10465
Thu Dec 18 17:41:32 2008     length 5 : 7976
Thu Dec 18 17:41:32 2008     length 6 : 5543
Thu Dec 18 17:41:32 2008     length 7 : 3515
Thu Dec 18 17:41:32 2008     length 9+: 4971
Thu Dec 18 17:41:32 2008  largest cycle: 19 relations
Thu Dec 18 17:41:32 2008  matrix is 77647 x 77942 (20.2 MB) with weight 4982155 (63.92/col)
Thu Dec 18 17:41:32 2008  sparse part has weight 4982155 (63.92/col)
Thu Dec 18 17:41:34 2008  filtering completed in 3 passes
Thu Dec 18 17:41:34 2008  matrix is 74265 x 74329 (19.3 MB) with weight 4766944 (64.13/col)
Thu Dec 18 17:41:34 2008  sparse part has weight 4766944 (64.13/col)
Thu Dec 18 17:41:34 2008  saving the first 48 matrix rows for later
Thu Dec 18 17:41:34 2008  matrix is 74217 x 74329 (12.1 MB) with weight 3736169 (50.27/col)
Thu Dec 18 17:41:34 2008  sparse part has weight 2737005 (36.82/col)
Thu Dec 18 17:41:34 2008  matrix includes 64 packed rows
Thu Dec 18 17:41:34 2008  using block size 29731 for processor cache size 1024 kB
Thu Dec 18 17:41:34 2008  commencing Lanczos iteration
Thu Dec 18 17:41:34 2008  memory use: 11.8 MB
Thu Dec 18 17:42:10 2008  lanczos halted after 1175 iterations (dim = 74213)
Thu Dec 18 17:42:10 2008  recovered 15 nontrivial dependencies
Thu Dec 18 17:42:11 2008  prp41 factor: 43086254634327649365606923085903856891003
Thu Dec 18 17:42:11 2008  prp54 factor: 226739972183122477267800170574550311949755005078106823
Thu Dec 18 17:42:11 2008  elapsed time 03:09:29

(38·10¹⁷⁶+7)/9 = 4(2)₁₇₅3_<177> = 3 · 29 · 54540943 · 4287368772178003_<16> · 8965485210842005636106031659_<28> · 2471951484413682939511067832881908139_<37> · C87

C87 = P43 · P45

P43 = 4366496618391640554655712516621488728265579_<43>

P45 = 214467496461094603037698726459970575067475919_<45>

Thu Dec 18 17:51:17 2008  Msieve v. 1.39
Thu Dec 18 17:51:17 2008  random seeds: 480a71e4 42ef3d6d
Thu Dec 18 17:51:17 2008  factoring 936471598052290722011809167208477610429304981302335238497256676307528852425786219092101 (87 digits)
Thu Dec 18 17:51:18 2008  searching for 15-digit factors
Thu Dec 18 17:51:20 2008  commencing quadratic sieve (87-digit input)
Thu Dec 18 17:51:20 2008  using multiplier of 1
Thu Dec 18 17:51:20 2008  using 32kb Intel Core sieve core
Thu Dec 18 17:51:20 2008  sieve interval: 22 blocks of size 32768
Thu Dec 18 17:51:20 2008  processing polynomials in batches of 10
Thu Dec 18 17:51:20 2008  using a sieve bound of 1493299 (57000 primes)
Thu Dec 18 17:51:20 2008  using large prime bound of 119463920 (26 bits)
Thu Dec 18 17:51:20 2008  using double large prime bound of 345960105556960 (42-49 bits)
Thu Dec 18 17:51:20 2008  using trial factoring cutoff of 49 bits
Thu Dec 18 17:51:20 2008  polynomial 'A' values have 11 factors
Thu Dec 18 18:41:03 2008  57227 relations (15776 full + 41451 combined from 604798 partial), need 57096
Thu Dec 18 18:41:04 2008  begin with 620574 relations
Thu Dec 18 18:41:05 2008  reduce to 138470 relations in 12 passes
Thu Dec 18 18:41:05 2008  attempting to read 138470 relations
Thu Dec 18 18:41:06 2008  recovered 138470 relations
Thu Dec 18 18:41:06 2008  recovered 117589 polynomials
Thu Dec 18 18:41:07 2008  attempting to build 57227 cycles
Thu Dec 18 18:41:07 2008  found 57227 cycles in 5 passes
Thu Dec 18 18:41:07 2008  distribution of cycle lengths:
Thu Dec 18 18:41:07 2008     length 1 : 15776
Thu Dec 18 18:41:07 2008     length 2 : 11054
Thu Dec 18 18:41:07 2008     length 3 : 9940
Thu Dec 18 18:41:07 2008     length 4 : 7535
Thu Dec 18 18:41:07 2008     length 5 : 5176
Thu Dec 18 18:41:07 2008     length 6 : 3384
Thu Dec 18 18:41:07 2008     length 7 : 2077
Thu Dec 18 18:41:07 2008     length 9+: 2285
Thu Dec 18 18:41:07 2008  largest cycle: 18 relations
Thu Dec 18 18:41:07 2008  matrix is 57000 x 57227 (13.2 MB) with weight 3225637 (56.37/col)
Thu Dec 18 18:41:07 2008  sparse part has weight 3225637 (56.37/col)
Thu Dec 18 18:41:08 2008  filtering completed in 4 passes
Thu Dec 18 18:41:08 2008  matrix is 52801 x 52864 (12.3 MB) with weight 3004794 (56.84/col)
Thu Dec 18 18:41:08 2008  sparse part has weight 3004794 (56.84/col)
Thu Dec 18 18:41:08 2008  saving the first 48 matrix rows for later
Thu Dec 18 18:41:08 2008  matrix is 52753 x 52864 (7.8 MB) with weight 2373010 (44.89/col)
Thu Dec 18 18:41:08 2008  sparse part has weight 1740382 (32.92/col)
Thu Dec 18 18:41:08 2008  matrix includes 64 packed rows
Thu Dec 18 18:41:08 2008  using block size 21145 for processor cache size 1024 kB
Thu Dec 18 18:41:08 2008  commencing Lanczos iteration
Thu Dec 18 18:41:08 2008  memory use: 7.7 MB
Thu Dec 18 18:41:24 2008  lanczos halted after 835 iterations (dim = 52753)
Thu Dec 18 18:41:24 2008  recovered 17 nontrivial dependencies
Thu Dec 18 18:41:25 2008  prp43 factor: 4366496618391640554655712516621488728265579
Thu Dec 18 18:41:25 2008  prp45 factor: 214467496461094603037698726459970575067475919
Thu Dec 18 18:41:25 2008  elapsed time 00:50:08

(38·10¹³⁰+7)/9 = 4(2)₁₂₉3_<131> = C131

C131 = P33 · P98

P33 = 678551793747462240865698141675319_<33>

P98 = 62224022707301452482853572488992317799268371175008642178618762222983732884341974062619005483162217_<98>

Number: 42223_130
N=42222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222223
  ( 131 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=678551793747462240865698141675319 (prp33)
 r2=62224022707301452482853572488992317799268371175008642178618762222983732884341974062619005483162217 (prp98)
Version: 
Total time: 3.60 hours.
Scaled time: 7.17 units (timescale=1.991).
Factorization parameters were as follows:
name: 42223_130
n: 42222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222223
m: 100000000000000000000000000
deg: 5
c5: 38
c0: 7
skew: 0.71
type: snfs
lss: 1
rlim: 1090000
alim: 1090000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1090000/1090000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [545000, 945001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 154826 x 155074
Total sieving time: 3.60 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1090000,1090000,26,26,47,47,2.3,2.3,50000
total time: 3.60 hours.
 --------- CPU info (if available) ----------

(38·10¹⁵⁵+7)/9 = 4(2)₁₅₄3_<156> = 3⁴ · 21247 · 405706541 · 8153054611907549_<16> · 3631636673976858283592464277485606931_<37> · C89

C89 = P34 · P56

P34 = 1420456107051505106563089043040989_<34>

P56 = 14377913877137253365446313866748979093357534901514687119_<56>

Thu Dec 18 19:12:15 2008  Msieve v. 1.39
Thu Dec 18 19:12:15 2008  random seeds: 766c50d8 0938bf95
Thu Dec 18 19:12:15 2008  factoring 20423195573440195206551390289801512611298882650218935717368875142211566032360322627320691 (89 digits)
Thu Dec 18 19:12:16 2008  searching for 15-digit factors
Thu Dec 18 19:12:17 2008  commencing quadratic sieve (89-digit input)
Thu Dec 18 19:12:17 2008  using multiplier of 1
Thu Dec 18 19:12:17 2008  using 32kb Intel Core sieve core
Thu Dec 18 19:12:17 2008  sieve interval: 30 blocks of size 32768
Thu Dec 18 19:12:17 2008  processing polynomials in batches of 7
Thu Dec 18 19:12:17 2008  using a sieve bound of 1546837 (58348 primes)
Thu Dec 18 19:12:17 2008  using large prime bound of 123746960 (26 bits)
Thu Dec 18 19:12:17 2008  using double large prime bound of 368605688486800 (42-49 bits)
Thu Dec 18 19:12:17 2008  using trial factoring cutoff of 49 bits
Thu Dec 18 19:12:17 2008  polynomial 'A' values have 11 factors
Thu Dec 18 20:18:08 2008  58635 relations (15460 full + 43175 combined from 627841 partial), need 58444
Thu Dec 18 20:18:09 2008  begin with 643301 relations
Thu Dec 18 20:18:09 2008  reduce to 144114 relations in 9 passes
Thu Dec 18 20:18:09 2008  attempting to read 144114 relations
Thu Dec 18 20:18:11 2008  recovered 144114 relations
Thu Dec 18 20:18:11 2008  recovered 123018 polynomials
Thu Dec 18 20:18:11 2008  attempting to build 58635 cycles
Thu Dec 18 20:18:11 2008  found 58635 cycles in 5 passes
Thu Dec 18 20:18:11 2008  distribution of cycle lengths:
Thu Dec 18 20:18:11 2008     length 1 : 15460
Thu Dec 18 20:18:11 2008     length 2 : 11059
Thu Dec 18 20:18:11 2008     length 3 : 10232
Thu Dec 18 20:18:11 2008     length 4 : 7813
Thu Dec 18 20:18:12 2008     length 5 : 5624
Thu Dec 18 20:18:12 2008     length 6 : 3705
Thu Dec 18 20:18:12 2008     length 7 : 2187
Thu Dec 18 20:18:12 2008     length 9+: 2555
Thu Dec 18 20:18:12 2008  largest cycle: 18 relations
Thu Dec 18 20:18:12 2008  matrix is 58348 x 58635 (14.3 MB) with weight 3505595 (59.79/col)
Thu Dec 18 20:18:12 2008  sparse part has weight 3505595 (59.79/col)
Thu Dec 18 20:18:13 2008  filtering completed in 3 passes
Thu Dec 18 20:18:13 2008  matrix is 54671 x 54735 (13.4 MB) with weight 3293020 (60.16/col)
Thu Dec 18 20:18:13 2008  sparse part has weight 3293020 (60.16/col)
Thu Dec 18 20:18:13 2008  saving the first 48 matrix rows for later
Thu Dec 18 20:18:13 2008  matrix is 54623 x 54735 (9.1 MB) with weight 2631716 (48.08/col)
Thu Dec 18 20:18:13 2008  sparse part has weight 2059013 (37.62/col)
Thu Dec 18 20:18:13 2008  matrix includes 64 packed rows
Thu Dec 18 20:18:13 2008  using block size 21894 for processor cache size 1024 kB
Thu Dec 18 20:18:13 2008  commencing Lanczos iteration
Thu Dec 18 20:18:13 2008  memory use: 8.6 MB
Thu Dec 18 20:18:32 2008  lanczos halted after 865 iterations (dim = 54621)
Thu Dec 18 20:18:32 2008  recovered 16 nontrivial dependencies
Thu Dec 18 20:18:33 2008  prp34 factor: 1420456107051505106563089043040989
Thu Dec 18 20:18:33 2008  prp56 factor: 14377913877137253365446313866748979093357534901514687119
Thu Dec 18 20:18:33 2008  elapsed time 01:06:18

(38·10¹³⁵+7)/9 = 4(2)₁₃₄3_<136> = 509 · C133

C133 = P38 · P46 · P51

P38 = 15913952422398244721190280306070085331_<38>

P46 = 1442361694262586816326270806420410498472186067_<46>

P51 = 361385788135949331769346686225100381937997477289411_<51>

Number: 42223_135
N=8295132067234228334424798079022047587862912027941497489631084915957214581969002401222440515171359965073128137961143855053481772538747
  ( 133 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=15913952422398244721190280306070085331 (prp38)
 r2=1442361694262586816326270806420410498472186067 (prp46)
 r3=361385788135949331769346686225100381937997477289411 (prp51)
Version: 
Total time: 5.58 hours.
Scaled time: 11.15 units (timescale=1.997).
Factorization parameters were as follows:
name: 42223_135
n: 8295132067234228334424798079022047587862912027941497489631084915957214581969002401222440515171359965073128137961143855053481772538747
m: 1000000000000000000000000000
deg: 5
c5: 38
c0: 7
skew: 0.71
type: snfs
lss: 1
rlim: 1320000
alim: 1320000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1320000/1320000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [660000, 1260001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 183860 x 184108
Total sieving time: 5.58 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1320000,1320000,26,26,48,48,2.3,2.3,75000
total time: 5.58 hours.
 --------- CPU info (if available) ----------

Dec 18, 2008 (7th)

By Serge Batalov / GMP-ECM 6.2.1

(38·10¹⁴²+7)/9 = 4(2)₁₄₁3_<143> = 59 · 5563 · 605464278196827737125597251068803_<33> · C105

C105 = P36 · P70

P36 = 108086691733104157882816618677785281_<36>

P70 = 1965709180424130529255869068846906640336734489270747363351530402366733_<70>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=519687493
Step 1 took 8384ms
Step 2 took 5062ms
********** Factor found in step 2: 108086691733104157882816618677785281
Found probable prime factor of 36 digits: 108086691733104157882816618677785281
Probable prime cofactor 1965709180424130529255869068846906640336734489270747363351530402366733 has 70 digits

Dec 18, 2008 (6th)

By Serge Batalov / PFGW

(8·10⁵³⁴¹¹+1)/9 = (8)₅₃₄₁₀9_<53411> is PRP.

Dec 18, 2008 (5th)

By Tyler Cadigan / GGNFS, Msieve

(43·10¹⁸⁵-7)/9 = 4(7)₁₈₅_<186> = 3 · 29 · 47 · 58170373640018484872008409_<26> · C157

C157 = P75 · P82

P75 = 711289181722006572964993391864934683586891620256502264874981119795063837321_<75>

P82 = 2823974552229371081708878262515141661878349230272684194999664683868033689289786137_<82>

Number: 47777_185
N=2008662548458999269449272053889738154785837004738744490237883895960497711975400967535628915609095715969831195102711489927429245865192787596589288254649018977
  ( 157 digits)
SNFS difficulty: 186 digits.
Divisors found:
 r1=711289181722006572964993391864934683586891620256502264874981119795063837321
 r2=2823974552229371081708878262515141661878349230272684194999664683868033689289786137
Version: 
Total time: 284.19 hours.
Scaled time: 728.96 units (timescale=2.565).
Factorization parameters were as follows:
n: 2008662548458999269449272053889738154785837004738744490237883895960497711975400967535628915609095715969831195102711489927429245865192787596589288254649018977
m: 10000000000000000000000000000000000000
deg: 5
c5: 43
c0: -7
skew: 0.70
type: snfs
lss: 1
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Y0: 10000000000000000000000000000000000000
Y1: -1
qintsize: 1000000Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4500000, 8500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1277651 x 1277899
Total sieving time: 284.19 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,54,54,2.5,2.5,100000
total time: 284.19 hours.
 --------- CPU info (if available) ----------

Dec 18, 2008 (4th)

By Robert Backstrom / GGNFS

(38·10¹⁰⁸+7)/9 = 4(2)₁₀₇3_<109> = 41 · 499 · C105

C105 = P47 · P59

P47 = 10295641543941343571168747279625193234146247799_<47>

P59 = 20044871255305051171624283732903041074399663885329714243003_<59>

Number: n
N=206374809239074354671402425447100162384389374955873807235066338639338297190587136332285166539040139900397
  ( 105 digits)
SNFS difficulty: 109 digits.
Divisors found:
 r1=10295641543941343571168747279625193234146247799 (pp47)
 r2=20044871255305051171624283732903041074399663885329714243003 (pp59)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.93 hours.
Scaled time: 1.70 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_4_2_107_3
n: 206374809239074354671402425447100162384389374955873807235066338639338297190587136332285166539040139900397
type: snfs
skew: 0.36
deg: 5
c5: 2375
c0: 14
m: 2000000000000000000000
rlim: 450000
alim: 450000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 450000/450000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [225000, 305001)
Primes: RFBsize:37706, AFBsize:38049, largePrimes:4928369 encountered
Relations: rels:4458518, finalFF:266912
Max relations in full relation-set: 48
Initial matrix: 75821 x 266912 with sparse part having weight 35358891.
Pruned matrix : 56879 x 57322 with weight 4347894.
Total sieving time: 0.83 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.01 hours.
Total square root time: 0.02 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,109,5,0,0,0,0,0,0,0,0,450000,450000,28,28,56,56,2.5,2.5,50000
total time: 0.93 hours.
 --------- CPU info (if available) ----------

(38·10¹¹⁶+7)/9 = 4(2)₁₁₅3_<117> = 3 · 352637 · C111

C111 = P43 · P68

P43 = 5573083583773648271800694651315923853073163_<43>

P68 = 71613747018533179366658876906680060578395225670235050033207926163611_<68>

Number: n
N=399109397881506310287181267821416189284563845372835921190177833695104996755135566434437511494088087015091271593
  ( 111 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=5573083583773648271800694651315923853073163 (pp43)
 r2=71613747018533179366658876906680060578395225670235050033207926163611 (pp68)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.18 hours.
Scaled time: 2.15 units (timescale=1.822).
Factorization parameters were as follows:
name: KA_4_2_115_3
n: 399109397881506310287181267821416189284563845372835921190177833695104996755135566434437511494088087015091271593
type: snfs
skew: 0.45
deg: 5
c5: 380
c0: 7
m: 100000000000000000000000
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [250000, 370001)
Primes: RFBsize:41538, AFBsize:41837, largePrimes:5004377 encountered
Relations: rels:4345290, finalFF:125163
Max relations in full relation-set: 48
Initial matrix: 83442 x 125163 with sparse part having weight 17533216.
Pruned matrix : 76901 x 77382 with weight 7526306.
Total sieving time: 1.04 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.03 hours.
Total square root time: 0.04 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,500000,500000,28,28,56,56,2.5,2.5,50000
total time: 1.18 hours.
 --------- CPU info (if available) ----------

Dec 18, 2008 (3rd)

By Sinkiti Sibata / GGNFS, Msieve

(37·10¹⁵³+53)/9 = 4(1)₁₅₂7_<154> = 29 · 167 · 2259934847_<10> · 699672253367_<12> · C129

C129 = P34 · P95

P34 = 8719756215598888403735903369151727_<34>

P95 = 61567260829717922876129222772484051350518977065235325715293890266317345837386780159662510836353_<95>

Number: 41117_153
N=536851505297330833256720241859282105348047475598159487710492234018066473949983864532710775744234875425075826135015294154924331631
  ( 129 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=8719756215598888403735903369151727 (pp34)
 r2=61567260829717922876129222772484051350518977065235325715293890266317345837386780159662510836353 (pp95)
Version: GGNFS-0.77.1-20060513-k8
Total time: 38.61 hours.
Scaled time: 75.95 units (timescale=1.967).
Factorization parameters were as follows:
name: 41117_153
n: 536851505297330833256720241859282105348047475598159487710492234018066473949983864532710775744234875425075826135015294154924331631
m: 5000000000000000000000000000000
deg: 5
c5: 296
c0: 1325
skew: 1.35
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2500001)
Primes: RFBsize:203362, AFBsize:203817, largePrimes:8308051 encountered
Relations: rels:8752937, finalFF:805926
Max relations in full relation-set: 28
Initial matrix: 407246 x 805926 with sparse part having weight 93645918.
Pruned matrix : 300178 x 302278 with weight 40667714.
Total sieving time: 36.68 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 1.51 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 38.61 hours.
 --------- CPU info (if available) ----------

(38·10¹⁵¹-11)/9 = 4(2)₁₅₀1_<152> = 41 · 53 · 26021 · 2914313 · C138

C138 = P46 · P92

P46 = 3159193923314794886124358434419958776363525831_<46>

P92 = 81104490278796803941574903528473981354882683238348933245451788515578216046199936350435152579_<92>

Number: 42221_151
N=256224812842318717545533857825918618214117908238051230838133636289935308342853369546321111379845635992526213941974521284389129356892768149
  ( 138 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=3159193923314794886124358434419958776363525831 (prp46)
 r2=81104490278796803941574903528473981354882683238348933245451788515578216046199936350435152579 (prp92)
Version: 
Total time: 15.14 hours.
Scaled time: 38.51 units (timescale=2.544).
Factorization parameters were as follows:
name: 42221_151
n: 256224812842318717545533857825918618214117908238051230838133636289935308342853369546321111379845635992526213941974521284389129356892768149
m: 2000000000000000000000000000000
deg: 5
c5: 95
c0: -88
skew: 0.98
type: snfs
lss: 1
rlim: 2500000
alim: 2500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1250000, 1950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 458616 x 458864
Total sieving time: 15.14 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2500000,2500000,27,27,50,50,2.4,2.4,100000
total time: 15.14 hours.
 --------- CPU info (if available) ----------

(38·10¹⁴¹+7)/9 = 4(2)₁₄₀3_<142> = 17 · 10799 · 14431 · 10551421125799_<14> · 3918960185104132736939080334753_<31> · C89

C89 = P37 · P53

P37 = 1208319630248751570624525558000988741_<37>

P53 = 31896906018545036923695174984522863360635051803331813_<53>

Thu Dec 18 08:07:13 2008  Msieve v. 1.39
Thu Dec 18 08:07:13 2008  random seeds: ba6ae35c e186a9eb
Thu Dec 18 08:07:13 2008  factoring 38541657686407517624151652150298002272942905139355928279567042796973174434731732100117433 (89 digits)
Thu Dec 18 08:07:14 2008  searching for 15-digit factors
Thu Dec 18 08:07:16 2008  commencing quadratic sieve (89-digit input)
Thu Dec 18 08:07:16 2008  using multiplier of 1
Thu Dec 18 08:07:16 2008  using 32kb Intel Core sieve core
Thu Dec 18 08:07:16 2008  sieve interval: 32 blocks of size 32768
Thu Dec 18 08:07:16 2008  processing polynomials in batches of 7
Thu Dec 18 08:07:16 2008  using a sieve bound of 1556189 (58802 primes)
Thu Dec 18 08:07:16 2008  using large prime bound of 124495120 (26 bits)
Thu Dec 18 08:07:16 2008  using double large prime bound of 372626841652480 (42-49 bits)
Thu Dec 18 08:07:16 2008  using trial factoring cutoff of 49 bits
Thu Dec 18 08:07:16 2008  polynomial 'A' values have 11 factors
Thu Dec 18 09:14:07 2008  59134 relations (15874 full + 43260 combined from 629696 partial), need 58898
Thu Dec 18 09:14:08 2008  begin with 645570 relations
Thu Dec 18 09:14:08 2008  reduce to 144306 relations in 11 passes
Thu Dec 18 09:14:08 2008  attempting to read 144306 relations
Thu Dec 18 09:14:10 2008  recovered 144306 relations
Thu Dec 18 09:14:10 2008  recovered 122188 polynomials
Thu Dec 18 09:14:10 2008  attempting to build 59134 cycles
Thu Dec 18 09:14:10 2008  found 59134 cycles in 5 passes
Thu Dec 18 09:14:10 2008  distribution of cycle lengths:
Thu Dec 18 09:14:10 2008     length 1 : 15874
Thu Dec 18 09:14:10 2008     length 2 : 11011
Thu Dec 18 09:14:10 2008     length 3 : 10357
Thu Dec 18 09:14:10 2008     length 4 : 8156
Thu Dec 18 09:14:10 2008     length 5 : 5506
Thu Dec 18 09:14:10 2008     length 6 : 3538
Thu Dec 18 09:14:10 2008     length 7 : 2140
Thu Dec 18 09:14:10 2008     length 9+: 2552
Thu Dec 18 09:14:10 2008  largest cycle: 17 relations
Thu Dec 18 09:14:11 2008  matrix is 58802 x 59134 (14.2 MB) with weight 3496057 (59.12/col)
Thu Dec 18 09:14:11 2008  sparse part has weight 3496057 (59.12/col)
Thu Dec 18 09:14:12 2008  filtering completed in 3 passes
Thu Dec 18 09:14:12 2008  matrix is 54893 x 54957 (13.3 MB) with weight 3263166 (59.38/col)
Thu Dec 18 09:14:12 2008  sparse part has weight 3263166 (59.38/col)
Thu Dec 18 09:14:12 2008  saving the first 48 matrix rows for later
Thu Dec 18 09:14:12 2008  matrix is 54845 x 54957 (9.1 MB) with weight 2632975 (47.91/col)
Thu Dec 18 09:14:12 2008  sparse part has weight 2067716 (37.62/col)
Thu Dec 18 09:14:12 2008  matrix includes 64 packed rows
Thu Dec 18 09:14:12 2008  using block size 21982 for processor cache size 1024 kB
Thu Dec 18 09:14:12 2008  commencing Lanczos iteration
Thu Dec 18 09:14:12 2008  memory use: 8.6 MB
Thu Dec 18 09:14:31 2008  lanczos halted after 869 iterations (dim = 54843)
Thu Dec 18 09:14:31 2008  recovered 16 nontrivial dependencies
Thu Dec 18 09:14:32 2008  prp37 factor: 1208319630248751570624525558000988741
Thu Dec 18 09:14:32 2008  prp53 factor: 31896906018545036923695174984522863360635051803331813
Thu Dec 18 09:14:32 2008  elapsed time 01:07:19

(38·10¹¹²+7)/9 = 4(2)₁₁₁3_<113> = 11677705261_<11> · C103

C103 = P46 · P58

P46 = 1945013057622469055928792403006550216266423129_<46>

P58 = 1858921524805644843829335015271915581157210985408240421667_<58>

Number: 42223_112
N=3615626638842449735144263478960074279461832207842552622738456544970528368794580610388486685596801536043
  ( 103 digits)
SNFS difficulty: 114 digits.
Divisors found:
 r1=1945013057622469055928792403006550216266423129 (prp46)
 r2=1858921524805644843829335015271915581157210985408240421667 (prp58)
Version: 
Total time: 1.45 hours.
Scaled time: 2.90 units (timescale=2.003).
Factorization parameters were as follows:
name: 42223_112
n: 3615626638842449735144263478960074279461832207842552622738456544970528368794580610388486685596801536043
m: 20000000000000000000000
deg: 5
c5: 475
c0: 28
skew: 0.57
type: snfs
lss: 1
rlim: 560000
alim: 560000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 560000/560000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [280000, 480001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 60412 x 60652
Total sieving time: 1.45 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,114,5,0,0,0,0,0,0,0,0,560000,560000,25,25,45,45,2.2,2.2,50000
total time: 1.45 hours.
 --------- CPU info (if available) ----------

(38·10¹¹⁵+7)/9 = 4(2)₁₁₄3_<116> = 251 · 15331533874127_<14> · C101

C101 = P34 · P67

P34 = 1634864409020671635063265717434331_<34>

P67 = 6711197497648071834292573110422804102757555587356032161168057878729_<67>

Number: 42223_115
N=10971897930813425274869156495205138122741990801162120520681589565626234907052249695702572980219245299
  ( 101 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=1634864409020671635063265717434331 (prp34)
 r2=6711197497648071834292573110422804102757555587356032161168057878729 (prp67)
Version: 
Total time: 1.49 hours.
Scaled time: 2.96 units (timescale=1.985).
Factorization parameters were as follows:
name: 42223_115
n: 10971897930813425274869156495205138122741990801162120520681589565626234907052249695702572980219245299
m: 100000000000000000000000
deg: 5
c5: 38
c0: 7
skew: 0.71
type: snfs
lss: 1
rlim: 610000
alim: 610000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 610000/610000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [305000, 505001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 62313 x 62551
Total sieving time: 1.49 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,610000,610000,25,25,45,45,2.2,2.2,50000
total time: 1.49 hours.
 --------- CPU info (if available) ----------

(38·10¹²³+7)/9 = 4(2)₁₂₂3_<124> = 41 · 16901347 · C115

C115 = P29 · P34 · P53

P29 = 95138006685886098469807972853_<29>

P34 = 1360440358306411252248900367385263_<34>

P53 = 47076303835257146062311650641289379426604433502131591_<53>

Number: 42223_123
N=6093066417149952780747582444056262558825062765883750556112368024929007747021759924212567087284879117048960830224349
  ( 115 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=95138006685886098469807972853 (prp29)
 r2=1360440358306411252248900367385263 (prp34)
 r3=47076303835257146062311650641289379426604433502131591 (prp53)
Version: 
Total time: 1.98 hours.
Scaled time: 5.07 units (timescale=2.564).
Factorization parameters were as follows:
name: 42223_123
n: 6093066417149952780747582444056262558825062765883750556112368024929007747021759924212567087284879117048960830224349
m: 10000000000000000000000000
deg: 5
c5: 19
c0: 350
skew: 1.79
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [445000, 745001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 122288 x 122535
Total sieving time: 1.98 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 1.98 hours.
 --------- CPU info (if available) ----------

(37·10¹⁴⁸+71)/9 = 4(1)₁₄₇9_<149> = 13 · 263 · 54907 · 83365277 · 4787540677386989927_<19> · C114

C114 = P45 · P69

P45 = 624271176245120850697276336102200832129446533_<45>

P69 = 878944475221714294164277298235867536498240189330190166674377210066449_<69>

Number: 42221_148
N=548699701400810060635961055722374030806191032906197312251591427155898046660410692341082608508184132862882522671317
  ( 114 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=624271176245120850697276336102200832129446533 (pp45)
 r2=878944475221714294164277298235867536498240189330190166674377210066449 (pp69)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 36.14 hours.
Scaled time: 17.10 units (timescale=0.473).
Factorization parameters were as follows:
name: 42221_148
n: 548699701400810060635961055722374030806191032906197312251591427155898046660410692341082608508184132862882522671317
m: 500000000000000000000000000000
deg: 5
c5: 296
c0: 1775
skew: 1.43
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 2050001)
Primes: RFBsize:169511, AFBsize:170002, largePrimes:7101805 encountered
Relations: rels:7231912, finalFF:593333
Max relations in full relation-set: 28
Initial matrix: 339580 x 593333 with sparse part having weight 65156158.
Pruned matrix : 267308 x 269069 with weight 28342252.
Total sieving time: 33.22 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 2.48 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 36.14 hours.
 --------- CPU info (if available) ----------

(38·10¹¹⁷+7)/9 = 4(2)₁₁₆3_<118> = 2657947 · 1142969897_<10> · 95220609140821_<14> · C89

C89 = P41 · P48

P41 = 69563816005530066987621201677220218900731_<41>

P48 = 209819392365296826977778796234537568048688935347_<48>

Thu Dec 18 12:29:54 2008  Msieve v. 1.39
Thu Dec 18 12:29:54 2008  random seeds: 83cedefc 8d8bdba6
Thu Dec 18 12:29:54 2008  factoring 14595837604891628552348108255737179313931799325177429616056819579069705362946879070038657 (89 digits)
Thu Dec 18 12:29:55 2008  searching for 15-digit factors
Thu Dec 18 12:29:56 2008  commencing quadratic sieve (89-digit input)
Thu Dec 18 12:29:56 2008  using multiplier of 73
Thu Dec 18 12:29:56 2008  using 32kb Intel Core sieve core
Thu Dec 18 12:29:56 2008  sieve interval: 28 blocks of size 32768
Thu Dec 18 12:29:56 2008  processing polynomials in batches of 8
Thu Dec 18 12:29:56 2008  using a sieve bound of 1537153 (58242 primes)
Thu Dec 18 12:29:56 2008  using large prime bound of 122972240 (26 bits)
Thu Dec 18 12:29:56 2008  using double large prime bound of 364462296550480 (42-49 bits)
Thu Dec 18 12:29:56 2008  using trial factoring cutoff of 49 bits
Thu Dec 18 12:29:56 2008  polynomial 'A' values have 12 factors
Thu Dec 18 13:23:00 2008  58458 relations (16648 full + 41810 combined from 606551 partial), need 58338
Thu Dec 18 13:23:01 2008  begin with 623199 relations
Thu Dec 18 13:23:01 2008  reduce to 137918 relations in 9 passes
Thu Dec 18 13:23:01 2008  attempting to read 137918 relations
Thu Dec 18 13:23:03 2008  recovered 137918 relations
Thu Dec 18 13:23:03 2008  recovered 115182 polynomials
Thu Dec 18 13:23:03 2008  attempting to build 58458 cycles
Thu Dec 18 13:23:03 2008  found 58458 cycles in 5 passes
Thu Dec 18 13:23:03 2008  distribution of cycle lengths:
Thu Dec 18 13:23:03 2008     length 1 : 16648
Thu Dec 18 13:23:03 2008     length 2 : 11814
Thu Dec 18 13:23:03 2008     length 3 : 10413
Thu Dec 18 13:23:03 2008     length 4 : 7579
Thu Dec 18 13:23:03 2008     length 5 : 5155
Thu Dec 18 13:23:03 2008     length 6 : 3172
Thu Dec 18 13:23:03 2008     length 7 : 1719
Thu Dec 18 13:23:03 2008     length 9+: 1958
Thu Dec 18 13:23:03 2008  largest cycle: 15 relations
Thu Dec 18 13:23:04 2008  matrix is 58242 x 58458 (13.7 MB) with weight 3359561 (57.47/col)
Thu Dec 18 13:23:04 2008  sparse part has weight 3359561 (57.47/col)
Thu Dec 18 13:23:04 2008  filtering completed in 3 passes
Thu Dec 18 13:23:04 2008  matrix is 53596 x 53660 (12.7 MB) with weight 3108809 (57.94/col)
Thu Dec 18 13:23:04 2008  sparse part has weight 3108809 (57.94/col)
Thu Dec 18 13:23:04 2008  saving the first 48 matrix rows for later
Thu Dec 18 13:23:04 2008  matrix is 53548 x 53660 (7.8 MB) with weight 2389963 (44.54/col)
Thu Dec 18 13:23:04 2008  sparse part has weight 1717555 (32.01/col)
Thu Dec 18 13:23:04 2008  matrix includes 64 packed rows
Thu Dec 18 13:23:04 2008  using block size 21464 for processor cache size 1024 kB
Thu Dec 18 13:23:05 2008  commencing Lanczos iteration
Thu Dec 18 13:23:05 2008  memory use: 7.7 MB
Thu Dec 18 13:23:21 2008  lanczos halted after 848 iterations (dim = 53545)
Thu Dec 18 13:23:21 2008  recovered 15 nontrivial dependencies
Thu Dec 18 13:23:22 2008  prp41 factor: 69563816005530066987621201677220218900731
Thu Dec 18 13:23:22 2008  prp48 factor: 209819392365296826977778796234537568048688935347
Thu Dec 18 13:23:22 2008  elapsed time 00:53:28

(38·10¹¹⁹+7)/9 = 4(2)₁₁₈3_<120> = 3² · C119

C119 = P32 · P88

P32 = 17796655303796507065144186379611_<32>

P88 = 2636089728439345957807003412593302655340134489266022323067968446022844599735148064148277_<88>

Number: 42223_119
N=46913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580247
  ( 119 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=17796655303796507065144186379611 (prp32)
 r2=2636089728439345957807003412593302655340134489266022323067968446022844599735148064148277 (prp88)
Version: 
Total time: 1.91 hours.
Scaled time: 3.77 units (timescale=1.978).
Factorization parameters were as follows:
name: 42223_119
n: 46913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580247
m: 1000000000000000000000000
deg: 5
c5: 19
c0: 35
skew: 1.13
type: snfs
lss: 1
rlim: 740000
alim: 740000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [370000, 620001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 81734 x 81967
Total sieving time: 1.91 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000
total time: 1.91 hours.
 --------- CPU info (if available) ----------

(37·10¹⁵³+71)/9 = 4(1)₁₅₂9_<154> = 3 · 47 · 42829 · 3356641 · C141

C141 = P36 · P48 · P58

P36 = 267585967846317503969097730621906439_<36>

P48 = 169083349998879656324913041735201585866792484537_<48>

P58 = 4482632066041583145692570283513003585998276879951383228217_<58>

Number: 41119_153
N=202813692784995100304654547000616001388351317469991900616989696292083774391262123814153905948868605435039400406739699971898527486293769126231
  ( 141 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=267585967846317503969097730621906439 (prp36)
 r2=169083349998879656324913041735201585866792484537 (prp48)
 r3=4482632066041583145692570283513003585998276879951383228217 (prp58)
Version: 
Total time: 23.52 hours.
Scaled time: 60.31 units (timescale=2.564).
Factorization parameters were as follows:
name: 41119_152
n: 202813692784995100304654547000616001388351317469991900616989696292083774391262123814153905948868605435039400406739699971898527486293769126231
m: 5000000000000000000000000000000
deg: 5
c5: 296
c0: 1775
skew: 1.43
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 481081 x 481329
Total sieving time: 23.52 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 23.52 hours.
 --------- CPU info (if available) ----------

(38·10¹²⁵+7)/9 = 4(2)₁₂₄3_<126> = 3 · 17 · 1901 · 32672306313541_<14> · C108

C108 = P45 · P64

P45 = 116295998349478982853156680832900513953293021_<45>

P64 = 1146157315974285019595546328596583393702116364957884428638802393_<64>

Number: 42223_125
N=133293509326788711666710854874444178050766096891403697830905172109269902185821542440145829581270460044999253
  ( 108 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=116295998349478982853156680832900513953293021 (prp45)
 r2=1146157315974285019595546328596583393702116364957884428638802393 (prp64)
Version: 
Total time: 2.03 hours.
Scaled time: 5.24 units (timescale=2.575).
Factorization parameters were as follows:
name: 42223_125
n: 133293509326788711666710854874444178050766096891403697830905172109269902185821542440145829581270460044999253
m: 10000000000000000000000000
deg: 5
c5: 38
c0: 7
skew: 0.71
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 112736 x 112984
Total sieving time: 2.03 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 2.03 hours.
 --------- CPU info (if available) ----------

(38·10¹²⁴+7)/9 = 4(2)₁₂₃3_<125> = 7529 · C121

C121 = P49 · P73

P49 = 2711151477562038629795543684920467598635043008193_<49>

P73 = 2068473716730609939247632473759947310004060663074300121852699702217549559_<73>

Number: 42223_124
N=5607945573412434881421466625344962441522409645666386269387996044922595593335399418544590546184383347353197266864420536887
  ( 121 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=2711151477562038629795543684920467598635043008193 (prp49)
 r2=2068473716730609939247632473759947310004060663074300121852699702217549559   (prp73)
Version: 
Total time: 2.63 hours.
Scaled time: 5.29 units (timescale=2.010).
Factorization parameters were as follows:
name: 42223_124
n: 5607945573412434881421466625344962441522409645666386269387996044922595593335399418544590546184383347353197266864420536887
m: 10000000000000000000000000
deg: 5
c5: 19
c0: 35
skew: 1.13
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [445000, 745001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 113109 x 113351
Total sieving time: 2.63 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 2.63 hours.
 --------- CPU info (if available) ----------

Dec 18, 2008 (2nd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39

(38·10¹⁰³+7)/9 = 4(2)₁₀₂3_<104> = 41 · 163 · 4120903 · C94

C94 = P35 · P60

P35 = 15228969283328568516002938499690549_<35>

P60 = 100671542589360374820010743674518363883167127317682185376623_<60>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2296685655
Step 1 took 1812ms
Step 2 took 1504ms
********** Factor found in step 2: 15228969283328568516002938499690549
Found probable prime factor of 35 digits: 15228969283328568516002938499690549
Probable prime cofactor 100671542589360374820010743674518363883167127317682185376623 has 60 digits

(38·10¹⁴³+7)/9 = 4(2)₁₄₂3_<144> = 3 · 41³ · 54667 · 84584933 · 2220749942527_<13> · C114

C114 = P28 · P86

P28 = 4866734418829920193805385751_<28>

P86 = 40861349391788987053960663317374360811603887138536668614277435169890368201323389007843_<86>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3725277577
Step 1 took 2220ms
Step 2 took 1784ms
********** Factor found in step 2: 4866734418829920193805385751
Found probable prime factor of 28 digits: 4866734418829920193805385751
Probable prime cofactor 40861349391788987053960663317374360811603887138536668614277435169890368201323389007843 has 86 digits

(38·10¹³⁴+7)/9 = 4(2)₁₃₃3_<135> = 3 · 274355461 · 7475083489_<10> · C116

C116 = P29 · P88

P29 = 13297128789458489611981711367_<29>

P88 = 5160981478476877174528191139543584005394929170028975707947883782299690148268479826942487_<88>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2193296238
Step 1 took 3614ms
Step 2 took 2463ms
********** Factor found in step 2: 13297128789458489611981711367
Found probable prime factor of 29 digits: 13297128789458489611981711367
Probable prime cofactor 5160981478476877174528191139543584005394929170028975707947883782299690148268479826942487 has 88 digits

(38·10¹⁷⁶+7)/9 = 4(2)₁₇₅3_<177> = 3 · 29 · 54540943 · 4287368772178003_<16> · 8965485210842005636106031659_<28> · C124

C124 = P37 · C87

P37 = 2471951484413682939511067832881908139_<37>

C87 = [936471598052290722011809167208477610429304981302335238497256676307528852425786219092101_<87>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1864500341
Step 1 took 3285ms
Step 2 took 2524ms
********** Factor found in step 2: 2471951484413682939511067832881908139
Found probable prime factor of 37 digits: 2471951484413682939511067832881908139
Composite cofactor has 87 digits

(38·10¹⁸⁸+7)/9 = 4(2)₁₈₇3_<189> = 3 · 41 · 161837827 · C179

C179 = P34 · C145

P34 = 4517407346651943696614538983948377_<34>

C145 = [4695336080119231002572034438003134103984773018851208689382346363956946707607387905336610628296559396105847033548036718431918869359857064027844119_<145>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2813434907
Step 1 took 5311ms
Step 2 took 3484ms
********** Factor found in step 2: 4517407346651943696614538983948377
Found probable prime factor of 34 digits: 4517407346651943696614538983948377

(38·10¹⁶²+7)/9 = 4(2)₁₆₁3_<163> = C163

C163 = P32 · C132

P32 = 22666112659648690795351599407939_<32>

C132 = [186279062741041885017985574573968873226228250750405652759785192197613040280790635024373857044630449303253807700550767095880568892357_<132>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4290004477
Step 1 took 4562ms
Step 2 took 2074ms
********** Factor found in step 2: 22666112659648690795351599407939
Found probable prime factor of 32 digits: 22666112659648690795351599407939
Composite cofactor has 132 digits

(38·10¹⁵⁵+7)/9 = 4(2)₁₅₄3_<156> = 3⁴ · 21247 · 405706541 · 8153054611907549_<16> · C125

C125 = P37 · C89

P37 = 3631636673976858283592464277485606931_<37>

C89 = [20423195573440195206551390289801512611298882650218935717368875142211566032360322627320691_<89>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2443936897
Step 1 took 9742ms
Step 2 took 5797ms
********** Factor found in step 2: 3631636673976858283592464277485606931
Found probable prime factor of 37 digits: 3631636673976858283592464277485606931
Composite cofactor has 89 digits

(38·10¹⁴²+7)/9 = 4(2)₁₄₁3_<143> = 59 · 5563 · C138

C138 = P33 · C105

P33 = 605464278196827737125597251068803_<33>

C105 = [212467002221435818816699426054912524005576609275217237202725667730873122816617802499885558317173191456973_<105>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=855237390
Step 1 took 11861ms
Step 2 took 6523ms
********** Factor found in step 2: 605464278196827737125597251068803
Found probable prime factor of 33 digits: 605464278196827737125597251068803
Composite cofactor has 105 digits

(38·10¹⁵³+7)/9 = 4(2)₁₅₂3_<154> = 41 · C153

C153 = P29 · P45 · P79

P29 = 56625770021249037961199832163_<29>

P45 = 188621649452113576484103965715195827806438457_<45>

P79 = 9641654643505460294402314031716939370932298867900541134767060848222202356644933_<79>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=485009599
Step 1 took 11845ms
Step 2 took 6774ms
********** Factor found in step 2: 56625770021249037961199832163
Found probable prime factor of 29 digits: 56625770021249037961199832163

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1546770427
Step 1 took 11724ms
Step 2 took 6721ms
********** Factor found in step 2: 188621649452113576484103965715195827806438457
Found probable prime factor of 45 digits: 188621649452113576484103965715195827806438457

(38·10¹⁷⁸+7)/9 = 4(2)₁₇₇3_<179> = 41 · C178

C178 = P31 · C147

P31 = 3831638300420149104517799143979_<31>

C147 = [268765007905380748598617247784989569226788294214434773423165473690567346198193202300914071893455165689330378310000725717652182828907168758369414757_<147>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1830987632
Step 1 took 15973ms
Step 2 took 8310ms
********** Factor found in step 2: 3831638300420149104517799143979
Found probable prime factor of 31 digits: 3831638300420149104517799143979
Composite cofactor has 147 digits

(38·10¹⁹⁵+7)/9 = 4(2)₁₉₄3_<196> = 23 · 18553 · 3149252376494183_<16> · C175

C175 = P32 · P143

P32 = 42889893988079578415478220866263_<32>

P143 = 73254898010487591881808968625718488656302684170273081444857108882017914768115541121202852664845950871593721116081377554264061422226124415883473_<143>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=400399179
Step 1 took 16303ms
Step 2 took 8309ms
********** Factor found in step 2: 42889893988079578415478220866263
Found probable prime factor of 32 digits: 42889893988079578415478220866263
Probable prime cofactor has 143 digits

(38·10¹⁹⁷+7)/9 = 4(2)₁₉₆3_<198> = 3 · 181 · C195

C195 = P32 · C164

P32 = 27947028349698781437164987540699_<32>

C164 = [27823106755181784284339819113194093003006848773401981584784546486000626197936927250194729311161601729645412862762131763250467738959280736054302716529829833142273539_<164>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4094683216
Step 1 took 18445ms
********** Factor found in step 1: 27947028349698781437164987540699
Found probable prime factor of 32 digits: 27947028349698781437164987540699
Composite cofactor has 164 digits

(38·10¹²⁸+7)/9 = 4(2)₁₂₇3_<129> = 3³ · 41 · 1567 · 9613 · 22153 · C115

C115 = P57 · P58

P57 = 205996789767280236842224092563294819222483899476019914763_<57>

P58 = 5548460870468833125139443648463825083675241175547040412381_<58>

SNFS difficulty: 131 digits.
Divisors found:
 r1=205996789767280236842224092563294819222483899476019914763 (pp57)
 r2=5548460870468833125139443648463825083675241175547040412381 (pp58)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.294).
Factorization parameters were as follows:
n: 1142965127465948919158699701485164461510638059759591797889499511512820592383071296850919410053462850517519989880703
m: 100000000000000000000000000
deg: 5
c5: 19
c0: 350
skew: 1.79
type: snfs
lss: 1
rlim: 1080000
alim: 1080000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1080000/1080000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [540000, 940001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 166698 x 166946
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1080000,1080000,26,26,49,49,2.3,2.3,50000
total time: 2.50 hours.

(38·10¹⁶¹+7)/9 = 4(2)₁₆₀3_<162> = 3 · 71 · 199 · 18133 · 3953923 · 102948767865281369_<18> · 223103459630440120241113301_<27> · C103

C103 = P36 · P68

P36 = 515054520953638018081451448555001699_<36>

P68 = 11744374101790571418852539848321630821275916011828441771173016482301_<68>

Number: 42223_161
N=6048992976898055544701500924282843318487253300729386621852067578882185467974673849952876192480058429399
  ( 103 digits)
Divisors found:
 r1=515054520953638018081451448555001699 (pp36)
 r2=11744374101790571418852539848321630821275916011828441771173016482301 (pp68)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.947).
Factorization parameters were as follows:
name: 42223_161
n: 6048992976898055544701500924282843318487253300729386621852067578882185467974673849952876192480058429399
skew: 9508.02
# norm 1.32e+14
c5: 65640
c4: 494004046
c3: -12223958194410
c2: -80219580147807645
c1: 377628040081781466140
c0: -5661552501923811834276
# alpha -5.67
Y1: 148027261
Y0: -39165430004865054515
# Murphy_E 2.38e-09
# M 1376237156667498328491122275652318259924145043912891828309343895588198824682229544879829222474450612280
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1850001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 251057 x 251305
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 5.00 hours.

(38·10¹⁶⁴+7)/9 = 4(2)₁₆₃3_<165> = 3² · 61 · 7682881 · 40818499 · 4453252165552267529490497_<25> · C123

C123 = P36 · P88

P36 = 425438812577715228012820656931311881_<36>

P88 = 1294414025611891599260150096076852317064818033104359921919372175404128601450000975774169_<88>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1663009270
Step 1 took 10333ms
Step 2 took 5828ms
********** Factor found in step 2: 425438812577715228012820656931311881
Found probable prime factor of 36 digits: 425438812577715228012820656931311881
Probable prime cofactor 1294414025611891599260150096076852317064818033104359921919372175404128601450000975774169 has 88 digits

(38·10¹⁸⁶+7)/9 = 4(2)₁₈₅3_<187> = 47 · 2767 · 359878883096258333_<18> · C164

C164 = P32 · C133

P32 = 17220926929820735919650444522083_<32>

C133 = [5238671693611155393110256636771215165291040871189770033614443601009113065979421595887797051522376438298628830110390256780678267308393_<133>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2089980357
Step 1 took 13584ms
Step 2 took 7373ms
********** Factor found in step 2: 17220926929820735919650444522083
Found probable prime factor of 32 digits: 17220926929820735919650444522083
Composite cofactor has 133 digits

Dec 18, 2008

Factorizations of 422...223 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Dec 17, 2008 (3rd)

By Sinkiti Sibata / Msieve

(37·10¹⁵¹+53)/9 = 4(1)₁₅₀7_<152> = 17 · 19 · 5424157 · 3012826135843_<13> · C130

C130 = P41 · P90

P41 = 30714188652462505796370832052921572228561_<41>

P90 = 253577854611776783427342074390532895866761571131753872950109269776119129811679765690447289_<90>

Number: 41117_151
N=7788438064632821574690358496362360897296483820042841122084535900504402571465752730134408241556280290071228582891922842992630821129
  ( 130 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=30714188652462505796370832052921572228561 (prp41)
 r2=253577854611776783427342074390532895866761571131753872950109269776119129811679765690447289 (prp90)
Version: 
Total time: 28.65 hours.
Scaled time: 56.71 units (timescale=1.979).
Factorization parameters were as follows:
name: 41117_151
n: 7788438064632821574690358496362360897296483820042841122084535900504402571465752730134408241556280290071228582891922842992630821129
m: 1000000000000000000000000000000
deg: 5
c5: 370
c0: 53
skew: 0.68
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1200000, 2300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 499116 x 499364
Total sieving time: 28.65 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000
total time: 28.65 hours.
 --------- CPU info (if available) ----------

(38·10¹³⁸-11)/9 = 4(2)₁₃₇1_<139> = 3² · 53 · 1021 · C133

C133 = P44 · P90

P44 = 51707817722286821429454583067769802912986421_<44>

P90 = 167664360523445916239872708231359971038766019984240649261322234707681832432375540040788753_<90>

Number: 42221_138
N=8669558192470123675810540950772195266740631686824530195500818702883517869442385424373732790071439440968636048068593544418823618523013
  ( 133 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=51707817722286821429454583067769802912986421 (prp44)
 r2=167664360523445916239872708231359971038766019984240649261322234707681832432375540040788753 (prp90)
Version: 
Total time: 9.44 hours.
Scaled time: 18.50 units (timescale=1.960).
Factorization parameters were as follows:
name: 42221_138
n: 8669558192470123675810540950772195266740631686824530195500818702883517869442385424373732790071439440968636048068593544418823618523013
m: 5000000000000000000000000000
deg: 5
c5: 304
c0: -275
skew: 0.98
type: snfs
lss: 1
rlim: 1570000
alim: 1570000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1570000/1570000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [785000, 1785001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 239659 x 239907
Total sieving time: 9.44 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000
total time: 9.44 hours.
 --------- CPU info (if available) ----------

(38·10¹⁴²-11)/9 = 4(2)₁₄₁1_<143> = 421 · 2062883 · 364018747 · C126

C126 = P60 · P66

P60 = 226667704464855786266160319294497767450305082964541295658331_<60>

P66 = 589211205531103317422879572675077629800058220084069542829565675771_<66>

Number: 42221_142
N=133555151402705527771020532470635570480603171803939263654479802422770269818472340168044144200161160806498395618241264340998201
  ( 126 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=226667704464855786266160319294497767450305082964541295658331 (prp60)
 r2=589211205531103317422879572675077629800058220084069542829565675771 (prp66)
Version: 
Total time: 9.54 hours.
Scaled time: 24.47 units (timescale=2.564).
Factorization parameters were as follows:
name: 42221_142
n: 133555151402705527771020532470635570480603171803939263654479802422770269818472340168044144200161160806498395618241264340998201
m: 20000000000000000000000000000
deg: 5
c5: 475
c0: -44
skew: 0.62
type: snfs
lss: 1
rlim: 1770000
alim: 1770000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1770000/1770000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [885000, 2185001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 317247 x 317495
Total sieving time: 9.54 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1770000,1770000,26,26,49,49,2.3,2.3,100000
total time: 9.54 hours.
 --------- CPU info (if available) ----------

(38·10¹⁴⁹-11)/9 = 4(2)₁₄₈1_<150> = C150

C150 = P34 · P53 · P65

P34 = 2156877309792813337917367804096273_<34>

P53 = 10692962417405779727963760437122579230977363713174343_<53>

P65 = 18307017852353217144257078631568701474589782475479036325318027739_<65>

Number: 42221_149
N=422222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
  ( 150 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=2156877309792813337917367804096273 (prp34)
 r2=10692962417405779727963760437122579230977363713174343 (prp53)
 r3=18307017852353217144257078631568701474589782475479036325318027739 (prp65)
Version: 
Total time: 16.63 hours.
Scaled time: 42.47 units (timescale=2.554).
Factorization parameters were as follows:
name: 42221_149
n: 422222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
m: 1000000000000000000000000000000
deg: 5
c5: 19
c0: -55
skew: 1.24
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 376776 x 377024
Total sieving time: 16.63 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 16.63 hours.
 --------- CPU info (if available) ----------

(38·10¹⁴⁰-11)/9 = 4(2)₁₃₉1_<141> = 167 · 569 · 101402387 · C128

C128 = P39 · P89

P39 = 804607420655732570446552759744605618923_<39>

P89 = 54460313579417670846316649744291707051749895931971216643706261352702388356635007215995827_<89>

Number: 42221_140
N=43819172437237618652820907786713083938238055391217746877124393262556917756829365265010678060634024257185753881011836909120234321
  ( 128 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=804607420655732570446552759744605618923 (prp39)
 r2=54460313579417670846316649744291707051749895931971216643706261352702388356635007215995827 (prp89)
Version: 
Total time: 5.35 hours.
Scaled time: 13.57 units (timescale=2.534).
Factorization parameters were as follows:
name: 42221_140
n: 43819172437237618652820907786713083938238055391217746877124393262556917756829365265010678060634024257185753881011836909120234321
m: 10000000000000000000000000000
deg: 5
c5: 38
c0: -11
skew: 0.78
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [800000, 1500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 218142 x 218390
Total sieving time: 5.35 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000
total time: 5.35 hours.
 --------- CPU info (if available) ----------

Dec 17, 2008 (2nd)

By Serge Batalov / Msieve-1.39, GMP-ECM 6.2.1

(38·10¹⁵²-11)/9 = 4(2)₁₅₁1_<153> = 47 · 740549 · 1388627 · C139

C139 = P55 · P85

P55 = 2244475534182952124033053975047362318980113940838127137_<55>

P85 = 3892144435855376728741091997536320056326825112992346851623166566331315178926518146493_<85>

SNFS difficulty: 154 digits.
Divisors found:
 r1=2244475534182952124033053975047362318980113940838127137 (pp55)
 r2=3892144435855376728741091997536320056326825112992346851623166566331315178926518146493 (pp85)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.280).
Factorization parameters were as follows:
n: 8735822961783701521595509383320306982142781207790003682501701235482336432672547155076594232653301349910915673274832506173076799918724680541
m: 2000000000000000000000000000000
deg: 5
c5: 475
c0: -44
skew: 0.62
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1300000, 2300001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 512153 x 512401
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,52,52,2.4,2.4,100000
total time: 18.00 hours.

(38·10¹⁶²-11)/9 = 4(2)₁₆₁1_<163> = 3 · 151 · 601 · 673 · 28551353 · 10361935027_<11> · 15788755231694576119999_<23> · C115

C115 = P39 · P77

P39 = 393004019300720895064649178102671858011_<39>

P77 = 12552808589729656412640688337363128700026916814005950670291119358728810118951_<77>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3477203104
Step 1 took 6473ms
Step 2 took 4044ms
********** Factor found in step 2: 393004019300720895064649178102671858011
Found probable prime factor of 39 digits: 393004019300720895064649178102671858011
Probable prime cofactor has 77 digits

(38·10¹⁵⁶-11)/9 = 4(2)₁₅₅1_<157> = 3² · 41 · 61 · 205450383023983_<15> · 868117700586089_<15> · C124

C124 = P36 · P88

P36 = 273415711927335176935345351670676383_<36>

P88 = 3846589586178820725082205888583716939157891153434790937819112111477628162272406784535689_<88>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=324217118
Step 1 took 7748ms
Step 2 took 4473ms
********** Factor found in step 2: 273415711927335176935345351670676383
Found probable prime factor of 36 digits: 273415711927335176935345351670676383
Probable prime cofactor 3846589586178820725082205888583716939157891153434790937819112111477628162272406784535689 has 88 digits

Dec 17, 2008

By Robert Backstrom / GGNFS, Msieve

(31·10¹⁸⁵+41)/9 = 3(4)₁₈₄9_<186> = 7 · 188753 · C180

C180 = P59 · P122

P59 = 11462491287896624764009877866815918899950651066846725626897_<59>

P122 = 22743026785569236152077669009125297268693301386451793502974838936091495987844715921550687164968936573229303616204234222327_<122>

Number: n
N=260691746389986947752917035524464280563521370290004430918747512391057129418903801297723513529355025914021002840783188645209381303642057113525116682682390247303122860067650349129319
  ( 180 digits)
SNFS difficulty: 186 digits.
Divisors found:

Wed Dec 17 02:46:14 2008  prp59 factor: 11462491287896624764009877866815918899950651066846725626897
Wed Dec 17 02:46:14 2008  prp122 factor: 22743026785569236152077669009125297268693301386451793502974838936091495987844715921550687164968936573229303616204234222327
Wed Dec 17 02:46:14 2008  elapsed time 03:13:45 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 58.50 hours.
Scaled time: 117.71 units (timescale=2.012).
Factorization parameters were as follows:
name: KA_3_4_184_9
n: 260691746389986947752917035524464280563521370290004430918747512391057129418903801297723513529355025914021002840783188645209381303642057113525116682682390247303122860067650349129319
type: snfs
skew: 1.06
deg: 5
c5: 31
c0: 41
m: 10000000000000000000000000000000000000
rlim: 8500000
alim: 8500000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 8500000/8500000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 4100001)
Primes: RFBsize:571119, AFBsize:571584, largePrimes:29344877 encountered
Relations: rels:26217521, finalFF:1026972
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 5676222 hash collisions in 31554904 relations
Msieve: matrix is 1493389 x 1493637 (408.6 MB)

Total sieving time: 57.58 hours.
Total relation processing time: 0.93 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,8500000,8500000,29,29,58,58,2.5,2.5,100000
total time: 58.50 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830490)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830462)
Total of 4 processors activated (22643.71 BogoMIPS).

(34·10¹⁸⁴+11)/9 = 3(7)₁₈₃9_<185> = 3 · 7 · C184

C184 = P70 · P114

P70 = 3153381182245925815602116031604202495320047121667445799461559645437791_<70>

P114 = 570480286072025881760890891024077848976969633603699632299856594817956338766406814897528070489702511123803391082489_<114>

Number: n
N=1798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941799
  ( 184 digits)
SNFS difficulty: 186 digits.
Divisors found:

Wed Dec 17 12:43:05 2008  prp70 factor: 3153381182245925815602116031604202495320047121667445799461559645437791
Wed Dec 17 12:43:05 2008  prp114 factor: 570480286072025881760890891024077848976969633603699632299856594817956338766406814897528070489702511123803391082489
Wed Dec 17 12:43:05 2008  elapsed time 04:13:42 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 28.87 hours.
Scaled time: 59.05 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_3_7_183_9
n: 1798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941799
type: snfs
skew: 1.26
deg: 5
c5: 17
c0: 55
m: 10000000000000000000000000000000000000
rlim: 8500000
alim: 8500000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 8500000/8500000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 4550001)
Primes: RFBsize:571119, AFBsize:571718, largePrimes:31863919 encountered
Relations: rels:29900533, finalFF:1289293
Max relations in full relation-set: 28
Initial matrix: 1142902 x 1289291 with sparse part having weight 139239900.
Pruned matrix : 1020687 x 1026465 with weight 109219622.

Msieve: found 5898080 hash collisions in 35099131 relations
Msieve: matrix is 1215906 x 1216154 (330.1 MB)

Total sieving time: 27.66 hours.
Total relation processing time: 1.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,8500000,8500000,29,29,58,58,2.5,2.5,100000
total time: 28.87 hours.
 --------- CPU info (if available) ----------

Dec 16, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve

(11·10²⁰⁴-17)/3 = 3(6)₂₀₃1_<205> = C205

C205 = P48 · P71 · P88

P48 = 221505090182582524572671341559157703350533777731_<48>

P71 = 13194273781235111004047017055681434596445649290434332958327191748518633_<71>

P88 = 1254591174776189824004158294987313249694792007124710608846927570746687005326132416330207_<88>

Number: n
N=3666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661
  ( 205 digits)
SNFS difficulty: 206 digits.
Divisors found:

Tue Dec 16 14:36:52 2008  prp48 factor: 221505090182582524572671341559157703350533777731
Tue Dec 16 14:36:52 2008  prp71 factor: 13194273781235111004047017055681434596445649290434332958327191748518633
Tue Dec 16 14:36:52 2008  prp88 factor: 1254591174776189824004158294987313249694792007124710608846927570746687005326132416330207
Tue Dec 16 14:36:52 2008  elapsed time 17:19:44 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 175.28 hours.
Scaled time: 352.66 units (timescale=2.012).
Factorization parameters were as follows:
name: KA_3_6_203_1
n: 3666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661
type: snfs
skew: 0.98
deg: 5
c5: 11
c0: -170
m: 100000000000000000000000000000000000000000
rlim: 10000000
alim: 10000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 29800001)
Primes: RFBsize:664579, AFBsize:664171, largePrimes:34554940 encountered
Relations: rels:27185260, finalFF:103021
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 13574584 hash collisions in 52206683 relations
Msieve: matrix is 3208382 x 3208630 (877.7 MB)

Total sieving time: 172.35 hours.
Total relation processing time: 2.93 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,206,5,0,0,0,0,0,0,0,0,10000000,10000000,29,29,58,58,2.5,2.5,100000
total time: 175.28 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830490)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830462)
Total of 4 processors activated (22643.71 BogoMIPS).

Dec 16, 2008 (3rd)

By Serge Batalov / Msieve-1.39, GMP-ECM 6.2.1

(37·10¹⁶⁸+53)/9 = 4(1)₁₆₇7_<169> = 61 · 48589 · 101917 · C158

C158 = P49 · P52 · P58

P49 = 1155470698301302268611468354403836671616459816573_<49>

P52 = 6382078797307035347345673498114642379600251847737301_<52>

P58 = 1845540960763765864183039787801984859962999384752383870553_<58>

SNFS difficulty: 170 digits.
Divisors found:
 r1=1155470698301302268611468354403836671616459816573 (pp49)
 r2=6382078797307035347345673498114642379600251847737301 (pp52)
 r3=1845540960763765864183039787801984859962999384752383870553 (pp58)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 13609582016862291049453137524723009045974398678080754559936713443116025299342216519110899671138279626636611560178417519813777040628623124578030888993199988569
m: 5000000000000000000000000000000000
deg: 5
c5: 296
c0: 1325
skew: 1.35
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2450000, 5450001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 919522 x 919770
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,200000
total time: 70.00 hours.

10²⁴⁵+3 = 1(0)₂₄₄3_<246> = 397 · C243

C243 = P37 · C207

P37 = 1523139408975506847609408057356772403_<37>

C207 = [165374992782288143099098664420190855135065524201790567845531019468290719579509530782801360420860492125166999904737069490397081057711442662739511913130562317785089919433785439437190546446326948947840039161333_<207>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1013441708
Step 1 took 88160ms
Step 2 took 36093ms
********** Factor found in step 2: 1523139408975506847609408057356772403
Found probable prime factor of 37 digits: 1523139408975506847609408057356772403
Composite cofactor has 207 digits

(38·10¹⁶⁰-11)/9 = 4(2)₁₅₉1_<161> = C161

C161 = P58 · P103

P58 = 4232810193853545342342065250180631557044686896193443565813_<58>

P103 = 9974985952248230050213644193474437703849918356907673850080379830337390210326473820200577856401733781817_<103>

SNFS difficulty: 161 digits.
Divisors found:
 r1=4232810193853545342342065250180631557044686896193443565813 (pp58)
 r2=9974985952248230050213644193474437703849918356907673850080379830337390210326473820200577856401733781817 (pp103)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.883).
Factorization parameters were as follows:
n: 42222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
m: 100000000000000000000000000000000
deg: 5
c5: 38
c0: -11
skew: 0.78
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1750000, 2950001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 559579 x 559827
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,52,52,2.4,2.4,200000
total time: 20.00 hours.

Dec 16, 2008 (2nd)

By Sinkiti Sibata / Msieve, GGNFS

(38·10¹⁵³-11)/9 = 4(2)₁₅₂1_<154> = 3 · 7 · 17 · 78517 · 4943441 · 129735240245090347741_<21> · 3871855789967261077355383_<25> · C95

C95 = P41 · P55

P41 = 15061311339269694752966969737951939626793_<41>

P55 = 4027540334331000455649132757502438402057856590453203831_<55>

Mon Dec 15 21:24:24 2008  Msieve v. 1.39
Mon Dec 15 21:24:24 2008  random seeds: d578aff0 13fce78b
Mon Dec 15 21:24:24 2008  factoring 60660038906825554637414355681564907507415461749948153955759950113103673417179000748613297843983 (95 digits)
Mon Dec 15 21:24:25 2008  searching for 15-digit factors
Mon Dec 15 21:24:27 2008  commencing quadratic sieve (95-digit input)
Mon Dec 15 21:24:27 2008  using multiplier of 7
Mon Dec 15 21:24:27 2008  using 64kb Pentium 4 sieve core
Mon Dec 15 21:24:27 2008  sieve interval: 18 blocks of size 65536
Mon Dec 15 21:24:27 2008  processing polynomials in batches of 6
Mon Dec 15 21:24:27 2008  using a sieve bound of 2162071 (79904 primes)
Mon Dec 15 21:24:27 2008  using large prime bound of 324310650 (28 bits)
Mon Dec 15 21:24:27 2008  using double large prime bound of 2087998231332900 (43-51 bits)
Mon Dec 15 21:24:27 2008  using trial factoring cutoff of 51 bits
Mon Dec 15 21:24:27 2008  polynomial 'A' values have 12 factors
Tue Dec 16 03:39:39 2008  80356 relations (19851 full + 60505 combined from 1194222 partial), need 80000
Tue Dec 16 03:39:44 2008  begin with 1214073 relations
Tue Dec 16 03:39:45 2008  reduce to 208410 relations in 12 passes
Tue Dec 16 03:39:45 2008  attempting to read 208410 relations
Tue Dec 16 03:39:52 2008  recovered 208410 relations
Tue Dec 16 03:39:52 2008  recovered 191316 polynomials
Tue Dec 16 03:39:52 2008  attempting to build 80356 cycles
Tue Dec 16 03:39:53 2008  found 80356 cycles in 7 passes
Tue Dec 16 03:39:53 2008  distribution of cycle lengths:
Tue Dec 16 03:39:53 2008     length 1 : 19851
Tue Dec 16 03:39:53 2008     length 2 : 14166
Tue Dec 16 03:39:53 2008     length 3 : 13601
Tue Dec 16 03:39:53 2008     length 4 : 10899
Tue Dec 16 03:39:53 2008     length 5 : 8038
Tue Dec 16 03:39:53 2008     length 6 : 5507
Tue Dec 16 03:39:53 2008     length 7 : 3514
Tue Dec 16 03:39:53 2008     length 9+: 4780
Tue Dec 16 03:39:53 2008  largest cycle: 22 relations
Tue Dec 16 03:39:53 2008  matrix is 79904 x 80356 (21.8 MB) with weight 5402198 (67.23/col)
Tue Dec 16 03:39:53 2008  sparse part has weight 5402198 (67.23/col)
Tue Dec 16 03:39:56 2008  filtering completed in 4 passes
Tue Dec 16 03:39:56 2008  matrix is 75825 x 75889 (20.6 MB) with weight 5108863 (67.32/col)
Tue Dec 16 03:39:56 2008  sparse part has weight 5108863 (67.32/col)
Tue Dec 16 03:39:56 2008  saving the first 48 matrix rows for later
Tue Dec 16 03:39:56 2008  matrix is 75777 x 75889 (14.5 MB) with weight 4195500 (55.28/col)
Tue Dec 16 03:39:56 2008  sparse part has weight 3350889 (44.16/col)
Tue Dec 16 03:39:56 2008  matrix includes 64 packed rows
Tue Dec 16 03:39:56 2008  using block size 21845 for processor cache size 512 kB
Tue Dec 16 03:39:57 2008  commencing Lanczos iteration
Tue Dec 16 03:39:57 2008  memory use: 13.1 MB
Tue Dec 16 03:40:59 2008  lanczos halted after 1200 iterations (dim = 75775)
Tue Dec 16 03:40:59 2008  recovered 16 nontrivial dependencies
Tue Dec 16 03:41:01 2008  prp41 factor: 15061311339269694752966969737951939626793
Tue Dec 16 03:41:01 2008  prp55 factor: 4027540334331000455649132757502438402057856590453203831
Tue Dec 16 03:41:01 2008  elapsed time 06:16:37

(38·10¹²⁵-11)/9 = 4(2)₁₂₄1_<126> = 53 · 2801 · 349499 · 1447098722403233_<16> · C100

C100 = P47 · P54

P47 = 26028553070102555153152006678575895714988264141_<47>

P54 = 216051847743155505973228004187461561967298916530089431_<54>

Mon Dec 15 19:29:51 2008  Msieve v. 1.39
Mon Dec 15 19:29:51 2008  random seeds: b14ae2d8 9d6205d9
Mon Dec 15 19:29:51 2008  factoring 5623516984876440046820940447597024505155242882926050220394806682266805082143873407184438266180393771 (100 digits)
Mon Dec 15 19:29:52 2008  searching for 15-digit factors
Mon Dec 15 19:29:53 2008  commencing quadratic sieve (100-digit input)
Mon Dec 15 19:29:53 2008  using multiplier of 19
Mon Dec 15 19:29:53 2008  using 32kb Intel Core sieve core
Mon Dec 15 19:29:53 2008  sieve interval: 36 blocks of size 32768
Mon Dec 15 19:29:53 2008  processing polynomials in batches of 6
Mon Dec 15 19:29:53 2008  using a sieve bound of 2747231 (100000 primes)
Mon Dec 15 19:29:53 2008  using large prime bound of 412084650 (28 bits)
Mon Dec 15 19:29:53 2008  using double large prime bound of 3213479781672900 (43-52 bits)
Mon Dec 15 19:29:53 2008  using trial factoring cutoff of 52 bits
Mon Dec 15 19:29:53 2008  polynomial 'A' values have 13 factors
Tue Dec 16 09:38:14 2008  100131 relations (23083 full + 77048 combined from 1514856 partial), need 100096
Tue Dec 16 09:38:16 2008  begin with 1537939 relations
Tue Dec 16 09:38:18 2008  reduce to 266334 relations in 11 passes
Tue Dec 16 09:38:18 2008  attempting to read 266334 relations
Tue Dec 16 09:38:23 2008  recovered 266334 relations
Tue Dec 16 09:38:23 2008  recovered 258695 polynomials
Tue Dec 16 09:38:23 2008  attempting to build 100131 cycles
Tue Dec 16 09:38:23 2008  found 100131 cycles in 7 passes
Tue Dec 16 09:38:23 2008  distribution of cycle lengths:
Tue Dec 16 09:38:23 2008     length 1 : 23083
Tue Dec 16 09:38:23 2008     length 2 : 16942
Tue Dec 16 09:38:23 2008     length 3 : 16845
Tue Dec 16 09:38:23 2008     length 4 : 13748
Tue Dec 16 09:38:23 2008     length 5 : 10569
Tue Dec 16 09:38:23 2008     length 6 : 7270
Tue Dec 16 09:38:23 2008     length 7 : 4676
Tue Dec 16 09:38:23 2008     length 9+: 6998
Tue Dec 16 09:38:23 2008  largest cycle: 23 relations
Tue Dec 16 09:38:24 2008  matrix is 100000 x 100131 (28.5 MB) with weight 7076937 (70.68/col)
Tue Dec 16 09:38:24 2008  sparse part has weight 7076937 (70.68/col)
Tue Dec 16 09:38:26 2008  filtering completed in 3 passes
Tue Dec 16 09:38:26 2008  matrix is 96437 x 96501 (27.6 MB) with weight 6861401 (71.10/col)
Tue Dec 16 09:38:26 2008  sparse part has weight 6861401 (71.10/col)
Tue Dec 16 09:38:26 2008  saving the first 48 matrix rows for later
Tue Dec 16 09:38:26 2008  matrix is 96389 x 96501 (17.9 MB) with weight 5506767 (57.06/col)
Tue Dec 16 09:38:26 2008  sparse part has weight 4110435 (42.59/col)
Tue Dec 16 09:38:26 2008  matrix includes 64 packed rows
Tue Dec 16 09:38:26 2008  using block size 38600 for processor cache size 1024 kB
Tue Dec 16 09:38:27 2008  commencing Lanczos iteration
Tue Dec 16 09:38:27 2008  memory use: 16.8 MB
Tue Dec 16 09:39:35 2008  lanczos halted after 1525 iterations (dim = 96384)
Tue Dec 16 09:39:35 2008  recovered 14 nontrivial dependencies
Tue Dec 16 09:39:36 2008  prp47 factor: 26028553070102555153152006678575895714988264141
Tue Dec 16 09:39:36 2008  prp54 factor: 216051847743155505973228004187461561967298916530089431
Tue Dec 16 09:39:36 2008  elapsed time 14:09:45

(37·10¹⁵⁰+71)/9 = 4(1)₁₄₉9_<151> = 3³ · 883 · 4889 · 1221948250643_<13> · C131

C131 = P64 · P67

P64 = 3287070246072146574864034007439682346444251917611909212297051483_<64>

P67 = 8781180623418817074662056980380019977887522124119819322642913307399_<67>

Number: 41119_150
N=28864357552625256507880498508537587718402715194719806825118503206248327918753286810133287358446407710796717272680968736991307822717
  ( 131 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=3287070246072146574864034007439682346444251917611909212297051483 (prp64)
 r2=8781180623418817074662056980380019977887522124119819322642913307399 (prp67)
Version: 
Total time: 16.83 hours.
Scaled time: 43.33 units (timescale=2.575).
Factorization parameters were as follows:
name: 41119_150
n: 28864357552625256507880498508537587718402715194719806825118503206248327918753286810133287358446407710796717272680968736991307822717
m: 1000000000000000000000000000000
deg: 5
c5: 37
c0: 71
skew: 1.14
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 2000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 389350 x 389598
Total sieving time: 16.83 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 16.83 hours.
 --------- CPU info (if available) ----------

(37·10¹⁴⁸+53)/9 = 4(1)₁₄₇7_<149> = 22669 · 107310918012420977_<18> · C128

C128 = P39 · P42 · P48

P39 = 244860118170382215335072280041384558599_<39>

P42 = 446917873259314622190911021433246558748781_<42>

P48 = 154431953041875888316954780441581808091078491811_<48>

Number: 41117_148
N=16899853584033955114950120383965912952947644853307839909495057609897055375198928097686899001618067828768496519047079737942880209
  ( 128 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=244860118170382215335072280041384558599 (prp39)
 r2=446917873259314622190911021433246558748781 (prp42)
 r3=154431953041875888316954780441581808091078491811 (prp48)
Version: 
Total time: 14.74 hours.
Scaled time: 37.79 units (timescale=2.564).
Factorization parameters were as follows:
name: 41117_148
n: 16899853584033955114950120383965912952947644853307839909495057609897055375198928097686899001618067828768496519047079737942880209
m: 500000000000000000000000000000
deg: 5
c5: 296
c0: 1325
skew: 1.35
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 405122 x 405370
Total sieving time: 14.74 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 14.74 hours.
 --------- CPU info (if available) ----------

(38·10¹⁰⁸-11)/9 = 4(2)₁₀₇1_<109> = 3 · C109

C109 = P39 · P70

P39 = 247611047803078395531865562134423674323_<39>

P70 = 5683944314660381557602633851722612401459653226858370362546598490499509_<70>

Number: 42221_108
N=1407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407
  ( 109 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=247611047803078395531865562134423674323 (pp39)
 r2=5683944314660381557602633851722612401459653226858370362546598490499509 (pp70)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 1.47 hours.
Scaled time: 0.70 units (timescale=0.474).
Factorization parameters were as follows:
name: 42221_108
n: 1407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407
m: 5000000000000000000000
deg: 5
c5: 304
c0: -275
skew: 0.98
type: snfs
lss: 1
rlim: 500000
alim: 500000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [250000, 400001)
Primes: RFBsize:41538, AFBsize:41548, largePrimes:1113852 encountered
Relations: rels:1058520, finalFF:113369
Max relations in full relation-set: 28
Initial matrix: 83153 x 113369 with sparse part having weight 4921853.
Pruned matrix : 70547 x 71026 with weight 2259018.
Total sieving time: 1.38 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000
total time: 1.47 hours.
 --------- CPU info (if available) ----------

(37·10¹⁵⁰+53)/9 = 4(1)₁₄₉7_<151> = 1953649038355327_<16> · C136

C136 = P68 · P69

P68 = 15528730282738141460510651909659560854080390256835141132996522651323_<68>

P69 = 135511677020391780462271499218014916556072164255270934647592478198377_<69>

Number: 41117_150
N=2104324282611188159960451123666380806055558797064658637231912660210061374031014998130279654083126691286869690704509007375842722395502771
  ( 136 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=15528730282738141460510651909659560854080390256835141132996522651323 (prp68)
 r2=135511677020391780462271499218014916556072164255270934647592478198377 (prp69)
Version: 
Total time: 19.54 hours.
Scaled time: 39.28 units (timescale=2.010).
Factorization parameters were as follows:
name: 41117_150
n: 2104324282611188159960451123666380806055558797064658637231912660210061374031014998130279654083126691286869690704509007375842722395502771
m: 1000000000000000000000000000000
deg: 5
c5: 37
c0: 53
skew: 1.07
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 1900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 350594 x 350842
Total sieving time: 19.54 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 19.54 hours.
 --------- CPU info (if available) ----------

(38·10¹³⁴-11)/9 = 4(2)₁₃₃1_<135> = 1491649 · 2946860149_<10> · C119

C119 = P52 · P68

P52 = 4149907820957241490972920909065030923841515609684853_<52>

P68 = 23146027777754951736573466939039243760546766431014482234227004890357_<68>

Number: 42221_134
N=96053881698998834395407603696803899148417871409640815733762490089278910746043202961580105229793209375622816062588662521
  ( 119 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=4149907820957241490972920909065030923841515609684853 (pp52)
 r2=23146027777754951736573466939039243760546766431014482234227004890357 (pp68)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 8.31 hours.
Scaled time: 3.93 units (timescale=0.473).
Factorization parameters were as follows:
name: 42221_134
n: 96053881698998834395407603696803899148417871409640815733762490089278910746043202961580105229793209375622816062588662521
m: 1000000000000000000000000000
deg: 5
c5: 19
c0: -55
skew: 1.24
type: snfs
lss: 1
rlim: 1310000
alim: 1310000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1310000/1310000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [655000, 1330001)
Primes: RFBsize:100730, AFBsize:100660, largePrimes:3230980 encountered
Relations: rels:3174985, finalFF:257716
Max relations in full relation-set: 28
Initial matrix: 201455 x 257716 with sparse part having weight 22148514.
Pruned matrix : 185025 x 186096 with weight 12827971.
Total sieving time: 7.51 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.60 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1310000,1310000,26,26,48,48,2.3,2.3,75000
total time: 8.31 hours.
 --------- CPU info (if available) ----------

Dec 16, 2008

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / Msieve v1.39

(38·10¹²⁰-11)/9 = 4(2)₁₁₉1_<121> = 3⁴ · C119

C119 = P42 · P78

P42 = 509139097395824952151373035566844707911509_<42>

P78 = 102381059598382098870388221982891747034455666681264121668445411723287964967049_<78>

Number: 42221_120
N=52126200274348422496570644718792866941015089163237311385459533607681755829903978052126200274348422496570644718792866941
  ( 119 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=509139097395824952151373035566844707911509
 r2=102381059598382098870388221982891747034455666681264121668445411723287964967049
Version: 
Total time: 0.90 hours.
Scaled time: 2.14 units (timescale=2.383).
Factorization parameters were as follows:
n: 52126200274348422496570644718792866941015089163237311385459533607681755829903978052126200274348422496570644718792866941
m: 1000000000000000000000000
deg: 5
c5: 38
c0: -11
skew: 0.78
type: snfs
lss: 1
rlim: 600000
alim: 600000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 510001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 69377 x 69607
Total sieving time: 0.84 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.2,2.2,30000
total time: 0.90 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(38·10¹²⁹-11)/9 = 4(2)₁₂₈1_<130> = 3² · 7 · 482513 · 6402719 · 23270251 · C108

C108 = P42 · P67

P42 = 125271917239803673135317586548283560303451_<42>

P67 = 7441702172870640836699293639239075973261209560036712761186574811061_<67>

Number: 42221_129
N=932236298723118086065258271081642050028750773492236275008624201179184424782920531697686204455679770151271511
  ( 108 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=125271917239803673135317586548283560303451
 r2=7441702172870640836699293639239075973261209560036712761186574811061
Version: 
Total time: 2.16 hours.
Scaled time: 5.17 units (timescale=2.393).
Factorization parameters were as follows:
n: 932236298723118086065258271081642050028750773492236275008624201179184424782920531697686204455679770151271511
m: 100000000000000000000000000
deg: 5
c5: 19
c0: -55
skew: 1.24
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [500000, 950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 147643 x 147891
Total sieving time: 1.98 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000
total time: 2.16 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(38·10¹³²-11)/9 = 4(2)₁₃₁1_<133> = 3 · 588953 · 1230907 · C121

C121 = P50 · P71

P50 = 26254955460944566172921225572697038732496864651657_<50>

P71 = 73943953476055737169732831407296594260590759605785391982027707547550781_<71>

Number: 42221_132
N=1941395205120000513014345070903776490531439352431330068809619602452852526039131860535958662912632755808985780565083294117
  ( 121 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=26254955460944566172921225572697038732496864651657
 r2=73943953476055737169732831407296594260590759605785391982027707547550781
Version: 
Total time: 3.02 hours.
Scaled time: 7.21 units (timescale=2.390).
Factorization parameters were as follows:
n: 1941395205120000513014345070903776490531439352431330068809619602452852526039131860535958662912632755808985780565083294117
m: 200000000000000000000000000
deg: 5
c5: 475
c0: -44
skew: 0.62
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [650000, 1250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 208908 x 209156
Total sieving time: 2.72 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,47,47,2.3,2.3,50000
total time: 3.02 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Dec 15, 2008 (10th)

By Wataru Sakai / Msieve

(8·10¹⁹⁹-17)/9 = (8)₁₉₈7_<199> = 7 · C199

C199 = P60 · P66 · P74

P60 = 165915290595704680698485074656900719922152047067184299154427_<60>

P66 = 209149051828140486987606736849824369901235273907179420942848736473_<66>

P74 = 36593767584410672419943796220646382293763887819649513105939916736712122971_<74>

Number: 88887_199
N=1269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841
  ( 199 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=165915290595704680698485074656900719922152047067184299154427
 r2=209149051828140486987606736849824369901235273907179420942848736473
 r3=36593767584410672419943796220646382293763887819649513105939916736712122971
Version: 
Total time: 755.47 hours.
Scaled time: 1492.80 units (timescale=1.976).
Factorization parameters were as follows:
n: 1269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841
m: 10000000000000000000000000000000000000000
deg: 5
c5: 4
c0: -85
skew: 1.84
type: snfs
lss: 1
rlim: 15400000
alim: 15400000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
Factor base limits: 15400000/15400000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [7700000, 15500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2674720 x 2674968
Total sieving time: 755.47 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,200,5,0,0,0,0,0,0,0,0,15400000,15400000,29,29,56,56,2.6,2.6,100000
total time: 755.47 hours.
 --------- CPU info (if available) ----------

(34·10¹⁹⁴+11)/9 = 3(7)₁₉₃9_<195> = C195

C195 = P49 · P147

P49 = 2691197740780502992199450526686456932840409619277_<49>

P147 = 140375332534358627509741440328961748053188124694231767125239461652617980761194328247328425405232588742773325753465604320143168823613280390506804927_<147>

Number: 37779_194
N=377777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
  ( 195 digits)
SNFS difficulty: 196 digits.
Divisors found:
 r1=2691197740780502992199450526686456932840409619277
 r2=140375332534358627509741440328961748053188124694231767125239461652617980761194328247328425405232588742773325753465604320143168823613280390506804927
Version: 
Total time: 658.53 hours.
Scaled time: 1313.11 units (timescale=1.994).
Factorization parameters were as follows:
n: 377777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
m: 1000000000000000000000000000000000000000
deg: 5
c5: 17
c0: 55
skew: 1.26
type: snfs
lss: 1
rlim: 13000000
alim: 13000000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5Factor base limits: 13000000/13000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6500000, 13600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2061273 x 2061521
Total sieving time: 658.53 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,196,5,0,0,0,0,0,0,0,0,13000000,13000000,28,28,55,55,2.5,2.5,100000
total time: 658.53 hours.
 --------- CPU info (if available) ----------

Dec 15, 2008 (9th)

By Sinkiti Sibata / Msieve

(38·10¹⁰³-11)/9 = 4(2)₁₀₂1_<104> = 733 · 1621 · 6029 · 367134413 · C86

C86 = P41 · P45

P41 = 28306816444502368825148383991347799490833_<41>

P45 = 567143149328791314070560484701937139507375317_<45>

Mon Dec 15 15:27:04 2008  Msieve v. 1.39
Mon Dec 15 15:27:04 2008  random seeds: 651d427f 9761b85e
Mon Dec 15 15:27:04 2008  factoring 16054017025807092569396169499940205222006738243601515768240784071360787770700831969061 (86 digits)
Mon Dec 15 15:27:06 2008  searching for 15-digit factors
Mon Dec 15 15:27:07 2008  commencing quadratic sieve (86-digit input)
Mon Dec 15 15:27:07 2008  using multiplier of 29
Mon Dec 15 15:27:07 2008  using 64kb Pentium 4 sieve core
Mon Dec 15 15:27:07 2008  sieve interval: 7 blocks of size 65536
Mon Dec 15 15:27:07 2008  processing polynomials in batches of 15
Mon Dec 15 15:27:07 2008  using a sieve bound of 1451119 (55333 primes)
Mon Dec 15 15:27:07 2008  using large prime bound of 116089520 (26 bits)
Mon Dec 15 15:27:07 2008  using double large prime bound of 328569561530240 (41-49 bits)
Mon Dec 15 15:27:07 2008  using trial factoring cutoff of 49 bits
Mon Dec 15 15:27:07 2008  polynomial 'A' values have 11 factors
Mon Dec 15 16:19:16 2008  55637 relations (16439 full + 39198 combined from 566957 partial), need 55429
Mon Dec 15 16:19:19 2008  begin with 583396 relations
Mon Dec 15 16:19:19 2008  reduce to 129329 relations in 9 passes
Mon Dec 15 16:19:19 2008  attempting to read 129329 relations
Mon Dec 15 16:19:22 2008  recovered 129329 relations
Mon Dec 15 16:19:22 2008  recovered 107195 polynomials
Mon Dec 15 16:19:23 2008  attempting to build 55637 cycles
Mon Dec 15 16:19:23 2008  found 55637 cycles in 5 passes
Mon Dec 15 16:19:23 2008  distribution of cycle lengths:
Mon Dec 15 16:19:23 2008     length 1 : 16439
Mon Dec 15 16:19:23 2008     length 2 : 11435
Mon Dec 15 16:19:23 2008     length 3 : 9924
Mon Dec 15 16:19:23 2008     length 4 : 7013
Mon Dec 15 16:19:23 2008     length 5 : 4754
Mon Dec 15 16:19:23 2008     length 6 : 2805
Mon Dec 15 16:19:23 2008     length 7 : 1625
Mon Dec 15 16:19:23 2008     length 9+: 1642
Mon Dec 15 16:19:23 2008  largest cycle: 19 relations
Mon Dec 15 16:19:23 2008  matrix is 55333 x 55637 (12.3 MB) with weight 2995743 (53.84/col)
Mon Dec 15 16:19:23 2008  sparse part has weight 2995743 (53.84/col)
Mon Dec 15 16:19:24 2008  filtering completed in 3 passes
Mon Dec 15 16:19:24 2008  matrix is 49885 x 49949 (11.1 MB) with weight 2716273 (54.38/col)
Mon Dec 15 16:19:24 2008  sparse part has weight 2716273 (54.38/col)
Mon Dec 15 16:19:24 2008  saving the first 48 matrix rows for later
Mon Dec 15 16:19:24 2008  matrix is 49837 x 49949 (6.8 MB) with weight 2078163 (41.61/col)
Mon Dec 15 16:19:24 2008  sparse part has weight 1495961 (29.95/col)
Mon Dec 15 16:19:24 2008  matrix includes 64 packed rows
Mon Dec 15 16:19:24 2008  using block size 19979 for processor cache size 512 kB
Mon Dec 15 16:19:25 2008  commencing Lanczos iteration
Mon Dec 15 16:19:25 2008  memory use: 6.9 MB
Mon Dec 15 16:19:48 2008  lanczos halted after 789 iterations (dim = 49837)
Mon Dec 15 16:19:48 2008  recovered 18 nontrivial dependencies
Mon Dec 15 16:19:49 2008  prp41 factor: 28306816444502368825148383991347799490833
Mon Dec 15 16:19:49 2008  prp45 factor: 567143149328791314070560484701937139507375317
Mon Dec 15 16:19:49 2008  elapsed time 00:52:45

(38·10¹⁰⁵-11)/9 = 4(2)₁₀₄1_<106> = 3 · 7² · 17 · 347 · 140986765379_<12> · C89

C89 = P41 · P48

P41 = 43871068211571581561965777755726137512439_<41>

P48 = 787206733759095811393840080371004503026881448697_<48>

Mon Dec 15 15:34:20 2008  Msieve v. 1.39
Mon Dec 15 15:34:20 2008  random seeds: 389128b0 b431d9bf
Mon Dec 15 15:34:20 2008  factoring 34535600313353761637815551285629476040788202504999833839791741988242343476339596177841983 (89 digits)
Mon Dec 15 15:34:21 2008  searching for 15-digit factors
Mon Dec 15 15:34:23 2008  commencing quadratic sieve (89-digit input)
Mon Dec 15 15:34:23 2008  using multiplier of 7
Mon Dec 15 15:34:23 2008  using 32kb Intel Core sieve core
Mon Dec 15 15:34:23 2008  sieve interval: 32 blocks of size 32768
Mon Dec 15 15:34:23 2008  processing polynomials in batches of 7
Mon Dec 15 15:34:23 2008  using a sieve bound of 1555999 (59000 primes)
Mon Dec 15 15:34:23 2008  using large prime bound of 124479920 (26 bits)
Mon Dec 15 15:34:23 2008  using double large prime bound of 372544998335040 (42-49 bits)
Mon Dec 15 15:34:23 2008  using trial factoring cutoff of 49 bits
Mon Dec 15 15:34:23 2008  polynomial 'A' values have 11 factors
Mon Dec 15 16:35:25 2008  59266 relations (15945 full + 43321 combined from 625351 partial), need 59096
Mon Dec 15 16:35:26 2008  begin with 641296 relations
Mon Dec 15 16:35:27 2008  reduce to 144178 relations in 10 passes
Mon Dec 15 16:35:27 2008  attempting to read 144178 relations
Mon Dec 15 16:35:29 2008  recovered 144178 relations
Mon Dec 15 16:35:29 2008  recovered 120576 polynomials
Mon Dec 15 16:35:29 2008  attempting to build 59266 cycles
Mon Dec 15 16:35:29 2008  found 59266 cycles in 6 passes
Mon Dec 15 16:35:29 2008  distribution of cycle lengths:
Mon Dec 15 16:35:29 2008     length 1 : 15945
Mon Dec 15 16:35:29 2008     length 2 : 11323
Mon Dec 15 16:35:29 2008     length 3 : 10530
Mon Dec 15 16:35:29 2008     length 4 : 7966
Mon Dec 15 16:35:29 2008     length 5 : 5549
Mon Dec 15 16:35:29 2008     length 6 : 3419
Mon Dec 15 16:35:29 2008     length 7 : 2034
Mon Dec 15 16:35:29 2008     length 9+: 2500
Mon Dec 15 16:35:29 2008  largest cycle: 21 relations
Mon Dec 15 16:35:29 2008  matrix is 59000 x 59266 (14.5 MB) with weight 3552330 (59.94/col)
Mon Dec 15 16:35:29 2008  sparse part has weight 3552330 (59.94/col)
Mon Dec 15 16:35:30 2008  filtering completed in 4 passes
Mon Dec 15 16:35:30 2008  matrix is 54944 x 55008 (13.5 MB) with weight 3325067 (60.45/col)
Mon Dec 15 16:35:30 2008  sparse part has weight 3325067 (60.45/col)
Mon Dec 15 16:35:30 2008  saving the first 48 matrix rows for later
Mon Dec 15 16:35:30 2008  matrix is 54896 x 55008 (9.8 MB) with weight 2725550 (49.55/col)
Mon Dec 15 16:35:30 2008  sparse part has weight 2235862 (40.65/col)
Mon Dec 15 16:35:30 2008  matrix includes 64 packed rows
Mon Dec 15 16:35:30 2008  using block size 22003 for processor cache size 1024 kB
Mon Dec 15 16:35:31 2008  commencing Lanczos iteration
Mon Dec 15 16:35:31 2008  memory use: 8.9 MB
Mon Dec 15 16:35:50 2008  lanczos halted after 870 iterations (dim = 54892)
Mon Dec 15 16:35:50 2008  recovered 15 nontrivial dependencies
Mon Dec 15 16:35:51 2008  prp41 factor: 43871068211571581561965777755726137512439
Mon Dec 15 16:35:51 2008  prp48 factor: 787206733759095811393840080371004503026881448697
Mon Dec 15 16:35:51 2008  elapsed time 01:01:31

(38·10¹²⁷-11)/9 = 4(2)₁₂₆1_<128> = 499 · 2386393 · 1606241281_<10> · 272625457405895818536527_<24> · C86

C86 = P35 · P52

P35 = 17366429354635051553800208947550843_<35>

P52 = 4662414176865757064462443642505119553194330890299483_<52>

Mon Dec 15 17:43:30 2008  Msieve v. 1.39
Mon Dec 15 17:43:30 2008  random seeds: 68905814 d1f19330
Mon Dec 15 17:43:30 2008  factoring 80969486424588104569192172741595063682559812789268173368043734892383445616679639114169 (86 digits)
Mon Dec 15 17:43:31 2008  searching for 15-digit factors
Mon Dec 15 17:43:33 2008  commencing quadratic sieve (86-digit input)
Mon Dec 15 17:43:33 2008  using multiplier of 1
Mon Dec 15 17:43:33 2008  using 32kb Intel Core sieve core
Mon Dec 15 17:43:33 2008  sieve interval: 17 blocks of size 32768
Mon Dec 15 17:43:33 2008  processing polynomials in batches of 12
Mon Dec 15 17:43:33 2008  using a sieve bound of 1469129 (56000 primes)
Mon Dec 15 17:43:33 2008  using large prime bound of 117530320 (26 bits)
Mon Dec 15 17:43:33 2008  using double large prime bound of 335946198551280 (41-49 bits)
Mon Dec 15 17:43:33 2008  using trial factoring cutoff of 49 bits
Mon Dec 15 17:43:33 2008  polynomial 'A' values have 11 factors
Mon Dec 15 18:13:35 2008  56158 relations (16674 full + 39484 combined from 575315 partial), need 56096
Mon Dec 15 18:13:36 2008  begin with 591989 relations
Mon Dec 15 18:13:37 2008  reduce to 130896 relations in 8 passes
Mon Dec 15 18:13:37 2008  attempting to read 130896 relations
Mon Dec 15 18:13:38 2008  recovered 130896 relations
Mon Dec 15 18:13:38 2008  recovered 102453 polynomials
Mon Dec 15 18:13:38 2008  attempting to build 56158 cycles
Mon Dec 15 18:13:38 2008  found 56158 cycles in 4 passes
Mon Dec 15 18:13:38 2008  distribution of cycle lengths:
Mon Dec 15 18:13:38 2008     length 1 : 16674
Mon Dec 15 18:13:38 2008     length 2 : 11381
Mon Dec 15 18:13:38 2008     length 3 : 10137
Mon Dec 15 18:13:38 2008     length 4 : 7151
Mon Dec 15 18:13:38 2008     length 5 : 4629
Mon Dec 15 18:13:38 2008     length 6 : 2845
Mon Dec 15 18:13:38 2008     length 7 : 1598
Mon Dec 15 18:13:38 2008     length 9+: 1743
Mon Dec 15 18:13:38 2008  largest cycle: 18 relations
Mon Dec 15 18:13:39 2008  matrix is 56000 x 56158 (12.1 MB) with weight 2944603 (52.43/col)
Mon Dec 15 18:13:39 2008  sparse part has weight 2944603 (52.43/col)
Mon Dec 15 18:13:39 2008  filtering completed in 3 passes
Mon Dec 15 18:13:39 2008  matrix is 50465 x 50527 (11.0 MB) with weight 2682817 (53.10/col)
Mon Dec 15 18:13:39 2008  sparse part has weight 2682817 (53.10/col)
Mon Dec 15 18:13:39 2008  saving the first 48 matrix rows for later
Mon Dec 15 18:13:39 2008  matrix is 50417 x 50527 (6.4 MB) with weight 2003995 (39.66/col)
Mon Dec 15 18:13:39 2008  sparse part has weight 1381607 (27.34/col)
Mon Dec 15 18:13:39 2008  matrix includes 64 packed rows
Mon Dec 15 18:13:39 2008  using block size 20210 for processor cache size 1024 kB
Mon Dec 15 18:13:40 2008  commencing Lanczos iteration
Mon Dec 15 18:13:40 2008  memory use: 6.8 MB
Mon Dec 15 18:13:53 2008  lanczos halted after 798 iterations (dim = 50413)
Mon Dec 15 18:13:54 2008  recovered 14 nontrivial dependencies
Mon Dec 15 18:13:54 2008  prp35 factor: 17366429354635051553800208947550843
Mon Dec 15 18:13:54 2008  prp52 factor: 4662414176865757064462443642505119553194330890299483
Mon Dec 15 18:13:54 2008  elapsed time 00:30:24

(37·10¹⁴³+71)/9 = 4(1)₁₄₂9_<144> = 31 · 151 · 1282121 · C134

C134 = P40 · P95

P40 = 3615287439291684894508158182767387665977_<40>

P95 = 18947360908062300940159800563451894341618031529231267746815252549335160149680738911882646397847_<95>

Number: 41119_143
N=68500155898643929386073770112198146916568725842649511299081359558885873252281044837718846546767740555072432009399126924327815887951519
  ( 134 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=3615287439291684894508158182767387665977 (prp40)
 r2=18947360908062300940159800563451894341618031529231267746815252549335160149680738911882646397847 (prp95)
Version: 
Total time: 9.91 hours.
Scaled time: 25.40 units (timescale=2.564).
Factorization parameters were as follows:
name: 41119_143
n: 68500155898643929386073770112198146916568725842649511299081359558885873252281044837718846546767740555072432009399126924327815887951519
m: 50000000000000000000000000000
deg: 5
c5: 296
c0: 1775
skew: 1.43
type: snfs
lss: 1
rlim: 1900000
alim: 1900000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1900000/1900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [950000, 2250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 328954 x 329202
Total sieving time: 9.91 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000
total time: 9.91 hours.
 --------- CPU info (if available) ----------

(37·10¹³⁸+71)/9 = 4(1)₁₃₇9_<139> = 3 · 969010793 · C130

C130 = P61 · P69

P61 = 3476796762562889019061094719588926077162359713038881374966959_<61>

P69 = 406752322152161834672358389592055437109529103077857683960073230597779_<69>

Number: 41119_138
N=1414195156823573553705887742749187696994382569658716247518999894535096649197353543171908066013017432273708813448035939853943784061
  ( 130 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=3476796762562889019061094719588926077162359713038881374966959 (prp61)
 r2=406752322152161834672358389592055437109529103077857683960073230597779(prp69)Version: 
Total time: 9.36 hours.
Scaled time: 18.63 units (timescale=1.991).
Factorization parameters were as follows:
name: 41119_138
n: 1414195156823573553705887742749187696994382569658716247518999894535096649197353543171908066013017432273708813448035939853943784061
m: 5000000000000000000000000000
deg: 5
c5: 296
c0: 1775
skew: 1.43
type: snfs
lss: 1
rlim: 1570000
alim: 1570000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1570000/1570000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [785000, 1785001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 237971 x 238219
Total sieving time: 9.36 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000
total time: 9.36 hours.
 --------- CPU info (if available) ----------

(37·10¹⁴¹+53)/9 = 4(1)₁₄₀7_<142> = 43 · C140

C140 = P43 · P98

P43 = 2344853697342225768244701403474970076911147_<43>

P98 = 40773219775069496196274797925205475166939330156666714576604063888238857689344930254975648637575477_<98>

Number: 41117_141
N=95607235142118863049095607235142118863049095607235142118863049095607235142118863049095607235142118863049095607235142118863049095607235142119
  ( 140 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=2344853697342225768244701403474970076911147 (prp43)
 r2=40773219775069496196274797925205475166939330156666714576604063888238857689344930254975648637575477 (prp98)
Version: 
Total time: 10.54 hours.
Scaled time: 26.09 units (timescale=2.475).
Factorization parameters were as follows:
name: 41117_141
n: 95607235142118863049095607235142118863049095607235142118863049095607235142118863049095607235142118863049095607235142118863049095607235142119
m: 10000000000000000000000000000
deg: 5
c5: 370
c0: 53
skew: 0.68
type: snfs
lss: 1
rlim: 1660000
alim: 1660000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1660000/1660000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [830000, 2330001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 306636 x 306884
Total sieving time: 10.54 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1660000,1660000,26,26,48,48,2.3,2.3,100000
total time: 10.54 hours.
 --------- CPU info (if available) ----------

(37·10¹⁴⁵+53)/9 = 4(1)₁₄₄7_<146> = 619 · 4360973 · 23951846117_<11> · C126

C126 = P59 · P68

P59 = 38350460235070243587880442271327734428299906979443252142693_<59>

P68 = 16579659029211224705104833603108275078319308270761472069498739409211_<68>

Number: 41117_145
N=635837554310788391204818689459763367605246338531582846149485015459484002376721164224273149663384689094348905037164216690545223
  ( 126 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=38350460235070243587880442271327734428299906979443252142693 (prp59)
 r2=16579659029211224705104833603108275078319308270761472069498739409211 (prp68)
Version: 
Total time: 11.28 hours.
Scaled time: 22.53 units (timescale=1.997).
Factorization parameters were as follows:
name: 41117_145
n: 635837554310788391204818689459763367605246338531582846149485015459484002376721164224273149663384689094348905037164216690545223
m: 100000000000000000000000000000
deg: 5
c5: 37
c0: 53
skew: 1.07
type: snfs
lss: 1
rlim: 1940000
alim: 1940000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1940000/1940000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [970000, 2070001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 307574 x 307822
Total sieving time: 11.28 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1940000,1940000,26,26,49,49,2.3,2.3,100000
total time: 11.28 hours.
 --------- CPU info (if available) ----------

Dec 15, 2008 (8th)

By Serge Batalov / GMP-ECM 6.2.1, msieve-1.39, GMP-ECM 6.2.1+msieve, Msieve-1.39

(38·10¹⁴⁵-11)/9 = 4(2)₁₄₄1_<146> = 389 · 785143 · 541988574965639_<15> · 11348765752211748977_<20> · C104

C104 = P34 · P35 · P36

P34 = 1325404641036859296643530875431267_<34>

P35 = 36103065167888294499984392024763463_<35>

P36 = 469690089725626719012031234061716021_<36>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2865957120
Step 1 took 8207ms
Step 2 took 4973ms
********** Factor found in step 2: 36103065167888294499984392024763463
Found probable prime factor of 35 digits: 36103065167888294499984392024763463
Composite cofactor has 69 digits

Sun Dec 14 22:43:05 2008
Sun Dec 14 22:43:05 2008  Msieve v. 1.39
Sun Dec 14 22:43:05 2008  random seeds: ecc3aec6 9d478ede
Sun Dec 14 22:43:05 2008  factoring 622529424771364516359872641106451889809872987897208805215742458228607 (69 digits)
Sun Dec 14 22:43:05 2008  searching for 15-digit factors
Sun Dec 14 22:43:05 2008  commencing quadratic sieve (69-digit input)
Sun Dec 14 22:43:05 2008  using multiplier of 7
Sun Dec 14 22:43:05 2008  using 64kb Opteron sieve core
Sun Dec 14 22:43:05 2008  sieve interval: 6 blocks of size 65536
Sun Dec 14 22:43:05 2008  processing polynomials in batches of 17
Sun Dec 14 22:43:06 2008  using a sieve bound of 204517 (9095 primes)
Sun Dec 14 22:43:06 2008  using large prime bound of 18406530 (24 bits)
Sun Dec 14 22:43:06 2008  using trial factoring cutoff of 24 bits
Sun Dec 14 22:43:06 2008  polynomial 'A' values have 9 factors
Sun Dec 14 22:44:53 2008  9225 relations (4203 full + 5022 combined from 51864 partial), need 9191
Sun Dec 14 22:44:53 2008  begin with 56067 relations
Sun Dec 14 22:44:53 2008  reduce to 13607 relations in 2 passes
Sun Dec 14 22:44:53 2008  attempting to read 13607 relations
Sun Dec 14 22:44:53 2008  recovered 13607 relations
Sun Dec 14 22:44:53 2008  recovered 11821 polynomials
Sun Dec 14 22:44:53 2008  attempting to build 9225 cycles
Sun Dec 14 22:44:53 2008  found 9225 cycles in 1 passes
Sun Dec 14 22:44:53 2008  distribution of cycle lengths:
Sun Dec 14 22:44:53 2008     length 1 : 4203
Sun Dec 14 22:44:53 2008     length 2 : 5022
Sun Dec 14 22:44:53 2008  largest cycle: 2 relations
Sun Dec 14 22:44:53 2008  matrix is 9095 x 9225 (1.3 MB) with weight 267721 (29.02/col)
Sun Dec 14 22:44:53 2008  sparse part has weight 267721 (29.02/col)
Sun Dec 14 22:44:53 2008  filtering completed in 3 passes
Sun Dec 14 22:44:53 2008  matrix is 8379 x 8443 (1.2 MB) with weight 242533 (28.73/col)
Sun Dec 14 22:44:53 2008  sparse part has weight 242533 (28.73/col)
Sun Dec 14 22:44:53 2008  commencing Lanczos iteration
Sun Dec 14 22:44:53 2008  memory use: 1.6 MB
Sun Dec 14 22:44:54 2008  lanczos halted after 134 iterations (dim = 8375)
Sun Dec 14 22:44:54 2008  recovered 63 nontrivial dependencies
Sun Dec 14 22:44:54 2008  prp34 factor: 1325404641036859296643530875431267
Sun Dec 14 22:44:54 2008  prp36 factor: 469690089725626719012031234061716021
Sun Dec 14 22:44:54 2008  elapsed time 00:01:49

(38·10¹⁶³-11)/9 = 4(2)₁₆₂1_<164> = 977 · 1399 · 126913957 · 1065053831_<10> · 1894635371_<10> · 1451688987955948106334132287_<28> · C104

C104 = P32 · P73

P32 = 15325232869025743468160027097037_<32>

P73 = 5421775857181523778303366997185264829240061910861849089673960276292566569_<73>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1701068307
Step 1 took 8199ms
Step 2 took 5108ms
********** Factor found in step 2: 15325232869025743468160027097037
Found probable prime factor of 32 digits: 15325232869025743468160027097037
Probable prime cofactor 5421775857181523778303366997185264829240061910861849089673960276292566569 has 73 digits

(38·10¹²⁸-11)/9 = 4(2)₁₂₇1_<129> = 83 · 7143462642221693_<16> · C111

C111 = P28 · P84

P28 = 3980015878546287994687508077_<28>

P84 = 178924335183058703221158270546770884637344930166891465712261296911583661673906338967_<84>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3096623199
Step 1 took 8208ms
Step 2 took 5205ms
********** Factor found in step 2: 3980015878546287994687508077
Found probable prime factor of 28 digits: 3980015878546287994687508077
Probable prime cofactor has 84 digits

(38·10¹⁴⁷-11)/9 = 4(2)₁₄₆1_<148> = 3³ · 7² · 47045659 · C137

C137 = P28 · P29 · P36 · P46

P28 = 2551902873964888480833926621_<28>

P29 = 25651567516317837264646215281_<29>

P36 = 140164536628756188314004991027646939_<36>

P46 = 7393421921628468039493253474311183298582706427_<46>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4033410296
Step 1 took 10041ms
Step 2 took 5472ms
********** Factor found in step 2: 2551902873964888480833926621
Found probable prime factor of 28 digits: 2551902873964888480833926621

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3869496862
Step 1 took 6981ms
Step 2 took 4380ms
********** Factor found in step 2: 25651567516317837264646215281
Found probable prime factor of 29 digits: 25651567516317837264646215281

Sun Dec 14 23:32:12 2008  Msieve v. 1.39
Sun Dec 14 23:32:12 2008  random seeds: c480db8c b034535a
Sun Dec 14 23:32:12 2008  factoring 1036295557745942373186723249313381729835841778863922580350252672039512028042176953 (82 digits)
Sun Dec 14 23:32:13 2008  searching for 15-digit factors
Sun Dec 14 23:32:14 2008  commencing quadratic sieve (82-digit input)
Sun Dec 14 23:32:14 2008  using multiplier of 1
Sun Dec 14 23:32:14 2008  using 64kb Opteron sieve core
Sun Dec 14 23:32:14 2008  sieve interval: 6 blocks of size 65536
Sun Dec 14 23:32:14 2008  processing polynomials in batches of 17
Sun Dec 14 23:32:14 2008  using a sieve bound of 1334341 (51025 primes)
Sun Dec 14 23:32:14 2008  using large prime bound of 126762395 (26 bits)
Sun Dec 14 23:32:14 2008  using trial factoring cutoff of 27 bits
Sun Dec 14 23:32:14 2008  polynomial 'A' values have 10 factors
Sun Dec 14 23:54:47 2008  51205 relations (26457 full + 24748 combined from 273052 partial), need 51121
Sun Dec 14 23:54:47 2008  begin with 299509 relations
Sun Dec 14 23:54:47 2008  reduce to 72932 relations in 2 passes
Sun Dec 14 23:54:47 2008  attempting to read 72932 relations
Sun Dec 14 23:54:48 2008  recovered 72932 relations
Sun Dec 14 23:54:48 2008  recovered 63151 polynomials
Sun Dec 14 23:54:48 2008  attempting to build 51205 cycles
Sun Dec 14 23:54:48 2008  found 51205 cycles in 1 passes
Sun Dec 14 23:54:48 2008  distribution of cycle lengths:
Sun Dec 14 23:54:48 2008     length 1 : 26457
Sun Dec 14 23:54:48 2008     length 2 : 24748
Sun Dec 14 23:54:48 2008  largest cycle: 2 relations
Sun Dec 14 23:54:49 2008  matrix is 51025 x 51205 (7.5 MB) with weight 1547321 (30.22/col)
Sun Dec 14 23:54:49 2008  sparse part has weight 1547321 (30.22/col)
Sun Dec 14 23:54:49 2008  filtering completed in 4 passes
Sun Dec 14 23:54:49 2008  matrix is 36298 x 36362 (5.8 MB) with weight 1237357 (34.03/col)
Sun Dec 14 23:54:49 2008  sparse part has weight 1237357 (34.03/col)
Sun Dec 14 23:54:49 2008  saving the first 48 matrix rows for later
Sun Dec 14 23:54:49 2008  matrix is 36250 x 36362 (4.4 MB) with weight 984802 (27.08/col)
Sun Dec 14 23:54:49 2008  sparse part has weight 795660 (21.88/col)
Sun Dec 14 23:54:49 2008  matrix includes 64 packed rows
Sun Dec 14 23:54:49 2008  using block size 14544 for processor cache size 1024 kB
Sun Dec 14 23:54:50 2008  commencing Lanczos iteration
Sun Dec 14 23:54:50 2008  memory use: 4.2 MB
Sun Dec 14 23:54:58 2008  lanczos halted after 575 iterations (dim = 36249)
Sun Dec 14 23:54:59 2008  recovered 16 nontrivial dependencies
Sun Dec 14 23:54:59 2008  prp36 factor: 140164536628756188314004991027646939
Sun Dec 14 23:54:59 2008  prp46 factor: 7393421921628468039493253474311183298582706427
Sun Dec 14 23:54:59 2008  elapsed time 00:22:47

(38·10¹³⁵-11)/9 = 4(2)₁₃₄1_<136> = 3 · 7 · 67 · 10709 · C129

C129 = P30 · P99

P30 = 937437808317976970693932416403_<30>

P99 = 298920435195374668796858613681629028190698771165759803331918105970884920720033436834219559330152989_<99>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4218461253
Step 1 took 8577ms
Step 2 took 4940ms
********** Factor found in step 2: 937437808317976970693932416403
Found probable prime factor of 30 digits: 937437808317976970693932416403
Probable prime cofactor 298920435195374668796858613681629028190698771165759803331918105970884920720033436834219559330152989 has 99 digits

(38·10¹³³-11)/9 = 4(2)₁₃₂1_<134> = 1259 · C131

C131 = P36 · P96

P36 = 227346354804397997449555013421517819_<36>

P96 = 147512003565082160996670532501548152339461769615196128904934077918830260161327461047769915156101_<96>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2551179353
Step 1 took 8385ms
Step 2 took 4932ms
********** Factor found in step 2: 227346354804397997449555013421517819
Found probable prime factor of 36 digits: 227346354804397997449555013421517819
Probable prime cofactor 147512003565082160996670532501548152339461769615196128904934077918830260161327461047769915156101 has 96 digits

(38·10¹⁹¹-11)/9 = 4(2)₁₉₀1_<192> = 41 · 2687 · 774334507 · C178

C178 = P33 · C146

P33 = 375832150285823251963801943606447_<33>

C146 = [13169431325495540700522931115085114511012173448511242545734463676942758815655542079711578357374161512954053203286078300190494821013860645706028447_<146>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3279824311
Step 1 took 15916ms
Step 2 took 8379ms
********** Factor found in step 2: 375832150285823251963801943606447
Found probable prime factor of 33 digits: 375832150285823251963801943606447
Composite cofactor has 146 digits

(38·10¹⁷⁴-11)/9 = 4(2)₁₇₃1_<175> = 3³ · 7629737812981_<13> · 31668315658185358241_<20> · C141

C141 = P38 · C104

P38 = 64583320974668012969282589628685014327_<38>

C104 = [10021260930390560266594511156264428707661578748567959642375971936717369835041789453030241615860197033469_<104>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3366280551
Step 1 took 14481ms
Step 2 took 6856ms
********** Factor found in step 2: 64583320974668012969282589628685014327
Found probable prime factor of 38 digits: 64583320974668012969282589628685014327
Composite cofactor has 104 digits

(38·10¹²²-11)/9 = 4(2)₁₂₁1_<123> = 23 · C122

C122 = P41 · P81

P41 = 22983221156969608220878678122685099656223_<41>

P81 = 798734337425041424415227498048707151445996691869167022100770362401392131327274149_<81>

SNFS difficulty: 124 digits.
Divisors found:
 r1=22983221156969608220878678122685099656223 (pp41)
 r2=798734337425041424415227498048707151445996691869167022100770362401392131327274149 (pp81)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.728).
Factorization parameters were as follows:
n: 18357487922705314009661835748792270531400966183574879227053140096618357487922705314009661835748792270531400966183574879227
m: 2000000000000000000000000
deg: 5
c5: 475
c0: -44
skew: 0.62
type: snfs
lss: 1
rlim: 820000
alim: 820000
lpbr: 25
lpba: 25
mfbr: 48
mfba: 48
rlambda: 2.2
alambda: 2.2
Factor base limits: 820000/820000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 48/48
Sieved rational special-q in [410000, 810001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 101881 x 102120
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,820000,820000,25,25,48,48,2.2,2.2,50000
total time: 1.20 hours.

(38·10¹⁸³-11)/9 = 4(2)₁₈₂1_<184> = 3² · 7 · 6514450079635017199_<19> · C164

C164 = P35 · P129

P35 = 75782147652784397005420137353528113_<35>

P129 = 135755010714898869452949025678199105972122459983334039812159735676716342059338321962469593013630612819204264542435169763895315341_<129>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=821134725
Step 1 took 11704ms
Step 2 took 6053ms
********** Factor found in step 2: 75782147652784397005420137353528113
Found probable prime factor of 35 digits: 75782147652784397005420137353528113
Probable prime cofactor 135755010714898869452949025678199105972122459983334039812159735676716342059338321962469593013630612819204264542435169763895315341 has 129 digits

(37·10¹⁶⁰+71)/9 = 4(1)₁₅₉9_<161> = 13 · 1164433 · 1927633 · C148

C148 = P34 · P49 · P67

P34 = 1302813942596384285247378345758543_<34>

P49 = 1023739102807287331415444498937198533190476003389_<49>

P67 = 1056343867181512794323328678468277917562204780290353805173030837321_<67>

SNFS difficulty: 161 digits.
Divisors found:
 r1=1302813942596384285247378345758543 (pp34)
 r2=1023739102807287331415444498937198533190476003389 (pp49)
 r3=1056343867181512794323328678468277917562204780290353805173030837321 (pp67)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.174).
Factorization parameters were as follows:
n: 1408889734971532832959813943795077767526643347374927297662390319135412350788559621130563324497189583241140762438987075704505540800628177844802413867
m: 100000000000000000000000000000000
deg: 5
c5: 37
c0: 71
skew: 1.14
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1750000, 3250001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 662073 x 662321
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,52,52,2.4,2.4,100000
total time: 35.00 hours.

(38·10¹⁹³-11)/9 = 4(2)₁₉₂1_<194> = 29 · 143251879 · C185

C185 = P32 · C153

P32 = 92238676107852763259816729714369_<32>

C153 = [110186833103092390774649090660008487821406637141568965549388610139834253319507062767249752482557653014855888025715777277839734871796910969834280443874599_<153>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4093897938
Step 1 took 13765ms
Step 2 took 7000ms
********** Factor found in step 2: 92238676107852763259816729714369
Found probable prime factor of 32 digits: 92238676107852763259816729714369
Composite cofactor has 153 digits

Dec 15, 2008 (7th)

By Jo Yeong Uk / GGNFS, Msieve

(11·10¹⁹¹-17)/3 = 3(6)₁₉₀1_<192> = C192

C192 = P50 · P142

P50 = 49192191343990162417715955038848218978279791366327_<50>

P142 = 7453757530390289043345066089546327493410373894631714762602742698136076516003603270057275757770990426540518320236664138941399118042301680339843_<142>

Number: 36661_191
N=366666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661
  ( 192 digits)
SNFS difficulty: 192 digits.
Divisors found:
 r1=49192191343990162417715955038848218978279791366327 (pp50)
 r2=7453757530390289043345066089546327493410373894631714762602742698136076516003603270057275757770990426540518320236664138941399118042301680339843 (pp142)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 333.93 hours.
Scaled time: 792.08 units (timescale=2.372).
Factorization parameters were as follows:
n: 366666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661
m: 100000000000000000000000000000000000000
deg: 5
c5: 110
c0: -17
skew: 0.69
type: snfs
lss: 1
rlim: 13000000
alim: 13000000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 13000000/13000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6500000, 11800001)
Primes: RFBsize:849252, AFBsize:848849, largePrimes:20997970 encountered
Relations: rels:22348036, finalFF:1980622
Max relations in full relation-set: 28
Initial matrix: 1698168 x 1980622 with sparse part having weight 222660520.
Pruned matrix : 1459606 x 1468160 with weight 178804439.
Total sieving time: 302.57 hours.
Total relation processing time: 0.57 hours.
Matrix solve time: 30.49 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,192,5,0,0,0,0,0,0,0,0,13000000,13000000,28,28,55,55,2.5,2.5,100000
total time: 333.93 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(37·10¹⁷⁹+53)/9 = 4(1)₁₇₈7_<180> = 3⁴ · 7 · 23 · 4751018479457_<13> · 13962759095755291_<17> · 49208248701391080839818523_<26> · 2119493083661110697017153309_<28> · C94

C94 = P43 · P52

P43 = 1231767907813054570880909901881618539628959_<43>

P52 = 3699061547272506851328690176815392273739868519354327_<52>

Sun Dec 14 23:07:19 2008  
Sun Dec 14 23:07:19 2008  
Sun Dec 14 23:07:19 2008  Msieve v. 1.39
Sun Dec 14 23:07:19 2008  random seeds: efc8f9c0 4a2a88b6
Sun Dec 14 23:07:19 2008  factoring 4556385302955576221884023543638349856512194802012137833352589947767890040676035957132831155593 (94 digits)
Sun Dec 14 23:07:20 2008  searching for 15-digit factors
Sun Dec 14 23:07:21 2008  commencing quadratic sieve (94-digit input)
Sun Dec 14 23:07:21 2008  using multiplier of 1
Sun Dec 14 23:07:21 2008  using VC8 32kb sieve core
Sun Dec 14 23:07:21 2008  sieve interval: 36 blocks of size 32768
Sun Dec 14 23:07:21 2008  processing polynomials in batches of 6
Sun Dec 14 23:07:21 2008  using a sieve bound of 2059511 (76377 primes)
Sun Dec 14 23:07:21 2008  using large prime bound of 284212518 (28 bits)
Sun Dec 14 23:07:21 2008  using double large prime bound of 1646484896014146 (42-51 bits)
Sun Dec 14 23:07:21 2008  using trial factoring cutoff of 51 bits
Sun Dec 14 23:07:21 2008  polynomial 'A' values have 12 factors
Mon Dec 15 02:09:04 2008  76723 relations (18644 full + 58079 combined from 1105235 partial), need 76473
Mon Dec 15 02:09:06 2008  begin with 1123879 relations
Mon Dec 15 02:09:06 2008  reduce to 199758 relations in 11 passes
Mon Dec 15 02:09:06 2008  attempting to read 199758 relations
Mon Dec 15 02:09:09 2008  recovered 199758 relations
Mon Dec 15 02:09:09 2008  recovered 183205 polynomials
Mon Dec 15 02:09:09 2008  attempting to build 76723 cycles
Mon Dec 15 02:09:09 2008  found 76723 cycles in 5 passes
Mon Dec 15 02:09:09 2008  distribution of cycle lengths:
Mon Dec 15 02:09:09 2008     length 1 : 18644
Mon Dec 15 02:09:09 2008     length 2 : 13569
Mon Dec 15 02:09:09 2008     length 3 : 12956
Mon Dec 15 02:09:09 2008     length 4 : 10464
Mon Dec 15 02:09:09 2008     length 5 : 7806
Mon Dec 15 02:09:09 2008     length 6 : 5369
Mon Dec 15 02:09:09 2008     length 7 : 3303
Mon Dec 15 02:09:09 2008     length 9+: 4612
Mon Dec 15 02:09:09 2008  largest cycle: 18 relations
Mon Dec 15 02:09:10 2008  matrix is 76377 x 76723 (20.7 MB) with weight 4802821 (62.60/col)
Mon Dec 15 02:09:10 2008  sparse part has weight 4802821 (62.60/col)
Mon Dec 15 02:09:11 2008  filtering completed in 3 passes
Mon Dec 15 02:09:11 2008  matrix is 72800 x 72864 (19.7 MB) with weight 4576855 (62.81/col)
Mon Dec 15 02:09:11 2008  sparse part has weight 4576855 (62.81/col)
Mon Dec 15 02:09:11 2008  saving the first 48 matrix rows for later
Mon Dec 15 02:09:11 2008  matrix is 72752 x 72864 (12.2 MB) with weight 3552283 (48.75/col)
Mon Dec 15 02:09:11 2008  sparse part has weight 2460376 (33.77/col)
Mon Dec 15 02:09:11 2008  matrix includes 64 packed rows
Mon Dec 15 02:09:11 2008  using block size 29145 for processor cache size 4096 kB
Mon Dec 15 02:09:11 2008  commencing Lanczos iteration
Mon Dec 15 02:09:11 2008  memory use: 11.2 MB
Mon Dec 15 02:09:41 2008  lanczos halted after 1151 iterations (dim = 72748)
Mon Dec 15 02:09:41 2008  recovered 14 nontrivial dependencies
Mon Dec 15 02:09:41 2008  prp43 factor: 1231767907813054570880909901881618539628959
Mon Dec 15 02:09:41 2008  prp52 factor: 3699061547272506851328690176815392273739868519354327
Mon Dec 15 02:09:41 2008  elapsed time 03:02:22

(37·10¹⁸¹+71)/9 = 4(1)₁₈₀9_<182> = 7 · 42323 · 33379705157_<11> · 24127822888595769062376049807_<29> · 47573256735105102134774568941200081_<35> · C103

C103 = P38 · P66

P38 = 10427180460429420252723196144751715523_<38>

P66 = 347339620026515181041293360623135033853462919353750340536712007667_<66>

Number: 41119_181
N=3621772899073458445059701652864566407076358975646712173315673909567467074401737345715255403591778914841
  ( 103 digits)
Divisors found:
 r1=10427180460429420252723196144751715523 (pp38)
 r2=347339620026515181041293360623135033853462919353750340536712007667 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.29 hours.
Scaled time: 10.21 units (timescale=2.382).
Factorization parameters were as follows:
name: 41119_181
n: 3621772899073458445059701652864566407076358975646712173315673909567467074401737345715255403591778914841
skew: 9782.55
# norm 4.14e+14
c5: 73080
c4: -2514835704
c3: 8790142461548
c2: 263294977153601755
c1: 196917554526018178456
c0: -2679866085058324682790127
# alpha -6.43
Y1: 7813826537
Y0: -34595945979182260752
# Murphy_E 2.51e-09
# M 1396009132050224762205095102224607140116956259471065740878701764748997185483488045420616203276518767234
type: gnfs
rlim: 1400000
alim: 1400000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved algebraic special-q in [700000, 1350001)
Primes: RFBsize:107126, AFBsize:107413, largePrimes:4760133 encountered
Relations: rels:4585963, finalFF:244161
Max relations in full relation-set: 28
Initial matrix: 214630 x 244161 with sparse part having weight 22152773.
Pruned matrix : 200512 x 201649 with weight 15853660.
Polynomial selection time: 0.25 hours.
Total sieving time: 3.76 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1400000,1400000,26,26,50,50,2.6,2.6,50000
total time: 4.29 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Dec 15, 2008 (6th)

By Serge Batalov / Msieve-1.39

(37·10¹⁵⁸+71)/9 = 4(1)₁₅₇9_<159> = 31 · C158

C158 = P38 · P47 · P73

P38 = 56252524761237276570987106972917336289_<38>

P47 = 37279445348853727722204385871231176114193568127_<47>

P73 = 6323915511918555012521989947661747244518565340773117237921653166093351183_<73>

SNFS difficulty: 160 digits.
Divisors found:
 r1=56252524761237276570987106972917336289 (pp38)
 r2=37279445348853727722204385871231176114193568127 (pp47)
 r3=6323915511918555012521989947661747244518565340773117237921653166093351183 (pp73)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.559).
Factorization parameters were as follows:
n: 13261648745519713261648745519713261648745519713261648745519713261648745519713261648745519713261648745519713261648745519713261648745519713261648745519713261649
m: 50000000000000000000000000000000
deg: 5
c5: 296
c0: 1775
skew: 1.43
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1700000, 3200001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 646811 x 647059
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,52,52,2.4,2.4,100000
total time: 21.00 hours.

(37·10¹⁵⁹+53)/9 = 4(1)₁₅₈7_<160> = 8473427 · C153

C153 = P42 · P42 · P70

P42 = 443323695339234757494089624823618634934581_<42>

P42 = 452780513252055747543767753370086491619059_<42>

P70 = 2417082367680574707369031567295805948468828136719998084989731464459249_<70>

SNFS difficulty: 161 digits.
Divisors found:
 r1=443323695339234757494089624823618634934581 (pp42)
 r2=452780513252055747543767753370086491619059 (pp42)
 r3=2417082367680574707369031567295805948468828136719998084989731464459249 (pp70)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.692).
Factorization parameters were as follows:
n: 485176907892298017214417627143198508833688082886783719398433610286736536599785554429289484775299428567816907033141503562975300443505456660110615352101471
m: 100000000000000000000000000000000
deg: 5
c5: 37
c0: 530
skew: 1.70
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1750000, 3650001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 723565 x 723813
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,52,52,2.4,2.4,100000
total time: 26.00 hours.

Dec 15, 2008 (5th)

By Robert Backstrom / GGNFS, Msieve

(37·10¹²⁰+71)/9 = 4(1)₁₁₉9_<121> = 3 · 17 · 257 · 169244578693_<12> · C106

C106 = P47 · P60

P47 = 15718212115607084073455098063640139764109946061_<47>

P60 = 117906569540261494882234034595775781192538671358262630919029_<60>

Number: n
N=1853280469857407409649560238135051795272682028566957745455654946359544378927120317253367823242200048494769
  ( 106 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=15718212115607084073455098063640139764109946061 (pp47)
 r2=117906569540261494882234034595775781192538671358262630919029 (pp60)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.52 hours.
Scaled time: 2.79 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_4_1_119_9
n: 1853280469857407409649560238135051795272682028566957745455654946359544378927120317253367823242200048494769
type: snfs
skew: 1.14
deg: 5
c5: 37
c0: 71
m: 1000000000000000000000000
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [250000, 450001)
Primes: RFBsize:41538, AFBsize:41148, largePrimes:5521859 encountered
Relations: rels:4970497, finalFF:209320
Max relations in full relation-set: 48
Initial matrix: 82751 x 209320 with sparse part having weight 32997515.
Pruned matrix : 71450 x 71927 with weight 7104504.
Total sieving time: 1.28 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.03 hours.
Total square root time: 0.14 hours, sqrts: 10.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,500000,500000,28,28,56,56,2.5,2.5,50000
total time: 1.52 hours.
 --------- CPU info (if available) ----------

(37·10¹²⁹+71)/9 = 4(1)₁₂₈9_<130> = 3 · 27774323 · 13031386588706799664801_<23> · C100

C100 = P42 · P59

P42 = 128123426410502970074948895719212965675887_<42>

P59 = 29551212498200826094631393040780112047335950040214922506473_<59>

Number: n
N=3786202599854369175101763795740950150675265207939197580619648859764781300033378615291421350577516551
  ( 100 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=128123426410502970074948895719212965675887 (pp42)
 r2=29551212498200826094631393040780112047335950040214922506473 (pp59)
Version: GGNFS-0.77.1-20051202-k8
Total time: 3.83 hours.
Scaled time: 7.71 units (timescale=2.013).
Factorization parameters were as follows:
name: KA_4_1_128_9
n: 3786202599854369175101763795740950150675265207939197580619648859764781300033378615291421350577516551
type: snfs
skew: 1.81
deg: 5
c5: 37
c0: 710
m: 100000000000000000000000000
rlim: 900000
alim: 900000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [100000, 650001)
Primes: RFBsize:71274, AFBsize:71376, largePrimes:7510334 encountered
Relations: rels:6777003, finalFF:229584
Max relations in full relation-set: 28
Initial matrix: 142715 x 229584 with sparse part having weight 24217375.
Pruned matrix : 123653 x 124430 with weight 10406862.
Total sieving time: 3.63 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,900000,900000,28,28,56,56,2.5,2.5,50000
total time: 3.83 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830490)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830462)
Total of 4 processors activated (22643.71 BogoMIPS).

(37·10¹³¹+53)/9 = 4(1)₁₃₀7_<132> = 3 · 7 · 26317 · 3455435628958223_<16> · C111

C111 = P49 · P62

P49 = 7972700383759441503881272449579513196474094885429_<49>

P62 = 27001959963243168853430820841180310949496723141495794009982343_<62>

Number: n
N=215278536561205887322108876493270186092609401846280407032882268561731174025745829832628911912346191386897980147
  ( 111 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=7972700383759441503881272449579513196474094885429 (pp49)
 r2=27001959963243168853430820841180310949496723141495794009982343 (pp62)
Version: GGNFS-0.77.1-20051202-k8
Total time: 4.34 hours.
Scaled time: 8.72 units (timescale=2.010).
Factorization parameters were as follows:
name: KA_4_1_130_7
n: 215278536561205887322108876493270186092609401846280407032882268561731174025745829832628911912346191386897980147
type: snfs
skew: 0.68
deg: 5
c5: 370
c0: 53
m: 100000000000000000000000000
rlim: 900000
alim: 900000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [100000, 750001)
Primes: RFBsize:71274, AFBsize:70980, largePrimes:7870308 encountered
Relations: rels:7124914, finalFF:201480
Max relations in full relation-set: 28
Initial matrix: 142321 x 201480 with sparse part having weight 21993173.
Pruned matrix : 129753 x 130528 with weight 11883302.
Total sieving time: 4.11 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,900000,900000,28,28,56,56,2.5,2.5,50000
total time: 4.34 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830490)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830462)
Total of 4 processors activated (22643.71 BogoMIPS).

(37·10¹³⁴+53)/9 = 4(1)₁₃₃7_<135> = 3² · 24986991259982899490059_<23> · C112

C112 = P50 · P62

P50 = 26997291767926798159853751308242719224871556251223_<50>

P62 = 67714634740461212531416188452742326805525020387462321160332809_<62>

Number: n
N=1828111751046823473729867845947611785538650552102639379539486366668748152605479610053566238562881946543093275407
  ( 112 digits)
SNFS difficulty: 136 digits.
Divisors found:

Mon Dec 15 05:57:05 2008  prp50 factor: 26997291767926798159853751308242719224871556251223
Mon Dec 15 05:57:05 2008  prp62 factor: 67714634740461212531416188452742326805525020387462321160332809
Mon Dec 15 05:57:05 2008  elapsed time 00:12:49 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20050930-k8
Total time: 4.50 hours.
Scaled time: 9.05 units (timescale=2.012).
Factorization parameters were as follows:
name: KA_4_1_133_7
n: 1828111751046823473729867845947611785538650552102639379539486366668748152605479610053566238562881946543093275407
type: snfs
skew: 1.70
deg: 5
c5: 37
c0: 530
m: 1000000000000000000000000000
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 800001)
Primes: RFBsize:78498, AFBsize:78716, largePrimes:7741734 encountered
Relations: rels:6703606, finalFF:108763
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 4.37 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,56,56,2.5,2.5,75000
total time: 4.50 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830490)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830462)
Total of 4 processors activated (22643.71 BogoMIPS).

Dec 15, 2008 (4th)

By Sinkiti Sibata / Msieve

(37·10¹²⁶+53)/9 = 4(1)₁₂₅7_<127> = 23429971 · C120

C120 = P55 · P65

P55 = 2385657431444900902593170998853579105307250401833124431_<55>

P65 = 73549442015086715345246777178084396489992122857979924708529445617_<65>

Number: 41117_126
N=175463772921917449710505877754228168319589943628658828092920435587014218289519483874355248289087131653347377643408568927
  ( 120 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=2385657431444900902593170998853579105307250401833124431 (prp55)
 r2=73549442015086715345246777178084396489992122857979924708529445617 (prp65)
Version: 
Total time: 4.07 hours.
Scaled time: 7.96 units (timescale=1.955).
Factorization parameters were as follows:
name: 41117_126
n: 175463772921917449710505877754228168319589943628658828092920435587014218289519483874355248289087131653347377643408568927
m: 10000000000000000000000000
deg: 5
c5: 370
c0: 53
skew: 0.68
type: snfs
lss: 1
rlim: 940000
alim: 940000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 940000/940000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [470000, 970001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 156346 x 156594
Total sieving time: 4.07 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,940000,940000,26,26,46,46,2.3,2.3,50000
total time: 4.07 hours.
 --------- CPU info (if available) ----------

(37·10¹²¹+53)/9 = 4(1)₁₂₀7_<122> = 4133 · 12448496033_<11> · 96559317121_<11> · C97

C97 = P42 · P56

P42 = 581119780975231635970058042786794126786889_<42>

P56 = 14240232483206706578295465829097659023799330370860981537_<56>

Sun Dec 14 17:44:52 2008  Msieve v. 1.39
Sun Dec 14 17:44:52 2008  random seeds: 558fa890 5a21134c
Sun Dec 14 17:44:52 2008  factoring 8275280781677460242495252428407518810499554171453232349711921873570895749085623666102478562668393 (97 digits)
Sun Dec 14 17:44:53 2008  searching for 15-digit factors
Sun Dec 14 17:44:55 2008  commencing quadratic sieve (97-digit input)
Sun Dec 14 17:44:55 2008  using multiplier of 1
Sun Dec 14 17:44:55 2008  using 32kb Intel Core sieve core
Sun Dec 14 17:44:55 2008  sieve interval: 36 blocks of size 32768
Sun Dec 14 17:44:55 2008  processing polynomials in batches of 6
Sun Dec 14 17:44:55 2008  using a sieve bound of 2404009 (88075 primes)
Sun Dec 14 17:44:55 2008  using large prime bound of 360601350 (28 bits)
Sun Dec 14 17:44:55 2008  using double large prime bound of 2527255810204800 (43-52 bits)
Sun Dec 14 17:44:55 2008  using trial factoring cutoff of 52 bits
Sun Dec 14 17:44:55 2008  polynomial 'A' values have 13 factors
Mon Dec 15 00:37:14 2008  88421 relations (20973 full + 67448 combined from 1337165 partial), need 88171
Mon Dec 15 00:37:16 2008  begin with 1358138 relations
Mon Dec 15 00:37:17 2008  reduce to 233452 relations in 11 passes
Mon Dec 15 00:37:17 2008  attempting to read 233452 relations
Mon Dec 15 00:37:21 2008  recovered 233452 relations
Mon Dec 15 00:37:21 2008  recovered 221954 polynomials
Mon Dec 15 00:37:21 2008  attempting to build 88421 cycles
Mon Dec 15 00:37:21 2008  found 88421 cycles in 7 passes
Mon Dec 15 00:37:21 2008  distribution of cycle lengths:
Mon Dec 15 00:37:21 2008     length 1 : 20973
Mon Dec 15 00:37:21 2008     length 2 : 15237
Mon Dec 15 00:37:21 2008     length 3 : 14842
Mon Dec 15 00:37:21 2008     length 4 : 12145
Mon Dec 15 00:37:21 2008     length 5 : 9070
Mon Dec 15 00:37:21 2008     length 6 : 6180
Mon Dec 15 00:37:21 2008     length 7 : 4123
Mon Dec 15 00:37:21 2008     length 9+: 5851
Mon Dec 15 00:37:21 2008  largest cycle: 21 relations
Mon Dec 15 00:37:22 2008  matrix is 88075 x 88421 (23.7 MB) with weight 5862504 (66.30/col)
Mon Dec 15 00:37:22 2008  sparse part has weight 5862504 (66.30/col)
Mon Dec 15 00:37:23 2008  filtering completed in 3 passes
Mon Dec 15 00:37:23 2008  matrix is 84357 x 84421 (22.7 MB) with weight 5613631 (66.50/col)
Mon Dec 15 00:37:23 2008  sparse part has weight 5613631 (66.50/col)
Mon Dec 15 00:37:23 2008  saving the first 48 matrix rows for later
Mon Dec 15 00:37:23 2008  matrix is 84309 x 84421 (13.9 MB) with weight 4399038 (52.11/col)
Mon Dec 15 00:37:23 2008  sparse part has weight 3132727 (37.11/col)
Mon Dec 15 00:37:23 2008  matrix includes 64 packed rows
Mon Dec 15 00:37:23 2008  using block size 33768 for processor cache size 1024 kB
Mon Dec 15 00:37:24 2008  commencing Lanczos iteration
Mon Dec 15 00:37:24 2008  memory use: 13.6 MB
Mon Dec 15 00:38:11 2008  lanczos halted after 1334 iterations (dim = 84309)
Mon Dec 15 00:38:11 2008  recovered 17 nontrivial dependencies
Mon Dec 15 00:38:12 2008  prp42 factor: 581119780975231635970058042786794126786889
Mon Dec 15 00:38:12 2008  prp56 factor: 14240232483206706578295465829097659023799330370860981537
Mon Dec 15 00:38:12 2008  elapsed time 06:53:20

(37·10¹³⁵+71)/9 = 4(1)₁₃₄9_<136> = 3 · 157 · 217858747 · C125

C125 = P39 · P86

P39 = 448527358525322314639414749099497098067_<39>

P86 = 89325276139362337612461557618510248967981249045371777169481861806222799110277558174761_<86>

Number: 41119_135
N=40064830156333189911356119025116378434156345249498865836143135288895502259163405215369647868960104691528229503292492741286987
  ( 125 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=448527358525322314639414749099497098067  (prp39)
 r2=89325276139362337612461557618510248967981249045371777169481861806222799110277558174761  (prp86)
Version: 
Total time: 4.72 hours.
Scaled time: 12.09 units (timescale=2.564).
Factorization parameters were as follows:
name: 41119_135
n: 40064830156333189911356119025116378434156345249498865836143135288895502259163405215369647868960104691528229503292492741286987
m: 1000000000000000000000000000
deg: 5
c5: 37
c0: 71
skew: 1.14
type: snfs
lss: 1
rlim: 1320000
alim: 1320000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1320000/1320000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [660000, 1335001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 193544 x 193792
Total sieving time: 4.72 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1320000,1320000,26,26,48,48,2.3,2.3,75000
total time: 4.72 hours.
 --------- CPU info (if available) ----------

(37·10¹³⁶+71)/9 = 4(1)₁₃₅9_<137> = 13 · 17 · 641 · C132

C132 = P56 · P76

P56 = 97340949537081992813353491071448672787822775697068133607_<56>

P76 = 2981352535792632774733519282793371700345256565006961199069479457120577812397_<76>

Number: 41119_136
N=290207686738842102703715991776925978999944311497950114082994692336713076366191902578063906870000290207686738842102703715991776925979
  ( 132 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=97340949537081992813353491071448672787822775697068133607  (prp56)
 r2=2981352535792632774733519282793371700345256565006961199069479457120577812397
 (prp76)
Version: 
Total time: 6.11 hours.
Scaled time: 15.68 units (timescale=2.564).
Factorization parameters were as follows:
name: 41119_136
n: 290207686738842102703715991776925978999944311497950114082994692336713076366191902578063906870000290207686738842102703715991776925979
m: 1000000000000000000000000000
deg: 5
c5: 370
c0: 71
skew: 0.72
type: snfs
lss: 1
rlim: 1370000
alim: 1370000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1370000/1370000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [685000, 1585001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 235989 x 236237
Total sieving time: 6.11 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1370000,1370000,26,26,48,48,2.3,2.3,75000
total time: 6.11 hours.
 --------- CPU info (if available) ----------

(37·10¹³⁷+53)/9 = 4(1)₁₃₆7_<138> = 3 · 7 · 71 · 349 · 17099 · 19001790168617_<14> · C115

C115 = P41 · P75

P41 = 19452637518709047440619598197258467357591_<41>

P75 = 125000692705880011030652701485196569731361764165251859204813732182028498671_<75>

Number: 41117_137
N=2431593164795021863019909687564068078352019780269255567935109822583356900993305863658209861643608160856750225261561
  ( 115 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=19452637518709047440619598197258467357591 (prp41)
 r2=125000692705880011030652701485196569731361764165251859204813732182028498671
 (prp75)
Version: 
Total time: 8.30 hours.
Scaled time: 16.37 units (timescale=1.972).
Factorization parameters were as follows:
name: 41117_137
n: 2431593164795021863019909687564068078352019780269255567935109822583356900993305863658209861643608160856750225261561
m: 2000000000000000000000000000
deg: 5
c5: 925
c0: 424
skew: 0.86
type: snfs
lss: 1
rlim: 1480000
alim: 1480000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1480000/1480000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [740000, 1640001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 247956 x 248204
Total sieving time: 8.30 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1480000,1480000,26,26,48,48,2.3,2.3,75000
total time: 8.30 hours.
 --------- CPU info (if available) ----------

(37·10¹⁴³+53)/9 = 4(1)₁₄₂7_<144> = 3² · 7 · 1093 · 6362389073_<10> · 224734168564901_<15> · 3210362852397241_<16> · C100

C100 = P42 · P58

P42 = 418741748016711844962144967395757153592003_<42>

P58 = 3106052477718236853520927156215139113532043711670312169297_<58>

Mon Dec 15 00:48:04 2008  Msieve v. 1.39
Mon Dec 15 00:48:04 2008  random seeds: dc2fd100 c9e6d64e
Mon Dec 15 00:48:04 2008  factoring 1300633843951373418973286402129012722051843503962648717536449548299399464906466570381194546601331891 (100 digits)
Mon Dec 15 00:48:05 2008  searching for 15-digit factors
Mon Dec 15 00:48:06 2008  commencing quadratic sieve (100-digit input)
Mon Dec 15 00:48:06 2008  using multiplier of 59
Mon Dec 15 00:48:06 2008  using 32kb Intel Core sieve core
Mon Dec 15 00:48:06 2008  sieve interval: 36 blocks of size 32768
Mon Dec 15 00:48:06 2008  processing polynomials in batches of 6
Mon Dec 15 00:48:06 2008  using a sieve bound of 2671787 (97647 primes)
Mon Dec 15 00:48:06 2008  using large prime bound of 400768050 (28 bits)
Mon Dec 15 00:48:06 2008  using double large prime bound of 3056381387395500 (43-52 bits)
Mon Dec 15 00:48:06 2008  using trial factoring cutoff of 52 bits
Mon Dec 15 00:48:06 2008  polynomial 'A' values have 13 factors
Mon Dec 15 12:57:16 2008  97874 relations (23045 full + 74829 combined from 1471490 partial), need 97743
Mon Dec 15 12:57:18 2008  begin with 1494535 relations
Mon Dec 15 12:57:20 2008  reduce to 259594 relations in 11 passes
Mon Dec 15 12:57:20 2008  attempting to read 259594 relations
Mon Dec 15 12:57:25 2008  recovered 259594 relations
Mon Dec 15 12:57:25 2008  recovered 251345 polynomials
Mon Dec 15 12:57:25 2008  attempting to build 97874 cycles
Mon Dec 15 12:57:25 2008  found 97874 cycles in 6 passes
Mon Dec 15 12:57:25 2008  distribution of cycle lengths:
Mon Dec 15 12:57:25 2008     length 1 : 23045
Mon Dec 15 12:57:25 2008     length 2 : 16691
Mon Dec 15 12:57:25 2008     length 3 : 16220
Mon Dec 15 12:57:25 2008     length 4 : 13422
Mon Dec 15 12:57:25 2008     length 5 : 10290
Mon Dec 15 12:57:25 2008     length 6 : 7121
Mon Dec 15 12:57:25 2008     length 7 : 4546
Mon Dec 15 12:57:25 2008     length 9+: 6539
Mon Dec 15 12:57:25 2008  largest cycle: 23 relations
Mon Dec 15 12:57:25 2008  matrix is 97647 x 97874 (27.4 MB) with weight 6794219 (69.42/col)
Mon Dec 15 12:57:25 2008  sparse part has weight 6794219 (69.42/col)
Mon Dec 15 12:57:27 2008  filtering completed in 3 passes
Mon Dec 15 12:57:27 2008  matrix is 93927 x 93990 (26.4 MB) with weight 6556190 (69.75/col)
Mon Dec 15 12:57:27 2008  sparse part has weight 6556190 (69.75/col)
Mon Dec 15 12:57:27 2008  saving the first 48 matrix rows for later
Mon Dec 15 12:57:27 2008  matrix is 93879 x 93990 (16.5 MB) with weight 5222311 (55.56/col)
Mon Dec 15 12:57:27 2008  sparse part has weight 3768024 (40.09/col)
Mon Dec 15 12:57:27 2008  matrix includes 64 packed rows
Mon Dec 15 12:57:27 2008  using block size 37596 for processor cache size 1024 kB
Mon Dec 15 12:57:28 2008  commencing Lanczos iteration
Mon Dec 15 12:57:28 2008  memory use: 15.9 MB
Mon Dec 15 12:58:34 2008  lanczos halted after 1485 iterations (dim = 93877)
Mon Dec 15 12:58:34 2008  recovered 16 nontrivial dependencies
Mon Dec 15 12:58:35 2008  prp42 factor: 418741748016711844962144967395757153592003
Mon Dec 15 12:58:35 2008  prp58 factor: 3106052477718236853520927156215139113532043711670312169297
Mon Dec 15 12:58:35 2008  elapsed time 12:10:31

Dec 15, 2008 (3rd)

Factorizations of 100...003 have been extended up to n=250. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Dec 15, 2008 (2nd)

Factorizations of 422...221 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Dec 15, 2008

By Serge Batalov / PFGW

(8·10¹²²⁶⁰+1)/9 = (8)₁₂₂₅₉9_<12260> is PRP.

(8·10¹²³⁴¹+1)/9 = (8)₁₂₃₄₀9_<12341> is PRP.

(8·10¹³⁷⁶⁰+1)/9 = (8)₁₃₇₅₉9_<13760> is PRP.

Dec 14, 2008 (5th)

By Robert Backstrom / Msieve, GMP-ECM

(37·10¹⁶⁵+71)/9 = 4(1)₁₆₄9_<166> = 3 · 5857 · 24499 · 299407691567021461_<18> · 64864715580932555437_<20> · 214518310799772616827199181657_<30> · C91

C91 = P37 · P54

P37 = 2456479326290440166586254085782156353_<37>

P54 = 933180006098833852846401252904487652104420827030262863_<54>

Sun Dec 14 14:20:07 2008  
Sun Dec 14 14:20:07 2008  
Sun Dec 14 14:20:07 2008  Msieve v. 1.39
Sun Dec 14 14:20:07 2008  random seeds: a9642068 c7f4fd37
Sun Dec 14 14:20:07 2008  factoring 2292337392689372228652417839233158652643250786585474807666277446662451849304779576555418639 (91 digits)
Sun Dec 14 14:20:08 2008  searching for 15-digit factors
Sun Dec 14 14:20:09 2008  commencing quadratic sieve (91-digit input)
Sun Dec 14 14:20:09 2008  using multiplier of 1
Sun Dec 14 14:20:09 2008  using 64kb Opteron sieve core
Sun Dec 14 14:20:09 2008  sieve interval: 18 blocks of size 65536
Sun Dec 14 14:20:09 2008  processing polynomials in batches of 6
Sun Dec 14 14:20:09 2008  using a sieve bound of 1682287 (63529 primes)
Sun Dec 14 14:20:09 2008  using large prime bound of 154770404 (27 bits)
Sun Dec 14 14:20:09 2008  using double large prime bound of 551363682974648 (42-49 bits)
Sun Dec 14 14:20:09 2008  using trial factoring cutoff of 49 bits
Sun Dec 14 14:20:09 2008  polynomial 'A' values have 12 factors
Sun Dec 14 15:25:56 2008  64164 relations (16520 full + 47644 combined from 732118 partial), need 63625
Sun Dec 14 15:25:57 2008  begin with 748638 relations
Sun Dec 14 15:25:57 2008  reduce to 159269 relations in 9 passes
Sun Dec 14 15:25:57 2008  attempting to read 159269 relations
Sun Dec 14 15:25:59 2008  recovered 159269 relations
Sun Dec 14 15:25:59 2008  recovered 138487 polynomials
Sun Dec 14 15:25:59 2008  attempting to build 64164 cycles
Sun Dec 14 15:25:59 2008  found 64164 cycles in 5 passes
Sun Dec 14 15:26:00 2008  distribution of cycle lengths:
Sun Dec 14 15:26:00 2008     length 1 : 16520
Sun Dec 14 15:26:00 2008     length 2 : 12059
Sun Dec 14 15:26:00 2008     length 3 : 11161
Sun Dec 14 15:26:00 2008     length 4 : 8627
Sun Dec 14 15:26:00 2008     length 5 : 6320
Sun Dec 14 15:26:00 2008     length 6 : 4020
Sun Dec 14 15:26:00 2008     length 7 : 2506
Sun Dec 14 15:26:00 2008     length 9+: 2951
Sun Dec 14 15:26:00 2008  largest cycle: 18 relations
Sun Dec 14 15:26:00 2008  matrix is 63529 x 64164 (16.0 MB) with weight 3927565 (61.21/col)
Sun Dec 14 15:26:00 2008  sparse part has weight 3927565 (61.21/col)
Sun Dec 14 15:26:01 2008  filtering completed in 4 passes
Sun Dec 14 15:26:01 2008  matrix is 59617 x 59681 (14.8 MB) with weight 3649747 (61.15/col)
Sun Dec 14 15:26:01 2008  sparse part has weight 3649747 (61.15/col)
Sun Dec 14 15:26:01 2008  saving the first 48 matrix rows for later
Sun Dec 14 15:26:01 2008  matrix is 59569 x 59681 (9.5 MB) with weight 2881639 (48.28/col)
Sun Dec 14 15:26:01 2008  sparse part has weight 2126116 (35.62/col)
Sun Dec 14 15:26:01 2008  matrix includes 64 packed rows
Sun Dec 14 15:26:01 2008  using block size 23872 for processor cache size 1024 kB
Sun Dec 14 15:26:01 2008  commencing Lanczos iteration
Sun Dec 14 15:26:01 2008  memory use: 9.2 MB
Sun Dec 14 15:26:22 2008  lanczos halted after 944 iterations (dim = 59567)
Sun Dec 14 15:26:22 2008  recovered 16 nontrivial dependencies
Sun Dec 14 15:26:23 2008  prp37 factor: 2456479326290440166586254085782156353
Sun Dec 14 15:26:23 2008  prp54 factor: 933180006098833852846401252904487652104420827030262863
Sun Dec 14 15:26:23 2008  elapsed time 01:06:16

(37·10¹⁴²+53)/9 = 4(1)₁₄₁7_<143> = 229 · 293 · 311363441 · 4290945583_<10> · 247255819459871080939110673_<27> · C94

C94 = P44 · P51

P44 = 16862793440103708198532263801272697174262183_<44>

P51 = 109991581016708918525866831687260181943473154034893_<51>

Sun Dec 14 18:57:25 2008  
Sun Dec 14 18:57:25 2008  
Sun Dec 14 18:57:25 2008  Msieve v. 1.39
Sun Dec 14 18:57:25 2008  random seeds: 0a9bc040 124024ef
Sun Dec 14 18:57:25 2008  factoring 1854765310835194710428440106540308919972924293904205223172756617211856527940960640436712351419 (94 digits)
Sun Dec 14 18:57:26 2008  searching for 15-digit factors
Sun Dec 14 18:57:26 2008  commencing quadratic sieve (94-digit input)
Sun Dec 14 18:57:27 2008  using multiplier of 11
Sun Dec 14 18:57:27 2008  using 64kb Opteron sieve core
Sun Dec 14 18:57:27 2008  sieve interval: 18 blocks of size 65536
Sun Dec 14 18:57:27 2008  processing polynomials in batches of 6
Sun Dec 14 18:57:27 2008  using a sieve bound of 1991609 (73982 primes)
Sun Dec 14 18:57:27 2008  using large prime bound of 256917561 (27 bits)
Sun Dec 14 18:57:27 2008  using double large prime bound of 1372868018887893 (42-51 bits)
Sun Dec 14 18:57:27 2008  using trial factoring cutoff of 51 bits
Sun Dec 14 18:57:27 2008  polynomial 'A' values have 12 factors
Sun Dec 14 21:16:14 2008  74176 relations (17786 full + 56390 combined from 1040543 partial), need 74078
Sun Dec 14 21:16:16 2008  begin with 1058329 relations
Sun Dec 14 21:16:17 2008  reduce to 194080 relations in 12 passes
Sun Dec 14 21:16:17 2008  attempting to read 194080 relations
Sun Dec 14 21:16:20 2008  recovered 194080 relations
Sun Dec 14 21:16:20 2008  recovered 179104 polynomials
Sun Dec 14 21:16:20 2008  attempting to build 74176 cycles
Sun Dec 14 21:16:20 2008  found 74176 cycles in 5 passes
Sun Dec 14 21:16:21 2008  distribution of cycle lengths:
Sun Dec 14 21:16:21 2008     length 1 : 17786
Sun Dec 14 21:16:21 2008     length 2 : 12925
Sun Dec 14 21:16:21 2008     length 3 : 12410
Sun Dec 14 21:16:21 2008     length 4 : 10031
Sun Dec 14 21:16:21 2008     length 5 : 7751
Sun Dec 14 21:16:21 2008     length 6 : 5177
Sun Dec 14 21:16:21 2008     length 7 : 3373
Sun Dec 14 21:16:21 2008     length 9+: 4723
Sun Dec 14 21:16:21 2008  largest cycle: 20 relations
Sun Dec 14 21:16:21 2008  matrix is 73982 x 74176 (19.3 MB) with weight 4766529 (64.26/col)
Sun Dec 14 21:16:21 2008  sparse part has weight 4766529 (64.26/col)
Sun Dec 14 21:16:22 2008  filtering completed in 3 passes
Sun Dec 14 21:16:22 2008  matrix is 70626 x 70690 (18.5 MB) with weight 4567849 (64.62/col)
Sun Dec 14 21:16:22 2008  sparse part has weight 4567849 (64.62/col)
Sun Dec 14 21:16:22 2008  saving the first 48 matrix rows for later
Sun Dec 14 21:16:22 2008  matrix is 70578 x 70690 (11.4 MB) with weight 3550378 (50.22/col)
Sun Dec 14 21:16:22 2008  sparse part has weight 2567736 (36.32/col)
Sun Dec 14 21:16:22 2008  matrix includes 64 packed rows
Sun Dec 14 21:16:22 2008  using block size 28276 for processor cache size 1024 kB
Sun Dec 14 21:16:23 2008  commencing Lanczos iteration
Sun Dec 14 21:16:23 2008  memory use: 11.2 MB
Sun Dec 14 21:16:55 2008  lanczos halted after 1117 iterations (dim = 70576)
Sun Dec 14 21:16:55 2008  recovered 17 nontrivial dependencies
Sun Dec 14 21:16:56 2008  prp44 factor: 16862793440103708198532263801272697174262183
Sun Dec 14 21:16:56 2008  prp51 factor: 109991581016708918525866831687260181943473154034893
Sun Dec 14 21:16:56 2008  elapsed time 02:19:31

(37·10¹²⁴+53)/9 = 4(1)₁₂₃7_<125> = 1277 · 47309 · 28722607534355557_<17> · C101

C101 = P36 · P66

P36 = 195169974164679173582454440992292441_<36>

P66 = 121391333009391162020765580291934643735513437889339216293015715737_<66>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 23691943327258839247481664570054627580787232775552733193324809100671477449073888934217058100029844017 (101 digits)
Using B1=1752000, B2=2140281790, polynomial Dickson(6), sigma=1759735969
Step 1 took 16760ms
Step 2 took 5941ms
********** Factor found in step 2: 195169974164679173582454440992292441
Found probable prime factor of 36 digits: 195169974164679173582454440992292441
Probable prime cofactor 121391333009391162020765580291934643735513437889339216293015715737 has 66 digits

Dec 14, 2008 (4th)

By Justin Card / ggnfs / msieve

(10¹⁸⁵+17)/9 = (1)₁₈₄3_<185> = 107 · 42403 · 4463369 · 97950977 · C163

C163 = P47 · P53 · P64

P47 = 15114737110291755253865525542276220443845732191_<47>

P53 = 62215924351208704620214741244687970502124398308107141_<53>

P64 = 5956668182002404597436168891848003944513400860278422888622352051_<64>

Sieve time, ~

Thu Dec 11 06:25:45 2008  Msieve v. 1.39
Thu Dec 11 06:25:45 2008  random seeds: c119b89d 3c60b76b
Thu Dec 11 06:25:45 2008  factoring 5601515784080136495058260409669476551922366725684158384351571184319213658664583664274625015281983236076984038434575826619948188356950956656183633054869264464184481 (163 digits)
Thu Dec 11 06:25:47 2008  searching for 15-digit factors
Thu Dec 11 06:25:48 2008  commencing number field sieve (163-digit input)
Thu Dec 11 06:25:48 2008  R0: -10000000000000000000000000000000000000
Thu Dec 11 06:25:48 2008  R1:  1
Thu Dec 11 06:25:48 2008  A0:  17
Thu Dec 11 06:25:48 2008  A1:  0
Thu Dec 11 06:25:48 2008  A2:  0
Thu Dec 11 06:25:48 2008  A3:  0
Thu Dec 11 06:25:48 2008  A4:  0
Thu Dec 11 06:25:48 2008  A5:  1
Thu Dec 11 06:25:48 2008  skew 0.00, size 1.649244e-12, alpha 1.047729, combined = 1.163083e-12
Thu Dec 11 06:25:48 2008
Thu Dec 11 06:25:48 2008  commencing relation filtering
Thu Dec 11 06:25:48 2008  commencing duplicate removal, pass 1
Thu Dec 11 06:28:46 2008  error -9 reading relation 14190429
Thu Dec 11 06:28:55 2008  error -9 reading relation 14949426
Thu Dec 11 06:29:13 2008  error -15 reading relation 16595032
Thu Dec 11 06:29:25 2008  error -9 reading relation 17527780
Thu Dec 11 06:29:35 2008  error -15 reading relation 18356803
Thu Dec 11 06:30:11 2008  found 3465609 hash collisions in 21585522 relations
Thu Dec 11 06:31:19 2008  added 24327 free relations
Thu Dec 11 06:31:19 2008  commencing duplicate removal, pass 2
Thu Dec 11 06:31:37 2008  found 3270865 duplicates and 18338984 unique relations
Thu Dec 11 06:31:37 2008  memory use: 94.6 MB
Thu Dec 11 06:31:37 2008  reading rational ideals above 8716288
Thu Dec 11 06:31:37 2008  reading algebraic ideals above 8716288
Thu Dec 11 06:31:37 2008  commencing singleton removal, pass 1
Thu Dec 11 06:35:35 2008  relations with 0 large ideals: 230675
Thu Dec 11 06:35:35 2008  relations with 1 large ideals: 1542279
Thu Dec 11 06:35:35 2008  relations with 2 large ideals: 4605346
Thu Dec 11 06:35:35 2008  relations with 3 large ideals: 6337724
Thu Dec 11 06:35:35 2008  relations with 4 large ideals: 3878423
Thu Dec 11 06:35:35 2008  relations with 5 large ideals: 969234
Thu Dec 11 06:35:35 2008  relations with 6 large ideals: 771397
Thu Dec 11 06:35:35 2008  relations with 7+ large ideals: 3906
Thu Dec 11 06:35:35 2008  18338984 relations and about 18219864 large ideals
Thu Dec 11 06:35:35 2008  commencing singleton removal, pass 2
Thu Dec 11 06:39:35 2008  found 6773463 singletons
Thu Dec 11 06:39:35 2008  current dataset: 11565521 relations and about 9662777 large ideals
Thu Dec 11 06:39:35 2008  commencing singleton removal, pass 3
Thu Dec 11 06:41:58 2008  found 1929828 singletons
Thu Dec 11 06:41:58 2008  current dataset: 9635693 relations and about 7596307 large ideals
Thu Dec 11 06:41:58 2008  commencing singleton removal, pass 4
Thu Dec 11 06:43:59 2008  found 559893 singletons
Thu Dec 11 06:43:59 2008  current dataset: 9075800 relations and about 7022668 large ideals
Thu Dec 11 06:43:59 2008  commencing singleton removal, pass 5
Thu Dec 11 06:45:52 2008  found 175568 singletons
Thu Dec 11 06:45:52 2008  current dataset: 8900232 relations and about 6845659 large ideals
Thu Dec 11 06:45:52 2008  commencing singleton removal, final pass
Thu Dec 11 06:47:54 2008  memory use: 157.8 MB
Thu Dec 11 06:47:55 2008  commencing in-memory singleton removal
Thu Dec 11 06:47:56 2008  begin with 8900232 relations and 7598828 unique ideals
Thu Dec 11 06:48:16 2008  reduce to 7009060 relations and 5642900 ideals in 18 passes
Thu Dec 11 06:48:16 2008  max relations containing the same ideal: 24
Thu Dec 11 06:48:18 2008  reading rational ideals above 720000
Thu Dec 11 06:48:18 2008  reading algebraic ideals above 720000
Thu Dec 11 06:48:18 2008  commencing singleton removal, final pass
Thu Dec 11 06:50:15 2008  keeping 6366128 ideals with weight <= 20, new excess is 589025
Thu Dec 11 06:50:21 2008  memory use: 183.7 MB
Thu Dec 11 06:50:21 2008  commencing in-memory singleton removal
Thu Dec 11 06:50:22 2008  begin with 7033399 relations and 6366128 unique ideals
Thu Dec 11 06:50:37 2008  reduce to 7004721 relations and 6218178 ideals in 11 passes
Thu Dec 11 06:50:37 2008  max relations containing the same ideal: 20
Thu Dec 11 06:50:43 2008  removing 599456 relations and 547819 ideals in 51637 cliques
Thu Dec 11 06:50:44 2008  commencing in-memory singleton removal
Thu Dec 11 06:50:45 2008  begin with 6405265 relations and 6218178 unique idealsThu Dec 11 06:50:57 2008  reduce to 6365591 relations and 5630271 ideals in 10 passes
Thu Dec 11 06:50:57 2008  max relations containing the same ideal: 20
Thu Dec 11 06:51:03 2008  removing 432595 relations and 380958 ideals in 51637 cliques
Thu Dec 11 06:51:03 2008  commencing in-memory singleton removal
Thu Dec 11 06:51:04 2008  begin with 5932996 relations and 5630271 unique ideals
Thu Dec 11 06:51:13 2008  reduce to 5909684 relations and 5225798 ideals in 8 passes
Thu Dec 11 06:51:13 2008  max relations containing the same ideal: 20
Thu Dec 11 06:51:20 2008  relations with 0 large ideals: 43999
Thu Dec 11 06:51:20 2008  relations with 1 large ideals: 279962
Thu Dec 11 06:51:20 2008  relations with 2 large ideals: 938340
Thu Dec 11 06:51:20 2008  relations with 3 large ideals: 1640855
Thu Dec 11 06:51:20 2008  relations with 4 large ideals: 1630210
Thu Dec 11 06:51:20 2008  relations with 5 large ideals: 952681
Thu Dec 11 06:51:20 2008  relations with 6 large ideals: 358387
Thu Dec 11 06:51:20 2008  relations with 7+ large ideals: 65250
Thu Dec 11 06:51:20 2008  commencing 2-way merge
Thu Dec 11 06:51:27 2008  reduce to 3478218 relation sets and 2794332 unique ideals
Thu Dec 11 06:51:27 2008  commencing full merge
Thu Dec 11 06:52:41 2008  memory use: 269.3 MB
Thu Dec 11 06:52:42 2008  found 1701886 cycles, need 1614532
Thu Dec 11 06:52:43 2008  weight of 1614532 cycles is about 113141746 (70.08/cycle)
Thu Dec 11 06:52:43 2008  distribution of cycle lengths:
Thu Dec 11 06:52:43 2008  1 relations: 209342
Thu Dec 11 06:52:43 2008  2 relations: 191075
Thu Dec 11 06:52:43 2008  3 relations: 185586
Thu Dec 11 06:52:43 2008  4 relations: 165144
Thu Dec 11 06:52:43 2008  5 relations: 146133
Thu Dec 11 06:52:43 2008  6 relations: 126188
Thu Dec 11 06:52:43 2008  7 relations: 106578
Thu Dec 11 06:52:43 2008  8 relations: 93386
Thu Dec 11 06:52:43 2008  9 relations: 78985
Thu Dec 11 06:52:43 2008  10+ relations: 312115
Thu Dec 11 06:52:43 2008  heaviest cycle: 20 relations
Thu Dec 11 06:52:44 2008  commencing cycle optimization
Thu Dec 11 06:52:48 2008  start with 9412575 relations
Thu Dec 11 06:53:15 2008  pruned 235166 relations
Thu Dec 11 06:53:15 2008  memory use: 315.3 MB
Thu Dec 11 06:53:15 2008  distribution of cycle lengths:
Thu Dec 11 06:53:15 2008  1 relations: 209342
Thu Dec 11 06:53:15 2008  2 relations: 195784
Thu Dec 11 06:53:15 2008  3 relations: 192349
Thu Dec 11 06:53:15 2008  4 relations: 169452
Thu Dec 11 06:53:15 2008  5 relations: 149844
Thu Dec 11 06:53:15 2008  6 relations: 127591
Thu Dec 11 06:53:15 2008  7 relations: 107695
Thu Dec 11 06:53:15 2008  8 relations: 93119
Thu Dec 11 06:53:15 2008  9 relations: 78380
Thu Dec 11 06:53:15 2008  10+ relations: 290976
Thu Dec 11 06:53:15 2008  heaviest cycle: 20 relations
Thu Dec 11 06:53:21 2008  elapsed time 00:27:36

Fri Dec 12 20:24:42 2008  Msieve v. 1.39
Fri Dec 12 20:24:42 2008  random seeds: 8a67411e b53fa8c3
Fri Dec 12 20:24:42 2008  factoring 5601515784080136495058260409669476551922366725684158384351571184319213658664583664274625015281983236076984038434575826619948188356950956656183633054869264464184481 (163 digits)
Fri Dec 12 20:24:45 2008  searching for 15-digit factors
Fri Dec 12 20:24:46 2008  commencing number field sieve (163-digit input)
Fri Dec 12 20:24:46 2008  R0: -10000000000000000000000000000000000000
Fri Dec 12 20:24:46 2008  R1:  1
Fri Dec 12 20:24:46 2008  A0:  17
Fri Dec 12 20:24:46 2008  A1:  0
Fri Dec 12 20:24:46 2008  A2:  0
Fri Dec 12 20:24:46 2008  A3:  0
Fri Dec 12 20:24:46 2008  A4:  0
Fri Dec 12 20:24:46 2008  A5:  1
Fri Dec 12 20:24:46 2008  skew 0.00, size 1.649244e-12, alpha 1.047729, combined = 1.163083e-12
Fri Dec 12 20:24:46 2008
Fri Dec 12 20:24:46 2008  commencing linear algebra
Fri Dec 12 20:24:47 2008  read 1599998 cycles
Fri Dec 12 20:24:54 2008  cycles contain 5294098 unique relations
Fri Dec 12 20:26:00 2008  read 5294098 relations
Fri Dec 12 20:26:14 2008  using 20 quadratic characters above 268434548
Fri Dec 12 20:27:04 2008  building initial matrix
Fri Dec 12 20:28:25 2008  memory use: 643.5 MB
Fri Dec 12 20:28:27 2008  read 1599998 cycles
Fri Dec 12 20:28:29 2008  matrix is 1599798 x 1599998 (480.2 MB) with weight 141340528 (88.34/col)
Fri Dec 12 20:28:29 2008  sparse part has weight 108280053 (67.68/col)
Fri Dec 12 20:28:55 2008  filtering completed in 1 passes
Fri Dec 12 20:28:55 2008  matrix is 1599798 x 1599998 (480.2 MB) with weight 141340528 (88.34/col)
Fri Dec 12 20:28:55 2008  sparse part has weight 108280053 (67.68/col)
Fri Dec 12 20:29:10 2008  read 1599998 cycles
Fri Dec 12 20:29:12 2008  matrix is 1599798 x 1599998 (480.2 MB) with weight 141340528 (88.34/col)
Fri Dec 12 20:29:12 2008  sparse part has weight 108280053 (67.68/col)
Fri Dec 12 20:29:12 2008  saving the first 48 matrix rows for later
Fri Dec 12 20:29:13 2008  matrix is 1599750 x 1599998 (452.7 MB) with weight 111950279 (69.97/col)
Fri Dec 12 20:29:13 2008  sparse part has weight 102665798 (64.17/col)
Fri Dec 12 20:29:13 2008  matrix includes 64 packed rows
Fri Dec 12 20:29:13 2008  using block size 10922 for processor cache size 256 kB
Fri Dec 12 20:29:23 2008  commencing Lanczos iteration (2 threads)
Fri Dec 12 20:29:23 2008  memory use: 448.0 MB
Sat Dec 13 00:51:35 2008  lanczos error: submatrix is not invertible
Sat Dec 13 00:51:35 2008  lanczos halted after 7210 iterations (dim = 455967)
Sat Dec 13 00:51:35 2008  linear algebra failed; retrying...
Sat Dec 13 00:51:35 2008  commencing Lanczos iteration (2 threads)
Sat Dec 13 00:51:35 2008  memory use: 448.0 MB
Sat Dec 13 16:07:31 2008  lanczos halted after 25302 iterations (dim = 1599744)
Sat Dec 13 16:07:38 2008  recovered 31 nontrivial dependencies
Sat Dec 13 16:07:38 2008  elapsed time 19:42:56
Sat Dec 13 18:12:48 2008
Sat Dec 13 18:12:48 2008
Sat Dec 13 18:12:48 2008  Msieve v. 1.39
Sat Dec 13 18:12:48 2008  random seeds: 595748d8 c5a6942b
Sat Dec 13 18:12:48 2008  factoring 5601515784080136495058260409669476551922366725684158384351571184319213658664583664274625015281983236076984038434575826619948188356950956656183633054869264464184481 (163 digits)
Sat Dec 13 18:12:49 2008  searching for 15-digit factors
Sat Dec 13 18:12:51 2008  commencing number field sieve (163-digit input)
Sat Dec 13 18:12:51 2008  R0: -10000000000000000000000000000000000000
Sat Dec 13 18:12:51 2008  R1:  1
Sat Dec 13 18:12:51 2008  A0:  17
Sat Dec 13 18:12:51 2008  A1:  0
Sat Dec 13 18:12:51 2008  A2:  0
Sat Dec 13 18:12:51 2008  A3:  0
Sat Dec 13 18:12:51 2008  A4:  0
Sat Dec 13 18:12:51 2008  A5:  1
Sat Dec 13 18:12:51 2008  skew 0.00, size 1.649244e-12, alpha 1.047729, combined = 1.163083e-12
Sat Dec 13 18:12:51 2008
Sat Dec 13 18:12:51 2008  commencing square root phase
Sat Dec 13 18:12:51 2008  reading relations for dependency 1
Sat Dec 13 18:12:51 2008  read 800041 cycles
Sat Dec 13 18:12:54 2008  cycles contain 3218627 unique relations
Sat Dec 13 18:13:39 2008  read 3218627 relations
Sat Dec 13 18:14:03 2008  multiplying 2646900 relations
Sat Dec 13 18:18:29 2008  multiply complete, coefficients have about 59.07 million bits
Sat Dec 13 18:18:31 2008  initial square root is modulo 301859771
Sat Dec 13 18:27:26 2008  reading relations for dependency 2
Sat Dec 13 18:27:27 2008  read 799909 cycles
Sat Dec 13 18:27:30 2008  cycles contain 3215839 unique relations
Sat Dec 13 18:28:13 2008  read 3215839 relations
Sat Dec 13 18:28:37 2008  multiplying 2645928 relations
Sat Dec 13 18:33:02 2008  multiply complete, coefficients have about 59.05 million bits
Sat Dec 13 18:33:04 2008  initial square root is modulo 299845591
Sat Dec 13 18:41:52 2008  Newton iteration failed to converge
Sat Dec 13 18:41:52 2008  algebraic square root failed
Sat Dec 13 18:41:52 2008  reading relations for dependency 3
Sat Dec 13 18:41:53 2008  read 800016 cycles
Sat Dec 13 18:41:56 2008  cycles contain 3214264 unique relations
Sat Dec 13 18:42:37 2008  read 3214264 relations
Sat Dec 13 18:43:02 2008  multiplying 2644520 relations
Sat Dec 13 18:47:26 2008  multiply complete, coefficients have about 59.01 million bits
Sat Dec 13 18:47:28 2008  initial square root is modulo 296690551
Sat Dec 13 18:56:23 2008  prp47 factor: 15114737110291755253865525542276220443845732191
Sat Dec 13 18:56:23 2008  prp53 factor: 62215924351208704620214741244687970502124398308107141
Sat Dec 13 18:56:23 2008  prp64 factor: 5956668182002404597436168891848003944513400860278422888622352051
Sat Dec 13 18:56:23 2008  elapsed time 00:43:35

Dec 14, 2008 (3rd)

By Serge Batalov / GMP-ECM 6.2.1, GMP-ECM 6.2.1; msieve/QS, Msieve-1.39

(37·10¹⁹¹+71)/9 = 4(1)₁₉₀9_<192> = 19 · 163 · 227 · 8221 · 220274727766969_<15> · 47092463385596851290407_<23> · 256080813541464866622802649_<27> · 16242434872628753856635344333_<29> · C91

C91 = P31 · P60

P31 = 4636700600036784458682270386851_<31>

P60 = 355561060921631143485837742682771800699261664861095825932721_<60>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2648465071
Step 1 took 5340ms
Step 2 took 3444ms
********** Factor found in step 2: 4636700600036784458682270386851
Found probable prime factor of 31 digits: 4636700600036784458682270386851
Probable prime cofactor 355561060921631143485837742682771800699261664861095825932721 has 60 digits

(37·10¹⁴⁴+71)/9 = 4(1)₁₄₃9_<145> = 3 · 23 · 7400711 · 408887911 · 20186612443_<11> · 29905721311256110223_<20> · C98

C98 = P36 · P62

P36 = 618775808407328473965636674049547033_<36>

P62 = 52708584683780887941137184058447905146401641743810396364826463_<62>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3429082305
Step 1 took 6624ms
Step 2 took 3648ms
********** Factor found in step 2: 618775808407328473965636674049547033
Found probable prime factor of 36 digits: 618775808407328473965636674049547033
Probable prime cofactor 52708584683780887941137184058447905146401641743810396364826463 has 62 digits

(37·10¹⁷⁶+53)/9 = 4(1)₁₇₅7_<177> = 3 · 45963274037027449_<17> · 218721874752653920697929367_<27> · 167559923470916489335366527497_<30> · C104

C104 = P32 · P32 · P41

P32 = 15102382275566300653137564378239_<32>

P32 = 91977583043394794293256969720219_<32>

P41 = 58564869249345584602048726485816313603829_<41>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3150125923
Step 1 took 6465ms
********** Factor found in step 1: 91977583043394794293256969720219
Found probable prime factor of 32 digits: 91977583043394794293256969720219
Composite cofactor has 72 digits

Sat Dec 13 15:36:47 2008  Msieve v. 1.39
Sat Dec 13 15:36:47 2008  random seeds: ff568006 9809a85b
Sat Dec 13 15:36:47 2008  factoring 884469043322174635950314079773456828426465440667479238633610773754677131 (72 digits)
Sat Dec 13 15:36:47 2008  searching for 15-digit factors
Sat Dec 13 15:36:48 2008  commencing quadratic sieve (72-digit input)
Sat Dec 13 15:36:48 2008  using multiplier of 1
Sat Dec 13 15:36:48 2008  using 64kb Opteron sieve core
Sat Dec 13 15:36:48 2008  sieve interval: 6 blocks of size 65536
Sat Dec 13 15:36:48 2008  processing polynomials in batches of 17
Sat Dec 13 15:36:48 2008  using a sieve bound of 414311 (17438 primes)
Sat Dec 13 15:36:48 2008  using large prime bound of 41431100 (25 bits)
Sat Dec 13 15:36:48 2008  using trial factoring cutoff of 25 bits
Sat Dec 13 15:36:48 2008  polynomial 'A' values have 9 factors
Sat Dec 13 15:39:26 2008  17777 relations (8871 full + 8906 combined from 97264 partial), need 17534
Sat Dec 13 15:39:27 2008  begin with 106135 relations
Sat Dec 13 15:39:27 2008  reduce to 25588 relations in 2 passes
Sat Dec 13 15:39:27 2008  attempting to read 25588 relations
Sat Dec 13 15:39:27 2008  recovered 25588 relations
Sat Dec 13 15:39:27 2008  recovered 19369 polynomials
Sat Dec 13 15:39:27 2008  attempting to build 17777 cycles
Sat Dec 13 15:39:27 2008  found 17777 cycles in 1 passes
Sat Dec 13 15:39:27 2008  distribution of cycle lengths:
Sat Dec 13 15:39:27 2008     length 1 : 8871
Sat Dec 13 15:39:27 2008     length 2 : 8906
Sat Dec 13 15:39:27 2008  largest cycle: 2 relations
Sat Dec 13 15:39:27 2008  matrix is 17438 x 17777 (2.5 MB) with weight 515169 (28.98/col)
Sat Dec 13 15:39:27 2008  sparse part has weight 515169 (28.98/col)
Sat Dec 13 15:39:27 2008  filtering completed in 3 passes
Sat Dec 13 15:39:27 2008  matrix is 12817 x 12880 (2.0 MB) with weight 411137 (31.92/col)
Sat Dec 13 15:39:27 2008  sparse part has weight 411137 (31.92/col)
Sat Dec 13 15:39:27 2008  saving the first 48 matrix rows for later
Sat Dec 13 15:39:27 2008  matrix is 12769 x 12880 (1.4 MB) with weight 303997 (23.60/col)
Sat Dec 13 15:39:27 2008  sparse part has weight 226977 (17.62/col)
Sat Dec 13 15:39:27 2008  matrix includes 64 packed rows
Sat Dec 13 15:39:27 2008  commencing Lanczos iteration
Sat Dec 13 15:39:27 2008  memory use: 1.8 MB
Sat Dec 13 15:39:31 2008  lanczos halted after 203 iterations (dim = 12764)
Sat Dec 13 15:39:31 2008  recovered 15 nontrivial dependencies
Sat Dec 13 15:39:31 2008  prp32 factor: 15102382275566300653137564378239
Sat Dec 13 15:39:31 2008  prp41 factor: 58564869249345584602048726485816313603829
Sat Dec 13 15:39:31 2008  elapsed time 00:02:44

(37·10¹³³+53)/9 = 4(1)₁₃₂7_<134> = 19² · 15163783 · 1587776027_<10> · C115

C115 = P32 · P84

P32 = 13869327544356415887390661584931_<32>

P84 = 341035670790310249149005077592957449976141974679492733387937361436382697840615082307_<84>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3785622199
Step 1 took 6436ms
Step 2 took 4048ms
********** Factor found in step 2: 13869327544356415887390661584931
Found probable prime factor of 32 digits: 13869327544356415887390661584931
Probable prime cofactor 341035670790310249149005077592957449976141974679492733387937361436382697840615082307 has 84 digits

(37·10¹⁷⁹+53)/9 = 4(1)₁₇₈7_<180> = 3⁴ · 7 · 23 · 4751018479457_<13> · 13962759095755291_<17> · 49208248701391080839818523_<26> · C121

C121 = P28 · C94

P28 = 2119493083661110697017153309_<28>

C94 = [4556385302955576221884023543638349856512194802012137833352589947767890040676035957132831155593_<94>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1915012220
Step 1 took 7824ms
Step 2 took 4376ms
********** Factor found in step 2: 2119493083661110697017153309
Found probable prime factor of 28 digits: 2119493083661110697017153309
Composite cofactor has 94 digits

(37·10¹⁸¹+71)/9 = 4(1)₁₈₀9_<182> = 7 · 42323 · 33379705157_<11> · 24127822888595769062376049807_<29> · C138

C138 = P35 · C103

P35 = 47573256735105102134774568941200081_<35>

C103 = [3621772899073458445059701652864566407076358975646712173315673909567467074401737345715255403591778914841_<103>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=721560188
Step 1 took 9244ms
Step 2 took 4985ms
********** Factor found in step 2: 47573256735105102134774568941200081
Found probable prime factor of 35 digits: 47573256735105102134774568941200081
Composite cofactor has 103 digits

(37·10¹⁰⁴+53)/9 = 4(1)₁₀₃7_<105> = 3 · 1289213 · C99

C99 = P35 · P64

P35 = 22837832423823428406549535979434663_<35>

P64 = 4654343177283332444580397105529579718882636552190002130060404781_<64>

SNFS difficulty: 105 digits.
Divisors found:
 r1=22837832423823428406549535979434663 (pp35)
 r2=4654343177283332444580397105529579718882636552190002130060404781 (pp64)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.314).
Factorization parameters were as follows:
n: 106295109525762645146331162528641145440696794895053832870935242692275859021773001852321561322323803
m: 100000000000000000000000000
deg: 4
c4: 37
c0: 53
skew: 1.09
type: snfs
lss: 1
rlim: 400000
alim: 400000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 400000/400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [200000, 250001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 42219 x 42456
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,105,4,0,0,0,0,0,0,0,0,400000,400000,25,25,45,45,2.2,2.2,50000
total time: 0.50 hours.

(37·10¹⁰⁹+53)/9 = 4(1)₁₀₈7_<110> = 151 · C108

C108 = P39 · P69

P39 = 345934149021961984853714355585332061497_<39>

P69 = 787025550240151752957429692905459301021394747512814523416460876641811_<69>

SNFS difficulty: 111 digits.
Divisors found:
 r1=345934149021961984853714355585332061497 (pp39)
 r2=787025550240151752957429692905459301021394747512814523416460876641811 (pp69)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.314).
Factorization parameters were as follows:
n: 272259013980868285504047093451066961000735835172921265636497424576894775570272259013980868285504047093451067
m: 10000000000000000000000
deg: 5
c5: 37
c0: 530
skew: 1.70
type: snfs
lss: 1
rlim: 510000
alim: 510000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 510000/510000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [255000, 405001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 63238 x 63485
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,510000,510000,25,25,44,44,2.2,2.2,50000
total time: 0.50 hours.

(37·10¹⁹⁴+71)/9 = 4(1)₁₉₃9_<195> = 116269 · 575551 · 474471463 · 16349135082988589810249_<23> · C153

C153 = P31 · C123

P31 = 7590690876337436335686621759791_<31>

C123 = [104333861145851641332524267483514811395721107982807617312384858364100696592011759800416745004248697924636939449966193271653_<123>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3439223145
Step 1 took 9237ms
Step 2 took 5184ms
********** Factor found in step 2: 7590690876337436335686621759791
Found probable prime factor of 31 digits: 7590690876337436335686621759791
Composite cofactor has 123 digits

(37·10¹⁸⁶+53)/9 = 4(1)₁₈₅7_<187> = 139 · 2017 · 109199 · 4908232860071_<13> · 704264442759638437_<18> · C146

C146 = P32 · C115

P32 = 10378488878367712824242152948117_<32>

C115 = [3743042944343746327051073365541314201342334703437542556352179663331113160500440981418270935251237401012936934788599_<115>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1287780505
Step 1 took 11689ms
Step 2 took 6736ms
********** Factor found in step 2: 10378488878367712824242152948117
Found probable prime factor of 32 digits: 10378488878367712824242152948117
Composite cofactor has 115 digits

(37·10¹⁸²+71)/9 = 4(1)₁₈₁9_<183> = 6554489 · 1825044564102727319125284089_<28> · C149

C149 = P37 · P112

P37 = 8755789092289348926356821244998051583_<37>

P112 = 3925107994217788084008788634318649563433570976255456089438348678247691568468116466972296949254207197157811247233_<112>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3972661220
Step 1 took 11736ms
Step 2 took 6719ms
********** Factor found in step 2: 8755789092289348926356821244998051583
Found probable prime factor of 37 digits: 8755789092289348926356821244998051583
Probable prime cofactor has 112 digits

(37·10¹⁶⁹+53)/9 = 4(1)₁₆₈7_<170> = 19 · C169

C169 = P33 · C136

P33 = 291511918341504324969778930777933_<33>

C136 = [7422484481487542405434963871001284300917097043855519001904556196162796366335291956314614258679614931018465138599301201369883800196508571_<136>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=104395819
Step 1 took 10737ms
Step 2 took 2968ms
********** Factor found in step 2: 291511918341504324969778930777933
Found probable prime factor of 33 digits: 291511918341504324969778930777933
Composite cofactor has 136 digits

(37·10¹⁹⁵+71)/9 = 4(1)₁₉₄9_<196> = 3² · 251 · 2291104455149_<13> · C180

C180 = P31 · C150

P31 = 2450016983244960343376200468679_<31>

C150 = [324211935613233135510755071528084489947422054060634139633546393659957487226795682741016274539652285925049436071103008421381656621387039362598589743471_<150>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=45812530
Step 1 took 12433ms
Step 2 took 6316ms
********** Factor found in step 2: 2450016983244960343376200468679
Found probable prime factor of 31 digits: 2450016983244960343376200468679
Composite cofactor has 150 digits

(37·10¹⁴¹+71)/9 = 4(1)₁₄₀9_<142> = 3² · 3816740789_<10> · C132

C132 = P39 · P94

P39 = 116328262062925150698065808106966699829_<39>

P94 = 1028818580921946643296788098261946277585679831371276345580742344707061170637149919562915568911_<94>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1887761298
Step 1 took 7593ms
Step 2 took 4548ms
********** Factor found in step 2: 116328262062925150698065808106966699829
Found probable prime factor of 39 digits: 116328262062925150698065808106966699829
Probable prime cofactor 1028818580921946643296788098261946277585679831371276345580742344707061170637149919562915568911 has 94 digits

(37·10¹⁹⁰+53)/9 = 4(1)₁₈₉7_<191> = 59 · 33366083669_<11> · 1038688946123696607997710239_<28> · C152

C152 = P33 · C119

P33 = 228822554008790119385212155709949_<33>

C119 = [87865347299839227077677777536365983116150872999131750437968032584396075641901842890425376739301590272179304048017141257_<119>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1937590972
Step 1 took 9284ms
Step 2 took 5233ms
********** Factor found in step 2: 228822554008790119385212155709949
Found probable prime factor of 33 digits: 228822554008790119385212155709949
Composite cofactor has 119 digits

(37·10¹⁵¹+71)/9 = 4(1)₁₅₀9_<152> = 7 · 29 · 719 · C147

C147 = P36 · P111

P36 = 493619702531188780719146460090685151_<36>

P111 = 570613182110476873637098969632150989726981775506952535058010084196523573240634138994101843197569157770130203517_<111>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1976020518
Step 1 took 9117ms
Step 2 took 5172ms
********** Factor found in step 2: 493619702531188780719146460090685151
Found probable prime factor of 36 digits: 493619702531188780719146460090685151
Probable prime cofactor 570613182110476873637098969632150989726981775506952535058010084196523573240634138994101843197569157770130203517 has 111 digits

(37·10²⁰⁵+71)/9 = 4(1)₂₀₄9_<206> = 7 · 2136133 · 64219024439_<11> · C188

C188 = P33 · P155

P33 = 811192614843691594162179215721103_<33>

P155 = 52777059952387829531805686963212177397005658748073113430271392340308625968747192771664150630058513871014711473629321309366475928080999258279957374370363597_<155>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2220468459
Step 1 took 15901ms
Step 2 took 8896ms
********** Factor found in step 2: 811192614843691594162179215721103
Found probable prime factor of 33 digits: 811192614843691594162179215721103
Probable prime cofactor has 155 digits

(37·10²⁰²+71)/9 = 4(1)₂₀₁9_<203> = 13 · 331 · 617 · 385329041 · 13678610652367342939958859931_<29> · C160

C160 = P33 · P128

P33 = 240415440947317746742029988668383_<33>

P128 = 12219870898197088877898626768426211369986433162099804061070145673200443592688273807744355365435476148474134453244176088463782133_<128>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=939060094
Step 1 took 10797ms
Step 2 took 5572ms
********** Factor found in step 2: 240415440947317746742029988668383
Found probable prime factor of 33 digits: 240415440947317746742029988668383
Probable prime cofactor 12219870898197088877898626768426211369986433162099804061070145673200443592688273807744355365435476148474134453244176088463782133 has 128 digits

(37·10¹¹²+53)/9 = 4(1)₁₁₁7_<113> = 67619 · 1002388368083_<13> · C96

C96 = P37 · P60

P37 = 1809172218365498113906379744251961009_<37>

P60 = 335254443186106734337422576507034330357097141008436045500069_<60>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1919125461
Step 1 took 6853ms
Step 2 took 4585ms
********** Factor found in step 2: 1809172218365498113906379744251961009
Found probable prime factor of 37 digits: 1809172218365498113906379744251961009
Probable prime cofactor 335254443186106734337422576507034330357097141008436045500069 has 60 digits

(37·10²⁰²+53)/9 = 4(1)₂₀₁7_<203> = 83 · 103969 · C196

C196 = P35 · C161

P35 = 83073232889032830958318021005925831_<35>

C161 = [57347718339390154926339184530294156960878348876030304573157521297170923496818684614574091715773458560271341921644399653208512139175830624309009733603768798562441_<161>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2223104446
Step 1 took 14353ms
Step 2 took 7001ms
********** Factor found in step 2: 83073232889032830958318021005925831
Found probable prime factor of 35 digits: 83073232889032830958318021005925831
Composite cofactor has 161 digits

(37·10¹⁶⁹+71)/9 = 4(1)₁₆₈9_<170> = 7² · 253366636945487563_<18> · C151

C151 = P32 · P119

P32 = 37501399965585490651118726058947_<32>

P119 = 88301123028773088784112825094403290394334942803635440323854002374944693073141336324975710529936256947568638512598023071_<119>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1399304808
Step 1 took 11746ms
Step 2 took 6891ms
********** Factor found in step 2: 37501399965585490651118726058947
Found probable prime factor of 32 digits: 37501399965585490651118726058947
Probable prime cofactor 88301123028773088784112825094403290394334942803635440323854002374944693073141336324975710529936256947568638512598023071 has 119 digits

Dec 14, 2008 (2nd)

By Sinkiti Sibata / GGNFS, Msieve

(37·10¹⁶²+17)/9 = 4(1)₁₆₁3_<163> = 3 · 19290329 · 66993539 · 288466127633_<12> · 2388806425599695184089_<22> · C115

C115 = P57 · P59

P57 = 130111273985304522814275954174641281081665867559899941167_<57>

P59 = 11827002600902938664289039732901650255844924476182741339279_<59>

Number: 41113_162
N=1538826375830991453057437176484248990299753945815650506175461641309026854092360282091108310398235858496090886198593
  ( 115 digits)
Divisors found:
 r1=130111273985304522814275954174641281081665867559899941167 (pp57)
 r2=11827002600902938664289039732901650255844924476182741339279 (pp59)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 57.40 hours.
Scaled time: 27.15 units (timescale=0.473).
Factorization parameters were as follows:
name: 41113_162
n: 1538826375830991453057437176484248990299753945815650506175461641309026854092360282091108310398235858496090886198593
skew: 68560.79
# norm 5.34e+15
c5: 16380
c4: -491501907
c3: -284502307743748
c2: 2095670281966397398
c1: 491009361245004074554604
c0: -4355927952840396465531407136
# alpha -5.95
Y1: 2733249033247
Y0: -9875881410257126254633
# Murphy_E 5.70e-10
# M 1019663148516304371654520437573394188902720054438743156392681884195776859271800520987608419626613033809430724205437
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2950001)
Primes: RFBsize:250150, AFBsize:250583, largePrimes:7640929 encountered
Relations: rels:7618928, finalFF:654352
Max relations in full relation-set: 28
Initial matrix: 500815 x 654352 with sparse part having weight 58437435.
Pruned matrix : 379734 x 382302 with weight 34243244.
Total sieving time: 50.65 hours.
Total relation processing time: 0.58 hours.
Matrix solve time: 5.82 hours.
Time per square root: 0.35 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 57.40 hours.
 --------- CPU info (if available) ----------

(37·10¹⁰³+53)/9 = 4(1)₁₀₂7_<104> = 17 · 113 · 89983 · 4032812257_<10> · C86

C86 = P38 · P49

P38 = 35314393767842084307850317582733171637_<38>

P49 = 1669981352997280313025282068382464491328210820391_<49>

Sun Dec 14 06:13:22 2008  Msieve v. 1.39
Sun Dec 14 06:13:22 2008  random seeds: 1925d00c b04ad9d7
Sun Dec 14 06:13:22 2008  factoring 58974379084699647746013481661671328339377519785913665155065638330419588046029182450067 (86 digits)
Sun Dec 14 06:13:22 2008  searching for 15-digit factors
Sun Dec 14 06:13:24 2008  commencing quadratic sieve (86-digit input)
Sun Dec 14 06:13:24 2008  using multiplier of 23
Sun Dec 14 06:13:24 2008  using 32kb Intel Core sieve core
Sun Dec 14 06:13:24 2008  sieve interval: 16 blocks of size 32768
Sun Dec 14 06:13:24 2008  processing polynomials in batches of 13
Sun Dec 14 06:13:24 2008  using a sieve bound of 1452827 (55667 primes)
Sun Dec 14 06:13:24 2008  using large prime bound of 116226160 (26 bits)
Sun Dec 14 06:13:24 2008  using double large prime bound of 329266038078320 (41-49 bits)
Sun Dec 14 06:13:24 2008  using trial factoring cutoff of 49 bits
Sun Dec 14 06:13:24 2008  polynomial 'A' values have 11 factors
Sun Dec 14 06:55:41 2008  55968 relations (15882 full + 40086 combined from 584002 partial), need 55763
Sun Dec 14 06:55:41 2008  begin with 599884 relations
Sun Dec 14 06:55:42 2008  reduce to 133031 relations in 9 passes
Sun Dec 14 06:55:42 2008  attempting to read 133031 relations
Sun Dec 14 06:55:43 2008  recovered 133031 relations
Sun Dec 14 06:55:43 2008  recovered 113790 polynomials
Sun Dec 14 06:55:44 2008  attempting to build 55968 cycles
Sun Dec 14 06:55:44 2008  found 55968 cycles in 5 passes
Sun Dec 14 06:55:44 2008  distribution of cycle lengths:
Sun Dec 14 06:55:44 2008     length 1 : 15882
Sun Dec 14 06:55:44 2008     length 2 : 10993
Sun Dec 14 06:55:44 2008     length 3 : 9934
Sun Dec 14 06:55:44 2008     length 4 : 7402
Sun Dec 14 06:55:44 2008     length 5 : 4990
Sun Dec 14 06:55:44 2008     length 6 : 3014
Sun Dec 14 06:55:44 2008     length 7 : 1771
Sun Dec 14 06:55:44 2008     length 9+: 1982
Sun Dec 14 06:55:44 2008  largest cycle: 18 relations
Sun Dec 14 06:55:44 2008  matrix is 55667 x 55968 (12.8 MB) with weight 3143787 (56.17/col)
Sun Dec 14 06:55:44 2008  sparse part has weight 3143787 (56.17/col)
Sun Dec 14 06:55:44 2008  filtering completed in 3 passes
Sun Dec 14 06:55:44 2008  matrix is 51132 x 51196 (11.9 MB) with weight 2902891 (56.70/col)
Sun Dec 14 06:55:44 2008  sparse part has weight 2902891 (56.70/col)
Sun Dec 14 06:55:44 2008  saving the first 48 matrix rows for later
Sun Dec 14 06:55:45 2008  matrix is 51084 x 51196 (7.8 MB) with weight 2292166 (44.77/col)
Sun Dec 14 06:55:45 2008  sparse part has weight 1727978 (33.75/col)
Sun Dec 14 06:55:45 2008  matrix includes 64 packed rows
Sun Dec 14 06:55:45 2008  using block size 20478 for processor cache size 1024 kB
Sun Dec 14 06:55:45 2008  commencing Lanczos iteration
Sun Dec 14 06:55:45 2008  memory use: 7.5 MB
Sun Dec 14 06:56:00 2008  lanczos halted after 809 iterations (dim = 51081)
Sun Dec 14 06:56:00 2008  recovered 15 nontrivial dependencies
Sun Dec 14 06:56:01 2008  prp38 factor: 35314393767842084307850317582733171637
Sun Dec 14 06:56:01 2008  prp49 factor: 1669981352997280313025282068382464491328210820391
Sun Dec 14 06:56:01 2008  elapsed time 00:42:39

(37·10¹⁰²+71)/9 = 4(1)₁₀₁9_<103> = 3 · 1244232153403207_<16> · C88

C88 = P34 · P54

P34 = 2649665594353355667701413432585159_<34>

P54 = 415666929362892300678012893291131874171779345720654421_<54>

Sun Dec 14 06:32:50 2008  Msieve v. 1.39
Sun Dec 14 06:32:50 2008  random seeds: 62e79a6d 45d19e2c
Sun Dec 14 06:32:50 2008  factoring 1101378361443362334800454697333708457237190352894806247424401857396076767882135292337939 (88 digits)
Sun Dec 14 06:32:51 2008  searching for 15-digit factors
Sun Dec 14 06:32:52 2008  commencing quadratic sieve (88-digit input)
Sun Dec 14 06:32:53 2008  using multiplier of 11
Sun Dec 14 06:32:53 2008  using 32kb Intel Core sieve core
Sun Dec 14 06:32:53 2008  sieve interval: 24 blocks of size 32768
Sun Dec 14 06:32:53 2008  processing polynomials in batches of 9
Sun Dec 14 06:32:53 2008  using a sieve bound of 1508383 (57226 primes)
Sun Dec 14 06:32:53 2008  using large prime bound of 120670640 (26 bits)
Sun Dec 14 06:32:53 2008  using double large prime bound of 352275850752880 (42-49 bits)
Sun Dec 14 06:32:53 2008  using trial factoring cutoff of 49 bits
Sun Dec 14 06:32:53 2008  polynomial 'A' values have 11 factors
Sun Dec 14 07:22:11 2008  57405 relations (15925 full + 41480 combined from 602836 partial), need 57322
Sun Dec 14 07:22:13 2008  begin with 618761 relations
Sun Dec 14 07:22:13 2008  reduce to 137376 relations in 9 passes
Sun Dec 14 07:22:13 2008  attempting to read 137376 relations
Sun Dec 14 07:22:16 2008  recovered 137376 relations
Sun Dec 14 07:22:16 2008  recovered 114537 polynomials
Sun Dec 14 07:22:16 2008  attempting to build 57405 cycles
Sun Dec 14 07:22:16 2008  found 57405 cycles in 6 passes
Sun Dec 14 07:22:16 2008  distribution of cycle lengths:
Sun Dec 14 07:22:16 2008     length 1 : 15925
Sun Dec 14 07:22:16 2008     length 2 : 11211
Sun Dec 14 07:22:16 2008     length 3 : 10151
Sun Dec 14 07:22:16 2008     length 4 : 7733
Sun Dec 14 07:22:16 2008     length 5 : 5182
Sun Dec 14 07:22:16 2008     length 6 : 3216
Sun Dec 14 07:22:16 2008     length 7 : 1838
Sun Dec 14 07:22:16 2008     length 9+: 2149
Sun Dec 14 07:22:16 2008  largest cycle: 20 relations
Sun Dec 14 07:22:16 2008  matrix is 57226 x 57405 (13.5 MB) with weight 3317254 (57.79/col)
Sun Dec 14 07:22:16 2008  sparse part has weight 3317254 (57.79/col)
Sun Dec 14 07:22:17 2008  filtering completed in 3 passes
Sun Dec 14 07:22:17 2008  matrix is 52706 x 52770 (12.6 MB) with weight 3079370 (58.35/col)
Sun Dec 14 07:22:17 2008  sparse part has weight 3079370 (58.35/col)
Sun Dec 14 07:22:17 2008  saving the first 48 matrix rows for later
Sun Dec 14 07:22:17 2008  matrix is 52658 x 52770 (8.6 MB) with weight 2474966 (46.90/col)
Sun Dec 14 07:22:17 2008  sparse part has weight 1945695 (36.87/col)
Sun Dec 14 07:22:17 2008  matrix includes 64 packed rows
Sun Dec 14 07:22:17 2008  using block size 21108 for processor cache size 2048 kB
Sun Dec 14 07:22:17 2008  commencing Lanczos iteration
Sun Dec 14 07:22:17 2008  memory use: 8.1 MB
Sun Dec 14 07:22:33 2008  lanczos halted after 834 iterations (dim = 52656)
Sun Dec 14 07:22:33 2008  recovered 17 nontrivial dependencies
Sun Dec 14 07:22:33 2008  prp34 factor: 2649665594353355667701413432585159
Sun Dec 14 07:22:33 2008  prp54 factor: 415666929362892300678012893291131874171779345720654421
Sun Dec 14 07:22:33 2008  elapsed time 00:49:43

(37·10¹¹⁰+71)/9 = 4(1)₁₀₉9_<111> = 163 · 3253 · 4993 · 115781 · 322350781 · C88

C88 = P38 · P50

P38 = 43729720990949949880600834845372658547_<38>

P50 = 95144404324151060163204535145958036377440540232891_<50>

Sun Dec 14 06:38:51 2008  Msieve v. 1.39
Sun Dec 14 06:38:51 2008  random seeds: 706bda11 1a3ccd2d
Sun Dec 14 06:38:51 2008  factoring 4160638254945257795077203040399477793071467096507626461078106980750015463188979201669377 (88 digits)
Sun Dec 14 06:38:52 2008  searching for 15-digit factors
Sun Dec 14 06:38:54 2008  commencing quadratic sieve (88-digit input)
Sun Dec 14 06:38:54 2008  using multiplier of 1
Sun Dec 14 06:38:54 2008  using 64kb Pentium 4 sieve core
Sun Dec 14 06:38:54 2008  sieve interval: 14 blocks of size 65536
Sun Dec 14 06:38:54 2008  processing polynomials in batches of 8
Sun Dec 14 06:38:54 2008  using a sieve bound of 1518589 (58000 primes)
Sun Dec 14 06:38:54 2008  using large prime bound of 121487120 (26 bits)
Sun Dec 14 06:38:54 2008  using double large prime bound of 356577817808960 (42-49 bits)
Sun Dec 14 06:38:54 2008  using trial factoring cutoff of 49 bits
Sun Dec 14 06:38:54 2008  polynomial 'A' values have 11 factors
Sun Dec 14 08:02:47 2008  58224 relations (16052 full + 42172 combined from 612983 partial), need 58096
Sun Dec 14 08:02:50 2008  begin with 629035 relations
Sun Dec 14 08:02:50 2008  reduce to 140474 relations in 9 passes
Sun Dec 14 08:02:50 2008  attempting to read 140474 relations
Sun Dec 14 08:02:54 2008  recovered 140474 relations
Sun Dec 14 08:02:54 2008  recovered 114957 polynomials
Sun Dec 14 08:02:54 2008  attempting to build 58224 cycles
Sun Dec 14 08:02:54 2008  found 58224 cycles in 6 passes
Sun Dec 14 08:02:54 2008  distribution of cycle lengths:
Sun Dec 14 08:02:54 2008     length 1 : 16052
Sun Dec 14 08:02:54 2008     length 2 : 11306
Sun Dec 14 08:02:54 2008     length 3 : 10232
Sun Dec 14 08:02:54 2008     length 4 : 7703
Sun Dec 14 08:02:54 2008     length 5 : 5269
Sun Dec 14 08:02:54 2008     length 6 : 3373
Sun Dec 14 08:02:54 2008     length 7 : 1952
Sun Dec 14 08:02:54 2008     length 9+: 2337
Sun Dec 14 08:02:54 2008  largest cycle: 17 relations
Sun Dec 14 08:02:54 2008  matrix is 58000 x 58224 (13.7 MB) with weight 3353101 (57.59/col)
Sun Dec 14 08:02:54 2008  sparse part has weight 3353101 (57.59/col)
Sun Dec 14 08:02:56 2008  filtering completed in 3 passes
Sun Dec 14 08:02:56 2008  matrix is 53684 x 53747 (12.7 MB) with weight 3122843 (58.10/col)
Sun Dec 14 08:02:56 2008  sparse part has weight 3122843 (58.10/col)
Sun Dec 14 08:02:56 2008  saving the first 48 matrix rows for later
Sun Dec 14 08:02:56 2008  matrix is 53636 x 53747 (8.7 MB) with weight 2504409 (46.60/col)
Sun Dec 14 08:02:56 2008  sparse part has weight 1952885 (36.33/col)
Sun Dec 14 08:02:56 2008  matrix includes 64 packed rows
Sun Dec 14 08:02:56 2008  using block size 21498 for processor cache size 512 kB
Sun Dec 14 08:02:57 2008  commencing Lanczos iteration
Sun Dec 14 08:02:57 2008  memory use: 8.2 MB
Sun Dec 14 08:03:27 2008  lanczos halted after 849 iterations (dim = 53632)
Sun Dec 14 08:03:27 2008  recovered 14 nontrivial dependencies
Sun Dec 14 08:03:28 2008  prp38 factor: 43729720990949949880600834845372658547
Sun Dec 14 08:03:28 2008  prp50 factor: 95144404324151060163204535145958036377440540232891
Sun Dec 14 08:03:28 2008  elapsed time 01:24:37

(37·10¹³⁴+71)/9 = 4(1)₁₃₃9_<135> = 22541 · 25579 · 9712652137_<10> · 44720537897489_<14> · 275014982787607_<15> · C88

C88 = P44 · P44

P44 = 76781171389640257460964238610947216532089199_<44>

P44 = 77740357280063944340382379702634468726758129_<44>

Sun Dec 14 08:13:01 2008  Msieve v. 1.39
Sun Dec 14 08:13:01 2008  random seeds: 9c481be0 3d650de5
Sun Dec 14 08:13:01 2008  factoring 5968995696212457427044842553502875786013425970251737697198124448731278272530146726348671 (88 digits)
Sun Dec 14 08:13:03 2008  searching for 15-digit factors
Sun Dec 14 08:13:05 2008  commencing quadratic sieve (88-digit input)
Sun Dec 14 08:13:05 2008  using multiplier of 1
Sun Dec 14 08:13:05 2008  using 64kb Pentium 4 sieve core
Sun Dec 14 08:13:05 2008  sieve interval: 14 blocks of size 65536
Sun Dec 14 08:13:05 2008  processing polynomials in batches of 8
Sun Dec 14 08:13:05 2008  using a sieve bound of 1527443 (57997 primes)
Sun Dec 14 08:13:05 2008  using large prime bound of 122195440 (26 bits)
Sun Dec 14 08:13:05 2008  using double large prime bound of 360328813713040 (42-49 bits)
Sun Dec 14 08:13:05 2008  using trial factoring cutoff of 49 bits
Sun Dec 14 08:13:05 2008  polynomial 'A' values have 11 factors
Sun Dec 14 09:46:40 2008  58202 relations (15835 full + 42367 combined from 613321 partial), need 58093
Sun Dec 14 09:46:42 2008  begin with 629156 relations
Sun Dec 14 09:46:43 2008  reduce to 141005 relations in 9 passes
Sun Dec 14 09:46:43 2008  attempting to read 141005 relations
Sun Dec 14 09:46:46 2008  recovered 141005 relations
Sun Dec 14 09:46:46 2008  recovered 118767 polynomials
Sun Dec 14 09:46:46 2008  attempting to build 58202 cycles
Sun Dec 14 09:46:46 2008  found 58202 cycles in 6 passes
Sun Dec 14 09:46:46 2008  distribution of cycle lengths:
Sun Dec 14 09:46:46 2008     length 1 : 15835
Sun Dec 14 09:46:46 2008     length 2 : 11324
Sun Dec 14 09:46:46 2008     length 3 : 10272
Sun Dec 14 09:46:46 2008     length 4 : 7605
Sun Dec 14 09:46:46 2008     length 5 : 5453
Sun Dec 14 09:46:46 2008     length 6 : 3261
Sun Dec 14 09:46:47 2008     length 7 : 2085
Sun Dec 14 09:46:47 2008     length 9+: 2367
Sun Dec 14 09:46:47 2008  largest cycle: 17 relations
Sun Dec 14 09:46:47 2008  matrix is 57997 x 58202 (13.9 MB) with weight 3398010 (58.38/col)
Sun Dec 14 09:46:47 2008  sparse part has weight 3398010 (58.38/col)
Sun Dec 14 09:46:48 2008  filtering completed in 4 passes
Sun Dec 14 09:46:48 2008  matrix is 53933 x 53997 (12.9 MB) with weight 3176190 (58.82/col)
Sun Dec 14 09:46:48 2008  sparse part has weight 3176190 (58.82/col)
Sun Dec 14 09:46:48 2008  saving the first 48 matrix rows for later
Sun Dec 14 09:46:48 2008  matrix is 53885 x 53997 (8.5 MB) with weight 2513844 (46.56/col)
Sun Dec 14 09:46:48 2008  sparse part has weight 1912992 (35.43/col)
Sun Dec 14 09:46:48 2008  matrix includes 64 packed rows
Sun Dec 14 09:46:48 2008  using block size 21598 for processor cache size 512 kB
Sun Dec 14 09:46:49 2008  commencing Lanczos iteration
Sun Dec 14 09:46:49 2008  memory use: 8.2 MB
Sun Dec 14 09:47:17 2008  lanczos halted after 853 iterations (dim = 53880)
Sun Dec 14 09:47:17 2008  recovered 14 nontrivial dependencies
Sun Dec 14 09:47:18 2008  prp44 factor: 76781171389640257460964238610947216532089199
Sun Dec 14 09:47:18 2008  prp44 factor: 77740357280063944340382379702634468726758129
Sun Dec 14 09:47:18 2008  elapsed time 01:34:17

(37·10¹⁰²+53)/9 = 4(1)₁₀₁7_<103> = 71 · 11839 · 7469039 · C90

C90 = P34 · P56

P34 = 7516248271660755869850274614285353_<34>

P56 = 87120428179153067595948563227353363024319865790575626979_<56>

un Dec 14 09:26:56 2008  Msieve v. 1.39
Sun Dec 14 09:26:56 2008  random seeds: 2832f164 98fb12c3
Sun Dec 14 09:26:56 2008  factoring 654818767727904256865639176292309801451437776014272230779785284420421232481315337991338587 (90 digits)
Sun Dec 14 09:26:57 2008  searching for 15-digit factors
Sun Dec 14 09:26:59 2008  commencing quadratic sieve (90-digit input)
Sun Dec 14 09:26:59 2008  using multiplier of 3
Sun Dec 14 09:26:59 2008  using 32kb Intel Core sieve core
Sun Dec 14 09:26:59 2008  sieve interval: 36 blocks of size 32768
Sun Dec 14 09:26:59 2008  processing polynomials in batches of 6
Sun Dec 14 09:26:59 2008  using a sieve bound of 1613867 (61176 primes)
Sun Dec 14 09:26:59 2008  using large prime bound of 135564828 (27 bits)
Sun Dec 14 09:26:59 2008  using double large prime bound of 434374788405180 (42-49 bits)
Sun Dec 14 09:26:59 2008  using trial factoring cutoff of 49 bits
Sun Dec 14 09:26:59 2008  polynomial 'A' values have 12 factors
Sun Dec 14 10:29:25 2008  61573 relations (17144 full + 44429 combined from 653984 partial), need 61272
Sun Dec 14 10:29:26 2008  begin with 671128 relations
Sun Dec 14 10:29:26 2008  reduce to 146946 relations in 11 passes
Sun Dec 14 10:29:26 2008  attempting to read 146946 relations
Sun Dec 14 10:29:28 2008  recovered 146946 relations
Sun Dec 14 10:29:28 2008  recovered 120493 polynomials
Sun Dec 14 10:29:28 2008  attempting to build 61573 cycles
Sun Dec 14 10:29:29 2008  found 61573 cycles in 5 passes
Sun Dec 14 10:29:29 2008  distribution of cycle lengths:
Sun Dec 14 10:29:29 2008     length 1 : 17144
Sun Dec 14 10:29:29 2008     length 2 : 12393
Sun Dec 14 10:29:29 2008     length 3 : 10791
Sun Dec 14 10:29:29 2008     length 4 : 8064
Sun Dec 14 10:29:29 2008     length 5 : 5463
Sun Dec 14 10:29:29 2008     length 6 : 3441
Sun Dec 14 10:29:29 2008     length 7 : 1974
Sun Dec 14 10:29:29 2008     length 9+: 2303
Sun Dec 14 10:29:29 2008  largest cycle: 18 relations
Sun Dec 14 10:29:29 2008  matrix is 61176 x 61573 (14.7 MB) with weight 3596232 (58.41/col)
Sun Dec 14 10:29:29 2008  sparse part has weight 3596232 (58.41/col)
Sun Dec 14 10:29:30 2008  filtering completed in 3 passes
Sun Dec 14 10:29:30 2008  matrix is 56580 x 56644 (13.5 MB) with weight 3322339 (58.65/col)
Sun Dec 14 10:29:30 2008  sparse part has weight 3322339 (58.65/col)
Sun Dec 14 10:29:30 2008  saving the first 48 matrix rows for later
Sun Dec 14 10:29:30 2008  matrix is 56532 x 56644 (8.3 MB) with weight 2561002 (45.21/col)
Sun Dec 14 10:29:30 2008  sparse part has weight 1840625 (32.49/col)
Sun Dec 14 10:29:30 2008  matrix includes 64 packed rows
Sun Dec 14 10:29:30 2008  using block size 22657 for processor cache size 1024 kB
Sun Dec 14 10:29:30 2008  commencing Lanczos iteration
Sun Dec 14 10:29:30 2008  memory use: 8.3 MB
Sun Dec 14 10:29:48 2008  lanczos halted after 895 iterations (dim = 56529)
Sun Dec 14 10:29:48 2008  recovered 16 nontrivial dependencies
Sun Dec 14 10:29:49 2008  prp34 factor: 7516248271660755869850274614285353
Sun Dec 14 10:29:49 2008  prp56 factor: 87120428179153067595948563227353363024319865790575626979
Sun Dec 14 10:29:49 2008  elapsed time 01:02:53

(37·10¹⁰⁵+53)/9 = 4(1)₁₀₄7_<106> = 111733 · 546863 · C95

C95 = P45 · P51

P45 = 204636041354677447482853109425426041565256449_<45>

P51 = 328788855581546082125121238993357453012048109411927_<51>

Sun Dec 14 08:15:04 2008  Msieve v. 1.39
Sun Dec 14 08:15:04 2008  random seeds: 868f8b33 3eb24c1e
Sun Dec 14 08:15:04 2008  factoring 67282049847742334963616862975582700215581962408551703345462075578114834596968610334356334267223 (95 digits)
Sun Dec 14 08:15:05 2008  searching for 15-digit factors
Sun Dec 14 08:15:06 2008  commencing quadratic sieve (95-digit input)
Sun Dec 14 08:15:06 2008  using multiplier of 3
Sun Dec 14 08:15:06 2008  using 32kb Intel Core sieve core
Sun Dec 14 08:15:06 2008  sieve interval: 36 blocks of size 32768
Sun Dec 14 08:15:06 2008  processing polynomials in batches of 6
Sun Dec 14 08:15:06 2008  using a sieve bound of 2196599 (80826 primes)
Sun Dec 14 08:15:06 2008  using large prime bound of 329489850 (28 bits)
Sun Dec 14 08:15:06 2008  using double large prime bound of 2148402323041500 (43-51 bits)
Sun Dec 14 08:15:06 2008  using trial factoring cutoff of 51 bits
Sun Dec 14 08:15:06 2008  polynomial 'A' values have 12 factors
Sun Dec 14 13:22:18 2008  81008 relations (19048 full + 61960 combined from 1237185 partial), need 80922
Sun Dec 14 13:22:23 2008  begin with 1256233 relations
Sun Dec 14 13:22:23 2008  reduce to 215120 relations in 13 passes
Sun Dec 14 13:22:23 2008  attempting to read 215120 relations
Sun Dec 14 13:22:29 2008  recovered 215120 relations
Sun Dec 14 13:22:29 2008  recovered 202169 polynomials
Sun Dec 14 13:22:29 2008  attempting to build 81008 cycles
Sun Dec 14 13:22:29 2008  found 81008 cycles in 6 passes
Sun Dec 14 13:22:29 2008  distribution of cycle lengths:
Sun Dec 14 13:22:29 2008     length 1 : 19048
Sun Dec 14 13:22:29 2008     length 2 : 13883
Sun Dec 14 13:22:29 2008     length 3 : 13540
Sun Dec 14 13:22:29 2008     length 4 : 11060
Sun Dec 14 13:22:29 2008     length 5 : 8465
Sun Dec 14 13:22:29 2008     length 6 : 5764
Sun Dec 14 13:22:29 2008     length 7 : 3725
Sun Dec 14 13:22:29 2008     length 9+: 5523
Sun Dec 14 13:22:29 2008  largest cycle: 20 relations
Sun Dec 14 13:22:30 2008  matrix is 80826 x 81008 (22.2 MB) with weight 5506807 (67.98/col)
Sun Dec 14 13:22:30 2008  sparse part has weight 5506807 (67.98/col)
Sun Dec 14 13:22:30 2008  filtering completed in 3 passes
Sun Dec 14 13:22:30 2008  matrix is 77469 x 77533 (21.4 MB) with weight 5302804 (68.39/col)
Sun Dec 14 13:22:30 2008  sparse part has weight 5302804 (68.39/col)
Sun Dec 14 13:22:31 2008  saving the first 48 matrix rows for later
Sun Dec 14 13:22:31 2008  matrix is 77421 x 77533 (14.7 MB) with weight 4320453 (55.72/col)
Sun Dec 14 13:22:31 2008  sparse part has weight 3383624 (43.64/col)
Sun Dec 14 13:22:31 2008  matrix includes 64 packed rows
Sun Dec 14 13:22:31 2008  using block size 31013 for processor cache size 2048 kB
Sun Dec 14 13:22:31 2008  commencing Lanczos iteration
Sun Dec 14 13:22:31 2008  memory use: 13.5 MB
Sun Dec 14 13:23:10 2008  lanczos halted after 1226 iterations (dim = 77418)
Sun Dec 14 13:23:10 2008  recovered 15 nontrivial dependencies
Sun Dec 14 13:23:11 2008  prp45 factor: 204636041354677447482853109425426041565256449
Sun Dec 14 13:23:11 2008  prp51 factor: 328788855581546082125121238993357453012048109411927
Sun Dec 14 13:23:11 2008  elapsed time 05:08:07

(37·10¹¹⁴+53)/9 = 4(1)₁₁₃7_<115> = C115

C115 = P54 · P62

P54 = 337537008280418766192929438347918809616735002757194727_<54>

P62 = 12179734400251853325768968702888321780028003904068045443286571_<62>

Number: 41117_114
N=4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117
  ( 115 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=337537008280418766192929438347918809616735002757194727 (prp54)
 r2=12179734400251853325768968702888321780028003904068045443286571 (prp62)
Version: 
Total time: 1.79 hours.
Scaled time: 3.50 units (timescale=1.960).
Factorization parameters were as follows:
name: 41117_114
n: 4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117
m: 100000000000000000000000
deg: 5
c5: 37
c0: 530
skew: 1.70
type: snfs
lss: 1
rlim: 610000
alim: 610000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 610000/610000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [305000, 555001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 79057 x 79305
Total sieving time: 1.79 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,610000,610000,25,25,45,45,2.2,2.2,50000
total time: 1.79 hours.
 --------- CPU info (if available) ----------

(37·10¹²³+71)/9 = 4(1)₁₂₂9_<124> = 3⁴ · 29 · 449 · C118

C118 = P41 · P78

P41 = 20695535029248947852717006458822002729677_<41>

P78 = 188344610965528230197952413898521617583890420834456669268656909688180223321047_<78>

Number: 41119_123
N=3897892493807354986020787987411703517026257784064973021843262793067524455851574153348779522453388316794154088325611819
  ( 118 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=20695535029248947852717006458822002729677  (prp41)
 r2=188344610965528230197952413898521617583890420834456669268656909688180223321047 (prp78)
Version: 
Total time: 1.94 hours.
Scaled time: 5.00 units (timescale=2.575).
Factorization parameters were as follows:
name: 41119_123
n: 3897892493807354986020787987411703517026257784064973021843262793067524455851574153348779522453388316794154088325611819
m: 5000000000000000000000000
deg: 5
c5: 296
c0: 1775
skew: 1.43
type: snfs
lss: 1
rlim: 880000
alim: 880000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 880000/880000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [440000, 740001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 123693 x 123934
Total sieving time: 1.94 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000
total time: 1.94 hours.
 --------- CPU info (if available) ----------

(37·10¹⁵⁵+71)/9 = 4(1)₁₅₄9_<156> = 19² · 449 · 203388431 · 434667323 · 21723500418352373_<17> · 195139313557545220666189_<24> · C94

C94 = P47 · P48

P47 = 14213129565745445748264000298044322650674765341_<47>

P48 = 476165733177193357196365532265201544599028821671_<48>

Sun Dec 14 10:37:40 2008  Msieve v. 1.39
Sun Dec 14 10:37:40 2008  random seeds: 992e376c 7d2779b2
Sun Dec 14 10:37:40 2008  factoring 6767805260415624010155217671358645841863341122871686405813495731920030225435926539273660504811 (94 digits)
Sun Dec 14 10:37:41 2008  searching for 15-digit factors
Sun Dec 14 10:37:43 2008  commencing quadratic sieve (94-digit input)
Sun Dec 14 10:37:43 2008  using multiplier of 3
Sun Dec 14 10:37:43 2008  using 64kb Pentium 4 sieve core
Sun Dec 14 10:37:43 2008  sieve interval: 18 blocks of size 65536
Sun Dec 14 10:37:43 2008  processing polynomials in batches of 6
Sun Dec 14 10:37:43 2008  using a sieve bound of 2059517 (76466 primes)
Sun Dec 14 10:37:43 2008  using large prime bound of 284213346 (28 bits)
Sun Dec 14 10:37:43 2008  using double large prime bound of 1646493387513360 (42-51 bits)
Sun Dec 14 10:37:43 2008  using trial factoring cutoff of 51 bits
Sun Dec 14 10:37:43 2008  polynomial 'A' values have 12 factors
Sun Dec 14 17:31:24 2008  76647 relations (18095 full + 58552 combined from 1115782 partial), need 76562
Sun Dec 14 17:31:28 2008  begin with 1133877 relations
Sun Dec 14 17:31:29 2008  reduce to 202780 relations in 11 passes
Sun Dec 14 17:31:29 2008  attempting to read 202780 relations
Sun Dec 14 17:31:35 2008  recovered 202780 relations
Sun Dec 14 17:31:35 2008  recovered 189693 polynomials
Sun Dec 14 17:31:36 2008  attempting to build 76647 cycles
Sun Dec 14 17:31:36 2008  found 76647 cycles in 6 passes
Sun Dec 14 17:31:36 2008  distribution of cycle lengths:
Sun Dec 14 17:31:36 2008     length 1 : 18095
Sun Dec 14 17:31:36 2008     length 2 : 12837
Sun Dec 14 17:31:36 2008     length 3 : 13006
Sun Dec 14 17:31:36 2008     length 4 : 10582
Sun Dec 14 17:31:36 2008     length 5 : 8026
Sun Dec 14 17:31:36 2008     length 6 : 5541
Sun Dec 14 17:31:36 2008     length 7 : 3467
Sun Dec 14 17:31:36 2008     length 9+: 5093
Sun Dec 14 17:31:36 2008  largest cycle: 19 relations
Sun Dec 14 17:31:36 2008  matrix is 76466 x 76647 (20.3 MB) with weight 5027332 (65.59/col)
Sun Dec 14 17:31:36 2008  sparse part has weight 5027332 (65.59/col)
Sun Dec 14 17:31:38 2008  filtering completed in 3 passes
Sun Dec 14 17:31:38 2008  matrix is 73269 x 73333 (19.6 MB) with weight 4838460 (65.98/col)
Sun Dec 14 17:31:38 2008  sparse part has weight 4838460 (65.98/col)
Sun Dec 14 17:31:38 2008  saving the first 48 matrix rows for later
Sun Dec 14 17:31:38 2008  matrix is 73221 x 73333 (12.3 MB) with weight 3830611 (52.24/col)
Sun Dec 14 17:31:38 2008  sparse part has weight 2772583 (37.81/col)
Sun Dec 14 17:31:38 2008  matrix includes 64 packed rows
Sun Dec 14 17:31:38 2008  using block size 21845 for processor cache size 512 kB
Sun Dec 14 17:31:39 2008  commencing Lanczos iteration
Sun Dec 14 17:31:39 2008  memory use: 11.9 MB
Sun Dec 14 17:32:34 2008  lanczos halted after 1159 iterations (dim = 73221)
Sun Dec 14 17:32:34 2008  recovered 18 nontrivial dependencies
Sun Dec 14 17:32:35 2008  prp47 factor: 14213129565745445748264000298044322650674765341
Sun Dec 14 17:32:35 2008  prp48 factor: 476165733177193357196365532265201544599028821671
Sun Dec 14 17:32:35 2008  elapsed time 06:54:55

(37·10¹¹⁸+71)/9 = 4(1)₁₁₇9_<119> = 13 · 61 · C116

C116 = P35 · P81

P35 = 69418872032971825675387608033297539_<35>

P81 = 746807162673007794573024730772402779877228065547662481262643057695893171999373197_<81>

Number: 41119_118
N=51842510858904301527252346924478072019055625613002662182990051842510858904301527252346924478072019055625613002662183
  ( 116 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=69418872032971825675387608033297539 (prp35)
 r2=746807162673007794573024730772402779877228065547662481262643057695893171999373197 (prp81)
Version: 
Total time: 2.26 hours.
Scaled time: 4.42 units (timescale=1.955).
Factorization parameters were as follows:
name: 41119_118
n: 51842510858904301527252346924478072019055625613002662182990051842510858904301527252346924478072019055625613002662183
m: 500000000000000000000000
deg: 5
c5: 296
c0: 1775
skew: 1.43
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 665001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 79104 x 79347
Total sieving time: 2.26 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 2.26 hours.
 --------- CPU info (if available) ----------

(37·10¹²⁹+53)/9 = 4(1)₁₂₈7_<130> = C130

C130 = P51 · P80

P51 = 145844390655749562788875940659676939529907563875789_<51>

P80 = 28188338904407774606901579652067711359624010893822103546405700927331945019978753_<80>

Number: 41117_129
N=4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117
  ( 130 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=145844390655749562788875940659676939529907563875789 (prp51)
 r2=28188338904407774606901579652067711359624010893822103546405700927331945019978753 (prp80)
Version: 
Total time: 3.90 hours.
Scaled time: 10.05 units (timescale=2.575).
Factorization parameters were as follows:
name: 41117_129
n: 4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117
m: 100000000000000000000000000
deg: 5
c5: 37
c0: 530
skew: 1.70
type: snfs
lss: 1
rlim: 1090000
alim: 1090000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1090000/1090000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [545000, 1145001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 168454 x 168702
Total sieving time: 3.90 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1090000,1090000,26,26,47,47,2.3,2.3,50000
total time: 3.90 hours.
 --------- CPU info (if available) ----------

Dec 14, 2008

Factorizations of 411...117 and Factorizations of 411...119 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Dec 13, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(37·10¹⁶⁰+17)/9 = 4(1)₁₅₉3_<161> = 2211071263_<10> · 230520570756165931_<18> · C134

C134 = P51 · P84

P51 = 182534298451988745491465996097413122160200468742407_<51>

P84 = 441877926343855694297910384601660321631744164035971667970314416322997130688858619603_<84>

Number: 41113_160
N=80657877286595255360501423871032632999300536701774910703390394464930393749780818957506729438603944423745442718258274615558035407604421
  ( 134 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=182534298451988745491465996097413122160200468742407 (pp51)
 r2=441877926343855694297910384601660321631744164035971667970314416322997130688858619603 (pp84)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 46.00 hours.
Scaled time: 117.48 units (timescale=2.554).
Factorization parameters were as follows:
name: 41113_160
n: 80657877286595255360501423871032632999300536701774910703390394464930393749780818957506729438603944423745442718258274615558035407604421
m: 100000000000000000000000000000000
deg: 5
c5: 37
c0: 17
skew: 0.86
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 3050001)
Primes: RFBsize:250150, AFBsize:250081, largePrimes:9043720 encountered
Relations: rels:9246377, finalFF:577662
Max relations in full relation-set: 28
Initial matrix: 500296 x 577662 with sparse part having weight 61823295.
Pruned matrix : 466400 x 468965 with weight 47236517.
Total sieving time: 43.14 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 2.53 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 46.00 hours.
 --------- CPU info (if available) ----------

(37·10¹⁵⁷+17)/9 = 4(1)₁₅₆3_<158> = 863 · 73607 · 2627737972449370281351927889_<28> · C123

C123 = P49 · P75

P49 = 2352669523486813031676403292583158308856321454209_<49>

P75 = 104685448438146196434694486111792280502604118654516603864565957058052394593_<75>

Number: 41113_157
N=246290264092976747496854725207962020306973824437463180894048095584859846285349289378058603553803801996749502615192448691937
  ( 123 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=2352669523486813031676403292583158308856321454209 (pp49)
 r2=104685448438146196434694486111792280502604118654516603864565957058052394593 (pp75)
Version: GGNFS-0.77.1-20060513-k8
Total time: 51.04 hours.
Scaled time: 99.79 units (timescale=1.955).
Factorization parameters were as follows:
name: 41113_157
n: 246290264092976747496854725207962020306973824437463180894048095584859846285349289378058603553803801996749502615192448691937
m: 20000000000000000000000000000000
deg: 5
c5: 925
c0: 136
skew: 0.68
type: snfs
lss: 1
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1600000, 3100001)
Primes: RFBsize:230209, AFBsize:229217, largePrimes:8087006 encountered
Relations: rels:8152494, finalFF:518868
Max relations in full relation-set: 28
Initial matrix: 459493 x 518868 with sparse part having weight 54487834.
Pruned matrix : 437407 x 439768 with weight 42949203.
Total sieving time: 47.24 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 3.31 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,50,50,2.4,2.4,100000
total time: 51.04 hours.
 --------- CPU info (if available) ----------

Dec 13, 2008

By Robert Backstrom / GGNFS, Msieve

(34·10¹⁸⁰+11)/9 = 3(7)₁₇₉9_<181> = C181

C181 = P64 · P117

P64 = 5574632468914608146858989470643476643459042798240453257348585029_<64>

P117 = 677672976441677150691405869835421581232568399868727814349136619956892166941871909050801747283982312193551902356049751_<117>

Number: n
N=3777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
  ( 181 digits)
SNFS difficulty: 181 digits.
Divisors found:

Sat Dec 13 03:26:24 2008  prp64 factor: 5574632468914608146858989470643476643459042798240453257348585029
Sat Dec 13 03:26:24 2008  prp117 factor: 677672976441677150691405869835421581232568399868727814349136619956892166941871909050801747283982312193551902356049751
Sat Dec 13 03:26:24 2008  elapsed time 03:25:41 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 37.44 hours.
Scaled time: 75.29 units (timescale=2.011).
Factorization parameters were as follows:
name: KA_3_7_179_9
n: 3777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
type: snfs
skew: 0.80
deg: 5
c5: 34
c0: 11
m: 1000000000000000000000000000000000000
rlim: 8500000
alim: 8500000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 8500000/8500000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 2900077)
Primes: RFBsize:571119, AFBsize:571308, largePrimes:28026071 encountered
Relations: rels:25436113, finalFF:1245495
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: 26132343 relations and about 26488749 large ideals
Msieve: matrix is 1120238 x 1120486 (303.3 MB)

Total sieving time: 36.85 hours.
Total relation processing time: 0.58 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,8500000,8500000,29,29,58,58,2.5,2.5,100000
total time: 37.44 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830490)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830462)
Total of 4 processors activated (22643.71 BogoMIPS).

Dec 12, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve

(35·10¹⁶³+1)/9 = 3(8)₁₆₂9_<164> = 3 · 13 · 22027 · C158

C158 = P61 · P98

P61 = 3772305601451741110693896034844369021299802372207123480191799_<61>

P98 = 12000482490194027628192717775525574707938989420059163916800025995974556673997774191103348024966187_<98>

Number: n
N=45269487317882469287563036144322747128394742686293964270992463665092711263320061613065653561408770924365422027382348806056074408550914657057118581611249700413
  ( 158 digits)
SNFS difficulty: 165 digits.
Divisors found:

Sat Dec 13 01:50:12 2008  prp61 factor: 3772305601451741110693896034844369021299802372207123480191799
Sat Dec 13 01:50:12 2008  prp98 factor: 12000482490194027628192717775525574707938989420059163916800025995974556673997774191103348024966187
Sat Dec 13 01:50:12 2008  elapsed time 02:21:03 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 29.93 hours.
Scaled time: 54.56 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_3_8_162_9
n: 45269487317882469287563036144322747128394742686293964270992463665092711263320061613065653561408770924365422027382348806056074408550914657057118581611249700413
type: snfs
skew: 0.62
deg: 5
c5: 56
c0: 5
m: 500000000000000000000000000000000
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 3850001)
Primes: RFBsize:348513, AFBsize:347941, largePrimes:18240387 encountered
Relations: rels:17162345, finalFF:870976
Max relations in full relation-set: 28
Initial matrix: 696520 x 870976 with sparse part having weight 111651568.
Pruned matrix : 577183 x 580729 with weight 75582274.

Msieve: found 1208921 hash collisions in 17899689 relations
Msieve: matrix is 725299 x 725547 (195.7 MB)

Total sieving time: 29.38 hours.
Total relation processing time: 0.54 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.5,2.5,100000
total time: 29.93 hours.
 --------- CPU info (if available) ----------

Dec 12, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(37·10¹⁵⁰+17)/9 = 4(1)₁₄₉3_<151> = 3 · 35322799 · 301866832776298641101058383_<27> · C117

C117 = P55 · P62

P55 = 2594925527914511341596318466274576379113700104320912139_<55>

P62 = 49527060558983801304162718190994337266256570404149672188885417_<62>

Number: 41113_150
N=128519033767075013780786115315087147448685727330032367627926634125513383045933845733508432136406988335267399195376963
  ( 117 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=2594925527914511341596318466274576379113700104320912139 (pp55)
 r2=49527060558983801304162718190994337266256570404149672188885417 (pp62)
Version: GGNFS-0.77.1-20060513-k8
Total time: 23.56 hours.
Scaled time: 47.36 units (timescale=2.010).
Factorization parameters were as follows:
name: 41113_146
n: 128519033767075013780786115315087147448685727330032367627926634125513383045933845733508432136406988335267399195376963
m: 1000000000000000000000000000000
deg: 5
c5: 37
c0: 17
skew: 0.86
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:175998, largePrimes:6927169 encountered
Relations: rels:6882552, finalFF:472100
Max relations in full relation-set: 28
Initial matrix: 352365 x 472100 with sparse part having weight 48448512.
Pruned matrix : 304761 x 306586 with weight 28267595.
Total sieving time: 21.83 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.40 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 23.56 hours.
 --------- CPU info (if available) ----------

(35·10¹⁶³-17)/9 = 3(8)₁₆₂7_<164> = 37 · 859433 · C157

C157 = P48 · P109

P48 = 307872788703161951907149258898808205952508429619_<48>

P109 = 3972285727489072042775156135135899166170668429731548228973478147815338273608566491300580895913110250732250113_<109>

Number: 41113_163
N=1222958684447829035016168859062953192454852270102557210452764847348252919135117049323275986669177296020807964147351859948420704174788553675564064971965296947
  ( 157 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=307872788703161951907149258898808205952508429619 (pp48)
 r2=3972285727489072042775156135135899166170668429731548228973478147815338273608566491300580895913110250732250113 (pp109)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 64.73 hours.
Scaled time: 165.98 units (timescale=2.564).
Factorization parameters were as follows:
name: 41113_163
n: 1222958684447829035016168859062953192454852270102557210452764847348252919135117049323275986669177296020807964147351859948420704174788553675564064971965296947
m: 500000000000000000000000000000000
deg: 5
c5: 56
c0: -85
skew: 1.09
type: snfs
lss: 1
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2000000, 4100001)
Primes: RFBsize:283146, AFBsize:282122, largePrimes:9360953 encountered
Relations: rels:9842272, finalFF:670189
Max relations in full relation-set: 28
Initial matrix: 565334 x 670189 with sparse part having weight 77009409.
Pruned matrix : 517749 x 520639 with weight 58596730.
Total sieving time: 61.13 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 3.23 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,51,51,2.4,2.4,100000
total time: 64.73 hours.
 --------- CPU info (if available) ----------

Dec 12, 2008 (2nd)

By Serge Batalov / Msieve-1.39

(37·10¹⁶⁴+17)/9 = 4(1)₁₆₃3_<165> = 7 · 293 · 76091 · C157

C157 = P77 · P80

P77 = 39322735725815644225314040621429171304048596658405725916552678760370150874401_<77>

P80 = 66991011921022211860576233057936764080376246489288267299249722416243173674326393_<80>

SNFS difficulty: 166 digits.
Divisors found:
 r1=39322735725815644225314040621429171304048596658405725916552678760370150874401 (pp77)
 r2=66991011921022211860576233057936764080376246489288267299249722416243173674326393 (pp80)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.944).
Factorization parameters were as follows:
n: 2634269857775321840869725580967908335673437123950190687283775436756264499657615758989437524071575279256687134437966554155078736051321283939511898373622365593
m: 1000000000000000000000000000000000
deg: 5
c5: 37
c0: 170
skew: 1.36
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2100000, 4700001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 805341 x 805588
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,52,52,2.4,2.4,200000
total time: 47.00 hours.

Dec 12, 2008

By matsui / GMP-ECM

(31·10¹⁸⁹+41)/9 = 3(4)₁₈₈9_<190> = 23² · 97 · C185

C185 = P39 · P147

P39 = 235132531583386114575877377394239306961_<39>

P147 = 285482215410488202454571268720246728545289583107834402404220895987309744040548884129366032393397755755971466525084701732853813236763453026420960993_<147>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]

67126156031501655417622131710179573294183626847863980754281457806880214457241721287869437461158857296288356643432355240279158194696167529562575652260527438357617844297633045123934372273
=
235132531583386114575877377394239306961* 285482215410488202454571268720246728545289583107834402404220895987309744040548884129366032393397755755971466525084701732853813236763453026420960993

Dec 11, 2008 (7th)

By Nechaev Sergey / Msieve v. 1.39

6·10¹⁷⁵+1 = 6(0)₁₇₄1_<176> = 31 · 227 · 18229 · 142965322616087752221825023_<27> · C142

C142 = P35 · P107

P35 = 78834246190375597401811445588639063_<35>

P107 = 41500681309919383885445995508284685803042892144778268185725040022437427106594917277468373401274522948400313_<107>

Wed Dec 10 22:56:36 2008  Msieve v. 1.39
Wed Dec 10 22:56:36 2008  random seeds: 37be8f74 a454187c
Wed Dec 10 22:56:36 2008  factoring 3271674927454503946351778908731093597432135074118241825266750809997264745464837343269894562027727499605259733648083021004609399100642593226719 (142 digits)
Wed Dec 10 22:56:41 2008  searching for 15-digit factors
Wed Dec 10 22:56:49 2008  searching for 20-digit factors
Wed Dec 10 22:58:23 2008  searching for 25-digit factors
Wed Dec 10 23:25:03 2008  searching for 30-digit factors
Thu Dec 11 02:28:30 2008  searching for 35-digit factors
Thu Dec 11 05:51:33 2008  ECM stage 2 factor found
Thu Dec 11 05:51:34 2008  prp35 factor: 78834246190375597401811445588639063
Thu Dec 11 05:51:34 2008  prp107 factor: 41500681309919383885445995508284685803042892144778268185725040022437427106594917277468373401274522948400313
Thu Dec 11 05:51:34 2008  elapsed time 06:54:58

Dec 11, 2008 (6th)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(34·10¹⁶¹+11)/9 = 3(7)₁₆₀9_<162> = 127 · 5981 · C156

C156 = P36 · P56 · P65

P36 = 452260176298104765469994838125306203_<36>

P56 = 39385795018549293522153408826555650505362558093119041313_<56>

P65 = 27920996888392742207968069111544861147664525260952212315370251203_<65>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 497346291837245473892757219091134758464504760847378612032298838418479749887475401471823211531763679180630760897405797858280589027692387807818956587958690417 (156 digits)
Using B1=2720000, B2=4281513610, polynomial Dickson(6), sigma=232161349
Step 1 took 34781ms
Step 2 took 14375ms
********** Factor found in step 2: 452260176298104765469994838125306203
Found probable prime factor of 36 digits: 452260176298104765469994838125306203
Composite cofactor 1099690660159789190804806713972128415259313977562867994302360024355993049387317737924061850452700979364367080663344949539 has 121 digits

Number: n
N=1099690660159789190804806713972128415259313977562867994302360024355993049387317737924061850452700979364367080663344949539
  ( 121 digits)
SNFS difficulty: 162 digits.
Divisors found:

Thu Dec 11 11:21:39 2008  prp56 factor: 39385795018549293522153408826555650505362558093119041313
Thu Dec 11 11:21:39 2008  prp65 factor: 27920996888392742207968069111544861147664525260952212315370251203
Thu Dec 11 11:21:39 2008  elapsed time 02:54:48 (Msieve 1.39 - dependency 9)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 31.55 hours.
Scaled time: 57.52 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_3_7_160_9
n: 1099690660159789190804806713972128415259313977562867994302360024355993049387317737924061850452700979364367080663344949539
type: snfs
skew: 0.50
deg: 5
c5: 340
c0: 11
m: 100000000000000000000000000000000
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 3350001)
Primes: RFBsize:315948, AFBsize:316667, largePrimes:16423876 encountered
Relations: rels:14735760, finalFF:661281
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1689980 hash collisions in 16193584 relations
Msieve: matrix is 714185 x 714433 (191.3 MB)

Total sieving time: 31.04 hours.
Total relation processing time: 0.51 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.5,2.5,100000
total time: 31.55 hours.
 --------- CPU info (if available) ----------

(37·10¹⁴⁹+17)/9 = 4(1)₁₄₈3_<150> = 127 · 11282083 · 2109610728710016200472049234081_<31> · C111

C111 = P34 · P77

P34 = 1422639995218516766085174683074889_<34>

P77 = 95602415156372339326148758212848196389050952859263144734499019891465623985877_<77>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 136007819440940199626993346046725191626984715365734593965157745676287529081814105333269047742828239066669342653 (111 digits)
Using B1=1474000, B2=2140044280, polynomial Dickson(6), sigma=4067917861
Step 1 took 11515ms
Step 2 took 6016ms
********** Factor found in step 2: 1422639995218516766085174683074889
Found probable prime factor of 34 digits: 1422639995218516766085174683074889
Probable prime cofactor 95602415156372339326148758212848196389050952859263144734499019891465623985877 has 77 digits

Dec 11, 2008 (5th)

By Sinkiti Sibata / GGNFS

(37·10¹³⁹+17)/9 = 4(1)₁₃₈3_<140> = 263 · 1129 · C135

C135 = P54 · P81

P54 = 776571400668482335948948936970269317882230994910909567_<54>

P81 = 178290470791338198590566039041674126404436054299479729486821730640619604606479657_<81>

Number: 41113_139
N=138455280628272643144985505228932064484237240503932317071573521812132649139724952971980019031988034470126027983683232279688647752178519
  ( 135 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=776571400668482335948948936970269317882230994910909567 (pp54)
 r2=178290470791338198590566039041674126404436054299479729486821730640619604606479657 (pp81)
Version: GGNFS-0.77.1-20060513-k8
Total time: 13.11 hours.
Scaled time: 25.69 units (timescale=1.960).
Factorization parameters were as follows:
name: 4113_139
n: 138455280628272643144985505228932064484237240503932317071573521812132649139724952971980019031988034470126027983683232279688647752178519
m: 10000000000000000000000000000
deg: 5
c5: 37
c0: 170
skew: 1.36
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [800000, 1900001)
Primes: RFBsize:121127, AFBsize:121245, largePrimes:3766307 encountered
Relations: rels:3795612, finalFF:280228
Max relations in full relation-set: 28
Initial matrix: 242437 x 280228 with sparse part having weight 27780523.
Pruned matrix : 230429 x 231705 with weight 20668622.
Total sieving time: 12.18 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.70 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000
total time: 13.11 hours.
 --------- CPU info (if available) ----------

(37·10¹³¹+17)/9 = 4(1)₁₃₀3_<132> = 23 · 71699265203561_<14> · C117

C117 = P51 · P66

P51 = 960213857480717092820466634798010164748470829921701_<51>

P66 = 259626312129121757923718106411025688347436635718952611864568981371_<66>

Number: 41113_131
N=249296782672996691184964141338283467690861101743854481919392655376932888711640627577602280819968177366623021257632071
  ( 117 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=960213857480717092820466634798010164748470829921701 (pp51)
 r2=259626312129121757923718106411025688347436635718952611864568981371 (pp66)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 6.36 hours.
Scaled time: 3.00 units (timescale=0.472).
Factorization parameters were as follows:
name: 41113_131
n: 249296782672996691184964141338283467690861101743854481919392655376932888711640627577602280819968177366623021257632071
m: 200000000000000000000000000
deg: 5
c5: 185
c0: 272
skew: 1.08
type: snfs
lss: 1
rlim: 1190000
alim: 1190000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1190000/1190000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [595000, 1120001)
Primes: RFBsize:92225, AFBsize:92052, largePrimes:3078150 encountered
Relations: rels:3091713, finalFF:318832
Max relations in full relation-set: 28
Initial matrix: 184344 x 318832 with sparse part having weight 25571817.
Pruned matrix : 147637 x 148622 with weight 8816635.
Total sieving time: 5.87 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.32 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1190000,1190000,26,26,47,47,2.3,2.3,75000
total time: 6.36 hours.
 --------- CPU info (if available) ----------

(37·10¹⁵³+17)/9 = 4(1)₁₅₂3_<154> = 3 · 23 · 53069057 · 287828909 · C136

C136 = P57 · P80

P57 = 147798446122814265682532579169586489229599427021466891689_<57>

P80 = 26391524244025315181901986791051403695472473000891951978687175963298942219564161_<80>

Number: 41113_153
N=3900626274079522038818045807979827636445703910575290215266426929996301350563243058786329016398052678670849180356191187091400100973157929
  ( 136 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=147798446122814265682532579169586489229599427021466891689 (pp57)
 r2=26391524244025315181901986791051403695472473000891951978687175963298942219564161 (pp80)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 41.73 hours.
Scaled time: 106.57 units (timescale=2.554).
Factorization parameters were as follows:
name: 41113_153
n: 3900626274079522038818045807979827636445703910575290215266426929996301350563243058786329016398052678670849180356191187091400100973157929
m: 5000000000000000000000000000000
deg: 5
c5: 296
c0: 425
skew: 1.08
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2700001)
Primes: RFBsize:203362, AFBsize:203142, largePrimes:8729745 encountered
Relations: rels:9617308, finalFF:1012297
Max relations in full relation-set: 28
Initial matrix: 406571 x 1012297 with sparse part having weight 128521276.
Pruned matrix : 295909 x 298005 with weight 56250693.
Total sieving time: 40.10 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.34 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 41.73 hours.
 --------- CPU info (if available) ----------

(37·10¹⁴⁶+17)/9 = 4(1)₁₄₅3_<147> = 7 · 71 · 7717 · 334793 · 627732433 · 356693996625943_<15> · C112

C112 = P49 · P63

P49 = 1766069054027965440964145667998262780071429651417_<49>

P63 = 809654824638086357101658646633649047759620702589883621852808083_<63>

Number: 41113_146
N=1429906330237763419256584585374257947640589473325192065862091090909240113617417060828411324961594265051290003611
  ( 112 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=1766069054027965440964145667998262780071429651417 (pp49)
 r2=809654824638086357101658646633649047759620702589883621852808083 (pp63)
Version: GGNFS-0.77.1-20060513-k8
Total time: 18.72 hours.
Scaled time: 37.16 units (timescale=1.985).
Factorization parameters were as follows:
name: 41113_146
n: 1429906330237763419256584585374257947640589473325192065862091090909240113617417060828411324961594265051290003611
m: 200000000000000000000000000000
deg: 5
c5: 185
c0: 272
skew: 1.08
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 2550001)
Primes: RFBsize:155805, AFBsize:155967, largePrimes:4338843 encountered
Relations: rels:4571767, finalFF:444860
Max relations in full relation-set: 28
Initial matrix: 311839 x 444860 with sparse part having weight 45290513.
Pruned matrix : 265410 x 267033 with weight 24710851.
Total sieving time: 17.66 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.78 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 18.72 hours.
 --------- CPU info (if available) ----------

(37·10¹⁵⁴+17)/9 = 4(1)₁₅₃3_<155> = 21089 · 2363861 · 474284206163_<12> · C133

C133 = P66 · P68

P66 = 131233336262996763208529705822455103762873856738445745721093470207_<66>

P68 = 13249468585707739286382083178667357680893222111820417576063166951417_<68>

Number: 41113_154
N=1738771966214195899844411429013914390022469286286495172486315067514102830946952647912317598944637037955520844369709805096681505933319
  ( 133 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=131233336262996763208529705822455103762873856738445745721093470207 (pp66)
 r2=13249468585707739286382083178667357680893222111820417576063166951417 (pp68)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 41.45 hours.
Scaled time: 106.29 units (timescale=2.564).
Factorization parameters were as follows:
name: 41113_154
n: 1738771966214195899844411429013914390022469286286495172486315067514102830946952647912317598944637037955520844369709805096681505933319
m: 10000000000000000000000000000000
deg: 5
c5: 37
c0: 170
skew: 1.36
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2700001)
Primes: RFBsize:203362, AFBsize:203707, largePrimes:8480197 encountered
Relations: rels:8996442, finalFF:695451
Max relations in full relation-set: 28
Initial matrix: 407134 x 695451 with sparse part having weight 87013355.
Pruned matrix : 330217 x 332316 with weight 45838888.
Total sieving time: 39.80 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 1.37 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 41.45 hours.
 --------- CPU info (if available) ----------

Dec 11, 2008 (4th)

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve

8·10¹⁹⁰+9 = 8(0)₁₈₉9_<191> = 10979 · 93384737 · 1829065993_<10> · 33295915167128085016755403_<26> · C145

C145 = P39 · P49 · P57

P39 = 538680813586121424240758361537710132899_<39>

P49 = 6350022202664860146059913355300429133521100785097_<49>

P57 = 374562434586295016714727912805051180637746786286264130259_<57>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 1281241420783814236840813769192768768968282355514739105615102519730239311445959678569274101458614659494795859882596971403016242617149021527396577 (145 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=329758939
Step 1 took 13980ms
Step 2 took 6087ms
********** Factor found in step 2: 538680813586121424240758361537710132899
Found probable prime factor of 39 digits: 538680813586121424240758361537710132899
Composite cofactor 2378479775907177676028084193338783974397321241121097388182329404628516816089088946894571346712074773950123 has 106 digits

Number: 80009_190
N=2378479775907177676028084193338783974397321241121097388182329404628516816089088946894571346712074773950123
  ( 106 digits)
Divisors found:
 r1=6350022202664860146059913355300429133521100785097 (pp49)
 r2=374562434586295016714727912805051180637746786286264130259 (pp57)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 8.41 hours.
Scaled time: 19.97 units (timescale=2.376).
Factorization parameters were as follows:
name: 80009_190
n: 2378479775907177676028084193338783974397321241121097388182329404628516816089088946894571346712074773950123
skew: 19335.04
# norm 1.36e+15
c5: 65520
c4: 27471564
c3: -107204221150694
c2: 210564676395091900
c1: 9948647454800704699109
c0: 23207652976387495420816781
# alpha -6.59
Y1: 21237383893
Y0: -129415146671552584386
# Murphy_E 1.68e-09
# M 824103466569355914939858143207610722275937838736571265540824437757076304596016719605159834285168869476384
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved algebraic special-q in [750000, 1250001)
Primes: RFBsize:114155, AFBsize:113854, largePrimes:5081953 encountered
Relations: rels:5214262, finalFF:385976
Max relations in full relation-set: 28
Initial matrix: 228095 x 385976 with sparse part having weight 41605213.
Pruned matrix : 170451 x 171655 with weight 16999266.
Polynomial selection time: 0.38 hours.
Total sieving time: 7.76 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000
total time: 8.41 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(37·10¹⁵²+17)/9 = 4(1)₁₅₁3_<153> = 7 · 19 · 44959 · 203910624271_<12> · 507610655507_<12> · 14460141021394288398859618298437_<32> · C92

C92 = P42 · P51

P42 = 151493134078234480918166746651747002165127_<42>

P51 = 303217922469936086150886963014441185305391540464493_<51>

Thu Dec 11 00:23:15 2008  
Thu Dec 11 00:23:15 2008  
Thu Dec 11 00:23:15 2008  Msieve v. 1.39
Thu Dec 11 00:23:15 2008  random seeds: e8ff7218 79ab8c9f
Thu Dec 11 00:23:15 2008  factoring 45935433383661735240212241640772496532456843193944056659319372052651886889596389102266335611 (92 digits)
Thu Dec 11 00:23:16 2008  searching for 15-digit factors
Thu Dec 11 00:23:16 2008  commencing quadratic sieve (92-digit input)
Thu Dec 11 00:23:16 2008  using multiplier of 7
Thu Dec 11 00:23:16 2008  using VC8 32kb sieve core
Thu Dec 11 00:23:16 2008  sieve interval: 36 blocks of size 32768
Thu Dec 11 00:23:16 2008  processing polynomials in batches of 6
Thu Dec 11 00:23:16 2008  using a sieve bound of 1815199 (68235 primes)
Thu Dec 11 00:23:16 2008  using large prime bound of 197856691 (27 bits)
Thu Dec 11 00:23:16 2008  using double large prime bound of 857889398643883 (42-50 bits)
Thu Dec 11 00:23:16 2008  using trial factoring cutoff of 50 bits
Thu Dec 11 00:23:16 2008  polynomial 'A' values have 12 factors
Thu Dec 11 02:03:10 2008  68560 relations (18147 full + 50413 combined from 851687 partial), need 68331
Thu Dec 11 02:03:15 2008  begin with 869834 relations
Thu Dec 11 02:03:16 2008  reduce to 170582 relations in 12 passes
Thu Dec 11 02:03:16 2008  attempting to read 170582 relations
Thu Dec 11 02:03:18 2008  recovered 170582 relations
Thu Dec 11 02:03:18 2008  recovered 148573 polynomials
Thu Dec 11 02:03:18 2008  attempting to build 68560 cycles
Thu Dec 11 02:03:18 2008  found 68560 cycles in 5 passes
Thu Dec 11 02:03:18 2008  distribution of cycle lengths:
Thu Dec 11 02:03:18 2008     length 1 : 18147
Thu Dec 11 02:03:18 2008     length 2 : 12790
Thu Dec 11 02:03:18 2008     length 3 : 11984
Thu Dec 11 02:03:18 2008     length 4 : 9132
Thu Dec 11 02:03:18 2008     length 5 : 6502
Thu Dec 11 02:03:18 2008     length 6 : 4199
Thu Dec 11 02:03:18 2008     length 7 : 2537
Thu Dec 11 02:03:18 2008     length 9+: 3269
Thu Dec 11 02:03:18 2008  largest cycle: 19 relations
Thu Dec 11 02:03:18 2008  matrix is 68235 x 68560 (18.0 MB) with weight 4182462 (61.00/col)
Thu Dec 11 02:03:18 2008  sparse part has weight 4182462 (61.00/col)
Thu Dec 11 02:03:19 2008  filtering completed in 4 passes
Thu Dec 11 02:03:19 2008  matrix is 63856 x 63920 (16.9 MB) with weight 3920443 (61.33/col)
Thu Dec 11 02:03:19 2008  sparse part has weight 3920443 (61.33/col)
Thu Dec 11 02:03:19 2008  saving the first 48 matrix rows for later
Thu Dec 11 02:03:19 2008  matrix is 63808 x 63920 (10.8 MB) with weight 3072139 (48.06/col)
Thu Dec 11 02:03:19 2008  sparse part has weight 2189768 (34.26/col)
Thu Dec 11 02:03:19 2008  matrix includes 64 packed rows
Thu Dec 11 02:03:19 2008  using block size 25568 for processor cache size 4096 kB
Thu Dec 11 02:03:20 2008  commencing Lanczos iteration
Thu Dec 11 02:03:20 2008  memory use: 9.7 MB
Thu Dec 11 02:03:46 2008  lanczos halted after 1011 iterations (dim = 63805)
Thu Dec 11 02:03:46 2008  recovered 16 nontrivial dependencies
Thu Dec 11 02:03:47 2008  prp42 factor: 151493134078234480918166746651747002165127
Thu Dec 11 02:03:47 2008  prp51 factor: 303217922469936086150886963014441185305391540464493
Thu Dec 11 02:03:47 2008  elapsed time 01:40:32

Dec 11, 2008 (3rd)

By JMB / GPM-ECM 6.1.3

(10¹⁷³+11)/3 = (3)₁₇₂7_<173> = 37 · 811 · 242712712761419_<15> · C154

C154 = P30 · C125

P30 = 381814249723112484682790856461_<30>

C125 = [11987027729406341483972295989694296404186466424267385001709299847430322285161979459109911425907788839466142164158747992679649_<125>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1501931023
Step 1 took 18828ms
Step 2 took 12468ms
********** Factor found in step 2: 381814249723112484682790856461
Found probable prime factor of 30 digits: 381814249723112484682790856461
Composite cofactor 11987027729406341483972295989694296404186466424267385001709299847430322285161979459109911425907788839466142164158747992679649 has 125 digits

Dec 11, 2008 (2nd)

By Serge Batalov / Msieve-1.39

(37·10¹⁶⁶+17)/9 = 4(1)₁₆₅3_<167> = 61 · C165

C165 = P79 · P87

P79 = 4188456316799221800062368322618682657246331640966662822479121968077244812718221_<79>

P87 = 160907167268914976547336082636897002177991578144842220208538078678074396886300458033073_<87>

SNFS difficulty: 168 digits.
Divisors found:
 r1=4188456316799221800062368322618682657246331640966662822479121968077244812718221 (pp79)
 r2=160907167268914976547336082636897002177991578144842220208538078678074396886300458033073 (pp87)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.949).
Factorization parameters were as follows:
n: 673952641165755919854280510018214936247723132969034608378870673952641165755919854280510018214936247723132969034608378870673952641165755919854280510018214936247723133
m: 2000000000000000000000000000000000
deg: 5
c5: 185
c0: 272
skew: 1.08
type: snfs
lss: 1
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2250000, 4650001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 806657 x 806905
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,52,52,2.4,2.4,200000
total time: 42.00 hours.

(37·10¹⁵⁵+17)/9 = 4(1)₁₅₄3_<156> = 457 · 1521973 · C147

C147 = P43 · P51 · P54

P43 = 4812749602630778901982598117461876860320447_<43>

P51 = 150708074931584761567153708706295660448302303155627_<51>

P54 = 814903676675932977298347920721395104373594560096382057_<54>

SNFS difficulty: 156 digits.
Divisors found:
 r1=4812749602630778901982598117461876860320447 (pp43)
 r2=150708074931584761567153708706295660448302303155627 (pp51)
 r3=814903676675932977298347920721395104373594560096382057 (pp54)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.730).
Factorization parameters were as follows:
n: 591066120352941893887663346036595083426801534338445775875833713878874483567579011073947892692959927688804698516989496494173497266774234406515458333
m: 10000000000000000000000000000000
deg: 5
c5: 37
c0: 17
skew: 0.86
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1400000, 2400001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 506992 x 507240
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,52,52,2.4,2.4,100000
total time: 11.00 hours.

(35·10¹⁶¹+1)/9 = 3(8)₁₆₀9_<162> = 157 · 3499 · 2162183 · C150

C150 = P42 · P108

P42 = 571876901252956296758416030882298904111353_<42>

P108 = 572515087772493770133642628444432834628357213143562046017527857271537229085382174829411992559101277600579177_<108>

SNFS difficulty: 164 digits.
Divisors found:
 r1=571876901252956296758416030882298904111353 (pp42)
 r2=572515087772493770133642628444432834628357213143562046017527857271537229085382174829411992559101277600579177 (pp108)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.535).
Factorization parameters were as follows:
n: 327408154315898026747083437461024067322294520449969657609780219617982316838421582776349431696677974649965426793135033707538303180431672196979301096481
m: 500000000000000000000000000000000
deg: 5
c5: 14
c0: 125
skew: 1.55
type: snfs
lss: 1
rlim: 3900000
alim: 3900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3900000/3900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1950000, 3750001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 701421 x 701669
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3900000,3900000,27,27,52,52,2.4,2.4,100000
total time: 22.00 hours.

Dec 11, 2008

By Erik Branger / Msieve

(37·10¹²⁷+17)/9 = 4(1)₁₂₆3_<128> = 43 · 2287 · 5402086163_<10> · 1496014728227396684836493981_<28> · C86

C86 = P33 · P54

P33 = 192989518424688578863761535141003_<33>

P54 = 268036227003025546179556250126925130151642985964735177_<54>

Tue Dec 09 17:21:54 2008  Msieve v. 1.38
Tue Dec 09 17:21:54 2008  random seeds: faf2f160 6a6e1ca0
Tue Dec 09 17:21:54 2008  factoring 51728182369684409028798805980087503755843503122413956066416778922363534304002249162531 (86 digits)
Tue Dec 09 17:21:55 2008  searching for 15-digit factors
Tue Dec 09 17:21:56 2008  commencing quadratic sieve (86-digit input)
Tue Dec 09 17:21:56 2008  using multiplier of 19
Tue Dec 09 17:21:56 2008  using 64kb Pentium 4 sieve core
Tue Dec 09 17:21:56 2008  sieve interval: 8 blocks of size 65536
Tue Dec 09 17:21:56 2008  processing polynomials in batches of 13
Tue Dec 09 17:21:56 2008  using a sieve bound of 1461403 (55606 primes)
Tue Dec 09 17:21:56 2008  using large prime bound of 116912240 (26 bits)
Tue Dec 09 17:21:56 2008  using double large prime bound of 332772803587280 (41-49 bits)
Tue Dec 09 17:21:56 2008  using trial factoring cutoff of 49 bits
Tue Dec 09 17:21:57 2008  polynomial 'A' values have 11 factors
Tue Dec 09 18:17:14 2008  55945 relations (16016 full + 39929 combined from 580933 partial), need 55702
Tue Dec 09 18:17:16 2008  begin with 596949 relations
Tue Dec 09 18:17:17 2008  reduce to 132179 relations in 10 passes
Tue Dec 09 18:17:17 2008  attempting to read 132179 relations
Tue Dec 09 18:17:22 2008  recovered 132179 relations
Tue Dec 09 18:17:22 2008  recovered 110384 polynomials
Tue Dec 09 18:17:22 2008  attempting to build 55945 cycles
Tue Dec 09 18:17:22 2008  found 55945 cycles in 5 passes
Tue Dec 09 18:17:22 2008  distribution of cycle lengths:
Tue Dec 09 18:17:22 2008     length 1 : 16016
Tue Dec 09 18:17:22 2008     length 2 : 11292
Tue Dec 09 18:17:22 2008     length 3 : 9885
Tue Dec 09 18:17:22 2008     length 4 : 7218
Tue Dec 09 18:17:22 2008     length 5 : 4903
Tue Dec 09 18:17:22 2008     length 6 : 2998
Tue Dec 09 18:17:22 2008     length 7 : 1772
Tue Dec 09 18:17:22 2008     length 9+: 1861
Tue Dec 09 18:17:22 2008  largest cycle: 18 relations
Tue Dec 09 18:17:22 2008  matrix is 55606 x 55945 (12.6 MB) with weight 3080958 (55.07/col)
Tue Dec 09 18:17:22 2008  sparse part has weight 3080958 (55.07/col)
Tue Dec 09 18:17:23 2008  filtering completed in 3 passes
Tue Dec 09 18:17:23 2008  matrix is 50632 x 50696 (11.5 MB) with weight 2810111 (55.43/col)
Tue Dec 09 18:17:23 2008  sparse part has weight 2810111 (55.43/col)
Tue Dec 09 18:17:23 2008  saving the first 48 matrix rows for later
Tue Dec 09 18:17:23 2008  matrix is 50584 x 50696 (7.2 MB) with weight 2173490 (42.87/col)
Tue Dec 09 18:17:23 2008  sparse part has weight 1570727 (30.98/col)
Tue Dec 09 18:17:23 2008  matrix includes 64 packed rows
Tue Dec 09 18:17:23 2008  using block size 20278 for processor cache size 512 kB
Tue Dec 09 18:17:24 2008  commencing Lanczos iteration
Tue Dec 09 18:17:24 2008  memory use: 7.2 MB
Tue Dec 09 18:17:48 2008  lanczos halted after 802 iterations (dim = 50583)
Tue Dec 09 18:17:48 2008  recovered 17 nontrivial dependencies
Tue Dec 09 18:17:48 2008  prp33 factor: 192989518424688578863761535141003
Tue Dec 09 18:17:48 2008  prp54 factor: 268036227003025546179556250126925130151642985964735177
Tue Dec 09 18:17:48 2008  elapsed time 00:55:54

(37·10¹⁷²-1)/9 = 4(1)₁₇₂_<173> = 7² · 49675493159_<11> · 581693342027508474141681883_<27> · 284058421196271016127648080138696939_<36> · C99

C99 = P47 · P52

P47 = 14637743314961305869395629399473422598403387829_<47>

P52 = 6983048497779176869298171805227564784303332803867877_<52>

Wed Dec 10 23:12:11 2008  Msieve v. 1.39
Wed Dec 10 23:12:11 2008  random seeds: dc7b48e4 819504a7
Wed Dec 10 23:12:12 2008  factoring 102216071466417735574182221688508636681384173985648829721984676231139297698278652475301191705869033 (99 digits)
Wed Dec 10 23:12:12 2008  searching for 15-digit factors
Wed Dec 10 23:12:13 2008  commencing quadratic sieve (99-digit input)
Wed Dec 10 23:12:13 2008  using multiplier of 1
Wed Dec 10 23:12:13 2008  using 64kb Opteron sieve core
Wed Dec 10 23:12:13 2008  sieve interval: 18 blocks of size 65536
Wed Dec 10 23:12:13 2008  processing polynomials in batches of 6
Wed Dec 10 23:12:13 2008  using a sieve bound of 2532769 (92941 primes)
Wed Dec 10 23:12:13 2008  using large prime bound of 379915350 (28 bits)
Wed Dec 10 23:12:13 2008  using double large prime bound of 2776107567720900 (43-52 bits)
Wed Dec 10 23:12:13 2008  using trial factoring cutoff of 52 bits
Wed Dec 10 23:12:13 2008  polynomial 'A' values have 13 factors
Thu Dec 11 05:03:51 2008  93374 relations (22224 full + 71150 combined from 1407528 partial), need 93037
Thu Dec 11 05:03:52 2008  begin with 1429752 relations
Thu Dec 11 05:03:53 2008  reduce to 246150 relations in 10 passes
Thu Dec 11 05:03:53 2008  attempting to read 246150 relations
Thu Dec 11 05:03:56 2008  recovered 246150 relations
Thu Dec 11 05:03:56 2008  recovered 235407 polynomials
Thu Dec 11 05:03:56 2008  attempting to build 93374 cycles
Thu Dec 11 05:03:56 2008  found 93374 cycles in 5 passes
Thu Dec 11 05:03:56 2008  distribution of cycle lengths:
Thu Dec 11 05:03:56 2008     length 1 : 22224
Thu Dec 11 05:03:56 2008     length 2 : 15847
Thu Dec 11 05:03:56 2008     length 3 : 15723
Thu Dec 11 05:03:56 2008     length 4 : 12743
Thu Dec 11 05:03:56 2008     length 5 : 9757
Thu Dec 11 05:03:56 2008     length 6 : 6633
Thu Dec 11 05:03:56 2008     length 7 : 4390
Thu Dec 11 05:03:56 2008     length 9+: 6057
Thu Dec 11 05:03:56 2008  largest cycle: 19 relations
Thu Dec 11 05:03:56 2008  matrix is 92941 x 93374 (25.0 MB) with weight 6190895 (66.30/col)
Thu Dec 11 05:03:56 2008  sparse part has weight 6190895 (66.30/col)
Thu Dec 11 05:03:58 2008  filtering completed in 3 passes
Thu Dec 11 05:03:58 2008  matrix is 89064 x 89128 (23.9 MB) with weight 5921326 (66.44/col)
Thu Dec 11 05:03:58 2008  sparse part has weight 5921326 (66.44/col)
Thu Dec 11 05:03:58 2008  saving the first 48 matrix rows for later
Thu Dec 11 05:03:58 2008  matrix is 89016 x 89128 (14.5 MB) with weight 4633284 (51.98/col)
Thu Dec 11 05:03:58 2008  sparse part has weight 3268814 (36.68/col)
Thu Dec 11 05:03:58 2008  matrix includes 64 packed rows
Thu Dec 11 05:03:58 2008  using block size 21845 for processor cache size 512 kB
Thu Dec 11 05:03:59 2008  commencing Lanczos iteration
Thu Dec 11 05:03:59 2008  memory use: 14.4 MB
Thu Dec 11 05:04:53 2008  lanczos halted after 1409 iterations (dim = 89012)
Thu Dec 11 05:04:53 2008  recovered 14 nontrivial dependencies
Thu Dec 11 05:04:53 2008  prp47 factor: 14637743314961305869395629399473422598403387829
Thu Dec 11 05:04:53 2008  prp52 factor: 6983048497779176869298171805227564784303332803867877
Thu Dec 11 05:04:53 2008  elapsed time 05:52:42

Dec 10, 2008 (7th)

By matsui / GMP-ECM

(16·10¹⁸⁷+11)/9 = 1(7)₁₈₆9_<188> = 61 · 67 · C184

C184 = P37 · P148

P37 = 1951924232335499171056484276290444999_<37>

P148 = 2228485844780820932821393203006312484951026177190765804027858301239457423520513255838839227297015998784342612223367264656633254640127530604744244083_<148>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
4349835521844330261261996030775086317048636598428621917733735693119103933882500067966180028817660332218687980860723703884946850447217464589620204985998966914063561971562950275942690917
=
1951924232335499171056484276290444999* 2228485844780820932821393203006312484951026177190765804027858301239457423520513255838839227297015998784342612223367264656633254640127530604744244083

Dec 10, 2008 (6th)

By Sinkiti Sibata / GGNFS, Msieve

(35·10¹⁶⁰+1)/9 = 3(8)₁₅₉9_<161> = 3 · 48889 · 14158995281_<11> · C146

C146 = P52 · P94

P52 = 3104396736833870181492437190327522026318664958142209_<52>

P94 = 6032307486523415111941507522986185399490762371629962271727902737700672557187363638130272688123_<94>

Number: 38889_160
N=18726675676741815199689758347265826045166743883791788145195661841811544319555874854046399069162508683551760254528733032677079437502130842539283707
  ( 146 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=3104396736833870181492437190327522026318664958142209 (pp52)
 r2=6032307486523415111941507522986185399490762371629962271727902737700672557187363638130272688123 (pp94)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 45.77 hours.
Scaled time: 117.35 units (timescale=2.564).
Factorization parameters were as follows:
name: 38889_160
n: 18726675676741815199689758347265826045166743883791788145195661841811544319555874854046399069162508683551760254528733032677079437502130842539283707
m: 100000000000000000000000000000000
deg: 5
c5: 35
c0: 1
skew: 0.49
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3000001)
Primes: RFBsize:243539, AFBsize:243354, largePrimes:9454508 encountered
Relations: rels:10260641, finalFF:981249
Max relations in full relation-set: 28
Initial matrix: 486959 x 981249 with sparse part having weight 118899122.
Pruned matrix : 354854 x 357352 with weight 58839652.
Total sieving time: 43.59 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.86 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 45.77 hours.
 --------- CPU info (if available) ----------

(37·10¹³⁸+17)/9 = 4(1)₁₃₇3_<139> = 3² · C138

C138 = P45 · P93

P45 = 510775719844408392390465528501098122071849389_<45>

P93 = 894306651059953932405219537564294331814846472823973070870460522554892046315226837865094032613_<93>

Number: 41113_138
N=456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123457
  ( 138 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=510775719844408392390465528501098122071849389 (pp45)
 r2=894306651059953932405219537564294331814846472823973070870460522554892046315226837865094032613 (pp93)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 13.91 hours.
Scaled time: 35.81 units (timescale=2.575).
Factorization parameters were as follows:
name: 41113_138
n: 456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123457
m: 5000000000000000000000000000
deg: 5
c5: 296
c0: 425
skew: 1.08
type: snfs
lss: 1
rlim: 1570000
alim: 1570000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1570000/1570000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [785000, 2085001)
Primes: RFBsize:119057, AFBsize:119140, largePrimes:4269723 encountered
Relations: rels:4901265, finalFF:728520
Max relations in full relation-set: 28
Initial matrix: 238264 x 728520 with sparse part having weight 84654973.
Pruned matrix : 173166 x 174421 with weight 29237746.
Total sieving time: 13.48 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000
total time: 13.91 hours.
 --------- CPU info (if available) ----------

(37·10¹³⁰+17)/9 = 4(1)₁₂₉3_<131> = 733 · 2755861 · C122

C122 = P43 · P79

P43 = 7976815312434325655010026496828210010899659_<43>

P79 = 2551340330232941042791734672815796033637758911848411720302531081819024948523739_<79>

Number: 41113_130
N=20351570613433373197016275791874020012092224506120029900085311127306483973869120833832723060768618756333861528591308505001
  ( 122 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=7976815312434325655010026496828210010899659 (pp43)
 r2=2551340330232941042791734672815796033637758911848411720302531081819024948523739 (pp79)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.22 hours.
Scaled time: 10.40 units (timescale=1.991).
Factorization parameters were as follows:
name: 41113_130
n: 20351570613433373197016275791874020012092224506120029900085311127306483973869120833832723060768618756333861528591308505001
m: 100000000000000000000000000
deg: 5
c5: 37
c0: 17
skew: 0.86
type: snfs
lss: 1
rlim: 1090000
alim: 1090000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1090000/1090000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [545000, 995001)
Primes: RFBsize:84976, AFBsize:84613, largePrimes:3064841 encountered
Relations: rels:3134879, finalFF:357436
Max relations in full relation-set: 28
Initial matrix: 169654 x 357436 with sparse part having weight 29515736.
Pruned matrix : 129023 x 129935 with weight 8435848.
Total sieving time: 4.95 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1090000,1090000,26,26,47,47,2.3,2.3,50000
total time: 5.22 hours.
 --------- CPU info (if available) ----------

(37·10¹⁴⁰+17)/9 = 4(1)₁₃₉3_<141> = 7² · 463 · 259452516097_<12> · 12224976615594643753028840051569_<32> · C94

C94 = P42 · P53

P42 = 349677359272427213877770746562063814121121_<42>

P53 = 16338369215819639791633317799316136066415149505855783_<53>

Wed Dec 10 08:05:54 2008  Msieve v. 1.39
Wed Dec 10 08:05:54 2008  random seeds: 6ad396f0 4eea3e53
Wed Dec 10 08:05:54 2008  factoring 5713157802205729067441731387747770291115643749641748842990579584482566967465904050235120292743 (94 digits)
Wed Dec 10 08:05:55 2008  searching for 15-digit factors
Wed Dec 10 08:05:56 2008  commencing quadratic sieve (94-digit input)
Wed Dec 10 08:05:56 2008  using multiplier of 2
Wed Dec 10 08:05:56 2008  using 32kb Intel Core sieve core
Wed Dec 10 08:05:56 2008  sieve interval: 36 blocks of size 32768
Wed Dec 10 08:05:56 2008  processing polynomials in batches of 6
Wed Dec 10 08:05:56 2008  using a sieve bound of 2059517 (76366 primes)
Wed Dec 10 08:05:56 2008  using large prime bound of 284213346 (28 bits)
Wed Dec 10 08:05:56 2008  using double large prime bound of 1646493387513360 (42-51 bits)
Wed Dec 10 08:05:56 2008  using trial factoring cutoff of 51 bits
Wed Dec 10 08:05:56 2008  polynomial 'A' values have 12 factors
Wed Dec 10 11:37:41 2008  76516 relations (18643 full + 57873 combined from 1110238 partial), need 76462
Wed Dec 10 11:37:42 2008  begin with 1128881 relations
Wed Dec 10 11:37:43 2008  reduce to 200010 relations in 10 passes
Wed Dec 10 11:37:43 2008  attempting to read 200010 relations
Wed Dec 10 11:37:46 2008  recovered 200010 relations
Wed Dec 10 11:37:46 2008  recovered 184776 polynomials
Wed Dec 10 11:37:46 2008  attempting to build 76516 cycles
Wed Dec 10 11:37:46 2008  found 76516 cycles in 5 passes
Wed Dec 10 11:37:46 2008  distribution of cycle lengths:
Wed Dec 10 11:37:46 2008     length 1 : 18643
Wed Dec 10 11:37:46 2008     length 2 : 13452
Wed Dec 10 11:37:46 2008     length 3 : 12666
Wed Dec 10 11:37:46 2008     length 4 : 10268
Wed Dec 10 11:37:46 2008     length 5 : 7802
Wed Dec 10 11:37:46 2008     length 6 : 5394
Wed Dec 10 11:37:46 2008     length 7 : 3439
Wed Dec 10 11:37:46 2008     length 9+: 4852
Wed Dec 10 11:37:46 2008  largest cycle: 19 relations
Wed Dec 10 11:37:46 2008  matrix is 76366 x 76516 (20.2 MB) with weight 4995764 (65.29/col)
Wed Dec 10 11:37:46 2008  sparse part has weight 4995764 (65.29/col)
Wed Dec 10 11:37:48 2008  filtering completed in 3 passes
Wed Dec 10 11:37:48 2008  matrix is 72912 x 72975 (19.4 MB) with weight 4801996 (65.80/col)
Wed Dec 10 11:37:48 2008  sparse part has weight 4801996 (65.80/col)
Wed Dec 10 11:37:48 2008  saving the first 48 matrix rows for later
Wed Dec 10 11:37:48 2008  matrix is 72864 x 72975 (12.3 MB) with weight 3807587 (52.18/col)
Wed Dec 10 11:37:48 2008  sparse part has weight 2779634 (38.09/col)
Wed Dec 10 11:37:48 2008  matrix includes 64 packed rows
Wed Dec 10 11:37:48 2008  using block size 29190 for processor cache size 1024 kB
Wed Dec 10 11:37:48 2008  commencing Lanczos iteration
Wed Dec 10 11:37:48 2008  memory use: 11.8 MB
Wed Dec 10 11:38:25 2008  lanczos halted after 1154 iterations (dim = 72861)
Wed Dec 10 11:38:25 2008  recovered 16 nontrivial dependencies
Wed Dec 10 11:38:26 2008  prp42 factor: 349677359272427213877770746562063814121121
Wed Dec 10 11:38:26 2008  prp53 factor: 16338369215819639791633317799316136066415149505855783
Wed Dec 10 11:38:26 2008  elapsed time 03:32:32

(35·10¹⁴⁵+1)/9 = 3(8)₁₄₄9_<146> = 3 · 13 · 173 · 46301 · 17045617 · 1842706471_<10> · 74365896181_<11> · C110

C110 = P47 · P63

P47 = 80482065692066908416612753751129845520716852307_<47>

P63 = 662190027785962142176186013718138487763144980919115337331166223_<63>

Number: 38889_145
N=53294421316901416528304760731530435279940035842458663214979262606185267085546269558410831973396800689958026461
  ( 110 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=80482065692066908416612753751129845520716852307 (pp47)
 r2=662190027785962142176186013718138487763144980919115337331166223 (pp63)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 16.16 hours.
Scaled time: 7.64 units (timescale=0.473).
Factorization parameters were as follows:
name: 38889_145
n: 53294421316901416528304760731530435279940035842458663214979262606185267085546269558410831973396800689958026461
m: 100000000000000000000000000000
deg: 5
c5: 35
c0: 1
skew: 0.49
type: snfs
lss: 1
rlim: 1940000
alim: 1940000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1940000/1940000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [970000, 2170001)
Primes: RFBsize:144810, AFBsize:144951, largePrimes:4110184 encountered
Relations: rels:4268857, finalFF:420980
Max relations in full relation-set: 28
Initial matrix: 289827 x 420980 with sparse part having weight 39373462.
Pruned matrix : 245719 x 247232 with weight 19897514.
Total sieving time: 14.30 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 1.58 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1940000,1940000,26,26,49,49,2.3,2.3,100000
total time: 16.16 hours.
 --------- CPU info (if available) ----------

(37·10¹³⁵+17)/9 = 4(1)₁₃₄3_<136> = 3 · 233 · 35533039 · C126

C126 = P38 · P89

P38 = 14641719656254489741568420087470167181_<38>

P89 = 11304662450032683330928990275564458178851499064755153440882955206425538566141385065716793_<89>

Number: 41113_135
N=165519698401965577994313589899056412124998401475059473398292465613085453691521316341029149043281052537325330258204555309170533
  ( 126 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=14641719656254489741568420087470167181 (pp38)
 r2=11304662450032683330928990275564458178851499064755153440882955206425538566141385065716793 (pp89)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 8.28 hours.
Scaled time: 21.24 units (timescale=2.564).
Factorization parameters were as follows:
name: 41113_135
n: 165519698401965577994313589899056412124998401475059473398292465613085453691521316341029149043281052537325330258204555309170533
m: 1000000000000000000000000000
deg: 5
c5: 37
c0: 17
skew: 0.86
type: snfs
lss: 1
rlim: 1320000
alim: 1320000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1320000/1320000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [660000, 1335001)
Primes: RFBsize:101433, AFBsize:100876, largePrimes:3892874 encountered
Relations: rels:4437698, finalFF:763666
Max relations in full relation-set: 28
Initial matrix: 202374 x 763666 with sparse part having weight 76985798.
Pruned matrix : 137533 x 138608 with weight 18297906.
Total sieving time: 8.03 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1320000,1320000,26,26,48,48,2.3,2.3,75000
total time: 8.28 hours.
 --------- CPU info (if available) ----------

(37·10¹²⁸+17)/9 = 4(1)₁₂₇3_<129> = 7 · 29 · 139 · 366317336179_<12> · C113

C113 = P43 · P70

P43 = 5892987442010330386722922517752335244214957_<43>

P70 = 6749248030263033399317509977913277782333557881183738908126529217567863_<70>

Number: 41113_128
N=39773233885353014121246197866071226793184898803915251469110066826582204106553428084166597044517372637684307126891
  ( 113 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=5892987442010330386722922517752335244214957 (pp43)
 r2=6749248030263033399317509977913277782333557881183738908126529217567863 (pp70)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.06 hours.
Scaled time: 9.91 units (timescale=1.960).
Factorization parameters were as follows:
name: 41113_128
n: 39773233885353014121246197866071226793184898803915251469110066826582204106553428084166597044517372637684307126891
m: 50000000000000000000000000
deg: 5
c5: 296
c0: 425
skew: 1.08
type: snfs
lss: 1
rlim: 1070000
alim: 1070000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1070000/1070000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [535000, 985001)
Primes: RFBsize:83548, AFBsize:83486, largePrimes:2816037 encountered
Relations: rels:2727760, finalFF:222088
Max relations in full relation-set: 28
Initial matrix: 167101 x 222088 with sparse part having weight 17817301.
Pruned matrix : 151342 x 152241 with weight 9260045.
Total sieving time: 4.76 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1070000,1070000,26,26,47,47,2.3,2.3,50000
total time: 5.06 hours.
 --------- CPU info (if available) ----------

(37·10¹²⁴+17)/9 = 4(1)₁₂₃3_<125> = 468623 · C119

C119 = P42 · P78

P42 = 112530124858026319235276321085291537757319_<42>

P78 = 779590994951787401614222560214997243616363930234312099703490458459408464798049_<78>

Number: 41113_124
N=87727472000117602232735292785695774878977581363081007784746184269895227317291535223646963787759267281185752963706670631
  ( 119 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=112530124858026319235276321085291537757319 (pp42)
 r2=779590994951787401614222560214997243616363930234312099703490458459408464798049 (pp78)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.54 hours.
Scaled time: 7.10 units (timescale=2.003).
Factorization parameters were as follows:
name: 41113_124
n: 87727472000117602232735292785695774878977581363081007784746184269895227317291535223646963787759267281185752963706670631
m: 10000000000000000000000000
deg: 5
c5: 37
c0: 170
skew: 1.36
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 800001)
Primes: RFBsize:71274, AFBsize:71110, largePrimes:2584163 encountered
Relations: rels:2495928, finalFF:206678
Max relations in full relation-set: 28
Initial matrix: 142449 x 206678 with sparse part having weight 16626795.
Pruned matrix : 126344 x 127120 with weight 7462678.
Total sieving time: 3.33 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 3.54 hours.
 --------- CPU info (if available) ----------

(37·10¹³⁷+17)/9 = 4(1)₁₃₆3_<138> = 37745119 · C131

C131 = P64 · P67

P64 = 3219321487884923385567438048156219294654507482548165761458705309_<64>

P67 = 3383249819657721642586538439401357021436968537987233098257618204803_<67>

Number: 41113_137
N=10891768843306895154075712706353134324761596621568767901118846945776250198366340058726827993603917664456458889720578470321185399127
  ( 131 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=3219321487884923385567438048156219294654507482548165761458705309 (pp64)
 r2=3383249819657721642586538439401357021436968537987233098257618204803 (pp67)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 10.43 hours.
Scaled time: 26.63 units (timescale=2.554).
Factorization parameters were as follows:
name: 41113_137
n: 10891768843306895154075712706353134324761596621568767901118846945776250198366340058726827993603917664456458889720578470321185399127
m: 2000000000000000000000000000
deg: 5
c5: 925
c0: 136
skew: 0.68
type: snfs
lss: 1
rlim: 1480000
alim: 1480000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1480000/1480000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [740000, 1715001)
Primes: RFBsize:112752, AFBsize:112144, largePrimes:3960082 encountered
Relations: rels:4364610, finalFF:588426
Max relations in full relation-set: 28
Initial matrix: 224963 x 588426 with sparse part having weight 63687211.
Pruned matrix : 163887 x 165075 with weight 21080585.
Total sieving time: 10.11 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1480000,1480000,26,26,48,48,2.3,2.3,75000
total time: 10.43 hours.
 --------- CPU info (if available) ----------

Dec 10, 2008 (5th)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39

5·10¹⁸⁸+9 = 5(0)₁₈₇9_<189> = 89 · 20644698707_<11> · 2095779451075181845289_<22> · C156

C156 = P35 · C121

P35 = 17069365974029360492115172688628301_<35>

C121 = [7606913553087904523289891655928436341384431709516903459521491661869372564112334503851881776661479063881775251744140099647_<121>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3476476497
Step 1 took 4752ms
Step 2 took 3258ms
********** Factor found in step 2: 17069365974029360492115172688628301
Found probable prime factor of 35 digits: 17069365974029360492115172688628301
Composite cofactor has 121 digits

(37·10¹⁶⁹+17)/9 = 4(1)₁₆₈3_<170> = 43 · 4651579 · 1017191121592337384843_<22> · 87039115464799111997365977317_<29> · C112

C112 = P31 · P81

P31 = 8425498979072827488852800911267_<31>

P81 = 275535586632481005658474330785623147493947560810087737672451637475014017044809677_<81>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1331634998
Step 1 took 2729ms
Step 2 took 2284ms
********** Factor found in step 2: 8425498979072827488852800911267
Found probable prime factor of 31 digits: 8425498979072827488852800911267
Probable prime cofactor 275535586632481005658474330785623147493947560810087737672451637475014017044809677 has 81 digits

(37·10¹⁵¹+17)/9 = 4(1)₁₅₀3_<152> = 8353 · 34386593 · 2039773586951292013_<19> · C122

C122 = P36 · P87

P36 = 273368539496778091201031494207412509_<36>

P87 = 256682989397362158875629863353292151892741767670591065562820018228860886687460955569841_<87>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3498479059
Step 1 took 3272ms
Step 2 took 2434ms
********** Factor found in step 2: 273368539496778091201031494207412509
Found probable prime factor of 36 digits: 273368539496778091201031494207412509
Probable prime cofactor 256682989397362158875629863353292151892741767670591065562820018228860886687460955569841 has 87 digits

(37·10¹⁴⁹+17)/9 = 4(1)₁₄₈3_<150> = 127 · 11282083 · C141

C141 = P31 · C111

P31 = 2109610728710016200472049234081_<31>

C111 = [136007819440940199626993346046725191626984715365734593965157745676287529081814105333269047742828239066669342653_<111>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=640405658
Step 1 took 3933ms
Step 2 took 2762ms
********** Factor found in step 2: 2109610728710016200472049234081
Found probable prime factor of 31 digits: 2109610728710016200472049234081
Composite cofactor has 111 digits

(37·10¹⁵²+17)/9 = 4(1)₁₅₁3_<153> = 7 · 19 · 44959 · 203910624271_<12> · 507610655507_<12> · C123

C123 = P32 · C92

P32 = 14460141021394288398859618298437_<32>

C92 = [45935433383661735240212241640772496532456843193944056659319372052651886889596389102266335611_<92>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2586452568
Step 1 took 9809ms
Step 2 took 5755ms
********** Factor found in step 2: 14460141021394288398859618298437
Found probable prime factor of 32 digits: 14460141021394288398859618298437
Composite cofactor has 92 digits

(37·10²⁰³+17)/9 = 4(1)₂₀₂3_<204> = 72317555052941212202437_<23> · 14037327305061710827375833007_<29> · C153

C153 = P34 · P119

P34 = 6140930812850915255314216030096973_<34>

P119 = 65947274112224700593650870901927012395470632038377646836641194000390957486841353488687312767513602066729431644202380359_<119>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1350806540
Step 1 took 6113ms
Step 2 took 4038ms
********** Factor found in step 2: 6140930812850915255314216030096973
Found probable prime factor of 34 digits: 6140930812850915255314216030096973

(37·10¹²⁵+17)/9 = 4(1)₁₂₄3_<126> = 223 · 8663 · C120

C120 = P54 · P67

P54 = 126466623195854517098346870112753670547872292270689591_<54>

P67 = 1682713250659195660607781542641572535401816555627858765330728147207_<67>

SNFS difficulty: 126 digits.
Divisors found:
 r1=126466623195854517098346870112753670547872292270689591 (pp54)
 r2=1682713250659195660607781542641572535401816555627858765330728147207 (pp67)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.725).
Factorization parameters were as follows:
n: 212807062617787990216166538436032583867119589114424114468113766195552090826514448650547279373859505122352270343650622337
m: 10000000000000000000000000
deg: 5
c5: 37
c0: 17
skew: 0.86
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [450000, 750001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 129306 x 129554
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,49,49,2.3,2.3,50000
total time: 1.50 hours.

(37·10¹⁴⁵+17)/9 = 4(1)₁₄₄3_<146> = 353 · 2131 · C140

C140 = P45 · P47 · P49

P45 = 527010246557101099424149801137279030430573559_<45>

P47 = 31339397888629582441406376485402492357432031637_<47>

P49 = 3308958741102845839413788208190473225543080012977_<49>

SNFS difficulty: 146 digits.
Divisors found:
 r1=527010246557101099424149801137279030430573559 (pp45)
 r2=31339397888629582441406376485402492357432031637 (pp47)
 r3=3308958741102845839413788208190473225543080012977 (pp49)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.315).
Factorization parameters were as follows:
n: 54651370781929657186721725707133348015350240694976372144521266546994935294992590308066822969587102985486220690802189068041990568355054299091
m: 100000000000000000000000000000
deg: 5
c5: 37
c0: 17
skew: 0.86
type: snfs
lss: 1
rlim: 1940000
alim: 1940000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1940000/1940000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [970000, 2270001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 299480 x 299728
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1940000,1940000,26,26,49,49,2.3,2.3,100000
total time: 8.00 hours.

(37·10¹⁶¹+17)/9 = 4(1)₁₆₀3_<162> = 45293 · C157

C157 = P54 · P104

P54 = 154488738576400451457982464398604103495508054393481467_<54>

P104 = 58753169523647679059266422943937672486812220399742768615027955753094899381427335186690263375374322360023_<104>

SNFS difficulty: 163 digits.
Divisors found:
 r1=154488738576400451457982464398604103495508054393481467 (pp54)
 r2=58753169523647679059266422943937672486812220399742768615027955753094899381427335186690263375374322360023 (pp104)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 9076703047073744532512995630916722476124591241717508469545208114081891486788490740536310491932773521539997595900274018305502199260616676111344161594752193741
m: 200000000000000000000000000000000
deg: 5
c5: 185
c0: 272
skew: 1.08
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1900000, 3500001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 728927 x 729175
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,52,52,2.4,2.4,200000
total time: 28.00 hours.

(37·10¹⁷²-1)/9 = 4(1)₁₇₂_<173> = 7² · 49675493159_<11> · 581693342027508474141681883_<27> · C134

C134 = P36 · C99

P36 = 284058421196271016127648080138696939_<36>

C99 = [102216071466417735574182221688508636681384173985648829721984676231139297698278652475301191705869033_<99>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2130306508
Step 1 took 9769ms
Step 2 took 5973ms
********** Factor found in step 2: 284058421196271016127648080138696939
Found probable prime factor of 36 digits: 284058421196271016127648080138696939
Composite cofactor has 99 digits

Dec 10, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve

(37·10¹⁰⁸+17)/9 = 4(1)₁₀₇3_<109> = 3 · 279294958181_<12> · C97

C97 = P48 · P50

P48 = 104182055552360290276887991646980292952367714049_<48>

P50 = 47095774354938298478289361041793337607914469549959_<50>

Number: n
N=4906534580127606927180094373743665249849469033907932112519677702181464751954187623632870631673991
  ( 97 digits)
SNFS difficulty: 111 digits.
Divisors found:

Wed Dec 10 07:21:09 2008  prp48 factor: 104182055552360290276887991646980292952367714049
Wed Dec 10 07:21:09 2008  prp50 factor: 47095774354938298478289361041793337607914469549959
Wed Dec 10 07:21:09 2008  elapsed time 00:06:28 (Msieve 1.39 - dependency 6)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.66 hours.
Scaled time: 1.20 units (timescale=1.827).
Factorization parameters were as follows:
name: KA_4_1_107_3
n: 4906534580127606927180094373743665249849469033907932112519677702181464751954187623632870631673991
type: snfs
skew: 2.15
deg: 5
c5: 37
c0: 1700
m: 10000000000000000000000
rlim: 460000
alim: 460000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 10000
Factor base limits: 460000/460000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 180001)
Primes: RFBsize:38458, AFBsize:38218, largePrimes:3390727 encountered
Relations: rels:2783996, finalFF:78182
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 0.62 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,460000,460000,28,28,56,56,2.5,2.5,50000
total time: 0.66 hours.
 --------- CPU info (if available) ----------

(37·10¹¹⁸+17)/9 = 4(1)₁₁₇3_<119> = 59 · 109 · 780433 · C109

C109 = P30 · P80

P30 = 369285778102739495137261341581_<30>

P80 = 22181070269155109783562069123105623896282019970639176229640191423908175990898051_<80>

Number: n
N=8191153793496486080155243826095227511849929831854706641774851002194663429312462621657955270889565525258158631
  ( 109 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=369285778102739495137261341581 (pp30)
 r2=22181070269155109783562069123105623896282019970639176229640191423908175990898051 (pp80)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.40 hours.
Scaled time: 2.56 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_4_1_117_3
n: 8191153793496486080155243826095227511849929831854706641774851002194663429312462621657955270889565525258158631
type: snfs
skew: 2.15
deg: 5
c5: 37
c0: 1700
m: 1000000000000000000000000
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 10000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [100000, 280001)
Primes: RFBsize:41538, AFBsize:41217, largePrimes:4239950 encountered
Relations: rels:3579601, finalFF:93820
Max relations in full relation-set: 48
Initial matrix: 82822 x 93820 with sparse part having weight 11495097.
Pruned matrix : 80528 x 81006 with weight 8340084.
Total sieving time: 1.29 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.04 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,500000,500000,28,28,56,56,2.5,2.5,50000
total time: 1.40 hours.
 --------- CPU info (if available) ----------

(35·10¹⁵⁷+1)/9 = 3(8)₁₅₆9_<158> = 3² · 13 · 19 · C155

C155 = P47 · P108

P47 = 48490980049404849877083686413436375909387700361_<47>

P108 = 360765592388035467312597513412831108601623865988953111824323565795743335616112041862817403331969655385010463_<108>

Number: n
N=17493877142999950017493877142999950017493877142999950017493877142999950017493877142999950017493877142999950017493877142999950017493877142999950017493877143
  ( 155 digits)
SNFS difficulty: 159 digits.
Divisors found:

Thu Dec 11 00:28:30 2008  prp47 factor: 48490980049404849877083686413436375909387700361
Thu Dec 11 00:28:30 2008  prp108 factor: 360765592388035467312597513412831108601623865988953111824323565795743335616112041862817403331969655385010463
Thu Dec 11 00:28:30 2008  elapsed time 01:44:59 (Msieve 1.39 - dependency 5)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.89 hours.
Scaled time: 36.05 units (timescale=1.813).
Factorization parameters were as follows:
name: KA_3_8_156_9
n: 17493877142999950017493877142999950017493877142999950017493877142999950017493877142999950017493877142999950017493877142999950017493877142999950017493877143
type: snfs
skew: 0.98
deg: 5
c5: 28
c0: 25
m: 50000000000000000000000000000000
rlim: 4000000
alim: 4000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 2650001)
Primes: RFBsize:283146, AFBsize:283487, largePrimes:14859643 encountered
Relations: rels:13076319, finalFF:601852
Max relations in full relation-set: 28

Msieve: found 1275837 hash collisions in 14147350 relations
Msieve: matrix is 569553 x 569801 (153.6 MB)

Initial matrix: 
Pruned matrix : 
Total sieving time: 19.53 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,56,56,2.5,2.5,100000
total time: 19.89 hours.
 --------- CPU info (if available) ----------

Dec 10, 2008 (3rd)

By Erik Branger / Msieve, GGNFS

(37·10¹⁰⁹+17)/9 = 4(1)₁₀₈3_<110> = 23 · 22115353963_<11> · 74107818511_<11> · C88

C88 = P29 · P59

P29 = 20288855357221307444588716847_<29>

P59 = 53754633920485650751518557177632083869545213561233239872861_<59>

Tue Dec 09 18:19:49 2008  Msieve v. 1.38
Tue Dec 09 18:19:49 2008  random seeds: 04da1f68 d6132000
Tue Dec 09 18:19:49 2008  factoring 1090619992393115507959322991878114317418422491212703526318350782022189627286829408789267 (88 digits)
Tue Dec 09 18:19:50 2008  searching for 15-digit factors
Tue Dec 09 18:19:52 2008  commencing quadratic sieve (88-digit input)
Tue Dec 09 18:19:52 2008  using multiplier of 3
Tue Dec 09 18:19:52 2008  using 64kb Pentium 4 sieve core
Tue Dec 09 18:19:52 2008  sieve interval: 12 blocks of size 65536
Tue Dec 09 18:19:52 2008  processing polynomials in batches of 9
Tue Dec 09 18:19:52 2008  using a sieve bound of 1501873 (57333 primes)
Tue Dec 09 18:19:52 2008  using large prime bound of 120149840 (26 bits)
Tue Dec 09 18:19:52 2008  using double large prime bound of 349543879472720 (42-49 bits)
Tue Dec 09 18:19:52 2008  using trial factoring cutoff of 49 bits
Tue Dec 09 18:19:52 2008  polynomial 'A' values have 11 factors
Tue Dec 09 19:32:43 2008  57703 relations (15932 full + 41771 combined from 603821 partial), need 57429
Tue Dec 09 19:32:44 2008  begin with 619753 relations
Tue Dec 09 19:32:45 2008  reduce to 138230 relations in 10 passes
Tue Dec 09 19:32:45 2008  attempting to read 138230 relations
Tue Dec 09 19:32:49 2008  recovered 138230 relations
Tue Dec 09 19:32:49 2008  recovered 115824 polynomials
Tue Dec 09 19:32:49 2008  attempting to build 57703 cycles
Tue Dec 09 19:32:49 2008  found 57703 cycles in 5 passes
Tue Dec 09 19:32:49 2008  distribution of cycle lengths:
Tue Dec 09 19:32:49 2008     length 1 : 15932
Tue Dec 09 19:32:49 2008     length 2 : 11388
Tue Dec 09 19:32:49 2008     length 3 : 10191
Tue Dec 09 19:32:49 2008     length 4 : 7570
Tue Dec 09 19:32:49 2008     length 5 : 5222
Tue Dec 09 19:32:49 2008     length 6 : 3299
Tue Dec 09 19:32:49 2008     length 7 : 1926
Tue Dec 09 19:32:49 2008     length 9+: 2175
Tue Dec 09 19:32:49 2008  largest cycle: 17 relations
Tue Dec 09 19:32:50 2008  matrix is 57333 x 57703 (13.6 MB) with weight 3330045 (57.71/col)
Tue Dec 09 19:32:50 2008  sparse part has weight 3330045 (57.71/col)
Tue Dec 09 19:32:50 2008  filtering completed in 3 passes
Tue Dec 09 19:32:50 2008  matrix is 52889 x 52953 (12.6 MB) with weight 3080639 (58.18/col)
Tue Dec 09 19:32:50 2008  sparse part has weight 3080639 (58.18/col)
Tue Dec 09 19:32:51 2008  saving the first 48 matrix rows for later
Tue Dec 09 19:32:51 2008  matrix is 52841 x 52953 (8.5 MB) with weight 2479242 (46.82/col)
Tue Dec 09 19:32:51 2008  sparse part has weight 1920939 (36.28/col)
Tue Dec 09 19:32:51 2008  matrix includes 64 packed rows
Tue Dec 09 19:32:51 2008  using block size 21181 for processor cache size 512 kB
Tue Dec 09 19:32:52 2008  commencing Lanczos iteration
Tue Dec 09 19:32:52 2008  memory use: 8.1 MB
Tue Dec 09 19:33:19 2008  lanczos halted after 837 iterations (dim = 52841)
Tue Dec 09 19:33:20 2008  recovered 18 nontrivial dependencies
Tue Dec 09 19:33:20 2008  prp29 factor: 20288855357221307444588716847
Tue Dec 09 19:33:20 2008  prp59 factor: 53754633920485650751518557177632083869545213561233239872861
Tue Dec 09 19:33:20 2008  elapsed time 01:13:31

(37·10¹¹⁵+17)/9 = 4(1)₁₁₄3_<116> = 269 · 322463 · C108

C108 = P46 · P62

P46 = 5497749320430187878858053736352893214180573673_<46>

P62 = 86206916448515400419165649243334368387994159291444142145800123_<62>

Number: 41113_115
N=473944016321207528193875966209651546329520519049447684665186406286999056081568726718516936228666551733961779
  ( 108 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=5497749320430187878858053736352893214180573673
 r2=86206916448515400419165649243334368387994159291444142145800123
Version: 
Total time: 1.75 hours.
Scaled time: 1.38 units (timescale=0.788).
Factorization parameters were as follows:
n: 473944016321207528193875966209651546329520519049447684665186406286999056081568726718516936228666551733961779
m: 100000000000000000000000
deg: 5
c5: 37
c0: 17
skew: 0.86
type: snfs
lss: 1
rlim: 610000
alim: 610000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 610000/610000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [305000, 505001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 63339 x 63557
Total sieving time: 1.75 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,610000,610000,25,25,45,45,2.2,2.2,50000
total time: 1.75 hours.
 --------- CPU info (if available) ----------

(37·10¹¹⁷+17)/9 = 4(1)₁₁₆3_<118> = 3 · C118

C118 = P39 · P80

P39 = 134559089698345633832840039614067963863_<39>

P80 = 10184153099151195348037371312804759219593045915950096947235927280552420123916917_<80>

Number: 41113_117
N=1370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370371
  ( 118 digits)
SNFS difficulty: 119 digits.
Divisors found:
 r1=134559089698345633832840039614067963863
 r2=10184153099151195348037371312804759219593045915950096947235927280552420123916917
Version: 
Total time: 2.12 hours.
Scaled time: 1.68 units (timescale=0.790).
Factorization parameters were as follows:
n: 1370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370371
m: 200000000000000000000000
deg: 5
c5: 925
c0: 136
skew: 0.68
type: snfs
lss: 1
rlim: 690000
alim: 690000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 690000/690000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [345000, 595001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 83361 x 83606
Total sieving time: 2.12 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,119,5,0,0,0,0,0,0,0,0,690000,690000,25,25,45,45,2.2,2.2,50000
total time: 2.12 hours.
 --------- CPU info (if available) ----------

(34·10¹⁶⁹-61)/9 = 3(7)₁₆₈1_<170> = C170

C170 = P56 · P115

P56 = 11317942006879836402511210783641114135063226371491831011_<56>

P115 = 3337866350155691145550968735711381661348565396657188332750832547393613263199497115692457216756403748695193991635161_<115>

Number: 37771_169
N=37777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777771
  ( 170 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=11317942006879836402511210783641114135063226371491831011
 r2=3337866350155691145550968735711381661348565396657188332750832547393613263199497115692457216756403748695193991635161
Version: 
Total time: 107.44 hours.
Scaled time: 231.85 units (timescale=2.158).
Factorization parameters were as follows:
n: 37777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777771
m: 10000000000000000000000000000000000
deg: 5
c5: 17
c0: -305
skew: 1.78
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 6000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 998386 x 998633
Total sieving time: 107.44 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 107.44 hours.
 --------- CPU info (if available) ----------

Dec 10, 2008 (2nd)

By Tyler Cadigan / ggnfs, msieve

(43·10¹⁸⁹-7)/9 = 4(7)₁₈₉_<190> = 409889 · 10279043 · 23144637364386847695553_<23> · C155

C155 = P53 · P103

P53 = 29909335929237981822985403260970890761599739765839699_<53>

P103 = 1638135600527218522474084632256993846436678807085787257035715605380077124636341859263839470084034319833_<103>

Number: 47777_189
N=48995547973812574793179189250193418592905049952135556886116149139211425752282423974271146284116043931349369118869012729947615449980688775331671793574450267
  ( 155 digits)
SNFS difficulty: 191 digits.
Divisors found:
 r1=29909335929237981822985403260970890761599739765839699
 r2=1638135600527218522474084632256993846436678807085787257035715605380077124636341859263839470084034319833
Version: 
Total time: 497.51 hours.
Scaled time: 1275.61 units (timescale=2.564).
Factorization parameters were as follows:
n: 48995547973812574793179189250193418592905049952135556886116149139211425752282423974271146284116043931349369118869012729947615449980688775331671793574450267
m: 100000000000000000000000000000000000000
deg: 5
c5: 43
c0: -70
Y0: 100000000000000000000000000000000000000
Y1: -1
skew: 1.10
type: snfs
lss: 1
rlim: 10900000
alim: 10900000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
qintsize: 1000000Factor base limits: 10900000/10900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5450000, 12450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1711650 x 1711898
Total sieving time: 497.51 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,10900000,10900000,28,28,54,54,2.5,2.5,100000
total time: 497.51 hours.
 --------- CPU info (if available) ----------

Dec 10, 2008

Factorizations of 411...113 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Dec 9, 2008 (6th)

By Wataru Sakai / Msieve

10¹⁹⁶+3 = 1(0)₁₉₅3_<197> = 7 · C196

C196 = P64 · P132

P64 = 2752508262761669324008667413574517577856587387092720436281875809_<64>

P132 = 519007135382076014806320192315848747738324564942772903565586965269516034842355760568492424090789108493561735010406846967181255450181_<132>

Number: 10003_196
N=1428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429
  ( 196 digits)
SNFS difficulty: 196 digits.
Divisors found:
 r1=2752508262761669324008667413574517577856587387092720436281875809
 r2=519007135382076014806320192315848747738324564942772903565586965269516034842355760568492424090789108493561735010406846967181255450181
Version: 
Total time: 642.69 hours.
Scaled time: 1295.02 units (timescale=2.015).
Factorization parameters were as follows:
n: 1428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429
m: 1000000000000000000000000000000000000000
deg: 5
c5: 10
c0: 3
skew: 0.79
type: snfs
lss: 1
rlim: 12900000
alim: 12900000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5Factor base limits: 12900000/12900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6450000, 13550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1916050 x 1916298
Total sieving time: 642.69 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,196,5,0,0,0,0,0,0,0,0,12900000,12900000,28,28,55,55,2.5,2.5,100000
total time: 642.69 hours.
 --------- CPU info (if available) ----------

Dec 9, 2008 (5th)

By Sinkiti Sibata / GGNFS

(35·10¹⁵¹-17)/9 = 3(8)₁₅₀7_<152> = 37 · 7607 · 549302680970858401_<18> · C129

C129 = P57 · P73

P57 = 118123717349038913397400950983195020461774566916898370759_<57>

P73 = 2129421183757089787810934958106849683297394566265161960072723588038834827_<73>

Number: 38887_151
N=251535146027178326982950809546578110289828500616900011712244631703787557941136548834954935449597346585500550412166434897007623693
  ( 129 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=118123717349038913397400950983195020461774566916898370759 (prp 57)
 r2=2129421183757089787810934958106849683297394566265161960072723588038834827 (prp  73)
Version: 
Total time: 18.97 hours.
Scaled time: 48.86 units (timescale=2.575).
Factorization parameters were as follows:
name: 38887_151
n: 251535146027178326982950809546578110289828500616900011712244631703787557941136548834954935449597346585500550412166434897007623693
m: 2000000000000000000000000000000
deg: 5
c5: 175
c0: -272
skew: 1.09
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 416757 x 417005
Total sieving time: 18.97 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 18.97 hours.
 --------- CPU info (if available) ----------

(35·10¹⁵²-17)/9 = 3(8)₁₅₁7_<153> = 3 · 32348688376499948062857708229_<29> · C124

C124 = P59 · P65

P59 = 42240598854390378377688655800680354702163772637296451470451_<59>

P65 = 94867517757021778096754297616255666172836797900280601682198483651_<65>

Number: 38887_152
N=4007260761886112998004137793495368715983783239142951653462846839189446808093663647938802239278248752261124422355781433096601
  ( 124 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=42240598854390378377688655800680354702163772637296451470451 (prp 59)
 r2=94867517757021778096754297616255666172836797900280601682198483651 (prp 65)
Version: 
Total time: 19.04 hours.
Scaled time: 48.82 units (timescale=2.564).
Factorization parameters were as follows:
name: 38887_152
n: 4007260761886112998004137793495368715983783239142951653462846839189446808093663647938802239278248752261124422355781433096601
m: 5000000000000000000000000000000
deg: 5
c5: 28
c0: -425
skew: 1.72
type: snfs
lss: 1
rlim: 2700000
alim: 2700000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2700000/2700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1350000, 2250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 521934 x 522182
Total sieving time: 19.04 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2700000,2700000,27,27,50,50,2.4,2.4,100000
total time: 19.04 hours.
 --------- CPU info (if available) ----------

(35·10¹⁵⁶-17)/9 = 3(8)₁₅₅7_<157> = 19 · 58096309927_<11> · 1859651820102671746966417186881408253_<37> · C109

C109 = P52 · P58

P52 = 1076928618506846748863383858027045833094779104071139_<52>

P58 = 1759157919925246744872768718883007727648687170851865993997_<58>

Number: 38887_156
N=1894487508440474112716213669780549012421849506804151246935164488038515303188473619404856596787335933634952583
  ( 109 digits)
Divisors found:
 r1=1076928618506846748863383858027045833094779104071139 (pp52)
 r2=1759157919925246744872768718883007727648687170851865993997 (pp58)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 25.17 hours.
Scaled time: 11.91 units (timescale=0.473).
Factorization parameters were as follows:
name: 38887_156
n: 1894487508440474112716213669780549012421849506804151246935164488038515303188473619404856596787335933634952583
skew: 44524.45
# norm 3.17e+15
c5: 10320
c4: 2068196878
c3: -65703351504663
c2: -745065446135219667
c1: 75575430184751883893503
c0: -677900066464869477272057091
# alpha -7.08
Y1: 258066449773
Y0: -712452811785165984766
# Murphy_E 1.22e-09
# M 409044238670812684725748569170621213081722672516267442206910112806419631766964042691786034651274577905956326
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2700001)
Primes: RFBsize:230209, AFBsize:230882, largePrimes:7115195 encountered
Relations: rels:6825408, finalFF:526305
Max relations in full relation-set: 28
Initial matrix: 461173 x 526305 with sparse part having weight 38038048.
Pruned matrix : 405124 x 407493 with weight 24200477.
Polynomial selection time: 1.37 hours.
Total sieving time: 17.86 hours.
Total relation processing time: 0.49 hours.
Matrix solve time: 5.16 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 25.17 hours.
 --------- CPU info (if available) ----------

Dec 9, 2008 (4th)

By Jo Yeong Uk / GGNFS

(35·10¹⁶⁹-17)/9 = 3(8)₁₆₈7_<170> = 37 · 9283 · 616717 · 7261187 · 2690791161620814877_<19> · 1203662182305387631696435974379_<31> · C103

C103 = P45 · P59

P45 = 111228175619580244012703383781260734185184707_<45>

P59 = 70184707899453055525548085720106885156447759916870224213803_<59>

Number: 38887_169
N=7806517016049305310583814338478114902043743974196109326508338472232780809105051328581261539459413910721
  ( 103 digits)
Divisors found:
 r1=111228175619580244012703383781260734185184707 (pp45)
 r2=70184707899453055525548085720106885156447759916870224213803 (pp59)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.67 hours.
Scaled time: 11.14 units (timescale=2.388).
Factorization parameters were as follows:
name: 38887_169
n: 7806517016049305310583814338478114902043743974196109326508338472232780809105051328581261539459413910721
skew: 6435.65
# norm 4.25e+14
c5: 327600
c4: 1341580360
c3: -28087535201805
c2: 27505657027816968
c1: -434236182625700756620
c0: -443139871734227666744928
# alpha -6.84
Y1: 24295412119
Y0: -29882876112108691223
# Murphy_E 2.39e-09
# M 5943626666779991075222796907480430371988929735998081121571940013048844424323463430802335138075319426611
type: gnfs
rlim: 1400000
alim: 1400000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved algebraic special-q in [700000, 1400001)
Primes: RFBsize:107126, AFBsize:107324, largePrimes:4895616 encountered
Relations: rels:4876186, finalFF:317090
Max relations in full relation-set: 28
Initial matrix: 214535 x 317090 with sparse part having weight 31970719.
Pruned matrix : 174914 x 176050 with weight 15170674.
Polynomial selection time: 0.35 hours.
Total sieving time: 4.07 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1400000,1400000,26,26,50,50,2.6,2.6,50000
total time: 4.67 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Dec 9, 2008 (3rd)

By Serge Batalov / GMP-ECM 6.2.1, GMP-ECM 6.2.1+Msieve-1.39/QS

(25·10¹⁹⁷-43)/9 = 2(7)₁₉₆3_<198> = 3² · 557 · 69708090293108587957264033909_<29> · 295129451897746307965079731115042417503_<39> · C127

C127 = P44 · P84

P44 = 10098350951856973961514524512537529605446767_<44>

P84 = 266718781518006085466517991346999437292650105384546657225926327572273641244537096069_<84>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=510398281
Step 1 took 36142ms
Step 2 took 18423ms
********** Factor found in step 2: 10098350951856973961514524512537529605446767
Found probable prime factor of 44 digits: 10098350951856973961514524512537529605446767
Probable prime cofactor 266718781518006085466517991346999437292650105384546657225926327572273641244537096069 has 84 digits

(22·10¹⁸¹+23)/9 = 2(4)₁₈₀7_<182> = 3² · 1858573 · 19707749 · 23468960719226551_<17> · 785195612198167577972729_<24> · C127

C127 = P38 · P39 · P51

P38 = 17785632801658181817419234383456954573_<38>

P39 = 828838352497750545369169782925386115193_<39>

P51 = 272966991471668803728822291820565994032634354475909_<51>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1242344107
Step 1 took 36137ms
Step 2 took 4961ms
********** Factor found in step 2: 828838352497750545369169782925386115193
Found probable prime factor of 39 digits: 828838352497750545369169782925386115193
Composite cofactor has 88 digits

Mon Dec  8 10:17:24 2008
Mon Dec  8 10:17:24 2008  Msieve v. 1.39
Mon Dec  8 10:17:24 2008  random seeds: dc424cf8 f5bcfa1e
Mon Dec  8 10:17:24 2008  factoring 4854890677288461848350056488138030029095188175960364440787486140231466977493816635881857 (88 digits)
Mon Dec  8 10:17:24 2008  searching for 15-digit factors
Mon Dec  8 10:17:25 2008  commencing quadratic sieve (88-digit input)
Mon Dec  8 10:17:25 2008  using multiplier of 1
Mon Dec  8 10:17:25 2008  using 64kb Opteron sieve core
Mon Dec  8 10:17:25 2008  sieve interval: 14 blocks of size 65536
Mon Dec  8 10:17:25 2008  processing polynomials in batches of 8
Mon Dec  8 10:17:25 2008  using a sieve bound of 1524851 (58000 primes)
Mon Dec  8 10:17:25 2008  using large prime bound of 121988080 (26 bits)
Mon Dec  8 10:17:25 2008  using double large prime bound of 359228912138960 (42-49 bits)
Mon Dec  8 10:17:25 2008  using trial factoring cutoff of 49 bits
Mon Dec  8 10:17:25 2008  polynomial 'A' values have 11 factors
Mon Dec  8 11:03:38 2008  58445 relations (15726 full + 42719 combined from 617079 partial), need 58096
Mon Dec  8 11:03:38 2008  begin with 632805 relations
Mon Dec  8 11:03:38 2008  reduce to 141869 relations in 9 passes
Mon Dec  8 11:03:38 2008  attempting to read 141869 relations
Mon Dec  8 11:03:39 2008  recovered 141869 relations
Mon Dec  8 11:03:39 2008  recovered 117476 polynomials
Mon Dec  8 11:03:40 2008  attempting to build 58445 cycles
Mon Dec  8 11:03:40 2008  found 58445 cycles in 5 passes
Mon Dec  8 11:03:40 2008  distribution of cycle lengths:
Mon Dec  8 11:03:40 2008     length 1 : 15726
Mon Dec  8 11:03:40 2008     length 2 : 11364
Mon Dec  8 11:03:40 2008     length 3 : 10248
Mon Dec  8 11:03:40 2008     length 4 : 7718
Mon Dec  8 11:03:40 2008     length 5 : 5531
Mon Dec  8 11:03:40 2008     length 6 : 3430
Mon Dec  8 11:03:40 2008     length 7 : 2045
Mon Dec  8 11:03:40 2008     length 9+: 2383
Mon Dec  8 11:03:40 2008  largest cycle: 18 relations
Mon Dec  8 11:03:40 2008  matrix is 58000 x 58445 (14.6 MB) with weight 3355288 (57.41/col)
Mon Dec  8 11:03:40 2008  sparse part has weight 3355288 (57.41/col)
Mon Dec  8 11:03:41 2008  filtering completed in 3 passes
Mon Dec  8 11:03:41 2008  matrix is 53938 x 54001 (13.5 MB) with weight 3108334 (57.56/col)
Mon Dec  8 11:03:41 2008  sparse part has weight 3108334 (57.56/col)
Mon Dec  8 11:03:41 2008  saving the first 48 matrix rows for later
Mon Dec  8 11:03:41 2008  matrix is 53890 x 54001 (9.1 MB) with weight 2445936 (45.29/col)
Mon Dec  8 11:03:41 2008  sparse part has weight 1852810 (34.31/col)
Mon Dec  8 11:03:41 2008  matrix includes 64 packed rows
Mon Dec  8 11:03:41 2008  using block size 21600 for processor cache size 1024 kB
Mon Dec  8 11:03:41 2008  commencing Lanczos iteration
Mon Dec  8 11:03:41 2008  memory use: 8.1 MB
Mon Dec  8 11:03:57 2008  lanczos halted after 854 iterations (dim = 53890)
Mon Dec  8 11:03:57 2008  recovered 17 nontrivial dependencies
Mon Dec  8 11:03:58 2008  prp38 factor: 17785632801658181817419234383456954573
Mon Dec  8 11:03:58 2008  prp51 factor: 272966991471668803728822291820565994032634354475909
Mon Dec  8 11:03:58 2008  elapsed time 00:46:34

(35·10¹³⁹+1)/9 = 3(8)₁₃₈9_<140> = 3² · 13 · 19 · C137

C137 = P37 · P100

P37 = 4711525053547959827836928818968407243_<37>

P100 = 3712996735489369150035175179729829418336017039152098603856719661184231606787193174795497182427779301_<100>

SNFS difficulty: 140 digits.
Divisors found:
 r1=4711525053547959827836928818968407243 (pp37)
 r2=3712996735489369150035175179729829418336017039152098603856719661184231606787193174795497182427779301 (pp100)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.314).
Factorization parameters were as follows:
n: 17493877142999950017493877142999950017493877142999950017493877142999950017493877142999950017493877142999950017493877142999950017493877143
m: 10000000000000000000000000000
deg: 5
c5: 7
c0: 2
skew: 0.78
type: snfs
lss: 1
rlim: 1560000
alim: 1560000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1560000/1560000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [780000, 1380001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 194565 x 194813
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1560000,1560000,26,26,49,49,2.3,2.3,100000
total time: 3.00 hours.

(35·10¹⁵⁵+1)/9 = 3(8)₁₅₄9_<156> = 17328426330280651_<17> · C140

C140 = P55 · P85

P55 = 8737120079789454811139398762185632204595767732620207073_<55>

P85 = 2568609627631786308344700400368235052270213245925487584490856911668202549658932772843_<85>

SNFS difficulty: 156 digits.
Divisors found:
 r1=8737120079789454811139398762185632204595767732620207073 (pp55)
 r2=2568609627631786308344700400368235052270213245925487584490856911668202549658932772843 (pp85)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.733).
Factorization parameters were as follows:
n: 22442250754722194601748660361573267317561028049968809187627893076057064731116896384383693819340329032336152489251152638084249145424730918539
m: 10000000000000000000000000000000
deg: 5
c5: 35
c0: 1
skew: 0.49
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1400000, 2300001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 485185 x 485433
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,52,52,2.4,2.4,100000
total time: 13.00 hours.

(35·10¹⁵⁹-17)/9 = 3(8)₁₅₈7_<160> = 13² · 65257 · 14268157 · C146

C146 = P36 · P44 · P66

P36 = 900723308910475183047680333245858277_<36>

P44 = 93911989316878837694411058288113772487947233_<44>

P66 = 292167163732202035035400549617558221929515408022408002322526037047_<66>

SNFS difficulty: 160 digits.
Divisors found:
 r1=900723308910475183047680333245858277 (pp36)
 r2=93911989316878837694411058288113772487947233 (pp44)
 r3=292167163732202035035400549617558221929515408022408002322526037047 (pp66)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 24714045752811968491542850976384650377766399465017040896140429801589203784478666528272728610806543632806391272680689057714714781765469735273001427
m: 100000000000000000000000000000000
deg: 5
c5: 7
c0: -34
skew: 1.37
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1700000, 2900001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 556589 x 556837
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,52,52,2.4,2.4,200000
total time: 20.00 hours.

(10¹⁸⁸+71)/9 = (1)₁₈₇9_<188> = 5051 · 11593 · 25889 · C175

C175 = P32 · C143

P32 = 77117398087105878766860647707673_<32>

C143 = [95042235417061342709137038769115156978823101279373950507224840278843986985720234251760664055691722544383397021632330291947586450809724093964989_<143>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=285739272
Step 1 took 5633ms
Step 2 took 3514ms
********** Factor found in step 2: 77117398087105878766860647707673
Found probable prime factor of 32 digits: 77117398087105878766860647707673
Composite cofactor has 143 digits

Dec 9, 2008 (2nd)

By Robert Backstrom / GGNFS

(35·10¹⁴²-17)/9 = 3(8)₁₄₁7_<143> = 37 · 24851 · 1638208606894922829008039249_<28> · C110

C110 = P51 · P60

P51 = 226680845566547999740279589713872828602549663480669_<51>

P60 = 113892706687805799382922156923032816068749972971507800267021_<60>

Number: n
N=25817295055854654959004012619776998646132580075897349544869694038625052469240774647237550816394496410471717049
  ( 110 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=226680845566547999740279589713872828602549663480669 (pp51)
 r2=113892706687805799382922156923032816068749972971507800267021 (pp60)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.50 hours.
Scaled time: 11.85 units (timescale=1.824).
Factorization parameters were as follows:
name: KA_3_8_141_7
n: 25817295055854654959004012619776998646132580075897349544869694038625052469240774647237550816394496410471717049
type: snfs
skew: 1.72
deg: 5
c5: 28
c0: -425
m: 50000000000000000000000000000
rlim: 1400000
alim: 1400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [100000, 1150001)
Primes: RFBsize:107126, AFBsize:106958, largePrimes:9584465 encountered
Relations: rels:8444842, finalFF:240314
Max relations in full relation-set: 48
Initial matrix: 214151 x 240314 with sparse part having weight 34092867.
Pruned matrix : 207603 x 208737 with weight 25906468.
Total sieving time: 5.70 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.46 hours.
Total square root time: 0.16 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1400000,1400000,28,28,56,56,2.5,2.5,100000
total time: 6.50 hours.
 --------- CPU info (if available) ----------

Dec 9, 2008

By Serge Batalov / PFGW

(28·10⁹⁶⁷⁴³+71)/9 = 3(1)₉₆₇₄₂9_<96744> is PRP.

It's the largest unprovable PRP in our tables so far. Congratulations!

Dec 8, 2008 (9th)

By Justin Card / msieve 1.39

(29·10¹⁰²+61)/9 = 3(2)₁₀₁9_<103> = 41232703 · C95

C95 = P35 · P61

P35 = 64818012805041651210696411371692207_<35>

P61 = 1205640894111136574747224703848636622066787269446361488487749_<61>

Sun Dec  7 16:27:13 2008
Sun Dec  7 16:27:13 2008
Sun Dec  7 16:27:13 2008  Msieve v. 1.39
Sun Dec  7 16:27:13 2008  random seeds: 246e521a 2bff3da1
Sun Dec  7 16:27:13 2008  factoring 78147246912777515997974283233922894218752096417792988789074105139850332446607301544655518272043 (95 digits)
Sun Dec  7 16:27:13 2008  searching for 15-digit factors
Sun Dec  7 16:27:14 2008  commencing quadratic sieve (95-digit input)
Sun Dec  7 16:27:14 2008  using multiplier of 3
Sun Dec  7 16:27:14 2008  using 64kb Opteron sieve core
Sun Dec  7 16:27:14 2008  sieve interval: 18 blocks of size 65536
Sun Dec  7 16:27:14 2008  processing polynomials in batches of 6
Sun Dec  7 16:27:14 2008  using a sieve bound of 2196599 (81146 primes)
Sun Dec  7 16:27:14 2008  using large prime bound of 329489850 (28 bits)
Sun Dec  7 16:27:14 2008  using double large prime bound of 2148402323041500 (43-51 bits)
Sun Dec  7 16:27:14 2008  using trial factoring cutoff of 51 bits
Sun Dec  7 16:27:14 2008  polynomial 'A' values have 12 factors
Sun Dec  7 16:27:26 2008
Sun Dec  7 16:27:26 2008
Sun Dec  7 16:27:26 2008  Msieve v. 1.39
Sun Dec  7 16:27:26 2008  random seeds: 666dd84d c9507886
Sun Dec  7 16:27:26 2008  factoring 78147246912777515997974283233922894218752096417792988789074105139850332446607301544655518272043 (95 digits)
Sun Dec  7 16:27:26 2008  searching for 15-digit factors
Sun Dec  7 16:27:27 2008  commencing quadratic sieve (95-digit input)
Sun Dec  7 16:27:27 2008  using multiplier of 3
Sun Dec  7 16:27:27 2008  using 64kb Opteron sieve core
Sun Dec  7 16:27:27 2008  sieve interval: 18 blocks of size 65536
Sun Dec  7 16:27:27 2008  processing polynomials in batches of 6
Sun Dec  7 16:27:27 2008  using a sieve bound of 2196599 (81146 primes)
Sun Dec  7 16:27:27 2008  using large prime bound of 329489850 (28 bits)
Sun Dec  7 16:27:27 2008  using double large prime bound of 2148402323041500 (43-51 bits)
Sun Dec  7 16:27:27 2008  using trial factoring cutoff of 51 bits
Sun Dec  7 16:27:27 2008  polynomial 'A' values have 12 factors
Sun Dec  7 17:49:22 2008  6019 relations (4845 full + 1174 combined from 298966 partial), need 81242
Sun Dec  7 17:49:22 2008  elapsed time 01:21:56
Sun Dec  7 17:49:42 2008  4760 relations (4760 full + 0 combined from 295056 partial), need 81242
Sun Dec  7 17:49:42 2008  elapsed time 01:22:29
Sun Dec  7 17:50:05 2008
Sun Dec  7 17:50:05 2008
Sun Dec  7 17:50:05 2008  Msieve v. 1.39
Sun Dec  7 17:50:05 2008  random seeds: 70f2f3d1 b7dd4591
Sun Dec  7 17:50:05 2008  factoring 78147246912777515997974283233922894218752096417792988789074105139850332446607301544655518272043 (95 digits)
Sun Dec  7 17:50:06 2008  searching for 15-digit factors
Sun Dec  7 17:50:06 2008  commencing quadratic sieve (95-digit input)
Sun Dec  7 17:50:07 2008  using multiplier of 3
Sun Dec  7 17:50:07 2008  using 64kb Opteron sieve core
Sun Dec  7 17:50:07 2008  sieve interval: 18 blocks of size 65536
Sun Dec  7 17:50:07 2008  processing polynomials in batches of 6
Sun Dec  7 17:50:07 2008  using a sieve bound of 2196599 (81146 primes)
Sun Dec  7 17:50:07 2008  using large prime bound of 329489850 (28 bits)
Sun Dec  7 17:50:07 2008  using double large prime bound of 2148402323041500 (43-51 bits)
Sun Dec  7 17:50:07 2008  using trial factoring cutoff of 51 bits
Sun Dec  7 17:50:07 2008  polynomial 'A' values have 12 factors
Sun Dec  7 17:50:07 2008  restarting with 9605 full and 594022 partial relations
Sun Dec  7 17:50:12 2008
Sun Dec  7 17:50:12 2008
Sun Dec  7 17:50:12 2008  Msieve v. 1.39
Sun Dec  7 17:50:12 2008  random seeds: a05eca4c 9a78ecf8
Sun Dec  7 17:50:12 2008  factoring 78147246912777515997974283233922894218752096417792988789074105139850332446607301544655518272043 (95 digits)
Sun Dec  7 17:50:13 2008  searching for 15-digit factors
Sun Dec  7 17:50:13 2008  commencing quadratic sieve (95-digit input)
Sun Dec  7 17:50:13 2008  using multiplier of 3
Sun Dec  7 17:50:13 2008  using 64kb Opteron sieve core
Sun Dec  7 17:50:13 2008  sieve interval: 18 blocks of size 65536
Sun Dec  7 17:50:13 2008  processing polynomials in batches of 6
Sun Dec  7 17:50:13 2008  using a sieve bound of 2196599 (81146 primes)
Sun Dec  7 17:50:13 2008  using large prime bound of 329489850 (28 bits)
Sun Dec  7 17:50:13 2008  using double large prime bound of 2148402323041500 (43-51 bits)
Sun Dec  7 17:50:13 2008  using trial factoring cutoff of 51 bits
Sun Dec  7 17:50:13 2008  polynomial 'A' values have 12 factors
Sun Dec  7 17:50:14 2008  restarting with 4760 full and 295056 partial relations
Sun Dec  7 17:53:50 2008  4992 relations (4992 full + 0 combined from 308433 partial), need 81242
Sun Dec  7 17:53:50 2008  elapsed time 00:03:38
Sun Dec  7 17:53:58 2008
Sun Dec  7 17:53:58 2008
Sun Dec  7 17:53:58 2008  Msieve v. 1.39
Sun Dec  7 17:53:58 2008  random seeds: 6485572e dc777515
Sun Dec  7 17:53:58 2008  factoring 78147246912777515997974283233922894218752096417792988789074105139850332446607301544655518272043 (95 digits)
Sun Dec  7 17:53:59 2008  searching for 15-digit factors
Sun Dec  7 17:54:00 2008  commencing quadratic sieve (95-digit input)
Sun Dec  7 17:54:00 2008  using multiplier of 3
Sun Dec  7 17:54:00 2008  using 64kb Opteron sieve core
Sun Dec  7 17:54:00 2008  sieve interval: 18 blocks of size 65536
Sun Dec  7 17:54:00 2008  processing polynomials in batches of 6
Sun Dec  7 17:54:00 2008  using a sieve bound of 2196599 (81146 primes)
Sun Dec  7 17:54:00 2008  using large prime bound of 329489850 (28 bits)
Sun Dec  7 17:54:00 2008  using double large prime bound of 2148402323041500 (43-51 bits)
Sun Dec  7 17:54:00 2008  using trial factoring cutoff of 51 bits
Sun Dec  7 17:54:00 2008  polynomial 'A' values have 12 factors
Sun Dec  7 18:45:27 2008  3104 relations (3104 full + 0 combined from 194276 partial), need 81242
Sun Dec  7 18:45:27 2008  elapsed time 00:51:29
Sun Dec  7 18:45:30 2008  28866 relations (12746 full + 16120 combined from 797473 partial), need 81242
Sun Dec  7 18:45:30 2008  elapsed time 00:55:25
Sun Dec  7 18:46:11 2008
Sun Dec  7 18:46:11 2008
Sun Dec  7 18:46:11 2008  Msieve v. 1.39
Sun Dec  7 18:46:11 2008  random seeds: edef846a 24c3dbe7
Sun Dec  7 18:46:11 2008  factoring 78147246912777515997974283233922894218752096417792988789074105139850332446607301544655518272043 (95 digits)
Sun Dec  7 18:46:11 2008  searching for 15-digit factors
Sun Dec  7 18:46:12 2008  commencing quadratic sieve (95-digit input)
Sun Dec  7 18:46:12 2008  using multiplier of 3
Sun Dec  7 18:46:12 2008  using 64kb Opteron sieve core
Sun Dec  7 18:46:12 2008  sieve interval: 18 blocks of size 65536
Sun Dec  7 18:46:12 2008  processing polynomials in batches of 6
Sun Dec  7 18:46:12 2008  using a sieve bound of 2196599 (81146 primes)
Sun Dec  7 18:46:12 2008  using large prime bound of 329489850 (28 bits)
Sun Dec  7 18:46:12 2008  using double large prime bound of 2148402323041500 (43-51 bits)
Sun Dec  7 18:46:12 2008  using trial factoring cutoff of 51 bits
Sun Dec  7 18:46:12 2008  polynomial 'A' values have 12 factors
Sun Dec  7 18:46:13 2008  restarting with 15850 full and 991749 partial relations
Sun Dec  7 18:49:30 2008
Sun Dec  7 18:49:30 2008
Sun Dec  7 18:49:30 2008  Msieve v. 1.39
Sun Dec  7 18:49:30 2008  random seeds: f2f6d37b b6eddc32
Sun Dec  7 18:49:30 2008  factoring 78147246912777515997974283233922894218752096417792988789074105139850332446607301544655518272043 (95 digits)
Sun Dec  7 18:49:30 2008  searching for 15-digit factors
Sun Dec  7 18:49:31 2008  commencing quadratic sieve (95-digit input)
Sun Dec  7 18:49:31 2008  using multiplier of 3
Sun Dec  7 18:49:31 2008  using 64kb Opteron sieve core
Sun Dec  7 18:49:31 2008  sieve interval: 18 blocks of size 65536
Sun Dec  7 18:49:31 2008  processing polynomials in batches of 6
Sun Dec  7 18:49:31 2008  using a sieve bound of 2196599 (81146 primes)
Sun Dec  7 18:49:31 2008  using large prime bound of 329489850 (28 bits)
Sun Dec  7 18:49:31 2008  using double large prime bound of 2148402323041500 (43-51 bits)
Sun Dec  7 18:49:31 2008  using trial factoring cutoff of 51 bits
Sun Dec  7 18:49:31 2008  polynomial 'A' values have 12 factors
Sun Dec  7 19:43:14 2008  79041 relations (19345 full + 59696 combined from 1210075 partial), need 81242
Sun Dec  7 19:43:14 2008  elapsed time 00:57:03
Sun Dec  7 19:43:18 2008  3309 relations (3309 full + 0 combined from 204475 partial), need 81242
Sun Dec  7 19:43:18 2008  elapsed time 00:53:48
Sun Dec  7 19:43:26 2008
Sun Dec  7 19:43:26 2008
Sun Dec  7 19:43:26 2008  Msieve v. 1.39
Sun Dec  7 19:43:26 2008  random seeds: 865ca451 35158040
Sun Dec  7 19:43:26 2008  factoring 78147246912777515997974283233922894218752096417792988789074105139850332446607301544655518272043 (95 digits)
Sun Dec  7 19:43:26 2008  searching for 15-digit factors
Sun Dec  7 19:43:27 2008  commencing quadratic sieve (95-digit input)
Sun Dec  7 19:43:27 2008  using multiplier of 3
Sun Dec  7 19:43:27 2008  using 64kb Opteron sieve core
Sun Dec  7 19:43:27 2008  sieve interval: 18 blocks of size 65536
Sun Dec  7 19:43:27 2008  processing polynomials in batches of 6
Sun Dec  7 19:43:27 2008  using a sieve bound of 2196599 (81146 primes)
Sun Dec  7 19:43:27 2008  using large prime bound of 329489850 (28 bits)
Sun Dec  7 19:43:27 2008  using double large prime bound of 2148402323041500 (43-51 bits)
Sun Dec  7 19:43:27 2008  using trial factoring cutoff of 51 bits
Sun Dec  7 19:43:27 2008  polynomial 'A' values have 12 factors
Sun Dec  7 19:43:28 2008  restarting with 22654 full and 1414550 partial relations
Sun Dec  7 19:43:28 2008  119699 relations (22654 full + 97045 combined from 1414550 partial), need 81242
Sun Dec  7 19:43:29 2008  begin with 1437204 relations
Sun Dec  7 19:43:31 2008  reduce to 316559 relations in 11 passes
Sun Dec  7 19:43:31 2008  attempting to read 316559 relations
Sun Dec  7 19:43:34 2008  recovered 316559 relations
Sun Dec  7 19:43:34 2008  recovered 292182 polynomials
Sun Dec  7 19:43:34 2008  attempting to build 119699 cycles
Sun Dec  7 19:43:34 2008  found 119699 cycles in 6 passes
Sun Dec  7 19:43:34 2008  distribution of cycle lengths:
Sun Dec  7 19:43:34 2008     length 1 : 22654
Sun Dec  7 19:43:34 2008     length 2 : 18504
Sun Dec  7 19:43:34 2008     length 3 : 20280
Sun Dec  7 19:43:34 2008     length 4 : 17688
Sun Dec  7 19:43:34 2008     length 5 : 14417
Sun Dec  7 19:43:34 2008     length 6 : 10278
Sun Dec  7 19:43:34 2008     length 7 : 6738
Sun Dec  7 19:43:34 2008     length 9+: 9140
Sun Dec  7 19:43:34 2008  largest cycle: 21 relations
Sun Dec  7 19:43:35 2008  matrix is 81146 x 119699 (37.0 MB) with weight 8736674 (72.99/col)
Sun Dec  7 19:43:35 2008  sparse part has weight 8736674 (72.99/col)
Sun Dec  7 19:43:38 2008  filtering completed in 4 passes
Sun Dec  7 19:43:38 2008  matrix is 74044 x 74108 (17.5 MB) with weight 4003119 (54.02/col)
Sun Dec  7 19:43:38 2008  sparse part has weight 4003119 (54.02/col)
Sun Dec  7 19:43:38 2008  saving the first 48 matrix rows for later
Sun Dec  7 19:43:38 2008  matrix is 73996 x 74108 (12.4 MB) with weight 3237909 (43.69/col)
Sun Dec  7 19:43:38 2008  sparse part has weight 2512684 (33.91/col)
Sun Dec  7 19:43:38 2008  matrix includes 64 packed rows
Sun Dec  7 19:43:38 2008  using block size 10922 for processor cache size 256 kB
Sun Dec  7 19:43:38 2008  commencing Lanczos iteration
Sun Dec  7 19:43:38 2008  memory use: 11.0 MB
Sun Dec  7 19:44:13 2008  lanczos halted after 1171 iterations (dim = 73996)
Sun Dec  7 19:44:13 2008  recovered 18 nontrivial dependencies
Sun Dec  7 19:44:15 2008  prp35 factor: 64818012805041651210696411371692207
Sun Dec  7 19:44:15 2008  prp61 factor: 1205640894111136574747224703848636622066787269446361488487749
Sun Dec  7 19:44:15 2008  elapsed time 00:00:49

Dec 8, 2008 (8th)

By Sinkiti Sibata /

(35·10¹³⁸-17)/9 = 3(8)₁₃₇7_<139> = 19 · 1049 · 309769 · 470663 · C124

C124 = P56 · P68

P56 = 38057395340621219550760269513883685643294306836546403397_<56>

P68 = 35164898775576928212777153301681488449949331239308314024794822219503_<68>

Number: 38887_138
N=1338284454815058216196354013354479303825956017779159462864869199752050231785163301790065223124319268085524058511255518851691
  ( 124 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=38057395340621219550760269513883685643294306836546403397 (prp56)
 r2=35164898775576928212777153301681488449949331239308314024794822219503 (prp68)
Version: 
Total time: 5.90 hours.
Scaled time: 15.19 units (timescale=2.575).
Factorization parameters were as follows:
name:38887_138
n: 1338284454815058216196354013354479303825956017779159462864869199752050231785163301790065223124319268085524058511255518851691
m: 5000000000000000000000000000
deg: 5
c5: 56
c0: -85
skew: 1.09
type: snfs
lss: 1
rlim: 1520000
alim: 1520000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1520000/1520000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [760000, 1585001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 251726 x 251974
Total sieving time: 5.90 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1520000,1520000,26,26,48,48,2.3,2.3,75000
total time: 5.90 hours.
 --------- CPU info (if available) ----------

(35·10¹⁴¹-17)/9 = 3(8)₁₄₀7_<142> = 13 · 2879 · 24457822001458490363244626531_<29> · C109

C109 = P53 · P56

P53 = 73820734517195491206986826554621892806273334976028047_<53>

P56 = 57549873803153056003497272592233619822725268242612595233_<56>

Number: 38887_141
N=4248373955520665359043123124769657924122696491420890193547031337963357606208311364487248645291710324866499951
  ( 109 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=73820734517195491206986826554621892806273334976028047 (prp 53)
 r2=57549873803153056003497272592233619822725268242612595233 (prp 56)
Version: 
Total time: 8.16 hours.
Scaled time: 20.91 units (timescale=2.564).
Factorization parameters were as follows:
name: 38887_141
n: 4248373955520665359043123124769657924122696491420890193547031337963357606208311364487248645291710324866499951
m: 20000000000000000000000000000
deg: 5
c5: 175
c0: -272
skew: 1.09
type: snfs
lss: 1
rlim: 1740000
alim: 1740000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1740000/1740000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [870000, 1970001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 264690 x 264938
Total sieving time: 8.16 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1740000,1740000,26,26,48,48,2.3,2.3,100000
total time: 8.16 hours.
 --------- CPU info (if available) ----------

Dec 8, 2008 (7th)

By Serge Batalov / Msieve-1.39

(35·10¹⁵⁰+1)/9 = 3(8)₁₄₉9_<151> = 449 · 2251 · 670051 · C139

C139 = P49 · P91

P49 = 2672290540824465915914614009423625553247516207069_<49>

P91 = 2148880004904170262568464197161540753125392466048489311759094604779127603367722353590597069_<91>

SNFS difficulty: 151 digits.
Divisors found:
 r1=2672290540824465915914614009423625553247516207069 (pp49)
 r2=2148880004904170262568464197161540753125392466048489311759094604779127603367722353590597069 (pp91)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 5742431710472246120644939956303442596465371964729863375287394745063218499520351618003208616411038581580501974256356707777534416781948480761
m: 1000000000000000000000000000000
deg: 5
c5: 35
c0: 1
skew: 0.49
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1150000, 1750001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 419644 x 419892
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,51,51,2.4,2.4,100000
total time: 9.00 hours.

(31·10¹⁶⁹+41)/9 = 3(4)₁₆₈9_<170> = 3² · 13 · 211 · 353 · C163

C163 = P48 · P52 · P64

P48 = 272869429905872532325536091824056889627588294853_<48>

P52 = 1797604110257900740437824679232652384721954009407117_<52>

P64 = 8057999312340717756148290734205967665222488391182536291058446159_<64>

SNFS difficulty: 171 digits.
Divisors found:
 r1=272869429905872532325536091824056889627588294853 (pp48)
 r2=1797604110257900740437824679232652384721954009407117 (pp52)
 r3=8057999312340717756148290734205967665222488391182536291058446159 (pp64)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.732).
Factorization parameters were as follows:
n: 3952538982903853634982438423044556882703394882907881399707274962926140599793200610389320117266986574971842303537679216245690027179315562794566952115206974257585359
m: 10000000000000000000000000000000000
deg: 5
c5: 31
c0: 410
skew: 1.68
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 5800001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 977723 x 977971
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 49.00 hours.

Dec 8, 2008 (6th)

By Justin Card / GGNFS, msieve

(29·10¹¹⁴+61)/9 = 3(2)₁₁₃9_<115> = 19 · 529043 · 131498189 · C100

C100 = P35 · P66

P35 = 13627837353418736230548561825683197_<35>

P66 = 178880994899876454053601851276075491188480810887295136045474447189_<66>

Number: 32229_114
N=2437761104113242789158014351988528630173349071448713576584407698125610142992752078271723965821183233
  ( 100 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=13627837353418736230548561825683197
 r2=178880994899876454053601851276075491188480810887295136045474447189
Version:
Total time: 0.38 hours.
Scaled time: 0.00 units (timescale=2.093).
Factorization parameters were as follows:
n: 2437761104113242789158014351988528630173349071448713576584407698125610142992752078271723965821183233
m: 50000000000000000000000
deg: 5
c5: 464
c0: 305
skew: 0.92
type: snfs
lss: 1
rlim: 600000
alim: 600000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2

Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [300000, 450001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 60867 x 61101
Total sieving time: 0.00 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.2,2.2,50000
total time: 0.00 hours.
 --------- CPU info (if available) ----------
[   26.316871] Memory: 3054544k/3111872k available (2523k kernel code, 56940k reserved, 1328k data, 328k init)
[   26.463157] Calibrating delay using timer specific routine.. 3982.78 BogoMIPS (lpj=19913938)
[   27.245296] Calibrating delay using timer specific routine.. 3979.63 BogoMIPS (lpj=19898169)

Dec 8, 2008 (5th)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39

(35·10¹⁸¹-17)/9 = 3(8)₁₈₀7_<182> = 37 · 5783 · 8291 · 6221154558239353306655743_<25> · 1259634470484335012059329643_<28> · C121

C121 = P36 · P86

P36 = 100287270379262073062534543329774973_<36>

P86 = 27893458439383066549646630630840407002770488829451805100233906262131129518370132230671_<86>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=730062768
Step 1 took 9937ms
Step 2 took 5714ms
********** Factor found in step 2: 100287270379262073062534543329774973
Found probable prime factor of 36 digits: 100287270379262073062534543329774973
Probable prime cofactor 27893458439383066549646630630840407002770488829451805100233906262131129518370132230671 has 86 digits

(35·10¹⁵⁹+1)/9 = 3(8)₁₅₈9_<160> = 7829 · 1982316236372128463169333701_<28> · C129

C129 = P41 · P89

P41 = 20276996658433163995117586251763240946991_<41>

P89 = 12357843020120421119265960598992168176546184213774282216299622263920595989161202430965951_<89>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=758478317
Step 1 took 9850ms
Step 2 took 6023ms
********** Factor found in step 2: 20276996658433163995117586251763240946991
Found probable prime factor of 41 digits: 20276996658433163995117586251763240946991
Probable prime cofactor 12357843020120421119265960598992168176546184213774282216299622263920595989161202430965951 has 89 digits

(35·10¹⁸⁷-17)/9 = 3(8)₁₈₆7_<188> = 37 · 293 · 44819 · 22323411871_<11> · 23575219891_<11> · C159

C159 = P31 · P128

P31 = 5405268658708132199635096286107_<31>

P128 = 28135874568677300735640012694914520710640214152856963017290900531616339376629182034845122781934860626430793955513760673461885739_<128>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3147506786
Step 1 took 10865ms
Step 2 took 5612ms
********** Factor found in step 2: 5405268658708132199635096286107
Found probable prime factor of 31 digits: 5405268658708132199635096286107
Probable prime cofactor 28135874568677300735640012694914520710640214152856963017290900531616339376629182034845122781934860626430793955513760673461885739 has 128 digits

(35·10¹⁶⁴+1)/9 = 3(8)₁₆₃9_<165> = 282833 · 347981 · C154

C154 = P31 · C124

P31 = 1195263561592703068137949500679_<31>

C124 = [3305797470684590126516118944166244859718767479459168848484632525243758609790874378955530593175883268566507494694347289345867_<124>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1440214857
Step 1 took 9229ms
Step 2 took 5176ms
********** Factor found in step 2: 1195263561592703068137949500679
Found probable prime factor of 31 digits: 1195263561592703068137949500679
Composite cofactor has 124 digits

(34·10¹⁶⁵+11)/9 = 3(7)₁₆₄9_<166> = 23 · 541 · 11059 · C158

C158 = P45 · P51 · P63

P45 = 132305034338835795699004205791407388620792643_<45>

P51 = 547267159590746377431429613203845746240770116543947_<51>

P63 = 379157534695536082042970312038325842573501978968316577268679027_<63>

SNFS difficulty: 166 digits.
Divisors found:
 r1=132305034338835795699004205791407388620792643 (pp45)
 r2=547267159590746377431429613203845746240770116543947 (pp51)
 r3=379157534695536082042970312038325842573501978968316577268679027 (pp63)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.726).
Factorization parameters were as follows:
n: 27453356418408572643857693062662714781848689852313239957734007486674021695384722507363682581215084634583871749164999906783743184612421503819077187673614470867
m: 1000000000000000000000000000000000
deg: 5
c5: 34
c0: 11
skew: 0.80
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2100000, 4000001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 732615 x 732863
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,52,52,2.4,2.4,100000
total time: 27.00 hours.

(35·10¹⁹⁶+1)/9 = 3(8)₁₉₅9_<197> = 3 · 332179 · C191

C191 = P35 · C157

P35 = 11088048895176551020181292564409681_<35>

C157 = [3519467624159191575455544285483961051122934211187407132902172790668680150206026331946662339397093151348832771154819848849822738248941373366285643225728428337_<157>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2788871739
Step 1 took 16422ms
Step 2 took 8551ms
********** Factor found in step 2: 11088048895176551020181292564409681
Found probable prime factor of 35 digits: 11088048895176551020181292564409681
Composite cofactor has 157 digits

(35·10¹⁷⁶-17)/9 = 3(8)₁₇₅7_<177> = 3 · 379 · 577 · 16633 · 8626865492539519_<16> · 72485366745861100910529372318687451_<35> · C116

C116 = P35 · P82

P35 = 16287071657624667201329691914058751_<35>

P82 = 3499228437398053869070314749177548455789874474953667584190158156018462102243163469_<82>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1452233116
Step 1 took 10696ms
Step 2 took 5610ms
********** Factor found in step 2: 16287071657624667201329691914058751
Found probable prime factor of 35 digits: 16287071657624667201329691914058751
Probable prime cofactor 3499228437398053869070314749177548455789874474953667584190158156018462102243163469 has 82 digits

(35·10¹⁵⁸+1)/9 = 3(8)₁₅₇9_<159> = 6479735363_<10> · C149

C149 = P43 · P107

P43 = 1930617658092374610982383853322441180442017_<43>

P107 = 31086511703887452946743635557423166013615764652218926546381262043929479546241125975302646673487898198639859_<107>

SNFS difficulty: 160 digits.
Divisors found:
 r1=1930617658092374610982383853322441180442017 (pp43)
 r2=31086511703887452946743635557423166013615764652218926546381262043929479546241125975302646673487898198639859 (pp107)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.698).
Factorization parameters were as follows:
n: 60016168424020388329073322510144754022555425291507987297549899784215753764400901026255212035406836859255372168644055917579436629361137829061814555603
m: 100000000000000000000000000000000
deg: 5
c5: 7
c0: 20
skew: 1.23
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1700000, 2600001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 555526 x 555774
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,52,52,2.4,2.4,100000
total time: 14.00 hours.

Dec 8, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve

(35·10¹⁴⁹-71)/9 = 3(8)₁₄₈1_<150> = 3² · 2203 · 669283 · 3873391 · 825404825109791_<15> · C118

C118 = P53 · P66

P53 = 21904388228641440264076699571380925440070866529091293_<53>

P66 = 418474754978414314848577390358111307476223571900094192394791077277_<66>

Number: n
N=9166433496932789469618650418665606801499463302417877899339615168342547900124545005831172681724367567313089423350849161
  ( 118 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=21904388228641440264076699571380925440070866529091293 (pp53)
 r2=418474754978414314848577390358111307476223571900094192394791077277 (pp66)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 10.17 hours.
Scaled time: 18.59 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_3_8_148_1
n: 9166433496932789469618650418665606801499463302417877899339615168342547900124545005831172681724367567313089423350849161
type: snfs
skew: 1.83
deg: 5
c5: 7
c0: -142
m: 1000000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [100000, 650001)
Primes: RFBsize:148933, AFBsize:148781, largePrimes:9739262 encountered
Relations: rels:8588387, finalFF:411950
Max relations in full relation-set: 48
Initial matrix: 297779 x 411950 with sparse part having weight 46016329.
Pruned matrix : 243037 x 244589 with weight 20701272.
Total sieving time: 9.51 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.46 hours.
Total square root time: 0.04 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,56,56,2.5,2.5,100000
total time: 10.17 hours.
 --------- CPU info (if available) ----------

(35·10¹⁸⁴+1)/9 = 3(8)₁₈₃9_<185> = 3² · 17 · 227 · 1237 · 3028427 · 6880873 · 106942088993_<12> · 938679944328740548919086924469_<30> · 8184269571777502631981099728373_<31> · C92

C92 = P44 · P48

P44 = 73116907767253706535802059911323219242216637_<44>

P48 = 723125958039174656868976766045499019103903811041_<48>

Mon Dec 08 04:06:31 2008  
Mon Dec 08 04:06:31 2008  
Mon Dec 08 04:06:31 2008  Msieve v. 1.39
Mon Dec 08 04:06:31 2008  random seeds: 65016500 55b5b456
Mon Dec 08 04:06:31 2008  factoring 52872733978057307340855511944849149533604403870713397705309533293503411357398195660834489117 (92 digits)
Mon Dec 08 04:06:31 2008  searching for 15-digit factors
Mon Dec 08 04:06:32 2008  commencing quadratic sieve (92-digit input)
Mon Dec 08 04:06:32 2008  using multiplier of 17
Mon Dec 08 04:06:32 2008  using 64kb Opteron sieve core
Mon Dec 08 04:06:32 2008  sieve interval: 18 blocks of size 65536
Mon Dec 08 04:06:32 2008  processing polynomials in batches of 6
Mon Dec 08 04:06:32 2008  using a sieve bound of 1821649 (68071 primes)
Mon Dec 08 04:06:32 2008  using large prime bound of 198559741 (27 bits)
Mon Dec 08 04:06:32 2008  using double large prime bound of 863384216847394 (42-50 bits)
Mon Dec 08 04:06:32 2008  using trial factoring cutoff of 50 bits
Mon Dec 08 04:06:32 2008  polynomial 'A' values have 12 factors
Mon Dec 08 05:39:54 2008  68410 relations (17341 full + 51069 combined from 862287 partial), need 68167
Mon Dec 08 05:39:56 2008  begin with 879628 relations
Mon Dec 08 05:39:56 2008  reduce to 173079 relations in 9 passes
Mon Dec 08 05:39:56 2008  attempting to read 173079 relations
Mon Dec 08 05:39:58 2008  recovered 173079 relations
Mon Dec 08 05:39:58 2008  recovered 155795 polynomials
Mon Dec 08 05:39:59 2008  attempting to build 68410 cycles
Mon Dec 08 05:39:59 2008  found 68410 cycles in 6 passes
Mon Dec 08 05:39:59 2008  distribution of cycle lengths:
Mon Dec 08 05:39:59 2008     length 1 : 17341
Mon Dec 08 05:39:59 2008     length 2 : 12441
Mon Dec 08 05:39:59 2008     length 3 : 11719
Mon Dec 08 05:39:59 2008     length 4 : 9251
Mon Dec 08 05:39:59 2008     length 5 : 6736
Mon Dec 08 05:39:59 2008     length 6 : 4614
Mon Dec 08 05:39:59 2008     length 7 : 2755
Mon Dec 08 05:39:59 2008     length 9+: 3553
Mon Dec 08 05:39:59 2008  largest cycle: 20 relations
Mon Dec 08 05:39:59 2008  matrix is 68071 x 68410 (16.5 MB) with weight 4054670 (59.27/col)
Mon Dec 08 05:39:59 2008  sparse part has weight 4054670 (59.27/col)
Mon Dec 08 05:40:00 2008  filtering completed in 3 passes
Mon Dec 08 05:40:00 2008  matrix is 64574 x 64638 (15.6 MB) with weight 3842697 (59.45/col)
Mon Dec 08 05:40:00 2008  sparse part has weight 3842697 (59.45/col)
Mon Dec 08 05:40:00 2008  saving the first 48 matrix rows for later
Mon Dec 08 05:40:00 2008  matrix is 64526 x 64638 (8.6 MB) with weight 2872762 (44.44/col)
Mon Dec 08 05:40:00 2008  sparse part has weight 1861575 (28.80/col)
Mon Dec 08 05:40:00 2008  matrix includes 64 packed rows
Mon Dec 08 05:40:00 2008  using block size 25855 for processor cache size 1024 kB
Mon Dec 08 05:40:01 2008  commencing Lanczos iteration
Mon Dec 08 05:40:01 2008  memory use: 9.2 MB
Mon Dec 08 05:40:22 2008  lanczos halted after 1022 iterations (dim = 64525)
Mon Dec 08 05:40:22 2008  recovered 17 nontrivial dependencies
Mon Dec 08 05:40:23 2008  prp44 factor: 73116907767253706535802059911323219242216637
Mon Dec 08 05:40:23 2008  prp48 factor: 723125958039174656868976766045499019103903811041
Mon Dec 08 05:40:23 2008  elapsed time 01:33:52

(35·10¹⁸⁷+1)/9 = 3(8)₁₈₆9_<188> = 3 · 13 · 229 · 6803 · 165946619 · 555455585147537219_<18> · 4965159428650814398623665321_<28> · 38675511208479660394046433269_<29> · C98

C98 = P38 · P61

P38 = 29605251527267858956304593927958498437_<38>

P61 = 1221431769936255690871056105778224165151337790826816109487361_<61>

Number: n
N=36160794772358817923915172072137409410750681709608392276080587830286144849317269422486703389754757
  ( 98 digits)
Divisors found:
 r1=29605251527267858956304593927958498437 (pp38)
 r2=1221431769936255690871056105778224165151337790826816109487361 (pp61)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.53 hours.
Scaled time: 6.43 units (timescale=1.822).
Factorization parameters were as follows:
name: KA_3_8_186_9
n: 36160794772358817923915172072137409410750681709608392276080587830286144849317269422486703389754757
type: gnfs
deg: 5
Y0: -7718508806807778569
Y1:  8556960283
c0: -1881440187227872704236700
c1: -245159569682553927924
c2:  9366265390438051
c3:  211495474264
c4: -8181476
c5:  1320
skew: 17788.81
rlim: 1800000
alim: 1800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [100000, 650001)
Primes: RFBsize:135072, AFBsize:135391, largePrimes:6590723 encountered
Relations: rels:5511512, finalFF:306759
Max relations in full relation-set: 48
Initial matrix: 270544 x 306759 with sparse part having weight 15239130.
Pruned matrix : 219444 x 220860 with weight 8001157.
Total sieving time: 3.19 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.16 hours.
Total square root time: 0.04 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,97,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,28,28,56,56,2.5,2.5,100000
total time: 3.53 hours.
 --------- CPU info (if available) ----------

Dec 8, 2008 (3rd)

By Erik Branger / GGNFS, Msieve

(35·10¹²⁶+1)/9 = 3(8)₁₂₅9_<127> = 191 · 67114366454671786121_<20> · C105

C105 = P35 · P71

P35 = 11448376571066039089838683423737211_<35>

P71 = 26499200218749713130300387657045233622273874435357161710361980927082109_<71>

Number: 38889_126
N=303372822936322273777801299985029471666532868396285446603379082502561345006703126181202303899414235657999
  ( 105 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=11448376571066039089838683423737211
 r2=26499200218749713130300387657045233622273874435357161710361980927082109
Version: 
Total time: 3.51 hours.
Scaled time: 2.74 units (timescale=0.781).
Factorization parameters were as follows:
n: 303372822936322273777801299985029471666532868396285446603379082502561345006703126181202303899414235657999
m: 50000000000000000000000000
deg: 5
c5: 14
c0: 125
skew: 1.55
type: snfs
lss: 1
rlim: 1010000
alim: 1010000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1010000/1010000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [505000, 855001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 146499 x 146741
Total sieving time: 3.51 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,1010000,1010000,26,26,47,47,2.3,2.3,50000
total time: 3.51 hours.
 --------- CPU info (if available) ----------

(35·10¹³³+1)/9 = 3(8)₁₃₂9_<134> = 3 · 13 · C132

C132 = P40 · P93

P40 = 2447766620080220042610121031721960294871_<40>

P93 = 407371760432911602911335890107629294263445550349909740419175681492591667237407264967405890681_<93>

Number: 38889_133
N=997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997151
  ( 132 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=2447766620080220042610121031721960294871
 r2=407371760432911602911335890107629294263445550349909740419175681492591667237407264967405890681
Version: 
Total time: 3.86 hours.
Scaled time: 8.25 units (timescale=2.137).
Factorization parameters were as follows:
n: 997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997151
m: 1000000000000000000000000000
deg: 5
c5: 7
c0: 20
skew: 1.23
type: snfs
lss: 1
rlim: 1290000
alim: 1290000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1290000/1290000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [645000, 1020001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 153527 x 153775
Total sieving time: 3.86 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1290000,1290000,26,26,47,47,2.3,2.3,75000
total time: 3.86 hours.
 --------- CPU info (if available) ----------

(35·10¹³⁹+1)/9 = 3(8)₁₃₈9_<140> = 3² · 13 · 19 · C137

C137 = P37 · P100

P37 = 4711525053547959827836928818968407243_<37>

P100 = 3712996735489369150035175179729829418336017039152098603856719661184231606787193174795497182427779301_<100>

Number: 38889_139
N=17493877142999950017493877142999950017493877142999950017493877142999950017493877142999950017493877142999950017493877142999950017493877143
  ( 137 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=4711525053547959827836928818968407243
 r2=3712996735489369150035175179729829418336017039152098603856719661184231606787193174795497182427779301
Version: 
Total time: 6.83 hours.
Scaled time: 5.38 units (timescale=0.788).
Factorization parameters were as follows:
n: 17493877142999950017493877142999950017493877142999950017493877142999950017493877142999950017493877142999950017493877142999950017493877143
m: 10000000000000000000000000000
deg: 5
c5: 7
c0: 2
skew: 0.78
type: snfs
lss: 1
rlim: 1560000
alim: 1560000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3

Factor base limits: 1560000/1560000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [780000, 1380001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 194234 x 194482
Total sieving time: 6.83 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1560000,1560000,26,26,48,48,2.3,2.3,100000
total time: 6.83 hours.
 --------- CPU info (if available) ----------

Dec 8, 2008 (2nd)

By Jo Yeong Uk / GGNFS

(35·10¹³⁰-17)/9 = 3(8)₁₂₉7_<131> = 37 · 1613 · 86467 · C121

C121 = P45 · P77

P45 = 127277577316998781516401903357718924380855137_<45>

P77 = 59208921733784673577031498471236697681202219803320125271724133270956593801213_<77>

Number: 38887_130
N=7535968113827908337130239897584722312102906490692631968995615240726178304140148339589240934436247096730415908026327881181
  ( 121 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=127277577316998781516401903357718924380855137 (pp45)
 r2=59208921733784673577031498471236697681202219803320125271724133270956593801213 (pp77)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.96 hours.
Scaled time: 4.69 units (timescale=2.390).
Factorization parameters were as follows:
n: 7535968113827908337130239897584722312102906490692631968995615240726178304140148339589240934436247096730415908026327881181
m: 100000000000000000000000000
deg: 5
c5: 35
c0: -17
skew: 0.87
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 950001)
Primes: RFBsize:85714, AFBsize:85279, largePrimes:2780587 encountered
Relations: rels:2677317, finalFF:215170
Max relations in full relation-set: 28
Initial matrix: 171059 x 215170 with sparse part having weight 16356712.
Pruned matrix : 154672 x 155591 with weight 9196114.
Total sieving time: 1.85 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 1.96 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(35·10¹⁵³+1)/9 = 3(8)₁₅₂9_<154> = 337 · 171847463083151491501_<21> · 38559715265314947042590710270001_<32> · C100

C100 = P47 · P54

P47 = 17390443877201234143891250701031139775259666719_<47>

P54 = 100140100604561495228549337527256127066996322341408163_<54>

Number: 38889_153
N=1741480799420912060381633191641537647280854501099135630013427896115275142592545214586443180526027197
  ( 100 digits)
Divisors found:
 r1=17390443877201234143891250701031139775259666719 (pp47)
 r2=100140100604561495228549337527256127066996322341408163 (pp54)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.09 hours.
Scaled time: 7.37 units (timescale=2.384).
Factorization parameters were as follows:
name: 38889_153
n: 1741480799420912060381633191641537647280854501099135630013427896115275142592545214586443180526027197
skew: 4056.81
# norm 1.30e+14
c5: 257760
c4: 2090628702
c3: -3214280028439
c2: 537488420607485
c1: -74787744966472671293
c0: -1601189094816443285975
# alpha -6.48
Y1: 47075126663
Y0: -5833577188547807742
# Murphy_E 3.59e-09
# M 697301709306757961896643942013299387594224137239616960663069866613643106139141792408406178409303908
type: gnfs
rlim: 1200000
alim: 1200000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [600000, 1100001)
Primes: RFBsize:92938, AFBsize:92632, largePrimes:4255351 encountered
Relations: rels:4164335, finalFF:279051
Max relations in full relation-set: 28
Initial matrix: 185648 x 279051 with sparse part having weight 25553704.
Pruned matrix : 147853 x 148845 with weight 10911122.
Polynomial selection time: 0.25 hours.
Total sieving time: 2.67 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,26,26,49,49,2.5,2.5,50000
total time: 3.09 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Dec 8, 2008

By Sinkiti Sibata / Msieve

(35·10¹²⁷-17)/9 = 3(8)₁₂₆7_<128> = 37 · 1649510569739_<13> · C114

C114 = P48 · P67

P48 = 390752729727494409677256101481138223351378730947_<48>

P67 = 1630672275638178028977091023427467641772116201128430345768992206347_<67>

Number: 38887_127
N=637189642996563245953103567105248123427011935586142479971519211497758129098842890558651615968037793670342418720609
  ( 114 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=390752729727494409677256101481138223351378730947 (pp48)
 r2=1630672275638178028977091023427467641772116201128430345768992206347 (pp67)
Version: 
Total time: 2.68 hours.
Scaled time: 6.87 units (timescale=2.564).
Factorization parameters were as follows:
name: 38887_127
n: 637189642996563245953103567105248123427011935586142479971519211497758129098842890558651615968037793670342418720609
m: 50000000000000000000000000
deg: 5
c5: 28
c0: -425
skew: 1.72
type: snfs
lss: 1
rlim: 1030000
alim: 1030000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1030000/1030000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [515000, 915001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 137200 x 137448
Total sieving time: 2.68 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,1030000,1030000,26,26,47,47,2.3,2.3,50000
total time: 2.68 hours.
 --------- CPU info (if available) ----------

(35·10¹²⁷+1)/9 = 3(8)₁₂₆9_<128> = 3 · 13 · 599 · 7151 · 35509 · 3897717493_<10> · 1968303984853_<13> · C93

C93 = P45 · P49

P45 = 157350569567152147220378732576837537803910029_<45>

P49 = 5430727809728405538160402721839618815472716167071_<49>

Mon Dec 08 00:32:03 2008  Msieve v. 1.39
Mon Dec 08 00:32:03 2008  random seeds: e7b531dc ad242115
Mon Dec 08 00:32:03 2008  factoring 854528114024937285149180181082706516562243298748907804692499306233913113780933046705816455059 (93 digits)
Mon Dec 08 00:32:04 2008  searching for 15-digit factors
Mon Dec 08 00:32:06 2008  commencing quadratic sieve (93-digit input)
Mon Dec 08 00:32:06 2008  using multiplier of 1
Mon Dec 08 00:32:06 2008  using 32kb Intel Core sieve core
Mon Dec 08 00:32:06 2008  sieve interval: 36 blocks of size 32768
Mon Dec 08 00:32:06 2008  processing polynomials in batches of 6
Mon Dec 08 00:32:06 2008  using a sieve bound of 1955507 (72941 primes)
Mon Dec 08 00:32:06 2008  using large prime bound of 244438375 (27 bits)
Mon Dec 08 00:32:06 2008  using double large prime bound of 1255176633760875 (42-51 bits)
Mon Dec 08 00:32:06 2008  using trial factoring cutoff of 51 bits
Mon Dec 08 00:32:06 2008  polynomial 'A' values have 12 factors
Mon Dec 08 00:32:07 2008  restarting with 18545 full and 992963 partial relations
Mon Dec 08 00:32:07 2008  73156 relations (18545 full + 54611 combined from 992963 partial), need 73037
Mon Dec 08 00:32:09 2008  begin with 1011508 relations
Mon Dec 08 00:32:09 2008  reduce to 186763 relations in 11 passes
Mon Dec 08 00:32:09 2008  attempting to read 186763 relations
Mon Dec 08 00:32:12 2008  recovered 186763 relations
Mon Dec 08 00:32:12 2008  recovered 167544 polynomials
Mon Dec 08 00:32:12 2008  attempting to build 73156 cycles
Mon Dec 08 00:32:12 2008  found 73156 cycles in 6 passes
Mon Dec 08 00:32:12 2008  distribution of cycle lengths:
Mon Dec 08 00:32:12 2008     length 1 : 18545
Mon Dec 08 00:32:12 2008     length 2 : 13105
Mon Dec 08 00:32:12 2008     length 3 : 12618
Mon Dec 08 00:32:12 2008     length 4 : 9872
Mon Dec 08 00:32:12 2008     length 5 : 7239
Mon Dec 08 00:32:12 2008     length 6 : 4869
Mon Dec 08 00:32:12 2008     length 7 : 2996
Mon Dec 08 00:32:12 2008     length 9+: 3912
Mon Dec 08 00:32:12 2008  largest cycle: 20 relations
Mon Dec 08 00:32:13 2008  matrix is 72941 x 73156 (17.9 MB) with weight 4398131 (60.12/col)
Mon Dec 08 00:32:13 2008  sparse part has weight 4398131 (60.12/col)
Mon Dec 08 00:32:14 2008  filtering completed in 3 passes
Mon Dec 08 00:32:14 2008  matrix is 69011 x 69075 (17.0 MB) with weight 4177621 (60.48/col)
Mon Dec 08 00:32:14 2008  sparse part has weight 4177621 (60.48/col)
Mon Dec 08 00:32:14 2008  saving the first 48 matrix rows for later
Mon Dec 08 00:32:14 2008  matrix is 68963 x 69075 (9.5 MB) with weight 3140818 (45.47/col)
Mon Dec 08 00:32:14 2008  sparse part has weight 2063060 (29.87/col)
Mon Dec 08 00:32:14 2008  matrix includes 64 packed rows
Mon Dec 08 00:32:14 2008  using block size 27630 for processor cache size 1024 kB
Mon Dec 08 00:32:14 2008  commencing Lanczos iteration
Mon Dec 08 00:32:14 2008  memory use: 10.0 MB
Mon Dec 08 00:32:42 2008  lanczos halted after 1092 iterations (dim = 68963)
Mon Dec 08 00:32:42 2008  recovered 18 nontrivial dependencies
Mon Dec 08 00:32:46 2008  prp45 factor: 157350569567152147220378732576837537803910029
Mon Dec 08 00:32:46 2008  prp49 factor: 5430727809728405538160402721839618815472716167071
Mon Dec 08 00:32:46 2008  elapsed time 00:00:43

(35·10¹²³+1)/9 = 3(8)₁₂₂9_<124> = 1381587624671_<13> · 163716152369726009_<18> · C95

C95 = P47 · P49

P47 = 10384299710970978120359331535825259223245131889_<47>

P49 = 1655687449944933127582920897860547628511068233359_<49>

Mon Dec 08 00:41:26 2008  Msieve v. 1.39
Mon Dec 08 00:41:26 2008  random seeds: 990eccb8 bafb8508
Mon Dec 08 00:41:26 2008  factoring 17193154707921444880778784466587728861787010649828655825384072319952296591978219433508184485151 (95 digits)
Mon Dec 08 00:41:27 2008  searching for 15-digit factors
Mon Dec 08 00:41:28 2008  commencing quadratic sieve (95-digit input)
Mon Dec 08 00:41:29 2008  using multiplier of 1
Mon Dec 08 00:41:29 2008  using 32kb Intel Core sieve core
Mon Dec 08 00:41:29 2008  sieve interval: 36 blocks of size 32768
Mon Dec 08 00:41:29 2008  processing polynomials in batches of 6
Mon Dec 08 00:41:29 2008  using a sieve bound of 2121809 (78824 primes)
Mon Dec 08 00:41:29 2008  using large prime bound of 309784114 (28 bits)
Mon Dec 08 00:41:29 2008  using double large prime bound of 1922677272029798 (43-51 bits)
Mon Dec 08 00:41:29 2008  using trial factoring cutoff of 51 bits
Mon Dec 08 00:41:29 2008  polynomial 'A' values have 12 factors
Mon Dec 08 03:57:17 2008  79248 relations (19467 full + 59781 combined from 1165661 partial), need 78920
Mon Dec 08 03:57:18 2008  begin with 1185128 relations
Mon Dec 08 03:57:19 2008  reduce to 205915 relations in 10 passes
Mon Dec 08 03:57:19 2008  attempting to read 205915 relations
Mon Dec 08 03:57:22 2008  recovered 205915 relations
Mon Dec 08 03:57:22 2008  recovered 187922 polynomials
Mon Dec 08 03:57:22 2008  attempting to build 79248 cycles
Mon Dec 08 03:57:23 2008  found 79248 cycles in 6 passes
Mon Dec 08 03:57:23 2008  distribution of cycle lengths:
Mon Dec 08 03:57:23 2008     length 1 : 19467
Mon Dec 08 03:57:23 2008     length 2 : 14006
Mon Dec 08 03:57:23 2008     length 3 : 13415
Mon Dec 08 03:57:23 2008     length 4 : 10803
Mon Dec 08 03:57:23 2008     length 5 : 7969
Mon Dec 08 03:57:23 2008     length 6 : 5401
Mon Dec 08 03:57:23 2008     length 7 : 3458
Mon Dec 08 03:57:23 2008     length 9+: 4729
Mon Dec 08 03:57:23 2008  largest cycle: 18 relations
Mon Dec 08 03:57:23 2008  matrix is 78824 x 79248 (20.8 MB) with weight 5128928 (64.72/col)
Mon Dec 08 03:57:23 2008  sparse part has weight 5128928 (64.72/col)
Mon Dec 08 03:57:24 2008  filtering completed in 3 passes
Mon Dec 08 03:57:24 2008  matrix is 74893 x 74957 (19.7 MB) with weight 4864632 (64.90/col)
Mon Dec 08 03:57:24 2008  sparse part has weight 4864632 (64.90/col)
Mon Dec 08 03:57:24 2008  saving the first 48 matrix rows for later
Mon Dec 08 03:57:25 2008  matrix is 74845 x 74957 (12.3 MB) with weight 3834680 (51.16/col)
Mon Dec 08 03:57:25 2008  sparse part has weight 2778669 (37.07/col)
Mon Dec 08 03:57:25 2008  matrix includes 64 packed rows
Mon Dec 08 03:57:25 2008  using block size 29982 for processor cache size 1024 kB
Mon Dec 08 03:57:25 2008  commencing Lanczos iteration
Mon Dec 08 03:57:25 2008  memory use: 11.9 MB
Mon Dec 08 03:58:03 2008  lanczos halted after 1185 iterations (dim = 74843)
Mon Dec 08 03:58:03 2008  recovered 16 nontrivial dependencies
Mon Dec 08 03:58:03 2008  prp47 factor: 10384299710970978120359331535825259223245131889
Mon Dec 08 03:58:03 2008  prp49 factor: 1655687449944933127582920897860547628511068233359
Mon Dec 08 03:58:03 2008  elapsed time 03:16:37

(35·10¹¹³-17)/9 = 3(8)₁₁₂7_<114> = 3 · 23 · 67 · 2361307315329023_<16> · C95

C95 = P39 · P56

P39 = 510712342028689440749924324396136884587_<39>

P56 = 69754587631347514921265069039903044640326990855644594869_<56>

Sun Dec 07 20:48:43 2008  Msieve v. 1.39
Sun Dec 07 20:48:43 2008  random seeds: 9d53de6c 2ca7d064
Sun Dec 07 20:48:43 2008  factoring 35624528816450942070204177663612725669850609496941878573455438512547059853912180811111425384103 (95 digits)
Sun Dec 07 20:48:45 2008  searching for 15-digit factors
Sun Dec 07 20:48:46 2008  commencing quadratic sieve (95-digit input)
Sun Dec 07 20:48:47 2008  using multiplier of 2
Sun Dec 07 20:48:47 2008  using 64kb Pentium 4 sieve core
Sun Dec 07 20:48:47 2008  sieve interval: 18 blocks of size 65536
Sun Dec 07 20:48:47 2008  processing polynomials in batches of 6
Sun Dec 07 20:48:47 2008  using a sieve bound of 2158631 (80000 primes)
Sun Dec 07 20:48:47 2008  using large prime bound of 323794650 (28 bits)
Sun Dec 07 20:48:47 2008  using double large prime bound of 2082022265125500 (43-51 bits)
Sun Dec 07 20:48:47 2008  using trial factoring cutoff of 51 bits
Sun Dec 07 20:48:47 2008  polynomial 'A' values have 12 factors
Mon Dec 08 03:33:54 2008  80284 relations (19242 full + 61042 combined from 1208021 partial), need 80096
Mon Dec 08 03:33:58 2008  begin with 1227263 relations
Mon Dec 08 03:34:00 2008  reduce to 211385 relations in 11 passes
Mon Dec 08 03:34:00 2008  attempting to read 211385 relations
Mon Dec 08 03:34:03 2008  recovered 211385 relations
Mon Dec 08 03:34:03 2008  recovered 196533 polynomials
Mon Dec 08 03:34:03 2008  attempting to build 80284 cycles
Mon Dec 08 03:34:03 2008  found 80284 cycles in 6 passes
Mon Dec 08 03:34:03 2008  distribution of cycle lengths:
Mon Dec 08 03:34:03 2008     length 1 : 19242
Mon Dec 08 03:34:03 2008     length 2 : 13846
Mon Dec 08 03:34:03 2008     length 3 : 13272
Mon Dec 08 03:34:03 2008     length 4 : 10949
Mon Dec 08 03:34:03 2008     length 5 : 8330
Mon Dec 08 03:34:03 2008     length 6 : 5672
Mon Dec 08 03:34:03 2008     length 7 : 3678
Mon Dec 08 03:34:03 2008     length 9+: 5295
Mon Dec 08 03:34:03 2008  largest cycle: 19 relations
Mon Dec 08 03:34:04 2008  matrix is 80000 x 80284 (21.6 MB) with weight 5346435 (66.59/col)
Mon Dec 08 03:34:04 2008  sparse part has weight 5346435 (66.59/col)
Mon Dec 08 03:34:06 2008  filtering completed in 3 passes
Mon Dec 08 03:34:06 2008  matrix is 76631 x 76695 (20.7 MB) with weight 5129508 (66.88/col)
Mon Dec 08 03:34:06 2008  sparse part has weight 5129508 (66.88/col)
Mon Dec 08 03:34:06 2008  saving the first 48 matrix rows for later
Mon Dec 08 03:34:06 2008  matrix is 76583 x 76695 (13.4 MB) with weight 4075545 (53.14/col)
Mon Dec 08 03:34:06 2008  sparse part has weight 3055081 (39.83/col)
Mon Dec 08 03:34:06 2008  matrix includes 64 packed rows
Mon Dec 08 03:34:06 2008  using block size 21845 for processor cache size 512 kB
Mon Dec 08 03:34:08 2008  commencing Lanczos iteration
Mon Dec 08 03:34:08 2008  memory use: 12.7 MB
Mon Dec 08 03:35:14 2008  lanczos halted after 1213 iterations (dim = 76581)
Mon Dec 08 03:35:14 2008  recovered 16 nontrivial dependencies
Mon Dec 08 03:35:17 2008  prp39 factor: 510712342028689440749924324396136884587
Mon Dec 08 03:35:17 2008  prp56 factor: 69754587631347514921265069039903044640326990855644594869
Mon Dec 08 03:35:17 2008  elapsed time 06:46:34

(35·10¹³⁶+1)/9 = 3(8)₁₃₅9_<137> = 3 · 17 · 5417 · 1119871 · 358467107 · C117

C117 = P39 · P78

P39 = 951810720294636454280684312778970536173_<39>

P78 = 368407634918623356591770151280494496467035113520864797303587770043237865921507_<78>

Number: 38889_136
N=350654336353938357728785501942232737329533148552772496868237294826954356212463033993097425351850866108036592522172711
  ( 117 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=951810720294636454280684312778970536173 (pp39)
 r2=368407634918623356591770151280494496467035113520864797303587770043237865921507 (pp78)
Version: 
Total time: 5.38 hours.
Scaled time: 13.86 units (timescale=2.575).
Factorization parameters were as follows:
name: 38889_136
n: 350654336353938357728785501942232737329533148552772496868237294826954356212463033993097425351850866108036592522172711
m: 5000000000000000000000000000
deg: 5
c5: 14
c0: 125
skew: 1.55
type: snfs
lss: 1
rlim: 1490000
alim: 1490000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1490000/1490000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [745000, 1495001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 217203 x 217451
Total sieving time: 5.38 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1490000,1490000,26,26,48,48,2.3,2.3,75000
total time: 5.38 hours.
 --------- CPU info (if available) ----------

(35·10¹⁴⁴-17)/9 = 3(8)₁₄₃7_<145> = 107590361 · 376107998117_<12> · C125

C125 = P59 · P67

P59 = 21426550966873432966355113684930427555362915856005664850821_<59>

P67 = 4485257002846199926844351970859416404519415299681016964991792241031_<67>

Number: 38887_144
N=96103587771010081120816982038935197024462227340896770922811350265604804162609970300269923694765800293325172370070865890236451
  ( 125 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=21426550966873432966355113684930427555362915856005664850821 (pp59)
 r2=4485257002846199926844351970859416404519415299681016964991792241031 (pp67)
Version: 
Total time: 7.82 hours.
Scaled time: 20.06 units (timescale=2.564).
Factorization parameters were as follows:
name: 38887_144
n: 96103587771010081120816982038935197024462227340896770922811350265604804162609970300269923694765800293325172370070865890236451
m: 100000000000000000000000000000
deg: 5
c5: 7
c0: -34
skew: 1.37
type: snfs
lss: 1
rlim: 1890000
alim: 1890000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1890000/1890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [945000, 1945001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 308413 x 308661
Total sieving time: 7.82 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1890000,1890000,26,26,49,49,2.3,2.3,100000
total time: 7.82 hours.
 --------- CPU info (if available) ----------

(35·10¹²⁸-17)/9 = 3(8)₁₂₇7_<129> = 3² · 43 · 2557 · 1744978463_<10> · 479702072115780301_<18> · C96

C96 = P48 · P48

P48 = 614114184448342236450430905615224850081743454187_<48>

P48 = 764492180582182386904576547379784128078297585553_<48>

Mon Dec 08 06:06:03 2008  Msieve v. 1.39
Mon Dec 08 06:06:03 2008  random seeds: 44322e90 aab5a9bf
Mon Dec 08 06:06:03 2008  factoring 469485491995361715464158650599678862392194433114786077454834953798678154555724651083604368560411 (96 digits)
Mon Dec 08 06:06:04 2008  searching for 15-digit factors
Mon Dec 08 06:06:05 2008  commencing quadratic sieve (96-digit input)
Mon Dec 08 06:06:05 2008  using multiplier of 1
Mon Dec 08 06:06:05 2008  using 32kb Intel Core sieve core
Mon Dec 08 06:06:05 2008  sieve interval: 36 blocks of size 32768
Mon Dec 08 06:06:05 2008  processing polynomials in batches of 6
Mon Dec 08 06:06:05 2008  using a sieve bound of 2258279 (83529 primes)
Mon Dec 08 06:06:05 2008  using large prime bound of 338741850 (28 bits)
Mon Dec 08 06:06:05 2008  using double large prime bound of 2258207977125450 (43-52 bits)
Mon Dec 08 06:06:05 2008  using trial factoring cutoff of 52 bits
Mon Dec 08 06:06:05 2008  polynomial 'A' values have 12 factors
Mon Dec 08 10:51:26 2008  83650 relations (19810 full + 63840 combined from 1265744 partial), need 83625
Mon Dec 08 10:51:28 2008  begin with 1285554 relations
Mon Dec 08 10:51:29 2008  reduce to 220757 relations in 10 passes
Mon Dec 08 10:51:29 2008  attempting to read 220757 relations
Mon Dec 08 10:51:32 2008  recovered 220757 relations
Mon Dec 08 10:51:32 2008  recovered 206454 polynomials
Mon Dec 08 10:51:32 2008  attempting to build 83650 cycles
Mon Dec 08 10:51:32 2008  found 83650 cycles in 6 passes
Mon Dec 08 10:51:32 2008  distribution of cycle lengths:
Mon Dec 08 10:51:32 2008     length 1 : 19810
Mon Dec 08 10:51:33 2008     length 2 : 14243
Mon Dec 08 10:51:33 2008     length 3 : 14030
Mon Dec 08 10:51:33 2008     length 4 : 11306
Mon Dec 08 10:51:33 2008     length 5 : 8908
Mon Dec 08 10:51:33 2008     length 6 : 6070
Mon Dec 08 10:51:33 2008     length 7 : 3862
Mon Dec 08 10:51:33 2008     length 9+: 5421
Mon Dec 08 10:51:33 2008  largest cycle: 21 relations
Mon Dec 08 10:51:33 2008  matrix is 83529 x 83650 (23.4 MB) with weight 5791731 (69.24/col)
Mon Dec 08 10:51:33 2008  sparse part has weight 5791731 (69.24/col)
Mon Dec 08 10:51:34 2008  filtering completed in 3 passes
Mon Dec 08 10:51:34 2008  matrix is 80003 x 80067 (22.5 MB) with weight 5587408 (69.78/col)
Mon Dec 08 10:51:34 2008  sparse part has weight 5587408 (69.78/col)
Mon Dec 08 10:51:34 2008  saving the first 48 matrix rows for later
Mon Dec 08 10:51:34 2008  matrix is 79955 x 80067 (16.1 MB) with weight 4638087 (57.93/col)
Mon Dec 08 10:51:34 2008  sparse part has weight 3734057 (46.64/col)
Mon Dec 08 10:51:34 2008  matrix includes 64 packed rows
Mon Dec 08 10:51:34 2008  using block size 32026 for processor cache size 1024 kB
Mon Dec 08 10:51:35 2008  commencing Lanczos iteration
Mon Dec 08 10:51:35 2008  memory use: 14.4 MB
Mon Dec 08 10:52:21 2008  lanczos halted after 1266 iterations (dim = 79955)
Mon Dec 08 10:52:22 2008  recovered 18 nontrivial dependencies
Mon Dec 08 10:52:22 2008  prp48 factor: 614114184448342236450430905615224850081743454187
Mon Dec 08 10:52:22 2008  prp48 factor: 764492180582182386904576547379784128078297585553
Mon Dec 08 10:52:22 2008  elapsed time 04:46:19

Dec 7, 2008 (11th)

By Erik Branger / GGNFS, Msieve

(35·10¹³⁴-17)/9 = 3(8)₁₃₃7_<135> = 3 · C135

C135 = P63 · P72

P63 = 969728384217945564797275207754143001546059800826738657962986323_<63>

P72 = 133676224950527476034793786904878991749286703030637898637843016107605423_<72>

Number: 38887_134
N=129629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629
  ( 135 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=969728384217945564797275207754143001546059800826738657962986323
 r2=133676224950527476034793786904878991749286703030637898637843016107605423
Version: 
Total time: 5.12 hours.
Scaled time: 10.84 units (timescale=2.116).
Factorization parameters were as follows:
n: 129629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629
m: 1000000000000000000000000000
deg: 5
c5: 7
c0: -34
skew: 1.37
type: snfs
lss: 1
rlim: 1290000
alim: 1290000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1290000/1290000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [645000, 1170001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 169326 x 169574
Total sieving time: 5.12 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1290000,1290000,26,26,47,47,2.3,2.3,75000
total time: 5.12 hours.
 --------- CPU info (if available) ----------

Dec 7, 2008 (10th)

By Jo Yeong Uk / GGNFS

(35·10¹⁶⁷+1)/9 = 3(8)₁₆₆9_<168> = 9399905186263_<13> · 1641584855370881_<16> · 117604162223291467981_<21> · 127461987854538798090991_<24> · C97

C97 = P39 · P58

P39 = 233497123122207430579337078165623812031_<39>

P58 = 7200353378046645802084948687027325444285796669256644994363_<58>

Number: 38889_167
N=1681261799237159840181193611414121235472148120751084549550605549646798210799635338358074566581253
  ( 97 digits)
Divisors found:
 r1=233497123122207430579337078165623812031 (pp39)
 r2=7200353378046645802084948687027325444285796669256644994363 (pp58)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.18 hours.
Scaled time: 5.22 units (timescale=2.390).
Factorization parameters were as follows:
name: 38889_167
n: 1681261799237159840181193611414121235472148120751084549550605549646798210799635338358074566581253
skew: 3433.58
# norm 1.68e+13
c5: 91320
c4: 360438986
c3: -610587742497
c2: -6706059088479814
c1: -187956054008070948
c0: 23649595112677456900133
# alpha -5.65
Y1: 10539400673
Y0: -1790654797890799296
# Murphy_E 5.13e-09
# M 511710912310871436142349479089457306917743183735526473683559315200237212626896620639101168005244
type: gnfs
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [500000, 850001)
Primes: RFBsize:78498, AFBsize:78521, largePrimes:3968793 encountered
Relations: rels:3760914, finalFF:213126
Max relations in full relation-set: 28
Initial matrix: 157102 x 213126 with sparse part having weight 18320617.
Pruned matrix : 132960 x 133809 with weight 8773894.
Polynomial selection time: 0.18 hours.
Total sieving time: 1.87 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
gnfs,96,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1000000,1000000,26,26,49,49,2.5,2.5,50000
total time: 2.18 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Dec 7, 2008 (9th)

By Sinkiti Sibata / Msieve

(35·10¹³²-17)/9 = 3(8)₁₃₁7_<133> = 61 · 167 · 197 · 1087 · 917117 · 349527261719_<12> · 381821911376033779003_<21> · C86

C86 = P37 · P49

P37 = 2618098890081871199911145483496466417_<37>

P49 = 5563278048469018825873033722128510859501955470983_<49>

Sun Dec 07 17:50:29 2008  Msieve v. 1.38
Sun Dec 07 17:50:29 2008  random seeds: 53c431d4 fec442a7
Sun Dec 07 17:50:29 2008  factoring 14565212083913576636674787221762602499347453906972766910220957675632824256961477477911 (86 digits)
Sun Dec 07 17:50:32 2008  searching for 15-digit factors
Sun Dec 07 17:50:37 2008  commencing quadratic sieve (86-digit input)
Sun Dec 07 17:50:38 2008  using multiplier of 11
Sun Dec 07 17:50:38 2008  using 64kb Pentium 2 sieve core
Sun Dec 07 17:50:38 2008  sieve interval: 6 blocks of size 65536
Sun Dec 07 17:50:38 2008  processing polynomials in batches of 17
Sun Dec 07 17:50:38 2008  using a sieve bound of 1438057 (55000 primes)
Sun Dec 07 17:50:38 2008  using large prime bound of 115044560 (26 bits)
Sun Dec 07 17:50:38 2008  using double large prime bound of 323265089678720 (41-49 bits)
Sun Dec 07 17:50:38 2008  using trial factoring cutoff of 49 bits
Sun Dec 07 17:50:38 2008  polynomial 'A' values have 11 factors
Sun Dec 07 22:58:04 2008  55301 relations (15869 full + 39432 combined from 573043 partial), need 55096
Sun Dec 07 22:58:09 2008  begin with 588912 relations
Sun Dec 07 22:58:10 2008  reduce to 130015 relations in 9 passes
Sun Dec 07 22:58:10 2008  attempting to read 130015 relations
Sun Dec 07 22:58:16 2008  recovered 130015 relations
Sun Dec 07 22:58:16 2008  recovered 112568 polynomials
Sun Dec 07 22:58:17 2008  attempting to build 55301 cycles
Sun Dec 07 22:58:17 2008  found 55301 cycles in 5 passes
Sun Dec 07 22:58:20 2008  distribution of cycle lengths:
Sun Dec 07 22:58:20 2008     length 1 : 15869
Sun Dec 07 22:58:20 2008     length 2 : 11102
Sun Dec 07 22:58:20 2008     length 3 : 9828
Sun Dec 07 22:58:20 2008     length 4 : 7335
Sun Dec 07 22:58:20 2008     length 5 : 4744
Sun Dec 07 22:58:20 2008     length 6 : 2982
Sun Dec 07 22:58:20 2008     length 7 : 1670
Sun Dec 07 22:58:20 2008     length 9+: 1771
Sun Dec 07 22:58:20 2008  largest cycle: 19 relations
Sun Dec 07 22:58:21 2008  matrix is 55000 x 55301 (12.5 MB) with weight 3043221 (55.03/col)
Sun Dec 07 22:58:21 2008  sparse part has weight 3043221 (55.03/col)
Sun Dec 07 22:58:25 2008  filtering completed in 3 passes
Sun Dec 07 22:58:25 2008  matrix is 49878 x 49941 (11.3 MB) with weight 2772025 (55.51/col)
Sun Dec 07 22:58:26 2008  sparse part has weight 2772025 (55.51/col)
Sun Dec 07 22:58:28 2008  saving the first 48 matrix rows for later
Sun Dec 07 22:58:28 2008  matrix is 49830 x 49941 (7.3 MB) with weight 2195446 (43.96/col)
Sun Dec 07 22:58:28 2008  sparse part has weight 1610296 (32.24/col)
Sun Dec 07 22:58:28 2008  matrix includes 64 packed rows
Sun Dec 07 22:58:28 2008  using block size 5461 for processor cache size 128 kB
Sun Dec 07 22:58:29 2008  commencing Lanczos iteration
Sun Dec 07 22:58:29 2008  memory use: 7.3 MB
Sun Dec 07 23:00:40 2008  lanczos halted after 789 iterations (dim = 49826)
Sun Dec 07 23:00:41 2008  recovered 15 nontrivial dependencies
Sun Dec 07 23:00:44 2008  prp37 factor: 2618098890081871199911145483496466417
Sun Dec 07 23:00:44 2008  prp49 factor: 5563278048469018825873033722128510859501955470983
Sun Dec 07 23:00:44 2008  elapsed time 05:10:15

Dec 7, 2008 (8th)

By Erik Branger / GGNFS, Msieve

(23·10¹⁷⁷+31)/9 = 2(5)₁₇₆9_<178> = 3³ · 53 · 20521 · 25177684816667351_<17> · C154

C154 = P42 · P112

P42 = 519620774710320798463766416667482050915119_<42>

P112 = 6651887165827614470553363180110159612057894005166560172816585853798701521249789037346745006909602267998822481361_<112>

Number: 25559_177
N=3456458762392985184684090100084040703301574082824617112870666857245245353646180549347304821656855905830979532981615933356972470985629517509741500370596959
  ( 154 digits)
SNFS difficulty: 179 digits.
Divisors found:
 r1=519620774710320798463766416667482050915119
 r2=6651887165827614470553363180110159612057894005166560172816585853798701521249789037346745006909602267998822481361
Version: 
Total time: 210.17 hours.
Scaled time: 444.73 units (timescale=2.116).
Factorization parameters were as follows:
n: 3456458762392985184684090100084040703301574082824617112870666857245245353646180549347304821656855905830979532981615933356972470985629517509741500370596959
m: 200000000000000000000000000000000000
deg: 5
c5: 575
c0: 248
skew: 0.85
type: snfs
lss: 1
rlim: 6800000
alim: 6800000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6800000/6800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3400000, 9900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1532523 x 1532771
Total sieving time: 210.17 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,179,5,0,0,0,0,0,0,0,0,6800000,6800000,28,28,53,53,2.5,2.5,100000
total time: 210.17 hours.
 --------- CPU info (if available) ----------

Dec 7, 2008 (7th)

By Jo Yeong Uk / GGNFS

(35·10¹⁶⁸-71)/9 = 3(8)₁₆₇1_<169> = 10873724311_<11> · 14303299735272000932427365334907044020341_<41> · C119

C119 = P49 · P70

P49 = 9393326677884059649378589506343491190606750272193_<49>

P70 = 2661898864995912156338864781434885655844161180750727978984078940447867_<70>

Number: 38881_168
N=25004085622395400531356004667950957578919315561901397443642967755502862141549701795225649125923569649521872339576262331
  ( 119 digits)
Divisors found:
 r1=9393326677884059649378589506343491190606750272193 (pp49)
 r2=2661898864995912156338864781434885655844161180750727978984078940447867 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 33.72 hours.
Scaled time: 80.17 units (timescale=2.378).
Factorization parameters were as follows:
name: 38881_168
n: 25004085622395400531356004667950957578919315561901397443642967755502862141549701795225649125923569649521872339576262331
skew: 55789.87
# norm 2.91e+16
c5: 50400
c4: -22670790084
c3: -576283113585857
c2: 77180010939996291587
c1: 1122099080230336208850255
c0: 321885631905066599984363475
# alpha -6.81
Y1: 3012571527971
Y0: -54842625079834511542186
# Murphy_E 3.61e-10
# M 11373750039980250020583137353018721562472880609089940211327385554674139944690464666740219551261430950451632264704464388
type: gnfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [2000000, 3900001)
Primes: RFBsize:283146, AFBsize:282457, largePrimes:9377636 encountered
Relations: rels:9555591, finalFF:780301
Max relations in full relation-set: 28
Initial matrix: 565684 x 780301 with sparse part having weight 80887021.
Pruned matrix : 416351 x 419243 with weight 55103470.
Polynomial selection time: 2.27 hours.
Total sieving time: 29.64 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.49 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,52,52,2.4,2.4,100000
total time: 33.72 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Dec 7, 2008 (6th)

By Sinkiti Sibata / GGNFS, Msieve

(35·10¹⁶⁵-71)/9 = 3(8)₁₆₄1_<166> = 347 · 683 · C161

C161 = P59 · P103

P59 = 13731007978254981814404167377815346660212103899723511183019_<59>

P103 = 1195013845155755906706283527067698572345276426831342688089512781690087911568759714098174429125702367099_<103>

Number: 38881_165
N=16408744641958847806080518178779367550722945847860932607410470373073906392331209104134112889350209023965674781494124028543714536600642566440179108480086113091881
  ( 161 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=13731007978254981814404167377815346660212103899723511183019 (pp59)
 r2=1195013845155755906706283527067698572345276426831342688089512781690087911568759714098174429125702367099 (pp103)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 84.76 hours.
Scaled time: 218.25 units (timescale=2.575).
Factorization parameters were as follows:
name: 38881_165
n: 16408744641958847806080518178779367550722945847860932607410470373073906392331209104134112889350209023965674781494124028543714536600642566440179108480086113091881
m: 1000000000000000000000000000000000
deg: 5
c5: 35
c0: -71
skew: 1.15
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 5000001)
Primes: RFBsize:296314, AFBsize:295812, largePrimes:9820806 encountered
Relations: rels:10979704, finalFF:994308
Max relations in full relation-set: 28
Initial matrix: 592192 x 994308 with sparse part having weight 129937602.
Pruned matrix : 457177 x 460201 with weight 81941478.
Total sieving time: 81.00 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.38 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 84.76 hours.
 --------- CPU info (if available) ----------

(35·10¹¹⁷+1)/9 = 3(8)₁₁₆9_<118> = 23671 · 27783859669_<11> · 586508325901909_<15> · C89

C89 = P43 · P46

P43 = 2220068530298034077903598290054113895052823_<43>

P46 = 4541253968601200953821721286835487419928638673_<46>

Sun Dec 07 17:46:57 2008  Msieve v. 1.39
Sun Dec 07 17:46:57 2008  random seeds: 3fb265a8 0d06a882
Sun Dec 07 17:46:57 2008  factoring 10081895023782582796843701887427849048952509971025379579156894880001019382626551815623879 (89 digits)
Sun Dec 07 17:46:58 2008  searching for 15-digit factors
Sun Dec 07 17:46:59 2008  commencing quadratic sieve (89-digit input)
Sun Dec 07 17:46:59 2008  using multiplier of 1
Sun Dec 07 17:46:59 2008  using 32kb Intel Core sieve core
Sun Dec 07 17:46:59 2008  sieve interval: 28 blocks of size 32768
Sun Dec 07 17:46:59 2008  processing polynomials in batches of 8
Sun Dec 07 17:46:59 2008  using a sieve bound of 1531987 (58333 primes)
Sun Dec 07 17:46:59 2008  using large prime bound of 122558960 (26 bits)
Sun Dec 07 17:46:59 2008  using double large prime bound of 362260509321760 (42-49 bits)
Sun Dec 07 17:46:59 2008  using trial factoring cutoff of 49 bits
Sun Dec 07 17:46:59 2008  polynomial 'A' values have 11 factors
Sun Dec 07 18:41:15 2008  58459 relations (15782 full + 42677 combined from 616373 partial), need 58429
Sun Dec 07 18:41:16 2008  begin with 632155 relations
Sun Dec 07 18:41:16 2008  reduce to 141998 relations in 9 passes
Sun Dec 07 18:41:16 2008  attempting to read 141998 relations
Sun Dec 07 18:41:18 2008  recovered 141998 relations
Sun Dec 07 18:41:18 2008  recovered 118175 polynomials
Sun Dec 07 18:41:18 2008  attempting to build 58459 cycles
Sun Dec 07 18:41:18 2008  found 58459 cycles in 5 passes
Sun Dec 07 18:41:18 2008  distribution of cycle lengths:
Sun Dec 07 18:41:18 2008     length 1 : 15782
Sun Dec 07 18:41:18 2008     length 2 : 11280
Sun Dec 07 18:41:18 2008     length 3 : 10154
Sun Dec 07 18:41:18 2008     length 4 : 7755
Sun Dec 07 18:41:18 2008     length 5 : 5534
Sun Dec 07 18:41:18 2008     length 6 : 3408
Sun Dec 07 18:41:18 2008     length 7 : 2047
Sun Dec 07 18:41:18 2008     length 9+: 2499
Sun Dec 07 18:41:18 2008  largest cycle: 19 relations
Sun Dec 07 18:41:18 2008  matrix is 58333 x 58459 (13.8 MB) with weight 3395424 (58.08/col)
Sun Dec 07 18:41:18 2008  sparse part has weight 3395424 (58.08/col)
Sun Dec 07 18:41:19 2008  filtering completed in 3 passes
Sun Dec 07 18:41:19 2008  matrix is 54314 x 54378 (13.0 MB) with weight 3193846 (58.73/col)
Sun Dec 07 18:41:19 2008  sparse part has weight 3193846 (58.73/col)
Sun Dec 07 18:41:19 2008  saving the first 48 matrix rows for later
Sun Dec 07 18:41:19 2008  matrix is 54266 x 54378 (8.4 MB) with weight 2474532 (45.51/col)
Sun Dec 07 18:41:19 2008  sparse part has weight 1876656 (34.51/col)
Sun Dec 07 18:41:19 2008  matrix includes 64 packed rows
Sun Dec 07 18:41:19 2008  using block size 21751 for processor cache size 1024 kB
Sun Dec 07 18:41:20 2008  commencing Lanczos iteration
Sun Dec 07 18:41:20 2008  memory use: 8.2 MB
Sun Dec 07 18:41:37 2008  lanczos halted after 859 iterations (dim = 54264)
Sun Dec 07 18:41:37 2008  recovered 16 nontrivial dependencies
Sun Dec 07 18:41:38 2008  prp43 factor: 2220068530298034077903598290054113895052823
Sun Dec 07 18:41:38 2008  prp46 factor: 4541253968601200953821721286835487419928638673
Sun Dec 07 18:41:38 2008  elapsed time 00:54:41

(35·10¹⁶¹-17)/9 = 3(8)₁₆₀7_<162> = 3 · 192799 · 242197863343_<12> · 13253282881361993_<17> · 186251389998046129_<18> · 2113037716029191144429_<22> · C90

C90 = P32 · P59

P32 = 28742297975313337803187625016407_<32>

P59 = 18517291741272127549515342256010461522539595944240811661567_<59>

Sun Dec 07 18:48:52 2008  Msieve v. 1.39
Sun Dec 07 18:48:52 2008  random seeds: 798680a8 b317973b
Sun Dec 07 18:48:52 2008  factoring 532229516923452263105571093994631719385926239719641669143819829745142516262461505306329769 (90 digits)
Sun Dec 07 18:48:53 2008  searching for 15-digit factors
Sun Dec 07 18:48:54 2008  commencing quadratic sieve (90-digit input)
Sun Dec 07 18:48:54 2008  using multiplier of 1
Sun Dec 07 18:48:54 2008  using 32kb Intel Core sieve core
Sun Dec 07 18:48:54 2008  sieve interval: 36 blocks of size 32768
Sun Dec 07 18:48:54 2008  processing polynomials in batches of 6
Sun Dec 07 18:48:54 2008  using a sieve bound of 1617079 (61176 primes)
Sun Dec 07 18:48:54 2008  using large prime bound of 135834636 (27 bits)
Sun Dec 07 18:48:54 2008  using double large prime bound of 435932059795260 (42-49 bits)
Sun Dec 07 18:48:54 2008  using trial factoring cutoff of 49 bits
Sun Dec 07 18:48:54 2008  polynomial 'A' values have 11 factors
Sun Dec 07 20:08:01 2008  61571 relations (16101 full + 45470 combined from 671969 partial), need 61272
Sun Dec 07 20:08:02 2008  begin with 688070 relations
Sun Dec 07 20:08:03 2008  reduce to 151577 relations in 10 passes
Sun Dec 07 20:08:03 2008  attempting to read 151577 relations
Sun Dec 07 20:08:05 2008  recovered 151577 relations
Sun Dec 07 20:08:05 2008  recovered 129782 polynomials
Sun Dec 07 20:08:05 2008  attempting to build 61571 cycles
Sun Dec 07 20:08:05 2008  found 61571 cycles in 5 passes
Sun Dec 07 20:08:05 2008  distribution of cycle lengths:
Sun Dec 07 20:08:05 2008     length 1 : 16101
Sun Dec 07 20:08:05 2008     length 2 : 11543
Sun Dec 07 20:08:05 2008     length 3 : 10855
Sun Dec 07 20:08:05 2008     length 4 : 8134
Sun Dec 07 20:08:05 2008     length 5 : 5893
Sun Dec 07 20:08:05 2008     length 6 : 3892
Sun Dec 07 20:08:05 2008     length 7 : 2429
Sun Dec 07 20:08:05 2008     length 9+: 2724
Sun Dec 07 20:08:05 2008  largest cycle: 16 relations
Sun Dec 07 20:08:05 2008  matrix is 61176 x 61571 (15.3 MB) with weight 3752165 (60.94/col)
Sun Dec 07 20:08:05 2008  sparse part has weight 3752165 (60.94/col)
Sun Dec 07 20:08:06 2008  filtering completed in 3 passes
Sun Dec 07 20:08:06 2008  matrix is 57444 x 57508 (14.3 MB) with weight 3515270 (61.13/col)
Sun Dec 07 20:08:06 2008  sparse part has weight 3515270 (61.13/col)
Sun Dec 07 20:08:06 2008  saving the first 48 matrix rows for later
Sun Dec 07 20:08:06 2008  matrix is 57396 x 57508 (10.7 MB) with weight 2954201 (51.37/col)
Sun Dec 07 20:08:06 2008  sparse part has weight 2467234 (42.90/col)
Sun Dec 07 20:08:06 2008  matrix includes 64 packed rows
Sun Dec 07 20:08:06 2008  using block size 23003 for processor cache size 1024 kB
Sun Dec 07 20:08:07 2008  commencing Lanczos iteration
Sun Dec 07 20:08:07 2008  memory use: 9.6 MB
Sun Dec 07 20:08:29 2008  lanczos halted after 909 iterations (dim = 57394)
Sun Dec 07 20:08:29 2008  recovered 16 nontrivial dependencies
Sun Dec 07 20:08:30 2008  prp32 factor: 28742297975313337803187625016407
Sun Dec 07 20:08:30 2008  prp59 factor: 18517291741272127549515342256010461522539595944240811661567
Sun Dec 07 20:08:30 2008  elapsed time 01:19:38

(35·10¹⁰³+1)/9 = 3(8)₁₀₂9_<104> = 3² · 13 · 19 · 7549 · 11351 · 167597 · C88

C88 = P42 · P47

P42 = 100755942974597228137872420680604757516957_<42>

P47 = 12089980789218005875422642451041062453834791133_<47>

Sun Dec 07 18:38:53 2008  Msieve v. 1.39
Sun Dec 07 18:38:53 2008  random seeds: e1c72794 2f91d1cc
Sun Dec 07 18:38:53 2008  factoring 1218137414962425390751738719549946610485828619899062995091669939678138120168291800742281 (88 digits)
Sun Dec 07 18:38:54 2008  searching for 15-digit factors
Sun Dec 07 18:38:56 2008  commencing quadratic sieve (88-digit input)
Sun Dec 07 18:38:57 2008  using multiplier of 29
Sun Dec 07 18:38:57 2008  using 64kb Pentium 4 sieve core
Sun Dec 07 18:38:57 2008  sieve interval: 12 blocks of size 65536
Sun Dec 07 18:38:57 2008  processing polynomials in batches of 9
Sun Dec 07 18:38:57 2008  using a sieve bound of 1505519 (57333 primes)
Sun Dec 07 18:38:57 2008  using large prime bound of 120441520 (26 bits)
Sun Dec 07 18:38:57 2008  using double large prime bound of 351072818700640 (42-49 bits)
Sun Dec 07 18:38:57 2008  using trial factoring cutoff of 49 bits
Sun Dec 07 18:38:57 2008  polynomial 'A' values have 11 factors
Sun Dec 07 20:11:02 2008  57705 relations (16284 full + 41421 combined from 602881 partial), need 57429
Sun Dec 07 20:11:03 2008  begin with 619165 relations
Sun Dec 07 20:11:04 2008  reduce to 137443 relations in 10 passes
Sun Dec 07 20:11:04 2008  attempting to read 137443 relations
Sun Dec 07 20:11:05 2008  recovered 137443 relations
Sun Dec 07 20:11:05 2008  recovered 114473 polynomials
Sun Dec 07 20:11:06 2008  attempting to build 57705 cycles
Sun Dec 07 20:11:06 2008  found 57705 cycles in 5 passes
Sun Dec 07 20:11:06 2008  distribution of cycle lengths:
Sun Dec 07 20:11:06 2008     length 1 : 16284
Sun Dec 07 20:11:06 2008     length 2 : 11518
Sun Dec 07 20:11:06 2008     length 3 : 10106
Sun Dec 07 20:11:06 2008     length 4 : 7429
Sun Dec 07 20:11:06 2008     length 5 : 5198
Sun Dec 07 20:11:06 2008     length 6 : 3293
Sun Dec 07 20:11:06 2008     length 7 : 1795
Sun Dec 07 20:11:06 2008     length 9+: 2082
Sun Dec 07 20:11:06 2008  largest cycle: 17 relations
Sun Dec 07 20:11:06 2008  matrix is 57333 x 57705 (13.6 MB) with weight 3344070 (57.95/col)
Sun Dec 07 20:11:06 2008  sparse part has weight 3344070 (57.95/col)
Sun Dec 07 20:11:07 2008  filtering completed in 3 passes
Sun Dec 07 20:11:07 2008  matrix is 52715 x 52779 (12.5 MB) with weight 3076848 (58.30/col)
Sun Dec 07 20:11:07 2008  sparse part has weight 3076848 (58.30/col)
Sun Dec 07 20:11:07 2008  saving the first 48 matrix rows for later
Sun Dec 07 20:11:07 2008  matrix is 52667 x 52779 (8.8 MB) with weight 2504264 (47.45/col)
Sun Dec 07 20:11:07 2008  sparse part has weight 1986421 (37.64/col)
Sun Dec 07 20:11:07 2008  matrix includes 64 packed rows
Sun Dec 07 20:11:07 2008  using block size 21111 for processor cache size 512 kB
Sun Dec 07 20:11:08 2008  commencing Lanczos iteration
Sun Dec 07 20:11:08 2008  memory use: 8.2 MB
Sun Dec 07 20:11:36 2008  lanczos halted after 834 iterations (dim = 52667)
Sun Dec 07 20:11:36 2008  recovered 18 nontrivial dependencies
Sun Dec 07 20:11:37 2008  prp42 factor: 100755942974597228137872420680604757516957
Sun Dec 07 20:11:37 2008  prp47 factor: 12089980789218005875422642451041062453834791133
Sun Dec 07 20:11:37 2008  elapsed time 01:32:44

(35·10¹¹⁴-17)/9 = 3(8)₁₁₃7_<115> = C115

C115 = P49 · P66

P49 = 4110160586637253424951061483322223671294257236029_<49>

P66 = 946164707416116073991311909742053789197323995598219236310578275203_<66>

Number: 38887_114
N=3888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887
  ( 115 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=4110160586637253424951061483322223671294257236029
 r2=946164707416116073991311909742053789197323995598219236310578275203
Version: 
Total time: 0.88 hours.
Scaled time: 2.25 units (timescale=2.554).
Factorization parameters were as follows:
name: 38887_114
n: 3888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887
m: 100000000000000000000000
deg: 5
c5: 7
c0: -34
skew: 1.37
type: snfs
lss: 1
rlim: 600000
alim: 600000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [300000, 450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 60810 x 61046
Total sieving time: 0.88 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.2,2.2,50000
total time: 0.88 hours.
 --------- CPU info (if available) ----------

(35·10¹²³-17)/9 = 3(8)₁₂₂7_<124> = 13 · 32514646135566929765652027227651_<32> · C91

C91 = P38 · P54

P38 = 11000509236102085663313836629757193677_<38>

P54 = 836354428344066072261132208793124499586090114853277237_<54>

Sun Dec 07 20:37:42 2008  Msieve v. 1.39
Sun Dec 07 20:37:42 2008  random seeds: 812bc180 6e8de99a
Sun Dec 07 20:37:42 2008  factoring 9200324613653778810285796898822436094804743580470879018126211975558105040781619379584430449 (91 digits)
Sun Dec 07 20:37:43 2008  searching for 15-digit factors
Sun Dec 07 20:37:44 2008  commencing quadratic sieve (91-digit input)
Sun Dec 07 20:37:44 2008  using multiplier of 1
Sun Dec 07 20:37:44 2008  using 32kb Intel Core sieve core
Sun Dec 07 20:37:44 2008  sieve interval: 36 blocks of size 32768
Sun Dec 07 20:37:44 2008  processing polynomials in batches of 6
Sun Dec 07 20:37:44 2008  using a sieve bound of 1748993 (65882 primes)
Sun Dec 07 20:37:44 2008  using large prime bound of 176648293 (27 bits)
Sun Dec 07 20:37:44 2008  using double large prime bound of 699514874899490 (42-50 bits)
Sun Dec 07 20:37:44 2008  using trial factoring cutoff of 50 bits
Sun Dec 07 20:37:44 2008  polynomial 'A' values have 12 factors
Sun Dec 07 21:34:58 2008  66992 relations (19108 full + 47884 combined from 769023 partial), need 65978
Sun Dec 07 21:34:59 2008  begin with 788131 relations
Sun Dec 07 21:35:00 2008  reduce to 159524 relations in 11 passes
Sun Dec 07 21:35:00 2008  attempting to read 159524 relations
Sun Dec 07 21:35:02 2008  recovered 159524 relations
Sun Dec 07 21:35:02 2008  recovered 122737 polynomials
Sun Dec 07 21:35:02 2008  attempting to build 66992 cycles
Sun Dec 07 21:35:02 2008  found 66992 cycles in 5 passes
Sun Dec 07 21:35:02 2008  distribution of cycle lengths:
Sun Dec 07 21:35:02 2008     length 1 : 19108
Sun Dec 07 21:35:02 2008     length 2 : 13518
Sun Dec 07 21:35:02 2008     length 3 : 11776
Sun Dec 07 21:35:02 2008     length 4 : 8599
Sun Dec 07 21:35:02 2008     length 5 : 5743
Sun Dec 07 21:35:02 2008     length 6 : 3648
Sun Dec 07 21:35:02 2008     length 7 : 2110
Sun Dec 07 21:35:02 2008     length 9+: 2490
Sun Dec 07 21:35:02 2008  largest cycle: 18 relations
Sun Dec 07 21:35:03 2008  matrix is 65882 x 66992 (15.8 MB) with weight 3873042 (57.81/col)
Sun Dec 07 21:35:03 2008  sparse part has weight 3873042 (57.81/col)
Sun Dec 07 21:35:04 2008  filtering completed in 4 passes
Sun Dec 07 21:35:04 2008  matrix is 60137 x 60201 (14.1 MB) with weight 3450170 (57.31/col)
Sun Dec 07 21:35:04 2008  sparse part has weight 3450170 (57.31/col)
Sun Dec 07 21:35:04 2008  saving the first 48 matrix rows for later
Sun Dec 07 21:35:04 2008  matrix is 60089 x 60201 (8.5 MB) with weight 2622071 (43.56/col)
Sun Dec 07 21:35:04 2008  sparse part has weight 1870073 (31.06/col)
Sun Dec 07 21:35:04 2008  matrix includes 64 packed rows
Sun Dec 07 21:35:04 2008  using block size 24080 for processor cache size 1024 kB
Sun Dec 07 21:35:04 2008  commencing Lanczos iteration
Sun Dec 07 21:35:04 2008  memory use: 8.6 MB
Sun Dec 07 21:35:24 2008  lanczos halted after 952 iterations (dim = 60088)
Sun Dec 07 21:35:25 2008  recovered 16 nontrivial dependencies
Sun Dec 07 21:35:28 2008  prp38 factor: 11000509236102085663313836629757193677
Sun Dec 07 21:35:28 2008  prp54 factor: 836354428344066072261132208793124499586090114853277237
Sun Dec 07 21:35:28 2008  elapsed time 00:57:46

Dec 7, 2008 (5th)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39

(35·10¹³⁹-17)/9 = 3(8)₁₃₈7_<140> = 37 · 23957 · 13997909 · 531167603 · 5324940143_<10> · 3808548267229_<13> · C96

C96 = P34 · P63

P34 = 1234471249886739306632069758085923_<34>

P63 = 235690164383998395752830997318697209446208726758860398731520089_<63>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1486614879
Step 1 took 6831ms
Step 2 took 4506ms
********** Factor found in step 2: 1234471249886739306632069758085923
Found probable prime factor of 34 digits: 1234471249886739306632069758085923
Probable prime cofactor 235690164383998395752830997318697209446208726758860398731520089 has 63 digits

(35·10¹⁹⁹+1)/9 = 3(8)₁₉₈9_<200> = 3 · 13² · 4861 · 152840603 · 1156566239497_<13> · 2515923827839_<13> · 217505594603821_<15> · 6497775628529706959_<19> · 24582654665588546304875938307_<29> · C100

C100 = P33 · P67

P33 = 521482237316465123045134535692157_<33>

P67 = 1958311477916142932716389871913675734578597034889255207588628076663_<67>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1731595855
Step 1 took 6408ms
Step 2 took 3796ms
********** Factor found in step 2: 521482237316465123045134535692157
Found probable prime factor of 33 digits: 521482237316465123045134535692157
Probable prime cofactor 1958311477916142932716389871913675734578597034889255207588628076663 has 67 digits

(35·10¹⁰³-17)/9 = 3(8)₁₀₂7_<104> = 37 · 131 · 1481 · 38299 · C93

C93 = P45 · P48

P45 = 202254561854416559848922039163312240405477011_<45>

P48 = 699377564266339266150223417648152119745082832369_<48>

SNFS difficulty: 104 digits.
Divisors found:
 r1=202254561854416559848922039163312240405477011 (pp45)
 r2=699377564266339266150223417648152119745082832369 (pp48)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.723).
Factorization parameters were as follows:
n: 141452302831497507848239580701056914824087857520121014274963999456081757918276165376396169059
m: 100000000000000000000000000
deg: 4
c4: 7
c0: -34
skew: 1.48
type: snfs
lss: 1
rlim: 390000
alim: 390000
lpbr: 25
lpba: 25
mfbr: 48
mfba: 48
rlambda: 2.2
alambda: 2.2
Factor base limits: 390000/390000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 48/48
Sieved rational special-q in [195000, 235001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 35012 x 35253
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,104,4,0,0,0,0,0,0,0,0,390000,390000,25,25,48,48,2.2,2.2,20000
total time: 0.20 hours.

(35·10²⁰⁴+1)/9 = 3(8)₂₀₃9_<205> = 71 · 359 · 10399 · 114531542096417446468313_<24> · C174

C174 = P32 · P142

P32 = 84236514375392918434791697369357_<32>

P142 = 1520742429925480309249157950965972233006436876279608768273203997250036059628029585673421815262936750036842572532516227046661639296824396080139_<142>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1498511238
Step 1 took 14159ms
Step 2 took 7539ms
********** Factor found in step 2: 84236514375392918434791697369357
Found probable prime factor of 32 digits: 84236514375392918434791697369357
Probable prime cofactor 1520742429925480309249157950965972233006436876279608768273203997250036059628029585673421815262936750036842572532516227046661639296824396080139 has 142 digits

(35·10¹⁸⁵-17)/9 = 3(8)₁₈₄7_<186> = 3 · 3242017 · 78781626947123_<14> · C165

C165 = P31 · C134

P31 = 5308091521661172993909954169669_<31>

C134 = [95614915315976341449915814671226342958300199565786370767219809757828964280275892186523976522697083942736597836961138778025419700393251_<134>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2815757366
Step 1 took 13757ms
Step 2 took 7741ms
********** Factor found in step 2: 5308091521661172993909954169669
Found probable prime factor of 31 digits: 5308091521661172993909954169669
Composite cofactor has 134 digits

(35·10¹⁶⁶-17)/9 = 3(8)₁₆₅7_<167> = 37 · 9967 · 37307 · 2354535121_<10> · 132127952267_<12> · 141133482721793_<15> · C122

C122 = P28 · P94

P28 = 8226444157972988141710931167_<28>

P94 = 7825767400812519208912071922939339970412517548592436550077410265971108080505948124839410842387_<94>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3714132238
Step 1 took 7741ms
Step 2 took 4408ms
********** Factor found in step 2: 8226444157972988141710931167
Found probable prime factor of 28 digits: 8226444157972988141710931167
Probable prime cofactor 7825767400812519208912071922939339970412517548592436550077410265971108080505948124839410842387 has 94 digits

(35·10¹⁷⁸-17)/9 = 3(8)₁₇₇7_<179> = 37 · 32969 · 189583 · 517981 · 3942871 · 10985291 · 22070273 · C141

C141 = P28 · P113

P28 = 6669335981879766458758192517_<28>

P113 = 50920232656772421298875597231096960594307229219521852623019622483583930275126623970795438847629543847126898487473_<113>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4196366601
Step 1 took 11768ms
Step 2 took 6458ms
********** Factor found in step 2: 6669335981879766458758192517
Found probable prime factor of 28 digits: 6669335981879766458758192517
Probable prime cofactor 50920232656772421298875597231096960594307229219521852623019622483583930275126623970795438847629543847126898487473 has 113 digits

(35·10¹¹⁴+1)/9 = 3(8)₁₁₃9_<115> = 832687381 · 15259609591_<11> · C96

C96 = P39 · P57

P39 = 690449786536111858913383994784646317701_<39>

P57 = 443269683332469302110610036873532000388386015468986749559_<57>

SNFS difficulty: 115 digits.
Divisors found:
 r1=690449786536111858913383994784646317701 (pp39)
 r2=443269683332469302110610036873532000388386015468986749559 (pp57)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.701).
Factorization parameters were as follows:
n: 306055458234833330425157231700400712933522790705374343481284656815000659951581236253030435643859
m: 100000000000000000000000
deg: 5
c5: 7
c0: 2
skew: 0.78
type: snfs
lss: 1
rlim: 600000
alim: 600000
lpbr: 25
lpba: 25
mfbr: 48
mfba: 48
rlambda: 2.2
alambda: 2.2
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 48/48
Sieved rational special-q in [300000, 450001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 51956 x 52170
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,600000,25,25,48,48,2.2,2.2,50000
total time: 0.50 hours.

(35·10¹⁵⁶+1)/9 = 3(8)₁₅₅9_<157> = 42879765185315430497_<20> · C137

C137 = P39 · P99

P39 = 292878855232275740887814418726995651773_<39>

P99 = 309660006169512256602650575144116413031660682773563091399663989195394753951491151864966823095355469_<99>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2088941172
Step 1 took 12424ms
Step 2 took 6633ms
********** Factor found in step 2: 292878855232275740887814418726995651773
Found probable prime factor of 39 digits: 292878855232275740887814418726995651773
Probable prime cofactor 309660006169512256602650575144116413031660682773563091399663989195394753951491151864966823095355469 has 99 digits

(35·10¹⁹⁴+1)/9 = 3(8)₁₉₃9_<195> = 1089969148057409_<16> · 10219198755552835523723_<23> · 9323979225759446991275928931_<28> · C130

C130 = P35 · P96

P35 = 12643344099626450719036094127714479_<35>

P96 = 296163291907625435082616666878492839479545213079224774475849163360422699627509912557439311446423_<96>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1697095651
Step 1 took 7693ms
Step 2 took 4596ms
********** Factor found in step 2: 12643344099626450719036094127714479
Found probable prime factor of 35 digits: 12643344099626450719036094127714479
Probable prime cofactor 296163291907625435082616666878492839479545213079224774475849163360422699627509912557439311446423 has 96 digits

(35·10¹²²-17)/9 = 3(8)₁₂₁7_<123> = 3 · 1667 · 200131 · 19180783 · C107

C107 = P49 · P59

P49 = 1127206542851648414760167029508360310343210538429_<49>

P59 = 17971506403106683410565933523865358418769645819039526418711_<59>

SNFS difficulty: 124 digits.
Divisors found:
 r1=1127206542851648414760167029508360310343210538429 (pp49)
 r2=17971506403106683410565933523865358418769645819039526418711 (pp59)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.724).
Factorization parameters were as follows:
n: 20257599602482147603370790428086817735513085831236870307396235699167569456996686633362298322208972410145019
m: 5000000000000000000000000
deg: 5
c5: 28
c0: -425
skew: 1.72
type: snfs
lss: 1
rlim: 850000
alim: 850000
lpbr: 25
lpba: 25
mfbr: 48
mfba: 48
rlambda: 2.2
alambda: 2.2
Factor base limits: 850000/850000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 48/48
Sieved rational special-q in [425000, 775001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 99712 x 99953
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,850000,850000,25,25,48,48,2.2,2.2,50000
total time: 1.10 hours.

(35·10¹⁴⁹+1)/9 = 3(8)₁₄₈9_<150> = 26091809 · 11465034896004908807461_<23> · C121

C121 = P34 · P88

P34 = 1088707817387439431350379964842563_<34>

P88 = 1194083292946011325405761931527911769362936033665647008316544335094461381186494573304247_<88>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2177793751
Step 1 took 9949ms
Step 2 took 5702ms
********** Factor found in step 2: 1088707817387439431350379964842563
Found probable prime factor of 34 digits: 1088707817387439431350379964842563
Probable prime cofactor 1194083292946011325405761931527911769362936033665647008316544335094461381186494573304247 has 88 digits

(35·10¹⁴²+1)/9 = 3(8)₁₄₁9_<143> = 3 · 1061 · C140

C140 = P41 · P99

P41 = 15860642001115756856472209121303190876727_<41>

P99 = 770314607968882846559673942076146333468438492173211262631406081919930865891145617675420812966181729_<99>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4239433639
Step 1 took 9320ms
Step 2 took 5009ms
********** Factor found in step 2: 15860642001115756856472209121303190876727
Found probable prime factor of 41 digits: 15860642001115756856472209121303190876727
Probable prime cofactor 770314607968882846559673942076146333468438492173211262631406081919930865891145617675420812966181729 has 99 digits

(35·10¹⁵⁶-17)/9 = 3(8)₁₅₅7_<157> = 19 · 58096309927_<11> · C145

C145 = P37 · C109

P37 = 1859651820102671746966417186881408253_<37>

C109 = [1894487508440474112716213669780549012421849506804151246935164488038515303188473619404856596787335933634952583_<109>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3652731674
Step 1 took 9300ms
Step 2 took 4985ms
********** Factor found in step 2: 1859651820102671746966417186881408253
Found probable prime factor of 37 digits: 1859651820102671746966417186881408253
Composite cofactor has 109 digits

(35·10¹⁵⁷-17)/9 = 3(8)₁₅₆7_<158> = 23 · 37 · 2069 · 1151733944305984141_<19> · 53292721252355927483_<20> · C114

C114 = P45 · P69

P45 = 951140256289141598794249013986046916487726837_<45>

P69 = 378330066980404354259155145077482265252602731240864591664915709201643_<69>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2131351972
Step 1 took 8217ms
Step 2 took 5288ms
********** Factor found in step 2: 951140256289141598794249013986046916487726837
Found probable prime factor of 45 digits: 951140256289141598794249013986046916487726837
Probable prime cofactor 378330066980404354259155145077482265252602731240864591664915709201643 has 69 digits

Dec 7, 2008 (4th)

Factorizations of 388...887 and Factorizations of 388...889 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Dec 7, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(34·10¹⁵⁶+11)/9 = 3(7)₁₅₅9_<157> = 431 · 20428085369379755054381161567133_<32> · C123

C123 = P40 · P84

P40 = 1641290498119364233612216509348496842037_<40>

P84 = 261424338685306378465746420265055797130828604401971263690053114734342542603363295229_<84>

Number: 37779_156
N=429073283061331887029373538382779736581251147921326448030495788175194522967423873919288084893891002909527976603344608741473
  ( 123 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=1641290498119364233612216509348496842037 (pp40)
 r2=261424338685306378465746420265055797130828604401971263690053114734342542603363295229 (pp84)
Version: GGNFS-0.77.1-20060513-k8
Total time: 50.25 hours.
Scaled time: 98.85 units (timescale=1.967).
Factorization parameters were as follows:
name: 37779_156
n: 429073283061331887029373538382779736581251147921326448030495788175194522967423873919288084893891002909527976603344608741473
m: 20000000000000000000000000000000
deg: 5
c5: 85
c0: 88
skew: 1.01
type: snfs
lss: 1
rlim: 3100000
alim: 3100000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3100000/3100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1550000, 3050001)
Primes: RFBsize:223492, AFBsize:224096, largePrimes:8479610 encountered
Relations: rels:9014923, finalFF:825935
Max relations in full relation-set: 28
Initial matrix: 447655 x 825935 with sparse part having weight 98632766.
Pruned matrix : 343747 x 346049 with weight 49427794.
Total sieving time: 47.33 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 2.44 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,50,50,2.4,2.4,100000
total time: 50.25 hours.
 --------- CPU info (if available) ----------

Dec 7, 2008 (2nd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39

(35·10¹⁶⁷-71)/9 = 3(8)₁₆₆1_<168> = 3⁴ · 146222004002926974466791407216706971_<36> · C131

C131 = P38 · P41 · P52

P38 = 81341906412392977262829851074413415931_<38>

P41 = 41635795095299879483137183719197356361501_<41>

P52 = 9694972354607531461319586026968019249490464567538301_<52>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=4289341784
Step 1 took 36615ms
Step 2 took 19160ms
********** Factor found in step 2: 41635795095299879483137183719197356361501
Found probable prime factor of 41 digits: 41635795095299879483137183719197356361501

Msieve v. 1.39
Sat Dec  6 12:40:47 2008
random seeds: 55056cf5 fb864dee
factoring 788607533939223004816128108651343184586583380585738621712061138366496488305796633086073231 (90 digits)
searching for 15-digit factors
commencing quadratic sieve (90-digit input)
using multiplier of 1
using 64kb Opteron sieve core
sieve interval: 18 blocks of size 65536
processing polynomials in batches of 6
using a sieve bound of 1608661 (61176 primes)
using large prime bound of 135127524 (27 bits)
using double large prime bound of 431855810609412 (42-49 bits)
using trial factoring cutoff of 49 bits
polynomial 'A' values have 11 factors

sieving in progress (press Ctrl-C to pause)
61329 relations (15844 full + 45485 combined from 667610 partial), need 61272
61329 relations (15844 full + 45485 combined from 667610 partial), need 61272
sieving complete, commencing postprocessing
begin with 683454 relations
reduce to 151862 relations in 10 passes
attempting to read 151862 relations
recovered 151862 relations
recovered 132888 polynomials
attempting to build 61329 cycles
found 61329 cycles in 6 passes
distribution of cycle lengths:
   length 1 : 15844
   length 2 : 11503
   length 3 : 10595
   length 4 : 8174
   length 5 : 5986
   length 6 : 4006
   length 7 : 2285
   length 9+: 2936
largest cycle: 20 relations
matrix is 61176 x 61329 (16.5 MB) with weight 3840633 (62.62/col)
sparse part has weight 3840633 (62.62/col)
filtering completed in 3 passes
matrix is 57546 x 57610 (15.6 MB) with weight 3639842 (63.18/col)
sparse part has weight 3639842 (63.18/col)
saving the first 48 matrix rows for later
matrix is 57498 x 57610 (12.1 MB) with weight 3077780 (53.42/col)
sparse part has weight 2589368 (44.95/col)
matrix includes 64 packed rows
using block size 23044 for processor cache size 1024 kB
commencing Lanczos iteration
memory use: 9.9 MB
lanczos halted after 911 iterations (dim = 57497)
recovered 17 nontrivial dependencies
prp38 factor: 81341906412392977262829851074413415931
prp52 factor: 9694972354607531461319586026968019249490464567538301
elapsed time 01:13:27

(16·10¹⁷²-7)/9 = 1(7)₁₇₂_<173> = 29 · 13646237777_<11> · 38365512482221_<14> · C148

C148 = P74 · P75

P74 = 11028341891571566346970754072658129784323506979873488661401005556161967581_<74>

P75 = 106173299975901986267593348697479150345163312613129043156754080131224341469_<75>

# a quasi-nice split (when factors r2/10<r1<r2)      :-)
#                              i.e. within 1 order of magnitude, BUT not the same length
#
SNFS difficulty: 173 digits.
Divisors found:
 r1=11028341891571566346970754072658129784323506979873488661401005556161967581 (pp74)
 r2=106173299975901986267593348697479150345163312613129043156754080131224341469 (pp75)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.699).
Factorization parameters were as follows:
n: 1170915451890634250878062812897650274435783395035731292758702557401427814481884711786286345110790218975486899180727931490597815191244770920051916489
m: 20000000000000000000000000000000000
deg: 5
c5: 50
c0: -7
skew: 0.67
type: snfs
lss: 1
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2700000, 6100001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1012460 x 1012702
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,5400000,5400000,27,27,52,52,2.4,2.4,100000
total time: 0.00 hours.

Dec 7, 2008

By Robert Backstrom / GGNFS, Msieve

(32·10²⁰⁴-41)/9 = 3(5)₂₀₃1_<205> = 73 · 863 · C200

C200 = P47 · P62 · P92

P47 = 14248427654041308826650517475730475139675651291_<47>

P62 = 39913387700709211382964131171098547802886843448472175066153267_<62>

P92 = 99240348514737227891488012650045657725921855844817056668365570013539644495922325704459609817_<92>

Number: n
N=56438285616526540985659384364125709226425110804227933071248044501588208631177567192424571113121725036199869133725226679083089502302505683511731226774322696480191043596811942341236457016072565525731449
  ( 200 digits)
SNFS difficulty: 206 digits.
Divisors found:

Sun Dec 07 04:22:58 2008  prp47 factor: 14248427654041308826650517475730475139675651291
Sun Dec 07 04:22:58 2008  prp62 factor: 39913387700709211382964131171098547802886843448472175066153267
Sun Dec 07 04:22:58 2008  prp92 factor: 99240348514737227891488012650045657725921855844817056668365570013539644495922325704459609817
Sun Dec 07 04:22:59 2008  elapsed time 28:19:21 (Msieve 1.39 - dependency 5)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 153.01 hours.
Scaled time: 312.90 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_3_5_203_1
n: 56438285616526540985659384364125709226425110804227933071248044501588208631177567192424571113121725036199869133725226679083089502302505683511731226774322696480191043596811942341236457016072565525731449
type: snfs
skew: 3.33
deg: 5
c5: 1
c0: -410
m: 200000000000000000000000000000000000000000
rlim: 10000000
alim: 10000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 25400001)
Primes: RFBsize:664579, AFBsize:665006, largePrimes:36354193 encountered
Relations: rels:27543760, finalFF:133156
Max relations in full relation-set: 28

Msieve: found 9558761 hash collisions in 45411678 relations
Msieve: matrix is 2874359 x 2874607 (781.1 MB)

Initial matrix: 
Pruned matrix : 
Total sieving time: 150.52 hours.
Total relation processing time: 2.49 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,206,5,0,0,0,0,0,0,0,0,10000000,10000000,29,29,58,58,2.5,2.5,100000
total time: 153.01 hours.
 --------- CPU info (if available) ----------

Dec 6, 2008 (4th)

By Jo Yeong Uk / GGNFS

(34·10¹⁵⁹-61)/9 = 3(7)₁₅₈1_<160> = 3 · 461 · 1424499695196759996786287319127759813_<37> · C121

C121 = P44 · P77

P44 = 70223475270970631308833714247375703978882183_<44>

P77 = 27306720714056958176389348613507388851630448512655938025187958253361469703103_<77>

Number: 37771_159
N=1917572826794880301937743521661713539970375827079494046314123580541938102384192570367828862969420055823648457470826513849
  ( 121 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=70223475270970631308833714247375703978882183 (pp44)
 r2=27306720714056958176389348613507388851630448512655938025187958253361469703103 (pp77)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 29.67 hours.
Scaled time: 70.50 units (timescale=2.376).
Factorization parameters were as follows:
n: 1917572826794880301937743521661713539970375827079494046314123580541938102384192570367828862969420055823648457470826513849
m: 100000000000000000000000000000000
deg: 5
c5: 17
c0: -305
skew: 1.78
type: snfs
lss: 1
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1800000, 3600001)
Primes: RFBsize:256726, AFBsize:257467, largePrimes:9103348 encountered
Relations: rels:9343195, finalFF:597134
Max relations in full relation-set: 28
Initial matrix: 514258 x 597134 with sparse part having weight 64218803.
Pruned matrix : 481231 x 483866 with weight 48798972.
Total sieving time: 27.66 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 1.83 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3600000,3600000,27,27,51,51,2.4,2.4,100000
total time: 29.67 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Dec 6, 2008 (3rd)

By Serge Batalov / Msieve-1.39, GMP-ECM 6.2.1

(35·10¹⁶⁴-71)/9 = 3(8)₁₆₃1_<165> = 3 · 40639 · C160

C160 = P64 · P96

P64 = 6729192217450863728598048618087237613653798990636162581422405139_<64>

P96 = 474021820032276344490729878036508269662859504739325818203395008676857889810899763775201694993287_<96>

SNFS difficulty: 165 digits.
Divisors found:
 r1=6729192217450863728598048618087237613653798990636162581422405139 (pp64)
 r2=474021820032276344490729878036508269662859504739325818203395008676857889810899763775201694993287 (pp96)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 3189783942263087911356815611349433539940196107916770334644790217023785763174035523256714723040173961702542622348719939703969822821172509895165472320421999301893
m: 500000000000000000000000000000000
deg: 5
c5: 112
c0: -71
skew: 0.91
type: snfs
lss: 1
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2000000, 3600001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 717162 x 717410
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,52,52,2.4,2.4,200000
total time: 33.00 hours.

(35·10¹⁵³-71)/9 = 3(8)₁₅₂1_<154> = 97 · 29683 · C148

C148 = P71 · P77

P71 = 27062252094015893891367821833925557921914470068002173930604051639604273_<71>

P77 = 49909368320669392065207112067360020697367464724002460386090056808636455973147_<77>

SNFS difficulty: 155 digits.
Divisors found:
 r1=27062252094015893891367821833925557921914470068002173930604051639604273 (pp71)
 r2=49909368320669392065207112067360020697367464724002460386090056808636455973147 (pp77)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.568).
Factorization parameters were as follows:
n: 1350659907347045772976683480838901814704202200116936275749800517179255608103944007969047814479838294365058443633045152676473460941365962498194457131
m: 5000000000000000000000000000000
deg: 5
c5: 56
c0: -355
skew: 1.45
type: snfs
lss: 1
rlim: 2700000
alim: 2700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 2700000/2700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1350000, 2350001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 594251 x 594499
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2700000,2700000,27,27,52,52,2.4,2.4,100000
total time: 16.00 hours.

(35·10²⁰⁰-71)/9 = 3(8)₁₉₉1_<201> = 3 · 16553 · 7927223 · 22704073853_<11> · 3979963552476295781_<19> · C161

C161 = P36 · P125

P36 = 395164945190857945350101909540564167_<36>

P125 = 27665924809055869339926234061280855054857483038403980884226624743443037940825917222475596589660592881576057076851168755649043_<125>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=3549987951
Step 1 took 50820ms
Step 2 took 23819ms
********** Factor found in step 2: 395164945190857945350101909540564167
Found probable prime factor of 36 digits: 395164945190857945350101909540564167
Probable prime cofactor has 125 digits

(35·10¹⁹⁹-71)/9 = 3(8)₁₉₈1_<200> = 433 · 5039 · 140389427623_<12> · 8357290475369752537_<19> · C164

C164 = P40 · P124

P40 = 1861468120897201492992872990658651081937_<40>

P124 = 8160894744665296943921251395162584241097643099470088044534647763466723548653244079777378652912656058510639793059446322808049_<124>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=449619090
Step 1 took 40186ms
Step 2 took 18013ms
********** Factor found in step 2: 1861468120897201492992872990658651081937
Found probable prime factor of 40 digits: 1861468120897201492992872990658651081937
Probable prime cofactor has 124 digits

(35·10¹⁷⁷-71)/9 = 3(8)₁₇₆1_<178> = 19 · 431 · 14192094360547_<14> · C161

C161 = P41 · P121

P41 = 16344822089886294631376367252687044228611_<41>

P121 = 2047236311811775237853370064349460550471296836642857788077745439397058049721082870618229704024096730530929819770762123837_<121>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=3439074722
Step 1 took 39858ms
Step 2 took 17981ms
********** Factor found in step 2: 16344822089886294631376367252687044228611
Found probable prime factor of 41 digits: 16344822089886294631376367252687044228611
Probable prime cofactor 2047236311811775237853370064349460550471296836642857788077745439397058049721082870618229704024096730530929819770762123837 has 121 digits

(35·10¹⁷⁹-71)/9 = 3(8)₁₇₈1_<180> = 3 · 26269883 · 8834314133_<10> · C162

C162 = P36 · P127

P36 = 160020693433359773518143219603912809_<36>

P127 = 3490576460850053450847907349976182625659172933180934406601688040579959555205761204584348481290922830235197726475366791229889077_<127>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1303534847
Step 1 took 51179ms
Step 2 took 23917ms
********** Factor found in step 2: 160020693433359773518143219603912809
Found probable prime factor of 36 digits: 160020693433359773518143219603912809
Probable prime cofactor 3490576460850053450847907349976182625659172933180934406601688040579959555205761204584348481290922830235197726475366791229889077 has 127 digits

Dec 6, 2008 (2nd)

By Sinkiti Sibata / GGNFS, Msieve

(35·10¹⁵⁷-71)/9 = 3(8)₁₅₆1_<158> = 2389 · 333630907000621_<15> · 589449675624851_<15> · 17403193705595170453363_<23> · C103

C103 = P42 · P62

P42 = 316077293436539492798483427174028217764847_<42>

P62 = 15047838586998004833845001684573837704128871608268602161556759_<62>

Number: 38881_157
N=4756280092648250188764199475728532994664874904397340967740470473080958604184638935560577270528905450873
  ( 103 digits)
Divisors found:
 r1=316077293436539492798483427174028217764847 (pp42)
 r2=15047838586998004833845001684573837704128871608268602161556759 (pp62)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 12.31 hours.
Scaled time: 5.82 units (timescale=0.473).
Factorization parameters were as follows:
name: 38881_157
n: 4756280092648250188764199475728532994664874904397340967740470473080958604184638935560577270528905450873
skew: 3602.91
# norm 2.89e+13
c5: 124320
c4: 635767801
c3: -5358051732169
c2: -6064988245481505
c1: 20352909303228765418
c0: -12588858375220797134080
# alpha -5.28
Y1: 10112432209
Y0: -32850739271467085601
# Murphy_E 2.80e-09
# M 4222018691528632760447361348847040396549466575631545691946562696264792403080906743535614308110637954375
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1750001)
Primes: RFBsize:169511, AFBsize:168817, largePrimes:4255453 encountered
Relations: rels:4207348, finalFF:391895
Max relations in full relation-set: 28
Initial matrix: 338411 x 391895 with sparse part having weight 26409720.
Pruned matrix : 291880 x 293636 with weight 15689274.
Polynomial selection time: 0.70 hours.
Total sieving time: 9.38 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 1.77 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 12.31 hours.
 --------- CPU info (if available) ----------

(35·10¹⁴⁸-71)/9 = 3(8)₁₄₇1_<149> = 23 · 139 · 167 · 359 · 24859 · 1899647 · C130

C130 = P47 · P84

P47 = 11005429562821160352220822132656618449470600567_<47>

P84 = 390398751300760287606065533166549932446704337286288865468217757117600799730398985751_<84>

Number: 38881_148
N=4296505958853853198420117289707372789332643113650127011567313181181692972509393851525932474511053618295318863339773930029645520817
  ( 130 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=11005429562821160352220822132656618449470600567 (pp47)
 r2=390398751300760287606065533166549932446704337286288865468217757117600799730398985751 (pp84)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 31.44 hours.
Scaled time: 80.61 units (timescale=2.564).
Factorization parameters were as follows:
name: 38881_148
n: 4296505958853853198420117289707372789332643113650127011567313181181692972509393851525932474511053618295318863339773930029645520817
m: 500000000000000000000000000000
deg: 5
c5: 56
c0: -355
skew: 1.45
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1100000, 2000001)
Primes: RFBsize:162662, AFBsize:162346, largePrimes:8114482 encountered
Relations: rels:9417140, finalFF:1578049
Max relations in full relation-set: 28
Initial matrix: 325074 x 1578049 with sparse part having weight 192518771.
Pruned matrix : 222168 x 223857 with weight 36995244.
Total sieving time: 30.70 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.50 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,49,49,2.4,2.4,100000
total time: 31.44 hours.
 --------- CPU info (if available) ----------

(35·10¹⁰⁵-71)/9 = 3(8)₁₀₄1_<106> = 19 · 67 · C103

C103 = P49 · P55

P49 = 1562267463406113328722074385809274805765951155247_<49>

P55 = 1955427611138011473211547323006830547632965613911300951_<55>

Fri Dec 05 17:00:31 2008  Msieve v. 1.39
Fri Dec 05 17:00:31 2008  random seeds: fc5576e8 64ab5ee6
Fri Dec 05 17:00:31 2008  factoring 3054900933926856943353408396613424107532512874225364406039975560792528585144453172732827092607139739897 (103 digits)
Fri Dec 05 17:00:32 2008  searching for 15-digit factors
Fri Dec 05 17:00:34 2008  commencing quadratic sieve (103-digit input)
Fri Dec 05 17:00:34 2008  using multiplier of 2
Fri Dec 05 17:00:34 2008  using 32kb Intel Core sieve core
Fri Dec 05 17:00:34 2008  sieve interval: 36 blocks of size 32768
Fri Dec 05 17:00:34 2008  processing polynomials in batches of 6
Fri Dec 05 17:00:34 2008  using a sieve bound of 3415309 (122500 primes)
Fri Dec 05 17:00:34 2008  using large prime bound of 512296350 (28 bits)
Fri Dec 05 17:00:34 2008  using double large prime bound of 4754865765116250 (44-53 bits)
Fri Dec 05 17:00:34 2008  using trial factoring cutoff of 53 bits
Fri Dec 05 17:00:34 2008  polynomial 'A' values have 13 factors
Sat Dec 06 10:39:04 2008  122696 relations (29594 full + 93102 combined from 1817556 partial), need 122596
Sat Dec 06 10:39:06 2008  begin with 1847150 relations
Sat Dec 06 10:39:09 2008  reduce to 320816 relations in 14 passes
Sat Dec 06 10:39:09 2008  attempting to read 320816 relations
Sat Dec 06 10:39:15 2008  recovered 320816 relations
Sat Dec 06 10:39:15 2008  recovered 311130 polynomials
Sat Dec 06 10:39:15 2008  attempting to build 122696 cycles
Sat Dec 06 10:39:15 2008  found 122696 cycles in 6 passes
Sat Dec 06 10:39:15 2008  distribution of cycle lengths:
Sat Dec 06 10:39:15 2008     length 1 : 29594
Sat Dec 06 10:39:15 2008     length 2 : 21278
Sat Dec 06 10:39:15 2008     length 3 : 20624
Sat Dec 06 10:39:15 2008     length 4 : 16624
Sat Dec 06 10:39:15 2008     length 5 : 12623
Sat Dec 06 10:39:15 2008     length 6 : 8645
Sat Dec 06 10:39:15 2008     length 7 : 5696
Sat Dec 06 10:39:15 2008     length 9+: 7612
Sat Dec 06 10:39:15 2008  largest cycle: 21 relations
Sat Dec 06 10:39:16 2008  matrix is 122500 x 122696 (36.3 MB) with weight 9015392 (73.48/col)
Sat Dec 06 10:39:16 2008  sparse part has weight 9015392 (73.48/col)
Sat Dec 06 10:39:18 2008  filtering completed in 3 passes
Sat Dec 06 10:39:18 2008  matrix is 117311 x 117374 (34.9 MB) with weight 8688006 (74.02/col)
Sat Dec 06 10:39:18 2008  sparse part has weight 8688006 (74.02/col)
Sat Dec 06 10:39:18 2008  saving the first 48 matrix rows for later
Sat Dec 06 10:39:18 2008  matrix is 117263 x 117374 (25.5 MB) with weight 7294140 (62.14/col)
Sat Dec 06 10:39:18 2008  sparse part has weight 5973790 (50.90/col)
Sat Dec 06 10:39:18 2008  matrix includes 64 packed rows
Sat Dec 06 10:39:18 2008  using block size 43690 for processor cache size 1024 kB
Sat Dec 06 10:39:20 2008  commencing Lanczos iteration
Sat Dec 06 10:39:20 2008  memory use: 22.3 MB
Sat Dec 06 10:41:08 2008  lanczos halted after 1856 iterations (dim = 117263)
Sat Dec 06 10:41:08 2008  recovered 18 nontrivial dependencies
Sat Dec 06 10:41:10 2008  prp49 factor: 1562267463406113328722074385809274805765951155247
Sat Dec 06 10:41:10 2008  prp55 factor: 1955427611138011473211547323006830547632965613911300951
Sat Dec 06 10:41:10 2008  elapsed time 17:40:39

(35·10¹⁵¹-71)/9 = 3(8)₁₅₀1_<152> = 31 · 1210922113_<10> · 4834258445689_<13> · C129

C129 = P53 · P77

P53 = 12358500842512959654534882662579877414220284948569179_<53>

P77 = 17340115058960026817035095906197024842383922831776749394279438959223915036517_<77>

Number: 38881_151
N=214297826565429150492910064568361695812555353202466228632291289065314164253707324199225375072353391618673584558585674182685709543
  ( 129 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=12358500842512959654534882662579877414220284948569179 (pp53)
 r2=17340115058960026817035095906197024842383922831776749394279438959223915036517 (pp77)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 32.66 hours.
Scaled time: 83.74 units (timescale=2.564).
Factorization parameters were as follows:
name: 38881_151
n: 214297826565429150492910064568361695812555353202466228632291289065314164253707324199225375072353391618673584558585674182685709543
m: 1000000000000000000000000000000
deg: 5
c5: 350
c0: -71
skew: 0.73
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176209, largePrimes:8615759 encountered
Relations: rels:9485023, finalFF:1053292
Max relations in full relation-set: 28
Initial matrix: 352578 x 1053292 with sparse part having weight 135303276.
Pruned matrix : 253374 x 255200 with weight 47792421.
Total sieving time: 31.55 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.85 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000
total time: 32.66 hours.
 --------- CPU info (if available) ----------

(35·10¹⁵⁸-71)/9 = 3(8)₁₅₇1_<159> = 3² · 872731 · 11263537857560226125063933208259_<32> · C121

C121 = P52 · P69

P52 = 5021903696133745830067411705044711834566746760809363_<52>

P69 = 875305020815140943837780270287316610643722751592004225362380010464867_<69>

Number: 38881_158
N=4395697519275981635190971269779667210646649147252567630493794524731924375810616348513154465968256408807779438490796149721
  ( 121 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=5021903696133745830067411705044711834566746760809363 (pp52)
 r2=875305020815140943837780270287316610643722751592004225362380010464867 (pp69)
Version: GGNFS-0.77.1-20060513-k8
Total time: 57.95 hours.
Scaled time: 113.58 units (timescale=1.960).
Factorization parameters were as follows:
name:  38881_158
n: 4395697519275981635190971269779667210646649147252567630493794524731924375810616348513154465968256408807779438490796149721
m: 50000000000000000000000000000000
deg: 5
c5: 56
c0: -355
skew: 1.45
type: snfs
lss: 1
rlim: 3300000
alim: 3300000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3300000/3300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1650000, 3350001)
Primes: RFBsize:236900, AFBsize:236893, largePrimes:9198456 encountered
Relations: rels:9588051, finalFF:598468
Max relations in full relation-set: 28
Initial matrix: 473859 x 598468 with sparse part having weight 69907364.
Pruned matrix : 429011 x 431444 with weight 48235210.
Total sieving time: 54.00 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 3.41 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3300000,3300000,27,27,51,51,2.4,2.4,100000
total time: 57.95 hours.
 --------- CPU info (if available) ----------

Dec 6, 2008

By Wataru Sakai / GGNFS

4·10²⁰⁰-3 = 3(9)₁₉₉7_<201> = 397 · C199

C199 = P55 · P144

P55 = 1591080945026496112917339112958930463606304590528911569_<55>

P144 = 633252932990278223069090414959637564981283096491029523470488470154265459768968029261042716837602446043281857774800232294214750266149540233317729_<144>

Number: 39997_200
N=1007556675062972292191435768261964735516372795969773299748110831234256926952141057934508816120906801007556675062972292191435768261964735516372795969773299748110831234256926952141057934508816120906801
  ( 199 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=1591080945026496112917339112958930463606304590528911569
 r2=633252932990278223069090414959637564981283096491029523470488470154265459768968029261042716837602446043281857774800232294214750266149540233317729
Version: 
Total time: 626.57 hours.
Scaled time: 1243.74 units (timescale=1.985).
Factorization parameters were as follows:
n: 1007556675062972292191435768261964735516372795969773299748110831234256926952141057934508816120906801007556675062972292191435768261964735516372795969773299748110831234256926952141057934508816120906801
m: 10000000000000000000000000000000000000000
deg: 5
c5: 4
c0: -3
skew: 0.94
type: snfs
lss: 1
rlim: 15400000
alim: 15400000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
Factor base limits: 15400000/15400000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [7700000, 14100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2802786 x 2803034
Total sieving time: 626.57 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,200,5,0,0,0,0,0,0,0,0,15400000,15400000,29,29,56,56,2.6,2.6,100000
total time: 626.57 hours.
 --------- CPU info (if available) ----------

Dec 5, 2008 (6th)

By Wataru Sakai / GGNFS

10¹⁷²+3 = 1(0)₁₇₁3_<173> = 7 · 103 · 4840357 · C163

C163 = P58 · P105

P58 = 6217133466469352588076049198728375528009389334759580516393_<58>

P105 = 460889856884875870260428947472281235450995348075280309946390712729504236795643811044642178283027609350143_<105>

Number: 10003_172
N=2865413753595232129398903356928690817897991056612143717989082187335148180002496503194474860373667312145337549589856896300037556662872859812044497192419895088394199
  ( 163 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=6217133466469352588076049198728375528009389334759580516393 (pp58)
 r2=460889856884875870260428947472281235450995348075280309946390712729504236795643811044642178283027609350143 (pp105)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 103.49 hours.
Scaled time: 208.53 units (timescale=2.015).
Factorization parameters were as follows:
n: 2865413753595232129398903356928690817897991056612143717989082187335148180002496503194474860373667312145337549589856896300037556662872859812044497192419895088394199
m: 20000000000000000000000000000000000
deg: 5
c5: 25
c0: 24
skew: 0.99
type: snfs
lss: 1
rlim: 5300000
alim: 5300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5300000/5300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2650000, 5550001)
Primes: RFBsize:367900, AFBsize:368047, largePrimes:10352551 encountered
Relations: rels:11115160, finalFF:896590
Max relations in full relation-set: 32
Initial matrix: 736012 x 896590 with sparse part having weight 113714104.
Pruned matrix : 642276 x 646020 with weight 89259004.
Total sieving time: 98.38 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 4.75 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,5300000,5300000,27,27,52,52,2.4,2.4,100000
total time: 103.49 hours.
 --------- CPU info (if available) ----------

Dec 5, 2008 (5th)

By Robert Backstrom / GGNFS, Msieve

(32·10¹⁶⁴+31)/9 = 3(5)₁₆₃9_<165> = 26711 · C161

C161 = P55 · P106

P55 = 9750124430174322079990785274701676614927947079446672633_<55>

P106 = 1365234213461941186730471721006005384005878692179369864168580091088793810524096380552387838598296089911993_<106>

Number: n
N=13311203457585098107729233482668397123116152729420671467019413558292671766521491353957379190429244713996314460542681125961422468479486187546537215213041651587569
  ( 161 digits)
SNFS difficulty: 166 digits.
Divisors found:

Fri Dec 05 18:46:41 2008  prp55 factor: 9750124430174322079990785274701676614927947079446672633
Fri Dec 05 18:46:41 2008  prp106 factor: 1365234213461941186730471721006005384005878692179369864168580091088793810524096380552387838598296089911993
Fri Dec 05 18:46:41 2008  elapsed time 02:08:47 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 31.27 hours.
Scaled time: 57.00 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_3_5_163_9
n: 13311203457585098107729233482668397123116152729420671467019413558292671766521491353957379190429244713996314460542681125961422468479486187546537215213041651587569
type: snfs
skew: 3.15
deg: 5
c5: 1
c0: 310
m: 2000000000000000000000000000000000
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 1900001)
Primes: RFBsize:348513, AFBsize:349532, largePrimes:14897284 encountered
Relations: rels:13440474, finalFF:731215
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 30.82 hours.
Total relation processing time: 0.45 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.5,2.5,100000
total time: 31.27 hours.
 --------- CPU info (if available) ----------

Dec 5, 2008 (4th)

By Sinkiti Sibata / GGNFS, Msieve

(35·10¹¹⁷-71)/9 = 3(8)₁₁₆1_<118> = 375643 · C113

C113 = P49 · P64

P49 = 2407192503767726283938093397877279814867330840593_<49>

P64 = 4300702608253451422223050521702143454051375448060420057356800819_<64>

Number: 38881_117
N=10352619079522016619207302914972164765186330875029985621691044126707775438085865805802021836927318994068540845667
  ( 113 digits)
SNFS difficulty: 119 digits.
Divisors found:
 r1=2407192503767726283938093397877279814867330840593 (pp49)
 r2=4300702608253451422223050521702143454051375448060420057356800819 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.98 hours.
Scaled time: 5.99 units (timescale=2.010).
Factorization parameters were as follows:
name: 38881_117
n: 10352619079522016619207302914972164765186330875029985621691044126707775438085865805802021836927318994068540845667
m: 200000000000000000000000
deg: 5
c5: 875
c0: -568
skew: 0.92
type: snfs
lss: 1
rlim: 690000
alim: 690000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 690000/690000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [345000, 695001)
Primes: RFBsize:55815, AFBsize:56064, largePrimes:1490570 encountered
Relations: rels:1555639, finalFF:231675
Max relations in full relation-set: 28
Initial matrix: 111946 x 231675 with sparse part having weight 13074136.
Pruned matrix : 84612 x 85235 with weight 3834904.
Total sieving time: 2.88 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,119,5,0,0,0,0,0,0,0,0,690000,690000,25,25,45,45,2.2,2.2,50000
total time: 2.98 hours.
 --------- CPU info (if available) ----------

(35·10¹³³-71)/9 = 3(8)₁₃₂1_<134> = 626636045531_<12> · C122

C122 = P57 · P65

P57 = 664661136625342072710172593992343671372176190170793922127_<57>

P65 = 93370541208729459632002309204427506540981356824207695672872397613_<65>

Number: 38881_133
N=62059770047117463525210261016827144517283034923743649863583909877584256653942798017061503606657721825998117614322502682851
  ( 122 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=664661136625342072710172593992343671372176190170793922127 (pp57)
 r2=93370541208729459632002309204427506540981356824207695672872397613 (pp65)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 6.39 hours.
Scaled time: 16.46 units (timescale=2.575).
Factorization parameters were as follows:
name: 38881_133
n: 62059770047117463525210261016827144517283034923743649863583909877584256653942798017061503606657721825998117614322502682851
m: 500000000000000000000000000
deg: 5
c5: 56
c0: -355
skew: 1.45
type: snfs
lss: 1
rlim: 1260000
alim: 1260000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1260000/1260000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [630000, 1305001)
Primes: RFBsize:97182, AFBsize:96764, largePrimes:3257937 encountered
Relations: rels:3274946, finalFF:296830
Max relations in full relation-set: 28
Initial matrix: 194012 x 296830 with sparse part having weight 27557581.
Pruned matrix : 168007 x 169041 with weight 12453978.
Total sieving time: 6.15 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1260000,1260000,26,26,47,47,2.3,2.3,75000
total time: 6.39 hours.
 --------- CPU info (if available) ----------

(35·10¹²⁵-71)/9 = 3(8)₁₂₄1_<126> = 3 · 55061 · C121

C121 = P42 · P80

P42 = 193777002671305679513189401385663005139429_<42>

P80 = 12149487304698154777013912556623553448883532470722295647430245883133644361392483_<80>

Number: 38881_125
N=2354291233897488778438997287183843911836501873006840225016429589539413189546677859639847253584744730928054877856007512207
  ( 121 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=193777002671305679513189401385663005139429 (pp42)
 r2=12149487304698154777013912556623553448883532470722295647430245883133644361392483 (pp80)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.60 hours.
Scaled time: 7.20 units (timescale=1.997).
Factorization parameters were as follows:
name: 38881_125
n: 2354291233897488778438997287183843911836501873006840225016429589539413189546677859639847253584744730928054877856007512207
m: 10000000000000000000000000
deg: 5
c5: 35
c0: -71
skew: 1.15
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 800001)
Primes: RFBsize:71274, AFBsize:71106, largePrimes:2741634 encountered
Relations: rels:2774104, finalFF:312654
Max relations in full relation-set: 28
Initial matrix: 142446 x 312654 with sparse part having weight 25875141.
Pruned matrix : 108667 x 109443 with weight 6866036.
Total sieving time: 3.42 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 3.60 hours.
 --------- CPU info (if available) ----------

(35·10¹⁴³-71)/9 = 3(8)₁₄₂1_<144> = 3 · 24877 · 2449308294863_<13> · 738760692290080903_<18> · 3043277453107840967_<19> · C90

C90 = P43 · P48

P43 = 6518639221073681222625258143211300772137541_<43>

P48 = 145164541708841951682791434372335409586197147397_<48>

Fri Dec 05 08:27:47 2008  Msieve v. 1.39
Fri Dec 05 08:27:47 2008  random seeds: 46401fa0 55a4e33b
Fri Dec 05 08:27:47 2008  factoring 946275275092443409644573949876196092691119058392272946735399730110850546130079032334130777 (90 digits)
Fri Dec 05 08:27:48 2008  searching for 15-digit factors
Fri Dec 05 08:27:50 2008  commencing quadratic sieve (90-digit input)
Fri Dec 05 08:27:50 2008  using multiplier of 1
Fri Dec 05 08:27:50 2008  using 32kb Intel Core sieve core
Fri Dec 05 08:27:50 2008  sieve interval: 36 blocks of size 32768
Fri Dec 05 08:27:50 2008  processing polynomials in batches of 6
Fri Dec 05 08:27:50 2008  using a sieve bound of 1616401 (61176 primes)
Fri Dec 05 08:27:50 2008  using large prime bound of 135777684 (27 bits)
Fri Dec 05 08:27:50 2008  using double large prime bound of 435603187807956 (42-49 bits)
Fri Dec 05 08:27:50 2008  using trial factoring cutoff of 49 bits
Fri Dec 05 08:27:50 2008  polynomial 'A' values have 11 factors
Fri Dec 05 10:03:38 2008  61574 relations (15651 full + 45923 combined from 675984 partial), need 61272
Fri Dec 05 10:03:39 2008  begin with 691635 relations
Fri Dec 05 10:03:39 2008  reduce to 153317 relations in 10 passes
Fri Dec 05 10:03:39 2008  attempting to read 153317 relations
Fri Dec 05 10:03:41 2008  recovered 153317 relations
Fri Dec 05 10:03:41 2008  recovered 135213 polynomials
Fri Dec 05 10:03:41 2008  attempting to build 61574 cycles
Fri Dec 05 10:03:42 2008  found 61574 cycles in 6 passes
Fri Dec 05 10:03:42 2008  distribution of cycle lengths:
Fri Dec 05 10:03:42 2008     length 1 : 15651
Fri Dec 05 10:03:42 2008     length 2 : 11589
Fri Dec 05 10:03:42 2008     length 3 : 10729
Fri Dec 05 10:03:42 2008     length 4 : 8341
Fri Dec 05 10:03:42 2008     length 5 : 5978
Fri Dec 05 10:03:42 2008     length 6 : 3884
Fri Dec 05 10:03:42 2008     length 7 : 2496
Fri Dec 05 10:03:42 2008     length 9+: 2906
Fri Dec 05 10:03:42 2008  largest cycle: 18 relations
Fri Dec 05 10:03:42 2008  matrix is 61176 x 61574 (15.5 MB) with weight 3815112 (61.96/col)
Fri Dec 05 10:03:42 2008  sparse part has weight 3815112 (61.96/col)
Fri Dec 05 10:03:43 2008  filtering completed in 3 passes
Fri Dec 05 10:03:43 2008  matrix is 57748 x 57812 (14.6 MB) with weight 3596094 (62.20/col)
Fri Dec 05 10:03:43 2008  sparse part has weight 3596094 (62.20/col)
Fri Dec 05 10:03:43 2008  saving the first 48 matrix rows for later
Fri Dec 05 10:03:43 2008  matrix is 57700 x 57812 (11.1 MB) with weight 3052248 (52.80/col)
Fri Dec 05 10:03:43 2008  sparse part has weight 2564465 (44.36/col)
Fri Dec 05 10:03:43 2008  matrix includes 64 packed rows
Fri Dec 05 10:03:43 2008  using block size 23124 for processor cache size 1024 kB
Fri Dec 05 10:03:43 2008  commencing Lanczos iteration
Fri Dec 05 10:03:43 2008  memory use: 9.9 MB
Fri Dec 05 10:04:06 2008  lanczos halted after 914 iterations (dim = 57697)
Fri Dec 05 10:04:06 2008  recovered 15 nontrivial dependencies
Fri Dec 05 10:04:07 2008  prp43 factor: 6518639221073681222625258143211300772137541
Fri Dec 05 10:04:07 2008  prp48 factor: 145164541708841951682791434372335409586197147397
Fri Dec 05 10:04:07 2008  elapsed time 01:36:20

(35·10¹³⁴-71)/9 = 3(8)₁₃₃1_<135> = 3 · 212281 · 552762764247593_<15> · C115

C115 = P50 · P65

P50 = 11472041308740830128226004319952938850730656734007_<50>

P65 = 96297203056272637468217470840571551206356271026255352522783960317_<65>

Number: 38881_134
N=1104725491377763414833483395718902424741972769207169290516839727448955235136688880837880013087427391950464312400219
  ( 115 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=11472041308740830128226004319952938850730656734007 (pp50)
 r2=96297203056272637468217470840571551206356271026255352522783960317 (pp65)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 11.67 hours.
Scaled time: 29.93 units (timescale=2.564).
Factorization parameters were as follows:
name: 38881_134
n: 1104725491377763414833483395718902424741972769207169290516839727448955235136688880837880013087427391950464312400219
m: 500000000000000000000000000
deg: 5
c5: 112
c0: -71
skew: 0.91
type: snfs
lss: 1
rlim: 1270000
alim: 1270000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1270000/1270000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [635000, 1310001)
Primes: RFBsize:97900, AFBsize:97920, largePrimes:4211322 encountered
Relations: rels:5361963, finalFF:1360672
Max relations in full relation-set: 28
Initial matrix: 195886 x 1360672 with sparse part having weight 120458970.
Pruned matrix : 121778 x 122821 with weight 12755672.
Total sieving time: 11.47 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1270000,1270000,26,26,47,47,2.3,2.3,75000
total time: 11.67 hours.
 --------- CPU info (if available) ----------

(35·10¹²⁹-71)/9 = 3(8)₁₂₈1_<130> = C130

C130 = P52 · P79

P52 = 3049419765225815668983930609536436633389526100014187_<52>

P79 = 1275288149318107683447556329379955502544080854576860051786719622599998534897363_<79>

Number: 38881_129
N=3888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888881
  ( 130 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=3049419765225815668983930609536436633389526100014187 (pp52)
 r2=1275288149318107683447556329379955502544080854576860051786719622599998534897363 (pp79)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.90 hours.
Scaled time: 7.81 units (timescale=2.003).
Factorization parameters were as follows:
name: 38881_129
n: 3888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888881
m: 50000000000000000000000000
deg: 5
c5: 112
c0: -71
skew: 0.91
type: snfs
lss: 1
rlim: 1050000
alim: 1050000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1050000/1050000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [525000, 875001)
Primes: RFBsize:82134, AFBsize:82218, largePrimes:2996541 encountered
Relations: rels:3114289, finalFF:403967
Max relations in full relation-set: 28
Initial matrix: 164418 x 403967 with sparse part having weight 31259082.
Pruned matrix : 111762 x 112648 with weight 7375178.
Total sieving time: 3.70 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1050000,1050000,26,26,47,47,2.3,2.3,50000
total time: 3.90 hours.
 --------- CPU info (if available) ----------

(35·10¹²⁴-71)/9 = 3(8)₁₂₃1_<125> = 126337 · 401536283195568182048119_<24> · C96

C96 = P40 · P57

P40 = 1569021033248296412077580593368762358459_<40>

P57 = 488586445919016114840133096706351415288180507783714125653_<57>

Fri Dec 05 16:43:00 2008  Msieve v. 1.39
Fri Dec 05 16:43:00 2008  random seeds: dc481b30 e523ea48
Fri Dec 05 16:43:00 2008  factoring 766602410206967560361540831523005387065159711107124604251139731533780707843870880275433353448727 (96 digits)
Fri Dec 05 16:43:01 2008  searching for 15-digit factors
Fri Dec 05 16:43:02 2008  commencing quadratic sieve (96-digit input)
Fri Dec 05 16:43:02 2008  using multiplier of 7
Fri Dec 05 16:43:02 2008  using 32kb Intel Core sieve core
Fri Dec 05 16:43:02 2008  sieve interval: 36 blocks of size 32768
Fri Dec 05 16:43:02 2008  processing polynomials in batches of 6
Fri Dec 05 16:43:02 2008  using a sieve bound of 2293831 (84706 primes)
Fri Dec 05 16:43:02 2008  using large prime bound of 344074650 (28 bits)
Fri Dec 05 16:43:02 2008  using double large prime bound of 2322601948775250 (43-52 bits)
Fri Dec 05 16:43:02 2008  using trial factoring cutoff of 52 bits
Fri Dec 05 16:43:02 2008  polynomial 'A' values have 12 factors
Fri Dec 05 16:43:04 2008  restarting with 20411 full and 1277790 partial relations
Fri Dec 05 16:43:04 2008  84995 relations (20411 full + 64584 combined from 1277790 partial), need 84802
Fri Dec 05 16:43:06 2008  begin with 1298201 relations
Fri Dec 05 16:43:07 2008  reduce to 223514 relations in 11 passes
Fri Dec 05 16:43:07 2008  attempting to read 223514 relations
Fri Dec 05 16:43:11 2008  recovered 223514 relations
Fri Dec 05 16:43:11 2008  recovered 209788 polynomials
Fri Dec 05 16:43:11 2008  attempting to build 84995 cycles
Fri Dec 05 16:43:11 2008  found 84995 cycles in 6 passes
Fri Dec 05 16:43:11 2008  distribution of cycle lengths:
Fri Dec 05 16:43:11 2008     length 1 : 20411
Fri Dec 05 16:43:11 2008     length 2 : 14457
Fri Dec 05 16:43:11 2008     length 3 : 14369
Fri Dec 05 16:43:11 2008     length 4 : 11606
Fri Dec 05 16:43:11 2008     length 5 : 8770
Fri Dec 05 16:43:11 2008     length 6 : 6098
Fri Dec 05 16:43:11 2008     length 7 : 3874
Fri Dec 05 16:43:11 2008     length 9+: 5410
Fri Dec 05 16:43:11 2008  largest cycle: 21 relations
Fri Dec 05 16:43:12 2008  matrix is 84706 x 84995 (23.8 MB) with weight 5903429 (69.46/col)
Fri Dec 05 16:43:12 2008  sparse part has weight 5903429 (69.46/col)
Fri Dec 05 16:43:13 2008  filtering completed in 3 passes
Fri Dec 05 16:43:13 2008  matrix is 80930 x 80994 (22.8 MB) with weight 5650897 (69.77/col)
Fri Dec 05 16:43:13 2008  sparse part has weight 5650897 (69.77/col)
Fri Dec 05 16:43:13 2008  saving the first 48 matrix rows for later
Fri Dec 05 16:43:13 2008  matrix is 80882 x 80994 (16.9 MB) with weight 4765904 (58.84/col)
Fri Dec 05 16:43:13 2008  sparse part has weight 3953034 (48.81/col)
Fri Dec 05 16:43:13 2008  matrix includes 64 packed rows
Fri Dec 05 16:43:13 2008  using block size 32397 for processor cache size 1024 kB
Fri Dec 05 16:43:14 2008  commencing Lanczos iteration
Fri Dec 05 16:43:14 2008  memory use: 14.8 MB
Fri Dec 05 16:44:03 2008  lanczos halted after 1280 iterations (dim = 80882)
Fri Dec 05 16:44:04 2008  recovered 18 nontrivial dependencies
Fri Dec 05 16:44:04 2008  prp40 factor: 1569021033248296412077580593368762358459
Fri Dec 05 16:44:04 2008  prp57 factor: 488586445919016114840133096706351415288180507783714125653
Fri Dec 05 16:44:04 2008  elapsed time 00:01:04

注、画面表示ミスしたので再演算したため分解時間は関係ありません。

(35·10¹⁴⁴-71)/9 = 3(8)₁₄₃1_<145> = 61 · 769207 · 7871627 · C131

C131 = P62 · P69

P62 = 28629087949393447456111133198620160036169315533071244148235903_<62>

P69 = 367773516809964708948000502851903761346423796515465049591887880180663_<69>

Number: 38881_144
N=10529020358210209126672419361319625913663990406421937265557556732693143120642454411467186326888174670644236643467251548108382943689
  ( 131 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=28629087949393447456111133198620160036169315533071244148235903 (pp62)
 r2=367773516809964708948000502851903761346423796515465049591887880180663 (pp69)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 10.01 hours.
Scaled time: 25.68 units (timescale=2.564).
Factorization parameters were as follows:
name: 38881_144
n: 10529020358210209126672419361319625913663990406421937265557556732693143120642454411467186326888174670644236643467251548108382943689
m: 50000000000000000000000000000
deg: 5
c5: 112
c0: -71
skew: 0.91
type: snfs
lss: 1
rlim: 1870000
alim: 1870000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1870000/1870000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [935000, 1835001)
Primes: RFBsize:139952, AFBsize:139833, largePrimes:3814117 encountered
Relations: rels:3832358, finalFF:342129
Max relations in full relation-set: 28
Initial matrix: 279851 x 342129 with sparse part having weight 28183205.
Pruned matrix : 255762 x 257225 with weight 17674466.
Total sieving time: 9.48 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.39 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1870000,1870000,26,26,49,49,2.3,2.3,100000
total time: 10.01 hours.
 --------- CPU info (if available) ----------

Dec 5, 2008 (3rd)

By Erik Branger / GGNFS, Msieve

(32·10¹⁶⁷+13)/9 = 3(5)₁₆₆7_<168> = 3 · 119293 · C162

C162 = P73 · P90

P73 = 4322911474401221003739959855382863867332867253351618140261790579201053693_<73>

P90 = 229823752646895330304729197086763575243943550018744050858962781324833714898204771186252031_<90>

Number: 35557_167
N=993507737407211810571605362582201122601649036561395207753334382725880969700808249591497560783269081325128201307021522792775087545107579812046964352631910661300483
  ( 162 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=4322911474401221003739959855382863867332867253351618140261790579201053693
 r2=229823752646895330304729197086763575243943550018744050858962781324833714898204771186252031
Version: 
Total time: 84.94 hours.
Scaled time: 66.94 units (timescale=0.788).
Factorization parameters were as follows:
n: 993507737407211810571605362582201122601649036561395207753334382725880969700808249591497560783269081325128201307021522792775087545107579812046964352631910661300483
m: 2000000000000000000000000000000000
deg: 5
c5: 100
c0: 13
skew: 0.66
type: snfs
lss: 1
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2250000, 4550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 883748 x 883996
Total sieving time: 84.94 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,52,52,2.4,2.4,100000
total time: 84.94 hours.
 --------- CPU info (if available) ----------

(35·10¹⁷⁸-71)/9 = 3(8)₁₇₇1_<179> = 59 · 30319 · 8784667 · 299262034171_<12> · 16932239622943_<14> · 2859919899229312168589_<22> · 3539940740859270898078487443_<28> · C92

C92 = P45 · P47

P45 = 852617991092640531706382587775687981367372409_<45>

P47 = 56580002638170283553528616716073383101107780277_<47>

Fri Dec 05 00:21:57 2008  Msieve v. 1.39
Fri Dec 05 00:21:57 2008  random seeds: 87820f18 cf45edda
Fri Dec 05 00:21:57 2008  factoring 48241128185373048607658534762192941159740389848374666344381904643854197316091606546004177293 (92 digits)
Fri Dec 05 00:21:58 2008  searching for 15-digit factors
Fri Dec 05 00:21:59 2008  commencing quadratic sieve (92-digit input)
Fri Dec 05 00:21:59 2008  using multiplier of 1
Fri Dec 05 00:21:59 2008  using 32kb Intel Core sieve core
Fri Dec 05 00:21:59 2008  sieve interval: 36 blocks of size 32768
Fri Dec 05 00:21:59 2008  processing polynomials in batches of 6
Fri Dec 05 00:21:59 2008  using a sieve bound of 1818667 (68235 primes)
Fri Dec 05 00:21:59 2008  using large prime bound of 198234703 (27 bits)
Fri Dec 05 00:21:59 2008  using double large prime bound of 860841928930917 (42-50 bits)
Fri Dec 05 00:21:59 2008  using trial factoring cutoff of 50 bits
Fri Dec 05 00:21:59 2008  polynomial 'A' values have 12 factors
Fri Dec 05 02:26:40 2008  68377 relations (17338 full + 51039 combined from 866466 partial), need 68331
Fri Dec 05 02:26:43 2008  begin with 883804 relations
Fri Dec 05 02:26:43 2008  reduce to 173971 relations in 11 passes
Fri Dec 05 02:26:43 2008  attempting to read 173971 relations
Fri Dec 05 02:26:47 2008  recovered 173971 relations
Fri Dec 05 02:26:47 2008  recovered 156247 polynomials
Fri Dec 05 02:26:48 2008  attempting to build 68377 cycles
Fri Dec 05 02:26:48 2008  found 68377 cycles in 5 passes
Fri Dec 05 02:26:48 2008  distribution of cycle lengths:
Fri Dec 05 02:26:48 2008     length 1 : 17338
Fri Dec 05 02:26:48 2008     length 2 : 12123
Fri Dec 05 02:26:48 2008     length 3 : 11729
Fri Dec 05 02:26:48 2008     length 4 : 9447
Fri Dec 05 02:26:48 2008     length 5 : 6839
Fri Dec 05 02:26:48 2008     length 6 : 4403
Fri Dec 05 02:26:48 2008     length 7 : 2764
Fri Dec 05 02:26:48 2008     length 9+: 3734
Fri Dec 05 02:26:48 2008  largest cycle: 21 relations
Fri Dec 05 02:26:48 2008  matrix is 68235 x 68377 (17.0 MB) with weight 4182839 (61.17/col)
Fri Dec 05 02:26:48 2008  sparse part has weight 4182839 (61.17/col)
Fri Dec 05 02:26:49 2008  filtering completed in 3 passes
Fri Dec 05 02:26:49 2008  matrix is 64604 x 64668 (16.2 MB) with weight 3981649 (61.57/col)
Fri Dec 05 02:26:49 2008  sparse part has weight 3981649 (61.57/col)
Fri Dec 05 02:26:49 2008  saving the first 48 matrix rows for later
Fri Dec 05 02:26:49 2008  matrix is 64556 x 64668 (10.0 MB) with weight 3102626 (47.98/col)
Fri Dec 05 02:26:49 2008  sparse part has weight 2234604 (34.56/col)
Fri Dec 05 02:26:49 2008  matrix includes 64 packed rows
Fri Dec 05 02:26:49 2008  using block size 25867 for processor cache size 2048 kB
Fri Dec 05 02:26:49 2008  commencing Lanczos iteration
Fri Dec 05 02:26:49 2008  memory use: 9.9 MB
Fri Dec 05 02:27:11 2008  lanczos halted after 1022 iterations (dim = 64554)
Fri Dec 05 02:27:12 2008  recovered 15 nontrivial dependencies
Fri Dec 05 02:27:12 2008  prp45 factor: 852617991092640531706382587775687981367372409
Fri Dec 05 02:27:12 2008  prp47 factor: 56580002638170283553528616716073383101107780277
Fri Dec 05 02:27:12 2008  elapsed time 02:05:15

Dec 5, 2008 (2nd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39

(35·10¹⁰²-71)/9 = 3(8)₁₀₁1_<103> = 139 · 2053 · 3421577921_<10> · C88

C88 = P36 · P53

P36 = 189655237882485713626855383164734829_<36>

P53 = 21000542262980580332387674910609858745830341198993427_<53>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3315921847
Step 1 took 9500ms
Step 2 took 7561ms
********** Factor found in step 2: 189655237882485713626855383164734829
Found probable prime factor of 36 digits: 189655237882485713626855383164734829
Probable prime cofactor 21000542262980580332387674910609858745830341198993427 has 53 digits

(35·10¹³⁹-71)/9 = 3(8)₁₃₈1_<140> = 17 · 813311 · 8018110624369_<13> · 6511228337017966632813877_<25> · C95

C95 = P35 · P61

P35 = 15649167451664818524155508294784231_<35>

P61 = 3442657041560301536979260219834848760144132407114779732793621_<61>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=344597253
Step 1 took 9148ms
Step 2 took 7897ms
********** Factor found in step 2: 15649167451664818524155508294784231
Found probable prime factor of 35 digits: 15649167451664818524155508294784231
Probable prime cofactor 3442657041560301536979260219834848760144132407114779732793621 has 61 digits

(35·10¹²⁰-71)/9 = 3(8)₁₁₉1_<121> = 59 · 83 · 1603184392344227670937_<22> · C96

C96 = P31 · P66

P31 = 2715369083178513050346546575239_<31>

P66 = 182424466924139797820704781550258524766594314753551564628143605311_<66>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1516650998
Step 1 took 10824ms
Step 2 took 9665ms
********** Factor found in step 2: 2715369083178513050346546575239
Found probable prime factor of 31 digits: 2715369083178513050346546575239
Probable prime cofactor 182424466924139797820704781550258524766594314753551564628143605311 has 66 digits

(35·10¹¹⁴-71)/9 = 3(8)₁₁₃1_<115> = 43284926261085623_<17> · C98

C98 = P31 · P68

P31 = 2076816267013609977133570087451_<31>

P68 = 43260424438253424573969100498590711648381570067561111971769414772597_<68>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4182817904
Step 1 took 14192ms
Step 2 took 10071ms
********** Factor found in step 2: 2076816267013609977133570087451
Found probable prime factor of 31 digits: 2076816267013609977133570087451
Probable prime cofactor 43260424438253424573969100498590711648381570067561111971769414772597 has 68 digits

(35·10¹⁴²-71)/9 = 3(8)₁₄₁1_<143> = 163 · 150313247296939_<15> · 490610474282534410031115979_<27> · C100

C100 = P43 · P58

P43 = 1223607960764791633345625934073632017268917_<43>

P58 = 2644000686310157989135261085141315838217069079769040285031_<58>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3800258058
Step 1 took 14387ms
Step 2 took 10768ms
********** Factor found in step 2: 1223607960764791633345625934073632017268917
Found probable prime factor of 43 digits: 1223607960764791633345625934073632017268917
Probable prime cofactor 2644000686310157989135261085141315838217069079769040285031 has 58 digits

(35·10¹⁸⁹-71)/9 = 3(8)₁₈₈1_<190> = 131 · 260207 · 616657957 · 11531893397_<11> · C164

C164 = P29 · P135

P29 = 17905448426118827495647659859_<29>

P135 = 895994002891375498633567347569959074995539442743484179100848856679581645115282341184169133920282804468223980864525066718672772643026463_<135>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=85049247
Step 1 took 20781ms
********** Factor found in step 1: 17905448426118827495647659859
Found probable prime factor of 29 digits: 17905448426118827495647659859
Probable prime cofactor has 135 digits

(35·10¹⁷³-71)/9 = 3(8)₁₇₂1_<174> = 3 · 29030340373_<11> · C163

C163 = P34 · C130

P34 = 1251570369921303065533447516226851_<34>

C130 = [3567770246554798335164904445667700393306498994538845244740178159103393362348826080981445946352887328882491821739754257930971069349_<130>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3008931572
Step 1 took 20686ms
********** Factor found in step 1: 1251570369921303065533447516226851
Found probable prime factor of 34 digits: 1251570369921303065533447516226851
Composite cofactor has 130 digits

(35·10¹⁶⁷-71)/9 = 3(8)₁₆₆1_<168> = 3⁴ · C166

C166 = P36 · C131

P36 = 146222004002926974466791407216706971_<36>

C131 = [32834301693703234431710291345676026682577433328676387101190552058950862612556701138015292983135095332969771365288049814825795079731_<131>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4195115374
Step 1 took 20989ms
Step 2 took 13929ms
********** Factor found in step 2: 146222004002926974466791407216706971
Found probable prime factor of 36 digits: 146222004002926974466791407216706971
Composite cofactor has 131 digits

(35·10¹⁹³-71)/9 = 3(8)₁₉₂1_<194> = 233 · 439 · 93332017 · 12287897372633_<14> · C168

C168 = P34 · P36 · P99

P34 = 1336274913064414490088424457113547_<34>

P36 = 305963866293796696968288607697488003_<36>

P99 = 810832058305497998180067142835268854471352451027447649649815204031597101164875882584961155023721063_<99>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1031670139
Step 1 took 21226ms
Step 2 took 13893ms
********** Factor found in step 2: 1336274913064414490088424457113547
Found probable prime factor of 34 digits: 1336274913064414490088424457113547
Composite cofactor 248085311474107357104588422474489869701555555453866907191475948275891744402980997431744271055640501443588456969084801898897862860907189 has 135 digits

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4250334491
Step 1 took 12049ms
Step 2 took 9732ms
********** Factor found in step 2: 305963866293796696968288607697488003
Found probable prime factor of 36 digits: 305963866293796696968288607697488003
Probable prime cofactor 
810832058305497998180067142835268854471352451027447649649815204031597101164875882584961155023721063 
has 99 digits

(35·10¹⁹⁷-71)/9 = 3(8)₁₉₆1_<198> = 3 · 41113 · 75642877643_<11> · C182

C182 = P27 · C155

P27 = 760313831104560253254183673_<27>

C155 = [54823174425482750926246594909658135020132072477274295276824574265817217975244637290064755167295711456097792543538115601269727309476437989059777953016700161_<155>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3978802356
Step 1 took 25553ms
Step 2 took 15409ms
********** Factor found in step 2: 760313831104560253254183673
Found probable prime factor of 27 digits: 760313831104560253254183673
Composite cofactor has 155 digits

(35·10¹⁹⁴-71)/9 = 3(8)₁₉₃1_<195> = 3³ · 139 · 10499 · C187

C187 = P28 · C160

P28 = 2695648747855838052012777127_<28>

C160 = [3661303521046606546298585518347392024070683888179286291517871209385493946781642011240660743528557012706441362886380290894705288545269001778754040289321222095749_<160>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=316825665
Step 1 took 25690ms
Step 2 took 15681ms
********** Factor found in step 2: 2695648747855838052012777127
Found probable prime factor of 28 digits: 2695648747855838052012777127
Composite cofactor has 160 digits

(35·10¹⁴¹-71)/9 = 3(8)₁₄₀1_<142> = 19 · C141

C141 = P55 · P87

P55 = 1319010200979302625048260303049985266255243144258099089_<55>

P87 = 155175723751897765150475110029731564711269841858076385450258470490538595269383272804091_<87>

SNFS difficulty: 142 digits.
Divisors found:
 r1=1319010200979302625048260303049985266255243144258099089 (pp55)
 r2=155175723751897765150475110029731564711269841858076385450258470490538595269383272804091 (pp87)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.735).
Factorization parameters were as follows:
n: 204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099
m: 10000000000000000000000000000
deg: 5
c5: 350
c0: -71
skew: 0.73
type: snfs
lss: 1
rlim: 1660000
alim: 1660000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1660000/1660000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [830000, 1930001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 268312 x 268560
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1660000,1660000,26,26,48,48,2.3,2.3,100000
total time: 6.00 hours.

(35·10¹¹⁹-71)/9 = 3(8)₁₁₈1_<120> = 3 · C120

C120 = P52 · P68

P52 = 9108048653773274900975019699685290610509871744551301_<52>

P68 = 14232426127404004736307046465996489398097073385511086633106988894527_<68>

SNFS difficulty: 120 digits.
Divisors found:
 r1=9108048653773274900975019699685290610509871744551301 (pp52)
 r2=14232426127404004736307046465996489398097073385511086633106988894527 (pp68)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.739).
Factorization parameters were as follows:
n: 129629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629627
m: 500000000000000000000000
deg: 5
c5: 112
c0: -71
skew: 0.91
type: snfs
lss: 1
rlim: 710000
alim: 710000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 710000/710000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [355000, 555001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 73362 x 73605
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,710000,710000,25,25,46,46,2.2,2.2,50000
total time: 1.00 hours.

(35·10²⁰¹-71)/9 = 3(8)₂₀₀1_<202> = 57690799 · 188013277 · C186

C186 = P31 · C156

P31 = 2417025011202852553830152157173_<31>

C156 = [148336940573693026676931953360768681251898110248037176988146673580884095938488249642040714732420381075108148432925737985713043549619431873238226401551617439_<156>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2143623369
Step 1 took 24053ms
Step 2 took 14537ms
********** Factor found in step 2: 2417025011202852553830152157173
Found probable prime factor of 31 digits: 2417025011202852553830152157173
Composite cofactor has 156 digits

(11·10¹⁵⁸+1)/3 = 3(6)₁₅₇7_<159> = 31 · 59 · 97 · 1237 · 2333 · C147

C147 = P68 · P80

P68 = 15611366323089686328149847587593711715540807434474824383064092790761_<68>

P80 = 45873369125111275439706510098906208237069667903072673179163397331530328855542839_<80>

SNFS difficulty: 160 digits.
Divisors found:
 r1=15611366323089686328149847587593711715540807434474824383064092790761 (pp68)
 r2=45873369125111275439706510098906208237069667903072673179163397331530328855542839 (pp80)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.939).
Factorization parameters were as follows:
n: 716145969886424353063705045345701423108319336840934696165230955448572566883712214497732483274991819051353486705377955571485029773507164775098910479
m: 50000000000000000000000000000000
deg: 5
c5: 88
c0: 25
skew: 0.78
type: snfs
lss: 1
rlim: 3300000
alim: 3300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3300000/3300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1650000, 2850001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 479736 x 479984
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3300000,3300000,27,27,52,52,2.4,2.4,200000
total time: 21.00 hours.

(35·10¹⁵²-71)/9 = 3(8)₁₅₁1_<153> = 3 · 593 · C150

C150 = P33 · P50 · P68

P33 = 196877064555228798257051976037937_<33>

P50 = 36533076470534038295304648507983428931265801937723_<50>

P68 = 30392625276083080315139642232573944572961068830522941570127555167489_<68>

SNFS difficulty: 154 digits.
Divisors found:
 r1=196877064555228798257051976037937 (pp33)
 r2=36533076470534038295304648507983428931265801937723 (pp50)
 r3=30392625276083080315139642232573944572961068830522941570127555167489 (pp68)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.737).
Factorization parameters were as follows:
n: 218599712697520454687402410842545749797014552495159577790269189931921803759915058397351820623321466491786896508650302916744737992630066829055024670539
m: 2000000000000000000000000000000
deg: 5
c5: 875
c0: -568
skew: 0.92
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1300000, 2400001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 547354 x 547602
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,52,52,2.4,2.4,100000
total time: 16.00 hours.

(35·10¹⁶⁸-71)/9 = 3(8)₁₆₇1_<169> = 10873724311_<11> · C159

C159 = P41 · C119

P41 = 14303299735272000932427365334907044020341_<41>

C119 = [25004085622395400531356004667950957578919315561901397443642967755502862141549701795225649125923569649521872339576262331_<119>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2451661041
Step 1 took 25935ms
Step 2 took 16777ms
********** Factor found in step 2: 14303299735272000932427365334907044020341
Found probable prime factor of 41 digits: 14303299735272000932427365334907044020341
Composite cofactor has 119 digits

Dec 5, 2008

Factorizations of 388...881 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Dec 4, 2008 (4th)

By Jo Yeong Uk / GGNFS

(14·10¹⁷⁰-23)/9 = 1(5)₁₆₉3_<171> = 3 · 691 · 22263472690475736337_<20> · 4140183215192466077295603949_<28> · C120

C120 = P51 · P70

P51 = 630117766017269648087725009336287261566800724122723_<51>

P70 = 1291968818028846496792599442959506376604417781810432273538694583529439_<70>

Number: 15553_170
N=814092505380309124943551135799902484909003478048353721821331357008460909965452505234824673882421566041432715888319342397
  ( 120 digits)
Divisors found:
 r1=630117766017269648087725009336287261566800724122723 (pp51)
 r2=1291968818028846496792599442959506376604417781810432273538694583529439 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 43.54 hours.
Scaled time: 103.89 units (timescale=2.386).
Factorization parameters were as follows:
name: 15553_170
n: 814092505380309124943551135799902484909003478048353721821331357008460909965452505234824673882421566041432715888319342397
skew: 28185.42
# norm 3.42e+15
c5: 95760
c4: 4567223691
c3: -133520678204283
c2: -3909924647066575861
c1: 67745503802752554587296
c0: -3003949084757309352275677
# alpha -3.63
Y1: 11054423741099
Y0: -96804924543965338047558
# Murphy_E 2.60e-10
# M 275705184235830591348662618029168213759719931670795570142473149118975745695546772170490093024576973858091779254759836679
type: gnfs
rlim: 4800000
alim: 4800000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved algebraic special-q in [2400000, 4800001)
Primes: RFBsize:335439, AFBsize:334032, largePrimes:10062010 encountered
Relations: rels:10266008, finalFF:849385
Max relations in full relation-set: 28
Initial matrix: 669551 x 849385 with sparse part having weight 84446630.
Pruned matrix : 532692 x 536103 with weight 58093567.
Polynomial selection time: 2.60 hours.
Total sieving time: 38.10 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 2.48 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4800000,4800000,27,27,53,53,2.4,2.4,100000
total time: 43.54 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Dec 4, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(32·10¹⁶⁴+13)/9 = 3(5)₁₆₃7_<165> = 3 · 7 · 43 · 1001485577_<10> · 6949169419_<10> · 603730695926738492922339797_<27> · C116

C116 = P57 · P60

P57 = 135668168107915602062507621783920751448705463501108031083_<57>

P60 = 690750012084541731056403382306042079849402924714875383489863_<60>

Number: n
N=93712788760030341200758687850157434280544815854859669843832571475209729383133361618332274540247415803878813219411629
  ( 116 digits)
Divisors found:

Thu Dec 04 13:22:30 2008  prp57 factor: 135668168107915602062507621783920751448705463501108031083
Thu Dec 04 13:22:30 2008  prp60 factor: 690750012084541731056403382306042079849402924714875383489863
Thu Dec 04 13:22:30 2008  elapsed time 01:13:36 (Msieve 1.39)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 32.16 hours.
Scaled time: 58.59 units (timescale=1.822).
Factorization parameters were as follows:
name: KA_3_5_163_7
n: 93712788760030341200758687850157434280544815854859669843832571475209729383133361618332274540247415803878813219411629

# Msieve 1.39 selections:

skew: 102302.32

Y0: -24003768776778299772686
Y1:  2470048358657

c0: -166645603175821687540475229795
c1:  4424225278037915341357178
c2:  33473491889923939705
c3: -767528885982384
c4: -1482191564
c5:  11760

# Ggnfs selections:

# skew: 46755.21
# norm 7.66e+15
#
# c5: 57960
# c4: -4378786561
# c3: -355222018770405
# c2: 6585478902930367520
# c1: 226574327938287993311037
# c0: 1873860926445465809121007730
#
# alpha -5.71
# Y1: 45119695357
# Y0: -17447536439140996067493
# Murphy_E 4.39e-10
# M 37118574491776789170758160355679680988337008512699570564323659979502457549970503778172089484588830310691125311224565

type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 1900001)
Primes: RFBsize:348513, AFBsize:348931, largePrimes:10449792 encountered
Relations: rels:9357171, finalFF:742303
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 31.83 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,28,28,56,56,2.4,2.4,60000
total time: 32.16 hours.
 --------- CPU info (if available) ----------

(11·10¹⁵¹-17)/3 = 3(6)₁₅₀1_<152> = 31 · 349 · 2861 · 8017 · 39843953 · 56011094759891_<14> · C119

C119 = P45 · P75

P45 = 112799423974289196481994738738050346143074439_<45>

P75 = 586963649074040777743311527397388588098323753426545891645978911779023424471_<75>

Number: n
N=66209161509398626028403506902594758492010827988105228259159168846744076206483165238543451191977366979540685390047196769
  ( 119 digits)
SNFS difficulty: 152 digits.
Divisors found:

Fri Dec 05 01:08:52 2008  prp45 factor: 112799423974289196481994738738050346143074439
Fri Dec 05 01:08:52 2008  prp75 factor: 586963649074040777743311527397388588098323753426545891645978911779023424471
Fri Dec 05 01:08:52 2008  elapsed time 00:49:53 (Msieve 1.39 - dependency 5)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 10.52 hours.
Scaled time: 19.24 units (timescale=1.828).
Factorization parameters were as follows:
name: KA_3_6_150_1
n: 66209161509398626028403506902594758492010827988105228259159168846744076206483165238543451191977366979540685390047196769
type: snfs
skew: 0.69
deg: 5
c5: 110
c0: -17
m: 1000000000000000000000000000000
rlim: 2400000
alim: 2400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 700001)
Primes: RFBsize:176302, AFBsize:176664, largePrimes:10025374 encountered
Relations: rels:8593859, finalFF:356069
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 10.34 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,28,28,56,56,2.5,2.5,100000
total time: 10.52 hours.
 --------- CPU info (if available) ----------

Dec 4, 2008 (2nd)

By Serge Batalov / Msieve-1.39

(34·10¹⁵⁰+11)/9 = 3(7)₁₄₉9_<151> = 613 · C148

C148 = P46 · P103

P46 = 5474723484518379372701766368967546866644000693_<46>

P103 = 1125676874566949097792931739812198215757230882784080543645476831099365405414404627756124731207967774331_<103>

SNFS difficulty: 151 digits.
Divisors found:
 r1=5474723484518379372701766368967546866644000693 (pp46)
 r2=1125676874566949097792931739812198215757230882784080543645476831099365405414404627756124731207967774331 (pp103)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.530).
Factorization parameters were as follows:
n: 6162769621170926228022475983324270436831611382998006162769621170926228022475983324270436831611382998006162769621170926228022475983324270436831611383
m: 1000000000000000000000000000000
deg: 5
c5: 34
c0: 11
skew: 0.80
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1150000, 1750001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 475351 x 475599
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,52,52,2.4,2.4,100000
total time: 9.00 hours.

Dec 4, 2008

By Sinkiti Sibata / GGNFS, Msieve

(34·10¹³⁶+11)/9 = 3(7)₁₃₅9_<137> = 3 · 7 · 163 · 526424108506853_<15> · 53655775625396912603_<20> · C99

C99 = P33 · P67

P33 = 129875636537331934293962710004963_<33>

P67 = 3008496924078089501053188927281925523873777858397632239079606003769_<67>

Wed Dec 03 13:56:27 2008  Msieve v. 1.38
Wed Dec 03 13:56:27 2008  random seeds: 2557077c 08d5cfb5
Wed Dec 03 13:56:27 2008  factoring 390730453035247059146522489228493483467865317468685394145951389981862136141644394648757538586705547 (99 digits)
Wed Dec 03 13:56:28 2008  searching for 15-digit factors
Wed Dec 03 13:56:29 2008  commencing quadratic sieve (99-digit input)
Wed Dec 03 13:56:30 2008  using multiplier of 3
Wed Dec 03 13:56:30 2008  using 32kb Intel Core sieve core
Wed Dec 03 13:56:30 2008  sieve interval: 36 blocks of size 32768
Wed Dec 03 13:56:30 2008  processing polynomials in batches of 6
Wed Dec 03 13:56:30 2008  using a sieve bound of 2612039 (95294 primes)
Wed Dec 03 13:56:30 2008  using large prime bound of 391805850 (28 bits)
Wed Dec 03 13:56:30 2008  using double large prime bound of 2934456164566950 (43-52 bits)
Wed Dec 03 13:56:30 2008  using trial factoring cutoff of 52 bits
Wed Dec 03 13:56:30 2008  polynomial 'A' values have 13 factors
Thu Dec 04 00:07:06 2008  95638 relations (22183 full + 73455 combined from 1444910 partial), need 95390
Thu Dec 04 00:07:08 2008  begin with 1467093 relations
Thu Dec 04 00:07:10 2008  reduce to 254155 relations in 10 passes
Thu Dec 04 00:07:10 2008  attempting to read 254155 relations
Thu Dec 04 00:07:14 2008  recovered 254155 relations
Thu Dec 04 00:07:14 2008  recovered 244846 polynomials
Thu Dec 04 00:07:14 2008  attempting to build 95638 cycles
Thu Dec 04 00:07:15 2008  found 95638 cycles in 6 passes
Thu Dec 04 00:07:15 2008  distribution of cycle lengths:
Thu Dec 04 00:07:15 2008     length 1 : 22183
Thu Dec 04 00:07:15 2008     length 2 : 16132
Thu Dec 04 00:07:15 2008     length 3 : 16184
Thu Dec 04 00:07:15 2008     length 4 : 13158
Thu Dec 04 00:07:15 2008     length 5 : 10093
Thu Dec 04 00:07:15 2008     length 6 : 6935
Thu Dec 04 00:07:15 2008     length 7 : 4505
Thu Dec 04 00:07:15 2008     length 9+: 6448
Thu Dec 04 00:07:15 2008  largest cycle: 20 relations
Thu Dec 04 00:07:15 2008  matrix is 95294 x 95638 (25.8 MB) with weight 6383703 (66.75/col)
Thu Dec 04 00:07:15 2008  sparse part has weight 6383703 (66.75/col)
Thu Dec 04 00:07:16 2008  filtering completed in 3 passes
Thu Dec 04 00:07:16 2008  matrix is 91652 x 91716 (24.8 MB) with weight 6140115 (66.95/col)
Thu Dec 04 00:07:16 2008  sparse part has weight 6140115 (66.95/col)
Thu Dec 04 00:07:17 2008  saving the first 48 matrix rows for later
Thu Dec 04 00:07:17 2008  matrix is 91604 x 91716 (14.6 MB) with weight 4748001 (51.77/col)
Thu Dec 04 00:07:17 2008  sparse part has weight 3267205 (35.62/col)
Thu Dec 04 00:07:17 2008  matrix includes 64 packed rows
Thu Dec 04 00:07:17 2008  using block size 36686 for processor cache size 1024 kB
Thu Dec 04 00:07:18 2008  commencing Lanczos iteration
Thu Dec 04 00:07:18 2008  memory use: 14.7 MB
Thu Dec 04 00:08:20 2008  lanczos halted after 1450 iterations (dim = 91602)
Thu Dec 04 00:08:21 2008  recovered 16 nontrivial dependencies
Thu Dec 04 00:08:21 2008  prp33 factor: 129875636537331934293962710004963
Thu Dec 04 00:08:21 2008  prp67 factor: 3008496924078089501053188927281925523873777858397632239079606003769
Thu Dec 04 00:08:21 2008  elapsed time 10:11:54

(34·10¹⁵²-61)/9 = 3(7)₁₅₁1_<153> = 7² · 1156845484056134377_<19> · C133

C133 = P56 · P78

P56 = 18140064527049332303648755303293357509352299892563197159_<56>

P78 = 367388996167468745630067954460328243858151569259818255011945437791324718164453_<78>

Number: 37771_152
N=6664460097005762889501326931842972589120882959363472910276971278563908576252337593941653650382664001497951582800929546255771624389027
  ( 133 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=18140064527049332303648755303293357509352299892563197159 (pp56)
 r2=367388996167468745630067954460328243858151569259818255011945437791324718164453 (pp78)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 48.81 hours.
Scaled time: 23.09 units (timescale=0.473).
Factorization parameters were as follows:
name: 37771_152
n: 6664460097005762889501326931842972589120882959363472910276971278563908576252337593941653650382664001497951582800929546255771624389027
m: 2000000000000000000000000000000
deg: 5
c5: 425
c0: -244
skew: 0.89
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2500001)
Primes: RFBsize:189880, AFBsize:190596, largePrimes:8108679 encountered
Relations: rels:8328593, finalFF:587648
Max relations in full relation-set: 28
Initial matrix: 380543 x 587648 with sparse part having weight 67736918.
Pruned matrix : 319755 x 321721 with weight 35454744.
Total sieving time: 44.15 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 4.12 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 48.81 hours.
 --------- CPU info (if available) ----------

(34·10¹⁵⁹+11)/9 = 3(7)₁₅₈9_<160> = 29 · 61 · 11092973448917077_<17> · C141

C141 = P32 · P36 · P73

P32 = 56960796213499206995819411589421_<32>

P36 = 653999055531658257880633332837128587_<36>

P73 = 5167820598800979524424252379458124776983707013484074238580352480196575329_<73>

Number: 37779_159
N=192513239084831126427408014469396118890961735454762306318816343869393433862102152227064049739804890063922442679003515268166854827647928928783
  ( 141 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=56960796213499206995819411589421 (pp32)
 r2=653999055531658257880633332837128587 (pp36)
 r3=5167820598800979524424252379458124776983707013484074238580352480196575329 (pp73)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 45.26 hours.
Scaled time: 116.53 units (timescale=2.575).
Factorization parameters were as follows:
name: 37779_159
n: 192513239084831126427408014469396118890961735454762306318816343869393433862102152227064049739804890063922442679003515268166854827647928928783
m: 100000000000000000000000000000000
deg: 5
c5: 17
c0: 55
skew: 1.26
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3000001)
Primes: RFBsize:243539, AFBsize:243460, largePrimes:9425000 encountered
Relations: rels:10213711, finalFF:981172
Max relations in full relation-set: 28
Initial matrix: 487064 x 981172 with sparse part having weight 116904325.
Pruned matrix : 354614 x 357113 with weight 57238682.
Total sieving time: 43.30 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.64 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 45.26 hours.
 --------- CPU info (if available) ----------

(11·10¹⁵⁷+1)/3 = 3(6)₁₅₆7_<158> = 37 · 1955047 · 25264817 · C143

C143 = P64 · P79

P64 = 8094731531159257114384118790068783897387029934394005132192109889_<64>

P79 = 2478528387941507389257903805559758966512411806020490482897963327234349291725481_<79>

Number: 36667_157
N=20063021892743443326478130818979587624195871689987254647969629230342545976216225090108921757143590322301830787962129778289720168589102773381609
  ( 143 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=8094731531159257114384118790068783897387029934394005132192109889 (pp64)
 r2=2478528387941507389257903805559758966512411806020490482897963327234349291725481 (pp79)
Version: GGNFS-0.77.1-20060513-k8
Total time: 51.97 hours.
Scaled time: 103.16 units (timescale=1.985).
Factorization parameters were as follows:
name: 36667_157
n: 20063021892743443326478130818979587624195871689987254647969629230342545976216225090108921757143590322301830787962129778289720168589102773381609
m: 50000000000000000000000000000000
deg: 5
c5: 44
c0: 125
skew: 1.23
type: snfs
lss: 1
rlim: 3300000
alim: 3300000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3300000/3300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1650000, 3150001)
Primes: RFBsize:236900, AFBsize:236813, largePrimes:9295256 encountered
Relations: rels:9908058, finalFF:836964
Max relations in full relation-set: 28
Initial matrix: 473780 x 836964 with sparse part having weight 98632399.
Pruned matrix : 366694 x 369126 with weight 50531157.
Total sieving time: 48.93 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 2.51 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3300000,3300000,27,27,51,51,2.4,2.4,100000
total time: 51.97 hours.
 --------- CPU info (if available) ----------

(34·10¹³⁴+11)/9 = 3(7)₁₃₃9_<135> = 19 · 374047 · 2174281046333862930037878901_<28> · C101

C101 = P30 · P71

P30 = 881826597797799257233689206803_<30>

P71 = 27724119158394433966044807026838624228049298969437410695567232496220401_<71>

Thu Dec 04 00:18:05 2008  Msieve v. 1.38
Thu Dec 04 00:18:05 2008  random seeds: c33abc40 4e1f0ddc
Thu Dec 04 00:18:05 2008  factoring 24447865674387749360043877876481953138437871115753646983888106437925276699437543296241688205156588003 (101 digits)
Thu Dec 04 00:18:06 2008  searching for 15-digit factors
Thu Dec 04 00:18:07 2008  commencing quadratic sieve (101-digit input)
Thu Dec 04 00:18:07 2008  using multiplier of 3
Thu Dec 04 00:18:07 2008  using 32kb Intel Core sieve core
Thu Dec 04 00:18:07 2008  sieve interval: 36 blocks of size 32768
Thu Dec 04 00:18:07 2008  processing polynomials in batches of 6
Thu Dec 04 00:18:07 2008  using a sieve bound of 2899627 (105000 primes)
Thu Dec 04 00:18:07 2008  using large prime bound of 434944050 (28 bits)
Thu Dec 04 00:18:07 2008  using double large prime bound of 3541441458762600 (43-52 bits)
Thu Dec 04 00:18:07 2008  using trial factoring cutoff of 52 bits
Thu Dec 04 00:18:07 2008  polynomial 'A' values have 13 factors
Thu Dec 04 15:35:22 2008  105169 relations (24457 full + 80712 combined from 1588835 partial), need 105096
Thu Dec 04 15:35:24 2008  begin with 1613292 relations
Thu Dec 04 15:35:26 2008  reduce to 279532 relations in 11 passes
Thu Dec 04 15:35:26 2008  attempting to read 279532 relations
Thu Dec 04 15:35:31 2008  recovered 279532 relations
Thu Dec 04 15:35:31 2008  recovered 271621 polynomials
Thu Dec 04 15:35:31 2008  attempting to build 105169 cycles
Thu Dec 04 15:35:32 2008  found 105169 cycles in 6 passes
Thu Dec 04 15:35:32 2008  distribution of cycle lengths:
Thu Dec 04 15:35:32 2008     length 1 : 24457
Thu Dec 04 15:35:32 2008     length 2 : 17837
Thu Dec 04 15:35:32 2008     length 3 : 17389
Thu Dec 04 15:35:32 2008     length 4 : 14579
Thu Dec 04 15:35:32 2008     length 5 : 11211
Thu Dec 04 15:35:32 2008     length 6 : 7688
Thu Dec 04 15:35:32 2008     length 7 : 4891
Thu Dec 04 15:35:32 2008     length 9+: 7117
Thu Dec 04 15:35:32 2008  largest cycle: 20 relations
Thu Dec 04 15:35:32 2008  matrix is 105000 x 105169 (29.4 MB) with weight 7290438 (69.32/col)
Thu Dec 04 15:35:32 2008  sparse part has weight 7290438 (69.32/col)
Thu Dec 04 15:35:33 2008  filtering completed in 3 passes
Thu Dec 04 15:35:33 2008  matrix is 101030 x 101094 (28.4 MB) with weight 7048029 (69.72/col)
Thu Dec 04 15:35:33 2008  sparse part has weight 7048029 (69.72/col)
Thu Dec 04 15:35:34 2008  saving the first 48 matrix rows for later
Thu Dec 04 15:35:34 2008  matrix is 100982 x 101094 (17.7 MB) with weight 5595506 (55.35/col)
Thu Dec 04 15:35:34 2008  sparse part has weight 4029442 (39.86/col)
Thu Dec 04 15:35:34 2008  matrix includes 64 packed rows
Thu Dec 04 15:35:34 2008  using block size 40437 for processor cache size 1024 kB
Thu Dec 04 15:35:35 2008  commencing Lanczos iteration
Thu Dec 04 15:35:35 2008  memory use: 17.1 MB
Thu Dec 04 15:37:01 2008  lanczos halted after 1598 iterations (dim = 100980)
Thu Dec 04 15:37:02 2008  recovered 16 nontrivial dependencies
Thu Dec 04 15:37:03 2008  prp30 factor: 881826597797799257233689206803
Thu Dec 04 15:37:03 2008  prp71 factor: 27724119158394433966044807026838624228049298969437410695567232496220401
Thu Dec 04 15:37:03 2008  elapsed time 15:18:58

(34·10¹⁶⁰+11)/9 = 3(7)₁₅₉9_<161> = 3² · 7 · 22543 · C155

C155 = P56 · P100

P56 = 15640944141321185099322247466507075594820802996029162961_<56>

P100 = 1700674430149138207643706969225336809928813149676112024635548084053368737429115806131547880354595571_<100>

Number: 37779_160
N=26600153764535908290806337502281549953406701251560705345324369707400655662495997263626535092917857708110410353530908322491814780625793652749544452807845731
  ( 155 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=15640944141321185099322247466507075594820802996029162961 (pp56)
 r2=1700674430149138207643706969225336809928813149676112024635548084053368737429115806131547880354595571 (pp100)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 45.26 hours.
Scaled time: 116.05 units (timescale=2.564).
Factorization parameters were as follows:
name: 37779_160
n: 26600153764535908290806337502281549953406701251560705345324369707400655662495997263626535092917857708110410353530908322491814780625793652749544452807845731
m: 100000000000000000000000000000000
deg: 5
c5: 34
c0: 11
skew: 0.80
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3000001)
Primes: RFBsize:243539, AFBsize:244010, largePrimes:9375477 encountered
Relations: rels:10101428, finalFF:940436
Max relations in full relation-set: 28
Initial matrix: 487615 x 940436 with sparse part having weight 112572943.
Pruned matrix : 359368 x 361870 with weight 55395426.
Total sieving time: 43.31 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.63 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 45.26 hours.
 --------- CPU info (if available) ----------

Dec 3, 2008 (6th)

By Wataru Sakai / GGNFS, Msieve

10¹⁸⁵+3 = 1(0)₁₈₄3_<186> = 23 · 503 · 1129 · C178

C178 = P47 · P132

P47 = 14664279305141722711057404987986284967512862293_<47>

P132 = 522094974805393808120588312898179627396251001923170837778218768489811574700366797020490210824166469329055959469753995440922219261071_<132>

Number: 10003_185
N=7656146534357225538056752104923507057167910241787998086882103994816482550378784021714056554882588782015038049899853775257340311349448654091548065938715150082292091024538638695803
  ( 178 digits)
SNFS difficulty: 185 digits.
Divisors found:
 r1=14664279305141722711057404987986284967512862293
 r2=522094974805393808120588312898179627396251001923170837778218768489811574700366797020490210824166469329055959469753995440922219261071
Version: 
Total time: 236.49 hours.
Scaled time: 475.81 units (timescale=2.012).
Factorization parameters were as follows:
n: 7656146534357225538056752104923507057167910241787998086882103994816482550378784021714056554882588782015038049899853775257340311349448654091548065938715150082292091024538638695803
m: 10000000000000000000000000000000000000
deg: 5
c5: 1
c0: 3
skew: 1.25
type: snfs
lss: 1
rlim: 8500000
alim: 8500000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 8500000/8500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4250000, 6450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1408605 x 1408853
Total sieving time: 236.49 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,185,5,0,0,0,0,0,0,0,0,8500000,8500000,28,28,54,54,2.5,2.5,100000
total time: 236.49 hours.
 --------- CPU info (if available) ----------

10¹⁷⁴+3 = 1(0)₁₇₃3_<175> = 9701827 · 2365502310860023_<16> · 27679823238177256411_<20> · C133

C133 = P60 · P73

P60 = 291422925891151054317621660625168167319857245759119095307699_<60>

P73 = 5401769776185501645973607904479822156071281325941785500003058562905410087_<73>

Number: 10003_174
N=1574199553166367063490716266281627928450579326253662047596012772199672959419105319917606262631145066135089965093226907594743043359813
  ( 133 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=291422925891151054317621660625168167319857245759119095307699 (pp60)
 r2=5401769776185501645973607904479822156071281325941785500003058562905410087 (pp73)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 123.13 hours.
Scaled time: 229.88 units (timescale=1.867).
Factorization parameters were as follows:
n: 1574199553166367063490716266281627928450579326253662047596012772199672959419105319917606262631145066135089965093226907594743043359813
m: 50000000000000000000000000000000000
deg: 5
c5: 16
c0: 15
skew: 0.99
type: snfs
lss: 1
rlim: 5700000
alim: 5700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5700000/5700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2850000, 6150001)
Primes: RFBsize:393606, AFBsize:392152, largePrimes:10860781 encountered
Relations: rels:12760960, finalFF:1797557
Max relations in full relation-set: 32
Initial matrix: 785822 x 1797557 with sparse part having weight 242784055.
Pruned matrix : 532971 x 536964 with weight 124499580.
Total sieving time: 117.44 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 5.32 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,174,5,0,0,0,0,0,0,0,0,5700000,5700000,27,27,52,52,2.4,2.4,100000
total time: 123.13 hours.
 --------- CPU info (if available) ----------

Dec 3, 2008 (5th)

By Sinkiti Sibata / Msieve, GGNFS

(34·10¹¹⁷+11)/9 = 3(7)₁₁₆9_<118> = 358289 · 10166759834121798343_<20> · C94

C94 = P43 · P51

P43 = 3169840304725009685413906056034592944278811_<43>

P51 = 327177165093027581456207742002827740502041351113407_<51>

Wed Dec 03 08:05:31 2008  Msieve v. 1.38
Wed Dec 03 08:05:31 2008  random seeds: f67d6428 21c1cf72
Wed Dec 03 08:05:31 2008  factoring 1037099364697547350622239844153508010917775411986117641986882008559440553594657077145488119077 (94 digits)
Wed Dec 03 08:05:32 2008  searching for 15-digit factors
Wed Dec 03 08:05:33 2008  commencing quadratic sieve (94-digit input)
Wed Dec 03 08:05:33 2008  using multiplier of 13
Wed Dec 03 08:05:33 2008  using 32kb Intel Core sieve core
Wed Dec 03 08:05:33 2008  sieve interval: 36 blocks of size 32768
Wed Dec 03 08:05:33 2008  processing polynomials in batches of 6
Wed Dec 03 08:05:33 2008  using a sieve bound of 1956883 (72881 primes)
Wed Dec 03 08:05:33 2008  using large prime bound of 244610375 (27 bits)
Wed Dec 03 08:05:33 2008  using double large prime bound of 1256766767596625 (42-51 bits)
Wed Dec 03 08:05:33 2008  using trial factoring cutoff of 51 bits
Wed Dec 03 08:05:33 2008  polynomial 'A' values have 12 factors
Wed Dec 03 10:37:52 2008  73001 relations (18382 full + 54619 combined from 986077 partial), need 72977
Wed Dec 03 10:37:55 2008  begin with 1004459 relations
Wed Dec 03 10:37:56 2008  reduce to 185777 relations in 10 passes
Wed Dec 03 10:37:56 2008  attempting to read 185777 relations
Wed Dec 03 10:37:59 2008  recovered 185777 relations
Wed Dec 03 10:37:59 2008  recovered 167454 polynomials
Wed Dec 03 10:37:59 2008  attempting to build 73001 cycles
Wed Dec 03 10:37:59 2008  found 73001 cycles in 6 passes
Wed Dec 03 10:37:59 2008  distribution of cycle lengths:
Wed Dec 03 10:37:59 2008     length 1 : 18382
Wed Dec 03 10:37:59 2008     length 2 : 13268
Wed Dec 03 10:37:59 2008     length 3 : 12616
Wed Dec 03 10:37:59 2008     length 4 : 9675
Wed Dec 03 10:37:59 2008     length 5 : 7349
Wed Dec 03 10:37:59 2008     length 6 : 4767
Wed Dec 03 10:37:59 2008     length 7 : 3037
Wed Dec 03 10:37:59 2008     length 9+: 3907
Wed Dec 03 10:37:59 2008  largest cycle: 18 relations
Wed Dec 03 10:38:00 2008  matrix is 72881 x 73001 (18.7 MB) with weight 4622762 (63.32/col)
Wed Dec 03 10:38:00 2008  sparse part has weight 4622762 (63.32/col)
Wed Dec 03 10:38:00 2008  filtering completed in 3 passes
Wed Dec 03 10:38:00 2008  matrix is 69106 x 69170 (17.9 MB) with weight 4413229 (63.80/col)
Wed Dec 03 10:38:00 2008  sparse part has weight 4413229 (63.80/col)
Wed Dec 03 10:38:01 2008  saving the first 48 matrix rows for later
Wed Dec 03 10:38:01 2008  matrix is 69058 x 69170 (11.1 MB) with weight 3457078 (49.98/col)
Wed Dec 03 10:38:01 2008  sparse part has weight 2486624 (35.95/col)
Wed Dec 03 10:38:01 2008  matrix includes 64 packed rows
Wed Dec 03 10:38:01 2008  using block size 27668 for processor cache size 1024 kB
Wed Dec 03 10:38:02 2008  commencing Lanczos iteration
Wed Dec 03 10:38:02 2008  memory use: 10.8 MB
Wed Dec 03 10:38:33 2008  lanczos halted after 1093 iterations (dim = 69054)
Wed Dec 03 10:38:33 2008  recovered 15 nontrivial dependencies
Wed Dec 03 10:38:34 2008  prp43 factor: 3169840304725009685413906056034592944278811
Wed Dec 03 10:38:34 2008  prp51 factor: 327177165093027581456207742002827740502041351113407
Wed Dec 03 10:38:34 2008  elapsed time 02:33:03

(34·10¹⁵⁸-61)/9 = 3(7)₁₅₇1_<159> = 7 · 53 · 3733 · 51058354870221649438611241_<26> · C127

C127 = P35 · P93

P35 = 15773686940889973900202381054990761_<35>

P93 = 338691637215285484915002611423828098986479112377345144665570421220398830743417389565760881397_<93>

Number: 37771_158
N=5342415854931393339113761235361305698914154448906483996879306276590440389544165947946307257339371354072751784092656669051773117
  ( 127 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=15773686940889973900202381054990761 (pp35)
 r2=338691637215285484915002611423828098986479112377345144665570421220398830743417389565760881397 (pp93)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 60.61 hours.
Scaled time: 155.40 units (timescale=2.564).
Factorization parameters were as follows:
name: 37771_158
n: 5342415854931393339113761235361305698914154448906483996879306276590440389544165947946307257339371354072751784092656669051773117
m: 50000000000000000000000000000000
deg: 5
c5: 272
c0: -1525
skew: 1.41
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3800001)
Primes: RFBsize:243539, AFBsize:243735, largePrimes:9779798 encountered
Relations: rels:10966987, finalFF:958393
Max relations in full relation-set: 28
Initial matrix: 487341 x 958393 with sparse part having weight 125995401.
Pruned matrix : 367954 x 370454 with weight 71973244.
Total sieving time: 58.31 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 1.94 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 60.61 hours.
 --------- CPU info (if available) ----------

(34·10¹³⁸+11)/9 = 3(7)₁₃₇9_<139> = 140076367 · C131

C131 = P42 · P89

P42 = 334616317985480536983994258642411534504181_<42>

P89 = 80598029134143922014930835608991813141358557739630559737319918330172366613804758172608777_<89>

Number: 37779_138
N=26969415745753727163539141315520967057760555553084681142378412611013660696795325779528375245324414915599415694281803994657983796637
  ( 131 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=334616317985480536983994258642411534504181 (pp42)
 r2=80598029134143922014930835608991813141358557739630559737319918330172366613804758172608777 (pp89)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 11.59 hours.
Scaled time: 29.73 units (timescale=2.564).
Factorization parameters were as follows:
name: 37779_138
n: 26969415745753727163539141315520967057760555553084681142378412611013660696795325779528375245324414915599415694281803994657983796637
m: 5000000000000000000000000000
deg: 5
c5: 272
c0: 275
skew: 1.00
type: snfs
lss: 1
rlim: 1560000
alim: 1560000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1560000/1560000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [780000, 1680001)
Primes: RFBsize:118376, AFBsize:118390, largePrimes:4197288 encountered
Relations: rels:4867657, finalFF:874717
Max relations in full relation-set: 28
Initial matrix: 236833 x 874717 with sparse part having weight 87846157.
Pruned matrix : 157212 x 158460 with weight 21375811.
Total sieving time: 11.28 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1560000,1560000,26,26,48,48,2.3,2.3,100000
total time: 11.59 hours.
 --------- CPU info (if available) ----------

(34·10¹³²+11)/9 = 3(7)₁₃₁9_<133> = 10018907 · 2005869806923_<13> · C114

C114 = P42 · P72

P42 = 704443609565155929330823351494758617941251_<42>

P72 = 266849926365080321478332525760082425809629672857355064497940552907853289_<72>

Number: 37779_132
N=187980725340813251363795528979449026243397065229977082464549401564536900145928473447874479402007304069611129124539
  ( 114 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=704443609565155929330823351494758617941251 (pp42)
 r2=266849926365080321478332525760082425809629672857355064497940552907853289 (pp72)
Version: GGNFS-0.77.1-20060513-k8
Total time: 7.58 hours.
Scaled time: 15.14 units (timescale=1.997).
Factorization parameters were as follows:
name: 37779_132
n: 187980725340813251363795528979449026243397065229977082464549401564536900145928473447874479402007304069611129124539
m: 200000000000000000000000000
deg: 5
c5: 425
c0: 44
skew: 0.64
type: snfs
lss: 1
rlim: 1200000
alim: 1200000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [600000, 1275001)
Primes: RFBsize:92938, AFBsize:93250, largePrimes:3205408 encountered
Relations: rels:3226583, finalFF:291905
Max relations in full relation-set: 28
Initial matrix: 186255 x 291905 with sparse part having weight 27574321.
Pruned matrix : 161015 x 162010 with weight 12254657.
Total sieving time: 7.17 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.24 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,47,47,2.3,2.3,75000
total time: 7.58 hours.
 --------- CPU info (if available) ----------

(34·10¹²⁵+11)/9 = 3(7)₁₂₄9_<126> = 1487² · 255487 · 1876151531_<10> · C105

C105 = P49 · P56

P49 = 5443398684485062745608459470540440836230952784999_<49>

P56 = 65479839726556724918536912328130937246647388805273851297_<56>

Number: 37779_125
N=356432873427831627112679318770660365172752354788089110074530458749791280922615989414199535547912738293703
  ( 105 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=5443398684485062745608459470540440836230952784999 (pp49)
 r2=65479839726556724918536912328130937246647388805273851297 (pp56)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.85 hours.
Scaled time: 5.70 units (timescale=2.003).
Factorization parameters were as follows:
name: 37779_125
n: 356432873427831627112679318770660365172752354788089110074530458749791280922615989414199535547912738293703
m: 10000000000000000000000000
deg: 5
c5: 34
c0: 11
skew: 0.80
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 700001)
Primes: RFBsize:71274, AFBsize:71741, largePrimes:2573592 encountered
Relations: rels:2543913, finalFF:259396
Max relations in full relation-set: 28
Initial matrix: 143081 x 259396 with sparse part having weight 19576840.
Pruned matrix : 111447 x 112226 with weight 6001097.
Total sieving time: 2.68 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 2.85 hours.
 --------- CPU info (if available) ----------

(34·10¹⁴⁰+11)/9 = 3(7)₁₃₉9_<141> = 461 · 1667 · 33013 · C131

C131 = P43 · P88

P43 = 5286853178190512842446697555047849243640583_<43>

P88 = 2816551137745142953027574742897451096765053262076789526378442459821368042472899695804823_<88>

Number: 37779_140
N=14890692334124013938426445413695471439527746160882064829320446619056609555256489725739314484031578937209695694518373562136729931809
  ( 131 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=5286853178190512842446697555047849243640583 (pp43)
 r2=2816551137745142953027574742897451096765053262076789526378442459821368042472899695804823 (pp88)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 11.70 hours.
Scaled time: 30.12 units (timescale=2.575).
Factorization parameters were as follows:
name: 37779_140
n: 14890692334124013938426445413695471439527746160882064829320446619056609555256489725739314484031578937209695694518373562136729931809
m: 10000000000000000000000000000
deg: 5
c5: 34
c0: 11
skew: 0.80
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [800000, 1700001)
Primes: RFBsize:121127, AFBsize:121741, largePrimes:4134768 encountered
Relations: rels:4641289, finalFF:712757
Max relations in full relation-set: 28
Initial matrix: 242934 x 712757 with sparse part having weight 74251615.
Pruned matrix : 167601 x 168879 with weight 21800021.
Total sieving time: 11.36 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000
total time: 11.70 hours.
 --------- CPU info (if available) ----------

Dec 3, 2008 (4th)

By Robert Backstrom / GMP-ECM, GGNFS

(34·10¹¹⁵+11)/9 = 3(7)₁₁₄9_<116> = 3³ · 13 · 1648813801501245593_<19> · C95

C95 = P35 · P61

P35 = 29415027840806636275258180245178147_<35>

P61 = 2219158965639345523025597599430986517293980929370944685537799_<61>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 65276622757457006081426432091868980663147198002143596564155708560164105572476967585475257278453 (95 digits)
Using B1=1164000, B2=1426247560, polynomial Dickson(6), sigma=3694281782
Step 1 took 7140ms
Step 2 took 4016ms
********** Factor found in step 2: 29415027840806636275258180245178147
Found probable prime factor of 35 digits: 29415027840806636275258180245178147
Probable prime cofactor 2219158965639345523025597599430986517293980929370944685537799 has 61 digits

(11·10¹⁶⁴+1)/3 = 3(6)₁₆₃7_<165> = 53 · 85121 · C158

C158 = P43 · P116

P43 = 1266188042683552938501666231379202970184373_<43>

P116 = 64189003840718731051789445749630286944004145691347328068960743453391971858994738506501705251623397446227743373324483_<116>

Number: n
N=81275349134886712138007907204830652096508713936557496878841876517770965918364527181764708012027865031790852814110937452781792903169509567549383456284464904159
  ( 158 digits)
SNFS difficulty: 166 digits.
Divisors found:

Wed Dec 03 09:12:58 2008  prp43 factor: 1266188042683552938501666231379202970184373
Wed Dec 03 09:12:58 2008  prp116 factor: 64189003840718731051789445749630286944004145691347328068960743453391971858994738506501705251623397446227743373324483
Wed Dec 03 09:12:58 2008  elapsed time 01:58:53 (Msiev 1.39)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 26.81 hours.
Scaled time: 49.04 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_3_6_163_7
n: 81275349134886712138007907204830652096508713936557496878841876517770965918364527181764708012027865031790852814110937452781792903169509567549383456284464904159
type: snfs
skew: 0.98
deg: 5
c5: 11
c0: 10
m: 1000000000000000000000000000000000
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 1500001)
Primes: RFBsize:348513, AFBsize:348432, largePrimes:14090709 encountered
Relations: rels:12617715, finalFF:733115
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 26.54 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.5,2.5,100000
total time: 26.81 hours.
 --------- CPU info (if available) ----------

Dec 3, 2008 (3rd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38, Msieve

(34·10¹³⁵+11)/9 = 3(7)₁₃₄9_<136> = 83 · 1271659 · 38820576214206694652531103157_<29> · C99

C99 = P31 · P69

P31 = 1841221420817442296175794794789_<31>

P69 = 500748491627872924290376533581931521233778005915252163983598241292459_<69>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=327529411
Step 1 took 12949ms
Step 2 took 10136ms
********** Factor found in step 2: 1841221420817442296175794794789
Found probable prime factor of 31 digits: 1841221420817442296175794794789
Probable prime cofactor 500748491627872924290376533581931521233778005915252163983598241292459 has 69 digits

(34·10¹⁶³+11)/9 = 3(7)₁₆₂9_<164> = 3 · 13 · 2995517639_<10> · 1786997605439027_<16> · 19883035843764619_<17> · 2414031517419368222581_<22> · C100

C100 = P30 · P70

P30 = 538538060804192975491860866957_<30>

P70 = 7000578264100615505009002316587714144643825814097360015482214397616419_<70>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=384210140
Step 1 took 12933ms
Step 2 took 10623ms
********** Factor found in step 2: 538538060804192975491860866957
Found probable prime factor of 30 digits: 538538060804192975491860866957
Probable prime cofactor 7000578264100615505009002316587714144643825814097360015482214397616419 has 70 digits

(34·10¹⁴⁸+11)/9 = 3(7)₁₄₇9_<149> = 3 · 7 · 126227 · 23834221709387491_<17> · C126

C126 = P30 · P97

P30 = 136061100348900004453193777393_<30>

P97 = 4394706727315139875544870349149726531886612053921328903129416402633146507216189846137880348388399_<97>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=452164895
Step 1 took 12205ms
Step 2 took 4977ms
********** Factor found in step 2: 136061100348900004453193777393
Found probable prime factor of 30 digits: 136061100348900004453193777393
Probable prime cofactor 4394706727315139875544870349149726531886612053921328903129416402633146507216189846137880348388399 has 97 digits

(34·10¹⁶²-61)/9 = 3(7)₁₆₁1_<163> = 3 · 521 · 7163179 · C153

C153 = P48 · P50 · P55

P48 = 508482292810519141237018117535724632563288268983_<48>

P50 = 69697565335453954183157841146626227272181807013267_<50>

P55 = 9520903958691570180369995997915148223742970595209791943_<55>

SNFS difficulty: 164 digits.
Divisors found:
 r1=508482292810519141237018117535724632563288268983 (pp48)
 r2=69697565335453954183157841146626227272181807013267 (pp50)
 r3=9520903958691570180369995997915148223742970595209791943 (pp55)
Version: Msieve-1.38
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.537).
Factorization parameters were as follows:
n: 337420625170770259299467660561244960872840414723192999695679851875816615851259950059949419759282795573495720737496191936943879016272865401591826039056723
m: 200000000000000000000000000000000
deg: 5
c5: 425
c0: -244
skew: 0.89
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1900000, 4000001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 768687 x 768929
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,52,52,2.4,2.4,100000
total time: 26.00 hours.

(34·10¹⁷⁰+11)/9 = 3(7)₁₆₉9_<171> = 19 · 601 · 673 · 8663 · 70439611822049_<14> · C146

C146 = P31 · P33 · P83

P31 = 5949365760417332575874777487329_<31>

P33 = 338927312633634574452868348574459_<33>

P83 = 39951286071499425676165028250701904891033092637792693030891274330699036140072514381_<83>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1331521538
Step 1 took 15177ms
Step 2 took 11309ms
********** Factor found in step 2: 338927312633634574452868348574459
Found probable prime factor of 33 digits: 338927312633634574452868348574459

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1686472867
Step 1 took 14489ms
Step 2 took 11065ms
********** Factor found in step 2: 5949365760417332575874777487329
Found probable prime factor of 31 digits: 5949365760417332575874777487329

(34·10¹⁶²+11)/9 = 3(7)₁₆₁9_<163> = 47 · 459443 · C156

C156 = P35 · C121

P35 = 67124546794083294248340603185287579_<35>

C121 = [2606306841918308784669025209898688038053573715705451307168694698444179234703434235423308619590868129220762915004730308381_<121>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2188203815
Step 1 took 24769ms
Step 2 took 16445ms
********** Factor found in step 2: 67124546794083294248340603185287579
Found probable prime factor of 35 digits: 67124546794083294248340603185287579
Composite cofactor has 121 digits

(34·10¹⁵⁵+11)/9 = 3(7)₁₅₄9_<156> = 109 · 38431 · 26314325321_<11> · C139

C139 = P31 · P109

P31 = 1367414235817844393835674902661_<31>

P109 = 2506316354241965358478287885021487172210327240182297461454627912939386465253844371489098898542813986043072421_<109>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=415686968
Step 1 took 6275ms
Step 2 took 4400ms
********** Factor found in step 2: 1367414235817844393835674902661
Found probable prime factor of 31 digits: 1367414235817844393835674902661
Probable prime cofactor 2506316354241965358478287885021487172210327240182297461454627912939386465253844371489098898542813986043072421 has 109 digits

(34·10¹⁵⁶+11)/9 = 3(7)₁₅₅9_<157> = 431 · C154

C154 = P32 · C123

P32 = 20428085369379755054381161567133_<32>

C123 = [429073283061331887029373538382779736581251147921326448030495788175194522967423873919288084893891002909527976603344608741473_<123>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=2478402618
Step 1 took 6442ms
Step 2 took 4452ms
********** Factor found in step 2: 20428085369379755054381161567133
Found probable prime factor of 32 digits: 20428085369379755054381161567133
Composite cofactor 429073283061331887029373538382779736581251147921326448030495788175194522967423873919288084893891002909527976603344608741473 has 123 digits

(34·10¹⁸⁸+11)/9 = 3(7)₁₈₇9_<189> = 19 · 3167 · 54673 · 6828917458921_<13> · C167

C167 = P30 · C138

P30 = 141522473677954575496709305193_<30>

C138 = [118818636354373834678341129976690275885036383831189369268516472576592786183983394505260652754963952768044196554737946327636300583734935967_<138>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=2017253979
Step 1 took 8272ms
Step 2 took 192ms
********** Factor found in step 2: 141522473677954575496709305193
Found probable prime factor of 30 digits: 141522473677954575496709305193
Composite cofactor 118818636354373834678341129976690275885036383831189369268516472576592786183983394505260652754963952768044196554737946327636300583734935967 has 138 digits

(34·10¹¹⁹+11)/9 = 3(7)₁₁₈9_<120> = 127 · 3467 · 1614479767_<10> · C105

C105 = P42 · P64

P42 = 134550578004032969503029919091315931135151_<42>

P64 = 3949668719875040095385887177491447940304626316925380622724998143_<64>

SNFS difficulty: 121 digits.
Divisors found:
 r1=134550578004032969503029919091315931135151 (pp42)
 r2=3949668719875040095385887177491447940304626316925380622724998143 (pp64)
Version: Msieve-1.38
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 531430209183635626101673509948954022583701742093667870559637533214565867046554682600715495943222357024593
m: 1000000000000000000000000
deg: 5
c5: 17
c0: 55
skew: 1.26
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 48
mfba: 48
rlambda: 2.2
alambda: 2.2
Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 48/48
Sieved rational special-q in [365000, 615001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 77656 x 77874
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,48,48,2.2,2.2,50000
total time: 1.00 hours.

(34·10²⁰³+11)/9 = 3(7)₂₀₂9_<204> = 127 · 4157 · 1084987 · 1576097849_<10> · 267522701219_<12> · C172

C172 = P33 · C139

P33 = 241852534709016633483041799377417_<33>

C139 = [6467458742747490908426758718543314878516214661999799045633580159444730768422463131124826108330789481076500407954611602955238945601019157889_<139>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=1984248884
Step 1 took 8287ms
Step 2 took 5223ms
********** Factor found in step 2: 241852534709016633483041799377417
Found probable prime factor of 33 digits: 241852534709016633483041799377417
Composite cofactor 6467458742747490908426758718543314878516214661999799045633580159444730768422463131124826108330789481076500407954611602955238945601019157889 has 139 digits

(34·10¹³⁷+11)/9 = 3(7)₁₃₆9_<138> = 313 · C136

C136 = P68 · P68

P68 = 24601879358045760753375775352802939606580539840588556396176557740009_<68>

P68 = 49059575445962897342059554987416196312658920843681835646967035583187_<68>

# Yes, Virginia, there is a Santa Claus. A Nice split for me, too, finally :-)
#
SNFS difficulty: 139 digits.
Divisors found:
 r1=24601879358045760753375775352802939606580539840588556396176557740009 (pp68)
 r2=49059575445962897342059554987416196312658920843681835646967035583187 (pp68)
Version: Msieve-1.38
Total time: 5.50 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
n: 1206957756478523251686190983315583954561590344337948171813986510472133475328363507277245296414625488107916222932197373091941782037628683
m: 2000000000000000000000000000
deg: 5
c5: 425
c0: 44
skew: 0.64
type: snfs
lss: 1
rlim: 1460000
alim: 1460000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.4
alambda: 2.4
Factor base limits: 1460000/1460000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [730000, 1630001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 240114 x 240356
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1460000,1460000,26,26,48,48,2.4,2.4,150000
total time: 5.50 hours.

(34·10¹⁷³+11)/9 = 3(7)₁₇₂9_<174> = 1451 · 23175336529_<11> · 6061403725747_<13> · C148

C148 = P38 · P110

P38 = 33356516879350872097959604347349217261_<38>

P110 = 55563428979535597429283367913886066893955421083855121284705414022229840742979307014569462000972114986360128703_<110>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=158554100
Step 1 took 6232ms
Step 2 took 4523ms
********** Factor found in step 2: 33356516879350872097959604347349217261
Found probable prime factor of 38 digits: 33356516879350872097959604347349217261
Probable prime cofactor 55563428979535597429283367913886066893955421083855121284705414022229840742979307014569462000972114986360128703 has 110 digits

(34·10²⁰¹+11)/9 = 3(7)₂₀₀9_<202> = 613 · 10463 · C195

C195 = P33 · C162

P33 = 947638487444381399137523776727917_<33>

C162 = [621551354039585113776369048662467374494877397995276706501347037287825921109330099815375691340299939198266932712737822293439082110528073781426306264610059081985773_<162>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3942574903
Step 1 took 35263ms
Step 2 took 21016ms
********** Factor found in step 2: 947638487444381399137523776727917
Found probable prime factor of 33 digits: 947638487444381399137523776727917
Composite cofactor 621551354039585113776369048662467374494877397995276706501347037287825921109330099815375691340299939198266932712737822293439082110528073781426306264610059081985773 has 162 digits

(34·10¹⁴¹+11)/9 = 3(7)₁₄₀9_<142> = 829 · C139

C139 = P38 · P102

P38 = 39514398764869549287206850885745348933_<38>

P102 = 115325806065567829009781861388333198225804023813540351062894513229056794230954742920893255484355270947_<102>

SNFS difficulty: 143 digits.
Divisors found:
 r1=39514398764869549287206850885745348933 (pp38)
 r2=115325806065567829009781861388333198225804023813540351062894513229056794230954742920893255484355270947 (pp102)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 4557029888754858598043157753652325425546173435196354376088996113121565473797078139659563061251842916499128803109502747620962337488272349551
m: 20000000000000000000000000000
deg: 5
c5: 85
c0: 88
skew: 1
type: snfs
lss: 1
rlim: 1720000
alim: 1720000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.4
alambda: 2.4
Factor base limits: 1720000/1720000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [860000, 1860001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 322040 x 322288
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1720000,1720000,26,26,48,48,2.4,2.4,200000
total time: 6.00 hours.

(34·10¹⁹⁸+11)/9 = 3(7)₁₉₇9_<199> = 110501 · 345944962629092687143_<21> · C173

C173 = P36 · P138

P36 = 487431470528644422733146459735402767_<36>

P138 = 202744752573318372422323054839304128700408443189463262974309331874473226300108176768945751786926898861429679103905594441113327049733804159_<138>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4272672805
Step 1 took 27411ms
Step 2 took 16584ms
********** Factor found in step 2: 487431470528644422733146459735402767
Found probable prime factor of 36 digits: 487431470528644422733146459735402767
Probable prime cofactor 202744752573318372422323054839304128700408443189463262974309331874473226300108176768945751786926898861429679103905594441113327049733804159 has 138 digits

Dec 3, 2008 (2nd)

By Erik Branger / Msieve

(34·10¹²²+11)/9 = 3(7)₁₂₁9_<123> = 5351 · 89620398463348176243456330223_<29> · C90

C90 = P42 · P49

P42 = 125930051109900781050517676232507094612633_<42>

P49 = 6255545776522447969252532683162886614264007977331_<49>

Tue Dec 02 17:23:35 2008  Msieve v. 1.38
Tue Dec 02 17:23:35 2008  random seeds: 8794fe44 d9316f60
Tue Dec 02 17:23:35 2008  factoring 787761199357795842149902004718574687702229628244577845033345679589374961514450685290222523 (90 digits)
Tue Dec 02 17:23:37 2008  searching for 15-digit factors
Tue Dec 02 17:23:38 2008  commencing quadratic sieve (90-digit input)
Tue Dec 02 17:23:38 2008  using multiplier of 35
Tue Dec 02 17:23:38 2008  using 32kb Intel Core sieve core
Tue Dec 02 17:23:38 2008  sieve interval: 36 blocks of size 32768
Tue Dec 02 17:23:38 2008  processing polynomials in batches of 6
Tue Dec 02 17:23:38 2008  using a sieve bound of 1613669 (61176 primes)
Tue Dec 02 17:23:38 2008  using large prime bound of 135548196 (27 bits)
Tue Dec 02 17:23:38 2008  using double large prime bound of 434278798718520 (42-49 bits)
Tue Dec 02 17:23:38 2008  using trial factoring cutoff of 49 bits
Tue Dec 02 17:23:38 2008  polynomial 'A' values have 12 factors
Tue Dec 02 18:51:53 2008  61673 relations (16166 full + 45507 combined from 667782 partial), need 61272
Tue Dec 02 18:51:54 2008  begin with 683948 relations
Tue Dec 02 18:51:54 2008  reduce to 151269 relations in 9 passes
Tue Dec 02 18:51:54 2008  attempting to read 151269 relations
Tue Dec 02 18:51:57 2008  recovered 151269 relations
Tue Dec 02 18:51:57 2008  recovered 131708 polynomials
Tue Dec 02 18:51:57 2008  attempting to build 61673 cycles
Tue Dec 02 18:51:57 2008  found 61673 cycles in 6 passes
Tue Dec 02 18:51:57 2008  distribution of cycle lengths:
Tue Dec 02 18:51:57 2008     length 1 : 16166
Tue Dec 02 18:51:57 2008     length 2 : 11786
Tue Dec 02 18:51:57 2008     length 3 : 10982
Tue Dec 02 18:51:57 2008     length 4 : 8304
Tue Dec 02 18:51:57 2008     length 5 : 5824
Tue Dec 02 18:51:57 2008     length 6 : 3724
Tue Dec 02 18:51:57 2008     length 7 : 2254
Tue Dec 02 18:51:57 2008     length 9+: 2633
Tue Dec 02 18:51:57 2008  largest cycle: 20 relations
Tue Dec 02 18:51:57 2008  matrix is 61176 x 61673 (15.1 MB) with weight 3720091 (60.32/col)
Tue Dec 02 18:51:57 2008  sparse part has weight 3720091 (60.32/col)
Tue Dec 02 18:51:57 2008  filtering completed in 3 passes
Tue Dec 02 18:51:57 2008  matrix is 57401 x 57465 (14.1 MB) with weight 3463249 (60.27/col)
Tue Dec 02 18:51:57 2008  sparse part has weight 3463249 (60.27/col)
Tue Dec 02 18:51:58 2008  saving the first 48 matrix rows for later
Tue Dec 02 18:51:58 2008  matrix is 57353 x 57465 (8.6 MB) with weight 2677561 (46.59/col)
Tue Dec 02 18:51:58 2008  sparse part has weight 1902579 (33.11/col)
Tue Dec 02 18:51:58 2008  matrix includes 64 packed rows
Tue Dec 02 18:51:58 2008  using block size 22986 for processor cache size 2048 kB
Tue Dec 02 18:51:58 2008  commencing Lanczos iteration
Tue Dec 02 18:51:58 2008  memory use: 8.5 MB
Tue Dec 02 18:52:16 2008  lanczos halted after 908 iterations (dim = 57350)
Tue Dec 02 18:52:17 2008  recovered 17 nontrivial dependencies
Tue Dec 02 18:52:17 2008  prp42 factor: 125930051109900781050517676232507094612633
Tue Dec 02 18:52:17 2008  prp49 factor: 6255545776522447969252532683162886614264007977331
Tue Dec 02 18:52:17 2008  elapsed time 01:28:42

(34·10¹³³+11)/9 = 3(7)₁₃₂9_<134> = 3² · 13 · 43 · 3041 · 7157041348997849_<16> · 3858971354503959667_<19> · C92

C92 = P40 · P53

P40 = 1611364825756490385391657092199601092037_<40>

P53 = 55483865437642055596519639266633036099126609006735619_<53>

Tue Dec 02 18:59:21 2008  Msieve v. 1.38
Tue Dec 02 18:59:21 2008  random seeds: db3297c8 282ae7cc
Tue Dec 02 18:59:21 2008  factoring 89404749163222650076866820667644652085586696566770446146303782255448909690029097440945165903 (92 digits)
Tue Dec 02 18:59:22 2008  searching for 15-digit factors
Tue Dec 02 18:59:24 2008  commencing quadratic sieve (92-digit input)
Tue Dec 02 18:59:24 2008  using multiplier of 3
Tue Dec 02 18:59:24 2008  using 32kb Intel Core sieve core
Tue Dec 02 18:59:24 2008  sieve interval: 36 blocks of size 32768
Tue Dec 02 18:59:24 2008  processing polynomials in batches of 6
Tue Dec 02 18:59:24 2008  using a sieve bound of 1853669 (69412 primes)
Tue Dec 02 18:59:24 2008  using large prime bound of 209464597 (27 bits)
Tue Dec 02 18:59:24 2008  using double large prime bound of 950602707335250 (42-50 bits)
Tue Dec 02 18:59:24 2008  using trial factoring cutoff of 50 bits
Tue Dec 02 18:59:24 2008  polynomial 'A' values have 12 factors
Tue Dec 02 21:27:12 2008  69578 relations (17573 full + 52005 combined from 892740 partial), need 69508
Tue Dec 02 21:27:16 2008  begin with 910313 relations
Tue Dec 02 21:27:16 2008  reduce to 176228 relations in 11 passes
Tue Dec 02 21:27:16 2008  attempting to read 176228 relations
Tue Dec 02 21:27:19 2008  recovered 176228 relations
Tue Dec 02 21:27:19 2008  recovered 158671 polynomials
Tue Dec 02 21:27:19 2008  attempting to build 69578 cycles
Tue Dec 02 21:27:19 2008  found 69578 cycles in 5 passes
Tue Dec 02 21:27:19 2008  distribution of cycle lengths:
Tue Dec 02 21:27:19 2008     length 1 : 17573
Tue Dec 02 21:27:19 2008     length 2 : 12601
Tue Dec 02 21:27:19 2008     length 3 : 11959
Tue Dec 02 21:27:19 2008     length 4 : 9471
Tue Dec 02 21:27:19 2008     length 5 : 6955
Tue Dec 02 21:27:19 2008     length 6 : 4600
Tue Dec 02 21:27:19 2008     length 7 : 2814
Tue Dec 02 21:27:19 2008     length 9+: 3605
Tue Dec 02 21:27:19 2008  largest cycle: 18 relations
Tue Dec 02 21:27:20 2008  matrix is 69412 x 69578 (17.6 MB) with weight 4325156 (62.16/col)
Tue Dec 02 21:27:20 2008  sparse part has weight 4325156 (62.16/col)
Tue Dec 02 21:27:20 2008  filtering completed in 3 passes
Tue Dec 02 21:27:20 2008  matrix is 65648 x 65712 (16.7 MB) with weight 4116478 (62.64/col)
Tue Dec 02 21:27:20 2008  sparse part has weight 4116478 (62.64/col)
Tue Dec 02 21:27:20 2008  saving the first 48 matrix rows for later
Tue Dec 02 21:27:21 2008  matrix is 65600 x 65712 (10.3 MB) with weight 3244072 (49.37/col)
Tue Dec 02 21:27:21 2008  sparse part has weight 2314877 (35.23/col)
Tue Dec 02 21:27:21 2008  matrix includes 64 packed rows
Tue Dec 02 21:27:21 2008  using block size 26284 for processor cache size 2048 kB
Tue Dec 02 21:27:21 2008  commencing Lanczos iteration
Tue Dec 02 21:27:21 2008  memory use: 10.1 MB
Tue Dec 02 21:27:47 2008  lanczos halted after 1039 iterations (dim = 65598)
Tue Dec 02 21:27:47 2008  recovered 17 nontrivial dependencies
Tue Dec 02 21:27:47 2008  prp40 factor: 1611364825756490385391657092199601092037
Tue Dec 02 21:27:47 2008  prp53 factor: 55483865437642055596519639266633036099126609006735619
Tue Dec 02 21:27:47 2008  elapsed time 02:28:26

Dec 3, 2008

Factorizations of 377...779 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Dec 2, 2008 (4th)

By Jo Yeong Uk / GGNFS

7·10¹⁸²-9 = 6(9)₁₈₁1_<183> = 47 · 2909 · 8412983 · 197529555280333365899_<21> · 551024823684035448740408536106657207_<36> · C115

C115 = P54 · P62

P54 = 120505114541548280042487841757872247892709036654778083_<54>

P62 = 46397835349507535301741903585430930023363737967949935765765821_<62>

Number: 69991_182
N=5591176463272303316615780966074659214096793163110886821777133410508295180383174336519509049157089247339837301301143
  ( 115 digits)
Divisors found:
 r1=120505114541548280042487841757872247892709036654778083 (pp54)
 r2=46397835349507535301741903585430930023363737967949935765765821 (pp62)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 22.15 hours.
Scaled time: 52.61 units (timescale=2.375).
Factorization parameters were as follows:
name: 69991_182
n: 5591176463272303316615780966074659214096793163110886821777133410508295180383174336519509049157089247339837301301143
skew: 17333.97
# norm 9.01e+15
c5: 97740
c4: 18416313678
c3: -212611237858754
c2: 202852738603153717
c1: 15507418452815452722844
c0: 58012158724999932663752355
# alpha -6.24
Y1: 2422555194829
Y0: -8942969295094779062108
# Murphy_E 5.46e-10
# M 2950275471248039864803529724056229443825261945017915189784971355597025064217620201603167612787728815854960471712106
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [1400000, 2660001)
Primes: RFBsize:203362, AFBsize:203456, largePrimes:9573195 encountered
Relations: rels:9505229, finalFF:506003
Max relations in full relation-set: 28
Initial matrix: 406897 x 506003 with sparse part having weight 54243052.
Pruned matrix : 348124 x 350222 with weight 36935690.
Polynomial selection time: 1.31 hours.
Total sieving time: 19.78 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.76 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,52,52,2.6,2.6,70000
total time: 22.15 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Dec 2, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(11·10¹⁴⁷+1)/3 = 3(6)₁₄₆7_<148> = 19 · 83791 · 753120798308864203_<18> · C124

C124 = P36 · P39 · P51

P36 = 153288443336301868304649866120256611_<36>

P39 = 170668247510580321448805603064473607653_<39>

P51 = 116894390737140603747245738094441350205229565084827_<51>

Number: 36667_147
N=3058129095015556371371520145905654136299614131214743883131326477092954523068559314933344152325533809154730720048680367745941
  ( 124 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=153288443336301868304649866120256611 (pp36)
 r2=170668247510580321448805603064473607653 (pp39)
 r3=116894390737140603747245738094441350205229565084827 (pp51)
Version: GGNFS-0.77.1-20060513-k8
Total time: 22.62 hours.
Scaled time: 44.91 units (timescale=1.985).
Factorization parameters were as follows:
name: 36667_147
n: 3058129095015556371371520145905654136299614131214743883131326477092954523068559314933344152325533809154730720048680367745941
m: 500000000000000000000000000000
deg: 5
c5: 44
c0: 125
skew: 1.23
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1100000, 1800001)
Primes: RFBsize:162662, AFBsize:162521, largePrimes:7150630 encountered
Relations: rels:7348652, finalFF:640645
Max relations in full relation-set: 28
Initial matrix: 325250 x 640645 with sparse part having weight 71451844.
Pruned matrix : 244711 x 246401 with weight 28421597.
Total sieving time: 21.33 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.97 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,49,49,2.4,2.4,100000
total time: 22.62 hours.
 --------- CPU info (if available) ----------

(34·10¹⁵⁶-61)/9 = 3(7)₁₅₅1_<157> = 3² · 43 · 6028933 · 1402421333_<10> · C139

C139 = P46 · P93

P46 = 9966402979697060305647496423630143597597319309_<46>

P93 = 115842529545143837157184112972896281967285587268931776950834834580235894383922902897517477333_<93>

Number: 37771_156
N=1154533331634366282678567732766953021488942489574034118414499319512603715875752034778388732687905581793683555211026274464001824176970722897
  ( 139 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=9966402979697060305647496423630143597597319309 (pp46)
 r2=115842529545143837157184112972896281967285587268931776950834834580235894383922902897517477333 (pp93)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 42.40 hours.
Scaled time: 108.71 units (timescale=2.564).
Factorization parameters were as follows:
name: 37771_156
n: 1154533331634366282678567732766953021488942489574034118414499319512603715875752034778388732687905581793683555211026274464001824176970722897
m: 10000000000000000000000000000000
deg: 5
c5: 340
c0: -61
skew: 0.71
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1500000, 2800001)
Primes: RFBsize:216816, AFBsize:216657, largePrimes:8653599 encountered
Relations: rels:9425471, finalFF:991033
Max relations in full relation-set: 28
Initial matrix: 433540 x 991033 with sparse part having weight 122448345.
Pruned matrix : 315934 x 318165 with weight 56320413.
Total sieving time: 40.85 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.25 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000
total time: 42.40 hours.
 --------- CPU info (if available) ----------

(34·10¹⁵⁷-61)/9 = 3(7)₁₅₆1_<158> = 108685226485233581851_<21> · C138

C138 = P51 · P87

P51 = 525635717350307831412930905071935105423234178396363_<51>

P87 = 661273356310180256351138419233820506936333700070566891354943514978567534279994118905267_<87>

Number: 37771_157
N=347588895008747308866544061102726069403307881613424404847414945687730332029210319944189517278502930044633182335397963047561247567174343921
  ( 138 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=525635717350307831412930905071935105423234178396363 (pp51)
 r2=661273356310180256351138419233820506936333700070566891354943514978567534279994118905267 (pp87)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 50.62 hours.
Scaled time: 129.79 units (timescale=2.564).
Factorization parameters were as follows:
name:37771_157
n: 347588895008747308866544061102726069403307881613424404847414945687730332029210319944189517278502930044633182335397963047561247567174343921
m: 20000000000000000000000000000000
deg: 5
c5: 425
c0: -244
skew: 0.89
type: snfs
lss: 1
rlim: 3100000
alim: 3100000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3100000/3100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1550000, 3250001)
Primes: RFBsize:223492, AFBsize:224441, largePrimes:8630791 encountered
Relations: rels:9318143, finalFF:799748
Max relations in full relation-set: 28
Initial matrix: 448000 x 799748 with sparse part having weight 101059944.
Pruned matrix : 351450 x 353754 with weight 55059506.
Total sieving time: 48.73 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.60 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,50,50,2.4,2.4,100000
total time: 50.62 hours.
 --------- CPU info (if available) ----------

(34·10¹⁴⁹-61)/9 = 3(7)₁₄₈1_<150> = 29 · 67 · C147

C147 = P39 · P108

P39 = 948232092733249950554056411032673040477_<39>

P108 = 205044893122722355563983803137691979462044995543930554941591189105064744137537173790203999128478533860189361_<108>

Number: 37771_149
N=194430148110024589695202150168696746154286041059072453822839823869159947389489334934522788357065248470292217075541831074512494996282953050837765197
  ( 147 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=948232092733249950554056411032673040477 (pp39)
 r2=205044893122722355563983803137691979462044995543930554941591189105064744137537173790203999128478533860189361 (pp108)
Version: GGNFS-0.77.1-20060513-k8
Total time: 28.30 hours.
Scaled time: 54.82 units (timescale=1.937).
Factorization parameters were as follows:
name:  37771_149
n: 194430148110024589695202150168696746154286041059072453822839823869159947389489334934522788357065248470292217075541831074512494996282953050837765197
m: 1000000000000000000000000000000
deg: 5
c5: 17
c0: -305
skew: 1.78
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 2050001)
Primes: RFBsize:169511, AFBsize:170222, largePrimes:7316415 encountered
Relations: rels:7619094, finalFF:707261
Max relations in full relation-set: 28
Initial matrix: 339798 x 707261 with sparse part having weight 82041141.
Pruned matrix : 254976 x 256738 with weight 33834665.
Total sieving time: 26.68 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.29 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 28.30 hours.
 --------- CPU info (if available) ----------

Dec 2, 2008 (2nd)

By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1

(11·10¹⁶⁰+1)/3 = 3(6)₁₅₉7_<161> = 37 · 4999 · C156

C156 = P63 · P94

P63 = 107806408315392186042834496039127146847357843939914262271423059_<63>

P94 = 1838831743539757907265990383385558921051444574734351440522190333306312386979892415634452042051_<94>

SNFS difficulty: 161 digits.
Divisors found:
 r1=107806408315392186042834496039127146847357843939914262271423059 (pp63)
 r2=1838831743539757907265990383385558921051444574734351440522190333306312386979892415634452042051 (pp94)
Version: Msieve-1.38
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 198237845767351668531904579114021002398677933784955189236045407279654129024002998797957789756149428083814961190436285455289256049408079814161030404279054009
m: 100000000000000000000000000000000
deg: 5
c5: 11
c0: 1
skew: 0.62
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1700000, 2600001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 589731 x 589973
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,52,52,2.4,2.4,100000
total time: 14.00 hours.

(11·10¹⁶¹+1)/3 = 3(6)₁₆₀7_<162> = 7 · 3583 · C158

C158 = P55 · P104

P55 = 1396874562526488259237574101449859344602907037597516643_<55>

P104 = 10465721494555841361661330014966716334135064147047311164221578603816109473930419270673010543406762793249_<104>

SNFS difficulty: 163 digits.
Divisors found:
 r1=1396874562526488259237574101449859344602907037597516643 (pp55)
 r2=10465721494555841361661330014966716334135064147047311164221578603816109473930419270673010543406762793249 (pp104)
Version: Msieve-1.38
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.316).
Factorization parameters were as follows:
n: 14619300134231755777946121233868931329160187658652632138537804181119838390282152492590672886514360139813670374652791621811995800273779620695612880932445543107
m: 200000000000000000000000000000000
deg: 5
c5: 55
c0: 16
skew: 0.78
type: snfs
lss: 1
rlim: 3700000
alim: 3700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3700000/3700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1850000, 3150001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 705916 x 706158
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3700000,3700000,27,27,52,52,2.4,2.4,100000
total time: 25.00 hours.

(34·10¹⁶¹-61)/9 = 3(7)₁₆₀1_<162> = 71 · C160

C160 = P61 · P100

P61 = 5248339198924568488090626332597551156263673436410591970891881_<61>

P100 = 1013809048890795600319731355237825745864782625364859636226664234782284012321457252955340518891623221_<100>

SNFS difficulty: 162 digits.
Divisors found:
 r1=5248339198924568488090626332597551156263673436410591970891881 (pp61)
 r2=1013809048890795600319731355237825745864782625364859636226664234782284012321457252955340518891623221 (pp100)
Version: Msieve-1.38
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.722).
Factorization parameters were as follows:
n: 5320813771517996870109546165884194053208137715179968701095461658841940532081377151799687010954616588419405320813771517996870109546165884194053208137715179968701
m: 100000000000000000000000000000000
deg: 5
c5: 340
c0: -61
skew: 0.71
type: snfs
lss: 1
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1800000, 3500001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 705065 x 705307
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3600000,3600000,27,27,52,52,2.4,2.4,100000
total time: 24.00 hours.

(64·10²⁴⁷-1)/9 = 7(1)₂₄₇_<248> = 10477 · 16879 · C240

C240 = P38 · P202

P38 = 63209533607698633158751402340598745883_<38>

P202 = 6361671236848233496152449269521854211349654871561806001705536258426388234147009847277835322217606481274315381488581580847083208285386176738103763445869615774430972147572743203317058290174392113785190999_<202>

Using B1=43000000, B2=582162027730, polynomial Dickson(30), sigma=2337050584
Step 1 took 491939ms
Step 2 took 244339ms
********** Factor found in step 2: 63209533607698633158751402340598745883
Found probable prime factor of 38 digits: 63209533607698633158751402340598745883
Probable prime cofactor has 202 digits

Dec 2, 2008

Msieve-1.39 has been released.

Dec 1, 2008 (6th)

By Robert Backstrom / GMP-ECM

(34·10¹⁴⁰-61)/9 = 3(7)₁₃₉1_<141> = 7 · 38729 · 1227075583_<10> · 113910217004608229_<18> · C109

C109 = P35 · P75

P35 = 19307640926740728658468249492603981_<35>

P75 = 516343693603233874370126179965698886505664770083775458430131775655309376971_<75>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 9969378630878273330209454988851072949503239070360101125655163488996390662293101007126290937779576661544321551 (109 digits)
Using B1=1040000, B2=1045563762, polynomial Dickson(6), sigma=3595781433
Step 1 took 8125ms
Step 2 took 4390ms
********** Factor found in step 2: 19307640926740728658468249492603981
Found probable prime factor of 35 digits: 19307640926740728658468249492603981
Probable prime cofactor 516343693603233874370126179965698886505664770083775458430131775655309376971 has 75 digits

Dec 1, 2008 (5th)

By Serge Batalov / GMP-ECM 6.2.1, pol51; Msieve-1.38 gnfs

(34·10¹⁴⁷-61)/9 = 3(7)₁₄₆1_<148> = 3⁵ · 136621 · C141

C141 = P36 · P105

P36 = 229396003666241020967296200838396591_<36>

P105 = 496051567622998067919651156246881008431154204658997849229474790386382145887920573758035262566826859064227_<105>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2648012166
Step 1 took 14589ms
Step 2 took 10677ms
********** Factor found in step 2: 229396003666241020967296200838396591
Found probable prime factor of 36 digits: 229396003666241020967296200838396591
Probable prime cofactor 496051567622998067919651156246881008431154204658997849229474790386382145887920573758035262566826859064227 has 105 digits

(11·10¹⁴²+1)/3 = 3(6)₁₄₁7_<143> = 37 · C141

C141 = P34 · P108

P34 = 2693334827130149692684600382468941_<34>

P108 = 367941995554607460375664696351964697590458986146034785229665363826072986598682216567858356117973188884575051_<108>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3012302675
Step 1 took 27684ms
Step 2 took 12805ms
********** Factor found in step 2: 2693334827130149692684600382468941
Found probable prime factor of 34 digits: 2693334827130149692684600382468941
Probable prime cofactor 367941995554607460375664696351964697590458986146034785229665363826072986598682216567858356117973188884575051 has 108 digits

(11·10¹⁵⁹+1)/3 = 3(6)₁₅₈7_<160> = 29 · C159

C159 = P34 · P125

P34 = 4579115157252350396251705660558469_<34>

P125 = 27611618678981302453420401159665729376211279209581066750141573274195794009038548402268649023166636612159131984086746695721467_<125>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2518271257
Step 1 took 20041ms
Step 2 took 12929ms
********** Factor found in step 2: 4579115157252350396251705660558469
Found probable prime factor of 34 digits: 4579115157252350396251705660558469
Probable prime cofactor 27611618678981302453420401159665729376211279209581066750141573274195794009038548402268649023166636612159131984086746695721467 has 125 digits

(11·10¹⁷⁴+1)/3 = 3(6)₁₇₃7_<175> = 25105507078193_<14> · C162

C162 = P34 · P129

P34 = 1431643137143289612013395042921649_<34>

P129 = 102015851080330394950115333716070269018964607525472741780280632981612360170145484208680248953025985904139335171265173737731269131_<129>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1752658758
Step 1 took 19541ms
Step 2 took 12577ms
********** Factor found in step 2: 1431643137143289612013395042921649
Found probable prime factor of 34 digits: 1431643137143289612013395042921649
Probable prime cofactor 102015851080330394950115333716070269018964607525472741780280632981612360170145484208680248953025985904139335171265173737731269131 has 129 digits

(34·10²⁰³-61)/9 = 3(7)₂₀₂1_<204> = 8831 · 72901 · 112501 · 10440322124787126683053_<23> · C168

C168 = P33 · P136

P33 = 194878783642531137396506518706737_<33>

P136 = 2563646825834120049987006706226367115513825431483244228135665471944472805150771543742942888716968688007800024055831525531246269818486481_<136>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=802463135
Step 1 took 20061ms
Step 2 took 12845ms
********** Factor found in step 2: 194878783642531137396506518706737
Found probable prime factor of 33 digits: 194878783642531137396506518706737
Probable prime cofactor 2563646825834120049987006706226367115513825431483244228135665471944472805150771543742942888716968688007800024055831525531246269818486481 has 136 digits

(34·10¹⁹²-61)/9 = 3(7)₁₉₁1_<193> = 3² · 3533 · 797439971587867_<15> · C174

C174 = P28 · C146

P28 = 5639483166306901179798816719_<28>

C146 = [26418791978814970831542819583891294783385354615760421669709934150784142724787661482579399836080971964830225870407234821376836573766640098403040291_<146>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4250593911
Step 1 took 25267ms
********** Factor found in step 1: 5639483166306901179798816719
Found probable prime factor of 28 digits: 5639483166306901179798816719
Composite cofactor

(11·10¹⁸⁶+1)/3 = 3(6)₁₈₅7_<187> = 184793114142475822975073_<24> · C164

C164 = P37 · C128

P37 = 1774927193533712492005677033453671123_<37>

C128 = [11179055258894793670224353164464161111390294918481458753128549105128717218169765741212056666252299726580644182426721221367136873_<128>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3358102994
Step 1 took 24726ms
Step 2 took 16644ms
********** Factor found in step 2: 1774927193533712492005677033453671123
Found probable prime factor of 37 digits: 1774927193533712492005677033453671123
Composite cofactor 11179055258894793670224353164464161111390294918481458753128549105128717218169765741212056666252299726580644182426721221367136873 has 128 digits

(34·10¹⁹⁸-61)/9 = 3(7)₁₉₇1_<199> = 3 · 43 · 2687 · 5968939 · C187

C187 = P32 · P155

P32 = 38105528752723700919153806322731_<32>

P155 = 47917472025515084936253091068040645829165545942645244660993199310349576589419386240479483830592013034148549763083512771249504720351602315724197904591349053_<155>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4028002106
Step 1 took 22017ms
Step 2 took 14649ms
********** Factor found in step 2: 38105528752723700919153806322731
Found probable prime factor of 32 digits: 38105528752723700919153806322731
Probable prime cofactor 47917472025515084936253091068040645829165545942645244660993199310349576589419386240479483830592013034148549763083512771249504720351602315724197904591349053 has 155 digits

(34·10²⁰⁴-61)/9 = 3(7)₂₀₃1_<205> = 3 · 456944495438603_<15> · C190

C190 = P31 · C160

P31 = 1512768834429399909066535514857_<31>

C160 = [1821709546286074516473557552513973715632831422256577038778502292556731957589880120180743562987930254113335165727299848149500511188794201681110980467838132947667_<160>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2899500130
Step 1 took 23289ms
Step 2 took 14553ms
********** Factor found in step 2: 1512768834429399909066535514857
Found probable prime factor of 31 digits: 1512768834429399909066535514857
Composite cofactor 1821709546286074516473557552513973715632831422256577038778502292556731957589880120180743562987930254113335165727299848149500511188794201681110980467838132947667 has 160 digits

(11·10²⁰⁵+1)/3 = 3(6)₂₀₄7_<206> = 37 · 967 · 193189 · 175495747251253477_<18> · C179

C179 = P34 · C145

P34 = 4216628214594391516805899817350621_<34>

C145 = [7168510581489893362061172533665932426911604966642096584491850386790355732112303191835701796670060964330568232485809019473596273412036396814696021_<145>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3119795829
Step 1 took 28545ms
Step 2 took 18593ms
********** Factor found in step 2: 4216628214594391516805899817350621
Found probable prime factor of 34 digits: 4216628214594391516805899817350621
Composite cofactor 7168510581489893362061172533665932426911604966642096584491850386790355732112303191835701796670060964330568232485809019473596273412036396814696021 has 145 digits

(34·10¹⁸⁹-61)/9 = 3(7)₁₈₈1_<190> = 3 · 19 · 1951 · 9199 · 140177 · 43664787877_<11> · 17268776936283601_<17> · 124302643102278005093_<21> · 3329405600056896389444381_<25> · C104

C104 = P44 · P61

P44 = 69966787580143993614754142851314738917569579_<44>

P61 = 1206576783959699309894410254281895913576361725987222092406549_<61>

Number: 37771_189
N=84420301542441572248655580080885734293394610747358405506554776579780343085112125886659786128138262772871
  ( 104 digits)
Divisors found:
 r1=69966787580143993614754142851314738917569579 (pp44)
 r2=1206576783959699309894410254281895913576361725987222092406549 (pp61)
Version: Msieve-1.38
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.730).
Factorization parameters were as follows:
name: 37771_189
n: 84420301542441572248655580080885734293394610747358405506554776579780343085112125886659786128138262772871
skew: 9787.26
# norm 1.05e+14
c5: 46080
c4: -602871736
c3: -7091880767194
c2: 80954041951701947
c1: 389451520411831702630
c0: -1537021221256345910714200
# alpha -5.48
Y1: 105296616953
Y0: -71217802010343892173
# Murphy_E 2.16e-09
# M 70169906179187845525575282802550724568150340856160222103856566810958666723249156632950463472826442865883
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1850001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 250586 x 250828
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 2.50 hours.

(11·10¹⁶⁹+1)/3 = 3(6)₁₆₈7_<170> = 37 · C168

C168 = P41 · P128

P41 = 11030812224377842345662744222070095528811_<41>

P128 = 89838442612677568783127992344632191440505401986005659153984016763066092470526608932676002858732238476800246754010447349587574381_<128>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1370658292
Step 1 took 24924ms
Step 2 took 16947ms
********** Factor found in step 2: 11030812224377842345662744222070095528811
Found probable prime factor of 41 digits: 11030812224377842345662744222070095528811
Probable prime cofactor 89838442612677568783127992344632191440505401986005659153984016763066092470526608932676002858732238476800246754010447349587574381 has 128 digits

(34·10¹⁵⁴-61)/9 = 3(7)₁₅₃1_<155> = 6379 · C151

C151 = P60 · P92

P60 = 183454113598076963373718986643971415060501020624289499571323_<60>

P92 = 32281696568612383429921930458932642651082130545296673862354073357067506441085413828479488563_<92>

SNFS difficulty: 156 digits.
Divisors found:
 r1=183454113598076963373718986643971415060501020624289499571323 (pp60)
 r2=32281696568612383429921930458932642651082130545296673862354073357067506441085413828479488563 (pp92)
Version: Msieve-1.38
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.316).
Factorization parameters were as follows:
n: 5922210029436867499259723746320391562592534531709951054675933183536256118165508352057967985229311455992754001846336068000905749769207991499886781278849
m: 10000000000000000000000000000000
deg: 5
c5: 17
c0: -305
skew: 1.78
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1400000, 2500001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 558486 x 558728
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,52,52,2.4,2.4,100000
total time: 20.00 hours.

Dec 1, 2008 (4th)

By Luigi Morelli / msieve 1.38

(34·10¹⁷⁴-43)/9 = 3(7)₁₇₃3_<175> = 23279 · 344848243 · 80308935953_<11> · 685748829763_<12> · 41268157890120643_<17> · C123

C123 = P53 · P70

P53 = 20911043547722046862836516832845716851816899295541089_<53>

P70 = 9902032167234716303717452177033910330401475786201296097689113927382553_<70>

Sat Nov 29 15:51:53 2008  Msieve v. 1.38
Sat Nov 29 15:51:53 2008  random seeds: be9f0478 86d8f760
Sat Nov 29 15:51:53 2008  factoring 207061825859989670459284623169677072047648707250318568804646243101328743888471612901950056737246672796156596706853633220217 (123 digits)
Sat Nov 29 15:51:55 2008  searching for 15-digit factors
Sat Nov 29 15:51:59 2008  commencing number field sieve (123-digit input)
Sat Nov 29 15:51:59 2008  R0: -679056770268448866920
Sat Nov 29 15:51:59 2008  R1:  1
Sat Nov 29 15:51:59 2008  A0: -9197281393885594503
Sat Nov 29 15:51:59 2008  A1:  11143000227051575216
Sat Nov 29 15:51:59 2008  A2: -1674590562615344430
Sat Nov 29 15:51:59 2008  A3: -13223622027949449591
Sat Nov 29 15:51:59 2008  A4:  3275463102756217972
Sat Nov 29 15:51:59 2008  A5:  1434067592525568000
Sat Nov 29 15:51:59 2008  size score = 4.498991e-013, Murphy alpha = -3.957239, combined = 1.682613e-012
Sat Nov 29 15:52:00 2008  
Sat Nov 29 15:52:00 2008  commencing relation filtering
Sat Nov 29 15:52:00 2008  commencing duplicate removal, pass 1
Sat Nov 29 15:59:48 2008  found 712206 hash collisions in 11479955 relations
Sat Nov 29 16:02:01 2008  added 60587 free relations
Sat Nov 29 16:02:01 2008  commencing duplicate removal, pass 2
Sat Nov 29 16:03:20 2008  found 615164 duplicates and 10925378 unique relations
Sat Nov 29 16:03:20 2008  memory use: 50.6 MB
Sat Nov 29 16:03:21 2008  reading rational ideals above 5046272
Sat Nov 29 16:03:21 2008  reading algebraic ideals above 5046272
Sat Nov 29 16:03:21 2008  commencing singleton removal, pass 1
Sat Nov 29 16:10:45 2008  relations with 0 large ideals: 68092
Sat Nov 29 16:10:45 2008  relations with 1 large ideals: 567434
Sat Nov 29 16:10:45 2008  relations with 2 large ideals: 1842955
Sat Nov 29 16:10:45 2008  relations with 3 large ideals: 3416912
Sat Nov 29 16:10:45 2008  relations with 4 large ideals: 3551459
Sat Nov 29 16:10:45 2008  relations with 5 large ideals: 1415110
Sat Nov 29 16:10:45 2008  relations with 6 large ideals: 63414
Sat Nov 29 16:10:45 2008  relations with 7+ large ideals: 2
Sat Nov 29 16:10:45 2008  10925378 relations and about 10213646 large ideals
Sat Nov 29 16:10:45 2008  commencing singleton removal, pass 2
Sat Nov 29 16:16:06 2008  found 3509153 singletons
Sat Nov 29 16:16:06 2008  current dataset: 7416225 relations and about 6209799 large ideals
Sat Nov 29 16:16:06 2008  commencing singleton removal, pass 3
Sat Nov 29 16:20:27 2008  found 810977 singletons
Sat Nov 29 16:20:27 2008  current dataset: 6605248 relations and about 5363239 large ideals
Sat Nov 29 16:20:27 2008  commencing singleton removal, pass 4
Sat Nov 29 16:24:50 2008  found 213706 singletons
Sat Nov 29 16:24:51 2008  current dataset: 6391542 relations and about 5146716 large ideals
Sat Nov 29 16:24:51 2008  commencing singleton removal, final pass
Sat Nov 29 16:28:04 2008  memory use: 125.2 MB
Sat Nov 29 16:28:05 2008  commencing in-memory singleton removal
Sat Nov 29 16:28:06 2008  begin with 6391542 relations and 5450488 unique ideals
Sat Nov 29 16:28:31 2008  reduce to 5793438 relations and 4842225 ideals in 13 passes
Sat Nov 29 16:28:31 2008  max relations containing the same ideal: 35
Sat Nov 29 16:28:36 2008  reading rational ideals above 720000
Sat Nov 29 16:28:36 2008  reading algebraic ideals above 720000
Sat Nov 29 16:28:36 2008  commencing singleton removal, final pass
Sat Nov 29 16:32:06 2008  keeping 5147907 ideals with weight <= 20, new excess is 399479
Sat Nov 29 16:32:22 2008  memory use: 178.3 MB
Sat Nov 29 16:32:22 2008  commencing in-memory singleton removal
Sat Nov 29 16:32:24 2008  begin with 5793911 relations and 5147907 unique ideals
Sat Nov 29 16:32:37 2008  reduce to 5793049 relations and 5144932 ideals in 6 passes
Sat Nov 29 16:32:37 2008  max relations containing the same ideal: 20
Sat Nov 29 16:32:48 2008  removing 653414 relations and 561053 ideals in 92361 cliques
Sat Nov 29 16:32:49 2008  commencing in-memory singleton removal
Sat Nov 29 16:32:51 2008  begin with 5139635 relations and 5144932 unique ideals
Sat Nov 29 16:33:07 2008  reduce to 5086560 relations and 4529693 ideals in 8 passes
Sat Nov 29 16:33:07 2008  max relations containing the same ideal: 20
Sat Nov 29 16:33:16 2008  removing 500648 relations and 408287 ideals in 92361 cliques
Sat Nov 29 16:33:16 2008  commencing in-memory singleton removal
Sat Nov 29 16:33:18 2008  begin with 4585912 relations and 4529693 unique ideals
Sat Nov 29 16:33:34 2008  reduce to 4547587 relations and 4082371 ideals in 9 passes
Sat Nov 29 16:33:34 2008  max relations containing the same ideal: 20
Sat Nov 29 16:33:43 2008  relations with 0 large ideals: 21617
Sat Nov 29 16:33:43 2008  relations with 1 large ideals: 179916
Sat Nov 29 16:33:44 2008  relations with 2 large ideals: 635257
Sat Nov 29 16:33:44 2008  relations with 3 large ideals: 1238278
Sat Nov 29 16:33:44 2008  relations with 4 large ideals: 1392824
Sat Nov 29 16:33:44 2008  relations with 5 large ideals: 824915
Sat Nov 29 16:33:44 2008  relations with 6 large ideals: 226256
Sat Nov 29 16:33:44 2008  relations with 7+ large ideals: 28524
Sat Nov 29 16:33:44 2008  commencing 2-way merge
Sat Nov 29 16:33:56 2008  reduce to 2954553 relation sets and 2489337 unique ideals
Sat Nov 29 16:33:56 2008  commencing full merge
Sat Nov 29 16:35:53 2008  memory use: 189.8 MB
Sat Nov 29 16:35:55 2008  found 1421189 cycles, need 1357537
Sat Nov 29 16:35:55 2008  weight of 1357537 cycles is about 95182674 (70.11/cycle)
Sat Nov 29 16:35:55 2008  distribution of cycle lengths:
Sat Nov 29 16:35:55 2008  1 relations: 127090
Sat Nov 29 16:35:55 2008  2 relations: 154422
Sat Nov 29 16:35:55 2008  3 relations: 165581
Sat Nov 29 16:35:56 2008  4 relations: 152485
Sat Nov 29 16:35:56 2008  5 relations: 139651
Sat Nov 29 16:35:56 2008  6 relations: 119549
Sat Nov 29 16:35:56 2008  7 relations: 103127
Sat Nov 29 16:35:56 2008  8 relations: 88323
Sat Nov 29 16:35:56 2008  9 relations: 74428
Sat Nov 29 16:35:56 2008  10+ relations: 232881
Sat Nov 29 16:35:56 2008  heaviest cycle: 17 relations
Sat Nov 29 16:35:57 2008  commencing cycle optimization
Sat Nov 29 16:36:07 2008  start with 7829053 relations
Sat Nov 29 16:37:04 2008  pruned 207954 relations
Sat Nov 29 16:37:04 2008  memory use: 204.9 MB
Sat Nov 29 16:37:04 2008  distribution of cycle lengths:
Sat Nov 29 16:37:04 2008  1 relations: 127090
Sat Nov 29 16:37:04 2008  2 relations: 158585
Sat Nov 29 16:37:04 2008  3 relations: 172435
Sat Nov 29 16:37:04 2008  4 relations: 156946
Sat Nov 29 16:37:04 2008  5 relations: 143689
Sat Nov 29 16:37:04 2008  6 relations: 121118
Sat Nov 29 16:37:04 2008  7 relations: 104106
Sat Nov 29 16:37:04 2008  8 relations: 88124
Sat Nov 29 16:37:05 2008  9 relations: 73703
Sat Nov 29 16:37:05 2008  10+ relations: 211741
Sat Nov 29 16:37:05 2008  heaviest cycle: 17 relations
Sat Nov 29 16:37:17 2008  
Sat Nov 29 16:37:17 2008  commencing linear algebra
Sat Nov 29 16:37:21 2008  read 1357537 cycles
Sat Nov 29 16:37:31 2008  cycles contain 4227276 unique relations
Sat Nov 29 16:41:02 2008  read 4227276 relations
Sat Nov 29 16:41:19 2008  using 32 quadratic characters above 134217650
Sat Nov 29 16:43:11 2008  building initial matrix
Sat Nov 29 16:45:39 2008  memory use: 491.8 MB
Sat Nov 29 16:45:52 2008  read 1357537 cycles
Sat Nov 29 16:47:00 2008  matrix is 1357304 x 1357537 (389.6 MB) with weight 134250650 (98.89/col)
Sat Nov 29 16:47:00 2008  sparse part has weight 91279211 (67.24/col)
Sat Nov 29 16:48:02 2008  filtering completed in 3 passes
Sat Nov 29 16:48:03 2008  matrix is 1350940 x 1351140 (388.9 MB) with weight 133898506 (99.10/col)
Sat Nov 29 16:48:03 2008  sparse part has weight 91134928 (67.45/col)
Sat Nov 29 16:48:56 2008  read 1351140 cycles
Sat Nov 29 16:53:10 2008  matrix is 1350940 x 1351140 (388.9 MB) with weight 133898506 (99.10/col)
Sat Nov 29 16:53:10 2008  sparse part has weight 91134928 (67.45/col)
Sat Nov 29 16:53:11 2008  saving the first 48 matrix rows for later
Sat Nov 29 16:53:12 2008  matrix is 1350892 x 1351140 (372.6 MB) with weight 103872555 (76.88/col)
Sat Nov 29 16:53:12 2008  sparse part has weight 89563605 (66.29/col)
Sat Nov 29 16:53:12 2008  matrix includes 64 packed rows
Sat Nov 29 16:53:12 2008  using block size 21845 for processor cache size 512 kB
Sat Nov 29 16:53:33 2008  commencing Lanczos iteration
Sat Nov 29 16:53:33 2008  memory use: 369.3 MB
Sun Nov 30 12:40:26 2008  lanczos halted after 21363 iterations (dim = 1350890)
Sun Nov 30 12:40:49 2008  recovered 42 nontrivial dependencies
Sun Nov 30 12:40:55 2008  
Sun Nov 30 12:40:55 2008  commencing square root phase
Sun Nov 30 12:40:55 2008  reading relations for dependency 1
Sun Nov 30 12:41:00 2008  read 675475 cycles
Sun Nov 30 12:41:07 2008  cycles contain 2624155 unique relations
Sun Nov 30 12:49:57 2008  read 2624155 relations
Sun Nov 30 12:51:04 2008  multiplying 2111948 relations
Sun Nov 30 14:03:49 2008  multiply complete, coefficients have about 174.29 million bits
Sun Nov 30 14:04:20 2008  initial square root is modulo 1797947
Sun Nov 30 15:42:24 2008  prp53 factor: 20911043547722046862836516832845716851816899295541089
Sun Nov 30 15:42:24 2008  prp70 factor: 9902032167234716303717452177033910330401475786201296097689113927382553
Sun Nov 30 15:42:24 2008  elapsed time 23:50:31

Dec 1, 2008 (3rd)

By Erik Branger / GGNFS, Msieve

(34·10¹²⁴-61)/9 = 3(7)₁₂₃1_<125> = 109 · 42875453 · C115

C115 = P48 · P68

P48 = 183902059423947183572586572945500757182382783851_<48>

P68 = 43955638737725434720351420594271267744658778646152810611533781011273_<68>

Number: 37771_124
N=8083532487162737666735497874469570726462998842225146757259227985958224006965198781856265773866351743424771753352323
  ( 115 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=183902059423947183572586572945500757182382783851
 r2=43955638737725434720351420594271267744658778646152810611533781011273
Version: 
Total time: 3.40 hours.
Scaled time: 2.68 units (timescale=0.789).
Factorization parameters were as follows:
n: 8083532487162737666735497874469570726462998842225146757259227985958224006965198781856265773866351743424771753352323
m: 10000000000000000000000000
deg: 5
c5: 17
c0: -305
skew: 1.78
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [445000, 795001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 123139 x 123376
Total sieving time: 3.40 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 3.40 hours.
 --------- CPU info (if available) ----------

(34·10¹²⁶-61)/9 = 3(7)₁₂₅1_<127> = 3 · 71 · 88852876601_<11> · C114

C114 = P56 · P58

P56 = 34432799348899478768254695087862221172954561711851166729_<56>

P58 = 5797129202738537298544666505195713087675830414976894319423_<58>

Number: 37771_126
N=199611386637541661542495056276037532975243649578791299977706603174046948493474101255739752477445195161194956077367
  ( 114 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=34432799348899478768254695087862221172954561711851166729
 r2=5797129202738537298544666505195713087675830414976894319423
Version: 
Total time: 3.47 hours.
Scaled time: 2.72 units (timescale=0.783).
Factorization parameters were as follows:
n: 199611386637541661542495056276037532975243649578791299977706603174046948493474101255739752477445195161194956077367
m: 10000000000000000000000000
deg: 5
c5: 340
c0: -61
skew: 0.71
type: snfs
lss: 1
rlim: 930000
alim: 930000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 930000/930000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [465000, 815001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 135078 x 135315
Total sieving time: 3.47 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,930000,930000,26,26,46,46,2.3,2.3,50000
total time: 3.47 hours.
 --------- CPU info (if available) ----------

Dec 1, 2008 (2nd)

By Jo Yeong Uk / GGNFS, GMP-ECM, Msieve

(5·10¹⁹⁸-17)/3 = 1(6)₁₉₇1_<199> = C199

C199 = P90 · P110

P90 = 119210534379624869888380873328590164795408717116498507216021846495878475022485775217297333_<90>

P110 = 13980867339787117486389823283545379889344751436236630206822306072817458470959671454043114394014893486370164017_<110>

Number: 16661_198
N=1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661
  ( 199 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=119210534379624869888380873328590164795408717116498507216021846495878475022485775217297333 (pp90)
 r2=13980867339787117486389823283545379889344751436236630206822306072817458470959671454043114394014893486370164017 (pp110)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 630.31 hours.
Scaled time: 1499.51 units (timescale=2.379).
Factorization parameters were as follows:
n: 1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661
m: 10000000000000000000000000000000000000000
deg: 5
c5: 1
c0: -340
skew: 3.21
type: snfs
rlim: 16000000
alim: 16000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.7
alambda: 2.7
Factor base limits: 16000000/16000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [8000000, 18400001)
Primes: RFBsize:1031130, AFBsize:1030468, largePrimes:21021002 encountered
Relations: rels:22530215, finalFF:2351886
Max relations in full relation-set: 28
Initial matrix: 2061662 x 2351886 with sparse part having weight 253898488.
Pruned matrix : 1821824 x 1832196 with weight 219935642.
Total sieving time: 576.62 hours.
Total relation processing time: 0.76 hours.
Matrix solve time: 52.69 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,200,5,0,0,0,0,0,0,0,0,16000000,16000000,28,28,56,56,2.7,2.7,100000
total time: 630.31 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(11·10¹²⁸+1)/3 = 3(6)₁₂₇7_<129> = 31 · 23902624069_<11> · C117

C117 = P45 · P73

P45 = 244685778733831624295445245539835854200298513_<45>

P73 = 2022345843767010726344409071701555602423554182366854872110064185709664481_<73>

Number: 36667_128
N=494839267651258805728615052976501211817190602021008465421943955351632370071553416982673598514685194886303419273216753
  ( 117 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=244685778733831624295445245539835854200298513 (pp45)
 r2=2022345843767010726344409071701555602423554182366854872110064185709664481 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.68 hours.
Scaled time: 4.01 units (timescale=2.391).
Factorization parameters were as follows:
n: 494839267651258805728615052976501211817190602021008465421943955351632370071553416982673598514685194886303419273216753
m: 100000000000000000000000000
deg: 5
c5: 11
c0: 100
skew: 1.55
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [450000, 800001)
Primes: RFBsize:71274, AFBsize:71561, largePrimes:2504135 encountered
Relations: rels:2386893, finalFF:184196
Max relations in full relation-set: 28
Initial matrix: 142902 x 184196 with sparse part having weight 14054047.
Pruned matrix : 129821 x 130599 with weight 7540241.
Total sieving time: 1.59 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,900000,900000,26,26,47,47,2.3,2.3,50000
total time: 1.68 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

7·10¹⁸²-9 = 6(9)₁₈₁1_<183> = 47 · 2909 · 8412983 · 197529555280333365899_<21> · C151

C151 = P36 · C115

P36 = 551024823684035448740408536106657207_<36>

C115 = [5591176463272303316615780966074659214096793163110886821777133410508295180383174336519509049157089247339837301301143_<115>]

GMP-ECM 6.2.1 [powered by GMP 4.2.3] [ECM]
Input number is 3080877024860949836881803991296662808651953686327894352408272117230457204223004198843440055196469778697272230530749827753879009022633410147845378287601 (151 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=820661537
Step 1 took 14820ms
Step 2 took 10654ms
********** Factor found in step 2: 551024823684035448740408536106657207
Found probable prime factor of 36 digits: 551024823684035448740408536106657207
Composite cofactor 5591176463272303316615780966074659214096793163110886821777133410508295180383174336519509049157089247339837301301143 has 115 digits

(34·10¹⁴⁴-61)/9 = 3(7)₁₄₃1_<145> = 3 · 56150330479_<11> · 372942956963322243857_<21> · C113

C113 = P50 · P64

P50 = 21661518727678594480814735512079782966721573328871_<50>

P64 = 2776077101002108005261699224078097855558784029617067090671671489_<64>

Number: 37771_144
N=60134046112836863621509113837401397903316783755784689699386716316543124790819035195276732807581757561615471258919
  ( 113 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=21661518727678594480814735512079782966721573328871 (pp50)
 r2=2776077101002108005261699224078097855558784029617067090671671489 (pp64)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.83 hours.
Scaled time: 25.86 units (timescale=2.387).
Factorization parameters were as follows:
n: 60134046112836863621509113837401397903316783755784689699386716316543124790819035195276732807581757561615471258919
m: 100000000000000000000000000000
deg: 5
c5: 17
c0: -305
skew: 1.78
type: snfs
lss: 1
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [750000, 1575001)
Primes: RFBsize:114155, AFBsize:114578, largePrimes:3725607 encountered
Relations: rels:3841660, finalFF:345565
Max relations in full relation-set: 28
Initial matrix: 228798 x 345565 with sparse part having weight 37940559.
Pruned matrix : 201967 x 203174 with weight 19049916.
Total sieving time: 10.58 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,49,49,2.3,2.3,75000
total time: 10.83 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(11·10¹⁶¹-17)/3 = 3(6)₁₆₀1_<162> = 1051 · 504111899 · 17405943367_<11> · 1435787357971_<13> · 1964614032373_<13> · C116

C116 = P35 · P39 · P43

P35 = 17664047353579579308310273713784361_<35>

P39 = 592554862419818603822736166692925446317_<39>

P43 = 1346660266522921163024397070941814596274577_<43>

GMP-ECM 6.2.1 [powered by GMP 4.2.3] [ECM]
Input number is 14095381438054049848194620343238446310043569438223828676882516142860471211671212343670224405889272698639578460886149 (116 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=702813065
Step 1 took 10671ms
Step 2 took 2620ms
********** Factor found in step 2: 17664047353579579308310273713784361
Found probable prime factor of 35 digits: 17664047353579579308310273713784361
Composite cofactor 797970088955725802508007644661910266369870917643959528519898754913208433205382909 has 81 digits

Mon Dec 01 21:34:18 2008  
Mon Dec 01 21:34:18 2008  
Mon Dec 01 21:34:18 2008  Msieve v. 1.32
Mon Dec 01 21:34:18 2008  random seeds: fa5ac99c bc59bc96
Mon Dec 01 21:34:18 2008  factoring 797970088955725802508007644661910266369870917643959528519898754913208433205382909 (81 digits)
Mon Dec 01 21:34:18 2008  no P-1/P+1/ECM available, skipping
Mon Dec 01 21:34:18 2008  commencing quadratic sieve (81-digit input)
Mon Dec 01 21:34:18 2008  using multiplier of 1
Mon Dec 01 21:34:18 2008  using VC8 32kb sieve core
Mon Dec 01 21:34:18 2008  sieve interval: 12 blocks of size 32768
Mon Dec 01 21:34:18 2008  processing polynomials in batches of 17
Mon Dec 01 21:34:18 2008  using a sieve bound of 1325659 (50882 primes)
Mon Dec 01 21:34:18 2008  using large prime bound of 127263264 (26 bits)
Mon Dec 01 21:34:18 2008  using trial factoring cutoff of 27 bits
Mon Dec 01 21:34:18 2008  polynomial 'A' values have 10 factors
Mon Dec 01 21:50:13 2008  51000 relations (25458 full + 25542 combined from 278893 partial), need 50978
Mon Dec 01 21:50:13 2008  begin with 304351 relations
Mon Dec 01 21:50:13 2008  reduce to 73391 relations in 2 passes
Mon Dec 01 21:50:13 2008  attempting to read 73391 relations
Mon Dec 01 21:50:14 2008  recovered 73391 relations
Mon Dec 01 21:50:14 2008  recovered 65369 polynomials
Mon Dec 01 21:50:14 2008  attempting to build 51000 cycles
Mon Dec 01 21:50:14 2008  found 51000 cycles in 1 passes
Mon Dec 01 21:50:14 2008  distribution of cycle lengths:
Mon Dec 01 21:50:14 2008     length 1 : 25458
Mon Dec 01 21:50:14 2008     length 2 : 25542
Mon Dec 01 21:50:14 2008  largest cycle: 2 relations
Mon Dec 01 21:50:14 2008  matrix is 50882 x 51000 with weight 1538386 (avg 30.16/col)
Mon Dec 01 21:50:14 2008  filtering completed in 4 passes
Mon Dec 01 21:50:14 2008  matrix is 44142 x 44206 with weight 1309465 (avg 29.62/col)
Mon Dec 01 21:50:14 2008  saving the first 48 matrix rows for later
Mon Dec 01 21:50:14 2008  matrix is 44094 x 44206 with weight 1037487 (avg 23.47/col)
Mon Dec 01 21:50:14 2008  matrix includes 64 packed rows
Mon Dec 01 21:50:14 2008  commencing Lanczos iteration
Mon Dec 01 21:50:36 2008  lanczos halted after 699 iterations (dim = 44084)
Mon Dec 01 21:50:36 2008  recovered 12 nontrivial dependencies
Mon Dec 01 21:50:37 2008  prp39 factor: 592554862419818603822736166692925446317
Mon Dec 01 21:50:37 2008  prp43 factor: 1346660266522921163024397070941814596274577
Mon Dec 01 21:50:37 2008  elapsed time 00:16:19

Dec 1, 2008

By Sinkiti Sibata / GGNFS, Msieve

(11·10¹⁵²-17)/3 = 3(6)₁₅₁1_<153> = 29 · 43 · 21289871 · C143

C143 = P35 · P108

P35 = 57368638108951067897882258416206337_<35>

P108 = 240745072480524105689094125373155362261200698502908150928447721048171065449125833957091710221823664394074069_<108>

Number: 36661_152
N=13811216939648382207457548841893009925631655326532384482575247278999696345718024918999933772590643167474122621636368843057734710342694765175253
  ( 143 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=57368638108951067897882258416206337 (pp35)
 r2=240745072480524105689094125373155362261200698502908150928447721048171065449125833957091710221823664394074069 (pp108)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 33.82 hours.
Scaled time: 86.38 units (timescale=2.554).
Factorization parameters were as follows:
name: 36661_152
n: 13811216939648382207457548841893009925631655326532384482575247278999696345718024918999933772590643167474122621636368843057734710342694765175253
m: 2000000000000000000000000000000
deg: 5
c5: 275
c0: -136
skew: 0.87
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2200001)
Primes: RFBsize:189880, AFBsize:189686, largePrimes:8729313 encountered
Relations: rels:9832054, finalFF:1374167
Max relations in full relation-set: 28
Initial matrix: 379633 x 1374167 with sparse part having weight 163279689.
Pruned matrix : 248100 x 250062 with weight 43412506.
Total sieving time: 32.92 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.65 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 33.82 hours.
 --------- CPU info (if available) ----------

(34·10¹²²-61)/9 = 3(7)₁₂₁1_<123> = 7 · C122

C122 = P54 · P68

P54 = 815245101135505697874744698170121827541490300092074703_<54>

P68 = 66198808055497474948864240487892379026886542832166295547558599332851_<68>

Number: 37771_122
N=53968253968253968253968253968253968253968253968253968253968253968253968253968253968253968253968253968253968253968253968253
  ( 122 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=815245101135505697874744698170121827541490300092074703 (pp54)
 r2=66198808055497474948864240487892379026886542832166295547558599332851 (pp68)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.14 hours.
Scaled time: 6.24 units (timescale=1.985).
Factorization parameters were as follows:
name: 37771_122
n: 53968253968253968253968253968253968253968253968253968253968253968253968253968253968253968253968253968253968253968253968253
m: 2000000000000000000000000
deg: 5
c5: 425
c0: -244
skew: 0.89
type: snfs
lss: 1
rlim: 820000
alim: 820000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 820000/820000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [410000, 760001)
Primes: RFBsize:65416, AFBsize:65749, largePrimes:1414200 encountered
Relations: rels:1399246, finalFF:162662
Max relations in full relation-set: 28
Initial matrix: 131232 x 162662 with sparse part having weight 8216881.
Pruned matrix : 120160 x 120880 with weight 4687522.
Total sieving time: 3.00 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,820000,820000,25,25,46,46,2.2,2.2,50000
total time: 3.14 hours.
 --------- CPU info (if available) ----------

(34·10¹¹⁹-61)/9 = 3(7)₁₁₈1_<120> = 53 · 97 · 569 · 409705573822798716046313501_<27> · C87

C87 = P36 · P51

P36 = 792246144585103935358792782500741713_<36>

P51 = 397873056847156620893313883848623187566975367724723_<51>

Sun Nov 30 18:04:40 2008  Msieve v. 1.38
Sun Nov 30 18:04:40 2008  random seeds: 93e01718 060378a8
Sun Nov 30 18:04:40 2008  factoring 315213395321449721601301773454983877531110347311256178703824935230238923212668707470499 (87 digits)
Sun Nov 30 18:04:43 2008  searching for 15-digit factors
Sun Nov 30 18:04:49 2008  commencing quadratic sieve (87-digit input)
Sun Nov 30 18:04:49 2008  using multiplier of 1
Sun Nov 30 18:04:49 2008  using 64kb Pentium 2 sieve core
Sun Nov 30 18:04:49 2008  sieve interval: 10 blocks of size 65536
Sun Nov 30 18:04:49 2008  processing polynomials in batches of 11
Sun Nov 30 18:04:49 2008  using a sieve bound of 1489661 (56508 primes)
Sun Nov 30 18:04:49 2008  using large prime bound of 119172880 (26 bits)
Sun Nov 30 18:04:49 2008  using double large prime bound of 344444540853840 (42-49 bits)
Sun Nov 30 18:04:49 2008  using trial factoring cutoff of 49 bits
Sun Nov 30 18:04:49 2008  polynomial 'A' values have 11 factors
Sun Nov 30 23:55:52 2008  56804 relations (15980 full + 40824 combined from 595193 partial), need 56604
Sun Nov 30 23:56:05 2008  begin with 611173 relations
Sun Nov 30 23:56:07 2008  reduce to 136055 relations in 11 passes
Sun Nov 30 23:56:07 2008  attempting to read 136055 relations
Sun Nov 30 23:56:18 2008  recovered 136055 relations
Sun Nov 30 23:56:18 2008  recovered 112570 polynomials
Sun Nov 30 23:56:18 2008  attempting to build 56804 cycles
Sun Nov 30 23:56:19 2008  found 56804 cycles in 6 passes
Sun Nov 30 23:56:22 2008  distribution of cycle lengths:
Sun Nov 30 23:56:22 2008     length 1 : 15980
Sun Nov 30 23:56:22 2008     length 2 : 11206
Sun Nov 30 23:56:22 2008     length 3 : 10018
Sun Nov 30 23:56:22 2008     length 4 : 7371
Sun Nov 30 23:56:22 2008     length 5 : 5154
Sun Nov 30 23:56:22 2008     length 6 : 3102
Sun Nov 30 23:56:22 2008     length 7 : 1843
Sun Nov 30 23:56:22 2008     length 9+: 2130
Sun Nov 30 23:56:22 2008  largest cycle: 18 relations
Sun Nov 30 23:56:23 2008  matrix is 56508 x 56804 (12.9 MB) with weight 3150716 (55.47/col)
Sun Nov 30 23:56:23 2008  sparse part has weight 3150716 (55.47/col)
Sun Nov 30 23:56:28 2008  filtering completed in 3 passes
Sun Nov 30 23:56:28 2008  matrix is 51954 x 52017 (11.9 MB) with weight 2910454 (55.95/col)
Sun Nov 30 23:56:28 2008  sparse part has weight 2910454 (55.95/col)
Sun Nov 30 23:56:30 2008  saving the first 48 matrix rows for later
Sun Nov 30 23:56:30 2008  matrix is 51906 x 52017 (7.2 MB) with weight 2240425 (43.07/col)
Sun Nov 30 23:56:30 2008  sparse part has weight 1578266 (30.34/col)
Sun Nov 30 23:56:30 2008  matrix includes 64 packed rows
Sun Nov 30 23:56:30 2008  using block size 5461 for processor cache size 128 kB
Sun Nov 30 23:56:32 2008  commencing Lanczos iteration
Sun Nov 30 23:56:32 2008  memory use: 7.4 MB
Sun Nov 30 23:58:53 2008  lanczos halted after 822 iterations (dim = 51905)
Sun Nov 30 23:58:54 2008  recovered 17 nontrivial dependencies
Sun Nov 30 23:58:55 2008  prp36 factor: 792246144585103935358792782500741713
Sun Nov 30 23:58:55 2008  prp51 factor: 397873056847156620893313883848623187566975367724723
Sun Nov 30 23:58:55 2008  elapsed time 05:54:15

(11·10¹⁰⁵+1)/3 = 3(6)₁₀₄7_<106> = 61 · 5807 · 3560329 · C94

C94 = P40 · P54

P40 = 5104021191531172673556798659086373586713_<40>

P54 = 569622543579183307943262520347190758832026542885980873_<54>

Sun Nov 30 21:45:06 2008  Msieve v. 1.38
Sun Nov 30 21:45:06 2008  random seeds: 942d4ef0 97db9756
Sun Nov 30 21:45:06 2008  factoring 2907365533602040519607069382815593864011076918018858165324571130743533984189529189206124940449 (94 digits)
Sun Nov 30 21:45:07 2008  searching for 15-digit factors
Sun Nov 30 21:45:09 2008  commencing quadratic sieve (94-digit input)
Sun Nov 30 21:45:09 2008  using multiplier of 1
Sun Nov 30 21:45:09 2008  using 32kb Intel Core sieve core
Sun Nov 30 21:45:09 2008  sieve interval: 36 blocks of size 32768
Sun Nov 30 21:45:09 2008  processing polynomials in batches of 6
Sun Nov 30 21:45:09 2008  using a sieve bound of 2019013 (75294 primes)
Sun Nov 30 21:45:09 2008  using large prime bound of 270547742 (28 bits)
Sun Nov 30 21:45:09 2008  using double large prime bound of 1506742330630918 (42-51 bits)
Sun Nov 30 21:45:09 2008  using trial factoring cutoff of 51 bits
Sun Nov 30 21:45:09 2008  polynomial 'A' values have 12 factors
Mon Dec 01 00:51:47 2008  75444 relations (18548 full + 56896 combined from 1064784 partial), need 75390
Mon Dec 01 00:51:48 2008  begin with 1083332 relations
Mon Dec 01 00:51:49 2008  reduce to 194974 relations in 10 passes
Mon Dec 01 00:51:49 2008  attempting to read 194974 relations
Mon Dec 01 00:51:52 2008  recovered 194974 relations
Mon Dec 01 00:51:52 2008  recovered 178130 polynomials
Mon Dec 01 00:51:53 2008  attempting to build 75444 cycles
Mon Dec 01 00:51:53 2008  found 75444 cycles in 5 passes
Mon Dec 01 00:51:53 2008  distribution of cycle lengths:
Mon Dec 01 00:51:53 2008     length 1 : 18548
Mon Dec 01 00:51:53 2008     length 2 : 13427
Mon Dec 01 00:51:53 2008     length 3 : 12752
Mon Dec 01 00:51:53 2008     length 4 : 10138
Mon Dec 01 00:51:53 2008     length 5 : 7733
Mon Dec 01 00:51:53 2008     length 6 : 5171
Mon Dec 01 00:51:53 2008     length 7 : 3285
Mon Dec 01 00:51:53 2008     length 9+: 4390
Mon Dec 01 00:51:53 2008  largest cycle: 24 relations
Mon Dec 01 00:51:53 2008  matrix is 75294 x 75444 (19.2 MB) with weight 4735552 (62.77/col)
Mon Dec 01 00:51:53 2008  sparse part has weight 4735552 (62.77/col)
Mon Dec 01 00:51:54 2008  filtering completed in 3 passes
Mon Dec 01 00:51:54 2008  matrix is 71559 x 71623 (18.4 MB) with weight 4532182 (63.28/col)
Mon Dec 01 00:51:54 2008  sparse part has weight 4532182 (63.28/col)
Mon Dec 01 00:51:54 2008  saving the first 48 matrix rows for later
Mon Dec 01 00:51:54 2008  matrix is 71511 x 71623 (11.2 MB) with weight 3557733 (49.67/col)
Mon Dec 01 00:51:54 2008  sparse part has weight 2500748 (34.92/col)
Mon Dec 01 00:51:54 2008  matrix includes 64 packed rows
Mon Dec 01 00:51:54 2008  using block size 28649 for processor cache size 1024 kB
Mon Dec 01 00:51:55 2008  commencing Lanczos iteration
Mon Dec 01 00:51:55 2008  memory use: 11.1 MB
Mon Dec 01 00:52:29 2008  lanczos halted after 1132 iterations (dim = 71510)
Mon Dec 01 00:52:29 2008  recovered 16 nontrivial dependencies
Mon Dec 01 00:52:30 2008  prp40 factor: 5104021191531172673556798659086373586713
Mon Dec 01 00:52:30 2008  prp54 factor: 569622543579183307943262520347190758832026542885980873
Mon Dec 01 00:52:30 2008  elapsed time 03:07:24

(34·10¹³²-61)/9 = 3(7)₁₃₁1_<133> = 3 · 53 · 103 · 353 · 1871 · 154959011 · C115

C115 = P37 · P79

P37 = 1467803989071718082013470577567538313_<37>

P79 = 1535566631427295729877492951417765852836324576562696402832211952890951456321847_<79>

Number: 37771_132
N=2253910827094405329406702177022748716235771695323783467639242509859558351198186072436492569535265639281513231424111
  ( 115 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=1467803989071718082013470577567538313 (pp37)
 r2=1535566631427295729877492951417765852836324576562696402832211952890951456321847 (pp79)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 6.28 hours.
Scaled time: 15.99 units (timescale=2.544).
Factorization parameters were as follows:
name: 37771_132
n: 2253910827094405329406702177022748716235771695323783467639242509859558351198186072436492569535265639281513231424111
m: 200000000000000000000000000
deg: 5
c5: 425
c0: -244
skew: 0.89
type: snfs
lss: 1
rlim: 1200000
alim: 1200000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3

Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [600000, 1275001)
Primes: RFBsize:92938, AFBsize:93360, largePrimes:3445412 encountered
Relations: rels:3691453, finalFF:487779
Max relations in full relation-set: 28
Initial matrix: 186365 x 487779 with sparse part having weight 48352330.
Pruned matrix : 135700 x 136695 with weight 13604336.
Total sieving time: 6.07 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,47,47,2.3,2.3,75000
total time: 6.28 hours.
 --------- CPU info (if available) ----------

(34·10¹²⁵-61)/9 = 3(7)₁₂₄1_<126> = C126

C126 = P32 · P95

P32 = 19740494857472588967332701859237_<32>

P95 = 19137198966153239867624204437561859299473983704016534407164186992343276916354282103061304370383_<95>

Number: 37771_125
N=377777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777771
  ( 126 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=19740494857472588967332701859237 (pp32)
 r2=19137198966153239867624204437561859299473983704016534407164186992343276916354282103061304370383 (pp95)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 3.62 hours.
Scaled time: 1.71 units (timescale=0.473).
Factorization parameters were as follows:
name: 37771_125
n: 377777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777771
m: 10000000000000000000000000
deg: 5
c5: 34
c0: -61
skew: 1.12
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 750001)
Primes: RFBsize:71274, AFBsize:71141, largePrimes:2435547 encountered
Relations: rels:2300446, finalFF:171358
Max relations in full relation-set: 28
Initial matrix: 142481 x 171358 with sparse part having weight 12544260.
Pruned matrix : 131947 x 132723 with weight 7646839.
Total sieving time: 3.26 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 3.62 hours.
 --------- CPU info (if available) ----------

(34·10¹²⁹-61)/9 = 3(7)₁₂₈1_<130> = 3² · 13693 · 349397 · C119

C119 = P36 · P84

P36 = 263963331926553076873883111669446861_<36>

P84 = 332378188548304164888481711164765467046216478192033437865048279353333268196436141599_<84>

Number: 37771_129
N=87735654108922455050335760232311461340278754717995692475831705299846130899251205478083642362964049338345940869402070739
  ( 119 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=263963331926553076873883111669446861 (pp36)
 r2=332378188548304164888481711164765467046216478192033437865048279353333268196436141599 (pp84)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 4.21 hours.
Scaled time: 10.85 units (timescale=2.575).
Factorization parameters were as follows:
name: 37771_129
n: 87735654108922455050335760232311461340278754717995692475831705299846130899251205478083642362964049338345940869402070739
m: 100000000000000000000000000
deg: 5
c5: 17
c0: -305
skew: 1.78
type: snfs
lss: 1
rlim: 1080000
alim: 1080000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1080000/1080000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [540000, 990001)
Primes: RFBsize:84270, AFBsize:84409, largePrimes:2848172 encountered
Relations: rels:2753101, finalFF:215201
Max relations in full relation-set: 28
Initial matrix: 168744 x 215201 with sparse part having weight 17637208.
Pruned matrix : 155362 x 156269 with weight 10004219.
Total sieving time: 4.02 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1080000,1080000,26,26,47,47,2.3,2.3,50000
total time: 4.21 hours.
 --------- CPU info (if available) ----------

(11·10¹⁴⁶+1)/3 = 3(6)₁₄₅7_<147> = 113 · 487 · 971 · 18871213290191_<14> · C126

C126 = P41 · P85

P41 = 55671965294353905409642364426584816346789_<41>

P85 = 6531432152866276879383268065912542982993709987799702322249068920766859531294563886133_<85>

Number: 36667_146
N=363617664136798578223631373800740555034454045808713398946590948965991187042710405434412718122742744048505165576401272036176937
  ( 126 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=55671965294353905409642364426584816346789 (pp41)
 r2=6531432152866276879383268065912542982993709987799702322249068920766859531294563886133 (pp85)
Version: GGNFS-0.77.1-20060513-k8
Total time: 16.88 hours.
Scaled time: 33.09 units (timescale=1.960).
Factorization parameters were as follows:
name: 36667_146
n: 363617664136798578223631373800740555034454045808713398946590948965991187042710405434412718122742744048505165576401272036176937
m: 200000000000000000000000000000
deg: 5
c5: 55
c0: 16
skew: 0.78
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 2350001)
Primes: RFBsize:155805, AFBsize:156098, largePrimes:4366036 encountered
Relations: rels:4680252, finalFF:535408
Max relations in full relation-set: 28
Initial matrix: 311970 x 535408 with sparse part having weight 52657743.
Pruned matrix : 242588 x 244211 with weight 22870955.
Total sieving time: 15.97 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.65 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 16.88 hours.
 --------- CPU info (if available) ----------

(34·10¹⁴³-61)/9 = 3(7)₁₄₂1_<144> = 163 · 60077 · 1387821481_<10> · C128

C128 = P38 · P90

P38 = 28217205843890219947899894994855070009_<38>

P90 = 985128659698187157995681645130669968509955434063183873242657897532139829137743789608925949_<90>

Number: 37771_143
N=27797578173419426475214525843686671620570526121700523721521450635809718455545362591787531239138156070259435426642397723691763541
  ( 128 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=28217205843890219947899894994855070009 (pp38)
 r2=985128659698187157995681645130669968509955434063183873242657897532139829137743789608925949 (pp90)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 17.77 hours.
Scaled time: 45.57 units (timescale=2.564).
Factorization parameters were as follows:
name: 37771_143
n: 27797578173419426475214525843686671620570526121700523721521450635809718455545362591787531239138156070259435426642397723691763541
m: 50000000000000000000000000000
deg: 5
c5: 272
c0: -1525
skew: 1.41
type: snfs
lss: 1
rlim: 1890000
alim: 1890000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1890000/1890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [945000, 2645001)
Primes: RFBsize:141338, AFBsize:141460, largePrimes:4295234 encountered
Relations: rels:4538118, finalFF:359878
Max relations in full relation-set: 28
Initial matrix: 282865 x 359878 with sparse part having weight 41888561.
Pruned matrix : 258253 x 259731 with weight 28460136.
Total sieving time: 17.03 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.57 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1890000,1890000,26,26,49,49,2.3,2.3,100000
total time: 17.77 hours.
 --------- CPU info (if available) ----------

(11·10¹³⁶+1)/3 = 3(6)₁₃₅7_<137> = 37 · 71 · 121993 · 47965921 · C121

C121 = P58 · P63

P58 = 8152366823116473223458206514088212059435658063000673614923_<58>

P63 = 292590314321289835234488595489015334328963631781252268897642259_<63>

Number: 36667_136
N=2385303571238103952394431723844548405578681842196340537735382861159899807041700551384403237187595381422841377585177831057
  ( 121 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=8152366823116473223458206514088212059435658063000673614923 (pp58)
 r2=292590314321289835234488595489015334328963631781252268897642259 (pp63)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.16 hours.
Scaled time: 12.35 units (timescale=2.003).
Factorization parameters were as follows:
name: 36667_136
n: 2385303571238103952394431723844548405578681842196340537735382861159899807041700551384403237187595381422841377585177831057
m: 2000000000000000000000000000
deg: 5
c5: 55
c0: 16
skew: 0.78
type: snfs
lss: 1
rlim: 1410000
alim: 1410000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1410000/1410000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [705000, 1230001)
Primes: RFBsize:107805, AFBsize:107895, largePrimes:3299822 encountered
Relations: rels:3294429, finalFF:313145
Max relations in full relation-set: 28
Initial matrix: 215767 x 313145 with sparse part having weight 25210536.
Pruned matrix : 182684 x 183826 with weight 11270363.
Total sieving time: 5.71 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1410000,1410000,26,26,48,48,2.3,2.3,75000
total time: 6.16 hours.
 --------- CPU info (if available) ----------

(34·10¹³⁶-61)/9 = 3(7)₁₃₅1_<137> = 31 · 523 · 5657 · 2879993487954253543_<19> · C111

C111 = P50 · P62

P50 = 12216635234419646814532430479735488014714813815991_<50>

P62 = 11706949192302675700783525796475048637254599157547420427413687_<62>

Number: 37771_136
N=143019527990245493495110490408170713644089509066703498854071034514709908212689381811169162212305619831252868817
  ( 111 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=12216635234419646814532430479735488014714813815991 (pp50)
 r2=11706949192302675700783525796475048637254599157547420427413687 (pp62)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 9.39 hours.
Scaled time: 4.44 units (timescale=0.473).
Factorization parameters were as follows:
name: 37771_136
n: 143019527990245493495110490408170713644089509066703498854071034514709908212689381811169162212305619831252868817
m: 1000000000000000000000000000
deg: 5
c5: 340
c0: -61
skew: 0.71
type: snfs
lss: 1
rlim: 1370000
alim: 1370000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1370000/1370000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [685000, 1435001)
Primes: RFBsize:104967, AFBsize:104789, largePrimes:3267455 encountered
Relations: rels:3187437, finalFF:238347
Max relations in full relation-set: 28
Initial matrix: 209823 x 238347 with sparse part having weight 20087998.
Pruned matrix : 201317 x 202430 with weight 14747372.
Total sieving time: 8.33 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.85 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1370000,1370000,26,26,48,48,2.3,2.3,75000
total time: 9.39 hours.
 --------- CPU info (if available) ----------

November 2008

Nov 30, 2008 (10th)

By Jo Yeong Uk / GGNFS

(11·10¹³⁹+1)/3 = 3(6)₁₃₈7_<140> = 17 · 37 · 167 · 3550454911_<10> · 577793052509_<12> · 18481830371284369_<17> · C97

C97 = P48 · P50

P48 = 186684117639574787528989733088753211050056946911_<48>

P50 = 49316885889471914935083459467994951356728795737709_<50>

Number: 36667_139
N=9206679327007660850305599792616297445143259412106374422712579360327352603261588284466462493766899
  ( 97 digits)
Divisors found:
 r1=186684117639574787528989733088753211050056946911 (pp48)
 r2=49316885889471914935083459467994951356728795737709 (pp50)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.36 hours.
Scaled time: 5.62 units (timescale=2.385).
Factorization parameters were as follows:
name: 36667_139
n: 9206679327007660850305599792616297445143259412106374422712579360327352603261588284466462493766899
skew: 1735.67
# norm 2.03e+13
c5: 592440
c4: -2146536287
c3: -4150159948542
c2: 6245351775971518
c1: 7030137616889093286
c0: -19054775817785412320
# alpha -5.87
Y1: 13808501069
Y0: -1730988725850774993
# Murphy_E 5.15e-09
# M 9026319937559876238802573127597355132016530503268299678618003208170456302899329542892731471298988
type: gnfs
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [500000, 850001)
Primes: RFBsize:78498, AFBsize:79035, largePrimes:4094354 encountered
Relations: rels:3942403, finalFF:241663
Max relations in full relation-set: 28
Initial matrix: 157611 x 241663 with sparse part having weight 21027438.
Pruned matrix : 125329 x 126181 with weight 8294614.
Polynomial selection time: 0.18 hours.
Total sieving time: 2.04 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
gnfs,96,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1000000,1000000,26,26,49,49,2.5,2.5,50000
total time: 2.36 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Nov 30, 2008 (9th)

By Erik Branger / GGNFS, Msieve

(11·10¹¹⁹+1)/3 = 3(6)₁₁₈7_<120> = 7 · 157 · 401 · 22478800580953_<14> · C101

C101 = P50 · P52

P50 = 12991913767799353249814912229358520152908976070653_<50>

P52 = 2848938679148128690045374612108836831282623299109037_<52>

Number: 36667_119
N=37013165649240677352188638468717285587168893121133951533421728005342231052746388846355743968062791161
  ( 101 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=12991913767799353249814912229358520152908976070653
 r2=2848938679148128690045374612108836831282623299109037
Version: 
Total time: 1.93 hours.
Scaled time: 1.52 units (timescale=0.788).
Factorization parameters were as follows:
n: 37013165649240677352188638468717285587168893121133951533421728005342231052746388846355743968062791161
m: 1000000000000000000000000
deg: 5
c5: 11
c0: 10
skew: 0.98
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2

Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 565001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 69857 x 70095
Total sieving time: 1.93 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 1.93 hours.
 --------- CPU info (if available) ----------

Nov 30, 2008 (8th)

By Sinkiti Sibata / Msieve, GGNFS

(11·10¹¹⁴+1)/3 = 3(6)₁₁₃7_<115> = 4084686562950884396339324671_<28> · C87

C87 = P44 · P44

P44 = 21099559767919706148965388700117758588600401_<44>

P44 = 42544095972337002803163257909814208720366277_<44>

Sun Nov 30 17:56:41 2008  Msieve v. 1.38
Sun Nov 30 17:56:41 2008  random seeds: 43c7e764 2d8bf80a
Sun Nov 30 17:56:41 2008  factoring 897661695740436635978921665840942462701571152708113448971815635450427880352253509077077 (87 digits)
Sun Nov 30 17:56:42 2008  searching for 15-digit factors
Sun Nov 30 17:56:43 2008  commencing quadratic sieve (87-digit input)
Sun Nov 30 17:56:43 2008  using multiplier of 1
Sun Nov 30 17:56:43 2008  using 32kb Intel Core sieve core
Sun Nov 30 17:56:43 2008  sieve interval: 22 blocks of size 32768
Sun Nov 30 17:56:43 2008  processing polynomials in batches of 10
Sun Nov 30 17:56:43 2008  using a sieve bound of 1499123 (56997 primes)
Sun Nov 30 17:56:43 2008  using large prime bound of 119929840 (26 bits)
Sun Nov 30 17:56:43 2008  using double large prime bound of 348392707234640 (42-49 bits)
Sun Nov 30 17:56:43 2008  using trial factoring cutoff of 49 bits
Sun Nov 30 17:56:43 2008  polynomial 'A' values have 11 factors
Sun Nov 30 18:50:59 2008  57411 relations (15553 full + 41858 combined from 607010 partial), need 57093
Sun Nov 30 18:50:59 2008  begin with 622563 relations
Sun Nov 30 18:51:00 2008  reduce to 138886 relations in 10 passes
Sun Nov 30 18:51:00 2008  attempting to read 138886 relations
Sun Nov 30 18:51:01 2008  recovered 138886 relations
Sun Nov 30 18:51:01 2008  recovered 118621 polynomials
Sun Nov 30 18:51:02 2008  attempting to build 57411 cycles
Sun Nov 30 18:51:02 2008  found 57411 cycles in 5 passes
Sun Nov 30 18:51:02 2008  distribution of cycle lengths:
Sun Nov 30 18:51:02 2008     length 1 : 15553
Sun Nov 30 18:51:02 2008     length 2 : 11104
Sun Nov 30 18:51:02 2008     length 3 : 10158
Sun Nov 30 18:51:02 2008     length 4 : 7663
Sun Nov 30 18:51:02 2008     length 5 : 5261
Sun Nov 30 18:51:02 2008     length 6 : 3377
Sun Nov 30 18:51:02 2008     length 7 : 1937
Sun Nov 30 18:51:02 2008     length 9+: 2358
Sun Nov 30 18:51:02 2008  largest cycle: 17 relations
Sun Nov 30 18:51:02 2008  matrix is 56997 x 57411 (13.3 MB) with weight 3247632 (56.57/col)
Sun Nov 30 18:51:02 2008  sparse part has weight 3247632 (56.57/col)
Sun Nov 30 18:51:02 2008  filtering completed in 4 passes
Sun Nov 30 18:51:02 2008  matrix is 52859 x 52923 (12.3 MB) with weight 3006031 (56.80/col)
Sun Nov 30 18:51:02 2008  sparse part has weight 3006031 (56.80/col)
Sun Nov 30 18:51:03 2008  saving the first 48 matrix rows for later
Sun Nov 30 18:51:03 2008  matrix is 52811 x 52923 (7.8 MB) with weight 2373089 (44.84/col)
Sun Nov 30 18:51:03 2008  sparse part has weight 1733530 (32.76/col)
Sun Nov 30 18:51:03 2008  matrix includes 64 packed rows
Sun Nov 30 18:51:03 2008  using block size 21169 for processor cache size 1024 kB
Sun Nov 30 18:51:03 2008  commencing Lanczos iteration
Sun Nov 30 18:51:03 2008  memory use: 7.7 MB
Sun Nov 30 18:51:20 2008  lanczos halted after 837 iterations (dim = 52811)
Sun Nov 30 18:51:20 2008  recovered 17 nontrivial dependencies
Sun Nov 30 18:51:21 2008  prp44 factor: 21099559767919706148965388700117758588600401
Sun Nov 30 18:51:21 2008  prp44 factor: 42544095972337002803163257909814208720366277
Sun Nov 30 18:51:21 2008  elapsed time 00:54:40

(11·10¹¹²+1)/3 = 3(6)₁₁₁7_<113> = 37 · 53 · 6053 · 121254179151355849_<18> · C89

C89 = P37 · P53

P37 = 2344658050851003644637589698792718697_<37>

P53 = 10865430383019248585841901328692422403234007461482983_<53>

Sun Nov 30 18:57:49 2008  Msieve v. 1.38
Sun Nov 30 18:57:49 2008  random seeds: 1760b75c 1e4aa34b
Sun Nov 30 18:57:49 2008  factoring 25475718823507185358250712731480185849953749457460003767658389018952004744064201971433151 (89 digits)
Sun Nov 30 18:57:50 2008  searching for 15-digit factors
Sun Nov 30 18:57:52 2008  commencing quadratic sieve (89-digit input)
Sun Nov 30 18:57:52 2008  using multiplier of 31
Sun Nov 30 18:57:52 2008  using 32kb Intel Core sieve core
Sun Nov 30 18:57:52 2008  sieve interval: 30 blocks of size 32768
Sun Nov 30 18:57:52 2008  processing polynomials in batches of 7
Sun Nov 30 18:57:52 2008  using a sieve bound of 1544489 (58667 primes)
Sun Nov 30 18:57:52 2008  using large prime bound of 123559120 (26 bits)
Sun Nov 30 18:57:52 2008  using double large prime bound of 367599255202560 (42-49 bits)
Sun Nov 30 18:57:52 2008  using trial factoring cutoff of 49 bits
Sun Nov 30 18:57:52 2008  polynomial 'A' values have 11 factors
Sun Nov 30 20:01:08 2008  59023 relations (16122 full + 42901 combined from 619206 partial), need 58763
Sun Nov 30 20:01:09 2008  begin with 635328 relations
Sun Nov 30 20:01:10 2008  reduce to 142320 relations in 10 passes
Sun Nov 30 20:01:10 2008  attempting to read 142320 relations
Sun Nov 30 20:01:12 2008  recovered 142320 relations
Sun Nov 30 20:01:12 2008  recovered 120307 polynomials
Sun Nov 30 20:01:12 2008  attempting to build 59023 cycles
Sun Nov 30 20:01:12 2008  found 59023 cycles in 6 passes
Sun Nov 30 20:01:12 2008  distribution of cycle lengths:
Sun Nov 30 20:01:12 2008     length 1 : 16122
Sun Nov 30 20:01:12 2008     length 2 : 11639
Sun Nov 30 20:01:12 2008     length 3 : 10383
Sun Nov 30 20:01:12 2008     length 4 : 7676
Sun Nov 30 20:01:12 2008     length 5 : 5403
Sun Nov 30 20:01:12 2008     length 6 : 3358
Sun Nov 30 20:01:12 2008     length 7 : 2090
Sun Nov 30 20:01:12 2008     length 9+: 2352
Sun Nov 30 20:01:12 2008  largest cycle: 20 relations
Sun Nov 30 20:01:12 2008  matrix is 58667 x 59023 (14.4 MB) with weight 3551446 (60.17/col)
Sun Nov 30 20:01:12 2008  sparse part has weight 3551446 (60.17/col)
Sun Nov 30 20:01:13 2008  filtering completed in 3 passes
Sun Nov 30 20:01:13 2008  matrix is 54455 x 54518 (13.4 MB) with weight 3299267 (60.52/col)
Sun Nov 30 20:01:13 2008  sparse part has weight 3299267 (60.52/col)
Sun Nov 30 20:01:13 2008  saving the first 48 matrix rows for later
Sun Nov 30 20:01:13 2008  matrix is 54407 x 54518 (10.2 MB) with weight 2772385 (50.85/col)
Sun Nov 30 20:01:13 2008  sparse part has weight 2337636 (42.88/col)
Sun Nov 30 20:01:13 2008  matrix includes 64 packed rows
Sun Nov 30 20:01:13 2008  using block size 21807 for processor cache size 1024 kB
Sun Nov 30 20:01:14 2008  commencing Lanczos iteration
Sun Nov 30 20:01:14 2008  memory use: 9.0 MB
Sun Nov 30 20:01:35 2008  lanczos halted after 862 iterations (dim = 54404)
Sun Nov 30 20:01:36 2008  recovered 15 nontrivial dependencies
Sun Nov 30 20:01:36 2008  prp37 factor: 2344658050851003644637589698792718697
Sun Nov 30 20:01:36 2008  prp53 factor: 10865430383019248585841901328692422403234007461482983
Sun Nov 30 20:01:36 2008  elapsed time 01:03:47

(11·10¹¹⁶+1)/3 = 3(6)₁₁₅7_<117> = 5923 · C113

C113 = P43 · P71

P43 = 1306986629179934599512414769208909338753123_<43>

P71 = 47365110316386599844519000083508998721829561294653165381499167296421523_<71>

Number: 36667_116
N=61905565873149867747200180088918903708706173673251167764083516236141594912488040970229050593730654510664640666329
  ( 113 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=1306986629179934599512414769208909338753123 (pp43)
 r2=47365110316386599844519000083508998721829561294653165381499167296421523 (pp71)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.39 hours.
Scaled time: 4.79 units (timescale=2.003).
Factorization parameters were as follows:
name: 36667_116
n: 61905565873149867747200180088918903708706173673251167764083516236141594912488040970229050593730654510664640666329
m: 200000000000000000000000
deg: 5
c5: 55
c0: 16
skew: 0.78
type: snfs
lss: 1
rlim: 650000
alim: 650000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 650000/650000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [325000, 575001)
Primes: RFBsize:52831, AFBsize:52923, largePrimes:1703942 encountered
Relations: rels:1982042, finalFF:430957
Max relations in full relation-set: 28
Initial matrix: 105821 x 430957 with sparse part having weight 20615305.
Pruned matrix : 61853 x 62446 with weight 3879059.
Total sieving time: 2.30 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,118,5,0,0,0,0,0,0,0,0,650000,650000,25,25,45,45,2.2,2.2,50000
total time: 2.39 hours.
 --------- CPU info (if available) ----------

(34·10¹⁵⁰-61)/9 = 3(7)₁₄₉1_<151> = 3 · 389 · 30137 · 38659272836953_<14> · 67606737734777_<14> · 100407816699053448695811907_<27> · C90

C90 = P43 · P48

P43 = 1973252236706869812819161804219996164666783_<43>

P48 = 207430084791366627386951998914230244772682187809_<48>

Sun Nov 30 20:11:43 2008  Msieve v. 1.38
Sun Nov 30 20:11:43 2008  random seeds: d7427efc dffe20ca
Sun Nov 30 20:11:43 2008  factoring 409311878774859856196618058713465886648346234120836517657865266347085566045370911909848447 (90 digits)
Sun Nov 30 20:11:43 2008  searching for 15-digit factors
Sun Nov 30 20:11:45 2008  commencing quadratic sieve (90-digit input)
Sun Nov 30 20:11:45 2008  using multiplier of 7
Sun Nov 30 20:11:45 2008  using 32kb Intel Core sieve core
Sun Nov 30 20:11:45 2008  sieve interval: 36 blocks of size 32768
Sun Nov 30 20:11:45 2008  processing polynomials in batches of 6
Sun Nov 30 20:11:45 2008  using a sieve bound of 1573717 (60000 primes)
Sun Nov 30 20:11:45 2008  using large prime bound of 125897360 (26 bits)
Sun Nov 30 20:11:45 2008  using double large prime bound of 380215566683840 (42-49 bits)
Sun Nov 30 20:11:45 2008  using trial factoring cutoff of 49 bits
Sun Nov 30 20:11:45 2008  polynomial 'A' values have 12 factors
Sun Nov 30 21:34:45 2008  60440 relations (16042 full + 44398 combined from 633475 partial), need 60096
Sun Nov 30 21:34:45 2008  begin with 649517 relations
Sun Nov 30 21:34:46 2008  reduce to 147373 relations in 10 passes
Sun Nov 30 21:34:46 2008  attempting to read 147373 relations
Sun Nov 30 21:34:48 2008  recovered 147373 relations
Sun Nov 30 21:34:48 2008  recovered 127487 polynomials
Sun Nov 30 21:34:48 2008  attempting to build 60440 cycles
Sun Nov 30 21:34:48 2008  found 60439 cycles in 5 passes
Sun Nov 30 21:34:48 2008  distribution of cycle lengths:
Sun Nov 30 21:34:48 2008     length 1 : 16042
Sun Nov 30 21:34:48 2008     length 2 : 11565
Sun Nov 30 21:34:48 2008     length 3 : 10681
Sun Nov 30 21:34:48 2008     length 4 : 8203
Sun Nov 30 21:34:48 2008     length 5 : 5747
Sun Nov 30 21:34:48 2008     length 6 : 3601
Sun Nov 30 21:34:48 2008     length 7 : 2155
Sun Nov 30 21:34:48 2008     length 9+: 2445
Sun Nov 30 21:34:48 2008  largest cycle: 20 relations
Sun Nov 30 21:34:48 2008  matrix is 60000 x 60439 (14.8 MB) with weight 3629462 (60.05/col)
Sun Nov 30 21:34:48 2008  sparse part has weight 3629462 (60.05/col)
Sun Nov 30 21:34:49 2008  filtering completed in 3 passes
Sun Nov 30 21:34:49 2008  matrix is 56097 x 56161 (13.7 MB) with weight 3376905 (60.13/col)
Sun Nov 30 21:34:49 2008  sparse part has weight 3376905 (60.13/col)
Sun Nov 30 21:34:49 2008  saving the first 48 matrix rows for later
Sun Nov 30 21:34:49 2008  matrix is 56049 x 56161 (8.8 MB) with weight 2662129 (47.40/col)
Sun Nov 30 21:34:49 2008  sparse part has weight 1959855 (34.90/col)
Sun Nov 30 21:34:49 2008  matrix includes 64 packed rows
Sun Nov 30 21:34:49 2008  using block size 22464 for processor cache size 1024 kB
Sun Nov 30 21:34:50 2008  commencing Lanczos iteration
Sun Nov 30 21:34:50 2008  memory use: 8.5 MB
Sun Nov 30 21:35:10 2008  lanczos halted after 888 iterations (dim = 56047)
Sun Nov 30 21:35:10 2008  recovered 16 nontrivial dependencies
Sun Nov 30 21:35:10 2008  prp43 factor: 1973252236706869812819161804219996164666783
Sun Nov 30 21:35:10 2008  prp48 factor: 207430084791366627386951998914230244772682187809
Sun Nov 30 21:35:10 2008  elapsed time 01:23:27

(11·10¹⁴³-17)/3 = 3(6)₁₄₂1_<144> = 59 · 103 · 197 · 219076802827792599331905203_<27> · C112

C112 = P37 · P75

P37 = 5820795363380476217942633647955613143_<37>

P75 = 240180222166092282236882706207457733262537991553564219984716625310194297761_<75>

Number: 36661_143
N=1398039923560082634828910420072859904457691715505441275759702220737789195249611934079696273591083487191067072823
  ( 112 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=5820795363380476217942633647955613143 (pp37)
 r2=240180222166092282236882706207457733262537991553564219984716625310194297761 (pp75)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 22.85 hours.
Scaled time: 10.81 units (timescale=0.473).
Factorization parameters were as follows:
name: 36661_143
n: 1398039923560082634828910420072859904457691715505441275759702220737789195249611934079696273591083487191067072823
m: 50000000000000000000000000000
deg: 5
c5: 88
c0: -425
skew: 1.37
type: snfs
lss: 1
rlim: 1860000
alim: 1860000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1860000/1860000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [930000, 2730001)
Primes: RFBsize:139249, AFBsize:139409, largePrimes:4151418 encountered
Relations: rels:4312026, finalFF:326401
Max relations in full relation-set: 28
Initial matrix: 278725 x 326401 with sparse part having weight 36068468.
Pruned matrix : 262731 x 264188 with weight 27157932.
Total sieving time: 20.04 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 2.47 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1860000,1860000,26,26,49,49,2.3,2.3,100000
total time: 22.85 hours.
 --------- CPU info (if available) ----------

(11·10¹²³+1)/3 = 3(6)₁₂₂7_<124> = 17 · 233 · 420319 · C115

C115 = P49 · P66

P49 = 9794999209502002672388914985834215568969898339847_<49>

P66 = 224844961786526402678113350024342711554948949791525830477913909179_<66>

Number: 36667_123
N=2202356222959534112779755467971839504883156015757536029981701961576441194628114329686083870245406553784502034755613
  ( 115 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=9794999209502002672388914985834215568969898339847 (pp49)
 r2=224844961786526402678113350024342711554948949791525830477913909179 (pp66)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.84 hours.
Scaled time: 5.64 units (timescale=1.985).
Factorization parameters were as follows:
name: 36667_123
n: 2202356222959534112779755467971839504883156015757536029981701961576441194628114329686083870245406553784502034755613
m: 5000000000000000000000000
deg: 5
c5: 88
c0: 25
skew: 0.78
type: snfs
lss: 1
rlim: 860000
alim: 860000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 860000/860000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [430000, 680001)
Primes: RFBsize:68342, AFBsize:68636, largePrimes:2725883 encountered
Relations: rels:2864348, finalFF:412312
Max relations in full relation-set: 28
Initial matrix: 137045 x 412312 with sparse part having weight 29982948.
Pruned matrix : 86555 x 87304 with weight 5897482.
Total sieving time: 2.70 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,860000,860000,26,26,46,46,2.3,2.3,50000
total time: 2.84 hours.
 --------- CPU info (if available) ----------

Nov 30, 2008 (7th)

By Robert Backstrom / Msieve, GGNFS

(11·10¹¹¹+1)/3 = 3(6)₁₁₀7_<112> = 19 · 4479173856329141155090247729_<28> · C83

C83 = P40 · P43

P40 = 5224631191091294072933327702528080958339_<40>

P43 = 8246397610153091399492664950103852314306803_<43>

Sun Nov 30 20:26:18 2008  
Sun Nov 30 20:26:18 2008  
Sun Nov 30 20:26:18 2008  Msieve v. 1.38
Sun Nov 30 20:26:18 2008  random seeds: 2bc1f670 7511cf85
Sun Nov 30 20:26:18 2008  factoring 43084386168146546835721754466890151824910052764435983250283044114671565568707280217 (83 digits)
Sun Nov 30 20:26:18 2008  searching for 15-digit factors
Sun Nov 30 20:26:19 2008  commencing quadratic sieve (83-digit input)
Sun Nov 30 20:26:19 2008  using multiplier of 5
Sun Nov 30 20:26:19 2008  using 64kb Opteron sieve core
Sun Nov 30 20:26:19 2008  sieve interval: 6 blocks of size 65536
Sun Nov 30 20:26:19 2008  processing polynomials in batches of 17
Sun Nov 30 20:26:19 2008  using a sieve bound of 1368167 (52647 primes)
Sun Nov 30 20:26:19 2008  using large prime bound of 121766863 (26 bits)
Sun Nov 30 20:26:19 2008  using trial factoring cutoff of 27 bits
Sun Nov 30 20:26:19 2008  polynomial 'A' values have 11 factors
Sun Nov 30 20:42:41 2008  52814 relations (27081 full + 25733 combined from 279284 partial), need 52743
Sun Nov 30 20:42:41 2008  begin with 306365 relations
Sun Nov 30 20:42:41 2008  reduce to 75332 relations in 2 passes
Sun Nov 30 20:42:41 2008  attempting to read 75332 relations
Sun Nov 30 20:42:42 2008  recovered 75332 relations
Sun Nov 30 20:42:42 2008  recovered 68175 polynomials
Sun Nov 30 20:42:42 2008  attempting to build 52814 cycles
Sun Nov 30 20:42:42 2008  found 52814 cycles in 1 passes
Sun Nov 30 20:42:42 2008  distribution of cycle lengths:
Sun Nov 30 20:42:42 2008     length 1 : 27081
Sun Nov 30 20:42:42 2008     length 2 : 25733
Sun Nov 30 20:42:42 2008  largest cycle: 2 relations
Sun Nov 30 20:42:42 2008  matrix is 52647 x 52814 (7.2 MB) with weight 1683721 (31.88/col)
Sun Nov 30 20:42:42 2008  sparse part has weight 1683721 (31.88/col)
Sun Nov 30 20:42:42 2008  filtering completed in 3 passes
Sun Nov 30 20:42:42 2008  matrix is 37904 x 37965 (5.7 MB) with weight 1347008 (35.48/col)
Sun Nov 30 20:42:42 2008  sparse part has weight 1347008 (35.48/col)
Sun Nov 30 20:42:43 2008  saving the first 48 matrix rows for later
Sun Nov 30 20:42:43 2008  matrix is 37856 x 37965 (3.8 MB) with weight 1039465 (27.38/col)
Sun Nov 30 20:42:43 2008  sparse part has weight 762472 (20.08/col)
Sun Nov 30 20:42:43 2008  matrix includes 64 packed rows
Sun Nov 30 20:42:43 2008  using block size 15186 for processor cache size 1024 kB
Sun Nov 30 20:42:43 2008  commencing Lanczos iteration
Sun Nov 30 20:42:43 2008  memory use: 4.3 MB
Sun Nov 30 20:42:49 2008  lanczos halted after 600 iterations (dim = 37854)
Sun Nov 30 20:42:49 2008  recovered 17 nontrivial dependencies
Sun Nov 30 20:42:49 2008  prp40 factor: 5224631191091294072933327702528080958339
Sun Nov 30 20:42:49 2008  prp43 factor: 8246397610153091399492664950103852314306803
Sun Nov 30 20:42:49 2008  elapsed time 00:16:31

(34·10¹³³-61)/9 = 3(7)₁₃₂1_<134> = 153962383 · 105954652313_<12> · 242858635321_<12> · 161803335731828507203_<21> · C83

C83 = P41 · P43

P41 = 26799939804329649021518979639474619438057_<41>

P43 = 2199008524395165291774974383767263037749039_<43>

Sun Nov 30 21:30:16 2008  
Sun Nov 30 21:30:16 2008  
Sun Nov 30 21:30:16 2008  Msieve v. 1.38
Sun Nov 30 21:30:16 2008  random seeds: e4438188 325b217a
Sun Nov 30 21:30:16 2008  factoring 58933296082998196336578171305363661582019073412603463167509046878466276668371777223 (83 digits)
Sun Nov 30 21:30:16 2008  searching for 15-digit factors
Sun Nov 30 21:30:17 2008  commencing quadratic sieve (83-digit input)
Sun Nov 30 21:30:17 2008  using multiplier of 23
Sun Nov 30 21:30:17 2008  using 64kb Opteron sieve core
Sun Nov 30 21:30:17 2008  sieve interval: 6 blocks of size 65536
Sun Nov 30 21:30:17 2008  processing polynomials in batches of 17
Sun Nov 30 21:30:17 2008  using a sieve bound of 1375981 (52647 primes)
Sun Nov 30 21:30:17 2008  using large prime bound of 122462309 (26 bits)
Sun Nov 30 21:30:17 2008  using trial factoring cutoff of 27 bits
Sun Nov 30 21:30:17 2008  polynomial 'A' values have 11 factors
Sun Nov 30 21:46:50 2008  52756 relations (27452 full + 25304 combined from 276041 partial), need 52743
Sun Nov 30 21:46:51 2008  begin with 303493 relations
Sun Nov 30 21:46:51 2008  reduce to 74861 relations in 2 passes
Sun Nov 30 21:46:51 2008  attempting to read 74861 relations
Sun Nov 30 21:46:51 2008  recovered 74861 relations
Sun Nov 30 21:46:51 2008  recovered 68059 polynomials
Sun Nov 30 21:46:51 2008  attempting to build 52756 cycles
Sun Nov 30 21:46:51 2008  found 52756 cycles in 1 passes
Sun Nov 30 21:46:51 2008  distribution of cycle lengths:
Sun Nov 30 21:46:51 2008     length 1 : 27452
Sun Nov 30 21:46:51 2008     length 2 : 25304
Sun Nov 30 21:46:51 2008  largest cycle: 2 relations
Sun Nov 30 21:46:51 2008  matrix is 52647 x 52756 (7.3 MB) with weight 1691578 (32.06/col)
Sun Nov 30 21:46:51 2008  sparse part has weight 1691578 (32.06/col)
Sun Nov 30 21:46:52 2008  filtering completed in 3 passes
Sun Nov 30 21:46:52 2008  matrix is 37816 x 37879 (5.7 MB) with weight 1347132 (35.56/col)
Sun Nov 30 21:46:52 2008  sparse part has weight 1347132 (35.56/col)
Sun Nov 30 21:46:52 2008  saving the first 48 matrix rows for later
Sun Nov 30 21:46:52 2008  matrix is 37768 x 37879 (3.6 MB) with weight 1000452 (26.41/col)
Sun Nov 30 21:46:52 2008  sparse part has weight 712309 (18.80/col)
Sun Nov 30 21:46:52 2008  matrix includes 64 packed rows
Sun Nov 30 21:46:52 2008  using block size 15151 for processor cache size 1024 kB
Sun Nov 30 21:46:53 2008  commencing Lanczos iteration
Sun Nov 30 21:46:53 2008  memory use: 4.2 MB
Sun Nov 30 21:46:58 2008  lanczos halted after 599 iterations (dim = 37768)
Sun Nov 30 21:46:58 2008  recovered 18 nontrivial dependencies
Sun Nov 30 21:46:58 2008  prp41 factor: 26799939804329649021518979639474619438057
Sun Nov 30 21:46:58 2008  prp43 factor: 2199008524395165291774974383767263037749039
Sun Nov 30 21:46:58 2008  elapsed time 00:16:42

(34·10¹⁰⁹-61)/9 = 3(7)₁₀₈1_<110> = 355457 · C105

C105 = P33 · P73

P33 = 102274718124055259233175468223737_<33>

P73 = 1039156707415436687110020687405007603981945643618063760550394061953391619_<73>

Number: n
N=106279459337635150743346671405480206544751623340594721099254699662062577970831289798140922186868672660203
  ( 105 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=102274718124055259233175468223737 (pp33)
 r2=1039156707415436687110020687405007603981945643618063760550394061953391619 (pp73)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.91 hours.
Scaled time: 1.65 units (timescale=1.817).
Factorization parameters were as follows:
name: KA_3_7_108_1
n: 106279459337635150743346671405480206544751623340594721099254699662062577970831289798140922186868672660203
type: snfs
skew: 1.78
deg: 5
c5: 17
c0: -305
m: 10000000000000000000000
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [100000, 200001)
Primes: RFBsize:41538, AFBsize:41418, largePrimes:4212687 encountered
Relations: rels:3752838, finalFF:255574
Max relations in full relation-set: 48
Initial matrix: 83021 x 255574 with sparse part having weight 23447240.
Pruned matrix : 53378 x 53857 with weight 2927628.
Total sieving time: 0.84 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.01 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,500000,500000,28,28,56,56,2.5,2.5,50000
total time: 0.91 hours.
 --------- CPU info (if available) ----------

Nov 30, 2008 (6th)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38

(34·10¹⁵¹-61)/9 = 3(7)₁₅₀1_<152> = 31 · 85413659 · 2512923666807739522019_<22> · 552414667069372497692778901_<27> · C95

C95 = P40 · P55

P40 = 4219687194429644317151362254455770822763_<40>

P55 = 2435693468651238851330439053636574682409976561582029267_<55>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2347407703
Step 1 took 8636ms
Step 2 took 404ms
********** Factor found in step 2: 4219687194429644317151362254455770822763
Found probable prime factor of 40 digits: 4219687194429644317151362254455770822763
Probable prime cofactor 2435693468651238851330439053636574682409976561582029267 has 55 digits

(11·10¹¹⁰+1)/3 = 3(6)₁₀₉7_<111> = 1730988986761_<13> · C99

C99 = P39 · P61

P39 = 190853932462516980462149362837947703859_<39>

P61 = 1109879967768032011225337624689665807633302433866174800966433_<61>

SNFS difficulty: 111 digits.
Divisors found:
 r1=190853932462516980462149362837947703859 (pp39)
 r2=1109879967768032011225337624689665807633302433866174800966433 (pp61)
Version: Msieve-1.38
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.403).
Factorization parameters were as follows:
n: 211824956409900504611721650005430185338299024638751288343886051876340119698931368923094866483564947
m: 10000000000000000000000
deg: 5
c5: 11
c0: 1
skew: 0.62
type: snfs
lss: 1
rlim: 500000
alim: 500000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [250000, 350001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 54411 x 54621
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,500000,500000,25,25,46,46,2.3,2.3,50000
total time: 0.30 hours.

Nov 30, 2008 (5th)

Factorizations of 366...667 and Factorizations of 377...771 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Nov 30, 2008 (4th)

By Sinkiti Sibata / Msieve, GGNFS

(11·10¹⁴⁸-17)/3 = 3(6)₁₄₇1_<149> = 127 · 6053 · 3527767 · 12713377 · 33380182777_<11> · 55504775997620393_<17> · C102

C102 = P43 · P60

P43 = 2948246018368709645486068483619884355791607_<43>

P60 = 194694387041111373270642545173578018166065623787751820262767_<60>

Sat Nov 29 19:58:25 2008  Msieve v. 1.38
Sat Nov 29 19:58:25 2008  random seeds: 0bb27454 e6c455c6
Sat Nov 29 19:58:25 2008  factoring 574006951392693106963739100431843481150210144630008572838701316332226314859054721325873107493033196569 (102 digits)
Sat Nov 29 19:58:26 2008  searching for 15-digit factors
Sat Nov 29 19:58:28 2008  commencing quadratic sieve (102-digit input)
Sat Nov 29 19:58:28 2008  using multiplier of 1
Sat Nov 29 19:58:28 2008  using 32kb Intel Core sieve core
Sat Nov 29 19:58:28 2008  sieve interval: 36 blocks of size 32768
Sat Nov 29 19:58:28 2008  processing polynomials in batches of 6
Sat Nov 29 19:58:28 2008  using a sieve bound of 3272219 (117500 primes)
Sat Nov 29 19:58:28 2008  using large prime bound of 490832850 (28 bits)
Sat Nov 29 19:58:28 2008  using double large prime bound of 4402308790788150 (44-52 bits)
Sat Nov 29 19:58:28 2008  using trial factoring cutoff of 52 bits
Sat Nov 29 19:58:28 2008  polynomial 'A' values have 13 factors
Sun Nov 30 09:52:49 2008  117762 relations (28907 full + 88855 combined from 1739700 partial), need 117596
Sun Nov 30 09:52:52 2008  begin with 1768607 relations
Sun Nov 30 09:52:53 2008  reduce to 305866 relations in 11 passes
Sun Nov 30 09:52:53 2008  attempting to read 305866 relations
Sun Nov 30 09:52:59 2008  recovered 305866 relations
Sun Nov 30 09:52:59 2008  recovered 294831 polynomials
Sun Nov 30 09:52:59 2008  attempting to build 117762 cycles
Sun Nov 30 09:52:59 2008  found 117762 cycles in 6 passes
Sun Nov 30 09:52:59 2008  distribution of cycle lengths:
Sun Nov 30 09:52:59 2008     length 1 : 28907
Sun Nov 30 09:53:00 2008     length 2 : 20776
Sun Nov 30 09:53:00 2008     length 3 : 19574
Sun Nov 30 09:53:00 2008     length 4 : 16039
Sun Nov 30 09:53:00 2008     length 5 : 12143
Sun Nov 30 09:53:00 2008     length 6 : 7941
Sun Nov 30 09:53:00 2008     length 7 : 5284
Sun Nov 30 09:53:00 2008     length 9+: 7098
Sun Nov 30 09:53:00 2008  largest cycle: 19 relations
Sun Nov 30 09:53:00 2008  matrix is 117500 x 117762 (33.6 MB) with weight 8326328 (70.70/col)
Sun Nov 30 09:53:00 2008  sparse part has weight 8326328 (70.70/col)
Sun Nov 30 09:53:02 2008  filtering completed in 4 passes
Sun Nov 30 09:53:02 2008  matrix is 112064 x 112128 (32.2 MB) with weight 7980133 (71.17/col)
Sun Nov 30 09:53:02 2008  sparse part has weight 7980133 (71.17/col)
Sun Nov 30 09:53:03 2008  saving the first 48 matrix rows for later
Sun Nov 30 09:53:03 2008  matrix is 112016 x 112128 (22.2 MB) with weight 6586527 (58.74/col)
Sun Nov 30 09:53:03 2008  sparse part has weight 5144383 (45.88/col)
Sun Nov 30 09:53:03 2008  matrix includes 64 packed rows
Sun Nov 30 09:53:03 2008  using block size 43690 for processor cache size 1024 kB
Sun Nov 30 09:53:04 2008  commencing Lanczos iteration
Sun Nov 30 09:53:04 2008  memory use: 20.1 MB
Sun Nov 30 09:54:49 2008  lanczos halted after 1774 iterations (dim = 112012)
Sun Nov 30 09:54:49 2008  recovered 14 nontrivial dependencies
Sun Nov 30 09:54:50 2008  prp43 factor: 2948246018368709645486068483619884355791607
Sun Nov 30 09:54:50 2008  prp60 factor: 194694387041111373270642545173578018166065623787751820262767
Sun Nov 30 09:54:50 2008  elapsed time 13:56:25

(11·10¹⁴⁷-17)/3 = 3(6)₁₄₆1_<148> = 7 · 20753 · 36857 · C138

C138 = P55 · P83

P55 = 8842698700184589568599008652313694532003883719628427533_<55>

P83 = 77443985378298208181284593151571674690130665279220978504034704045989491535203645511_<83>

Number: 36661_147
N=684813828841791925548542636326045013960593236516865610758561616214614337734306773754040675593517862354982976147348950128332745010084254363
  ( 138 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=8842698700184589568599008652313694532003883719628427533 (pp55)
 r2=77443985378298208181284593151571674690130665279220978504034704045989491535203645511 (pp83)
Version: GGNFS-0.77.1-20060513-k8
Total time: 19.10 hours.
Scaled time: 37.43 units (timescale=1.960).
Factorization parameters were as follows:
name: 36661_147
n: 684813828841791925548542636326045013960593236516865610758561616214614337734306773754040675593517862354982976147348950128332745010084254363
m: 200000000000000000000000000000
deg: 5
c5: 275
c0: -136
skew: 0.87
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 2550001)
Primes: RFBsize:155805, AFBsize:155548, largePrimes:4285623 encountered
Relations: rels:4471418, finalFF:407942
Max relations in full relation-set: 28
Initial matrix: 311420 x 407942 with sparse part having weight 41248728.
Pruned matrix : 275681 x 277302 with weight 25234510.
Total sieving time: 17.84 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.96 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 19.10 hours.
 --------- CPU info (if available) ----------

Nov 30, 2008 (3rd)

By Wataru Sakai /

(29·10¹⁹⁸+61)/9 = 3(2)₁₉₇9_<199> = C199

C199 = P34 · P80 · P86

P34 = 2095371728411637326523016514560361_<34>

P80 = 74843311724277390714103497997979276379695056502313658840857218754233651055714689_<80>

P86 = 20546668414495269636043870873401510005927188389041146706716965258195301264107264535501_<86>

Number: 32229_198
N=3222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229
  ( 199 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=2095371728411637326523016514560361
 r2=74843311724277390714103497997979276379695056502313658840857218754233651055714689
 r3=20546668414495269636043870873401510005927188389041146706716965258195301264107264535501
Version: 
Total time: 1037.76 hours.
Scaled time: 2075.52 units (timescale=2.000).
Factorization parameters were as follows:
n: 3222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229
m: 5000000000000000000000000000000000000000
deg: 5
c5: 232
c0: 1525
skew: 1.46
type: snfs
lss: 1
rlim: 15600000
alim: 15600000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6Factor base limits: 15600000/15600000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [7800000, 19100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3123383 x 3123631
Total sieving time: 1037.76 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,200,5,0,0,0,0,0,0,0,0,15600000,15600000,29,29,56,56,2.6,2.6,100000
total time: 1037.76 hours.
 --------- CPU info (if available) ----------

Nov 30, 2008 (2nd)

By Robert Backstrom / GGNFS

(11·10¹⁴⁹-17)/3 = 3(6)₁₄₈1_<150> = 113 · 2789 · C145

C145 = P52 · P93

P52 = 1749531190763715955891758353574118748596593649502417_<52>

P93 = 665001742324150244386503948550084957227608454300070908441392564284028975306968875042947440769_<93>

Number: n
N=1163441290108316384109084255360555744174067739782605706573760591282017111048355793038601924331893839155299316425358366359200863908041600429838673
  ( 145 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=1749531190763715955891758353574118748596593649502417 (pp52)
 r2=665001742324150244386503948550084957227608454300070908441392564284028975306968875042947440769 (pp93)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 12.50 hours.
Scaled time: 22.78 units (timescale=1.822).
Factorization parameters were as follows:
name: KA_3_6_148_1
n: 1163441290108316384109084255360555744174067739782605706573760591282017111048355793038601924331893839155299316425358366359200863908041600429838673
type: snfs
skew: 1.73
deg: 5
c5: 11
c0: -170
m: 1000000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:148933, AFBsize:149101, largePrimes:9843134 encountered
Relations: rels:8711625, finalFF:409868
Max relations in full relation-set: 48
Initial matrix: 298099 x 409868 with sparse part having weight 47976057.
Pruned matrix : 244058 x 245612 with weight 21718722.
Total sieving time: 11.67 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.50 hours.
Total square root time: 0.13 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,56,56,2.5,2.5,100000
total time: 12.50 hours.
 --------- CPU info (if available) ----------

Nov 30, 2008

By Serge Batalov / Msieve-1.38

(11·10¹⁵⁹-17)/3 = 3(6)₁₅₈1_<160> = 7 · C159

C159 = P43 · P116

P43 = 9605698962417846290315464856568118961559197_<43>

P116 = 54531120104733736426800532979622712211483081760295270849348053571911942643371024243440985426930821251996580938007759_<116>

SNFS difficulty: 161 digits.
Divisors found:
 r1=9605698962417846290315464856568118961559197 (pp43)
 r2=54531120104733736426800532979622712211483081760295270849348053571911942643371024243440985426930821251996580938007759 (pp116)
Version: Msieve-1.38
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.552).
Factorization parameters were as follows:
n: 523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523
m: 100000000000000000000000000000000
deg: 5
c5: 11
c0: -170
skew: 1.73
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1700000, 3000001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 617903 x 618145
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,52,52,2.4,2.4,100000
total time: 17.00 hours.

Nov 29, 2008 (4th)

By Sinkiti Sibata / GGNFS, Msieve

(29·10¹⁶¹-11)/9 = 3(2)₁₆₀1_<162> = 3² · 107 · 12829059953513_<14> · 378530381329301986746325121_<27> · C119

C119 = P40 · P80

P40 = 2546623150563877412685398371793679334001_<40>

P80 = 27056333382115000182457185576833611392251799115728017548960989369903042621465479_<80>

Number: 32221_161
N=68902284960268310691160272909882658392427741164950225050125505847630985571103442660751760239191044441082947519332451479
  ( 119 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=2546623150563877412685398371793679334001 (pp40)
 r2=27056333382115000182457185576833611392251799115728017548960989369903042621465479 (pp80)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 55.10 hours.
Scaled time: 141.29 units (timescale=2.564).
Factorization parameters were as follows:
name: 32221_161
n: 68902284960268310691160272909882658392427741164950225050125505847630985571103442660751760239191044441082947519332451479
m: 200000000000000000000000000000000
deg: 5
c5: 145
c0: -176
skew: 1.04
type: snfs
lss: 1
rlim: 3700000
alim: 3700000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3700000/3700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1850000, 3550001)
Primes: RFBsize:263397, AFBsize:262673, largePrimes:9228731 encountered
Relations: rels:9590220, finalFF:635440
Max relations in full relation-set: 28
Initial matrix: 526137 x 635440 with sparse part having weight 70868979.
Pruned matrix : 480579 x 483273 with weight 51758556.
Total sieving time: 52.00 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 2.75 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3700000,3700000,27,27,51,51,2.4,2.4,100000
total time: 55.10 hours.
 --------- CPU info (if available) ----------

(11·10¹³⁵-17)/3 = 3(6)₁₃₄1_<136> = 7 · 643 · 98953 · 1598539 · C121

C121 = P54 · P68

P54 = 463899733528641667300807588409536956588227985148592021_<54>

P68 = 11101613225813972447215283066867552276042114840195309698943540163023_<68>

Number: 36661_135
N=5150035417193145851355521736539756677829975768640092551076918709929398652640501243150621028631411539736512996373257039483
  ( 121 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=463899733528641667300807588409536956588227985148592021 (pp54)
 r2=11101613225813972447215283066867552276042114840195309698943540163023 (pp68)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.75 hours.
Scaled time: 13.32 units (timescale=1.972).
Factorization parameters were as follows:
name: 36661_135
n: 5150035417193145851355521736539756677829975768640092551076918709929398652640501243150621028631411539736512996373257039483
m: 1000000000000000000000000000
deg: 5
c5: 11
c0: -17
skew: 1.09
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1175001)
Primes: RFBsize:100021, AFBsize:100129, largePrimes:3397345 encountered
Relations: rels:3539165, finalFF:431299
Max relations in full relation-set: 28
Initial matrix: 200215 x 431299 with sparse part having weight 37332250.
Pruned matrix : 146610 x 147675 with weight 10914158.
Total sieving time: 6.42 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000
total time: 6.75 hours.
 --------- CPU info (if available) ----------

(11·10¹²⁰-17)/3 = 3(6)₁₁₉1_<121> = 277 · 6048409 · 233162350530541_<15> · C97

C97 = P49 · P49

P49 = 2105127696207944911022798679968833991726314291117_<49>

P49 = 4458755319605430079360836851668789221417006597841_<49>

Sat Nov 29 07:45:04 2008  Msieve v. 1.38
Sat Nov 29 07:45:04 2008  random seeds: 3c84e488 28be6288
Sat Nov 29 07:45:04 2008  factoring 9386249313915898130261757082745844486257562853489685991325229137610986951325811514789997817678397 (97 digits)
Sat Nov 29 07:45:05 2008  searching for 15-digit factors
Sat Nov 29 07:45:07 2008  commencing quadratic sieve (97-digit input)
Sat Nov 29 07:45:07 2008  using multiplier of 13
Sat Nov 29 07:45:07 2008  using 32kb Intel Core sieve core
Sat Nov 29 07:45:07 2008  sieve interval: 36 blocks of size 32768
Sat Nov 29 07:45:07 2008  processing polynomials in batches of 6
Sat Nov 29 07:45:07 2008  using a sieve bound of 2433061 (89412 primes)
Sat Nov 29 07:45:07 2008  using large prime bound of 364959150 (28 bits)
Sat Nov 29 07:45:07 2008  using double large prime bound of 2582495835375450 (43-52 bits)
Sat Nov 29 07:45:07 2008  using trial factoring cutoff of 52 bits
Sat Nov 29 07:45:07 2008  polynomial 'A' values have 13 factors
Sat Nov 29 13:54:17 2008  89905 relations (21674 full + 68231 combined from 1343247 partial), need 89508
Sat Nov 29 13:54:22 2008  begin with 1364921 relations
Sat Nov 29 13:54:23 2008  reduce to 235606 relations in 10 passes
Sat Nov 29 13:54:23 2008  attempting to read 235606 relations
Sat Nov 29 13:54:27 2008  recovered 235606 relations
Sat Nov 29 13:54:27 2008  recovered 222456 polynomials
Sat Nov 29 13:54:27 2008  attempting to build 89905 cycles
Sat Nov 29 13:54:28 2008  found 89905 cycles in 6 passes
Sat Nov 29 13:54:28 2008  distribution of cycle lengths:
Sat Nov 29 13:54:28 2008     length 1 : 21674
Sat Nov 29 13:54:28 2008     length 2 : 15506
Sat Nov 29 13:54:28 2008     length 3 : 15138
Sat Nov 29 13:54:28 2008     length 4 : 12293
Sat Nov 29 13:54:28 2008     length 5 : 9307
Sat Nov 29 13:54:28 2008     length 6 : 6256
Sat Nov 29 13:54:28 2008     length 7 : 4136
Sat Nov 29 13:54:28 2008     length 9+: 5595
Sat Nov 29 13:54:28 2008  largest cycle: 20 relations
Sat Nov 29 13:54:28 2008  matrix is 89412 x 89905 (24.4 MB) with weight 6028665 (67.06/col)
Sat Nov 29 13:54:28 2008  sparse part has weight 6028665 (67.06/col)
Sat Nov 29 13:54:29 2008  filtering completed in 3 passes
Sat Nov 29 13:54:29 2008  matrix is 85386 x 85449 (23.2 MB) with weight 5736383 (67.13/col)
Sat Nov 29 13:54:29 2008  sparse part has weight 5736383 (67.13/col)
Sat Nov 29 13:54:30 2008  saving the first 48 matrix rows for later
Sat Nov 29 13:54:30 2008  matrix is 85338 x 85449 (14.2 MB) with weight 4515452 (52.84/col)
Sat Nov 29 13:54:30 2008  sparse part has weight 3212893 (37.60/col)
Sat Nov 29 13:54:30 2008  matrix includes 64 packed rows
Sat Nov 29 13:54:30 2008  using block size 34179 for processor cache size 1024 kB
Sat Nov 29 13:54:30 2008  commencing Lanczos iteration
Sat Nov 29 13:54:30 2008  memory use: 13.8 MB
Sat Nov 29 13:55:24 2008  lanczos halted after 1350 iterations (dim = 85336)
Sat Nov 29 13:55:24 2008  recovered 17 nontrivial dependencies
Sat Nov 29 13:55:24 2008  prp49 factor: 2105127696207944911022798679968833991726314291117
Sat Nov 29 13:55:24 2008  prp49 factor: 4458755319605430079360836851668789221417006597841
Sat Nov 29 13:55:24 2008  elapsed time 06:10:20

(11·10¹³⁴-17)/3 = 3(6)₁₃₃1_<135> = 10093 · 24133 · 8598394367382957958478995153_<28> · C99

C99 = P42 · P58

P42 = 108612463794649131001183112199859161618563_<42>

P58 = 1611917530744212293292156513540070557954192544839381684071_<58>

Number: 36661_134
N=175074334447915985220800658956999547881339884018263365077774518425860165827877515202679577075009973
  ( 99 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=108612463794649131001183112199859161618563 (pp42)
 r2=1611917530744212293292156513540070557954192544839381684071 (pp58)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.99 hours.
Scaled time: 12.03 units (timescale=2.010).
Factorization parameters were as follows:
name: 36661_134
n: 175074334447915985220800658956999547881339884018263365077774518425860165827877515202679577075009973
m: 1000000000000000000000000000
deg: 5
c5: 11
c0: -170
skew: 1.73
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1175001)
Primes: RFBsize:100021, AFBsize:99724, largePrimes:3190511 encountered
Relations: rels:3153954, finalFF:278438
Max relations in full relation-set: 28
Initial matrix: 199810 x 278438 with sparse part having weight 23194464.
Pruned matrix : 175657 x 176720 with weight 11268879.
Total sieving time: 5.57 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000
total time: 5.99 hours.
 --------- CPU info (if available) ----------

(11·10¹⁴⁴-17)/3 = 3(6)₁₄₃1_<145> = 157 · 10136260877_<11> · C133

C133 = P61 · P72

P61 = 5065705850886976495988343132418566289486969861509620415150181_<61>

P72 = 454835161040530031250813026453337616614594591416830701515656087243041929_<72>

Number: 36661_144
N=2304061136472133163799949453218864216324962170621676146520944921910783356238101620691422131265770593846200318144699849557627814939149
  ( 133 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=5065705850886976495988343132418566289486969861509620415150181 (pp61)
 r2=454835161040530031250813026453337616614594591416830701515656087243041929 (pp72)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 15.29 hours.
Scaled time: 39.21 units (timescale=2.564).
Factorization parameters were as follows:
name: 36661_144
n: 2304061136472133163799949453218864216324962170621676146520944921910783356238101620691422131265770593846200318144699849557627814939149
m: 100000000000000000000000000000
deg: 5
c5: 11
c0: -170
skew: 1.73
type: snfs
lss: 1
rlim: 1900000
alim: 1900000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1900000/1900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [950000, 2250001)
Primes: RFBsize:142029, AFBsize:142163, largePrimes:4461462 encountered
Relations: rels:5018508, finalFF:688348
Max relations in full relation-set: 28
Initial matrix: 284257 x 688348 with sparse part having weight 77522317.
Pruned matrix : 203776 x 205261 with weight 29271991.
Total sieving time: 14.79 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.35 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000
total time: 15.29 hours.
 --------- CPU info (if available) ----------

(11·10¹⁶⁰-17)/3 = 3(6)₁₅₉1_<161> = 21766998733_<11> · 629345781923007387639337_<24> · 146878709199615825406227598069_<30> · C98

C98 = P45 · P53

P45 = 957664442926109750412572273548012986189861349_<45>

P53 = 19028797420494901463586438810592233217404823016337961_<53>

Sat Nov 29 14:03:27 2008  Msieve v. 1.38
Sat Nov 29 14:03:27 2008  random seeds: 27020444 ac7423e9
Sat Nov 29 14:03:27 2008  factoring 18223202681252044003716422527687772043697950467962637572786101774796419825519335769749720315369389 (98 digits)
Sat Nov 29 14:03:28 2008  searching for 15-digit factors
Sat Nov 29 14:03:29 2008  commencing quadratic sieve (98-digit input)
Sat Nov 29 14:03:30 2008  using multiplier of 13
Sat Nov 29 14:03:30 2008  using 32kb Intel Core sieve core
Sat Nov 29 14:03:30 2008  sieve interval: 36 blocks of size 32768
Sat Nov 29 14:03:30 2008  processing polynomials in batches of 6
Sat Nov 29 14:03:30 2008  using a sieve bound of 2457703 (90588 primes)
Sat Nov 29 14:03:30 2008  using large prime bound of 368655450 (28 bits)
Sat Nov 29 14:03:30 2008  using double large prime bound of 2629766418374550 (43-52 bits)
Sat Nov 29 14:03:30 2008  using trial factoring cutoff of 52 bits
Sat Nov 29 14:03:30 2008  polynomial 'A' values have 13 factors
Sat Nov 29 19:47:07 2008  91084 relations (22967 full + 68117 combined from 1341174 partial), need 90684
Sat Nov 29 19:47:09 2008  begin with 1364141 relations
Sat Nov 29 19:47:11 2008  reduce to 234288 relations in 10 passes
Sat Nov 29 19:47:11 2008  attempting to read 234288 relations
Sat Nov 29 19:47:14 2008  recovered 234288 relations
Sat Nov 29 19:47:14 2008  recovered 219976 polynomials
Sat Nov 29 19:47:15 2008  attempting to build 91084 cycles
Sat Nov 29 19:47:15 2008  found 91084 cycles in 6 passes
Sat Nov 29 19:47:15 2008  distribution of cycle lengths:
Sat Nov 29 19:47:15 2008     length 1 : 22967
Sat Nov 29 19:47:15 2008     length 2 : 16339
Sat Nov 29 19:47:15 2008     length 3 : 15478
Sat Nov 29 19:47:15 2008     length 4 : 12139
Sat Nov 29 19:47:15 2008     length 5 : 8966
Sat Nov 29 19:47:15 2008     length 6 : 6133
Sat Nov 29 19:47:15 2008     length 7 : 3870
Sat Nov 29 19:47:15 2008     length 9+: 5192
Sat Nov 29 19:47:15 2008  largest cycle: 20 relations
Sat Nov 29 19:47:15 2008  matrix is 90588 x 91084 (24.4 MB) with weight 6028326 (66.18/col)
Sat Nov 29 19:47:15 2008  sparse part has weight 6028326 (66.18/col)
Sat Nov 29 19:47:16 2008  filtering completed in 3 passes
Sat Nov 29 19:47:16 2008  matrix is 85968 x 86032 (23.1 MB) with weight 5709069 (66.36/col)
Sat Nov 29 19:47:16 2008  sparse part has weight 5709069 (66.36/col)
Sat Nov 29 19:47:17 2008  saving the first 48 matrix rows for later
Sat Nov 29 19:47:17 2008  matrix is 85920 x 86032 (14.3 MB) with weight 4507429 (52.39/col)
Sat Nov 29 19:47:17 2008  sparse part has weight 3219825 (37.43/col)
Sat Nov 29 19:47:17 2008  matrix includes 64 packed rows
Sat Nov 29 19:47:17 2008  using block size 34412 for processor cache size 1024 kB
Sat Nov 29 19:47:18 2008  commencing Lanczos iteration
Sat Nov 29 19:47:18 2008  memory use: 13.8 MB
Sat Nov 29 19:48:11 2008  lanczos halted after 1360 iterations (dim = 85918)
Sat Nov 29 19:48:11 2008  recovered 17 nontrivial dependencies
Sat Nov 29 19:48:12 2008  prp45 factor: 957664442926109750412572273548012986189861349
Sat Nov 29 19:48:12 2008  prp53 factor: 19028797420494901463586438810592233217404823016337961
Sat Nov 29 19:48:12 2008  elapsed time 05:44:45

(11·10¹⁴²-17)/3 = 3(6)₁₄₁1_<143> = 53 · 7852775608472349923_<19> · 2209134768103327026461_<22> · C101

C101 = P36 · P65

P36 = 485358917513402248806445046758915291_<36>

P65 = 82165054748679947348480555740015151916804192014196841159896556469_<65>

Number: 36661_142
N=39879542030248730305952505549511479412491993196918291201620186809045469006365085989027975256569067479
  ( 101 digits)
Divisors found:
 r1=485358917513402248806445046758915291 (pp36)
 r2=82165054748679947348480555740015151916804192014196841159896556469 (pp65)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 9.38 hours.
Scaled time: 4.44 units (timescale=0.473).
Factorization parameters were as follows:
name: 36661_142
n: 39879542030248730305952505549511479412491993196918291201620186809045469006365085989027975256569067479
skew: 2082.32
# norm 1.23e+14
c5: 694260
c4: 3381224247
c3: -23801353228510
c2: -9926089970119084
c1: 21900716397827144332
c0: 6005824574800108133350
# alpha -5.93
Y1: 18094922549
Y0: -8950447478689257681
# Murphy_E 3.20e-09
# M 22311532077896101791765456491507583033848276516459723976941369835133769069388259434247533295035075598
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1500001)
Primes: RFBsize:135072, AFBsize:135291, largePrimes:4019335 encountered
Relations: rels:4151080, finalFF:480080
Max relations in full relation-set: 28
Initial matrix: 270451 x 480080 with sparse part having weight 37267957.
Pruned matrix : 158606 x 160022 with weight 13822330.
Total sieving time: 8.40 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.52 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 9.38 hours.
 --------- CPU info (if available) ----------

(11·10¹⁴⁰-17)/3 = 3(6)₁₃₉1_<141> = 19937 · 85087 · 38421740169819971_<17> · C115

C115 = P46 · P70

P46 = 4310159630862946677025293676143401052048035549_<46>

P70 = 1305202882733129400361734021700020844652399098566959423983108286773661_<70>

Number: 36661_140
N=5625632775242278895503641449999420022802034367450748010214474861781619745325974560260325834412849046572994244874889
  ( 115 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=4310159630862946677025293676143401052048035549 (pp46)
 r2=1305202882733129400361734021700020844652399098566959423983108286773661 (pp70)
Version: GGNFS-0.77.1-20060513-k8
Total time: 8.34 hours.
Scaled time: 16.51 units (timescale=1.979).
Factorization parameters were as follows:
name: 36661_140
n: 5625632775242278895503641449999420022802034367450748010214474861781619745325974560260325834412849046572994244874889
m: 10000000000000000000000000000
deg: 5
c5: 11
c0: -17
skew: 1.09
type: snfs
lss: 1
rlim: 1570000
alim: 1570000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1570000/1570000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [785000, 1485001)
Primes: RFBsize:119057, AFBsize:119011, largePrimes:3601073 encountered
Relations: rels:3633049, finalFF:338910
Max relations in full relation-set: 28
Initial matrix: 238133 x 338910 with sparse part having weight 29665582.
Pruned matrix : 207023 x 208277 with weight 14398096.
Total sieving time: 7.81 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.35 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000
total time: 8.34 hours.
 --------- CPU info (if available) ----------

(11·10¹⁴⁵-17)/3 = 3(6)₁₄₄1_<146> = 64879 · 184043 · 5941489091849_<13> · C123

C123 = P55 · P69

P55 = 2408472121547289871373542292920092592599029191777402247_<55>

P69 = 214590776583004188735108491680326897863212133273819137444936868883071_<69>

Number: 36661_145
N=516835902941348589508791970092043654132499949138794905474603269728655539745759808332443712734409744644426855368404775660537
  ( 123 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=2408472121547289871373542292920092592599029191777402247 (pp55)
 r2=214590776583004188735108491680326897863212133273819137444936868883071 (pp69)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 16.26 hours.
Scaled time: 41.87 units (timescale=2.575).
Factorization parameters were as follows:
name: 36661_145
n: 516835902941348589508791970092043654132499949138794905474603269728655539745759808332443712734409744644426855368404775660537
m: 100000000000000000000000000000
deg: 5
c5: 11
c0: -17
skew: 1.09
type: snfs
lss: 1
rlim: 1900000
alim: 1900000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1900000/1900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [950000, 2250001)
Primes: RFBsize:142029, AFBsize:142108, largePrimes:4619974 encountered
Relations: rels:5424522, finalFF:914310
Max relations in full relation-set: 28
Initial matrix: 284202 x 914310 with sparse part having weight 103851334.
Pruned matrix : 196007 x 197492 with weight 31950170.
Total sieving time: 15.71 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.38 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000
total time: 16.26 hours.
 --------- CPU info (if available) ----------

Nov 29, 2008 (3rd)

By Serge Batalov / Msieve-1.38, GMP-ECM, GMP-ECM 6.2.1

(34·10¹⁷¹-7)/9 = 3(7)₁₇₁_<172> = 3 · 117917 · 471774240006282373987_<21> · C146

C146 = P67 · P80

P67 = 1872405935270522689357066301818617011650603001455113126945903699221_<67>

P80 = 12089393077978057072487459330648278729512042675916075725904232034926240219356201_<80>

SNFS difficulty: 173 digits.
Divisors found:
 r1=1872405935270522689357066301818617011650603001455113126945903699221 (pp67)
 r2=12089393077978057072487459330648278729512042675916075725904232034926240219356201 (pp80)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.561).
Factorization parameters were as follows:
n: 22636251353024486990443569623606952139781589234140446733973661409451373214880172157489920365589050835529237199414251961233190439964627012965219421
m: 20000000000000000000000000000000000
deg: 5
c5: 85
c0: -56
skew: 0.92
type: snfs
lss: 1
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2700000, 6600001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1025183 x 1025425
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,5400000,5400000,27,27,52,52,2.4,2.4,100000
total time: 60.00 hours.

(11·10¹³⁷-17)/3 = 3(6)₁₃₆1_<138> = 457 · 25282613101_<11> · 70540502984696358345035712479_<29> · C96

C96 = P30 · P67

P30 = 225068055414946500455101512413_<30>

P67 = 1998853021220465571838973633604944432837054563410179737705368297499_<67>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3848341359
Step 1 took 20041ms
Step 2 took 8402ms
********** Factor found in step 2: 225068055414946500455101512413
Found probable prime factor of 30 digits: 225068055414946500455101512413
Probable prime cofactor 1998853021220465571838973633604944432837054563410179737705368297499 has 67 digits

(11·10¹⁷⁸-17)/3 = 3(6)₁₇₇1_<179> = 419 · 875323 · 160850805730055940026013323_<27> · C144

C144 = P32 · P113

P32 = 25564389165499286775537881549053_<32>

P113 = 24312544101470344889522583008595898850613862866972797747589406600656397524145120318815543370098395903890481926987_<113>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4102962534
Step 1 took 19473ms
Step 2 took 13973ms
********** Factor found in step 2: 25564389165499286775537881549053
Found probable prime factor of 32 digits: 25564389165499286775537881549053
Probable prime cofactor 24312544101470344889522583008595898850613862866972797747589406600656397524145120318815543370098395903890481926987 has 113 digits

(11·10¹¹⁹-17)/3 = 3(6)₁₁₈1_<120> = 95339 · 106454485737497_<15> · C101

C101 = P33 · P69

P33 = 201591097540583059899592638756229_<33>

P69 = 179211354572697613407122682853275301429002320329115019253778195188123_<69>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1995292405
Step 1 took 17977ms
Step 2 took 8827ms
********** Factor found in step 2: 201591097540583059899592638756229
Found probable prime factor of 33 digits: 201591097540583059899592638756229
Probable prime cofactor 179211354572697613407122682853275301429002320329115019253778195188123 has 69 digits

(11·10¹⁹⁹-17)/3 = 3(6)₁₉₈1_<200> = 47 · 167 · 809 · 897231271 · C184

C184 = P33 · P152

P33 = 620849510886121014996653223133973_<33>

P152 = 10366158259157309433389410520769455172640438054800073452130936958194069123240087142681724227125048990871767365225139184688088979862324552054539230787287_<152>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3437716281
Step 1 took 29551ms
Step 2 took 19011ms
********** Factor found in step 2: 620849510886121014996653223133973
Found probable prime factor of 33 digits: 620849510886121014996653223133973
Probable prime cofactor 10366158259157309433389410520769455172640438054800073452130936958194069123240087142681724227125048990871767365225139184688088979862324552054539230787287 has 152 digits

(11·10¹²⁶-17)/3 = 3(6)₁₂₅1_<127> = 2387939232349009_<16> · C112

C112 = P53 · P60

P53 = 14087763858732627321101608034056487645098264034924687_<53>

P60 = 108994879691177420849768695576009997842287982075496976611867_<60>

SNFS difficulty: 127 digits.
Divisors found:
 r1=14087763858732627321101608034056487645098264034924687 (pp53)
 r2=108994879691177420849768695576009997842287982075496976611867 (pp60)
Version: Msieve-1.38
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.554).
Factorization parameters were as follows:
n: 1535494126900280097634966453816017651318018197457135481071718189164248955722438293136152218641345776503775460629
m: 10000000000000000000000000
deg: 5
c5: 110
c0: -17
skew: 0.69
type: snfs
lss: 1
rlim: 980000
alim: 980000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 980000/980000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [490000, 740001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 130283 x 130515
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,980000,980000,26,26,49,49,2.4,2.4,50000
total time: 2.00 hours.

(11·10¹⁸³-17)/3 = 3(6)₁₈₂1_<184> = 7² · C182

C182 = P31 · P152

P31 = 3223571118646144467773535158267_<31>

P152 = 23213364687364694423071285117959366924827885485071481831459700304705661130344587728525748337616731300987146031291571492942419541892201351763828235946767_<152>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1551405898
Step 1 took 28124ms
Step 2 took 18519ms
********** Factor found in step 2: 3223571118646144467773535158267
Found probable prime factor of 31 digits: 3223571118646144467773535158267
Probable prime cofactor 23213364687364694423071285117959366924827885485071481831459700304705661130344587728525748337616731300987146031291571492942419541892201351763828235946767 has 152 digits

(11·10¹⁹⁷-17)/3 = 3(6)₁₉₆1_<198> = 155539 · 23359738123_<11> · C183

C183 = P38 · P145

P38 = 27255285980819546400270342287438245231_<38>

P145 = 3702656423765222191449953291983165896174333193450106467327364998558250919653147210340654247030518342692904270634997845089652018632377252248552123_<145>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2963924375
Step 1 took 30017ms
Step 2 took 18759ms
********** Factor found in step 2: 27255285980819546400270342287438245231
Found probable prime factor of 38 digits: 27255285980819546400270342287438245231
Probable prime cofactor 3702656423765222191449953291983165896174333193450106467327364998558250919653147210340654247030518342692904270634997845089652018632377252248552123 has 145 digits

(11·10¹⁶²-17)/3 = 3(6)₁₆₁1_<163> = 229 · 6461041 · 6240128181383599_<16> · 87674584682570693_<17> · C121

C121 = P33 · P88

P33 = 731052435518075457940546324433539_<33>

P88 = 6196089676534327845925392116638898810470739385870543386025115721853192452315915758888913_<88>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2785932908
Step 1 took 22539ms
Step 2 took 10481ms
********** Factor found in step 2: 731052435518075457940546324433539
Found probable prime factor of 33 digits: 731052435518075457940546324433539
Probable prime cofactor 6196089676534327845925392116638898810470739385870543386025115721853192452315915758888913 has 88 digits

(11·10¹³⁶-17)/3 = 3(6)₁₃₅1_<137> = 31 · C136

C136 = P36 · P45 · P56

P36 = 110448053390064403764987276605352253_<36>

P45 = 169097178743797369834770845207818629319141307_<45>

P56 = 63330848811647738103769089974633221625010035821186883861_<56>

SNFS difficulty: 137 digits.
Divisors found:
 r1=110448053390064403764987276605352253 (pp36)
 r2=169097178743797369834770845207818629319141307 (pp45)
 r3=63330848811647738103769089974633221625010035821186883861 (pp56)
Version: Msieve-1.38
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.558).
Factorization parameters were as follows:
n: 1182795698924731182795698924731182795698924731182795698924731182795698924731182795698924731182795698924731182795698924731182795698924731
m: 1000000000000000000000000000
deg: 5
c5: 110
c0: -17
skew: 0.69
type: snfs
lss: 1
rlim: 1350000
alim: 1350000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1350000/1350000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [675000, 1200001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 204242 x 204484
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1350000,1350000,26,26,49,49,2.3,2.3,75000
total time: 2.40 hours.

(11·10¹⁷⁷-17)/3 = 3(6)₁₇₆1_<178> = 7 · 103 · 151 · C173

C173 = P31 · P142

P31 = 5556832887851812076162476070701_<31>

P142 = 6060826921814296872914390472209730923182376228115283211788582114118810150036488088797677147810237162263095022865241892934485730623618870717791_<142>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3024729889
Step 1 took 24813ms
Step 2 took 17166ms
********** Factor found in step 2: 5556832887851812076162476070701
Found probable prime factor of 31 digits: 5556832887851812076162476070701
Probable prime cofactor 6060826921814296872914390472209730923182376228115283211788582114118810150036488088797677147810237162263095022865241892934485730623618870717791 has 142 digits

(11·10¹⁷¹-17)/3 = 3(6)₁₇₀1_<172> = 7 · 83 · 89 · 37879493 · C160

C160 = P38 · C122

P38 = 83385999899891719865878511313987222461_<38>

C122 = [22449568247593753184083167533291975290884854540034547605076554357224725377782546501707146485392713868517979960233913402073_<122>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=718240080
Step 1 took 24841ms
Step 2 took 16811ms
********** Factor found in step 2: 83385999899891719865878511313987222461
Found probable prime factor of 38 digits: 83385999899891719865878511313987222461
Composite cofactor 22449568247593753184083167533291975290884854540034547605076554357224725377782546501707146485392713868517979960233913402073 has 122 digits

(11·10¹⁷⁵-17)/3 = 3(6)₁₇₄1_<176> = 29201 · 2933501 · 588474961 · 32750153572057_<14> · C143

C143 = P40 · P104

P40 = 1109870810744795934280775949391017001109_<40>

P104 = 20011226434218264569802564557860035959581832711691655219245543666648061801344742292178573885646208347277_<104>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2854008978
Step 1 took 19162ms
Step 2 took 13841ms
********** Factor found in step 2: 1109870810744795934280775949391017001109
Found probable prime factor of 40 digits: 1109870810744795934280775949391017001109
Probable prime cofactor 20011226434218264569802564557860035959581832711691655219245543666648061801344742292178573885646208347277 has 104 digits

(11·10¹⁶⁵-17)/3 = 3(6)₁₆₄1_<166> = 7 · 179 · 649915076007329393_<18> · 2371711292610209065707512288131_<31> · C115

C115 = P32 · P83

P32 = 26297757323118614671519055263267_<32>

P83 = 72191025851228490858060062036302772473383497526433611076929831488505843922709835817_<83>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2265542806
Step 1 took 12957ms
Step 2 took 11043ms
********** Factor found in step 2: 26297757323118614671519055263267
Found probable prime factor of 32 digits: 26297757323118614671519055263267
Probable prime cofactor 72191025851228490858060062036302772473383497526433611076929831488505843922709835817 has 83 digits

(11·10¹⁵⁶-17)/3 = 3(6)₁₅₅1_<157> = 1619 · 2520183811697_<13> · C141

C141 = P39 · P103

P39 = 384665774755265922540245230014640845803_<39>

P103 = 2336193530902535449760773143184500147895336647884600817095444483766385399109723704479196726601653355909_<103>

SNFS difficulty: 157 digits.
Divisors found:
 r1=384665774755265922540245230014640845803 (pp39)
 r2=2336193530902535449760773143184500147895336647884600817095444483766385399109723704479196726601653355909 (pp103)
Version: Msieve-1.38
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.316).
Factorization parameters were as follows:
n: 898653694542864079694322256023889802504426131617625176516182040256382815496843564561485283796472486632464351154376228436806719058721147899927
m: 10000000000000000000000000000000
deg: 5
c5: 110
c0: -17
skew: 0.69
type: snfs
lss: 1
rlim: 2900000
alim: 2900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 2900000/2900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1450000, 2350001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 538024 x 538266
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,52,52,2.4,2.4,100000
total time: 16.00 hours.

Nov 29, 2008 (2nd)

By Erik Branger / GGNFS, Msieve

(11·10¹⁰⁹-17)/3 = 3(6)₁₀₈1_<110> = 103 · C108

C108 = P32 · P76

P32 = 55686128876513198408165347351459_<32>

P76 = 6392742002332402976749775654819971481286309835724565111795563996899029411793_<76>

Number: 36661_109
N=355987055016181229773462783171521035598705501618122977346278317152103559870550161812297734627831715210355987
  ( 108 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=55686128876513198408165347351459
 r2=6392742002332402976749775654819971481286309835724565111795563996899029411793
Version: 
Total time: 1.33 hours.
Scaled time: 1.04 units (timescale=0.784).
Factorization parameters were as follows:
n: 355987055016181229773462783171521035598705501618122977346278317152103559870550161812297734627831715210355987
m: 10000000000000000000000
deg: 5
c5: 11
c0: -170
skew: 1.73
type: snfs
lss: 1
rlim: 500000
alim: 500000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [250000, 400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 46578 x 46805
Total sieving time: 1.33 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000
total time: 1.33 hours.
 --------- CPU info (if available) ----------

(11·10¹¹⁰-17)/3 = 3(6)₁₀₉1_<111> = 19 · 43 · 359 · 3413 · 6037 · C98

C98 = P32 · P66

P32 = 80031387200864474276826335774639_<32>

P66 = 758118538179302738564118749660544653553657027889141216006719903893_<66>

Number: 36661_110
N=60673278273181134471086551243482531992281681325714658104638326655668739103398066074480921786769627
  ( 98 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=80031387200864474276826335774639
 r2=758118538179302738564118749660544653553657027889141216006719903893
Version: 
Total time: 0.92 hours.
Scaled time: 0.72 units (timescale=0.792).
Factorization parameters were as follows:
n: 60673278273181134471086551243482531992281681325714658104638326655668739103398066074480921786769627
m: 10000000000000000000000
deg: 5
c5: 11
c0: -17
skew: 1.09
type: snfs
lss: 1
rlim: 500000
alim: 500000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [250000, 350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 49726 x 49945
Total sieving time: 0.92 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000
total time: 0.92 hours.
 --------- CPU info (if available) ----------

(11·10¹²³-17)/3 = 3(6)₁₂₂1_<124> = 7 · 23070065599136107_<17> · C107

C107 = P42 · P65

P42 = 668886617714639215408779843398589318361601_<42>

P65 = 33944706176884080583579775103068072235776993030794292237369985689_<65>

Number: 36661_123
N=22705159703973214452236063687756023515217752056680576539032965607066094137200662015975910403773494297128089
  ( 107 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=668886617714639215408779843398589318361601
 r2=33944706176884080583579775103068072235776993030794292237369985689
Version: 
Total time: 3.21 hours.
Scaled time: 2.53 units (timescale=0.787).
Factorization parameters were as follows:
n: 22705159703973214452236063687756023515217752056680576539032965607066094137200662015975910403773494297128089
m: 5000000000000000000000000
deg: 5
c5: 88
c0: -425
skew: 1.37
type: snfs
lss: 1
rlim: 860000
alim: 860000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 860000/860000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [430000, 780001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 136821 x 137069
Total sieving time: 3.21 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,860000,860000,26,26,46,46,2.3,2.3,50000
total time: 3.21 hours.
 --------- CPU info (if available) ----------

(11·10¹³²-17)/3 = 3(6)₁₃₁1_<133> = 199 · C131

C131 = P59 · P72

P59 = 23458969553533159486261373436846041377784456048254245377789_<59>

P72 = 785433503141268669465977030069961182458200542220187279043681975728135151_<72>

Number: 36661_132
N=18425460636515912897822445561139028475711892797319932998324958123953098827470686767169179229480737018425460636515912897822445561139
  ( 131 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=23458969553533159486261373436846041377784456048254245377789
 r2=785433503141268669465977030069961182458200542220187279043681975728135151
Version: 
Total time: 4.67 hours.
Scaled time: 3.69 units (timescale=0.789).
Factorization parameters were as follows:
n: 18425460636515912897822445561139028475711892797319932998324958123953098827470686767169179229480737018425460636515912897822445561139
m: 200000000000000000000000000
deg: 5
c5: 275
c0: -136
skew: 0.87
type: snfs
lss: 1
rlim: 1200000
alim: 1200000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [600000, 1050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 181650 x 181898
Total sieving time: 4.67 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,47,47,2.3,2.3,75000
total time: 4.67 hours.
 --------- CPU info (if available) ----------

Nov 29, 2008

By Robert Backstrom / GMP-ECM, Msieve, GGNFS

(11·10¹⁰¹-17)/3 = 3(6)₁₀₀1_<102> = 138913373 · C94

C94 = P32 · P63

P32 = 15362996616432738906443983605163_<32>

P63 = 171811187227657721764594149916169855418000979165505985718980539_<63>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 2639534688043797386351468599547047688969921324037439265596600743879904684674719306302256922857 (94 digits)
Using B1=1200000, B2=1426326730, polynomial Dickson(6), sigma=1460276515
Step 1 took 7406ms
Step 2 took 3875ms
********** Factor found in step 2: 15362996616432738906443983605163
Found probable prime factor of 32 digits: 15362996616432738906443983605163
Probable prime cofactor 171811187227657721764594149916169855418000979165505985718980539 has 63 digits

(11·10¹¹⁶-17)/3 = 3(6)₁₁₅1_<117> = 53 · 3461 · 84201513116637056621653_<23> · C89

C89 = P35 · P54

P35 = 73977684816291194925607695803441513_<35>

P54 = 320902669571158779992693858038181395877039064352464353_<54>

Sat Nov 29 04:02:03 2008  
Sat Nov 29 04:02:03 2008  
Sat Nov 29 04:02:03 2008  Msieve v. 1.38
Sat Nov 29 04:02:03 2008  random seeds: 46a032e0 bae8cfdf
Sat Nov 29 04:02:03 2008  factoring 23739636546241623339183677581442267087364438127319553630046719804948907173444660052886089 (89 digits)
Sat Nov 29 04:02:04 2008  searching for 15-digit factors
Sat Nov 29 04:02:04 2008  commencing quadratic sieve (89-digit input)
Sat Nov 29 04:02:05 2008  using multiplier of 1
Sat Nov 29 04:02:05 2008  using 64kb Opteron sieve core
Sat Nov 29 04:02:05 2008  sieve interval: 15 blocks of size 65536
Sat Nov 29 04:02:05 2008  processing polynomials in batches of 7
Sat Nov 29 04:02:05 2008  using a sieve bound of 1542239 (58667 primes)
Sat Nov 29 04:02:05 2008  using large prime bound of 123379120 (26 bits)
Sat Nov 29 04:02:05 2008  using double large prime bound of 366635860574400 (42-49 bits)
Sat Nov 29 04:02:05 2008  using trial factoring cutoff of 49 bits
Sat Nov 29 04:02:05 2008  polynomial 'A' values have 11 factors
Sat Nov 29 04:46:12 2008  58992 relations (15923 full + 43069 combined from 620929 partial), need 58763
Sat Nov 29 04:46:12 2008  begin with 636852 relations
Sat Nov 29 04:46:13 2008  reduce to 142375 relations in 12 passes
Sat Nov 29 04:46:13 2008  attempting to read 142375 relations
Sat Nov 29 04:46:14 2008  recovered 142375 relations
Sat Nov 29 04:46:14 2008  recovered 117564 polynomials
Sat Nov 29 04:46:14 2008  attempting to build 58992 cycles
Sat Nov 29 04:46:14 2008  found 58992 cycles in 5 passes
Sat Nov 29 04:46:14 2008  distribution of cycle lengths:
Sat Nov 29 04:46:14 2008     length 1 : 15923
Sat Nov 29 04:46:14 2008     length 2 : 11484
Sat Nov 29 04:46:14 2008     length 3 : 10494
Sat Nov 29 04:46:14 2008     length 4 : 7817
Sat Nov 29 04:46:14 2008     length 5 : 5387
Sat Nov 29 04:46:14 2008     length 6 : 3465
Sat Nov 29 04:46:14 2008     length 7 : 2026
Sat Nov 29 04:46:14 2008     length 9+: 2396
Sat Nov 29 04:46:14 2008  largest cycle: 16 relations
Sat Nov 29 04:46:14 2008  matrix is 58667 x 58992 (14.0 MB) with weight 3438927 (58.29/col)
Sat Nov 29 04:46:14 2008  sparse part has weight 3438927 (58.29/col)
Sat Nov 29 04:46:15 2008  filtering completed in 3 passes
Sat Nov 29 04:46:15 2008  matrix is 54349 x 54413 (13.0 MB) with weight 3197994 (58.77/col)
Sat Nov 29 04:46:15 2008  sparse part has weight 3197994 (58.77/col)
Sat Nov 29 04:46:15 2008  saving the first 48 matrix rows for later
Sat Nov 29 04:46:15 2008  matrix is 54301 x 54413 (8.9 MB) with weight 2565338 (47.15/col)
Sat Nov 29 04:46:15 2008  sparse part has weight 2018746 (37.10/col)
Sat Nov 29 04:46:15 2008  matrix includes 64 packed rows
Sat Nov 29 04:46:15 2008  using block size 21765 for processor cache size 1024 kB
Sat Nov 29 04:46:16 2008  commencing Lanczos iteration
Sat Nov 29 04:46:16 2008  memory use: 8.4 MB
Sat Nov 29 04:46:35 2008  lanczos halted after 860 iterations (dim = 54297)
Sat Nov 29 04:46:35 2008  recovered 13 nontrivial dependencies
Sat Nov 29 04:46:35 2008  prp35 factor: 73977684816291194925607695803441513
Sat Nov 29 04:46:35 2008  prp54 factor: 320902669571158779992693858038181395877039064352464353
Sat Nov 29 04:46:35 2008  elapsed time 00:44:32

(11·10¹³⁰-17)/3 = 3(6)₁₂₉1_<131> = 83 · 109 · 26529247 · 80947637321_<11> · 381304712411819489_<18> · C91

C91 = P35 · P57

P35 = 26119835504853257224991747510790013_<35>

P57 = 189493854350681751333427226811128589700254398242977884057_<57>

Sat Nov 29 04:56:17 2008  
Sat Nov 29 04:56:17 2008  
Sat Nov 29 04:56:17 2008  Msieve v. 1.38
Sat Nov 29 04:56:17 2008  random seeds: c7f8ab60 3c0d8e28
Sat Nov 29 04:56:17 2008  factoring 4949548304820429075400004912874089555561546276186079877477197022930758447185728135187522741 (91 digits)
Sat Nov 29 04:56:17 2008  searching for 15-digit factors
Sat Nov 29 04:56:18 2008  commencing quadratic sieve (91-digit input)
Sat Nov 29 04:56:18 2008  using multiplier of 29
Sat Nov 29 04:56:18 2008  using 64kb Opteron sieve core
Sat Nov 29 04:56:18 2008  sieve interval: 18 blocks of size 65536
Sat Nov 29 04:56:18 2008  processing polynomials in batches of 6
Sat Nov 29 04:56:18 2008  using a sieve bound of 1716263 (64706 primes)
Sat Nov 29 04:56:18 2008  using large prime bound of 164761248 (27 bits)
Sat Nov 29 04:56:18 2008  using double large prime bound of 617076512625696 (42-50 bits)
Sat Nov 29 04:56:18 2008  using trial factoring cutoff of 50 bits
Sat Nov 29 04:56:18 2008  polynomial 'A' values have 12 factors
Sat Nov 29 06:06:22 2008  65132 relations (17203 full + 47929 combined from 761920 partial), need 64802
Sat Nov 29 06:06:23 2008  begin with 779123 relations
Sat Nov 29 06:06:24 2008  reduce to 162114 relations in 10 passes
Sat Nov 29 06:06:24 2008  attempting to read 162114 relations
Sat Nov 29 06:06:26 2008  recovered 162114 relations
Sat Nov 29 06:06:26 2008  recovered 141428 polynomials
Sat Nov 29 06:06:27 2008  attempting to build 65132 cycles
Sat Nov 29 06:06:27 2008  found 65132 cycles in 5 passes
Sat Nov 29 06:06:27 2008  distribution of cycle lengths:
Sat Nov 29 06:06:27 2008     length 1 : 17203
Sat Nov 29 06:06:27 2008     length 2 : 12059
Sat Nov 29 06:06:27 2008     length 3 : 11019
Sat Nov 29 06:06:27 2008     length 4 : 8801
Sat Nov 29 06:06:27 2008     length 5 : 6314
Sat Nov 29 06:06:27 2008     length 6 : 4210
Sat Nov 29 06:06:27 2008     length 7 : 2421
Sat Nov 29 06:06:27 2008     length 9+: 3105
Sat Nov 29 06:06:27 2008  largest cycle: 19 relations
Sat Nov 29 06:06:27 2008  matrix is 64706 x 65132 (15.8 MB) with weight 3894254 (59.79/col)
Sat Nov 29 06:06:27 2008  sparse part has weight 3894254 (59.79/col)
Sat Nov 29 06:06:28 2008  filtering completed in 3 passes
Sat Nov 29 06:06:28 2008  matrix is 60808 x 60872 (14.9 MB) with weight 3650160 (59.96/col)
Sat Nov 29 06:06:28 2008  sparse part has weight 3650160 (59.96/col)
Sat Nov 29 06:06:28 2008  saving the first 48 matrix rows for later
Sat Nov 29 06:06:28 2008  matrix is 60760 x 60872 (8.7 MB) with weight 2777885 (45.63/col)
Sat Nov 29 06:06:28 2008  sparse part has weight 1912037 (31.41/col)
Sat Nov 29 06:06:28 2008  matrix includes 64 packed rows
Sat Nov 29 06:06:28 2008  using block size 24348 for processor cache size 1024 kB
Sat Nov 29 06:06:29 2008  commencing Lanczos iteration
Sat Nov 29 06:06:29 2008  memory use: 8.9 MB
Sat Nov 29 06:06:50 2008  lanczos halted after 962 iterations (dim = 60758)
Sat Nov 29 06:06:50 2008  recovered 16 nontrivial dependencies
Sat Nov 29 06:06:51 2008  prp35 factor: 26119835504853257224991747510790013
Sat Nov 29 06:06:51 2008  prp57 factor: 189493854350681751333427226811128589700254398242977884057
Sat Nov 29 06:06:51 2008  elapsed time 01:10:34

(11·10¹²⁸-17)/3 = 3(6)₁₂₇1_<129> = 19 · C128

C128 = P64 · P65

P64 = 1090272986019580928374762912685367956622743722256057747557165627_<64>

P65 = 17700379502650997404470878861782680291067945187883910993616729797_<65>

Number: n
N=19298245614035087719298245614035087719298245614035087719298245614035087719298245614035087719298245614035087719298245614035087719
  ( 128 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=1090272986019580928374762912685367956622743722256057747557165627 (pp64)
 r2=17700379502650997404470878861782680291067945187883910993616729797 (pp65)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.84 hours.
Scaled time: 5.16 units (timescale=1.816).
Factorization parameters were as follows:
name: KA_3_6_127_1
n: 19298245614035087719298245614035087719298245614035087719298245614035087719298245614035087719298245614035087719298245614035087719
type: snfs
skew: 2.74
deg: 5
c5: 11
c0: -1700
m: 100000000000000000000000000
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [100000, 550001)
Primes: RFBsize:63951, AFBsize:63749, largePrimes:6492214 encountered
Relations: rels:5659445, finalFF:184434
Max relations in full relation-set: 48
Initial matrix: 127767 x 184434 with sparse part having weight 26352058.
Pruned matrix : 116709 x 117411 with weight 12205227.
Total sieving time: 2.63 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.09 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,28,28,56,56,2.5,2.5,50000
total time: 2.84 hours.
 --------- CPU info (if available) ----------

(10¹⁷⁰+11)/3 = (3)₁₆₉7_<170> = 37 · 163 · 1291 · 23038909286259871_<17> · C147

C147 = P47 · P101

P47 = 11678389683627973847213584321368447993233911399_<47>

P101 = 15911762839346654192692129977862432931562688321822699857420110352345615549508686305420162237407946893_<101>

Number: n
N=185823766991360923710679129196544755596402591828367442331733798414239140090653102165527343177897437971975078078955898882605783639735498740459333307
  ( 147 digits)
SNFS difficulty: 170 digits.
Divisors found:

Sat Nov 29 17:02:34 2008  prp47 factor: 11678389683627973847213584321368447993233911399
Sat Nov 29 17:02:34 2008  prp101 factor: 15911762839346654192692129977862432931562688321822699857420110352345615549508686305420162237407946893
Sat Nov 29 17:02:34 2008  elapsed time 05:16:03 (Msieve 1.38)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 46.56 hours.
Scaled time: 60.72 units (timescale=1.304).
Factorization parameters were as follows:
name: KA_3_169_7
n: 185823766991360923710679129196544755596402591828367442331733798414239140090653102165527343177897437971975078078955898882605783639735498740459333307
type: snfs
skew: 1.62
deg: 5
c5: 1
c0: 11
m: 10000000000000000000000000000000000
rlim: 6000000
alim: 6000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 1900001)
Primes: RFBsize:412849, AFBsize:412887, largePrimes:14693738 encountered
Relations: rels:13330852, finalFF:847863
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 46.08 hours.
Total relation processing time: 0.48 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,56,56,2.5,2.5,100000
total time: 46.56 hours.
 --------- CPU info (if available) ----------

Nov 28, 2008 (8th)

By Erik Branger / GGNFS; Msieve

(32·10¹⁴⁹+31)/9 = 3(5)₁₄₈9_<150> = 23 · 1192127 · 3454681 · 5814839 · C129

C129 = P44 · P86

P44 = 36079668826573699943490114729420937250109313_<44>

P86 = 17891589284599087776495371368847733054140180147919739353006755447057290876475925057937_<86>

Number: 35559_149
N=645522616169409752919180544786267715281071636514574448021532325578189047306661052443515232321172943154564141276747304249108267281
  ( 129 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=36079668826573699943490114729420937250109313
 r2=17891589284599087776495371368847733054140180147919739353006755447057290876475925057937
Version: 
Total time: 24.26 hours.
Scaled time: 19.26 units (timescale=0.794).
Factorization parameters were as follows:
n: 645522616169409752919180544786267715281071636514574448021532325578189047306661052443515232321172943154564141276747304249108267281
m: 1000000000000000000000000000000
deg: 5
c5: 16
c0: 155
skew: 1.57
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 332704 x 332952
Total sieving time: 24.26 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 24.26 hours.
 --------- CPU info (if available) ----------

Nov 28, 2008 (7th)

By Sinkiti Sibata / GGNFS

(32·10¹⁵⁸+31)/9 = 3(5)₁₅₇9_<159> = 1847 · 3271 · 782689767414187_<15> · C137

C137 = P57 · P81

P57 = 728383830613617901512898035711531200163111814922121405509_<57>

P81 = 103230986344316631452156190293703543504210710933180145720843938503614168819071729_<81>

Number: 35559_158
N=75191781271495427961526192435963176611571086648507863294028382067951511505660654447069167461791164580416202384221687140995631470166755061
  ( 137 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=728383830613617901512898035711531200163111814922121405509 (pp57)
 r2=103230986344316631452156190293703543504210710933180145720843938503614168819071729 (pp81)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 61.27 hours.
Scaled time: 61.94 units (timescale=1.011).
Factorization parameters were as follows:
name: 35559_158
n: 75191781271495427961526192435963176611571086648507863294028382067951511505660654447069167461791164580416202384221687140995631470166755061
m: 40000000000000000000000000000000
deg: 5
c5: 125
c0: 124
skew: 1.00
type: snfs
lss: 1
rlim: 3300000
alim: 3300000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3300000/3300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1650000, 3350001)
Primes: RFBsize:236900, AFBsize:237133, largePrimes:10009512 encountered
Relations: rels:11723424, finalFF:1603464
Max relations in full relation-set: 28
Initial matrix: 474099 x 1603464 with sparse part having weight 209003057.
Pruned matrix : 327083 x 329517 with weight 65552425.
Total sieving time: 59.47 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 1.51 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3300000,3300000,27,27,51,51,2.4,2.4,100000
total time: 61.27 hours.
 --------- CPU info (if available) ----------

(32·10¹⁵⁵+13)/9 = 3(5)₁₅₄7_<156> = 3 · 9745711663_<10> · 836420183209442561075511309839_<30> · C116

C116 = P41 · P75

P41 = 23094872044969571779279121773911112181383_<41>

P75 = 629553425817664516608346615262883641525165764299729025538826136158686426449_<75>

Number: 35557_155
N=14539455814731205321210177525875969087182313619367490212466311977932541637996102085909142345349193136322821376598967
  ( 116 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=23094872044969571779279121773911112181383 (pp41)
 r2=629553425817664516608346615262883641525165764299729025538826136158686426449 (pp75)
Version: GGNFS-0.77.1-20060513-k8
Total time: 25.53 hours.
Scaled time: 50.99 units (timescale=1.997).
Factorization parameters were as follows:
name: 35557_155
n: 14539455814731205321210177525875969087182313619367490212466311977932541637996102085909142345349193136322821376598967
m: 20000000000000000000000000000000
deg: 5
c5: 1
c0: 13
skew: 1.67
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2100001)
Primes: RFBsize:203362, AFBsize:202632, largePrimes:7931710 encountered
Relations: rels:8033044, finalFF:597631
Max relations in full relation-set: 28
Initial matrix: 406058 x 597631 with sparse part having weight 61275731.
Pruned matrix : 323038 x 325132 with weight 32326940.
Total sieving time: 23.64 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.53 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 25.53 hours.
 --------- CPU info (if available) ----------

Nov 28, 2008 (6th)

By Jo Yeong Uk / GGNFS

(32·10¹⁵⁷+31)/9 = 3(5)₁₅₆9_<158> = 3² · 13 · 3343 · 314771 · 107802232591_<12> · 11902574766281436363312409_<26> · C111

C111 = P47 · P64

P47 = 34721041154083197424198540840683236213110001909_<47>

P64 = 6482299664938003634923870800254260917289099912150023501829586029_<64>

Number: 35559_157
N=225072193439412145701799215959772861124655915684613894776517073007926147419114083683529204169407787632869729361
  ( 111 digits)
Divisors found:
 r1=34721041154083197424198540840683236213110001909 (pp47)
 r2=6482299664938003634923870800254260917289099912150023501829586029 (pp64)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 15.38 hours.
Scaled time: 36.67 units (timescale=2.384).
Factorization parameters were as follows:
name: 35559_157
n: 225072193439412145701799215959772861124655915684613894776517073007926147419114083683529204169407787632869729361
skew: 28795.49
# norm 1.13e+16
c5: 46800
c4: 1274979120
c3: -523803857097587
c2: -954455472874104530
c1: 68225153952563267555272
c0: 198863934818240337723728640
# alpha -6.89
Y1: 444567509023
Y0: -1369034617122522968939
# Murphy_E 9.23e-10
# M 11475828137743923857118331731015828543479728004221583302539558888654103715022607496554975749211705474898107198
type: gnfs
rlim: 2100000
alim: 2100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1050000, 1950001)
Primes: RFBsize:155805, AFBsize:155375, largePrimes:8686731 encountered
Relations: rels:8631688, finalFF:456376
Max relations in full relation-set: 28
Initial matrix: 311259 x 456376 with sparse part having weight 50491100.
Pruned matrix : 250053 x 251673 with weight 27602004.
Polynomial selection time: 0.84 hours.
Total sieving time: 13.96 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.35 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000
total time: 15.38 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Nov 28, 2008 (5th)

By Tyler Cadigan / GGNFS, Msieve

(43·10¹⁹²-7)/9 = 4(7)₁₉₂_<193> = 4451 · 5827 · 940903127 · 12835951153_<11> · 2701303725402363678544195517_<28> · C139

C139 = P54 · P86

P54 = 135427060717739009170914297860127597169429975010164729_<54>

P86 = 41693801642367404962648784775123910677444951042004634952791915483103489484160391387347_<86>

Number: 47777_192
N=5646469006574256973282355219285673016714439033035136874206463329954028779275555920105596499863540512205308966627980373468257697311316283963
  ( 139 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=135427060717739009170914297860127597169429975010164729
 r2=41693801642367404962648784775123910677444951042004634952791915483103489484160391387347
Version: 
Total time: 593.99 hours.
Scaled time: 1495.67 units (timescale=2.518).
Factorization parameters were as follows:
n: 5646469006574256973282355219285673016714439033035136874206463329954028779275555920105596499863540512205308966627980373468257697311316283963
m: 500000000000000000000000000000000000000
deg: 5
c5: 172
c0: -875
Y0: 500000000000000000000000000000000000000
Y1: -1
skew: 1.38
type: snfs
lss: 1
rlim: 12800000
alim: 12800000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
qintsize: 1000000

Factor base limits: 12800000/12800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6400000, 1
)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2014456 x 2014704
Total sieving time: 593.99 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,195,5,0,0,0,0,0,0,0,0,12800000,12800000,28,28,55,55,2.5,2.5,100000
total time: 593.99 hours.
 --------- CPU info (if available) ----------

Nov 28, 2008 (4th)

By Serge Batalov / Msieve-1.38+pol51 gnfs

8·10¹⁸⁵+9 = 8(0)₁₈₄9_<186> = 7 · 24329 · 53381 · 25502165263849_<14> · 1303028394848660857467715486468010946754987_<43> · C121

C121 = P38 · P84

P38 = 11958203612381011725704592874030579567_<38>

P84 = 221454293090384742218717863326746087344454398748013997486958446978047338608032823703_<84>

Number: 80009_185
N=2648195527610722149244619035624215921962390457850886740531905304699190651782516458062408766925167070534368118892625076601
  ( 121 digits)
Divisors found:
 r1=11958203612381011725704592874030579567 (pp38)
 r2=221454293090384742218717863326746087344454398748013997486958446978047338608032823703 (pp84)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.315).
Factorization parameters were as follows:
name: 80009_185
n: 2648195527610722149244619035624215921962390457850886740531905304699190651782516458062408766925167070534368118892625076601
skew: 97324.20
# norm 6.02e+16
c5: 31560
c4: -20257094952
c3: -869302950855308
c2: 173746730595733330327
c1: 2705646423516967148423142
c0: -146634980995403207875729446336
# alpha -6.61
Y1: 4019354345677
Y0: -153025594366465211457007
# Murphy_E 2.66e-10
# M 2084414786921268954617093831981252894697800350894014333202808952118001393556414218128011869192530578591410857486809023958
type: gnfs
rlim: 5200000
alim: 5200000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5200000/5200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [2600000, 4700001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 699597 x 699839
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 1.70 hours.
Time per square root: 0.50 hours.
Prototype def-par.txt line would be:
gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5200000,5200000,27,27,52,52,2.5,2.5,100000
total time: 70.00 hours.

(32·10¹⁶³+31)/9 = 3(5)₁₆₂9_<164> = 3 · 13 · 33533 · 13815635357301430349027_<23> · C136

C136 = P52 · P84

P52 = 7298831326676946646025396317875694511838180349179983_<52>

P84 = 269616373803723615329708115913185862970918638097728700348675818639575345943982545577_<84>

SNFS difficulty: 165 digits.
Divisors found:
 r1=7298831326676946646025396317875694511838180349179983 (pp52)
 r2=269616373803723615329708115913185862970918638097728700348675818639575345943982545577 (pp84)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.310).
Factorization parameters were as follows:
n: 1967884435303659598974407641705651605895826214331689001349496161987105599499654836345057185351290971556047757091915941837674076873585191
m: 400000000000000000000000000000000
deg: 5
c5: 125
c0: 124
skew: 1.00
type: snfs
lss: 1
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2000000, 3800001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 751201 x 751443
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,52,52,2.4,2.4,100000
total time: 32.00 hours.

(32·10¹⁷²+13)/9 = 3(5)₁₇₁7_<173> = 37 · 2987983 · 15505397 · C158

C158 = P46 · P112

P46 = 3223320654117369921102155773727518551111001831_<46>

P112 = 6434891389908080526697096790304309578136358069732443055338000019495154297132988986043062674697587170436074188981_<112>

SNFS difficulty: 173 digits.
Divisors found:
 r1=3223320654117369921102155773727518551111001831 (pp46)
 r2=6434891389908080526697096790304309578136358069732443055338000019495154297132988986043062674697587170436074188981 (pp112)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.729).
Factorization parameters were as follows:
n: 20741718324092745817932403403493671875317896729662839811155637583900644726621173514191415102199691204642649327958919643967405329532734416609470589959731024211
m: 20000000000000000000000000000000000
deg: 5
c5: 100
c0: 13
skew: 0.66
type: snfs
lss: 1
rlim: 5500000
alim: 5500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2750000, 6150001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1033757 x 1033999
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,52,52,2.4,2.4,100000
total time: 52.00 hours.

Nov 28, 2008 (3rd)

By Markus Tervooren / GGNFS

(32·10¹⁶⁰+31)/9 = 3(5)₁₅₉9_<161> = 3 · 43 · 139 · 20629781705287_<14> · 2019091759073720141_<19> · C125

C125 = P41 · P84

P41 = 49505366525422020814016668476770343965501_<41>

P84 = 961612254795298853587706824117737416378847326019848732349508624487390819019261139067_<84>

N=47604967128978778980308853599287784927336120234905235004022738211686430159655031390012816340428481995268348789459939011327567
  ( 125 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=49505366525422020814016668476770343965501 (pp41)
 r2=961612254795298853587706824117737416378847326019848732349508624487390819019261139067 (pp84)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 30.26 hours.
Scaled time: 46.29 units (timescale=1.530).
Factorization parameters were as follows:
n: 47604967128978778980308853599287784927336120234905235004022738211686430159655031390012816340428481995268348789459939011327567
m: 200000000000000000000000000000000
deg: 5
c5: 1
c0: 31
skew: 1.99
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
qintsize: 5000
type: snfs
rlambda: 2.4
alambda: 2.4

Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 1985001)
Primes: RFBsize:243539, AFBsize:243245, largePrimes:10208774 encountered
Relations: rels:12323629, finalFF:1513653
Max relations in full relation-set: 32
Initial matrix: 486848 x 1513653 with sparse part having weight 217147940.
Pruned matrix : 344986 x 347484 with weight 86395308.
Total sieving time: 27.94 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 2.14 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 30.26 hours.
 --------- CPU info (if available) ----------
Intel(R) Xeon(R) CPU           E5335  @ 2.00GHz stepping 0b
Intel(R) Xeon(R) CPU           E5335  @ 2.00GHz stepping 0b
Intel(R) Xeon(R) CPU           E5335  @ 2.00GHz stepping 0b
Memory: 16428772k/17825792k available (1928k kernel code, 343260k reserved, 867k data, 176k init)
Calibrating delay using timer specific routine.. 3993.74 BogoMIPS (lpj=7987498)
Calibrating delay using timer specific routine.. 3990.12 BogoMIPS (lpj=7980241)
Calibrating delay using timer specific routine.. 3990.13 BogoMIPS (lpj=7980276)
Calibrating delay using timer specific routine.. 3990.04 BogoMIPS (lpj=7980080)

Nov 28, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(29·10¹⁶⁶-11)/9 = 3(2)₁₆₅1_<167> = 7 · 31 · 53 · 35251 · 497346601 · 213701737408337603_<18> · C132

C132 = P62 · P71

P62 = 18906556686684146433835881345695559366409569958898328591881699_<62>

P71 = 39552031510187221770337793580470173334223496149600838342975909506856043_<71>

Number: n
N=747792725820872276182403763957411243471551527733257813413020576660548430228202239146613462924753798426754801343957204384310879257057
  ( 132 digits)
SNFS difficulty: 167 digits.
Divisors found:

Fri Nov 28 03:42:05 2008  prp62 factor: 18906556686684146433835881345695559366409569958898328591881699
Fri Nov 28 03:42:05 2008  prp71 factor: 39552031510187221770337793580470173334223496149600838342975909506856043
Fri Nov 28 03:42:05 2008  elapsed time 02:47:08 (Msieve 1.38)

Version: GGNFS-0.77.1-20050930-k8
Total time: 44.06 hours.
Scaled time: 36.96 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_3_2_165_1
n: 747792725820872276182403763957411243471551527733257813413020576660548430228202239146613462924753798426754801343957204384310879257057
type: snfs
skew: 0.52
deg: 5
c5: 290
c0: -11
m: 1000000000000000000000000000000000
rlim: 5400000
alim: 5400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 2200001)
Primes: RFBsize:374362, AFBsize:373593, largePrimes:15524089 encountered
Relations: rels:14102407, finalFF:767427
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 43.53 hours.
Total relation processing time: 0.53 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5400000,5400000,28,28,56,56,2.5,2.5,100000
total time: 44.06 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(32·10¹⁵¹+13)/9 = 3(5)₁₅₀7_<152> = 37 · 2137 · 10781 · 158906947 · C135

C135 = P56 · P79

P56 = 35286918260832971119796069080905050350002961841266080149_<56>

P79 = 7438503322170209816946556791363220387621438800981627959820246469138811695379971_<79>

Number: n
N=262481858712354698059517611967957792929674054710118423170194967391373575737986775226844972214369983360318353897435684826276256295295679
  ( 135 digits)
SNFS difficulty: 152 digits.
Divisors found:

Fri Nov 28 13:16:03 2008  prp56 factor: 35286918260832971119796069080905050350002961841266080149
Fri Nov 28 13:16:03 2008  prp79 factor: 7438503322170209816946556791363220387621438800981627959820246469138811695379971
Fri Nov 28 13:16:03 2008  elapsed time 00:30:14 (Msieve 1.38)

Version: GGNFS-0.77.1-20050930-k8
Total time: 12.47 hours.
Scaled time: 10.43 units (timescale=0.836).
Factorization parameters were as follows:
name: KA_3_5_150_7
n: 262481858712354698059517611967957792929674054710118423170194967391373575737986775226844972214369983360318353897435684826276256295295679
type: snfs
skew: 1.05
deg: 5
c5: 10
c0: 13
m: 2000000000000000000000000000000
rlim: 2400000
alim: 2400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 700001)
Primes: RFBsize:176302, AFBsize:176888, largePrimes:10574079 encountered
Relations: rels:9335262, finalFF:404813
Max relations in full relation-set: 28
Initial matrix: 353256 x 404813 with sparse part having weight 34304116.
Pruned matrix : 315684 x 317514 with weight 23782300.
Total sieving time: 12.27 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,28,28,56,56,2.5,2.5,100000
total time: 12.47 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(28·10¹⁷⁹+71)/9 = 3(1)₁₇₈9_<180> = 41 · C178

C178 = P78 · P101

P78 = 463075775995206321032650596711128078474740747807397760979408995670133078825749_<78>

P101 = 16386250963897014588548079794123952353280585186116441103459154761169411054261602389191949558824062491_<101>

Number: n
N=7588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880759
  ( 178 digits)
SNFS difficulty: 181 digits.
Divisors found:

Fri Nov 28 18:24:07 2008  prp78 factor: 463075775995206321032650596711128078474740747807397760979408995670133078825749
Fri Nov 28 18:24:08 2008  prp101 factor: 16386250963897014588548079794123952353280585186116441103459154761169411054261602389191949558824062491
Fri Nov 28 18:24:08 2008  elapsed time 04:22:22 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 31.62 hours.
Scaled time: 64.66 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_3_1_178_9
n: 7588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880759
type: snfs
skew: 1.91
deg: 5
c5: 14
c0: 355
m: 1000000000000000000000000000000000000
rlim: 8000000
alim: 8000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 2100001)
Primes: RFBsize:539777, AFBsize:539736, largePrimes:16473243 encountered
Relations: rels:15646828, finalFF:1184593
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 31.20 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,56,56,2.5,2.5,100000
total time: 31.62 hours.
 --------- CPU info (if available) ----------

Nov 28, 2008

Factorizations of 366...661 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Nov 27, 2008 (4th)

By Jo Yeong Uk / GGNFS

(32·10¹⁵⁰+31)/9 = 3(5)₁₄₉9_<151> = 7 · 15073 · 920219 · 4319202413_<10> · 265240094732112281_<18> · C113

C113 = P43 · P70

P43 = 9328504925290444441822005205016085050202529_<43>

P70 = 3426602734277911210608358720760753470015484796145599102726577084452023_<70>

Number: 35559_150
N=31965080483725198765375891316094958518982027309305547961910175720694233352383936555933314648188090942893133766167
  ( 113 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=9328504925290444441822005205016085050202529 (pp43)
 r2=3426602734277911210608358720760753470015484796145599102726577084452023 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 9.37 hours.
Scaled time: 22.29 units (timescale=2.379).
Factorization parameters were as follows:
n: 31965080483725198765375891316094958518982027309305547961910175720694233352383936555933314648188090942893133766167
m: 2000000000000000000000000000000
deg: 5
c5: 1
c0: 31
skew: 1.99
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 1600001)
Primes: RFBsize:148933, AFBsize:148876, largePrimes:6640709 encountered
Relations: rels:6470040, finalFF:365507
Max relations in full relation-set: 28
Initial matrix: 297873 x 365507 with sparse part having weight 36847502.
Pruned matrix : 270279 x 271832 with weight 24272165.
Total sieving time: 8.90 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.37 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000
total time: 9.37 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(32·10¹⁵⁹+31)/9 = 3(5)₁₅₈9_<160> = 71 · 4099 · 2686673839_<10> · 2236273950894083539_<19> · 142399011313204411709_<21> · C107

C107 = P42 · P65

P42 = 691801292122926124619142949686718950073469_<42>

P65 = 20641578597385298121235556805106391775954256529093190003746261231_<65>

Number: 35559_159
N=14279870745128086325073949925715343467378244321563381991867004239842949568432183034744786374363261516380339
  ( 107 digits)
Divisors found:
 r1=691801292122926124619142949686718950073469 (pp42)
 r2=20641578597385298121235556805106391775954256529093190003746261231 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 9.48 hours.
Scaled time: 22.54 units (timescale=2.378).
Factorization parameters were as follows:
name: 35559_159
n: 14279870745128086325073949925715343467378244321563381991867004239842949568432183034744786374363261516380339
skew: 6610.55
# norm 1.46e+14
c5: 25440
c4: -137352764
c3: 14140130325568
c2: 11186446944255427
c1: -256581559691255668326
c0: 88625683951583427259919
# alpha -5.09
Y1: 6223772741
Y0: -223790397110437034630
# Murphy_E 1.59e-09
# M 11583433849997306632283936826464805133153048936625287091066066575029620600574454972810926420293069935986582
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 51/51
Sieved algebraic special-q in [900000, 1450001)
Primes: RFBsize:135072, AFBsize:134928, largePrimes:5377820 encountered
Relations: rels:5449762, finalFF:384816
Max relations in full relation-set: 28
Initial matrix: 270076 x 384816 with sparse part having weight 38468322.
Pruned matrix : 215248 x 216662 with weight 19235135.
Polynomial selection time: 0.55 hours.
Total sieving time: 8.62 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,51,51,2.6,2.6,50000
total time: 9.48 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Nov 27, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(32·10¹⁴²+31)/9 = 3(5)₁₄₁9_<143> = 3 · 64561841 · 104257759 · 377994599 · C118

C118 = P37 · P82

P37 = 1213740532142468235120515988563847529_<37>

P82 = 3837871883887678543854926447937643139346902671587478192888671244047886126346297597_<82>

Number: 35559_142
N=4658180662644448017979591182199206192957275439326873380189147999176379892124261928899928390307204730058222534367087813
  ( 118 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=1213740532142468235120515988563847529 (pp37)
 r2=3837871883887678543854926447937643139346902671587478192888671244047886126346297597 (pp82)
Version: GGNFS-0.77.1-20060513-k8
Total time: 10.65 hours.
Scaled time: 21.34 units (timescale=2.003).
Factorization parameters were as follows:
name: 35559_142
n: 4658180662644448017979591182199206192957275439326873380189147999176379892124261928899928390307204730058222534367087813
m: 20000000000000000000000000000
deg: 5
c5: 100
c0: 31
skew: 0.79
type: snfs
lss: 1
rlim: 1730000
alim: 1730000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1730000/1730000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [865000, 1765001)
Primes: RFBsize:130213, AFBsize:130606, largePrimes:3697321 encountered
Relations: rels:3696975, finalFF:308074
Max relations in full relation-set: 28
Initial matrix: 260883 x 308074 with sparse part having weight 26725119.
Pruned matrix : 243807 x 245175 with weight 18265017.
Total sieving time: 9.84 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.61 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1730000,1730000,26,26,48,48,2.3,2.3,100000
total time: 10.65 hours.
 --------- CPU info (if available) ----------

(32·10¹⁴⁷+13)/9 = 3(5)₁₄₆7_<148> = 577 · 3003359 · 455596076143783_<15> · C124

C124 = P38 · P42 · P45

P38 = 72519105901762960424586887146043201269_<38>

P42 = 237393285754289721684399278650422527285701_<42>

P45 = 261591459190022276610663797779771133402539237_<45>

Number: 35557_147
N=4503440539192284694080254631636649733208049606510396053663091715437410543570581827078424255488049582122601901054604325523853
  ( 124 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=72519105901762960424586887146043201269 (pp38)
 r2=237393285754289721684399278650422527285701 (pp42)
 r3=261591459190022276610663797779771133402539237 (pp45)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 19.05 hours.
Scaled time: 19.22 units (timescale=1.009).
Factorization parameters were as follows:
name: 35557_147
n: 4503440539192284694080254631636649733208049606510396053663091715437410543570581827078424255488049582122601901054604325523853
m: 200000000000000000000000000000
deg: 5
c5: 100
c0: 13
skew: 0.66
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 2750001)
Primes: RFBsize:155805, AFBsize:156147, largePrimes:4692420 encountered
Relations: rels:5382227, finalFF:751102
Max relations in full relation-set: 28
Initial matrix: 312016 x 751102 with sparse part having weight 87947570.
Pruned matrix : 224954 x 226578 with weight 36935309.
Total sieving time: 18.48 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.43 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 19.05 hours.
 --------- CPU info (if available) ----------

(32·10¹³⁸+13)/9 = 3(5)₁₃₇7_<139> = 151 · 239070938762608352011_<21> · C116

C116 = P35 · P82

P35 = 38286075216383022257640191847520543_<35>

P82 = 2572544443884594548631930409137038593963600087065351749783286536175566198407004759_<82>

Number: 35557_138
N=98492630076053819893362066775404397948947703796013667845436549228724048750081144551122623075631307653019377351264137
  ( 116 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=38286075216383022257640191847520543 (pp35)
 r2=2572544443884594548631930409137038593963600087065351749783286536175566198407004759 (pp82)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 11.96 hours.
Scaled time: 5.64 units (timescale=0.472).
Factorization parameters were as follows:
name: 35557_138
n: 98492630076053819893362066775404397948947703796013667845436549228724048750081144551122623075631307653019377351264137
m: 4000000000000000000000000000
deg: 5
c5: 125
c0: 52
skew: 0.84
type: snfs
lss: 1
rlim: 1510000
alim: 1510000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1510000/1510000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [755000, 1730001)
Primes: RFBsize:114886, AFBsize:114462, largePrimes:3597792 encountered
Relations: rels:3646300, finalFF:319530
Max relations in full relation-set: 28
Initial matrix: 229414 x 319530 with sparse part having weight 29910094.
Pruned matrix : 203028 x 204239 with weight 15985370.
Total sieving time: 10.78 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.94 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1510000,1510000,26,26,48,48,2.3,2.3,75000
total time: 11.96 hours.
 --------- CPU info (if available) ----------

(32·10¹⁴³+13)/9 = 3(5)₁₄₂7_<144> = 3² · 43 · 136300339079_<12> · C130

C130 = P54 · P77

P54 = 129540884783737232563732791036117978164375414441872727_<54>

P77 = 52034658491669865443373273867237919313125763903812941156376897881115098465367_<77>

Number: 35557_143
N=6740615700430520249355904501258211265810098697425404834449623922044888793184621364778853022916598827039769466350315646703231345809
  ( 130 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=129540884783737232563732791036117978164375414441872727 (pp54)
 r2=52034658491669865443373273867237919313125763903812941156376897881115098465367 (pp77)
Version: GGNFS-0.77.1-20060513-k8
Total time: 17.48 hours.
Scaled time: 34.27 units (timescale=1.960).
Factorization parameters were as follows:
name: 35557_143
n: 6740615700430520249355904501258211265810098697425404834449623922044888793184621364778853022916598827039769466350315646703231345809
m: 40000000000000000000000000000
deg: 5
c5: 125
c0: 52
skew: 0.84
type: snfs
lss: 1
rlim: 1830000
alim: 1830000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1830000/1830000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [915000, 2415001)
Primes: RFBsize:137166, AFBsize:136949, largePrimes:4152822 encountered
Relations: rels:4421422, finalFF:440986
Max relations in full relation-set: 28
Initial matrix: 274181 x 440986 with sparse part having weight 48070702.
Pruned matrix : 226240 x 227674 with weight 23821835.
Total sieving time: 16.49 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.74 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1830000,1830000,26,26,49,49,2.3,2.3,100000
total time: 17.48 hours.
 --------- CPU info (if available) ----------

(32·10¹⁴⁴+13)/9 = 3(5)₁₄₃7_<145> = 1562829649_<10> · C136

C136 = P53 · P84

P53 = 21343091280175666099265930659020264876344915006263847_<53>

P84 = 106595410233811335107263401150127469936167809467849002202851268941550486159081360419_<84>

Number: 35557_144
N=2275075570668006667408416664582715217962668403122646130164091579475502742753222207109250686832570806669892884503086078549022687216471893
  ( 136 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=21343091280175666099265930659020264876344915006263847 (pp53)
 r2=106595410233811335107263401150127469936167809467849002202851268941550486159081360419 (pp84)
Version: GGNFS-0.77.1-20060513-k8
Total time: 14.18 hours.
Scaled time: 27.80 units (timescale=1.960).
Factorization parameters were as follows:
name: 35557_144
n: 2275075570668006667408416664582715217962668403122646130164091579475502742753222207109250686832570806669892884503086078549022687216471893
m: 100000000000000000000000000000
deg: 5
c5: 16
c0: 65
skew: 1.32
type: snfs
lss: 1
rlim: 1910000
alim: 1910000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1910000/1910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [955000, 2055001)
Primes: RFBsize:142718, AFBsize:142665, largePrimes:4190102 encountered
Relations: rels:4488048, finalFF:534806
Max relations in full relation-set: 28
Initial matrix: 285447 x 534806 with sparse part having weight 51597395.
Pruned matrix : 216011 x 217502 with weight 20112430.
Total sieving time: 13.43 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.53 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1910000,1910000,26,26,49,49,2.3,2.3,100000
total time: 14.18 hours.
 --------- CPU info (if available) ----------

Nov 27, 2008 (2nd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38

(32·10²⁰¹+13)/9 = 3(5)₂₀₀7_<202> = 71 · C200

C200 = P35 · P165

P35 = 64499300335345945772569335465848633_<35>

P165 = 776415356460893542572148430011329803890783961378327293176367619348587721447168535503721077213200924311601722917814388070780548658836862919766647808745906924624959499_<165>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2420471301
Step 1 took 35354ms
Step 2 took 21406ms
********** Factor found in step 2: 64499300335345945772569335465848633
Found probable prime factor of 35 digits: 64499300335345945772569335465848633
Probable prime cofactor 776415356460893542572148430011329803890783961378327293176367619348587721447168535503721077213200924311601722917814388070780548658836862919766647808745906924624959499 has 165 digits

(32·10¹⁸⁹+13)/9 = 3(5)₁₈₈7_<190> = 19 · 107 · C187

C187 = P39 · P148

P39 = 843460198256475257121613143362568122851_<39>

P148 = 2073506955858448830349465499436664370903520495707406284060409753621333767261713347013056871399165319114052676049692680217196117332798366844122275079_<148>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3643605157
Step 1 took 28189ms
Step 2 took 19369ms
********** Factor found in step 2: 843460198256475257121613143362568122851
Found probable prime factor of 39 digits: 843460198256475257121613143362568122851
Probable prime cofactor 2073506955858448830349465499436664370903520495707406284060409753621333767261713347013056871399165319114052676049692680217196117332798366844122275079 has 148 digits

(32·10¹⁶⁸+13)/9 = 3(5)₁₆₇7_<169> = 2293 · C166

C166 = P68 · P98

P68 = 34830569746839257317899826291328772117731947319522284446012964814699_<68>

P98 = 44518737073861990630104024619714585669202122565337947057601576528643764758484259563116570090807251_<98>

SNFS difficulty: 170 digits.
Divisors found:
 r1=34830569746839257317899826291328772117731947319522284446012964814699 (pp68)
 r2=44518737073861990630104024619714585669202122565337947057601576528643764758484259563116570090807251 (pp98)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.949).
Factorization parameters were as follows:
n: 1550612976692348694093133691912584193438968842370499588118428066094878131511363085719823617773901245336046906042544943547996317294180355671851528807481707612540582449
m: 4000000000000000000000000000000000
deg: 5
c5: 125
c0: 52
skew: 0.84
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved rational special-q in [2400000, 5400001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 924774 x 925016
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,53,53,2.5,2.5,200000
total time: 60.00 hours.

(32·10¹⁶¹+31)/9 = 3(5)₁₆₀9_<162> = 19 · 47692016535428836243_<20> · C141

C141 = P66 · P76

P66 = 110241649022448520071238394292360412717056973196080358021493292843_<66>

P76 = 3559282679293368344699238534100485608179773689995381905642703269366099354989_<76>

SNFS difficulty: 162 digits.
Divisors found:
 r1=110241649022448520071238394292360412717056973196080358021493292843 (pp66)
 r2=3559282679293368344699238534100485608179773689995381905642703269366099354989 (pp76)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.729).
Factorization parameters were as follows:
n: 392381191902339709749372813102397984185725242296439646480483642273917995502467744884092300496990794306058047534341998381451290475411990043727
m: 200000000000000000000000000000000
deg: 5
c5: 10
c0: 31
skew: 1.25
type: snfs
lss: 1
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1800000, 3100001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 689147 x 689389
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3600000,3600000,27,27,52,52,2.4,2.4,100000
total time: 19.00 hours.

Nov 27, 2008

By Robert Backstrom / GGNFS, Msieve

(14·10¹⁷⁵-23)/9 = 1(5)₁₇₄3_<176> = 13 · 7573 · C171

C171 = P43 · P128

P43 = 2038700949876497258819164740062522064954709_<43>

P128 = 77503388727423169575714188322817654539111949909475491882640338731051584806905658501368959790339414055676600291226770718963064333_<128>

Number: n
N=158006232217245025907379003906139783599178819038848089422498507405413519238951696366195243786687072042941579452869562469456831004434332045582540762786372188194451498294097
  ( 171 digits)
SNFS difficulty: 176 digits.
Divisors found:

Thu Nov 27 04:51:58 2008  prp43 factor: 2038700949876497258819164740062522064954709
Thu Nov 27 04:51:58 2008  prp128 factor: 77503388727423169575714188322817654539111949909475491882640338731051584806905658501368959790339414055676600291226770718963064333
Thu Nov 27 04:51:59 2008  elapsed time 03:36:08 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.92 hours.
Scaled time: 40.86 units (timescale=2.051).
Factorization parameters were as follows:
name: KA_1_5_174_3
n: 158006232217245025907379003906139783599178819038848089422498507405413519238951696366195243786687072042941579452869562469456831004434332045582540762786372188194451498294097
type: snfs
skew: 1.10
deg: 5
c5: 14
c0: -23
m: 100000000000000000000000000000000000
rlim: 7500000
alim: 7500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 7500000/7500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 3800001)
Primes: RFBsize:508261, AFBsize:508901, largePrimes:18196504 encountered
Relations: rels:17583392, finalFF:1197106
Max relations in full relation-set: 28
Initial matrix: 1017230 x 1197106 with sparse part having weight 109758757.
Pruned matrix : 
Total sieving time: 19.33 hours.
Total relation processing time: 0.59 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,7500000,7500000,28,28,56,56,2.5,2.5,100000
total time: 19.92 hours.
 --------- CPU info (if available) ----------

9·10¹⁶⁷+1 = 9(0)₁₆₆1_<168> = 65011 · 331853765402124003677_<21> · C143

C143 = P55 · P88

P55 = 7113900758268929663283411570479354669535798745893423331_<55>

P88 = 5864096533496964606518020454924687639490103035820928855353490102504942263905443892896093_<88>

Number: n
N=41716600776206258411222477166102973461160042517623071486739187464549952517470294390048761365003310345273758999726780709270940796628119644945783
  ( 143 digits)
SNFS difficulty: 167 digits.
Divisors found:

Thu Nov 27 10:01:19 2008  prp55 factor: 7113900758268929663283411570479354669535798745893423331
Thu Nov 27 10:01:19 2008  prp88 factor: 5864096533496964606518020454924687639490103035820928855353490102504942263905443892896093
Thu Nov 27 10:01:19 2008  elapsed time 02:38:18 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 31.92 hours.
Scaled time: 57.87 units (timescale=1.813).
Factorization parameters were as follows:
name: KA_9_0_166_1
n: 41716600776206258411222477166102973461160042517623071486739187464549952517470294390048761365003310345273758999726780709270940796628119644945783
type: snfs
skew: 0.26
deg: 5
c5: 900
c0: 1
m: 1000000000000000000000000000000000
rlim: 5500000
alim: 5500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 1850001)
Primes: RFBsize:380800, AFBsize:379512, largePrimes:14682360 encountered
Relations: rels:13224417, finalFF:760889
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 31.46 hours.
Total relation processing time: 0.45 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,56,56,2.5,2.5,100000
total time: 31.92 hours.
 --------- CPU info (if available) ----------

(29·10¹⁶²-11)/9 = 3(2)₁₆₁1_<163> = 893147 · 19471057 · 746734138448512777471322756059_<30> · C120

C120 = P53 · P67

P53 = 46463222638182568129303288420608644739547623874362397_<53>

P67 = 5340324918609786317635870057618451405996157273164823665163903114313_<67>

Number: n
N=248128705653600704252183940981166727591290446648117130564206869724052667609229038959837362742059371119512152905479688261
  ( 120 digits)
SNFS difficulty: 163 digits.
Divisors found:

Thu Nov 27 22:04:17 2008  prp53 factor: 46463222638182568129303288420608644739547623874362397
Thu Nov 27 22:04:17 2008  prp67 factor: 5340324918609786317635870057618451405996157273164823665163903114313
Thu Nov 27 22:04:17 2008  elapsed time 02:32:33 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 42.18 hours.
Scaled time: 61.20 units (timescale=1.451).
Factorization parameters were as follows:
name: KA_3_2_161_1
n: 248128705653600704252183940981166727591290446648117130564206869724052667609229038959837362742059371119512152905479688261
type: snfs
skew: 0.33
deg: 5
c5: 2900
c0: -11
m: 100000000000000000000000000000000
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 1800001)
Primes: RFBsize:315948, AFBsize:316467, largePrimes:14976512 encountered
Relations: rels:13784661, finalFF:723023
Max relations in full relation-set: 28
Initial matrix: 632482 x 723023 with sparse part having weight 64151002.
Pruned matrix : 558893 x 562119 with weight 45340058.
Total sieving time: 41.44 hours.
Total relation processing time: 0.73 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.5,2.5,100000
total time: 42.18 hours.
 --------- CPU info (if available) ----------

Nov 26, 2008 (6th)

By Robert Backstrom / GGNFS, Msieve

(31·10¹⁶²+41)/9 = 3(4)₁₆₁9_<163> = 4829107 · 227519218577615844600233_<24> · C133

C133 = P64 · P69

P64 = 4497256276942913708784333111919888344610032022987466112890666921_<64>

P69 = 697086435613153702704174629418486140293389147332010155586147216393899_<69>

Number: n
N=3134976348133017753986237508264591675227397506931118169753747860898160990515607185310712968530556574409882478282528797528962745514979
  ( 133 digits)
SNFS difficulty: 163 digits.
Divisors found:

Thu Nov 27 01:18:58 2008  prp64 factor: 4497256276942913708784333111919888344610032022987466112890666921
Thu Nov 27 01:18:58 2008  prp69 factor: 697086435613153702704174629418486140293389147332010155586147216393899
Thu Nov 27 01:18:58 2008  elapsed time 02:47:55 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 46.31 hours.
Scaled time: 93.82 units (timescale=2.026).
Factorization parameters were as follows:
name: KA_3_4_161_9
n: 3134976348133017753986237508264591675227397506931118169753747860898160990515607185310712968530556574409882478282528797528962745514979
type: snfs
skew: 0.42
deg: 5
c5: 3100
c0: 41
m: 100000000000000000000000000000000
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 2400001)
Primes: RFBsize:315948, AFBsize:316018, largePrimes:15816324 encountered
Relations: rels:14466655, finalFF:677553
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 45.67 hours.
Total relation processing time: 0.63 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.5,2.5,100000
total time: 46.31 hours.
 --------- CPU info (if available) ----------

Nov 26, 2008 (5th)

By Jo Yeong Uk / GGNFS

(28·10¹⁶⁵+71)/9 = 3(1)₁₆₄9_<166> = 1753 · 6055958639980063027_<19> · 965316807436900108524947_<24> · C120

C120 = P35 · P85

P35 = 70439990548456091885222669101231123_<35>

P85 = 4309843978488043509530024860013260980329590471359429014805762306586306512837214055029_<85>

Number: 31119_165
N=303585369110018185007471879360898991168929903700924426959244422935273048194869215246139424974107724672809347382969467567
  ( 120 digits)
Divisors found:
 r1=70439990548456091885222669101231123 (pp35)
 r2=4309843978488043509530024860013260980329590471359429014805762306586306512837214055029 (pp85)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 40.96 hours.
Scaled time: 97.08 units (timescale=2.370).
Factorization parameters were as follows:
name: 31119_165
n: 303585369110018185007471879360898991168929903700924426959244422935273048194869215246139424974107724672809347382969467567
skew: 33667.21
# norm 1.82e+16
c5: 32340
c4: -23522374526
c3: 310860150727100
c2: 20865714667004567049
c1: -32102243520844357032692
c0: -2872046884747467271572696700
# alpha -5.20
Y1: 976166667797
Y0: -98743561855902881885457
# Murphy_E 2.75e-10
# M 153187704591743685195168053080016067196268183713315786138378510697769178895803432423620387704969606083977056054982934738
type: gnfs
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved algebraic special-q in [2100000, 4400001)
Primes: RFBsize:296314, AFBsize:297542, largePrimes:9896798 encountered
Relations: rels:10038568, finalFF:728716
Max relations in full relation-set: 28
Initial matrix: 593938 x 728716 with sparse part having weight 78608378.
Pruned matrix : 495863 x 498896 with weight 56165481.
Polynomial selection time: 2.65 hours.
Total sieving time: 35.87 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.08 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4200000,4200000,27,27,53,53,2.4,2.4,100000
total time: 40.96 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Nov 26, 2008 (4th)

By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1

(32·10¹⁰⁵+13)/9 = 3(5)₁₀₄7_<106> = 6943591 · 11775493 · C92

C92 = P35 · P58

P35 = 16322666212462824649542261200640023_<35>

P58 = 2664116050279468052227828533131936012933075971887327880993_<58>

SNFS difficulty: 106 digits.
Divisors found:
 r1=16322666212462824649542261200640023 (pp35)
 r2=2664116050279468052227828533131936012933075971887327880993 (pp58)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.565).
Factorization parameters were as follows:
n: 43485477039976584910743136045130133133538428294391933903186090881596753760752964623976782839
m: 200000000000000000000000000
deg: 4
c4: 20
c0: 13
skew: 0.90
type: snfs
lss: 1
rlim: 420000
alim: 420000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 420000/420000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [210000, 270001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 38130 x 38343
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,106,4,0,0,0,0,0,0,0,0,420000,420000,25,25,46,46,2.2,2.2,20000
total time: 0.50 hours.

(32·10¹⁷⁰+13)/9 = 3(5)₁₆₉7_<171> = 3² · 7 · 5540993 · 12984208595306517726286012309466401_<35> · C128

C128 = P29 · P99

P29 = 79463930140396661143010131997_<29>

P99 = 987174192828764409699802414185584254672009061795451677369777853855095127393439210182651571314227959_<99>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4231249235
Step 1 took 27069ms
Step 2 took 20682ms
********** Factor found in step 2: 79463930140396661143010131997
Found probable prime factor of 29 digits: 79463930140396661143010131997

(32·10¹⁵⁰+13)/9 = 3(5)₁₄₉7_<151> = 34178423 · C144

C144 = P52 · P92

P52 = 2431428001729590940164509177974037642037881794664501_<52>

P92 = 42785246111212653779850385352873604265492028686791920253084903971196032603178702127108172759_<92>

SNFS difficulty: 151 digits.
Divisors found:
 r1=2431428001729590940164509177974037642037881794664501 (pp52)
 r2=42785246111212653779850385352873604265492028686791920253084903971196032603178702127108172759 (pp92)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 104029245455694534401296266815925227315360792262286517887485784688063447384788805368684083392482899388177024889520372416116318636338357552528259
m: 2000000000000000000000000000000
deg: 5
c5: 1
c0: 13
skew: 1.67
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1150000, 1750001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 289384 x 289626
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,52,52,2.4,2.4,200000
total time: 10.00 hours.

(32·10¹⁷⁶+31)/9 = 3(5)₁₇₅9_<177> = 857 · 1303 · C171

C171 = P40 · P131

P40 = 3660718354755801093405249716097352669909_<40>

P131 = 86979301255766846910552733876279826203666396318195941678536718624178967053141838401347217342937724437358746417149543025182392182581_<131>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3906121173
Step 1 took 24827ms
Step 2 took 17271ms
********** Factor found in step 2: 3660718354755801093405249716097352669909
Found probable prime factor of 40 digits: 3660718354755801093405249716097352669909
Probable prime cofactor 86979301255766846910552733876279826203666396318195941678536718624178967053141838401347217342937724437358746417149543025182392182581 has 131 digits

(32·10¹⁵⁹+13)/9 = 3(5)₁₅₈7_<160> = 23 · 59 · 489677 · C151

C151 = P61 · P91

P61 = 1232966069094936177518596294215111397980392397178880244356891_<61>

P91 = 4339770769793435292184566514528285478018485043899804024027687412872122711201864678555927143_<91>

SNFS difficulty: 161 digits.
Divisors found:
 r1=1232966069094936177518596294215111397980392397178880244356891 (pp61)
 r2=4339770769793435292184566514528285478018485043899804024027687412872122711201864678555927143 (pp91)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.949).
Factorization parameters were as follows:
n: 5350790106805317102401796263181789103694200689326538071352094150203217297960148837249875002658694735842746643525823775285104514761742272980566285992413
m: 100000000000000000000000000000000
deg: 5
c5: 16
c0: 65
skew: 1.32
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1700000, 2900001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 503048 x 503290
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,52,52,2.5,2.5,200000
total time: 22.00 hours.

(32·10¹⁵³+13)/9 = 3(5)₁₅₂7_<154> = 19 · 218143 · 70572269 · C140

C140 = P42 · P98

P42 = 403967241451444975239778660111155267040127_<42>

P98 = 30090704578648225872257958579041618055553664570878690395590884572436070064354330906165968391395267_<98>

SNFS difficulty: 155 digits.
Divisors found:
 r1=403967241451444975239778660111155267040127 (pp42)
 r2=30090704578648225872257958579041618055553664570878690395590884572436070064354330906165968391395267 (pp98)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.723).
Factorization parameters were as follows:
n: 12155658921966888698616208655832446688236837622138948118055634331019789700340514206626868868857159960301790182378014050733043219562806878909
m: 4000000000000000000000000000000
deg: 5
c5: 125
c0: 52
skew: 0.84
type: snfs
lss: 1
rlim: 2700000
alim: 2700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 2700000/2700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1350000, 2250001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 563951 x 564193
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2700000,2700000,27,27,52,52,2.5,2.5,100000
total time: 13.00 hours.

(32·10²⁰⁰+31)/9 = 3(5)₁₉₉9_<201> = 47 · 18951629 · 486479627 · 3127490721447603892747013_<25> · C159

C159 = P31 · P128

P31 = 4028141074602949806622803794063_<31>

P128 = 65132493605364354978645976959047691248910542452002211669809096765307018582702503470064768992992787394098368670588376753466133461_<128>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=251454589
Step 1 took 24715ms
Step 2 took 16344ms
********** Factor found in step 2: 4028141074602949806622803794063
Found probable prime factor of 31 digits: 4028141074602949806622803794063
Probable prime cofactor 65132493605364354978645976959047691248910542452002211669809096765307018582702503470064768992992787394098368670588376753466133461 has 128 digits

Nov 26, 2008 (3rd)

By Erik Branger / GGNFS, Msieve

8·10¹⁶⁸+3 = 8(0)₁₆₇3_<169> = 11 · 7508952959070127_<16> · 67190157772167649_<17> · C136

C136 = P50 · P87

P50 = 13469805809745432155725685004278020183984235651737_<50>

P87 = 107016544227351834704803055140285312688017262106116130497648324056315093035478326557023_<87>

Number: 80003_168
N=1441492069172462733055271981772212297398850822494070561575278242939498872337270030684777421160455311668790312909413094797598647699498951
  ( 136 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=13469805809745432155725685004278020183984235651737
 r2=107016544227351834704803055140285312688017262106116130497648324056315093035478326557023
Version: 
Total time: 78.19 hours.
Scaled time: 61.54 units (timescale=0.787).
Factorization parameters were as follows:
n: 1441492069172462733055271981772212297398850822494070561575278242939498872337270030684777421160455311668790312909413094797598647699498951
m: 10000000000000000000000000000000000
deg: 5
c5: 2
c0: 75
skew: 2.06
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4

Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2400000, 4400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 809243 x 809491
Total sieving time: 78.19 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,52,52,2.4,2.4,100000
total time: 78.19 hours.
 --------- CPU info (if available) ----------

(32·10¹³⁶+31)/9 = 3(5)₁₃₅9_<137> = 3 · 496891 · 1122571 · 4761415135792806704700849085613258322433_<40> · C85

C85 = P35 · P50

P35 = 92123373788344372285635615769596739_<35>

P50 = 48440139168210650866664274877353596332333457620279_<50>

Tue Nov 25 20:57:27 2008  Msieve v. 1.38
Tue Nov 25 20:57:27 2008  random seeds: cf745a60 a52fd4cc
Tue Nov 25 20:57:27 2008  factoring 4462469046952490638354343160769488971248707524461871437573226959519017881746418670181 (85 digits)
Tue Nov 25 20:57:28 2008  searching for 15-digit factors
Tue Nov 25 20:57:30 2008  commencing quadratic sieve (85-digit input)
Tue Nov 25 20:57:30 2008  using multiplier of 1
Tue Nov 25 20:57:30 2008  using 64kb Pentium 4 sieve core
Tue Nov 25 20:57:30 2008  sieve interval: 6 blocks of size 65536
Tue Nov 25 20:57:30 2008  processing polynomials in batches of 17
Tue Nov 25 20:57:30 2008  using a sieve bound of 1434241 (54676 primes)
Tue Nov 25 20:57:30 2008  using large prime bound of 116173521 (26 bits)
Tue Nov 25 20:57:30 2008  using double large prime bound of 328997602795950 (41-49 bits)
Tue Nov 25 20:57:30 2008  using trial factoring cutoff of 49 bits
Tue Nov 25 20:57:30 2008  polynomial 'A' values have 11 factors
Tue Nov 25 21:50:59 2008  54899 relations (15846 full + 39053 combined from 576302 partial), need 54772
Tue Nov 25 21:51:02 2008  begin with 592148 relations
Tue Nov 25 21:51:02 2008  reduce to 130381 relations in 10 passes
Tue Nov 25 21:51:02 2008  attempting to read 130381 relations
Tue Nov 25 21:51:06 2008  recovered 130381 relations
Tue Nov 25 21:51:06 2008  recovered 111038 polynomials
Tue Nov 25 21:51:07 2008  attempting to build 54899 cycles
Tue Nov 25 21:51:07 2008  found 54899 cycles in 5 passes
Tue Nov 25 21:51:07 2008  distribution of cycle lengths:
Tue Nov 25 21:51:07 2008     length 1 : 15846
Tue Nov 25 21:51:07 2008     length 2 : 10901
Tue Nov 25 21:51:07 2008     length 3 : 9452
Tue Nov 25 21:51:07 2008     length 4 : 7155
Tue Nov 25 21:51:07 2008     length 5 : 4909
Tue Nov 25 21:51:07 2008     length 6 : 2926
Tue Nov 25 21:51:07 2008     length 7 : 1730
Tue Nov 25 21:51:07 2008     length 9+: 1980
Tue Nov 25 21:51:07 2008  largest cycle: 16 relations
Tue Nov 25 21:51:07 2008  matrix is 54676 x 54899 (11.8 MB) with weight 2881914 (52.49/col)
Tue Nov 25 21:51:07 2008  sparse part has weight 2881914 (52.49/col)
Tue Nov 25 21:51:08 2008  filtering completed in 3 passes
Tue Nov 25 21:51:08 2008  matrix is 49850 x 49914 (10.9 MB) with weight 2649803 (53.09/col)
Tue Nov 25 21:51:08 2008  sparse part has weight 2649803 (53.09/col)
Tue Nov 25 21:51:08 2008  saving the first 48 matrix rows for later
Tue Nov 25 21:51:08 2008  matrix is 49802 x 49914 (6.4 MB) with weight 2011559 (40.30/col)
Tue Nov 25 21:51:08 2008  sparse part has weight 1389929 (27.85/col)
Tue Nov 25 21:51:08 2008  matrix includes 64 packed rows
Tue Nov 25 21:51:08 2008  using block size 19965 for processor cache size 512 kB
Tue Nov 25 21:51:09 2008  commencing Lanczos iteration
Tue Nov 25 21:51:09 2008  memory use: 6.8 MB
Tue Nov 25 21:51:32 2008  lanczos halted after 790 iterations (dim = 49799)
Tue Nov 25 21:51:32 2008  recovered 15 nontrivial dependencies
Tue Nov 25 21:51:34 2008  prp35 factor: 92123373788344372285635615769596739
Tue Nov 25 21:51:34 2008  prp50 factor: 48440139168210650866664274877353596332333457620279
Tue Nov 25 21:51:34 2008  elapsed time 00:54:07

(32·10¹⁴⁸+13)/9 = 3(5)₁₄₇7_<149> = 37 · 1015690043_<10> · 21788482138371211_<17> · 331676232498798305313287633537_<30> · C93

C93 = P38 · P55

P38 = 94903203682704040124208587387626991143_<38>

P55 = 1379502043103630182118926944969415246125508853045791327_<55>

Wed Nov 26 12:04:05 2008  Msieve v. 1.38
Wed Nov 26 12:04:05 2008  random seeds: ba40a840 d9ff2749
Wed Nov 26 12:04:05 2008  factoring 130919163377370183397007958071376655425247437752619741439878676248451252269473992284455216761 (93 digits)
Wed Nov 26 12:04:06 2008  searching for 15-digit factors
Wed Nov 26 12:04:07 2008  commencing quadratic sieve (93-digit input)
Wed Nov 26 12:04:07 2008  using multiplier of 1
Wed Nov 26 12:04:07 2008  using 32kb Intel Core sieve core
Wed Nov 26 12:04:07 2008  sieve interval: 36 blocks of size 32768
Wed Nov 26 12:04:07 2008  processing polynomials in batches of 6
Wed Nov 26 12:04:07 2008  using a sieve bound of 1885753 (70588 primes)
Wed Nov 26 12:04:07 2008  using large prime bound of 220633101 (27 bits)
Wed Nov 26 12:04:07 2008  using double large prime bound of 1043775707505921 (42-50 bits)
Wed Nov 26 12:04:07 2008  using trial factoring cutoff of 50 bits
Wed Nov 26 12:04:07 2008  polynomial 'A' values have 12 factors
Wed Nov 26 13:42:50 2008  70721 relations (18727 full + 51994 combined from 909015 partial), need 70684
Wed Nov 26 13:42:51 2008  begin with 927742 relations
Wed Nov 26 13:42:52 2008  reduce to 175950 relations in 10 passes
Wed Nov 26 13:42:52 2008  attempting to read 175950 relations
Wed Nov 26 13:42:54 2008  recovered 175950 relations
Wed Nov 26 13:42:54 2008  recovered 151728 polynomials
Wed Nov 26 13:42:54 2008  attempting to build 70721 cycles
Wed Nov 26 13:42:54 2008  found 70721 cycles in 6 passes
Wed Nov 26 13:42:54 2008  distribution of cycle lengths:
Wed Nov 26 13:42:54 2008     length 1 : 18727
Wed Nov 26 13:42:54 2008     length 2 : 13332
Wed Nov 26 13:42:54 2008     length 3 : 12178
Wed Nov 26 13:42:54 2008     length 4 : 9387
Wed Nov 26 13:42:54 2008     length 5 : 6780
Wed Nov 26 13:42:54 2008     length 6 : 4296
Wed Nov 26 13:42:54 2008     length 7 : 2643
Wed Nov 26 13:42:54 2008     length 9+: 3378
Wed Nov 26 13:42:54 2008  largest cycle: 19 relations
Wed Nov 26 13:42:55 2008  matrix is 70588 x 70721 (17.1 MB) with weight 4196924 (59.34/col)
Wed Nov 26 13:42:55 2008  sparse part has weight 4196924 (59.34/col)
Wed Nov 26 13:42:55 2008  filtering completed in 3 passes
Wed Nov 26 13:42:55 2008  matrix is 66187 x 66251 (16.1 MB) with weight 3964446 (59.84/col)
Wed Nov 26 13:42:55 2008  sparse part has weight 3964446 (59.84/col)
Wed Nov 26 13:42:56 2008  saving the first 48 matrix rows for later
Wed Nov 26 13:42:56 2008  matrix is 66139 x 66251 (9.5 MB) with weight 3022847 (45.63/col)
Wed Nov 26 13:42:56 2008  sparse part has weight 2093712 (31.60/col)
Wed Nov 26 13:42:56 2008  matrix includes 64 packed rows
Wed Nov 26 13:42:56 2008  using block size 26500 for processor cache size 2048 kB
Wed Nov 26 13:42:56 2008  commencing Lanczos iteration
Wed Nov 26 13:42:56 2008  memory use: 9.7 MB
Wed Nov 26 13:43:19 2008  lanczos halted after 1047 iterations (dim = 66133)
Wed Nov 26 13:43:20 2008  recovered 13 nontrivial dependencies
Wed Nov 26 13:43:20 2008  prp38 factor: 94903203682704040124208587387626991143
Wed Nov 26 13:43:20 2008  prp55 factor: 1379502043103630182118926944969415246125508853045791327
Wed Nov 26 13:43:20 2008  elapsed time 01:39:15

Nov 26, 2008 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(32·10¹⁴⁵+13)/9 = 3(5)₁₄₄7_<146> = 37 · 3197004779_<10> · 254681218216645409818996342939_<30> · C106

C106 = P34 · P72

P34 = 5229918696886448659761231433046467_<34>

P72 = 225668323907862446214856345291670054173175166345927281111241519005977043_<72>

GMP-ECM 6.0.1 [powered by GMP 4.1.4] [ECM]
Input number is 1180226986500756972134059759800332242451110673451530099017680638918163275649167707645548036671643354257081 (106 digits)
Using B1=882000, B2=702018447, polynomial Dickson(3), sigma=923708382
Step 1 took 8610ms
Step 2 took 6406ms
********** Factor found in step 2: 5229918696886448659761231433046467
Found probable prime factor of 34 digits: 5229918696886448659761231433046467
Probable prime cofactor 225668323907862446214856345291670054173175166345927281111241519005977043 has 72 digits

(32·10¹⁶⁶-41)/9 = 3(5)₁₆₅1_<167> = 31 · 10531 · 5788583 · C155

C155 = P40 · P115

P40 = 9792135022795704973814420716717552208387_<40>

P115 = 1921438569531190489372181741560709835825907604892997957330053823094539017344979860619343704918741149830171856900671_<115>

Number: n
N=18814985910856850738989493552015668813724344381955732627780744427450386269838098108337739752472791134671475386080902144478651310281628482623249021352127677
  ( 155 digits)
SNFS difficulty: 167 digits.
Divisors found:

Wed Nov 26 09:08:30 2008  prp40 factor: 9792135022795704973814420716717552208387
Wed Nov 26 09:08:30 2008  prp115 factor: 1921438569531190489372181741560709835825907604892997957330053823094539017344979860619343704918741149830171856900671
Wed Nov 26 09:08:30 2008  elapsed time 02:15:55 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 37.41 hours.
Scaled time: 68.08 units (timescale=1.820).
Factorization parameters were as follows:
name: KA_3_5_165_1
n: 18814985910856850738989493552015668813724344381955732627780744427450386269838098108337739752472791134671475386080902144478651310281628482623249021352127677
type: snfs
skew: 1.33
deg: 5
c5: 10
c0: -41
m: 2000000000000000000000000000000000
rlim: 5200000
alim: 5200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 5200000/5200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 2150001)
Primes: RFBsize:361407, AFBsize:361403, largePrimes:15647474 encountered
Relations: rels:14410609, finalFF:836059
Max relations in full relation-set: 28
Initial matrix: 722876 x 836059 with sparse part having weight 94388964.
Pruned matrix : 631595 x 635273 with weight 62761233.
Total sieving time: 36.91 hours.
Total relation processing time: 0.49 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5200000,5200000,28,28,56,56,2.5,2.5,100000
total time: 37.41 hours.
 --------- CPU info (if available) ----------

(32·10¹⁵⁸+13)/9 = 3(5)₁₅₇7_<159> = 3 · 7 · 4889 · 6761 · 1812937883_<10> · 5326454155007_<13> · 29917160077671362567875821596807351_<35> · C94

C94 = P40 · P54

P40 = 6043839649643906935863300584811449219393_<40>

P54 = 293361275238573998016222754474394638893197836210505131_<54>

Number: n
N=1773028506956992823270714966016153997533707382744774221590296026068158413217827561776171205483
  ( 94 digits)
Divisors found:
 r1=6043839649643906935863300584811449219393 (pp40)
 r2=293361275238573998016222754474394638893197836210505131 (pp54)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 6.60 hours.
Scaled time: 8.65 units (timescale=1.310).
Factorization parameters were as follows:
name: KA_3_5_157_7
n:  1773028506956992823270714966016153997533707382744774221590296026068158413217827561776171205483
m:  3101524404745634812660
deg: 4
c4: 19160856
c3: 80284134
c2: -135811583081129561
c1: -160852531582126458026
c0: 1407163380862846602243
skew: 1635.250
type: gnfs
# adj. I(F,S) = 55.938
# E(F1,F2) = 5.489594e-05
# GGNFS version 0.77.1-20060513-athlon-xp polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1227641341.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [100000, 880001)
Primes: RFBsize:92938, AFBsize:93100, largePrimes:1766464 encountered
Relations: rels:1793660, finalFF:209859
Max relations in full relation-set: 28
Initial matrix: 186117 x 209859 with sparse part having weight 12840070.
Pruned matrix : 168779 x 169773 with weight 8560939.
Polynomial selection time: 0.17 hours.
Total sieving time: 5.89 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.40 hours.
Total square root time: 0.04 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,93,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 6.60 hours.
 --------- CPU info (if available) ----------

(31·10¹⁶⁷+41)/9 = 3(4)₁₆₆9_<168> = 7⁴ · 23 · 107 · 443 · C159

C159 = P47 · P112

P47 = 82428469360546100817236547386728121355817832071_<47>

P112 = 1596373276554398260694282851868805545175066253459654053153617203305739262457720934111478909609962402182895680953_<112>

Number: n
N=131586605714458804155816928144361334942782011803697417116828042223841300323604186069384933706935671232760809125303351106872422993136724453506518546845747243663
  ( 159 digits)
SNFS difficulty: 168 digits.
Divisors found:

Wed Nov 26 13:09:28 2008  prp47 factor: 82428469360546100817236547386728121355817832071
Wed Nov 26 13:09:28 2008  prp112 factor: 1596373276554398260694282851868805545175066253459654053153617203305739262457720934111478909609962402182895680953
Wed Nov 26 13:09:28 2008  elapsed time 03:20:59 (Msieve 1.38)

Version: GGNFS-0.77.1-20050930-k8
Total time: 64.94 hours.
Scaled time: 54.35 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_3_4_166_9
n: 131586605714458804155816928144361334942782011803697417116828042223841300323604186069384933706935671232760809125303351106872422993136724453506518546845747243663
type: snfs
skew: 0.42
deg: 5
c5: 3100
c0: 41
m: 1000000000000000000000000000000000
rlim: 5500000
alim: 5500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 3250001)
Primes: RFBsize:380800, AFBsize:380784, largePrimes:16898141 encountered
Relations: rels:15611597, finalFF:778444
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 64.09 hours.
Total relation processing time: 0.85 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,56,56,2.5,2.5,100000
total time: 64.94 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

Nov 26, 2008

By Sinkiti Sibata / GGNFS, Msieve

(32·10¹²⁵+31)/9 = 3(5)₁₂₄9_<126> = 19 · 3067 · 134807213061289_<15> · C107

C107 = P42 · P65

P42 = 855863039493258726374436148063275096378011_<42>

P65 = 52883804346368337523551464619943154719770857071655107899081988477_<65>

Number: 35559_125
N=45261293527849611944009007470516564747912317071464403030095643688236704332954890087226456720792950338179247
  ( 107 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=855863039493258726374436148063275096378011 (pp42)
 r2=52883804346368337523551464619943154719770857071655107899081988477 (pp65)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.93 hours.
Scaled time: 5.68 units (timescale=1.937).
Factorization parameters were as follows:
name: 35559_125
n: 45261293527849611944009007470516564747912317071464403030095643688236704332954890087226456720792950338179247
m: 20000000000000000000000000
deg: 5
c5: 1
c0: 31
skew: 1.99
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 700001)
Primes: RFBsize:71274, AFBsize:71376, largePrimes:2868761 encountered
Relations: rels:3072916, finalFF:475953
Max relations in full relation-set: 28
Initial matrix: 142714 x 475953 with sparse part having weight 34254737.
Pruned matrix : 85856 x 86633 with weight 6376451.
Total sieving time: 2.80 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 2.93 hours.
 --------- CPU info (if available) ----------

(32·10¹²⁸+31)/9 = 3(5)₁₂₇9_<129> = 25000147 · 4170310365607_<13> · 3288676168058609_<16> · C94

C94 = P46 · P48

P46 = 8411554247231991338364718226661881690595399127_<46>

P48 = 123281857069967884883915224017233748896454151597_<48>

Wed Nov 26 00:36:44 2008  Msieve v. 1.38
Wed Nov 26 00:36:44 2008  random seeds: 7e6bef0c f76e70b4
Wed Nov 26 00:36:44 2008  factoring 1036992028443535661266653954091510658049072752976818609735661966213284022836424574186379455819 (94 digits)
Wed Nov 26 00:36:45 2008  searching for 15-digit factors
Wed Nov 26 00:36:46 2008  commencing quadratic sieve (94-digit input)
Wed Nov 26 00:36:47 2008  using multiplier of 3
Wed Nov 26 00:36:47 2008  using 32kb Intel Core sieve core
Wed Nov 26 00:36:47 2008  sieve interval: 36 blocks of size 32768
Wed Nov 26 00:36:47 2008  processing polynomials in batches of 6
Wed Nov 26 00:36:47 2008  using a sieve bound of 1956287 (72941 primes)
Wed Nov 26 00:36:47 2008  using large prime bound of 244535875 (27 bits)
Wed Nov 26 00:36:47 2008  using double large prime bound of 1256078084807500 (42-51 bits)
Wed Nov 26 00:36:47 2008  using trial factoring cutoff of 51 bits
Wed Nov 26 00:36:47 2008  polynomial 'A' values have 12 factors
Wed Nov 26 00:36:47 2008  restarting with 10856 full and 592550 partial relations
Wed Nov 26 01:45:42 2008  73117 relations (18244 full + 54873 combined from 1001025 partial), need 73037
Wed Nov 26 01:45:44 2008  begin with 1019269 relations
Wed Nov 26 01:45:45 2008  reduce to 187744 relations in 12 passes
Wed Nov 26 01:45:45 2008  attempting to read 187744 relations
Wed Nov 26 01:45:47 2008  recovered 187744 relations
Wed Nov 26 01:45:47 2008  recovered 170550 polynomials
Wed Nov 26 01:45:48 2008  attempting to build 73117 cycles
Wed Nov 26 01:45:48 2008  found 73117 cycles in 5 passes
Wed Nov 26 01:45:48 2008  distribution of cycle lengths:
Wed Nov 26 01:45:48 2008     length 1 : 18244
Wed Nov 26 01:45:48 2008     length 2 : 13033
Wed Nov 26 01:45:48 2008     length 3 : 12520
Wed Nov 26 01:45:48 2008     length 4 : 10040
Wed Nov 26 01:45:48 2008     length 5 : 7217
Wed Nov 26 01:45:48 2008     length 6 : 4975
Wed Nov 26 01:45:48 2008     length 7 : 3133
Wed Nov 26 01:45:48 2008     length 9+: 3955
Wed Nov 26 01:45:48 2008  largest cycle: 18 relations
Wed Nov 26 01:45:48 2008  matrix is 72941 x 73117 (18.6 MB) with weight 4579830 (62.64/col)
Wed Nov 26 01:45:48 2008  sparse part has weight 4579830 (62.64/col)
Wed Nov 26 01:45:49 2008  filtering completed in 3 passes
Wed Nov 26 01:45:49 2008  matrix is 69223 x 69287 (17.7 MB) with weight 4366954 (63.03/col)
Wed Nov 26 01:45:49 2008  sparse part has weight 4366954 (63.03/col)
Wed Nov 26 01:45:49 2008  saving the first 48 matrix rows for later
Wed Nov 26 01:45:49 2008  matrix is 69175 x 69287 (10.6 MB) with weight 3397331 (49.03/col)
Wed Nov 26 01:45:49 2008  sparse part has weight 2369792 (34.20/col)
Wed Nov 26 01:45:49 2008  matrix includes 64 packed rows
Wed Nov 26 01:45:49 2008  using block size 27714 for processor cache size 1024 kB
Wed Nov 26 01:45:50 2008  commencing Lanczos iteration
Wed Nov 26 01:45:50 2008  memory use: 10.6 MB
Wed Nov 26 01:46:21 2008  lanczos halted after 1096 iterations (dim = 69175)
Wed Nov 26 01:46:21 2008  recovered 18 nontrivial dependencies
Wed Nov 26 01:46:22 2008  prp46 factor: 8411554247231991338364718226661881690595399127
Wed Nov 26 01:46:22 2008  prp48 factor: 123281857069967884883915224017233748896454151597
Wed Nov 26 01:46:22 2008  elapsed time 01:09:38

(32·10¹²⁷+31)/9 = 3(5)₁₂₆9_<128> = 3 · 13 · 23 · 1857797 · 42403008773_<11> · C108

C108 = P50 · P58

P50 = 93598957773679097998335210590339756869624650269513_<50>

P58 = 5375874010147014698096140847150062199888070164109434270599_<58>

Number: 35559_127
N=503176204472369347528704149914346319811344140205384244788935122030122608807740644710994427251286623921948287
  ( 108 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=93598957773679097998335210590339756869624650269513 (pp50)
 r2=5375874010147014698096140847150062199888070164109434270599 (pp58)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.91 hours.
Scaled time: 5.49 units (timescale=1.885).
Factorization parameters were as follows:
name: 35559_127
n: 503176204472369347528704149914346319811344140205384244788935122030122608807740644710994427251286623921948287
m: 20000000000000000000000000
deg: 5
c5: 100
c0: 31
skew: 0.79
type: snfs
lss: 1
rlim: 970000
alim: 970000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 970000/970000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [485000, 735001)
Primes: RFBsize:76350, AFBsize:76308, largePrimes:2524019 encountered
Relations: rels:2393135, finalFF:184054
Max relations in full relation-set: 28
Initial matrix: 152722 x 184054 with sparse part having weight 12789703.
Pruned matrix : 140139 x 140966 with weight 7598605.
Total sieving time: 2.69 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,970000,970000,26,26,47,47,2.3,2.3,50000
total time: 2.91 hours.
 --------- CPU info (if available) ----------

(32·10¹²⁶+13)/9 = 3(5)₁₂₅7_<127> = 380191666015952176443593_<24> · C103

C103 = P32 · P72

P32 = 11501538774057476031056012458627_<32>

P72 = 813109299918853671165561790980638470245413633332066936422499433992993087_<72>

Number: 35557_126
N=9352008140563424847917023294566006210147916989237119692496652400268872388438878951389661139693484511549
  ( 103 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=11501538774057476031056012458627 (pp32)
 r2=813109299918853671165561790980638470245413633332066936422499433992993087 (pp72)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 3.65 hours.
Scaled time: 1.73 units (timescale=0.473).
Factorization parameters were as follows:
name: 35557_126
n: 9352008140563424847917023294566006210147916989237119692496652400268872388438878951389661139693484511549
m: 20000000000000000000000000
deg: 5
c5: 10
c0: 13
skew: 1.05
type: snfs
lss: 1
rlim: 930000
alim: 930000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 930000/930000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [465000, 765001)
Primes: RFBsize:73474, AFBsize:73352, largePrimes:2549493 encountered
Relations: rels:2483110, finalFF:230404
Max relations in full relation-set: 28
Initial matrix: 146892 x 230404 with sparse part having weight 17391688.
Pruned matrix : 120843 x 121641 with weight 6495539.
Total sieving time: 3.35 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,930000,930000,26,26,46,46,2.3,2.3,50000
total time: 3.65 hours.
 --------- CPU info (if available) ----------

(32·10¹³⁰+13)/9 = 3(5)₁₂₉7_<131> = 17 · 37 · 1777 · 100591304997342587_<18> · C108

C108 = P37 · P72

P37 = 1050271947861286918310443412512133053_<37>

P72 = 301097526163687219478040228435943897480969623432826469142619137934601839_<72>

Number: 35557_130
N=316234285300150577120637906765190725260228622770227425697921490435194156409281796327578461287310422146484467
  ( 108 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=1050271947861286918310443412512133053 (pp37)
 r2=301097526163687219478040228435943897480969623432826469142619137934601839 (pp72)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.12 hours.
Scaled time: 6.11 units (timescale=1.955).
Factorization parameters were as follows:
name: 35557_130
n: 316234285300150577120637906765190725260228622770227425697921490435194156409281796327578461287310422146484467
m: 200000000000000000000000000
deg: 5
c5: 1
c0: 13
skew: 1.67
type: snfs
lss: 1
rlim: 1090000
alim: 1090000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1090000/1090000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [545000, 795001)
Primes: RFBsize:84976, AFBsize:85103, largePrimes:2811907 encountered
Relations: rels:2795363, finalFF:289791
Max relations in full relation-set: 28
Initial matrix: 170143 x 289791 with sparse part having weight 20768407.
Pruned matrix : 128435 x 129349 with weight 6660177.
Total sieving time: 2.93 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1090000,1090000,26,26,47,47,2.3,2.3,50000
total time: 3.12 hours.
 --------- CPU info (if available) ----------

(32·10¹³⁴+13)/9 = 3(5)₁₃₃7_<135> = 3² · 7 · 88560727 · 2289483979_<10> · C116

C116 = P49 · P67

P49 = 3196374879110325254657478673654847444267746688383_<49>

P67 = 8708240782305831710840887083343494810399416878830148384579837357001_<67>

Number: 35557_134
N=27834802077806407057659935627871990894848877408888265744552298958093842386798039849894726455952568910653769070419383
  ( 116 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=3196374879110325254657478673654847444267746688383 (pp49)
 r2=8708240782305831710840887083343494810399416878830148384579837357001 (pp67)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.00 hours.
Scaled time: 12.05 units (timescale=2.010).
Factorization parameters were as follows:
name: 35557_134
n: 27834802077806407057659935627871990894848877408888265744552298958093842386798039849894726455952568910653769070419383
m: 1000000000000000000000000000
deg: 5
c5: 16
c0: 65
skew: 1.32
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1175001)
Primes: RFBsize:100021, AFBsize:100193, largePrimes:3501357 encountered
Relations: rels:3766590, finalFF:544316
Max relations in full relation-set: 28
Initial matrix: 200278 x 544316 with sparse part having weight 44663294.
Pruned matrix : 133071 x 134136 with weight 11084208.
Total sieving time: 5.73 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000
total time: 6.00 hours.
 --------- CPU info (if available) ----------

(32·10¹³⁷+13)/9 = 3(5)₁₃₆7_<138> = 3 · 23 · 45337 · 145847851 · 159472373 · 9568191913142298047_<19> · C96

C96 = P44 · P52

P44 = 88546528817072023971206079968369863534097279_<44>

P52 = 5767912849452179312919971545551350229311180122030031_<52>

Wed Nov 26 05:14:00 2008  Msieve v. 1.38
Wed Nov 26 05:14:00 2008  random seeds: cf0e7240 51db047a
Wed Nov 26 05:14:00 2008  factoring 510728661338377406183907643299278443750079883884964732152000041361727719148120748810880513385649 (96 digits)
Wed Nov 26 05:14:00 2008  searching for 15-digit factors
Wed Nov 26 05:14:02 2008  commencing quadratic sieve (96-digit input)
Wed Nov 26 05:14:02 2008  using multiplier of 1
Wed Nov 26 05:14:02 2008  using 32kb Intel Core sieve core
Wed Nov 26 05:14:02 2008  sieve interval: 36 blocks of size 32768
Wed Nov 26 05:14:02 2008  processing polynomials in batches of 6
Wed Nov 26 05:14:02 2008  using a sieve bound of 2265611 (83418 primes)
Wed Nov 26 05:14:02 2008  using large prime bound of 339841650 (28 bits)
Wed Nov 26 05:14:02 2008  using double large prime bound of 2271422065653900 (43-52 bits)
Wed Nov 26 05:14:02 2008  using trial factoring cutoff of 52 bits
Wed Nov 26 05:14:02 2008  polynomial 'A' values have 12 factors
Wed Nov 26 09:51:26 2008  83756 relations (20168 full + 63588 combined from 1271970 partial), need 83514
Wed Nov 26 09:51:28 2008  begin with 1292138 relations
Wed Nov 26 09:51:29 2008  reduce to 221157 relations in 13 passes
Wed Nov 26 09:51:29 2008  attempting to read 221157 relations
Wed Nov 26 09:51:33 2008  recovered 221157 relations
Wed Nov 26 09:51:33 2008  recovered 206126 polynomials
Wed Nov 26 09:51:33 2008  attempting to build 83756 cycles
Wed Nov 26 09:51:33 2008  found 83756 cycles in 7 passes
Wed Nov 26 09:51:33 2008  distribution of cycle lengths:
Wed Nov 26 09:51:33 2008     length 1 : 20168
Wed Nov 26 09:51:33 2008     length 2 : 14206
Wed Nov 26 09:51:33 2008     length 3 : 13951
Wed Nov 26 09:51:33 2008     length 4 : 11416
Wed Nov 26 09:51:33 2008     length 5 : 8719
Wed Nov 26 09:51:33 2008     length 6 : 6047
Wed Nov 26 09:51:33 2008     length 7 : 3746
Wed Nov 26 09:51:33 2008     length 9+: 5503
Wed Nov 26 09:51:33 2008  largest cycle: 20 relations
Wed Nov 26 09:51:34 2008  matrix is 83418 x 83756 (23.2 MB) with weight 5751541 (68.67/col)
Wed Nov 26 09:51:34 2008  sparse part has weight 5751541 (68.67/col)
Wed Nov 26 09:51:34 2008  filtering completed in 3 passes
Wed Nov 26 09:51:34 2008  matrix is 79674 x 79736 (22.2 MB) with weight 5495801 (68.92/col)
Wed Nov 26 09:51:34 2008  sparse part has weight 5495801 (68.92/col)
Wed Nov 26 09:51:35 2008  saving the first 48 matrix rows for later
Wed Nov 26 09:51:35 2008  matrix is 79626 x 79736 (16.3 MB) with weight 4608485 (57.80/col)
Wed Nov 26 09:51:35 2008  sparse part has weight 3785457 (47.47/col)
Wed Nov 26 09:51:35 2008  matrix includes 64 packed rows
Wed Nov 26 09:51:35 2008  using block size 31894 for processor cache size 1024 kB
Wed Nov 26 09:51:36 2008  commencing Lanczos iteration
Wed Nov 26 09:51:36 2008  memory use: 14.4 MB
Wed Nov 26 09:52:30 2008  lanczos halted after 1261 iterations (dim = 79624)
Wed Nov 26 09:52:30 2008  recovered 16 nontrivial dependencies
Wed Nov 26 09:52:32 2008  prp44 factor: 88546528817072023971206079968369863534097279
Wed Nov 26 09:52:32 2008  prp52 factor: 5767912849452179312919971545551350229311180122030031
Wed Nov 26 09:52:32 2008  elapsed time 04:38:32

(32·10¹²⁶+31)/9 = 3(5)₁₂₅9_<127> = 7 · 16476983 · C119

C119 = P51 · P68

P51 = 680997224473041479842187137587524564706549553049407_<51>

P68 = 45267487816196178055544763426310297914032845214592067327606904162777_<68>

Number: 35559_126
N=30827033561696818920547317912296682985467455294243365821760968493838218835810931402703270162258254920607002902651323239
  ( 119 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=680997224473041479842187137587524564706549553049407 (pp51)
 r2=45267487816196178055544763426310297914032845214592067327606904162777 (pp68)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 3.64 hours.
Scaled time: 1.72 units (timescale=0.472).
Factorization parameters were as follows:
name: 35559_126
n: 30827033561696818920547317912296682985467455294243365821760968493838218835810931402703270162258254920607002902651323239
m: 20000000000000000000000000
deg: 5
c5: 10
c0: 31
skew: 1.25
type: snfs
lss: 1
rlim: 930000
alim: 930000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 930000/930000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [465000, 765001)
Primes: RFBsize:73474, AFBsize:73628, largePrimes:2612797 encountered
Relations: rels:2582628, finalFF:264069
Max relations in full relation-set: 28
Initial matrix: 147168 x 264069 with sparse part having weight 19890177.
Pruned matrix : 113591 x 114390 with weight 6088730.
Total sieving time: 3.36 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,930000,930000,26,26,46,46,2.3,2.3,50000
total time: 3.64 hours.
 --------- CPU info (if available) ----------

(32·10¹³⁷+31)/9 = 3(5)₁₃₆9_<138> = 17² · 167 · 370663 · C128

C128 = P44 · P85

P44 = 13381285655013871857765308443020945443852381_<44>

P85 = 1485306483235108080529520897277681421570533714769036651190820055852516640157660621731_<85>

Number: 35559_137
N=19875310337413053710637590695530793527882282744921895395807157800777667144452785946358436075296632143126961352653038140244691511
  ( 128 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=13381285655013871857765308443020945443852381 (pp44)
 r2=1485306483235108080529520897277681421570533714769036651190820055852516640157660621731 (pp85)
Version: GGNFS-0.77.1-20060513-k8
Total time: 7.53 hours.
Scaled time: 14.94 units (timescale=1.985).
Factorization parameters were as follows:
name: 35559_137
n: 19875310337413053710637590695530793527882282744921895395807157800777667144452785946358436075296632143126961352653038140244691511
m: 2000000000000000000000000000
deg: 5
c5: 100
c0: 31
skew: 0.79
type: snfs
lss: 1
rlim: 1420000
alim: 1420000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1420000/1420000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [710000, 1385001)
Primes: RFBsize:108487, AFBsize:108634, largePrimes:3522102 encountered
Relations: rels:3644702, finalFF:410418
Max relations in full relation-set: 28
Initial matrix: 217185 x 410418 with sparse part having weight 36113840.
Pruned matrix : 168501 x 169650 with weight 12265564.
Total sieving time: 7.10 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1420000,1420000,26,26,48,48,2.3,2.3,75000
total time: 7.53 hours.
 --------- CPU info (if available) ----------

(32·10¹³¹+31)/9 = 3(5)₁₃₀9_<132> = 266066510143035541_<18> · C115

C115 = P42 · P73

P42 = 844138519262383556289425467818988709704541_<42>

P73 = 1583082461247132173875334710522972730177912267910497115891734314149580039_<73>

Number: 35559_131
N=1336340884707403852333814649696063832094289430719468240561408485925328779819885140490430012885296587458038921257099
  ( 115 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=844138519262383556289425467818988709704541 (pp42)
 r2=1583082461247132173875334710522972730177912267910497115891734314149580039 (pp73)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 5.16 hours.
Scaled time: 2.43 units (timescale=0.471).
Factorization parameters were as follows:
name: 35559_131
n: 1336340884707403852333814649696063832094289430719468240561408485925328779819885140490430012885296587458038921257099
m: 200000000000000000000000000
deg: 5
c5: 10
c0: 31
skew: 1.25
type: snfs
lss: 1
rlim: 1130000
alim: 1130000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1130000/1130000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [565000, 965001)
Primes: RFBsize:87884, AFBsize:88119, largePrimes:2834235 encountered
Relations: rels:2738680, finalFF:224186
Max relations in full relation-set: 28
Initial matrix: 176069 x 224186 with sparse part having weight 17121575.
Pruned matrix : 157598 x 158542 with weight 9354096.
Total sieving time: 4.65 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.36 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1130000,1130000,26,26,47,47,2.3,2.3,50000
total time: 5.16 hours.
 --------- CPU info (if available) ----------

Nov 25, 2008 (6th)

By Sinkiti Sibata / Msieve, GGNFS

(32·10¹¹¹+31)/9 = 3(5)₁₁₀9_<112> = 83 · 479 · 221059673 · 213133327019_<12> · C88

C88 = P36 · P52

P36 = 487569966093755841400317894390408449_<36>

P52 = 3893104217967748849798424193291740807807864809580849_<52>

Tue Nov 25 16:11:38 2008  Msieve v. 1.38
Tue Nov 25 16:11:38 2008  random seeds: 4901283c 27d5cc06
Tue Nov 25 16:11:38 2008  factoring 1898160691553993157407449678245732393464881155578512112540299285983401084722145598193201 (88 digits)
Tue Nov 25 16:11:39 2008  searching for 15-digit factors
Tue Nov 25 16:11:41 2008  commencing quadratic sieve (88-digit input)
Tue Nov 25 16:11:41 2008  using multiplier of 1
Tue Nov 25 16:11:41 2008  using 32kb Intel Core sieve core
Tue Nov 25 16:11:41 2008  sieve interval: 24 blocks of size 32768
Tue Nov 25 16:11:41 2008  processing polynomials in batches of 9
Tue Nov 25 16:11:41 2008  using a sieve bound of 1508383 (57034 primes)
Tue Nov 25 16:11:41 2008  using large prime bound of 120670640 (26 bits)
Tue Nov 25 16:11:41 2008  using double large prime bound of 352275850752880 (42-49 bits)
Tue Nov 25 16:11:41 2008  using trial factoring cutoff of 49 bits
Tue Nov 25 16:11:41 2008  polynomial 'A' values have 11 factors
Tue Nov 25 17:12:53 2008  57299 relations (14815 full + 42484 combined from 613221 partial), need 57130
Tue Nov 25 17:12:56 2008  begin with 628036 relations
Tue Nov 25 17:12:56 2008  reduce to 140932 relations in 10 passes
Tue Nov 25 17:12:56 2008  attempting to read 140932 relations
Tue Nov 25 17:12:59 2008  recovered 140932 relations
Tue Nov 25 17:12:59 2008  recovered 122059 polynomials
Tue Nov 25 17:12:59 2008  attempting to build 57299 cycles
Tue Nov 25 17:12:59 2008  found 57299 cycles in 5 passes
Tue Nov 25 17:12:59 2008  distribution of cycle lengths:
Tue Nov 25 17:12:59 2008     length 1 : 14815
Tue Nov 25 17:12:59 2008     length 2 : 11055
Tue Nov 25 17:12:59 2008     length 3 : 10130
Tue Nov 25 17:12:59 2008     length 4 : 7717
Tue Nov 25 17:12:59 2008     length 5 : 5412
Tue Nov 25 17:12:59 2008     length 6 : 3622
Tue Nov 25 17:12:59 2008     length 7 : 2122
Tue Nov 25 17:12:59 2008     length 9+: 2426
Tue Nov 25 17:12:59 2008  largest cycle: 20 relations
Tue Nov 25 17:12:59 2008  matrix is 57034 x 57299 (13.4 MB) with weight 3274244 (57.14/col)
Tue Nov 25 17:12:59 2008  sparse part has weight 3274244 (57.14/col)
Tue Nov 25 17:13:00 2008  filtering completed in 3 passes
Tue Nov 25 17:13:00 2008  matrix is 53372 x 53436 (12.5 MB) with weight 3072775 (57.50/col)
Tue Nov 25 17:13:00 2008  sparse part has weight 3072775 (57.50/col)
Tue Nov 25 17:13:00 2008  saving the first 48 matrix rows for later
Tue Nov 25 17:13:00 2008  matrix is 53324 x 53436 (8.0 MB) with weight 2417387 (45.24/col)
Tue Nov 25 17:13:00 2008  sparse part has weight 1766360 (33.06/col)
Tue Nov 25 17:13:00 2008  matrix includes 64 packed rows
Tue Nov 25 17:13:00 2008  using block size 21374 for processor cache size 2048 kB
Tue Nov 25 17:13:00 2008  commencing Lanczos iteration
Tue Nov 25 17:13:00 2008  memory use: 7.9 MB
Tue Nov 25 17:13:17 2008  lanczos halted after 845 iterations (dim = 53320)
Tue Nov 25 17:13:17 2008  recovered 14 nontrivial dependencies
Tue Nov 25 17:13:18 2008  prp36 factor: 487569966093755841400317894390408449
Tue Nov 25 17:13:18 2008  prp52 factor: 3893104217967748849798424193291740807807864809580849
Tue Nov 25 17:13:18 2008  elapsed time 01:01:40

(32·10¹¹³+13)/9 = 3(5)₁₁₂7_<114> = 3 · 367 · 8039 · 260363 · 4472974792621_<13> · C89

C89 = P42 · P47

P42 = 722805190445538559579755657850210987340009_<42>

P47 = 47722275212804886755544319503545804388116823209_<47>

Tue Nov 25 17:21:51 2008  Msieve v. 1.38
Tue Nov 25 17:21:51 2008  random seeds: 73861c22 a47e1017
Tue Nov 25 17:21:51 2008  factoring 34493908223685840362451462065513046847262683445436352847040664541897484049027610225468881 (89 digits)
Tue Nov 25 17:21:52 2008  searching for 15-digit factors
Tue Nov 25 17:21:53 2008  commencing quadratic sieve (89-digit input)
Tue Nov 25 17:21:53 2008  using multiplier of 1
Tue Nov 25 17:21:53 2008  using 32kb Intel Core sieve core
Tue Nov 25 17:21:53 2008  sieve interval: 32 blocks of size 32768
Tue Nov 25 17:21:53 2008  processing polynomials in batches of 7
Tue Nov 25 17:21:53 2008  using a sieve bound of 1556083 (58841 primes)
Tue Nov 25 17:21:53 2008  using large prime bound of 124486640 (26 bits)
Tue Nov 25 17:21:53 2008  using double large prime bound of 372581168808240 (42-49 bits)
Tue Nov 25 17:21:53 2008  using trial factoring cutoff of 49 bits
Tue Nov 25 17:21:53 2008  polynomial 'A' values have 11 factors
Tue Nov 25 18:01:21 2008  59297 relations (17170 full + 42127 combined from 608482 partial), need 58937
Tue Nov 25 18:01:23 2008  begin with 625652 relations
Tue Nov 25 18:01:23 2008  reduce to 138778 relations in 10 passes
Tue Nov 25 18:01:23 2008  attempting to read 138778 relations
Tue Nov 25 18:01:26 2008  recovered 138778 relations
Tue Nov 25 18:01:26 2008  recovered 102781 polynomials
Tue Nov 25 18:01:26 2008  attempting to build 59297 cycles
Tue Nov 25 18:01:26 2008  found 59297 cycles in 5 passes
Tue Nov 25 18:01:26 2008  distribution of cycle lengths:
Tue Nov 25 18:01:26 2008     length 1 : 17170
Tue Nov 25 18:01:26 2008     length 2 : 12193
Tue Nov 25 18:01:26 2008     length 3 : 10649
Tue Nov 25 18:01:26 2008     length 4 : 7548
Tue Nov 25 18:01:26 2008     length 5 : 4978
Tue Nov 25 18:01:26 2008     length 6 : 3084
Tue Nov 25 18:01:26 2008     length 7 : 1791
Tue Nov 25 18:01:26 2008     length 9+: 1884
Tue Nov 25 18:01:26 2008  largest cycle: 16 relations
Tue Nov 25 18:01:26 2008  matrix is 58841 x 59297 (13.8 MB) with weight 3372407 (56.87/col)
Tue Nov 25 18:01:26 2008  sparse part has weight 3372407 (56.87/col)
Tue Nov 25 18:01:26 2008  filtering completed in 3 passes
Tue Nov 25 18:01:26 2008  matrix is 53403 x 53467 (12.5 MB) with weight 3061639 (57.26/col)
Tue Nov 25 18:01:26 2008  sparse part has weight 3061639 (57.26/col)
Tue Nov 25 18:01:27 2008  saving the first 48 matrix rows for later
Tue Nov 25 18:01:27 2008  matrix is 53355 x 53467 (8.5 MB) with weight 2428743 (45.43/col)
Tue Nov 25 18:01:27 2008  sparse part has weight 1915838 (35.83/col)
Tue Nov 25 18:01:27 2008  matrix includes 64 packed rows
Tue Nov 25 18:01:27 2008  using block size 21386 for processor cache size 2048 kB
Tue Nov 25 18:01:27 2008  commencing Lanczos iteration
Tue Nov 25 18:01:27 2008  memory use: 8.0 MB
Tue Nov 25 18:01:45 2008  lanczos halted after 846 iterations (dim = 53348)
Tue Nov 25 18:01:45 2008  recovered 13 nontrivial dependencies
Tue Nov 25 18:01:46 2008  prp42 factor: 722805190445538559579755657850210987340009
Tue Nov 25 18:01:46 2008  prp47 factor: 47722275212804886755544319503545804388116823209
Tue Nov 25 18:01:46 2008  elapsed time 00:39:55

(31·10¹⁴⁷+41)/9 = 3(4)₁₄₆9_<148> = 30619519171_<11> · C138

C138 = P38 · P50 · P50

P38 = 52645699521864232841037910835053332133_<38>

P50 = 26284555383594257254292409604368589956841814276767_<50>

P50 = 81293773300248697922814898301342394783351214050929_<50>

Number: 34449_147
N=112491787516595175094248525044692787688858788070759429119202756420202848274323231189071647765374520630627849399171887618027300225120326219
  ( 138 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=52645699521864232841037910835053332133 (pp38)
 r2=26284555383594257254292409604368589956841814276767 (pp50)
 r3=81293773300248697922814898301342394783351214050929 (pp50)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 39.23 hours.
Scaled time: 18.52 units (timescale=0.472).
Factorization parameters were as follows:
name: 34449_147
n: 112491787516595175094248525044692787688858788070759429119202756420202848274323231189071647765374520630627849399171887618027300225120326219
m: 200000000000000000000000000000
deg: 5
c5: 775
c0: 328
skew: 0.84
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1100000, 4100001)
Primes: RFBsize:162662, AFBsize:163207, largePrimes:4709465 encountered
Relations: rels:5141491, finalFF:384765
Max relations in full relation-set: 28
Initial matrix: 325936 x 384765 with sparse part having weight 47733275.
Pruned matrix : 306013 x 307706 with weight 36858857.
Total sieving time: 34.63 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 4.11 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,49,49,2.3,2.3,100000
total time: 39.23 hours.
 --------- CPU info (if available) ----------

(32·10¹²²+31)/9 = 3(5)₁₂₁9_<123> = 328781 · 2504008107923036641496791213_<28> · C90

C90 = P35 · P56

P35 = 42723292270746693182558544322045801_<35>

P56 = 10108816517969606422105778729319311803504197245858958103_<56>

Tue Nov 25 18:15:00 2008  Msieve v. 1.38
Tue Nov 25 18:15:00 2008  random seeds: d1551f0c 1ce83f3a
Tue Nov 25 18:15:00 2008  factoring 431881922608567386526197281175982703937335426667558565328396228433888608545324127306075503 (90 digits)
Tue Nov 25 18:15:01 2008  searching for 15-digit factors
Tue Nov 25 18:15:03 2008  commencing quadratic sieve (90-digit input)
Tue Nov 25 18:15:03 2008  using multiplier of 7
Tue Nov 25 18:15:03 2008  using 32kb Intel Core sieve core
Tue Nov 25 18:15:03 2008  sieve interval: 36 blocks of size 32768
Tue Nov 25 18:15:03 2008  processing polynomials in batches of 6
Tue Nov 25 18:15:03 2008  using a sieve bound of 1584929 (59679 primes)
Tue Nov 25 18:15:03 2008  using large prime bound of 126794320 (26 bits)
Tue Nov 25 18:15:03 2008  using double large prime bound of 385105414448400 (42-49 bits)
Tue Nov 25 18:15:03 2008  using trial factoring cutoff of 49 bits
Tue Nov 25 18:15:03 2008  polynomial 'A' values have 12 factors
Tue Nov 25 19:31:03 2008  60194 relations (15958 full + 44236 combined from 638107 partial), need 59775
Tue Nov 25 19:31:05 2008  begin with 654065 relations
Tue Nov 25 19:31:05 2008  reduce to 146856 relations in 10 passes
Tue Nov 25 19:31:05 2008  attempting to read 146856 relations
Tue Nov 25 19:31:08 2008  recovered 146856 relations
Tue Nov 25 19:31:08 2008  recovered 125328 polynomials
Tue Nov 25 19:31:08 2008  attempting to build 60194 cycles
Tue Nov 25 19:31:08 2008  found 60194 cycles in 5 passes
Tue Nov 25 19:31:08 2008  distribution of cycle lengths:
Tue Nov 25 19:31:08 2008     length 1 : 15958
Tue Nov 25 19:31:08 2008     length 2 : 11650
Tue Nov 25 19:31:08 2008     length 3 : 10547
Tue Nov 25 19:31:08 2008     length 4 : 8074
Tue Nov 25 19:31:08 2008     length 5 : 5654
Tue Nov 25 19:31:08 2008     length 6 : 3590
Tue Nov 25 19:31:08 2008     length 7 : 2148
Tue Nov 25 19:31:08 2008     length 9+: 2573
Tue Nov 25 19:31:08 2008  largest cycle: 20 relations
Tue Nov 25 19:31:09 2008  matrix is 59679 x 60194 (14.7 MB) with weight 3625687 (60.23/col)
Tue Nov 25 19:31:09 2008  sparse part has weight 3625687 (60.23/col)
Tue Nov 25 19:31:09 2008  filtering completed in 3 passes
Tue Nov 25 19:31:09 2008  matrix is 55677 x 55741 (13.7 MB) with weight 3363925 (60.35/col)
Tue Nov 25 19:31:09 2008  sparse part has weight 3363925 (60.35/col)
Tue Nov 25 19:31:09 2008  saving the first 48 matrix rows for later
Tue Nov 25 19:31:09 2008  matrix is 55629 x 55741 (8.7 MB) with weight 2647142 (47.49/col)
Tue Nov 25 19:31:09 2008  sparse part has weight 1945354 (34.90/col)
Tue Nov 25 19:31:09 2008  matrix includes 64 packed rows
Tue Nov 25 19:31:09 2008  using block size 22296 for processor cache size 2048 kB
Tue Nov 25 19:31:10 2008  commencing Lanczos iteration
Tue Nov 25 19:31:10 2008  memory use: 8.4 MB
Tue Nov 25 19:31:28 2008  lanczos halted after 881 iterations (dim = 55626)
Tue Nov 25 19:31:29 2008  recovered 16 nontrivial dependencies
Tue Nov 25 19:31:29 2008  prp35 factor: 42723292270746693182558544322045801
Tue Nov 25 19:31:29 2008  prp56 factor: 10108816517969606422105778729319311803504197245858958103
Tue Nov 25 19:31:29 2008  elapsed time 01:16:29

(32·10¹¹⁹+13)/9 = 3(5)₁₁₈7_<120> = 3 · 207637403 · 1000206492930416143935716239_<28> · C84

C84 = P33 · P51

P33 = 640277981563769011474718630122289_<33>

P51 = 891296885887495874319183654447578766973756482284363_<51>

Tue Nov 25 16:25:35 2008  Msieve v. 1.38
Tue Nov 25 16:25:35 2008  random seeds: ac2b7704 f677277a
Tue Nov 25 16:25:35 2008  factoring 570677771070118815842205302870178050917454543396455013477008232333098780244762466907 (84 digits)
Tue Nov 25 16:25:38 2008  searching for 15-digit factors
Tue Nov 25 16:25:42 2008  commencing quadratic sieve (84-digit input)
Tue Nov 25 16:25:43 2008  using multiplier of 43
Tue Nov 25 16:25:43 2008  using 64kb Pentium 2 sieve core
Tue Nov 25 16:25:43 2008  sieve interval: 6 blocks of size 65536
Tue Nov 25 16:25:43 2008  processing polynomials in batches of 17
Tue Nov 25 16:25:43 2008  using a sieve bound of 1407293 (53824 primes)
Tue Nov 25 16:25:43 2008  using large prime bound of 119619905 (26 bits)
Tue Nov 25 16:25:43 2008  using double large prime bound of 346773678658515 (41-49 bits)
Tue Nov 25 16:25:43 2008  using trial factoring cutoff of 49 bits
Tue Nov 25 16:25:43 2008  polynomial 'A' values have 11 factors
Tue Nov 25 20:30:12 2008  53931 relations (16424 full + 37507 combined from 568412 partial), need 53920
Tue Nov 25 20:30:18 2008  begin with 584836 relations
Tue Nov 25 20:30:20 2008  reduce to 124724 relations in 10 passes
Tue Nov 25 20:30:20 2008  attempting to read 124724 relations
Tue Nov 25 20:30:26 2008  recovered 124724 relations
Tue Nov 25 20:30:26 2008  recovered 100563 polynomials
Tue Nov 25 20:30:26 2008  attempting to build 53931 cycles
Tue Nov 25 20:30:26 2008  found 53931 cycles in 4 passes
Tue Nov 25 20:30:30 2008  distribution of cycle lengths:
Tue Nov 25 20:30:30 2008     length 1 : 16424
Tue Nov 25 20:30:30 2008     length 2 : 11082
Tue Nov 25 20:30:30 2008     length 3 : 9630
Tue Nov 25 20:30:30 2008     length 4 : 6837
Tue Nov 25 20:30:30 2008     length 5 : 4320
Tue Nov 25 20:30:30 2008     length 6 : 2598
Tue Nov 25 20:30:30 2008     length 7 : 1463
Tue Nov 25 20:30:30 2008     length 9+: 1577
Tue Nov 25 20:30:30 2008  largest cycle: 18 relations
Tue Nov 25 20:30:31 2008  matrix is 53824 x 53931 (11.3 MB) with weight 2739791 (50.80/col)
Tue Nov 25 20:30:31 2008  sparse part has weight 2739791 (50.80/col)
Tue Nov 25 20:30:35 2008  filtering completed in 3 passes
Tue Nov 25 20:30:35 2008  matrix is 48144 x 48208 (10.2 MB) with weight 2482659 (51.50/col)
Tue Nov 25 20:30:35 2008  sparse part has weight 2482659 (51.50/col)
Tue Nov 25 20:30:37 2008  saving the first 48 matrix rows for later
Tue Nov 25 20:30:37 2008  matrix is 48096 x 48208 (5.6 MB) with weight 1823977 (37.84/col)
Tue Nov 25 20:30:37 2008  sparse part has weight 1189151 (24.67/col)
Tue Nov 25 20:30:37 2008  matrix includes 64 packed rows
Tue Nov 25 20:30:38 2008  using block size 5461 for processor cache size 128 kB
Tue Nov 25 20:30:39 2008  commencing Lanczos iteration
Tue Nov 25 20:30:39 2008  memory use: 6.2 MB
Tue Nov 25 20:32:29 2008  lanczos halted after 762 iterations (dim = 48096)
Tue Nov 25 20:32:30 2008  recovered 18 nontrivial dependencies
Tue Nov 25 20:32:32 2008  prp33 factor: 640277981563769011474718630122289
Tue Nov 25 20:32:32 2008  prp51 factor: 891296885887495874319183654447578766973756482284363
Tue Nov 25 20:32:32 2008  elapsed time 04:06:57

(32·10¹²⁰+31)/9 = 3(5)₁₁₉9_<121> = 7 · 5807 · C116

C116 = P31 · P86

P31 = 3113032816097266174778764676807_<31>

P86 = 28097902683758787473437650239350518110448549347179343214543208493496692074850718804313_<86>

Number: 35559_120
N=87469693118048551146536336823920774325458327524799024712921733758654716119844413283366271139648098490874450922668591
  ( 116 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=3113032816097266174778764676807 (pp31)
 r2=28097902683758787473437650239350518110448549347179343214543208493496692074850718804313 (pp86)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.50 hours.
Scaled time: 5.00 units (timescale=2.003).
Factorization parameters were as follows:
name: 35559_120
n: 87469693118048551146536336823920774325458327524799024712921733758654716119844413283366271139648098490874450922668591
m: 2000000000000000000000000
deg: 5
c5: 1
c0: 31
skew: 1.99
type: snfs
lss: 1
rlim: 740000
alim: 740000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [370000, 620001)
Primes: RFBsize:59531, AFBsize:59539, largePrimes:1702979 encountered
Relations: rels:1960859, finalFF:410760
Max relations in full relation-set: 28
Initial matrix: 119134 x 410760 with sparse part having weight 19379073.
Pruned matrix : 67073 x 67732 with weight 3827093.
Total sieving time: 2.41 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000
total time: 2.50 hours.
 --------- CPU info (if available) ----------

(32·10¹²⁴+13)/9 = 3(5)₁₂₃7_<125> = 31 · 37 · 111150343 · 3992206561597_<13> · C101

C101 = P41 · P61

P41 = 10402125562044091642484846822078823468091_<41>

P61 = 6715806088535023166394807724616174297101621140015673344377671_<61>

Number: 35557_124
N=69858658183281510532470852601943169332228650358787493281055371585330045221451803823211994604321396061
  ( 101 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=10402125562044091642484846822078823468091 (pp41)
 r2=6715806088535023166394807724616174297101621140015673344377671 (pp61)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 3.20 hours.
Scaled time: 1.51 units (timescale=0.472).
Factorization parameters were as follows:
name: 35557_124
n: 69858658183281510532470852601943169332228650358787493281055371585330045221451803823211994604321396061
m: 10000000000000000000000000
deg: 5
c5: 16
c0: 65
skew: 1.32
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [445000, 695001)
Primes: RFBsize:70555, AFBsize:70488, largePrimes:2519735 encountered
Relations: rels:2495783, finalFF:266363
Max relations in full relation-set: 28
Initial matrix: 141107 x 266363 with sparse part having weight 18696002.
Pruned matrix : 104070 x 104839 with weight 5169750.
Total sieving time: 2.97 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 3.20 hours.
 --------- CPU info (if available) ----------

(32·10¹¹³+31)/9 = 3(5)₁₁₂9_<114> = 6871 · 5101787 · C104

C104 = P31 · P73

P31 = 2169685434607141957872712202903_<31>

P73 = 4674858004238930698030761281227982249602384821440497976576836629122533589_<73>

Number: 35559_113
N=10142971320653820632723339542539382492089008306725584839857993969919889375979466051668360765372800808867
  ( 104 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=2169685434607141957872712202903 (pp31)
 r2=4674858004238930698030761281227982249602384821440497976576836629122533589 (pp73)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1.57 hours.
Scaled time: 3.08 units (timescale=1.967).
Factorization parameters were as follows:
name: 35559_113
n: 10142971320653820632723339542539382492089008306725584839857993969919889375979466051668360765372800808867
m: 40000000000000000000000
deg: 5
c5: 125
c0: 124
skew: 1.00
type: snfs
lss: 1
rlim: 580000
alim: 580000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 580000/580000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [290000, 440001)
Primes: RFBsize:47588, AFBsize:47780, largePrimes:1340429 encountered
Relations: rels:1372204, finalFF:195899
Max relations in full relation-set: 28
Initial matrix: 95434 x 195899 with sparse part having weight 9478162.
Pruned matrix : 67455 x 67996 with weight 2513133.
Total sieving time: 1.49 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,580000,580000,25,25,45,45,2.2,2.2,50000
total time: 1.57 hours.
 --------- CPU info (if available) ----------

9·10²¹³-1 = 8(9)₂₁₃_<214> = 293 · 31517 · 297630677 · 653240602737601_<15> · 2763180643414756163_<19> · 1880839632718006855987957867_<28> · 179481389251375241524195452694409_<33> · C106

C106 = P30 · P77

P30 = 240517498236320119968635920027_<30>

P77 = 22343541377353884509643293353805591669647127166940550303134256458298751571009_<77>

Mon Nov 24 00:11:51 2008  Msieve v. 1.38
Mon Nov 24 00:11:51 2008  random seeds: a24e6aa0 3eb03746
Mon Nov 24 00:11:51 2008  factoring 5374012673820858541660812441083032124477051306670520962378248708789456585274457770479061617280814335697243 (106 digits)
Mon Nov 24 00:11:52 2008  searching for 15-digit factors
Mon Nov 24 00:11:54 2008  commencing quadratic sieve (106-digit input)
Mon Nov 24 00:11:54 2008  using multiplier of 3
Mon Nov 24 00:11:54 2008  using 32kb Intel Core sieve core
Mon Nov 24 00:11:54 2008  sieve interval: 41 blocks of size 32768
Mon Nov 24 00:11:54 2008  processing polynomials in batches of 5
Mon Nov 24 00:11:54 2008  using a sieve bound of 4519019 (158667 primes)
Mon Nov 24 00:11:54 2008  using large prime bound of 677852850 (29 bits)
Mon Nov 24 00:11:54 2008  using double large prime bound of 7871251019049750 (45-53 bits)
Mon Nov 24 00:11:54 2008  using trial factoring cutoff of 53 bits
Mon Nov 24 00:11:54 2008  polynomial 'A' values have 14 factors
Tue Nov 25 22:27:00 2008  158913 relations (37698 full + 121215 combined from 2331858 partial), need 158763
Tue Nov 25 22:27:03 2008  begin with 2369556 relations
Tue Nov 25 22:27:06 2008  reduce to 417220 relations in 11 passes
Tue Nov 25 22:27:06 2008  attempting to read 417220 relations
Tue Nov 25 22:27:16 2008  recovered 417220 relations
Tue Nov 25 22:27:16 2008  recovered 409284 polynomials
Tue Nov 25 22:27:16 2008  attempting to build 158913 cycles
Tue Nov 25 22:27:16 2008  found 158913 cycles in 6 passes
Tue Nov 25 22:27:16 2008  distribution of cycle lengths:
Tue Nov 25 22:27:16 2008     length 1 : 37698
Tue Nov 25 22:27:16 2008     length 2 : 27255
Tue Nov 25 22:27:16 2008     length 3 : 26726
Tue Nov 25 22:27:16 2008     length 4 : 21725
Tue Nov 25 22:27:16 2008     length 5 : 16730
Tue Nov 25 22:27:16 2008     length 6 : 11228
Tue Nov 25 22:27:16 2008     length 7 : 7302
Tue Nov 25 22:27:16 2008     length 9+: 10249
Tue Nov 25 22:27:16 2008  largest cycle: 20 relations
Tue Nov 25 22:27:17 2008  matrix is 158667 x 158913 (42.9 MB) with weight 10612023 (66.78/col)
Tue Nov 25 22:27:17 2008  sparse part has weight 10612023 (66.78/col)
Tue Nov 25 22:27:20 2008  filtering completed in 3 passes
Tue Nov 25 22:27:20 2008  matrix is 152562 x 152626 (41.4 MB) with weight 10241543 (67.10/col)
Tue Nov 25 22:27:20 2008  sparse part has weight 10241543 (67.10/col)
Tue Nov 25 22:27:21 2008  saving the first 48 matrix rows for later
Tue Nov 25 22:27:21 2008  matrix is 152514 x 152626 (22.7 MB) with weight 7745078 (50.75/col)
Tue Nov 25 22:27:21 2008  sparse part has weight 5042413 (33.04/col)
Tue Nov 25 22:27:21 2008  matrix includes 64 packed rows
Tue Nov 25 22:27:21 2008  using block size 43690 for processor cache size 1024 kB
Tue Nov 25 22:27:22 2008  commencing Lanczos iteration
Tue Nov 25 22:27:22 2008  memory use: 24.2 MB
Tue Nov 25 22:30:07 2008  lanczos halted after 2415 iterations (dim = 152514)
Tue Nov 25 22:30:08 2008  recovered 18 nontrivial dependencies
Tue Nov 25 22:30:09 2008  prp30 factor: 240517498236320119968635920027
Tue Nov 25 22:30:09 2008  prp77 factor: 22343541377353884509643293353805591669647127166940550303134256458298751571009
Tue Nov 25 22:30:09 2008  elapsed time 46:18:18

Nov 25, 2008 (5th)

By Serge Batalov / Msieve, GMP-ECM 6.2.1, Msieve-1.39, Msieve-1.39/QS, Msieve-1.38

(32·10¹³³+13)/9 = 3(5)₁₃₂7_<134> = 37 · 28229087 · 26252902873_<11> · 1807579431701_<13> · 672131425700807858561_<21> · C82

C82 = P40 · P42

P40 = 3701932676318776884096888982145290362881_<40>

P42 = 288304533842512763257586489293524587911771_<42>

Mon Nov 24 21:44:24 2008  Msieve v. 1.39
Mon Nov 24 21:44:24 2008  random seeds: 53b7fae1 4fe02420
Mon Nov 24 21:44:24 2008  factoring 1067283974562450657219633927845179417913759582844266707522004006708319194601372251 (82 digits)
Mon Nov 24 21:44:25 2008  searching for 15-digit factors
Mon Nov 24 21:44:25 2008  commencing quadratic sieve (82-digit input)
Mon Nov 24 21:44:26 2008  using multiplier of 11
Mon Nov 24 21:44:26 2008  using 64kb Opteron sieve core
Mon Nov 24 21:44:26 2008  sieve interval: 6 blocks of size 65536
Mon Nov 24 21:44:26 2008  processing polynomials in batches of 17
Mon Nov 24 21:44:26 2008  using a sieve bound of 1334341 (51074 primes)
Mon Nov 24 21:44:26 2008  using large prime bound of 126762395 (26 bits)
Mon Nov 24 21:44:26 2008  using trial factoring cutoff of 27 bits
Mon Nov 24 21:44:26 2008  polynomial 'A' values have 10 factors
Mon Nov 24 21:57:27 2008  51230 relations (26672 full + 24558 combined from 272144 partial), need 51170
Mon Nov 24 21:57:28 2008  begin with 298816 relations
Mon Nov 24 21:57:28 2008  reduce to 72630 relations in 2 passes
Mon Nov 24 21:57:28 2008  attempting to read 72630 relations
Mon Nov 24 21:57:28 2008  recovered 72630 relations
Mon Nov 24 21:57:28 2008  recovered 62674 polynomials
Mon Nov 24 21:57:28 2008  attempting to build 51230 cycles
Mon Nov 24 21:57:28 2008  found 51230 cycles in 1 passes
Mon Nov 24 21:57:28 2008  distribution of cycle lengths:
Mon Nov 24 21:57:28 2008     length 1 : 26672
Mon Nov 24 21:57:28 2008     length 2 : 24558
Mon Nov 24 21:57:28 2008  largest cycle: 2 relations
Mon Nov 24 21:57:28 2008  matrix is 51074 x 51230 (7.6 MB) with weight 1577987 (30.80/col)
Mon Nov 24 21:57:28 2008  sparse part has weight 1577987 (30.80/col)
Mon Nov 24 21:57:29 2008  filtering completed in 3 passes
Mon Nov 24 21:57:29 2008  matrix is 36236 x 36299 (5.9 MB) with weight 1256664 (34.62/col)
Mon Nov 24 21:57:29 2008  sparse part has weight 1256664 (34.62/col)
Mon Nov 24 21:57:29 2008  saving the first 48 matrix rows for later
Mon Nov 24 21:57:29 2008  matrix is 36188 x 36299 (4.6 MB) with weight 1006135 (27.72/col)
Mon Nov 24 21:57:29 2008  sparse part has weight 834315 (22.98/col)
Mon Nov 24 21:57:29 2008  matrix includes 64 packed rows
Mon Nov 24 21:57:29 2008  using block size 14519 for processor cache size 1024 kB
Mon Nov 24 21:57:29 2008  commencing Lanczos iteration
Mon Nov 24 21:57:29 2008  memory use: 4.3 MB
Mon Nov 24 21:57:34 2008  lanczos halted after 573 iterations (dim = 36186)
Mon Nov 24 21:57:34 2008  recovered 16 nontrivial dependencies
Mon Nov 24 21:57:34 2008  prp40 factor: 3701932676318776884096888982145290362881
Mon Nov 24 21:57:34 2008  prp42 factor: 288304533842512763257586489293524587911771
Mon Nov 24 21:57:34 2008  elapsed time 00:13:10

(32·10¹²⁰+13)/9 = 3(5)₁₁₉7_<121> = 4937 · 12451 · 1016780899_<10> · 666585174041787950087_<21> · C83

C83 = P30 · P54

P30 = 750956733862170017094819057059_<30>

P54 = 113642862248618823692705891243347504507404736593836833_<54>

Factor found in step 2: 750956733862170017094819057059

(32·10¹⁵⁷+13)/9 = 3(5)₁₅₆7_<158> = 29 · 37 · 4001 · 10345641860816323_<17> · 1998968244836228509_<19> · 1730927190715608520160070713867_<31> · C87

C87 = P31 · P57

P31 = 1037983176934327212428494372699_<31>

P57 = 222898294402775465729776596045681470561860226927431308539_<57>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1740884508
Step 1 took 9068ms
Step 2 took 7069ms
********** Factor found in step 2: 1037983176934327212428494372699
Found probable prime factor of 31 digits: 1037983176934327212428494372699
Probable prime cofactor 222898294402775465729776596045681470561860226927431308539 has 57 digits

(32·10¹¹²+31)/9 = 3(5)₁₁₁9_<113> = 3³ · C112

C112 = P36 · P76

P36 = 779171800996810039027022481680618939_<36>

P76 = 1690092513998630224825837674006645536944911498054409463644922048126340665503_<76>

SNFS difficulty: 113 digits.
Divisors found:
 r1=779171800996810039027022481680618939 (pp36)
 r2=1690092513998630224825837674006645536944911498054409463644922048126340665503 (pp76)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.530).
Factorization parameters were as follows:
n: 1316872427983539094650205761316872427983539094650205761316872427983539094650205761316872427983539094650205761317
m: 20000000000000000000000
deg: 5
c5: 100
c0: 31
skew: 0.79
type: snfs
lss: 1
rlim: 550000
alim: 550000
lpbr: 25
lpba: 25
mfbr: 47
mfba: 47
rlambda: 2.4
alambda: 2.4
Factor base limits: 550000/550000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved rational special-q in [275000, 375001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 70160 x 70392
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,550000,550000,25,25,47,47,2.4,2.4,50000
total time: 0.40 hours.

(32·10²⁰⁴+31)/9 = 3(5)₂₀₃9_<205> = 7 · C204

C204 = P32 · P173

P32 = 14637538698830902307625620189239_<32>

P173 = 34700950643913702365065874534902278676298261512243498500603317994747009402362554449670858232087763450045141503365706972462373562457470861965763765551899124491831749801274983_<173>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3260985831
Step 1 took 27673ms
Step 2 took 17877ms
********** Factor found in step 2: 14637538698830902307625620189239
Found probable prime factor of 32 digits: 14637538698830902307625620189239
Probable prime cofactor 34700950643913702365065874534902278676298261512243498500603317994747009402362554449670858232087763450045141503365706972462373562457470861965763765551899124491831749801274983 has 173 digits

(32·10¹¹⁰+13)/9 = 3(5)₁₀₉7_<111> = 3 · 7 · 9887 · 1530281 · 20230061 · C92

C92 = P31 · P61

P31 = 7606386568876402013092015181731_<31>

P61 = 7272385101382534798671686555514012222568303439645131667835121_<61>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2507754419
Step 1 took 12573ms
Step 2 took 9527ms
********** Factor found in step 2: 7606386568876402013092015181731
Found probable prime factor of 31 digits: 7606386568876402013092015181731
Probable prime cofactor 7272385101382534798671686555514012222568303439645131667835121 has 61 digits

(32·10¹⁹¹+13)/9 = 3(5)₁₉₀7_<192> = 3 · 397 · 11399 · 9912175103_<10> · 1107141154793_<13> · 34670318910569_<14> · 2487293749934501_<16> · 6876334367075809644387659601569_<31> · C103

C103 = P32 · P72

P32 = 29910520760937869999189622935359_<32>

P72 = 134552297455318840469145844020671821216847923472351025231267535414587713_<72>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3521872813
Step 1 took 10297ms
Step 2 took 8073ms
********** Factor found in step 2: 29910520760937869999189622935359
Found probable prime factor of 32 digits: 29910520760937869999189622935359
Probable prime cofactor 134552297455318840469145844020671821216847923472351025231267535414587713 has 72 digits

(32·10¹⁰⁷+13)/9 = 3(5)₁₀₆7_<108> = 3² · 848868677 · C98

C98 = P27 · P72

P27 = 238802620593963929748934177_<27>

P72 = 194888118356224715493353351777762026261476308030109023440212914292340537_<72>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4219071836
Step 1 took 11769ms
Step 2 took 7820ms
********** Factor found in step 2: 238802620593963929748934177
Found probable prime factor of 27 digits: 238802620593963929748934177
Probable prime cofactor 194888118356224715493353351777762026261476308030109023440212914292340537 has 72 digits

(32·10¹³⁸+31)/9 = 3(5)₁₃₇9_<139> = 7 · 29 · 28547 · 6549012698471_<13> · 318047692355660734589_<21> · C99

C99 = P35 · P65

P35 = 12106920853579459070424999289438561_<35>

P65 = 24330395648365789996989790128333355913417874067772163713318487061_<65>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1141709438
Step 1 took 10100ms
Step 2 took 8013ms
********** Factor found in step 2: 12106920853579459070424999289438561
Found probable prime factor of 35 digits: 12106920853579459070424999289438561
Probable prime cofactor 24330395648365789996989790128333355913417874067772163713318487061 has 65 digits

(32·10¹⁰⁶+31)/9 = 3(5)₁₀₅9_<107> = 3 · 1821487 · C100

C100 = P28 · P73

P28 = 3571013824957159595463095741_<28>

P73 = 1822084889737849498179943594910491438357264930935924835236634397925820159_<73>

Factor found in step 2: 3571013824957159595463095741

(32·10¹¹⁶+31)/9 = 3(5)₁₁₅9_<117> = 491 · 175661008871473_<15> · C100

C100 = P43 · P58

P43 = 1726129193205343241018771466495207041016209_<43>

P58 = 2388236362175239596226223470142158679479256151585078511157_<58>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2138698920
Step 1 took 11101ms
Step 2 took 8108ms
********** Factor found in step 2: 1726129193205343241018771466495207041016209
Found probable prime factor of 43 digits: 1726129193205343241018771466495207041016209
Probable prime cofactor 2388236362175239596226223470142158679479256151585078511157 has 58 digits

(32·10¹³²+13)/9 = 3(5)₁₃₁7_<133> = 148794791 · 2833366320968183379087743_<25> · C100

C100 = P30 · P71

P30 = 661868311318946194599394724447_<30>

P71 = 12742229569126623063338124721065029231175785715234648227686968662772787_<71>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3096332453
Step 1 took 10644ms
Step 2 took 8337ms
********** Factor found in step 2: 661868311318946194599394724447
Found probable prime factor of 30 digits: 661868311318946194599394724447
Probable prime cofactor 12742229569126623063338124721065029231175785715234648227686968662772787 has 71 digits

(32·10¹⁴⁹+13)/9 = 3(5)₁₄₈7_<150> = 3 · 9234772121_<10> · 100360203094699379549_<21> · C120

C120 = P32 · P34 · P55

P32 = 25145039467698927171165751342183_<32>

P34 = 3767430535319777861990133738332443_<34>

P55 = 1349897908339817126731715201675741182458631650813620119_<55>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2310493951
Step 1 took 16384ms
********** Factor found in step 1: 25145039467698927171165751342183
Found probable prime factor of 32 digits: 25145039467698927171165751342183

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=169416394
Step 1 took 15265ms
Step 2 took 12202ms
********** Factor found in step 2: 3767430535319777861990133738332443
Found probable prime factor of 34 digits: 3767430535319777861990133738332443

(32·10¹⁴¹+31)/9 = 3(5)₁₄₀9_<142> = 383 · 5477 · 16602920627_<11> · 6586700235426342488768387_<25> · C101

C101 = P31 · P35 · P36

P31 = 3688852328182643226043829314643_<31>

P35 = 17459840163246399172064730922660979_<35>

P36 = 240647874318475240136761574757014533_<36>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1536110132
Step 1 took 10029ms
Step 2 took 8096ms
********** Factor found in step 2: 3688852328182643226043829314643
Found probable prime factor of 31 digits: 3688852328182643226043829314643

Mon Nov 24 22:45:24 2008  Msieve v. 1.39
Mon Nov 24 22:45:24 2008  random seeds: 5e5c56b8 b847632e
Mon Nov 24 22:45:25 2008  factoring 4201673421225585687652109078110886743277008789701716681609806135007807 (70 digits)
Mon Nov 24 22:45:25 2008  searching for 15-digit factors
Mon Nov 24 22:45:25 2008  commencing quadratic sieve (70-digit input)
Mon Nov 24 22:45:25 2008  using multiplier of 23
Mon Nov 24 22:45:25 2008  using 64kb Opteron sieve core
Mon Nov 24 22:45:25 2008  sieve interval: 6 blocks of size 65536
Mon Nov 24 22:45:25 2008  processing polynomials in batches of 17
Mon Nov 24 22:45:25 2008  using a sieve bound of 218287 (9781 primes)
Mon Nov 24 22:45:25 2008  using large prime bound of 21392126 (24 bits)
Mon Nov 24 22:45:25 2008  using trial factoring cutoff of 24 bits
Mon Nov 24 22:45:25 2008  polynomial 'A' values have 9 factors
Mon Nov 24 22:46:20 2008  10026 relations (4844 full + 5182 combined from 54427 partial), need 9877
Mon Nov 24 22:46:20 2008  begin with 59271 relations
Mon Nov 24 22:46:20 2008  reduce to 14536 relations in 2 passes
Mon Nov 24 22:46:20 2008  attempting to read 14536 relations
Mon Nov 24 22:46:20 2008  recovered 14536 relations
Mon Nov 24 22:46:20 2008  recovered 11729 polynomials
Mon Nov 24 22:46:20 2008  attempting to build 10026 cycles
Mon Nov 24 22:46:20 2008  found 10026 cycles in 1 passes
Mon Nov 24 22:46:20 2008  distribution of cycle lengths:
Mon Nov 24 22:46:20 2008     length 1 : 4844
Mon Nov 24 22:46:20 2008     length 2 : 5182
Mon Nov 24 22:46:20 2008  largest cycle: 2 relations
Mon Nov 24 22:46:20 2008  matrix is 9781 x 10026 (1.4 MB) with weight 292831 (29.21/col)
Mon Nov 24 22:46:20 2008  sparse part has weight 292831 (29.21/col)
Mon Nov 24 22:46:20 2008  filtering completed in 3 passes
Mon Nov 24 22:46:20 2008  matrix is 7725 x 7789 (1.2 MB) with weight 243518 (31.26/col)
Mon Nov 24 22:46:20 2008  sparse part has weight 243518 (31.26/col)
Mon Nov 24 22:46:20 2008  commencing Lanczos iteration
Mon Nov 24 22:46:20 2008  memory use: 1.5 MB
Mon Nov 24 22:46:20 2008  lanczos halted after 123 iterations (dim = 7717)
Mon Nov 24 22:46:20 2008  recovered 59 nontrivial dependencies
Mon Nov 24 22:46:20 2008  prp35 factor: 17459840163246399172064730922660979
Mon Nov 24 22:46:20 2008  prp36 factor: 240647874318475240136761574757014533
Mon Nov 24 22:46:20 2008  elapsed time 00:00:56

(32·10¹⁴⁸+13)/9 = 3(5)₁₄₇7_<149> = 37 · 1015690043_<10> · 21788482138371211_<17> · C122

C122 = P30 · C93

P30 = 331676232498798305313287633537_<30>

C93 = [130919163377370183397007958071376655425247437752619741439878676248451252269473992284455216761_<93>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1788152846
Step 1 took 15351ms
Step 2 took 12352ms
********** Factor found in step 2: 331676232498798305313287633537
Found probable prime factor of 30 digits: 331676232498798305313287633537
Composite cofactor 130919163377370183397007958071376655425247437752619741439878676248451252269473992284455216761 has 93 digits

(32·10¹⁴⁵+13)/9 = 3(5)₁₄₄7_<146> = 37 · 3197004779_<10> · C135

C135 = P30 · C106

P30 = 254681218216645409818996342939_<30>

C106 = [1180226986500756972134059759800332242451110673451530099017680638918163275649167707645548036671643354257081_<106>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=905853048
Step 1 took 15690ms
Step 2 took 12502ms
********** Factor found in step 2: 254681218216645409818996342939
Found probable prime factor of 30 digits: 254681218216645409818996342939
Composite cofactor 1180226986500756972134059759800332242451110673451530099017680638918163275649167707645548036671643354257081 has 106 digits

(32·10¹⁷⁶+13)/9 = 3(5)₁₇₅7_<177> = 3 · 7 · 9925220777_<10> · 2226740461727_<13> · 12954658312101283688035155697_<29> · C125

C125 = P36 · P89

P36 = 670617771284617422568164672853882771_<36>

P89 = 88181478626904046575951572845551494672796981698068302152918697596211551701623415862806429_<89>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=447520435
Step 1 took 13533ms
********** Factor found in step 1: 670617771284617422568164672853882771
Found probable prime factor of 36 digits: 670617771284617422568164672853882771
Probable prime cofactor 88181478626904046575951572845551494672796981698068302152918697596211551701623415862806429 has 89 digits

(32·10¹⁵⁸+13)/9 = 3(5)₁₅₇7_<159> = 3 · 7 · 4889 · 6761 · 1812937883_<10> · 5326454155007_<13> · C128

C128 = P35 · C94

P35 = 29917160077671362567875821596807351_<35>

C94 = [1773028506956992823270714966016153997533707382744774221590296026068158413217827561776171205483_<94>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2227927754
Step 1 took 13273ms
Step 2 took 9689ms
********** Factor found in step 2: 29917160077671362567875821596807351
Found probable prime factor of 35 digits: 29917160077671362567875821596807351
Composite cofactor 1773028506956992823270714966016153997533707382744774221590296026068158413217827561776171205483 has 94 digits

(32·10¹³⁶+31)/9 = 3(5)₁₃₅9_<137> = 3 · 496891 · 1122571 · C125

C125 = P40 · C85

P40 = 4761415135792806704700849085613258322433_<40>

C85 = [4462469046952490638354343160769488971248707524461871437573226959519017881746418670181_<85>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1947702416
Step 1 took 15638ms
Step 2 took 12168ms
********** Factor found in step 2: 4761415135792806704700849085613258322433
Found probable prime factor of 40 digits: 4761415135792806704700849085613258322433
Composite cofactor 4462469046952490638354343160769488971248707524461871437573226959519017881746418670181 has 85 digits

(32·10²⁰⁵+13)/9 = 3(5)₂₀₄7_<206> = 37 · 967379807683_<12> · 1184417920426891_<16> · C177

C177 = P33 · C145

P33 = 795593320256493401773149644687597_<33>

C145 = [1054174796839763600251173148992151267392532166265351897868569865399104713716754192260199669134941216435023948497548183846373245867966030763646021_<145>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3026039895
Step 1 took 31370ms
Step 2 took 23237ms
********** Factor found in step 2: 795593320256493401773149644687597
Found probable prime factor of 33 digits: 795593320256493401773149644687597
Composite cofactor 1054174796839763600251173148992151267392532166265351897868569865399104713716754192260199669134941216435023948497548183846373245867966030763646021 has 145 digits

(32·10¹⁶⁶+13)/9 = 3(5)₁₆₅7_<167> = 37 · 71 · 1061 · 522009982599416239_<18> · C143

C143 = P33 · P110

P33 = 245652995118526324744360953023587_<33>

P110 = 99478938010092014586431984516395488503049535368699230296313702892077298924404182342090564617201312578520899767_<110>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3389241046
Step 1 took 18884ms
Step 2 took 13969ms
********** Factor found in step 2: 245652995118526324744360953023587
Found probable prime factor of 33 digits: 245652995118526324744360953023587
Probable prime cofactor 99478938010092014586431984516395488503049535368699230296313702892077298924404182342090564617201312578520899767 has 110 digits

(32·10¹⁵⁵+13)/9 = 3(5)₁₅₄7_<156> = 3 · 9745711663_<10> · C146

C146 = P30 · C116

P30 = 836420183209442561075511309839_<30>

C116 = [14539455814731205321210177525875969087182313619367490212466311977932541637996102085909142345349193136322821376598967_<116>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3636140472
Step 1 took 19495ms
Step 2 took 14178ms
********** Factor found in step 2: 836420183209442561075511309839
Found probable prime factor of 30 digits: 836420183209442561075511309839
Composite cofactor 14539455814731205321210177525875969087182313619367490212466311977932541637996102085909142345349193136322821376598967 has 116 digits

(32·10²⁰²+31)/9 = 3(5)₂₀₁9_<203> = 3² · 43 · 389 · 10429 · 1464390643_<10> · 164985366343084789_<18> · C167

C167 = P33 · P135

P33 = 466182519781633765887136567956083_<33>

P135 = 201069352542540042650344508717518021638710606851507419933772379949081681365191326619697562625614660401936804153516374403184966817798817_<135>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=430933424
Step 1 took 20917ms
Step 2 took 13093ms
********** Factor found in step 2: 466182519781633765887136567956083
Found probable prime factor of 33 digits: 466182519781633765887136567956083
Probable prime cofactor 201069352542540042650344508717518021638710606851507419933772379949081681365191326619697562625614660401936804153516374403184966817798817 has 135 digits

(32·10¹⁸⁹+31)/9 = 3(5)₁₈₈9_<190> = 701 · 2383 · 2376873324384917_<16> · 4759383136642136198432852719_<28> · C141

C141 = P33 · P108

P33 = 333814150829410815649737373435823_<33>

P108 = 563642797085802332383830652856064364475273552193519508492141508999800002809776410596006504633051870472710537_<108>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1257938415
Step 1 took 14609ms
Step 2 took 10712ms
********** Factor found in step 2: 333814150829410815649737373435823
Found probable prime factor of 33 digits: 333814150829410815649737373435823
Probable prime cofactor 563642797085802332383830652856064364475273552193519508492141508999800002809776410596006504633051870472710537 has 108 digits

(32·10¹⁷⁰+13)/9 = 3(5)₁₆₉7_<171> = 3² · 7 · 5540993 · C163

C163 = P35 · C128

P35 = 12984208595306517726286012309466401_<35>

C128 = [78444741095347397678580999552636074583338295133502838361927571852405256534421658239002539572952571276956284929552098180737904123_<128>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2815647174
Step 1 took 22088ms
Step 2 took 13643ms
********** Factor found in step 2: 12984208595306517726286012309466401
Found probable prime factor of 35 digits: 12984208595306517726286012309466401
Composite cofactor 78444741095347397678580999552636074583338295133502838361927571852405256534421658239002539572952571276956284929552098180737904123 has 128 digits

(32·10¹⁷¹+31)/9 = 3(5)₁₇₀9_<172> = 23 · 769 · 17417 · 159589 · C158

C158 = P33 · P126

P33 = 107987834546806140945454007205523_<33>

P126 = 669733704346118779197931924293208612028416461194287929094971953976142368895751217073718031774189697036538650671648735737179543_<126>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3083652194
Step 1 took 19369ms
Step 2 took 12661ms
********** Factor found in step 2: 107987834546806140945454007205523
Found probable prime factor of 33 digits: 107987834546806140945454007205523
Probable prime cofactor 669733704346118779197931924293208612028416461194287929094971953976142368895751217073718031774189697036538650671648735737179543 has 126 digits

(32·10¹⁹⁰+13)/9 = 3(5)₁₈₉7_<191> = 37 · 113 · 485964719904233782920111577_<27> · C161

C161 = P36 · C125

P36 = 699056118054564041970473612040807401_<36>

C125 = [25032862789153365018478740251724706852131249447149089422041868395151290097102441153373002551131680579832018686146524928049361_<125>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4191816949
Step 1 took 27021ms
Step 2 took 20674ms
********** Factor found in step 2: 699056118054564041970473612040807401
Found probable prime factor of 36 digits: 699056118054564041970473612040807401
Composite cofactor 25032862789153365018478740251724706852131249447149089422041868395151290097102441153373002551131680579832018686146524928049361 has 125 digits

(32·10¹⁴³+31)/9 = 3(5)₁₄₂9_<144> = 19 · 59 · 1747 · 10253 · C134

C134 = P53 · P81

P53 = 23079352820141598249619821678406829423352705026772569_<53>

P81 = 767245531149285575267317899340707869952195439658557920669800614699184607306931801_<81>

SNFS difficulty: 145 digits.
Divisors found:
 r1=23079352820141598249619821678406829423352705026772569 (pp53)
 r2=767245531149285575267317899340707869952195439658557920669800614699184607306931801 (pp81)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.729).
Factorization parameters were as follows:
n: 17707530313071302506770464821911341751421185586262790520373820609700536492625271455568848575873804968724781806697706346734440820566769
m: 40000000000000000000000000000
deg: 5
c5: 125
c0: 124
skew: 1.00
type: snfs
lss: 1
rlim: 1830000
alim: 1830000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.3
alambda: 2.3
Factor base limits: 1830000/1830000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved rational special-q in [915000, 2015001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 280603 x 280845
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1830000,1830000,26,26,50,50,2.3,2.3,100000
total time: 8.00 hours.

(32·10¹⁸⁵+31)/9 = 3(5)₁₈₄9_<186> = 17 · 347 · 4323883 · C176

C176 = P31 · P145

P31 = 3568420194938534766279266855287_<31>

P145 = 3906421938835330886237170731851398038761864173604013154645274793931398036626799143927453920469689066686149317964345952393979283699104118805078521_<145>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2825353847
Step 1 took 22174ms
Step 2 took 14393ms
********** Factor found in step 2: 3568420194938534766279266855287
Found probable prime factor of 31 digits: 3568420194938534766279266855287
Probable prime cofactor 3906421938835330886237170731851398038761864173604013154645274793931398036626799143927453920469689066686149317964345952393979283699104118805078521 has 145 digits

(32·10¹⁸⁶+31)/9 = 3(5)₁₈₅9_<187> = 7² · 11888401325164912805825621_<26> · 6024171809472740969693719777_<28> · C133

C133 = P36 · P97

P36 = 426892186754019709687986691410122407_<36>

P97 = 2373407857358874412233536608360417319692140812876644426471548027819447985400508358165919646993389_<97>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4039017758
Step 1 took 13817ms
Step 2 took 10652ms
********** Factor found in step 2: 426892186754019709687986691410122407
Found probable prime factor of 36 digits: 426892186754019709687986691410122407
Probable prime cofactor 2373407857358874412233536608360417319692140812876644426471548027819447985400508358165919646993389 has 97 digits

(32·10¹⁸¹+31)/9 = 3(5)₁₈₀9_<182> = 3 · 13² · 43 · 359 · 40039 · C171

C171 = P39 · P132

P39 = 372638789975169574957214534210894523011_<39>

P132 = 304484593113223482635726534234166940008636199680134144356572163201145489184394894990238818475119649638851178460186072715697294579669_<132>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=742742276
Step 1 took 24819ms
Step 2 took 16777ms
********** Factor found in step 2: 372638789975169574957214534210894523011
Found probable prime factor of 39 digits: 372638789975169574957214534210894523011
Probable prime cofactor 304484593113223482635726534234166940008636199680134144356572163201145489184394894990238818475119649638851178460186072715697294579669 has 132 digits

(32·10¹⁸⁵+13)/9 = 3(5)₁₈₄7_<186> = 3 · 29 · 43 · 168832608157_<12> · C171

C171 = P33 · C139

P33 = 290495865583715280417753050377727_<33>

C139 = [1937864805353253318005736959102344995714626766253850408250067765460602155724470008087217876606783341886236558661754693541740125223893701443_<139>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3377039204
Step 1 took 24625ms
Step 2 took 16884ms
********** Factor found in step 2: 290495865583715280417753050377727
Found probable prime factor of 33 digits: 290495865583715280417753050377727
Composite cofactor 1937864805353253318005736959102344995714626766253850408250067765460602155724470008087217876606783341886236558661754693541740125223893701443 has 139 digits

Nov 25, 2008 (4th)

By Sinkiti Sibata / GGNFS

(31·10¹⁵¹+41)/9 = 3(4)₁₅₀9_<152> = 3² · 13 · 5813021873_<10> · C140

C140 = P50 · P91

P50 = 25159023166929253852356966287189982699044095992221_<50>

P91 = 2012971334982969607587578984544165589319626732300682305366828685278214905844400647139065009_<91>

Number: 34449_151
N=50644392451201039940486898811919837806947292225271785123798546055054166195530666819430997570993822590013111807604058720118930867542077294989
  ( 140 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=25159023166929253852356966287189982699044095992221 (pp50)
 r2=2012971334982969607587578984544165589319626732300682305366828685278214905844400647139065009 (pp91)
Version: GGNFS-0.77.1-20060513-k8
Total time: 29.07 hours.
Scaled time: 53.88 units (timescale=1.853).
Factorization parameters were as follows:
name: 34449_151
n: 50644392451201039940486898811919837806947292225271785123798546055054166195530666819430997570993822590013111807604058720118930867542077294989
m: 1000000000000000000000000000000
deg: 5
c5: 310
c0: 41
skew: 0.67
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176735, largePrimes:7906736 encountered
Relations: rels:7966289, finalFF:469567
Max relations in full relation-set: 28
Initial matrix: 353104 x 469567 with sparse part having weight 52765137.
Pruned matrix : 314785 x 316614 with weight 32293031.
Total sieving time: 27.06 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 1.63 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000
total time: 29.07 hours.
 --------- CPU info (if available) ----------

Nov 25, 2008 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(32·10¹⁶⁵-41)/9 = 3(5)₁₆₄1_<166> = 28933 · 77017 · 1481692160913415043336153_<25> · C133

C133 = P45 · P88

P45 = 952732027174124881625503241681651225883485593_<45>

P88 = 1130312827031637517531129402173147614032500164417042066514785305877661651415227444360379_<88>

GMP-ECM 6.0.1 [powered by GMP 4.1.4] [ECM]
Input number is 1076885231038767992413352754329605253167257680508027092947125535368173098885445945137010069761323421743188297144152194724878946519747 (133 digits)
Using B1=2114000, B2=2439300909, polynomial Dickson(6), sigma=2117395774
Step 1 took 28031ms
Step 2 took 15469ms
********** Factor found in step 2: 952732027174124881625503241681651225883485593
Found probable prime factor of 45 digits: 952732027174124881625503241681651225883485593
Probable prime cofactor 1130312827031637517531129402173147614032500164417042066514785305877661651415227444360379 has 88 digits

(31·10¹⁶⁵+41)/9 = 3(4)₁₆₄9_<166> = 3571 · 21693282270189289_<17> · 1201928900749666965658298861489_<31> · C116

C116 = P44 · P72

P44 = 52360156332128908550551752115093402369791409_<44>

P72 = 706519827658752527682749389034573409857980191378297593467378048714187971_<72>

Number: n
N=36993488627961056344488479201846311208466483880832964717932506627895049398002594345347037447623735419557550086941139
  ( 116 digits)
Divisors found:

Tue Nov 25 04:40:41 2008  prp44 factor: 52360156332128908550551752115093402369791409
Tue Nov 25 04:40:41 2008  prp72 factor: 706519827658752527682749389034573409857980191378297593467378048714187971
Tue Nov 25 04:40:41 2008  elapsed time 00:49:14 (Msieve 1.38)

Version: GGNFS-0.77.1-20050930-k8
Total time: 34.13 hours.
Scaled time: 28.63 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_3_4_164_9
n: 36993488627961056344488479201846311208466483880832964717932506627895049398002594345347037447623735419557550086941139
skew: 27554.71
# norm 2.12e+15
c5: 73080
c4: -270741138
c3: -118636966223308
c2: -1515144755494934221
c1: 37855017221866213730472
c0: 462963681614409640635618000
# alpha -5.09
Y1: 2124809634343
Y0: -13831376378547203326429
# Murphy_E 4.86e-10
# M 9599321862410283898123100379616895623818960450150469167051830326877405946979609366726360656345165674977990457946100
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 2020001)
Primes: RFBsize:315948, AFBsize:315804, largePrimes:6353259 encountered
Relations: rels:6186586, finalFF:669899
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 33.85 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 34.13 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(31·10¹⁵⁸+41)/9 = 3(4)₁₅₇9_<159> = 17 · 341656622449638885049_<21> · C137

C137 = P51 · P87

P51 = 403369120592280214906680606143906456903218042215967_<51>

P87 = 147020458057331909160593920488882803957838848951345662283367806977244326092173137116359_<87>

Number: n
N=59303512875660190239903873838592225362043522656415163955070689963128025148740225659345164492560895282613090072407941118087658052686704153
  ( 137 digits)
SNFS difficulty: 159 digits.
Divisors found:

Tue Nov 25 07:05:02 2008  prp51 factor: 403369120592280214906680606143906456903218042215967
Tue Nov 25 07:05:03 2008  prp87 factor: 147020458057331909160593920488882803957838848951345662283367806977244326092173137116359
Tue Nov 25 07:05:03 2008  elapsed time 01:23:00 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 32.75 hours.
Scaled time: 67.17 units (timescale=2.051).
Factorization parameters were as follows:
name: KA_3_4_157_9
n: 59303512875660190239903873838592225362043522656415163955070689963128025148740225659345164492560895282613090072407941118087658052686704153
type: snfs
skew: 0.27
deg: 5
c5: 31000
c0: 41
m: 10000000000000000000000000000000
rlim: 4000000
alim: 4000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 1750001)
Primes: RFBsize:283146, AFBsize:283059, largePrimes:14395021 encountered
Relations: rels:12895344, finalFF:596990
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 32.42 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,56,56,2.5,2.5,100000
total time: 32.75 hours.
 --------- CPU info (if available) ----------

Nov 25, 2008 (2nd)

By Serge Batalov / ***Msieve-1.39-beta (and it's own poly. select!)***, GMP-ECM 6.2.1

(29·10¹⁹³+43)/9 = 3(2)₁₉₂7_<194> = 37 · 376545742538947_<15> · 5277015119215697866479228169_<28> · 12855017410089438631794603630041_<32> · C119

C119 = P55 · P64

P55 = 5149427821374870752051649514844128520721202945360567979_<55>

P64 = 6620884931864348748165073996244706685224112510911662888370567223_<64>

Number: 32227_193
N=34093769070263942955503177408570636568154822681818558606509181335014782811074308996491335063579593027737149761680752317
  ( 119 digits)
Divisors found:
 r1=5149427821374870752051649514844128520721202945360567979 (pp55)
 r2=6620884931864348748165073996244706685224112510911662888370567223 (pp64)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
name: 32227_193
n: 34093769070263942955503177408570636568154822681818558606509181335014782811074308996491335063579593027737149761680752317
Y0: -78144654374057956235581
Y1:  3845840165363
c0: -1871596898878390306911020084352
c1: -15959543399998484701121224
c2:  195713673571504411046
c3:  1015716197615315
c4: -3952249560
c5: 11700
skew: 142699.88
# norm 6.915e+16
# alpha -7.327632
# Murphy_E 2.169e-11
# M
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4050001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 618901 x 619149
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.5,2.5,100000
total time: 50.00 hours.

7·10¹⁷⁴+9 = 7(0)₁₇₃9_<175> = 2417 · 62141 · 24597884160931_<14> · 238162287627716653181_<21> · C133

C133 = P34 · P100

P34 = 1927956018365591441032402945607921_<34>

P100 = 4126437621140930568054372656781264192663859088452172703723803757169122245662645278492526385498425387_<100>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3558391417
Step 1 took 12353ms
Step 2 took 9712ms
********** Factor found in step 2: 1927956018365591441032402945607921
Found probable prime factor of 34 digits: 1927956018365591441032402945607921
Probable prime cofactor 4126437621140930568054372656781264192663859088452172703723803757169122245662645278492526385498425387 has 100 digits

Nov 25, 2008

Factorizations of 355...557 and Factorizations of 355...559 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Nov 24, 2008 (6th)

By Wataru Sakai / GGNFS

(13·10¹⁸¹+41)/9 = 1(4)₁₈₀9_<182> = 17 · 19 · C179

C179 = P50 · P130

P50 = 27562524394914669598711172166617269924884888204961_<50>

P130 = 1622479915196479736876798893912635377625993367732178502949268365993143847383362621642915177047839771381675513828189657496747215083_<130>

Number: 14449_181
N=44719642242862057103543171654626762985896112831097351221190230478156174750601995184038527691778465772273821809425524595803233574131406948744410044719642242862057103543171654626763
  ( 179 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=27562524394914669598711172166617269924884888204961 (pp50)
 r2=1622479915196479736876798893912635377625993367732178502949268365993143847383362621642915177047839771381675513828189657496747215083 (pp130)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 351.70 hours.
Scaled time: 697.77 units (timescale=1.984).
Factorization parameters were as follows:
n: 44719642242862057103543171654626762985896112831097351221190230478156174750601995184038527691778465772273821809425524595803233574131406948744410044719642242862057103543171654626763
m: 1000000000000000000000000000000000000
deg: 5
c5: 130
c0: 41
skew: 0.79
type: snfs
lss: 1
rlim: 7600000
alim: 7600000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7600000/7600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3800000, 7100001)
Primes: RFBsize:514565, AFBsize:513133, largePrimes:19008871 encountered
Relations: rels:21296485, finalFF:2344194
Max relations in full relation-set: 32
Initial matrix: 1027765 x 2344193 with sparse part having weight 350900025.
Pruned matrix : 721846 x 727048 with weight 202326012.
Total sieving time: 336.70 hours.
Total relation processing time: 0.39 hours.
Matrix solve time: 14.25 hours.
Time per square root: 0.35 hours.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,7600000,7600000,28,28,53,53,2.5,2.5,100000
total time: 351.70 hours.
 --------- CPU info (if available) ----------

Nov 24, 2008 (5th)

By Jo Yeong Uk / GGNFS, Msieve

(32·10¹⁴⁷-41)/9 = 3(5)₁₄₆1_<148> = 1559 · 4523 · 6029 · 59237052585780701417_<20> · C118

C118 = P36 · P82

P36 = 577085991676888579048591258886894351_<36>

P82 = 2446557956931734686843641738363522287338694689153264217316360714289132931884914001_<82>

Number: 35551_147
N=1411874324770932570133784077882139868858237151608737458865903660716993942523655638259947462944967839507201267607708351
  ( 118 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=577085991676888579048591258886894351 (pp36)
 r2=2446557956931734686843641738363522287338694689153264217316360714289132931884914001 (pp82)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.61 hours.
Scaled time: 27.56 units (timescale=2.374).
Factorization parameters were as follows:
n: 1411874324770932570133784077882139868858237151608737458865903660716993942523655638259947462944967839507201267607708351
m: 200000000000000000000000000000
deg: 5
c5: 100
c0: -41
skew: 0.84
type: snfs
lss: 1
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [900000, 1800001)
Primes: RFBsize:135072, AFBsize:134269, largePrimes:3907862 encountered
Relations: rels:3974260, finalFF:333414
Max relations in full relation-set: 28
Initial matrix: 269405 x 333414 with sparse part having weight 32597540.
Pruned matrix : 250682 x 252093 with weight 21205303.
Total sieving time: 11.00 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.52 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,49,49,2.3,2.3,75000
total time: 11.61 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(29·10¹⁶¹+43)/9 = 3(2)₁₆₀7_<162> = 3 · 127 · 1303 · 81017 · 2764441 · 723581991738401_<15> · C130

C130 = P41 · P44 · P46

P41 = 65731665480805222595720071261961910422471_<41>

P44 = 19465377701474799653076880016239617879270773_<44>

P46 = 3130238241711695725511513679546855990923798339_<46>

I used Serge Batalov's ECM result.Thanks for him to prevent wasting my resources.

Mon Nov 24 20:15:36 2008  
Mon Nov 24 20:15:36 2008  
Mon Nov 24 20:15:36 2008  Msieve v. 1.34
Mon Nov 24 20:15:36 2008  random seeds: ab854081 b2e8a7f3
Mon Nov 24 20:15:36 2008  factoring 205755772979417104595082042547315417057596909369989234543823785687942743680835498075669 (87 digits)
Mon Nov 24 20:15:37 2008  no P-1/P+1/ECM available, skipping
Mon Nov 24 20:15:37 2008  commencing quadratic sieve (87-digit input)
Mon Nov 24 20:15:37 2008  using multiplier of 13
Mon Nov 24 20:15:37 2008  using 32kb Intel Core sieve core
Mon Nov 24 20:15:37 2008  sieve interval: 19 blocks of size 32768
Mon Nov 24 20:15:37 2008  processing polynomials in batches of 11
Mon Nov 24 20:15:37 2008  using a sieve bound of 1480243 (56155 primes)
Mon Nov 24 20:15:37 2008  using large prime bound of 118419440 (26 bits)
Mon Nov 24 20:15:37 2008  using double large prime bound of 340534638927600 (41-49 bits)
Mon Nov 24 20:15:37 2008  using trial factoring cutoff of 49 bits
Mon Nov 24 20:15:37 2008  polynomial 'A' values have 11 factors
Mon Nov 24 20:51:07 2008  56540 relations (15918 full + 40622 combined from 591093 partial), need 56251
Mon Nov 24 20:51:07 2008  begin with 607011 relations
Mon Nov 24 20:51:08 2008  reduce to 134507 relations in 10 passes
Mon Nov 24 20:51:08 2008  attempting to read 134507 relations
Mon Nov 24 20:51:09 2008  recovered 134507 relations
Mon Nov 24 20:51:09 2008  recovered 112909 polynomials
Mon Nov 24 20:51:09 2008  attempting to build 56540 cycles
Mon Nov 24 20:51:09 2008  found 56540 cycles in 6 passes
Mon Nov 24 20:51:09 2008  distribution of cycle lengths:
Mon Nov 24 20:51:09 2008     length 1 : 15918
Mon Nov 24 20:51:09 2008     length 2 : 11285
Mon Nov 24 20:51:09 2008     length 3 : 10098
Mon Nov 24 20:51:09 2008     length 4 : 7501
Mon Nov 24 20:51:09 2008     length 5 : 4854
Mon Nov 24 20:51:09 2008     length 6 : 3068
Mon Nov 24 20:51:09 2008     length 7 : 1807
Mon Nov 24 20:51:09 2008     length 9+: 2009
Mon Nov 24 20:51:09 2008  largest cycle: 19 relations
Mon Nov 24 20:51:09 2008  matrix is 56155 x 56540 (13.9 MB) with weight 3179419 (56.23/col)
Mon Nov 24 20:51:09 2008  sparse part has weight 3179419 (56.23/col)
Mon Nov 24 20:51:09 2008  filtering completed in 3 passes
Mon Nov 24 20:51:09 2008  matrix is 51433 x 51497 (12.7 MB) with weight 2910899 (56.53/col)
Mon Nov 24 20:51:09 2008  sparse part has weight 2910899 (56.53/col)
Mon Nov 24 20:51:09 2008  saving the first 48 matrix rows for later
Mon Nov 24 20:51:09 2008  matrix is 51385 x 51497 (8.4 MB) with weight 2277388 (44.22/col)
Mon Nov 24 20:51:09 2008  sparse part has weight 1697155 (32.96/col)
Mon Nov 24 20:51:09 2008  matrix includes 64 packed rows
Mon Nov 24 20:51:09 2008  using block size 20598 for processor cache size 4096 kB
Mon Nov 24 20:51:10 2008  commencing Lanczos iteration
Mon Nov 24 20:51:10 2008  memory use: 7.5 MB
Mon Nov 24 20:51:19 2008  lanczos halted after 814 iterations (dim = 51385)
Mon Nov 24 20:51:19 2008  recovered 18 nontrivial dependencies
Mon Nov 24 20:51:20 2008  prp41 factor: 65731665480805222595720071261961910422471
Mon Nov 24 20:51:20 2008  prp46 factor: 3130238241711695725511513679546855990923798339
Mon Nov 24 20:51:20 2008  elapsed time 00:35:44

Nov 24, 2008 (4th)

By Erik Branger / GGNFS, Msieve

(31·10¹²⁹+23)/9 = 3(4)₁₂₈7_<130> = 3² · 113 · 1307 · 2023778357_<10> · C115

C115 = P40 · P75

P40 = 1808155721885738375046960285070261414171_<40>

P75 = 708147729052792909331890541107232260936223443052897711922138946192172196179_<75>

Number: 34447_129
N=1280441368227199028861108069600156146599223949765701089268336067031998884839311050344612389229259445048883382652609
  ( 115 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=1808155721885738375046960285070261414171
 r2=708147729052792909331890541107232260936223443052897711922138946192172196179
Version: 
Total time: 5.59 hours.
Scaled time: 11.52 units (timescale=2.061).
Factorization parameters were as follows:
n: 1280441368227199028861108069600156146599223949765701089268336067031998884839311050344612389229259445048883382652609
m: 100000000000000000000000000
deg: 5
c5: 31
c0: 230
skew: 1.49
type: snfs
lss: 1
rlim: 1090000
alim: 1090000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1090000/1090000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [545000, 1095001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 179344 x 179592
Total sieving time: 5.59 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1090000,1090000,26,26,47,47,2.3,2.3,50000
total time: 5.59 hours.
 --------- CPU info (if available) ----------

Nov 24, 2008 (3rd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38

(32·10¹⁸⁰-41)/9 = 3(5)₁₇₉1_<181> = 73 · 227 · 1693 · C174

C174 = P37 · C137

P37 = 1782454901553614650304098655062208111_<37>

C137 = [71102233465445408409612382583042372098046406252784713936200060362115527942842424757820993742113288336936350920262904289486346645532474047_<137>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1778025856
Step 1 took 25039ms
Step 2 took 16297ms
********** Factor found in step 2: 1782454901553614650304098655062208111
Found probable prime factor of 37 digits: 1782454901553614650304098655062208111
Composite cofactor 71102233465445408409612382583042372098046406252784713936200060362115527942842424757820993742113288336936350920262904289486346645532474047 has 137 digits

(31·10¹⁷³+41)/9 = 3(4)₁₇₂9_<174> = 7 · 19 · 4691 · 7782742866519634973_<19> · C149

C149 = P32 · P117

P32 = 83377522136045683392304271789693_<32>

P117 = 850786214026242067189873714302933069285863191449712790626418410523447559037456956822189265479193369646179402708251047_<117>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=526494384
Step 1 took 20116ms
Step 2 took 14285ms
********** Factor found in step 2: 83377522136045683392304271789693
Found probable prime factor of 32 digits: 83377522136045683392304271789693
Probable prime cofactor 850786214026242067189873714302933069285863191449712790626418410523447559037456956822189265479193369646179402708251047 has 117 digits

(32·10¹⁷⁸-41)/9 = 3(5)₁₇₇1_<179> = 28156920554652720527_<20> · 5210329393120129261464619_<25> · C135

C135 = P33 · P103

P33 = 125024948769124296559864649242229_<33>

P103 = 1938476088265407267608468946830297300218344442829662873259342913111548879306471757099239916369185285863_<103>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3121908314
Step 1 took 11952ms
Step 2 took 9541ms
********** Factor found in step 2: 125024948769124296559864649242229
Found probable prime factor of 33 digits: 125024948769124296559864649242229
Probable prime cofactor 1938476088265407267608468946830297300218344442829662873259342913111548879306471757099239916369185285863 has 103 digits

(31·10¹⁹¹+41)/9 = 3(4)₁₉₀9_<192> = 7 · 19 · C190

C190 = P32 · P159

P32 = 16352608158325280068530540592321_<32>

P159 = 158372770134973853451453319258450143367925711568851708222095631882900541087769377379856401740310931607028215689622351972876314002803779729804456699654096482093_<159>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3712999241
Step 1 took 30616ms
Step 2 took 19179ms
********** Factor found in step 2: 16352608158325280068530540592321
Found probable prime factor of 32 digits: 16352608158325280068530540592321
Probable prime cofactor 158372770134973853451453319258450143367925711568851708222095631882900541087769377379856401740310931607028215689622351972876314002803779729804456699654096482093 has 159 digits

(31·10¹⁹⁹+23)/9 = 3(4)₁₉₈7_<200> = 37 · 269 · 1171 · 2131 · 5335974706151_<13> · C177

C177 = P36 · P141

P36 = 587694556997297870644186569026808713_<36>

P141 = 442241408781365201047390169107407138612743617495375426139753485106195550727452708337636024716855229535778626601983057531826393257778505615673_<141>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1953325660
Step 1 took 28043ms
Step 2 took 4695ms
********** Factor found in step 2: 587694556997297870644186569026808713
Found probable prime factor of 36 digits: 587694556997297870644186569026808713
Probable prime cofactor 442241408781365201047390169107407138612743617495375426139753485106195550727452708337636024716855229535778626601983057531826393257778505615673 has 141 digits

(32·10¹⁸⁷-41)/9 = 3(5)₁₈₆1_<188> = 3533 · 3739 · C181

C181 = P36 · P145

P36 = 827294513452956265618762024603598903_<36>

P145 = 3253480605332184680921640377891870384597854099985062122053939956180523797724675112907904366651740113627813901481730040593855626571502160884709191_<145>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3710936791
Step 1 took 28301ms
Step 2 took 18753ms
********** Factor found in step 2: 827294513452956265618762024603598903
Found probable prime factor of 36 digits: 827294513452956265618762024603598903
Probable prime cofactor 3253480605332184680921640377891870384597854099985062122053939956180523797724675112907904366651740113627813901481730040593855626571502160884709191 has 145 digits

(31·10¹⁹²+23)/9 = 3(4)₁₉₁7_<193> = 3² · 232982699 · 5557520236851780468690203_<25> · C159

C159 = P41 · P118

P41 = 68847142672712911758410719469952112423811_<41>

P118 = 4293248525452453558473029420197389416256988299456207145251790401469095489360510382530193461098608464957750681137104549_<118>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1102381511
Step 1 took 24753ms
Step 2 took 16493ms
********** Factor found in step 2: 68847142672712911758410719469952112423811
Found probable prime factor of 41 digits: 68847142672712911758410719469952112423811
Probable prime cofactor 4293248525452453558473029420197389416256988299456207145251790401469095489360510382530193461098608464957750681137104549 has 118 digits

(32·10¹⁹⁴-41)/9 = 3(5)₁₉₃1_<195> = 3 · 13 · 10067 · 157427 · 172969 · 6254734808027557837_<19> · 1569299852534710883524631_<25> · C136

C136 = P35 · P102

P35 = 10833599953333206062513961588376283_<35>

P102 = 312757454475848459879503203836292897307277646250554042188313990627705705745444626647351015419658382929_<102>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2633261084
Step 1 took 18932ms
Step 2 took 13679ms
********** Factor found in step 2: 10833599953333206062513961588376283
Found probable prime factor of 35 digits: 10833599953333206062513961588376283
Probable prime cofactor 312757454475848459879503203836292897307277646250554042188313990627705705745444626647351015419658382929 has 102 digits

(31·10¹⁹⁴+23)/9 = 3(4)₁₉₃7_<195> = 67939 · 3215447 · 4483159 · C177

C177 = P35 · C143

P35 = 19142262145430902451199177266387881_<35>

C143 = [18373050867731199376514309341207865522577073846536752888979846972728248598440480445014355515199596125693843553423683088903672752641169831356221_<143>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2790789935
Step 1 took 28016ms
Step 2 took 18710ms
********** Factor found in step 2: 19142262145430902451199177266387881
Found probable prime factor of 35 digits: 19142262145430902451199177266387881
Composite cofactor 18373050867731199376514309341207865522577073846536752888979846972728248598440480445014355515199596125693843553423683088903672752641169831356221 has 143 digits

(32·10²⁰³-41)/9 = 3(5)₂₀₂1_<204> = 3 · 7 · 61 · 22739 · 379837 · 536563509683722190583327839_<27> · C164

C164 = P33 · P132

P33 = 354102979541164110880003592212481_<33>

P132 = 169137144852597308225618316511538561476577202292669595418051665587776733341784913636767253699943916968786779942651786094067252427383_<132>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4180862736
Step 1 took 24856ms
Step 2 took 16720ms
********** Factor found in step 2: 354102979541164110880003592212481
Found probable prime factor of 33 digits: 354102979541164110880003592212481
Probable prime cofactor 169137144852597308225618316511538561476577202292669595418051665587776733341784913636767253699943916968786779942651786094067252427383 has 132 digits

(32·10¹⁷⁰-41)/9 = 3(5)₁₆₉1_<171> = 3 · 13 · C169

C169 = P60 · P109

P60 = 998043704380098602044869755178934572557337371599512013922099_<60>

P109 = 9134679249814733560138714436517929988836887392421258951330673846471491717924198918470826456585941620511614291_<109>

SNFS difficulty: 171 digits.
Divisors found:
 r1=998043704380098602044869755178934572557337371599512013922099 (pp60)
 r2=9134679249814733560138714436517929988836887392421258951330673846471491717924198918470826456585941620511614291 (pp109)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 9116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809
m: 20000000000000000000000000000000000
deg: 5
c5: 1
c0: -41
skew: 2.10
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [2550000, 4550001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 962406 x 962647
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,54,54,2.5,2.5,200000
total time: 42.00 hours.

(26·10¹⁷⁵-71)/9 = 2(8)₁₇₄1_<176> = 3² · 7² · 51396937 · C166

C166 = P34 · C132

P34 = 5485541467765331185793932059381071_<34>

C132 = [232346165013524035407277568756740617921650712557593860807267789156818500888584376591986045173426639312451934844830078298810503320383_<132>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1753223694
Step 1 took 19425ms
Step 2 took 12913ms
********** Factor found in step 2: 5485541467765331185793932059381071
Found probable prime factor of 34 digits: 5485541467765331185793932059381071
Composite cofactor 232346165013524035407277568756740617921650712557593860807267789156818500888584376591986045173426639312451934844830078298810503320383 has 132 digits

(29·10¹⁶⁶+43)/9 = 3(2)₁₆₅7_<167> = 13 · 37 · 61 · 139 · 577 · 52967429 · 80517401 · 84663716459138949752951_<23> · C119

C119 = P33 · P86

P33 = 761702925310844258565528121716823_<33>

P86 = 49786130187401782926117076264729435237188242647832592699115744065130471304676109804097_<86>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1084544580
Step 1 took 11941ms
Step 2 took 9369ms
********** Factor found in step 2: 761702925310844258565528121716823
Found probable prime factor of 33 digits: 761702925310844258565528121716823
Probable prime cofactor 49786130187401782926117076264729435237188242647832592699115744065130471304676109804097 has 86 digits

(17·10¹⁶⁸+1)/9 = 1(8)₁₆₇9_<169> = 1722973771_<10> · 441744465139454537703640231879_<30> · C130

C130 = P38 · P92

P38 = 62067659878874716493548893843727505309_<38>

P92 = 39984462054234271226059897447734856516947654297265965031547710425930629429688197202520858369_<92>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3404844789
Step 1 took 14129ms
Step 2 took 9713ms
********** Factor found in step 2: 62067659878874716493548893843727505309
Found probable prime factor of 38 digits: 62067659878874716493548893843727505309
Probable prime cofactor 39984462054234271226059897447734856516947654297265965031547710425930629429688197202520858369 has 92 digits

(22·10¹⁹⁸-13)/9 = 2(4)₁₉₇3_<199> = 761 · C196

C196 = P40 · C157

P40 = 1116164463888701212766808462545049455171_<40>

C157 = [2877844495788575168113607192129997691026661911215134817394216371163195475768528619368913071644015537645015736907890065295017724885610399161647249281604057553_<157>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2917915214
Step 1 took 32189ms
Step 2 took 20917ms
********** Factor found in step 2: 1116164463888701212766808462545049455171
Found probable prime factor of 40 digits: 1116164463888701212766808462545049455171
Composite cofactor 2877844495788575168113607192129997691026661911215134817394216371163195475768528619368913071644015537645015736907890065295017724885610399161647249281604057553 has 157 digits

7·10¹⁶⁸+3 = 7(0)₁₆₇3_<169> = 341870677521159820404771314461_<30> · C140

C140 = P67 · P73

P67 = 5749965473293729696597801765242916256625281553550128309455278186337_<67>

P73 = 3560991610105122471722990488660298925687905168583791168409158735294004479_<73>

SNFS difficulty: 170 digits.
Divisors found:
 r1=5749965473293729696597801765242916256625281553550128309455278186337 (pp67)
 r2=3560991610105122471722990488660298925687905168583791168409158735294004479 (pp73)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.723).
Factorization parameters were as follows:
n: 20475578808793101098067109352302136241947465332363736170498450833112663592480281217974216315890803341249803045346825107415291040669074603423
m: 5000000000000000000000000000000000
deg: 5
c5: 56
c0: 75
skew: 1.06
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.4
alambda: 2.4
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved rational special-q in [2400000, 4800001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 917860 x 918102
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,53,53,2.4,2.4,100000
total time: 36.00 hours.

(17·10¹⁷⁰+1)/9 = 1(8)₁₆₉9_<171> = 3 · 7 · 23 · 37501 · 1307923 · 46512393772229041_<17> · C141

C141 = P37 · P104

P37 = 4807025903651954567691869159809598947_<37>

P104 = 35660637429904587067911820002302375560227157892722747763245437688750495106878532185673868322404000400823_<104>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3211483261
Step 1 took 14620ms
Step 2 took 10677ms
********** Factor found in step 2: 4807025903651954567691869159809598947
Found probable prime factor of 37 digits: 4807025903651954567691869159809598947
Probable prime cofactor 35660637429904587067911820002302375560227157892722747763245437688750495106878532185673868322404000400823 has 104 digits

(26·10¹⁹⁸-71)/9 = 2(8)₁₉₇1_<199> = 281 · 7743557 · 15794094665352108651876851_<26> · 56141214127490815204720556917_<29> · C136

C136 = P34 · P102

P34 = 6672158345324570924911004640070319_<34>

P102 = 224409447889967492996585171782030978009865301467761627115443269401396865659446660091646883625181321541_<102>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=234056921
Step 1 took 16085ms
Step 2 took 11441ms
********** Factor found in step 2: 6672158345324570924911004640070319
Found probable prime factor of 34 digits: 6672158345324570924911004640070319
Probable prime cofactor 224409447889967492996585171782030978009865301467761627115443269401396865659446660091646883625181321541 has 102 digits

4·10¹⁷²+7 = 4(0)₁₇₁7_<173> = 11 · 107 · 109 · 28109 · 4110437 · 37009237580533_<14> · C143

C143 = P45 · P99

P45 = 100305578557150326645901431665213886002442319_<45>

P99 = 726923004900429115307541442670226086141573640361924923419646985297364567603919585356657165361801089_<99>

SNFS difficulty: 172 digits.
Divisors found:
 r1=100305578557150326645901431665213886002442319 (pp45)
 r2=726923004900429115307541442670226086141573640361924923419646985297364567603919585356657165361801089 (pp99)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.538).
Factorization parameters were as follows:
n: 72914432573039764485645880875045651008927003853729473970414449958165524809692232914487279677657403075526865507092416340315342944171122673885391
m: 20000000000000000000000000000000000
deg: 5
c5: 25
c0: 14
skew: 0.89
type: snfs
lss: 1
rlim: 5300000
alim: 5300000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 5300000/5300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved rational special-q in [2650000, 4950001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 965179 x 965421
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,5300000,5300000,27,27,53,53,2.5,2.5,100000
total time: 37.00 hours.

(14·10¹⁷⁰-23)/9 = 1(5)₁₆₉3_<171> = 3 · 691 · 22263472690475736337_<20> · C148

C148 = P28 · C120

P28 = 4140183215192466077295603949_<28>

C120 = [814092505380309124943551135799902484909003478048353721821331357008460909965452505234824673882421566041432715888319342397_<120>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2712233381
Step 1 took 14573ms
********** Factor found in step 1: 4140183215192466077295603949
Found probable prime factor of 28 digits: 4140183215192466077295603949
Composite cofactor 814092505380309124943551135799902484909003478048353721821331357008460909965452505234824673882421566041432715888319342397 has 120 digits

(67·10¹⁶⁹+23)/9 = 7(4)₁₆₈7_<170> = 7 · 11³ · 47 · 9634504347070848704094689_<25> · C140

C140 = P44 · P96

P44 = 36355850834570118053133951458400315996827161_<44>

P96 = 485349570832950084927284102664391171870708737358204755442100584286328162153818832105814831878757_<96>

SNFS difficulty: 171 digits.
Divisors found:
 r1=36355850834570118053133951458400315996827161 (pp44)
 r2=485349570832950084927284102664391171870708737358204755442100584286328162153818832105814831878757 (pp96)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.728).
Factorization parameters were as follows:
n: 17645296599825356972196652946718116402721679125350513178441215898893463560972287693021794077117749728905327359821616360176301061848636518877
m: 10000000000000000000000000000000000
deg: 5
c5: 67
c0: 230
skew: 1.28
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved rational special-q in [2550000, 5150001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 954924 x 955166
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,53,53,2.5,2.5,100000
total time: 40.00 hours.

(8·10²⁰⁹+1)/9 = (8)₂₀₈9_<209> = 47 · 103 · 2237941 · 4609345901_<10> · 30497201569_<11> · 6734479233509927143_<19> · 20018060180487237540114636047_<29> · C132

C132 = P33 · P100

P33 = 287944218227248700481818032174301_<33>

P100 = 1503592325881574908416447589270613098491254186484255698064601081514562926755107233101700906147750381_<100>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1801430418
Step 1 took 15665ms
Step 2 took 12740ms
********** Factor found in step 2: 287944218227248700481818032174301
Found probable prime factor of 33 digits: 287944218227248700481818032174301
Probable prime cofactor 1503592325881574908416447589270613098491254186484255698064601081514562926755107233101700906147750381 has 100 digits

(25·10¹⁷⁶-43)/9 = 2(7)₁₇₅3_<177> = 3 · 7 · 13 · 281 · C172

C172 = P35 · P138

P35 = 17117031548021844777195855517637263_<35>

P138 = 211543692732147083754486058627421714563422861284785083503461250666691057398802310212309971774486900777685438889359113718536082788821389067_<138>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=387572664
Step 1 took 24831ms
Step 2 took 16880ms
********** Factor found in step 2: 17117031548021844777195855517637263
Found probable prime factor of 35 digits: 17117031548021844777195855517637263
Probable prime cofactor 211543692732147083754486058627421714563422861284785083503461250666691057398802310212309971774486900777685438889359113718536082788821389067 has 138 digits

Nov 24, 2008 (2nd)

By Robert Backstrom / GGNFS, GMP-ECM, Msieve

(32·10¹⁵⁵-41)/9 = 3(5)₁₅₄1_<156> = 3² · 7 · 577 · 1458547 · 44654861 · 168236298229207179798289_<24> · C114

C114 = P49 · P66

P49 = 6589889674901733654324033821990327559794316422291_<49>

P66 = 135457821999390469099670401531267201792965530673937169973854234797_<66>

Number: n
N=892652102578460163452218925109299370287832470891244205426080081902444565148626159311884218437879316318892518659927
  ( 114 digits)
Divisors found:
 r1=6589889674901733654324033821990327559794316422291 (pp49)
 r2=135457821999390469099670401531267201792965530673937169973854234797 (pp66)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 31.44 hours.
Scaled time: 64.30 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_3_5_154_1
n: 892652102578460163452218925109299370287832470891244205426080081902444565148626159311884218437879316318892518659927
skew: 17881.72
# norm 1.65e+15
c5: 124740
c4: -3305249242
c3: -66180629234238
c2: 941123426736639434
c1: 18068018182754986939935
c0: 56736548028175370430747650
# alpha -4.71
Y1: 627207758323
Y0: -5901134905459535117853
# Murphy_E 5.87e-10
# M 875948648962425620048330212363563760145461037216438232018025505669232687984754761478672507962506218253364299892481
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [100000, 1700001)
Primes: RFBsize:250150, AFBsize:250601, largePrimes:7261061 encountered
Relations: rels:7091857, finalFF:612715
Max relations in full relation-set: 28
Initial matrix: 500833 x 612715 with sparse part having weight 46311257.
Pruned matrix : 402233 x 404801 with weight 24686433.
Total sieving time: 29.94 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.71 hours.
Total square root time: 0.58 hours, sqrts: 3.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 31.44 hours.
 --------- CPU info (if available) ----------

(29·10¹⁵⁶+61)/9 = 3(2)₁₅₅9_<157> = 1583 · 13954570914080293172207179192384157_<35> · C120

C120 = P40 · P80

P40 = 1891857657521508354844909719281960503397_<40>

P80 = 77102707610175432125304673350243785044485094386824629693426617726158095364091947_<80>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 145867347807952268579412120037241313649196025306635310236169952952796714365773755203936139204221987693598990373913843959 (120 digits)
Using B1=4516000, B2=8562077170, polynomial Dickson(6), sigma=3701885376
Step 1 took 59297ms
Step 2 took 18375ms
********** Factor found in step 2: 1891857657521508354844909719281960503397
Found probable prime factor of 40 digits: 1891857657521508354844909719281960503397
Probable prime cofactor 77102707610175432125304673350243785044485094386824629693426617726158095364091947 has 80 digits

(31·10¹⁵²+23)/9 = 3(4)₁₅₁7_<153> = 107 · 677 · 487387 · C142

C142 = P62 · P81

P62 = 73614591348542831536038340486350437160072591338127130900413721_<62>

P81 = 132528380627864005990141182168512501174418120784716384110004695241628977470486099_<81>

Number: n
N=9756022582004349047507364507499921946225366500848674640456733416082136242417803225035612096644979843850061570187862543328775065391426079364379
  ( 142 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=73614591348542831536038340486350437160072591338127130900413721 (pp62)
 r2=132528380627864005990141182168512501174418120784716384110004695241628977470486099 (pp81)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 29.59 hours.
Scaled time: 38.64 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_3_4_151_7
n: 9756022582004349047507364507499921946225366500848674640456733416082136242417803225035612096644979843850061570187862543328775065391426079364379
type: snfs
skew: 0.38
deg: 5
c5: 3100
c0: 23
m: 1000000000000000000000000000000
rlim: 2400000
alim: 2400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [100000, 1150001)
Primes: RFBsize:176302, AFBsize:176014, largePrimes:12206874 encountered
Relations: rels:11170380, finalFF:458117
Max relations in full relation-set: 28
Initial matrix: 352383 x 458117 with sparse part having weight 46424684.
Pruned matrix : 296745 x 298570 with weight 28529175.
Total sieving time: 26.27 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 2.66 hours.
Total square root time: 0.25 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,28,28,56,56,2.5,2.5,100000
total time: 29.59 hours.
 --------- CPU info (if available) ----------

(32·10¹⁶⁰-41)/9 = 3(5)₁₅₉1_<161> = 47527409 · 1059981455713_<13> · 24745675942864343054205647_<26> · C116

C116 = P57 · P60

P57 = 163875404876858976588551599658128966517628862360417550081_<57>

P60 = 174041157702382505971591718344739887639052132484582251616929_<60>

Number: n
N=28521065183715196355824844085452176849021322513407806760569274498363666847451583590806239126414388837306251084921249
  ( 116 digits)
Divisors found:

Mon Nov 24 21:52:43 2008  prp57 factor: 163875404876858976588551599658128966517628862360417550081
Mon Nov 24 21:52:43 2008  prp60 factor: 174041157702382505971591718344739887639052132484582251616929
Mon Nov 24 21:52:43 2008  elapsed time 00:43:19 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 36.70 hours.
Scaled time: 53.17 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_3_5_159_1
n: 28521065183715196355824844085452176849021322513407806760569274498363666847451583590806239126414388837306251084921249
skew: 115436.32
# norm 1.36e+16
c5: 4800
c4: -783522220
c3: -300581098722771
c2: 10441071344211345536
c1: -17790501904306421094330
c0: -14839347986275999951931807367
# alpha -6.62
Y1: 1602120061993
Y0: -22635281731215525167408
# Murphy_E 5.30e-10
# M 3583062506374066250087638677111738450689527918815593869953971918521088312084087884886850189552142664315250577447483
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1720001)
Primes: RFBsize:315948, AFBsize:316284, largePrimes:6170251 encountered
Relations: rels:6123996, finalFF:749005
Max relations in full relation-set: 28
Initial matrix: 632311 x 749005 with sparse part having weight 34439405.
Pruned matrix : 499348 x 502573 with weight 16557018.
Total sieving time: 36.45 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 36.70 hours.
 --------- CPU info (if available) ----------

(31·10¹⁶¹+41)/9 = 3(4)₁₆₀9_<162> = 7 · 174672715331411159_<18> · C144

C144 = P50 · P95

P50 = 19271833543064282432963298327790989181455280173613_<50>

P95 = 14617497794949856808550674252675297489036964937095681265244845906085208668384217430630196277221_<95>

Number: n
N=281705984320382834768168838574043320101246180179813501104002009710698781848409531013928771698738236445365657545494019832461744291094443157169473
  ( 144 digits)
SNFS difficulty: 162 digits.
Divisors found:

Mon Nov 24 23:56:29 2008  prp50 factor: 19271833543064282432963298327790989181455280173613
Mon Nov 24 23:56:29 2008  prp95 factor: 14617497794949856808550674252675297489036964937095681265244845906085208668384217430630196277221
Mon Nov 24 23:56:29 2008  elapsed time 01:55:56 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 30.90 hours.
Scaled time: 56.45 units (timescale=1.827).
Factorization parameters were as follows:
name: KA_3_4_160_9
n: 281705984320382834768168838574043320101246180179813501104002009710698781848409531013928771698738236445365657545494019832461744291094443157169473
type: snfs
skew: 0.67
deg: 5
c5: 310
c0: 41
m: 100000000000000000000000000000000
rlim: 4400000
alim: 4400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 1800001)
Primes: RFBsize:309335, AFBsize:309440, largePrimes:14840002 encountered
Relations: rels:13480228, finalFF:698255
Max relations in full relation-set: 28
Initial matrix: 618842 x 698255 with sparse part having weight 80958662.
Pruned matrix : 558849 x 562007 with weight 56988131.
Total sieving time: 30.47 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4400000,4400000,28,28,56,56,2.5,2.5,100000
total time: 30.90 hours.
 --------- CPU info (if available) ----------

Nov 24, 2008

By Sinkiti Sibata / GGNFS

(31·10¹⁴⁶+41)/9 = 3(4)₁₄₅9_<147> = 587 · 3001 · 10030451 · C134

C134 = P30 · P50 · P55

P30 = 224989048861303607305990760947_<30>

P50 = 10690526136524945934822924019667842419697205995921_<50>

P55 = 8104648192327214100807766498210552641603797424899038771_<55>

Number: 34449_146
N=19493715659669137717634283501866598231174008195488279686946974479242646515513142646151978243163268222141919758885399329471406009037177
  ( 134 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=224989048861303607305990760947 (pp30)
 r2=10690526136524945934822924019667842419697205995921 (pp50)
 r3=8104648192327214100807766498210552641603797424899038771 (pp55)
Version: GGNFS-0.77.1-20060513-k8
Total time: 22.19 hours.
Scaled time: 43.77 units (timescale=1.972).
Factorization parameters were as follows:
name: 34449_146
n: 19493715659669137717634283501866598231174008195488279686946974479242646515513142646151978243163268222141919758885399329471406009037177
m: 100000000000000000000000000000
deg: 5
c5: 310
c0: 41
skew: 0.67
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 2900001)
Primes: RFBsize:148933, AFBsize:149232, largePrimes:4381484 encountered
Relations: rels:4654922, finalFF:390109
Max relations in full relation-set: 28
Initial matrix: 298232 x 390109 with sparse part having weight 45287677.
Pruned matrix : 267944 x 269499 with weight 29530201.
Total sieving time: 20.88 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.02 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,49,49,2.3,2.3,100000
total time: 22.19 hours.
 --------- CPU info (if available) ----------

(32·10¹⁴⁸-41)/9 = 3(5)₁₄₇1_<149> = 73 · 7883 · 9419 · 16411 · 77309956598999_<14> · C121

C121 = P52 · P70

P52 = 4843514337760459572815534254707218514959785263884641_<52>

P70 = 1067473790535875080479232281288764753614270973659955842797287456129819_<70>

Number: 35551_148
N=5170324609644016527884881041706215829565526794526256285437584956636903529022585551794141982832094977765160463535536209979
  ( 121 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=4843514337760459572815534254707218514959785263884641 (pp52)
 r2=1067473790535875080479232281288764753614270973659955842797287456129819 (pp70)
Version: GGNFS-0.77.1-20060513-k8
Total time: 23.00 hours.
Scaled time: 45.79 units (timescale=1.991).
Factorization parameters were as follows:
name: 35551_148
n: 5170324609644016527884881041706215829565526794526256285437584956636903529022585551794141982832094977765160463535536209979
m: 400000000000000000000000000000
deg: 5
c5: 125
c0: -164
skew: 1.06
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1100000, 1800001)
Primes: RFBsize:162662, AFBsize:162616, largePrimes:7413483 encountered
Relations: rels:7905348, finalFF:907301
Max relations in full relation-set: 28
Initial matrix: 325344 x 907301 with sparse part having weight 102751201.
Pruned matrix : 217844 x 219534 with weight 33552730.
Total sieving time: 21.78 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.91 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,49,49,2.4,2.4,100000
total time: 23.00 hours.
 --------- CPU info (if available) ----------

Nov 23, 2008 (7th)

By Markus Tervooren / GGNFS

(79·10¹⁶⁸-7)/9 = 8(7)₁₆₈_<169> = 67 · 503 · 557 · 1205760657098941451_<19> · C144

C144 = P61 · P83

P61 = 7759395761065552324116951099007858595802868200287671942463351_<61>

P83 = 49980153610709556948637712835820984645682617068092949162535061366397670901309487461_<83>

N=387815792064344895618351800343352262605326578940255711093416077885722827353065727386705918821842903745588255225110877887373958010723171586541811
  ( 144 digits)
SNFS difficulty: 171 digits.
Divisors found:
r1=7759395761065552324116951099007858595802868200287671942463351 (pp61)
r2=49980153610709556948637712835820984645682617068092949162535061366397670901309487461 (pp83)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 67.86 hours.
Scaled time: 137.82 units (timescale=2.031).
Factorization parameters were as follows:
n: 387815792064344895618351800343352262605326578940255711093416077885722827353065727386705918821842903745588255225110877887373958010723171586541811
m: 5000000000000000000000000000000000
deg: 5
c5: 632
c0: -175
skew: 0.77
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4

Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 7400001)
Primes: RFBsize:348513, AFBsize:348556, largePrimes:10510580 encountered
Relations: rels:11477264, finalFF:824020
Max relations in full relation-set: 32
Initial matrix: 697136 x 824020 with sparse part having weight 113502940.
Pruned matrix : 630588 x 634137 with weight 91303413.
Total sieving time: 61.15 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 6.27 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 67.86 hours.
 --------- CPU info (if available) ----------

Nov 23, 2008 (6th)

By Wataru Sakai / Msieve

(7·10¹⁹⁹-61)/9 = (7)₁₉₈1_<199> = C199

C199 = P54 · P73 · P74

P54 = 162977242689074237420617781730238377969785419608250633_<54>

P73 = 1078499033126045544619923456125343966895163031786125650645190344488551801_<73>

P74 = 44249544503388844859222475426113422020799712625769378619900612613079145387_<74>

Number: 77771_199
N=7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777771
  ( 199 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=162977242689074237420617781730238377969785419608250633
 r2=1078499033126045544619923456125343966895163031786125650645190344488551801
 r3=44249544503388844859222475426113422020799712625769378619900612613079145387
Version: 
Total time: 931.32 hours.
Scaled time: 1842.15 units (timescale=1.978).
Factorization parameters were as follows:
n: 7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777771
m: 5000000000000000000000000000000000000000
deg: 5
c5: 112
c0: -305
skew: 1.22
type: snfs
lss: 1
rlim: 15400000
alim: 15400000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
Factor base limits: 15400000/15400000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [7700000, 17600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3166635 x 3166882
Total sieving time: 931.32 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,200,5,0,0,0,0,0,0,0,0,15400000,15400000,29,29,56,56,2.6,2.6,100000
total time: 931.32 hours.
 --------- CPU info (if available) ----------

Nov 23, 2008 (5th)

By Kenji Ibusuki / GGNFS-0.77.1

(29·10¹⁹¹-11)/9 = 3(2)₁₉₀1_<192> = 3 · C192

C192 = P78 · P114

P78 = 234962048155245284311390320134874392608349302915475444887775014352507137133437_<78>

P114 = 457126622153211121929472840043706090744226808049801534743653872091775669361431051141638973630223980189775046870811_<114>

Number: 32221_191
N=107407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407
  ( 192 digits)
SNFS difficulty: 193 digits.
Divisors found:
 r1=234962048155245284311390320134874392608349302915475444887775014352507137133437 (pp78)
 r2=457126622153211121929472840043706090744226808049801534743653872091775669361431051141638973630223980189775046870811 (pp114)
Version: GGNFS-0.77.1
Total time: 665.59 hours.
Scaled time: 1474.28 units (timescale=2.215).
Factorization parameters were as follows:
number: 32221_191
n: 107407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407
m: 200000000000000000000000000000000000000
type: snfs
deg: 5
skew: 1.040
c0: -176
c5: 145
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6
qintsize: 10000
q0: 10000
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Sieved special-q in [10000, 10420001)
Relations: rels:16881690, finalFF:1351631
Initial matrix: 1203472 x 1351631 with sparse part having weight 178964056.
Pruned matrix : 1169451 x 1175532 with weight 141697409.
Total sieving time: 641.10 hours.
Total relation processing time: 5.50 hours.
Matrix solve time: 18.74 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,193,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.6,2.6,100000
total time: 665.59 hours.
 --------- CPU info (if available) ----------

Nov 23, 2008 (4th)

By Sinkiti Sibata / GGNFS

(31·10¹⁴³+41)/9 = 3(4)₁₄₂9_<144> = 7 · 233 · 1506781 · 512151545029_<12> · C123

C123 = P46 · P77

P46 = 2763241941388641272813974675010137882804144873_<46>

P77 = 99037048435115939648404395098604147324333042396077440279511597887787486342327_<77>

Number: 34449_143
N=273663325987250666193658535831565708877585280399160212059319626415796731264203768483627142893257335731842059187153779939471
  ( 123 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=2763241941388641272813974675010137882804144873 (pp46)
 r2=99037048435115939648404395098604147324333042396077440279511597887787486342327 (pp77)
Version: GGNFS-0.77.1-20060513-k8
Total time: 21.55 hours.
Scaled time: 42.13 units (timescale=1.955).
Factorization parameters were as follows:
name: 34449_143
n: 273663325987250666193658535831565708877585280399160212059319626415796731264203768483627142893257335731842059187153779939471
m: 50000000000000000000000000000
deg: 5
c5: 248
c0: 1025
skew: 1.33
type: snfs
lss: 1
rlim: 1890000
alim: 1890000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1890000/1890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [945000, 2845001)
Primes: RFBsize:141338, AFBsize:141131, largePrimes:4261266 encountered
Relations: rels:4491050, finalFF:353932
Max relations in full relation-set: 28
Initial matrix: 282536 x 353932 with sparse part having weight 41049959.
Pruned matrix : 259250 x 260726 with weight 28392947.
Total sieving time: 20.22 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.03 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1890000,1890000,26,26,49,49,2.3,2.3,100000
total time: 21.55 hours.
 --------- CPU info (if available) ----------

(31·10¹⁴²+41)/9 = 3(4)₁₄₁9_<143> = 3² · 17 · 809 · 3037 · C134

C134 = P51 · P84

P51 = 249013338986204435097585192153943981947080710065557_<51>

P84 = 367969504790916776725533016892666807229583043626074786102746866272342615210332238593_<84>

Number: 34449_142
N=91629315033086336258089934120092012703910322193113037170545087138342097380259920272842329508498424035340485686522479420891591595441301
  ( 134 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=249013338986204435097585192153943981947080710065557 (pp51)
 r2=367969504790916776725533016892666807229583043626074786102746866272342615210332238593 (pp84)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 22.54 hours.
Scaled time: 10.66 units (timescale=0.473).
Factorization parameters were as follows:
name: 34449_142
n: 91629315033086336258089934120092012703910322193113037170545087138342097380259920272842329508498424035340485686522479420891591595441301
m: 20000000000000000000000000000
deg: 5
c5: 775
c0: 328
skew: 0.84
type: snfs
lss: 1
rlim: 1790000
alim: 1790000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1790000/1790000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [895000, 2695001)
Primes: RFBsize:134359, AFBsize:134584, largePrimes:4106423 encountered
Relations: rels:4251420, finalFF:308391
Max relations in full relation-set: 28
Initial matrix: 269010 x 308391 with sparse part having weight 34555699.
Pruned matrix : 256408 x 257817 with weight 26898094.
Total sieving time: 20.05 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 2.15 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1790000,1790000,26,26,49,49,2.3,2.3,100000
total time: 22.54 hours.
 --------- CPU info (if available) ----------

Nov 23, 2008 (3rd)

By matsui / GMP-ECM

(26·10¹⁹⁴-71)/9 = 2(8)₁₉₃1_<195> = 127 · C193

C193 = P32 · P162

P32 = 11413826722781612615066149463171_<32>

P162 = 199294742752855759616595652474247599588531861457327919786234813849577319328816218083242071052288301464688708144297554003022214681904207255725793885068388792538693_<162>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
2274715660542432195975503062117235345581802274715660542432195975503062117235345581802274715660542432195975503062117235345581802274715660542432195975503062117235345581802274715660542432195975503
=
11413826722781612615066149463171* 199294742752855759616595652474247599588531861457327919786234813849577319328816218083242071052288301464688708144297554003022214681904207255725793885068388792538693

Nov 23, 2008 (2nd)

By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1

(31·10¹⁶⁶+41)/9 = 3(4)₁₆₅9_<167> = 3 · 1669 · C163

C163 = P69 · P95

P69 = 181349445677364300441878201566985382903693854106708508967491099295051_<69>

P95 = 37933713566617419532751041365089999565596259225341362011623253271472207437090733501918061961357_<95>

SNFS difficulty: 167 digits.
Divisors found:
 r1=181349445677364300441878201566985382903693854106708508967491099295051 (pp69)
 r2=37933713566617419532751041365089999565596259225341362011623253271472207437090733501918061961357 (pp95)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.953).
Factorization parameters were as follows:
n: 6879257927789982912810953553913410114728269311852295674943967334620420300468233362181834320839713290282493398131504782193817544326831325033841510773805561103344207
m: 1000000000000000000000000000000000
deg: 5
c5: 310
c0: 41
skew: 0.67
type: snfs
lss: 1
rlim: 4300000
alim: 4300000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 4300000/4300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved rational special-q in [2150000, 4750001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 888968 x 889210
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,4300000,4300000,27,27,53,53,2.5,2.5,200000
total time: 50.00 hours.

9·10²¹³-1 = 8(9)₂₁₃_<214> = 293 · 31517 · 297630677 · 653240602737601_<15> · 2763180643414756163_<19> · 1880839632718006855987957867_<28> · C138

C138 = P33 · C106

P33 = 179481389251375241524195452694409_<33>

C106 = [5374012673820858541660812441083032124477051306670520962378248708789456585274457770479061617280814335697243_<106>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3144849970
Step 1 took 21095ms
Step 2 took 13861ms
********** Factor found in step 2: 179481389251375241524195452694409
Found probable prime factor of 33 digits: 179481389251375241524195452694409
Composite cofactor 5374012673820858541660812441083032124477051306670520962378248708789456585274457770479061617280814335697243 has 106 digits

(32·10¹⁹⁶-41)/9 = 3(5)₁₉₅1_<197> = 31 · 73 · 11463757430011_<14> · 155869784726978437957_<21> · 84293380190754159708341_<23> · C138

C138 = P43 · P95

P43 = 2621005805007976677279163475247999795539713_<43>

P95 = 39799034734136717395774185493040870102947697545992386055866170111726118412127304962406603538947_<95>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=983927123
Step 1 took 18737ms
Step 2 took 14050ms
********** Factor found in step 2: 2621005805007976677279163475247999795539713
Found probable prime factor of 43 digits: 2621005805007976677279163475247999795539713
Probable prime cofactor 39799034734136717395774185493040870102947697545992386055866170111726118412127304962406603538947 has 95 digits

Nov 23, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(29·10¹⁶³+61)/9 = 3(2)₁₆₂9_<164> = 3 · 13 · 11518110473_<11> · C152

C152 = P59 · P94

P59 = 28968902095765974876176251537052725076837212300626871212011_<59>

P94 = 2476153740130391749632672210156842557311791559372719993391286077470404443761638984392106323937_<94>

Number: n
N=71731455271902062683594372416193981301312252677751010734398503646894671594995286707459435462753685485581660198251757661434457299653547628447564971207307
  ( 152 digits)
SNFS difficulty: 164 digits.
Divisors found:

Sun Nov 23 02:19:40 2008  prp59 factor: 28968902095765974876176251537052725076837212300626871212011
Sun Nov 23 02:19:40 2008  prp94 factor: 2476153740130391749632672210156842557311791559372719993391286077470404443761638984392106323937
Sun Nov 23 02:19:40 2008  elapsed time 02:27:09 (Msieve 1.38)

Version: GGNFS-0.77.1-20050930-k8
Total time: 45.02 hours.
Scaled time: 37.68 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_3_2_162_9
n: 71731455271902062683594372416193981301312252677751010734398503646894671594995286707459435462753685485581660198251757661434457299653547628447564971207307
type: snfs
skew: 0.29
deg: 5
c5: 29000
c0: 61
m: 100000000000000000000000000000000
rlim: 4600000
alim: 4600000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 2350001)
Primes: RFBsize:322441, AFBsize:321512, largePrimes:15532518 encountered
Relations: rels:14047608, finalFF:643166
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 44.42 hours.
Total relation processing time: 0.60 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,4600000,4600000,28,28,56,56,2.5,2.5,100000
total time: 45.02 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(31·10¹³¹+41)/9 = 3(4)₁₃₀9_<132> = 7 · 347 · 9920299856931027199537861_<25> · C104

C104 = P46 · P59

P46 = 1248935601417172450982864120557249528038055829_<46>

P59 = 11445290611232355952658107212384022849920784550095471386349_<59>

Number: n
N=14294430912933799768877945621994775259320155089090998487296732530834015369018161723244761086025290478321
  ( 104 digits)
Divisors found:
 r1=1248935601417172450982864120557249528038055829 (pp46)
 r2=11445290611232355952658107212384022849920784550095471386349 (pp59)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.75 hours.
Scaled time: 15.85 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_3_4_130_9
n: 14294430912933799768877945621994775259320155089090998487296732530834015369018161723244761086025290478321
skew: 3390.65
# norm 2.31e+13
c5: 91800
c4: 6859206
c3: -4725006547371
c2: -2699552177629954
c1: 27385722727592109576
c0: -21567600773132452286336
# alpha -4.55
Y1: 91767493427
Y0: -43497552812811424329
# Murphy_E 2.47e-09
# M 7075543479495724653964217112395499653546303942025095148589176977474698349047121752729839508576224373702
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [100000, 1000001)
Primes: RFBsize:169511, AFBsize:169506, largePrimes:4076820 encountered
Relations: rels:4026657, finalFF:415113
Max relations in full relation-set: 28
Initial matrix: 339097 x 415113 with sparse part having weight 23662065.
Pruned matrix : 265650 x 267409 with weight 11101962.
Polynomial selection time: 0.98 hours.
Total sieving time: 6.36 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.20 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 7.75 hours.
 --------- CPU info (if available) ----------

(31·10¹⁵⁹+41)/9 = 3(4)₁₅₈9_<160> = 89 · 283 · 67447 · 110291 · 162901069 · C138

C138 = P33 · P105

P33 = 519200074012305510805012666334819_<33>

P105 = 217360863393650894273483985147045926746949619702827516312957917248727025467082747527790644449593568212041_<105>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 112853776361362171890036514539513706755461921707305238431624689696835446173126379474301045848075084708611487263335709392706447626493355579 (138 digits)
Using B1=1428000, B2=2140044280, polynomial Dickson(6), sigma=3811119449
Step 1 took 15585ms
Step 2 took 7162ms
********** Factor found in step 2: 519200074012305510805012666334819
Found probable prime factor of 33 digits: 519200074012305510805012666334819
Probable prime cofactor 217360863393650894273483985147045926746949619702827516312957917248727025467082747527790644449593568212041 has 105 digits

(32·10¹⁶⁸-41)/9 = 3(5)₁₆₇1_<169> = 67 · 91159 · C162

C162 = P40 · P123

P40 = 2071061672414038887327862478162760144139_<40>

P123 = 281086561073560727550682470459751650208883734024290695333856539193174433441099866200434115946299221513714137236518465529753_<123>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 582147603270119562384365247265284317160054042945065077461924499567273313587978157167009251435134830933511703358975297967247902845095416448111173892091701273067667 (162 digits)
Using B1=2658000, B2=4281434440, polynomial Dickson(6), sigma=79681721
Step 1 took 53859ms
Step 2 took 19406ms
********** Factor found in step 2: 2071061672414038887327862478162760144139
Found probable prime factor of 40 digits: 2071061672414038887327862478162760144139
Probable prime cofactor 281086561073560727550682470459751650208883734024290695333856539193174433441099866200434115946299221513714137236518465529753 has 123 digits

(32·10¹⁶²-41)/9 = 3(5)₁₆₁1_<163> = 23 · 29 · 1213 · 22133 · 16724402733491_<14> · 147843987594734310011684362061_<30> · C110

C110 = P47 · P64

P47 = 22564381405754882879509950206984140408804091429_<47>

P64 = 3558793866027322837892334872232527090837570341500904949191061183_<64>

Number: n
N=80301982137501457226438683808161823698010328552916864791826396744849000596280781712481044585978795444664900507
  ( 110 digits)
Divisors found:
 r1=22564381405754882879509950206984140408804091429 (pp47)
 r2=3558793866027322837892334872232527090837570341500904949191061183 (pp64)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 17.19 hours.
Scaled time: 35.03 units (timescale=2.038).
Factorization parameters were as follows:
name: KA_3_5_161_1
n: 80301982137501457226438683808161823698010328552916864791826396744849000596280781712481044585978795444664900507
skew: 20941.36
# norm 3.03e+15
c5: 80160
c4: -178494500
c3: -208866880738614
c2: 1010698957953137416
c1: 26388170788187158703673
c0: 67057988088281024513967838
# alpha -6.73
Y1: 2999771929
Y0: -1000353997470729914547
# Murphy_E 1.09e-09
# M 51387382130815976307384603189548897007283674985944576533889534954907903830011786739793269560296316131041848063
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [100000, 1000001)
Primes: RFBsize:230209, AFBsize:229814, largePrimes:6650753 encountered
Relations: rels:6415890, finalFF:611905
Max relations in full relation-set: 28
Initial matrix: 460107 x 611905 with sparse part having weight 37008769.
Pruned matrix : 312942 x 315306 with weight 13812048.
Total sieving time: 16.59 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.29 hours.
Total square root time: 0.11 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 17.19 hours.
 --------- CPU info (if available) ----------

(29·10¹⁶⁸+43)/9 = 3(2)₁₆₇7_<169> = 23 · 701 · C165

C165 = P51 · P114

P51 = 977639558746409933281005872314517859936176961237157_<51>

P114 = 204423522793514430218662211232552454622248740088943549859241400069576142068391696971781870504041640804809998425557_<114>

Number: n
N=199852522621238120834970056578938300702240415693247052175291336737717684191665460660064641953868524605980414452783118664158172934455264046531180439262061788886821449
  ( 165 digits)
SNFS difficulty: 169 digits.
Divisors found:

Sun Nov 23 17:05:15 2008  prp51 factor: 977639558746409933281005872314517859936176961237157
Sun Nov 23 17:05:15 2008  prp114 factor: 204423522793514430218662211232552454622248740088943549859241400069576142068391696971781870504041640804809998425557
Sun Nov 23 17:05:15 2008  elapsed time 03:41:45 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 60.15 hours.
Scaled time: 110.02 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_3_2_167_7
n: 199852522621238120834970056578938300702240415693247052175291336737717684191665460660064641953868524605980414452783118664158172934455264046531180439262061788886821449
type: snfs
skew: 0.27
deg: 5
c5: 29000
c0: 43
m: 1000000000000000000000000000000000
rlim: 6000000
alim: 6000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 3400001)
Primes: RFBsize:412849, AFBsize:412761, largePrimes:17173952 encountered
Relations: rels:16036227, finalFF:897904
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 59.30 hours.
Total relation processing time: 0.85 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,56,56,2.5,2.5,100000
total time: 60.15 hours.
 --------- CPU info (if available) ----------

(32·10¹⁵⁶-41)/9 = 3(5)₁₅₅1_<157> = 73 · 4871 · 7159 · 8814419 · 380665371239696891267261_<24> · C117

C117 = P36 · P82

P36 = 277097866660463929160851656157857587_<36>

P82 = 1502255740059705391542146623564628296144683429311981707835983561439257940088530651_<82>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 416271860748980805269299319690524959322893202639117708912412035001294381766873523256418067451244226313074070942399137 (117 digits)
Using B1=2456000, B2=3567875230, polynomial Dickson(6), sigma=3741657175
Step 1 took 32438ms
Step 2 took 11703ms
********** Factor found in step 2: 277097866660463929160851656157857587
Found probable prime factor of 36 digits: 277097866660463929160851656157857587
Probable prime cofactor 1502255740059705391542146623564628296144683429311981707835983561439257940088530651 has 82 digits

Nov 22, 2008 (10th)

By Markus Tervooren / GGNFS

7·10¹⁶⁷-9 = 6(9)₁₆₆1_<168> = 1315096889_<10> · 2924704534089087990741564307_<28> · C132

C132 = P44 · P88

P44 = 32171713835165356860545627602731658117138163_<44>

P88 = 5656972847387801199256068528668241589373474506207018297434013731023661520263653791197559_<88>

N=181994511619460886722571958133515667928438683353276929634860147537918477950452863619794044389350713131234957248455222391689631344117
  ( 132 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=32171713835165356860545627602731658117138163 (pp44)
 r2=5656972847387801199256068528668241589373474506207018297434013731023661520263653791197559 (pp88)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 76.94 hours.
Scaled time: 157.33 units (timescale=2.045).
Factorization parameters were as follows:
n: 181994511619460886722571958133515667928438683353276929634860147537918477950452863619794044389350713131234957248455222391689631344117
m: 2000000000000000000000000000000000
deg: 5
c5: 175
c0: -72
skew: 0.84
type: snfs
lss: 1
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4

Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2250000, 5150001)
Primes: RFBsize:315948, AFBsize:315881, largePrimes:10450786 encountered
Relations: rels:11438283, finalFF:947465
Max relations in full relation-set: 32
Initial matrix: 631897 x 947465 with sparse part having weight 126994170.
Pruned matrix : 515741 x 518964 with weight 79936325.
Total sieving time: 72.97 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 3.65 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,52,52,2.4,2.4,100000
total time: 76.94 hours.
 --------- CPU info (if available) ----------

Nov 22, 2008 (9th)

By Robert Backstrom / GGNFS, GMP-ECM, Msieve

(31·10¹³⁹+41)/9 = 3(4)₁₃₈9_<140> = 3 · 13² · 151 · 211 · 263887980827_<12> · 65802951844819631490175873_<26> · C96

C96 = P41 · P55

P41 = 17751030558599310472733314763851239959047_<41>

P55 = 6917724541519043115256611096093267885584506550050379251_<55>

Number: n
N=122796739732476938843056250443218226969682997756544001036135289144535313607829770602408058533797
  ( 96 digits)
Divisors found:
 r1=17751030558599310472733314763851239959047 (pp41)
 r2=6917724541519043115256611096093267885584506550050379251 (pp55)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 9.83 hours.
Scaled time: 12.88 units (timescale=1.310).
Factorization parameters were as follows:
name: KA_3_4_138_9
n:  122796739732476938843056250443218226969682997756544001036135289144535313607829770602408058533797
m:  7243743645372881631714
deg: 4
c4: 44599968
c3: 106520161388
c2: -859752888831163147
c1: -226792341741364904
c0: 453710617209311880093505
skew: 1635.250
type: gnfs
# adj. I(F,S) = 56.152
# E(F1,F2) = 2.818535e-05
# GGNFS version 0.77.1-20060513-athlon-xp polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1227291941.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:92938, AFBsize:92030, largePrimes:1875231 encountered
Relations: rels:1947293, finalFF:232210
Max relations in full relation-set: 28
Initial matrix: 185049 x 232210 with sparse part having weight 18482100.
Pruned matrix : 164303 x 165292 with weight 10782603.
Polynomial selection time: 0.17 hours.
Total sieving time: 8.95 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.51 hours.
Total square root time: 0.09 hours, sqrts: 2.
Prototype def-par.txt line would be:
gnfs,95,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 9.83 hours.
 --------- CPU info (if available) ----------

(31·10¹⁴⁸+41)/9 = 3(4)₁₄₇9_<149> = 3 · 5101 · 75389 · 4525837 · C133

C133 = P28 · P33 · P73

P28 = 7423689621961529739231158597_<28>

P33 = 702766731950884884431830689726431_<33>

P73 = 1264458890754132592520292456614107767172350023484547611212032793438177533_<73>

GMP-ECM 6.2.1 [powered by GMP 4.1.4] [ECM]
Input number is 6596836416721928663206667563446461274548082634185610745446412601130224788147677008292567890044088794576244499948181477445864362643631 (133 digits)
Using B1=68000, B2=20337252, polynomial x^2, sigma=1865824268
Step 1 took 906ms
********** Factor found in step 1: 7423689621961529739231158597
Found probable prime factor of 28 digits: 7423689621961529739231158597
Composite cofactor 888619642341522732989585178583008347765811867881469147602770976994452953369611679679482249149798980474723 has 105 digits

GMP-ECM 6.2.1 [powered by GMP 4.1.4] [ECM]
Input number is 888619642341522732989585178583008347765811867881469147602770976994452953369611679679482249149798980474723 (105 digits)
Using B1=2118000, B2=2854078510, polynomial Dickson(6), sigma=2632614283
Step 1 took 20141ms
Step 2 took 10594ms
********** Factor found in step 2: 702766731950884884431830689726431
Found probable prime factor of 33 digits: 702766731950884884431830689726431
Probable prime cofactor 1264458890754132592520292456614107767172350023484547611212032793438177533 has 73 digits

(31·10¹⁷⁶+23)/9 = 3(4)₁₇₅7_<177> = 61 · 127 · 6269 · 93623059 · 328309320318647_<15> · 202720502544193253155472756683183303_<36> · C112

C112 = P52 · P60

P52 = 2266172878279014315730607731434242315087398795693843_<52>

P60 = 502262330982835789656318035407776239301869911590546746313137_<60>

Number: n
N=1138213272254499930643296820016032059483757432491990061526260841951018280753405751022578969878813592572060915491
  ( 112 digits)
Divisors found:
 r1=2266172878279014315730607731434242315087398795693843 (pp52)
 r2=502262330982835789656318035407776239301869911590546746313137 (pp60)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 21.91 hours.
Scaled time: 39.61 units (timescale=1.808).
Factorization parameters were as follows:
name: KA_3_4_175_7
n: 1138213272254499930643296820016032059483757432491990061526260841951018280753405751022578969878813592572060915491
skew: 53039.99
# norm 7.36e+15
c5: 17460
c4: 5859327786
c3: -118467216522632
c2: -13760853615378600227
c1: 187861473514694524755838
c0: 4487634284275327949310944367
# alpha -6.95
Y1: 227078131093
Y0: -2305860398873277449270
# Murphy_E 8.45e-10
# M 2024995312728739307273871443214848386906755758974582669400508108420435202603172697573663281195273174673215143
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:250150, AFBsize:249691, largePrimes:7037075 encountered
Relations: rels:6984182, finalFF:754863
Max relations in full relation-set: 48
Initial matrix: 499918 x 754863 with sparse part having weight 51708575.
Pruned matrix : 264371 x 266934 with weight 16537923.
Polynomial selection time: 1.90 hours.
Total sieving time: 19.21 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.46 hours.
Total square root time: 0.14 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 21.91 hours.
 --------- CPU info (if available) ----------

(31·10¹²⁷+41)/9 = 3(4)₁₂₆9_<128> = 3 · 13 · 5082719021_<10> · C117

C117 = P43 · P74

P43 = 9973580693615855217576522026614909705580359_<43>

P74 = 17422375492504637407894128118367596750344220464668292825505166710628246069_<74>

Number: n
N=173763467848970278713974750561149146568806736167382405237857999467581269407965348000471968423452003995969697905358771
  ( 117 digits)
SNFS difficulty: 128 digits.
Divisors found:

Sat Nov 22 21:21:13 2008  prp43 factor: 9973580693615855217576522026614909705580359
Sat Nov 22 21:21:13 2008  prp74 factor: 17422375492504637407894128118367596750344220464668292825505166710628246069
Sat Nov 22 21:21:13 2008  elapsed time 00:09:04 (Msieve 1.38)

Version: GGNFS-0.77.1-20050930-k8
Total time: 2.73 hours.
Scaled time: 2.28 units (timescale=0.836).
Factorization parameters were as follows:
name: KA_3_4_126_9
n: 173763467848970278713974750561149146568806736167382405237857999467581269407965348000471968423452003995969697905358771
type: snfs
skew: 0.42
deg: 5
c5: 3100
c0: 41
m: 10000000000000000000000000
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 550001)
Primes: RFBsize:63951, AFBsize:63920, largePrimes:5985205 encountered
Relations: rels:5100087, finalFF:107496
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 2.62 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,28,28,56,56,2.5,2.5,50000
total time: 2.73 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(31·10¹⁵⁷+23)/9 = 3(4)₁₅₆7_<158> = 37 · 5003 · C153

C153 = P39 · P115

P39 = 137062009031584687162325943108145597979_<39>

P115 = 1357593856795359123077509588134425961575969533810088621185776166177182280010278618966059027685150731758000076456763_<115>

Number: n
N=186074541461309400545858670983596028569044759330587833486094529468505083136304403544059750335984595428928828888852874461509280617815496888053354173681977
  ( 153 digits)
SNFS difficulty: 158 digits.
Divisors found:

Sat Nov 22 22:31:01 2008  prp39 factor: 137062009031584687162325943108145597979
Sat Nov 22 22:31:01 2008  prp115 factor: 1357593856795359123077509588134425961575969533810088621185776166177182280010278618966059027685150731758000076456763
Sat Nov 22 22:31:01 2008  elapsed time 01:49:31 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 25.37 hours.
Scaled time: 51.88 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_3_4_156_7
n: 186074541461309400545858670983596028569044759330587833486094529468505083136304403544059750335984595428928828888852874461509280617815496888053354173681977
type: snfs
skew: 0.38
deg: 5
c5: 3100
c0: 23
m: 10000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 1400001)
Primes: RFBsize:250150, AFBsize:249137, largePrimes:13233651 encountered
Relations: rels:11691766, finalFF:516629
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 25.07 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,56,56,2.5,2.5,100000
total time: 25.37 hours.
 --------- CPU info (if available) ----------

Nov 22, 2008 (8th)

By Serge Batalov / GMP-ECM 6.2.1

(32·10¹⁵²-41)/9 = 3(5)₁₅₁1_<153> = 3 · 13 · 1069 · 4057 · C145

C145 = P30 · P30 · P86

P30 = 177032885146535852618476212619_<30>

P30 = 183767390539545233362133693209_<30>

P86 = 64615655324137978437197139681674314373675816817502284960654218102416791281648499460663_<86>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=524982478
Step 1 took 18886ms
Step 2 took 14066ms
********** Factor found in step 2: 183767390539545233362133693209
Found probable prime factor of 30 digits: 183767390539545233362133693209

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1337943101
Step 1 took 19191ms
Step 2 took 14563ms
********** Factor found in step 2: 177032885146535852618476212619
Found probable prime factor of 30 digits: 177032885146535852618476212619

Nov 22, 2008 (7th)

By Sinkiti Sibata / GGNFS

(32·10¹¹⁵-41)/9 = 3(5)₁₁₄1_<116> = 1553881626764981_<16> · C101

C101 = P40 · P62

P40 = 1874364695456994437787812330948654894281_<40>

P62 = 12207744796954647002836007977637501893348342131034571999208491_<62>

Number: 35551_115
N=22881765858560605328444758333732016135351937111017680153991433819602314108836986599559243845282539971
  ( 101 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=1874364695456994437787812330948654894281 (pp40)
 r2=12207744796954647002836007977637501893348342131034571999208491 (pp62)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 1.63 hours.
Scaled time: 0.77 units (timescale=0.473).
Factorization parameters were as follows:
name: 35551_115
n: 22881765858560605328444758333732016135351937111017680153991433819602314108836986599559243845282539971
m: 200000000000000000000000
deg: 5
c5: 1
c0: -41
skew: 2.10
type: snfs
lss: 1
rlim: 610000
alim: 610000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 610000/610000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [305000, 455001)
Primes: RFBsize:49861, AFBsize:49970, largePrimes:1339209 encountered
Relations: rels:1376013, finalFF:204044
Max relations in full relation-set: 28
Initial matrix: 99895 x 204044 with sparse part having weight 8657884.
Pruned matrix : 64281 x 64844 with weight 2194412.
Total sieving time: 1.55 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,610000,610000,25,25,45,45,2.2,2.2,50000
total time: 1.63 hours.
 --------- CPU info (if available) ----------

(32·10¹³⁸-41)/9 = 3(5)₁₃₇1_<139> = 157 · 1854331 · C131

C131 = P43 · P88

P43 = 3614408098329054255724340417243253779450081_<43>

P88 = 3378962493146452219447414756610095654554526360880050718178161743928515403049413915028913_<88>

Number: 35551_138
N=12212949399178668390243576524554600576571890847483782236527906299510402361140498997671220687341868711013028609162572245802355191953
  ( 131 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=3614408098329054255724340417243253779450081 (pp43)
 r2=3378962493146452219447414756610095654554526360880050718178161743928515403049413915028913 (pp88)
Version: GGNFS-0.77.1-20060513-k8
Total time: 8.53 hours.
Scaled time: 16.67 units (timescale=1.955).
Factorization parameters were as follows:
name: 35551_138
n: 12212949399178668390243576524554600576571890847483782236527906299510402361140498997671220687341868711013028609162572245802355191953
m: 4000000000000000000000000000
deg: 5
c5: 125
c0: -164
skew: 1.06
type: snfs
lss: 1
rlim: 1510000
alim: 1510000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1510000/1510000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [755000, 1430001)
Primes: RFBsize:114886, AFBsize:114908, largePrimes:3334696 encountered
Relations: rels:3259503, finalFF:260977
Max relations in full relation-set: 28
Initial matrix: 229860 x 260977 with sparse part having weight 20373065.
Pruned matrix : 219199 x 220412 with weight 14602189.
Total sieving time: 7.87 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.48 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1510000,1510000,26,26,48,48,2.3,2.3,75000
total time: 8.53 hours.
 --------- CPU info (if available) ----------

(31·10¹⁴¹+41)/9 = 3(4)₁₄₀9_<142> = 2143 · 21736275811319_<14> · C125

C125 = P36 · P90

P36 = 250844864487752569642988214862325027_<36>

P90 = 294785870231812031961140657885418584096523225421107367822479810640014905616838732440253811_<90>

Number: 34449_141
N=73945521671203103330866766193284634285998509123366560370612765483356140853530412183713691765269584991516030247771197457427897
  ( 125 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=250844864487752569642988214862325027 (pp36)
 r2=294785870231812031961140657885418584096523225421107367822479810640014905616838732440253811 (pp90)
Version: GGNFS-0.77.1-20060513-k8
Total time: 15.03 hours.
Scaled time: 29.39 units (timescale=1.955).
Factorization parameters were as follows:
name: 34449_141
n: 73945521671203103330866766193284634285998509123366560370612765483356140853530412183713691765269584991516030247771197457427897
m: 10000000000000000000000000000
deg: 5
c5: 310
c0: 41
skew: 0.67
type: snfs
lss: 1
rlim: 1660000
alim: 1660000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1660000/1660000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [830000, 2130001)
Primes: RFBsize:125335, AFBsize:125478, largePrimes:4027860 encountered
Relations: rels:4257982, finalFF:408568
Max relations in full relation-set: 28
Initial matrix: 250880 x 408568 with sparse part having weight 45738650.
Pruned matrix : 209515 x 210833 with weight 22135631.
Total sieving time: 14.18 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.62 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1660000,1660000,26,26,48,48,2.3,2.3,100000
total time: 15.03 hours.
 --------- CPU info (if available) ----------

Nov 22, 2008 (6th)

By Wataru Sakai / GGNFS

9·10¹⁸⁵+7 = 9(0)₁₈₄7_<186> = 3260111 · C180

C180 = P89 · P92

P89 = 16002389063807038301896669024272082879641164981792275113754829766261058133472766404528443_<89>

P92 = 17251437819596683036560616627382651350704560527929204910892350271133158669382239777179811659_<92>

Number: 90007_185
N=276064219899261098778538522154613753948868612142347300444678110653287572110274772852826176777416474469734312727388730015634436986961486894157898304689625598637592400994935448516937
  ( 180 digits)
SNFS difficulty: 185 digits.
Divisors found:
 r1=16002389063807038301896669024272082879641164981792275113754829766261058133472766404528443
 r2=17251437819596683036560616627382651350704560527929204910892350271133158669382239777179811659
Version: 
Total time: 307.81 hours.
Scaled time: 612.84 units (timescale=1.991).
Factorization parameters were as follows:
n: 276064219899261098778538522154613753948868612142347300444678110653287572110274772852826176777416474469734312727388730015634436986961486894157898304689625598637592400994935448516937
m: 10000000000000000000000000000000000000
deg: 5
c5: 9
c0: 7
skew: 0.95
type: snfs
lss: 1
rlim: 10500000
alim: 10500000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.7
alambda: 2.7
Factor base limits: 10500000/10500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [5250000, 8150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1277949 x 1278197
Total sieving time: 307.81 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,185,5,0,0,0,0,0,0,0,0,10500000,10500000,28,28,55,55,2.7,2.7,100000
total time: 307.81 hours.
 --------- CPU info (if available) ----------

(29·10¹⁷⁷-11)/9 = 3(2)₁₇₆1_<178> = C178

C178 = P46 · P52 · P80

P46 = 4238791109846768319832989175973237807031692293_<46>

P52 = 9122678024342822606413342521202266190898888619350609_<52>

P80 = 83328032289291372193606565637887001304378576354453021528093000914205072237905433_<80>

Number: 32221_177
N=3222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
  ( 178 digits)
SNFS difficulty: 179 digits.
Divisors found:
 r1=4238791109846768319832989175973237807031692293 (pp46)
 r2=9122678024342822606413342521202266190898888619350609 (pp52)
 r3=83328032289291372193606565637887001304378576354453021528093000914205072237905433 (pp80)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 216.80 hours.
Scaled time: 436.41 units (timescale=2.013).
Factorization parameters were as follows:
n: 3222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
m: 200000000000000000000000000000000000
deg: 5
c5: 725
c0: -88
skew: 0.66
type: snfs
lss: 1
rlim: 6800000
alim: 6800000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6800000/6800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3400000, 9900001)
Primes: RFBsize:463872, AFBsize:464782, largePrimes:18589630 encountered
Relations: rels:20197980, finalFF:1175338
Max relations in full relation-set: 32
Initial matrix: 928721 x 1175338 with sparse part having weight 172348679.
Pruned matrix : 767940 x 772647 with weight 161025116.
Total sieving time: 204.87 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 11.23 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,179,5,0,0,0,0,0,0,0,0,6800000,6800000,28,28,53,53,2.5,2.5,100000
total time: 216.80 hours.
 --------- CPU info (if available) ----------

Nov 22, 2008 (5th)

By Jo Yeong Uk / GGNFS

(29·10¹⁵⁷+43)/9 = 3(2)₁₅₆7_<158> = 37 · 18143 · 198323 · 120011103804224805681823546153_<30> · C118

C118 = P52 · P66

P52 = 3779316950432087251769608243853000617761392165509961_<52>

P66 = 533625819775685716703761578486849254082415913206193590187082495683_<66>

Number: 32227_157
N=2016741105866467140951604570336781152331001527925371904341000515480857002518308891930313959772708022278077300275998363
  ( 118 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=3779316950432087251769608243853000617761392165509961 (pp52)
 r2=533625819775685716703761578486849254082415913206193590187082495683 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 28.09 hours.
Scaled time: 66.75 units (timescale=2.376).
Factorization parameters were as follows:
n: 2016741105866467140951604570336781152331001527925371904341000515480857002518308891930313959772708022278077300275998363
m: 10000000000000000000000000000000
deg: 5
c5: 2900
c0: 43
skew: 0.43
type: snfs
lss: 1
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1600000, 3400001)
Primes: RFBsize:230209, AFBsize:230182, largePrimes:8236119 encountered
Relations: rels:8439376, finalFF:550147
Max relations in full relation-set: 28
Initial matrix: 460458 x 550147 with sparse part having weight 61945056.
Pruned matrix : 427466 x 429832 with weight 45595021.
Total sieving time: 26.52 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 1.40 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,50,50,2.4,2.4,100000
total time: 28.09 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Nov 22, 2008 (4th)

By Sinkiti Sibata / GGNFS, Msieve

(32·10¹²⁵-41)/9 = 3(5)₁₂₄1_<126> = 3 · 7 · C125

C125 = P49 · P76

P49 = 4101642359788017039736531885784855474095010630123_<49>

P76 = 4127911564696239905743837315670797719255008130849857537912706158500072765097_<76>

Number: 35551_125
N=16931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931
  ( 125 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=4101642359788017039736531885784855474095010630123 (pp49)
 r2=4127911564696239905743837315670797719255008130849857537912706158500072765097 (pp76)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 2.61 hours.
Scaled time: 1.23 units (timescale=0.473).
Factorization parameters were as follows:
name: 35551_125
n: 16931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931
m: 20000000000000000000000000
deg: 5
c5: 1
c0: -41
skew: 2.10
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 650001)
Primes: RFBsize:71274, AFBsize:71351, largePrimes:2368602 encountered
Relations: rels:2262222, finalFF:197699
Max relations in full relation-set: 28
Initial matrix: 142689 x 197699 with sparse part having weight 12662606.
Pruned matrix : 119300 x 120077 with weight 5455752.
Total sieving time: 2.36 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 2.61 hours.
 --------- CPU info (if available) ----------

(32·10¹³²-41)/9 = 3(5)₁₃₁1_<133> = 73 · C131

C131 = P32 · P35 · P65

P32 = 53253233532503110182693787985653_<32>

P35 = 20444379394590998327962375579649849_<35>

P65 = 44736777108005239501416276185226616696706068766867655030020027971_<65>

Number: 35551_132
N=48706240487062404870624048706240487062404870624048706240487062404870624048706240487062404870624048706240487062404870624048706240487
  ( 131 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=53253233532503110182693787985653 (pp32)
 r2=20444379394590998327962375579649849 (pp35)
 r3=44736777108005239501416276185226616696706068766867655030020027971 (pp65)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.33 hours.
Scaled time: 12.59 units (timescale=1.991).
Factorization parameters were as follows:
name: 35551_132
n: 48706240487062404870624048706240487062404870624048706240487062404870624048706240487062404870624048706240487062404870624048706240487
m: 200000000000000000000000000
deg: 5
c5: 100
c0: -41
skew: 0.84
type: snfs
lss: 1
rlim: 1180000
alim: 1180000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1180000/1180000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [590000, 1115001)
Primes: RFBsize:91490, AFBsize:90768, largePrimes:3152382 encountered
Relations: rels:3171737, finalFF:314254
Max relations in full relation-set: 28
Initial matrix: 182322 x 314254 with sparse part having weight 26946203.
Pruned matrix : 151286 x 152261 with weight 9842261.
Total sieving time: 6.01 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1180000,1180000,26,26,47,47,2.3,2.3,75000
total time: 6.33 hours.
 --------- CPU info (if available) ----------

(32·10¹²¹-41)/9 = 3(5)₁₂₀1_<122> = 31 · 97 · 624613195527409379246773_<24> · C95

C95 = P46 · P49

P46 = 7302277230608177321336738676050278849209010349_<46>

P49 = 2592415258819787071229728638616500578052858667409_<49>

Fri Nov 21 23:38:37 2008  Msieve v. 1.38
Fri Nov 21 23:38:37 2008  random seeds: 0d4af2ec 94d26f7d
Fri Nov 21 23:38:37 2008  factoring 18930534916760935971590741741646619489241142175356386448608577960372293068418528062763830015741 (95 digits)
Fri Nov 21 23:38:37 2008  searching for 15-digit factors
Fri Nov 21 23:38:39 2008  commencing quadratic sieve (95-digit input)
Fri Nov 21 23:38:39 2008  using multiplier of 1
Fri Nov 21 23:38:39 2008  using 32kb Intel Core sieve core
Fri Nov 21 23:38:39 2008  sieve interval: 36 blocks of size 32768
Fri Nov 21 23:38:39 2008  processing polynomials in batches of 6
Fri Nov 21 23:38:39 2008  using a sieve bound of 2125181 (78824 primes)
Fri Nov 21 23:38:39 2008  using large prime bound of 310276426 (28 bits)
Fri Nov 21 23:38:39 2008  using double large prime bound of 1928180890905122 (43-51 bits)
Fri Nov 21 23:38:39 2008  using trial factoring cutoff of 51 bits
Fri Nov 21 23:38:39 2008  polynomial 'A' values have 12 factors
Sat Nov 22 02:33:35 2008  78924 relations (20057 full + 58867 combined from 1153943 partial), need 78920
Sat Nov 22 02:33:36 2008  begin with 1174000 relations
Sat Nov 22 02:33:37 2008  reduce to 202550 relations in 9 passes
Sat Nov 22 02:33:37 2008  attempting to read 202550 relations
Sat Nov 22 02:33:40 2008  recovered 202550 relations
Sat Nov 22 02:33:40 2008  recovered 182655 polynomials
Sat Nov 22 02:33:40 2008  attempting to build 78924 cycles
Sat Nov 22 02:33:40 2008  found 78924 cycles in 6 passes
Sat Nov 22 02:33:40 2008  distribution of cycle lengths:
Sat Nov 22 02:33:40 2008     length 1 : 20057
Sat Nov 22 02:33:40 2008     length 2 : 14148
Sat Nov 22 02:33:40 2008     length 3 : 13467
Sat Nov 22 02:33:40 2008     length 4 : 10622
Sat Nov 22 02:33:40 2008     length 5 : 7732
Sat Nov 22 02:33:40 2008     length 6 : 5123
Sat Nov 22 02:33:40 2008     length 7 : 3320
Sat Nov 22 02:33:40 2008     length 9+: 4455
Sat Nov 22 02:33:40 2008  largest cycle: 20 relations
Sat Nov 22 02:33:40 2008  matrix is 78824 x 78924 (20.4 MB) with weight 5044100 (63.91/col)
Sat Nov 22 02:33:40 2008  sparse part has weight 5044100 (63.91/col)
Sat Nov 22 02:33:41 2008  filtering completed in 3 passes
Sat Nov 22 02:33:41 2008  matrix is 74614 x 74678 (19.5 MB) with weight 4821220 (64.56/col)
Sat Nov 22 02:33:41 2008  sparse part has weight 4821220 (64.56/col)
Sat Nov 22 02:33:42 2008  saving the first 48 matrix rows for later
Sat Nov 22 02:33:42 2008  matrix is 74566 x 74678 (12.6 MB) with weight 3859562 (51.68/col)
Sat Nov 22 02:33:42 2008  sparse part has weight 2866657 (38.39/col)
Sat Nov 22 02:33:42 2008  matrix includes 64 packed rows
Sat Nov 22 02:33:42 2008  using block size 29871 for processor cache size 1024 kB
Sat Nov 22 02:33:43 2008  commencing Lanczos iteration
Sat Nov 22 02:33:43 2008  memory use: 12.1 MB
Sat Nov 22 02:34:22 2008  lanczos halted after 1180 iterations (dim = 74564)
Sat Nov 22 02:34:22 2008  recovered 16 nontrivial dependencies
Sat Nov 22 02:34:23 2008  prp46 factor: 7302277230608177321336738676050278849209010349
Sat Nov 22 02:34:23 2008  prp49 factor: 2592415258819787071229728638616500578052858667409
Sat Nov 22 02:34:23 2008  elapsed time 02:55:46

(32·10¹²³-41)/9 = 3(5)₁₂₂1_<124> = 167 · 293 · 2268001 · 259137899539_<12> · 260503293345466609_<18> · C84

C84 = P42 · P43

P42 = 167982103839853336193445278263392698635919_<42>

P43 = 2825354631611978018062501736888645582464009_<43>

Fri Nov 21 21:28:02 2008  Msieve v. 1.38
Fri Nov 21 21:28:02 2008  random seeds: b8cb3a44 4d4e9d2a
Fri Nov 21 21:28:02 2008  factoring 474609015111853860752833336137112158853448747727127472704320673550969428561212139271 (84 digits)
Fri Nov 21 21:28:04 2008  searching for 15-digit factors
Fri Nov 21 21:28:09 2008  commencing quadratic sieve (84-digit input)
Fri Nov 21 21:28:10 2008  using multiplier of 15
Fri Nov 21 21:28:10 2008  using 64kb Pentium 2 sieve core
Fri Nov 21 21:28:10 2008  sieve interval: 6 blocks of size 65536
Fri Nov 21 21:28:10 2008  processing polynomials in batches of 17
Fri Nov 21 21:28:10 2008  using a sieve bound of 1390619 (53529 primes)
Fri Nov 21 21:28:10 2008  using large prime bound of 119593234 (26 bits)
Fri Nov 21 21:28:10 2008  using double large prime bound of 346634530714364 (41-49 bits)
Fri Nov 21 21:28:10 2008  using trial factoring cutoff of 49 bits
Fri Nov 21 21:28:10 2008  polynomial 'A' values have 11 factors
Sat Nov 22 01:02:21 2008  53629 relations (17104 full + 36525 combined from 561999 partial), need 53625
Sat Nov 22 01:02:31 2008  begin with 579103 relations
Sat Nov 22 01:02:32 2008  reduce to 121584 relations in 10 passes
Sat Nov 22 01:02:32 2008  attempting to read 121584 relations
Sat Nov 22 01:02:37 2008  recovered 121584 relations
Sat Nov 22 01:02:37 2008  recovered 93293 polynomials
Sat Nov 22 01:02:38 2008  attempting to build 53629 cycles
Sat Nov 22 01:02:38 2008  found 53629 cycles in 4 passes
Sat Nov 22 01:02:41 2008  distribution of cycle lengths:
Sat Nov 22 01:02:41 2008     length 1 : 17104
Sat Nov 22 01:02:41 2008     length 2 : 11333
Sat Nov 22 01:02:41 2008     length 3 : 9269
Sat Nov 22 01:02:41 2008     length 4 : 6572
Sat Nov 22 01:02:41 2008     length 5 : 4225
Sat Nov 22 01:02:41 2008     length 6 : 2400
Sat Nov 22 01:02:41 2008     length 7 : 1329
Sat Nov 22 01:02:41 2008     length 9+: 1397
Sat Nov 22 01:02:41 2008  largest cycle: 16 relations
Sat Nov 22 01:02:42 2008  matrix is 53529 x 53629 (11.4 MB) with weight 2782077 (51.88/col)
Sat Nov 22 01:02:42 2008  sparse part has weight 2782077 (51.88/col)
Sat Nov 22 01:02:46 2008  filtering completed in 3 passes
Sat Nov 22 01:02:46 2008  matrix is 47011 x 47075 (10.2 MB) with weight 2486567 (52.82/col)
Sat Nov 22 01:02:46 2008  sparse part has weight 2486567 (52.82/col)
Sat Nov 22 01:02:48 2008  saving the first 48 matrix rows for later
Sat Nov 22 01:02:48 2008  matrix is 46963 x 47075 (6.2 MB) with weight 1901594 (40.39/col)
Sat Nov 22 01:02:48 2008  sparse part has weight 1340469 (28.48/col)
Sat Nov 22 01:02:48 2008  matrix includes 64 packed rows
Sat Nov 22 01:02:48 2008  using block size 5461 for processor cache size 128 kB
Sat Nov 22 01:02:49 2008  commencing Lanczos iteration
Sat Nov 22 01:02:49 2008  memory use: 6.4 MB
Sat Nov 22 01:04:39 2008  lanczos halted after 744 iterations (dim = 46954)
Sat Nov 22 01:04:40 2008  recovered 14 nontrivial dependencies
Sat Nov 22 01:04:41 2008  prp42 factor: 167982103839853336193445278263392698635919
Sat Nov 22 01:04:41 2008  prp43 factor: 2825354631611978018062501736888645582464009
Sat Nov 22 01:04:41 2008  elapsed time 03:36:39

(32·10¹¹¹-41)/9 = 3(5)₁₁₀1_<112> = 46560268009_<11> · C101

C101 = P51 · P51

P51 = 250725206151227572491375889110383529086023607868659_<51>

P51 = 304574822852910071162849414423941486520137105717021_<51>

Number: 35551_111
N=76364585248269496393816506554713280356615130143710070231171455531033722911050513054523245829788744839
  ( 101 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=250725206151227572491375889110383529086023607868659 (pp51)
 r2=304574822852910071162849414423941486520137105717021 (pp51)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 1.54 hours.
Scaled time: 0.73 units (timescale=0.473).
Factorization parameters were as follows:
name: 35551_111
n: 76364585248269496393816506554713280356615130143710070231171455531033722911050513054523245829788744839
m: 20000000000000000000000
deg: 5
c5: 10
c0: -41
skew: 1.33
type: snfs
lss: 1
rlim: 530000
alim: 530000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 530000/530000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [265000, 415001)
Primes: RFBsize:43825, AFBsize:43507, largePrimes:1230717 encountered
Relations: rels:1219885, finalFF:156266
Max relations in full relation-set: 28
Initial matrix: 87398 x 156266 with sparse part having weight 7026889.
Pruned matrix : 64055 x 64555 with weight 2168146.
Total sieving time: 1.46 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,112,5,0,0,0,0,0,0,0,0,530000,530000,25,25,45,45,2.2,2.2,50000
total time: 1.54 hours.
 --------- CPU info (if available) ----------

(31·10¹¹⁶+41)/9 = 3(4)₁₁₅9_<117> = 4159 · 5309 · 1265569807591063802657_<22> · C89

C89 = P38 · P51

P38 = 24351976690366456440494140268150735011_<38>

P51 = 506170946785176908374198765538995513913432276329177_<51>

Sat Nov 22 05:22:34 2008  Msieve v. 1.38
Sat Nov 22 05:22:34 2008  random seeds: 1a24b790 2ab2abb3
Sat Nov 22 05:22:34 2008  factoring 12326263097453348113695198957819947847469270526475883181784504535093721446219669534715947 (89 digits)
Sat Nov 22 05:22:35 2008  searching for 15-digit factors
Sat Nov 22 05:22:36 2008  commencing quadratic sieve (89-digit input)
Sat Nov 22 05:22:36 2008  using multiplier of 3
Sat Nov 22 05:22:36 2008  using 32kb Intel Core sieve core
Sat Nov 22 05:22:36 2008  sieve interval: 28 blocks of size 32768
Sat Nov 22 05:22:36 2008  processing polynomials in batches of 8
Sat Nov 22 05:22:36 2008  using a sieve bound of 1533107 (58333 primes)
Sat Nov 22 05:22:36 2008  using large prime bound of 122648560 (26 bits)
Sat Nov 22 05:22:36 2008  using double large prime bound of 362737408899600 (42-49 bits)
Sat Nov 22 05:22:36 2008  using trial factoring cutoff of 49 bits
Sat Nov 22 05:22:36 2008  polynomial 'A' values have 11 factors
Sat Nov 22 06:30:13 2008  58550 relations (15565 full + 42985 combined from 620271 partial), need 58429
Sat Nov 22 06:30:14 2008  begin with 635836 relations
Sat Nov 22 06:30:14 2008  reduce to 142791 relations in 11 passes
Sat Nov 22 06:30:14 2008  attempting to read 142791 relations
Sat Nov 22 06:30:16 2008  recovered 142791 relations
Sat Nov 22 06:30:16 2008  recovered 123483 polynomials
Sat Nov 22 06:30:16 2008  attempting to build 58550 cycles
Sat Nov 22 06:30:16 2008  found 58550 cycles in 5 passes
Sat Nov 22 06:30:16 2008  distribution of cycle lengths:
Sat Nov 22 06:30:16 2008     length 1 : 15565
Sat Nov 22 06:30:16 2008     length 2 : 11170
Sat Nov 22 06:30:16 2008     length 3 : 10250
Sat Nov 22 06:30:16 2008     length 4 : 7878
Sat Nov 22 06:30:16 2008     length 5 : 5508
Sat Nov 22 06:30:16 2008     length 6 : 3522
Sat Nov 22 06:30:16 2008     length 7 : 2079
Sat Nov 22 06:30:16 2008     length 9+: 2578
Sat Nov 22 06:30:16 2008  largest cycle: 18 relations
Sat Nov 22 06:30:17 2008  matrix is 58333 x 58550 (14.2 MB) with weight 3493391 (59.67/col)
Sat Nov 22 06:30:17 2008  sparse part has weight 3493391 (59.67/col)
Sat Nov 22 06:30:17 2008  filtering completed in 3 passes
Sat Nov 22 06:30:17 2008  matrix is 54459 x 54523 (13.4 MB) with weight 3283171 (60.22/col)
Sat Nov 22 06:30:17 2008  sparse part has weight 3283171 (60.22/col)
Sat Nov 22 06:30:17 2008  saving the first 48 matrix rows for later
Sat Nov 22 06:30:18 2008  matrix is 54411 x 54523 (9.4 MB) with weight 2678963 (49.13/col)
Sat Nov 22 06:30:18 2008  sparse part has weight 2139290 (39.24/col)
Sat Nov 22 06:30:18 2008  matrix includes 64 packed rows
Sat Nov 22 06:30:18 2008  using block size 21809 for processor cache size 1024 kB
Sat Nov 22 06:30:18 2008  commencing Lanczos iteration
Sat Nov 22 06:30:18 2008  memory use: 8.7 MB
Sat Nov 22 06:30:38 2008  lanczos halted after 861 iterations (dim = 54411)
Sat Nov 22 06:30:38 2008  recovered 18 nontrivial dependencies
Sat Nov 22 06:30:38 2008  prp38 factor: 24351976690366456440494140268150735011
Sat Nov 22 06:30:38 2008  prp51 factor: 506170946785176908374198765538995513913432276329177
Sat Nov 22 06:30:38 2008  elapsed time 01:08:04

Nov 22, 2008 (3rd)

By Serge Batalov / GMP-ECM 6.2.1, GMP-ECM 6.2.1; Msieve-1.38

(31·10¹⁹⁹+41)/9 = 3(4)₁₉₈9_<200> = 3 · 13 · 211 · 4933314511_<10> · 108886162810849_<15> · C172

C172 = P30 · P143

P30 = 142018885622971503634552823639_<30>

P143 = 54867418150082322617178305566660740301855900348368997744658055286701238044662021541391733259709740789882218697925348449694048592355472049447861_<143>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1592717021
Step 1 took 24586ms
Step 2 took 16761ms
********** Factor found in step 2: 142018885622971503634552823639
Found probable prime factor of 30 digits: 142018885622971503634552823639
Probable prime cofactor 54867418150082322617178305566660740301855900348368997744658055286701238044662021541391733259709740789882218697925348449694048592355472049447861 has 143 digits

(32·10¹³⁵-41)/9 = 3(5)₁₃₄1_<136> = 17 · 67 · 541 · 631 · 646855311531991_<15> · C113

C113 = P30 · P31 · P52

P30 = 395238694440067346506321051229_<30>

P31 = 4607584230616385795106992439653_<31>

P52 = 7762779182268771788520111353675163478851612794868937_<52>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=978761011
Step 1 took 56903ms
Step 2 took 20658ms
********** Factor found in step 2: 4607584230616385795106992439653
Found probable prime factor of 31 digits: 4607584230616385795106992439653
Composite cofactor 3068150709226442954934260179839783913836305853892991916706470823431308919117773573 has 82 digits

Fri Nov 21 11:32:35 2008  Msieve v. 1.38
Fri Nov 21 11:32:35 2008  random seeds: f61d4527 abcf05c9
Fri Nov 21 11:32:35 2008  factoring 3068150709226442954934260179839783913836305853892991916706470823431308919117773573 (82 digits)
Fri Nov 21 11:32:35 2008  no P-1/P+1/ECM available, skipping
Fri Nov 21 11:32:35 2008  commencing quadratic sieve (82-digit input)
Fri Nov 21 11:32:35 2008  using multiplier of 13
Fri Nov 21 11:32:35 2008  using 64kb Opteron sieve core
Fri Nov 21 11:32:35 2008  sieve interval: 6 blocks of size 65536
Fri Nov 21 11:32:35 2008  processing polynomials in batches of 17
Fri Nov 21 11:32:35 2008  using a sieve bound of 1339157 (51471 primes)
Fri Nov 21 11:32:35 2008  using large prime bound of 125880758 (26 bits)
Fri Nov 21 11:32:35 2008  using trial factoring cutoff of 27 bits
Fri Nov 21 11:32:35 2008  polynomial 'A' values have 11 factors
Fri Nov 21 11:46:18 2008  51761 relations (27110 full + 24651 combined from 267857 partial), need 51567
Fri Nov 21 11:46:18 2008  begin with 294967 relations
Fri Nov 21 11:46:18 2008  reduce to 73333 relations in 2 passes
Fri Nov 21 11:46:18 2008  attempting to read 73333 relations
Fri Nov 21 11:46:18 2008  recovered 73333 relations
Fri Nov 21 11:46:18 2008  recovered 64668 polynomials
Fri Nov 21 11:46:19 2008  attempting to build 51761 cycles
Fri Nov 21 11:46:19 2008  found 51761 cycles in 1 passes
Fri Nov 21 11:46:19 2008  distribution of cycle lengths:
Fri Nov 21 11:46:19 2008     length 1 : 27110
Fri Nov 21 11:46:19 2008     length 2 : 24651
Fri Nov 21 11:46:19 2008  largest cycle: 2 relations
Fri Nov 21 11:46:19 2008  matrix is 51471 x 51761 (7.9 MB) with weight 1651481 (31.91/col)
Fri Nov 21 11:46:19 2008  sparse part has weight 1651481 (31.91/col)
Fri Nov 21 11:46:19 2008  filtering completed in 3 passes
Fri Nov 21 11:46:19 2008  matrix is 36514 x 36576 (6.1 MB) with weight 1302933 (35.62/col)
Fri Nov 21 11:46:19 2008  sparse part has weight 1302933 (35.62/col)
Fri Nov 21 11:46:19 2008  saving the first 48 matrix rows for later
Fri Nov 21 11:46:19 2008  matrix is 36466 x 36576 (4.2 MB) with weight 993167 (27.15/col)
Fri Nov 21 11:46:19 2008  sparse part has weight 731232 (19.99/col)
Fri Nov 21 11:46:19 2008  matrix includes 64 packed rows
Fri Nov 21 11:46:19 2008  using block size 14630 for processor cache size 1024 kB
Fri Nov 21 11:46:19 2008  commencing Lanczos iteration
Fri Nov 21 11:46:19 2008  memory use: 4.1 MB
Fri Nov 21 11:46:24 2008  lanczos halted after 578 iterations (dim = 36464)
Fri Nov 21 11:46:24 2008  recovered 17 nontrivial dependencies
Fri Nov 21 11:46:24 2008  prp30 factor: 395238694440067346506321051229
Fri Nov 21 11:46:24 2008  prp52 factor: 7762779182268771788520111353675163478851612794868937
Fri Nov 21 11:46:24 2008  elapsed time 00:13:49

(32·10¹³⁹-41)/9 = 3(5)₁₃₈1_<140> = C140

C140 = P51 · P89

P51 = 464526285610532197573410910418540500603849191853171_<51>

P89 = 76541536306873319748687998204768071820486616615213271404046353568746662919813194493399781_<89>

SNFS difficulty: 141 digits.
Divisors found:
 r1=464526285610532197573410910418540500603849191853171 (pp51)
 r2=76541536306873319748687998204768071820486616615213271404046353568746662919813194493399781 (pp89)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.949).
Factorization parameters were as follows:
n: 35555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555551
m: 10000000000000000000000000000
deg: 5
c5: 16
c0: -205
skew: 1.67
type: snfs
lss: 1
rlim: 1580000
alim: 1580000
lpbr: 25
lpba: 25
mfbr: 48
mfba: 48
rlambda: 2.4
alambda: 2.4
Factor base limits: 1580000/1580000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 48/48
Sieved rational special-q in [790000, 1590001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 220033 x 220275
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1580000,1580000,25,25,48,48,2.4,2.4,200000
total time: 4.50 hours.

(32·10¹⁵⁷-41)/9 = 3(5)₁₅₆1_<158> = 254050733 · C150

C150 = P29 · P121

P29 = 82152423305033592348298831619_<29>

P121 = 1703596103003294419723782049965196114125342318793393470606475103127644906981867365346338961594764303306093223734477470313_<121>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1517652325
Step 1 took 18518ms
Step 2 took 14281ms
********** Factor found in step 2: 82152423305033592348298831619
Found probable prime factor of 29 digits: 82152423305033592348298831619
Probable prime cofactor 1703596103003294419723782049965196114125342318793393470606475103127644906981867365346338961594764303306093223734477470313 has 121 digits

(32·10¹⁵⁰-41)/9 = 3(5)₁₄₉1_<151> = 7229 · C147

C147 = P57 · P91

P57 = 151630060370265312596023804982270143882259787233401865167_<57>

P91 = 3243724314599321778834666368665223817246547329724430342376155329768224196716824187092053957_<91>

SNFS difficulty: 151 digits.
Divisors found:
 r1=151630060370265312596023804982270143882259787233401865167 (pp57)
 r2=3243724314599321778834666368665223817246547329724430342376155329768224196716824187092053957 (pp91)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
n: 491846113647192634604448133290296798389203977805444121670432363474277985275356972687170501529334009621739598223205914449516607491431118488802815819
m: 2000000000000000000000000000000
deg: 5
c5: 1
c0: -41
skew: 2.10
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved rational special-q in [1150000, 1750001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 350251 x 350493
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,53,53,2.5,2.5,200000
total time: 10.00 hours.

Nov 22, 2008 (2nd)

By Erik Branger / GGNFS, Msieve

(31·10¹²⁵+41)/9 = 3(4)₁₂₄9_<126> = 7² · 487 · 1133565895591_<13> · C110

C110 = P42 · P68

P42 = 874649588582602018285507418779006331185511_<42>

P68 = 14558387529805029615527432457618027810773080096835070639069566035223_<68>

Number: 34449_125
N=12733487663370052831395840247528589876745259188248257431076297252867117599646478553622394464399720261573253953
  ( 110 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=874649588582602018285507418779006331185511
 r2=14558387529805029615527432457618027810773080096835070639069566035223
Version: 
Total time: 2.26 hours.
Scaled time: 4.52 units (timescale=1.997).
Factorization parameters were as follows:
n: 12733487663370052831395840247528589876745259188248257431076297252867117599646478553622394464399720261573253953
m: 10000000000000000000000000
deg: 5
c5: 31
c0: 41
skew: 1.06
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 121472 x 121697
Total sieving time: 2.26 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 2.26 hours.
 --------- CPU info (if available) ----------

Nov 22, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(32·10¹⁵⁴-41)/9 = 3(5)₁₅₃1_<155> = 19 · 1997 · 5903 · 48647 · 8841960503_<10> · 12814998923_<11> · 1194009122626689491_<19> · C104

C104 = P37 · P67

P37 = 7152201341862591428684838599721619649_<37>

P67 = 3372348398945690607950846917414070323884300578481012329068619483687_<67>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 24119714744167530175826743896080551920044617404588160851068750109106326746284237447175478123245774165863 (104 digits)
Using B1=1766000, B2=2140281790, polynomial Dickson(6), sigma=647106178
Step 1 took 12632ms
Step 2 took 5157ms
********** Factor found in step 2: 7152201341862591428684838599721619649
Found probable prime factor of 37 digits: 7152201341862591428684838599721619649
Probable prime cofactor 3372348398945690607950846917414070323884300578481012329068619483687 has 67 digits

(29·10¹⁶⁰+61)/9 = 3(2)₁₅₉9_<161> = 3 · 18658042499_<11> · 173087931043_<12> · 68198980432302694162763_<23> · C116

C116 = P46 · P71

P46 = 3392334564486724377686000326486270997623824929_<46>

P71 = 14375561255610661870862903525731472575001154792532546013717693189769037_<71>

Number: n
N=48766713331304223297469209004162040855423177792331628693848084378802536364064355176272991837831834801871342032923373
  ( 116 digits)
Divisors found:

Sat Nov 22 06:14:15 2008  prp46 factor: 3392334564486724377686000326486270997623824929
Sat Nov 22 06:14:15 2008  prp71 factor: 14375561255610661870862903525731472575001154792532546013717693189769037
Sat Nov 22 06:14:16 2008  elapsed time 00:37:16 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 33.08 hours.
Scaled time: 67.65 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_3_2_159_9
n: 48766713331304223297469209004162040855423177792331628693848084378802536364064355176272991837831834801871342032923373
skew: 40631.40
# norm 1.28e+16
c5: 48960
c4: -3677136100
c3: -580854246872754
c2: 4669045965929046074
c1: 201689939828851083322901
c0: -1049108959979503795077868296
# alpha -6.13
Y1: 3663644112433
Y0: -15836453313678855586037
# Murphy_E 4.96e-10
# M 5020676239017025116654576699585057370287755122455090683803015253454311247305124917305425540222722612575777110676580
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1900001)
Primes: RFBsize:315948, AFBsize:316550, largePrimes:6201115 encountered
Relations: rels:6010949, finalFF:652204
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 32.85 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 33.08 hours.
 --------- CPU info (if available) ----------

(32·10¹²⁸-41)/9 = 3(5)₁₂₇1_<129> = 3² · 13 · 2383 · 17203 · 44439431 · 12342097267987_<14> · C99

C99 = P45 · P54

P45 = 401832657422981661467753981794828719551127827_<45>

P54 = 336349426550456762380413783163560600207935723362612513_<54>

Number: n
N=135156183893466024666977800451768589430551510931312422361412184461027826326223292573670614332699251
  ( 99 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=401832657422981661467753981794828719551127827 (pp45)
 r2=336349426550456762380413783163560600207935723362612513 (pp54)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.24 hours.
Scaled time: 4.58 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_3_5_127_1
n: 135156183893466024666977800451768589430551510931312422361412184461027826326223292573670614332699251
type: snfs
skew: 5.28
deg: 5
c5: 1
c0: -4100
m: 200000000000000000000000000
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [100000, 380001)
Primes: RFBsize:63951, AFBsize:64074, largePrimes:5795056 encountered
Relations: rels:4973051, finalFF:148600
Max relations in full relation-set: 28
Initial matrix: 128089 x 148600 with sparse part having weight 12143336.
Pruned matrix : 120774 x 121478 with weight 8312350.
Total sieving time: 2.07 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.04 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,28,28,56,56,2.5,2.5,50000
total time: 2.24 hours.
 --------- CPU info (if available) ----------

(32·10¹⁴⁰-41)/9 = 3(5)₁₃₉1_<141> = 3 · 13 · 23 · 73 · 1301 · 3109 · 2055125448574067128165337723_<28> · C102

C102 = P47 · P55

P47 = 81534190191088785562703437179631417594742467373_<47>

P55 = 8011540784187013965767181696517537757246380887244496561_<55>

Number: n
N=653214490021568591153880136071698042579076844847058983336996288582169963418227578858397724804353204253
  ( 102 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=81534190191088785562703437179631417594742467373 (pp47)
 r2=8011540784187013965767181696517537757246380887244496561 (pp55)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.74 hours.
Scaled time: 6.86 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_3_5_139_1
n: 653214490021568591153880136071698042579076844847058983336996288582169963418227578858397724804353204253
type: snfs
skew: 2.10
deg: 5
c5: 1
c0: -41
m: 20000000000000000000000000000
rlim: 1200000
alim: 1200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [100000, 600001)
Primes: RFBsize:92938, AFBsize:93090, largePrimes:7573396 encountered
Relations: rels:6550842, finalFF:211514
Max relations in full relation-set: 28
Initial matrix: 186092 x 211514 with sparse part having weight 17096091.
Pruned matrix : 174635 x 175629 with weight 12149381.
Total sieving time: 3.84 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.64 hours.
Total square root time: 0.10 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,56,56,2.5,2.5,100000
total time: 4.74 hours.
 --------- CPU info (if available) ----------

(31·10¹⁴⁰+41)/9 = 3(4)₁₃₉9_<141> = 59 · 10228703 · 221997037441_<12> · 247948902336703103_<18> · C104

C104 = P37 · P67

P37 = 1788847380174561304042465308411568243_<37>

P67 = 5796474718390466137267505980824046764103166906082630165666673013633_<67>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 10369008614240863352321120069636994460028391623281167738181012372516588639848686662393445079840448856819 (104 digits)
Using B1=2156000, B2=2854157680, polynomial Dickson(6), sigma=3161595063
Step 1 took 22047ms
Step 2 took 8375ms
********** Factor found in step 2: 1788847380174561304042465308411568243
Found probable prime factor of 37 digits: 1788847380174561304042465308411568243
Probable prime cofactor 5796474718390466137267505980824046764103166906082630165666673013633 has 67 digits

Nov 21, 2008 (10th)

By Sinkiti Sibata / Msieve

(32·10¹⁴⁹-41)/9 = 3(5)₁₄₈1_<150> = 3 · 7 · 419 · 34729 · 533793222600156067_<18> · 1324836958983859085546653940413_<31> · C94

C94 = P41 · P53

P41 = 80114216324581510271381545232553255062473_<41>

P53 = 20536990094074404442694620736817421850163590286243607_<53>

Fri Nov 21 20:27:25 2008  Msieve v. 1.38
Fri Nov 21 20:27:25 2008  random seeds: 57771344 631fd988
Fri Nov 21 20:27:25 2008  factoring 1645304867052464418756468820263549672476733372189469658647398655789212312830417506743281860111 (94 digits)
Fri Nov 21 20:27:25 2008  searching for 15-digit factors
Fri Nov 21 20:27:27 2008  commencing quadratic sieve (94-digit input)
Fri Nov 21 20:27:27 2008  using multiplier of 31
Fri Nov 21 20:27:27 2008  using 32kb Intel Core sieve core
Fri Nov 21 20:27:27 2008  sieve interval: 36 blocks of size 32768
Fri Nov 21 20:27:27 2008  processing polynomials in batches of 6
Fri Nov 21 20:27:27 2008  using a sieve bound of 1986293 (74118 primes)
Fri Nov 21 20:27:27 2008  using large prime bound of 256231797 (27 bits)
Fri Nov 21 20:27:27 2008  using double large prime bound of 1366278931731603 (42-51 bits)
Fri Nov 21 20:27:27 2008  using trial factoring cutoff of 51 bits
Fri Nov 21 20:27:27 2008  polynomial 'A' values have 12 factors
Fri Nov 21 20:27:27 2008  restarting with 338 full and 17985 partial relations
Fri Nov 21 23:26:19 2008  74250 relations (18366 full + 55884 combined from 1032480 partial), need 74214
Fri Nov 21 23:26:20 2008  begin with 1050846 relations
Fri Nov 21 23:26:21 2008  reduce to 191860 relations in 12 passes
Fri Nov 21 23:26:21 2008  attempting to read 191860 relations
Fri Nov 21 23:26:24 2008  recovered 191860 relations
Fri Nov 21 23:26:24 2008  recovered 175246 polynomials
Fri Nov 21 23:26:24 2008  attempting to build 74250 cycles
Fri Nov 21 23:26:24 2008  found 74250 cycles in 5 passes
Fri Nov 21 23:26:24 2008  distribution of cycle lengths:
Fri Nov 21 23:26:24 2008     length 1 : 18366
Fri Nov 21 23:26:24 2008     length 2 : 13089
Fri Nov 21 23:26:24 2008     length 3 : 12660
Fri Nov 21 23:26:24 2008     length 4 : 10071
Fri Nov 21 23:26:24 2008     length 5 : 7558
Fri Nov 21 23:26:24 2008     length 6 : 5099
Fri Nov 21 23:26:24 2008     length 7 : 3181
Fri Nov 21 23:26:24 2008     length 9+: 4226
Fri Nov 21 23:26:24 2008  largest cycle: 21 relations
Fri Nov 21 23:26:24 2008  matrix is 74118 x 74250 (19.6 MB) with weight 4844671 (65.25/col)
Fri Nov 21 23:26:24 2008  sparse part has weight 4844671 (65.25/col)
Fri Nov 21 23:26:25 2008  filtering completed in 3 passes
Fri Nov 21 23:26:25 2008  matrix is 70475 x 70539 (18.8 MB) with weight 4640189 (65.78/col)
Fri Nov 21 23:26:25 2008  sparse part has weight 4640189 (65.78/col)
Fri Nov 21 23:26:25 2008  saving the first 48 matrix rows for later
Fri Nov 21 23:26:26 2008  matrix is 70427 x 70539 (12.2 MB) with weight 3705494 (52.53/col)
Fri Nov 21 23:26:26 2008  sparse part has weight 2781041 (39.43/col)
Fri Nov 21 23:26:26 2008  matrix includes 64 packed rows
Fri Nov 21 23:26:26 2008  using block size 28215 for processor cache size 1024 kB
Fri Nov 21 23:26:26 2008  commencing Lanczos iteration
Fri Nov 21 23:26:26 2008  memory use: 11.5 MB
Fri Nov 21 23:27:02 2008  lanczos halted after 1116 iterations (dim = 70427)
Fri Nov 21 23:27:02 2008  recovered 18 nontrivial dependencies
Fri Nov 21 23:27:02 2008  prp41 factor: 80114216324581510271381545232553255062473
Fri Nov 21 23:27:02 2008  prp53 factor: 20536990094074404442694620736817421850163590286243607
Fri Nov 21 23:27:02 2008  elapsed time 02:59:37

Nov 21, 2008 (9th)

By Robert Backstrom / GGNFS

(31·10¹⁰⁵+41)/9 = 3(4)₁₀₄9_<106> = 353 · 5431 · 128291 · C95

C95 = P36 · P59

P36 = 594693148785308211822209674660147831_<36>

P59 = 23549167060302104560864919762949010499061378501200898045083_<59>

Number: n
N=14004528310362318666354244575991794858089633112257439635385050554676123620105734472655682664973
  ( 95 digits)
SNFS difficulty: 106 digits.
Divisors found:
 r1=594693148785308211822209674660147831 (pp36)
 r2=23549167060302104560864919762949010499061378501200898045083 (pp59)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.64 hours.
Scaled time: 1.30 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_3_4_104_9
n: 14004528310362318666354244575991794858089633112257439635385050554676123620105734472655682664973
type: snfs
skew: 1.06
deg: 5
c5: 31
c0: 41
m: 1000000000000000000000
rlim: 400000
alim: 400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 400000/400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [100000, 160001)
Primes: RFBsize:33860, AFBsize:34095, largePrimes:3193883 encountered
Relations: rels:2701320, finalFF:112185
Max relations in full relation-set: 28
Initial matrix: 68020 x 112185 with sparse part having weight 7919858.
Pruned matrix : 55163 x 55567 with weight 2392508.
Total sieving time: 0.51 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.01 hours.
Total square root time: 0.08 hours, sqrts: 5.
Prototype def-par.txt line would be:
snfs,106,5,0,0,0,0,0,0,0,0,400000,400000,28,28,56,56,2.5,2.5,50000
total time: 0.64 hours.
 --------- CPU info (if available) ----------

(32·10¹⁰⁷-41)/9 = 3(5)₁₀₆1_<108> = 3 · 7 · 53 · 323093 · C99

C99 = P43 · P57

P43 = 4969113507692915159830820858462998480110977_<43>

P57 = 198978356029457891142388803820629371983665753967882940507_<57>

Number: n
N=988746036684509216134405657207346002014562016183139466236470434514002669418403739656765174448645339
  ( 99 digits)
SNFS difficulty: 108 digits.
Divisors found:
 r1=4969113507692915159830820858462998480110977 (pp43)
 r2=198978356029457891142388803820629371983665753967882940507 (pp57)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.88 hours.
Scaled time: 1.27 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_3_5_106_1
n: 988746036684509216134405657207346002014562016183139466236470434514002669418403739656765174448645339
type: snfs
skew: 0.84
deg: 5
c5: 100
c0: -41
m: 2000000000000000000000
rlim: 450000
alim: 450000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 450000/450000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [100000, 160001)
Primes: RFBsize:37706, AFBsize:37550, largePrimes:3672853 encountered
Relations: rels:3166359, finalFF:149304
Max relations in full relation-set: 28
Initial matrix: 75320 x 149304 with sparse part having weight 10857343.
Pruned matrix : 56531 x 56971 with weight 2447010.
Total sieving time: 0.79 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.02 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,108,5,0,0,0,0,0,0,0,0,450000,450000,28,28,56,56,2.5,2.5,50000
total time: 0.88 hours.
 --------- CPU info (if available) ----------

Nov 21, 2008 (8th)

By Erik Branger / GGNFS, Msieve

(31·10¹¹²+41)/9 = 3(4)₁₁₁9_<113> = 3 · 163 · 21187 · C106

C106 = P48 · P59

P48 = 258792217686256918312919174969009069760596232037_<48>

P59 = 12846642731570680842788982699578386236853374596065485513239_<59>

Number: 34449_112
N=3324611162326209839139546875017259826094737883741500671780583556556842641231117669818215731165592479437843
  ( 106 digits)
SNFS difficulty: 114 digits.
Divisors found:
 r1=258792217686256918312919174969009069760596232037
 r2=12846642731570680842788982699578386236853374596065485513239
Version: 
Total time: 1.68 hours.
Scaled time: 3.69 units (timescale=2.195).
Factorization parameters were as follows:
n: 3324611162326209839139546875017259826094737883741500671780583556556842641231117669818215731165592479437843
m: 20000000000000000000000
deg: 5
c5: 775
c0: 328
skew: 0.84
type: snfs
lss: 1
rlim: 560000
alim: 560000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 560000/560000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [280000, 530001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 66642 x 66860
Total sieving time: 1.68 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,114,5,0,0,0,0,0,0,0,0,560000,560000,25,25,45,45,2.2,2.2,50000
total time: 1.68 hours.
 --------- CPU info (if available) ----------

(31·10¹⁵³+41)/9 = 3(4)₁₅₂9_<154> = 5835739554532332869_<19> · 50158851041600162665093_<23> · 4032687920589908329955267_<25> · C88

C88 = P41 · P47

P41 = 44486831924067687045714216542322079414577_<41>

P47 = 65591809150534983525158372279246902373496543283_<47>

Fri Nov 21 12:35:16 2008  Msieve v. 1.36
Fri Nov 21 12:35:16 2008  random seeds: 21ecf6b8 72b652fe
Fri Nov 21 12:35:16 2008  factoring 2917971789275374742550279961408364217439585732684651363096861229810434025847121781636291 (88 digits)
Fri Nov 21 12:35:17 2008  searching for 15-digit factors
Fri Nov 21 12:35:18 2008  commencing quadratic sieve (88-digit input)
Fri Nov 21 12:35:19 2008  using multiplier of 19
Fri Nov 21 12:35:19 2008  using 64kb Pentium 4 sieve core
Fri Nov 21 12:35:19 2008  sieve interval: 13 blocks of size 65536
Fri Nov 21 12:35:19 2008  processing polynomials in batches of 8
Fri Nov 21 12:35:19 2008  using a sieve bound of 1517699 (57619 primes)
Fri Nov 21 12:35:19 2008  using large prime bound of 121415920 (26 bits)
Fri Nov 21 12:35:19 2008  using double large prime bound of 356201769813440 (42-49 bits)
Fri Nov 21 12:35:19 2008  using trial factoring cutoff of 49 bits
Fri Nov 21 12:35:19 2008  polynomial 'A' values have 11 factors
Fri Nov 21 13:46:13 2008  58029 relations (16470 full + 41559 combined from 601969 partial), need 57715
Fri Nov 21 13:46:15 2008  begin with 618438 relations
Fri Nov 21 13:46:16 2008  reduce to 137673 relations in 12 passes
Fri Nov 21 13:46:16 2008  attempting to read 137673 relations
Fri Nov 21 13:46:21 2008  recovered 137673 relations
Fri Nov 21 13:46:21 2008  recovered 112399 polynomials
Fri Nov 21 13:46:22 2008  attempting to build 58029 cycles
Fri Nov 21 13:46:22 2008  found 58029 cycles in 5 passes
Fri Nov 21 13:46:22 2008  distribution of cycle lengths:
Fri Nov 21 13:46:22 2008     length 1 : 16470
Fri Nov 21 13:46:22 2008     length 2 : 11704
Fri Nov 21 13:46:22 2008     length 3 : 10218
Fri Nov 21 13:46:22 2008     length 4 : 7559
Fri Nov 21 13:46:22 2008     length 5 : 5181
Fri Nov 21 13:46:22 2008     length 6 : 3198
Fri Nov 21 13:46:22 2008     length 7 : 1770
Fri Nov 21 13:46:22 2008     length 9+: 1929
Fri Nov 21 13:46:22 2008  largest cycle: 19 relations
Fri Nov 21 13:46:22 2008  matrix is 57619 x 58029 (13.8 MB) with weight 3380613 (58.26/col)
Fri Nov 21 13:46:22 2008  sparse part has weight 3380613 (58.26/col)
Fri Nov 21 13:46:23 2008  filtering completed in 3 passes
Fri Nov 21 13:46:23 2008  matrix is 52792 x 52855 (12.6 MB) with weight 3099871 (58.65/col)
Fri Nov 21 13:46:23 2008  sparse part has weight 3099871 (58.65/col)
Fri Nov 21 13:46:23 2008  saving the first 48 matrix rows for later
Fri Nov 21 13:46:23 2008  matrix is 52744 x 52855 (9.0 MB) with weight 2535635 (47.97/col)
Fri Nov 21 13:46:23 2008  sparse part has weight 2054683 (38.87/col)
Fri Nov 21 13:46:23 2008  matrix includes 64 packed rows
Fri Nov 21 13:46:23 2008  using block size 21142 for processor cache size 512 kB
Fri Nov 21 13:46:24 2008  commencing Lanczos iteration
Fri Nov 21 13:46:24 2008  memory use: 8.3 MB
Fri Nov 21 13:46:52 2008  lanczos halted after 836 iterations (dim = 52742)
Fri Nov 21 13:46:53 2008  recovered 16 nontrivial dependencies
Fri Nov 21 13:46:53 2008  prp41 factor: 44486831924067687045714216542322079414577
Fri Nov 21 13:46:53 2008  prp47 factor: 65591809150534983525158372279246902373496543283
Fri Nov 21 13:46:53 2008  elapsed time 01:11:37

Nov 21, 2008 (7th)

By Sinkiti Sibata / GGNFS

(31·10¹⁴⁴+23)/9 = 3(4)₁₄₃7_<145> = 3 · 28081 · 12198479 · 74631544459542509715103237_<26> · C107

C107 = P45 · P63

P45 = 159211005704693000085823595910997363902059699_<45>

P63 = 282087708148123545945056068424813008842460110880541912155624277_<63>

Number: 34447_144
N=44911467711194671956311458873486555830635215692557289809449257051105516413906070946575439201768427467712623
  ( 107 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=159211005704693000085823595910997363902059699 (pp45)
 r2=282087708148123545945056068424813008842460110880541912155624277 (pp63)
Version: GGNFS-0.77.1-20060513-k8
Total time: 21.60 hours.
Scaled time: 42.60 units (timescale=1.972).
Factorization parameters were as follows:
name: 34447_144
n: 44911467711194671956311458873486555830635215692557289809449257051105516413906070946575439201768427467712623
m: 100000000000000000000000000000
deg: 5
c5: 31
c0: 230
skew: 1.49
type: snfs
lss: 1
rlim: 1930000
alim: 1930000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1930000/1930000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [965000, 2865001)
Primes: RFBsize:144125, AFBsize:144048, largePrimes:4340864 encountered
Relations: rels:4606753, finalFF:371261
Max relations in full relation-set: 28
Initial matrix: 288238 x 371261 with sparse part having weight 43229078.
Pruned matrix : 261658 x 263163 with weight 28833069.
Total sieving time: 20.36 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.96 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1930000,1930000,26,26,49,49,2.3,2.3,100000
total time: 21.60 hours.
 --------- CPU info (if available) ----------

(32·10¹²⁶-41)/9 = 3(5)₁₂₅1_<127> = 409 · C124

C124 = P57 · P68

P57 = 171194598333615048222366566893522206348126341433869776357_<57>

P68 = 50780164511633549798402123157855699628021684842890883339859369480427_<68>

Number: 35551_126
N=8693289866883998913338766639500135832654170062483020918228742189622385221407226297201847324096712849769084487910893778864439
  ( 124 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=171194598333615048222366566893522206348126341433869776357 (pp57)
 r2=50780164511633549798402123157855699628021684842890883339859369480427 (pp68)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.84 hours.
Scaled time: 5.41 units (timescale=1.902).
Factorization parameters were as follows:
name: 35551_126
n: 8693289866883998913338766639500135832654170062483020918228742189622385221407226297201847324096712849769084487910893778864439
m: 20000000000000000000000000
deg: 5
c5: 10
c0: -41
skew: 1.33
type: snfs
lss: 1
rlim: 930000
alim: 930000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 930000/930000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [465000, 715001)
Primes: RFBsize:73474, AFBsize:72978, largePrimes:2463207 encountered
Relations: rels:2336543, finalFF:179494
Max relations in full relation-set: 28
Initial matrix: 146518 x 179494 with sparse part having weight 13010167.
Pruned matrix : 134193 x 134989 with weight 7615669.
Total sieving time: 2.63 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,930000,930000,26,26,46,46,2.3,2.3,50000
total time: 2.84 hours.
 --------- CPU info (if available) ----------

(32·10¹¹⁹-41)/9 = 3(5)₁₁₈1_<120> = 3² · 7 · 17 · 317 · 1109 · 1223 · 4241 · C105

C105 = P34 · P71

P34 = 5146035129801747950200491709940393_<34>

P71 = 35380153561359894771496352426470646393927511422671498242115915382113823_<71>

Number: 35551_119
N=182067513124538441101462579812715985235713896251223737793957929646967334531924025154370350419725671352439
  ( 105 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=5146035129801747950200491709940393 (pp34)
 r2=35380153561359894771496352426470646393927511422671498242115915382113823 (pp71)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 2.15 hours.
Scaled time: 1.02 units (timescale=0.473).
Factorization parameters were as follows:
name: 35551_119
n: 182067513124538441101462579812715985235713896251223737793957929646967334531924025154370350419725671352439
m: 1000000000000000000000000
deg: 5
c5: 16
c0: -205
skew: 1.67
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 565001)
Primes: RFBsize:58789, AFBsize:58897, largePrimes:1264545 encountered
Relations: rels:1228338, finalFF:140700
Max relations in full relation-set: 28
Initial matrix: 117750 x 140700 with sparse part having weight 5817576.
Pruned matrix : 103103 x 103755 with weight 3356003.
Total sieving time: 2.00 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 2.15 hours.
 --------- CPU info (if available) ----------

Nov 21, 2008 (6th)

By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1

(32·10¹²⁷-41)/9 = 3(5)₁₂₆1_<128> = 401 · 2917 · 17987 · 3229901922977237_<16> · 2071025562653464453843_<22> · C81

C81 = P33 · P48

P33 = 400338547831239941807329391891749_<33>

P48 = 631052844269568196604006040863340283212860511491_<48>

Fri Nov 21 00:20:47 2008  Msieve v. 1.38
Fri Nov 21 00:20:47 2008  random seeds: b84c8010 b8809f02
Fri Nov 21 00:20:47 2008  factoring 252634779279652537693843677634751731140715269848712613595857696355762680242587759 (81 digits)
Fri Nov 21 00:20:48 2008  no P-1/P+1/ECM available, skipping
Fri Nov 21 00:20:48 2008  commencing quadratic sieve (81-digit input)
Fri Nov 21 00:20:48 2008  using multiplier of 39
Fri Nov 21 00:20:48 2008  using 64kb Opteron sieve core
Fri Nov 21 00:20:48 2008  sieve interval: 6 blocks of size 65536
Fri Nov 21 00:20:48 2008  processing polynomials in batches of 17
Fri Nov 21 00:20:48 2008  using a sieve bound of 1315507 (50588 primes)
Fri Nov 21 00:20:48 2008  using large prime bound of 128919686 (26 bits)
Fri Nov 21 00:20:48 2008  using trial factoring cutoff of 27 bits
Fri Nov 21 00:20:48 2008  polynomial 'A' values have 10 factors
Fri Nov 21 00:38:56 2008  50811 relations (26310 full + 24501 combined from 269737 partial), need 50684
Fri Nov 21 00:38:56 2008  begin with 296047 relations
Fri Nov 21 00:38:57 2008  reduce to 72222 relations in 2 passes
Fri Nov 21 00:38:57 2008  attempting to read 72222 relations
Fri Nov 21 00:38:57 2008  recovered 72222 relations
Fri Nov 21 00:38:57 2008  recovered 62442 polynomials
Fri Nov 21 00:38:57 2008  attempting to build 50811 cycles
Fri Nov 21 00:38:57 2008  found 50811 cycles in 1 passes
Fri Nov 21 00:38:57 2008  distribution of cycle lengths:
Fri Nov 21 00:38:57 2008     length 1 : 26310
Fri Nov 21 00:38:57 2008     length 2 : 24501
Fri Nov 21 00:38:57 2008  largest cycle: 2 relations
Fri Nov 21 00:38:57 2008  matrix is 50588 x 50811 (7.6 MB) with weight 1577942 (31.06/col)
Fri Nov 21 00:38:57 2008  sparse part has weight 1577942 (31.06/col)
Fri Nov 21 00:38:58 2008  filtering completed in 3 passes
Fri Nov 21 00:38:58 2008  matrix is 35841 x 35905 (5.9 MB) with weight 1254482 (34.94/col)
Fri Nov 21 00:38:58 2008  sparse part has weight 1254482 (34.94/col)
Fri Nov 21 00:38:58 2008  saving the first 48 matrix rows for later
Fri Nov 21 00:38:58 2008  matrix is 35793 x 35905 (4.6 MB) with weight 1006660 (28.04/col)
Fri Nov 21 00:38:58 2008  sparse part has weight 834359 (23.24/col)
Fri Nov 21 00:38:58 2008  matrix includes 64 packed rows
Fri Nov 21 00:38:58 2008  using block size 14362 for processor cache size 1024 kB
Fri Nov 21 00:38:58 2008  commencing Lanczos iteration
Fri Nov 21 00:38:58 2008  memory use: 4.2 MB
Fri Nov 21 00:39:06 2008  lanczos halted after 567 iterations (dim = 35789)
Fri Nov 21 00:39:06 2008  recovered 16 nontrivial dependencies
Fri Nov 21 00:39:06 2008  prp33 factor: 400338547831239941807329391891749
Fri Nov 21 00:39:06 2008  prp48 factor: 631052844269568196604006040863340283212860511491
Fri Nov 21 00:39:06 2008  elapsed time 00:18:19

(31·10¹¹¹+41)/9 = 3(4)₁₁₀9_<112> = 88327 · C107

C107 = P50 · P57

P50 = 41454123728155760979248725791099159638505634915673_<50>

P57 = 940714774807484928843711276649544526402883573778713355119_<57>

SNFS difficulty: 112 digits.
Divisors found:
 r1=41454123728155760979248725791099159638505634915673 (pp50)
 r2=940714774807484928843711276649544526402883573778713355119 (pp57)
Version: Msieve-1.38
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.949).
Factorization parameters were as follows:
n: 38996506667773664275300241652546157397448622102465208197317291931622770437628861440380002088200034467880087
m: 10000000000000000000000
deg: 5
c5: 310
c0: 41
skew: 0.67
type: snfs
lss: 1
rlim: 520000
alim: 520000
lpbr: 25
lpba: 25
mfbr: 47
mfba: 47
rlambda: 2.4
alambda: 2.4
Factor base limits: 520000/520000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved rational special-q in [260000, 360001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 90705 x 90947
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,112,5,0,0,0,0,0,0,0,0,520000,520000,25,25,47,47,2.4,2.4,50000
total time: 0.50 hours.

(31·10¹²⁴+41)/9 = 3(4)₁₂₃9_<125> = 3² · 95544360543089_<14> · 2649780403203617373383_<22> · C89

C89 = P29 · P60

P29 = 48404523956151107959172206679_<29>

P60 = 312302729254556267292136300344926518307355113530119444922057_<60>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2358009462
Step 1 took 11056ms
********** Factor found in step 1: 48404523956151107959172206679
Found probable prime factor of 29 digits: 48404523956151107959172206679
Probable prime cofactor 312302729254556267292136300344926518307355113530119444922057 has 60 digits

(32·10¹⁹⁷-41)/9 = 3(5)₁₉₆1_<198> = 3 · 7 · 47 · 139 · 1283 · 69001 · 7465399 · 52789594305359_<14> · 5704587641284886551_<19> · C146

C146 = P32 · P114

P32 = 25381539827219968939889818942099_<32>

P114 = 513038436540897283961126919502212025962143546345330531503056737906022207414185764428308211340282304133292693358681_<114>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2785240796
Step 1 took 83890ms
Step 2 took 28611ms
********** Factor found in step 2: 25381539827219968939889818942099
Found probable prime factor of 32 digits: 25381539827219968939889818942099
Probable prime cofactor 513038436540897283961126919502212025962143546345330531503056737906022207414185764428308211340282304133292693358681 has 114 digits

(31·10¹¹⁸+41)/9 = 3(4)₁₁₇9_<119> = 3 · 349 · 7559 · 25033 · 142330839643_<12> · C97

C97 = P39 · P58

P39 = 667275628520032946456406704929974171499_<39>

P58 = 1830589570099598722655453913313123714527630752671977509873_<58>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4183339842
Step 1 took 11372ms
Step 2 took 9026ms
********** Factor found in step 2: 667275628520032946456406704929974171499
Found probable prime factor of 39 digits: 667275628520032946456406704929974171499
Probable prime cofactor 1830589570099598722655453913313123714527630752671977509873 has 58 digits

(31·10¹¹⁷+41)/9 = 3(4)₁₁₆9_<118> = 2939 · 15300092001869737_<17> · C98

C98 = P35 · P64

P35 = 39060798498707080488288532923358921_<35>

P64 = 1961030909115423998982595692229352015289040401796279581247674883_<64>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=406823575
Step 1 took 13031ms
********** Factor found in step 1: 39060798498707080488288532923358921
Found probable prime factor of 35 digits: 39060798498707080488288532923358921
Probable prime cofactor 1961030909115423998982595692229352015289040401796279581247674883 has 64 digits

Nov 21, 2008 (5th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(29·10¹⁵²+43)/9 = 3(2)₁₅₁7_<153> = 3 · 40296437249_<11> · 17122663123552071584377558151_<29> · C114

C114 = P39 · P75

P39 = 220220544173356641441005461809174158519_<39>

P75 = 706868192209211965355505466528845063936170712012029710240294391113595495089_<75>

Number: n
N=155666897947149516564762656348434456049373366190782014151391987567686593948726747795044131944426787108190772013191
  ( 114 digits)
Divisors found:
 r1=220220544173356641441005461809174158519 (pp39)
 r2=706868192209211965355505466528845063936170712012029710240294391113595495089 (pp75)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 26.06 hours.
Scaled time: 53.11 units (timescale=2.038).
Factorization parameters were as follows:
name: KA_3_2_151_7
n: 155666897947149516564762656348434456049373366190782014151391987567686593948726747795044131944426787108190772013191
skew: 40305.29
# norm 4.06e+15
c5: 33600
c4: 662166430
c3: -119500018998054
c2: -5194326731023833722
c1: 90592809296439845948331
c0: -5694511903865148553261982
# alpha -6.17
Y1: 1852807172777
Y0: -5409670490352917931165
# Murphy_E 6.68e-10
# M 23888537930743219166264097391624569843008903802972367072493419719091397771460949961003863560930060113166770635755
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:250150, AFBsize:250862, largePrimes:6935471 encountered
Relations: rels:6699692, finalFF:603533
Max relations in full relation-set: 28
Initial matrix: 501089 x 603533 with sparse part having weight 37743944.
Pruned matrix : 402062 x 404631 with weight 18813363.
Polynomial selection time: 2.34 hours.
Total sieving time: 22.66 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.69 hours.
Total square root time: 0.16 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 26.06 hours.
 --------- CPU info (if available) ----------

(29·10¹⁵¹+43)/9 = 3(2)₁₅₀7_<152> = 37 · 1759 · 15563627912986965137034736448411_<32> · C116

C116 = P54 · P62

P54 = 975096392303048933102454301118670269267371089773626501_<54>

P62 = 32623423650910648679172594020763946317343258487506521412621679_<62>

Number: n
N=31810982706576934772998608605741160071516082639197877089858403102494412714121865479732665846484350034366517761515179
  ( 116 digits)
SNFS difficulty: 152 digits.
Divisors found:

Fri Nov 21 20:16:11 2008  prp54 factor: 975096392303048933102454301118670269267371089773626501
Fri Nov 21 20:16:11 2008  prp62 factor: 32623423650910648679172594020763946317343258487506521412621679
Fri Nov 21 20:16:11 2008  elapsed time 00:07:22 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.51 hours.
Scaled time: 28.33 units (timescale=1.452).
Factorization parameters were as follows:
name: KA_3_2_150_7
n: 31810982706576934772998608605741160071516082639197877089858403102494412714121865479732665846484350034366517761515179
type: snfs
skew: 0.68
deg: 5
c5: 290
c0: 43
m: 1000000000000000000000000000000
rlim: 2200000
alim: 2200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 1000001)
Primes: RFBsize:162662, AFBsize:162100, largePrimes:10824027 encountered
Relations: rels:9422016, finalFF:331070
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 19.24 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2200000,2200000,28,28,56,56,2.5,2.5,100000
total time: 19.51 hours.
 --------- CPU info (if available) ----------

(31·10¹⁶⁶+23)/9 = 3(4)₁₆₅7_<167> = 7 · 19 · 37 · 3191371129640080919489_<22> · 30931033777436558908625985247_<29> · C113

C113 = P38 · P76

P38 = 61798914931319480887285014377816703853_<38>

P76 = 1147395711679263505648383683460557746640664861931176587561400962806755863693_<76>

Number: n
N=70907809978627579542331612890992534418293146708040921479541278492523484270210998457654446469974744522569415909129
  ( 113 digits)
Divisors found:

Fri Nov 21 22:03:23 2008  prp38 factor: 61798914931319480887285014377816703853
Fri Nov 21 22:03:23 2008  prp76 factor: 1147395711679263505648383683460557746640664861931176587561400962806755863693
Fri Nov 21 22:03:23 2008  elapsed time 00:56:46 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 24.47 hours.
Scaled time: 50.05 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_3_4_165_7
n: 70907809978627579542331612890992534418293146708040921479541278492523484270210998457654446469974744522569415909129
skew: 32881.19
# norm 7.28e+15
c5: 83160
c4: -668967376
c3: -458058952759210
c2: 3172828514069222313
c1: 170324935437936606139530
c0: 758285338230349101156775464
# alpha -6.22
Y1: 1248999244049
Y0: -3856169760807240084551
# Murphy_E 6.59e-10
# M 31637108997680505828204905949716122300136356195570654326165134163816097965750691160478327792426738914491526610890
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1600001)
Primes: RFBsize:250150, AFBsize:250251, largePrimes:6877052 encountered
Relations: rels:6547858, finalFF:553182
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 24.23 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 24.47 hours.
 --------- CPU info (if available) ----------

(29·10¹⁵⁴+61)/9 = 3(2)₁₅₃9_<155> = 3 · 17 · 139 · 1155721321_<10> · C142

C142 = P66 · P76

P66 = 986372713677326998182527307992767279549974733724897913803676371177_<66>

P76 = 3987276352659791668600404809219191996642277325038493061533106729035862222933_<76>

Number: n
N=3932940596154473397043411029640516430303803401489513592173945327232225973966600528391700714282673182011623756607136363687254410051134029602141
  ( 142 digits)
SNFS difficulty: 156 digits.
Divisors found:

Fri Nov 21 22:18:20 2008  prp66 factor: 986372713677326998182527307992767279549974733724897913803676371177
Fri Nov 21 22:18:20 2008  prp76 factor: 3987276352659791668600404809219191996642277325038493061533106729035862222933
Fri Nov 21 22:18:20 2008  elapsed time 01:37:29 (Msieve 1.38)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 21.20 hours.
Scaled time: 27.66 units (timescale=1.305).
Factorization parameters were as follows:
name: KA_3_2_153_9
n: 3932940596154473397043411029640516430303803401489513592173945327232225973966600528391700714282673182011623756607136363687254410051134029602141
type: snfs
skew: 1.84
deg: 5
c5: 29
c0: 610
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 900001)
Primes: RFBsize:216816, AFBsize:216747, largePrimes:11290316 encountered
Relations: rels:9758502, finalFF:438402
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 20.89 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,56,56,2.5,2.5,100000
total time: 21.20 hours.
 --------- CPU info (if available) ----------

(32·10¹⁵¹-41)/9 = 3(5)₁₅₀1_<152> = 17 · 31 · 47 · 139 · 4091 · 32293129663_<11> · 4851519655528868117_<19> · 29189954590458934457859397_<26> · C87

C87 = P39 · P49

P39 = 180480728295344801238466336014947707069_<39>

P49 = 3058458065007834303252286311493510914433449868357_<49>

Fri Nov 21 22:15:27 2008  
Fri Nov 21 22:15:27 2008  
Fri Nov 21 22:15:28 2008  Msieve v. 1.38
Fri Nov 21 22:15:28 2008  random seeds: a89c3cd0 547fa8f3
Fri Nov 21 22:15:28 2008  factoring 551992739033384950060268575515588763406213000287167928339052156947081662679297048315633 (87 digits)
Fri Nov 21 22:15:29 2008  searching for 15-digit factors
Fri Nov 21 22:15:31 2008  commencing quadratic sieve (87-digit input)
Fri Nov 21 22:15:31 2008  using multiplier of 1
Fri Nov 21 22:15:31 2008  using 32kb Intel Core sieve core
Fri Nov 21 22:15:31 2008  sieve interval: 22 blocks of size 32768
Fri Nov 21 22:15:31 2008  processing polynomials in batches of 10
Fri Nov 21 22:15:32 2008  using a sieve bound of 1499123 (56843 primes)
Fri Nov 21 22:15:32 2008  using large prime bound of 119929840 (26 bits)
Fri Nov 21 22:15:32 2008  using double large prime bound of 348392707234640 (42-49 bits)
Fri Nov 21 22:15:32 2008  using trial factoring cutoff of 49 bits
Fri Nov 21 22:15:32 2008  polynomial 'A' values have 11 factors
Fri Nov 21 22:48:17 2008  56958 relations (16178 full + 40780 combined from 596856 partial), need 56939
Fri Nov 21 22:48:17 2008  begin with 613034 relations
Fri Nov 21 22:48:18 2008  reduce to 135437 relations in 9 passes
Fri Nov 21 22:48:18 2008  attempting to read 135437 relations
Fri Nov 21 22:48:20 2008  recovered 135437 relations
Fri Nov 21 22:48:20 2008  recovered 110021 polynomials
Fri Nov 21 22:48:20 2008  attempting to build 56958 cycles
Fri Nov 21 22:48:20 2008  found 56958 cycles in 5 passes
Fri Nov 21 22:48:20 2008  distribution of cycle lengths:
Fri Nov 21 22:48:21 2008     length 1 : 16178
Fri Nov 21 22:48:21 2008     length 2 : 11310
Fri Nov 21 22:48:21 2008     length 3 : 9937
Fri Nov 21 22:48:21 2008     length 4 : 7424
Fri Nov 21 22:48:21 2008     length 5 : 5053
Fri Nov 21 22:48:21 2008     length 6 : 3174
Fri Nov 21 22:48:22 2008     length 7 : 1914
Fri Nov 21 22:48:22 2008     length 9+: 1968
Fri Nov 21 22:48:22 2008  largest cycle: 17 relations
Fri Nov 21 22:48:22 2008  matrix is 56843 x 56958 (12.9 MB) with weight 3155406 (55.40/col)
Fri Nov 21 22:48:22 2008  sparse part has weight 3155406 (55.40/col)
Fri Nov 21 22:48:23 2008  filtering completed in 4 passes
Fri Nov 21 22:48:23 2008  matrix is 52253 x 52317 (12.0 MB) with weight 2938923 (56.18/col)
Fri Nov 21 22:48:23 2008  sparse part has weight 2938923 (56.18/col)
Fri Nov 21 22:48:24 2008  saving the first 48 matrix rows for later
Fri Nov 21 22:48:24 2008  matrix is 52205 x 52317 (7.7 MB) with weight 2303617 (44.03/col)
Fri Nov 21 22:48:24 2008  sparse part has weight 1692532 (32.35/col)
Fri Nov 21 22:48:24 2008  matrix includes 64 packed rows
Fri Nov 21 22:48:24 2008  using block size 20926 for processor cache size 4096 kB
Fri Nov 21 22:48:25 2008  commencing Lanczos iteration
Fri Nov 21 22:48:25 2008  memory use: 7.6 MB
Fri Nov 21 22:48:37 2008  lanczos halted after 828 iterations (dim = 52203)
Fri Nov 21 22:48:38 2008  recovered 16 nontrivial dependencies
Fri Nov 21 22:48:38 2008  prp39 factor: 180480728295344801238466336014947707069
Fri Nov 21 22:48:38 2008  prp49 factor: 3058458065007834303252286311493510914433449868357
Fri Nov 21 22:48:38 2008  elapsed time 00:33:10

(28·10¹⁵⁹+71)/9 = 3(1)₁₅₈9_<160> = 41 · 91084690499731_<14> · C144

C144 = P68 · P77

P68 = 23171439760163422371111675724153326581658778372287070365863549514077_<68>

P77 = 35952844688261045591447954066332986440191163322054061900169489973005924718257_<77>

Number: n
N=833079174900552296204015274726708994720787603658384837712899528402125685009777275008418875429543491560512280381394998443766749291297875480403789
  ( 144 digits)
SNFS difficulty: 161 digits.
Divisors found:

Sat Nov 22 00:10:35 2008  prp68 factor: 23171439760163422371111675724153326581658778372287070365863549514077
Sat Nov 22 00:10:35 2008  prp77 factor: 35952844688261045591447954066332986440191163322054061900169489973005924718257
Sat Nov 22 00:10:35 2008  elapsed time 01:06:10 (Msieve 1.38)

Version: GGNFS-0.77.1-20050930-k8
Total time: 21.41 hours.
Scaled time: 17.94 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_3_1_158_9
n: 833079174900552296204015274726708994720787603658384837712899528402125685009777275008418875429543491560512280381394998443766749291297875480403789
type: snfs
skew: 1.91
deg: 5
c5: 14
c0: 355
m: 100000000000000000000000000000000
rlim: 4000000
alim: 4000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 1150001)
Primes: RFBsize:283146, AFBsize:282603, largePrimes:13023992 encountered
Relations: rels:11576174, finalFF:592990
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 21.08 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,56,56,2.5,2.5,100000
total time: 21.41 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(31·10¹⁴⁹+41)/9 = 3(4)₁₄₈9_<150> = 7 · 42824491 · 9158260301_<10> · 22224985260767827_<17> · 1112929878226468993_<19> · C97

C97 = P38 · P60

P38 = 22521545757000487584780938305372935523_<38>

P60 = 225220787774420230975891805254681225718909593400875653913409_<60>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 5072320277289301240298525799177849702522387783534603072805642037340932334501433151881909182127907 (97 digits)
Using B1=1328000, B2=1426405900, polynomial Dickson(6), sigma=4224044251
Step 1 took 13875ms
Step 2 took 5313ms
********** Factor found in step 2: 22521545757000487584780938305372935523
Found probable prime factor of 38 digits: 22521545757000487584780938305372935523
Probable prime cofactor 225220787774420230975891805254681225718909593400875653913409 has 60 digits

Nov 21, 2008 (4th)

Factorizations of 344...449 and Factorizations of 355...551 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Nov 21, 2008 (3rd)

By Sinkiti Sibata / Msieve

(31·10¹³²+23)/9 = 3(4)₁₃₁7_<133> = 3 · 2297 · 193937 · 113221838034086314271_<21> · C104

C104 = P42 · P63

P42 = 128001041209174255487204192912085552014267_<42>

P63 = 177841272808507424123091401292295891898695805385853038162258313_<63>

Thu Nov 20 05:27:39 2008  Msieve v. 1.38
Thu Nov 20 05:27:39 2008  random seeds: 06aef7d0 3491eb82
Thu Nov 20 05:27:39 2008  factoring 22763868089453759778600523391606177381637960434520514072517380420776039653079075638988500274654715351571 (104 digits)
Thu Nov 20 05:27:40 2008  searching for 15-digit factors
Thu Nov 20 05:27:42 2008  commencing quadratic sieve (104-digit input)
Thu Nov 20 05:27:42 2008  using multiplier of 11
Thu Nov 20 05:27:42 2008  using 32kb Intel Core sieve core
Thu Nov 20 05:27:42 2008  sieve interval: 36 blocks of size 32768
Thu Nov 20 05:27:42 2008  processing polynomials in batches of 6
Thu Nov 20 05:27:42 2008  using a sieve bound of 3650509 (129768 primes)
Thu Nov 20 05:27:42 2008  using large prime bound of 547576350 (29 bits)
Thu Nov 20 05:27:42 2008  using double large prime bound of 5360439540079200 (44-53 bits)
Thu Nov 20 05:27:42 2008  using trial factoring cutoff of 53 bits
Thu Nov 20 05:27:42 2008  polynomial 'A' values have 14 factors
Fri Nov 21 11:27:11 2008  130009 relations (30765 full + 99244 combined from 1944400 partial), need 129864
Fri Nov 21 11:27:14 2008  begin with 1975165 relations
Fri Nov 21 11:27:16 2008  reduce to 343309 relations in 13 passes
Fri Nov 21 11:27:16 2008  attempting to read 343309 relations
Fri Nov 21 11:27:24 2008  recovered 343309 relations
Fri Nov 21 11:27:24 2008  recovered 336630 polynomials
Fri Nov 21 11:27:25 2008  attempting to build 130009 cycles
Fri Nov 21 11:27:25 2008  found 130009 cycles in 6 passes
Fri Nov 21 11:27:25 2008  distribution of cycle lengths:
Fri Nov 21 11:27:25 2008     length 1 : 30765
Fri Nov 21 11:27:25 2008     length 2 : 22047
Fri Nov 21 11:27:25 2008     length 3 : 21707
Fri Nov 21 11:27:25 2008     length 4 : 17738
Fri Nov 21 11:27:25 2008     length 5 : 13868
Fri Nov 21 11:27:25 2008     length 6 : 9322
Fri Nov 21 11:27:25 2008     length 7 : 6050
Fri Nov 21 11:27:25 2008     length 9+: 8512
Fri Nov 21 11:27:25 2008  largest cycle: 21 relations
Fri Nov 21 11:27:26 2008  matrix is 129768 x 130009 (36.9 MB) with weight 9152557 (70.40/col)
Fri Nov 21 11:27:26 2008  sparse part has weight 9152557 (70.40/col)
Fri Nov 21 11:27:28 2008  filtering completed in 3 passes
Fri Nov 21 11:27:28 2008  matrix is 124950 x 125013 (35.6 MB) with weight 8843121 (70.74/col)
Fri Nov 21 11:27:28 2008  sparse part has weight 8843121 (70.74/col)
Fri Nov 21 11:27:29 2008  saving the first 48 matrix rows for later
Fri Nov 21 11:27:29 2008  matrix is 124902 x 125013 (22.0 MB) with weight 7005702 (56.04/col)
Fri Nov 21 11:27:29 2008  sparse part has weight 5022897 (40.18/col)
Fri Nov 21 11:27:29 2008  matrix includes 64 packed rows
Fri Nov 21 11:27:29 2008  using block size 43690 for processor cache size 1024 kB
Fri Nov 21 11:27:30 2008  commencing Lanczos iteration
Fri Nov 21 11:27:30 2008  memory use: 21.4 MB
Fri Nov 21 11:29:34 2008  lanczos halted after 1976 iterations (dim = 124902)
Fri Nov 21 11:29:34 2008  recovered 18 nontrivial dependencies
Fri Nov 21 11:29:35 2008  prp42 factor: 128001041209174255487204192912085552014267
Fri Nov 21 11:29:35 2008  prp63 factor: 177841272808507424123091401292295891898695805385853038162258313
Fri Nov 21 11:29:35 2008  elapsed time 30:01:56

Nov 21, 2008 (2nd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38

(29·10¹⁵⁸-11)/9 = 3(2)₁₅₇1_<159> = 3 · 17 · 599 · 3320365643961975314499641_<25> · C130

C130 = P37 · P94

P37 = 3113310324647811275855004400415874517_<37>

P94 = 1020352344078143226664091214916101776213040500244838288298165298571081699060386378588779843357_<94>

Run 58 out of 100:
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2684999099
Step 1 took 33625ms
********** Factor found in step 1: 3113310324647811275855004400415874517
Found probable prime factor of 37 digits: 3113310324647811275855004400415874517
Probable prime cofactor 1020352344078143226664091214916101776213040500244838288298165298571081699060386378588779843357 has 94 digits

(8·10²⁴¹+1)/9 = (8)₂₄₀9_<241> = 3 · 240542009 · 36048817474529_<14> · 2236835197411007_<16> · 619328809218826631987_<21> · 2307994439692107818518677103_<28> · C156

C156 = P30 · P126

P30 = 139271372194463204233517633963_<30>

P126 = 767348030659914881516899932516529213904508061822198690776663718238208342560952835364792234120627533932150190654837531132325483_<126>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3302111522
Step 1 took 26889ms
Step 2 took 16389ms
********** Factor found in step 2: 139271372194463204233517633963
Found probable prime factor of 30 digits: 139271372194463204233517633963
Probable prime cofactor 767348030659914881516899932516529213904508061822198690776663718238208342560952835364792234120627533932150190654837531132325483 has 126 digits

4·10²³⁴+1 = 4(0)₂₃₃1_<235> = 101844481261409_<15> · 15083067110761453_<17> · 166470474810555341081321_<24> · 281722440676563078737805904561_<30> · C152

C152 = P35 · P117

P35 = 59520510316289955705069974366831129_<35>

P117 = 932840774605491827367365884272243625937825837089740051536226422913469229092335449597657018460854220557450573143028437_<117>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3553856087
Step 1 took 14589ms
Step 2 took 10980ms
********** Factor found in step 2: 59520510316289955705069974366831129
Found probable prime factor of 35 digits: 59520510316289955705069974366831129
Probable prime cofactor 932840774605491827367365884272243625937825837089740051536226422913469229092335449597657018460854220557450573143028437 has 117 digits

(31·10¹⁵³+23)/9 = 3(4)₁₅₂7_<154> = 3 · 33179 · 20826677 · C142

C142 = P43 · P99

P43 = 8057751421933845833175419115668072017469321_<43>

P99 = 206205758933494869507949855300183014699121320329094444631862433555090877799400218997532783562912443_<99>

SNFS difficulty: 155 digits.
Divisors found:
 r1=8057751421933845833175419115668072017469321 (pp43)
 r2=206205758933494869507949855300183014699121320329094444631862433555090877799400218997532783562912443 (pp99)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.948).
Factorization parameters were as follows:
n: 1661554747257316118030711657236449112247555007148199909420522176066246632447220815227217524487168894168556200871108421492188390703937161661203
m: 5000000000000000000000000000000
deg: 5
c5: 248
c0: 575
skew: 1.18
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved rational special-q in [1400000, 2600001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 625976 x 626218
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,53,53,2.5,2.5,100000
total time: 20.00 hours.

Nov 21, 2008

By Robert Backstrom / GGNFS, GMP-ECM

(28·10¹⁵⁵+71)/9 = 3(1)₁₅₄9_<156> = 3911 · 17762298559_<11> · 1654368234481259210641757_<25> · C118

C118 = P58 · P60

P58 = 5207543179028634894163598836860089001918725016663488946821_<58>

P60 = 519832559697601779512517512681427527642437186726029598257623_<60>

Number: n
N=2707050500490241799888406019421296662760926921905251579321279923412603805121355417444843351066830762011792020904866483
  ( 118 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=5207543179028634894163598836860089001918725016663488946821 (pp58)
 r2=519832559697601779512517512681427527642437186726029598257623 (pp60)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 15.17 hours.
Scaled time: 27.73 units (timescale=1.828).
Factorization parameters were as follows:
name: KA_3_1_154_9
n: 2707050500490241799888406019421296662760926921905251579321279923412603805121355417444843351066830762011792020904866483
type: snfs
skew: 1.20
deg: 5
c5: 28
c0: 71
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [100000, 850001)
Primes: RFBsize:216816, AFBsize:216157, largePrimes:11660197 encountered
Relations: rels:10375245, finalFF:578312
Max relations in full relation-set: 48
Initial matrix: 433041 x 578312 with sparse part having weight 56231987.
Pruned matrix : 323328 x 325557 with weight 28767447.
Total sieving time: 13.85 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 1.02 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,56,56,2.5,2.5,100000
total time: 15.17 hours.
 --------- CPU info (if available) ----------

(29·10¹⁵⁹-11)/9 = 3(2)₁₅₈1_<160> = 113 · 127 · 439 · 647 · 2930064630617_<13> · C138

C138 = P32 · P107

P32 = 19376489485924470209262041162989_<32>

P107 = 13923622050520029560513560197456375374993934656664684892227903781263511730077220792928335238140859671738599_<107>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 269790916267887465351909992767559683801135115291189777213727431952734734185276613939457571274588620565285534217037470149479822257561512411 (138 digits)
Using B1=800000, B2=696806892, polynomial Dickson(3), sigma=2305516098
Step 1 took 8563ms
Step 2 took 3640ms
********** Factor found in step 2: 19376489485924470209262041162989
Found probable prime factor of 32 digits: 19376489485924470209262041162989
Probable prime cofactor 13923622050520029560513560197456375374993934656664684892227903781263511730077220792928335238140859671738599 has 107 digits

Nov 20, 2008 (9th)

By Jo Yeong Uk / GGNFS

(31·10¹⁵¹+23)/9 = 3(4)₁₅₀7_<152> = 37 · 813097 · C145

C145 = P51 · P94

P51 = 661308922236046130574180250788845131268232439494137_<51>

P94 = 1731293583610207200485057312737901737674537238871160790344877979353997153175128440849742800979_<94>

Number: 34447_151
N=1144919893851448143248506550793977755336609200293360977756566474763688626241310607382552058279554506941891226915030963010478369654458116228360123
  ( 145 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=661308922236046130574180250788845131268232439494137 (pp51)
 r2=1731293583610207200485057312737901737674537238871160790344877979353997153175128440849742800979 (pp94)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.38 hours.
Scaled time: 27.00 units (timescale=2.373).
Factorization parameters were as follows:
n: 1144919893851448143248506550793977755336609200293360977756566474763688626241310607382552058279554506941891226915030963010478369654458116228360123
m: 1000000000000000000000000000000
deg: 5
c5: 310
c0: 23
skew: 0.59
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:176064, largePrimes:7721639 encountered
Relations: rels:7779627, finalFF:545693
Max relations in full relation-set: 28
Initial matrix: 352433 x 545693 with sparse part having weight 57523083.
Pruned matrix : 282021 x 283847 with weight 27602538.
Total sieving time: 10.80 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.45 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000
total time: 11.38 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Nov 20, 2008 (8th)

By Robert Backstrom / Msieve

(31·10¹⁴¹+23)/9 = 3(4)₁₄₀7_<142> = 3 · 89 · 151 · 26064697 · 2350566219110645571032862479372843_<34> · C97

C97 = P43 · P54

P43 = 1549081274511290351303642137676399869628903_<43>

P54 = 900184644644614901232675640022748801919586985760172207_<54>

Thu Nov 20 16:38:07 2008  
Thu Nov 20 16:38:07 2008  
Thu Nov 20 16:38:07 2008  Msieve v. 1.38
Thu Nov 20 16:38:08 2008  random seeds: 9bc7b380 5b2b56c3
Thu Nov 20 16:38:08 2008  factoring 1394459176621573051639386763789651414147839796257994686093167116726624290897405719337770464498921 (97 digits)
Thu Nov 20 16:38:09 2008  searching for 15-digit factors
Thu Nov 20 16:38:10 2008  commencing quadratic sieve (97-digit input)
Thu Nov 20 16:38:11 2008  using multiplier of 13
Thu Nov 20 16:38:11 2008  using 32kb Intel Core sieve core
Thu Nov 20 16:38:11 2008  sieve interval: 36 blocks of size 32768
Thu Nov 20 16:38:11 2008  processing polynomials in batches of 6
Thu Nov 20 16:38:11 2008  using a sieve bound of 2334863 (85703 primes)
Thu Nov 20 16:38:12 2008  using large prime bound of 350229450 (28 bits)
Thu Nov 20 16:38:12 2008  using double large prime bound of 2397920528297850 (43-52 bits)
Thu Nov 20 16:38:12 2008  using trial factoring cutoff of 52 bits
Thu Nov 20 16:38:12 2008  polynomial 'A' values have 13 factors
Thu Nov 20 20:11:57 2008  85990 relations (22065 full + 63925 combined from 1278641 partial), need 85799
Thu Nov 20 20:11:58 2008  begin with 1300706 relations
Thu Nov 20 20:11:59 2008  reduce to 220755 relations in 11 passes
Thu Nov 20 20:11:59 2008  attempting to read 220755 relations
Thu Nov 20 20:12:02 2008  recovered 220755 relations
Thu Nov 20 20:12:02 2008  recovered 205400 polynomials
Thu Nov 20 20:12:03 2008  attempting to build 85990 cycles
Thu Nov 20 20:12:03 2008  found 85990 cycles in 6 passes
Thu Nov 20 20:12:03 2008  distribution of cycle lengths:
Thu Nov 20 20:12:03 2008     length 1 : 22065
Thu Nov 20 20:12:04 2008     length 2 : 15290
Thu Nov 20 20:12:04 2008     length 3 : 14451
Thu Nov 20 20:12:04 2008     length 4 : 11510
Thu Nov 20 20:12:04 2008     length 5 : 8566
Thu Nov 20 20:12:04 2008     length 6 : 5640
Thu Nov 20 20:12:05 2008     length 7 : 3598
Thu Nov 20 20:12:05 2008     length 9+: 4870
Thu Nov 20 20:12:05 2008  largest cycle: 24 relations
Thu Nov 20 20:12:05 2008  matrix is 85703 x 85990 (23.2 MB) with weight 5738545 (66.74/col)
Thu Nov 20 20:12:05 2008  sparse part has weight 5738545 (66.74/col)
Thu Nov 20 20:12:06 2008  filtering completed in 3 passes
Thu Nov 20 20:12:06 2008  matrix is 81042 x 81106 (22.0 MB) with weight 5441103 (67.09/col)
Thu Nov 20 20:12:07 2008  sparse part has weight 5441103 (67.09/col)
Thu Nov 20 20:12:07 2008  saving the first 48 matrix rows for later
Thu Nov 20 20:12:07 2008  matrix is 80994 x 81106 (14.4 MB) with weight 4384075 (54.05/col)
Thu Nov 20 20:12:08 2008  sparse part has weight 3281672 (40.46/col)
Thu Nov 20 20:12:08 2008  matrix includes 64 packed rows
Thu Nov 20 20:12:08 2008  using block size 32442 for processor cache size 4096 kB
Thu Nov 20 20:12:09 2008  commencing Lanczos iteration
Thu Nov 20 20:12:09 2008  memory use: 13.4 MB
Thu Nov 20 20:12:46 2008  lanczos halted after 1283 iterations (dim = 80993)
Thu Nov 20 20:12:46 2008  recovered 17 nontrivial dependencies
Thu Nov 20 20:12:47 2008  prp43 factor: 1549081274511290351303642137676399869628903
Thu Nov 20 20:12:47 2008  prp54 factor: 900184644644614901232675640022748801919586985760172207
Thu Nov 20 20:12:47 2008  elapsed time 03:34:39

Nov 20, 2008 (7th)

By Serge Batalov / GMP-ECM 6.2.1

(31·10¹⁷⁶+23)/9 = 3(4)₁₇₅7_<177> = 61 · 127 · 6269 · 93623059 · 328309320318647_<15> · C147

C147 = P36 · C112

P36 = 202720502544193253155472756683183303_<36>

C112 = [1138213272254499930643296820016032059483757432491990061526260841951018280753405751022578969878813592572060915491_<112>]

Factor found in step 2: 202720502544193253155472756683183303

Nov 20, 2008 (6th)

By Sinkiti Sibata / GGNFS

(31·10¹³⁵+23)/9 = 3(4)₁₃₄7_<136> = 3 · 53 · 14827 · 80153 · 175333 · C120

C120 = P55 · P65

P55 = 5320146285913004033923822786340081282766713399367469351_<55>

P65 = 19541673492807033009504105677720911572680933743819569639669768521_<65>

Number: 34447_135
N=103964561653281937615940698397888792368105511524925163767455307432152372393741558475751641975328714898867866571732099871
  ( 120 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=5320146285913004033923822786340081282766713399367469351 (pp55)
 r2=19541673492807033009504105677720911572680933743819569639669768521 (pp65)
Version: GGNFS-0.77.1-20060513-k8
Total time: 7.27 hours.
Scaled time: 14.60 units (timescale=2.010).
Factorization parameters were as follows:
name: 34447_135
n: 103964561653281937615940698397888792368105511524925163767455307432152372393741558475751641975328714898867866571732099871
m: 1000000000000000000000000000
deg: 5
c5: 31
c0: 23
skew: 0.94
type: snfs
lss: 1
rlim: 1320000
alim: 1320000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1320000/1320000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [660000, 1335001)
Primes: RFBsize:101433, AFBsize:101212, largePrimes:3455437 encountered
Relations: rels:3558281, finalFF:377834
Max relations in full relation-set: 28
Initial matrix: 202710 x 377834 with sparse part having weight 34651730.
Pruned matrix : 162371 x 163448 with weight 12239877.
Total sieving time: 6.87 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1320000,1320000,26,26,48,48,2.3,2.3,75000
total time: 7.27 hours.
 --------- CPU info (if available) ----------

(31·10¹³⁶+23)/9 = 3(4)₁₃₅7_<137> = 7 · 37 · 191 · 76280803889_<11> · C121

C121 = P48 · P74

P48 = 230857778558202023809686931408875980413732116091_<48>

P74 = 39539054474929483767587850106894599968633750590814267323704018007244123137_<74>

Number: 34447_136
N=9127898282373957556699495805501989405108267715924648355714034125424503203800344076649701860823029148177829292694783097467
  ( 121 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=230857778558202023809686931408875980413732116091 (pp48)
 r2=39539054474929483767587850106894599968633750590814267323704018007244123137 (pp74)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.15 hours.
Scaled time: 12.09 units (timescale=1.967).
Factorization parameters were as follows:
name: 34447_136
n: 9127898282373957556699495805501989405108267715924648355714034125424503203800344076649701860823029148177829292694783097467
m: 1000000000000000000000000000
deg: 5
c5: 310
c0: 23
skew: 0.59
type: snfs
lss: 1
rlim: 1370000
alim: 1370000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1370000/1370000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [685000, 1210001)
Primes: RFBsize:104967, AFBsize:104854, largePrimes:3408938 encountered
Relations: rels:3538159, finalFF:429663
Max relations in full relation-set: 28
Initial matrix: 209888 x 429663 with sparse part having weight 35074190.
Pruned matrix : 151114 x 152227 with weight 10313401.
Total sieving time: 5.80 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1370000,1370000,26,26,48,48,2.3,2.3,75000
total time: 6.15 hours.
 --------- CPU info (if available) ----------

(29·10¹⁸⁶+61)/9 = 3(2)₁₈₅9_<187> = 17 · 19³ · 47 · 3718068359279171_<16> · 113058097714385228025180839_<27> · 181946415457142894948928977_<27> · C112

C112 = P39 · P74

P39 = 234409202006688255034232774122567068593_<39>

P74 = 32795231563991643406708561831148438339108461899856497446365159781924774941_<74>

Number: 32229_186
N=7687504060539835938241812108807707610084134351196074491195907286991355483346098423276905938072695145759634528013
  ( 112 digits)
Divisors found:
 r1=234409202006688255034232774122567068593 (pp39)
 r2=32795231563991643406708561831148438339108461899856497446365159781924774941 (pp74)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 40.91 hours.
Scaled time: 19.31 units (timescale=0.472).
Factorization parameters were as follows:
name: 32229_186
n: 7687504060539835938241812108807707610084134351196074491195907286991355483346098423276905938072695145759634528013
skew: 133187.17
# norm 2.88e+15
c5: 1320
c4: -514310512
c3: -50979482068505
c2: 8010119441520019056
c1: 457410820682172058593724
c0: -16837277770970666611448064400
# alpha -6.23
Y1: 25966459357
Y0: -5662946263637765414111
# Murphy_E 8.13e-10
# M 4200585395635473684294363244070652105637947337899380732823859960862627643749087323514256470378064353059671242202
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2550001)
Primes: RFBsize:250150, AFBsize:250898, largePrimes:7476257 encountered
Relations: rels:7404514, finalFF:659120
Max relations in full relation-set: 28
Initial matrix: 501131 x 659120 with sparse part having weight 54630815.
Pruned matrix : 365685 x 368254 with weight 28525788.
Total sieving time: 35.12 hours.
Total relation processing time: 0.53 hours.
Matrix solve time: 4.97 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 40.91 hours.
 --------- CPU info (if available) ----------

Nov 20, 2008 (5th)

By Robert Backstrom / GGNFS, Msieve

(25·10²⁰⁵-43)/9 = 2(7)₂₀₄3_<206> = C206

C206 = P68 · P139

P68 = 12466231636846188520451920609929604004464475715294728532343200023149_<68>

P139 = 2228241748346433917452944401867292639290089338373380648762414423835950014659934220490400787972385728917030277626747350491446963613906059777_<139>

Number: n
N=27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773
  ( 206 digits)
SNFS difficulty: 206 digits.
Divisors found:

Thu Nov 20 11:21:24 2008  prp68 factor: 12466231636846188520451920609929604004464475715294728532343200023149
Thu Nov 20 11:21:24 2008  prp139 factor: 2228241748346433917452944401867292639290089338373380648762414423835950014659934220490400787972385728917030277626747350491446963613906059777
Thu Nov 20 11:21:24 2008  elapsed time 32:26:42 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 163.61 hours.
Scaled time: 335.55 units (timescale=2.051).
Factorization parameters were as follows:
name: KA_2_7_204_3
n: 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773
type: snfs
skew: 1.11
deg: 5
c5: 25
c0: -43
m: 100000000000000000000000000000000000000000
rlim: 10000000
alim: 10000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 26500001)
Primes: RFBsize:664579, AFBsize:663590, largePrimes:35068129 encountered
Relations: rels:27426805, finalFF:95765
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 160.78 hours.
Total relation processing time: 2.82 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,206,5,0,0,0,0,0,0,0,0,10000000,10000000,29,29,58,58,2.5,2.5,100000
total time: 163.61 hours.
 --------- CPU info (if available) ----------

Nov 20, 2008 (4th)

By Jo Yeong Uk / GGNFS

(29·10¹⁵⁸+43)/9 = 3(2)₁₅₇7_<159> = 3² · 977 · 279212959 · 583872380142192551079643634844427_<33> · C114

C114 = P44 · P70

P44 = 33962717422558397652469099314595771182277901_<44>

P70 = 6618544311658850749222168864793307787858976179228968556878226516680923_<70>

Number: 32227_158
N=224783750205550827667498520536546643814178594317883134181700329233660310038101302061860511369018574239773131182623
  ( 114 digits)
Divisors found:
 r1=33962717422558397652469099314595771182277901 (pp44)
 r2=6618544311658850749222168864793307787858976179228968556878226516680923 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 18.70 hours.
Scaled time: 44.51 units (timescale=2.380).
Factorization parameters were as follows:
name: 32227_158
n: 224783750205550827667498520536546643814178594317883134181700329233660310038101302061860511369018574239773131182623
skew: 43507.31
# norm 7.70e+15
c5: 46800
c4: 3439852684
c3: 141662054244854
c2: -10328543654556641841
c1: -230815965196408801245766
c0: 3056223806377708494279690880
# alpha -6.76
Y1: 513516312733
Y0: -5448829395459177655763
# Murphy_E 6.35e-10
# M 56906511998489966154066701174603629338226874494165166046143718999847722194005330214456027652359019840763477811026
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1400000, 2450001)
Primes: RFBsize:203362, AFBsize:203841, largePrimes:7664084 encountered
Relations: rels:7562037, finalFF:540171
Max relations in full relation-set: 28
Initial matrix: 407282 x 540171 with sparse part having weight 53460198.
Pruned matrix : 315279 x 317379 with weight 32717958.
Polynomial selection time: 1.20 hours.
Total sieving time: 16.65 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.61 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000
total time: 18.70 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Nov 20, 2008 (3rd)

By Sinkiti Sibata / GGNFS, Msieve

(31·10¹³⁹+23)/9 = 3(4)₁₃₈7_<140> = 29 · 37 · 359 · 331313810704688044833753059_<27> · C108

C108 = P52 · P57

P52 = 2473477119213667851398376330277761733597789180593671_<52>

P57 = 109113271405889587593078488061443066335576018058528503189_<57>

Number: 34447_139
N=269889180225018855012170244562663159435434265133670879679303009495874480796357848143053362681804370036716819
  ( 108 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=2473477119213667851398376330277761733597789180593671
 r2=109113271405889587593078488061443066335576018058528503189
Version: 
Total time: 10.22 hours.
Scaled time: 20.28 units (timescale=1.985).
Factorization parameters were as follows:
name: 34447_139
n: 269889180225018855012170244562663159435434265133670879679303009495874480796357848143053362681804370036716819
m: 10000000000000000000000000000
deg: 5
c5: 31
c0: 230
skew: 1.49
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [800000, 1900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 258735 x 258983
Total sieving time: 10.22 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000
total time: 10.22 hours.
 --------- CPU info (if available) ----------

(31·10¹²⁸+23)/9 = 3(4)₁₂₇7_<129> = 16843 · C125

C125 = P56 · P69

P56 = 85379477275895844315105998660497969913412719107941553679_<56>

P69 = 239522460420870238976438445828349706474920058303140588513872318793651_<69>

Number: 34447_128
N=20450302466570352338920883716941426375612684465026684346282992604906753217624202603125597841503559012316359582286079940892029
  ( 125 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=85379477275895844315105998660497969913412719107941553679 (pp56)
 r2=239522460420870238976438445828349706474920058303140588513872318793651 (pp69)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 6.36 hours.
Scaled time: 3.01 units (timescale=0.473).
Factorization parameters were as follows:
name: 34447_128
n: 20450302466570352338920883716941426375612684465026684346282992604906753217624202603125597841503559012316359582286079940892029
m: 50000000000000000000000000
deg: 5
c5: 248
c0: 575
skew: 1.18
type: snfs
lss: 1
rlim: 1060000
alim: 1060000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1060000/1060000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [530000, 1080001)
Primes: RFBsize:82832, AFBsize:82914, largePrimes:2809394 encountered
Relations: rels:2710118, finalFF:206536
Max relations in full relation-set: 28
Initial matrix: 165813 x 206536 with sparse part having weight 16995812.
Pruned matrix : 155210 x 156103 with weight 10273925.
Total sieving time: 5.81 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.37 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1060000,1060000,26,26,47,47,2.3,2.3,50000
total time: 6.36 hours.
 --------- CPU info (if available) ----------

(31·10¹⁴²+23)/9 = 3(4)₁₄₁7_<143> = 7 · 37 · 173 · 32031673 · 12736060439_<11> · 372546828293_<12> · 35106681140227_<14> · C96

C96 = P32 · P64

P32 = 63064060992753333563442403816667_<32>

P64 = 2284578076622266880180728159657091165236588456548603773699038939_<64>

Wed Nov 19 23:30:19 2008  Msieve v. 1.38
Wed Nov 19 23:30:19 2008  random seeds: 53c0fa20 5250e793
Wed Nov 19 23:30:19 2008  factoring 144074771166813737220443242018141597913702894796079291182385820547606367181066983636203450196313 (96 digits)
Wed Nov 19 23:30:20 2008  searching for 15-digit factors
Wed Nov 19 23:30:21 2008  commencing quadratic sieve (96-digit input)
Wed Nov 19 23:30:21 2008  using multiplier of 33
Wed Nov 19 23:30:21 2008  using 32kb Intel Core sieve core
Wed Nov 19 23:30:21 2008  sieve interval: 36 blocks of size 32768
Wed Nov 19 23:30:21 2008  processing polynomials in batches of 6
Wed Nov 19 23:30:21 2008  using a sieve bound of 2231371 (82274 primes)
Wed Nov 19 23:30:21 2008  using large prime bound of 334705650 (28 bits)
Wed Nov 19 23:30:21 2008  using double large prime bound of 2210005845812100 (43-51 bits)
Wed Nov 19 23:30:21 2008  using trial factoring cutoff of 51 bits
Wed Nov 19 23:30:21 2008  polynomial 'A' values have 12 factors
Thu Nov 20 04:17:48 2008  82540 relations (19965 full + 62575 combined from 1229050 partial), need 82370
Thu Nov 20 04:17:50 2008  begin with 1249015 relations
Thu Nov 20 04:17:51 2008  reduce to 216101 relations in 11 passes
Thu Nov 20 04:17:51 2008  attempting to read 216101 relations
Thu Nov 20 04:17:54 2008  recovered 216101 relations
Thu Nov 20 04:17:54 2008  recovered 202340 polynomials
Thu Nov 20 04:17:55 2008  attempting to build 82540 cycles
Thu Nov 20 04:17:55 2008  found 82540 cycles in 7 passes
Thu Nov 20 04:17:55 2008  distribution of cycle lengths:
Thu Nov 20 04:17:55 2008     length 1 : 19965
Thu Nov 20 04:17:55 2008     length 2 : 14267
Thu Nov 20 04:17:55 2008     length 3 : 13826
Thu Nov 20 04:17:55 2008     length 4 : 11224
Thu Nov 20 04:17:55 2008     length 5 : 8457
Thu Nov 20 04:17:55 2008     length 6 : 5889
Thu Nov 20 04:17:55 2008     length 7 : 3845
Thu Nov 20 04:17:55 2008     length 9+: 5067
Thu Nov 20 04:17:55 2008  largest cycle: 20 relations
Thu Nov 20 04:17:55 2008  matrix is 82274 x 82540 (23.3 MB) with weight 5769700 (69.90/col)
Thu Nov 20 04:17:55 2008  sparse part has weight 5769700 (69.90/col)
Thu Nov 20 04:17:56 2008  filtering completed in 3 passes
Thu Nov 20 04:17:56 2008  matrix is 78492 x 78556 (22.3 MB) with weight 5524149 (70.32/col)
Thu Nov 20 04:17:56 2008  sparse part has weight 5524149 (70.32/col)
Thu Nov 20 04:17:57 2008  saving the first 48 matrix rows for later
Thu Nov 20 04:17:57 2008  matrix is 78444 x 78556 (16.6 MB) with weight 4648272 (59.17/col)
Thu Nov 20 04:17:57 2008  sparse part has weight 3874818 (49.33/col)
Thu Nov 20 04:17:57 2008  matrix includes 64 packed rows
Thu Nov 20 04:17:57 2008  using block size 31422 for processor cache size 1024 kB
Thu Nov 20 04:17:58 2008  commencing Lanczos iteration
Thu Nov 20 04:17:58 2008  memory use: 14.4 MB
Thu Nov 20 04:18:49 2008  lanczos halted after 1242 iterations (dim = 78439)
Thu Nov 20 04:18:49 2008  recovered 15 nontrivial dependencies
Thu Nov 20 04:18:51 2008  prp32 factor: 63064060992753333563442403816667
Thu Nov 20 04:18:51 2008  prp64 factor: 2284578076622266880180728159657091165236588456548603773699038939
Thu Nov 20 04:18:51 2008  elapsed time 04:48:32

(31·10¹¹⁶+23)/9 = 3(4)₁₁₅7_<117> = 61 · 103 · 1539511135911716295637_<22> · C92

C92 = P44 · P49

P44 = 16577521209685874321282377576121847403429763_<44>

P49 = 2148076271608348625324510255199205373704302291139_<49>

Wed Nov 19 13:44:43 2008  Msieve v. 1.38
Wed Nov 19 13:44:43 2008  random seeds: 127574c0 4e76b20c
Wed Nov 19 13:44:43 2008  factoring 35609779952610354232635219525330182100718764866412978203425728886616766922185519127563770057 (92 digits)
Wed Nov 19 13:44:47 2008  searching for 15-digit factors
Wed Nov 19 13:44:52 2008  commencing quadratic sieve (92-digit input)
Wed Nov 19 13:44:52 2008  using multiplier of 1
Wed Nov 19 13:44:52 2008  using 64kb Pentium 2 sieve core
Wed Nov 19 13:44:52 2008  sieve interval: 18 blocks of size 65536
Wed Nov 19 13:44:52 2008  processing polynomials in batches of 6
Wed Nov 19 13:44:52 2008  using a sieve bound of 1815629 (68235 primes)
Wed Nov 19 13:44:52 2008  using large prime bound of 197903561 (27 bits)
Wed Nov 19 13:44:52 2008  using double large prime bound of 858255299613335 (42-50 bits)
Wed Nov 19 13:44:52 2008  using trial factoring cutoff of 50 bits
Wed Nov 19 13:44:53 2008  polynomial 'A' values have 12 factors
Thu Nov 20 04:07:44 2008  68500 relations (17925 full + 50575 combined from 860511 partial), need 68331
Thu Nov 20 04:08:43 2008  begin with 878436 relations
Thu Nov 20 04:12:02 2008  reduce to 171780 relations in 10 passes
Thu Nov 20 04:12:03 2008  attempting to read 171780 relations
Thu Nov 20 04:12:22 2008  recovered 171780 relations
Thu Nov 20 04:12:22 2008  recovered 152027 polynomials
Thu Nov 20 04:12:23 2008  attempting to build 68500 cycles
Thu Nov 20 04:12:23 2008  found 68500 cycles in 5 passes
Thu Nov 20 04:12:29 2008  distribution of cycle lengths:
Thu Nov 20 04:12:29 2008     length 1 : 17925
Thu Nov 20 04:12:29 2008     length 2 : 12533
Thu Nov 20 04:12:29 2008     length 3 : 11759
Thu Nov 20 04:12:29 2008     length 4 : 9188
Thu Nov 20 04:12:29 2008     length 5 : 6726
Thu Nov 20 04:12:29 2008     length 6 : 4359
Thu Nov 20 04:12:29 2008     length 7 : 2639
Thu Nov 20 04:12:29 2008     length 9+: 3371
Thu Nov 20 04:12:29 2008  largest cycle: 20 relations
Thu Nov 20 04:12:32 2008  matrix is 68235 x 68500 (16.8 MB) with weight 4127308 (60.25/col)
Thu Nov 20 04:12:32 2008  sparse part has weight 4127308 (60.25/col)
Thu Nov 20 04:12:38 2008  filtering completed in 3 passes
Thu Nov 20 04:12:38 2008  matrix is 64376 x 64440 (15.9 MB) with weight 3905357 (60.60/col)
Thu Nov 20 04:12:38 2008  sparse part has weight 3905357 (60.60/col)
Thu Nov 20 04:12:41 2008  saving the first 48 matrix rows for later
Thu Nov 20 04:12:41 2008  matrix is 64328 x 64440 (9.6 MB) with weight 3020114 (46.87/col)
Thu Nov 20 04:12:41 2008  sparse part has weight 2138073 (33.18/col)
Thu Nov 20 04:12:41 2008  matrix includes 64 packed rows
Thu Nov 20 04:12:41 2008  using block size 5461 for processor cache size 128 kB
Thu Nov 20 04:12:43 2008  commencing Lanczos iteration
Thu Nov 20 04:12:43 2008  memory use: 9.8 MB
Thu Nov 20 04:16:45 2008  lanczos halted after 1019 iterations (dim = 64327)
Thu Nov 20 04:16:46 2008  recovered 16 nontrivial dependencies
Thu Nov 20 04:16:48 2008  prp44 factor: 16577521209685874321282377576121847403429763
Thu Nov 20 04:16:48 2008  prp49 factor: 2148076271608348625324510255199205373704302291139
Thu Nov 20 04:16:48 2008  elapsed time 14:32:05

(31·10¹³¹+23)/9 = 3(4)₁₃₀7_<132> = 7176048337_<10> · C122

C122 = P47 · P75

P47 = 58814456815850728043978098245622984007914608133_<47>

P75 = 816111952757307914009314203227325907496851007454861051529854391178893476707_<75>

Number: 34447_131
N=47999181202344295809394914398337119847140801727914063860415220673623570722116283376484793101867374509638067456685868258031
  ( 122 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=58814456815850728043978098245622984007914608133 (pp47)
 r2=816111952757307914009314203227325907496851007454861051529854391178893476707 (pp75)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.01 hours.
Scaled time: 8.02 units (timescale=2.003).
Factorization parameters were as follows:
name: 34447_131
n: 47999181202344295809394914398337119847140801727914063860415220673623570722116283376484793101867374509638067456685868258031
m: 100000000000000000000000000
deg: 5
c5: 310
c0: 23
skew: 0.59
type: snfs
lss: 1
rlim: 1130000
alim: 1130000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1130000/1130000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [565000, 915001)
Primes: RFBsize:87884, AFBsize:87884, largePrimes:2901244 encountered
Relations: rels:2868121, finalFF:277844
Max relations in full relation-set: 28
Initial matrix: 175835 x 277844 with sparse part having weight 21171464.
Pruned matrix : 142532 x 143475 with weight 7923435.
Total sieving time: 3.74 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1130000,1130000,26,26,47,47,2.3,2.3,50000
total time: 4.01 hours.
 --------- CPU info (if available) ----------

Nov 20, 2008 (2nd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38

(31·10¹⁶⁴+23)/9 = 3(4)₁₆₃7_<165> = 1187 · 19751765838087181_<17> · 77076343049421473843_<20> · 97197921667542870019_<20> · C106

C106 = P29 · P77

P29 = 26225390858497213055695898321_<29>

P77 = 74776044450002424378739770286018531603258310157404917007158902194661257092993_<77>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1882111869
Step 1 took 12978ms
Step 2 took 10583ms
********** Factor found in step 2: 26225390858497213055695898321
Found probable prime factor of 29 digits: 26225390858497213055695898321
Probable prime cofactor 74776044450002424378739770286018531603258310157404917007158902194661257092993 has 77 digits

(31·10¹⁸⁴+23)/9 = 3(4)₁₈₃7_<185> = 7 · 19 · 37 · 103 · 355441 · C174

C174 = P33 · P141

P33 = 237349828833458037266370999935411_<33>

P141 = 805512250524160053024218670593153283285936169981890369660778171822088933584384586054521660133841097184028353756005935093638355078054636670619_<141>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3841333516
Step 1 took 25970ms
Step 2 took 16530ms
********** Factor found in step 2: 237349828833458037266370999935411
Found probable prime factor of 33 digits: 237349828833458037266370999935411
Probable prime cofactor 805512250524160053024218670593153283285936169981890369660778171822088933584384586054521660133841097184028353756005935093638355078054636670619 has 141 digits

(31·10¹⁹⁰+23)/9 = 3(4)₁₈₉7_<191> = 7 · 37 · 18679 · 196277 · 212561 · C174

C174 = P39 · P135

P39 = 938939424276220156588067577227983963633_<39>

P135 = 181750338188017966926585180534245271074438087656727304705093140750638388807143161919233728286312335186618226569058027162361635240453127_<135>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2726623914
Step 1 took 26296ms
Step 2 took 16438ms
********** Factor found in step 2: 938939424276220156588067577227983963633
Found probable prime factor of 39 digits: 938939424276220156588067577227983963633
Probable prime cofactor 181750338188017966926585180534245271074438087656727304705093140750638388807143161919233728286312335186618226569058027162361635240453127 has 135 digits

(28·10¹⁷¹+71)/9 = 3(1)₁₇₀9_<172> = 47 · 1033 · C167

C167 = P67 · P101

P67 = 1031742911944581497755340763716442950404686881912645644675482631607_<67>

P101 = 62107757478836297627513604933143884731071612237300177074100586545875135390795675774103399514937355567_<101>

SNFS difficulty: 172 digits.
Divisors found:
 r1=1031742911944581497755340763716442950404686881912645644675482631607 (pp67)
 r2=62107757478836297627513604933143884731071612237300177074100586545875135390795675774103399514937355567 (pp101)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.947).
Factorization parameters were as follows:
n: 64079238555562421188257937243540011763117363413958746701635622564130730800830283848141358800253570701141297009559249265949436903691192995223808183376472392146631606169
m: 10000000000000000000000000000000000
deg: 5
c5: 280
c0: 71
skew: 0.76
type: snfs
lss: 1
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 54
mfba: 54
rlambda: 2.4
alambda: 2.4
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [2700000, 5700001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 888418 x 888659
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,5400000,5400000,27,27,54,54,2.4,2.4,200000
total time: 63.00 hours.

Nov 20, 2008

By Erik Branger / GGNFS, Msieve

(29·10¹⁵⁵+43)/9 = 3(2)₁₅₄7_<156> = 3 · 47 · 382091287 · 296664877073318110962662865089_<30> · C116

C116 = P53 · P63

P53 = 29920707085237350653801260567698459993581560517223127_<53>

P63 = 673800388051418068178170290945972346896872151144996313704183727_<63>

Number: 32227_155
N=20160584044805740899471140024147275272088678695425246681184859208290589691014527207371887769660562776824980261454329
  ( 116 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=29920707085237350653801260567698459993581560517223127
 r2=673800388051418068178170290945972346896872151144996313704183727
Version: 
Total time: 23.30 hours.
Scaled time: 48.98 units (timescale=2.102).
Factorization parameters were as follows:
n: 20160584044805740899471140024147275272088678695425246681184859208290589691014527207371887769660562776824980261454329
m: 10000000000000000000000000000000
deg: 5
c5: 29
c0: 43
skew: 1.08
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4

Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 501993 x 502241
Total sieving time: 23.30 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 23.30 hours.
 --------- CPU info (if available) ----------

Nov 19, 2008 (9th)

By matsui / GMP-ECM

5·10¹⁸⁵-7 = 4(9)₁₈₄3_<186> = 13 · 67867 · C180

C180 = P37 · C144

P37 = 3447997960776944762766553717092214661_<37>

C144 = [164361841986391913741776198251558299154755901642009269837282938194472792768129370249771101946669967081043628829357623935904923280758172290316603_<144>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]

566719295998621738672131351931549376552102471916225286788299740102530855032070644960562004191455913205806379219083478885739188979349882292402221086264877798318203817194490128316583
=
3447997960776944762766553717092214661* 164361841986391913741776198251558299154755901642009269837282938194472792768129370249771101946669967081043628829357623935904923280758172290316603

Nov 19, 2008 (8th)

By Serge Batalov / GMP-ECM 6.2.1, Msieve, Msieve-1.38

(31·10¹⁵⁶+23)/9 = 3(4)₁₅₅7_<157> = 3² · 4289 · 7215659571846059_<16> · 303956505946913182950607_<24> · 51649903737974328420181129_<26> · C87

C87 = P32 · P56

P32 = 30062121943635127503267133496219_<32>

P56 = 26202576715893157235293141992702086950253009011391537369_<56>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1420406366
Step 1 took 11306ms
Step 2 took 9180ms
********** Factor found in step 2: 30062121943635127503267133496219
Found probable prime factor of 32 digits: 30062121943635127503267133496219
Probable prime cofactor 26202576715893157235293141992702086950253009011391537369 has 56 digits

(31·10¹⁰⁵+23)/9 = 3(4)₁₀₄7_<106> = 3 · 87415901 · C98

C98 = P49 · P49

P49 = 3198714675065427922561621520496084003147464052427_<49>

P49 = 4106123321616776594835801868588745437723505467787_<49>

Tue Nov 18 21:23:34 2008  Msieve v. 1.38
Tue Nov 18 21:23:34 2008  random seeds: 88f8d981 9b86cb57
Tue Nov 18 21:23:34 2008  factoring 131343169264839831388130192486164290424478739645793749600332798508608650976227785851
92963327669049 (98 digits)
Tue Nov 18 21:23:35 2008  searching for 15-digit factors
Tue Nov 18 21:23:35 2008  commencing number field sieve (98-digit input)
Tue Nov 18 21:23:35 2008  R0: -200000000000000000000000000
Tue Nov 18 21:23:35 2008  R1:  1
Tue Nov 18 21:23:35 2008  A0:  184
Tue Nov 18 21:23:35 2008  A1:  0
Tue Nov 18 21:23:35 2008  A2:  0
Tue Nov 18 21:23:35 2008  A3:  0
Tue Nov 18 21:23:35 2008  A4:  155
Tue Nov 18 21:23:35 2008  size score = 1.988154e-11, Murphy alpha = -0.372646, combined = 2.307732e-11
Tue Nov 18 21:23:35 2008
Tue Nov 18 21:23:35 2008  commencing linear algebra
Tue Nov 18 21:23:35 2008  read 61369 cycles
Tue Nov 18 21:23:35 2008  cycles contain 223451 unique relations
Tue Nov 18 21:23:37 2008  read 223451 relations
Tue Nov 18 21:23:37 2008  using 32 quadratic characters above 33553800
Tue Nov 18 21:23:40 2008  building initial matrix
Tue Nov 18 21:23:41 2008  memory use: 33.2 MB
Tue Nov 18 21:23:42 2008  read 61369 cycles
Tue Nov 18 21:23:42 2008  matrix is 61200 x 61369 (18.8 MB) with weight 6127987 (99.85/col)
Tue Nov 18 21:23:42 2008  sparse part has weight 4258924 (69.40/col)
Tue Nov 18 21:23:42 2008  filtering completed in 2 passes
Tue Nov 18 21:23:42 2008  matrix is 60983 x 61152 (18.8 MB) with weight 6114373 (99.99/col)
Tue Nov 18 21:23:42 2008  sparse part has weight 4252319 (69.54/col)
Tue Nov 18 21:23:43 2008  read 61152 cycles
Tue Nov 18 21:23:43 2008  matrix is 60983 x 61152 (18.8 MB) with weight 6114373 (99.99/col)
Tue Nov 18 21:23:43 2008  sparse part has weight 4252319 (69.54/col)
Tue Nov 18 21:23:43 2008  saving the first 42 matrix rows for later
Tue Nov 18 21:23:43 2008  matrix is 60941 x 61152 (18.1 MB) with weight 4859342 (79.46/col)
Tue Nov 18 21:23:43 2008  sparse part has weight 4127287 (67.49/col)
Tue Nov 18 21:23:43 2008  matrix includes 64 packed rows
Tue Nov 18 21:23:43 2008  using block size 24460 for processor cache size 1024 kB
Tue Nov 18 21:23:44 2008  commencing Lanczos iteration
Tue Nov 18 21:23:44 2008  memory use: 15.9 MB
Tue Nov 18 21:24:21 2008  lanczos halted after 965 iterations (dim = 60941)
Tue Nov 18 21:24:22 2008  recovered 56 nontrivial dependencies
Tue Nov 18 21:24:22 2008  elapsed time 00:00:48
...
Tue Nov 18 21:26:26 2008  reading relations for dependency 9
Tue Nov 18 21:26:26 2008  read 30637 cycles
Tue Nov 18 21:26:26 2008  cycles contain 142049 unique relations
Tue Nov 18 21:26:27 2008  read 142049 relations
Tue Nov 18 21:26:28 2008  multiplying 112056 relations
Tue Nov 18 21:26:32 2008  multiply complete, coefficients have about 2.92 million bits
Tue Nov 18 21:26:32 2008  initial square root is modulo 5340481
Tue Nov 18 21:26:40 2008  prp49 factor: 3198714675065427922561621520496084003147464052427
Tue Nov 18 21:26:40 2008  prp49 factor: 4106123321616776594835801868588745437723505467787
Tue Nov 18 21:26:40 2008  elapsed time 00:02:14
Total time: 0.20 hr

(31·10¹⁰⁹+23)/9 = 3(4)₁₀₈7_<110> = 37 · 53 · 1260520284383_<13> · C95

C95 = P41 · P54

P41 = 69802549992863458713524079329578454901797_<41>

P54 = 199627543953063622202577954734848009773487912524010277_<54>

SNFS difficulty: 111 digits.
Divisors found:
 r1=69802549992863458713524079329578454901797 (pp41)
 r2=199627543953063622202577954734848009773487912524010277 (pp54)
Version: Msieve-1.38
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
n: 13934511616736270932637732753690812614764701004280694412608764883229631350012507024186653767769
m: 10000000000000000000000
deg: 5
c5: 31
c0: 230
skew: 1.49
type: snfs
lss: 1
rlim: 500000
alim: 500000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.4
alambda: 2.4
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [250000, 350001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 85464 x 85706
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,500000,500000,25,25,46,46,2.4,2.4,50000
total time: 0.44 hours.

(31·10¹³⁸+23)/9 = 3(4)₁₃₇7_<139> = 3² · 17 · 35449 · 76597193 · C124

C124 = P33 · P92

P33 = 425331164615134287079987318339223_<33>

P92 = 19493225429670552729857527935947134128408399799387896828008900400424185200391198127920568609_<92>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2764368724
Step 1 took 15565ms
Step 2 took 12189ms
********** Factor found in step 2: 425331164615134287079987318339223
Found probable prime factor of 33 digits: 425331164615134287079987318339223
Probable prime cofactor 19493225429670552729857527935947134128408399799387896828008900400424185200391198127920568609 has 92 digits

(31·10¹⁴¹+23)/9 = 3(4)₁₄₀7_<142> = 3 · 89 · 151 · 26064697 · C130

C130 = P34 · C97

P34 = 2350566219110645571032862479372843_<34>

C97 = [1394459176621573051639386763789651414147839796257994686093167116726624290897405719337770464498921_<97>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2830981924
Step 1 took 15701ms
Step 2 took 12881ms
********** Factor found in step 2: 2350566219110645571032862479372843
Found probable prime factor of 34 digits: 2350566219110645571032862479372843
Composite cofactor 1394459176621573051639386763789651414147839796257994686093167116726624290897405719337770464498921 has 97 digits

(31·10¹⁵⁵+23)/9 = 3(4)₁₅₄7_<156> = 743 · 3877 · 320293 · 87542518061_<11> · C133

C133 = P29 · P105

P29 = 23516095857499575558307056793_<29>

P105 = 181343864352268877571212976251901069010084878705008449185231497922778887753953648570248794590546447878493_<105>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=980145216
Step 1 took 15599ms
********** Factor found in step 1: 23516095857499575558307056793
Found probable prime factor of 29 digits: 23516095857499575558307056793
Probable prime cofactor 181343864352268877571212976251901069010084878705008449185231497922778887753953648570248794590546447878493 has 105 digits

(31·10¹²⁷+23)/9 = 3(4)₁₂₆7_<128> = 37 · C126

C126 = P32 · P94

P32 = 97270187898068637736016992651793_<32>

P94 = 9570567828104454237196160316745951642829132145921976310013121355514932688368360314674485545667_<94>

SNFS difficulty: 129 digits.
Divisors found:
 r1=97270187898068637736016992651793 (pp32)
 r2=9570567828104454237196160316745951642829132145921976310013121355514932688368360314674485545667 (pp94)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 930930930930930930930930930930930930930930930930930930930930930930930930930930930930930930930930930930930930930930930930930931
m: 20000000000000000000000000
deg: 5
c5: 775
c0: 184
skew: 0.75
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 25
lpba: 25
mfbr: 47
mfba: 47
rlambda: 2.5
alambda: 2.5
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved rational special-q in [500000, 900001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 154652 x 154894
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,47,47,2.5,2.5,50000
total time: 2.40 hours.

(31·10¹⁷⁷+23)/9 = 3(4)₁₇₆7_<178> = 3 · 111581 · 886833227724343_<15> · C158

C158 = P35 · P123

P35 = 13254045645043572257091523693520891_<35>

P123 = 875421607153306863297223929188753906423199002422805403873143557144062180284928718909392945416795016973639695922753727364733_<123>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3001664386
Step 1 took 25730ms
Step 2 took 16394ms
********** Factor found in step 2: 13254045645043572257091523693520891
Found probable prime factor of 35 digits: 13254045645043572257091523693520891
Probable prime cofactor

(31·10¹⁷³+23)/9 = 3(4)₁₇₂7_<174> = 9492103471_<10> · 27069297163_<11> · C154

C154 = P32 · C122

P32 = 92908475405229428506788810564397_<32>

C122 = [14428607099022432673306409823918546390880687001008211285748959062244918989746704433598578584157419146708891361260189029887_<122>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=205771521
Step 1 took 19722ms
Step 2 took 14238ms
********** Factor found in step 2: 92908475405229428506788810564397
Found probable prime factor of 32 digits: 92908475405229428506788810564397
Composite cofactor 14428607099022432673306409823918546390880687001008211285748959062244918989746704433598578584157419146708891361260189029887 has 122 digits

(31·10¹⁵⁴+23)/9 = 3(4)₁₅₃7_<155> = 7 · 17 · 37 · 917585479980913_<15> · C136

C136 = P32 · P105

P32 = 67709218824799436689325098690159_<32>

P105 = 125914621130509991249162570949745545096358619356950620399456369625999088541498055440116472305188849960347_<105>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=145261113
Step 1 took 19260ms
Step 2 took 13617ms
********** Factor found in step 2: 67709218824799436689325098690159
Found probable prime factor of 32 digits: 67709218824799436689325098690159
Probable prime cofactor 125914621130509991249162570949745545096358619356950620399456369625999088541498055440116472305188849960347 has 105 digits

Nov 19, 2008 (7th)

By Sinkiti Sibata / GGNFS, Msieve

(29·10¹⁵³+61)/9 = 3(2)₁₅₂9_<154> = 85365372191133803232236248682377_<32> · C122

C122 = P43 · P79

P43 = 4471016885284892094064428969844082669284823_<43>

P79 = 8442429452871492723847244029989852385037808762793079404839902174013864671881499_<79>

Number: 32229_153
N=37746244636614937109295441126432534233511429209331063518631294297155763315859691710659339462548995062900226905080135189677
  ( 122 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=4471016885284892094064428969844082669284823 (pp43)
 r2=8442429452871492723847244029989852385037808762793079404839902174013864671881499 (pp79)
Version: GGNFS-0.77.1-20060513-k8
Total time: 43.51 hours.
Scaled time: 85.59 units (timescale=1.967).
Factorization parameters were as follows:
name: 32229_153
n: 37746244636614937109295441126432534233511429209331063518631294297155763315859691710659339462548995062900226905080135189677
m: 5000000000000000000000000000000
deg: 5
c5: 232
c0: 1525
skew: 1.46
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2700001)
Primes: RFBsize:203362, AFBsize:202463, largePrimes:8126931 encountered
Relations: rels:8269642, finalFF:531820
Max relations in full relation-set: 28
Initial matrix: 405892 x 531820 with sparse part having weight 59695479.
Pruned matrix : 365508 x 367601 with weight 38014697.
Total sieving time: 40.79 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 2.27 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 43.51 hours.
 --------- CPU info (if available) ----------

(31·10¹¹⁵+23)/9 = 3(4)₁₁₄7_<116> = 37 · 47807 · 139312449151957889_<18> · C93

C93 = P43 · P50

P43 = 3975100330099347670994035324751549335101971_<43>

P50 = 35163164054974719903847065656342696717857873144607_<50>

Wed Nov 19 13:41:10 2008  Msieve v. 1.38
Wed Nov 19 13:41:10 2008  random seeds: bfad5480 388ed57c
Wed Nov 19 13:41:10 2008  factoring 139777105042267525685082956492088152402569060014210488994392747415396006411028434868773720397 (93 digits)
Wed Nov 19 13:41:11 2008  searching for 15-digit factors
Wed Nov 19 13:41:12 2008  commencing quadratic sieve (93-digit input)
Wed Nov 19 13:41:12 2008  using multiplier of 13
Wed Nov 19 13:41:12 2008  using 32kb Intel Core sieve core
Wed Nov 19 13:41:12 2008  sieve interval: 36 blocks of size 32768
Wed Nov 19 13:41:12 2008  processing polynomials in batches of 6
Wed Nov 19 13:41:12 2008  using a sieve bound of 1883459 (70588 primes)
Wed Nov 19 13:41:12 2008  using large prime bound of 220364703 (27 bits)
Wed Nov 19 13:41:12 2008  using double large prime bound of 1041491185153848 (42-50 bits)
Wed Nov 19 13:41:12 2008  using trial factoring cutoff of 50 bits
Wed Nov 19 13:41:12 2008  polynomial 'A' values have 12 factors
Wed Nov 19 15:56:38 2008  70878 relations (17907 full + 52971 combined from 923444 partial), need 70684
Wed Nov 19 15:56:39 2008  begin with 941351 relations
Wed Nov 19 15:56:40 2008  reduce to 179498 relations in 11 passes
Wed Nov 19 15:56:40 2008  attempting to read 179498 relations
Wed Nov 19 15:56:42 2008  recovered 179498 relations
Wed Nov 19 15:56:42 2008  recovered 160366 polynomials
Wed Nov 19 15:56:42 2008  attempting to build 70878 cycles
Wed Nov 19 15:56:42 2008  found 70878 cycles in 6 passes
Wed Nov 19 15:56:42 2008  distribution of cycle lengths:
Wed Nov 19 15:56:42 2008     length 1 : 17907
Wed Nov 19 15:56:42 2008     length 2 : 13088
Wed Nov 19 15:56:42 2008     length 3 : 12320
Wed Nov 19 15:56:42 2008     length 4 : 9634
Wed Nov 19 15:56:42 2008     length 5 : 6870
Wed Nov 19 15:56:42 2008     length 6 : 4475
Wed Nov 19 15:56:42 2008     length 7 : 2898
Wed Nov 19 15:56:42 2008     length 9+: 3686
Wed Nov 19 15:56:42 2008  largest cycle: 18 relations
Wed Nov 19 15:56:43 2008  matrix is 70588 x 70878 (17.4 MB) with weight 4284487 (60.45/col)
Wed Nov 19 15:56:43 2008  sparse part has weight 4284487 (60.45/col)
Wed Nov 19 15:56:43 2008  filtering completed in 3 passes
Wed Nov 19 15:56:43 2008  matrix is 66684 x 66747 (16.5 MB) with weight 4055106 (60.75/col)
Wed Nov 19 15:56:43 2008  sparse part has weight 4055106 (60.75/col)
Wed Nov 19 15:56:44 2008  saving the first 48 matrix rows for later
Wed Nov 19 15:56:44 2008  matrix is 66636 x 66747 (9.6 MB) with weight 3057518 (45.81/col)
Wed Nov 19 15:56:44 2008  sparse part has weight 2109132 (31.60/col)
Wed Nov 19 15:56:44 2008  matrix includes 64 packed rows
Wed Nov 19 15:56:44 2008  using block size 26698 for processor cache size 1024 kB
Wed Nov 19 15:56:44 2008  commencing Lanczos iteration
Wed Nov 19 15:56:44 2008  memory use: 9.8 MB
Wed Nov 19 15:57:12 2008  lanczos halted after 1056 iterations (dim = 66632)
Wed Nov 19 15:57:12 2008  recovered 14 nontrivial dependencies
Wed Nov 19 15:57:13 2008  prp43 factor: 3975100330099347670994035324751549335101971
Wed Nov 19 15:57:13 2008  prp50 factor: 35163164054974719903847065656342696717857873144607
Wed Nov 19 15:57:13 2008  elapsed time 02:16:03

(31·10¹⁶⁷+23)/9 = 3(4)₁₆₆7_<168> = 29 · 446166146755871_<15> · 35859278686887841_<17> · 17261346807760160851_<20> · 166754940289037004609267911_<27> · C90

C90 = P43 · P47

P43 = 2903916704097012988465468787854787906046359_<43>

P47 = 88814828170411516711524534020787854062092569687_<47>

Wed Nov 19 16:04:44 2008  Msieve v. 1.38
Wed Nov 19 16:04:44 2008  random seeds: f2d00950 012536f3
Wed Nov 19 16:04:44 2008  factoring 257910863095563953833429968486591780704085942063711414587033921966560265416374354860119633 (90 digits)
Wed Nov 19 16:04:44 2008  searching for 15-digit factors
Wed Nov 19 16:04:46 2008  commencing quadratic sieve (90-digit input)
Wed Nov 19 16:04:46 2008  using multiplier of 1
Wed Nov 19 16:04:46 2008  using 32kb Intel Core sieve core
Wed Nov 19 16:04:46 2008  sieve interval: 36 blocks of size 32768
Wed Nov 19 16:04:46 2008  processing polynomials in batches of 6
Wed Nov 19 16:04:46 2008  using a sieve bound of 1584943 (59970 primes)
Wed Nov 19 16:04:46 2008  using large prime bound of 126795440 (26 bits)
Wed Nov 19 16:04:46 2008  using double large prime bound of 385111478867040 (42-49 bits)
Wed Nov 19 16:04:46 2008  using trial factoring cutoff of 49 bits
Wed Nov 19 16:04:46 2008  polynomial 'A' values have 11 factors
Wed Nov 19 17:18:57 2008  60222 relations (15932 full + 44290 combined from 639005 partial), need 60066
Wed Nov 19 17:18:58 2008  begin with 654937 relations
Wed Nov 19 17:18:58 2008  reduce to 147348 relations in 11 passes
Wed Nov 19 17:18:58 2008  attempting to read 147348 relations
Wed Nov 19 17:19:00 2008  recovered 147348 relations
Wed Nov 19 17:19:00 2008  recovered 125152 polynomials
Wed Nov 19 17:19:00 2008  attempting to build 60222 cycles
Wed Nov 19 17:19:00 2008  found 60222 cycles in 5 passes
Wed Nov 19 17:19:00 2008  distribution of cycle lengths:
Wed Nov 19 17:19:00 2008     length 1 : 15932
Wed Nov 19 17:19:00 2008     length 2 : 11294
Wed Nov 19 17:19:00 2008     length 3 : 10744
Wed Nov 19 17:19:00 2008     length 4 : 8003
Wed Nov 19 17:19:00 2008     length 5 : 5793
Wed Nov 19 17:19:00 2008     length 6 : 3669
Wed Nov 19 17:19:00 2008     length 7 : 2184
Wed Nov 19 17:19:00 2008     length 9+: 2603
Wed Nov 19 17:19:00 2008  largest cycle: 19 relations
Wed Nov 19 17:19:01 2008  matrix is 59970 x 60222 (14.9 MB) with weight 3652250 (60.65/col)
Wed Nov 19 17:19:01 2008  sparse part has weight 3652250 (60.65/col)
Wed Nov 19 17:19:01 2008  filtering completed in 4 passes
Wed Nov 19 17:19:01 2008  matrix is 56279 x 56343 (14.0 MB) with weight 3444010 (61.13/col)
Wed Nov 19 17:19:01 2008  sparse part has weight 3444010 (61.13/col)
Wed Nov 19 17:19:02 2008  saving the first 48 matrix rows for later
Wed Nov 19 17:19:02 2008  matrix is 56231 x 56343 (10.5 MB) with weight 2895002 (51.38/col)
Wed Nov 19 17:19:02 2008  sparse part has weight 2407788 (42.73/col)
Wed Nov 19 17:19:02 2008  matrix includes 64 packed rows
Wed Nov 19 17:19:02 2008  using block size 22537 for processor cache size 1024 kB
Wed Nov 19 17:19:02 2008  commencing Lanczos iteration
Wed Nov 19 17:19:02 2008  memory use: 9.4 MB
Wed Nov 19 17:19:25 2008  lanczos halted after 891 iterations (dim = 56227)
Wed Nov 19 17:19:25 2008  recovered 15 nontrivial dependencies
Wed Nov 19 17:19:26 2008  prp43 factor: 2903916704097012988465468787854787906046359
Wed Nov 19 17:19:26 2008  prp47 factor: 88814828170411516711524534020787854062092569687
Wed Nov 19 17:19:26 2008  elapsed time 01:14:42

(31·10¹²³+23)/9 = 3(4)₁₂₂7_<124> = 3 · 84606897082627201_<17> · C107

C107 = P52 · P55

P52 = 6319917590226352894125890044416029503902005597444263_<52>

P55 = 2147240780066801934686523205080673857557725977524797123_<55>

Number: 34447_123
N=13570384776395537087024643508148141126686711527749785820838572030632082729852778921557351096188596375255349
  ( 107 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=6319917590226352894125890044416029503902005597444263 (pp52)
 r2=2147240780066801934686523205080673857557725977524797123 (pp55)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 4.46 hours.
Scaled time: 2.00 units (timescale=0.449).
Factorization parameters were as follows:
name: 34447_123
n: 13570384776395537087024643508148141126686711527749785820838572030632082729852778921557351096188596375255349
m: 5000000000000000000000000
deg: 5
c5: 248
c0: 575
skew: 1.18
type: snfs
lss: 1
rlim: 880000
alim: 880000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 880000/880000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [440000, 840001)
Primes: RFBsize:69823, AFBsize:69924, largePrimes:2526981 encountered
Relations: rels:2448972, finalFF:213919
Max relations in full relation-set: 28
Initial matrix: 139814 x 213919 with sparse part having weight 16840551.
Pruned matrix : 121656 x 122419 with weight 6886973.
Total sieving time: 4.10 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000
total time: 4.46 hours.
 --------- CPU info (if available) ----------

(31·10¹⁰⁸+23)/9 = 3(4)₁₀₇7_<109> = 3 · 223 · 613 · 26321 · 32363 · C94

C94 = P38 · P57

P38 = 66660839637703797959802996348497475557_<38>

P57 = 147914467409319341807551757070456364919452883686409154841_<57>

Wed Nov 19 17:28:28 2008  Msieve v. 1.38
Wed Nov 19 17:28:28 2008  random seeds: a1a1aef0 7bf371c4
Wed Nov 19 17:28:28 2008  factoring 9860102592069001383943623141214283234414689376330949043038392340073766181537242128302425721437 (94 digits)
Wed Nov 19 17:28:29 2008  searching for 15-digit factors
Wed Nov 19 17:28:30 2008  commencing quadratic sieve (94-digit input)
Wed Nov 19 17:28:31 2008  using multiplier of 5
Wed Nov 19 17:28:31 2008  using 32kb Intel Core sieve core
Wed Nov 19 17:28:31 2008  sieve interval: 36 blocks of size 32768
Wed Nov 19 17:28:31 2008  processing polynomials in batches of 6
Wed Nov 19 17:28:31 2008  using a sieve bound of 2090159 (77647 primes)
Wed Nov 19 17:28:31 2008  using large prime bound of 296802578 (28 bits)
Wed Nov 19 17:28:31 2008  using double large prime bound of 1780089192091634 (42-51 bits)
Wed Nov 19 17:28:31 2008  using trial factoring cutoff of 51 bits
Wed Nov 19 17:28:31 2008  polynomial 'A' values have 12 factors
Wed Nov 19 20:37:28 2008  78136 relations (19584 full + 58552 combined from 1130179 partial), need 77743
Wed Nov 19 20:37:29 2008  begin with 1149763 relations
Wed Nov 19 20:37:30 2008  reduce to 201982 relations in 10 passes
Wed Nov 19 20:37:30 2008  attempting to read 201982 relations
Wed Nov 19 20:37:33 2008  recovered 201982 relations
Wed Nov 19 20:37:33 2008  recovered 183781 polynomials
Wed Nov 19 20:37:33 2008  attempting to build 78136 cycles
Wed Nov 19 20:37:33 2008  found 78136 cycles in 5 passes
Wed Nov 19 20:37:33 2008  distribution of cycle lengths:
Wed Nov 19 20:37:33 2008     length 1 : 19584
Wed Nov 19 20:37:33 2008     length 2 : 13798
Wed Nov 19 20:37:33 2008     length 3 : 13098
Wed Nov 19 20:37:33 2008     length 4 : 10641
Wed Nov 19 20:37:33 2008     length 5 : 7922
Wed Nov 19 20:37:33 2008     length 6 : 5134
Wed Nov 19 20:37:33 2008     length 7 : 3396
Wed Nov 19 20:37:33 2008     length 9+: 4563
Wed Nov 19 20:37:33 2008  largest cycle: 20 relations
Wed Nov 19 20:37:33 2008  matrix is 77647 x 78136 (20.8 MB) with weight 5127022 (65.62/col)
Wed Nov 19 20:37:33 2008  sparse part has weight 5127022 (65.62/col)
Wed Nov 19 20:37:34 2008  filtering completed in 3 passes
Wed Nov 19 20:37:34 2008  matrix is 73700 x 73764 (19.6 MB) with weight 4846871 (65.71/col)
Wed Nov 19 20:37:34 2008  sparse part has weight 4846871 (65.71/col)
Wed Nov 19 20:37:35 2008  saving the first 48 matrix rows for later
Wed Nov 19 20:37:35 2008  matrix is 73652 x 73764 (13.0 MB) with weight 3892828 (52.77/col)
Wed Nov 19 20:37:35 2008  sparse part has weight 2964524 (40.19/col)
Wed Nov 19 20:37:35 2008  matrix includes 64 packed rows
Wed Nov 19 20:37:35 2008  using block size 29505 for processor cache size 1024 kB
Wed Nov 19 20:37:36 2008  commencing Lanczos iteration
Wed Nov 19 20:37:36 2008  memory use: 12.2 MB
Wed Nov 19 20:38:15 2008  lanczos halted after 1166 iterations (dim = 73647)
Wed Nov 19 20:38:15 2008  recovered 14 nontrivial dependencies
Wed Nov 19 20:38:16 2008  prp38 factor: 66660839637703797959802996348497475557
Wed Nov 19 20:38:16 2008  prp57 factor: 147914467409319341807551757070456364919452883686409154841
Wed Nov 19 20:38:16 2008  elapsed time 03:09:48

(31·10¹²⁰+23)/9 = 3(4)₁₁₉7_<121> = 3³ · 19725851 · 157137530004674651_<18> · C95

C95 = P44 · P51

P44 = 54204446176358550691331299450593801518802911_<44>

P51 = 759285031162886117655652650922885658998240238735051_<51>

Wed Nov 19 20:58:35 2008  Msieve v. 1.38
Wed Nov 19 20:58:35 2008  random seeds: eee04af0 6d939a12
Wed Nov 19 20:58:35 2008  factoring 41156624604183385426124387483809375623717575938202142871748189374889762552463441751930416533461 (95 digits)
Wed Nov 19 20:58:36 2008  searching for 15-digit factors
Wed Nov 19 20:58:37 2008  commencing quadratic sieve (95-digit input)
Wed Nov 19 20:58:37 2008  using multiplier of 1
Wed Nov 19 20:58:37 2008  using 32kb Intel Core sieve core
Wed Nov 19 20:58:37 2008  sieve interval: 36 blocks of size 32768
Wed Nov 19 20:58:37 2008  processing polynomials in batches of 6
Wed Nov 19 20:58:37 2008  using a sieve bound of 2154077 (80000 primes)
Wed Nov 19 20:58:37 2008  using large prime bound of 323111550 (28 bits)
Wed Nov 19 20:58:37 2008  using double large prime bound of 2074122508433250 (43-51 bits)
Wed Nov 19 20:58:37 2008  using trial factoring cutoff of 51 bits
Wed Nov 19 20:58:37 2008  polynomial 'A' values have 12 factors
Wed Nov 19 23:22:16 2008  80202 relations (21178 full + 59024 combined from 1172046 partial), need 80096
Wed Nov 19 23:22:17 2008  begin with 1193224 relations
Wed Nov 19 23:22:18 2008  reduce to 202098 relations in 12 passes
Wed Nov 19 23:22:18 2008  attempting to read 202098 relations
Wed Nov 19 23:22:21 2008  recovered 202098 relations
Wed Nov 19 23:22:21 2008  recovered 177771 polynomials
Wed Nov 19 23:22:21 2008  attempting to build 80202 cycles
Wed Nov 19 23:22:22 2008  found 80202 cycles in 5 passes
Wed Nov 19 23:22:22 2008  distribution of cycle lengths:
Wed Nov 19 23:22:22 2008     length 1 : 21178
Wed Nov 19 23:22:22 2008     length 2 : 14727
Wed Nov 19 23:22:22 2008     length 3 : 13766
Wed Nov 19 23:22:22 2008     length 4 : 10752
Wed Nov 19 23:22:22 2008     length 5 : 7658
Wed Nov 19 23:22:22 2008     length 6 : 5080
Wed Nov 19 23:22:22 2008     length 7 : 3122
Wed Nov 19 23:22:22 2008     length 9+: 3919
Wed Nov 19 23:22:22 2008  largest cycle: 21 relations
Wed Nov 19 23:22:22 2008  matrix is 80000 x 80202 (20.8 MB) with weight 5124249 (63.89/col)
Wed Nov 19 23:22:22 2008  sparse part has weight 5124249 (63.89/col)
Wed Nov 19 23:22:23 2008  filtering completed in 3 passes
Wed Nov 19 23:22:23 2008  matrix is 75017 x 75080 (19.6 MB) with weight 4833095 (64.37/col)
Wed Nov 19 23:22:23 2008  sparse part has weight 4833095 (64.37/col)
Wed Nov 19 23:22:23 2008  saving the first 48 matrix rows for later
Wed Nov 19 23:22:23 2008  matrix is 74969 x 75080 (12.9 MB) with weight 3879732 (51.67/col)
Wed Nov 19 23:22:23 2008  sparse part has weight 2943325 (39.20/col)
Wed Nov 19 23:22:23 2008  matrix includes 64 packed rows
Wed Nov 19 23:22:23 2008  using block size 30032 for processor cache size 1024 kB
Wed Nov 19 23:22:24 2008  commencing Lanczos iteration
Wed Nov 19 23:22:24 2008  memory use: 12.1 MB
Wed Nov 19 23:23:04 2008  lanczos halted after 1187 iterations (dim = 74969)
Wed Nov 19 23:23:04 2008  recovered 17 nontrivial dependencies
Wed Nov 19 23:23:05 2008  prp44 factor: 54204446176358550691331299450593801518802911
Wed Nov 19 23:23:05 2008  prp51 factor: 759285031162886117655652650922885658998240238735051
Wed Nov 19 23:23:05 2008  elapsed time 02:24:30

Nov 19, 2008 (6th)

Factorizations of 344...447 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Nov 19, 2008 (5th)

By Jo Yeong Uk / GMP-ECM, GGNFS

8·10¹⁷²+9 = 8(0)₁₇₁9_<173> = 4201 · 31121 · 5041411 · 346459071611_<12> · C147

C147 = P42 · P42 · P64

P42 = 122454245483536330061045540807347553945459_<42>

P42 = 608296663654957875693373827303732266946233_<42>

P64 = 4703167420425903988646488862192041281322859917358747628829697267_<64>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 350331928621527728761081949351918869573565424827174645006780581369818827638825443432238620811811976063345620759127952586071954864671857213232146849 (147 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2462122556
Step 1 took 13971ms
Step 2 took 6377ms
********** Factor found in step 2: 122454245483536330061045540807347553945459
Found probable prime factor of 42 digits: 122454245483536330061045540807347553945459
Composite cofactor 2860921050455771977764483927646944768955414366666151492991326927020143373266369210679921533070327956045211 has 106 digits

Number: 80009_172
N=2860921050455771977764483927646944768955414366666151492991326927020143373266369210679921533070327956045211
  ( 106 digits)
Divisors found:
 r1=608296663654957875693373827303732266946233 (pp42)
 r2=4703167420425903988646488862192041281322859917358747628829697267 (pp64)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 7.72 hours.
Scaled time: 18.45 units (timescale=2.390).
Factorization parameters were as follows:
name: 80009_172
n: 2860921050455771977764483927646944768955414366666151492991326927020143373266369210679921533070327956045211
skew: 11678.31
# norm 1.72e+15
c5: 120600
c4: 6819803985
c3: 37057788054551
c2: -1151675053026808358
c1: 2909342933569088464627
c0: 324963623916431255748839
# alpha -6.59
Y1: 10640649107
Y0: -118858781408249484738
# Murphy_E 1.72e-09
# M 541327409357061061008302996406796774326480382613132409656102290302813857792902919658625814147961415995838
type: gnfs
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [800000, 1250001)
Primes: RFBsize:121127, AFBsize:121169, largePrimes:4551667 encountered
Relations: rels:4587757, finalFF:357886
Max relations in full relation-set: 28
Initial matrix: 242379 x 357886 with sparse part having weight 34663704.
Pruned matrix : 188093 x 189368 with weight 15680682.
Polynomial selection time: 0.49 hours.
Total sieving time: 6.98 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1600000,1600000,26,26,49,49,2.6,2.6,50000
total time: 7.72 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Nov 19, 2008 (4th)

By Serge Batalov / Msieve-1.38

(29·10¹⁶²+43)/9 = 3(2)₁₆₁7_<163> = 2281 · 1380524160241_<13> · C148

C148 = P47 · P101

P47 = 24338504945142473597830485802111060049232775711_<47>

P101 = 42042864161506593485661228298579117459637482156761211650372648834901725871855061061337359033326914517_<101>

SNFS difficulty: 164 digits.
Divisors found:
 r1=24338504945142473597830485802111060049232775711 (pp47)
 r2=42042864161506593485661228298579117459637482156761211650372648834901725871855061061337359033326914517 (pp101)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 1023260457302781502321058826619075853267150618701104376101655793590908734618042775416104799906803554891849404419821230807109285753121776555130896587
m: 200000000000000000000000000000000
deg: 5
c5: 725
c0: 344
skew: 0.86
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 27
lpba: 27
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [1900000, 4100001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 872891 x 873133
Total sieving time: 20.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 6.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,54,54,2.5,2.5,200000
total time: 27.00 hours.

Nov 19, 2008 (3rd)

By Erik Branger / GGNFS, Msieve

(35·10¹⁸¹-53)/9 = 3(8)₁₈₀3_<182> = 3 · 11 · 71 · 881 · 208945537457941_<15> · 791365109293020169_<18> · 21778263350111446027_<20> · C124

C124 = P43 · P82

P43 = 1252919402408328755421374091254262320800303_<43>

P82 = 4175619906214193298947641749972535268213753641612635366469178981999800565253855349_<82>

Number: 38883_181
N=5231715197578208831447042887178669531402910572998083330570601096456072639171819460414476215122280855020505800755505877370747
  ( 124 digits)
Divisors found:
 r1=1252919402408328755421374091254262320800303
 r2=4175619906214193298947641749972535268213753641612635366469178981999800565253855349
Version: 
Total time: 107.58 hours.
Scaled time: 197.62 units (timescale=1.837).
Factorization parameters were as follows:
name: 38883_181
n: 5231715197578208831447042887178669531402910572998083330570601096456072639171819460414476215122280855020505800755505877370747
skew: 66716.52
# norm 3.33e+017
c5: 1075020
c4: -78698768752
c3: -17021611594094501
c2: 281519712989601017903
c1: 28582653678799695610438785
c0: 160056945615395880888497141625
# alpha -7.11
Y1: 54913199080289
Y0: -344704158686954209701182
# Murphy_E 1.72e-010
# M 1136309453548721671272440661601553980613918152128772920480184792812545192504107872685614962152046899738781232436031973902978
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 6040001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 744744 x 744992
Total sieving time: 107.58 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 107.58 hours.
 --------- CPU info (if available) ----------

Nov 19, 2008 (2nd)

By Robert Backstrom / GMP-ECM

(28·10¹⁵²+71)/9 = 3(1)₁₅₁9_<153> = 11 · 2141 · C149

C149 = P46 · P47 · P57

P46 = 1226316957498029579045870019792441755337618589_<46>

P47 = 80940410630738976725326885455402605922641740003_<47>

P57 = 133087734524800559082620074043187468597248350842161192407_<57>

Number: n
N=13210101953679721078133035162460664562486141187682523506904637217575097070659891771521850923999452724347633268698191631400412343896697002722224581169
  ( 149 digits)
SNFS difficulty: 153 digits.
Divisors found:

 r1=1226316957498029579045870019792441755337618589 (pp46)
 r2=80940410630738976725326885455402605922641740003 (pp47)
 r3=133087734524800559082620074043187468597248350842161192407 (pp57)

Ggnfs  : 0.77.1-20051202-athlon
Msieve : 1.38
Total time:  16.33 hours.
Scaled time: 29.77 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_3_1_151_9
n: 13210101953679721078133035162460664562486141187682523506904637217575097070659891771521850923999452724347633268698191631400412343896697002722224581169
type: snfs
skew: 0.96
deg: 5
c5: 175
c0: 142
m: 2000000000000000000000000000000
rlim: 2500000
alim: 2500000
lpbr: 27
lpba: 27
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved algebraic special-q in [1250000, 2200000)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 10053756
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 533108 x 533356
Total sieving time: 16.33 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2500000,2500000,27,27,54,54,2.5,2.5,100000
total time: 16.33 hours.
 --------- CPU info (if available) ----------

(29·10¹⁵⁷+61)/9 = 3(2)₁₅₆9_<158> = 3³ · 13 · 2531 · 111491 · C147

C147 = P37 · P110

P37 = 3790426175780289902379082348729368317_<37>

P110 = 85827877663886217686624927713596100146431875154647473222853714845318268952376104728527063396257347348391319247_<110>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 325324234108862798024888672602227669818231185557939007019477225308521689758051408804150529854512300441954587776525928341252624651350941132594097299 (147 digits)
Using B1=2790000, B2=4281592780, polynomial Dickson(6), sigma=4021036377
Step 1 took 33667ms
Step 2 took 12747ms
********** Factor found in step 2: 3790426175780289902379082348729368317
Found probable prime factor of 37 digits: 3790426175780289902379082348729368317
Probable prime cofactor 85827877663886217686624927713596100146431875154647473222853714845318268952376104728527063396257347348391319247 has 110 digits

Nov 19, 2008

By Serge Batalov / PFGW

(28·10⁵⁹¹³⁵+53)/9 = 3(1)₅₉₁₃₄7_<59136> is PRP.

It's the largest unprovable quasi-repdigit PRP (except Plateau and Depression PRPs) in our tables so far. Congratulations!

Nov 18, 2008 (3rd)

By Jo Yeong Uk / GGNFS, GMP-ECM

(29·10¹⁴⁶+61)/9 = 3(2)₁₄₅9_<147> = 7 · 3467 · 259507 · 13624175111_<11> · 138313582440049_<15> · C113

C113 = P40 · P73

P40 = 3169810222981727600466968272956709187527_<40>

P73 = 8565371832817375392513756344491664934115448215655694538143590743210533971_<73>

Number: 32229_146
N=27150603199304253514940527210781393490679512341427106122393417249589472947324497432458764591434516158903242979717
  ( 113 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=3169810222981727600466968272956709187527 (pp40)
 r2=8565371832817375392513756344491664934115448215655694538143590743210533971 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.07 hours.
Scaled time: 26.45 units (timescale=2.390).
Factorization parameters were as follows:
n: 27150603199304253514940527210781393490679512341427106122393417249589472947324497432458764591434516158903242979717
m: 100000000000000000000000000000
deg: 5
c5: 290
c0: 61
skew: 0.73
type: snfs
rlim: 1950000
alim: 1950000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1950000/1950000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [975000, 1725001)
Primes: RFBsize:145502, AFBsize:145972, largePrimes:3960898 encountered
Relations: rels:4039693, finalFF:373641
Max relations in full relation-set: 28
Initial matrix: 291541 x 373641 with sparse part having weight 34601105.
Pruned matrix : 260365 x 261886 with weight 20668004.
Total sieving time: 10.41 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.58 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1950000,1950000,26,26,49,49,2.3,2.3,75000
total time: 11.07 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

8·10¹⁸⁵+9 = 8(0)₁₈₄9_<186> = 7 · 24329 · 53381 · 25502165263849_<14> · C163

C163 = P43 · C121

P43 = 1303028394848660857467715486468010946754987_<43>

C121 = [2648195527610722149244619035624215921962390457850886740531905304699190651782516458062408766925167070534368118892625076601_<121>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 3450673967588001826514728936156930978629571495727208135592960907082200888074468826445788854167633653862786053882083856937104121316034686491932860587742803253759187 (163 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=927156312
Step 1 took 16545ms
Step 2 took 6975ms
********** Factor found in step 2: 1303028394848660857467715486468010946754987
Found probable prime factor of 43 digits: 1303028394848660857467715486468010946754987
Composite cofactor 2648195527610722149244619035624215921962390457850886740531905304699190651782516458062408766925167070534368118892625076601 has 121 digits

Nov 18, 2008 (2nd)

By Sinkiti Sibata / GGNFS, Msieve

(29·10¹⁴¹+61)/9 = 3(2)₁₄₀9_<142> = 13183 · 387197 · 71847667 · 133889624761_<12> · C113

C113 = P35 · P37 · P42

P35 = 23326022163441896017355332795484893_<35>

P37 = 8095744849338993975408132622174877891_<37>

P42 = 347497881729904362093602551567166189462659_<42>

Number: 32229_141
N=65622029498022402511370121818645478725599093924522418761938954240567698309562351507030435140498203033268335542917
  ( 113 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=23326022163441896017355332795484893 (pp35)
 r2=8095744849338993975408132622174877891 (pp37)
 r3=347497881729904362093602551567166189462659 (pp42)
Version: GGNFS-0.77.1-20060513-k8
Total time: 13.27 hours.
Scaled time: 26.42 units (timescale=1.991).
Factorization parameters were as follows:
name: 32229_141
n: 65622029498022402511370121818645478725599093924522418761938954240567698309562351507030435140498203033268335542917
m: 10000000000000000000000000000
deg: 5
c5: 290
c0: 61
skew: 0.73
type: snfs
lss: 1
rlim: 1660000
alim: 1660000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1660000/1660000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [830000, 1930001)
Primes: RFBsize:125335, AFBsize:125722, largePrimes:3887765 encountered
Relations: rels:4017215, finalFF:365741
Max relations in full relation-set: 28
Initial matrix: 251124 x 365741 with sparse part having weight 37586099.
Pruned matrix : 216769 x 218088 with weight 19575455.
Total sieving time: 12.54 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.52 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1660000,1660000,26,26,48,48,2.3,2.3,100000
total time: 13.27 hours.
 --------- CPU info (if available) ----------

(29·10¹³⁷+61)/9 = 3(2)₁₃₆9_<138> = 36865611488038198486792207_<26> · C112

C112 = P43 · P70

P43 = 1876509566605769011012478535021817151398357_<43>

P70 = 4657826031403067538249012839543823016247868013413400768902393511194671_<70>

Number: 32229_137
N=8740455107513239305779557493730510918834594330157676536378650217243444178655936857371578307479790099541296555547
  ( 112 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=1876509566605769011012478535021817151398357 (pp43)
 r2=4657826031403067538249012839543823016247868013413400768902393511194671 (pp70)
Version: GGNFS-0.77.1-20060513-k8
Total time: 10.97 hours.
Scaled time: 21.91 units (timescale=1.997).
Factorization parameters were as follows:
name: 32229_137
n: 8740455107513239305779557493730510918834594330157676536378650217243444178655936857371578307479790099541296555547
m: 2000000000000000000000000000
deg: 5
c5: 725
c0: 488
skew: 0.92
type: snfs
lss: 1
rlim: 1470000
alim: 1470000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1470000/1470000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [735000, 1710001)
Primes: RFBsize:112047, AFBsize:112565, largePrimes:3586545 encountered
Relations: rels:3620639, finalFF:294457
Max relations in full relation-set: 28
Initial matrix: 224679 x 294457 with sparse part having weight 29193083.
Pruned matrix : 204167 x 205354 with weight 17484458.
Total sieving time: 10.30 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.47 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1470000,1470000,26,26,48,48,2.3,2.3,75000
total time: 10.97 hours.
 --------- CPU info (if available) ----------

(29·10¹⁴²+43)/9 = 3(2)₁₄₁7_<143> = 13 · 37 · 90071 · 271177 · 83701033319_<11> · 2639074956201911_<16> · C104

C104 = P35 · P70

P35 = 11669805408573726208797777707700553_<35>

P70 = 1063962733182911001767833547303540722494502663962209251203781021064213_<70>

Mon Nov 17 14:13:57 2008  Msieve v. 1.38
Mon Nov 17 14:13:57 2008  random seeds: 514256f8 8e3d4afb
Mon Nov 17 14:13:57 2008  factoring 12416238058218819166824114540569901613579126526613903387203375857785433658967700039267592952549188609789 (104 digits)
Mon Nov 17 14:13:58 2008  searching for 15-digit factors
Mon Nov 17 14:13:59 2008  commencing quadratic sieve (104-digit input)
Mon Nov 17 14:14:00 2008  using multiplier of 1
Mon Nov 17 14:14:00 2008  using 32kb Intel Core sieve core
Mon Nov 17 14:14:00 2008  sieve interval: 36 blocks of size 32768
Mon Nov 17 14:14:00 2008  processing polynomials in batches of 6
Mon Nov 17 14:14:00 2008  using a sieve bound of 3575519 (127357 primes)
Mon Nov 17 14:14:00 2008  using large prime bound of 536327850 (28 bits)
Mon Nov 17 14:14:00 2008  using double large prime bound of 5163861615140850 (44-53 bits)
Mon Nov 17 14:14:00 2008  using trial factoring cutoff of 53 bits
Mon Nov 17 14:14:00 2008  polynomial 'A' values have 13 factors
Tue Nov 18 16:04:28 2008  127591 relations (30004 full + 97587 combined from 1915668 partial), need 127453
Tue Nov 18 16:04:31 2008  begin with 1945672 relations
Tue Nov 18 16:04:33 2008  reduce to 338988 relations in 12 passes
Tue Nov 18 16:04:33 2008  attempting to read 338988 relations
Tue Nov 18 16:04:39 2008  recovered 338988 relations
Tue Nov 18 16:04:39 2008  recovered 331435 polynomials
Tue Nov 18 16:04:40 2008  attempting to build 127591 cycles
Tue Nov 18 16:04:40 2008  found 127591 cycles in 6 passes
Tue Nov 18 16:04:40 2008  distribution of cycle lengths:
Tue Nov 18 16:04:40 2008     length 1 : 30004
Tue Nov 18 16:04:40 2008     length 2 : 21534
Tue Nov 18 16:04:40 2008     length 3 : 21139
Tue Nov 18 16:04:40 2008     length 4 : 17316
Tue Nov 18 16:04:40 2008     length 5 : 13424
Tue Nov 18 16:04:40 2008     length 6 : 9343
Tue Nov 18 16:04:40 2008     length 7 : 6168
Tue Nov 18 16:04:40 2008     length 9+: 8663
Tue Nov 18 16:04:40 2008  largest cycle: 22 relations
Tue Nov 18 16:04:41 2008  matrix is 127357 x 127591 (37.6 MB) with weight 9357482 (73.34/col)
Tue Nov 18 16:04:41 2008  sparse part has weight 9357482 (73.34/col)
Tue Nov 18 16:04:42 2008  filtering completed in 3 passes
Tue Nov 18 16:04:42 2008  matrix is 122629 x 122693 (36.4 MB) with weight 9050763 (73.77/col)
Tue Nov 18 16:04:42 2008  sparse part has weight 9050763 (73.77/col)
Tue Nov 18 16:04:43 2008  saving the first 48 matrix rows for later
Tue Nov 18 16:04:44 2008  matrix is 122581 x 122693 (26.3 MB) with weight 7597616 (61.92/col)
Tue Nov 18 16:04:44 2008  sparse part has weight 6160501 (50.21/col)
Tue Nov 18 16:04:44 2008  matrix includes 64 packed rows
Tue Nov 18 16:04:44 2008  using block size 43690 for processor cache size 1024 kB
Tue Nov 18 16:04:45 2008  commencing Lanczos iteration
Tue Nov 18 16:04:45 2008  memory use: 23.3 MB
Tue Nov 18 16:06:57 2008  lanczos halted after 1940 iterations (dim = 122581)
Tue Nov 18 16:06:57 2008  recovered 17 nontrivial dependencies
Tue Nov 18 16:06:58 2008  prp35 factor: 11669805408573726208797777707700553
Tue Nov 18 16:06:58 2008  prp70 factor: 1063962733182911001767833547303540722494502663962209251203781021064213
Tue Nov 18 16:06:58 2008  elapsed time 25:53:01

Nov 18, 2008

By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1

(29·10¹⁵⁶+43)/9 = 3(2)₁₅₅7_<157> = 30859 · 1534343971_<10> · C143

C143 = P37 · P107

P37 = 1377552754580720316751868668303903781_<37>

P107 = 49401788191707908150553066353759600516135856958908205391836521851420399804418285516707499280068724331113303_<107>

SNFS difficulty: 157 digits.
Divisors found:
 r1=1377552754580720316751868668303903781 (pp37)
 r2=49401788191707908150553066353759600516135856958908205391836521851420399804418285516707499280068724331113303 (pp107)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.729).
Factorization parameters were as follows:
n: 68053569404700530923170764879185371978510877788928882861160627284981640913973139213450909040663507340468157232348646363524761347762432721098643
m: 10000000000000000000000000000000
deg: 5
c5: 290
c0: 43
skew: 0.68
type: snfs
lss: 1
rlim: 2900000
alim: 2900000
lpbr: 27
lpba: 27
Factor base limits: 2900000/2900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [1450000, 2650001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 633376 x 633618
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,54,54,2.5,2.5,100000
total time: 28.00 hours.

(29·10¹⁶⁷+61)/9 = 3(2)₁₆₆9_<168> = 1110413 · C162

C162 = P45 · P118

P45 = 126809889244639021357268589157526459258405033_<45>

P118 = 2288325644641308471859080040799162906181921781791384079876889249717810058558308565164012974877788941034747528288278401_<118>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1566598641
Step 1 took 25314ms
Step 2 took 16576ms
********** Factor found in step 2: 126809889244639021357268589157526459258405033
Found probable prime factor of 45 digits: 126809889244639021357268589157526459258405033
Probable prime cofactor 2288325644641308471859080040799162906181921781791384079876889249717810058558308565164012974877788941034747528288278401 has 118 digits

(28·10¹⁷⁰+71)/9 = 3(1)₁₆₉9_<171> = 11 · 29 · 331 · C166

C166 = P41 · C126

P41 = 19859450154315389409262513980231995152171_<41>

C126 = [148364372806478843118018056613754483141353836691388837731243793211133214062412958758919222671776635993740297014703909886184601_<126>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3158295896
Step 1 took 20529ms
Step 2 took 13133ms
********** Factor found in step 2: 19859450154315389409262513980231995152171
Found probable prime factor of 41 digits: 19859450154315389409262513980231995152171
Composite cofactor 148364372806478843118018056613754483141353836691388837731243793211133214062412958758919222671776635993740297014703909886184601 has 126 digits

(29·10¹⁶⁴+61)/9 = 3(2)₁₆₃9_<165> = 7 · 18296071169_<11> · C154

C154 = P39 · P52 · P64

P39 = 529139710257486136769165693925353727749_<39>

P52 = 3543247599221912697675370851675835652468863948412567_<52>

P64 = 1341923476483577207953314651919037091986443271975979972818618161_<64>

SNFS difficulty: 166 digits.
Divisors found:
 r1=529139710257486136769165693925353727749 (pp39)
 r2=3543247599221912697675370851675835652468863948412567 (pp52)
 r3=1341923476483577207953314651919037091986443271975979972818618161 (pp64)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.946).
Factorization parameters were as follows:
n: 2515936104891199319210067619722540648914314792789491894987050267728767367587831338728546445895809907785893339078962457426043899864092512251094629857784963
m: 1000000000000000000000000000000000
deg: 5
c5: 29
c0: 610
skew: 1.84
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2050000, 3850001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 712823 x 713065
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,52,52,2.5,2.5,200000
total time: 23.00 hours.

Nov 17, 2008 (6th)

By Robert Backstrom / GMP-ECM, GGNFS+Msieve

(29·10¹⁷²+43)/9 = 3(2)₁₇₁7_<173> = 13² · 19 · 37 · 3119131 · 307874741 · 39577769389383443_<17> · 185683336923165787_<18> · 5188305348860178155851_<22> · C97

C97 = P36 · P62

P36 = 242134544099255329284789632330728687_<36>

P62 = 30591393340298415649850547843758728559625979373492486617641223_<62>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 7407233079814152516570865935671655828908744097439146872132648689700405980714588309617488719864201 (97 digits)
Using B1=3346000, B2=5707365310, polynomial Dickson(6), sigma=1782536042
Step 1 took 23719ms
Step 2 took 9297ms
********** Factor found in step 2: 242134544099255329284789632330728687
Found probable prime factor of 36 digits: 242134544099255329284789632330728687
Probable prime cofactor 30591393340298415649850547843758728559625979373492486617641223 has 62 digits

(29·10¹⁴⁰+43)/9 = 3(2)₁₃₉7_<141> = 3² · 82219597700479507_<17> · C123

C123 = P58 · P65

P58 = 7543301094605391045064977941022620892585184652931249322841_<58>

P65 = 57726627832506193799633496599134618772751262475665405484205686369_<65>

Number: n
N=435449334916822004002149338747365465555272793113051889143398338029024260586100943664452029185844079320320641739892874054329
  ( 123 digits)
SNFS difficulty: 141 digits.
Divisors found:

 r1=7543301094605391045064977941022620892585184652931249322841 (pp58)
 r2=57726627832506193799633496599134618772751262475665405484205686369 (pp65)

Ggnfs  : 0.77.1-20051202-athlon
Msieve : 1.38
Total time:  3.64 hours.
Scaled time: 6.64 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_3_2_139_7
n: 435449334916822004002149338747365465555272793113051889143398338029024260586100943664452029185844079320320641739892874054329
type: snfs
skew: 1.08
deg: 5
c5: 29
c0: 43
m: 10000000000000000000000000000
rlim: 1200000
alim: 1200000
lpbr: 27
lpba: 27
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved algebraic special-q in [600000, 1220000)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7001824
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 293297 x 293545
Total sieving time: 3.64 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1200000,1200000,27,27,54,54,2.5,2.5,100000
total time: 3.64 hours.
 --------- CPU info (if available) ----------

Nov 17, 2008 (5th)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38+pol51

(29·10¹⁹²+61)/9 = 3(2)₁₉₁9_<193> = 482527 · 3278369 · 187750647274994433763849699_<27> · C155

C155 = P37 · P118

P37 = 2316834160594153819667107946835624439_<37>

P118 = 4682735670925414078866118621047739953536644987195349759769350594785717948649737367633121436688424842703068559636997103_<118>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=114559045
Step 1 took 54535ms
Step 2 took 19111ms
********** Factor found in step 2: 2316834160594153819667107946835624439
Found probable prime factor of 37 digits: 2316834160594153819667107946835624439
Probable prime cofactor 4682735670925414078866118621047739953536644987195349759769350594785717948649737367633121436688424842703068559636997103 has 118 digits

(29·10¹⁸⁴+61)/9 = 3(2)₁₈₃9_<185> = 3³ · 255256602685706526999458973095231_<33> · C151

C151 = P32 · P120

P32 = 37296769389789298779684908001329_<32>

P120 = 125355537759404243933982601729318974211996976487902842604447040165178893665367161257179742437444317012524654252728521473_<120>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2120548678
Step 1 took 15802ms
Step 2 took 12328ms
********** Factor found in step 2: 37296769389789298779684908001329
Found probable prime factor of 32 digits: 37296769389789298779684908001329
Probable prime cofactor 125355537759404243933982601729318974211996976487902842604447040165178893665367161257179742437444317012524654252728521473 has 120 digits

(29·10¹⁷³+43)/9 = 3(2)₁₇₂7_<174> = 3 · 1279 · 13627 · 13236833 · 148688385509304503_<18> · C142

C142 = P39 · P104

P39 = 278125250251433947903850622262669172867_<39>

P104 = 11258016445427235313011794263716183664680139091861609109861704266670446050131750455666720671537249609881_<104>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=54860734
Step 1 took 18960ms
Step 2 took 13876ms
********** Factor found in step 2: 278125250251433947903850622262669172867
Found probable prime factor of 39 digits: 278125250251433947903850622262669172867
Probable prime cofactor 11258016445427235313011794263716183664680139091861609109861704266670446050131750455666720671537249609881 has 104 digits

(29·10¹⁵⁸+43)/9 = 3(2)₁₅₇7_<159> = 3² · 977 · 279212959 · C147

C147 = P33 · C114

P33 = 583872380142192551079643634844427_<33>

C114 = [224783750205550827667498520536546643814178594317883134181700329233660310038101302061860511369018574239773131182623_<114>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2559564766
Step 1 took 15907ms
Step 2 took 12072ms
********** Factor found in step 2: 583872380142192551079643634844427
Found probable prime factor of 33 digits: 583872380142192551079643634844427
Composite cofactor 224783750205550827667498520536546643814178594317883134181700329233660310038101302061860511369018574239773131182623 has 114 digits

(29·10¹⁵⁸+61)/9 = 3(2)₁₅₇9_<159> = 7 · 607 · 21379 · 2095201 · C145

C145 = P32 · P113

P32 = 21190175341877706602064263755067_<32>

P113 = 79895280719012847910673786448020987976586641161452917808757752436610586187445750827143161492493875865710083529997_<113>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1456372488
Step 1 took 71098ms
Step 2 took 27177ms
********** Factor found in step 2: 21190175341877706602064263755067
Found probable prime factor of 32 digits: 21190175341877706602064263755067
Probable prime cofactor 79895280719012847910673786448020987976586641161452917808757752436610586187445750827143161492493875865710083529997 has 113 digits

(29·10¹⁸⁷+43)/9 = 3(2)₁₈₆7_<188> = 37 · 397 · 1223 · 9093324433_<10> · C171

C171 = P30 · C141

P30 = 225672697957802240071355869943_<30>

C141 = [874047617631760391195304292247147019956812512118441877235264029120636815503492744210942204168382928019415331396254518104266298927433445990339_<141>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3637906633
Step 1 took 66450ms
Step 2 took 22651ms
********** Factor found in step 2: 225672697957802240071355869943
Found probable prime factor of 30 digits: 225672697957802240071355869943
Composite cofactor 874047617631760391195304292247147019956812512118441877235264029120636815503492744210942204168382928019415331396254518104266298927433445990339 has 141 digits

(29·10¹⁶⁴+43)/9 = 3(2)₁₆₃7_<165> = 3 · 11491 · 473869683961_<12> · C149

C149 = P31 · P119

P31 = 1942716736615818038402338174021_<31>

P119 = 10153318318372036964823232567936373358103425158864543912265807365285383606461019955365281439089858072132176984882382679_<119>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=940592037
Step 1 took 16658ms
Step 2 took 12377ms
********** Factor found in step 2: 1942716736615818038402338174021
Found probable prime factor of 31 digits: 1942716736615818038402338174021
Probable prime cofactor 10153318318372036964823232567936373358103425158864543912265807365285383606461019955365281439089858072132176984882382679 has 119 digits

(29·10¹⁷⁹+43)/9 = 3(2)₁₇₈7_<180> = 3 · 42594067205378886809_<20> · 248608775267040116745474127_<27> · C134

C134 = P31 · P103

P31 = 2769319232990930018823920363173_<31>

P103 = 3662651907484122160682225291966783394252544467675339129918900995332581468906429399627651838257437808331_<103>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2974743075
Step 1 took 43872ms
Step 2 took 16146ms
********** Factor found in step 2: 2769319232990930018823920363173
Found probable prime factor of 31 digits: 2769319232990930018823920363173
Probable prime cofactor 3662651907484122160682225291966783394252544467675339129918900995332581468906429399627651838257437808331 has 103 digits

(29·10¹⁸¹+43)/9 = 3(2)₁₈₀7_<182> = 37 · 647 · 3104071 · 11680004471_<11> · 53808065626583_<14> · 10907159084372867669_<20> · 82972673688786008924639_<23> · C105

C105 = P43 · P63

P43 = 3601458746009011119542948899535711107790437_<43>

P63 = 211690940233967989813862201243570845426363639153268518613816993_<63>

Number: 32227_181
N=762396188156494875567780473147586708249017071732373530428771402196001592862502726153090821862990913495941
  ( 105 digits)
Divisors found:
 r1=3601458746009011119542948899535711107790437 (pp43)
 r2=211690940233967989813862201243570845426363639153268518613816993 (pp63)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.733).
Factorization parameters were as follows:
name: 32227_181
n: 762396188156494875567780473147586708249017071732373530428771402196001592862502726153090821862990913495941
skew: 9844.65
# norm 3.11e+14
c5: 29640
c4: 1117679122
c3: 19394260346651
c2: -117325550455593525
c1: -630322423049171911239
c0: 2106398969892741411195903
# alpha -5.82
Y1: 24663503227
Y0: -120798025239544098128
# Murphy_E 1.83e-09
# M 584676753022640349010774396889405223318803062446763465583310243513069604242056769938892601179638601221218
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2150001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 273203 x 273445
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 8.50 hours.

Nov 17, 2008 (4th)

By Sinkiti Sibata / GGNFS

(29·10¹²⁶+61)/9 = 3(2)₁₂₅9_<127> = 22246373 · 8154448405163_<13> · C107

C107 = P37 · P70

P37 = 5260246663870249816139402148927464621_<37>

P70 = 3376724080941819078597386914245768715629794334600094008745661189453951_<70>

Number: 32229_126
N=17762401581584539215934748989254245111000743713326681417675537217984098385505054330098797056958065861167571
  ( 107 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=5260246663870249816139402148927464621 (pp37)
 r2=3376724080941819078597386914245768715629794334600094008745661189453951 (pp70)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.66 hours.
Scaled time: 7.29 units (timescale=1.991).
Factorization parameters were as follows:
name: 32229_126
n: 17762401581584539215934748989254245111000743713326681417675537217984098385505054330098797056958065861167571
m: 10000000000000000000000000
deg: 5
c5: 290
c0: 61
skew: 0.73
type: snfs
lss: 1
rlim: 930000
alim: 930000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 930000/930000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [465000, 815001)
Primes: RFBsize:73474, AFBsize:73758, largePrimes:2693813 encountered
Relations: rels:2675287, finalFF:270666
Max relations in full relation-set: 28
Initial matrix: 147299 x 270666 with sparse part having weight 22074441.
Pruned matrix : 118461 x 119261 with weight 6932569.
Total sieving time: 3.45 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,930000,930000,26,26,46,46,2.3,2.3,50000
total time: 3.66 hours.
 --------- CPU info (if available) ----------

(29·10¹²⁷+43)/9 = 3(2)₁₂₆7_<128> = 17 · 37 · 12823747462269174161_<20> · C106

C106 = P52 · P54

P52 = 6579167382533500938426829892675558224130541575894473_<52>

P54 = 607182087000918396013785605242613558361173964633582271_<54>

Number: 32227_127
N=3994752582055060728308608112517264856218214939170946070765465949859566855109944727334903191216111059688183
  ( 106 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=6579167382533500938426829892675558224130541575894473 (pp52)
 r2=607182087000918396013785605242613558361173964633582271 (pp54)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 5.72 hours.
Scaled time: 2.71 units (timescale=0.473).
Factorization parameters were as follows:
name: 32227_127
n: 3994752582055060728308608112517264856218214939170946070765465949859566855109944727334903191216111059688183
m: 20000000000000000000000000
deg: 5
c5: 725
c0: 344
skew: 0.86
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [500000, 1000001)
Primes: RFBsize:78498, AFBsize:78406, largePrimes:2713685 encountered
Relations: rels:2627655, finalFF:216772
Max relations in full relation-set: 28
Initial matrix: 156971 x 216772 with sparse part having weight 17221769.
Pruned matrix : 142113 x 142961 with weight 8478682.
Total sieving time: 5.27 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000
total time: 5.72 hours.
 --------- CPU info (if available) ----------

(29·10¹¹⁹+61)/9 = 3(2)₁₁₈9_<120> = 197 · 36736277 · C110

C110 = P55 · P56

P55 = 3039594091840195741412652558969397930858942438694303563_<55>

P56 = 14648006686402284380989446730512633636716046580374198407_<56>

Number: 32229_119
N=44523994581224066491456374407948378951798095334630452372072088876207730565761711381108873202032068093249024141
  ( 110 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=3039594091840195741412652558969397930858942438694303563 (pp55)
 r2=14648006686402284380989446730512633636716046580374198407 (pp56)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.47 hours.
Scaled time: 2.49 units (timescale=1.009).
Factorization parameters were as follows:
name: 32229_119
n: 44523994581224066491456374407948378951798095334630452372072088876207730565761711381108873202032068093249024141
m: 500000000000000000000000
deg: 5
c5: 464
c0: 305
skew: 0.92
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 615001)
Primes: RFBsize:58789, AFBsize:58572, largePrimes:1393640 encountered
Relations: rels:1416113, finalFF:193824
Max relations in full relation-set: 28
Initial matrix: 117427 x 193824 with sparse part having weight 8753871.
Pruned matrix : 87703 x 88354 with weight 3029773.
Total sieving time: 2.42 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 2.47 hours.
 --------- CPU info (if available) ----------

(28·10¹⁵³+71)/9 = 3(1)₁₅₂9_<154> = 857 · 85103 · 3976032114275161_<16> · 1086768939743010205380688859_<28> · C103

C103 = P38 · P66

P38 = 11186157647009820408220827313507101889_<38>

P66 = 882514385602616930882416082547517692492045139519424234560724804899_<66>

Number: 31119_153
N=9871945043104886736129379424657667897317895638682689885689875888250427703761523754328418040160439354211
  ( 103 digits)
Divisors found:
 r1=11186157647009820408220827313507101889 (pp38)
 r2=882514385602616930882416082547517692492045139519424234560724804899 (pp66)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 12.56 hours.
Scaled time: 5.94 units (timescale=0.473).
Factorization parameters were as follows:
name: 31119_153
n: 9871945043104886736129379424657667897317895638682689885689875888250427703761523754328418040160439354211
skew: 3705.13
# norm 8.60e+13
c5: 129720
c4: 263511244
c3: -12960973898930
c2: -3893806066263409
c1: 35118915354322524346
c0: -4785904810680555345056
# alpha -5.01
Y1: 55039345009
Y0: -37694579262082979205
# Murphy_E 2.40e-09
# M 2829306139617020241602336734220383744679524675451341332199799705151743481356617341779517768513448671065
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1850001)
Primes: RFBsize:169511, AFBsize:169312, largePrimes:4329475 encountered
Relations: rels:4333401, finalFF:422619
Max relations in full relation-set: 28
Initial matrix: 338906 x 422619 with sparse part having weight 29252220.
Pruned matrix : 269922 x 271680 with weight 15139323.
Total sieving time: 10.49 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 1.61 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 12.56 hours.
 --------- CPU info (if available) ----------

(29·10¹⁴⁹+61)/9 = 3(2)₁₄₈9_<150> = 89 · 829 · 138445203817_<12> · 175012803491_<12> · C123

C123 = P51 · P72

P51 = 635113194319765417239064874330432842193149404260779_<51>

P72 = 283799796263498656912659353956895657512659811644817238669954795620677593_<72>

Number: 32229_149
N=180244995152209257871068513860892740771751549462287974955233441702277009188183769637702407052589249184897134811269254024947
  ( 123 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=635113194319765417239064874330432842193149404260779 (pp51)
 r2=283799796263498656912659353956895657512659811644817238669954795620677593 (pp72)
Version: GGNFS-0.77.1-20060513-k8
Total time: 23.35 hours.
Scaled time: 46.77 units (timescale=2.003).
Factorization parameters were as follows:
name: 32229_149
n: 180244995152209257871068513860892740771751549462287974955233441702277009188183769637702407052589249184897134811269254024947
m: 500000000000000000000000000000
deg: 5
c5: 464
c0: 305
skew: 0.92
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1850001)
Primes: RFBsize:169511, AFBsize:169392, largePrimes:7334238 encountered
Relations: rels:7738710, finalFF:851885
Max relations in full relation-set: 28
Initial matrix: 338969 x 851885 with sparse part having weight 94817796.
Pruned matrix : 226765 x 228523 with weight 32842570.
Total sieving time: 22.25 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.76 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 23.35 hours.
 --------- CPU info (if available) ----------

Nov 17, 2008 (3rd)

By Jo Yeong Uk / GGNFS, GMP-ECM

(29·10¹²⁹+43)/9 = 3(2)₁₂₈7_<130> = 7 · 306239 · 718373555133336532322597_<24> · C100

C100 = P42 · P59

P42 = 197169997628234206028002430469013231337207_<42>

P59 = 10612208709773598061794748776121946417518003303981281232681_<59>

Number: 32227_129
N=2092409166136386713511344885436572573281938920501205545052096177131300751195392629414994502939661967
  ( 100 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=197169997628234206028002430469013231337207 (pp42)
 r2=10612208709773598061794748776121946417518003303981281232681 (pp59)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.60 hours.
Scaled time: 6.17 units (timescale=2.374).
Factorization parameters were as follows:
n: 2092409166136386713511344885436572573281938920501205545052096177131300751195392629414994502939661967
m: 100000000000000000000000000
deg: 5
c5: 29
c0: 430
skew: 1.71
type: snfs
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [550000, 1100001)
Primes: RFBsize:85714, AFBsize:85644, largePrimes:2923915 encountered
Relations: rels:2858952, finalFF:236548
Max relations in full relation-set: 28
Initial matrix: 171423 x 236548 with sparse part having weight 19778267.
Pruned matrix : 153220 x 154141 with weight 10177188.
Total sieving time: 2.46 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 2.60 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(29·10¹⁴⁵+43)/9 = 3(2)₁₄₄7_<146> = 37 · 1213 · 478417 · 503297 · 2951288533_<10> · C121

C121 = P32 · P89

P32 = 10247291001622018635859955972609_<32>

P89 = 98591909628755490844286807124291083231007250711599438141935321983826363535987763218040039_<89>

GMP-ECM 6.2.1 [powered by GMP 4.2.3] [ECM]
Input number is 1010299988371477397292104639607664043256850275108263217380788857381139510032913034000182354177943480725818782472949291751 (121 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1291799851
Step 1 took 4555ms
Step 2 took 4149ms
********** Factor found in step 2: 10247291001622018635859955972609
Found probable prime factor of 32 digits: 10247291001622018635859955972609
Probable prime cofactor 98591909628755490844286807124291083231007250711599438141935321983826363535987763218040039 has 89 digits

(29·10¹³¹+61)/9 = 3(2)₁₃₀9_<132> = 241 · 338610521 · C121

C121 = P41 · P81

P41 = 14968664333421247762182979421624958274117_<41>

P81 = 263787947249239008750674692352237210954998800730439204974507833660087043354398217_<81>

Number: 32229_131
N=3948553237576089494148082911757301899278468894475833811454137708324984302175421052876280537476334555392850421077462049389
  ( 121 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=14968664333421247762182979421624958274117 (pp41)
 r2=263787947249239008750674692352237210954998800730439204974507833660087043354398217 (pp81)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.55 hours.
Scaled time: 6.09 units (timescale=2.388).
Factorization parameters were as follows:
n: 3948553237576089494148082911757301899278468894475833811454137708324984302175421052876280537476334555392850421077462049389
m: 100000000000000000000000000
deg: 5
c5: 290
c0: 61
skew: 0.73
type: snfs
rlim: 1200000
alim: 1200000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [600000, 1100001)
Primes: RFBsize:92938, AFBsize:93085, largePrimes:2913374 encountered
Relations: rels:2807722, finalFF:218137
Max relations in full relation-set: 28
Initial matrix: 186090 x 218137 with sparse part having weight 17086563.
Pruned matrix : 174542 x 175536 with weight 11234838.
Total sieving time: 2.38 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,47,47,2.3,2.3,50000
total time: 2.55 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(29·10¹³⁴+43)/9 = 3(2)₁₃₃7_<135> = 3 · C135

C135 = P41 · P94

P41 = 24372631993284051383227862131227688564753_<41>

P94 = 4406885864317149925873449272788362430802606540713671318887298946932319069202758466259102283553_<94>

Number: 32227_134
N=107407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407409
  ( 135 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=24372631993284051383227862131227688564753 (pp41)
 r2=4406885864317149925873449272788362430802606540713671318887298946932319069202758466259102283553 (pp94)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.94 hours.
Scaled time: 9.40 units (timescale=2.385).
Factorization parameters were as follows:
n: 107407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407409
m: 1000000000000000000000000000
deg: 5
c5: 29
c0: 430
skew: 1.71
type: snfs
rlim: 1400000
alim: 1400000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [700000, 1500001)
Primes: RFBsize:107126, AFBsize:107158, largePrimes:3362035 encountered
Relations: rels:3311708, finalFF:255252
Max relations in full relation-set: 28
Initial matrix: 214349 x 255252 with sparse part having weight 22476192.
Pruned matrix : 201959 x 203094 with weight 15236621.
Total sieving time: 3.69 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,26,26,48,48,2.3,2.3,50000
total time: 3.94 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Nov 17, 2008 (2nd)

By Serge Batalov / PFGW

(28·10¹⁸⁷⁹¹+71)/9 = 3(1)₁₈₇₉₀9_<18792> is PRP.

(28·10²⁰⁷⁶³+71)/9 = 3(1)₂₀₇₆₂9_<20764> is PRP.

Nov 17, 2008

By Robert Backstrom / GMP-ECM

(29·10¹³¹+43)/9 = 3(2)₁₃₀7_<132> = 3² · C131

C131 = P31 · P37 · P63

P31 = 7584921469716321237382514976833_<31>

P37 = 8330184288131855349587745711089547313_<37>

P63 = 566640068052964565594590690160024017167002613447500354812611307_<63>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 35802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135803 (131 digits)
Using B1=472000, B2=348010752, polynomial Dickson(3), sigma=3433028033
Step 1 took 4547ms
Step 2 took 2187ms
********** Factor found in step 2: 7584921469716321237382514976833
Found probable prime factor of 31 digits: 7584921469716321237382514976833
Composite cofactor 4720216191920770700400352407972835561265887236702533952800013993816315322996122970739370238055268091 has 100 digits

Number: n
N=4720216191920770700400352407972835561265887236702533952800013993816315322996122970739370238055268091
  ( 100 digits)
Divisors found:

 r1=8330184288131855349587745711089547313 (pp37)
 r2=566640068052964565594590690160024017167002613447500354812611307 (pp63)

Ggnfs  : 0.77.1-20051202-athlon
Msieve : 1.38
Total time:  3.78 hours.
Scaled time: 6.91 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_3_2_130_7
n: 4720216191920770700400352407972835561265887236702533952800013993816315322996122970739370238055268091
skew: 2650.89
# norm 7.14e+12
c5: 61800
c4: 170288854
c3: -1889121659039
c2: -933543355282307
c1: 5169234448736335351
c0: 141071289371110253349
# alpha -3.69
Y1: 14551090609
Y0: -9475329373998954166
# Murphy_E 3.22e-09
# M 2632774819720813873582616960242094899627781404542663414337763497216335352857576220471051099846799530
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1500000)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4318987
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 195671 x 195919
Total sieving time: 3.78 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 3.78 hours.
 --------- CPU info (if available) ----------

Nov 16, 2008 (13th)

By Jo Yeong Uk / GGNFS

(29·10¹³⁰+61)/9 = 3(2)₁₂₉9_<131> = 3⁴ · 9677 · 23747 · C121

C121 = P29 · P92

P29 = 79670731472298078269193701411_<29>

P92 = 21728121032288311484210768531278542120403106435158017147982447424462035210929072787288822001_<92>

Number: 32229_130
N=1731095296161034186652985668204719951318539695468105962876040531421889024048732585255272712583375416756926743955121543411
  ( 121 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=79670731472298078269193701411 (pp29)
 r2=21728121032288311484210768531278542120403106435158017147982447424462035210929072787288822001 (pp92)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.36 hours.
Scaled time: 5.59 units (timescale=2.369).
Factorization parameters were as follows:
n: 1731095296161034186652985668204719951318539695468105962876040531421889024048732585255272712583375416756926743955121543411
m: 100000000000000000000000000
deg: 5
c5: 29
c0: 61
skew: 1.16
type: snfs
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [550000, 1050001)
Primes: RFBsize:85714, AFBsize:85120, largePrimes:2938526 encountered
Relations: rels:2911673, finalFF:271253
Max relations in full relation-set: 28
Initial matrix: 170899 x 271253 with sparse part having weight 22254580.
Pruned matrix : 141772 x 142690 with weight 9219822.
Total sieving time: 2.21 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 2.36 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Nov 17, 2008 (12th)

By Sinkiti Sibata /

(29·10¹⁵²-11)/9 = 3(2)₁₅₁1_<153> = 3³ · 977 · 1307 · 94219 · 548062798963_<12> · 22854258046007_<14> · C115

C115 = P40 · P76

P40 = 4717553768781855497144740383059502295079_<40>

P76 = 1678683310635184185657719324978438526481246512191333254586664692875578138677_<76>

Number: 32221_152
N=7919278778678215402808835942419335646076742583669425379121773732292567486392354026273870461341449652731280436670483
  ( 115 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=4717553768781855497144740383059502295079
 r2=1678683310635184185657719324978438526481246512191333254586664692875578138677
Version: 
Total time: 27.99 hours.
Scaled time: 55.20 units (timescale=1.972).
Factorization parameters were as follows:
name: 32221_152
n: 7919278778678215402808835942419335646076742583669425379121773732292567486392354026273870461341449652731280436670483
m: 2000000000000000000000000000000
deg: 5
c5: 725
c0: -88
skew: 0.66
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 421269 x 421517
Total sieving time: 27.99 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 27.99 hours.
 --------- CPU info (if available) ----------

Nov 16, 2008 (11th)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38

(29·10¹⁵⁹+61)/9 = 3(2)₁₅₈9_<160> = 284253271 · 8753968849_<10> · C142

C142 = P33 · P109

P33 = 923043599565278593919200163621863_<33>

P109 = 1402887370268419205442411169734934628646967237570845327816811121807097837271907420111192258792588754204879877_<109>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3890356734
Step 1 took 48566ms
Step 2 took 17644ms
********** Factor found in step 2: 923043599565278593919200163621863
Found probable prime factor of 33 digits: 923043599565278593919200163621863
Probable prime cofactor 1402887370268419205442411169734934628646967237570845327816811121807097837271907420111192258792588754204879877 has 109 digits

(29·10¹⁵⁰+43)/9 = 3(2)₁₄₉7_<151> = 83 · C149

C149 = P68 · P82

P68 = 13184528625225371145509156973829622318872182632582330804323609162489_<68>

P82 = 2944508339139919747974481716312002253485663596863910707778125382058769232843539721_<82>

SNFS difficulty: 151 digits.
Divisors found:
 r1=13184528625225371145509156973829622318872182632582330804323609162489 (pp68)
 r2=2944508339139919747974481716312002253485663596863910707778125382058769232843539721 (pp82)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.725).
Factorization parameters were as follows:
n: 38821954484605087014725568942436412315930388219544846050870147255689424364123159303882195448460508701472556894243641231593038821954484605087014725569
m: 1000000000000000000000000000000
deg: 5
c5: 29
c0: 43
skew: 1.08
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [1150000, 1650001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 515146 x 515385
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,54,54,2.5,2.5,100000
total time: 13.00 hours.

Nov 16, 2008 (10th)

By Robert Backstrom /

(29·10¹¹⁶+43)/9 = 3(2)₁₁₅7_<117> = 3 · 3037 · 4339 · 29873118019_<11> · C99

C99 = P41 · P58

P41 = 99874899971989533339685090697244290059031_<41>

P58 = 2731887932168763902826965323517225176982061431632091727067_<58>

Number: n
N=272847033960040622074723079272278317230415122000585289300524483935019799965138736854378204170492077
  ( 99 digits)
SNFS difficulty: 117 digits.
Divisors found:

 r1=99874899971989533339685090697244290059031 (pp41)
 r2=2731887932168763902826965323517225176982061431632091727067 (pp58)

Ggnfs  : 0.77.1-20051202-athlon
Msieve : 1.38
Total time:  1.15 hours.
Scaled time: 2.10 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_3_2_115_7
n: 272847033960040622074723079272278317230415122000585289300524483935019799965138736854378204170492077
type: snfs
skew: 0.68
deg: 5
c5: 290
c0: 43
m: 100000000000000000000000
rlim: 500000
alim: 500000
lpbr: 27
lpba: 27
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved algebraic special-q in [250000, 390000)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4115193
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 98798 x 99046
Total sieving time: 1.15 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,500000,500000,27,27,54,54,2.5,2.5,50000
total time: 1.15 hours.
 --------- CPU info (if available) ----------

Nov 16, 2008 (9th)

By Sinkiti Sibata / GGNFS, Msieve

(29·10¹⁴⁵+61)/9 = 3(2)₁₄₄9_<146> = 3 · 13 · 163 · 96893 · 145056683 · C129

C129 = P34 · P34 · P62

P34 = 1598708070484988358112518328305521_<34>

P34 = 3121609285825117168137150203040509_<34>

P62 = 72264569656054347511539909116190943810928844213628642438944667_<62>

Number: 32229_145
N=360639366956156084287866810171610783624733976547008333737357618447101472770979423032269917976079514554428256628648259060290992063
  ( 129 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=1598708070484988358112518328305521 (pp34)
 r2=3121609285825117168137150203040509 (pp34)
 r3=72264569656054347511539909116190943810928844213628642438944667 (pp62)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 12.90 hours.
Scaled time: 12.94 units (timescale=1.003).
Factorization parameters were as follows:
name: 32229_145
n: 360639366956156084287866810171610783624733976547008333737357618447101472770979423032269917976079514554428256628648259060290992063
m: 100000000000000000000000000000
deg: 5
c5: 29
c0: 61
skew: 1.16
type: snfs
lss: 1
rlim: 1930000
alim: 1930000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1930000/1930000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [965000, 2265001)
Primes: RFBsize:144125, AFBsize:143518, largePrimes:4161349 encountered
Relations: rels:4324735, finalFF:378250
Max relations in full relation-set: 28
Initial matrix: 287708 x 378250 with sparse part having weight 38595962.
Pruned matrix : 256620 x 258122 with weight 23578229.
Total sieving time: 12.36 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1930000,1930000,26,26,49,49,2.3,2.3,100000
total time: 12.90 hours.
 --------- CPU info (if available) ----------

(29·10¹²⁵+43)/9 = 3(2)₁₂₄7_<126> = 3 · 89 · 6620287 · 441521601703305421777_<21> · C96

C96 = P38 · P58

P38 = 56859860542308708942407652168957800861_<38>

P58 = 7261221136568621182260260341158450281310685998983145054179_<58>

Sun Nov 16 13:04:27 2008  Msieve v. 1.38
Sun Nov 16 13:04:27 2008  random seeds: c8c1a59c 298fb242
Sun Nov 16 13:04:27 2008  factoring 412872021192156140734203756448061606220965801339505983006757502536443923903739248267452537848119 (96 digits)
Sun Nov 16 13:04:28 2008  searching for 15-digit factors
Sun Nov 16 13:04:30 2008  commencing quadratic sieve (96-digit input)
Sun Nov 16 13:04:30 2008  using multiplier of 1
Sun Nov 16 13:04:30 2008  using 32kb Intel Core sieve core
Sun Nov 16 13:04:30 2008  sieve interval: 36 blocks of size 32768
Sun Nov 16 13:04:30 2008  processing polynomials in batches of 6
Sun Nov 16 13:04:30 2008  using a sieve bound of 2259407 (83529 primes)
Sun Nov 16 13:04:30 2008  using large prime bound of 338911050 (28 bits)
Sun Nov 16 13:04:30 2008  using double large prime bound of 2260238461776000 (43-52 bits)
Sun Nov 16 13:04:30 2008  using trial factoring cutoff of 52 bits
Sun Nov 16 13:04:30 2008  polynomial 'A' values have 12 factors
Sun Nov 16 18:14:23 2008  83838 relations (19958 full + 63880 combined from 1275546 partial), need 83625
Sun Nov 16 18:14:25 2008  begin with 1295504 relations
Sun Nov 16 18:14:26 2008  reduce to 223204 relations in 10 passes
Sun Nov 16 18:14:26 2008  attempting to read 223204 relations
Sun Nov 16 18:14:29 2008  recovered 223204 relations
Sun Nov 16 18:14:29 2008  recovered 209662 polynomials
Sun Nov 16 18:14:30 2008  attempting to build 83838 cycles
Sun Nov 16 18:14:30 2008  found 83838 cycles in 7 passes
Sun Nov 16 18:14:30 2008  distribution of cycle lengths:
Sun Nov 16 18:14:30 2008     length 1 : 19958
Sun Nov 16 18:14:30 2008     length 2 : 14066
Sun Nov 16 18:14:30 2008     length 3 : 13727
Sun Nov 16 18:14:30 2008     length 4 : 11385
Sun Nov 16 18:14:30 2008     length 5 : 8736
Sun Nov 16 18:14:30 2008     length 6 : 6200
Sun Nov 16 18:14:30 2008     length 7 : 3978
Sun Nov 16 18:14:30 2008     length 9+: 5788
Sun Nov 16 18:14:30 2008  largest cycle: 21 relations
Sun Nov 16 18:14:30 2008  matrix is 83529 x 83838 (23.5 MB) with weight 5822185 (69.45/col)
Sun Nov 16 18:14:30 2008  sparse part has weight 5822185 (69.45/col)
Sun Nov 16 18:14:31 2008  filtering completed in 3 passes
Sun Nov 16 18:14:31 2008  matrix is 80047 x 80111 (22.5 MB) with weight 5581828 (69.68/col)
Sun Nov 16 18:14:31 2008  sparse part has weight 5581828 (69.68/col)
Sun Nov 16 18:14:31 2008  saving the first 48 matrix rows for later
Sun Nov 16 18:14:32 2008  matrix is 79999 x 80111 (16.0 MB) with weight 4614078 (57.60/col)
Sun Nov 16 18:14:32 2008  sparse part has weight 3704461 (46.24/col)
Sun Nov 16 18:14:32 2008  matrix includes 64 packed rows
Sun Nov 16 18:14:32 2008  using block size 32044 for processor cache size 1024 kB
Sun Nov 16 18:14:32 2008  commencing Lanczos iteration
Sun Nov 16 18:14:32 2008  memory use: 14.3 MB
Sun Nov 16 18:15:26 2008  lanczos halted after 1267 iterations (dim = 79997)
Sun Nov 16 18:15:26 2008  recovered 17 nontrivial dependencies
Sun Nov 16 18:15:29 2008  prp38 factor: 56859860542308708942407652168957800861
Sun Nov 16 18:15:29 2008  prp58 factor: 7261221136568621182260260341158450281310685998983145054179
Sun Nov 16 18:15:29 2008  elapsed time 05:11:02

(29·10¹³²+61)/9 = 3(2)₁₃₁9_<133> = 19 · 47903 · 2492909802066469_<16> · C112

C112 = P46 · P67

P46 = 1160506834037004778363069891034036545878599561_<46>

P67 = 1223728028587715881592422848454136462283332040500297843381391947533_<67>

Number: 32229_132
N=1420144740178675433512906399968811958294246897026011140899170620946895100478122156953533633651982314156428833013
  ( 112 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=1160506834037004778363069891034036545878599561 (pp46)
 r2=1223728028587715881592422848454136462283332040500297843381391947533 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.34 hours.
Scaled time: 6.41 units (timescale=1.011).
Factorization parameters were as follows:
name: 32229_132
n: 1420144740178675433512906399968811958294246897026011140899170620946895100478122156953533633651982314156428833013
m: 200000000000000000000000000
deg: 5
c5: 725
c0: 488
skew: 0.92
type: snfs
lss: 1
rlim: 1210000
alim: 1210000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1210000/1210000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [605000, 1280001)
Primes: RFBsize:93614, AFBsize:94015, largePrimes:3067360 encountered
Relations: rels:3002294, finalFF:240316
Max relations in full relation-set: 28
Initial matrix: 187696 x 240316 with sparse part having weight 20724710.
Pruned matrix : 172796 x 173798 with weight 12064795.
Total sieving time: 6.13 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1210000,1210000,26,26,47,47,2.3,2.3,75000
total time: 6.34 hours.
 --------- CPU info (if available) ----------

(29·10¹³³+43)/9 = 3(2)₁₃₂7_<134> = 37 · 2081 · 103963 · 2134514597004855986172183061829_<31> · C94

C94 = P43 · P51

P43 = 3775743651125883485686895208096141403943177_<43>

P51 = 499460619014383808795366865959525045010382778481929_<51>

Sun Nov 16 13:14:08 2008  Msieve v. 1.38
Sun Nov 16 13:14:08 2008  random seeds: 1ebe208c e5af2b58
Sun Nov 16 13:14:08 2008  factoring 1885835261230963387421169407174891911074651744191347548716932886403570847964280662066637348433 (94 digits)
Sun Nov 16 13:14:10 2008  searching for 15-digit factors
Sun Nov 16 13:14:11 2008  commencing quadratic sieve (94-digit input)
Sun Nov 16 13:14:12 2008  using multiplier of 1
Sun Nov 16 13:14:12 2008  using 64kb Pentium 4 sieve core
Sun Nov 16 13:14:12 2008  sieve interval: 18 blocks of size 65536
Sun Nov 16 13:14:12 2008  processing polynomials in batches of 6
Sun Nov 16 13:14:12 2008  using a sieve bound of 1984331 (74118 primes)
Sun Nov 16 13:14:12 2008  using large prime bound of 255978699 (27 bits)
Sun Nov 16 13:14:12 2008  using double large prime bound of 1363850668591515 (42-51 bits)
Sun Nov 16 13:14:12 2008  using trial factoring cutoff of 51 bits
Sun Nov 16 13:14:12 2008  polynomial 'A' values have 12 factors
Sun Nov 16 18:51:29 2008  74241 relations (17907 full + 56334 combined from 1041351 partial), need 74214
Sun Nov 16 18:51:33 2008  begin with 1059258 relations
Sun Nov 16 18:51:34 2008  reduce to 194588 relations in 11 passes
Sun Nov 16 18:51:34 2008  attempting to read 194588 relations
Sun Nov 16 18:51:41 2008  recovered 194588 relations
Sun Nov 16 18:51:41 2008  recovered 179574 polynomials
Sun Nov 16 18:51:41 2008  attempting to build 74241 cycles
Sun Nov 16 18:51:42 2008  found 74241 cycles in 6 passes
Sun Nov 16 18:51:42 2008  distribution of cycle lengths:
Sun Nov 16 18:51:42 2008     length 1 : 17907
Sun Nov 16 18:51:42 2008     length 2 : 12882
Sun Nov 16 18:51:42 2008     length 3 : 12370
Sun Nov 16 18:51:42 2008     length 4 : 10061
Sun Nov 16 18:51:42 2008     length 5 : 7799
Sun Nov 16 18:51:42 2008     length 6 : 5175
Sun Nov 16 18:51:42 2008     length 7 : 3426
Sun Nov 16 18:51:42 2008     length 9+: 4621
Sun Nov 16 18:51:42 2008  largest cycle: 23 relations
Sun Nov 16 18:51:42 2008  matrix is 74118 x 74241 (18.5 MB) with weight 4540294 (61.16/col)
Sun Nov 16 18:51:42 2008  sparse part has weight 4540294 (61.16/col)
Sun Nov 16 18:51:43 2008  filtering completed in 3 passes
Sun Nov 16 18:51:43 2008  matrix is 70904 x 70968 (17.8 MB) with weight 4369985 (61.58/col)
Sun Nov 16 18:51:43 2008  sparse part has weight 4369985 (61.58/col)
Sun Nov 16 18:51:44 2008  saving the first 48 matrix rows for later
Sun Nov 16 18:51:44 2008  matrix is 70856 x 70968 (10.5 MB) with weight 3286505 (46.31/col)
Sun Nov 16 18:51:44 2008  sparse part has weight 2322199 (32.72/col)
Sun Nov 16 18:51:44 2008  matrix includes 64 packed rows
Sun Nov 16 18:51:44 2008  using block size 21845 for processor cache size 512 kB
Sun Nov 16 18:51:45 2008  commencing Lanczos iteration
Sun Nov 16 18:51:45 2008  memory use: 10.8 MB
Sun Nov 16 18:52:43 2008  lanczos halted after 1122 iterations (dim = 70852)
Sun Nov 16 18:52:44 2008  recovered 13 nontrivial dependencies
Sun Nov 16 18:52:46 2008  prp43 factor: 3775743651125883485686895208096141403943177
Sun Nov 16 18:52:46 2008  prp51 factor: 499460619014383808795366865959525045010382778481929
Sun Nov 16 18:52:46 2008  elapsed time 05:38:38

(29·10¹³³+61)/9 = 3(2)₁₃₂9_<134> = 3 · 13 · 582167 · 1731979 · 5736235911224029_<16> · C105

C105 = P26 · P37 · P43

P26 = 82102399405226866715133641_<26>

P37 = 1695378156926123401429032448812952661_<37>

P43 = 1026245436017454986714853921405601157067463_<43>

Number: 32229_133
N=142847837933854366350820670655655652951557243538670005984715501589767377406377382448365027428597346275563
  ( 105 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=82102399405226866715133641 (pp26)
 r2=1695378156926123401429032448812952661 (pp37)
 r3=1026245436017454986714853921405601157067463 (pp43)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.46 hours.
Scaled time: 6.46 units (timescale=1.000).
Factorization parameters were as follows:
name: 32229_133
n: 142847837933854366350820670655655652951557243538670005984715501589767377406377382448365027428597346275563
m: 500000000000000000000000000
deg: 5
c5: 232
c0: 1525
skew: 1.46
type: snfs
lss: 1
rlim: 1290000
alim: 1290000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1290000/1290000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [645000, 1320001)
Primes: RFBsize:99332, AFBsize:99274, largePrimes:3176509 encountered
Relations: rels:3103563, finalFF:236151
Max relations in full relation-set: 28
Initial matrix: 198673 x 236151 with sparse part having weight 20552066.
Pruned matrix : 187588 x 188645 with weight 13829174.
Total sieving time: 6.20 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1290000,1290000,26,26,47,47,2.3,2.3,75000
total time: 6.46 hours.
 --------- CPU info (if available) ----------

Nov 16, 2008 (8th)

By Jo Yeong Uk / GGNFS, Msieve

(29·10¹¹⁵+61)/9 = 3(2)₁₁₄9_<116> = 3 · 13 · 151 · 229 · 673 · C107

C107 = P43 · P65

P43 = 1063452127633539612140587509270470321829037_<43>

P65 = 33384543579129404191599943967015786740223790494495006249744297909_<65>

Number: 32229_115
N=35502863899299788486411859804062433981468144340963035042836030019285950199708977711430221600636122294583633
  ( 107 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=1063452127633539612140587509270470321829037 (pp43)
 r2=33384543579129404191599943967015786740223790494495006249744297909 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.85 hours.
Scaled time: 2.01 units (timescale=2.375).
Factorization parameters were as follows:
n: 35502863899299788486411859804062433981468144340963035042836030019285950199708977711430221600636122294583633
m: 100000000000000000000000
deg: 5
c5: 29
c0: 61
skew: 1.16
type: snfs
rlim: 500000
alim: 500000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [250000, 450001)
Primes: RFBsize:41538, AFBsize:41313, largePrimes:1204513 encountered
Relations: rels:1160406, finalFF:127665
Max relations in full relation-set: 28
Initial matrix: 82916 x 127665 with sparse part having weight 5990211.
Pruned matrix : 68199 x 68677 with weight 2335623.
Total sieving time: 0.82 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,500000,500000,25,25,45,45,2.2,2.2,25000
total time: 0.85 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(29·10¹²⁸+43)/9 = 3(2)₁₂₇7_<129> = 3 · 18439 · 3095474729470628159_<19> · C106

C106 = P39 · P68

P39 = 185807551282157802207924187206548772493_<39>

P68 = 10127593155997007580574631471356904823047086838039899837659475915613_<68>

Number: 32227_128
N=1881783284697744368427137799251912955332064804310096537998332492135742752227798084851148356130562403633209
  ( 106 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=185807551282157802207924187206548772493 (pp39)
 r2=10127593155997007580574631471356904823047086838039899837659475915613 (pp68)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.50 hours.
Scaled time: 5.99 units (timescale=2.393).
Factorization parameters were as follows:
n: 1881783284697744368427137799251912955332064804310096537998332492135742752227798084851148356130562403633209
m: 100000000000000000000000000
deg: 5
c5: 29
c0: 4300
skew: 2.72
type: snfs
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [550000, 1100001)
Primes: RFBsize:85714, AFBsize:85364, largePrimes:2902642 encountered
Relations: rels:2851314, finalFF:251074
Max relations in full relation-set: 28
Initial matrix: 171145 x 251074 with sparse part having weight 20525122.
Pruned matrix : 148506 x 149425 with weight 9532221.
Total sieving time: 2.38 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 2.50 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(29·10¹⁴³+61)/9 = 3(2)₁₄₂9_<144> = 251 · 11633 · 681557 · 33617387310889_<14> · 25135555715017400562491_<23> · C96

C96 = P47 · P49

P47 = 53090111509500046699970834294540168315452678951_<47>

P49 = 3609289928327873103344992856542781257387147830791_<49>

Sun Nov 16 15:51:06 2008  
Sun Nov 16 15:51:06 2008  
Sun Nov 16 15:51:06 2008  Msieve v. 1.32
Sun Nov 16 15:51:06 2008  random seeds: 9ccb8280 d7bc4d77
Sun Nov 16 15:51:06 2008  factoring 
191617604765042214487285873627042372065144419378891933069732010892507288599184754668089395380241 
(96 digits)
Sun Nov 16 15:51:07 2008  no P-1/P+1/ECM available, skipping
Sun Nov 16 15:51:07 2008  commencing quadratic sieve (95-digit input)
Sun Nov 16 15:51:07 2008  using multiplier of 1
Sun Nov 16 15:51:07 2008  using VC8 32kb sieve core
Sun Nov 16 15:51:07 2008  sieve interval: 36 blocks of size 32768
Sun Nov 16 15:51:07 2008  processing polynomials in batches of 6
Sun Nov 16 15:51:07 2008  using a sieve bound of 2231357 (82229 primes)
Sun Nov 16 15:51:07 2008  using large prime bound of 334703550 (28 bits)
Sun Nov 16 15:51:07 2008  using double large prime bound of 2209980934643550 (43-51 bits)
Sun Nov 16 15:51:07 2008  using trial factoring cutoff of 51 bits
Sun Nov 16 15:51:07 2008  polynomial 'A' values have 12 factors
Sun Nov 16 19:33:07 2008  82402 relations (19628 full + 62774 combined from 1248672 partial), need 
82325
Sun Nov 16 19:33:14 2008  begin with 1268300 relations
Sun Nov 16 19:33:15 2008  reduce to 217896 relations in 11 passes
Sun Nov 16 19:33:15 2008  attempting to read 217896 relations
Sun Nov 16 19:33:17 2008  recovered 217896 relations
Sun Nov 16 19:33:17 2008  recovered 204851 polynomials
Sun Nov 16 19:33:18 2008  attempting to build 82402 cycles
Sun Nov 16 19:33:18 2008  found 82402 cycles in 6 passes
Sun Nov 16 19:33:18 2008  distribution of cycle lengths:
Sun Nov 16 19:33:18 2008     length 1 : 19628
Sun Nov 16 19:33:18 2008     length 2 : 14107
Sun Nov 16 19:33:18 2008     length 3 : 13863
Sun Nov 16 19:33:18 2008     length 4 : 11127
Sun Nov 16 19:33:18 2008     length 5 : 8442
Sun Nov 16 19:33:18 2008     length 6 : 5983
Sun Nov 16 19:33:18 2008     length 7 : 3779
Sun Nov 16 19:33:18 2008     length 9+: 5473
Sun Nov 16 19:33:18 2008  largest cycle: 26 relations
Sun Nov 16 19:33:18 2008  matrix is 82229 x 82402 with weight 5568133 (avg 67.57/col)
Sun Nov 16 19:33:18 2008  filtering completed in 3 passes
Sun Nov 16 19:33:18 2008  matrix is 78797 x 78861 with weight 5364790 (avg 68.03/col)
Sun Nov 16 19:33:19 2008  saving the first 48 matrix rows for later
Sun Nov 16 19:33:19 2008  matrix is 78749 x 78861 with weight 4403567 (avg 55.84/col)
Sun Nov 16 19:33:19 2008  matrix includes 64 packed rows
Sun Nov 16 19:33:19 2008  using block size 31544 for processor cache size 4096 kB
Sun Nov 16 19:33:19 2008  commencing Lanczos iteration
Sun Nov 16 19:33:53 2008  lanczos halted after 1247 iterations (dim = 78749)
Sun Nov 16 19:33:53 2008  recovered 17 nontrivial dependencies
Sun Nov 16 19:33:55 2008  prp47 factor: 53090111509500046699970834294540168315452678951
Sun Nov 16 19:33:55 2008  prp49 factor: 3609289928327873103344992856542781257387147830791
Sun Nov 16 19:33:55 2008  elapsed time 03:42:49

Nov 16, 2008 (7th)

By matsui / GMP-ECM

(5·10¹⁷⁷-41)/9 = (5)₁₇₆1_<177> = 149 · 1019 · C172

C172 = P38 · P134

P38 = 45582849447613703454457875647438960999_<38>

P134 = 80272275170111359836295192620380467552432000219410208483930158874634645594592204074048358771739052488635823849168122734568346120654879_<134>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]

3659039033896605802211376830525752682624467701296543891270923299955579266128495205561153885277417362432938962106259957159970991138539267709200068204487591832732153220064121
=
45582849447613703454457875647438960999* 80272275170111359836295192620380467552432000219410208483930158874634645594592204074048358771739052488635823849168122734568346120654879

Nov 16, 2008 (6th)

By Justin Card / ggnfs/msieve

(29·10¹¹²+61)/9 = 3(2)₁₁₁9_<113> = 3² · 306034303429_<12> · C101

C101 = P44 · P57

P44 = 21348808706404288248596941574025542992564873_<44>

P57 = 547985698001970931910634724148480216575854589619614950593_<57>

Sat Nov 15 18:09:25 2008
Sat Nov 15 18:09:25 2008
Sat Nov 15 18:09:25 2008  Msieve v. 1.38
Sat Nov 15 18:09:25 2008  random seeds: 218a7e97 15c2ba48
Sat Nov 15 18:09:25 2008  factoring 11698841840489508014434081186604843067304024535141148500613325712108587327498587470710278150242319689 (101 digits)
Sat Nov 15 18:09:26 2008  no P-1/P+1/ECM available, skipping
Sat Nov 15 18:09:26 2008  commencing number field sieve (101-digit input)
Sat Nov 15 18:09:26 2008  R0: -20000000000000000000000
Sat Nov 15 18:09:26 2008  R1:  1
Sat Nov 15 18:09:26 2008  A0:  488
Sat Nov 15 18:09:26 2008  A1:  0
Sat Nov 15 18:09:26 2008  A2:  0
Sat Nov 15 18:09:26 2008  A3:  0
Sat Nov 15 18:09:26 2008  A4:  0
Sat Nov 15 18:09:26 2008  A5:  725
Sat Nov 15 18:09:26 2008  size score = 2.241186e-08, Murphy alpha = 0.280014, combined = 2.041464e-08
Sat Nov 15 18:09:26 2008  generating factor base
Sat Nov 15 18:09:26 2008  factor base complete:
Sat Nov 15 18:09:26 2008  46072 rational roots (max prime = 559991)
Sat Nov 15 18:09:26 2008  46427 algebraic roots (max prime = 559973)
Sat Nov 15 18:09:26 2008  a range: [-2000000, 2000000]
Sat Nov 15 18:09:26 2008  b range: [1, 200]
Sat Nov 15 18:09:26 2008  number of hash buckets: 9
Sat Nov 15 18:09:26 2008  sieve block size: 65536
Sat Nov 15 18:09:26 2008
Sat Nov 15 18:09:26 2008  maximum RFB prime: 559991
Sat Nov 15 18:09:26 2008  RFB entries: 46072
Sat Nov 15 18:09:26 2008  medium RFB entries: 6542
Sat Nov 15 18:09:26 2008  resieved RFB entries: 6374
Sat Nov 15 18:09:26 2008  small RFB prime powers: 28
Sat Nov 15 18:09:26 2008  projective RFB roots: 0
Sat Nov 15 18:09:26 2008  RFB trial factoring cutoff: 52 or 77 bits
Sat Nov 15 18:09:26 2008  single large prime RFB range: 19 - 25 bits
Sat Nov 15 18:09:26 2008  double large prime RFB range: 39 - 48 bits
Sat Nov 15 18:09:26 2008  triple large prime RFB range: 60 - 73 bits
Sat Nov 15 18:09:26 2008
Sat Nov 15 18:09:26 2008  maximum AFB prime: 559973
Sat Nov 15 18:09:26 2008  AFB entries: 46427
Sat Nov 15 18:09:26 2008  medium AFB entries: 6538
Sat Nov 15 18:09:26 2008  resieved AFB entries: 6349
Sat Nov 15 18:09:26 2008  small AFB prime powers: 18
Sat Nov 15 18:09:26 2008  projective AFB roots: 2
Sat Nov 15 18:09:26 2008  AFB trial factoring cutoff: 52 or 77 bits
Sat Nov 15 18:09:26 2008  single large prime AFB range: 19 - 25 bits
Sat Nov 15 18:09:26 2008  double large prime AFB range: 39 - 48 bits
Sat Nov 15 18:09:26 2008  triple large prime AFB range: 60 - 73 bits
Sat Nov 15 18:09:26 2008
Sat Nov 15 18:09:26 2008  multiplying 518093 primes from 559973 to 8388608
Sat Nov 15 18:09:28 2008  multiply complete, product has 11290805 bits
Sat Nov 15 18:10:25 2008  completed b = 200, found 22538 relations
Sat Nov 15 18:10:25 2008  elapsed time 00:01:00
-> makeJobFile(): Adjusted to q0=280000, q1=330000.
->               client 1 q0: 280000
-> makeJobFile(): Adjusted to q0=330001, q1=380000.
->               client 1 q0: 330001
-> makeJobFile(): Adjusted to q0=380001, q1=430000.
->               client 1 q0: 380001
...
Sat Nov 15 18:32:28 2008
Sat Nov 15 18:32:28 2008
Sat Nov 15 18:32:28 2008  Msieve v. 1.38
Sat Nov 15 18:32:28 2008  random seeds: f76655f8 ef663562
Sat Nov 15 18:32:28 2008  factoring 11698841840489508014434081186604843067304024535141148500613325712108587327498587470710278150242319689 (101 digits)
Sat Nov 15 18:32:29 2008  no P-1/P+1/ECM available, skipping
Sat Nov 15 18:32:29 2008  commencing number field sieve (101-digit input)
Sat Nov 15 18:32:29 2008  R0: -20000000000000000000000
Sat Nov 15 18:32:29 2008  R1:  1
Sat Nov 15 18:32:29 2008  A0:  488
Sat Nov 15 18:32:29 2008  A1:  0
Sat Nov 15 18:32:29 2008  A2:  0
Sat Nov 15 18:32:29 2008  A3:  0
Sat Nov 15 18:32:29 2008  A4:  0
Sat Nov 15 18:32:29 2008  A5:  725
Sat Nov 15 18:32:29 2008  size score = 2.241186e-08, Murphy alpha = 0.280014, combined = 2.041464e-08
Sat Nov 15 18:32:29 2008
Sat Nov 15 18:32:29 2008  commencing relation filtering
Sat Nov 15 18:32:29 2008  commencing duplicate removal, pass 1
Sat Nov 15 18:32:29 2008  error -9 reading relation 59
Sat Nov 15 18:32:44 2008  found 63675 hash collisions in 1248000 relations
Sat Nov 15 18:32:48 2008  added 7620 free relations
Sat Nov 15 18:32:48 2008  commencing duplicate removal, pass 2
Sat Nov 15 18:32:49 2008  found 63659 duplicates and 1191961 unique relations
Sat Nov 15 18:32:49 2008  memory use: 36.9 MB
Sat Nov 15 18:32:49 2008  reading rational ideals above 458752
Sat Nov 15 18:32:49 2008  reading algebraic ideals above 458752
Sat Nov 15 18:32:49 2008  commencing singleton removal, pass 1
Sat Nov 15 18:33:04 2008  relations with 0 large ideals: 17696
Sat Nov 15 18:33:04 2008  relations with 1 large ideals: 173887
Sat Nov 15 18:33:04 2008  relations with 2 large ideals: 515230
Sat Nov 15 18:33:04 2008  relations with 3 large ideals: 324501
Sat Nov 15 18:33:04 2008  relations with 4 large ideals: 79115
Sat Nov 15 18:33:04 2008  relations with 5 large ideals: 9087
Sat Nov 15 18:33:04 2008  relations with 6 large ideals: 72432
Sat Nov 15 18:33:04 2008  relations with 7+ large ideals: 13
Sat Nov 15 18:33:04 2008  1191961 relations and about 1443170 large ideals
Sat Nov 15 18:33:04 2008  commencing singleton removal, pass 2
Sat Nov 15 18:33:19 2008  found 685993 singletons
Sat Nov 15 18:33:19 2008  current dataset: 505968 relations and about 411140 large ideals
Sat Nov 15 18:33:19 2008  commencing singleton removal, pass 3
Sat Nov 15 18:33:25 2008  found 143942 singletons
Sat Nov 15 18:33:25 2008  current dataset: 362026 relations and about 255076 large ideals
Sat Nov 15 18:33:25 2008  commencing singleton removal, final pass
Sat Nov 15 18:33:29 2008  memory use: 11.7 MB
Sat Nov 15 18:33:29 2008  commencing in-memory singleton removal
Sat Nov 15 18:33:29 2008  begin with 362026 relations and 257434 unique ideals
Sat Nov 15 18:33:30 2008  reduce to 320101 relations and 214542 ideals in 9 passes
Sat Nov 15 18:33:30 2008  max relations containing the same ideal: 41
Sat Nov 15 18:33:30 2008  reading rational ideals above 229376
Sat Nov 15 18:33:30 2008  reading algebraic ideals above 229376
Sat Nov 15 18:33:30 2008  commencing singleton removal, final pass
Sat Nov 15 18:33:34 2008  keeping 285136 ideals with weight <= 20, new excess is 52070
Sat Nov 15 18:33:34 2008  memory use: 11.7 MB
Sat Nov 15 18:33:34 2008  commencing in-memory singleton removal
Sat Nov 15 18:33:34 2008  begin with 327721 relations and 285136 unique ideals
Sat Nov 15 18:33:34 2008  reduce to 320027 relations and 239459 ideals in 4 passes
Sat Nov 15 18:33:34 2008  max relations containing the same ideal: 20
Sat Nov 15 18:33:35 2008  removing 51059 relations and 40976 ideals in 10083 cliques
Sat Nov 15 18:33:35 2008  commencing in-memory singleton removal
Sat Nov 15 18:33:35 2008  begin with 268968 relations and 239459 unique ideals
Sat Nov 15 18:33:35 2008  reduce to 265294 relations and 194677 ideals in 6 passes
Sat Nov 15 18:33:35 2008  max relations containing the same ideal: 20
Sat Nov 15 18:33:35 2008  removing 38841 relations and 28758 ideals in 10083 cliques
Sat Nov 15 18:33:35 2008  commencing in-memory singleton removal
Sat Nov 15 18:33:35 2008  begin with 226453 relations and 194677 unique ideals
Sat Nov 15 18:33:35 2008  reduce to 223585 relations and 162960 ideals in 6 passes
Sat Nov 15 18:33:35 2008  max relations containing the same ideal: 20
Sat Nov 15 18:33:35 2008  relations with 0 large ideals: 5758
Sat Nov 15 18:33:35 2008  relations with 1 large ideals: 30159
Sat Nov 15 18:33:35 2008  relations with 2 large ideals: 65781
Sat Nov 15 18:33:35 2008  relations with 3 large ideals: 67806
Sat Nov 15 18:33:35 2008  relations with 4 large ideals: 37624
Sat Nov 15 18:33:35 2008  relations with 5 large ideals: 12603
Sat Nov 15 18:33:35 2008  relations with 6 large ideals: 3578
Sat Nov 15 18:33:35 2008  relations with 7+ large ideals: 276
Sat Nov 15 18:33:35 2008  commencing 2-way merge
Sat Nov 15 18:33:36 2008  reduce to 148691 relation sets and 88066 unique ideals
Sat Nov 15 18:33:36 2008  commencing full merge
Sat Nov 15 18:33:38 2008  memory use: 8.5 MB
Sat Nov 15 18:33:38 2008  found 71214 cycles, need 64266
Sat Nov 15 18:33:38 2008  weight of 64266 cycles is about 4962297 (77.21/cycle)
Sat Nov 15 18:33:38 2008  distribution of cycle lengths:
Sat Nov 15 18:33:38 2008  1 relations: 6680
Sat Nov 15 18:33:38 2008  2 relations: 4853
Sat Nov 15 18:33:38 2008  3 relations: 4936
Sat Nov 15 18:33:38 2008  4 relations: 4889
Sat Nov 15 18:33:38 2008  5 relations: 4903
Sat Nov 15 18:33:38 2008  6 relations: 4875
Sat Nov 15 18:33:38 2008  7 relations: 4593
Sat Nov 15 18:33:38 2008  8 relations: 4278
Sat Nov 15 18:33:38 2008  9 relations: 3838
Sat Nov 15 18:33:38 2008  10+ relations: 20421
Sat Nov 15 18:33:38 2008  heaviest cycle: 21 relations
Sat Nov 15 18:33:38 2008  commencing cycle optimization
Sat Nov 15 18:33:38 2008  start with 472140 relations
Sat Nov 15 18:33:39 2008  pruned 29547 relations
Sat Nov 15 18:33:39 2008  memory use: 12.9 MB
Sat Nov 15 18:33:39 2008  distribution of cycle lengths:
Sat Nov 15 18:33:39 2008  1 relations: 6680
Sat Nov 15 18:33:39 2008  2 relations: 5031
Sat Nov 15 18:33:39 2008  3 relations: 5275
Sat Nov 15 18:33:39 2008  4 relations: 5267
Sat Nov 15 18:33:39 2008  5 relations: 5379
Sat Nov 15 18:33:39 2008  6 relations: 5261
Sat Nov 15 18:33:39 2008  7 relations: 4932
Sat Nov 15 18:33:39 2008  8 relations: 4655
Sat Nov 15 18:33:39 2008  9 relations: 4114
Sat Nov 15 18:33:39 2008  10+ relations: 17672
Sat Nov 15 18:33:39 2008  heaviest cycle: 21 relations
Sat Nov 15 18:33:39 2008  elapsed time 00:01:11
Sat Nov 15 18:33:39 2008
Sat Nov 15 18:33:39 2008
Sat Nov 15 18:33:39 2008  Msieve v. 1.38
Sat Nov 15 18:33:39 2008  random seeds: bb1f69ce 1efc98ad
Sat Nov 15 18:33:39 2008  factoring 11698841840489508014434081186604843067304024535141148500613325712108587327498587470710278150242319689 (101 digits)
Sat Nov 15 18:33:40 2008  no P-1/P+1/ECM available, skipping
Sat Nov 15 18:33:40 2008  commencing number field sieve (101-digit input)
Sat Nov 15 18:33:40 2008  R0: -20000000000000000000000
Sat Nov 15 18:33:40 2008  R1:  1
Sat Nov 15 18:33:40 2008  A0:  488
Sat Nov 15 18:33:40 2008  A1:  0
Sat Nov 15 18:33:40 2008  A2:  0
Sat Nov 15 18:33:40 2008  A3:  0
Sat Nov 15 18:33:40 2008  A4:  0
Sat Nov 15 18:33:40 2008  A5:  725
Sat Nov 15 18:33:40 2008  size score = 2.241186e-08, Murphy alpha = 0.280014, combined = 2.041464e-08
Sat Nov 15 18:33:40 2008
Sat Nov 15 18:33:40 2008  commencing linear algebra
Sat Nov 15 18:33:40 2008  read 64266 cycles
Sat Nov 15 18:33:40 2008  cycles contain 194789 unique relations
Sat Nov 15 18:33:43 2008  read 194789 relations
Sat Nov 15 18:33:43 2008  using 32 quadratic characters above 33549128
Sat Nov 15 18:33:46 2008  building initial matrix
Sat Nov 15 18:33:49 2008  memory use: 30.8 MB
Sat Nov 15 18:33:49 2008  read 64266 cycles
Sat Nov 15 18:33:49 2008  matrix is 64090 x 64266 (19.8 MB) with weight 6291711 (97.90/col)
Sat Nov 15 18:33:49 2008  sparse part has weight 4485523 (69.80/col)
Sat Nov 15 18:33:50 2008  filtering completed in 2 passes
Sat Nov 15 18:33:50 2008  matrix is 63969 x 64145 (19.8 MB) with weight 6283910 (97.96/col)
Sat Nov 15 18:33:50 2008  sparse part has weight 4481088 (69.86/col)
Sat Nov 15 18:33:50 2008  read 64145 cycles
Sat Nov 15 18:33:50 2008  matrix is 63969 x 64145 (19.8 MB) with weight 6283910 (97.96/col)
Sat Nov 15 18:33:50 2008  sparse part has weight 4481088 (69.86/col)
Sat Nov 15 18:33:50 2008  saving the first 48 matrix rows for later
Sat Nov 15 18:33:50 2008  matrix is 63921 x 64145 (18.7 MB) with weight 4867505 (75.88/col)
Sat Nov 15 18:33:50 2008  sparse part has weight 4263391 (66.46/col)
Sat Nov 15 18:33:50 2008  matrix includes 64 packed rows
Sat Nov 15 18:33:50 2008  using block size 10922 for processor cache size 256 kB
Sat Nov 15 18:33:51 2008  commencing Lanczos iteration
Sat Nov 15 18:33:51 2008  memory use: 16.6 MB
Sat Nov 15 18:34:31 2008  lanczos halted after 1012 iterations (dim = 63917)
Sat Nov 15 18:34:32 2008  recovered 47 nontrivial dependencies
Sat Nov 15 18:34:32 2008  elapsed time 00:00:53
Sat Nov 15 18:34:32 2008
Sat Nov 15 18:34:32 2008
Sat Nov 15 18:34:32 2008  Msieve v. 1.38
Sat Nov 15 18:34:32 2008  random seeds: cb8bea23 c471f78a
Sat Nov 15 18:34:32 2008  factoring 11698841840489508014434081186604843067304024535141148500613325712108587327498587470710278150242319689 (101 digits)
Sat Nov 15 18:34:32 2008  no P-1/P+1/ECM available, skipping
Sat Nov 15 18:34:32 2008  commencing number field sieve (101-digit input)
Sat Nov 15 18:34:32 2008  R0: -20000000000000000000000
Sat Nov 15 18:34:32 2008  R1:  1
Sat Nov 15 18:34:32 2008  A0:  488
Sat Nov 15 18:34:32 2008  A1:  0
Sat Nov 15 18:34:32 2008  A2:  0
Sat Nov 15 18:34:32 2008  A3:  0
Sat Nov 15 18:34:32 2008  A4:  0
Sat Nov 15 18:34:32 2008  A5:  725
Sat Nov 15 18:34:32 2008  size score = 2.241186e-08, Murphy alpha = 0.280014, combined = 2.041464e-08
Sat Nov 15 18:34:32 2008
Sat Nov 15 18:34:32 2008  commencing square root phase
Sat Nov 15 18:34:32 2008  reading relations for dependency 1
Sat Nov 15 18:34:32 2008  read 32049 cycles
Sat Nov 15 18:34:33 2008  cycles contain 123676 unique relations
Sat Nov 15 18:34:34 2008  read 123676 relations
Sat Nov 15 18:34:35 2008  multiplying 97168 relations
Sat Nov 15 18:34:44 2008  multiply complete, coefficients have about 2.74 million bits
Sat Nov 15 18:34:44 2008  initial square root is modulo 2061551
Sat Nov 15 18:35:00 2008  prp44 factor: 21348808706404288248596941574025542992564873
Sat Nov 15 18:35:00 2008  prp57 factor: 547985698001970931910634724148480216575854589619614950593
Sat Nov 15 18:35:00 2008  elapsed time 00:00:28

Nov 16, 2008 (5th)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38

(29·10¹⁷⁶+61)/9 = 3(2)₁₇₅9_<177> = 7 · 134835929 · 318777664839839039_<18> · 2973592313226154031_<19> · 44151885111614554195911529_<26> · C106

C106 = P29 · P78

P29 = 13242551548213967681766393163_<29>

P78 = 615972868251949379864943710198946868352151531886241396399834277242076818280601_<78>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3363816077
Step 1 took 13026ms
Step 2 took 10539ms
********** Factor found in step 2: 13242551548213967681766393163
Found probable prime factor of 29 digits: 13242551548213967681766393163
Probable prime cofactor 615972868251949379864943710198946868352151531886241396399834277242076818280601 has 78 digits

(29·10¹⁰⁴+61)/9 = 3(2)₁₀₃9_<105> = 7 · 71 · C102

C102 = P29 · P35 · P40

P29 = 14751591942611498717745397159_<29>

P35 = 41209480987075384610005546822286843_<35>

P40 = 1066505413986600338073968613179955167561_<40>

SNFS difficulty: 105 digits.
Divisors found:
 r1=14751591942611498717745397159 (pp29)
 r2=41209480987075384610005546822286843 (pp35)
 r3=1066505413986600338073968613179955167561 (pp40)
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.712).
Factorization parameters were as follows:
n: 648334451151352559803264028616141292197630225799239883746926000447127207690587972278113123183545718757
m: 100000000000000000000000000
deg: 4
c4: 29
c0: 61
skew: 1.20
type: snfs
lss: 1
rlim: 400000
alim: 400000
lpbr: 25
lpba: 25
Factor base limits: 400000/400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [200000, 260001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 33864 x 34074
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,105,4,0,0,0,0,0,0,0,0,400000,400000,25,25,44,44,2.2,2.2,20000
total time: 0.20 hours.

(29·10¹⁷⁰+43)/9 = 3(2)₁₆₉7_<171> = 3 · C171

C171 = P34 · C137

P34 = 1954336561162450967604444406439339_<34>

C137 = [54958500773030027645652315828411893842541871854764460247889669905548548420516193561916002544292592741336996889228227378146037689161386131_<137>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2151013859
Step 1 took 25368ms
Step 2 took 16923ms
********** Factor found in step 2: 1954336561162450967604444406439339
Found probable prime factor of 34 digits: 1954336561162450967604444406439339
Composite cofactor 54958500773030027645652315828411893842541871854764460247889669905548548420516193561916002544292592741336996889228227378146037689161386131 has 137 digits

(29·10²⁰⁰+43)/9 = 3(2)₁₉₉7_<201> = 3 · 221317 · C195

C195 = P35 · C161

P35 = 16654256710134409897367986445675537_<35>

C161 = [29140312477557268243815160436071115345823312713892485599178823150597069361988015232115946254249741167966868789607546618400348250638379344509930808316538620381421_<161>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1534676880
Step 1 took 155712ms
Step 2 took 48401ms
********** Factor found in step 2: 16654256710134409897367986445675537
Found probable prime factor of 35 digits: 16654256710134409897367986445675537
Composite cofactor 29140312477557268243815160436071115345823312713892485599178823150597069361988015232115946254249741167966868789607546618400348250638379344509930808316538620381421 has 161 digits

(29·10¹⁵¹+43)/9 = 3(2)₁₅₀7_<152> = 37 · 1759 · C147

C147 = P32 · C116

P32 = 15563627912986965137034736448411_<32>

C116 = [31810982706576934772998608605741160071516082639197877089858403102494412714121865479732665846484350034366517761515179_<116>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1187595953
Step 1 took 18643ms
Step 2 took 14422ms
********** Factor found in step 2: 15563627912986965137034736448411
Found probable prime factor of 32 digits: 15563627912986965137034736448411
Composite cofactor 31810982706576934772998608605741160071516082639197877089858403102494412714121865479732665846484350034366517761515179 has 116 digits

(29·10¹⁵⁴+43)/9 = 3(2)₁₅₃7_<155> = 13 · 19 · 37 · 59 · 197 · C147

C147 = P29 · P118

P29 = 39419331049028519665646376229_<29>

P118 = 7695366765062327363947327794059688249986301193294977945234544298004013084172419459774322031488971864398013417772286379_<118>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=39788821
Step 1 took 18634ms
Step 2 took 14366ms
********** Factor found in step 2: 39419331049028519665646376229
Found probable prime factor of 29 digits: 39419331049028519665646376229
Probable prime cofactor 7695366765062327363947327794059688249986301193294977945234544298004013084172419459774322031488971864398013417772286379 has 118 digits

(29·10¹⁵⁷+43)/9 = 3(2)₁₅₆7_<158> = 37 · 18143 · 198323 · C147

C147 = P30 · C118

P30 = 120011103804224805681823546153_<30>

C118 = [2016741105866467140951604570336781152331001527925371904341000515480857002518308891930313959772708022278077300275998363_<118>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3866990487
Step 1 took 18482ms
Step 2 took 14415ms
********** Factor found in step 2: 120011103804224805681823546153
Found probable prime factor of 30 digits: 120011103804224805681823546153
Composite cofactor 2016741105866467140951604570336781152331001527925371904341000515480857002518308891930313959772708022278077300275998363 has 118 digits

(29·10¹⁵²+43)/9 = 3(2)₁₅₁7_<153> = 3 · 40296437249_<11> · C142

C142 = P29 · C114

P29 = 17122663123552071584377558151_<29>

C114 = [155666897947149516564762656348434456049373366190782014151391987567686593948726747795044131944426787108190772013191_<114>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3087136349
Step 1 took 18829ms
Step 2 took 13886ms
********** Factor found in step 2: 17122663123552071584377558151
Found probable prime factor of 29 digits: 17122663123552071584377558151
Composite cofactor 155666897947149516564762656348434456049373366190782014151391987567686593948726747795044131944426787108190772013191 has 114 digits

Nov 16, 2008 (4th)

By Sinkiti Sibata / GGNFS, Msieve

(29·10¹⁵³-11)/9 = 3(2)₁₅₂1_<154> = 53 · 1916921 · 794286653 · C137

C137 = P60 · P78

P60 = 179960253364535182856090133804477727808273167171138429030663_<60>

P78 = 221881729778503414210444550530112268200498799466442770208768757814706434720003_<78>

Number: 32221_153
N=39929892307900805319907718077544036658921544690767565938858130177962346727983580345761301594137429455745885939198391814545711703106451989
  ( 137 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=179960253364535182856090133804477727808273167171138429030663 (pp60)
 r2=221881729778503414210444550530112268200498799466442770208768757814706434720003 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 42.37 hours.
Scaled time: 42.76 units (timescale=1.009).
Factorization parameters were as follows:
name: 32221_153
n: 39929892307900805319907718077544036658921544690767565938858130177962346727983580345761301594137429455745885939198391814545711703106451989
m: 5000000000000000000000000000000
deg: 5
c5: 232
c0: -275
skew: 1.03
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2700001)
Primes: RFBsize:203362, AFBsize:202388, largePrimes:8891593 encountered
Relations: rels:10028067, finalFF:1233699
Max relations in full relation-set: 28
Initial matrix: 405817 x 1233699 with sparse part having weight 157935020.
Pruned matrix : 286415 x 288508 with weight 58412974.
Total sieving time: 41.14 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.99 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 42.37 hours.
 --------- CPU info (if available) ----------

(29·10¹⁰³+61)/9 = 3(2)₁₀₂9_<104> = 3³ · 13 · 4003 · 5901160009_<10> · C88

C88 = P32 · P57

P32 = 13955405739252974791819323206909_<32>

P57 = 278472891040044154124888430675886431365951225649379875653_<57>

Sun Nov 16 07:43:35 2008  Msieve v. 1.38
Sun Nov 16 07:43:35 2008  random seeds: 55ae4f0c d5804962
Sun Nov 16 07:43:35 2008  factoring 3886202181846600488926048772833634100539737551849176875626859169440252679270183610486577 (88 digits)
Sun Nov 16 07:43:37 2008  searching for 15-digit factors
Sun Nov 16 07:43:39 2008  commencing quadratic sieve (88-digit input)
Sun Nov 16 07:43:39 2008  using multiplier of 1
Sun Nov 16 07:43:39 2008  using 64kb Pentium 4 sieve core
Sun Nov 16 07:43:39 2008  sieve interval: 13 blocks of size 65536
Sun Nov 16 07:43:39 2008  processing polynomials in batches of 8
Sun Nov 16 07:43:39 2008  using a sieve bound of 1517707 (57413 primes)
Sun Nov 16 07:43:39 2008  using large prime bound of 121416560 (26 bits)
Sun Nov 16 07:43:39 2008  using double large prime bound of 356205104400640 (42-49 bits)
Sun Nov 16 07:43:39 2008  using trial factoring cutoff of 49 bits
Sun Nov 16 07:43:39 2008  polynomial 'A' values have 11 factors
Sun Nov 16 09:12:50 2008  57725 relations (15367 full + 42358 combined from 612926 partial), need 57509
Sun Nov 16 09:12:53 2008  begin with 628293 relations
Sun Nov 16 09:12:53 2008  reduce to 140381 relations in 11 passes
Sun Nov 16 09:12:53 2008  attempting to read 140381 relations
Sun Nov 16 09:12:57 2008  recovered 140381 relations
Sun Nov 16 09:12:57 2008  recovered 118548 polynomials
Sun Nov 16 09:12:57 2008  attempting to build 57725 cycles
Sun Nov 16 09:12:57 2008  found 57725 cycles in 6 passes
Sun Nov 16 09:12:57 2008  distribution of cycle lengths:
Sun Nov 16 09:12:57 2008     length 1 : 15367
Sun Nov 16 09:12:57 2008     length 2 : 11258
Sun Nov 16 09:12:57 2008     length 3 : 10201
Sun Nov 16 09:12:57 2008     length 4 : 7596
Sun Nov 16 09:12:57 2008     length 5 : 5450
Sun Nov 16 09:12:57 2008     length 6 : 3418
Sun Nov 16 09:12:57 2008     length 7 : 2045
Sun Nov 16 09:12:57 2008     length 9+: 2390
Sun Nov 16 09:12:57 2008  largest cycle: 20 relations
Sun Nov 16 09:12:58 2008  matrix is 57413 x 57725 (13.7 MB) with weight 3348390 (58.01/col)
Sun Nov 16 09:12:58 2008  sparse part has weight 3348390 (58.01/col)
Sun Nov 16 09:12:59 2008  filtering completed in 3 passes
Sun Nov 16 09:12:59 2008  matrix is 53477 x 53540 (12.7 MB) with weight 3122622 (58.32/col)
Sun Nov 16 09:12:59 2008  sparse part has weight 3122622 (58.32/col)
Sun Nov 16 09:12:59 2008  saving the first 48 matrix rows for later
Sun Nov 16 09:12:59 2008  matrix is 53429 x 53540 (8.5 MB) with weight 2501947 (46.73/col)
Sun Nov 16 09:12:59 2008  sparse part has weight 1919087 (35.84/col)
Sun Nov 16 09:12:59 2008  matrix includes 64 packed rows
Sun Nov 16 09:12:59 2008  using block size 21416 for processor cache size 512 kB
Sun Nov 16 09:13:00 2008  commencing Lanczos iteration
Sun Nov 16 09:13:00 2008  memory use: 8.2 MB
Sun Nov 16 09:13:30 2008  lanczos halted after 846 iterations (dim = 53429)
Sun Nov 16 09:13:30 2008  recovered 17 nontrivial dependencies
Sun Nov 16 09:13:31 2008  prp32 factor: 13955405739252974791819323206909
Sun Nov 16 09:13:31 2008  prp57 factor: 278472891040044154124888430675886431365951225649379875653
Sun Nov 16 09:13:31 2008  elapsed time 01:29:56

(29·10¹²²+43)/9 = 3(2)₁₂₁7_<123> = 3⁵ · 22709 · 1871960749_<10> · 220404736035126967_<18> · C90

C90 = P37 · P53

P37 = 9577067301489216188060274467072296429_<37>

P53 = 14777501242913200839830140856588531939556504474729203_<53>

Sun Nov 16 08:29:56 2008  Msieve v. 1.38
Sun Nov 16 08:29:56 2008  random seeds: 4209dae2 8044089e
Sun Nov 16 08:29:56 2008  factoring 141525123951220266571496944533675051004574403815120627762290662529117960797405243118916087 (90 digits)
Sun Nov 16 08:29:57 2008  searching for 15-digit factors
Sun Nov 16 08:29:58 2008  commencing quadratic sieve (90-digit input)
Sun Nov 16 08:29:58 2008  using multiplier of 23
Sun Nov 16 08:29:58 2008  using 32kb Intel Core sieve core
Sun Nov 16 08:29:58 2008  sieve interval: 35 blocks of size 32768
Sun Nov 16 08:29:58 2008  processing polynomials in batches of 6
Sun Nov 16 08:29:58 2008  using a sieve bound of 1569301 (59667 primes)
Sun Nov 16 08:29:58 2008  using large prime bound of 125544080 (26 bits)
Sun Nov 16 08:29:58 2008  using double large prime bound of 378297205588960 (42-49 bits)
Sun Nov 16 08:29:58 2008  using trial factoring cutoff of 49 bits
Sun Nov 16 08:29:58 2008  polynomial 'A' values have 12 factors
Sun Nov 16 09:47:59 2008  60278 relations (15890 full + 44388 combined from 633235 partial), need 59763
Sun Nov 16 09:48:02 2008  begin with 649125 relations
Sun Nov 16 09:48:02 2008  reduce to 146863 relations in 9 passes
Sun Nov 16 09:48:02 2008  attempting to read 146863 relations
Sun Nov 16 09:48:05 2008  recovered 146863 relations
Sun Nov 16 09:48:05 2008  recovered 126298 polynomials
Sun Nov 16 09:48:05 2008  attempting to build 60278 cycles
Sun Nov 16 09:48:05 2008  found 60278 cycles in 5 passes
Sun Nov 16 09:48:05 2008  distribution of cycle lengths:
Sun Nov 16 09:48:05 2008     length 1 : 15890
Sun Nov 16 09:48:05 2008     length 2 : 11426
Sun Nov 16 09:48:05 2008     length 3 : 10906
Sun Nov 16 09:48:05 2008     length 4 : 7999
Sun Nov 16 09:48:05 2008     length 5 : 5805
Sun Nov 16 09:48:05 2008     length 6 : 3659
Sun Nov 16 09:48:05 2008     length 7 : 2092
Sun Nov 16 09:48:05 2008     length 9+: 2501
Sun Nov 16 09:48:05 2008  largest cycle: 18 relations
Sun Nov 16 09:48:05 2008  matrix is 59667 x 60278 (14.6 MB) with weight 3598260 (59.69/col)
Sun Nov 16 09:48:05 2008  sparse part has weight 3598260 (59.69/col)
Sun Nov 16 09:48:06 2008  filtering completed in 3 passes
Sun Nov 16 09:48:06 2008  matrix is 55839 x 55903 (13.6 MB) with weight 3338960 (59.73/col)
Sun Nov 16 09:48:06 2008  sparse part has weight 3338960 (59.73/col)
Sun Nov 16 09:48:06 2008  saving the first 48 matrix rows for later
Sun Nov 16 09:48:06 2008  matrix is 55791 x 55903 (8.5 MB) with weight 2604416 (46.59/col)
Sun Nov 16 09:48:06 2008  sparse part has weight 1900399 (33.99/col)
Sun Nov 16 09:48:06 2008  matrix includes 64 packed rows
Sun Nov 16 09:48:06 2008  using block size 22361 for processor cache size 2048 kB
Sun Nov 16 09:48:07 2008  commencing Lanczos iteration
Sun Nov 16 09:48:07 2008  memory use: 8.4 MB
Sun Nov 16 09:48:25 2008  lanczos halted after 884 iterations (dim = 55787)
Sun Nov 16 09:48:25 2008  recovered 16 nontrivial dependencies
Sun Nov 16 09:48:26 2008  prp37 factor: 9577067301489216188060274467072296429
Sun Nov 16 09:48:26 2008  prp53 factor: 14777501242913200839830140856588531939556504474729203
Sun Nov 16 09:48:26 2008  elapsed time 01:18:30

(29·10¹³⁰+43)/9 = 3(2)₁₂₉7_<131> = 13 · 37 · 13397 · C124

C124 = P37 · P87

P37 = 6563660505566349382251069574930863659_<37>

P87 = 761827674362837670889483686123403408305860263945563318952163418498829415650821416567029_<87>

Number: 32227_130
N=5000378218262819292900654399497424055160861908641262227886098901997983881987763453763304476150635738603194003656793833699111
  ( 124 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=6563660505566349382251069574930863659 (pp37)
 r2=761827674362837670889483686123403408305860263945563318952163418498829415650821416567029 (pp87)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.65 hours.
Scaled time: 5.68 units (timescale=1.006).
Factorization parameters were as follows:
name: 32227_130
n: 5000378218262819292900654399497424055160861908641262227886098901997983881987763453763304476150635738603194003656793833699111
m: 100000000000000000000000000
deg: 5
c5: 29
c0: 43
skew: 1.08
type: snfs
lss: 1
rlim: 1090000
alim: 1090000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1090000/1090000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [545000, 995001)
Primes: RFBsize:84976, AFBsize:85268, largePrimes:3648337 encountered
Relations: rels:4312746, finalFF:913559
Max relations in full relation-set: 28
Initial matrix: 170309 x 913559 with sparse part having weight 70893609.
Pruned matrix : 105040 x 105955 with weight 10185065.
Total sieving time: 5.52 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1090000,1090000,26,26,47,47,2.3,2.3,50000
total time: 5.65 hours.
 --------- CPU info (if available) ----------

(29·10¹⁰³+43)/9 = 3(2)₁₀₂7_<104> = 37 · 67 · 937 · 180623 · C92

C92 = P46 · P47

P46 = 5903435180099898704490423374514522415338172223_<46>

P47 = 13009527410669058115242501966183259978431586981_<47>

Sun Nov 16 08:45:25 2008  Msieve v. 1.38
Sun Nov 16 08:45:25 2008  random seeds: b2d53890 b00bac8c
Sun Nov 16 08:45:25 2008  factoring 76800901792617659949345571350578332419923141299538313055437365070058025792039820937782628763 (92 digits)
Sun Nov 16 08:45:26 2008  searching for 15-digit factors
Sun Nov 16 08:45:27 2008  commencing quadratic sieve (92-digit input)
Sun Nov 16 08:45:28 2008  using multiplier of 2
Sun Nov 16 08:45:28 2008  using 32kb Intel Core sieve core
Sun Nov 16 08:45:28 2008  sieve interval: 36 blocks of size 32768
Sun Nov 16 08:45:28 2008  processing polynomials in batches of 6
Sun Nov 16 08:45:28 2008  using a sieve bound of 1853281 (69412 primes)
Sun Nov 16 08:45:28 2008  using large prime bound of 209420753 (27 bits)
Sun Nov 16 08:45:28 2008  using double large prime bound of 950244572529970 (42-50 bits)
Sun Nov 16 08:45:28 2008  using trial factoring cutoff of 50 bits
Sun Nov 16 08:45:28 2008  polynomial 'A' values have 12 factors
Sun Nov 16 10:49:37 2008  69959 relations (17732 full + 52227 combined from 892618 partial), need 69508
Sun Nov 16 10:49:38 2008  begin with 910350 relations
Sun Nov 16 10:49:38 2008  reduce to 177464 relations in 10 passes
Sun Nov 16 10:49:38 2008  attempting to read 177464 relations
Sun Nov 16 10:49:41 2008  recovered 177464 relations
Sun Nov 16 10:49:41 2008  recovered 157168 polynomials
Sun Nov 16 10:49:41 2008  attempting to build 69959 cycles
Sun Nov 16 10:49:41 2008  found 69959 cycles in 6 passes
Sun Nov 16 10:49:41 2008  distribution of cycle lengths:
Sun Nov 16 10:49:41 2008     length 1 : 17732
Sun Nov 16 10:49:41 2008     length 2 : 12853
Sun Nov 16 10:49:41 2008     length 3 : 11981
Sun Nov 16 10:49:41 2008     length 4 : 9439
Sun Nov 16 10:49:41 2008     length 5 : 6861
Sun Nov 16 10:49:41 2008     length 6 : 4532
Sun Nov 16 10:49:41 2008     length 7 : 2862
Sun Nov 16 10:49:41 2008     length 9+: 3699
Sun Nov 16 10:49:41 2008  largest cycle: 19 relations
Sun Nov 16 10:49:41 2008  matrix is 69412 x 69959 (17.5 MB) with weight 4316157 (61.70/col)
Sun Nov 16 10:49:41 2008  sparse part has weight 4316157 (61.70/col)
Sun Nov 16 10:49:42 2008  filtering completed in 3 passes
Sun Nov 16 10:49:42 2008  matrix is 65468 x 65532 (16.4 MB) with weight 4042304 (61.68/col)
Sun Nov 16 10:49:42 2008  sparse part has weight 4042304 (61.68/col)
Sun Nov 16 10:49:42 2008  saving the first 48 matrix rows for later
Sun Nov 16 10:49:42 2008  matrix is 65420 x 65532 (9.8 MB) with weight 3128711 (47.74/col)
Sun Nov 16 10:49:42 2008  sparse part has weight 2186706 (33.37/col)
Sun Nov 16 10:49:42 2008  matrix includes 64 packed rows
Sun Nov 16 10:49:42 2008  using block size 26212 for processor cache size 1024 kB
Sun Nov 16 10:49:43 2008  commencing Lanczos iteration
Sun Nov 16 10:49:43 2008  memory use: 9.8 MB
Sun Nov 16 10:50:10 2008  lanczos halted after 1036 iterations (dim = 65419)
Sun Nov 16 10:50:10 2008  recovered 17 nontrivial dependencies
Sun Nov 16 10:50:11 2008  prp46 factor: 5903435180099898704490423374514522415338172223
Sun Nov 16 10:50:11 2008  prp47 factor: 13009527410669058115242501966183259978431586981
Sun Nov 16 10:50:11 2008  elapsed time 02:04:46

(29·10¹²⁹+61)/9 = 3(2)₁₂₈9_<130> = 97 · 91035070031_<11> · C117

C117 = P33 · P84

P33 = 702397047936012971295827907183563_<33>

P84 = 519508127036019215068898992290694168510514114774183232879983195042107161939072988369_<84>

Number: 32229_129
N=364900974808867104898967325221905613343552291848563833088459135235478973892663263256448468989776474935458668646978747
  ( 117 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=702397047936012971295827907183563 (pp33)
 r2=519508127036019215068898992290694168510514114774183232879983195042107161939072988369 (pp84)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.40 hours.
Scaled time: 4.45 units (timescale=1.011).
Factorization parameters were as follows:
name: 32229_129
n: 364900974808867104898967325221905613343552291848563833088459135235478973892663263256448468989776474935458668646978747
m: 50000000000000000000000000
deg: 5
c5: 464
c0: 305
skew: 0.92
type: snfs
lss: 1
rlim: 1070000
alim: 1070000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1070000/1070000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [535000, 985001)
Primes: RFBsize:83548, AFBsize:83187, largePrimes:2867311 encountered
Relations: rels:2842564, finalFF:280905
Max relations in full relation-set: 28
Initial matrix: 166801 x 280905 with sparse part having weight 21547482.
Pruned matrix : 133491 x 134389 with weight 7371408.
Total sieving time: 4.27 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1070000,1070000,26,26,47,47,2.3,2.3,50000
total time: 4.40 hours.
 --------- CPU info (if available) ----------

(29·10¹¹³+43)/9 = 3(2)₁₁₂7_<114> = 3² · 20797883 · 269631728192171_<15> · C91

C91 = P37 · P55

P37 = 1230125378660460641412156544039754279_<37>

P55 = 5190073096884926489334879139819915251892446474164708549_<55>

Sun Nov 16 11:02:01 2008  Msieve v. 1.38
Sun Nov 16 11:02:01 2008  random seeds: 4a2d7900 8d9ddbb5
Sun Nov 16 11:02:01 2008  factoring 6384440633581039826739877413765078122967424829684569361832030989027519066449604771610631171 (91 digits)
Sun Nov 16 11:02:02 2008  searching for 15-digit factors
Sun Nov 16 11:02:03 2008  commencing quadratic sieve (91-digit input)
Sun Nov 16 11:02:04 2008  using multiplier of 1
Sun Nov 16 11:02:04 2008  using 32kb Intel Core sieve core
Sun Nov 16 11:02:04 2008  sieve interval: 36 blocks of size 32768
Sun Nov 16 11:02:04 2008  processing polynomials in batches of 6
Sun Nov 16 11:02:04 2008  using a sieve bound of 1710419 (64706 primes)
Sun Nov 16 11:02:04 2008  using large prime bound of 164200224 (27 bits)
Sun Nov 16 11:02:04 2008  using double large prime bound of 613299659056128 (42-50 bits)
Sun Nov 16 11:02:04 2008  using trial factoring cutoff of 50 bits
Sun Nov 16 11:02:04 2008  polynomial 'A' values have 12 factors
Sun Nov 16 12:49:14 2008  65008 relations (16520 full + 48488 combined from 767657 partial), need 64802
Sun Nov 16 12:49:15 2008  begin with 784177 relations
Sun Nov 16 12:49:15 2008  reduce to 163114 relations in 10 passes
Sun Nov 16 12:49:15 2008  attempting to read 163114 relations
Sun Nov 16 12:49:18 2008  recovered 163114 relations
Sun Nov 16 12:49:18 2008  recovered 143897 polynomials
Sun Nov 16 12:49:18 2008  attempting to build 65008 cycles
Sun Nov 16 12:49:18 2008  found 65008 cycles in 5 passes
Sun Nov 16 12:49:18 2008  distribution of cycle lengths:
Sun Nov 16 12:49:18 2008     length 1 : 16520
Sun Nov 16 12:49:18 2008     length 2 : 11927
Sun Nov 16 12:49:18 2008     length 3 : 11315
Sun Nov 16 12:49:18 2008     length 4 : 8818
Sun Nov 16 12:49:18 2008     length 5 : 6414
Sun Nov 16 12:49:18 2008     length 6 : 4171
Sun Nov 16 12:49:18 2008     length 7 : 2538
Sun Nov 16 12:49:18 2008     length 9+: 3305
Sun Nov 16 12:49:18 2008  largest cycle: 18 relations
Sun Nov 16 12:49:18 2008  matrix is 64706 x 65008 (16.3 MB) with weight 4013865 (61.74/col)
Sun Nov 16 12:49:18 2008  sparse part has weight 4013865 (61.74/col)
Sun Nov 16 12:49:19 2008  filtering completed in 3 passes
Sun Nov 16 12:49:19 2008  matrix is 61072 x 61136 (15.4 MB) with weight 3794033 (62.06/col)
Sun Nov 16 12:49:19 2008  sparse part has weight 3794033 (62.06/col)
Sun Nov 16 12:49:19 2008  saving the first 48 matrix rows for later
Sun Nov 16 12:49:19 2008  matrix is 61024 x 61136 (9.7 MB) with weight 2988624 (48.88/col)
Sun Nov 16 12:49:19 2008  sparse part has weight 2182842 (35.70/col)
Sun Nov 16 12:49:19 2008  matrix includes 64 packed rows
Sun Nov 16 12:49:19 2008  using block size 24454 for processor cache size 1024 kB
Sun Nov 16 12:49:20 2008  commencing Lanczos iteration
Sun Nov 16 12:49:20 2008  memory use: 9.4 MB
Sun Nov 16 12:49:44 2008  lanczos halted after 966 iterations (dim = 61020)
Sun Nov 16 12:49:45 2008  recovered 15 nontrivial dependencies
Sun Nov 16 12:49:45 2008  prp37 factor: 1230125378660460641412156544039754279
Sun Nov 16 12:49:45 2008  prp55 factor: 5190073096884926489334879139819915251892446474164708549
Sun Nov 16 12:49:45 2008  elapsed time 01:47:44

(29·10¹²³+61)/9 = 3(2)₁₂₂9_<124> = 1093 · 20197097 · 945337638045691432687_<21> · C93

C93 = P35 · P58

P35 = 23784786456749368257820483421526223_<35>

P58 = 6491725823707635239534358637976596616815241340171667425449_<58>

Sun Nov 16 09:29:45 2008  Msieve v. 1.38
Sun Nov 16 09:29:45 2008  random seeds: eb06c0eb dee408f7
Sun Nov 16 09:29:45 2008  factoring 154404312452651499619825162391679781184038198256602725705528105359351435732648813328651049127 (93 digits)
Sun Nov 16 09:29:46 2008  searching for 15-digit factors
Sun Nov 16 09:29:48 2008  commencing quadratic sieve (93-digit input)
Sun Nov 16 09:29:48 2008  using multiplier of 2
Sun Nov 16 09:29:48 2008  using 64kb Pentium 4 sieve core
Sun Nov 16 09:29:48 2008  sieve interval: 18 blocks of size 65536
Sun Nov 16 09:29:48 2008  processing polynomials in batches of 6
Sun Nov 16 09:29:48 2008  using a sieve bound of 1889117 (70571 primes)
Sun Nov 16 09:29:48 2008  using large prime bound of 221026689 (27 bits)
Sun Nov 16 09:29:48 2008  using double large prime bound of 1047129632032419 (42-50 bits)
Sun Nov 16 09:29:48 2008  using trial factoring cutoff of 50 bits
Sun Nov 16 09:29:48 2008  polynomial 'A' values have 12 factors
Sun Nov 16 12:59:39 2008  71078 relations (18371 full + 52707 combined from 918971 partial), need 70667
Sun Nov 16 12:59:42 2008  begin with 937342 relations
Sun Nov 16 12:59:43 2008  reduce to 178871 relations in 11 passes
Sun Nov 16 12:59:43 2008  attempting to read 178871 relations
Sun Nov 16 12:59:49 2008  recovered 178871 relations
Sun Nov 16 12:59:49 2008  recovered 158299 polynomials
Sun Nov 16 12:59:49 2008  attempting to build 71078 cycles
Sun Nov 16 12:59:49 2008  found 71078 cycles in 6 passes
Sun Nov 16 12:59:49 2008  distribution of cycle lengths:
Sun Nov 16 12:59:49 2008     length 1 : 18371
Sun Nov 16 12:59:49 2008     length 2 : 13084
Sun Nov 16 12:59:49 2008     length 3 : 12391
Sun Nov 16 12:59:49 2008     length 4 : 9547
Sun Nov 16 12:59:49 2008     length 5 : 6908
Sun Nov 16 12:59:49 2008     length 6 : 4395
Sun Nov 16 12:59:49 2008     length 7 : 2773
Sun Nov 16 12:59:49 2008     length 9+: 3609
Sun Nov 16 12:59:49 2008  largest cycle: 21 relations
Sun Nov 16 12:59:49 2008  matrix is 70571 x 71078 (17.7 MB) with weight 4345835 (61.14/col)
Sun Nov 16 12:59:49 2008  sparse part has weight 4345835 (61.14/col)
Sun Nov 16 12:59:51 2008  filtering completed in 3 passes
Sun Nov 16 12:59:51 2008  matrix is 66437 x 66501 (16.6 MB) with weight 4076816 (61.30/col)
Sun Nov 16 12:59:51 2008  sparse part has weight 4076816 (61.30/col)
Sun Nov 16 12:59:51 2008  saving the first 48 matrix rows for later
Sun Nov 16 12:59:51 2008  matrix is 66389 x 66501 (9.8 MB) with weight 3136378 (47.16/col)
Sun Nov 16 12:59:51 2008  sparse part has weight 2167002 (32.59/col)
Sun Nov 16 12:59:51 2008  matrix includes 64 packed rows
Sun Nov 16 12:59:51 2008  using block size 21845 for processor cache size 512 kB
Sun Nov 16 12:59:52 2008  commencing Lanczos iteration
Sun Nov 16 12:59:52 2008  memory use: 9.9 MB
Sun Nov 16 13:00:36 2008  lanczos halted after 1051 iterations (dim = 66389)
Sun Nov 16 13:00:36 2008  recovered 18 nontrivial dependencies
Sun Nov 16 13:00:37 2008  prp35 factor: 23784786456749368257820483421526223
Sun Nov 16 13:00:37 2008  prp58 factor: 6491725823707635239534358637976596616815241340171667425449
Sun Nov 16 13:00:37 2008  elapsed time 03:30:52

Nov 16, 2008 (3rd)

By Erik Branger / Msieve

(29·10¹⁰⁹+61)/9 = 3(2)₁₀₈9_<110> = 3 · 13 · 157 · 1181 · 157201157 · 574932409 · C86

C86 = P42 · P44

P42 = 650901737212776005468142288693299353882937_<42>

P44 = 75744895730524561665714325673543185447690943_<44>

Sat Nov 15 19:25:48 2008  Msieve v. 1.38
Sat Nov 15 19:25:48 2008  random seeds: f6a352b0 53563743
Sat Nov 15 19:25:48 2008  factoring 49302484215999017457519029556422881048788318162661963404252646628561929655487777139591 (86 digits)
Sat Nov 15 19:25:49 2008  searching for 15-digit factors
Sat Nov 15 19:25:50 2008  commencing quadratic sieve (86-digit input)
Sat Nov 15 19:25:50 2008  using multiplier of 1
Sat Nov 15 19:25:50 2008  using 32kb Intel Core sieve core
Sat Nov 15 19:25:50 2008  sieve interval: 16 blocks of size 32768
Sat Nov 15 19:25:50 2008  processing polynomials in batches of 13
Sat Nov 15 19:25:50 2008  using a sieve bound of 1457683 (55667 primes)
Sat Nov 15 19:25:50 2008  using large prime bound of 116614640 (26 bits)
Sat Nov 15 19:25:50 2008  using double large prime bound of 331249715652000 (41-49 bits)
Sat Nov 15 19:25:50 2008  using trial factoring cutoff of 49 bits
Sat Nov 15 19:25:50 2008  polynomial 'A' values have 11 factors
Sat Nov 15 20:02:11 2008  55832 relations (16024 full + 39808 combined from 583767 partial), need 55763
Sat Nov 15 20:02:12 2008  begin with 599791 relations
Sat Nov 15 20:02:12 2008  reduce to 132574 relations in 9 passes
Sat Nov 15 20:02:12 2008  attempting to read 132574 relations
Sat Nov 15 20:02:14 2008  recovered 132574 relations
Sat Nov 15 20:02:14 2008  recovered 109344 polynomials
Sat Nov 15 20:02:14 2008  attempting to build 55832 cycles
Sat Nov 15 20:02:14 2008  found 55832 cycles in 5 passes
Sat Nov 15 20:02:14 2008  distribution of cycle lengths:
Sat Nov 15 20:02:14 2008     length 1 : 16024
Sat Nov 15 20:02:14 2008     length 2 : 11211
Sat Nov 15 20:02:14 2008     length 3 : 9906
Sat Nov 15 20:02:14 2008     length 4 : 7001
Sat Nov 15 20:02:14 2008     length 5 : 4890
Sat Nov 15 20:02:14 2008     length 6 : 3061
Sat Nov 15 20:02:14 2008     length 7 : 1767
Sat Nov 15 20:02:14 2008     length 9+: 1972
Sat Nov 15 20:02:14 2008  largest cycle: 16 relations
Sat Nov 15 20:02:14 2008  matrix is 55667 x 55832 (12.0 MB) with weight 2931997 (52.51/col)
Sat Nov 15 20:02:14 2008  sparse part has weight 2931997 (52.51/col)
Sat Nov 15 20:02:14 2008  filtering completed in 3 passes
Sat Nov 15 20:02:14 2008  matrix is 50974 x 51038 (11.1 MB) with weight 2709335 (53.08/col)
Sat Nov 15 20:02:14 2008  sparse part has weight 2709335 (53.08/col)
Sat Nov 15 20:02:15 2008  saving the first 48 matrix rows for later
Sat Nov 15 20:02:15 2008  matrix is 50926 x 51038 (6.1 MB) with weight 1988059 (38.95/col)
Sat Nov 15 20:02:15 2008  sparse part has weight 1294362 (25.36/col)
Sat Nov 15 20:02:15 2008  matrix includes 64 packed rows
Sat Nov 15 20:02:15 2008  using block size 20415 for processor cache size 2048 kB
Sat Nov 15 20:02:15 2008  commencing Lanczos iteration
Sat Nov 15 20:02:15 2008  memory use: 6.7 MB
Sat Nov 15 20:02:28 2008  lanczos halted after 807 iterations (dim = 50918)
Sat Nov 15 20:02:28 2008  recovered 13 nontrivial dependencies
Sat Nov 15 20:02:29 2008  prp42 factor: 650901737212776005468142288693299353882937
Sat Nov 15 20:02:29 2008  prp44 factor: 75744895730524561665714325673543185447690943
Sat Nov 15 20:02:29 2008  elapsed time 00:36:41

(29·10¹²¹+43)/9 = 3(2)₁₂₀7_<122> = 37 · 1409 · 116273 · 49986259 · 268484505653234917_<18> · C87

C87 = P39 · P48

P39 = 532697136187481881341266254372747070933_<39>

P48 = 743555976503052776395768756045694514223915261397_<48>

Sat Nov 15 20:07:42 2008  Msieve v. 1.38
Sat Nov 15 20:07:42 2008  random seeds: a4ecc3a8 54553869
Sat Nov 15 20:07:42 2008  factoring 396090139278262782600209118642442432563590971291144371671691191910055716222928795673401 (87 digits)
Sat Nov 15 20:07:43 2008  searching for 15-digit factors
Sat Nov 15 20:07:44 2008  commencing quadratic sieve (87-digit input)
Sat Nov 15 20:07:44 2008  using multiplier of 19
Sat Nov 15 20:07:44 2008  using 32kb Intel Core sieve core
Sat Nov 15 20:07:44 2008  sieve interval: 20 blocks of size 32768
Sat Nov 15 20:07:44 2008  processing polynomials in batches of 11
Sat Nov 15 20:07:44 2008  using a sieve bound of 1485751 (56667 primes)
Sat Nov 15 20:07:44 2008  using large prime bound of 118860080 (26 bits)
Sat Nov 15 20:07:44 2008  using double large prime bound of 342818857657760 (42-49 bits)
Sat Nov 15 20:07:44 2008  using trial factoring cutoff of 49 bits
Sat Nov 15 20:07:44 2008  polynomial 'A' values have 11 factors
Sat Nov 15 20:59:12 2008  56965 relations (15586 full + 41379 combined from 598785 partial), need 56763
Sat Nov 15 20:59:12 2008  begin with 614371 relations
Sat Nov 15 20:59:13 2008  reduce to 137532 relations in 9 passes
Sat Nov 15 20:59:13 2008  attempting to read 137532 relations
Sat Nov 15 20:59:14 2008  recovered 137532 relations
Sat Nov 15 20:59:14 2008  recovered 118192 polynomials
Sat Nov 15 20:59:15 2008  attempting to build 56965 cycles
Sat Nov 15 20:59:15 2008  found 56965 cycles in 5 passes
Sat Nov 15 20:59:15 2008  distribution of cycle lengths:
Sat Nov 15 20:59:15 2008     length 1 : 15586
Sat Nov 15 20:59:15 2008     length 2 : 11049
Sat Nov 15 20:59:15 2008     length 3 : 9917
Sat Nov 15 20:59:15 2008     length 4 : 7588
Sat Nov 15 20:59:15 2008     length 5 : 5204
Sat Nov 15 20:59:15 2008     length 6 : 3481
Sat Nov 15 20:59:15 2008     length 7 : 1910
Sat Nov 15 20:59:15 2008     length 9+: 2230
Sat Nov 15 20:59:15 2008  largest cycle: 19 relations
Sat Nov 15 20:59:15 2008  matrix is 56667 x 56965 (13.6 MB) with weight 3346291 (58.74/col)
Sat Nov 15 20:59:15 2008  sparse part has weight 3346291 (58.74/col)
Sat Nov 15 20:59:15 2008  filtering completed in 3 passes
Sat Nov 15 20:59:15 2008  matrix is 52509 x 52573 (12.7 MB) with weight 3107546 (59.11/col)
Sat Nov 15 20:59:15 2008  sparse part has weight 3107546 (59.11/col)
Sat Nov 15 20:59:15 2008  saving the first 48 matrix rows for later
Sat Nov 15 20:59:15 2008  matrix is 52461 x 52573 (8.5 MB) with weight 2464123 (46.87/col)
Sat Nov 15 20:59:15 2008  sparse part has weight 1915121 (36.43/col)
Sat Nov 15 20:59:15 2008  matrix includes 64 packed rows
Sat Nov 15 20:59:15 2008  using block size 21029 for processor cache size 2048 kB
Sat Nov 15 20:59:16 2008  commencing Lanczos iteration
Sat Nov 15 20:59:16 2008  memory use: 8.1 MB
Sat Nov 15 20:59:32 2008  lanczos halted after 831 iterations (dim = 52457)
Sat Nov 15 20:59:33 2008  recovered 16 nontrivial dependencies
Sat Nov 15 20:59:34 2008  prp39 factor: 532697136187481881341266254372747070933
Sat Nov 15 20:59:34 2008  prp48 factor: 743555976503052776395768756045694514223915261397
Sat Nov 15 20:59:34 2008  elapsed time 00:51:52

(29·10¹³⁹+61)/9 = 3(2)₁₃₈9_<140> = 3² · 13 · 71 · 2069 · 2051849603_<10> · 76632406965209_<14> · 45612363410902054681_<20> · C90

C90 = P36 · P54

P36 = 526346512135981262865057629649851747_<36>

P54 = 496636312759644324545696307974594420148439259761254067_<54>

Sat Nov 15 21:31:02 2008  Msieve v. 1.38
Sat Nov 15 21:31:02 2008  random seeds: 52e51600 39bdff75
Sat Nov 15 21:31:02 2008  factoring 261402791021113117578925405750467260032219345544353197182924360382793355544864901350805049 (90 digits)
Sat Nov 15 21:31:03 2008  searching for 15-digit factors
Sat Nov 15 21:31:05 2008  commencing quadratic sieve (90-digit input)
Sat Nov 15 21:31:05 2008  using multiplier of 1
Sat Nov 15 21:31:05 2008  using 32kb Intel Core sieve core
Sat Nov 15 21:31:05 2008  sieve interval: 36 blocks of size 32768
Sat Nov 15 21:31:05 2008  processing polynomials in batches of 6
Sat Nov 15 21:31:05 2008  using a sieve bound of 1577909 (60000 primes)
Sat Nov 15 21:31:05 2008  using large prime bound of 126232720 (26 bits)
Sat Nov 15 21:31:05 2008  using double large prime bound of 382040549960160 (42-49 bits)
Sat Nov 15 21:31:05 2008  using trial factoring cutoff of 49 bits
Sat Nov 15 21:31:05 2008  polynomial 'A' values have 11 factors
Sat Nov 15 22:47:12 2008  60109 relations (15701 full + 44408 combined from 638898 partial), need 60096
Sat Nov 15 22:47:12 2008  begin with 654599 relations
Sat Nov 15 22:47:13 2008  reduce to 147530 relations in 10 passes
Sat Nov 15 22:47:13 2008  attempting to read 147530 relations
Sat Nov 15 22:47:15 2008  recovered 147530 relations
Sat Nov 15 22:47:15 2008  recovered 127332 polynomials
Sat Nov 15 22:47:15 2008  attempting to build 60109 cycles
Sat Nov 15 22:47:15 2008  found 60109 cycles in 5 passes
Sat Nov 15 22:47:15 2008  distribution of cycle lengths:
Sat Nov 15 22:47:15 2008     length 1 : 15701
Sat Nov 15 22:47:15 2008     length 2 : 11329
Sat Nov 15 22:47:15 2008     length 3 : 10720
Sat Nov 15 22:47:15 2008     length 4 : 8056
Sat Nov 15 22:47:15 2008     length 5 : 5760
Sat Nov 15 22:47:15 2008     length 6 : 3736
Sat Nov 15 22:47:15 2008     length 7 : 2134
Sat Nov 15 22:47:15 2008     length 9+: 2673
Sat Nov 15 22:47:15 2008  largest cycle: 19 relations
Sat Nov 15 22:47:15 2008  matrix is 60000 x 60109 (14.8 MB) with weight 3640661 (60.57/col)
Sat Nov 15 22:47:15 2008  sparse part has weight 3640661 (60.57/col)
Sat Nov 15 22:47:15 2008  filtering completed in 3 passes
Sat Nov 15 22:47:15 2008  matrix is 56304 x 56368 (14.0 MB) with weight 3451440 (61.23/col)
Sat Nov 15 22:47:15 2008  sparse part has weight 3451440 (61.23/col)
Sat Nov 15 22:47:16 2008  saving the first 48 matrix rows for later
Sat Nov 15 22:47:16 2008  matrix is 56256 x 56368 (10.3 MB) with weight 2869705 (50.91/col)
Sat Nov 15 22:47:16 2008  sparse part has weight 2356081 (41.80/col)
Sat Nov 15 22:47:16 2008  matrix includes 64 packed rows
Sat Nov 15 22:47:16 2008  using block size 22547 for processor cache size 2048 kB
Sat Nov 15 22:47:16 2008  commencing Lanczos iteration
Sat Nov 15 22:47:16 2008  memory use: 9.3 MB
Sat Nov 15 22:47:37 2008  lanczos halted after 891 iterations (dim = 56255)
Sat Nov 15 22:47:38 2008  recovered 16 nontrivial dependencies
Sat Nov 15 22:47:38 2008  prp36 factor: 526346512135981262865057629649851747
Sat Nov 15 22:47:38 2008  prp54 factor: 496636312759644324545696307974594420148439259761254067
Sat Nov 15 22:47:38 2008  elapsed time 01:16:36

Nov 16, 2008 (2nd)

By Robert Backstrom / Msieve, GMP-ECM

(29·10¹¹⁶+61)/9 = 3(2)₁₁₅9_<117> = 7 · 257 · 491747 · 247097692151858136343213913_<27> · C82

C82 = P34 · P48

P34 = 2178729077434916503736133330125321_<34>

P48 = 676566807283536166402708627290220286482051675841_<48>

Sun Nov 16 04:52:04 2008  
Sun Nov 16 04:52:04 2008  
Sun Nov 16 04:52:04 2008  Msieve v. 1.38
Sun Nov 16 04:52:04 2008  random seeds: b5630310 0b7d1da0
Sun Nov 16 04:52:04 2008  factoring 1474055775855945699490365633699736543007749056604429799681281685914133078598069961 (82 digits)
Sun Nov 16 04:52:04 2008  searching for 15-digit factors
Sun Nov 16 04:52:05 2008  commencing quadratic sieve (82-digit input)
Sun Nov 16 04:52:05 2008  using multiplier of 1
Sun Nov 16 04:52:05 2008  using 64kb Opteron sieve core
Sun Nov 16 04:52:05 2008  sieve interval: 6 blocks of size 65536
Sun Nov 16 04:52:05 2008  processing polynomials in batches of 17
Sun Nov 16 04:52:05 2008  using a sieve bound of 1325183 (51176 primes)
Sun Nov 16 04:52:05 2008  using large prime bound of 125892385 (26 bits)
Sun Nov 16 04:52:05 2008  using trial factoring cutoff of 27 bits
Sun Nov 16 04:52:05 2008  polynomial 'A' values have 10 factors
Sun Nov 16 05:03:43 2008  51289 relations (25932 full + 25357 combined from 276904 partial), need 51272
Sun Nov 16 05:03:43 2008  begin with 302836 relations
Sun Nov 16 05:03:43 2008  reduce to 73495 relations in 2 passes
Sun Nov 16 05:03:43 2008  attempting to read 73495 relations
Sun Nov 16 05:03:44 2008  recovered 73495 relations
Sun Nov 16 05:03:44 2008  recovered 64316 polynomials
Sun Nov 16 05:03:44 2008  attempting to build 51289 cycles
Sun Nov 16 05:03:44 2008  found 51289 cycles in 1 passes
Sun Nov 16 05:03:44 2008  distribution of cycle lengths:
Sun Nov 16 05:03:44 2008     length 1 : 25932
Sun Nov 16 05:03:44 2008     length 2 : 25357
Sun Nov 16 05:03:44 2008  largest cycle: 2 relations
Sun Nov 16 05:03:44 2008  matrix is 51176 x 51289 (6.7 MB) with weight 1557069 (30.36/col)
Sun Nov 16 05:03:44 2008  sparse part has weight 1557069 (30.36/col)
Sun Nov 16 05:03:45 2008  filtering completed in 3 passes
Sun Nov 16 05:03:45 2008  matrix is 37092 x 37156 (5.4 MB) with weight 1261642 (33.96/col)
Sun Nov 16 05:03:45 2008  sparse part has weight 1261642 (33.96/col)
Sun Nov 16 05:03:45 2008  saving the first 48 matrix rows for later
Sun Nov 16 05:03:45 2008  matrix is 37044 x 37156 (4.0 MB) with weight 1002066 (26.97/col)
Sun Nov 16 05:03:45 2008  sparse part has weight 813973 (21.91/col)
Sun Nov 16 05:03:45 2008  matrix includes 64 packed rows
Sun Nov 16 05:03:45 2008  using block size 14862 for processor cache size 1024 kB
Sun Nov 16 05:03:45 2008  commencing Lanczos iteration
Sun Nov 16 05:03:45 2008  memory use: 4.3 MB
Sun Nov 16 05:03:51 2008  lanczos halted after 587 iterations (dim = 37042)
Sun Nov 16 05:03:51 2008  recovered 15 nontrivial dependencies
Sun Nov 16 05:03:51 2008  prp34 factor: 2178729077434916503736133330125321
Sun Nov 16 05:03:51 2008  prp48 factor: 676566807283536166402708627290220286482051675841
Sun Nov 16 05:03:51 2008  elapsed time 00:11:47

(29·10¹⁰⁷+43)/9 = 3(2)₁₀₆7_<108> = 3 · 157 · 2411 · 3499 · 3685209051242203_<16> · C83

C83 = P40 · P44

P40 = 1425282736544390826810125421049919685529_<40>

P44 = 15439394862943373275259839417275417587690959_<44>

Sun Nov 16 06:01:28 2008  
Sun Nov 16 06:01:28 2008  
Sun Nov 16 06:01:28 2008  Msieve v. 1.38
Sun Nov 16 06:01:28 2008  random seeds: ce7c0a8c 72132a61
Sun Nov 16 06:01:28 2008  factoring 22005502960845341009717371068217949500020830757589908888394504033728427454516432311 (83 digits)
Sun Nov 16 06:01:29 2008  searching for 15-digit factors
Sun Nov 16 06:01:30 2008  commencing quadratic sieve (83-digit input)
Sun Nov 16 06:01:30 2008  using multiplier of 19
Sun Nov 16 06:01:30 2008  using 64kb Opteron sieve core
Sun Nov 16 06:01:30 2008  sieve interval: 6 blocks of size 65536
Sun Nov 16 06:01:30 2008  processing polynomials in batches of 17
Sun Nov 16 06:01:30 2008  using a sieve bound of 1362629 (52353 primes)
Sun Nov 16 06:01:30 2008  using large prime bound of 123999239 (26 bits)
Sun Nov 16 06:01:30 2008  using trial factoring cutoff of 27 bits
Sun Nov 16 06:01:30 2008  polynomial 'A' values have 11 factors
Sun Nov 16 06:17:11 2008  52512 relations (26925 full + 25587 combined from 276907 partial), need 52449
Sun Nov 16 06:17:11 2008  begin with 303832 relations
Sun Nov 16 06:17:11 2008  reduce to 74921 relations in 2 passes
Sun Nov 16 06:17:11 2008  attempting to read 74921 relations
Sun Nov 16 06:17:12 2008  recovered 74921 relations
Sun Nov 16 06:17:12 2008  recovered 67669 polynomials
Sun Nov 16 06:17:12 2008  attempting to build 52512 cycles
Sun Nov 16 06:17:12 2008  found 52512 cycles in 1 passes
Sun Nov 16 06:17:12 2008  distribution of cycle lengths:
Sun Nov 16 06:17:12 2008     length 1 : 26925
Sun Nov 16 06:17:12 2008     length 2 : 25587
Sun Nov 16 06:17:12 2008  largest cycle: 2 relations
Sun Nov 16 06:17:12 2008  matrix is 52353 x 52512 (7.2 MB) with weight 1681244 (32.02/col)
Sun Nov 16 06:17:12 2008  sparse part has weight 1681244 (32.02/col)
Sun Nov 16 06:17:13 2008  filtering completed in 4 passes
Sun Nov 16 06:17:13 2008  matrix is 37946 x 38010 (5.7 MB) with weight 1348944 (35.49/col)
Sun Nov 16 06:17:13 2008  sparse part has weight 1348944 (35.49/col)
Sun Nov 16 06:17:14 2008  saving the first 48 matrix rows for later
Sun Nov 16 06:17:14 2008  matrix is 37898 x 38010 (3.5 MB) with weight 1001632 (26.35/col)
Sun Nov 16 06:17:14 2008  sparse part has weight 694996 (18.28/col)
Sun Nov 16 06:17:14 2008  matrix includes 64 packed rows
Sun Nov 16 06:17:14 2008  using block size 15204 for processor cache size 1024 kB
Sun Nov 16 06:17:14 2008  commencing Lanczos iteration
Sun Nov 16 06:17:14 2008  memory use: 4.1 MB
Sun Nov 16 06:17:19 2008  lanczos halted after 601 iterations (dim = 37896)
Sun Nov 16 06:17:19 2008  recovered 17 nontrivial dependencies
Sun Nov 16 06:17:19 2008  prp40 factor: 1425282736544390826810125421049919685529
Sun Nov 16 06:17:19 2008  prp44 factor: 15439394862943373275259839417275417587690959
Sun Nov 16 06:17:19 2008  elapsed time 00:15:51

(29·10¹¹¹+61)/9 = 3(2)₁₁₀9_<112> = 227 · 1229 · 2531 · 4517 · 553355006146379_<15> · C85

C85 = P36 · P49

P36 = 276993852075149363427098229130204721_<36>

P49 = 6591155221914261426440632501639332054792978851191_<49>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 1825709474543267205420856555959842362192321944249866230555968943131807164817224672711 (85 digits)
Using B1=2950000, B2=4281751120, polynomial Dickson(6), sigma=4015980292
Step 1 took 15688ms
Step 2 took 7359ms
********** Factor found in step 2: 276993852075149363427098229130204721
Found probable prime factor of 36 digits: 276993852075149363427098229130204721
Probable prime cofactor 6591155221914261426440632501639332054792978851191 has 49 digits

(29·10¹³⁶+61)/9 = 3(2)₁₃₅9_<137> = 3 · 421 · 62099 · 19123277 · 5872671531578717594595674662340908259_<37> · C85

C85 = P35 · P50

P35 = 44422204522463800558090885913108389_<35>

P50 = 82351098639585552850344538095782597161862158898771_<50>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 3658217346417259879542882504552540988176513141181323018991027486329660954453801889919 (85 digits)
Using B1=1160000, B2=1426247560, polynomial Dickson(6), sigma=2802654316
Step 1 took 6094ms
Step 2 took 3515ms
********** Factor found in step 2: 44422204522463800558090885913108389
Found probable prime factor of 35 digits: 44422204522463800558090885913108389
Probable prime cofactor 82351098639585552850344538095782597161862158898771 has 50 digits

Nov 16, 2008

Factorizations of 322...227 and Factorizations of 322...229 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Nov 15, 2008 (2nd)

By Sinkiti Sibata / Msieve, GGNFS

(29·10¹⁶⁷-11)/9 = 3(2)₁₆₆1_<168> = 3 · 19 · 1217 · 545375959 · 20778919487_<11> · 45602021140493_<14> · 14614344872681959582619366399806329959_<38> · C93

C93 = P33 · P61

P33 = 227175975763318381887575509543877_<33>

P61 = 2707355331188622324443371660128309350699561584856921482876427_<61>

Fri Nov 14 23:43:08 2008  Msieve v. 1.38
Fri Nov 14 23:43:08 2008  random seeds: 4e9568c4 8f996ae3
Fri Nov 14 23:43:08 2008  factoring 615046089100797276059789575087661813724676267821413765385904915681332714128994363968725487479 (93 digits)
Fri Nov 14 23:43:09 2008  searching for 15-digit factors
Fri Nov 14 23:43:10 2008  commencing quadratic sieve (93-digit input)
Fri Nov 14 23:43:10 2008  using multiplier of 31
Fri Nov 14 23:43:10 2008  using 32kb Intel Core sieve core
Fri Nov 14 23:43:10 2008  sieve interval: 36 blocks of size 32768
Fri Nov 14 23:43:10 2008  processing polynomials in batches of 6
Fri Nov 14 23:43:10 2008  using a sieve bound of 1954087 (72941 primes)
Fri Nov 14 23:43:10 2008  using large prime bound of 244260875 (27 bits)
Fri Nov 14 23:43:10 2008  using double large prime bound of 1253536551543250 (42-51 bits)
Fri Nov 14 23:43:10 2008  using trial factoring cutoff of 51 bits
Fri Nov 14 23:43:10 2008  polynomial 'A' values have 12 factors
Sat Nov 15 02:11:46 2008  73182 relations (18600 full + 54582 combined from 987308 partial), need 73037
Sat Nov 15 02:11:47 2008  begin with 1005908 relations
Sat Nov 15 02:11:48 2008  reduce to 185908 relations in 10 passes
Sat Nov 15 02:11:48 2008  attempting to read 185908 relations
Sat Nov 15 02:11:50 2008  recovered 185908 relations
Sat Nov 15 02:11:50 2008  recovered 166941 polynomials
Sat Nov 15 02:11:51 2008  attempting to build 73182 cycles
Sat Nov 15 02:11:51 2008  found 73182 cycles in 5 passes
Sat Nov 15 02:11:51 2008  distribution of cycle lengths:
Sat Nov 15 02:11:51 2008     length 1 : 18600
Sat Nov 15 02:11:51 2008     length 2 : 13208
Sat Nov 15 02:11:51 2008     length 3 : 12719
Sat Nov 15 02:11:51 2008     length 4 : 9789
Sat Nov 15 02:11:51 2008     length 5 : 7149
Sat Nov 15 02:11:51 2008     length 6 : 4812
Sat Nov 15 02:11:51 2008     length 7 : 3000
Sat Nov 15 02:11:51 2008     length 9+: 3905
Sat Nov 15 02:11:51 2008  largest cycle: 18 relations
Sat Nov 15 02:11:51 2008  matrix is 72941 x 73182 (18.6 MB) with weight 4581116 (62.60/col)
Sat Nov 15 02:11:51 2008  sparse part has weight 4581116 (62.60/col)
Sat Nov 15 02:11:52 2008  filtering completed in 3 passes
Sat Nov 15 02:11:52 2008  matrix is 69064 x 69128 (17.7 MB) with weight 4355016 (63.00/col)
Sat Nov 15 02:11:52 2008  sparse part has weight 4355016 (63.00/col)
Sat Nov 15 02:11:52 2008  saving the first 48 matrix rows for later
Sat Nov 15 02:11:52 2008  matrix is 69016 x 69128 (10.7 MB) with weight 3362251 (48.64/col)
Sat Nov 15 02:11:52 2008  sparse part has weight 2402551 (34.76/col)
Sat Nov 15 02:11:52 2008  matrix includes 64 packed rows
Sat Nov 15 02:11:52 2008  using block size 27651 for processor cache size 1024 kB
Sat Nov 15 02:11:53 2008  commencing Lanczos iteration
Sat Nov 15 02:11:53 2008  memory use: 10.6 MB
Sat Nov 15 02:12:24 2008  lanczos halted after 1093 iterations (dim = 69012)
Sat Nov 15 02:12:24 2008  recovered 15 nontrivial dependencies
Sat Nov 15 02:12:26 2008  prp33 factor: 227175975763318381887575509543877
Sat Nov 15 02:12:26 2008  prp61 factor: 2707355331188622324443371660128309350699561584856921482876427
Sat Nov 15 02:12:26 2008  elapsed time 02:29:18

(28·10¹³³+71)/9 = 3(1)₁₃₂9_<134> = 3² · 13 · 59 · 179 · 6307979 · 13229898216989522059_<20> · C102

C102 = P49 · P54

P49 = 1839668211284057814365396705452504160370049234991_<49>

P54 = 163997932016769164501097073245953747850978841901913637_<54>

Thu Nov 13 21:43:44 2008  Msieve v. 1.38
Thu Nov 13 21:43:44 2008  random seeds: 521c9724 bf061dcd
Thu Nov 13 21:43:44 2008  factoring 301701782247574244986826324546458933509775232068798905009039077203737957765388348419560196830800472267 (102 digits)
Thu Nov 13 21:43:45 2008  searching for 15-digit factors
Thu Nov 13 21:43:47 2008  commencing quadratic sieve (102-digit input)
Thu Nov 13 21:43:48 2008  using multiplier of 11
Thu Nov 13 21:43:48 2008  using 64kb Pentium 4 sieve core
Thu Nov 13 21:43:48 2008  sieve interval: 18 blocks of size 65536
Thu Nov 13 21:43:48 2008  processing polynomials in batches of 6
Thu Nov 13 21:43:48 2008  using a sieve bound of 3198409 (114807 primes)
Thu Nov 13 21:43:48 2008  using large prime bound of 479761350 (28 bits)
Thu Nov 13 21:43:48 2008  using double large prime bound of 4225182407156700 (44-52 bits)
Thu Nov 13 21:43:48 2008  using trial factoring cutoff of 52 bits
Thu Nov 13 21:43:48 2008  polynomial 'A' values have 13 factors
Thu Nov 13 21:43:48 2008  restarting with 107 full and 6750 partial relations
Sat Nov 15 03:49:44 2008  114918 relations (27221 full + 87697 combined from 1725189 partial), need 114903
Sat Nov 15 03:49:51 2008  begin with 1752410 relations
Sat Nov 15 03:49:53 2008  reduce to 304089 relations in 12 passes
Sat Nov 15 03:49:53 2008  attempting to read 304089 relations
Sat Nov 15 03:50:04 2008  recovered 304089 relations
Sat Nov 15 03:50:04 2008  recovered 296040 polynomials
Sat Nov 15 03:50:05 2008  attempting to build 114918 cycles
Sat Nov 15 03:50:05 2008  found 114918 cycles in 6 passes
Sat Nov 15 03:50:05 2008  distribution of cycle lengths:
Sat Nov 15 03:50:05 2008     length 1 : 27221
Sat Nov 15 03:50:05 2008     length 2 : 19398
Sat Nov 15 03:50:05 2008     length 3 : 19281
Sat Nov 15 03:50:05 2008     length 4 : 15830
Sat Nov 15 03:50:05 2008     length 5 : 11903
Sat Nov 15 03:50:05 2008     length 6 : 8287
Sat Nov 15 03:50:05 2008     length 7 : 5303
Sat Nov 15 03:50:05 2008     length 9+: 7695
Sat Nov 15 03:50:05 2008  largest cycle: 22 relations
Sat Nov 15 03:50:06 2008  matrix is 114807 x 114918 (33.9 MB) with weight 8425186 (73.31/col)
Sat Nov 15 03:50:06 2008  sparse part has weight 8425186 (73.31/col)
Sat Nov 15 03:50:08 2008  filtering completed in 3 passes
Sat Nov 15 03:50:08 2008  matrix is 110420 x 110484 (32.8 MB) with weight 8161255 (73.87/col)
Sat Nov 15 03:50:08 2008  sparse part has weight 8161255 (73.87/col)
Sat Nov 15 03:50:09 2008  saving the first 48 matrix rows for later
Sat Nov 15 03:50:10 2008  matrix is 110372 x 110484 (23.4 MB) with weight 6834160 (61.86/col)
Sat Nov 15 03:50:10 2008  sparse part has weight 5464671 (49.46/col)
Sat Nov 15 03:50:10 2008  matrix includes 64 packed rows
Sat Nov 15 03:50:10 2008  using block size 21845 for processor cache size 512 kB
Sat Nov 15 03:50:11 2008  commencing Lanczos iteration
Sat Nov 15 03:50:11 2008  memory use: 20.8 MB
Sat Nov 15 03:52:44 2008  lanczos halted after 1746 iterations (dim = 110372)
Sat Nov 15 03:52:45 2008  recovered 18 nontrivial dependencies
Sat Nov 15 03:52:49 2008  prp49 factor: 1839668211284057814365396705452504160370049234991
Sat Nov 15 03:52:49 2008  prp54 factor: 163997932016769164501097073245953747850978841901913637
Sat Nov 15 03:52:49 2008  elapsed time 30:09:05

(28·10¹⁴⁷+71)/9 = 3(1)₁₄₆9_<148> = 186701 · 588820003 · 659034703250019414229_<21> · C113

C113 = P33 · P36 · P45

P33 = 303971445136473294348591356602429_<33>

P36 = 208410345381267237307086484257560467_<36>

P45 = 677838101450885656471927399373596982235245059_<45>

Number: 31119_147
N=42941581840169851306496911799165463946002022848074130658861492367490343781164497312063584313924117589654966921237
  ( 113 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=303971445136473294348591356602429 (pp33)
 r2=208410345381267237307086484257560467 (pp36)
 r3=677838101450885656471927399373596982235245059 (pp45)
Version: GGNFS-0.77.1-20060513-k8
Total time: 24.69 hours.
Scaled time: 48.56 units (timescale=1.967).
Factorization parameters were as follows:
name: 31119_147
n: 42941581840169851306496911799165463946002022848074130658861492367490343781164497312063584313924117589654966921237
m: 200000000000000000000000000000
deg: 5
c5: 175
c0: 142
skew: 0.96
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 3150001)
Primes: RFBsize:155805, AFBsize:155838, largePrimes:4543525 encountered
Relations: rels:4873763, finalFF:401796
Max relations in full relation-set: 28
Initial matrix: 311709 x 401796 with sparse part having weight 47172161.
Pruned matrix : 281859 x 283481 with weight 31778198.
Total sieving time: 23.36 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.03 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 24.69 hours.
 --------- CPU info (if available) ----------

(28·10¹⁷²+53)/9 = 3(1)₁₇₁7_<173> = 29 · 37 · 397 · 953 · 1249 · 152441 · 760164647237041_<15> · C141

C141 = P41 · P101

P41 = 14515566495965381484432908137188917611379_<41>

P101 = 36477621053825863236530826318706660402494626746122190956217533559432562151205757871210576748577472619_<101>

Number: 31117_172
N=529493334021436111922162637254840759809513964430346448697227563102473589227446184240143681531113116238112526127602307738122013166310255331601
  ( 141 digits)
SNFS difficulty: 173 digits.
Divisors found:
 r1=14515566495965381484432908137188917611379 (pp41)
 r2=36477621053825863236530826318706660402494626746122190956217533559432562151205757871210576748577472619 (pp101)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 164.10 hours.
Scaled time: 164.92 units (timescale=1.005).
Factorization parameters were as follows:
name: 31117_172
n: 529493334021436111922162637254840759809513964430346448697227563102473589227446184240143681531113116238112526127602307738122013166310255331601
m: 20000000000000000000000000000000000
deg: 5
c5: 175
c0: 106
skew: 0.90
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.6
alambda: 2.6
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved rational special-q in [3000000, 7900001)
Primes: RFBsize:412849, AFBsize:412611, largePrimes:11459526 encountered
Relations: rels:13076347, finalFF:1093514
Max relations in full relation-set: 28
Initial matrix: 825526 x 1093514 with sparse part having weight 138828364.
Pruned matrix : 651933 x 656124 with weight 130144864.
Total sieving time: 155.40 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 8.23 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,53,53,2.6,2.6,100000
total time: 164.10 hours.
 --------- CPU info (if available) ----------

(29·10¹⁴²-11)/9 = 3(2)₁₄₁1_<143> = 7 · 17 · 351229883 · 5178567259_<10> · 255467237901787825132567_<24> · C99

C99 = P35 · P65

P35 = 45143496014853321725780216738462753_<35>

P65 = 12908537643623924412394518260364827954583231327679114647926028197_<65>

Sat Nov 15 05:00:32 2008  Msieve v. 1.38
Sat Nov 15 05:00:32 2008  random seeds: bade0d0f 2d3a8c11
Sat Nov 15 05:00:32 2008  factoring 582736517672520719845325286851715855979999310291647305857501595762410574799373037350831074712246341 (99 digits)
Sat Nov 15 05:00:34 2008  searching for 15-digit factors
Sat Nov 15 05:00:36 2008  commencing quadratic sieve (99-digit input)
Sat Nov 15 05:00:36 2008  using multiplier of 19
Sat Nov 15 05:00:36 2008  using 64kb Pentium 4 sieve core
Sat Nov 15 05:00:36 2008  sieve interval: 18 blocks of size 65536
Sat Nov 15 05:00:36 2008  processing polynomials in batches of 6
Sat Nov 15 05:00:36 2008  using a sieve bound of 2644451 (96471 primes)
Sat Nov 15 05:00:36 2008  using large prime bound of 396667650 (28 bits)
Sat Nov 15 05:00:36 2008  using double large prime bound of 3000324291093600 (43-52 bits)
Sat Nov 15 05:00:36 2008  using trial factoring cutoff of 52 bits
Sat Nov 15 05:00:36 2008  polynomial 'A' values have 13 factors
Sat Nov 15 20:32:14 2008  96672 relations (23219 full + 73453 combined from 1449879 partial), need 96567
Sat Nov 15 20:32:20 2008  begin with 1473098 relations
Sat Nov 15 20:32:22 2008  reduce to 254199 relations in 11 passes
Sat Nov 15 20:32:22 2008  attempting to read 254199 relations
Sat Nov 15 20:32:31 2008  recovered 254199 relations
Sat Nov 15 20:32:31 2008  recovered 243572 polynomials
Sat Nov 15 20:32:31 2008  attempting to build 96672 cycles
Sat Nov 15 20:32:31 2008  found 96672 cycles in 6 passes
Sat Nov 15 20:32:31 2008  distribution of cycle lengths:
Sat Nov 15 20:32:31 2008     length 1 : 23219
Sat Nov 15 20:32:31 2008     length 2 : 16773
Sat Nov 15 20:32:31 2008     length 3 : 16143
Sat Nov 15 20:32:31 2008     length 4 : 13311
Sat Nov 15 20:32:31 2008     length 5 : 9835
Sat Nov 15 20:32:31 2008     length 6 : 6818
Sat Nov 15 20:32:31 2008     length 7 : 4392
Sat Nov 15 20:32:31 2008     length 9+: 6181
Sat Nov 15 20:32:31 2008  largest cycle: 20 relations
Sat Nov 15 20:32:32 2008  matrix is 96471 x 96672 (26.5 MB) with weight 6549247 (67.75/col)
Sat Nov 15 20:32:32 2008  sparse part has weight 6549247 (67.75/col)
Sat Nov 15 20:32:34 2008  filtering completed in 3 passes
Sat Nov 15 20:32:34 2008  matrix is 92288 x 92352 (25.4 MB) with weight 6297598 (68.19/col)
Sat Nov 15 20:32:34 2008  sparse part has weight 6297598 (68.19/col)
Sat Nov 15 20:32:35 2008  saving the first 48 matrix rows for later
Sat Nov 15 20:32:35 2008  matrix is 92240 x 92352 (15.0 MB) with weight 4898487 (53.04/col)
Sat Nov 15 20:32:35 2008  sparse part has weight 3376150 (36.56/col)
Sat Nov 15 20:32:35 2008  matrix includes 64 packed rows
Sat Nov 15 20:32:35 2008  using block size 21845 for processor cache size 512 kB
Sat Nov 15 20:32:36 2008  commencing Lanczos iteration
Sat Nov 15 20:32:36 2008  memory use: 14.9 MB
Sat Nov 15 20:34:08 2008  lanczos halted after 1460 iterations (dim = 92240)
Sat Nov 15 20:34:08 2008  recovered 19 nontrivial dependencies
Sat Nov 15 20:34:09 2008  prp35 factor: 45143496014853321725780216738462753
Sat Nov 15 20:34:09 2008  prp65 factor: 12908537643623924412394518260364827954583231327679114647926028197
Sat Nov 15 20:34:09 2008  elapsed time 15:33:37

Nov 15, 2008

By Tyler Cadigan / GGNFS, Msieve 1.38

(71·10¹⁷¹-17)/9 = 7(8)₁₇₀7_<172> = 3 · 11² · 107 · 239 · 41617 · C161

C161 = P51 · P53 · P57

P51 = 743770934175463115201037183333790751921305348910579_<51>

P53 = 82351698218466862057837603678567544986836853816071383_<53>

P57 = 333384192006290094571037308928858215235936225349216967277_<57>

Number: 78887_171
N=20420048306009174199433788969740439342448980838301017872131156786256424455380537910470509179869439410058419671254422931255136857208344475008636852033785021448689
  ( 161 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=743770934175463115201037183333790751921305348910579
 r2=82351698218466862057837603678567544986836853816071383
 r3=333384192006290094571037308928858215235936225349216967277
Version: 
Total time: 98.26 hours.
Scaled time: 248.98 units (timescale=2.534).
Factorization parameters were as follows:
n: 20420048306009174199433788969740439342448980838301017872131156786256424455380537910470509179869439410058419671254422931255136857208344475008636852033785021448689
m: 20000000000000000000000000000000000
deg: 5
c5: 355
c0: -272
skew: 0.95
Y0: 20000000000000000000000000000000000
Y1: -1
type: snfs
lss: 1
rlim: 6100000
alim: 6100000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.6
alambda: 2.6
qintsize: 1000000
Factor base limits: 6100000/6100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved rational special-q in [3050000, 7050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 996316 x 996564
Total sieving time: 98.26 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,174,5,0,0,0,0,0,0,0,0,6100000,6100000,27,27,53,53,2.6,2.6,100000
total time: 98.26 hours.
 --------- CPU info (if available) ----------

Nov 14, 2008 (6th)

By Sinkiti Sibata / GGNFS

(28·10¹⁴⁴+71)/9 = 3(1)₁₄₃9_<145> = 11 · 41 · 18269 · 154083203 · C130

C130 = P64 · P66

P64 = 8988041621249801554077485816065408422877758581642567645054836559_<64>

P66 = 272648951321970616039365589773091933223612684510617694429149896013_<66>

Number: 31119_144
N=2450580122471983000458653136037293800989706180239195005066168357353833426832036294754567817490052925818651778913076348977560739267
  ( 130 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=8988041621249801554077485816065408422877758581642567645054836559 (pp64)
 r2=272648951321970616039365589773091933223612684510617694429149896013 (pp66)
Version: GGNFS-0.77.1-20060513-k8
Total time: 11.25 hours.
Scaled time: 22.40 units (timescale=1.991).
Factorization parameters were as follows:
name: 31119_144
n: 2450580122471983000458653136037293800989706180239195005066168357353833426832036294754567817490052925818651778913076348977560739267
m: 100000000000000000000000000000
deg: 5
c5: 14
c0: 355
skew: 1.91
type: snfs
lss: 1
rlim: 1910000
alim: 1910000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1910000/1910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [955000, 1855001)
Primes: RFBsize:142718, AFBsize:142781, largePrimes:3919763 encountered
Relations: rels:3994994, finalFF:387236
Max relations in full relation-set: 28
Initial matrix: 285565 x 387236 with sparse part having weight 32964282.
Pruned matrix : 247981 x 249472 with weight 17297811.
Total sieving time: 10.41 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.63 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1910000,1910000,26,26,49,49,2.3,2.3,100000
total time: 11.25 hours.
 --------- CPU info (if available) ----------

Nov 14, 2008 (5th)

By Sinkiti Sibata / GGNFS

(29·10¹⁴⁵-11)/9 = 3(2)₁₄₄1_<146> = 503 · 5701 · 17491 · 33713 · 221709130896523847_<18> · C113

C113 = P39 · P75

P39 = 135401502323718758207541890954286813529_<39>

P75 = 634771412258360352784225937469269688580613867062470480811701781026293841083_<75>

Number: 32221_145
N=85949002851930617146158121584271921387063936434731256105680849591756257694871998711424728459121527841533980411907
  ( 113 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=135401502323718758207541890954286813529 (pp39)
 r2=634771412258360352784225937469269688580613867062470480811701781026293841083 (pp75)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 18.25 hours.
Scaled time: 18.45 units (timescale=1.011).
Factorization parameters were as follows:
name: 32221_145
n: 85949002851930617146158121584271921387063936434731256105680849591756257694871998711424728459121527841533980411907
m: 100000000000000000000000000000
deg: 5
c5: 29
c0: -11
skew: 0.82
type: snfs
lss: 1
rlim: 1930000
alim: 1930000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1930000/1930000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [965000, 2265001)
Primes: RFBsize:144125, AFBsize:143858, largePrimes:4789852 encountered
Relations: rels:5894049, finalFF:1229568
Max relations in full relation-set: 28
Initial matrix: 288048 x 1229568 with sparse part having weight 133674564.
Pruned matrix : 187931 x 189435 with weight 30832138.
Total sieving time: 17.83 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1930000,1930000,26,26,49,49,2.3,2.3,100000
total time: 18.25 hours.
 --------- CPU info (if available) ----------

(29·10¹⁴¹-11)/9 = 3(2)₁₄₀1_<142> = 83 · 263 · 397 · C135

C135 = P41 · P95

P41 = 12804731909514238216319764752004572447961_<41>

P95 = 29037595469567804574615307737073820889361614690525154000942625597804357574692524096735208662997_<95>

Number: 32221_141
N=371818625284740946976138232010385996838746762501506987298945008243283029222238646348394282675776581983436198238151547553352030168799117
  ( 135 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=12804731909514238216319764752004572447961 (pp41)
 r2=29037595469567804574615307737073820889361614690525154000942625597804357574692524096735208662997 (pp95)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 16.98 hours.
Scaled time: 17.13 units (timescale=1.009).
Factorization parameters were as follows:
name: 32221_141
n: 371818625284740946976138232010385996838746762501506987298945008243283029222238646348394282675776581983436198238151547553352030168799117
m: 20000000000000000000000000000
deg: 5
c5: 145
c0: -176
skew: 1.04
type: snfs
lss: 1
rlim: 1740000
alim: 1740000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
Factor base limits: 1740000/1740000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [870000, 2170001)
Primes: RFBsize:130902, AFBsize:129901, largePrimes:4460730 encountered
Relations: rels:5208342, finalFF:863036
Max relations in full relation-set: 28
Initial matrix: 260870 x 863036 with sparse part having weight 99152444.
Pruned matrix : 181833 x 183201 with weight 30124554.
Total sieving time: 16.57 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.27 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1740000,1740000,26,26,48,48,2.3,2.3,100000
total time: 16.98 hours.
 --------- CPU info (if available) ----------

(29·10¹²⁹-11)/9 = 3(2)₁₂₈1_<130> = 23 · 1213 · 1447 · 723389347 · C114

C114 = P35 · P79

P35 = 14136908388814870635901620792537073_<35>

P79 = 7804979522579487282216412714267347177075015773931605314775746515999118728496747_<79>

Number: 32221_129
N=110338280487282237783468003594113762991473241073633009146320341846348322084077083770113293431200809692433557401531
  ( 114 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=14136908388814870635901620792537073 (pp35)
 r2=7804979522579487282216412714267347177075015773931605314775746515999118728496747 (pp79)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.61 hours.
Scaled time: 9.24 units (timescale=2.003).
Factorization parameters were as follows:
name: 32221_129
n: 110338280487282237783468003594113762991473241073633009146320341846348322084077083770113293431200809692433557401531
m: 100000000000000000000000000
deg: 5
c5: 29
c0: -110
skew: 1.31
type: snfs
lss: 1
rlim: 1090000
alim: 1090000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1090000/1090000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [545000, 995001)
Primes: RFBsize:84976, AFBsize:84869, largePrimes:2838036 encountered
Relations: rels:2727089, finalFF:203434
Max relations in full relation-set: 28
Initial matrix: 169910 x 203434 with sparse part having weight 16356166.
Pruned matrix : 159952 x 160865 with weight 10455858.
Total sieving time: 4.32 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1090000,1090000,26,26,47,47,2.3,2.3,50000
total time: 4.61 hours.
 --------- CPU info (if available) ----------

(29·10¹³⁰-11)/9 = 3(2)₁₂₉1_<131> = 7 · 661 · 12490000153_<11> · C117

C117 = P50 · P67

P50 = 84078455171865397847467760865288765955666013538007_<50>

P67 = 6631454921038865667129918457268982086762167608648817336351681684513_<67>

Number: 32221_130
N=557562485302812458556720381686020624493646449535865520700068302534868504103654261098408140968189266407221764708785591
  ( 117 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=84078455171865397847467760865288765955666013538007 (pp50)
 r2=6631454921038865667129918457268982086762167608648817336351681684513 (pp67)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.00 hours.
Scaled time: 8.03 units (timescale=2.010).
Factorization parameters were as follows:
name: 32221_130
n: 557562485302812458556720381686020624493646449535865520700068302534868504103654261098408140968189266407221764708785591
m: 100000000000000000000000000
deg: 5
c5: 29
c0: -11
skew: 0.82
type: snfs
lss: 1
rlim: 1090000
alim: 1090000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1090000/1090000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [545000, 895001)
Primes: RFBsize:84976, AFBsize:84739, largePrimes:3093783 encountered
Relations: rels:3249328, finalFF:441711
Max relations in full relation-set: 28
Initial matrix: 169780 x 441711 with sparse part having weight 34736385.
Pruned matrix : 110817 x 111729 with weight 7836212.
Total sieving time: 3.80 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1090000,1090000,26,26,47,47,2.3,2.3,50000
total time: 4.00 hours.
 --------- CPU info (if available) ----------

(29·10¹³⁹-11)/9 = 3(2)₁₃₈1_<140> = 60577859 · C132

C132 = P54 · P79

P54 = 281767272770529021750867390333886008734104756792620853_<54>

P79 = 1887778432180578846158888755050078279456816964415040725088239206457139407989523_<79>

Number: 32221_139
N=531914180430546781493585341506080996065282238222090718363325158491029242585516636073622579203768529063105749944418177971958735323119
  ( 132 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=281767272770529021750867390333886008734104756792620853 (pp54)
 r2=1887778432180578846158888755050078279456816964415040725088239206457139407989523 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 14.17 hours.
Scaled time: 14.30 units (timescale=1.009).
Factorization parameters were as follows:
name: 32221_139
n: 531914180430546781493585341506080996065282238222090718363325158491029242585516636073622579203768529063105749944418177971958735323119
m: 10000000000000000000000000000
deg: 5
c5: 29
c0: -110
skew: 1.31
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [800000, 2100001)
Primes: RFBsize:121127, AFBsize:121406, largePrimes:4348465 encountered
Relations: rels:5015081, finalFF:747625
Max relations in full relation-set: 28
Initial matrix: 242598 x 747625 with sparse part having weight 87264402.
Pruned matrix : 176117 x 177393 with weight 29807612.
Total sieving time: 13.78 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.27 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000
total time: 14.17 hours.
 --------- CPU info (if available) ----------

(29·10¹³¹-11)/9 = 3(2)₁₃₀1_<132> = 3 · 19² · 97 · 269 · 1523 · 56817259 · C114

C114 = P47 · P67

P47 = 17995042551372841939533353574619370418923120791_<47>

P67 = 7322678345243243790674472867484716011829823748915723894088465209557_<67>

Number: 32221_131
N=131771908412668642055273055352670569886186700122328238744264724206595060935364524814258713765988320913048238599587
  ( 114 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=17995042551372841939533353574619370418923120791 (pp47)
 r2=7322678345243243790674472867484716011829823748915723894088465209557 (pp67)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.68 hours.
Scaled time: 11.38 units (timescale=2.003).
Factorization parameters were as follows:
name: 32221_131
n: 131771908412668642055273055352670569886186700122328238744264724206595060935364524814258713765988320913048238599587
m: 200000000000000000000000000
deg: 5
c5: 145
c0: -176
skew: 1.04
type: snfs
lss: 1
rlim: 1180000
alim: 1180000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1180000/1180000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [590000, 1115001)
Primes: RFBsize:91490, AFBsize:90773, largePrimes:3248433 encountered
Relations: rels:3371748, finalFF:409329
Max relations in full relation-set: 28
Initial matrix: 182330 x 409329 with sparse part having weight 35732054.
Pruned matrix : 135105 x 136080 with weight 9984945.
Total sieving time: 5.40 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1180000,1180000,26,26,47,47,2.3,2.3,75000
total time: 5.68 hours.
 --------- CPU info (if available) ----------

(29·10¹³⁸-11)/9 = 3(2)₁₃₇1_<139> = 163 · 191 · 53591 · 15463122908501011867111_<23> · C108

C108 = P53 · P55

P53 = 37790779259699711501744662535598103375993317541545193_<53>

P55 = 3304909721696979379133654104517864011655110436713126409_<55>

Number: 32221_138
N=124895113765886153948413921083715265507933979125035450661884648697806100529531289100210133846332979795301937
  ( 108 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=37790779259699711501744662535598103375993317541545193 (pp53)
 r2=3304909721696979379133654104517864011655110436713126409 (pp55)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 16.18 hours.
Scaled time: 16.27 units (timescale=1.006).
Factorization parameters were as follows:
name: 32221_138
n: 124895113765886153948413921083715265507933979125035450661884648697806100529531289100210133846332979795301937
m: 5000000000000000000000000000
deg: 5
c5: 232
c0: -275
skew: 1.03
type: snfs
lss: 1
rlim: 1560000
alim: 1560000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1560000/1560000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [780000, 2080001)
Primes: RFBsize:118376, AFBsize:117850, largePrimes:4386409 encountered
Relations: rels:5202691, finalFF:916162
Max relations in full relation-set: 28
Initial matrix: 236293 x 916162 with sparse part having weight 106553532.
Pruned matrix : 166193 x 167438 with weight 30853001.
Total sieving time: 15.80 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.24 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1560000,1560000,26,26,48,48,2.3,2.3,100000
total time: 16.18 hours.
 --------- CPU info (if available) ----------

Nov 14, 2008 (4th)

By Robert Backstrom /

(29·10¹¹⁸-11)/9 = 3(2)₁₁₇1_<119> = 7² · 1783 · 8791755381953_<13> · C101

C101 = P50 · P52

P50 = 16265156725388180254811666957299274188190461943863_<50>

P52 = 2579135842593250281246313099668077876980060807295117_<52>

Number: n
N=41950048695845315860193362149200760634222247656007637390076886198570583579181328177989365034928016971
  ( 101 digits)
SNFS difficulty: 119 digits.
Divisors found:

 r1=16265156725388180254811666957299274188190461943863 (pp50)
 r2=2579135842593250281246313099668077876980060807295117 (pp52)

Ggnfs  : 0.77.1-20051202-athlon
Msieve : 1.38
Total time:  1.25 hours.
Scaled time: 1.62 units (timescale=1.298).
Factorization parameters were as follows:
name: KA_3_2_117_1
n: 41950048695845315860193362149200760634222247656007637390076886198570583579181328177989365034928016971
type: snfs
skew: 0.21
deg: 5
c5: 29000
c0: -11
m: 100000000000000000000000
rlim: 500000
alim: 500000
lpbr: 27
lpba: 27
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved algebraic special-q in [250000, 410000)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3902474
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 114032 x 114276
Total sieving time: 1.25 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,119,5,0,0,0,0,0,0,0,0,500000,500000,27,27,54,54,2.5,2.5,50000
total time: 1.25 hours.
 --------- CPU info (if available) ----------

Nov 14, 2008 (3rd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38

(29·10¹⁷²-11)/9 = 3(2)₁₇₁1_<173> = 7 · 911 · 2137 · 51674677 · C158

C158 = P30 · P128

P30 = 686837002770721101814315002743_<30>

P128 = 66619764671176635087249126590613431344175126180553448850764036499467766258915040323962972670825895791557302195078744381102836239_<128>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=321248721
Step 1 took 19977ms
Step 2 took 12745ms
********** Factor found in step 2: 686837002770721101814315002743
Found probable prime factor of 30 digits: 686837002770721101814315002743
Probable prime cofactor 66619764671176635087249126590613431344175126180553448850764036499467766258915040323962972670825895791557302195078744381102836239 has 128 digits

(29·10¹⁶⁷-11)/9 = 3(2)₁₆₆1_<168> = 3 · 19 · 1217 · 545375959 · 20778919487_<11> · 45602021140493_<14> · C130

C130 = P38 · C93

P38 = 14614344872681959582619366399806329959_<38>

C93 = [615046089100797276059789575087661813724676267821413765385904915681332714128994363968725487479_<93>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2608115933
Step 1 took 14061ms
Step 2 took 9717ms
********** Factor found in step 2: 14614344872681959582619366399806329959
Found probable prime factor of 38 digits: 14614344872681959582619366399806329959
Composite cofactor 615046089100797276059789575087661813724676267821413765385904915681332714128994363968725487479 has 93 digits

(29·10¹⁷⁹-11)/9 = 3(2)₁₇₈1_<180> = 3³ · 53 · 3549619 · C170

C170 = P35 · P136

P35 = 13310355728458018191436051090311587_<35>

P136 = 4765894801948423367811395504889628582659434826497324644479808786421859894569556486917950969689887532292510529531422667771365530802998547_<136>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4238845314
Step 1 took 19462ms
Step 2 took 12928ms
********** Factor found in step 2: 13310355728458018191436051090311587
Found probable prime factor of 35 digits: 13310355728458018191436051090311587
Probable prime cofactor 4765894801948423367811395504889628582659434826497324644479808786421859894569556486917950969689887532292510529531422667771365530802998547 has 136 digits

(29·10¹¹⁷-11)/9 = 3(2)₁₁₆1_<118> = 127 · 1782527232461_<13> · C104

C104 = P37 · P67

P37 = 4553468733578991760986408024122748403_<37>

P67 = 3125886718200121590683661018583279104542738986002111542287194104581_<67>

SNFS difficulty: 118 digits.
Divisors found:
 r1=4553468733578991760986408024122748403
 r2=3125886718200121590683661018583279104542738986002111542287194104581
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
n: 14233627436034098355590986715425150232984508544339962709686067006412690267978679376207813601632332734143
m: 100000000000000000000000
deg: 5
c5: 2900
c0: -11
skew: 0.33
type: snfs
lss: 1
rlim: 680000
alim: 680000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.4
alambda: 2.4
Factor base limits: 680000/680000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [340000, 490001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 92898 x 93126
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,118,5,0,0,0,0,0,0,0,0,680000,680000,25,25,46,46,2.4,2.4,50000
total time: 0.90 hours.

(28·10¹⁵⁷+71)/9 = 3(1)₁₅₆9_<158> = 3 · 13 · 1997 · C153

C153 = P44 · P110

P44 = 36350485135267436326923615816470359590281339_<44>

P110 = 10989112985873334669406170921657814512909467293608141635001759927342856073118693439074001322936654769906256487_<110>

SNFS difficulty: 158 digits.
Divisors found:
 r1=36350485135267436326923615816470359590281339
 r2=10989112985873334669406170921657814512909467293608141635001759927342856073118693439074001322936654769906256487
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
n: 399459588242763004906219728453078478116034450536203165146580269264295303353891235713969815121542712929793550724947820591285789082484125047970816623796093
m: 20000000000000000000000000000000
deg: 5
c5: 175
c0: 142
skew: 0.96
type: snfs
lss: 1
rlim: 3100000
alim: 3100000
lpbr: 27
lpba: 27
Factor base limits: 3100000/3100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [1550000, 2850001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 600523 x 600765
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,54,54,2.5,2.5,100000
total time: 20.00 hours.

(8·10¹⁸²-17)/9 = (8)₁₈₁7_<182> = 3 · 47 · 29443147 · 245690237799029_<15> · C158

C158 = P31 · C128

P31 = 1409781315068910934903369464751_<31>

C128 = [61816510636424402556322751316069604684810286368811027148055645738587135263914950492193568745510518427867118128501016167399497339_<128>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=109125358
Step 1 took 19337ms
Step 2 took 12585ms
********** Factor found in step 2: 1409781315068910934903369464751
Found probable prime factor of 31 digits: 1409781315068910934903369464751
Composite cofactor 61816510636424402556322751316069604684810286368811027148055645738587135263914950492193568745510518427867118128501016167399497339 has 128 digits

(10¹⁸⁶+11)/3 = (3)₁₈₅7_<186> = 4931 · 73081788083755769363_<20> · C162

C162 = P33 · C130

P33 = 119082595147331902970137026564983_<33>

C130 = [7767589884898905584453846627616528735466833665717627569798152437068183984890392285268361811654098469581336926528022496076374393063_<130>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3868127526
Step 1 took 25004ms
Step 2 took 16416ms
********** Factor found in step 2: 119082595147331902970137026564983
Found probable prime factor of 33 digits: 119082595147331902970137026564983
Composite cofactor 7767589884898905584453846627616528735466833665717627569798152437068183984890392285268361811654098469581336926528022496076374393063 has 130 digits

8·10¹⁸⁵-3 = 7(9)₁₈₄7_<186> = 11 · 1380647833218789973997_<22> · C164

C164 = P31 · P134

P31 = 3200915410197558946108301126563_<31>

P134 = 16456602869353096430189233547034000220094751192335801441349696122224558115436230108977366054340110982446113898104412344324225790271057_<134>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3050675837
Step 1 took 20201ms
********** Factor found in step 1: 3200915410197558946108301126563
Found probable prime factor of 31 digits: 3200915410197558946108301126563
Probable prime cofactor 16456602869353096430189233547034000220094751192335801441349696122224558115436230108977366054340110982446113898104412344324225790271057 has 134 digits

(14·10¹⁸⁶-41)/9 = 1(5)₁₈₅1_<187> = 3² · 29 · 449 · 7534276176716793611_<19> · C163

C163 = P29 · P134

P29 = 32588984944879249360239874831_<29>

P134 = 54061278057400452561143167961063501861872785250750941089820142488320368986133543167855544550220331678923941602572569248399536665621399_<134>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=319754870
Step 1 took 19249ms
Step 2 took 12557ms
********** Factor found in step 2: 32588984944879249360239874831
Found probable prime factor of 29 digits: 32588984944879249360239874831
Probable prime cofactor 54061278057400452561143167961063501861872785250750941089820142488320368986133543167855544550220331678923941602572569248399536665621399 has 134 digits

Nov 14, 2008 (2nd)

By Jo Yeong Uk / GGNFS, Msieve

(28·10¹¹⁹+71)/9 = 3(1)₁₁₈9_<120> = 41 · 46716180536895694963_<20> · C99

C99 = P35 · P65

P35 = 15752862529566178334162706383037239_<35>

P65 = 10311096562260032607624715134869831170912033798303420229926003387_<65>

Number: 31119_119
N=162429286674364702693980728505753820793032235270959101041564195163550081532685326692686733661128493
  ( 99 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=15752862529566178334162706383037239 (pp35)
 r2=10311096562260032607624715134869831170912033798303420229926003387 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.88 hours.
Scaled time: 2.10 units (timescale=2.386).
Factorization parameters were as follows:
n: 162429286674364702693980728505753820793032235270959101041564195163550081532685326692686733661128493
m: 1000000000000000000000000
deg: 5
c5: 14
c0: 355
skew: 1.91
type: snfs
rlim: 600000
alim: 600000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 510001)
Primes: RFBsize:49098, AFBsize:49132, largePrimes:1240702 encountered
Relations: rels:1201057, finalFF:133899
Max relations in full relation-set: 28
Initial matrix: 98296 x 133899 with sparse part having weight 6510018.
Pruned matrix : 84104 x 84659 with weight 3043212.
Total sieving time: 0.85 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.2,2.2,30000
total time: 0.88 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.62 BogoMIPS (lpj=2673810)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.36 BogoMIPS (lpj=2672182)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672336)

(29·10¹⁵⁶-11)/9 = 3(2)₁₅₅1_<157> = 595877 · 33067975599667_<14> · 583036481857549_<15> · 44705744025044195944187429_<26> · C97

C97 = P46 · P52

P46 = 1841104617768553066539921824820814632819354673_<46>

P52 = 3407640197035790755600685336333428103580485026012643_<52>

Thu Nov 13 23:11:53 2008  
Thu Nov 13 23:11:53 2008  
Thu Nov 13 23:11:53 2008  Msieve v. 1.32
Thu Nov 13 23:11:53 2008  random seeds: 09471290 f9ff2327
Thu Nov 13 23:11:53 2008  factoring 6273822102456336397478900791555360195036548821463081823181815408929116357407108429062361599130739 (97 digits)
Thu Nov 13 23:11:54 2008  no P-1/P+1/ECM available, skipping
Thu Nov 13 23:11:54 2008  commencing quadratic sieve (97-digit input)
Thu Nov 13 23:11:54 2008  using multiplier of 11
Thu Nov 13 23:11:54 2008  using VC8 32kb sieve core
Thu Nov 13 23:11:54 2008  sieve interval: 36 blocks of size 32768
Thu Nov 13 23:11:54 2008  processing polynomials in batches of 6
Thu Nov 13 23:11:54 2008  using a sieve bound of 2404009 (88134 primes)
Thu Nov 13 23:11:54 2008  using large prime bound of 360601350 (28 bits)
Thu Nov 13 23:11:54 2008  using double large prime bound of 2527255810204800 (43-52 bits)
Thu Nov 13 23:11:54 2008  using trial factoring cutoff of 52 bits
Thu Nov 13 23:11:54 2008  polynomial 'A' values have 13 factors
Fri Nov 14 03:12:20 2008  88297 relations (21728 full + 66569 combined from 1312671 partial), need 88230
Fri Nov 14 03:12:26 2008  begin with 1334399 relations
Fri Nov 14 03:12:27 2008  reduce to 228127 relations in 11 passes
Fri Nov 14 03:12:27 2008  attempting to read 228127 relations
Fri Nov 14 03:12:30 2008  recovered 228127 relations
Fri Nov 14 03:12:30 2008  recovered 213806 polynomials
Fri Nov 14 03:12:30 2008  attempting to build 88297 cycles
Fri Nov 14 03:12:30 2008  found 88297 cycles in 5 passes
Fri Nov 14 03:12:30 2008  distribution of cycle lengths:
Fri Nov 14 03:12:30 2008     length 1 : 21728
Fri Nov 14 03:12:30 2008     length 2 : 15697
Fri Nov 14 03:12:30 2008     length 3 : 15092
Fri Nov 14 03:12:30 2008     length 4 : 11939
Fri Nov 14 03:12:30 2008     length 5 : 8880
Fri Nov 14 03:12:30 2008     length 6 : 6119
Fri Nov 14 03:12:30 2008     length 7 : 3766
Fri Nov 14 03:12:30 2008     length 9+: 5076
Fri Nov 14 03:12:30 2008  largest cycle: 21 relations
Fri Nov 14 03:12:30 2008  matrix is 88134 x 88297 with weight 5871621 (avg 66.50/col)
Fri Nov 14 03:12:30 2008  filtering completed in 3 passes
Fri Nov 14 03:12:30 2008  matrix is 83870 x 83934 with weight 5623519 (avg 67.00/col)
Fri Nov 14 03:12:31 2008  saving the first 48 matrix rows for later
Fri Nov 14 03:12:31 2008  matrix is 83822 x 83934 with weight 4447168 (avg 52.98/col)
Fri Nov 14 03:12:31 2008  matrix includes 64 packed rows
Fri Nov 14 03:12:31 2008  using block size 33573 for processor cache size 4096 kB
Fri Nov 14 03:12:32 2008  commencing Lanczos iteration
Fri Nov 14 03:13:05 2008  lanczos halted after 1328 iterations (dim = 83821)
Fri Nov 14 03:13:05 2008  recovered 17 nontrivial dependencies
Fri Nov 14 03:13:05 2008  prp46 factor: 1841104617768553066539921824820814632819354673
Fri Nov 14 03:13:05 2008  prp52 factor: 3407640197035790755600685336333428103580485026012643
Fri Nov 14 03:13:05 2008  elapsed time 04:01:12

Nov 14, 2008

By Wataru Sakai / Msieve

(23·10¹⁹⁸-41)/9 = 2(5)₁₉₇1_<199> = C199

C199 = P48 · P69 · P83

P48 = 330048488040326643281297069715026424433630199177_<48>

P69 = 515268873558507774234780986872212218799351367544094804445562015097943_<69>

P83 = 15027047896934639118130321753833927516048042040409791293930953426741283723690424241_<83>

Number: 25551_198
N=2555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555551
  ( 199 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=330048488040326643281297069715026424433630199177
 r2=515268873558507774234780986872212218799351367544094804445562015097943
 r3=15027047896934639118130321753833927516048042040409791293930953426741283723690424241
Version: 
Total time: 993.45 hours.
Scaled time: 2000.80 units (timescale=2.014).
Factorization parameters were as follows:
n: 2555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555551
m: 5000000000000000000000000000000000000000
deg: 5
c5: 184
c0: -1025
skew: 1.41
type: snfs
lss: 1
rlim: 21000000
alim: 21000000
lpbr: 29
lpba: 29
mfbr: 57
mfba: 57
rlambda: 2.8
alambda: 2.8
Factor base limits: 21000000/21000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 57/57
Sieved rational special-q in [10500000, 19700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3481118 x 3481365
Total sieving time: 993.45 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,200,5,0,0,0,0,0,0,0,0,21000000,21000000,29,29,57,57,2.8,2.8,100000
total time: 993.45 hours.
 --------- CPU info (if available) ----------

Nov 13, 2008 (8th)

By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1

(28·10¹⁵⁶+71)/9 = 3(1)₁₅₅9_<157> = 11 · 373 · 3461 · 2009315225524317079_<19> · 43732513694910445326617_<23> · 87679139790976199399319247097_<29> · C80

C80 = P37 · P44

P37 = 1163077854391997881426801097760029323_<37>

P44 = 24448646588930130118660551617391962100587321_<44>

Wed Nov 12 23:31:56 2008  factoring 28435679417441093560965677996084063055357095027467175103552861928042176482013683 (80 digits)
Wed Nov 12 23:31:56 2008  no P-1/P+1/ECM available, skipping
Wed Nov 12 23:31:56 2008  commencing quadratic sieve (80-digit input)
Wed Nov 12 23:31:56 2008  using multiplier of 11
Wed Nov 12 23:31:56 2008  using 64kb Opteron sieve core
Wed Nov 12 23:31:56 2008  sieve interval: 6 blocks of size 65536
Wed Nov 12 23:31:56 2008  processing polynomials in batches of 17
Wed Nov 12 23:31:56 2008  using a sieve bound of 1224919 (47235 primes)
Wed Nov 12 23:31:56 2008  using large prime bound of 122491900 (26 bits)
Wed Nov 12 23:31:56 2008  using trial factoring cutoff of 27 bits
Wed Nov 12 23:31:56 2008  polynomial 'A' values have 10 factors
Wed Nov 12 23:42:08 2008  47423 relations (24196 full + 23227 combined from 259919 partial), need 47331
Wed Nov 12 23:42:08 2008  begin with 284115 relations
Wed Nov 12 23:42:08 2008  reduce to 67756 relations in 2 passes
Wed Nov 12 23:42:08 2008  attempting to read 67756 relations
Wed Nov 12 23:42:08 2008  recovered 67756 relations
Wed Nov 12 23:42:08 2008  recovered 58044 polynomials
Wed Nov 12 23:42:08 2008  attempting to build 47423 cycles
Wed Nov 12 23:42:08 2008  found 47423 cycles in 1 passes
Wed Nov 12 23:42:08 2008  distribution of cycle lengths:
Wed Nov 12 23:42:08 2008     length 1 : 24196
Wed Nov 12 23:42:08 2008     length 2 : 23227
Wed Nov 12 23:42:08 2008  largest cycle: 2 relations
Wed Nov 12 23:42:08 2008  matrix is 47235 x 47423 (6.9 MB) with weight 1438142 (30.33/col)
Wed Nov 12 23:42:09 2008  sparse part has weight 1438142 (30.33/col)
Wed Nov 12 23:42:09 2008  filtering completed in 3 passes
Wed Nov 12 23:42:09 2008  matrix is 33614 x 33676 (5.4 MB) with weight 1147203 (34.07/col)
Wed Nov 12 23:42:09 2008  sparse part has weight 1147203 (34.07/col)
Wed Nov 12 23:42:09 2008  saving the first 48 matrix rows for later
Wed Nov 12 23:42:09 2008  matrix is 33566 x 33676 (3.9 MB) with weight 886098 (26.31/col)
Wed Nov 12 23:42:09 2008  sparse part has weight 683492 (20.30/col)
Wed Nov 12 23:42:09 2008  matrix includes 64 packed rows
Wed Nov 12 23:42:09 2008  using block size 13470 for processor cache size 1024 kB
Wed Nov 12 23:42:09 2008  commencing Lanczos iteration
Wed Nov 12 23:42:09 2008  memory use: 3.8 MB
Wed Nov 12 23:42:13 2008  lanczos halted after 532 iterations (dim = 33562)
Wed Nov 12 23:42:13 2008  recovered 16 nontrivial dependencies
Wed Nov 12 23:42:13 2008  prp37 factor: 1163077854391997881426801097760029323
Wed Nov 12 23:42:13 2008  prp44 factor: 24448646588930130118660551617391962100587321
Wed Nov 12 23:42:13 2008  elapsed time 00:10:17

(29·10¹²⁰-11)/9 = 3(2)₁₁₉1_<121> = 929 · 3529 · 93603969731_<11> · C104

C104 = P47 · P57

P47 = 15773947874373735667035781810915813703050741501_<47>

P57 = 665661512203010225589354648368830774478561194130089746851_<57>

SNFS difficulty: 121 digits.
Divisors found:
 r1=15773947874373735667035781810915813703050741501
 r2=665661512203010225589354648368830774478561194130089746851
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
n: 10500109995467079653618700393101576418348639811018615193020274232640086317642184622406460042272929763351
m: 1000000000000000000000000
deg: 5
c5: 29
c0: -11
skew: 0.82
type: snfs
lss: 1
rlim: 740000
alim: 740000
lpbr: 25
lpba: 25
Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [370000, 520001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 93804 x 94038
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.4,2.4,50000
total time: 1.10 hours.

(28·10¹⁵⁰+71)/9 = 3(1)₁₄₉9_<151> = 11² · 17 · 78658003 · C140

C140 = P43 · P46 · P52

P43 = 1505435896944076504911748169972217944553047_<43>

P46 = 1471581719349738533115955225275854247106676533_<46>

P52 = 8679439141512810986119574471702663143711519334849039_<52>

SNFS difficulty: 151 digits.
Divisors found:
 r1=1505435896944076504911748169972217944553047
 r2=1471581719349738533115955225275854247106676533
 r3=8679439141512810986119574471702663143711519334849039
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 19228185977613401633369694166969387451300507364563153637761353934453891234971683412314329153263211485477792708635663610248791317482884594989
m: 1000000000000000000000000000000
deg: 5
c5: 28
c0: 71
skew: 1.20
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [1150000, 1950001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 343246 x 343488
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,54,54,2.5,2.5,100000
total time: 10.00 hours.

(28·10¹²¹+71)/9 = 3(1)₁₂₀9_<122> = 3 · 13 · C120

C120 = P32 · P88

P32 = 88250508996934421910237303503471_<32>

P88 = 9039277017070896785066121746411140231987821216816813125338426885493714376603735640821751_<88>

SNFS difficulty: 123 digits.
Divisors found:
 r1=88250508996934421910237303503471
 r2=9039277017070896785066121746411140231987821216816813125338426885493714376603735640821751
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 797720797720797720797720797720797720797720797720797720797720797720797720797720797720797720797720797720797720797720797721
m: 2000000000000000000000000
deg: 5
c5: 35
c0: 284
skew: 1.52
type: snfs
lss: 1
rlim: 790000
alim: 790000
lpbr: 25
lpba: 25
Factor base limits: 790000/790000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [395000, 595001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 95126 x 95352
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,790000,790000,25,25,46,46,2.4,2.4,50000
total time: 1.20 hours.

(28·10¹²⁰+71)/9 = 3(1)₁₁₉9_<121> = 11 · 435181 · 18265558777_<11> · C104

C104 = P36 · P68

P36 = 442460566136144594370009127235877449_<36>

P68 = 80416538963720077560264003230693394349183018398367267759796577012833_<68>

SNFS difficulty: 121 digits.
Divisors found:
 r1=442460566136144594370009127235877449
 r2=80416538963720077560264003230693394349183018398367267759796577012833
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 35581147356596916060734014065265079727475129640192670336805045603048589526584395617189367471510088303017
m: 1000000000000000000000000
deg: 5
c5: 28
c0: 71
skew: 1.20
type: snfs
lss: 1
rlim: 740000
alim: 740000
lpbr: 25
lpba: 25
Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [370000, 520001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 86191 x 86420
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.4,2.4,50000
total time: 1.00 hours.

(28·10¹⁸⁹+71)/9 = 3(1)₁₈₈9_<190> = 41 · C188

C188 = P36 · P153

P36 = 154404198802585779625548736654848061_<36>

P153 = 491442327320423324677368836487922152089885148164851026168352045646964403454221159385528666500912510299956883818830016131844263490242213578840344716671619_<153>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2777304898
Step 1 took 22057ms
Step 2 took 14793ms
********** Factor found in step 2: 154404198802585779625548736654848061
Found probable prime factor of 36 digits: 154404198802585779625548736654848061
Probable prime cofactor 491442327320423324677368836487922152089885148164851026168352045646964403454221159385528666500912510299956883818830016131844263490242213578840344716671619 has 153 digits

To be, or not to be: that is the question:
Whether 'tis nobler in the mind to suffer
The slings and arrows of outrageous fortune,
Or to take arms against a sea of troubles,
And by opposing end them? To die: to sleep;
No more; and by a sleep to say we end
The heart-ache and the thousand natural shocks
That flesh is heir to, 'tis a consummation
Devoutly to be wish'd. To die, to sleep;
To sleep: perchance to dream: ay, there's the rub!

Nov 13, 2008 (7th)

By Robert Backstrom / Msieve, GGNFS

(28·10¹⁸²+71)/9 = 3(1)₁₈₁9_<183> = 11 · 17 · 17937235419397613597_<20> · 1240051552825565617766747_<25> · 3209888690684034869163037_<25> · 4136832651683704203599999_<25> · C88

C88 = P40 · P49

P40 = 1769146270425716073999738991617358320203_<40>

P49 = 3183882267929421411122992492160640617807896639987_<49>

Thu Nov 13 17:49:42 2008  
Thu Nov 13 17:49:42 2008  
Thu Nov 13 17:49:42 2008  Msieve v. 1.38
Thu Nov 13 17:49:42 2008  random seeds: 51185410 c757fac6
Thu Nov 13 17:49:42 2008  factoring 5632753439781906371926677051017548102999369398501852290406917367586148830928022159757361 (88 digits)
Thu Nov 13 17:49:42 2008  searching for 15-digit factors
Thu Nov 13 17:49:43 2008  commencing quadratic sieve (88-digit input)
Thu Nov 13 17:49:43 2008  using multiplier of 15
Thu Nov 13 17:49:43 2008  using 64kb Opteron sieve core
Thu Nov 13 17:49:43 2008  sieve interval: 14 blocks of size 65536
Thu Nov 13 17:49:43 2008  processing polynomials in batches of 8
Thu Nov 13 17:49:43 2008  using a sieve bound of 1518311 (58000 primes)
Thu Nov 13 17:49:43 2008  using large prime bound of 121464880 (26 bits)
Thu Nov 13 17:49:43 2008  using double large prime bound of 356460311108640 (42-49 bits)
Thu Nov 13 17:49:43 2008  using trial factoring cutoff of 49 bits
Thu Nov 13 17:49:43 2008  polynomial 'A' values have 11 factors
Thu Nov 13 18:29:52 2008  58287 relations (16307 full + 41980 combined from 608396 partial), need 58096
Thu Nov 13 18:29:53 2008  begin with 624703 relations
Thu Nov 13 18:29:53 2008  reduce to 139184 relations in 10 passes
Thu Nov 13 18:29:53 2008  attempting to read 139184 relations
Thu Nov 13 18:29:54 2008  recovered 139184 relations
Thu Nov 13 18:29:54 2008  recovered 116779 polynomials
Thu Nov 13 18:29:54 2008  attempting to build 58287 cycles
Thu Nov 13 18:29:54 2008  found 58287 cycles in 6 passes
Thu Nov 13 18:29:55 2008  distribution of cycle lengths:
Thu Nov 13 18:29:55 2008     length 1 : 16307
Thu Nov 13 18:29:55 2008     length 2 : 11401
Thu Nov 13 18:29:55 2008     length 3 : 10285
Thu Nov 13 18:29:55 2008     length 4 : 7674
Thu Nov 13 18:29:55 2008     length 5 : 5269
Thu Nov 13 18:29:55 2008     length 6 : 3307
Thu Nov 13 18:29:55 2008     length 7 : 1957
Thu Nov 13 18:29:55 2008     length 9+: 2087
Thu Nov 13 18:29:55 2008  largest cycle: 21 relations
Thu Nov 13 18:29:55 2008  matrix is 58000 x 58287 (14.3 MB) with weight 3515841 (60.32/col)
Thu Nov 13 18:29:55 2008  sparse part has weight 3515841 (60.32/col)
Thu Nov 13 18:29:55 2008  filtering completed in 3 passes
Thu Nov 13 18:29:55 2008  matrix is 53538 x 53602 (13.3 MB) with weight 3259658 (60.81/col)
Thu Nov 13 18:29:55 2008  sparse part has weight 3259658 (60.81/col)
Thu Nov 13 18:29:56 2008  saving the first 48 matrix rows for later
Thu Nov 13 18:29:56 2008  matrix is 53490 x 53602 (9.6 MB) with weight 2670563 (49.82/col)
Thu Nov 13 18:29:56 2008  sparse part has weight 2192693 (40.91/col)
Thu Nov 13 18:29:56 2008  matrix includes 64 packed rows
Thu Nov 13 18:29:56 2008  using block size 21440 for processor cache size 1024 kB
Thu Nov 13 18:29:56 2008  commencing Lanczos iteration
Thu Nov 13 18:29:56 2008  memory use: 8.7 MB
Thu Nov 13 18:30:16 2008  lanczos halted after 847 iterations (dim = 53484)
Thu Nov 13 18:30:17 2008  recovered 16 nontrivial dependencies
Thu Nov 13 18:30:17 2008  prp40 factor: 1769146270425716073999738991617358320203
Thu Nov 13 18:30:17 2008  prp49 factor: 3183882267929421411122992492160640617807896639987
Thu Nov 13 18:30:17 2008  elapsed time 00:40:35

(29·10¹¹⁵-11)/9 = 3(2)₁₁₄1_<116> = 491 · 49464953330747879_<17> · C97

C97 = P42 · P55

P42 = 521485095599320202335987001799276507049523_<42>

P55 = 2544101840587878969578582280072469936142006701535179643_<55>

Number: n
N=1326711191553376550163673662779438743163331933916517632567212608197880091269011163554673702460289
  ( 97 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=521485095599320202335987001799276507049523 (pp42)
 r2=2544101840587878969578582280072469936142006701535179643 (pp55)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.82 hours.
Scaled time: 1.50 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_3_2_114_1
n: 1326711191553376550163673662779438743163331933916517632567212608197880091269011163554673702460289
type: snfs
skew: 0.82
deg: 5
c5: 29
c0: -11
m: 100000000000000000000000
rlim: 500000
alim: 500000
lpbr: 27
lpba: 27
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved algebraic special-q in [100000, 180001)
Primes: RFBsize:41538, AFBsize:41708, largePrimes:3125611 encountered
Relations: rels:2743279, finalFF:139616
Max relations in full relation-set: 48
Initial matrix: 83311 x 139616 with sparse part having weight 13302111.
Pruned matrix : 68753 x 69233 with weight 3681833.
Total sieving time: 0.74 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.02 hours.
Total square root time: 0.02 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,500000,500000,27,27,54,54,2.5,2.5,50000
total time: 0.82 hours.
 --------- CPU info (if available) ----------

Nov 13, 2008 (6th)

By Sinkiti Sibata / GGNFS, Msieve

(28·10¹²⁸+71)/9 = 3(1)₁₂₇9_<129> = 11² · 40591 · 2076617 · C116

C116 = P49 · P68

P49 = 1759361168535800593722424780888255616232128643859_<49>

P68 = 17337600581458520378695677885782595812103597467631586975360877316443_<68>

Number: 31119_128
N=30503101218601838242281562486678231891968486574615790895383405789704114369495831474670624493780031992478388791673537
  ( 116 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=1759361168535800593722424780888255616232128643859 (pp49)
 r2=17337600581458520378695677885782595812103597467631586975360877316443 (pp68)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.81 hours.
Scaled time: 7.58 units (timescale=1.991).
Factorization parameters were as follows:
name: 31119_128
n: 30503101218601838242281562486678231891968486574615790895383405789704114369495831474670624493780031992478388791673537
m: 20000000000000000000000000
deg: 5
c5: 875
c0: 71
skew: 0.61
type: snfs
lss: 1
rlim: 1010000
alim: 1010000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1010000/1010000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [505000, 855001)
Primes: RFBsize:79251, AFBsize:79577, largePrimes:2837693 encountered
Relations: rels:2869586, finalFF:323357
Max relations in full relation-set: 28
Initial matrix: 158894 x 323357 with sparse part having weight 25840052.
Pruned matrix : 119292 x 120150 with weight 7146188.
Total sieving time: 3.60 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,1010000,1010000,26,26,47,47,2.3,2.3,50000
total time: 3.81 hours.
 --------- CPU info (if available) ----------

(28·10¹²⁴+71)/9 = 3(1)₁₂₃9_<125> = 3³ · 11 · 41 · 21023 · 426161 · 711317 · 463869692723597_<15> · C90

C90 = P32 · P59

P32 = 61034350822028682568383479322877_<32>

P59 = 14160327778718875019797795731954549923748306637725290915413_<59>

Thu Nov 13 13:19:25 2008  Msieve v. 1.38
Thu Nov 13 13:19:25 2008  random seeds: 12c89b69 9a9ad8a5
Thu Nov 13 13:19:25 2008  factoring 864266413401245958241356446200346615110630641383201062809846268652697374724364416722803201 (90 digits)
Thu Nov 13 13:19:27 2008  searching for 15-digit factors
Thu Nov 13 13:19:28 2008  commencing quadratic sieve (90-digit input)
Thu Nov 13 13:19:28 2008  using multiplier of 1
Thu Nov 13 13:19:28 2008  using 64kb Pentium 4 sieve core
Thu Nov 13 13:19:28 2008  sieve interval: 18 blocks of size 65536
Thu Nov 13 13:19:28 2008  processing polynomials in batches of 6
Thu Nov 13 13:19:28 2008  using a sieve bound of 1613099 (61176 primes)
Thu Nov 13 13:19:28 2008  using large prime bound of 135500316 (27 bits)
Thu Nov 13 13:19:28 2008  using double large prime bound of 434002769636940 (42-49 bits)
Thu Nov 13 13:19:28 2008  using trial factoring cutoff of 49 bits
Thu Nov 13 13:19:28 2008  polynomial 'A' values have 11 factors
Thu Nov 13 14:59:16 2008  61273 relations (16965 full + 44308 combined from 655697 partial), need 61272
Thu Nov 13 14:59:18 2008  begin with 672662 relations
Thu Nov 13 14:59:19 2008  reduce to 146911 relations in 12 passes
Thu Nov 13 14:59:19 2008  attempting to read 146911 relations
Thu Nov 13 14:59:23 2008  recovered 146911 relations
Thu Nov 13 14:59:23 2008  recovered 118929 polynomials
Thu Nov 13 14:59:23 2008  attempting to build 61273 cycles
Thu Nov 13 14:59:23 2008  found 61273 cycles in 5 passes
Thu Nov 13 14:59:23 2008  distribution of cycle lengths:
Thu Nov 13 14:59:23 2008     length 1 : 16965
Thu Nov 13 14:59:23 2008     length 2 : 12014
Thu Nov 13 14:59:23 2008     length 3 : 10823
Thu Nov 13 14:59:23 2008     length 4 : 8074
Thu Nov 13 14:59:23 2008     length 5 : 5686
Thu Nov 13 14:59:23 2008     length 6 : 3488
Thu Nov 13 14:59:23 2008     length 7 : 1983
Thu Nov 13 14:59:23 2008     length 9+: 2240
Thu Nov 13 14:59:23 2008  largest cycle: 18 relations
Thu Nov 13 14:59:24 2008  matrix is 61176 x 61273 (14.8 MB) with weight 3641345 (59.43/col)
Thu Nov 13 14:59:24 2008  sparse part has weight 3641345 (59.43/col)
Thu Nov 13 14:59:25 2008  filtering completed in 3 passes
Thu Nov 13 14:59:25 2008  matrix is 56752 x 56816 (13.9 MB) with weight 3427126 (60.32/col)
Thu Nov 13 14:59:25 2008  sparse part has weight 3427126 (60.32/col)
Thu Nov 13 14:59:25 2008  saving the first 48 matrix rows for later
Thu Nov 13 14:59:25 2008  matrix is 56704 x 56816 (10.4 MB) with weight 2857107 (50.29/col)
Thu Nov 13 14:59:25 2008  sparse part has weight 2375998 (41.82/col)
Thu Nov 13 14:59:25 2008  matrix includes 64 packed rows
Thu Nov 13 14:59:25 2008  using block size 21845 for processor cache size 512 kB
Thu Nov 13 14:59:26 2008  commencing Lanczos iteration
Thu Nov 13 14:59:26 2008  memory use: 9.3 MB
Thu Nov 13 15:00:03 2008  lanczos halted after 898 iterations (dim = 56700)
Thu Nov 13 15:00:03 2008  recovered 15 nontrivial dependencies
Thu Nov 13 15:00:04 2008  prp32 factor: 61034350822028682568383479322877
Thu Nov 13 15:00:04 2008  prp59 factor: 14160327778718875019797795731954549923748306637725290915413
Thu Nov 13 15:00:04 2008  elapsed time 01:40:39

(28·10¹⁴²+71)/9 = 3(1)₁₄₁9_<143> = 3² · 11 · 29 · 173 · 1170549383_<10> · C128

C128 = P53 · P75

P53 = 98956011461166233106158495680143819212663834594612911_<53>

P75 = 540759681615055896653927742171404547325622441779817255231447555411397200261_<75>

Number: 31119_142
N=53511421251636074461001855116575692241530928222593843976577478578526658990658578980492834986144528791340522330374752498443169771
  ( 128 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=98956011461166233106158495680143819212663834594612911 (pp53)
 r2=540759681615055896653927742171404547325622441779817255231447555411397200261 (pp75)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 14.53 hours.
Scaled time: 14.69 units (timescale=1.011).
Factorization parameters were as follows:
name: 31119_142
n: 53511421251636074461001855116575692241530928222593843976577478578526658990658578980492834986144528791340522330374752498443169771
m: 20000000000000000000000000000
deg: 5
c5: 175
c0: 142
skew: 0.96
type: snfs
lss: 1
rlim: 1740000
alim: 1740000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1740000/1740000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [870000, 2170001)
Primes: RFBsize:130902, AFBsize:130971, largePrimes:4300379 encountered
Relations: rels:4782240, finalFF:601062
Max relations in full relation-set: 28
Initial matrix: 261939 x 601062 with sparse part having weight 69303084.
Pruned matrix : 195615 x 196988 with weight 27282474.
Total sieving time: 14.12 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1740000,1740000,26,26,48,48,2.3,2.3,100000
total time: 14.53 hours.
 --------- CPU info (if available) ----------

(29·10¹²⁴-11)/9 = 3(2)₁₂₃1_<125> = 7 · 50091271 · 40363075974930714377108729_<26> · C91

C91 = P41 · P51

P41 = 18249620940906744369260499117790083340667_<41>

P51 = 124754808339746480688040731128208190032343004178751_<51>

Thu Nov 13 15:18:50 2008  Msieve v. 1.38
Thu Nov 13 15:18:50 2008  random seeds: d4f311d8 1a1720a9
Thu Nov 13 15:18:50 2008  factoring 2276727962755844728256011612134281078047322333991346968381899355391434077181621330895566917 (91 digits)
Thu Nov 13 15:18:52 2008  searching for 15-digit factors
Thu Nov 13 15:18:53 2008  commencing quadratic sieve (91-digit input)
Thu Nov 13 15:18:53 2008  using multiplier of 2
Thu Nov 13 15:18:53 2008  using 64kb Pentium 4 sieve core
Thu Nov 13 15:18:53 2008  sieve interval: 18 blocks of size 65536
Thu Nov 13 15:18:53 2008  processing polynomials in batches of 6
Thu Nov 13 15:18:54 2008  using a sieve bound of 1680377 (63529 primes)
Thu Nov 13 15:18:54 2008  using large prime bound of 154594684 (27 bits)
Thu Nov 13 15:18:54 2008  using double large prime bound of 550237418754584 (42-49 bits)
Thu Nov 13 15:18:54 2008  using trial factoring cutoff of 49 bits
Thu Nov 13 15:18:54 2008  polynomial 'A' values have 12 factors
Thu Nov 13 16:23:57 2008  10634 relations (6786 full + 3848 combined from 305664 partial), need 63625
Thu Nov 13 16:23:57 2008  elapsed time 01:05:07
Thu Nov 13 16:33:29 2008  
Thu Nov 13 16:33:29 2008  
Thu Nov 13 16:33:29 2008  Msieve v. 1.38
Thu Nov 13 16:33:29 2008  random seeds: 2f4d82cd b2c5050e
Thu Nov 13 16:33:29 2008  factoring 2276727962755844728256011612134281078047322333991346968381899355391434077181621330895566917 (91 digits)
Thu Nov 13 16:33:30 2008  searching for 15-digit factors
Thu Nov 13 16:33:32 2008  commencing quadratic sieve (91-digit input)
Thu Nov 13 16:33:32 2008  using multiplier of 2
Thu Nov 13 16:33:32 2008  using 64kb Pentium 4 sieve core
Thu Nov 13 16:33:32 2008  sieve interval: 18 blocks of size 65536
Thu Nov 13 16:33:32 2008  processing polynomials in batches of 6
Thu Nov 13 16:33:32 2008  using a sieve bound of 1680377 (63529 primes)
Thu Nov 13 16:33:32 2008  using large prime bound of 154594684 (27 bits)
Thu Nov 13 16:33:32 2008  using double large prime bound of 550237418754584 (42-49 bits)
Thu Nov 13 16:33:32 2008  using trial factoring cutoff of 49 bits
Thu Nov 13 16:33:32 2008  polynomial 'A' values have 12 factors
Thu Nov 13 16:33:33 2008  restarting with 6786 full and 305664 partial relations
Thu Nov 13 18:03:34 2008  63740 relations (16320 full + 47420 combined from 728152 partial), need 63625
Thu Nov 13 18:03:37 2008  begin with 744472 relations
Thu Nov 13 18:03:38 2008  reduce to 158551 relations in 10 passes
Thu Nov 13 18:03:38 2008  attempting to read 158551 relations
Thu Nov 13 18:03:42 2008  recovered 158551 relations
Thu Nov 13 18:03:42 2008  recovered 138092 polynomials
Thu Nov 13 18:03:42 2008  attempting to build 63740 cycles
Thu Nov 13 18:03:42 2008  found 63740 cycles in 6 passes
Thu Nov 13 18:03:42 2008  distribution of cycle lengths:
Thu Nov 13 18:03:42 2008     length 1 : 16320
Thu Nov 13 18:03:42 2008     length 2 : 11921
Thu Nov 13 18:03:42 2008     length 3 : 11266
Thu Nov 13 18:03:42 2008     length 4 : 8632
Thu Nov 13 18:03:42 2008     length 5 : 6259
Thu Nov 13 18:03:42 2008     length 6 : 4000
Thu Nov 13 18:03:42 2008     length 7 : 2396
Thu Nov 13 18:03:42 2008     length 9+: 2946
Thu Nov 13 18:03:42 2008  largest cycle: 16 relations
Thu Nov 13 18:03:42 2008  matrix is 63529 x 63740 (15.8 MB) with weight 3885568 (60.96/col)
Thu Nov 13 18:03:42 2008  sparse part has weight 3885568 (60.96/col)
Thu Nov 13 18:03:44 2008  filtering completed in 3 passes
Thu Nov 13 18:03:44 2008  matrix is 59875 x 59938 (14.9 MB) with weight 3676757 (61.34/col)
Thu Nov 13 18:03:44 2008  sparse part has weight 3676757 (61.34/col)
Thu Nov 13 18:03:44 2008  saving the first 48 matrix rows for later
Thu Nov 13 18:03:44 2008  matrix is 59827 x 59938 (9.3 MB) with weight 2874020 (47.95/col)
Thu Nov 13 18:03:44 2008  sparse part has weight 2084673 (34.78/col)
Thu Nov 13 18:03:44 2008  matrix includes 64 packed rows
Thu Nov 13 18:03:44 2008  using block size 21845 for processor cache size 512 kB
Thu Nov 13 18:03:45 2008  commencing Lanczos iteration
Thu Nov 13 18:03:45 2008  memory use: 9.1 MB
Thu Nov 13 18:04:21 2008  lanczos halted after 948 iterations (dim = 59824)
Thu Nov 13 18:04:22 2008  recovered 15 nontrivial dependencies
Thu Nov 13 18:04:22 2008  prp41 factor: 18249620940906744369260499117790083340667
Thu Nov 13 18:04:22 2008  prp51 factor: 124754808339746480688040731128208190032343004178751
Thu Nov 13 18:04:22 2008  elapsed time 01:30:53

(29·10¹¹⁶-11)/9 = 3(2)₁₁₅1_<117> = 3² · C116

C116 = P37 · P79

P37 = 9688360407028247869586928337915901923_<37>

P79 = 3695410537146224236337805119314202453465253249831680260806032183583448457242903_<79>

Number: 32221_116
N=35802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469
  ( 116 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=9688360407028247869586928337915901923 (pp37)
 r2=3695410537146224236337805119314202453465253249831680260806032183583448457242903 (pp79)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.34 hours.
Scaled time: 4.67 units (timescale=1.997).
Factorization parameters were as follows:
name: 32221_116
n: 35802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469
m: 200000000000000000000000
deg: 5
c5: 145
c0: -176
skew: 1.04
type: snfs
lss: 1
rlim: 670000
alim: 670000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 670000/670000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [335000, 585001)
Primes: RFBsize:54309, AFBsize:53853, largePrimes:1347054 encountered
Relations: rels:1350498, finalFF:174389
Max relations in full relation-set: 28
Initial matrix: 108229 x 174389 with sparse part having weight 8537228.
Pruned matrix : 85073 x 85678 with weight 3131755.
Total sieving time: 2.25 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,118,5,0,0,0,0,0,0,0,0,670000,670000,25,25,45,45,2.2,2.2,50000
total time: 2.34 hours.
 --------- CPU info (if available) ----------

(28·10¹²⁹+71)/9 = 3(1)₁₂₈9_<130> = 41 · 773 · 445141 · C120

C120 = P57 · P63

P57 = 998661353734226691201162008429721923263380151711856352253_<57>

P63 = 220818944841654637670697572402532957665466840826897976978866571_<63>

Number: 31119_129
N=220523346385730354440563592134768481002827585182170729750542538185950859037739379422434695266187802376393347502462234463
  ( 120 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=998661353734226691201162008429721923263380151711856352253 (pp57)
 r2=220818944841654637670697572402532957665466840826897976978866571 (pp63)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.54 hours.
Scaled time: 4.55 units (timescale=1.002).
Factorization parameters were as follows:
name: 31119_129
n: 220523346385730354440563592134768481002827585182170729750542538185950859037739379422434695266187802376393347502462234463
m: 100000000000000000000000000
deg: 5
c5: 14
c0: 355
skew: 1.91
type: snfs
lss: 1
rlim: 1070000
alim: 1070000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1070000/1070000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [535000, 985001)
Primes: RFBsize:83548, AFBsize:83662, largePrimes:3295145 encountered
Relations: rels:3630249, finalFF:604759
Max relations in full relation-set: 28
Initial matrix: 167276 x 604759 with sparse part having weight 47640109.
Pruned matrix : 104073 x 104973 with weight 9222543.
Total sieving time: 4.42 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1070000,1070000,26,26,47,47,2.3,2.3,50000
total time: 4.54 hours.
 --------- CPU info (if available) ----------

(28·10¹²⁶+71)/9 = 3(1)₁₂₅9_<127> = 11 · 367 · 27521237 · C116

C116 = P33 · P84

P33 = 260219561015023904073125637011407_<33>

P84 = 107609071054194816684961875836184239251131272684730456080520869226989494139859803993_<84>

Number: 31119_126
N=28001985230957090767152638224044590284972366033375119079078864782444846527652567332098129248206933089336649325148151
  ( 116 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=260219561015023904073125637011407 (pp33)
 r2=107609071054194816684961875836184239251131272684730456080520869226989494139859803993 (pp84)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.93 hours.
Scaled time: 5.83 units (timescale=1.991).
Factorization parameters were as follows:
name: 31119_126
n: 28001985230957090767152638224044590284972366033375119079078864782444846527652567332098129248206933089336649325148151
m: 20000000000000000000000000
deg: 5
c5: 35
c0: 284
skew: 1.52
type: snfs
lss: 1
rlim: 950000
alim: 950000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 950000/950000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [475000, 725001)
Primes: RFBsize:74907, AFBsize:74969, largePrimes:2608741 encountered
Relations: rels:2550505, finalFF:242470
Max relations in full relation-set: 28
Initial matrix: 149943 x 242470 with sparse part having weight 18053980.
Pruned matrix : 120623 x 121436 with weight 6350642.
Total sieving time: 2.74 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,950000,950000,26,26,47,47,2.3,2.3,50000
total time: 2.93 hours.
 --------- CPU info (if available) ----------

(29·10¹³⁷-11)/9 = 3(2)₁₃₆1_<138> = 3 · 720703 · 175418193893329959997_<21> · 833113457520160415741_<21> · C91

C91 = P37 · P54

P37 = 4775676152509569129014103327365320999_<37>

P54 = 213532630462205808407077683016256587935549400085341903_<54>

Thu Nov 13 18:23:32 2008  Msieve v. 1.38
Thu Nov 13 18:23:32 2008  random seeds: c41d1ad7 11a0be03
Thu Nov 13 18:23:32 2008  factoring 1019762691080994653046278600591474071223441368709160737667020953237916146217839070260521097 (91 digits)
Thu Nov 13 18:23:33 2008  searching for 15-digit factors
Thu Nov 13 18:23:35 2008  commencing quadratic sieve (91-digit input)
Thu Nov 13 18:23:35 2008  using multiplier of 1
Thu Nov 13 18:23:35 2008  using 64kb Pentium 4 sieve core
Thu Nov 13 18:23:35 2008  sieve interval: 18 blocks of size 65536
Thu Nov 13 18:23:35 2008  processing polynomials in batches of 6
Thu Nov 13 18:23:35 2008  using a sieve bound of 1652503 (62230 primes)
Thu Nov 13 18:23:35 2008  using large prime bound of 145420264 (27 bits)
Thu Nov 13 18:23:35 2008  using double large prime bound of 492861412574344 (42-49 bits)
Thu Nov 13 18:23:35 2008  using trial factoring cutoff of 49 bits
Thu Nov 13 18:23:35 2008  polynomial 'A' values have 11 factors
Thu Nov 13 21:02:39 2008  62350 relations (16199 full + 46151 combined from 703587 partial), need 62326
Thu Nov 13 21:02:42 2008  begin with 719786 relations
Thu Nov 13 21:02:43 2008  reduce to 154720 relations in 9 passes
Thu Nov 13 21:02:43 2008  attempting to read 154720 relations
Thu Nov 13 21:02:47 2008  recovered 154720 relations
Thu Nov 13 21:02:47 2008  recovered 134659 polynomials
Thu Nov 13 21:02:47 2008  attempting to build 62350 cycles
Thu Nov 13 21:02:47 2008  found 62350 cycles in 5 passes
Thu Nov 13 21:02:47 2008  distribution of cycle lengths:
Thu Nov 13 21:02:47 2008     length 1 : 16199
Thu Nov 13 21:02:47 2008     length 2 : 11735
Thu Nov 13 21:02:47 2008     length 3 : 10711
Thu Nov 13 21:02:47 2008     length 4 : 8301
Thu Nov 13 21:02:47 2008     length 5 : 6078
Thu Nov 13 21:02:47 2008     length 6 : 3919
Thu Nov 13 21:02:47 2008     length 7 : 2405
Thu Nov 13 21:02:47 2008     length 9+: 3002
Thu Nov 13 21:02:47 2008  largest cycle: 17 relations
Thu Nov 13 21:02:48 2008  matrix is 62230 x 62350 (15.6 MB) with weight 3828185 (61.40/col)
Thu Nov 13 21:02:48 2008  sparse part has weight 3828185 (61.40/col)
Thu Nov 13 21:02:49 2008  filtering completed in 3 passes
Thu Nov 13 21:02:49 2008  matrix is 58550 x 58614 (14.8 MB) with weight 3635067 (62.02/col)
Thu Nov 13 21:02:49 2008  sparse part has weight 3635067 (62.02/col)
Thu Nov 13 21:02:49 2008  saving the first 48 matrix rows for later
Thu Nov 13 21:02:49 2008  matrix is 58502 x 58614 (11.3 MB) with weight 3100494 (52.90/col)
Thu Nov 13 21:02:49 2008  sparse part has weight 2605874 (44.46/col)
Thu Nov 13 21:02:49 2008  matrix includes 64 packed rows
Thu Nov 13 21:02:49 2008  using block size 21845 for processor cache size 512 kB
Thu Nov 13 21:02:50 2008  commencing Lanczos iteration
Thu Nov 13 21:02:50 2008  memory use: 10.0 MB
Thu Nov 13 21:03:30 2008  lanczos halted after 926 iterations (dim = 58500)
Thu Nov 13 21:03:31 2008  recovered 15 nontrivial dependencies
Thu Nov 13 21:03:31 2008  prp37 factor: 4775676152509569129014103327365320999
Thu Nov 13 21:03:31 2008  prp54 factor: 213532630462205808407077683016256587935549400085341903
Thu Nov 13 21:03:31 2008  elapsed time 02:39:59

(29·10¹²⁸-11)/9 = 3(2)₁₂₇1_<129> = 3 · 2560764391879_<13> · C116

C116 = P57 · P60

P57 = 195630407555737641475441597959544100446483683136103342557_<57>

P60 = 214401713467205088259322269652181056024814754718303452106669_<60>

Number: 32221_128
N=41943494586237815139200117024764776394705485795105030962417067283970524902850117778680933664992870761876614211212633
  ( 116 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=195630407555737641475441597959544100446483683136103342557 (pp57)
 r2=214401713467205088259322269652181056024814754718303452106669 (pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 7.51 hours.
Scaled time: 7.60 units (timescale=1.011).
Factorization parameters were as follows:
name: 32221_128
n: 41943494586237815139200117024764776394705485795105030962417067283970524902850117778680933664992870761876614211212633
m: 50000000000000000000000000
deg: 5
c5: 232
c0: -275
skew: 1.03
type: snfs
lss: 1
rlim: 1060000
alim: 1060000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1060000/1060000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [530000, 1180001)
Primes: RFBsize:82832, AFBsize:82349, largePrimes:3595337 encountered
Relations: rels:4154092, finalFF:780966
Max relations in full relation-set: 28
Initial matrix: 165248 x 780966 with sparse part having weight 77798435.
Pruned matrix : 113944 x 114834 with weight 15153460.
Total sieving time: 7.34 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1060000,1060000,26,26,47,47,2.3,2.3,50000
total time: 7.51 hours.
 --------- CPU info (if available) ----------

Nov 13, 2008 (5th)

By Sinkiti Sibata / Msieve

(28·10¹³⁴+71)/9 = 3(1)₁₃₃9_<135> = 11 · 17 · 41 · 21157 · 707563 · 53267801 · 62076811 · 977221428389_<12> · C93

C93 = P45 · P49

P45 = 139170240895771901265496748581032926011617269_<45>

P49 = 6027501546530032936138143435351272065230728470777_<49>

Thu Nov 13 07:24:34 2008  Msieve v. 1.38
Thu Nov 13 07:24:34 2008  random seeds: c0092a71 e53f1a57
Thu Nov 13 07:24:34 2008  factoring 838848842230222371146179714520208650316197768760776722992556595071439398757036723212975048013 (93 digits)
Thu Nov 13 07:24:35 2008  searching for 15-digit factors
Thu Nov 13 07:24:37 2008  commencing quadratic sieve (93-digit input)
Thu Nov 13 07:24:37 2008  using multiplier of 5
Thu Nov 13 07:24:37 2008  using 64kb Pentium 4 sieve core
Thu Nov 13 07:24:37 2008  sieve interval: 18 blocks of size 65536
Thu Nov 13 07:24:37 2008  processing polynomials in batches of 6
Thu Nov 13 07:24:37 2008  using a sieve bound of 1951709 (72941 primes)
Thu Nov 13 07:24:37 2008  using large prime bound of 243963625 (27 bits)
Thu Nov 13 07:24:37 2008  using double large prime bound of 1250791990793625 (42-51 bits)
Thu Nov 13 07:24:37 2008  using trial factoring cutoff of 51 bits
Thu Nov 13 07:24:37 2008  polynomial 'A' values have 12 factors
Thu Nov 13 12:49:08 2008  73213 relations (17770 full + 55443 combined from 1006720 partial), need 73037
Thu Nov 13 12:49:12 2008  begin with 1024490 relations
Thu Nov 13 12:49:13 2008  reduce to 190804 relations in 10 passes
Thu Nov 13 12:49:13 2008  attempting to read 190804 relations
Thu Nov 13 12:49:19 2008  recovered 190804 relations
Thu Nov 13 12:49:19 2008  recovered 175954 polynomials
Thu Nov 13 12:49:19 2008  attempting to build 73213 cycles
Thu Nov 13 12:49:19 2008  found 73213 cycles in 5 passes
Thu Nov 13 12:49:19 2008  distribution of cycle lengths:
Thu Nov 13 12:49:19 2008     length 1 : 17770
Thu Nov 13 12:49:19 2008     length 2 : 12760
Thu Nov 13 12:49:19 2008     length 3 : 12259
Thu Nov 13 12:49:19 2008     length 4 : 9947
Thu Nov 13 12:49:19 2008     length 5 : 7382
Thu Nov 13 12:49:19 2008     length 6 : 5192
Thu Nov 13 12:49:19 2008     length 7 : 3351
Thu Nov 13 12:49:19 2008     length 9+: 4552
Thu Nov 13 12:49:19 2008  largest cycle: 18 relations
Thu Nov 13 12:49:20 2008  matrix is 72941 x 73213 (18.6 MB) with weight 4591029 (62.71/col)
Thu Nov 13 12:49:20 2008  sparse part has weight 4591029 (62.71/col)
Thu Nov 13 12:49:21 2008  filtering completed in 3 passes
Thu Nov 13 12:49:21 2008  matrix is 69751 x 69815 (17.8 MB) with weight 4396443 (62.97/col)
Thu Nov 13 12:49:21 2008  sparse part has weight 4396443 (62.97/col)
Thu Nov 13 12:49:22 2008  saving the first 48 matrix rows for later
Thu Nov 13 12:49:22 2008  matrix is 69703 x 69815 (10.6 MB) with weight 3385564 (48.49/col)
Thu Nov 13 12:49:22 2008  sparse part has weight 2353687 (33.71/col)
Thu Nov 13 12:49:22 2008  matrix includes 64 packed rows
Thu Nov 13 12:49:22 2008  using block size 21845 for processor cache size 512 kB
Thu Nov 13 12:49:23 2008  commencing Lanczos iteration
Thu Nov 13 12:49:23 2008  memory use: 10.7 MB
Thu Nov 13 12:50:13 2008  lanczos halted after 1104 iterations (dim = 69703)
Thu Nov 13 12:50:13 2008  recovered 18 nontrivial dependencies
Thu Nov 13 12:50:14 2008  prp45 factor: 139170240895771901265496748581032926011617269
Thu Nov 13 12:50:14 2008  prp49 factor: 6027501546530032936138143435351272065230728470777
Thu Nov 13 12:50:14 2008  elapsed time 05:25:40

Nov 13, 2008 (4th)

By Robert Backstrom / Msieve

(29·10¹²⁷-11)/9 = 3(2)₁₂₆1_<128> = 53 · 2070737 · 87683177 · 110869756429_<12> · 84607104219193_<14> · C87

C87 = P41 · P46

P41 = 95070682214954468326311130551196839108947_<41>

P46 = 3754670784430775196082684395797432868827232127_<46>

Thu Nov 13 11:10:56 2008  
Thu Nov 13 11:10:56 2008  
Thu Nov 13 11:10:56 2008  Msieve v. 1.38
Thu Nov 13 11:10:56 2008  random seeds: 43f61fc0 27f42988
Thu Nov 13 11:10:56 2008  factoring 356959112968392041887915367515924314281826255548460137183739424614888414281767011540269 (87 digits)
Thu Nov 13 11:10:56 2008  searching for 15-digit factors
Thu Nov 13 11:10:57 2008  commencing quadratic sieve (87-digit input)
Thu Nov 13 11:10:57 2008  using multiplier of 5
Thu Nov 13 11:10:57 2008  using 64kb Opteron sieve core
Thu Nov 13 11:10:57 2008  sieve interval: 10 blocks of size 65536
Thu Nov 13 11:10:57 2008  processing polynomials in batches of 11
Thu Nov 13 11:10:57 2008  using a sieve bound of 1489637 (56536 primes)
Thu Nov 13 11:10:57 2008  using large prime bound of 119170960 (26 bits)
Thu Nov 13 11:10:57 2008  using double large prime bound of 344434582165760 (42-49 bits)
Thu Nov 13 11:10:57 2008  using trial factoring cutoff of 49 bits
Thu Nov 13 11:10:57 2008  polynomial 'A' values have 11 factors
Thu Nov 13 11:13:36 2008  
Thu Nov 13 11:13:36 2008  
Thu Nov 13 11:13:36 2008  Msieve v. 1.38
Thu Nov 13 11:13:36 2008  random seeds: 1e468de8 f26209d1
Thu Nov 13 11:13:36 2008  factoring 356959112968392041887915367515924314281826255548460137183739424614888414281767011540269 (87 digits)
Thu Nov 13 11:13:37 2008  searching for 15-digit factors
Thu Nov 13 11:13:37 2008  commencing quadratic sieve (87-digit input)
Thu Nov 13 11:13:37 2008  using multiplier of 5
Thu Nov 13 11:13:37 2008  using 64kb Opteron sieve core
Thu Nov 13 11:13:37 2008  sieve interval: 10 blocks of size 65536
Thu Nov 13 11:13:37 2008  processing polynomials in batches of 11
Thu Nov 13 11:13:37 2008  using a sieve bound of 1489637 (56536 primes)
Thu Nov 13 11:13:37 2008  using large prime bound of 119170960 (26 bits)
Thu Nov 13 11:13:37 2008  using double large prime bound of 344434582165760 (42-49 bits)
Thu Nov 13 11:13:37 2008  using trial factoring cutoff of 49 bits
Thu Nov 13 11:13:37 2008  polynomial 'A' values have 11 factors
Thu Nov 13 11:13:37 2008  restarting with 1035 full and 38221 partial relations
Thu Nov 13 11:41:13 2008  56955 relations (16306 full + 40649 combined from 591487 partial), need 56632
Thu Nov 13 11:41:14 2008  begin with 607793 relations
Thu Nov 13 11:41:14 2008  reduce to 135178 relations in 9 passes
Thu Nov 13 11:41:14 2008  attempting to read 135178 relations
Thu Nov 13 11:41:15 2008  recovered 135178 relations
Thu Nov 13 11:41:15 2008  recovered 110766 polynomials
Thu Nov 13 11:41:15 2008  attempting to build 56955 cycles
Thu Nov 13 11:41:15 2008  found 56955 cycles in 6 passes
Thu Nov 13 11:41:16 2008  distribution of cycle lengths:
Thu Nov 13 11:41:16 2008     length 1 : 16306
Thu Nov 13 11:41:16 2008     length 2 : 11296
Thu Nov 13 11:41:16 2008     length 3 : 10050
Thu Nov 13 11:41:16 2008     length 4 : 7430
Thu Nov 13 11:41:16 2008     length 5 : 4980
Thu Nov 13 11:41:16 2008     length 6 : 3050
Thu Nov 13 11:41:16 2008     length 7 : 1794
Thu Nov 13 11:41:16 2008     length 9+: 2049
Thu Nov 13 11:41:16 2008  largest cycle: 20 relations
Thu Nov 13 11:41:16 2008  matrix is 56536 x 56955 (13.2 MB) with weight 3235569 (56.81/col)
Thu Nov 13 11:41:16 2008  sparse part has weight 3235569 (56.81/col)
Thu Nov 13 11:41:16 2008  filtering completed in 3 passes
Thu Nov 13 11:41:16 2008  matrix is 51499 x 51562 (12.0 MB) with weight 2951835 (57.25/col)
Thu Nov 13 11:41:16 2008  sparse part has weight 2951835 (57.25/col)
Thu Nov 13 11:41:17 2008  saving the first 48 matrix rows for later
Thu Nov 13 11:41:17 2008  matrix is 51451 x 51562 (8.2 MB) with weight 2368789 (45.94/col)
Thu Nov 13 11:41:17 2008  sparse part has weight 1827722 (35.45/col)
Thu Nov 13 11:41:17 2008  matrix includes 64 packed rows
Thu Nov 13 11:41:17 2008  using block size 20624 for processor cache size 1024 kB
Thu Nov 13 11:41:17 2008  commencing Lanczos iteration
Thu Nov 13 11:41:17 2008  memory use: 7.7 MB
Thu Nov 13 11:41:33 2008  lanczos halted after 816 iterations (dim = 51445)
Thu Nov 13 11:41:34 2008  recovered 14 nontrivial dependencies
Thu Nov 13 11:41:34 2008  prp41 factor: 95070682214954468326311130551196839108947
Thu Nov 13 11:41:34 2008  prp46 factor: 3754670784430775196082684395797432868827232127
Thu Nov 13 11:41:34 2008  elapsed time 00:27:58

Nov 13, 2008 (3rd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38

(29·10¹³²-11)/9 = 3(2)₁₃₁1_<133> = 1104974417_<10> · 832689448153946153171357026481_<30> · C94

C94 = P32 · P62

P32 = 80414506743700883354190522171791_<32>

P62 = 43549763580334770575095184643964731287732358444855048847732003_<62>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1855890600
Step 1 took 8644ms
Step 2 took 7541ms
********** Factor found in step 2: 80414506743700883354190522171791
Found probable prime factor of 32 digits: 80414506743700883354190522171791
Probable prime cofactor 43549763580334770575095184643964731287732358444855048847732003 has 62 digits
Input number is 1326711191553376550163673662779438743163331933916517632567212608197880091269011163554673702460289 (97 digits)

(79·10¹⁷⁹-7)/9 = 8(7)₁₇₉_<180> = 69191 · C176

C176 = P55 · P121

P55 = 1323486772291042062347767853173796187473215598039738449_<55>

P121 = 9585513195744228583885902560617274532350803556151073635205582699852643964350412161988989141326678149345407852327055036503_<121>

SNFS difficulty: 181 digits.
Divisors found:
 r1=1323486772291042062347767853173796187473215598039738449
 r2=9585513195744228583885902560617274532350803556151073635205582699852643964350412161988989141326678149345407852327055036503
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.946).
Factorization parameters were as follows:
n: 12686299920188720755268427653564448812385682787902729802687889722330617822806113190700781572426728588657163182751770862941390900229477501087970657712387128062577181682267603847
m: 1000000000000000000000000000000000000
deg: 5
c5: 79
c0: -70
skew: 0.98
type: snfs
lss: 1
rlim: 8600000
alim: 8600000
lpbr: 27
lpba: 27
mfbr: 54
mfba: 54
rlambda: 2.6
alambda: 2.6
Factor base limits: 8600000/8600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [4300000, 7100001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1428957 x 1429196
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,8600000,8600000,27,27,54,54,2.6,2.6,200000
total time: 110.00 hours.

(28·10¹²⁵+71)/9 = 3(1)₁₂₄9_<126> = 47 · 7013 · 865807 · 637454432903_<12> · C103

C103 = P33 · P70

P33 = 948155035316114812542048781151683_<33>

P70 = 1803699691397314578497043401639521953896001046423413462657696894175703_<70>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2536211752
Step 1 took 10052ms
Step 2 took 8101ms
********** Factor found in step 2: 948155035316114812542048781151683
Found probable prime factor of 33 digits: 948155035316114812542048781151683
Probable prime cofactor 1803699691397314578497043401639521953896001046423413462657696894175703 has 70 digits

(28·10¹⁵⁶+71)/9 = 3(1)₁₅₅9_<157> = 11 · 373 · 3461 · 2009315225524317079_<19> · 43732513694910445326617_<23> · C109

C109 = P29 · C80

P29 = 87679139790976199399319247097_<29>

C80 = [28435679417441093560965677996084063055357095027467175103552861928042176482013683_<80>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3986050529
Step 1 took 10257ms
Step 2 took 8464ms
********** Factor found in step 2: 87679139790976199399319247097
Found probable prime factor of 29 digits: 87679139790976199399319247097
Composite cofactor 28435679417441093560965677996084063055357095027467175103552861928042176482013683 has 80 digits

(28·10¹⁵⁴+71)/9 = 3(1)₁₅₃9_<155> = 3 · 11 · 19 · 41 · 61 · 10665502717136462501_<20> · C130

C130 = P34 · P96

P34 = 3425426951621600515042987227307069_<34>

P96 = 543048037030329582597213809565029194214444433430756712726409932533669420532810099590456505890913_<96>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1358792107
Step 1 took 13989ms
Step 2 took 9636ms
********** Factor found in step 2: 3425426951621600515042987227307069
Found probable prime factor of 34 digits: 3425426951621600515042987227307069
Probable prime cofactor 543048037030329582597213809565029194214444433430756712726409932533669420532810099590456505890913 has 96 digits

(28·10¹⁰⁹+71)/9 = 3(1)₁₀₈9_<110> = 3 · 13 · 41 · 4729 · C103

C103 = P34 · P70

P34 = 1316470743289074900325002514828393_<34>

P70 = 3125262725179705400651545045523261800581464400858076755340556648062673_<70>

SNFS difficulty: 110 digits.
Divisors found:
 r1=1316470743289074900325002514828393
 r2=3125262725179705400651545045523261800581464400858076755340556648062673
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 4114316942790966588087621256083623726966051698243828792751114285600512255969760005574311697918503874489
m: 2000000000000000000000000000
c4: 35
c0: 142
skew: 1.42
type: snfs
lss: 1
rlim: 500000
alim: 500000
lpbr: 25
lpba: 25
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [250000, 350001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 52229 x 52471
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,110,4,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,20000
total time: 0.40 hours.

(29·10¹¹²-11)/9 = 3(2)₁₁₁1_<113> = 7 · 25183 · C108

C108 = P32 · P76

P32 = 42623589369304135120774617930199_<32>

P76 = 4288446176859474104734338555208678726328744931833395919458818562976729123059_<76>

SNFS difficulty: 114 digits.
Divisors found:
 r1=42623589369304135120774617930199
 r2=4288446176859474104734338555208678726328744931833395919458818562976729123059
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
n: 182788968874820441353419950092308429281784322883477074796615756787301083056155922772290957177587046943358741
m: 20000000000000000000000
deg: 5
c5: 725
c0: -88
skew: 0.66
type: snfs
lss: 1
rlim: 560000
alim: 560000
lpbr: 25
lpba: 25
Factor base limits: 560000/560000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [280000, 380001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 83409 x 83622
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,114,5,0,0,0,0,0,0,0,0,560000,560000,25,25,46,46,2.4,2.4,100000
total time: 0.40 hours.

(29·10¹⁵¹-11)/9 = 3(2)₁₅₀1_<152> = 23 · 31 · 5783540629_<10> · C139

C139 = P34 · P106

P34 = 6030710732056972996146796583655799_<34>

P106 = 1295697647062495140482578388904535513056221855990277044863111841403601357591160208257520544152967493582327_<106>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1393290503
Step 1 took 16349ms
Step 2 took 10892ms
********** Factor found in step 2: 6030710732056972996146796583655799
Found probable prime factor of 34 digits: 6030710732056972996146796583655799
Probable prime cofactor 1295697647062495140482578388904535513056221855990277044863111841403601357591160208257520544152967493582327 has 106 digits

(29·10¹⁶²-11)/9 = 3(2)₁₆₁1_<163> = 893147 · 19471057 · C150

C150 = P30 · C120

P30 = 746734138448512777471322756059_<30>

C120 = [248128705653600704252183940981166727591290446648117130564206869724052667609229038959837362742059371119512152905479688261_<120>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3179040063
Step 1 took 17441ms
Step 2 took 12113ms
********** Factor found in step 2: 746734138448512777471322756059
Found probable prime factor of 30 digits: 746734138448512777471322756059
Composite cofactor 248128705653600704252183940981166727591290446648117130564206869724052667609229038959837362742059371119512152905479688261 has 120 digits

(29·10¹⁴⁷-11)/9 = 3(2)₁₄₆1_<148> = 15227 · 1590949 · C138

C138 = P59 · P79

P59 = 16431167000761097086608455694019255023550612169609099680183_<59>

P79 = 8094992916345143796027360708747750051847185126894636439636003383767537995429069_<79>

SNFS difficulty: 149 digits.
Divisors found:
 r1=16431167000761097086608455694019255023550612169609099680183
 r2=8094992916345143796027360708747750051847185126894636439636003383767537995429069
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
n: 133010180478445162876285875621075782279046451208838555303715084293857993803205185778981738891730353497872177551901811974373807843761439627
m: 200000000000000000000000000000
deg: 5
c5: 725
c0: -88
skew: 0.66
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 26
lpba: 26
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved rational special-q in [1100000, 3500001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 293099 x 293332
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,45,45,2.3,2.3,200000
total time: 10.00 hours.

Nov 13, 2008 (2nd)

By Jo Yeong Uk / GMP-ECM, GGNFS

(28·10¹⁶⁷+71)/9 = 3(1)₁₆₆9_<168> = C168

C168 = P46 · P122

P46 = 6361593299461195600022136270359902423389375773_<46>

P122 = 48904589851328773139603224038629125897433045861866521152439579001132682680657170685564747035658736348401899828271484240603_<122>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111119 (168 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3590283382
Step 1 took 16371ms
Step 2 took 7173ms
********** Factor found in step 2: 6361593299461195600022136270359902423389375773
Found probable prime factor of 46 digits: 6361593299461195600022136270359902423389375773
Probable prime cofactor 48904589851328773139603224038629125897433045861866521152439579001132682680657170685564747035658736348401899828271484240603 has 122 digits

(29·10¹⁰²-11)/9 = 3(2)₁₀₁1_<103> = C103

C103 = P46 · P58

P46 = 2086989367377430338068718358517067554766449659_<46>

P58 = 1543957181857307441236327584868144774614328996585231159319_<58>

Number: 32221_102
N=3222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
  ( 103 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=2086989367377430338068718358517067554766449659 (pp46)
 r2=1543957181857307441236327584868144774614328996585231159319 (pp58)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.32 hours.
Scaled time: 0.77 units (timescale=2.389).
Factorization parameters were as follows:
n: 3222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
m: 100000000000000000000
deg: 5
c5: 2900
c0: -11
skew: 0.33
type: snfs
rlim: 210000
alim: 210000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 210000/210000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [105000, 180001)
Primes: RFBsize:18807, AFBsize:18986, largePrimes:788369 encountered
Relations: rels:676681, finalFF:44263
Max relations in full relation-set: 28
Initial matrix: 37860 x 44263 with sparse part having weight 1931482.
Pruned matrix : 35761 x 36014 with weight 1237693.
Total sieving time: 0.30 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,103,5,0,0,0,0,0,0,0,0,210000,210000,25,25,44,44,2.2,2.2,15000
total time: 0.32 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047212k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673807)
Calibrating delay using timer specific routine.. 5344.58 BogoMIPS (lpj=2672293)
Calibrating delay using timer specific routine.. 5344.06 BogoMIPS (lpj=2672032)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672362)

(29·10¹⁰³-11)/9 = 3(2)₁₀₂1_<104> = C104

C104 = P38 · P67

P38 = 26042266802856807831656958190462844209_<38>

P67 = 1237304819359560517371280897725082910678283633399794566410902570269_<67>

Number: 32221_103
N=32222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
  ( 104 digits)
SNFS difficulty: 106 digits.
Divisors found:
 r1=26042266802856807831656958190462844209 (pp38)
 r2=1237304819359560517371280897725082910678283633399794566410902570269 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.49 hours.
Scaled time: 1.16 units (timescale=2.386).
Factorization parameters were as follows:
n: 32222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
m: 1000000000000000000000
deg: 5
c5: 29
c0: -1100
skew: 2.07
type: snfs
rlim: 240000
alim: 240000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 240000/240000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [120000, 240001)
Primes: RFBsize:21221, AFBsize:21040, largePrimes:923530 encountered
Relations: rels:825591, finalFF:66348
Max relations in full relation-set: 28
Initial matrix: 42328 x 66348 with sparse part having weight 3320261.
Pruned matrix : 37600 x 37875 with weight 1286928.
Total sieving time: 0.47 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,106,5,0,0,0,0,0,0,0,0,240000,240000,25,25,44,44,2.2,2.2,20000
total time: 0.49 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047212k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673807)
Calibrating delay using timer specific routine.. 5344.58 BogoMIPS (lpj=2672293)
Calibrating delay using timer specific routine.. 5344.06 BogoMIPS (lpj=2672032)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672362)

(28·10¹⁰¹+71)/9 = 3(1)₁₀₀9_<102> = 769 · C99

C99 = P40 · P60

P40 = 1695778772641719924507116262361629971059_<40>

P60 = 238572283552329116530644795001097412229139123623034647675189_<60>

Number: 31119_101
N=404565814188701054760872706256321340846698453980638636035255020950729663343447478688050859702355151
  ( 99 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=1695778772641719924507116262361629971059 (pp40)
 r2=238572283552329116530644795001097412229139123623034647675189 (pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.27 hours.
Scaled time: 0.64 units (timescale=2.375).
Factorization parameters were as follows:
n: 404565814188701054760872706256321340846698453980638636035255020950729663343447478688050859702355151
m: 200000000000000000000
deg: 5
c5: 35
c0: 284
skew: 1.52
type: snfs
rlim: 210000
alim: 210000
lpbr: 25
lpba: 25
mfbr: 43
mfba: 43
rlambda: 2.2
alambda: 2.2
Factor base limits: 210000/210000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [105000, 165001)
Primes: RFBsize:18807, AFBsize:18956, largePrimes:778541 encountered
Relations: rels:667610, finalFF:45305
Max relations in full relation-set: 28
Initial matrix: 37830 x 45305 with sparse part having weight 1882153.
Pruned matrix : 34902 x 35155 with weight 1133450.
Total sieving time: 0.25 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,103,5,0,0,0,0,0,0,0,0,210000,210000,25,25,43,43,2.2,2.2,15000
total time: 0.27 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047212k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673807)
Calibrating delay using timer specific routine.. 5344.58 BogoMIPS (lpj=2672293)
Calibrating delay using timer specific routine.. 5344.06 BogoMIPS (lpj=2672032)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672362)

(28·10¹⁰²+71)/9 = 3(1)₁₀₁9_<103> = 11 · 17 · C101

C101 = P42 · P59

P42 = 463851615188877878495082182287898341551647_<42>

P59 = 35866982605318560939327970256787851946906520438716252355171_<59>

Number: 31119_102
N=16636957813428401663695781342840166369578134284016636957813428401663695781342840166369578134284016637
  ( 101 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=463851615188877878495082182287898341551647 (pp42)
 r2=35866982605318560939327970256787851946906520438716252355171 (pp59)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.38 hours.
Scaled time: 0.90 units (timescale=2.388).
Factorization parameters were as follows:
n: 16636957813428401663695781342840166369578134284016636957813428401663695781342840166369578134284016637
m: 200000000000000000000
deg: 5
c5: 175
c0: 142
skew: 0.96
type: snfs
rlim: 210000
alim: 210000
lpbr: 25
lpba: 25
mfbr: 43
mfba: 43
rlambda: 2.2
alambda: 2.2
Factor base limits: 210000/210000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [105000, 195001)
Primes: RFBsize:18807, AFBsize:18966, largePrimes:830664 encountered
Relations: rels:719934, finalFF:49081
Max relations in full relation-set: 28
Initial matrix: 37839 x 49081 with sparse part having weight 2309008.
Pruned matrix : 35235 x 35488 with weight 1202455.
Total sieving time: 0.36 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,103,5,0,0,0,0,0,0,0,0,210000,210000,25,25,43,43,2.2,2.2,15000
total time: 0.38 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047212k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673807)
Calibrating delay using timer specific routine.. 5344.58 BogoMIPS (lpj=2672293)
Calibrating delay using timer specific routine.. 5344.06 BogoMIPS (lpj=2672032)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672362)

(28·10¹⁰⁶+71)/9 = 3(1)₁₀₅9_<107> = 3² · 11³ · 249973 · C98

C98 = P47 · P51

P47 = 27460086117550751749087163860396849317232970491_<47>

P51 = 378355420066750802279410132926190270342218870699227_<51>

Number: 31119_106
N=10389672418075066828349813766233229893431917013549229277563750358988553253478769015714223427510457
  ( 98 digits)
SNFS difficulty: 108 digits.
Divisors found:
 r1=27460086117550751749087163860396849317232970491 (pp47)
 r2=378355420066750802279410132926190270342218870699227 (pp51)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.38 hours.
Scaled time: 0.91 units (timescale=2.377).
Factorization parameters were as follows:
n: 10389672418075066828349813766233229893431917013549229277563750358988553253478769015714223427510457
m: 2000000000000000000000
deg: 5
c5: 35
c0: 284
skew: 1.52
type: snfs
rlim: 320000
alim: 320000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 320000/320000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [160000, 240001)
Primes: RFBsize:27608, AFBsize:27871, largePrimes:930525 encountered
Relations: rels:840330, finalFF:73159
Max relations in full relation-set: 28
Initial matrix: 55546 x 73159 with sparse part having weight 3198123.
Pruned matrix : 48492 x 48833 with weight 1561054.
Total sieving time: 0.36 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,108,5,0,0,0,0,0,0,0,0,320000,320000,25,25,44,44,2.2,2.2,20000
total time: 0.38 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047212k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673807)
Calibrating delay using timer specific routine.. 5344.58 BogoMIPS (lpj=2672293)
Calibrating delay using timer specific routine.. 5344.06 BogoMIPS (lpj=2672032)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672362)

Nov 13, 2008

Factorizations of 311...119 and Factorizations of 322...221 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Nov 12, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(28·10¹⁶⁹+53)/9 = 3(1)₁₆₈7_<170> = 37 · 1559 · 11087 · C161

C161 = P34 · P127

P34 = 6576167450442864942395733867530623_<34>

P127 = 7397428427374041743927780007395203806290373475751794436242704677858412169289099564434772924989179618665154751237931963740230799_<127>

Number: 31117_169
N=48646728041077924005724671205968957561369156107673263345588005301636479110713015476859754027802663836764184743803402759019577727848826228525699147956502220257777
  ( 161 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=6576167450442864942395733867530623 (pp34)
 r2=7397428427374041743927780007395203806290373475751794436242704677858412169289099564434772924989179618665154751237931963740230799 (pp127)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 88.61 hours.
Scaled time: 88.88 units (timescale=1.003).
Factorization parameters were as follows:
name: 31117_169
n: 48646728041077924005724671205968957561369156107673263345588005301636479110713015476859754027802663836764184743803402759019577727848826228525699147956502220257777
m: 10000000000000000000000000000000000
deg: 5
c5: 14
c0: 265
skew: 1.80
type: snfs
lss: 1
rlim: 5300000
alim: 5300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6
Factor base limits: 5300000/5300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2650000, 5150001)
Primes: RFBsize:367900, AFBsize:368397, largePrimes:10227866 encountered
Relations: rels:10849454, finalFF:903116
Max relations in full relation-set: 28
Initial matrix: 736363 x 903116 with sparse part having weight 95364440.
Pruned matrix : 628184 x 631929 with weight 73827870.
Total sieving time: 83.40 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 4.88 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5300000,5300000,27,27,52,52,2.6,2.6,100000
total time: 88.61 hours.
 --------- CPU info (if available) ----------

Nov 12, 2008

By Serge Batalov / Msieve-1.38

4·10¹⁸³-9 = 3(9)₁₈₂1_<184> = 13 · 291521 · C178

C178 = P84 · P94

P84 = 175760151760128614736111330301882810113296736746728352650439858811633452129329386893_<84>

P94 = 6005184777904143133368396782495819629853737419435935288123825152255604348922994197853024855519_<94>

SNFS difficulty: 183 digits.
Divisors found:
 r1=175760151760128614736111330301882810113296736746728352650439858811633452129329386893
 r2=6005184777904143133368396782495819629853737419435935288123825152255604348922994197853024855519
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.621).
Factorization parameters were as follows:
n: 1055472187912046447109101257515951483109938246960965735942495764258175885468601945288015931297204344429072664774380945771686061407899628816818316031065712906815263077762177312467
m: 2000000000000000000000000000000000000
deg: 5
c5: 125
c0: -9
skew: 0.59
type: snfs
lss: 1
rlim: 9400000
alim: 9400000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.6
alambda: 2.6
Factor base limits: 9400000/9400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4700000, 7200001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1611547 x 1611789
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 6.00 hours (4 threads)
Time per square root: 0.50 hours.
Prototype def-par.txt line would be:
snfs,183,5,0,0,0,0,0,0,0,0,9400000,9400000,28,28,54,54,2.6,2.6,100000
total time: 120.00 hours.

Nov 11, 2008 (4th)

By Sinkiti Sibata / GGNFS

4·10¹⁸⁷-9 = 3(9)₁₈₆1_<188> = 53 · 10684013423190202598370871_<26> · 1626349888286077666713489931346081_<34> · C128

C128 = P46 · P83

P46 = 1156412510086878791154526581085081807094186719_<46>

P83 = 37559770618664727055350154373325301900026821932736805523253002218736318566782328163_<83>

Number: 39991_187
N=43434588619417477329933277408700569125776242676471321059204704968470235596379158309505822359339758001320385530719040417854267197
  ( 128 digits)
Divisors found:
 r1=1156412510086878791154526581085081807094186719 (pp46)
 r2=37559770618664727055350154373325301900026821932736805523253002218736318566782328163 (pp83)
Version: GGNFS-0.77.1-20060513-k8
Total time: 246.89 hours.
Scaled time: 485.63 units (timescale=1.967).
Factorization parameters were as follows:
name: 39991_187
n: 43434588619417477329933277408700569125776242676471321059204704968470235596379158309505822359339758001320385530719040417854267197
skew: 41234.70
# norm 4.47e+17
c5: 179760
c4: -468322242646
c3: 7158562425476123
c2: 706920016882918004321
c1: -8997659448553333649363
c0: -81193830374116964234607252355
# alpha -6.59
Y1: 69625650657497
Y0: -2996634592095948845052744
# Murphy_E 1.05e-10
# M 27377686138790807889789438251685435821041056178393248572664212912808568040467964210247533237064438040348735126973249238361678525
type: gnfs
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.5
alambda: 2.5
qintsize: 60000
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [2700000, 9840001)
Primes: RFBsize:374362, AFBsize:374718, largePrimes:9599165 encountered
Relations: rels:10656209, finalFF:859521
Max relations in full relation-set: 28
Initial matrix: 749166 x 859521 with sparse part having weight 120586918.
Pruned matrix : 668643 x 672452 with weight 99995938.
Total sieving time: 233.91 hours.
Total relation processing time: 1.48 hours.
Matrix solve time: 10.85 hours.
Time per square root: 0.65 hours.
Prototype def-par.txt line would be:
gnfs,127,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5400000,5400000,27,27,51,51,2.5,2.5,60000
total time: 246.89 hours.
 --------- CPU info (if available) ----------

Nov 11, 2008 (3rd)

By Serge Batalov / GMP-ECM 6.2.1

(26·10¹⁷³+1)/9 = 2(8)₁₇₂9_<174> = 458557838989194890719_<21> · C153

C153 = P35 · P118

P35 = 73305096001558563409944288559304387_<35>

P118 = 8594142483414908579347938546811251556448886758055864089876219871162756829401458004039178884223538718178148112968531213_<118>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=512132224
Step 1 took 14765ms
Step 2 took 11009ms
********** Factor found in step 2: 73305096001558563409944288559304387
Found probable prime factor of 35 digits: 73305096001558563409944288559304387
Probable prime cofactor 8594142483414908579347938546811251556448886758055864089876219871162756829401458004039178884223538718178148112968531213 has 118 digits

Nov 11, 2008 (2nd)

By Serge Batalov / Msieve-1.38

(7·10¹⁸²+11)/9 = (7)₁₈₁9_<182> = 7162907 · C176

C176 = P74 · P102

P74 = 21099773409773806293781644425845956947197905609054762376378049489953181671_<74>

P102 = 514622092833430760457080826490332986070853295140251661480075572933304449397750105423250483183378081807_<102>

SNFS difficulty: 182 digits.
Divisors found:
 r1=21099773409773806293781644425845956947197905609054762376378049489953181671
 r2=514622092833430760457080826490332986070853295140251661480075572933304449397750105423250483183378081807
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
n: 10858409550448969640088553122046367177149972459195376650538360721111942089681993327259139030812179716667796716860595534435638739659439635022174345943312928365226266064570959497
m: 1000000000000000000000000000000000000
c5: 700
c0: 11
skew: 0.44
type: snfs
lss: 1
rlim: 9400000
alim: 9400000
lpbr: 27
lpba: 27
mfbr: 54
mfba: 54
rlambda: 2.6
alambda: 2.6
Factor base limits: 9400000/9400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [4700000, 8300001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1465939 x 1466181
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,9400000,9400000,27,27,54,54,2.6,2.6,400000
total time: 160.00 hours.

Nov 11, 2008

By Tyler Cadigan / GGNFS, msieve 1.38

(64·10¹⁹³-1)/9 = 7(1)₁₉₃_<194> = 48841603 · 4147149761_<10> · 6136607557_<10> · 31737283837445080249_<20> · C148

C148 = P72 · P77

P72 = 106827244682461422181234170696232476853829433128839704733530965299009843_<72>

P77 = 16873986719788660126221030932544026486472905100620508524512200329945569875883_<77>

Number: 71111_193
N=1802601508083467798391112388078070476447733455722798735220424812749725790627450776795649250070797201074189953860549742051929399404960264228305316369
  ( 148 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=106827244682461422181234170696232476853829433128839704733530965299009843
 r2=16873986719788660126221030932544026486472905100620508524512200329945569875883
Version: 
Total time: 989.65 hours.
Scaled time: 2544.40 units (timescale=2.571).
Factorization parameters were as follows:
n: 1802601508083467798391112388078070476447733455722798735220424812749725790627450776795649250070797201074189953860549742051929399404960264228305316369
m: 400000000000000000000000000000000000000
c5: 125
c0: -2
skew: 0.44
type: snfs
Y0: 400000000000000000000000000000000000000
Y1: -1
rlambda: 2.6
alambda: 2.6
rlim: 20000000
alim: 20000000
qintsize: 1000000Factor base limits: 20000000/20000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [10000000, 24000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1589990 x 1590207
Total sieving time: 989.65 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,195,5,0,0,0,0,0,0,0,0,20000000,20000000,27,27,48,48,2.6,2.6,100000
total time: 989.65 hours.
 --------- CPU info (if available) ----------

Nov 10, 2008 (5th)

By Robert Backstrom / GGNFS, Msieve

(16·10²⁰⁵-1)/3 = 5(3)₂₀₅_<206> = C206

C206 = P67 · P139

P67 = 7253816360547696746337226052876346580763518857600573480425639193467_<67>

P139 = 7352451548595092851587671278219896892562021515468240661156973439665968776976024454455251948173889966313752479891086480528562516539317420399_<139>

Number: n
N=53333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333
  ( 206 digits)
SNFS difficulty: 206 digits.
Divisors found:

Mon Nov 10 22:35:48 2008  prp67 factor: 7253816360547696746337226052876346580763518857600573480425639193467
Mon Nov 10 22:35:48 2008  prp139 factor: 7352451548595092851587671278219896892562021515468240661156973439665968776976024454455251948173889966313752479891086480528562516539317420399
Mon Nov 10 22:35:48 2008  elapsed time 35:33:32 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 120.07 hours.
Scaled time: 243.98 units (timescale=2.032).
Factorization parameters were as follows:
name: KA_5_3_205
n: 53333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333
type: snfs
skew: 1.15
deg: 5
c5: 1
c0: -2
m: 200000000000000000000000000000000000000000
rlim: 10000000
alim: 10000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 18900001)
Primes: RFBsize:664579, AFBsize:664630, largePrimes:35868282 encountered
Relations: rels:27817726, finalFF:172962
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 117.89 hours.
Total relation processing time: 2.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,206,5,0,0,0,0,0,0,0,0,10000000,10000000,29,29,58,58,2.5,2.5,100000
total time: 120.07 hours.
 --------- CPU info (if available) ----------

Nov 11, 2008 (4th)

By Sinkiti Sibata / GGNFS

(28·10¹⁶⁷+53)/9 = 3(1)₁₆₆7_<168> = 173 · 1033 · 861933138290293_<15> · 396782411899824648671_<21> · C127

C127 = P48 · P80

P48 = 130895819870043557515711359581289161373022640261_<48>

P80 = 38888154047693150598352587316342929490928032042224238309930286093662401799559311_<80>

Number: 31117_167
N=5090296807305347901135661154211531213234907790899800177923121847419165500383051328464658675418849569729412119386322895486020171
  ( 127 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=130895819870043557515711359581289161373022640261 (pp48)
 r2=38888154047693150598352587316342929490928032042224238309930286093662401799559311 (pp80)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 102.72 hours.
Scaled time: 103.65 units (timescale=1.009).
Factorization parameters were as follows:
name: 31117_167
n: 5090296807305347901135661154211531213234907790899800177923121847419165500383051328464658675418849569729412119386322895486020171
m: 2000000000000000000000000000000000
deg: 5
c5: 175
c0: 106
skew: 0.90
type: snfs
lss: 1
rlim: 4700000
alim: 4700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6
Factor base limits: 4700000/4700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2350000, 5650001)
Primes: RFBsize:328964, AFBsize:328714, largePrimes:10621873 encountered
Relations: rels:11700619, finalFF:787911
Max relations in full relation-set: 28
Initial matrix: 657744 x 787911 with sparse part having weight 98221720.
Pruned matrix : 589848 x 593200 with weight 78569950.
Total sieving time: 97.88 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 4.48 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.6,2.6,100000
total time: 102.72 hours.
 --------- CPU info (if available) ----------

Nov 10, 2008 (3rd)

By Erik Branger / GGNFS,Msieve

(26·10¹⁶⁷+1)/9 = 2(8)₁₆₆9_<168> = 23 · 97 · 7440716741_<10> · C155

C155 = P33 · P40 · P82

P33 = 994429931053939659460376462395301_<33>

P40 = 8171083938783497384303320933326590394457_<40>

P82 = 2141719727669073859289699777557563993829652102083579639846097856848841724268160287_<82>

Number: 28889_167
N=17402694505373145372496501874332254808264964601515213995881884682345882922122957369781299658358690100048182317099152378155908918093570308072669512206881859
  ( 155 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=994429931053939659460376462395301
 r2=8171083938783497384303320933326590394457
 r3=2141719727669073859289699777557563993829652102083579639846097856848841724268160287
Version: 
Total time: 72.08 hours.
Scaled time: 158.51 units (timescale=2.199).
Factorization parameters were as follows:
n: 17402694505373145372496501874332254808264964601515213995881884682345882922122957369781299658358690100048182317099152378155908918093570308072669512206881859
m: 5000000000000000000000000000000000
deg: 5
c5: 104
c0: 125
skew: 1.04
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6
Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 5050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 947021 x 947269
Total sieving time: 72.08 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.6,2.6,100000
total time: 72.08 hours.
 --------- CPU info (if available) ----------

Nov 10, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(28·10¹⁵³+53)/9 = 3(1)₁₅₂7_<154> = 3⁴ · 56249 · 730095898313_<12> · 9965171834443050233424291971_<28> · C107

C107 = P52 · P56

P52 = 1714948088665204519589713916720465015747178714196217_<52>

P56 = 54726795393356620267708850472075073689756000982100900023_<56>

Number: 31117_153
N=93853613158608655468571700499385796554488640891821409187467158885149908174643438256355936087132602721812991
  ( 107 digits)
Divisors found:
 r1=1714948088665204519589713916720465015747178714196217 (pp52)
 r2=54726795393356620267708850472075073689756000982100900023 (pp56)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 21.87 hours.
Scaled time: 10.35 units (timescale=0.473).
Factorization parameters were as follows:
name: 31117_153
n: 93853613158608655468571700499385796554488640891821409187467158885149908174643438256355936087132602721812991
skew: 16073.92
# norm 2.25e+15
c5: 178800
c4: 1666354780
c3: -225587937339236
c2: -156790534487345883
c1: 20270929971815814767584
c0: 3054437511647271308857872
# alpha -6.78
Y1: 145494130243
Y0: -220808690967853528205
# Murphy_E 1.36e-09
# M 9503772141216026415551950007863591962513804742151124620315633056092138605998778437390332844898982587770367
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2450001)
Primes: RFBsize:183072, AFBsize:183884, largePrimes:4470428 encountered
Relations: rels:4574255, finalFF:472428
Max relations in full relation-set: 28
Initial matrix: 367035 x 472428 with sparse part having weight 35488964.
Pruned matrix : 288904 x 290803 with weight 19736749.
Polynomial selection time: 1.08 hours.
Total sieving time: 18.07 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 2.19 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 21.87 hours.
 --------- CPU info (if available) ----------

Nov 10, 2008

By Serge Batalov / GMP-ECM 6.2.1

(5·10¹⁸¹-11)/3 = 1(6)₁₈₀3_<182> = 13² · 10463 · C175

C175 = P41 · P135

P41 = 19735873762848979923788343262746910415597_<41>

P135 = 477583661777319114348974410080105808146987308682331423638268730772140428005311952962423539714530787220806113863148497059834874873525557_<135>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2126843982
Step 1 took 25957ms
Step 2 took 15589ms
********** Factor found in step 2: 19735873762848979923788343262746910415597
Found probable prime factor of 41 digits: 19735873762848979923788343262746910415597
Probable prime cofactor 477583661777319114348974410080105808146987308682331423638268730772140428005311952962423539714530787220806113863148497059834874873525557 has 135 digits

(34·10¹⁷³-43)/9 = 3(7)₁₇₂3_<174> = 11 · 4090017086037300067260361867_<28> · C145

C145 = P60 · P86

P60 = 107626043102279955648663040733162113867786338310868288276113_<60>

P86 = 78019152169372766771630568934861109861574756452212059302706443287700884816615566155333_<86>

SNFS difficulty: 175 digits.
Divisors found:
 r1=107626043102279955648663040733162113867786338310868288276113
 r2=7801915216937276677163056893486110986157475645221205930270644328770088481661                                           5566155333
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 83968926341842521032222222375343161902382575858720800562857080406878660082583                                           64078713992722606690854088987379490701900885592654783285597751460629
m: 50000000000000000000000000000000000
deg: 5
c5: 272
c0: -1075
skew: 1.32
type: snfs
lss: 1
rlim: 6600000
alim: 6600000
lpbr: 27
lpba: 27
Factor base limits: 6600000/6600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [3300000, 7600001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1186854 x 1187096
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,6600000,6600000,27,27,54,54,2.6,2.6,100000
total time: 96.00 hours.

Nov 9, 2008 (4th)

By matsui / GMP-ECM

2·10¹⁹³-9 = 1(9)₁₉₂1_<194> = 11² · 229 · 751 · C186

C186 = P34 · C153

P34 = 1389008490432229693915637396036821_<34>

C153 = [691933417297017957104478334368940847492681960800916503025598061193956200601528866970042838166170253705478669766997332550958436576230148828520831637814969_<153>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]

961101391439344963268867297318974030031246847887780263773315779136785824177360881895103568045666155953405612322742268311732659652516675229279146565030835256216896364292795886716708973549
=
1389008490432229693915637396036821* 691933417297017957104478334368940847492681960800916503025598061193956200601528866970042838166170253705478669766997332550958436576230148828520831637814969

Nov 9, 2008 (3rd)

By Justin Card / GGNFS / msieve 1.38

(10¹⁸³+17)/9 = (1)₁₈₂3_<183> = 109 · 233 · 107149391 · C170

C170 = P63 · P108

P63 = 168065510093738558138055116999214544462198890554682324748107419_<63>

P108 = 242944329426849970997180630477373752133478580556976677728940298344363173643729480362319651902123233317150001_<108>

Fri Nov  7 17:54:24 2008  Msieve v. 1.38
Fri Nov  7 17:54:24 2008  random seeds: e74a4bc0 27e1dda1
Fri Nov  7 17:54:24 2008  factoring 40830562649504799217415961810238391197943215134935430982426238285068266711842023010787621084797361781299076622938184082903429550547622347219167653925734308110219683957419 (170 digits)
Fri Nov  7 17:54:26 2008  no P-1/P+1/ECM available, skipping
Fri Nov  7 17:54:26 2008  commencing number field sieve (170-digit input)
Fri Nov  7 17:54:26 2008  R0: -2000000000000000000000000000000000000
Fri Nov  7 17:54:26 2008  R1:  1
Fri Nov  7 17:54:26 2008  A0:  68
Fri Nov  7 17:54:26 2008  A1:  0
Fri Nov  7 17:54:26 2008  A2:  0
Fri Nov  7 17:54:26 2008  A3:  0
Fri Nov  7 17:54:26 2008  A4:  0
Fri Nov  7 17:54:26 2008  A5:  125
Fri Nov  7 17:54:26 2008  size score = 8.925208e-13, Murphy alpha = 0.098689, combined = 8.636379e-13
Fri Nov  7 17:54:26 2008
Fri Nov  7 17:54:26 2008  commencing relation filtering
Fri Nov  7 17:54:26 2008  commencing duplicate removal, pass 1
Fri Nov  7 17:59:19 2008  found 2177390 hash collisions in 23154021 relations
Fri Nov  7 18:00:40 2008  added 3465 free relations
Fri Nov  7 18:00:40 2008  commencing duplicate removal, pass 2
Fri Nov  7 18:00:57 2008  found 1506103 duplicates and 21651383 unique relations
Fri Nov  7 18:00:57 2008  memory use: 94.6 MB
Fri Nov  7 18:00:57 2008  reading rational ideals above 10944512
Fri Nov  7 18:00:57 2008  reading algebraic ideals above 10944512
Fri Nov  7 18:00:57 2008  commencing singleton removal, pass 1
Fri Nov  7 18:05:37 2008  relations with 0 large ideals: 392628
Fri Nov  7 18:05:37 2008  relations with 1 large ideals: 2450350
Fri Nov  7 18:05:37 2008  relations with 2 large ideals: 6519546
Fri Nov  7 18:05:37 2008  relations with 3 large ideals: 7895436
Fri Nov  7 18:05:37 2008  relations with 4 large ideals: 3690112
Fri Nov  7 18:05:37 2008  relations with 5 large ideals: 19077
Fri Nov  7 18:05:37 2008  relations with 6 large ideals: 684234
Fri Nov  7 18:05:37 2008  relations with 7+ large ideals: 0
Fri Nov  7 18:05:37 2008  21651383 relations and about 19194176 large ideals
Fri Nov  7 18:05:37 2008  commencing singleton removal, pass 2
Fri Nov  7 18:10:16 2008  found 6735403 singletons
Fri Nov  7 18:10:16 2008  current dataset: 14915980 relations and about 11124611 large ideals
Fri Nov  7 18:10:16 2008  commencing singleton removal, pass 3
Fri Nov  7 18:13:22 2008  found 1602906 singletons
Fri Nov  7 18:13:22 2008  current dataset: 13313074 relations and about 9447761 large ideals
Fri Nov  7 18:13:22 2008  commencing singleton removal, pass 4
Fri Nov  7 18:16:08 2008  found 370857 singletons
Fri Nov  7 18:16:08 2008  current dataset: 12942217 relations and about 9072150 large ideals
Fri Nov  7 18:16:08 2008  commencing singleton removal, final pass
Fri Nov  7 18:19:10 2008  memory use: 219.5 MB
Fri Nov  7 18:19:10 2008  commencing in-memory singleton removal
Fri Nov  7 18:19:12 2008  begin with 12942217 relations and 10108568 unique ideals
Fri Nov  7 18:19:38 2008  reduce to 11020221 relations and 8131732 ideals in 15 passes
Fri Nov  7 18:19:38 2008  max relations containing the same ideal: 43
Fri Nov  7 18:19:40 2008  reading rational ideals above 720000
Fri Nov  7 18:19:40 2008  reading algebraic ideals above 720000
Fri Nov  7 18:19:40 2008  commencing singleton removal, final pass
Fri Nov  7 18:23:19 2008  keeping 8734777 ideals with weight <= 20, new excess is 864903
Fri Nov  7 18:23:29 2008  memory use: 256.8 MB
Fri Nov  7 18:23:29 2008  commencing in-memory singleton removal
Fri Nov  7 18:23:31 2008  begin with 11023686 relations and 8734777 unique ideals
Fri Nov  7 18:23:45 2008  reduce to 11019203 relations and 8713341 ideals in 7 passes
Fri Nov  7 18:23:45 2008  max relations containing the same ideal: 20
Fri Nov  7 18:23:56 2008  removing 2136396 relations and 1736396 ideals in 400000 cliques
Fri Nov  7 18:23:57 2008  commencing in-memory singleton removal
Fri Nov  7 18:23:58 2008  begin with 8882807 relations and 8713341 unique ideals
Fri Nov  7 18:24:12 2008  reduce to 8621173 relations and 6704103 ideals in 9 passes
Fri Nov  7 18:24:12 2008  max relations containing the same ideal: 20
Fri Nov  7 18:24:20 2008  removing 1619607 relations and 1219607 ideals in 400000 cliques
Fri Nov  7 18:24:21 2008  commencing in-memory singleton removal
Fri Nov  7 18:24:22 2008  begin with 7001566 relations and 6704103 unique ideals
Fri Nov  7 18:24:33 2008  reduce to 6797292 relations and 5271165 ideals in 9 passes
Fri Nov  7 18:24:33 2008  max relations containing the same ideal: 20
Fri Nov  7 18:24:39 2008  removing 1463385 relations and 1063385 ideals in 400000 cliques
Fri Nov  7 18:24:40 2008  commencing in-memory singleton removal
Fri Nov  7 18:24:40 2008  begin with 5333907 relations and 5271165 unique ideals
Fri Nov  7 18:24:48 2008  reduce to 5118087 relations and 3980297 ideals in 9 passes
Fri Nov  7 18:24:48 2008  max relations containing the same ideal: 19
Fri Nov  7 18:24:52 2008  removing 616616 relations and 482114 ideals in 134502 cliques
Fri Nov  7 18:24:53 2008  commencing in-memory singleton removal
Fri Nov  7 18:24:54 2008  begin with 4501471 relations and 3980297 unique ideals
Fri Nov  7 18:24:59 2008  reduce to 4451213 relations and 3446730 ideals in 7 passes
Fri Nov  7 18:24:59 2008  max relations containing the same ideal: 19
Fri Nov  7 18:25:03 2008  relations with 0 large ideals: 128141
Fri Nov  7 18:25:03 2008  relations with 1 large ideals: 644668
Fri Nov  7 18:25:03 2008  relations with 2 large ideals: 1377524
Fri Nov  7 18:25:03 2008  relations with 3 large ideals: 1403644
Fri Nov  7 18:25:03 2008  relations with 4 large ideals: 700436
Fri Nov  7 18:25:03 2008  relations with 5 large ideals: 159255
Fri Nov  7 18:25:03 2008  relations with 6 large ideals: 36585
Fri Nov  7 18:25:03 2008  relations with 7+ large ideals: 960
Fri Nov  7 18:25:03 2008  commencing 2-way merge
Fri Nov  7 18:25:08 2008  reduce to 2874971 relation sets and 1870488 unique ideals
Fri Nov  7 18:25:08 2008  commencing full merge
Fri Nov  7 18:25:42 2008  memory use: 163.5 MB
Fri Nov  7 18:25:43 2008  found 1409399 cycles, need 1272688
Fri Nov  7 18:25:44 2008  weight of 1272688 cycles is about 89474158 (70.30/cycle)
Fri Nov  7 18:25:44 2008  distribution of cycle lengths:
Fri Nov  7 18:25:44 2008  1 relations: 165517
Fri Nov  7 18:25:44 2008  2 relations: 128117
Fri Nov  7 18:25:44 2008  3 relations: 131193
Fri Nov  7 18:25:44 2008  4 relations: 129223
Fri Nov  7 18:25:44 2008  5 relations: 124960
Fri Nov  7 18:25:44 2008  6 relations: 114579
Fri Nov  7 18:25:44 2008  7 relations: 104913
Fri Nov  7 18:25:44 2008  8 relations: 91673
Fri Nov  7 18:25:44 2008  9 relations: 79160
Fri Nov  7 18:25:44 2008  10+ relations: 203353
Fri Nov  7 18:25:44 2008  heaviest cycle: 16 relations
Fri Nov  7 18:25:44 2008  commencing cycle optimization
Fri Nov  7 18:25:47 2008  start with 7122735 relations
Fri Nov  7 18:26:05 2008  pruned 235546 relations
Fri Nov  7 18:26:06 2008  memory use: 233.5 MB
Fri Nov  7 18:26:06 2008  distribution of cycle lengths:
Fri Nov  7 18:26:06 2008  1 relations: 165517
Fri Nov  7 18:26:06 2008  2 relations: 132065
Fri Nov  7 18:26:06 2008  3 relations: 137489
Fri Nov  7 18:26:06 2008  4 relations: 134742
Fri Nov  7 18:26:06 2008  5 relations: 130671
Fri Nov  7 18:26:06 2008  6 relations: 119077
Fri Nov  7 18:26:06 2008  7 relations: 108667
Fri Nov  7 18:26:06 2008  8 relations: 93246
Fri Nov  7 18:26:06 2008  9 relations: 78451
Fri Nov  7 18:26:06 2008  10+ relations: 172763
Fri Nov  7 18:26:06 2008  heaviest cycle: 16 relations
Fri Nov  7 18:26:07 2008

Sat Nov  8 11:39:25 2008  Msieve v. 1.38
Sat Nov  8 11:39:25 2008  random seeds: 51fa03ca 0994addc
Sat Nov  8 11:39:25 2008  factoring 40830562649504799217415961810238391197943215134935430982426238285068266711842023010787621084797361781299076622938184082903429550547622347219167653925734308110219683957419 (170 digits)
Sat Nov  8 11:39:27 2008  no P-1/P+1/ECM available, skipping
Sat Nov  8 11:39:27 2008  commencing number field sieve (170-digit input)
Sat Nov  8 11:39:27 2008  R0: -2000000000000000000000000000000000000
Sat Nov  8 11:39:27 2008  R1:  1
Sat Nov  8 11:39:27 2008  A0:  68
Sat Nov  8 11:39:27 2008  A1:  0
Sat Nov  8 11:39:27 2008  A2:  0
Sat Nov  8 11:39:27 2008  A3:  0
Sat Nov  8 11:39:27 2008  A4:  0
Sat Nov  8 11:39:27 2008  A5:  125
Sat Nov  8 11:39:27 2008  size score = 8.925208e-13, Murphy alpha = 0.098689, combined = 8.636379e-13
Sat Nov  8 11:39:27 2008
Sat Nov  8 11:39:27 2008  commencing linear algebra
Sat Nov  8 11:39:28 2008  read 1266783 cycles
Sat Nov  8 11:39:35 2008  matrix is 1266583 x 1266783 (376.6 MB) with weight 119213116 (94.11/col)
Sat Nov  8 11:39:35 2008  sparse part has weight 84786181 (66.93/col)
Sat Nov  8 11:39:35 2008  saving the first 48 matrix rows for later
Sat Nov  8 11:39:36 2008  matrix is 1266535 x 1266783 (359.5 MB) with weight 91770370 (72.44/col)
Sat Nov  8 11:39:36 2008  sparse part has weight 81564776 (64.39/col)
Sat Nov  8 11:39:36 2008  matrix includes 64 packed rows
Sat Nov  8 11:39:36 2008  using block size 10922 for processor cache size 256 kB
Sat Nov  8 11:39:44 2008  commencing Lanczos iteration (2 threads)
Sat Nov  8 11:39:44 2008  memory use: 354.5 MB
Sat Nov  8 11:39:45 2008  restarting at iteration 7907 (dim = 500003)
Sat Nov  8 16:25:01 2008  lanczos halted after 20032 iterations (dim = 1266533)
Sat Nov  8 16:25:05 2008  recovered 49 nontrivial dependencies
Sat Nov  8 16:25:05 2008  elapsed time 04:45:40

Sat Nov  8 17:55:09 2008  Msieve v. 1.38
Sat Nov  8 17:55:09 2008  random seeds: a64a7e10 af28163f
Sat Nov  8 17:55:09 2008  factoring 40830562649504799217415961810238391197943215134935430982426238285068266711842023010787621084797361781299076622938184082903429550547622347219167653925734308110219683957419 (170 digits)
Sat Nov  8 17:55:11 2008  no P-1/P+1/ECM available, skipping
Sat Nov  8 17:55:11 2008  commencing number field sieve (170-digit input)
Sat Nov  8 17:55:11 2008  R0: -2000000000000000000000000000000000000
Sat Nov  8 17:55:11 2008  R1:  1
Sat Nov  8 17:55:11 2008  A0:  68
Sat Nov  8 17:55:11 2008  A1:  0
Sat Nov  8 17:55:11 2008  A2:  0
Sat Nov  8 17:55:11 2008  A3:  0
Sat Nov  8 17:55:11 2008  A4:  0
Sat Nov  8 17:55:11 2008  A5:  125
Sat Nov  8 17:55:11 2008  size score = 8.925208e-13, Murphy alpha = 0.098689, combined = 8.636379e-13
Sat Nov  8 17:55:11 2008
Sat Nov  8 17:55:11 2008  commencing square root phase
Sat Nov  8 17:55:11 2008  reading relations for dependency 1
Sat Nov  8 17:55:14 2008  read 633249 cycles
Sat Nov  8 17:55:16 2008  cycles contain 2386887 unique relations
Sat Nov  8 17:56:05 2008  read 2386887 relations
Sat Nov  8 17:56:22 2008  multiplying 1941296 relations
Sat Nov  8 18:00:50 2008  multiply complete, coefficients have about 58.10 million bits
Sat Nov  8 18:00:52 2008  initial square root is modulo 219677771
Sat Nov  8 18:09:53 2008  reading relations for dependency 2
Sat Nov  8 18:09:53 2008  read 633768 cycles
Sat Nov  8 18:09:55 2008  cycles contain 2389302 unique relations
Sat Nov  8 18:10:28 2008  read 2389302 relations
Sat Nov  8 18:10:46 2008  multiplying 1944182 relations
Sat Nov  8 18:15:13 2008  multiply complete, coefficients have about 58.19 million bits
Sat Nov  8 18:15:14 2008  initial square root is modulo 225957161
Sat Nov  8 18:24:15 2008  prp63 factor: 168065510093738558138055116999214544462198890554682324748107419
Sat Nov  8 18:24:15 2008  prp108 factor: 242944329426849970997180630477373752133478580556976677728940298344363173643729480362319651902123233317150001
Sat Nov  8 18:24:15 2008  elapsed time 00:29:06

Nov 9, 2008 (2nd)

By Sinkiti Sibata / GGNFS, Msieve

(28·10¹⁵⁴+53)/9 = 3(1)₁₅₃7_<155> = 37 · 118253 · 2590601425843_<13> · 104351236022329_<15> · C122

C122 = P59 · P63

P59 = 31380690453138880931657560889514420126566353542603767728673_<59>

P63 = 838187032860531496732431247159491568872050528936039746282768087_<63>

Number: 31117_154
N=26302887820031286216044163151544987536670418340903126268617853632435901087122766307269609832111146982541812236687199258551
  ( 122 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=31380690453138880931657560889514420126566353542603767728673 (pp59)
 r2=838187032860531496732431247159491568872050528936039746282768087 (pp63)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 35.76 hours.
Scaled time: 36.08 units (timescale=1.009).
Factorization parameters were as follows:
name: 31117_154
n: 26302887820031286216044163151544987536670418340903126268617853632435901087122766307269609832111146982541812236687199258551
m: 10000000000000000000000000000000
deg: 5
c5: 14
c0: 265
skew: 1.80
type: snfs
lss: 1
rlim: 2700000
alim: 2700000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
Factor base limits: 2700000/2700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1350000, 2250001)
Primes: RFBsize:196645, AFBsize:196555, largePrimes:8974694 encountered
Relations: rels:10185021, finalFF:1418892
Max relations in full relation-set: 28
Initial matrix: 393266 x 1418892 with sparse part having weight 172397834.
Pruned matrix : 261743 x 263773 with weight 46680093.
Total sieving time: 34.83 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.70 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2700000,2700000,27,27,50,50,2.5,2.5,100000
total time: 35.76 hours.
 --------- CPU info (if available) ----------

(28·10¹⁵⁷+53)/9 = 3(1)₁₅₆7_<158> = 37 · 47 · 26331439648529_<14> · 21571218020531989_<17> · 918246836096301808177139_<24> · C101

C101 = P44 · P57

P44 = 39831015768787321623763565201624873814103751_<44>

P57 = 861163957056282450067185221723079940753436194438560270367_<57>

Sat Nov  8 08:51:48 2008  Msieve v. 1.38
Sat Nov  8 08:51:48 2008  random seeds: 31e6e1ba bd1041bd
Sat Nov  8 08:51:48 2008  factoring 34301035153020074137083936657263640461196013812649453311158553740296304575991971202189293536348846617 (101 digits)
Sat Nov  8 08:51:50 2008  searching for 15-digit factors
Sat Nov  8 08:51:52 2008  commencing quadratic sieve (101-digit input)
Sat Nov  8 08:51:52 2008  using multiplier of 65
Sat Nov  8 08:51:52 2008  using 64kb Pentium 4 sieve core
Sat Nov  8 08:51:52 2008  sieve interval: 18 blocks of size 65536
Sat Nov  8 08:51:52 2008  processing polynomials in batches of 6
Sat Nov  8 08:51:52 2008  using a sieve bound of 2893831 (105000 primes)
Sat Nov  8 08:51:52 2008  using large prime bound of 434074650 (28 bits)
Sat Nov  8 08:51:52 2008  using double large prime bound of 3528709595930850 (43-52 bits)
Sat Nov  8 08:51:52 2008  using trial factoring cutoff of 52 bits
Sat Nov  8 08:51:52 2008  polynomial 'A' values have 13 factors
Sun Nov  9 06:18:37 2008  105394 relations (26049 full + 79345 combined from 1560756 partial), need 105096
Sun Nov  9 06:18:44 2008  begin with 1586805 relations
Sun Nov  9 06:18:46 2008  reduce to 274428 relations in 11 passes
Sun Nov  9 06:18:46 2008  attempting to read 274428 relations
Sun Nov  9 06:18:56 2008  recovered 274428 relations
Sun Nov  9 06:18:56 2008  recovered 265233 polynomials
Sun Nov  9 06:18:57 2008  attempting to build 105394 cycles
Sun Nov  9 06:18:57 2008  found 105394 cycles in 6 passes
Sun Nov  9 06:18:57 2008  distribution of cycle lengths:
Sun Nov  9 06:18:57 2008     length 1 : 26049
Sun Nov  9 06:18:57 2008     length 2 : 18219
Sun Nov  9 06:18:57 2008     length 3 : 17760
Sun Nov  9 06:18:57 2008     length 4 : 14238
Sun Nov  9 06:18:57 2008     length 5 : 10838
Sun Nov  9 06:18:57 2008     length 6 : 7183
Sun Nov  9 06:18:57 2008     length 7 : 4587
Sun Nov  9 06:18:57 2008     length 9+: 6520
Sun Nov  9 06:18:57 2008  largest cycle: 19 relations
Sun Nov  9 06:18:58 2008  matrix is 105000 x 105394 (31.0 MB) with weight 7696930 (73.03/col)
Sun Nov  9 06:18:58 2008  sparse part has weight 7696930 (73.03/col)
Sun Nov  9 06:19:00 2008  filtering completed in 3 passes
Sun Nov  9 06:19:00 2008  matrix is 100434 x 100498 (29.6 MB) with weight 7363818 (73.27/col)
Sun Nov  9 06:19:00 2008  sparse part has weight 7363818 (73.27/col)
Sun Nov  9 06:19:01 2008  saving the first 48 matrix rows for later
Sun Nov  9 06:19:02 2008  matrix is 100386 x 100498 (21.3 MB) with weight 6154040 (61.24/col)
Sun Nov  9 06:19:02 2008  sparse part has weight 4981615 (49.57/col)
Sun Nov  9 06:19:02 2008  matrix includes 64 packed rows
Sun Nov  9 06:19:02 2008  using block size 21845 for processor cache size 512 kB
Sun Nov  9 06:19:03 2008  commencing Lanczos iteration
Sun Nov  9 06:19:03 2008  memory use: 18.7 MB
Sun Nov  9 06:21:11 2008  lanczos halted after 1589 iterations (dim = 100386)
Sun Nov  9 06:21:11 2008  recovered 19 nontrivial dependencies
Sun Nov  9 06:21:15 2008  prp44 factor: 39831015768787321623763565201624873814103751
Sun Nov  9 06:21:15 2008  prp57 factor: 861163957056282450067185221723079940753436194438560270367
Sun Nov  9 06:21:15 2008  elapsed time 21:29:27

Nov 9, 2008

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38, Msieve-1.38+pol51

(28·10¹⁹⁴+53)/9 = 3(1)₁₉₃7_<195> = 31 · C194

C194 = P33 · P161

P33 = 472354746844406776569684827121259_<33>

P161 = 21246409316201086781223560802188507623529576386381183964277856707558320818501394634593007351163955614343818211309876908233391721201139215075947346247649789438073_<161>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1052466718
Step 1 took 34838ms
Step 2 took 20685ms
********** Factor found in step 2: 472354746844406776569684827121259
Found probable prime factor of 33 digits: 472354746844406776569684827121259
Probable prime cofactor 21246409316201086781223560802188507623529576386381183964277856707558320818501394634593007351163955614343818211309876908233391721201139215075947346247649789438073 has 161 digits

(28·10²⁰⁰+53)/9 = 3(1)₁₉₉7_<201> = 29 · 43 · 107 · 1823 · 21328421210758970543_<20> · C173

C173 = P38 · P136

P38 = 45942003104423641964369130794226732463_<38>

P136 = 1305298942936638231265444090741388866280605981251391488376841472424640754825434217341481496796729350040386008942938650151794702274016839_<136>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2885641489
Step 1 took 26947ms
Step 2 took 16809ms
********** Factor found in step 2: 45942003104423641964369130794226732463
Found probable prime factor of 38 digits: 45942003104423641964369130794226732463
Probable prime cofactor 1305298942936638231265444090741388866280605981251391488376841472424640754825434217341481496796729350040386008942938650151794702274016839 has 136 digits

(82·10¹⁷²+71)/9 = 9(1)₁₇₁9_<173> = 3³ · 7 · 896417753761291537_<18> · C153

C153 = P75 · P78

P75 = 579334939143750224236552153827979527517295282518316257376055224005179129017_<75>

P78 = 928259426815593672223170317132445806904486312024907035248560376926499575246499_<78>

SNFS difficulty: 174 digits.
Divisors found:
 r1=579334939143750224236552153827979527517295282518316257376055224005179129017
 r2=928259426815593672223170317132445806904486312024907035248560376926499575246499
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.947).
Factorization parameters were as follows:
n: 537773118543824425100631333861953876307574301213434419754952037963832301306473338612108363514158650784044233408704123947175704195086527887173317898561483
m: 20000000000000000000000000000000000
deg: 5
c5: 1025
c0: 284
skew: 0.77
type: snfs
lss: 1
rlim: 6200000
alim: 6200000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.6
alambda: 2.6
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved rational special-q in [3100000, 7500001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1165120 x 1165362
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,174,5,0,0,0,0,0,0,0,0,6200000,6200000,27,27,53,53,2.6,2.6,200000
total time: 75.00 hours.

6·10¹⁷³-1 = 5(9)₁₇₃_<174> = 446221 · 13201045994383692917_<20> · 20546681584297179439544553169075952341_<38> · C112

C112 = P53 · P59

P53 = 53428999410989900919046470530953734472804557616368781_<53>

P59 = 92784230298861313197303857948581192121788284162444016808767_<59>

Number: 59999_173
N=4957368585987012421336435230959147904107104720246843895074059519403671637558839501911510239834859772382225903027
  ( 112 digits)
Divisors found:
 r1=53428999410989900919046470530953734472804557616368781
 r2=92784230298861313197303857948581192121788284162444016808767
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.314).
Factorization parameters were as follows:
name: 59999_173
n: 4957368585987012421336435230959147904107104720246843895074059519403671637558839501911510239834859772382225903027
skew: 12484.82
# norm 9.97e+14
c5: 50400
c4: -5841185348
c3: -54516924114116
c2: 799289440818286359
c1: 1836172894286450032140
c0: -11508237231544326150287190
# alpha -5.31
Y1: 359724270407
Y0: -2503603679782615335551
# Murphy_E 8.14e-10
# M 2940404575292636002365519038296432669014495572869498409424791177403342616136593791228801633381886273626809455453
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 3650001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 447391 x 447633
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.61 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 22.00 hours.

(28·10¹⁶⁶+53)/9 = 3(1)₁₆₅7_<167> = 37 · 26380692011_<11> · C155

C155 = P38 · P118

P38 = 31871524461533362268482655663519284247_<38>

P118 = 1000057053409639797383976464291592486851338028888291608314213688558051361960864430945141648685927217381257608105340573_<118>

SNFS difficulty: 168 digits.
Divisors found:
 r1=31871524461533362268482655663519284247
 r2=1000057053409639797383976464291592486851338028888291608314213688558051361960864430945141648685927217381257608105340573
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.533).
Factorization parameters were as follows:
n: 31873342840674310954141135507184131116113838051086325646002434611450452479217977434763390174088062167810918568584961174877682053116208561040117775128853531
m: 2000000000000000000000000000000000
deg: 5
c5: 35
c0: 212
skew: 1.43
type: snfs
lss: 1
rlim: 4600000
alim: 4600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2300000, 4600001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 888006 x 888248
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,52,52,2.6,2.6,100000
total time: 36.00 hours.

Nov 8, 2008 (5th)

By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1

(28·10¹⁴⁷+53)/9 = 3(1)₁₄₆7_<148> = 3 · 107 · C145

C145 = P69 · P77

P69 = 617019353343065071168771290868633532184628741719601748697702907156201_<69>

P77 = 15707667633224193663795893478004311722269116087274668192009165707756038371077_<77>

SNFS difficulty: 148 digits.
Divisors found:
 r1=617019353343065071168771290868633532184628741719601748697702907156201
 r2=15707667633224193663795893478004311722269116087274668192009165707756038371077
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.514).
Factorization parameters were as follows:
n: 9691934925579785392869505019037729318103149878850813430252682589131187262028383523710626514364832121841467635860159224645205953617168570439598477
m: 200000000000000000000000000000
deg: 5
c5: 175
c0: 106
skew: 0.90
type: snfs
lss: 1
rlim: 1890000
alim: 1890000
lpbr: 26
lpba: 26
Factor base limits: 1890000/1890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved rational special-q in [945000, 3945001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 301855 x 302082
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1890000,1890000,26,26,45,45,2.3,2.3,100000
total time: 10.00 hours.
 --------- CPU info (if available) ----------
Intel(R) Xeon(R) CPU            3060  @ 2.40GHz stepping 06
Memory: 2056692k/2095936k available (1918k kernel code, 38852k reserved, 886k data, 196k init)
Calibrating delay using timer specific routine.. 4807.99 BogoMIPS

(28·10¹⁶¹+53)/9 = 3(1)₁₆₀7_<162> = C162

C162 = P71 · P91

P71 = 63139457581438896942328825069550851208784856399796968332441478404066551_<71>

P91 = 4927364330139073419051913860536580547607886284960417140375152137364545183145321257120242267_<91>

SNFS difficulty: 163 digits.
Divisors found:
 r1=63139457581438896942328825069550851208784856399796968332441478404066551
 r2=4927364330139073419051913860536580547607886284960417140375152137364545183145321257120242267
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.944).
Factorization parameters were as follows:
n: 311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117
m: 200000000000000000000000000000000
deg: 5
c5: 35
c0: 212
skew: 1.43
type: snfs
lss: 1
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [1800000, 3400001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 719458 x 719700
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3600000,3600000,27,27,54,54,2.5,2.5,200000
total time: 40.00 hours.

(28·10¹⁹⁵+53)/9 = 3(1)₁₉₄7_<196> = 3 · 59 · 395953 · 42767503850028819725441309_<26> · C163

C163 = P33 · C130

P33 = 352426542677057137608275426464363_<33>

C130 = [2945208906366052236932459156515487535676983279100897646113232542808115418940071695405800723228208432134601112336948955530984723571_<130>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3148797574
Step 1 took 26541ms
Step 2 took 16432ms
********** Factor found in step 2: 352426542677057137608275426464363
Found probable prime factor of 33 digits: 352426542677057137608275426464363
Composite cofactor 2945208906366052236932459156515487535676983279100897646113232542808115418940071695405800723228208432134601112336948955530984723571 has 130 digits

Nov 8, 2008 (4th)

By Sinkiti Sibata / GGNFS

(28·10¹⁴⁰+53)/9 = 3(1)₁₃₉7_<141> = 719 · 59073839760124597826003_<23> · C115

C115 = P46 · P70

P46 = 2325698751206860496055539668188983558068752811_<46>

P70 = 3149473592196775785669922329386782368714203572482622242212803781186771_<70>

Number: 31117_140
N=7324726800331026460555229546626895219469339431616719423307207640327309385610323420792409886859810566259237422263281
  ( 115 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=2325698751206860496055539668188983558068752811 (pp46)
 r2=3149473592196775785669922329386782368714203572482622242212803781186771 (pp70)
Version: GGNFS-0.77.1-20060513-k8
Total time: 8.49 hours.
Scaled time: 17.00 units (timescale=2.003).
Factorization parameters were as follows:
name: 31117_140
n: 7324726800331026460555229546626895219469339431616719423307207640327309385610323420792409886859810566259237422263281
m: 10000000000000000000000000000
deg: 5
c5: 28
c0: 53
skew: 1.14
type: snfs
lss: 1
rlim: 1350000
alim: 1350000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.4
alambda: 2.4
Factor base limits: 1350000/1350000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [675000, 1375001)
Primes: RFBsize:103544, AFBsize:103270, largePrimes:4313541 encountered
Relations: rels:4578665, finalFF:422100
Max relations in full relation-set: 28
Initial matrix: 206882 x 422100 with sparse part having weight 46272349.
Pruned matrix : 164150 x 165248 with weight 16293575.
Total sieving time: 8.06 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1350000,1350000,26,26,48,48,2.4,2.4,100000
total time: 8.49 hours.
 --------- CPU info (if available) ----------

(28·10¹⁵²+53)/9 = 3(1)₁₅₁7_<153> = 872135881 · 136844792064663015857067456487_<30> · C115

C115 = P36 · P38 · P42

P36 = 114533644517486766460031592704008207_<36>

P38 = 56375440480817404918936792134365039519_<38>

P42 = 403719814376655975729160398310593574509667_<42>

Number: 31117_152
N=2606772276203660697254409655413048199786310727961846805755009726182143624168623495955434049796287923822321057129811
  ( 115 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=114533644517486766460031592704008207 (pp36)
 r2=56375440480817404918936792134365039519 (pp38)
 r3=403719814376655975729160398310593574509667 (pp42)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 26.92 hours.
Scaled time: 26.70 units (timescale=0.992).
Factorization parameters were as follows:
name: 31117_152
n: 2606772276203660697254409655413048199786310727961846805755009726182143624168623495955434049796287923822321057129811
m: 2000000000000000000000000000000
deg: 5
c5: 175
c0: 106
skew: 0.90
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176208, largePrimes:8391475 encountered
Relations: rels:8688664, finalFF:539001
Max relations in full relation-set: 28
Initial matrix: 352576 x 539001 with sparse part having weight 65291586.
Pruned matrix : 304897 x 306723 with weight 35556743.
Total sieving time: 25.88 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.83 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.5,2.5,100000
total time: 26.92 hours.
 --------- CPU info (if available) ----------

(28·10¹⁴²+53)/9 = 3(1)₁₄₁7_<143> = 37 · 21761759 · 3427015200061_<13> · 7239626494033_<13> · C109

C109 = P43 · P66

P43 = 4073940241111780673209337589037246877679337_<43>

P66 = 382272411123968825071696930766321451979064764499216758783281040379_<66>

Number: 31117_142
N=1557354958744763303553869743002788354621146330435429684510646550677472783934229634700695460059986438510948723
  ( 109 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=4073940241111780673209337589037246877679337 (pp43)
 r2=382272411123968825071696930766321451979064764499216758783281040379 (pp66)
Version: GGNFS-0.77.1-20060513-k8
Total time: 18.26 hours.
Scaled time: 35.79 units (timescale=1.960).
Factorization parameters were as follows:
name: 31117_142
n: 1557354958744763303553869743002788354621146330435429684510646550677472783934229634700695460059986438510948723
m: 20000000000000000000000000000
deg: 5
c5: 175
c0: 106
skew: 0.90
type: snfs
lss: 1
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [750000, 2250001)
Primes: RFBsize:114155, AFBsize:114057, largePrimes:5047803 encountered
Relations: rels:5660295, finalFF:369277
Max relations in full relation-set: 28
Initial matrix: 228278 x 369277 with sparse part having weight 46453510.
Pruned matrix : 197234 x 198439 with weight 24900215.
Total sieving time: 17.33 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.64 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,49,49,2.4,2.4,100000
total time: 18.26 hours.
 --------- CPU info (if available) ----------

Nov 8, 2008 (3rd)

By Sinkiti Sibata / GGNFS, Msieve

(28·10¹²⁸+53)/9 = 3(1)₁₂₇7_<129> = 823 · 1975073 · C120

C120 = P50 · P70

P50 = 30607483775884291734596015945273931066369402323623_<50>

P70 = 6253237255550603811574584544677820651991885965657489332025148605514701_<70>

Number: 31117_128
N=191395857846020320873773527336765612421294401257995866913221361603843495576689394582324007362426924566750274741286081723
  ( 120 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=30607483775884291734596015945273931066369402323623 (pp50)
 r2=6253237255550603811574584544677820651991885965657489332025148605514701 (pp70)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.79 hours.
Scaled time: 9.57 units (timescale=1.997).
Factorization parameters were as follows:
name: 31117_128
n: 191395857846020320873773527336765612421294401257995866913221361603843495576689394582324007362426924566750274741286081723
m: 20000000000000000000000000
deg: 5
c5: 875
c0: 53
skew: 0.57
type: snfs
lss: 1
rlim: 780000
alim: 780000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 780000/780000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [390000, 940001)
Primes: RFBsize:62468, AFBsize:62810, largePrimes:2579675 encountered
Relations: rels:2521660, finalFF:182401
Max relations in full relation-set: 28
Initial matrix: 125344 x 182401 with sparse part having weight 18617405.
Pruned matrix : 114418 x 115108 with weight 9577816.
Total sieving time: 4.58 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,780000,780000,26,26,47,47,2.3,2.3,50000
total time: 4.79 hours.
 --------- CPU info (if available) ----------

(28·10¹⁰⁸+53)/9 = 3(1)₁₀₇7_<109> = 3² · 4907921 · 37050317 · C94

C94 = P46 · P48

P46 = 1931237577332861098630296640300992774105967417_<46>

P48 = 984346083423077363780925917466614052933358283377_<48>

Fri Nov  7 22:53:20 2008  Msieve v. 1.38
Fri Nov  7 22:53:20 2008  random seeds: 03d23b23 6279e046
Fri Nov  7 22:53:20 2008  factoring 1901006145407074312672458086786796553506794510767066812919746527396777575054770568223014727209 (94 digits)
Fri Nov  7 22:53:21 2008  searching for 15-digit factors
Fri Nov  7 22:53:23 2008  commencing quadratic sieve (94-digit input)
Fri Nov  7 22:53:23 2008  using multiplier of 1
Fri Nov  7 22:53:23 2008  using 64kb Pentium 4 sieve core
Fri Nov  7 22:53:23 2008  sieve interval: 18 blocks of size 65536
Fri Nov  7 22:53:23 2008  processing polynomials in batches of 6
Fri Nov  7 22:53:23 2008  using a sieve bound of 1991603 (74066 primes)
Fri Nov  7 22:53:23 2008  using large prime bound of 256916787 (27 bits)
Fri Nov  7 22:53:23 2008  using double large prime bound of 1372860543013200 (42-51 bits)
Fri Nov  7 22:53:23 2008  using trial factoring cutoff of 51 bits
Fri Nov  7 22:53:23 2008  polynomial 'A' values have 12 factors
Sat Nov  8 03:09:08 2008  74573 relations (19040 full + 55533 combined from 1026486 partial), need 74162
Sat Nov  8 03:09:12 2008  begin with 1045526 relations
Sat Nov  8 03:09:13 2008  reduce to 189639 relations in 11 passes
Sat Nov  8 03:09:13 2008  attempting to read 189639 relations
Sat Nov  8 03:09:19 2008  recovered 189639 relations
Sat Nov  8 03:09:19 2008  recovered 169450 polynomials
Sat Nov  8 03:09:19 2008  attempting to build 74573 cycles
Sat Nov  8 03:09:19 2008  found 74573 cycles in 6 passes
Sat Nov  8 03:09:19 2008  distribution of cycle lengths:
Sat Nov  8 03:09:19 2008     length 1 : 19040
Sat Nov  8 03:09:19 2008     length 2 : 13395
Sat Nov  8 03:09:19 2008     length 3 : 12886
Sat Nov  8 03:09:19 2008     length 4 : 10012
Sat Nov  8 03:09:19 2008     length 5 : 7431
Sat Nov  8 03:09:19 2008     length 6 : 4891
Sat Nov  8 03:09:19 2008     length 7 : 3036
Sat Nov  8 03:09:19 2008     length 9+: 3882
Sat Nov  8 03:09:19 2008  largest cycle: 19 relations
Sat Nov  8 03:09:19 2008  matrix is 74066 x 74573 (18.4 MB) with weight 4517834 (60.58/col)
Sat Nov  8 03:09:19 2008  sparse part has weight 4517834 (60.58/col)
Sat Nov  8 03:09:21 2008  filtering completed in 3 passes
Sat Nov  8 03:09:21 2008  matrix is 69972 x 70036 (17.3 MB) with weight 4245086 (60.61/col)
Sat Nov  8 03:09:21 2008  sparse part has weight 4245086 (60.61/col)
Sat Nov  8 03:09:21 2008  saving the first 48 matrix rows for later
Sat Nov  8 03:09:21 2008  matrix is 69924 x 70036 (10.1 MB) with weight 3230928 (46.13/col)
Sat Nov  8 03:09:21 2008  sparse part has weight 2236863 (31.94/col)
Sat Nov  8 03:09:21 2008  matrix includes 64 packed rows
Sat Nov  8 03:09:21 2008  using block size 21845 for processor cache size 512 kB
Sat Nov  8 03:09:22 2008  commencing Lanczos iteration
Sat Nov  8 03:09:22 2008  memory use: 10.4 MB
Sat Nov  8 03:10:12 2008  lanczos halted after 1107 iterations (dim = 69924)
Sat Nov  8 03:10:13 2008  recovered 17 nontrivial dependencies
Sat Nov  8 03:10:14 2008  prp46 factor: 1931237577332861098630296640300992774105967417
Sat Nov  8 03:10:14 2008  prp48 factor: 984346083423077363780925917466614052933358283377
Sat Nov  8 03:10:14 2008  elapsed time 04:16:54

(28·10¹⁴³+53)/9 = 3(1)₁₄₂7_<144> = 1243709 · 11719818916387_<14> · C125

C125 = P51 · P75

P51 = 139558811476406019376315978192641107859922180202419_<51>

P75 = 152939117966647388107012028728804903280976039746938346857297256825895223321_<75>

Number: 31117_143
N=21344001531675163537885430218438044701516671558893408325921998331850660509258825767152980916233004254820610666222044989413499
  ( 125 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=139558811476406019376315978192641107859922180202419 (pp51)
 r2=152939117966647388107012028728804903280976039746938346857297256825895223321 (pp75)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 19.54 hours.
Scaled time: 19.75 units (timescale=1.011).
Factorization parameters were as follows:
name: 31117_143
n: 21344001531675163537885430218438044701516671558893408325921998331850660509258825767152980916233004254820610666222044989413499
m: 20000000000000000000000000000
deg: 5
c5: 875
c0: 53
skew: 0.57
type: snfs
lss: 1
rlim: 1550000
alim: 1550000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 1550000/1550000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [775000, 2475001)
Primes: RFBsize:117663, AFBsize:118152, largePrimes:5232574 encountered
Relations: rels:6112263, finalFF:427100
Max relations in full relation-set: 28
Initial matrix: 235881 x 427100 with sparse part having weight 56912828.
Pruned matrix : 198063 x 199306 with weight 29198534.
Total sieving time: 19.06 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.32 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1550000,1550000,26,26,49,49,2.4,2.4,100000
total time: 19.54 hours.
 --------- CPU info (if available) ----------

(28·10¹³⁸+53)/9 = 3(1)₁₃₇7_<139> = 3 · 40163749 · 1067050114723_<13> · C119

C119 = P39 · P81

P39 = 173513712361751799126894410308232788697_<39>

P81 = 139457348692700593839066377349755448264601276654137754769730514781494124225439881_<81>

Number: 31117_138
N=24197762287797774132671833763509209261000805563687269801999221277019703970067711180492955984427133208292289632149825057
  ( 119 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=173513712361751799126894410308232788697 (pp39)
 r2=139457348692700593839066377349755448264601276654137754769730514781494124225439881 (pp81)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.27 hours.
Scaled time: 10.36 units (timescale=1.009).
Factorization parameters were as follows:
name: 31117_138
n: 24197762287797774132671833763509209261000805563687269801999221277019703970067711180492955984427133208292289632149825057
m: 2000000000000000000000000000
deg: 5
c5: 875
c0: 53
skew: 0.57
type: snfs
lss: 1
rlim: 1230000
alim: 1230000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.4
alambda: 2.4
Factor base limits: 1230000/1230000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [615000, 1590001)
Primes: RFBsize:95051, AFBsize:95403, largePrimes:4440909 encountered
Relations: rels:4779332, finalFF:277914
Max relations in full relation-set: 28
Initial matrix: 190520 x 277914 with sparse part having weight 34069845.
Pruned matrix : 171927 x 172943 with weight 19626049.
Total sieving time: 9.97 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1230000,1230000,26,26,48,48,2.4,2.4,75000
total time: 10.27 hours.
 --------- CPU info (if available) ----------

Nov 8, 2008 (2nd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38

(28·10²⁰²+53)/9 = 3(1)₂₀₁7_<203> = 37 · C201

C201 = P38 · C163

P38 = 91866284775493228069434109183838987923_<38>

C163 = [9152877390173378596782581355965337582944051950902417469327670863123664533552791783821206064629832232208439415653989500470516623203715818866856565652662067477550067_<163>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4095180192
Step 1 took 25202ms
Step 2 took 15917ms
********** Factor found in step 2: 91866284775493228069434109183838987923
Found probable prime factor of 38 digits: 91866284775493228069434109183838987923
Composite cofactor 9152877390173378596782581355965337582944051950902417469327670863123664533552791783821206064629832232208439415653989500470516623203715818866856565652662067477550067 has 163 digits

(28·10¹⁷⁰+53)/9 = 3(1)₁₆₉7_<171> = 149417 · 235813 · 4601871629_<10> · 111482586841_<12> · 194134469367409_<15> · C125

C125 = P32 · P94

P32 = 12769617743782569896315990123137_<32>

P94 = 6942656510920124686297865042790016163877551842396123531581415155016514192117788659172759034621_<94>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=340735920
Step 1 took 14909ms
Step 2 took 10265ms
********** Factor found in step 2: 12769617743782569896315990123137
Found probable prime factor of 32 digits: 12769617743782569896315990123137
Probable prime cofactor 6942656510920124686297865042790016163877551842396123531581415155016514192117788659172759034621 has 94 digits

9·10¹⁷¹+1 = 9(0)₁₇₀1_<172> = 47 · 53 · 3036861280810645404931_<22> · C148

C148 = P71 · P77

P71 = 51385746424530178231491293825778690117107805206225197788441809802689717_<71>

P77 = 23152674067043755161598533865974421832973091656998852143841113795270050798893_<77>

SNFS difficulty: 173 digits.
Divisors found:
 r1=51385746424530178231491293825778690117107805206225197788441809802689717
 r2=23152674067043755161598533865974421832973091656998852143841113795270050798893
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 1189717438658906221837803003057716463192750863131280020458027692162119895901034234571473853525200925763890756580925220048957727612205131776046083281
m: 30000000000000000000000000000000000
deg: 5
c5: 10
c0: 27
skew: 1.22
type: snfs
lss: 1
rlim: 5900000
alim: 5900000
lpbr: 27
lpba: 27
Factor base limits: 5900000/5900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [2950000, 5950001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 925788 x 926024
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,5900000,5900000,27,27,54,54,2.6,2.6,200000
total time: 57.00 hours.

(28·10¹⁶⁵+53)/9 = 3(1)₁₆₄7_<166> = 3 · 17 · 20599 · 42307735637_<11> · C149

C149 = P36 · P114

P36 = 208720416688403262065547116196411199_<36>

P114 = 335362495860118079509073756035043621112786235039869783125073326414207323154348853911331252003615499742569012909291_<114>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3789916067
Step 1 took 15833ms
Step 2 took 11917ms
********** Factor found in step 2: 208720416688403262065547116196411199
Found probable prime factor of 36 digits: 208720416688403262065547116196411199
Probable prime cofactor 335362495860118079509073756035043621112786235039869783125073326414207323154348853911331252003615499742569012909291 has 114 digits

Nov 8, 2008

By Jo Yeong Uk / GMP-ECM, GGNFS

(28·10¹⁵²+53)/9 = 3(1)₁₅₁7_<153> = 872135881 · C144

C144 = P30 · C115

P30 = 136844792064663015857067456487_<30>

C115 = [2606772276203660697254409655413048199786310727961846805755009726182143624168623495955434049796287923822321057129811_<115>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 356723210097018254786275799505961515544056730663408069448654080901312110000335040808980442705935534271535275947568898511023548991113130353033957 (144 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2746676296
Step 1 took 4682ms
Step 2 took 2686ms
********** Factor found in step 2: 136844792064663015857067456487
Found probable prime factor of 30 digits: 136844792064663015857067456487
Composite cofactor 2606772276203660697254409655413048199786310727961846805755009726182143624168623495955434049796287923822321057129811 has 115 digits

(28·10¹³⁵+53)/9 = 3(1)₁₃₄7_<136> = 3² · 83 · 431 · 8087 · 15161227190718442273135561_<26> · C101

C101 = P49 · P53

P49 = 2922137826713607622269773183748540216869810114279_<49>

P53 = 26970882371737256355684501901258381151689194528523777_<53>

Number: 31117_135
N=78812635598296657370217757450351375173358243975867836682922680479192841333176715123460559997538711783
  ( 101 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=2922137826713607622269773183748540216869810114279 (pp49)
 r2=26970882371737256355684501901258381151689194528523777 (pp53)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.68 hours.
Scaled time: 6.40 units (timescale=2.389).
Factorization parameters were as follows:
n: 78812635598296657370217757450351375173358243975867836682922680479192841333176715123460559997538711783
m: 1000000000000000000000000000
deg: 5
c5: 28
c0: 53
skew: 1.14
type: snfs
rlim: 1400000
alim: 1400000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.4
alambda: 2.4
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [700000, 1200001)
Primes: RFBsize:107126, AFBsize:106993, largePrimes:4037153 encountered
Relations: rels:4104975, finalFF:363639
Max relations in full relation-set: 28
Initial matrix: 214187 x 363639 with sparse part having weight 32434851.
Pruned matrix : 166326 x 167460 with weight 12502137.
Total sieving time: 2.52 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,26,26,48,48,2.4,2.4,50000
total time: 2.68 hours.
 --------- CPU info (if available) ----------

Nov 7, 2008 (8th)

By Sinkiti Sibata / GGNFS

(28·10¹²⁰+53)/9 = 3(1)₁₁₉7_<121> = 3 · 281 · C118

C118 = P52 · P66

P52 = 4105934781114179790682630177253734108415115748517159_<52>

P66 = 898826566961578901544842173483989959828342532935837448597526095841_<66>

Number: 31117_120
N=3690523263477000131804402267035718993014366679847106893370238565968103334651377356003690523263477000131804402267035719
  ( 118 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=4105934781114179790682630177253734108415115748517159 (pp52)
 r2=898826566961578901544842173483989959828342532935837448597526095841 (pp66)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.54 hours.
Scaled time: 5.04 units (timescale=1.985).
Factorization parameters were as follows:
name: 31117_120
n: 3690523263477000131804402267035718993014366679847106893370238565968103334651377356003690523263477000131804402267035719
m: 1000000000000000000000000
deg: 5
c5: 28
c0: 53
skew: 1.14
type: snfs
lss: 1
rlim: 540000
alim: 540000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 540000/540000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [270000, 520001)
Primes: RFBsize:44572, AFBsize:44410, largePrimes:1875081 encountered
Relations: rels:2235457, finalFF:487174
Max relations in full relation-set: 28
Initial matrix: 89050 x 487174 with sparse part having weight 37948118.
Pruned matrix : 60589 x 61098 with weight 5269980.
Total sieving time: 2.44 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,540000,540000,25,25,46,46,2.3,2.3,50000
total time: 2.54 hours.
 --------- CPU info (if available) ----------

(28·10¹³⁶+53)/9 = 3(1)₁₃₅7_<137> = 37 · 347 · 102337 · 17903296250182927_<17> · C112

C112 = P49 · P63

P49 = 8262742876604125785993929334225872346805456960693_<49>

P63 = 160064272475974357804672783623195800906136858641291346710222129_<63>

Number: 31117_136
N=1322569927199678960528329520717663211682527542022221236361147165058047340734026215153086442092281054219251775397
  ( 112 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=8262742876604125785993929334225872346805456960693 (pp49)
 r2=160064272475974357804672783623195800906136858641291346710222129 (pp63)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.17 hours.
Scaled time: 11.29 units (timescale=1.011).
Factorization parameters were as follows:
name: 31117_136
n: 1322569927199678960528329520717663211682527542022221236361147165058047340734026215153086442092281054219251775397
m: 2000000000000000000000000000
deg: 5
c5: 35
c0: 212
skew: 1.43
type: snfs
lss: 1
rlim: 1150000
alim: 1150000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.4
alambda: 2.4
Factor base limits: 1150000/1150000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [575000, 1250001)
Primes: RFBsize:89302, AFBsize:88935, largePrimes:4501050 encountered
Relations: rels:5029597, finalFF:512488
Max relations in full relation-set: 28
Initial matrix: 178304 x 512488 with sparse part having weight 62033230.
Pruned matrix : 136367 x 137322 with weight 19496822.
Total sieving time: 10.84 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1150000,1150000,26,26,48,48,2.4,2.4,75000
total time: 11.17 hours.
 --------- CPU info (if available) ----------

Nov 7, 2008 (7th)

By Sinkiti Sibata / Msieve

(28·10¹¹²+53)/9 = 3(1)₁₁₁7_<113> = 37 · 16633 · 44383 · 2469734135509_<13> · C90

C90 = P33 · P58

P33 = 395435569143484867490894919534871_<33>

P58 = 1166274071028520668668288925686227131278424555746468179621_<58>

Fri Nov  7 20:01:38 2008  Msieve v. 1.38
Fri Nov  7 20:01:38 2008  random seeds: d2743c6c 67763d3d
Fri Nov  7 20:01:38 2008  factoring 461186251054452166382699161188904523720824103903067004694882992496446997534797427401063891 (90 digits)
Fri Nov  7 20:01:39 2008  searching for 15-digit factors
Fri Nov  7 20:01:41 2008  commencing quadratic sieve (90-digit input)
Fri Nov  7 20:01:41 2008  using multiplier of 1
Fri Nov  7 20:01:41 2008  using 64kb Pentium 4 sieve core
Fri Nov  7 20:01:41 2008  sieve interval: 18 blocks of size 65536
Fri Nov  7 20:01:41 2008  processing polynomials in batches of 6
Fri Nov  7 20:01:41 2008  using a sieve bound of 1584943 (59901 primes)
Fri Nov  7 20:01:41 2008  using large prime bound of 126795440 (26 bits)
Fri Nov  7 20:01:41 2008  using double large prime bound of 385111478867040 (42-49 bits)
Fri Nov  7 20:01:41 2008  using trial factoring cutoff of 49 bits
Fri Nov  7 20:01:41 2008  polynomial 'A' values have 11 factors
Fri Nov  7 22:45:19 2008  60002 relations (15224 full + 44778 combined from 645399 partial), need 59997
Fri Nov  7 22:45:22 2008  begin with 660623 relations
Fri Nov  7 22:45:22 2008  reduce to 149497 relations in 9 passes
Fri Nov  7 22:45:22 2008  attempting to read 149497 relations
Fri Nov  7 22:45:26 2008  recovered 149497 relations
Fri Nov  7 22:45:26 2008  recovered 132340 polynomials
Fri Nov  7 22:45:26 2008  attempting to build 60002 cycles
Fri Nov  7 22:45:27 2008  found 60002 cycles in 5 passes
Fri Nov  7 22:45:27 2008  distribution of cycle lengths:
Fri Nov  7 22:45:27 2008     length 1 : 15224
Fri Nov  7 22:45:27 2008     length 2 : 11087
Fri Nov  7 22:45:27 2008     length 3 : 10502
Fri Nov  7 22:45:27 2008     length 4 : 8273
Fri Nov  7 22:45:27 2008     length 5 : 5908
Fri Nov  7 22:45:27 2008     length 6 : 3771
Fri Nov  7 22:45:27 2008     length 7 : 2323
Fri Nov  7 22:45:27 2008     length 9+: 2914
Fri Nov  7 22:45:27 2008  largest cycle: 19 relations
Fri Nov  7 22:45:27 2008  matrix is 59901 x 60002 (15.2 MB) with weight 3754339 (62.57/col)
Fri Nov  7 22:45:27 2008  sparse part has weight 3754339 (62.57/col)
Fri Nov  7 22:45:28 2008  filtering completed in 3 passes
Fri Nov  7 22:45:28 2008  matrix is 56596 x 56660 (14.5 MB) with weight 3580652 (63.20/col)
Fri Nov  7 22:45:28 2008  sparse part has weight 3580652 (63.20/col)
Fri Nov  7 22:45:28 2008  saving the first 48 matrix rows for later
Fri Nov  7 22:45:28 2008  matrix is 56548 x 56660 (11.1 MB) with weight 3044810 (53.74/col)
Fri Nov  7 22:45:28 2008  sparse part has weight 2569359 (45.35/col)
Fri Nov  7 22:45:28 2008  matrix includes 64 packed rows
Fri Nov  7 22:45:28 2008  using block size 21845 for processor cache size 512 kB
Fri Nov  7 22:45:29 2008  commencing Lanczos iteration
Fri Nov  7 22:45:29 2008  memory use: 9.8 MB
Fri Nov  7 22:46:08 2008  lanczos halted after 896 iterations (dim = 56548)
Fri Nov  7 22:46:08 2008  recovered 18 nontrivial dependencies
Fri Nov  7 22:46:09 2008  prp33 factor: 395435569143484867490894919534871
Fri Nov  7 22:46:09 2008  prp58 factor: 1166274071028520668668288925686227131278424555746468179621
Fri Nov  7 22:46:09 2008  elapsed time 02:44:31

Nov 7, 2008 (6th)

By Jo Yeong Uk / GGNFS

(28·10¹¹⁵+53)/9 = 3(1)₁₁₄7_<116> = 37 · 205256992907_<12> · C103

C103 = P31 · P72

P31 = 4787445483439776346028961749113_<31>

P72 = 855681207848006406767942996887982170459469817221116001387245364253552851_<72>

Number: 31117_115
N=4096527133776230777589294135068251708248440771554837269760844186821928888996635683528346142189547871163
  ( 103 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=4787445483439776346028961749113 (pp31)
 r2=855681207848006406767942996887982170459469817221116001387245364253552851 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.62 hours.
Scaled time: 1.48 units (timescale=2.391).
Factorization parameters were as follows:
n: 4096527133776230777589294135068251708248440771554837269760844186821928888996635683528346142189547871163
m: 100000000000000000000000
deg: 5
c5: 28
c0: 53
skew: 1.14
type: snfs
rlim: 400000
alim: 400000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 400000/400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [200000, 350001)
Primes: RFBsize:33860, AFBsize:33683, largePrimes:1016983 encountered
Relations: rels:927514, finalFF:78875
Max relations in full relation-set: 28
Initial matrix: 67611 x 78875 with sparse part having weight 3665373.
Pruned matrix : 63462 x 63864 with weight 2334000.
Total sieving time: 0.59 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,400000,400000,25,25,45,45,2.2,2.2,25000
total time: 0.62 hours.
 --------- CPU info (if available) ----------

Nov 7, 2008 (5th)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.36, Msieve-1.38

6·10¹⁷³-1 = 5(9)₁₇₃_<174> = 446221 · 13201045994383692917_<20> · C150

C150 = P38 · C112

P38 = 20546681584297179439544553169075952341_<38>

C112 = [4957368585987012421336435230959147904107104720246843895074059519403671637558839501911510239834859772382225903027_<112>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1624081815
Step 1 took 14453ms
Step 2 took 10996ms
********** Factor found in step 2: 20546681584297179439544553169075952341
Found probable prime factor of 38 digits: 20546681584297179439544553169075952341
Composite cofactor 4957368585987012421336435230959147904107104720246843895074059519403671637558839501911510239834859772382225903027 has 112 digits

(28·10¹³³+53)/9 = 3(1)₁₃₂7_<134> = 17 · 37 · 749600825894593_<15> · 13929457418707948000477141189_<29> · C88

C88 = P35 · P53

P35 = 55835930141245976683222796488170859_<35>

P53 = 84837305159319719171718948795925775107018829665616111_<53>

Thu Nov  6 23:40:27 2008  Msieve v. 1.36
Thu Nov  6 23:40:27 2008  random seeds: 54cf9356 c494cfbf
Thu Nov  6 23:40:27 2008  factoring 4736969844247342713692487312568994509752670296668692844534636602543519427104855671109349 (88 digits)
Thu Nov  6 23:40:28 2008  no P-1/P+1/ECM available, skipping
Thu Nov  6 23:40:28 2008  commencing quadratic sieve (88-digit input)
Thu Nov  6 23:40:28 2008  using multiplier of 5
Thu Nov  6 23:40:28 2008  using 64kb Opteron sieve core
Thu Nov  6 23:40:28 2008  sieve interval: 14 blocks of size 65536
Thu Nov  6 23:40:28 2008  processing polynomials in batches of 8
Thu Nov  6 23:40:28 2008  using a sieve bound of 1525877 (58000 primes)
Thu Nov  6 23:40:28 2008  using large prime bound of 122070160 (26 bits)
Thu Nov  6 23:40:28 2008  using double large prime bound of 359664101459520 (42-49 bits)
Thu Nov  6 23:40:28 2008  using trial factoring cutoff of 49 bits
Thu Nov  6 23:40:28 2008  polynomial 'A' values have 11 factors
Fri Nov  7 00:30:10 2008  58354 relations (15926 full + 42428 combined from 613752 partial), need 58096
Fri Nov  7 00:30:10 2008  begin with 629678 relations
Fri Nov  7 00:30:11 2008  reduce to 141165 relations in 10 passes
Fri Nov  7 00:30:11 2008  attempting to read 141165 relations
Fri Nov  7 00:30:12 2008  recovered 141165 relations
Fri Nov  7 00:30:12 2008  recovered 118180 polynomials
Fri Nov  7 00:30:12 2008  attempting to build 58354 cycles
Fri Nov  7 00:30:12 2008  found 58354 cycles in 5 passes
Fri Nov  7 00:30:12 2008  distribution of cycle lengths:
Fri Nov  7 00:30:12 2008     length 1 : 15926
Fri Nov  7 00:30:12 2008     length 2 : 11392
Fri Nov  7 00:30:12 2008     length 3 : 10319
Fri Nov  7 00:30:12 2008     length 4 : 7680
Fri Nov  7 00:30:12 2008     length 5 : 5293
Fri Nov  7 00:30:12 2008     length 6 : 3351
Fri Nov  7 00:30:12 2008     length 7 : 1984
Fri Nov  7 00:30:12 2008     length 9+: 2409
Fri Nov  7 00:30:12 2008  largest cycle: 18 relations
Fri Nov  7 00:30:12 2008  matrix is 58000 x 58354 (14.9 MB) with weight 3436843 (58.90/col)
Fri Nov  7 00:30:12 2008  sparse part has weight 3436843 (58.90/col)
Fri Nov  7 00:30:13 2008  filtering completed in 3 passes
Fri Nov  7 00:30:13 2008  matrix is 53777 x 53841 (13.8 MB) with weight 3192836 (59.30/col)
Fri Nov  7 00:30:13 2008  sparse part has weight 3192836 (59.30/col)
Fri Nov  7 00:30:13 2008  saving the first 48 matrix rows for later
Fri Nov  7 00:30:13 2008  matrix is 53729 x 53841 (10.0 MB) with weight 2609810 (48.47/col)
Fri Nov  7 00:30:13 2008  sparse part has weight 2070838 (38.46/col)
Fri Nov  7 00:30:13 2008  matrix includes 64 packed rows
Fri Nov  7 00:30:13 2008  using block size 21536 for processor cache size 1024 kB
Fri Nov  7 00:30:13 2008  commencing Lanczos iteration
Fri Nov  7 00:30:13 2008  memory use: 8.5 MB
Fri Nov  7 00:30:31 2008  lanczos halted after 851 iterations (dim = 53729)
Fri Nov  7 00:30:31 2008  recovered 18 nontrivial dependencies
Fri Nov  7 00:30:31 2008  prp35 factor: 55835930141245976683222796488170859
Fri Nov  7 00:30:31 2008  prp53 factor: 84837305159319719171718948795925775107018829665616111
Fri Nov  7 00:30:31 2008  elapsed time 00:50:04

(28·10¹⁰⁷+53)/9 = 3(1)₁₀₆7_<108> = C108

C108 = P40 · P69

P40 = 1345714267619735241622083592355939803453_<40>

P69 = 231186603721900367868902363880488891351271265076613106810523648244689_<69>

SNFS difficulty: 109 digits.
Divisors found:
 r1=1345714267619735241622083592355939803453
 r2=231186603721900367868902363880488891351271265076613106810523648244689
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.729).
Factorization parameters were as follows:
n: 311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117
m: 1000000000000000000000000000
c4: 14
c0: 265
skew: 4
type: snfs
lss: 1
rlim: 300000
alim: 300000
lpbr: 25
lpba: 25
Factor base limits: 300000/300000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [150000, 250001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 38073 x 38309
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,109,4,0,0,0,0,0,0,0,0,300000,300000,25,25,44,44,2.2,2.2,20000
total time: 0.40 hours.

(28·10¹⁷⁹+53)/9 = 3(1)₁₇₈7_<180> = 31 · 43 · 229 · 7104109 · 74812941392011_<14> · 16507413285958541278577807_<26> · 910115883072350972734038341_<27> · C102

C102 = P33 · P69

P33 = 251657724546775776918487145183357_<33>

P69 = 507198032429569287477765065713930617795719443082782575395300656664341_<69>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1657388960
Step 1 took 10353ms
********** Factor found in step 1: 251657724546775776918487145183357
Found probable prime factor of 33 digits: 251657724546775776918487145183357
Probable prime cofactor 507198032429569287477765065713930617795719443082782575395300656664341 has 69 digits

Nov 7, 2008 (4th)

Factorizations of 311...117 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Nov 7, 2008 (3rd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38

4·10²²²+1 = 4(0)₂₂₁1_<223> = C223

C223 = P46 · C177

P46 = 6097015972179447612468707229921763686040066157_<46>

C177 = [656058638890223304734304814532016364046521353594428916682596906758480771159191063541717990626390717402033424938857168466764328812593445093132882486910603381621639064614968488293_<177>]

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=2238052366
Step 1 took 107815ms
Step 2 took 45211ms
********** Factor found in step 2: 6097015972179447612468707229921763686040066157
Found probable prime factor of 46 digits: 6097015972179447612468707229921763686040066157
Composite cofactor 656058638890223304734304814532016364046521353594428916682596906758480771159191063541717990626390717402033424938857168466764328812593445093132882486910603381621639064614968488293 has 177 digits

(19·10¹⁷⁰+53)/9 = 2(1)₁₆₉7_<171> = 7 · 67 · 1813327 · 272195657 · 8028230032164739_<16> · C138

C138 = P54 · P84

P54 = 134974717201857773930368940820113637270129245125087339_<54>

P84 = 841605752110865393463396741998699499596686714405178738438815370274632079228373494047_<84>

SNFS difficulty: 171 digits.
Divisors found:
 r1=134974717201857773930368940820113637270129245125087339
 r2=841605752110865393463396741998699499596686714405178738438815370274632079228373494047
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.728).
Factorization parameters were as follows:
n: 113595498386620872755908814716787455791745380513425714228053550210917871632865906879922244374810697121827475171977159458642518183471570933
m: 10000000000000000000000000000000000
deg: 5
c5: 19
c0: 53
skew: 1.23
type: snfs
lss: 1
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [3000000, 6000001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1001530 x 1001766
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000
total time: 49.00 hours.

(25·10²²³-1)/3 = 8(3)₂₂₃_<224> = 157 · C222

C222 = P55 · P55 · P114

P55 = 1306957603596747155756205207527556392595787608690473329_<55>

P55 = 3610883731712362153383889046706233893569388374490811951_<55>

P114 = 112471916936323581687912526226250477697448549238152945555808403830365255115368282256825791178690625431891025219111_<114>

SNFS difficulty: 224.398 digits.
Divisors found:
 r1=1306957603596747155756205207527556392595787608690473329 (p55)
 r2=3610883731712362153383889046706233893569388374490811951 (p55)
 r3=112471916936323581687912526226250477697448549238152945555808403830365255115368282256825791178690625431891025219111 (p114)
Version: Msieve v. 1.38
Total time: 4000.00 hours. (~ 1/2 year)
Scaled time: 10936.00 units (timescale=2.734).
Factorization parameters were as follows:
m: 10000000000000000000000000000000000000
c0: -1
c6: 250
skew: 0.40
type: snfs
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
rlim: 20000000
alim: 20000000
Factor base limits: 20000000/20000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved R and A special-q in [5000000, 39000001)
# found 25418178 duplicates and 44624814 unique relations in 70042435 relations
Relations: 44624814 unique relations
Max relations in full relation-set: 18
Initial matrix: 5093347 x 5093664 (1562.6 MB) with weight 492190544 (96.63/col)
sparse part has weight 353583836 (69.42/col)
Pruned matrix : 5072806 x 5073054 (1502.9 MB) with weight 379638576 (74.83/col)
Total sieving time: 3600.00 hours.
Total relation processing time: 2.00 hours.
Matrix solve time: 79.90 hours * 4 threads
Time per square root: 1.50 hours * 7
Prototype def-par.txt line would be:
snfs,224,6,0,0,0,0,0,0,0,0,20000000,20000000,29,29,58,58,2.6,2.6,200000
total time: 4000.00 hours.
 --------- CPU info (if available) ----------
Memory: 4050412k/4718592k available (1919k kernel code, 143268k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5208.19 BogoMIPS

Msieve v. 1.38
random seeds: 275aa104 d1ec624c
factoring 530785562...492569 (222 digits)
commencing number field sieve (222-digit input)
R0: -10000000000000000000000000000000000000
R1:  1
A0: -1
A6:  250
size score = 5.526797e-11, Murphy alpha = 0.888228, combined = 4.288037e-11

commencing relation filtering
commencing duplicate removal, pass 1
found 20690166 hash collisions in 70042435 relations
added 557 free relations
commencing duplicate removal, pass 2
found 25418178 duplicates and 44624814 unique relations
memory use: 504.8 MB
reading rational ideals above 20000000
reading algebraic ideals above 20000000
commencing singleton removal, pass 1
relations with 0 large ideals: 300151
relations with 1 large ideals: 1709036
relations with 2 large ideals: 6485441
relations with 3 large ideals: 13135534
relations with 4 large ideals: 14398569
relations with 5 large ideals: 7482640
relations with 6 large ideals: 0
relations with 7+ large ideals: 1113443
44624814 relations and about 37264844 large ideals
commencing singleton removal, pass 2
found 10269225 singletons
current dataset: 34355589 relations and about 25836557 large ideals
commencing singleton removal, pass 3
found 2285083 singletons
current dataset: 32070506 relations and about 23483970 large ideals
commencing singleton removal, pass 4
found 506556 singletons
current dataset: 31563950 relations and about 22973862 large ideals
commencing singleton removal, pass 5
found 105787 singletons
current dataset: 31458163 relations and about 22867923 large ideals
commencing singleton removal, final pass
memory use: 646.6 MB
commencing in-memory singleton removal
begin with 31458163 relations and 28073717 unique ideals
reduce to 23820147 relations and 20055302 ideals in 17 passes
max relations containing the same ideal: 34
reading rational ideals above 720000
reading algebraic ideals above 720000
commencing singleton removal, final pass
keeping 20738892 ideals with weight <= 20, new excess is 1857987
memory use: 691.1 MB
commencing in-memory singleton removal
begin with 23820560 relations and 20738892 unique ideals
reduce to 23820146 relations and 20736293 ideals in 2 passes
max relations containing the same ideal: 20
removing 3105558 relations and 2705558 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 20714588 relations and 20736293 unique ideals
reduce to 20388570 relations and 17697237 ideals in 9 passes
max relations containing the same ideal: 20
removing 2311009 relations and 1911009 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 18077561 relations and 17697237 unique ideals
reduce to 17874198 relations and 15578752 ideals in 9 passes
max relations containing the same ideal: 20
removing 1258394 relations and 1043894 ideals in 214500 cliques
commencing in-memory singleton removal
begin with 16615804 relations and 15578752 unique ideals
reduce to 16547775 relations and 14466038 ideals in 8 passes
max relations containing the same ideal: 20
relations with 0 large ideals: 143138
relations with 1 large ideals: 715795
relations with 2 large ideals: 2446351
relations with 3 large ideals: 4567315
relations with 4 large ideals: 4875853
relations with 5 large ideals: 2857270
relations with 6 large ideals: 666675
relations with 7+ large ideals: 275378
commencing 2-way merge
reduce to 10525201 relation sets and 8443464 unique ideals
commencing full merge
memory use: 831.4 MB
found 5312709 cycles, need 5093664
weight of 5093664 cycles is about 366772863 (72.01/cycle)
distribution of cycle lengths:
1 relations: 649763
2 relations: 609230
3 relations: 607283
4 relations: 549747
5 relations: 496237
6 relations: 424834
7 relations: 367364
8 relations: 314101
9 relations: 265067
10+ relations: 810038
heaviest cycle: 18 relations
commencing cycle optimization
start with 27980174 relations
pruned 708656 relations
memory use: 928.6 MB
distribution of cycle lengths:
1 relations: 649763
2 relations: 623356
3 relations: 630091
4 relations: 564773
5 relations: 509179
6 relations: 431489
7 relations: 371358
8 relations: 314199
9 relations: 262906
10+ relations: 736550
heaviest cycle: 18 relations
elapsed time 01:10:33

Msieve v. 1.38
random seeds: 64904535 aade4bbb
factoring 530785562...492569 (222 digits)
commencing number field sieve (222-digit input)
R0: -10000000000000000000000000000000000000
R1:  1
A0: -1
A6:  250
size score = 5.526797e-11, Murphy alpha = 0.888228, combined = 4.288037e-11

commencing linear algebra
read 5093664 cycles
cycles contain 15477814 unique relations
read 15477814 relations
using 32 quadratic characters above 536870600
building initial matrix
memory use: 1946.3 MB
read 5093664 cycles
matrix is 5093347 x 5093664 (1562.6 MB) with weight 492190544 (96.63/col)
sparse part has weight 353583836 (69.42/col)
filtering completed in 3 passes
matrix is 5072854 x 5073054 (1560.0 MB) with weight 491181101 (96.82/col)
sparse part has weight 353137144 (69.61/col)
read 5073054 cycles
matrix is 5072854 x 5073054 (1560.0 MB) with weight 491181101 (96.82/col)
sparse part has weight 353137144 (69.61/col)
saving the first 48 matrix rows for later
matrix is 5072806 x 5073054 (1502.9 MB) with weight 379638576 (74.83/col)
sparse part has weight 343236700 (67.66/col)
matrix includes 64 packed rows
using block size 43690 for processor cache size 1024 kB
commencing Lanczos iteration (4 threads)
memory use: 1649.6 MB
lanczos halted after 80220 iterations (dim = 5072803)
recovered 47 nontrivial dependencies
elapsed time 79:55:38

Msieve v. 1.38
random seeds: 8e04b69d de095e6b
...
commencing square root phase
reading relations for dependency 1, 6, 7, 8, 9, 10, 11, 12
read 2537586 cycles
cycles contain 9477386 unique relations
read 9477386 relations
multiplying 7731564 relations
multiply complete, coefficients have about 241.77 million bits
initial square root is modulo 474860731
commencing number field sieve (168-digit input)
prp55 factor: 1306957603596747155756205207527556392595787608690473329
prp55 factor: 3610883731712362153383889046706233893569388374490811951
prp114 factor: 112471916936323581687912526226250477697448549238152945555808403830365255115368282256825791178690625431891025219111
Thu Nov  6 21:53:18 2008  elapsed time 01:24:31

C205 is the largest snfs-factored composite number in our tables so far.

Nov 7, 2008 (2nd)

By Jo Yeong Uk / GGNFS

7·10¹⁷¹+3 = 7(0)₁₇₀3_<172> = 193663 · 1870021 · 5209480256572103393851_<22> · 2894880042580604713105118836471073339_<37> · C103

C103 = P41 · P62

P41 = 80382204556821276120047494428888590479349_<41>

P62 = 15944834639689281626909755621895853382079436807483057371958301_<62>

Number: 70003_171
N=1281680959632193503942635352586274267558015554322256712727649413867069609775801786926191322876429626049
  ( 103 digits)
Divisors found:
 r1=80382204556821276120047494428888590479349 (pp41)
 r2=15944834639689281626909755621895853382079436807483057371958301 (pp62)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.35 hours.
Scaled time: 10.35 units (timescale=2.380).
Factorization parameters were as follows:
name: 70003_171
n: 1281680959632193503942635352586274267558015554322256712727649413867069609775801786926191322876429626049
skew: 12451.75
# norm 3.14e+14
c5: 28800
c4: -1396556640
c3: -21383349502937
c2: 102977721717798824
c1: 1369617770306240302888
c0: -3004456949011618764265560
# alpha -6.63
Y1: 66033646709
Y0: -33859902537347602823
# Murphy_E 2.62e-09
# M 353806601918654332315014283607060409901318680890166882125174584860899677165461883132592572648288552241
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [750000, 1400001)
Primes: RFBsize:114155, AFBsize:114273, largePrimes:4440046 encountered
Relations: rels:4417859, finalFF:331596
Max relations in full relation-set: 28
Initial matrix: 228507 x 331596 with sparse part having weight 29476847.
Pruned matrix : 180731 x 181937 with weight 13703494.
Polynomial selection time: 0.35 hours.
Total sieving time: 3.76 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,49,49,2.6,2.6,50000
total time: 4.35 hours.
 --------- CPU info (if available) ----------

Nov 7, 2008

By Erik Branger / GGNFS, Msieve

(89·10¹⁶⁶+1)/9 = 9(8)₁₆₅9_<167> = 3 · 7 · 2145267415169671460471822733293_<31> · C136

C136 = P51 · P85

P51 = 787295564822051341879920685703659778682875348470397_<51>

P85 = 2788103947756805820487521573803396169483071780461221984528675501647444463826993994429_<85>

Number: 98889_166
N=2195061872331785564833392556541334193678898931031362398283536977263473924321435784902869096812578999064592069887228245952439930289418313
  ( 136 digits)
SNFS difficulty: 169 digits.
Divisors found:
 r1=787295564822051341879920685703659778682875348470397
 r2=2788103947756805820487521573803396169483071780461221984528675501647444463826993994429
Version: 
Total time: 57.30 hours.
Scaled time: 127.08 units (timescale=2.218).
Factorization parameters were as follows:
n: 2195061872331785564833392556541334193678898931031362398283536977263473924321435784902869096812578999064592069887228245952439930289418313
m: 2000000000000000000000000000000000
deg: 5
c5: 445
c0: 16
skew: 0.51
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2400000, 4300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 821410 x 821658
Total sieving time: 57.30 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,52,52,2.6,2.6,100000
total time: 57.30 hours.
 --------- CPU info (if available) ----------

Nov 6, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(10¹⁷⁴-7)/3 = (3)₁₇₃1_<174> = 19 · 88547903 · 65493648547_<11> · 473223671792563487_<18> · C136

C136 = P58 · P79

P58 = 2729972876973264473407668709958466870137231132087382318011_<58>

P79 = 2341654867528510756347386808613808840739845101672864629948634132731214827586577_<79>

Number: 33331_174
N=6392654275585257013050251073760484734035868446531489738443496605400817805956429239525447040560721507485657356110288987765692807048938347
  ( 136 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=2729972876973264473407668709958466870137231132087382318011 (pp58)
 r2=2341654867528510756347386808613808840739845101672864629948634132731214827586577 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 128.43 hours.
Scaled time: 128.81 units (timescale=1.003).
Factorization parameters were as follows:
name: 33331_174
n: 6392654275585257013050251073760484734035868446531489738443496605400817805956429239525447040560721507485657356110288987765692807048938347
m: 50000000000000000000000000000000000
deg: 5
c5: 16
c0: -35
skew: 1.17
type: snfs
lss: 1
rlim: 6200000
alim: 6200000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.6
alambda: 2.6
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved rational special-q in [3100000, 6800001)
Primes: RFBsize:425648, AFBsize:427427, largePrimes:11270398 encountered
Relations: rels:12623695, finalFF:1249159
Max relations in full relation-set: 28
Initial matrix: 853139 x 1249159 with sparse part having weight 145713480.
Pruned matrix : 624977 x 629306 with weight 130223134.
Total sieving time: 120.48 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 7.55 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,174,5,0,0,0,0,0,0,0,0,6200000,6200000,27,27,53,53,2.6,2.6,100000
total time: 128.43 hours.
 --------- CPU info (if available) ----------

Nov 6, 2008

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38

8·10¹⁹⁴+9 = 8(0)₁₉₃9_<195> = 36288787236817_<14> · 1733287778383420857881_<22> · C161

C161 = P34 · P127

P34 = 4640813787596588296684196149207787_<34>

P127 = 2740644562907019485541894329504307053275818363204588691032659775150280382696305597977509234141114088628824622335852067596963491_<127>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=636370792
Step 1 took 20942ms
Step 2 took 13761ms
********** Factor found in step 2: 4640813787596588296684196149207787
Found probable prime factor of 34 digits: 4640813787596588296684196149207787
Probable prime cofactor 2740644562907019485541894329504307053275818363204588691032659775150280382696305597977509234141114088628824622335852067596963491 has 127 digits

(13·10¹⁹²-1)/3 = 4(3)₁₉₂_<193> = 2009095013_<10> · C184

C184 = P33 · C151

P33 = 453354899999051385638164148236283_<33>

C151 = [4757549415156671793718885360940066592028321069345124332444285713214129510247713968209634548850809460784818990083255411472660105494008435800994319257027_<151>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1455303559
Step 1 took 28365ms
Step 2 took 18987ms
********** Factor found in step 2: 453354899999051385638164148236283
Found probable prime factor of 33 digits: 453354899999051385638164148236283
Composite cofactor 4757549415156671793718885360940066592028321069345124332444285713214129510247713968209634548850809460784818990083255411472660105494008435800994319257027 has 151 digits

(13·10¹⁹³-1)/3 = 4(3)₁₉₃_<194> = 1283 · 211241938696927_<15> · C177

C177 = P28 · C150

P28 = 1179454721985069238526884189_<28>

C150 = [135560768795315666479420567155372787318773966104575598566882947784980396196359198484042923902019314266173918223948245743345587089475901721819107886317_<150>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3284095331
Step 1 took 28060ms
Step 2 took 18525ms
********** Factor found in step 2: 1179454721985069238526884189
Found probable prime factor of 28 digits: 1179454721985069238526884189
Composite cofactor 135560768795315666479420567155372787318773966104575598566882947784980396196359198484042923902019314266173918223948245743345587089475901721819107886317 has 150 digits

(23·10¹⁶⁷+13)/9 = 2(5)₁₆₆7_<168> = 277 · 48691157895576045683_<20> · C146

C146 = P44 · P102

P44 = 27443969039133904169298446115216292040204117_<44>

P102 = 690412323075362557285027197597598433223412453613402784609440766686898486315079882183222803599157306431_<102>

SNFS difficulty: 169 digits.
Divisors found:
 r1=27443969039133904169298446115216292040204117
 r2=690412323075362557285027197597598433223412453613402784609440766686898486315079882183222803599157306431
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.723).
Factorization parameters were as follows:
n: 18947654418716764374424967132467690542553161009686042491058061789733340248529530439004902748518528032044865890752042000493770430656115301156776427
m: 2000000000000000000000000000000000
deg: 5
c5: 575
c0: 104
skew: 0.71
type: snfs
lss: 1
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [3000000, 5900001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1107113 x 1107361
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000
total time: 24.00 hours.

(8·10¹⁷³+7)/3 = 2(6)₁₇₂9_<174> = 13 · 73 · 281 · 6326603 · C162

C162 = P74 · P88

P74 = 42814776790459658722187417517510814215270667144107978173935095857975270761_<74>

P88 = 3691747018154731514901278255388629875677249064619370992864317356367999540966374768013547_<88>

SNFS difficulty: 173 digits.
Divisors found:
 r1=42814776790459658722187417517510814215270667144107978173935095857975270761
 r2=3691747018154731514901278255388629875677249064619370992864317356367999540966374768013547
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 158061324549139851209881000137957958908466176625143650125935232571582776824866705772982079747177766026516809926412204131385899417709255574554361914986549440999267
m: 20000000000000000000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
lpbr: 27
lpba: 27
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [4500000, 7900001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1270477 x 1270725
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 8.00 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,54,54,2.6,2.6,200000
total time: 80.00 hours.

3·10¹⁷⁰+7 = 3(0)₁₆₉7_<171> = 11900149 · 116810359621_<12> · 333724949161_<12> · C141

C141 = P69 · P73

P69 = 351770377281652245322691967098920378125785292375511986421626711343961_<69>

P73 = 1838398065903311066272707877014113500727599586799929165989126913413817423_<73>

SNFS difficulty: 170 digits.
Divisors found:
 r1=351770377281652245322691967098920378125785292375511986421626711343961
 r2=1838398065903311066272707877014113500727599586799929165989126913413817423
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.529).
Factorization parameters were as follows:
n: 646693981236667522389584237654366407875221788717974285764394693434647990177604896070899093925014128846041367813074214479167782278715807632503
m: 10000000000000000000000000000000000
deg: 5
c5: 3
c0: 7
skew: 1.18
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6
Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 4550001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 944170 x 944418
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.6,2.6,100000
total time: 35.00 hours.

Nov 5, 2008 (2nd)

By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1

(8·10²⁴⁶+1)/9 = (8)₂₄₅9_<246> = 19 · 43 · 1123 · 1201 · 54049 · 374953 · 238863187 · 254423276921041_<15> · 249878855847304998235057_<24> · 1140131831316969859162651_<25> · C157

C157 = P49 · P108

P49 = 8415713706200900127931199895379743806544075670969_<49>

P108 = 273184820763160944148394055954587276134525002594293166787252148081315618120301142706791530493734100974000787_<108>

SNFS difficulty: 164 digits.
Divisors found:
 r1=8415713706200900127931199895379743806544075670969
 r2=273184820763160944148394055954587276134525002594293166787252148081315618120301142706791530493734100974000787
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.507).
Factorization parameters were as follows:
n: 2299045240422569802993721301700792860811599639640751880445141369355142007512624617692485421768499513237520278081936673408099549026757535740080796611359052603
m: 1000000000000000000000000000
deg: 6
c6: 400
c3: -20
c0: 1
skew: 0.37
type: snfs
lss: 0
rlim: 3900000
alim: 3900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 3900000/3900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [1950000, 4050001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 837829 x 838077
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,164,6,0,0,0,0,0,0,0,0,3900000,3900000,27,27,52,52,2.5,2.5,100000
total time: 20.00 hours.

(26·10¹⁶⁴+1)/9 = 2(8)₁₆₃9_<165> = 1297 · 411676655521_<12> · C150

C150 = P46 · P105

P46 = 4990807523509232364418465886288926752428403251_<46>

P105 = 108408616165558846036225029730435357616003437405601641863437365460786398813070202087637446096562159822547_<105>

SNFS difficulty: 166 digits.
Divisors found:
 r1=4990807523509232364418465886288926752428403251
 r2=108408616165558846036225029730435357616003437405601641863437365460786398813070202087637446096562159822547
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.467).
Factorization parameters were as follows:
n: 541046537172295678230112063092771000976403890919093220360728609248413825135794521816996517561591797000086121973304077595149385152379890268904717900297
m: 1000000000000000000000000000000000
deg: 5
c5: 13
c0: 5
skew: 0.83
type: snfs
lss: 1
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [2500000, 4200001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 822500 x 822748
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,54,54,2.5,2.5,100000
total time: 22.00 hours.

7·10¹⁷¹+3 = 7(0)₁₇₀3_<172> = 193663 · 1870021 · 5209480256572103393851_<22> · C139

C139 = P37 · C103

P37 = 2894880042580604713105118836471073339_<37>

C103 = [1281680959632193503942635352586274267558015554322256712727649413867069609775801786926191322876429626049_<103>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=799800686
Step 1 took 14613ms
Step 2 took 10661ms
********** Factor found in step 2: 2894880042580604713105118836471073339
Found probable prime factor of 37 digits: 2894880042580604713105118836471073339
Composite cofactor 1281680959632193503942635352586274267558015554322256712727649413867069609775801786926191322876429626049 has 103 digits

(17·10¹⁹⁷-71)/9 = 1(8)₁₉₆1_<198> = 7² · 11 · 154740857 · C187

C187 = P31 · C156

P31 = 6484318817072200664220252344377_<31>

C156 = [349259549226120898816318561825819172354659038159561997366757349200839837492502651538230943161399611740470482506153445896948591808813671085174887996739488211_<156>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1746000186
Step 1 took 23750ms
Step 2 took 15893ms
********** Factor found in step 2: 6484318817072200664220252344377
Found probable prime factor of 31 digits: 6484318817072200664220252344377
Composite cofactor 349259549226120898816318561825819172354659038159561997366757349200839837492502651538230943161399611740470482506153445896948591808813671085174887996739488211 has 156 digits

(11·10¹⁹⁶+43)/9 = 1(2)₁₉₅7_<197> = 275729 · 459212683 · C182

C182 = P31 · P152

P31 = 6008741759849951709826487049587_<31>

P152 = 16064614786695207086436049790472937530349258514440848160108671782788638591989327765703152163679992909068260214239814718499452514400361031807712665514003_<152>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1330018205
Step 1 took 23833ms
Step 2 took 15449ms
********** Factor found in step 2: 6008741759849951709826487049587
Found probable prime factor of 31 digits: 6008741759849951709826487049587
Probable prime cofactor 16064614786695207086436049790472937530349258514440848160108671782788638591989327765703152163679992909068260214239814718499452514400361031807712665514003 has 152 digits

Nov 5, 2008

By matsui / GMP-ECM

(26·10¹⁹⁴-53)/9 = 2(8)₁₉₃3_<195> = 9181 · C191

C191 = P38 · C153

P38 = 33131310762757534463314113982209864083_<38>

C153 = [949734540734059667011737519492193550057699281014965411093905490630203178374931330861533970341294050228827482597677330651031537089155308322620878537348821_<153>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]

31465950211184935071221968074162824190054339275557007830180687167943458107928209224364327294291350494378486971886383715160536857519756986046061310193757639569642619419332195718210313570296143
=
33131310762757534463314113982209864083* 949734540734059667011737519492193550057699281014965411093905490630203178374931330861533970341294050228827482597677330651031537089155308322620878537348821

(5·10¹⁹⁵-23)/9 = (5)₁₉₄3_<195> = 7 · 1423 · C191

C191 = P33 · P159

P33 = 129336462421879849754069060926489_<33>

P159 = 431224648380284309612865232874969422125228889747146931488227823268960765271677558591003604362740223454092783275191554461980340501715000408162796413157813991457_<159>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]

55773070530624993028366183671875871454227041015516068221619873060491472297515867438565962810516570179254648685428727593168914321409050853885709823868643264286272016419591964215997947551004473
=
129336462421879849754069060926489* 431224648380284309612865232874969422125228889747146931488227823268960765271677558591003604362740223454092783275191554461980340501715000408162796413157813991457

Nov 4, 2008 (5th)

By Wataru Sakai / GGNFS, Msieve

(23·10¹⁸⁸+13)/9 = 2(5)₁₈₇7_<189> = 29 · C187

C187 = P82 · P106

P82 = 4202259808550773907971885337983361678177345697627240201969519646276349756458518887_<82>

P106 = 2097028964860108572050467604009417142331875365403029617600254671056087250436376223344983146072314679901359_<106>

Number: 25557_188
N=8812260536398467432950191570881226053639846743295019157088122605363984674329501915708812260536398467432950191570881226053639846743295019157088122605363984674329501915708812260536398467433
  ( 187 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=4202259808550773907971885337983361678177345697627240201969519646276349756458518887 (pp82)
 r2=2097028964860108572050467604009417142331875365403029617600254671056087250436376223344983146072314679901359 (pp106)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 617.09 hours.
Scaled time: 1241.59 units (timescale=2.012).
Factorization parameters were as follows:
n: 8812260536398467432950191570881226053639846743295019157088122605363984674329501915708812260536398467432950191570881226053639846743295019157088122605363984674329501915708812260536398467433
m: 50000000000000000000000000000000000000
deg: 5
c5: 184
c0: 325
skew: 1.12
type: snfs
lss: 1
rlim: 13100000
alim: 13100000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.7
alambda: 2.7Factor base limits: 13100000/13100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6550000, 12250001)
Primes: RFBsize:855281, AFBsize:852904, largePrimes:21516523 encountered
Relations: rels:23769795, finalFF:2632176
Max relations in full relation-set: 32
Initial matrix: 1708252 x 2632176 with sparse part having weight 341771835.
Pruned matrix : 1206863 x 1215468 with weight 293848552.
Total sieving time: 578.38 hours.
Total relation processing time: 0.51 hours.
Matrix solve time: 37.66 hours.
Time per square root: 0.54 hours.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,13100000,13100000,28,28,55,55,2.7,2.7,100000
total time: 617.09 hours.
 --------- CPU info (if available) ----------

(8·10¹⁹⁷+1)/9 = (8)₁₉₆9_<197> = C197

C197 = P54 · P144

P54 = 106311392897166500371783359424653869114814020003048227_<54>

P144 = 836118185140042779513129418862402364113623638373731957714431877766932382409809916330540749485034097969436866621225052370275032773495280814961907_<144>

Number: 88889_197
N=88888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889
  ( 197 digits)
SNFS difficulty: 197 digits.
Divisors found:
 r1=106311392897166500371783359424653869114814020003048227
 r2=836118185140042779513129418862402364113623638373731957714431877766932382409809916330540749485034097969436866621225052370275032773495280814961907
Version: 
Total time: 624.61 hours.
Scaled time: 1221.73 units (timescale=1.956).
Factorization parameters were as follows:
n: 88888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889
m: 2000000000000000000000000000000000000000
deg: 5
c5: 25
c0: 1
skew: 0.53
type: snfs
lss: 1
rlim: 18200000
alim: 18200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.7
alambda: 2.7
Factor base limits: 18200000/18200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [9100000, 14800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2170422 x 2170670
Total sieving time: 624.61 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,197,5,0,0,0,0,0,0,0,0,18200000,18200000,28,28,56,56,2.7,2.7,100000
total time: 624.61 hours.
 --------- CPU info (if available) ----------

Nov 4, 2008 (4th)

By Sinkiti Sibata / GGNFS

4·10¹⁷¹-9 = 3(9)₁₇₀1_<172> = 13 · 1481551 · 2094373 · 35330951 · C151

C151 = P41 · P41 · P70

P41 = 23561463756765050201124699355493115971879_<41>

P41 = 28941009474935683843948897020903479139997_<41>

P70 = 4115993992441463544706180751361765698756507413749483861195184714376893_<70>

Number: 39991_171
N=2806665622118214847710924039293177763744010593873768497634226553742291244426872708427320284461062478088337028837972880775444239881356186539391699404159
  ( 151 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=23561463756765050201124699355493115971879 (pp41)
 r2=28941009474935683843948897020903479139997 (pp41)
 r3=4115993992441463544706180751361765698756507413749483861195184714376893 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 96.52 hours.
Scaled time: 97.29 units (timescale=1.008).
Factorization parameters were as follows:
name: 39991_171
n: 2806665622118214847710924039293177763744010593873768497634226553742291244426872708427320284461062478088337028837972880775444239881356186539391699404159
m: 20000000000000000000000000000000000
deg: 5
c5: 5
c0: -36
skew: 1.48
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.6
alambda: 2.6
Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved rational special-q in [2800000, 4900001)
Primes: RFBsize:387202, AFBsize:386584, largePrimes:10808797 encountered
Relations: rels:11331818, finalFF:919917
Max relations in full relation-set: 28
Initial matrix: 773853 x 919917 with sparse part having weight 94060144.
Pruned matrix : 669033 x 672966 with weight 71217464.
Total sieving time: 90.71 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 5.41 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,53,53,2.6,2.6,100000
total time: 96.52 hours.
 --------- CPU info (if available) ----------

Nov 4, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

4·10²⁰¹+1 = 4(0)₂₀₀1_<202> = 41 · 5121931 · 103849329299_<12> · 13503675809573_<14> · 587861201947289_<15> · 1860750042755447209_<19> · 2795453108496978738236562037_<28> · C109

C109 = P40 · P70

P40 = 1684776046154235009517333610464790582051_<40>

P70 = 2636510377862930365366650606354695539107142487471106263373162893880619_<70>

Number: n
N=4441929530060515954157998847314184112685903495876036134220205683443732187676153908597962620364198451118169569
  ( 109 digits)
Divisors found:

 r1=1684776046154235009517333610464790582051 (pp40)
 r2=2636510377862930365366650606354695539107142487471106263373162893880619 (pp70)

Ggnfs  : 0.77.1-20051202-athlon
Msieve : 1.38
Total time:  13.15 hours.
Scaled time: 17.22 units (timescale=1.310).
Factorization parameters were as follows:
name: KA_4_0_200_1
n: 4441929530060515954157998847314184112685903495876036134220205683443732187676153908597962620364198451118169569
skew: 31421.32
# norm 1.12e+15
c5: 33300
c4: 67891188
c3: -92107347697813
c2: -71140811831309675
c1: 45923596748289206796281
c0: 99335048402119309697832255
# alpha -6.17
Y1: 260512343659
Y0: -668383033680763864204
# Murphy_E 1.16e-09
# M 59806822586170241890647397341851243665361596419283843288752444232521072743104971604544561288048719651220781
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2800000)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7320359
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 422921 x 423169
Total sieving time: 13.15 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 13.15 hours.
 --------- CPU info (if available) ----------

(64·10²⁰³-1)/9 = 7(1)₂₀₃_<204> = 3 · C204

C204 = P66 · P138

P66 = 792832704173552914410162539337802386344011510373910197870659268159_<66>

P138 = 298974847769585802645309063405649477128051560575355074174346983441282122866725297765250335898742915030739786008659822640863906581190981843_<138>

Number: n
N=237037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037
  ( 204 digits)
SNFS difficulty: 205 digits.
Divisors found:

Tue Nov 04 22:50:14 2008  prp66 factor: 792832704173552914410162539337802386344011510373910197870659268159
Tue Nov 04 22:50:15 2008  prp138 factor: 298974847769585802645309063405649477128051560575355074174346983441282122866725297765250335898742915030739786008659822640863906581190981843
Tue Nov 04 22:50:15 2008  elapsed time 32:38:00 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 86.80 hours.
Scaled time: 176.89 units (timescale=2.038).
Factorization parameters were as follows:
name: KA_7_1_203
n: 237037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037
type: snfs
skew: 0.44
deg: 5
c5: 125
c0: -2
m: 40000000000000000000000000000000000000000
rlim: 9800000
alim: 9800000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9800000/9800000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 14400001)
Primes: RFBsize:652265, AFBsize:651935, largePrimes:34202822 encountered
Relations: rels:29031060, finalFF:202074
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 84.55 hours.
Total relation processing time: 2.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,205,5,0,0,0,0,0,0,0,0,9800000,9800000,29,29,58,58,2.5,2.5,100000
total time: 86.80 hours.
 --------- CPU info (if available) ----------

Nov 4, 2008 (2nd)

By Jo Yeong Uk / GMP-ECM

7·10¹⁷⁶-9 = 6(9)₁₇₅1_<177> = 31 · 284227 · C170

C170 = P34 · P137

P34 = 1471607402359269526317161020368119_<34>

P137 = 53985739075515634697915501772688348506596820268762244897523775610785131164014476184599853349601190834688415144297768454969091079778009397_<137>

GMP-ECM 6.2.1 [powered by GMP 4.2.3] [ECM]
Input number is 79445813245364875893722838753259122620867441596261597811926110399944978099626638725952461668246314253362004949020189110543968888111580963739001436493797495118905981214243 (170 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3920796782
Step 1 took 5865ms
Step 2 took 5148ms
********** Factor found in step 2: 1471607402359269526317161020368119
Found probable prime factor of 34 digits: 1471607402359269526317161020368119
Probable prime cofactor 53985739075515634697915501772688348506596820268762244897523775610785131164014476184599853349601190834688415144297768454969091079778009397 has 137 digits

7·10¹⁸⁷-9 = 6(9)₁₈₆1_<188> = 461 · 923371 · 473554153625182489683337_<24> · C156

C156 = P34 · C122

P34 = 4690476648547345168326374837406127_<34>

C122 = [74034518384334417089817067969336107865932654799596895823511091185372389129149571176376292605794361402236374912345491675039_<122>]

GMP-ECM 6.2.1 [powered by GMP 4.2.3] [ECM]
Input number is 347257179668169708309514689892335853744363566614245519657579625393249342784866390835895774677123656675961762660717974357244997314882524228703848091151563953 (156 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=603318502
Step 1 took 5912ms
Step 2 took 4961ms
********** Factor found in step 2: 4690476648547345168326374837406127
Found probable prime factor of 34 digits: 4690476648547345168326374837406127
Composite cofactor 74034518384334417089817067969336107865932654799596895823511091185372389129149571176376292605794361402236374912345491675039 has 122 digits

Nov 4, 2008

By Serge Batalov / GMP-ECM 6.2.1

4·10²⁰⁹-9 = 3(9)₂₀₈1_<210> = 43 · 157 · 1344799 · 43219643 · 456637813 · C184

C184 = P35 · C149

P35 = 52186574700410202710543580507939239_<35>

C149 = [42778215758823271283365202134828897965312572658602223157505026013428737320090590105223875557676570260944693618416666386090018930911972785693795598359_<149>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1610337776
Step 1 took 22446ms
Step 2 took 14608ms
********** Factor found in step 2: 52186574700410202710543580507939239
Found probable prime factor of 35 digits: 52186574700410202710543580507939239
Composite cofactor 42778215758823271283365202134828897965312572658602223157505026013428737320090590105223875557676570260944693618416666386090018930911972785693795598359 has 149 digits

4·10²²¹-9 = 3(9)₂₂₀1_<222> = 151 · 1481 · 43987 · C212

C212 = P37 · C175

P37 = 4520901491708664102216490947309660917_<37>

C175 = [8994532558579486158422478107666038614484587159727739139328919647030809782442864806400623275472680285761731651257616798378038630894161355548480113921301545753585088558529303159_<175>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3686803269
Step 1 took 27678ms
Step 2 took 16249ms
********** Factor found in step 2: 4520901491708664102216490947309660917
Found probable prime factor of 37 digits: 4520901491708664102216490947309660917
Composite cofactor 8994532558579486158422478107666038614484587159727739139328919647030809782442864806400623275472680285761731651257616798378038630894161355548480113921301545753585088558529303159 has 175 digits

Nov 3, 2008 (3rd)

By Jo Yeong Uk / GGNFS

(26·10¹⁶⁵+1)/9 = 2(8)₁₆₄9_<166> = 3³ · 117851 · 518327 · 58366361 · 17084746139318579_<17> · C130

C130 = P49 · P82

P49 = 1461695095426919438797142366846476947894188853677_<49>

P82 = 1201716525739254573467518321801984231101319213539948807673545053111692159046723257_<82>

Number: 28889_165
N=1756543151766545803755642925450589171778542028876884396660299422169027097780703495647142664349931068706672888482955013259885865989
  ( 130 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=1461695095426919438797142366846476947894188853677 (pp49)
 r2=1201716525739254573467518321801984231101319213539948807673545053111692159046723257 (pp82)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 31.99 hours.
Scaled time: 75.89 units (timescale=2.372).
Factorization parameters were as follows:
n: 1756543151766545803755642925450589171778542028876884396660299422169027097780703495647142664349931068706672888482955013259885865989
m: 1000000000000000000000000000000000
deg: 5
c5: 26
c0: 1
skew: 0.52
type: snfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [2000000, 3900001)
Primes: RFBsize:283146, AFBsize:283472, largePrimes:9788810 encountered
Relations: rels:9959778, finalFF:681236
Max relations in full relation-set: 28
Initial matrix: 566686 x 681236 with sparse part having weight 69626447.
Pruned matrix : 514482 x 517379 with weight 50794316.
Total sieving time: 29.63 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 2.17 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,52,52,2.6,2.6,100000
total time: 31.99 hours.
 --------- CPU info (if available) ----------

Nov 3, 2008 (2nd)

By Sinkiti Sibata / GGNFS, Msieve

(10¹⁶⁸-7)/3 = (3)₁₆₇1_<168> = 131 · 49129598861427367631541486362214571_<35> · C131

C131 = P61 · P71

P61 = 1228202233579388080561140656681357992984908574006806994870721_<61>

P71 = 42169101600404796800299427212024531725642501882767388509831772835550611_<71>

Number: 33331_168
N=51792184773653319969285271375059174848183340563143297361801486678007691346322178986782793210838274087534397894208901070916797560531
  ( 131 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=1228202233579388080561140656681357992984908574006806994870721 (pp61)
 r2=42169101600404796800299427212024531725642501882767388509831772835550611 (pp71)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 77.82 hours.
Scaled time: 78.52 units (timescale=1.009).
Factorization parameters were as follows:
name: 33331_168
n: 51792184773653319969285271375059174848183340563143297361801486678007691346322178986782793210838274087534397894208901070916797560531
m: 2000000000000000000000000000000000
deg: 5
c5: 125
c0: -28
skew: 0.74
type: snfs
lss: 1
rlim: 4700000
alim: 4700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6
Factor base limits: 4700000/4700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2350000, 4050001)
Primes: RFBsize:328964, AFBsize:328714, largePrimes:10042513 encountered
Relations: rels:10368230, finalFF:738492
Max relations in full relation-set: 28
Initial matrix: 657744 x 738492 with sparse part having weight 74336497.
Pruned matrix : 605532 x 608884 with weight 58986195.
Total sieving time: 73.14 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 4.31 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.6,2.6,100000
total time: 77.82 hours.
 --------- CPU info (if available) ----------

4·10²⁴⁸+1 = 4(0)₂₄₇1_<249> = 317 · 4349 · 25633 · 1115580458177_<13> · C109 · 2461338222207399496484039883032285004259961128085456678539752052171509493196922687274302976705525864295840055350573941_<118>

C109 = P54 · P56

P54 = 234046722213975127327184686613228150778995773714719821_<54>

P56 = 17613153769512112517578753541630628864236833323216296297_<56>

Number: 40001_248
N=4122300907605030294499111843600161364770012937047971593160000464298405090920832309716980944454539014674802837
  ( 109 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=234046722213975127327184686613228150778995773714719821
 r2=17613153769512112517578753541630628864236833323216296297
Version: 
Total time: 6.26 hours.
Scaled time: 6.52 units (timescale=1.041).
Factorization parameters were as follows:
name: 40001_248
n: 4122300907605030294499111843600161364770012937047971593160000464298405090920832309716980944454539014674802837
m: 10000000000000000000000000000000
deg: 4
c4: 2
c2: -2
c0: 1
skew: 0.84
type: snfs
lss: 1
rlim: 610000
alim: 610000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 610000/610000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [305000, 680001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 85089 x 85326
Total sieving time: 6.26 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,124,4,0,0,0,0,0,0,0,0,610000,610000,25,25,46,46,2.3,2.3,75000
total time: 6.26 hours.
 --------- CPU info (if available) ----------

Nov 3, 2008

Factorizations of 399...991 and Factorizations of 400...001 have been extended up to n=250. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Nov 2, 2008 (5th)

By Sinkiti Sibata / GGNFS

(8·10¹⁷²+1)/9 = (8)₁₇₁9_<172> = 3⁶ · 735571 · 301300931 · 2921457841539294443_<19> · C137

C137 = P44 · P46 · P48

P44 = 14123871181080477763897946609418072128713121_<44>

P46 = 2956392197812963543895136286012007490917219747_<46>

P48 = 451003028266667406944543619427456332464089161001_<48>

Number: 88889_172
N=18831948303162667244590918998815998979388665461180031905468570772382957770384992951626941042510712833480481908158471365601449643984507387
  ( 137 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=14123871181080477763897946609418072128713121 (pp44)
 r2=2956392197812963543895136286012007490917219747 (pp46)
 r3=451003028266667406944543619427456332464089161001 (pp48)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 100.01 hours.
Scaled time: 100.61 units (timescale=1.006).
Factorization parameters were as follows:
name: 88889_172
n: 18831948303162667244590918998815998979388665461180031905468570772382957770384992951626941042510712833480481908158471365601449643984507387
m: 20000000000000000000000000000000000
deg: 5
c5: 25
c0: 1
skew: 0.53
type: snfs
lss: 1
rlim: 5700000
alim: 5700000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.6
alambda: 2.6
Factor base limits: 5700000/5700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved rational special-q in [2850000, 5350001)
Primes: RFBsize:393606, AFBsize:392982, largePrimes:11092016 encountered
Relations: rels:12144422, finalFF:1245359
Max relations in full relation-set: 28
Initial matrix: 786652 x 1245359 with sparse part having weight 133842613.
Pruned matrix : 559260 x 563257 with weight 95031013.
Total sieving time: 94.74 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 4.90 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,5700000,5700000,27,27,53,53,2.6,2.6,100000
total time: 100.01 hours.
 --------- CPU info (if available) ----------

Nov 2, 2008 (4th)

By Serge Batalov / PFGW

(13·10⁶⁷⁰³⁸-31)/9 = 1(4)₆₇₀₃₇1_<67039> is PRP.

This is the new record of the largest known Plateau and Depression PRPs. Congratulations!

See also Patrick De Geest's Plateau and Depression Primes and Henri & Renaud Lifchitz's PRP Top records.

Nov 2, 2008 (3rd)

By Serge Batalov / GMP-ECM 6.2.1

9·10²⁴⁹-1 = 8(9)₂₄₉_<250> = 1239961 · 17567289930891241_<17> · 2211131180516999698877_<22> · 132852679081112049264025722783994751_<36> · C172

C172 = P36 · C136

P36 = 173971508153106043979381596158458837_<36>

C136 = [8084753086520734729835410115388355154353484488692121661133313572891265091227154991684283911329904836521257457036748584838069340122707201_<136>]

# ain't no such thing as a GNFS-172 :-)
#
Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2491863350
Step 1 took 21203ms
Step 2 took 14217ms
********** Factor found in step 2: 173971508153106043979381596158458837
Found probable prime factor of 36 digits: 173971508153106043979381596158458837
Composite cofactor 8084753086520734729835410115388355154353484488692121661133313572891265091227154991684283911329904836521257457036748584838069340122707201 has 136 digits

Nov 2, 2008 (2nd)

By Serge Batalov / PFGW

(58·10²⁶²⁶³-31)/9 = 6(4)₂₆₂₆₂1_<26264> is PRP.

Nov 2, 2008

By Jo Yeong Uk / GGNFS

(8·10²³⁷+1)/9 = (8)₂₃₆9_<237> = 7 · 67 · 79843 · 810282229 · 25235288443_<11> · 65577779623_<11> · 207290260327_<12> · 2316545454492717520441_<22> · 583350087044270793536476261956509179115137398672510361_<54> · C113

C113 = P43 · P71

P43 = 1487191291700791041015131345158905072042727_<43>

P71 = 42493320513341915820527305465165793249803276165861201738045955147117383_<71>

Number: 88889_237
N=63195696222892684832277844391928328946821188206823261379133646682788995464468527739880731086293082863637460423441
  ( 113 digits)
Divisors found:
 r1=1487191291700791041015131345158905072042727 (pp43)
 r2=42493320513341915820527305465165793249803276165861201738045955147117383 (pp71)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 20.14 hours.
Scaled time: 48.09 units (timescale=2.388).
Factorization parameters were as follows:
name: 88889_237
n: 63195696222892684832277844391928328946821188206823261379133646682788995464468527739880731086293082863637460423441
skew: 27018.80
# norm 7.50e+15
c5: 123120
c4: 15962790444
c3: -173345636186388
c2: -9974465700677868059
c1: 72237218500103757733458
c0: 896261119410555873154720925
# alpha -6.43
Y1: 402453350621
Y0: -3483938486140772011098
# Murphy_E 6.73e-10
# M 16365498609173863858154545566911789076320402775766839248454106356650596401781867323838807040660698237825956707642
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1200000, 2400001)
Primes: RFBsize:176302, AFBsize:176053, largePrimes:7835106 encountered
Relations: rels:7790839, finalFF:486106
Max relations in full relation-set: 28
Initial matrix: 352440 x 486106 with sparse part having weight 54607869.
Pruned matrix : 287389 x 289215 with weight 33631177.
Polynomial selection time: 1.05 hours.
Total sieving time: 18.36 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.49 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000
total time: 20.14 hours.
 --------- CPU info (if available) ----------

Nov 1, 2008 (8th)

By Jo Yeong Uk / GMP-ECM, Msieve

(8·10²⁴³+1)/9 = (8)₂₄₂9_<243> = 7 · 103 · 10987 · 2208760504147_<13> · 17177677368619642846441_<23> · 2399421520626029861918272171940676301643_<40> · 277844747550954514120814179402028087323169_<42> · C121

C121 = P36 · P42 · P44

P36 = 570594377243591599388686219119749929_<36>

P42 = 485954209612491624876956921153428347098089_<42>

P44 = 15998838028061921724000945081009795138974083_<44>

GMP-ECM 6.2.1 [powered by GMP 4.2.3] [ECM]
Input number is 4436201638881531080820121090024595020987461248035884770887711417896929274628629764144793641653411786281356411430875505523 (121 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2085848685
Step 1 took 12792ms
Step 2 took 9578ms
********** Factor found in step 2: 570594377243591599388686219119749929
Found probable prime factor of 36 digits: 570594377243591599388686219119749929
Composite cofactor 7774702688645105274357691330510344294773167446766755376698913587511041625917629827387 has 85 digits

Sat Nov 01 20:06:03 2008  
Sat Nov 01 20:06:03 2008  
Sat Nov 01 20:06:03 2008  Msieve v. 1.32
Sat Nov 01 20:06:03 2008  random seeds: f05f1888 7a2ed8fe
Sat Nov 01 20:06:03 2008  factoring 7774702688645105274357691330510344294773167446766755376698913587511041625917629827387 (85 digits)
Sat Nov 01 20:06:04 2008  no P-1/P+1/ECM available, skipping
Sat Nov 01 20:06:04 2008  commencing quadratic sieve (85-digit input)
Sat Nov 01 20:06:04 2008  using multiplier of 67
Sat Nov 01 20:06:04 2008  using VC8 32kb sieve core
Sat Nov 01 20:06:04 2008  sieve interval: 12 blocks of size 32768
Sat Nov 01 20:06:04 2008  processing polynomials in batches of 17
Sat Nov 01 20:06:04 2008  using a sieve bound of 1442509 (54745 primes)
Sat Nov 01 20:06:04 2008  using large prime bound of 115400720 (26 bits)
Sat Nov 01 20:06:04 2008  using double large prime bound of 325068826146400 (41-49 bits)
Sat Nov 01 20:06:04 2008  using trial factoring cutoff of 49 bits
Sat Nov 01 20:06:04 2008  polynomial 'A' values have 11 factors
Sat Nov 01 20:32:05 2008  55096 relations (16088 full + 39008 combined from 569882 partial), need 54841
Sat Nov 01 20:32:05 2008  begin with 585970 relations
Sat Nov 01 20:32:05 2008  reduce to 129381 relations in 9 passes
Sat Nov 01 20:32:05 2008  attempting to read 129381 relations
Sat Nov 01 20:32:07 2008  recovered 129381 relations
Sat Nov 01 20:32:07 2008  recovered 111770 polynomials
Sat Nov 01 20:32:07 2008  attempting to build 55096 cycles
Sat Nov 01 20:32:07 2008  found 55096 cycles in 5 passes
Sat Nov 01 20:32:07 2008  distribution of cycle lengths:
Sat Nov 01 20:32:07 2008     length 1 : 16088
Sat Nov 01 20:32:07 2008     length 2 : 11156
Sat Nov 01 20:32:07 2008     length 3 : 9817
Sat Nov 01 20:32:07 2008     length 4 : 6949
Sat Nov 01 20:32:07 2008     length 5 : 4796
Sat Nov 01 20:32:07 2008     length 6 : 2849
Sat Nov 01 20:32:07 2008     length 7 : 1602
Sat Nov 01 20:32:07 2008     length 9+: 1839
Sat Nov 01 20:32:07 2008  largest cycle: 17 relations
Sat Nov 01 20:32:07 2008  matrix is 54745 x 55096 with weight 3015660 (avg 54.73/col)
Sat Nov 01 20:32:07 2008  filtering completed in 3 passes
Sat Nov 01 20:32:07 2008  matrix is 49581 x 49645 with weight 2734730 (avg 55.09/col)
Sat Nov 01 20:32:07 2008  saving the first 48 matrix rows for later
Sat Nov 01 20:32:07 2008  matrix is 49533 x 49645 with weight 2135984 (avg 43.03/col)
Sat Nov 01 20:32:07 2008  matrix includes 64 packed rows
Sat Nov 01 20:32:07 2008  commencing Lanczos iteration
Sat Nov 01 20:32:40 2008  lanczos halted after 785 iterations (dim = 49530)
Sat Nov 01 20:32:41 2008  recovered 16 nontrivial dependencies
Sat Nov 01 20:32:41 2008  prp42 factor: 485954209612491624876956921153428347098089
Sat Nov 01 20:32:41 2008  prp44 factor: 15998838028061921724000945081009795138974083
Sat Nov 01 20:32:41 2008  elapsed time 00:26:38

Nov 1, 2008 (7th)

By Jo Yeong Uk / GMP-ECM, Msieve

(8·10²⁴⁰+1)/9 = (8)₂₃₉9_<240> = 499 · 2593 · 4153 · 37537 · 157907 · 592027 · 25143931 · 953529450602823737857_<21> · 63206919651724498591265539_<26> · 180916423539264977164887047686482530123_<39> · C123

C123 = P38 · P43 · P43

P38 = 59644893805996916150715795095302049977_<38>

P43 = 1072585571895690212926242783522064352375233_<43>

P43 = 2687601656653192547082463793848796171321257_<43>

GMP-ECM 6.2.1 [powered by GMP 4.2.3] [ECM]
Input number is 171937307092353385967400546721317067525746091830138769938460004457841338344298987572006993464275252473429109785647831808737 (123 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3843108160
Step 1 took 13198ms
Step 2 took 9251ms
********** Factor found in step 2: 59644893805996916150715795095302049977
Found probable prime factor of 38 digits: 59644893805996916150715795095302049977
Composite cofactor 2882682759929168977194009694842213855041748885584302599479357366656409353283853227881 has 85 digits

Sat Nov 01 18:46:36 2008  
Sat Nov 01 18:46:36 2008  
Sat Nov 01 18:46:36 2008  Msieve v. 1.32
Sat Nov 01 18:46:36 2008  random seeds: 7b2a1340 77511deb
Sat Nov 01 18:46:36 2008  factoring 2882682759929168977194009694842213855041748885584302599479357366656409353283853227881 (85 digits)
Sat Nov 01 18:46:37 2008  no P-1/P+1/ECM available, skipping
Sat Nov 01 18:46:37 2008  commencing quadratic sieve (85-digit input)
Sat Nov 01 18:46:37 2008  using multiplier of 1
Sat Nov 01 18:46:37 2008  using VC8 32kb sieve core
Sat Nov 01 18:46:37 2008  sieve interval: 12 blocks of size 32768
Sat Nov 01 18:46:37 2008  processing polynomials in batches of 17
Sat Nov 01 18:46:37 2008  using a sieve bound of 1423453 (54412 primes)
Sat Nov 01 18:46:37 2008  using large prime bound of 116723146 (26 bits)
Sat Nov 01 18:46:37 2008  using trial factoring cutoff of 27 bits
Sat Nov 01 18:46:37 2008  polynomial 'A' values have 11 factors
Sat Nov 01 19:03:03 2008  54673 relations (28990 full + 25683 combined from 274856 partial), need 54508
Sat Nov 01 19:03:03 2008  begin with 303846 relations
Sat Nov 01 19:03:03 2008  reduce to 77135 relations in 2 passes
Sat Nov 01 19:03:03 2008  attempting to read 77135 relations
Sat Nov 01 19:03:04 2008  recovered 77135 relations
Sat Nov 01 19:03:04 2008  recovered 69084 polynomials
Sat Nov 01 19:03:04 2008  attempting to build 54673 cycles
Sat Nov 01 19:03:04 2008  found 54673 cycles in 1 passes
Sat Nov 01 19:03:04 2008  distribution of cycle lengths:
Sat Nov 01 19:03:04 2008     length 1 : 28990
Sat Nov 01 19:03:04 2008     length 2 : 25683
Sat Nov 01 19:03:04 2008  largest cycle: 2 relations
Sat Nov 01 19:03:04 2008  matrix is 54412 x 54673 with weight 1751130 (avg 32.03/col)
Sat Nov 01 19:03:04 2008  filtering completed in 3 passes
Sat Nov 01 19:03:04 2008  matrix is 39912 x 39976 with weight 1384330 (avg 34.63/col)
Sat Nov 01 19:03:04 2008  saving the first 48 matrix rows for later
Sat Nov 01 19:03:04 2008  matrix is 39864 x 39976 with weight 1001281 (avg 25.05/col)
Sat Nov 01 19:03:04 2008  matrix includes 64 packed rows
Sat Nov 01 19:03:04 2008  commencing Lanczos iteration
Sat Nov 01 19:03:21 2008  lanczos halted after 632 iterations (dim = 39862)
Sat Nov 01 19:03:21 2008  recovered 16 nontrivial dependencies
Sat Nov 01 19:03:21 2008  prp43 factor: 1072585571895690212926242783522064352375233
Sat Nov 01 19:03:21 2008  prp43 factor: 2687601656653192547082463793848796171321257
Sat Nov 01 19:03:21 2008  elapsed time 00:16:45

Nov 1, 2008 (6th)

By Wataru Sakai / GGNFS

(2·10¹⁹⁷+1)/3 = (6)₁₉₆7_<197> = 220392158565284374291688840255616335178470607209821260561705899731767149903089665630652594920421_<96> · 302491100866089681760705045981867175663870543867735929938582966213623707361104074371799068296165909327_<102>

C197 = P96 · P102

P96 = 220392158565284374291688840255616335178470607209821260561705899731767149903089665630652594920421_<96>

P102 = 302491100866089681760705045981867175663870543867735929938582966213623707361104074371799068296165909327_<102>

Number: 66667_197
N=66666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667
  ( 197 digits)
SNFS difficulty: 197 digits.
Divisors found:
 r1=220392158565284374291688840255616335178470607209821260561705899731767149903089665630652594920421 (pp96)
 r2=302491100866089681760705045981867175663870543867735929938582966213623707361104074371799068296165909327 (pp102)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 2956.25 hours.
Scaled time: 5581.40 units (timescale=1.888).
Factorization parameters were as follows:
n: 66666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667
m: 1000000000000000000000000000000000000000
c5: 200
c0: 1
skew: 0.35
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 50700001)
Primes: RFBsize:501962, AFBsize:501861, largePrimes:8502861 encountered
Relations: rels:9534666, finalFF:1152190
Max relations in full relation-set: 32
Initial matrix: 1003888 x 1152190 with sparse part having weight 195186395.
Pruned matrix : 916465 x 921548 with weight 179477863.
Total sieving time: 2935.44 hours.
Total relation processing time: 0.48 hours.
Matrix solve time: 19.96 hours.
Time per square root: 0.36 hours.
Prototype def-par.txt line would be:
snfs,197,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 2956.25 hours.
 --------- CPU info (if available) ----------

Nov 1, 2008 (5th)

By Sinkiti Sibata / GGNFS

(26·10¹⁵⁵+1)/9 = 2(8)₁₅₄9_<156> = 31 · 59 · 72383 · 229093 · C142

C142 = P42 · P46 · P56

P42 = 538963150673787390706865573661610521092599_<42>

P46 = 1528601204716243697472593549862635099435041001_<46>

P56 = 11561534087493686424248097003525027478147253178845840561_<56>

Number: 28889_155
N=9525082252482793999323102663610381687328364089726663768981685048839219164389556307565161122064185071206368574553912285043224680366061665707039
  ( 142 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=538963150673787390706865573661610521092599 (pp42)
 r2=1528601204716243697472593549862635099435041001 (pp46)
 r3=11561534087493686424248097003525027478147253178845840561 (pp56)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 20.88 hours.
Scaled time: 20.63 units (timescale=0.988).
Factorization parameters were as follows:
name: 28889_155
n: 9525082252482793999323102663610381687328364089726663768981685048839219164389556307565161122064185071206368574553912285043224680366061665707039
m: 20000000000000000000000000000000
deg: 5
c5: 13
c0: 16
skew: 1.04
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.5
alambda: 2.5
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1400000, 1900001)
Primes: RFBsize:203362, AFBsize:203722, largePrimes:9222201 encountered
Relations: rels:9617408, finalFF:720314
Max relations in full relation-set: 28
Initial matrix: 407152 x 720314 with sparse part having weight 80380800.
Pruned matrix : 302612 x 304711 with weight 34968755.
Total sieving time: 19.87 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.78 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,51,51,2.5,2.5,100000
total time: 20.88 hours.
 --------- CPU info (if available) ----------

Nov 1, 2008 (4th)

By Serge Batalov / Msieve-1.38

(8·10²³⁴+1)/9 = (8)₂₃₃9_<234> = 17 · 811 · 12000751417_<11> · 554504489139892891_<18> · 4029308550879030630103503316721468381681617562125360827105876473_<64> · C139

C139 = P36 · P50 · P54

P36 = 708452754409146374529483146787025747_<36>

P50 = 22620385990634069598730260876721948262835656222041_<50>

P54 = 150045427642136409744783106387616892839332104918312931_<54>

SNFS difficulty: 156 digits.
Divisors found:
 r1=708452754409146374529483146787025747
 r2=22620385990634069598730260876721948262835656222041
 r3=150045427642136409744783106387616892839332104918312931
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 2404549213661918600414415840219982246832209037094558163654197849879077303245717353071130110863139553088219578414824432195743107120942866737
m: 100000000000000000000000000
deg: 6
c6: 4
c3: -2
c0: 1
skew: 0.79
type: snfs
lss: 0
rlim: 2700000
alim: 2700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 2700000/2700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [1350000, 2650001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 632870 x 633118
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,6,0,0,0,0,0,0,0,0,2700000,2700000,27,27,52,52,2.5,2.5,100000
total time: 18.00 hours.

Nov 1, 2008 (3rd)

By Jo Yeong Uk / GGNFS

(26·10¹⁶⁹+1)/9 = 2(8)₁₆₈9_<170> = 29 · 100913 · 21379041680182019_<17> · 629791800841938978959882287717_<30> · C117

C117 = P39 · P79

P39 = 237851355259520245767693083629268399033_<39>

P79 = 3082441596275624181609734228458130179747319199386915262705645132263828924699723_<79>

Number: 28889_169
N=733162911182476165696651536719886879504049082501597874078847443074443075794267486433599185290529361536401602468567859
  ( 117 digits)
Divisors found:
 r1=237851355259520245767693083629268399033 (pp39)
 r2=3082441596275624181609734228458130179747319199386915262705645132263828924699723 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 29.59 hours.
Scaled time: 70.74 units (timescale=2.391).
Factorization parameters were as follows:
name: 28889_169
n: 733162911182476165696651536719886879504049082501597874078847443074443075794267486433599185290529361536401602468567859
skew: 108187.70
# norm 1.20e+16
c5: 2280
c4: -2795606378
c3: 91661920058231
c2: 32492461028090342176
c1: 190596168568149965665252
c0: -22722389176983656882853269024
# alpha -6.02
Y1: 1799589968209
Y0: -50287140329669627061855
# Murphy_E 4.21e-10
# M 32639685845805564224093647946773830579766880893555582023928404958121945799986229313304601184884548131897019900486115
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 70000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 3500001)
Primes: RFBsize:250150, AFBsize:250319, largePrimes:7797872 encountered
Relations: rels:7841679, finalFF:647316
Max relations in full relation-set: 28
Initial matrix: 500549 x 647316 with sparse part having weight 63689992.
Pruned matrix : 398906 x 401472 with weight 42503958.
Polynomial selection time: 1.72 hours.
Total sieving time: 26.52 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 1.06 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.4,2.4,70000
total time: 29.59 hours.
 --------- CPU info (if available) ----------

Nov 1, 2008 (2nd)

By Serge Batalov / GMP-ECM 6.2.1

(16·10²²⁹-1)/3 = 5(3)₂₂₉_<230> = C230

C230 = P36 · C195

P36 = 138587157716002611881874212016797719_<36>

C195 = [384836042619661515037583365602420853804947706362741067724480589885195095790677520451016462477007474961684527089033394907416313251084718861869219905548092763513236834002103979070093897973877134707_<195>]

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2575188952
Step 1 took 13664ms
Step 2 took 7337ms
********** Factor found in step 2: 138587157716002611881874212016797719
Found probable prime factor of 36 digits: 138587157716002611881874212016797719
Composite cofactor 384836042619661515037583365602420853804947706362741067724480589885195095790677520451016462477007474961684527089033394907416313251084718861869219905548092763513236834002103979070093897973877134707 has 195 digits

(16·10²²⁷-1)/3 = 5(3)₂₂₇_<228> = 41 · 1101419432827217431_<19> · 837939824157522113713403_<24> · C185

C185 = P32 · C153

P32 = 50951806998599951488548848592191_<32>

C153 = [276623909222459955262062365246498315145753233845762190081926880984539629653558336897979021461117054738370602081856376552137256435890922353288561621777151_<153>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2751728905
Step 1 took 22017ms
Step 2 took 14817ms
********** Factor found in step 2: 50951806998599951488548848592191
Found probable prime factor of 32 digits: 50951806998599951488548848592191
Composite cofactor 276623909222459955262062365246498315145753233845762190081926880984539629653558336897979021461117054738370602081856376552137256435890922353288561621777151 has 153 digits

Nov 1, 2008

By Jo Yeong Uk / GGNFS

(8·10²⁰⁴+1)/9 = (8)₂₀₃9_<204> = 43 · 67 · 1291 · 24907 · 327345587 · 8061929011849_<13> · 94532204264734580251505661306547825138854107742779_<50> · C122

C122 = P38 · P39 · P46

P38 = 82897411705071064047937967244636410137_<38>

P39 = 191569661445027288713112719046241871161_<39>

P46 = 2421941276018788705974103400089367990086645033_<46>

Number: 88889_204
N=38461951094348424889796919695047691873076556376697842828616885689987407536284091576355196737748437367339041253075869613881
  ( 122 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=82897411705071064047937967244636410137 (pp38)
 r2=191569661445027288713112719046241871161 (pp39)
 r3=2421941276018788705974103400089367990086645033 (pp46)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.67 hours.
Scaled time: 11.11 units (timescale=2.381).
Factorization parameters were as follows:
n: 38461951094348424889796919695047691873076556376697842828616885689987407536284091576355196737748437367339041253075869613881
m: 100000000000000000000000
deg: 6
c6: 1
c3: -5
c0: 25
skew: 1.71
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.4
alambda: 2.4
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1650001)
Primes: RFBsize:114155, AFBsize:113645, largePrimes:3608661 encountered
Relations: rels:3614398, finalFF:283594
Max relations in full relation-set: 28
Initial matrix: 227865 x 283594 with sparse part having weight 25287404.
Pruned matrix : 206933 x 208136 with weight 15893379.
Total sieving time: 4.43 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,138,6,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.4,2.4,50000
total time: 4.67 hours.
 --------- CPU info (if available) ----------

(8·10²⁰⁷+1)/9 = (8)₂₀₆9_<207> = 7 · 23 · 109 · 307 · 297674527070399026203749_<24> · 2909875173333171111479969227134609531967_<40> · C138

C138 = P34 · P104

P34 = 5582664782691969404374014480446767_<34>

P104 = 34119224042741568474837497946520829604804791221870890569522792743145229666446531659254662634444747964243_<104>

Number: 88889_207
N=190476190476190476190476190476190476190476190476190476190476190476190380952380952380952380952380952380952380952380952380952380952380952381
  ( 138 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=5582664782691969404374014480446767 (pp34)
 r2=34119224042741568474837497946520829604804791221870890569522792743145229666446531659254662634444747964243 (pp104)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.72 hours.
Scaled time: 11.27 units (timescale=2.388).
Factorization parameters were as follows:
n: 190476190476190476190476190476190476190476190476190476190476190476190380952380952380952380952380952380952380952380952380952380952380952381
m: 100000000000000000000000
deg: 6
c6: 4
c3: -2
c0: 1
skew: 0.79
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.4
alambda: 2.4
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1650001)
Primes: RFBsize:114155, AFBsize:113945, largePrimes:3605300 encountered
Relations: rels:3601927, finalFF:271303
Max relations in full relation-set: 28
Initial matrix: 228165 x 271303 with sparse part having weight 24454403.
Pruned matrix : 212282 x 213486 with weight 16741789.
Total sieving time: 4.47 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,138,6,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.4,2.4,50000
total time: 4.72 hours.
 --------- CPU info (if available) ----------

October 2008

Oct 31, 2008 (4th)

By Jo Yeong Uk / GMP-ECM

(8·10²²⁵+1)/9 = (8)₂₂₄9_<225> = 7² · 43 · 8228029 · 24020107 · 14857882856581287529_<20> · 3258352894056569900803_<22> · 5000236399743388811370403_<25> · 320247123017961326534531395337587_<33> · C110

C110 = P32 · P78

P32 = 50532169039234753564210908503389_<32>

P78 = 544895758886235998604351913304690160474307653093573978373738315850473064776483_<78>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 27534764596801380073444030684382856370143345530480298090729657481328086634802851751249267898435076081333000887 (110 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3291085960
Step 1 took 3256ms
Step 2 took 2058ms
********** Factor found in step 2: 50532169039234753564210908503389
Found probable prime factor of 32 digits: 50532169039234753564210908503389
Probable prime cofactor 544895758886235998604351913304690160474307653093573978373738315850473064776483 has 78 digits

Oct 31, 2008 (3rd)

Factorizations of 899...99, Factorizations of 88...889, Factorizations of 533...33 were extended to n=250. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Oct 31, 2008 (2nd)

By matsui / GMP-ECM

(7·10¹⁹⁰-61)/9 = (7)₁₈₉1_<190> = 23² · C188

C188 = P31 · C157

P31 = 2688905664266052337484729565917_<31>

C157 = [5467946951863048473626887020863645023766677773365149383086724143142152008359250701849934634922233312157204345407319371930536542980234660828386982636456713847_<157>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]

14702793530770846460827557235874816215080865364419239655534551564797311489182944759504305818105440033606385213190506196177273681999579920184835118672547784078975005250997689561016593152699
=2688905664266052337484729565917* 5467946951863048473626887020863645023766677773365149383086724143142152008359250701849934634922233312157204345407319371930536542980234660828386982636456713847

Oct 31, 2008

By Serge Batalov / GMP-ECM 6.2.1

6·10¹⁶⁸-1 = 5(9)₁₆₈_<169> = 4799 · 2017177 · 4202161651613_<13> · 10503821362051_<14> · C134

C134 = P34 · P100

P34 = 6720571008125216270124997913782507_<34>

P100 = 2089441596792376491620750374295583364339925722989928143182632024080598639760461288200867439741680893_<100>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3109165435
Step 1 took 12077ms
Step 2 took 9621ms
********** Factor found in step 2: 6720571008125216270124997913782507
Found probable prime factor of 34 digits: 6720571008125216270124997913782507
Probable prime cofactor 2089441596792376491620750374295583364339925722989928143182632024080598639760461288200867439741680893 has 100 digits

Oct 30, 2008 (7th)

By Jo Yeong Uk / GGNFS

(26·10¹⁵⁹+1)/9 = 2(8)₁₅₈9_<160> = 3 · 19 · 2897 · 47530117865256101258279_<23> · C132

C132 = P53 · P79

P53 = 63372486529335247949657526960405508372415068972242089_<53>

P79 = 5808150331783600012048251978464509513167533255570748146548143492258533560391311_<79>

Number: 28889_159
N=368076928661310242796685223052351194474178929325136743683341593384751145819507087501554444508127876795316137199592189505603864088679
  ( 132 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=63372486529335247949657526960405508372415068972242089 (pp53)
 r2=5808150331783600012048251978464509513167533255570748146548143492258533560391311 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.36 hours.
Scaled time: 57.78 units (timescale=2.372).
Factorization parameters were as follows:
n: 368076928661310242796685223052351194474178929325136743683341593384751145819507087501554444508127876795316137199592189505603864088679
m: 100000000000000000000000000000000
deg: 5
c5: 13
c0: 5
skew: 0.83
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.5
alambda: 2.5
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1500000, 3100001)
Primes: RFBsize:216816, AFBsize:217321, largePrimes:9125240 encountered
Relations: rels:9381690, finalFF:582288
Max relations in full relation-set: 28
Initial matrix: 434202 x 582288 with sparse part having weight 65760285.
Pruned matrix : 383610 x 385845 with weight 43352181.
Total sieving time: 23.04 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 1.15 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,51,51,2.5,2.5,100000
total time: 24.36 hours.
 --------- CPU info (if available) ----------

Oct 30, 2008 (6th)

By matsui / GMP-ECM

5·10¹⁷⁷-3 = 4(9)₁₇₆7_<178> = 29 · 71 · 647 · 11597 · 32257 · 11155845410727571_<17> · C147

C147 = P31 · P117

P31 = 4116890636843482409367503214379_<31>

P117 = 218457987170696445427188464234004646047913220813017808820800049784287693771198669963461651749956944384214219693687749_<117>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]

899367641926713799141991352700853887454818241078024680408131394423372550185069563049583638222675661519098771870475781201357007143856873533832942871

=4116890636843482409367503214379* 218457987170696445427188464234004646047913220813017808820800049784287693771198669963461651749956944384214219693687749

Oct 30, 2008 (5th)

By Wataru Sakai / GGNFS

(4·10¹⁸⁷+17)/3 = 1(3)₁₈₆9_<188> = 227 · C185

C185 = P62 · P123

P62 = 68965476147814636902426765565516035764069141667886618893443389_<62>

P123 = 851689200583090792929308232980079439143509638878237547282829962931049006405070726814731704503101259053470178580894789150813_<123>

Number: 13339_187
N=58737151248164464023494860499265785609397944199706314243759177679882525697503671071953010279001468428781204111600587371512481644640234948604992657856093979441997063142437591776798825257
  ( 185 digits)
SNFS difficulty: 187 digits.
Divisors found:
 r1=68965476147814636902426765565516035764069141667886618893443389 (pp62)
 r2=851689200583090792929308232980079439143509638878237547282829962931049006405070726814731704503101259053470178580894789150813 (pp123)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 1042.92 hours.
Scaled time: 2087.93 units (timescale=2.002).
Factorization parameters were as follows:
n: 58737151248164464023494860499265785609397944199706314243759177679882525697503671071953010279001468428781204111600587371512481644640234948604992657856093979441997063142437591776798825257
m: 20000000000000000000000000000000000000
c5: 25
c0: 34
skew: 1.06
type: snfsFactor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 18500001)
Primes: RFBsize:501962, AFBsize:503361, largePrimes:7202596 encountered
Relations: rels:7831073, finalFF:1219969
Max relations in full relation-set: 32
Initial matrix: 1005387 x 1219969 with sparse part having weight 139107803.
Pruned matrix : 846533 x 851623 with weight 122408733.
Total sieving time: 1030.97 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 11.53 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 1042.92 hours.
 --------- CPU info (if available) ----------

2·10¹⁹⁰+9 = 2(0)₁₈₉9_<191> = 11 · 2267 · C186

C186 = P43 · P144

P43 = 3598257171209322387124035246065550912037121_<43>

P144 = 222891543042545298957116640948488621345212099759851442244790596744882493938600415976943482712976628381818095574564453234501990920912116689990817_<144>

Number: 20009_190
N=802021093154749969924209006696876127842162248867145205918915667482054778040662469422945823475157396639531619681597626017564261940089024341340177246661587199743353250190480009624253117857
  ( 186 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=3598257171209322387124035246065550912037121 (pp43)
 r2=222891543042545298957116640948488621345212099759851442244790596744882493938600415976943482712976628381818095574564453234501990920912116689990817 (pp144)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 868.84 hours.
Scaled time: 1750.70 units (timescale=2.015).
Factorization parameters were as follows:
n: 802021093154749969924209006696876127842162248867145205918915667482054778040662469422945823475157396639531619681597626017564261940089024341340177246661587199743353250190480009624253117857
m: 100000000000000000000000000000000000000
c5: 2
c0: 9
skew: 1.35
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 15700001)
Primes: RFBsize:501962, AFBsize:502156, largePrimes:6947303 encountered
Relations: rels:7503487, finalFF:1184004
Max relations in full relation-set: 32
Initial matrix: 1004183 x 1184004 with sparse part having weight 117312846.
Pruned matrix : 866921 x 872005 with weight 96822749.
Total sieving time: 860.03 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 8.42 hours.
Time per square root: 0.26 hours.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 868.84 hours.
 --------- CPU info (if available) ----------

Oct 30, 2008 (4th)

By Sinkiti Sibata / GGNFS

(26·10¹⁷⁹-17)/9 = 2(8)₁₇₈7_<180> = 577 · 2011439 · 27778159 · 98699849 · 1653903478537_<13> · C143

C143 = P49 · P94

P49 = 5568917968267078138899173830351221759908557861721_<49>

P94 = 9857056137728383106952550168939175812236563857884385884810595206543334545507467963339269590847_<94>

Number: 28887_179
N=54893137039612879596184897392530603975543294236018838293195344236899356693945768816826702494078297548438412058402012173090931238202908873267687
  ( 143 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=5568917968267078138899173830351221759908557861721 (pp49)
 r2=9857056137728383106952550168939175812236563857884385884810595206543334545507467963339269590847 (pp94)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 548.54 hours.
Scaled time: 553.48 units (timescale=1.009).
Factorization parameters were as follows:
name: 28887_179
n: 54893137039612879596184897392530603975543294236018838293195344236899356693945768816826702494078297548438412058402012173090931238202908873267687
m: 1000000000000000000000000000000000000
c5: 13
c0: -85
skew: 1.46
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 11000001)
Primes: RFBsize:501962, AFBsize:501546, largePrimes:6747299 encountered
Relations: rels:7249285, finalFF:1172045
Max relations in full relation-set: 28
Initial matrix: 1003573 x 1172045 with sparse part having weight 87126144.
Pruned matrix : 865254 x 870335 with weight 67813684.
Total sieving time: 540.27 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 7.96 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 548.54 hours.
 --------- CPU info (if available) ----------

Oct 30, 2008 (3rd)

By Serge Batalov / GMP-ECM 6.2.1

(28·10¹⁹⁰+17)/9 = 3(1)₁₈₉3_<191> = 3 · 53 · 2324869405289_<13> · C176

C176 = P30 · P147

P30 = 189344953281801099289844032523_<30>

P147 = 444494202776565721977201120940522199860059753010149064714369456018500463217163672442226792310654799092430889759491584962078996666281704027405100381_<147>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=732919934
Step 1 took 22026ms
Step 2 took 16557ms
********** Factor found in step 2: 189344953281801099289844032523
Found probable prime factor of 30 digits: 189344953281801099289844032523
Probable prime cofactor 444494202776565721977201120940522199860059753010149064714369456018500463217163672442226792310654799092430889759491584962078996666281704027405100381 has 147 digits

(10¹⁹⁵-7)/3 = (3)₁₉₄1_<195> = 181 · 269 · 8124997885001_<13> · 74717295626884435829_<20> · 326293390169303271462521_<24> · C134

C134 = P38 · P97

P38 = 29260605544995388086468822651950635609_<38>

P97 = 1181168628435656755332100955486268041776709445145430749775935359970677708462298380422465750774959_<97>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3346586215
Step 1 took 11984ms
Step 2 took 11253ms
********** Factor found in step 2: 29260605544995388086468822651950635609
Found probable prime factor of 38 digits: 29260605544995388086468822651950635609
Probable prime cofactor 1181168628435656755332100955486268041776709445145430749775935359970677708462298380422465750774959 has 97 digits

(2·10²⁰⁰-17)/3 = (6)₁₉₉1_<200> = 273765949 · 189134477377_<12> · C181

C181 = P33 · C148

P33 = 522353457577022509514639952407329_<33>

C148 = [2464870651612724961793238428217840495900981675124347834528712637053912675622666484609096621861583916321050830926456254813740600462323677340559278633_<148>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3352591208
Step 1 took 22005ms
Step 2 took 16481ms
********** Factor found in step 2: 522353457577022509514639952407329
Found probable prime factor of 33 digits: 522353457577022509514639952407329
Composite cofactor 2464870651612724961793238428217840495900981675124347834528712637053912675622666484609096621861583916321050830926456254813740600462323677340559278633 has 148 digits

Oct 30, 2008 (2nd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve

(28·10¹⁷¹+17)/9 = 3(1)₁₇₀3_<172> = 11 · 98671529155359905029_<20> · C151

C151 = P30 · P121

P30 = 568989076397229877436168709083_<30>

P121 = 5037639078551312735260150274259076408128833763875038399879050906215408406462219863760359907480071781960561895317179882669_<121>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3387344901
Step 1 took 16665ms
Step 2 took 13201ms
********** Factor found in step 2: 568989076397229877436168709083
Found probable prime factor of 30 digits: 568989076397229877436168709083
Probable prime cofactor 5037639078551312735260150274259076408128833763875038399879050906215408406462219863760359907480071781960561895317179882669 has 121 digits

(28·10¹⁸¹+17)/9 = 3(1)₁₈₀3_<182> = 3 · 11 · 59 · 1013 · 14321 · 25444583528418949967_<20> · C152

C152 = P33 · P35 · P35 · P50

P33 = 487786121583417478031377245240619_<33>

P35 = 23713943396205054814260936625106267_<35>

P35 = 74651041133013577781884111541307929_<35>

P50 = 50130535731281299048808262966371781007594617903457_<50>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=80191738
Step 1 took 14481ms
Step 2 took 12853ms
********** Factor found in step 2: 23713943396205054814260936625106267
Found probable prime factor of 35 digits: 23713943396205054814260936625106267

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=392881417
Step 1 took 15425ms
Step 2 took 12941ms
********** Factor found in step 2: 487786121583417478031377245240619
Found probable prime factor of 33 digits: 487786121583417478031377245240619

Wed Oct 29 19:41:35 2008  Msieve v. 1.36
Wed Oct 29 19:41:35 2008  random seeds: 6270e78e 23782657
Wed Oct 29 19:41:35 2008  factoring 
3742296684895887151566152410872755963617683239627020475047963724780736160593630610553 (85 digits)
Wed Oct 29 19:41:35 2008  no P-1/P+1/ECM available, skipping
Wed Oct 29 19:41:35 2008  commencing quadratic sieve (85-digit input)
Wed Oct 29 19:41:35 2008  using multiplier of 3
Wed Oct 29 19:41:35 2008  using 64kb Opteron sieve core
Wed Oct 29 19:41:35 2008  sieve interval: 6 blocks of size 65536
Wed Oct 29 19:41:35 2008  processing polynomials in batches of 17
Wed Oct 29 19:41:35 2008  using a sieve bound of 1426129 (54330 primes)
Wed Oct 29 19:41:35 2008  using large prime bound of 116942578 (26 bits)
Wed Oct 29 19:41:35 2008  using double large prime bound of 332928269126164 (41-49 bits)
Wed Oct 29 19:41:35 2008  using trial factoring cutoff of 49 bits
Wed Oct 29 19:41:35 2008  polynomial 'A' values have 11 factors
Wed Oct 29 20:07:14 2008  54749 relations (16077 full + 38672 combined from 569767 partial), need 
54426
Wed Oct 29 20:07:14 2008  begin with 585844 relations
Wed Oct 29 20:07:14 2008  reduce to 128305 relations in 9 passes
Wed Oct 29 20:07:14 2008  attempting to read 128305 relations
Wed Oct 29 20:07:15 2008  recovered 128305 relations
Wed Oct 29 20:07:15 2008  recovered 107033 polynomials
Wed Oct 29 20:07:15 2008  attempting to build 54749 cycles
Wed Oct 29 20:07:15 2008  found 54749 cycles in 6 passes
Wed Oct 29 20:07:15 2008  distribution of cycle lengths:
Wed Oct 29 20:07:15 2008     length 1 : 16077
Wed Oct 29 20:07:15 2008     length 2 : 11191
Wed Oct 29 20:07:15 2008     length 3 : 9634
Wed Oct 29 20:07:15 2008     length 4 : 7021
Wed Oct 29 20:07:15 2008     length 5 : 4652
Wed Oct 29 20:07:15 2008     length 6 : 2817
Wed Oct 29 20:07:15 2008     length 7 : 1583
Wed Oct 29 20:07:15 2008     length 9+: 1774
Wed Oct 29 20:07:15 2008  largest cycle: 17 relations
Wed Oct 29 20:07:15 2008  matrix is 54330 x 54749 (12.7 MB) with weight 2892970 (52.84/col)
Wed Oct 29 20:07:16 2008  sparse part has weight 2892970 (52.84/col)
Wed Oct 29 20:07:16 2008  filtering completed in 4 passes
Wed Oct 29 20:07:16 2008  matrix is 48985 x 49049 (11.5 MB) with weight 2610556 (53.22/col)
Wed Oct 29 20:07:16 2008  sparse part has weight 2610556 (53.22/col)
Wed Oct 29 20:07:16 2008  saving the first 48 matrix rows for later
Wed Oct 29 20:07:16 2008  matrix is 48937 x 49049 (6.8 MB) with weight 1947250 (39.70/col)
Wed Oct 29 20:07:16 2008  sparse part has weight 1294865 (26.40/col)
Wed Oct 29 20:07:16 2008  matrix includes 64 packed rows
Wed Oct 29 20:07:16 2008  using block size 19619 for processor cache size 1024 kB
Wed Oct 29 20:07:17 2008  commencing Lanczos iteration
Wed Oct 29 20:07:17 2008  memory use: 6.5 MB
Wed Oct 29 20:07:27 2008  lanczos halted after 775 iterations (dim = 48935)
Wed Oct 29 20:07:27 2008  recovered 18 nontrivial dependencies
Wed Oct 29 20:07:28 2008  prp35 factor: 74651041133013577781884111541307929
Wed Oct 29 20:07:28 2008  prp50 factor: 50130535731281299048808262966371781007594617903457
Wed Oct 29 20:07:28 2008  elapsed time 00:25:53

Oct 30, 2008

By Robert Backstrom / GGNFS, Msieve

(14·10²⁰⁰-23)/9 = 1(5)₁₉₉3_<201> = 3² · C200

C200 = P52 · P65 · P84

P52 = 3033496037622857307870842268067364837548775059726949_<52>

P65 = 12252998283212933037938412743529586470315179061764978083771647637_<65>

P84 = 465004560406171829084976708697089017173510355031372707962704278582642195060480525009_<84>

Number: n
N=17283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617
  ( 200 digits)
SNFS difficulty: 201 digits.
Divisors found:

Thu Oct 30 08:57:29 2008  prp52 factor: 3033496037622857307870842268067364837548775059726949
Thu Oct 30 08:57:29 2008  prp65 factor: 12252998283212933037938412743529586470315179061764978083771647637
Thu Oct 30 08:57:29 2008  prp84 factor: 465004560406171829084976708697089017173510355031372707962704278582642195060480525009
Thu Oct 30 08:57:30 2008  elapsed time 26:37:36 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 83.40 hours.
Scaled time: 170.54 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_1_5_199_3
n: 17283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617
type: snfs
skew: 1.10
deg: 5
c5: 14
c0: -23
m: 10000000000000000000000000000000000000000
rlim: 9600000
alim: 9600000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9600000/9600000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 13300001)
Primes: RFBsize:639851, AFBsize:640823, largePrimes:35380027 encountered
Relations: rels:26823768, finalFF:263116
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 81.43 hours.
Total relation processing time: 1.97 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,201,5,0,0,0,0,0,0,0,0,9600000,9600000,29,29,58,58,2.5,2.5,100000
total time: 83.40 hours.
 --------- CPU info (if available) ----------

Oct 29, 2008 (5th)

By Jo Yeong Uk / GGNFS

(26·10¹⁸³-17)/9 = 2(8)₁₈₂7_<184> = C184

C184 = P90 · P94

P90 = 571191356051002418872131436996090915923457383067405912592086693050165007850808002169422749_<90>

P94 = 5057655124302924926840820612415887462963794902802707794326442625485636705143562806846593819363_<94>

Number: 28887_183
N=2888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887
  ( 184 digits)
SNFS difficulty: 186 digits.
Divisors found:
 r1=571191356051002418872131436996090915923457383067405912592086693050165007850808002169422749 (pp90)
 r2=5057655124302924926840820612415887462963794902802707794326442625485636705143562806846593819363 (pp94)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 296.85 hours.
Scaled time: 704.43 units (timescale=2.373).
Factorization parameters were as follows:
n: 2888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887
m: 10000000000000000000000000000000000000
c5: 13
c0: -850
skew: 2.31
type: snfs
Factor base limits: 12000000/12000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 51/51
Sieved algebraic special-q in [6000000, 11300001)
Primes: RFBsize:788060, AFBsize:788454, largePrimes:12608406 encountered
Relations: rels:13159127, finalFF:1768281
Max relations in full relation-set: 28
Initial matrix: 1576580 x 1768281 with sparse part having weight 117863959.
Pruned matrix : 1406297 x 1414243 with weight 86507487.
Total sieving time: 280.09 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 16.38 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,12000000,12000000,28,28,51,51,2.6,2.6,100000
total time: 296.85 hours.
 --------- CPU info (if available) ----------

Oct 29, 2008 (4th)

By Justin Card / GGNFS for sieving, msieve for linear algebra

(10¹⁷⁹+17)/9 = (1)₁₇₈3_<179> = 19 · 1439 · 11791673 · 350355007 · 41417257495760776071419_<23> · C136

C136 = P56 · P80

P56 = 64359895320324138046847817077342166028615808217898933063_<56>

P80 = 36903084954015880064848993395715905165599046095682487205693219081526100375034279_<80>

Tue Oct 28 18:11:06 2008  Msieve v. 1.38
Tue Oct 28 18:11:06 2008  random seeds: d81d15f7 8c4cc99f
Tue Oct 28 18:11:06 2008  factoring 2375078684637490748471009799403460903791906373419845536550774278476483193823770338103403225837841896931094354587473006789445556151466577 (136 digits)
Tue Oct 28 18:11:07 2008  no P-1/P+1/ECM available, skipping
Tue Oct 28 18:11:07 2008  commencing number field sieve (136-digit input)
Tue Oct 28 18:11:07 2008  R0: -1000000000000000000000000000000000000
Tue Oct 28 18:11:07 2008  R1:  1
Tue Oct 28 18:11:07 2008  A0:  170
Tue Oct 28 18:11:07 2008  A1:  0
Tue Oct 28 18:11:07 2008  A2:  0
Tue Oct 28 18:11:07 2008  A3:  0
Tue Oct 28 18:11:07 2008  A4:  0
Tue Oct 28 18:11:07 2008  A5:  1
Tue Oct 28 18:11:07 2008  size score = 2.613876e-12, Murphy alpha = 0.851423, combined = 1.968017e-12
Tue Oct 28 18:11:07 2008
Tue Oct 28 18:11:07 2008  commencing relation filtering
Tue Oct 28 18:11:07 2008  commencing duplicate removal, pass 1
Tue Oct 28 18:14:06 2008  error -9 reading relation 16302560
Tue Oct 28 18:14:58 2008  error -15 reading relation 21041764
Tue Oct 28 18:15:19 2008  found 1848518 hash collisions in 22933637 relations
Tue Oct 28 18:16:47 2008  added 721562 free relations
Tue Oct 28 18:16:47 2008  commencing duplicate removal, pass 2
Tue Oct 28 18:17:06 2008  found 1107318 duplicates and 22547881 unique relations
Tue Oct 28 18:17:06 2008  memory use: 94.6 MB
Tue Oct 28 18:17:06 2008  reading rational ideals above 18415616
Tue Oct 28 18:17:06 2008  reading algebraic ideals above 18415616
Tue Oct 28 18:17:06 2008  commencing singleton removal, pass 1
Tue Oct 28 18:21:41 2008  relations with 0 large ideals: 922249
Tue Oct 28 18:21:41 2008  relations with 1 large ideals: 4236483
Tue Oct 28 18:21:41 2008  relations with 2 large ideals: 7900596
Tue Oct 28 18:21:41 2008  relations with 3 large ideals: 6655370
Tue Oct 28 18:21:41 2008  relations with 4 large ideals: 2152524
Tue Oct 28 18:21:41 2008  relations with 5 large ideals: 17717
Tue Oct 28 18:21:41 2008  relations with 6 large ideals: 662941
Tue Oct 28 18:21:41 2008  relations with 7+ large ideals: 1
Tue Oct 28 18:21:41 2008  22547881 relations and about 18723100 large ideals
Tue Oct 28 18:21:41 2008  commencing singleton removal, pass 2
Tue Oct 28 18:26:16 2008  found 6186686 singletons
Tue Oct 28 18:26:16 2008  current dataset: 16361195 relations and about 11312019 large ideals
Tue Oct 28 18:26:16 2008  commencing singleton removal, pass 3
Tue Oct 28 18:29:28 2008  found 1867860 singletons
Tue Oct 28 18:29:28 2008  current dataset: 14493335 relations and about 9370319 large ideals
Tue Oct 28 18:29:28 2008  commencing singleton removal, pass 4
Tue Oct 28 18:32:18 2008  found 423643 singletons
Tue Oct 28 18:32:18 2008  current dataset: 14069692 relations and about 8941622 large ideals
Tue Oct 28 18:32:18 2008  commencing singleton removal, final pass
Tue Oct 28 18:35:28 2008  memory use: 218.4 MB
Tue Oct 28 18:35:28 2008  commencing in-memory singleton removal
Tue Oct 28 18:35:30 2008  begin with 14069692 relations and 9950674 unique ideals
Tue Oct 28 18:35:54 2008  reduce to 12261335 relations and 8095900 ideals in 14 passes
Tue Oct 28 18:35:54 2008  max relations containing the same ideal: 64
Tue Oct 28 18:35:57 2008  reading rational ideals above 720000
Tue Oct 28 18:35:57 2008  reading algebraic ideals above 720000
Tue Oct 28 18:35:57 2008  commencing singleton removal, final pass
Tue Oct 28 18:39:45 2008  keeping 9433782 ideals with weight <= 20, new excess is 1020107
Tue Oct 28 18:39:55 2008  memory use: 348.3 MB
Tue Oct 28 18:39:56 2008  commencing in-memory singleton removal
Tue Oct 28 18:39:58 2008  begin with 12262644 relations and 9433782 unique ideals
Tue Oct 28 18:40:25 2008  reduce to 12250914 relations and 9415970 ideals in 11 passes
Tue Oct 28 18:40:25 2008  max relations containing the same ideal: 20
Tue Oct 28 18:40:37 2008  removing 2080308 relations and 1680308 ideals in 400000 cliques
Tue Oct 28 18:40:38 2008  commencing in-memory singleton removal
Tue Oct 28 18:40:39 2008  begin with 10170606 relations and 9415970 unique ideals
Tue Oct 28 18:40:55 2008  reduce to 9954338 relations and 7510988 ideals in 8 passes
Tue Oct 28 18:40:55 2008  max relations containing the same ideal: 20
Tue Oct 28 18:41:05 2008  removing 1568488 relations and 1168488 ideals in 400000 cliques
Tue Oct 28 18:41:05 2008  commencing in-memory singleton removal
Tue Oct 28 18:41:07 2008  begin with 8385850 relations and 7510988 unique ideals
Tue Oct 28 18:41:18 2008  reduce to 8228753 relations and 6179332 ideals in 7 passes
Tue Oct 28 18:41:18 2008  max relations containing the same ideal: 20
Tue Oct 28 18:41:25 2008  removing 1410938 relations and 1010938 ideals in 400000 cliques
Tue Oct 28 18:41:26 2008  commencing in-memory singleton removal
Tue Oct 28 18:41:27 2008  begin with 6817815 relations and 6179332 unique ideals
Tue Oct 28 18:41:36 2008  reduce to 6663133 relations and 5006972 ideals in 7 passes
Tue Oct 28 18:41:36 2008  max relations containing the same ideal: 19
Tue Oct 28 18:41:42 2008  removing 1327964 relations and 927964 ideals in 400000 cliques
Tue Oct 28 18:41:42 2008  commencing in-memory singleton removal
Tue Oct 28 18:41:43 2008  begin with 5335169 relations and 5006972 unique ideals
Tue Oct 28 18:41:51 2008  reduce to 5164439 relations and 3899279 ideals in 9 passes
Tue Oct 28 18:41:51 2008  max relations containing the same ideal: 19
Tue Oct 28 18:41:56 2008  removing 377053 relations and 295218 ideals in 81835 cliques
Tue Oct 28 18:41:56 2008  commencing in-memory singleton removal
Tue Oct 28 18:41:57 2008  begin with 4787386 relations and 3899279 unique ideals
Tue Oct 28 18:42:02 2008  reduce to 4769762 relations and 3586176 ideals in 6 passes
Tue Oct 28 18:42:02 2008  max relations containing the same ideal: 18
Tue Oct 28 18:42:07 2008  relations with 0 large ideals: 142358
Tue Oct 28 18:42:07 2008  relations with 1 large ideals: 686352
Tue Oct 28 18:42:07 2008  relations with 2 large ideals: 1396880
Tue Oct 28 18:42:07 2008  relations with 3 large ideals: 1417942
Tue Oct 28 18:42:07 2008  relations with 4 large ideals: 792619
Tue Oct 28 18:42:07 2008  relations with 5 large ideals: 262925
Tue Oct 28 18:42:07 2008  relations with 6 large ideals: 65802
Tue Oct 28 18:42:07 2008  relations with 7+ large ideals: 4884
Tue Oct 28 18:42:07 2008  commencing 2-way merge
Tue Oct 28 18:42:12 2008  reduce to 3246628 relation sets and 2063042 unique ideals
Tue Oct 28 18:42:12 2008  commencing full merge
Tue Oct 28 18:42:58 2008  memory use: 188.1 MB
Tue Oct 28 18:42:59 2008  found 1609067 cycles, need 1449242
Tue Oct 28 18:43:00 2008  weight of 1449242 cycles is about 101702624 (70.18/cycle)
Tue Oct 28 18:43:00 2008  distribution of cycle lengths:
Tue Oct 28 18:43:00 2008  1 relations: 183967
Tue Oct 28 18:43:00 2008  2 relations: 144810
Tue Oct 28 18:43:00 2008  3 relations: 147743
Tue Oct 28 18:43:00 2008  4 relations: 142868
Tue Oct 28 18:43:00 2008  5 relations: 138666
Tue Oct 28 18:43:00 2008  6 relations: 127732
Tue Oct 28 18:43:00 2008  7 relations: 116050
Tue Oct 28 18:43:00 2008  8 relations: 102946
Tue Oct 28 18:43:00 2008  9 relations: 90027
Tue Oct 28 18:43:00 2008  10+ relations: 254433
Tue Oct 28 18:43:00 2008  heaviest cycle: 17 relations
Tue Oct 28 18:43:00 2008  commencing cycle optimization
Tue Oct 28 18:43:04 2008  start with 8311173 relations
Tue Oct 28 18:43:28 2008  pruned 344021 relations
Tue Oct 28 18:43:28 2008  memory use: 259.1 MB
Tue Oct 28 18:43:28 2008  distribution of cycle lengths:
Tue Oct 28 18:43:28 2008  1 relations: 183967
Tue Oct 28 18:43:28 2008  2 relations: 150111
Tue Oct 28 18:43:28 2008  3 relations: 156291
Tue Oct 28 18:43:28 2008  4 relations: 150605
Tue Oct 28 18:43:28 2008  5 relations: 147049
Tue Oct 28 18:43:28 2008  6 relations: 134232
Tue Oct 28 18:43:28 2008  7 relations: 121130
Tue Oct 28 18:43:28 2008  8 relations: 105413
Tue Oct 28 18:43:28 2008  9 relations: 89711
Tue Oct 28 18:43:28 2008  10+ relations: 210733
Tue Oct 28 18:43:28 2008  heaviest cycle: 16 relations
Tue Oct 28 18:43:30 2008  elapsed time 00:32:24

Tue Oct 28 18:49:39 2008  commencing linear algebra
Tue Oct 28 18:49:39 2008  read 1449242 cycles
Tue Oct 28 18:49:45 2008  cycles contain 4205356 unique relations
Tue Oct 28 18:50:50 2008  read 4205356 relations
Tue Oct 28 18:51:02 2008  using 32 quadratic characters above 268434108
Tue Oct 28 18:52:08 2008  building initial matrix
Tue Oct 28 18:53:21 2008  memory use: 535.9 MB
Tue Oct 28 18:53:22 2008  read 1449242 cycles
Tue Oct 28 18:53:24 2008  matrix is 1448913 x 1449242 (426.1 MB) with weight 135761514 (93.68/col)
Tue Oct 28 18:53:24 2008  sparse part has weight 95768962 (66.08/col)
Tue Oct 28 18:54:31 2008  filtering completed in 3 passes
Tue Oct 28 18:54:31 2008  matrix is 1445023 x 1445223 (425.4 MB) with weight 135504932 (93.76/col)
Tue Oct 28 18:54:31 2008  sparse part has weight 95625280 (66.17/col)
Tue Oct 28 18:54:54 2008  read 1445223 cycles
Tue Oct 28 18:54:56 2008  matrix is 1445023 x 1445223 (425.4 MB) with weight 135504932 (93.76/col)
Tue Oct 28 18:54:56 2008  sparse part has weight 95625280 (66.17/col)
Tue Oct 28 18:54:56 2008  saving the first 48 matrix rows for later
Tue Oct 28 18:54:57 2008  matrix is 1444975 x 1445223 (407.0 MB) with weight 103303242 (71.48/col)
Tue Oct 28 18:54:57 2008  sparse part has weight 92233447 (63.82/col)
Tue Oct 28 18:54:57 2008  matrix includes 64 packed rows
Tue Oct 28 18:54:57 2008  using block size 10922 for processor cache size 256 kB
Tue Oct 28 18:55:08 2008  commencing Lanczos iteration (2 threads)
Tue Oct 28 18:55:08 2008  memory use: 401.3 MB
Wed Oct 29 05:44:13 2008  lanczos halted after 22851 iterations (dim = 1444972)
Wed Oct 29 05:44:18 2008  recovered 49 nontrivial dependencies
Wed Oct 29 05:44:18 2008  elapsed time 10:54:41

Wed Oct 29 06:58:26 2008  commencing square root phase
Wed Oct 29 06:58:26 2008  reading relations for dependency 1
Wed Oct 29 06:58:26 2008  read 722524 cycles
Wed Oct 29 06:58:28 2008  cycles contain 2614791 unique relations
Wed Oct 29 06:59:15 2008  read 2614791 relations
Wed Oct 29 06:59:34 2008  multiplying 2100892 relations
Wed Oct 29 07:03:48 2008  multiply complete, coefficients have about 49.51 million bits
Wed Oct 29 07:03:49 2008  initial square root is modulo 12816931
Wed Oct 29 07:10:19 2008  prp56 factor: 64359895320324138046847817077342166028615808217898933063
Wed Oct 29 07:10:19 2008  prp80 factor: 36903084954015880064848993395715905165599046095682487205693219081526100375034279
Wed Oct 29 07:10:19 2008  elapsed time 00:11:55

Oct 29, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(26·10¹⁵⁶+1)/9 = 2(8)₁₅₅9_<157> = 3² · 223 · 233769517 · 134568092601416937915213119_<27> · C119

C119 = P52 · P67

P52 = 4694190438486921544482209313363107731432206332676001_<52>

P67 = 9747489708959753624184848714122459667180630977918143237919612742549_<67>

Number: 28889_156
N=45756572991048541133395486566429369623153492393720523352242534418823215640644591834205930308998136427613459753843866549
  ( 119 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=4694190438486921544482209313363107731432206332676001 (pp52)
 r2=9747489708959753624184848714122459667180630977918143237919612742549 (pp67)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 48.37 hours.
Scaled time: 22.88 units (timescale=0.473).
Factorization parameters were as follows:
name: 28889_156
n: 45756572991048541133395486566429369623153492393720523352242534418823215640644591834205930308998136427613459753843866549
m: 10000000000000000000000000000000
c5: 260
c0: 1
skew: 0.33
type: snfs
lss: 1
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved rational special-q in [1500000, 2700001)
Primes: RFBsize:216816, AFBsize:217216, largePrimes:5794216 encountered
Relations: rels:5821754, finalFF:597590
Max relations in full relation-set: 28
Initial matrix: 434099 x 597590 with sparse part having weight 50890701.
Pruned matrix : 346420 x 348654 with weight 28861073.
Total sieving time: 43.83 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 4.10 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 48.37 hours.
 --------- CPU info (if available) ----------

Oct 29, 2008 (2nd)

By Markus Tervooren / GGNFS

(5·10¹⁶⁹-11)/3 = 1(6)₁₆₈3_<170> = 13 · 89 · 22391 · 23029 · 461413 · 1819826843737381_<16> · 4550168374230307_<16> · C121

C121 = P60 · P62

P60 = 342855645862195973177653413327612398418129301253722970119969_<60>

P62 = 21325938610287432927341056805305788973239926323324136910316219_<62>

Number: 16663_169
N=7311718455847639845721422994958497742937731902430134270627579900735868508985975918296890634287583350087847104844156477211
  ( 121 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=342855645862195973177653413327612398418129301253722970119969 (pp60)
 r2=21325938610287432927341056805305788973239926323324136910316219 (pp62)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 93.56 hours.
Scaled time: 188.44 units (timescale=2.014).
Factorization parameters were as follows:
n: 7311718455847639845721422994958497742937731902430134270627579900735868508985975918296890634287583350087847104844156477211
m: 10000000000000000000000000000000000
c5: 1
c0: -22
skew: 1.86
type: snfs

Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 7000001)
Primes: RFBsize:412849, AFBsize:413702, largePrimes:6022667 encountered
Relations: rels:6293835, finalFF:938359
Max relations in full relation-set: 32
Initial matrix: 826615 x 938359 with sparse part having weight 53816742.
Pruned matrix : 732721 x 736918 with weight 39211480.
Total sieving time: 89.30 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 4.04 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 93.56 hours.
 --------- CPU info (if available) ----------

Oct 29, 2008

By Markus Tervooren / GGNFS

(26·10¹⁶⁶+1)/9 = 2(8)₁₆₅9_<167> = 7 · 1667 · C163

C163 = P31 · P132

P31 = 6479340028054522941348709917163_<31>

P132 = 382090664543561576649417393525054205485383414004188396956282953099429824152707303462083388779904441883425715160662357958463678303487_<132>

Number: 28889_166
N=2475695337123051580160158444501575875301130250140448100856019272336008988678454785233429504575275421106254939488292817626950800316127250740328124851220232144047381
  ( 163 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=6479340028054522941348709917163 (pp31)
 r2=382090664543561576649417393525054205485383414004188396956282953099429824152707303462083388779904441883425715160662357958463678303487 (pp132)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 78.56 hours.
Scaled time: 159.94 units (timescale=2.036).
Factorization parameters were as follows:
n: 2475695337123051580160158444501575875301130250140448100856019272336008988678454785233429504575275421106254939488292817626950800316127250740328124851220232144047381
m: 1000000000000000000000000000000000
c5: 260
c0: 1
skew: 0.33
type: snfs

Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 6150001)
Primes: RFBsize:380800, AFBsize:380647, largePrimes:5982858 encountered
Relations: rels:6228346, finalFF:897352
Max relations in full relation-set: 32
Initial matrix: 761514 x 897352 with sparse part having weight 55066587.
Pruned matrix : 649767 x 653638 with weight 38510994.
Total sieving time: 73.75 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 4.58 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 78.56 hours.
 --------- CPU info (if available) ----------

Oct 28, 2008 (2nd)

By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1

(64·10²⁴⁹-1)/9 = 7(1)₂₄₉_<250> = 13⁴ · 31 · 79 · 575149723 · 1750665933361_<13> · 133333333333333333333333333333333333333333333333333333333333333333333333333333333333_<84> · C138

C138 = P44 · P95

P44 = 27086436208081622110852425797559383058724969_<44>

P95 = 27957637508878218719963598621020965070748187141715745023108986130986591894311142081697805427129_<95>

SNFS difficulty: 168 digits.
Divisors found:
 r1=27086436208081622110852425797559383058724969
 r2=27957637508878218719963598621020965070748187141715745023108986130986591894311142081697805427129
Version: Msieve-1.38
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.953).
Factorization parameters were as follows:
n: 757272764912899866386887025526747705214803310378892063447463012260184658852997426333940202723454900300368209126720821842355792483182284001
m: 10000000000000000000000000000
c6: 4
c3: 10
c0: 25
skew: 1.36
type: snfs
lss: 0
rlim: 4400000
alim: 4400000
lpbr: 27
lpba: 27
mfbr: 54
mfba: 54
rlambda: 2.6
alambda: 2.6
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved algebraic special-q in [2200000, 4600001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 872724 x 872972
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,168,6,0,0,0,0,0,0,0,0,4400000,4400000,27,27,54,54,2.6,2.6,100000
total time: 40.00 hours.

(64·10²²⁹-1)/9 = 7(1)₂₂₉_<230> = C230

C230 = P40 · P191

P40 = 4034369654841644099524570966777671875083_<40>

P191 = 17626325100321612372043581868911704206480250854797206110017885233003976436117257470546278972236787342059112346427096034798397900124082888413527743045616320435222095135066126658177229500020917_<191>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=72303299
Step 1 took 111927ms
Step 2 took 31142ms
********** Factor found in step 2: 4034369654841644099524570966777671875083
Found probable prime factor of 40 digits: 4034369654841644099524570966777671875083
Probable prime cofactor 17626325100321612372043581868911704206480250854797206110017885233003976436117257470546278972236787342059112346427096034798397900124082888413527743045616320435222095135066126658177229500020917 has 191 digits

Oct 28, 2008

By Jo Yeong Uk / msieve v1.32 for x86_64

(64·10²⁴³-1)/9 = 7(1)₂₄₃_<244> = 13 · 67 · 12373 · 380557 · 47182356220003_<14> · 6517738858382209_<16> · 54699974406060473236679_<23> · 11669402665120428032569628031827203_<35> · 24375392270487185471964198611176415474970434465429475617027_<59> · C87

C87 = P41 · P47

P41 = 17158834697255184376964105105887004062117_<41>

P47 = 21118975572183169191742372770186676720387518241_<47>

Mon Oct 27 20:54:49 2008  
Mon Oct 27 20:54:49 2008  
Mon Oct 27 20:54:49 2008  Msieve v. 1.32
Mon Oct 27 20:54:49 2008  random seeds: 115608e0 5cb23f87
Mon Oct 27 20:54:49 2008  factoring 362377010818461224190198188942329063958140704637401162426736098893805128375151434576197 (87 digits)
Mon Oct 27 20:54:49 2008  no P-1/P+1/ECM available, skipping
Mon Oct 27 20:54:49 2008  commencing quadratic sieve (87-digit input)
Mon Oct 27 20:54:49 2008  using multiplier of 13
Mon Oct 27 20:54:49 2008  using VC8 32kb sieve core
Mon Oct 27 20:54:49 2008  sieve interval: 20 blocks of size 32768
Mon Oct 27 20:54:49 2008  processing polynomials in batches of 11
Mon Oct 27 20:54:49 2008  using a sieve bound of 1489097 (56667 primes)
Mon Oct 27 20:54:49 2008  using large prime bound of 119127760 (26 bits)
Mon Oct 27 20:54:49 2008  using double large prime bound of 344209894043680 (42-49 bits)
Mon Oct 27 20:54:49 2008  using trial factoring cutoff of 49 bits
Mon Oct 27 20:54:49 2008  polynomial 'A' values have 11 factors
Mon Oct 27 21:25:48 2008  56817 relations (16105 full + 40712 combined from 594294 partial), need 56763
Mon Oct 27 21:25:51 2008  begin with 610399 relations
Mon Oct 27 21:25:51 2008  reduce to 135207 relations in 9 passes
Mon Oct 27 21:25:51 2008  attempting to read 135207 relations
Mon Oct 27 21:25:53 2008  recovered 135207 relations
Mon Oct 27 21:25:53 2008  recovered 113112 polynomials
Mon Oct 27 21:25:53 2008  attempting to build 56817 cycles
Mon Oct 27 21:25:53 2008  found 56817 cycles in 6 passes
Mon Oct 27 21:25:53 2008  distribution of cycle lengths:
Mon Oct 27 21:25:53 2008     length 1 : 16105
Mon Oct 27 21:25:53 2008     length 2 : 11391
Mon Oct 27 21:25:53 2008     length 3 : 10003
Mon Oct 27 21:25:53 2008     length 4 : 7238
Mon Oct 27 21:25:53 2008     length 5 : 5067
Mon Oct 27 21:25:53 2008     length 6 : 3127
Mon Oct 27 21:25:53 2008     length 7 : 1795
Mon Oct 27 21:25:53 2008     length 9+: 2091
Mon Oct 27 21:25:53 2008  largest cycle: 19 relations
Mon Oct 27 21:25:53 2008  matrix is 56667 x 56817 with weight 3227551 (avg 56.81/col)
Mon Oct 27 21:25:53 2008  filtering completed in 3 passes
Mon Oct 27 21:25:53 2008  matrix is 51992 x 52056 with weight 2991184 (avg 57.46/col)
Mon Oct 27 21:25:53 2008  saving the first 48 matrix rows for later
Mon Oct 27 21:25:53 2008  matrix is 51944 x 52056 with weight 2392846 (avg 45.97/col)
Mon Oct 27 21:25:53 2008  matrix includes 64 packed rows
Mon Oct 27 21:25:53 2008  using block size 20822 for processor cache size 4096 kB
Mon Oct 27 21:25:54 2008  commencing Lanczos iteration
Mon Oct 27 21:26:06 2008  lanczos halted after 823 iterations (dim = 51940)
Mon Oct 27 21:26:06 2008  recovered 15 nontrivial dependencies
Mon Oct 27 21:26:06 2008  prp41 factor: 17158834697255184376964105105887004062117
Mon Oct 27 21:26:06 2008  prp47 factor: 21118975572183169191742372770186676720387518241
Mon Oct 27 21:26:06 2008  elapsed time 00:31:17

Oct 27, 2008 (2nd)

By Jo Yeong Uk / GMP-ECM, GGNFS

(64·10²⁴³-1)/9 = 7(1)₂₄₃_<244> = 13 · 67 · 12373 · 380557 · 47182356220003_<14> · 6517738858382209_<16> · 54699974406060473236679_<23> · 24375392270487185471964198611176415474970434465429475617027_<59> · C121

C121 = P35 · C87

P35 = 11669402665120428032569628031827203_<35>

C87 = [362377010818461224190198188942329063958140704637401162426736098893805128375151434576197_<87>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 4228723255823325591225591310871269787909747181710337388679437779965558548033222618556156136920285183366078808713840886991 (121 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1941427008
Step 1 took 3928ms
Step 2 took 2305ms
********** Factor found in step 2: 11669402665120428032569628031827203
Found probable prime factor of 35 digits: 11669402665120428032569628031827203
Composite cofactor 362377010818461224190198188942329063958140704637401162426736098893805128375151434576197 has 87 digits

(64·10²¹³-1)/9 = 7(1)₂₁₃_<214> = 13 · 382523701896683_<15> · 4067453597354015437_<19> · 348562279075051256093224790444794552907778175157643567551_<57> · C124

C124 = P30 · P94

P30 = 567258301292899201186210025281_<30>

P94 = 1778082503370430610274480465861532259362412214947513681455173686500912615751057885081460445747_<94>

Number: 71111_213
N=1008632060420536186503070653401950661490631137612965301768555874785722944164613998799848275106831807902913290493950398929907
  ( 124 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=567258301292899201186210025281 (pp30)
 r2=1778082503370430610274480465861532259362412214947513681455173686500912615751057885081460445747 (pp94)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.56 hours.
Scaled time: 25.03 units (timescale=2.371).
Factorization parameters were as follows:
n: 1008632060420536186503070653401950661490631137612965301768555874785722944164613998799848275106831807902913290493950398929907
m: 1000000000000000000000000
c6: 4
c3: 10
c0: 25
skew: 1.36
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1550001)
Primes: RFBsize:114155, AFBsize:113529, largePrimes:3493047 encountered
Relations: rels:3529121, finalFF:303069
Max relations in full relation-set: 28
Initial matrix: 227750 x 303069 with sparse part having weight 30082344.
Pruned matrix : 203350 x 204552 with weight 17555191.
Total sieving time: 10.30 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,144,6,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 10.56 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673800)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Calibrating delay using timer specific routine.. 5344.40 BogoMIPS (lpj=2672204)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)

Oct 27, 2008

By Sinkiti Sibata / GGNFS

(26·10¹⁶³+1)/9 = 2(8)₁₆₂9_<164> = 7457 · 18506641791872782624357_<23> · 40079919846728870051247378643_<29> · C109

C109 = P41 · P69

P41 = 28009093238970577101538416824495651053679_<41>

P69 = 186471808485408531378078405605085883074515478870902537239877522909513_<69>

Number: 28889_163
N=5222906270307272385287641264035510040058867306663010966297297185700537761242664898692400059453720580222748327
  ( 109 digits)
Divisors found:
 r1=28009093238970577101538416824495651053679 (pp41)
 r2=186471808485408531378078405605085883074515478870902537239877522909513 (pp69)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 28.21 hours.
Scaled time: 13.34 units (timescale=0.473).
Factorization parameters were as follows:
name: 28889_163
n: 5222906270307272385287641264035510040058867306663010966297297185700537761242664898692400059453720580222748327
skew: 14112.08
# norm 1.79e+15
c5: 223200
c4: -6134129468
c3: -76619933374282
c2: 612536663203801749
c1: 11856328080881592151098
c0: 35073061741902416693402160
# alpha -6.38
Y1: 311615672159
Y0: -471894792419104682383
# Murphy_E 1.14e-09
# M 2569326901361743041309263714221806126383752657397438348950049127272982709113883339738467089251094412998729618
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 3000001)
Primes: RFBsize:230209, AFBsize:230072, largePrimes:7400735 encountered
Relations: rels:7297161, finalFF:627508
Max relations in full relation-set: 28
Initial matrix: 460365 x 627508 with sparse part having weight 50506885.
Pruned matrix : 330047 x 332412 with weight 27258385.
Polynomial selection time: 1.35 hours.
Total sieving time: 22.24 hours.
Total relation processing time: 0.62 hours.
Matrix solve time: 3.71 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 28.21 hours.
 --------- CPU info (if available) ----------

(26·10¹⁵³+1)/9 = 2(8)₁₅₂9_<154> = 3 · 263 · 171697 · 217829018959_<12> · C134

C134 = P37 · P37 · P62

P37 = 1799406072605487269788642443251985797_<37>

P37 = 3155029794925095373974038518269034733_<37>

P62 = 17244187886143827169731047895923370766606567965331126953137387_<62>

Number: 28889_153
N=97898354655912498577542654582672781408023360921519599642012823005388701296746551513056855209262153547431585837515028847674767970483787
  ( 134 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=1799406072605487269788642443251985797 (pp37)
 r2=3155029794925095373974038518269034733 (pp37)
 r3=17244187886143827169731047895923370766606567965331126953137387 (pp62)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 37.34 hours.
Scaled time: 29.20 units (timescale=0.782).
Factorization parameters were as follows:
name: 28889_153
n: 97898354655912498577542654582672781408023360921519599642012823005388701296746551513056855209262153547431585837515028847674767970483787
m: 2000000000000000000000000000000
c5: 1625
c0: 2
skew: 0.26
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2800001)
Primes: RFBsize:216816, AFBsize:217126, largePrimes:5838600 encountered
Relations: rels:5918466, finalFF:645652
Max relations in full relation-set: 28
Initial matrix: 434008 x 645652 with sparse part having weight 54622944.
Pruned matrix : 325218 x 327452 with weight 33994766.
Total sieving time: 35.64 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.43 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 37.34 hours.
 --------- CPU info (if available) ----------

Oct 26, 2008 (3rd)

Factorizations of 711...11 were extended to n=250. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Oct 26, 2008 (2nd)

By Serge Batalov / GMP-ECM 6.2.1

4·10¹⁸⁷-9 = 3(9)₁₈₆1_<188> = 53 · 10684013423190202598370871_<26> · C161

C161 = P34 · C128

P34 = 1626349888286077666713489931346081_<34>

C128 = [43434588619417477329933277408700569125776242676471321059204704968470235596379158309505822359339758001320385530719040417854267197_<128>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1057010532
Step 1 took 19422ms
Step 2 took 12488ms
********** Factor found in step 2: 1626349888286077666713489931346081
Found probable prime factor of 34 digits: 1626349888286077666713489931346081
Composite cofactor 43434588619417477329933277408700569125776242676471321059204704968470235596379158309505822359339758001320385530719040417854267197 has 128 digits

Oct 26, 2008

By Sinkiti Sibata / GGNFS

(26·10¹⁵⁰+1)/9 = 2(8)₁₄₉9_<151> = 3 · 71 · C149

C149 = P55 · P94

P55 = 3017003463910021527742494989600535726691290449142078503_<55>

P94 = 4495473338205509039310196795964079881302715548106765302223250101153564129630339087731808697251_<94>

Number: 28889_150
N=13562858633281168492436098069900886802295252999478351591027647365675534689619196661450182576943140323422013562858633281168492436098069900886802295253
  ( 149 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=3017003463910021527742494989600535726691290449142078503 (pp55)
 r2=4495473338205509039310196795964079881302715548106765302223250101153564129630339087731808697251 (pp94)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 21.15 hours.
Scaled time: 16.37 units (timescale=0.774).
Factorization parameters were as follows:
name: 28889_150
n: 13562858633281168492436098069900886802295252999478351591027647365675534689619196661450182576943140323422013562858633281168492436098069900886802295253
m: 1000000000000000000000000000000
c5: 26
c0: 1
skew: 0.52
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:176443, largePrimes:5632146 encountered
Relations: rels:5707812, finalFF:631681
Max relations in full relation-set: 28
Initial matrix: 352813 x 631681 with sparse part having weight 54511948.
Pruned matrix : 239959 x 241787 with weight 23574679.
Total sieving time: 20.32 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.62 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 21.15 hours.
 --------- CPU info (if available) ----------

Oct 25, 2008 (4th)

By Jo Yeong Uk / GMP-ECM

(26·10¹⁶¹+1)/9 = 2(8)₁₆₀9_<162> = 76423 · 220372643 · 1474229971_<10> · 147156782343257_<15> · C125

C125 = P35 · P91

P35 = 10361570462978943081240648695403377_<35>

P91 = 7630938828349621287861991098515099831174529504441192479176022590263801165241085184406853279_<91>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 79068510368626578914580689981349106518885530717911113165602486185883192699712154881358461884808530837102009408078304160123183 (125 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4091174184
Step 1 took 3914ms
Step 2 took 2300ms
********** Factor found in step 2: 10361570462978943081240648695403377
Found probable prime factor of 35 digits: 10361570462978943081240648695403377
Probable prime cofactor 7630938828349621287861991098515099831174529504441192479176022590263801165241085184406853279 has 91 digits

Oct 25, 2008 (3rd)

By Robert Backstrom / GMP-ECM

(13·10²⁰⁰-31)/9 = 1(4)₁₉₉1_<201> = 3 · C200

C200 = P42 · P159

P42 = 114479882131369179149234001603952546215491_<42>

P159 = 420581741103617402874421898652662038794499187212832147446391522348358265479791351017478571599457943977151584144697838957610036655579567326450207149555866212817_<159>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 48148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148147 (200 digits)
Using B1=5144000, B2=11416472350, polynomial Dickson(12), sigma=3111509481
Step 1 took 94705ms
Step 2 took 35047ms
********** Factor found in step 2: 114479882131369179149234001603952546215491
Found probable prime factor of 42 digits: 114479882131369179149234001603952546215491
Probable prime cofactor 420581741103617402874421898652662038794499187212832147446391522348358265479791351017478571599457943977151584144697838957610036655579567326450207149555866212817 has 159 digits

Oct 25, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(26·10¹⁴⁹+1)/9 = 2(8)₁₄₈9_<150> = 20179355711_<11> · 106315628013331801_<18> · C123

C123 = P38 · P85

P38 = 15750235873838074915509902031059707619_<38>

P85 = 8549473520716549201848743714153027681604986908351797552246043947706893694574847601621_<85>

Number: 28889_149
N=134656224548418501202256267790773535854432105692255442723175176680010180799465933023419580788851221043186204159831650450399
  ( 123 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=15750235873838074915509902031059707619 (pp38)
 r2=8549473520716549201848743714153027681604986908351797552246043947706893694574847601621 (pp85)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.14 hours.
Scaled time: 24.36 units (timescale=1.009).
Factorization parameters were as follows:
name: 28889_149
n: 134656224548418501202256267790773535854432105692255442723175176680010180799465933023419580788851221043186204159831650450399
m: 1000000000000000000000000000000
c5: 13
c0: 5
skew: 0.83
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:177028, largePrimes:5838819 encountered
Relations: rels:6030865, finalFF:724886
Max relations in full relation-set: 28
Initial matrix: 353395 x 724886 with sparse part having weight 65294965.
Pruned matrix : 231892 x 233722 with weight 29627846.
Total sieving time: 23.59 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 24.14 hours.
 --------- CPU info (if available) ----------

(26·10¹⁴³+1)/9 = 2(8)₁₄₂9_<144> = 61 · 1187 · 117617 · 63544867 · 163152643 · 5008510873_<10> · C108

C108 = P51 · P58

P51 = 242354794037594091064567695394505940331886690503589_<51>

P58 = 2695537401622218909188582052352420335657517229979365604083_<58>

Number: 28889_143
N=653276411790784408103837393616365788765257143439082180152626896708423506902293078416685615987036100464553887
  ( 108 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=242354794037594091064567695394505940331886690503589 (pp51)
 r2=2695537401622218909188582052352420335657517229979365604083 (pp58)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 17.79 hours.
Scaled time: 13.79 units (timescale=0.775).
Factorization parameters were as follows:
name: 28889_143
n: 653276411790784408103837393616365788765257143439082180152626896708423506902293078416685615987036100464553887
m: 20000000000000000000000000000
c5: 1625
c0: 2
skew: 0.26
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2750001)
Primes: RFBsize:100021, AFBsize:99838, largePrimes:2898969 encountered
Relations: rels:2922932, finalFF:246910
Max relations in full relation-set: 28
Initial matrix: 199925 x 246910 with sparse part having weight 29217163.
Pruned matrix : 187821 x 188884 with weight 20844043.
Total sieving time: 17.28 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.34 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 17.79 hours.
 --------- CPU info (if available) ----------

(26·10¹²⁴+1)/9 = 2(8)₁₂₃9_<125> = 7 · 46359253 · 7190093831059_<13> · C104

C104 = P36 · P68

P36 = 773275929802648482592761218854738987_<36>

P68 = 16011326705494942557586789847113370037134298211097213575458840860723_<68>

Number: 28889_124
N=12381173545565578195482031153109208249880322714939240951946839415492096378310151279966671538102585107601
  ( 104 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=773275929802648482592761218854738987 (pp36)
 r2=16011326705494942557586789847113370037134298211097213575458840860723 (pp68)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 2.98 hours.
Scaled time: 1.41 units (timescale=0.473).
Factorization parameters were as follows:
name:  28889_124
n: 12381173545565578195482031153109208249880322714939240951946839415492096378310151279966671538102585107601
m: 10000000000000000000000000
c5: 13
c0: 5
skew: 0.83
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:64323, largePrimes:2131178 encountered
Relations: rels:2175070, finalFF:179780
Max relations in full relation-set: 28
Initial matrix: 113486 x 179780 with sparse part having weight 16502796.
Pruned matrix : 98778 x 99409 with weight 6491834.
Total sieving time: 2.75 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.98 hours.
 --------- CPU info (if available) ----------

Oct 25, 2008

By matsui / GGNFS

9·10¹⁶⁹+1 = 9(0)₁₆₈1_<170> = 7 · 13 · 23 · 26680727 · 2783029903_<10> · C150

C150 = P59 · P92

P59 = 11273267512862863753557060067341695659241008487576093151619_<59>

P92 = 51369807273759613054098903544267959129913929401519425473243091409904983605073403539507467663_<92>

GGNFS-0.77.1-20060513-pentium-m
579105579481300680664203254199355666978495794312124657905662485914995879034725283343220643005997344743212838687825264828908375906570902705963398596397
=
11273267512862863753557060067341695659241008487576093151619* 51369807273759613054098903544267959129913929401519425473243091409904983605073403539507467663

Oct 24, 2008 (5th)

By Jo Yeong Uk / GMP-ECM

(26·10¹⁵⁸+1)/9 = 2(8)₁₅₇9_<159> = 105188220778305713_<18> · 24222934745760446147_<20> · C123

C123 = P33 · P90

P33 = 417696229209318550390360676653337_<33>

P90 = 271441605526889400486767802727114167273548745703371791610999906296442521703183253981680827_<90>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 113380135079105024067914279723335761157532854479549372542241163306012886790982389958922970574426694448602106850588458469699 (123 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1028318472
Step 1 took 3951ms
Step 2 took 2281ms
********** Factor found in step 2: 417696229209318550390360676653337
Found probable prime factor of 33 digits: 417696229209318550390360676653337
Probable prime cofactor 271441605526889400486767802727114167273548745703371791610999906296442521703183253981680827 has 90 digits

Oct 24, 2008 (4th)

By Sinkiti Sibata / GGNFS

(26·10¹³²+1)/9 = 2(8)₁₃₁9_<133> = 3 · 229 · 2651273 · 36877893731033_<14> · C110

C110 = P55 · P56

P55 = 2726275397938340164900433126360846604110296672882596679_<55>

P56 = 15775524934216280471244052315246368790827525421860015377_<56>

Number: 28889_132
N=43008425517716697593767624874994058946918870477503849624665527408666408016173678755798405053073648918629132983
  ( 110 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=2726275397938340164900433126360846604110296672882596679 (pp55)
 r2=15775524934216280471244052315246368790827525421860015377 (pp56)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.84 hours.
Scaled time: 4.59 units (timescale=0.786).
Factorization parameters were as follows:
name: 28889_132
n: 43008425517716697593767624874994058946918870477503849624665527408666408016173678755798405053073648918629132983
m: 100000000000000000000000000
c5: 2600
c0: 1
skew: 0.21
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1150001)
Primes: RFBsize:63951, AFBsize:64003, largePrimes:1522242 encountered
Relations: rels:1518630, finalFF:162295
Max relations in full relation-set: 28
Initial matrix: 128021 x 162295 with sparse part having weight 14413076.
Pruned matrix : 119236 x 119940 with weight 8876334.
Total sieving time: 5.66 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.84 hours.
 --------- CPU info (if available) ----------

Oct 24, 2008 (3rd)

By Sinkiti Sibata / Msieve, GGNFS

(26·10¹⁰⁹+1)/9 = 2(8)₁₀₈9_<110> = 107 · 2185727459_<10> · 3764215737119_<13> · C86

C86 = P40 · P47

P40 = 2352715497850448405626204828134063318937_<40>

P47 = 13947845666568227036142246713980273600953265951_<47>

Fri Oct 24 07:38:35 2008  Msieve v. 1.38
Fri Oct 24 07:38:35 2008  random seeds: 27520f42 5012447c
Fri Oct 24 07:38:35 2008  factoring 32815312661361285664799561745417563767797352627553000827562716332375330588420695614087 (86 digits)
Fri Oct 24 07:38:36 2008  searching for 15-digit factors
Fri Oct 24 07:38:38 2008  commencing quadratic sieve (86-digit input)
Fri Oct 24 07:38:38 2008  using multiplier of 7
Fri Oct 24 07:38:38 2008  using 64kb Pentium 4 sieve core
Fri Oct 24 07:38:38 2008  sieve interval: 8 blocks of size 65536
Fri Oct 24 07:38:38 2008  processing polynomials in batches of 13
Fri Oct 24 07:38:38 2008  using a sieve bound of 1461403 (55577 primes)
Fri Oct 24 07:38:38 2008  using large prime bound of 116912240 (26 bits)
Fri Oct 24 07:38:38 2008  using double large prime bound of 332772803587280 (41-49 bits)
Fri Oct 24 07:38:38 2008  using trial factoring cutoff of 49 bits
Fri Oct 24 07:38:38 2008  polynomial 'A' values have 11 factors
Fri Oct 24 08:44:54 2008  55888 relations (15735 full + 40153 combined from 584474 partial), need 55673
Fri Oct 24 08:44:57 2008  begin with 600209 relations
Fri Oct 24 08:44:57 2008  reduce to 133634 relations in 11 passes
Fri Oct 24 08:44:57 2008  attempting to read 133634 relations
Fri Oct 24 08:45:01 2008  recovered 133634 relations
Fri Oct 24 08:45:01 2008  recovered 114115 polynomials
Fri Oct 24 08:45:01 2008  attempting to build 55888 cycles
Fri Oct 24 08:45:01 2008  found 55887 cycles in 5 passes
Fri Oct 24 08:45:01 2008  distribution of cycle lengths:
Fri Oct 24 08:45:01 2008     length 1 : 15735
Fri Oct 24 08:45:01 2008     length 2 : 10950
Fri Oct 24 08:45:01 2008     length 3 : 9687
Fri Oct 24 08:45:01 2008     length 4 : 7328
Fri Oct 24 08:45:01 2008     length 5 : 5058
Fri Oct 24 08:45:01 2008     length 6 : 3109
Fri Oct 24 08:45:01 2008     length 7 : 1856
Fri Oct 24 08:45:01 2008     length 9+: 2164
Fri Oct 24 08:45:01 2008  largest cycle: 19 relations
Fri Oct 24 08:45:01 2008  matrix is 55577 x 55887 (12.5 MB) with weight 3052144 (54.61/col)
Fri Oct 24 08:45:01 2008  sparse part has weight 3052144 (54.61/col)
Fri Oct 24 08:45:02 2008  filtering completed in 3 passes
Fri Oct 24 08:45:02 2008  matrix is 51138 x 51202 (11.5 MB) with weight 2815779 (54.99/col)
Fri Oct 24 08:45:02 2008  sparse part has weight 2815779 (54.99/col)
Fri Oct 24 08:45:02 2008  saving the first 48 matrix rows for later
Fri Oct 24 08:45:03 2008  matrix is 51090 x 51202 (6.9 MB) with weight 2162007 (42.23/col)
Fri Oct 24 08:45:03 2008  sparse part has weight 1511643 (29.52/col)
Fri Oct 24 08:45:03 2008  matrix includes 64 packed rows
Fri Oct 24 08:45:03 2008  using block size 20480 for processor cache size 512 kB
Fri Oct 24 08:45:03 2008  commencing Lanczos iteration
Fri Oct 24 08:45:03 2008  memory use: 7.1 MB
Fri Oct 24 08:45:30 2008  lanczos halted after 809 iterations (dim = 51090)
Fri Oct 24 08:45:30 2008  recovered 18 nontrivial dependencies
Fri Oct 24 08:45:30 2008  prp40 factor: 2352715497850448405626204828134063318937
Fri Oct 24 08:45:30 2008  prp47 factor: 13947845666568227036142246713980273600953265951
Fri Oct 24 08:45:30 2008  elapsed time 01:06:55

(26·10¹⁴⁰+1)/9 = 2(8)₁₃₉9_<141> = 31 · 4973 · 13349257 · 146756720381_<12> · C117

C117 = P41 · P77

P41 = 16946406410302077950728265839823308474681_<41>

P77 = 56444025048774398773331902576688228725404795527707944697772162262625763068639_<77>

Number: 28889_140
N=956523387909801529433876566582169079255855390436023481092130570669948064133375135303153768545553242649095876996629159
  ( 117 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=16946406410302077950728265839823308474681 (pp41)
 r2=56444025048774398773331902576688228725404795527707944697772162262625763068639 (pp77)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 7.86 hours.
Scaled time: 7.93 units (timescale=1.009).
Factorization parameters were as follows:
name: 28889_140
n: 956523387909801529433876566582169079255855390436023481092130570669948064133375135303153768545553242649095876996629159
m: 10000000000000000000000000000
c5: 26
c0: 1
skew: 0.52
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1550001)
Primes: RFBsize:100021, AFBsize:100158, largePrimes:2845541 encountered
Relations: rels:2958063, finalFF:396703
Max relations in full relation-set: 28
Initial matrix: 200247 x 396703 with sparse part having weight 33108599.
Pruned matrix : 147491 x 148556 with weight 12955765.
Total sieving time: 7.67 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 7.86 hours.
 --------- CPU info (if available) ----------

(26·10¹¹⁸+1)/9 = 2(8)₁₁₇9_<119> = 7 · 43 · 347 · 18493 · 142596099014873898701_<21> · C90

C90 = P39 · P51

P39 = 310504758589188668868039465733010830759_<39>

P51 = 337793737293839609947074217344570551540349654109001_<51>

Fri Oct 24 08:55:48 2008  Msieve v. 1.38
Fri Oct 24 08:55:48 2008  random seeds: a74e622f fe874ab3
Fri Oct 24 08:55:48 2008  factoring 104886562851363485405548252303473041147564571797863156376514452609058806792242120949561759 (90 digits)
Fri Oct 24 08:55:49 2008  searching for 15-digit factors
Fri Oct 24 08:55:51 2008  commencing quadratic sieve (90-digit input)
Fri Oct 24 08:55:51 2008  using multiplier of 41
Fri Oct 24 08:55:51 2008  using 64kb Pentium 4 sieve core
Fri Oct 24 08:55:51 2008  sieve interval: 17 blocks of size 65536
Fri Oct 24 08:55:51 2008  processing polynomials in batches of 6
Fri Oct 24 08:55:51 2008  using a sieve bound of 1561267 (59333 primes)
Fri Oct 24 08:55:51 2008  using large prime bound of 124901360 (26 bits)
Fri Oct 24 08:55:51 2008  using double large prime bound of 374818364744400 (42-49 bits)
Fri Oct 24 08:55:51 2008  using trial factoring cutoff of 49 bits
Fri Oct 24 08:55:51 2008  polynomial 'A' values have 12 factors
Fri Oct 24 11:06:35 2008  59936 relations (15999 full + 43937 combined from 627733 partial), need 59429
Fri Oct 24 11:06:37 2008  begin with 643732 relations
Fri Oct 24 11:06:38 2008  reduce to 145799 relations in 9 passes
Fri Oct 24 11:06:38 2008  attempting to read 145799 relations
Fri Oct 24 11:06:42 2008  recovered 145799 relations
Fri Oct 24 11:06:42 2008  recovered 126067 polynomials
Fri Oct 24 11:06:42 2008  attempting to build 59936 cycles
Fri Oct 24 11:06:42 2008  found 59936 cycles in 5 passes
Fri Oct 24 11:06:42 2008  distribution of cycle lengths:
Fri Oct 24 11:06:42 2008     length 1 : 15999
Fri Oct 24 11:06:42 2008     length 2 : 11788
Fri Oct 24 11:06:42 2008     length 3 : 10497
Fri Oct 24 11:06:42 2008     length 4 : 7907
Fri Oct 24 11:06:42 2008     length 5 : 5609
Fri Oct 24 11:06:42 2008     length 6 : 3532
Fri Oct 24 11:06:42 2008     length 7 : 2083
Fri Oct 24 11:06:42 2008     length 9+: 2521
Fri Oct 24 11:06:42 2008  largest cycle: 22 relations
Fri Oct 24 11:06:42 2008  matrix is 59333 x 59936 (14.6 MB) with weight 3594607 (59.97/col)
Fri Oct 24 11:06:42 2008  sparse part has weight 3594607 (59.97/col)
Fri Oct 24 11:06:43 2008  filtering completed in 3 passes
Fri Oct 24 11:06:43 2008  matrix is 55352 x 55416 (13.5 MB) with weight 3320978 (59.93/col)
Fri Oct 24 11:06:43 2008  sparse part has weight 3320978 (59.93/col)
Fri Oct 24 11:06:44 2008  saving the first 48 matrix rows for later
Fri Oct 24 11:06:44 2008  matrix is 55304 x 55416 (8.4 MB) with weight 2564229 (46.27/col)
Fri Oct 24 11:06:44 2008  sparse part has weight 1857421 (33.52/col)
Fri Oct 24 11:06:44 2008  matrix includes 64 packed rows
Fri Oct 24 11:06:44 2008  using block size 21845 for processor cache size 512 kB
Fri Oct 24 11:06:44 2008  commencing Lanczos iteration
Fri Oct 24 11:06:44 2008  memory use: 8.2 MB
Fri Oct 24 11:07:15 2008  lanczos halted after 876 iterations (dim = 55304)
Fri Oct 24 11:07:15 2008  recovered 19 nontrivial dependencies
Fri Oct 24 11:07:16 2008  prp39 factor: 310504758589188668868039465733010830759
Fri Oct 24 11:07:16 2008  prp51 factor: 337793737293839609947074217344570551540349654109001
Fri Oct 24 11:07:16 2008  elapsed time 02:11:28

(26·10¹³⁵+1)/9 = 2(8)₁₃₄9_<136> = 3 · 3623 · 8298691 · C125

C125 = P55 · P71

P55 = 2984924145121567481231370167761731005911594902352492537_<55>

P71 = 10729966269440986387424384155216021254035129543325817268738099540010143_<71>

Number: 28889_135
N=32028135393994390893512870715772478008650433931356742226952684544130115555067978734842948059021629198081409882507694311802791
  ( 125 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=2984924145121567481231370167761731005911594902352492537 (pp55)
 r2=10729966269440986387424384155216021254035129543325817268738099540010143 (pp71)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.86 hours.
Scaled time: 4.26 units (timescale=0.728).
Factorization parameters were as follows:
name: 28889_135
n: 32028135393994390893512870715772478008650433931356742226952684544130115555067978734842948059021629198081409882507694311802791
m: 1000000000000000000000000000
c5: 26
c0: 1
skew: 0.52
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:63993, largePrimes:1584823 encountered
Relations: rels:1636631, finalFF:222218
Max relations in full relation-set: 28
Initial matrix: 142559 x 222218 with sparse part having weight 16894199.
Pruned matrix : 118197 x 118973 with weight 7602832.
Total sieving time: 5.70 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.86 hours.
 --------- CPU info (if available) ----------

(26·10¹⁴⁴+1)/9 = 2(8)₁₄₃9_<145> = 3 · C144

C144 = P40 · P105

P40 = 3868456166380275987258850199506057417163_<40>

P105 = 248926941794460034322836458820266164478157735098297360503167305646685102364493278068850644610523325296601_<105>

Number: 28889_144
N=962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962963
  ( 144 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=3868456166380275987258850199506057417163 (pp40)
 r2=248926941794460034322836458820266164478157735098297360503167305646685102364493278068850644610523325296601 (pp105)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 13.04 hours.
Scaled time: 13.00 units (timescale=0.997).
Factorization parameters were as follows:
name: 28889_144
n: 962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962963
m: 100000000000000000000000000000
c5: 13
c0: 5
skew: 0.83
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2450001)
Primes: RFBsize:114155, AFBsize:114927, largePrimes:2920308 encountered
Relations: rels:2974362, finalFF:340461
Max relations in full relation-set: 28
Initial matrix: 229147 x 340461 with sparse part having weight 34112156.
Pruned matrix : 196490 x 197699 with weight 18660001.
Total sieving time: 12.72 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.22 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 13.04 hours.
 --------- CPU info (if available) ----------

(26·10¹³⁶+1)/9 = 2(8)₁₃₅9_<137> = 7² · 1009163 · 92173330259_<11> · C118

C118 = P39 · P80

P39 = 109003884098615801826326739083592367603_<39>

P80 = 58146849261168928709085037160922928516795192130437343258069237123101709831491811_<80>

Number: 28889_136
N=6338232417564141772974103575750162136421796142704203282418999024391507789321722903633658782706570980626231650996199033
  ( 118 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=109003884098615801826326739083592367603 (pp39)
 r2=58146849261168928709085037160922928516795192130437343258069237123101709831491811 (pp80)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.84 hours.
Scaled time: 8.22 units (timescale=0.759).
Factorization parameters were as follows:
name: 28889_136
n: 6338232417564141772974103575750162136421796142704203282418999024391507789321722903633658782706570980626231650996199033
m: 1000000000000000000000000000
c5: 260
c0: 1
skew: 0.33
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1375001)
Primes: RFBsize:78498, AFBsize:64178, largePrimes:1540035 encountered
Relations: rels:1534558, finalFF:167204
Max relations in full relation-set: 28
Initial matrix: 142743 x 167204 with sparse part having weight 14162172.
Pruned matrix : 135478 x 136255 with weight 9964494.
Total sieving time: 10.56 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 10.84 hours.
 --------- CPU info (if available) ----------

(26·10¹⁴⁶+1)/9 = 2(8)₁₄₅9_<147> = 17 · 1367 · 185599 · 5265763 · 20930509 · C123

C123 = P58 · P66

P58 = 1124073153303578585771807081716025889983932995108149151131_<58>

P66 = 540632434021785268234902288892949509330978466439075267476173783637_<66>

Number: 28889_146
N=607710404889057066896460732610797716908669403889768225367727440828283420463903579304033251169460502873600370283178007843447
  ( 123 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=1124073153303578585771807081716025889983932995108149151131 (pp58)
 r2=540632434021785268234902288892949509330978466439075267476173783637 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 15.54 hours.
Scaled time: 15.59 units (timescale=1.003).
Factorization parameters were as follows:
name: 28889_146
n: 607710404889057066896460732610797716908669403889768225367727440828283420463903579304033251169460502873600370283178007843447
m: 100000000000000000000000000000
c5: 260
c0: 1
skew: 0.33
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2850001)
Primes: RFBsize:114155, AFBsize:114352, largePrimes:2879800 encountered
Relations: rels:2888648, finalFF:289991
Max relations in full relation-set: 28
Initial matrix: 228574 x 289991 with sparse part having weight 30172774.
Pruned matrix : 209836 x 211042 with weight 20187694.
Total sieving time: 15.18 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.27 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 15.54 hours.
 --------- CPU info (if available) ----------

Oct 24, 2008 (2nd)

By Jo Yeong Uk / GGNFS

(26·10¹²⁷+1)/9 = 2(8)₁₂₆9_<128> = C128

C128 = P33 · P46 · P49

P33 = 458085681516861371474360406126427_<33>

P46 = 7023583414196555680661945198122510555776461537_<46>

P49 = 8978946353297513072321536821597066798123200152411_<49>

Number: 28889_127
N=28888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889
  ( 128 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=458085681516861371474360406126427 (pp33)
 r2=7023583414196555680661945198122510555776461537 (pp46)
 r3=8978946353297513072321536821597066798123200152411 (pp49)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.91 hours.
Scaled time: 4.57 units (timescale=2.386).
Factorization parameters were as follows:
n: 28888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889
m: 20000000000000000000000000
c5: 325
c0: 4
skew: 0.41
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 950001)
Primes: RFBsize:78498, AFBsize:78521, largePrimes:1556455 encountered
Relations: rels:1594578, finalFF:212343
Max relations in full relation-set: 28
Initial matrix: 157086 x 212343 with sparse part having weight 10787721.
Pruned matrix : 132986 x 133835 with weight 5333440.
Total sieving time: 1.85 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 1.91 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673800)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Calibrating delay using timer specific routine.. 5344.40 BogoMIPS (lpj=2672204)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)

Oct 24, 2008

By Serge Batalov / Msieve, GMP-ECM 6.2.1, Msieve-1.38

(26·10¹⁴⁵+1)/9 = 2(8)₁₄₄9_<146> = 23 · 16034479 · 187957327080463607012417_<24> · 588289017691633394319116788695937_<33> · C81

C81 = P32 · P50

P32 = 54896618346979991955469420943911_<32>

P50 = 12904837953364134191960473735409301929999830768343_<50>

Thu Oct 23 10:29:56 2008  Msieve v. 1.38
Thu Oct 23 10:29:56 2008  random seeds: bf8006ca f25a0719
Thu Oct 23 10:29:56 2008  factoring 708431963955453258881716546076869813358455186906357975700925723287910831437409473 (81 digits)
Thu Oct 23 10:29:57 2008  searching for 15-digit factors
Thu Oct 23 10:29:57 2008  commencing quadratic sieve (81-digit input)
Thu Oct 23 10:29:57 2008  using multiplier of 29
Thu Oct 23 10:29:57 2008  using 64kb Opteron sieve core
Thu Oct 23 10:29:57 2008  sieve interval: 6 blocks of size 65536
Thu Oct 23 10:29:57 2008  processing polynomials in batches of 17
Thu Oct 23 10:29:57 2008  using a sieve bound of 1319687 (50882 primes)
Thu Oct 23 10:29:57 2008  using large prime bound of 126689952 (26 bits)
Thu Oct 23 10:29:57 2008  using trial factoring cutoff of 27 bits
Thu Oct 23 10:29:57 2008  polynomial 'A' values have 10 factors
Thu Oct 23 10:42:21 2008  51080 relations (26277 full + 24803 combined from 272800 partial), need 50978
Thu Oct 23 10:42:21 2008  begin with 299077 relations
Thu Oct 23 10:42:21 2008  reduce to 72762 relations in 2 passes
Thu Oct 23 10:42:21 2008  attempting to read 72762 relations
Thu Oct 23 10:42:22 2008  recovered 72762 relations
Thu Oct 23 10:42:22 2008  recovered 63176 polynomials
Thu Oct 23 10:42:22 2008  attempting to build 51080 cycles
Thu Oct 23 10:42:22 2008  found 51080 cycles in 1 passes
Thu Oct 23 10:42:22 2008  distribution of cycle lengths:
Thu Oct 23 10:42:22 2008     length 1 : 26277
Thu Oct 23 10:42:22 2008     length 2 : 24803
Thu Oct 23 10:42:22 2008  largest cycle: 2 relations
Thu Oct 23 10:42:22 2008  matrix is 50882 x 51080 (7.6 MB) with weight 1575931 (30.85/col)
Thu Oct 23 10:42:22 2008  sparse part has weight 1575931 (30.85/col)
Thu Oct 23 10:42:22 2008  filtering completed in 3 passes
Thu Oct 23 10:42:22 2008  matrix is 36078 x 36141 (5.9 MB) with weight 1255285 (34.73/col)
Thu Oct 23 10:42:22 2008  sparse part has weight 1255285 (34.73/col)
Thu Oct 23 10:42:22 2008  saving the first 48 matrix rows for later
Thu Oct 23 10:42:22 2008  matrix is 36030 x 36141 (4.6 MB) with weight 1016694 (28.13/col)
Thu Oct 23 10:42:22 2008  sparse part has weight 840697 (23.26/col)
Thu Oct 23 10:42:22 2008  matrix includes 64 packed rows
Thu Oct 23 10:42:22 2008  using block size 14456 for processor cache size 1024 kB
Thu Oct 23 10:42:22 2008  commencing Lanczos iteration
Thu Oct 23 10:42:22 2008  memory use: 4.3 MB
Thu Oct 23 10:42:27 2008  lanczos halted after 571 iterations (dim = 36030)
Thu Oct 23 10:42:27 2008  recovered 18 nontrivial dependencies
Thu Oct 23 10:42:27 2008  prp32 factor: 54896618346979991955469420943911
Thu Oct 23 10:42:27 2008  prp50 factor: 12904837953364134191960473735409301929999830768343
Thu Oct 23 10:42:27 2008  elapsed time 00:12:31

(26·10¹⁴¹+1)/9 = 2(8)₁₄₀9_<142> = 3 · 19 · 29 · 3296148577_<10> · 5839065893291_<13> · 35712359448084329_<17> · 144912971424315491_<18> · C83

C83 = P37 · P46

P37 = 7537297685684934579476791673851030409_<37>

P46 = 2327910906718027614464758526910877086171667909_<46>

Thu Oct 23 10:32:00 2008  Msieve v. 1.38
Thu Oct 23 10:32:00 2008  random seeds: f4ffedc8 bb9bb07a
Thu Oct 23 10:32:00 2008  factoring 17546157489686507164223646012583316051508274916630319119035081251725924541808444781 (83 digits)
Thu Oct 23 10:32:01 2008  searching for 15-digit factors
Thu Oct 23 10:32:01 2008  commencing quadratic sieve (83-digit input)
Thu Oct 23 10:32:01 2008  using multiplier of 69
Thu Oct 23 10:32:01 2008  using 64kb Opteron sieve core
Thu Oct 23 10:32:01 2008  sieve interval: 6 blocks of size 65536
Thu Oct 23 10:32:01 2008  processing polynomials in batches of 17
Thu Oct 23 10:32:01 2008  using a sieve bound of 1367749 (52320 primes)
Thu Oct 23 10:32:01 2008  using large prime bound of 124465159 (26 bits)
Thu Oct 23 10:32:01 2008  using trial factoring cutoff of 27 bits
Thu Oct 23 10:32:01 2008  polynomial 'A' values have 11 factors
Thu Oct 23 10:49:00 2008  52549 relations (27310 full + 25239 combined from 272691 partial), need 52416
Thu Oct 23 10:49:01 2008  begin with 300001 relations
Thu Oct 23 10:49:01 2008  reduce to 74599 relations in 2 passes
Thu Oct 23 10:49:01 2008  attempting to read 74599 relations
Thu Oct 23 10:49:01 2008  recovered 74599 relations
Thu Oct 23 10:49:01 2008  recovered 67221 polynomials
Thu Oct 23 10:49:01 2008  attempting to build 52549 cycles
Thu Oct 23 10:49:01 2008  found 52549 cycles in 1 passes
Thu Oct 23 10:49:01 2008  distribution of cycle lengths:
Thu Oct 23 10:49:01 2008     length 1 : 27310
Thu Oct 23 10:49:01 2008     length 2 : 25239
Thu Oct 23 10:49:01 2008  largest cycle: 2 relations
Thu Oct 23 10:49:01 2008  matrix is 52320 x 52549 (8.1 MB) with weight 1707055 (32.49/col)
Thu Oct 23 10:49:01 2008  sparse part has weight 1707055 (32.49/col)
Thu Oct 23 10:49:02 2008  filtering completed in 3 passes
Thu Oct 23 10:49:02 2008  matrix is 37474 x 37538 (6.3 MB) with weight 1347017 (35.88/col)
Thu Oct 23 10:49:02 2008  sparse part has weight 1347017 (35.88/col)
Thu Oct 23 10:49:02 2008  saving the first 48 matrix rows for later
Thu Oct 23 10:49:02 2008  matrix is 37426 x 37538 (4.0 MB) with weight 985377 (26.25/col)
Thu Oct 23 10:49:02 2008  sparse part has weight 680625 (18.13/col)
Thu Oct 23 10:49:02 2008  matrix includes 64 packed rows
Thu Oct 23 10:49:02 2008  using block size 15015 for processor cache size 1024 kB
Thu Oct 23 10:49:02 2008  commencing Lanczos iteration
Thu Oct 23 10:49:02 2008  memory use: 4.1 MB
Thu Oct 23 10:49:06 2008  lanczos halted after 593 iterations (dim = 37426)
Thu Oct 23 10:49:06 2008  recovered 19 nontrivial dependencies
Thu Oct 23 10:49:06 2008  prp37 factor: 7537297685684934579476791673851030409
Thu Oct 23 10:49:06 2008  prp46 factor: 2327910906718027614464758526910877086171667909
Thu Oct 23 10:49:06 2008  elapsed time 00:17:06

(26·10¹²³+1)/9 = 2(8)₁₂₂9_<124> = 3 · 19 · 23 · 293673451 · 14086235410802221_<17> · C96

C96 = P31 · P66

P31 = 2260206644216843897235550228849_<31>

P66 = 235678719982591680453016546251331940361325353146335698040419053881_<66>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1715797540
Step 1 took 8517ms
Step 2 took 8480ms
********** Factor found in step 2: 2260206644216843897235550228849
Found probable prime factor of 31 digits: 2260206644216843897235550228849
Probable prime cofactor 235678719982591680453016546251331940361325353146335698040419053881 has 66 digits

(26·10¹⁶⁸+1)/9 = 2(8)₁₆₇9_<169> = 3 · 156641 · 21214442884961_<14> · 23964088941151470239380261199_<29> · C122

C122 = P35 · P87

P35 = 26698194639575122525661827534142287_<35>

P87 = 452928540577266887157236259134255076239219768187618558929062743927670190164498760454451_<87>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=274814543
Step 1 took 13361ms
Step 2 took 10905ms
********** Factor found in step 2: 26698194639575122525661827534142287
Found probable prime factor of 35 digits: 26698194639575122525661827534142287
Probable prime cofactor 452928540577266887157236259134255076239219768187618558929062743927670190164498760454451 has 87 digits

(26·10¹⁵¹+1)/9 = 2(8)₁₅₀9_<152> = 367 · 11399 · 6075767 · 959734623010792392437077357_<27> · C112

C112 = P34 · P38 · P40

P34 = 7947880915750697011047998057190331_<34>

P38 = 51027845668162402739414306998386845861_<38>

P40 = 2920028986625899746912414355924945584277_<40>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1288646471
Step 1 took 11085ms
Step 2 took 9828ms
********** Factor found in step 2: 7947880915750697011047998057190331
Found probable prime factor of 34 digits: 7947880915750697011047998057190331
#
Thu Oct 23 11:52:40 2008  Msieve v. 1.38
Thu Oct 23 11:52:40 2008  random seeds: 55b14030 4ff574bf
Thu Oct 23 11:52:40 2008  factoring 149002788476107069043684168199295287350958471236577922876144705896373784127497 (78 digits)
Thu Oct 23 11:52:41 2008  searching for 15-digit factors
Thu Oct 23 11:52:41 2008  commencing quadratic sieve (78-digit input)
Thu Oct 23 11:52:41 2008  using multiplier of 5
Thu Oct 23 11:52:41 2008  using 64kb Opteron sieve core
Thu Oct 23 11:52:41 2008  sieve interval: 6 blocks of size 65536
Thu Oct 23 11:52:41 2008  processing polynomials in batches of 17
Thu Oct 23 11:52:41 2008  using a sieve bound of 958687 (37824 primes)
Thu Oct 23 11:52:41 2008  using large prime bound of 95868700 (26 bits)
Thu Oct 23 11:52:41 2008  using trial factoring cutoff of 27 bits
Thu Oct 23 11:52:41 2008  polynomial 'A' values have 10 factors
Thu Oct 23 11:57:36 2008  38199 relations (20007 full + 18192 combined from 205677 partial), need 37920
Thu Oct 23 11:57:36 2008  begin with 225684 relations
Thu Oct 23 11:57:37 2008  reduce to 54082 relations in 2 passes
Thu Oct 23 11:57:37 2008  attempting to read 54082 relations
Thu Oct 23 11:57:37 2008  recovered 54082 relations
Thu Oct 23 11:57:37 2008  recovered 42175 polynomials
Thu Oct 23 11:57:37 2008  attempting to build 38199 cycles
Thu Oct 23 11:57:37 2008  found 38199 cycles in 1 passes
Thu Oct 23 11:57:37 2008  distribution of cycle lengths:
Thu Oct 23 11:57:37 2008     length 1 : 20007
Thu Oct 23 11:57:37 2008     length 2 : 18192
Thu Oct 23 11:57:37 2008  largest cycle: 2 relations
Thu Oct 23 11:57:37 2008  matrix is 37824 x 38199 (5.5 MB) with weight 1141071 (29.87/col)
Thu Oct 23 11:57:37 2008  sparse part has weight 1141071 (29.87/col)
Thu Oct 23 11:57:37 2008  filtering completed in 4 passes
Thu Oct 23 11:57:37 2008  matrix is 27598 x 27662 (4.3 MB) with weight 893917 (32.32/col)
Thu Oct 23 11:57:37 2008  sparse part has weight 893917 (32.32/col)
Thu Oct 23 11:57:37 2008  saving the first 48 matrix rows for later
Thu Oct 23 11:57:37 2008  matrix is 27550 x 27662 (2.8 MB) with weight 652298 (23.58/col)
Thu Oct 23 11:57:37 2008  sparse part has weight 456512 (16.50/col)
Thu Oct 23 11:57:37 2008  matrix includes 64 packed rows
Thu Oct 23 11:57:37 2008  commencing Lanczos iteration
Thu Oct 23 11:57:37 2008  memory use: 3.9 MB
Thu Oct 23 11:57:54 2008  lanczos halted after 437 iterations (dim = 27550)
Thu Oct 23 11:57:54 2008  recovered 18 nontrivial dependencies
Thu Oct 23 11:57:55 2008  prp38 factor: 51027845668162402739414306998386845861
Thu Oct 23 11:57:55 2008  prp40 factor: 2920028986625899746912414355924945584277
Thu Oct 23 11:57:55 2008  elapsed time 00:05:15

(26·10¹²²+1)/9 = 2(8)₁₂₁9_<123> = 74162267 · 237038273947153447_<18> · C98

C98 = P38 · P60

P38 = 46879667831372870430779365910146268011_<38>

P60 = 350545857881710086313544549379318576471907638151859610638951_<60>

Using B1=4000000, B2=14268967450, polynomial Dickson(12), sigma=2427505608
Step 1 took 13613ms
Step 2 took 9084ms
********** Factor found in step 2: 46879667831372870430779365910146268011
Found probable prime factor of 38 digits: 46879667831372870430779365910146268011
Probable prime cofactor 350545857881710086313544549379318576471907638151859610638951 has 60 digits

10²³⁷-9 = (9)₂₃₆1_<237> = 107 · 7561 · 57235347277_<11> · 672331504409_<12> · 4675438610011439_<16> · C193

C193 = P33 · P161

P33 = 124195659693998352897446580594911_<33>

P161 = 55317229683125179811055047825566314237250570327459404598417890762364651604901335574716743377299431025304065892097911840931358872788401832572008373559390024256489_<161>

Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=1344070187
Step 1 took 16461ms
Step 2 took 8449ms
********** Factor found in step 2: 124195659693998352897446580594911
Found probable prime factor of 33 digits: 124195659693998352897446580594911
Probable prime cofactor 55317229683125179811055047825566314237250570327459404598417890762364651604901335574716743377299431025304065892097911840931358872788401832572008373559390024256489 has 161 digits

10²⁰⁹-9 = (9)₂₀₈1_<209> = 6199 · 1098311 · 8749770522229013046664029725719_<31> · C169

C169 = P32 · P138

P32 = 11779221979625493750760591465889_<32>

P138 = 142508169351112330751625366154027236299106678544471738141095195169427914114649935286029433461028125436734063605464802185882769616072838209_<138>

Using B1=6000000, B2=35128842850, polynomial Dickson(12), sigma=2769882817
Step 1 took 40563ms
********** Factor found in step 1: 11779221979625493750760591465889
Found probable prime factor of 32 digits: 11779221979625493750760591465889
Probable prime cofactor 142508169351112330751625366154027236299106678544471738141095195169427914114649935286029433461028125436734063605464802185882769616072838209 has 138 digits

10²²⁷-9 = (9)₂₂₆1_<227> = 43 · 925733 · 1415114047290409_<16> · C205

C205 = P41 · P164

P41 = 17786640496933624840678534245662351596213_<41>

P164 = 99806868526225823221956954125006142277499588289181858360905874746351256925536418640176658497489042909882373987832308907586475427226873597370517730462039750438400917_<164>

Using B1=6000000, B2=35128842850, polynomial Dickson(12), sigma=1970878906
Step 1 took 50263ms
Step 2 took 28402ms
********** Factor found in step 2: 17786640496933624840678534245662351596213
Found probable prime factor of 41 digits: 17786640496933624840678534245662351596213
Probable prime cofactor 99806868526225823221956954125006142277499588289181858360905874746351256925536418640176658497489042909882373987832308907586475427226873597370517730462039750438400917 has 164 digits

(26·10¹²⁸+1)/9 = 2(8)₁₂₇9_<129> = 47 · 587621 · C122

C122 = P36 · P86

P36 = 608854427798862595293365769991723889_<36>

P86 = 17179962200419555232686564654540718862779882714985860187643887329996349818496153104123_<86>

SNFS difficulty: 129 digits.
Divisors found:
 r1=608854427798862595293365769991723889
 r2=17179962200419555232686564654540718862779882714985860187643887329996349818496153104123
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 10460096055142536651261318814623454062675761044303483385382570148029227584304823806460897990475945755921230053547283494347
m: 20000000000000000000000000
c5: 1625
c0: 2
skew: 0.26
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [400000, 950001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 111088 x 111310
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 2.00 hours.

Oct 23, 2008 (5th)

Factorizations of 288...889 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Oct 23, 2008 (4th)

The following PRPs were imported from Henri & Renaud Lifchitz's PRP Top records (www.primenumbers.net).

10²⁶⁹²⁷+3 = 1(0)₂₆₉₂₆3_<26928> is PRP. (Jason Earls / Dec 2007)

10²³⁶³⁶+7 = 1(0)₂₃₆₃₅7_<23637> is PRP. (Jason Earls / Nov 2007)

10³⁰²²¹+7 = 1(0)₃₀₂₂₀7_<30222> is PRP. (Jason Earls / Nov 2007)

10⁵⁰⁷¹¹+7 = 1(0)₅₀₇₁₀7_<50712> is PRP. (Jason Earls / Dec 2007)

10⁴³¹⁸⁶+9 = 1(0)₄₃₁₈₅9_<43187> is PRP. (Jason Earls / Dec 2007)

10⁴⁸¹⁰⁹+9 = 1(0)₄₈₁₀₈9_<48110> is PRP. (Jason Earls / Dec 2007)

(10²⁰⁰¹⁶+17)/9 = (1)₂₀₀₁₅3_<20016> is PRP. (Lelio R Paula / Oct 2008)

(10²²⁹⁷³+53)/9 = (1)₂₂₉₇₂7_<22973> is PRP. (Lelio R Paula / Oct 2008)

(10¹⁰⁶⁸³+11)/3 = (3)₁₀₆₈₂7_<10683> is PRP. (Lelio R Paula / Oct 2008)

(10¹²⁸⁹¹+11)/3 = (3)₁₂₈₉₀7_<12891> is PRP. (Lelio R Paula / Oct 2008)

(10¹⁴¹¹⁸+11)/3 = (3)₁₄₁₁₇7_<14118> is PRP. (Lelio R Paula / Oct 2008)

(61·10³⁰⁹⁷⁶-7)/9 = 6(7)₃₀₉₇₆_<30977> is PRP. (Maksym Voznyy / Jan 2008)

(61·10³¹⁶³¹-7)/9 = 6(7)₃₁₆₃₁_<31632> is PRP. (Maksym Voznyy / Jan 2008)

(61·10⁴³²⁷¹-7)/9 = 6(7)₄₃₂₇₁_<43272> is PRP. (Maksym Voznyy / Jan 2008)

10³⁵⁹²⁵-9 = (9)₃₅₉₂₄1_<35925> is PRP. (Jason Earls / Jan 2008)

10³⁷⁵⁹⁷-9 = (9)₃₇₅₉₆1_<37597> is PRP. (Jason Earls / Jan 2008)

Oct 23, 2008 (3rd)

Factorizations of 99...991 were extended to n=250. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Oct 23, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(64·10¹⁹⁷-1)/9 = 7(1)₁₉₇_<198> = 3 · 79 · C196

C196 = P55 · P141

P55 = 3210403733699042628385928154786408307073629412536388653_<55>

P141 = 934607940975846911851800500250432186081148964077948364953109571678411737172955610971512851456158708210894860371172826511957783213489964794351_<141>

Number: n
N=3000468823253633380215658696671354899203000468823253633380215658696671354899203000468823253633380215658696671354899203000468823253633380215658696671354899203000468823253633380215658696671354899203
  ( 196 digits)
SNFS difficulty: 199 digits.
Divisors found:

Thu Oct 23 20:51:46 2008  prp55 factor: 3210403733699042628385928154786408307073629412536388653
Thu Oct 23 20:51:46 2008  prp141 factor: 934607940975846911851800500250432186081148964077948364953109571678411737172955610971512851456158708210894860371172826511957783213489964794351
Thu Oct 23 20:51:47 2008  elapsed time 11:12:22 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 84.04 hours.
Scaled time: 171.86 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_7_1_197
n: 3000468823253633380215658696671354899203000468823253633380215658696671354899203000468823253633380215658696671354899203000468823253633380215658696671354899203000468823253633380215658696671354899203
type: snfs
skew: 0.69
deg: 5
c5: 25
c0: -4
m: 4000000000000000000000000000000000000000
rlim: 9500000
alim: 9500000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9500000/9500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 15500001)
Primes: RFBsize:633578, AFBsize:632788, largePrimes:15523414 encountered
Relations: rels:15938365, finalFF:1374724
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 83.45 hours.
Total relation processing time: 0.58 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,199,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,52,52,2.5,2.5,100000
total time: 84.04 hours.
 --------- CPU info (if available) ----------

Oct 23, 2008

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38

(25·10²⁴¹-1)/3 = 8(3)₂₄₁_<242> = 2203 · 3533 · 3139573 · 1058961517_<10> · 2936784733_<10> · 59760373009_<11> · 119276608278517969_<18> · 166630678549184691608467541279_<30> · 372622263768407797404826574707693_<33> · C121

C121 = P41 · P80

P41 = 54171639063846133845831310427219878076359_<41>

P80 = 45737605300666532796752786676494483427340987650457306599587100372839171400797483_<80>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3548948731
Step 1 took 14409ms
Step 2 took 5545ms
********** Factor found in step 2: 54171639063846133845831310427219878076359
Found probable prime factor of 41 digits: 54171639063846133845831310427219878076359
Probable prime cofactor 45737605300666532796752786676494483427340987650457306599587100372839171400797483 has 80 digits

6·10¹⁹⁴+7 = 6(0)₁₉₃7_<195> = 4880807929_<10> · C186

C186 = P33 · P153

P33 = 126110244771031557278809682152871_<33>

P153 = 974785733093042308010396782144898734663233985206820852016727149290684723767326775717208198754930119035872196205293376228506927605092858346962533362269673_<153>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1132209484
Step 1 took 21881ms
Step 2 took 14389ms
********** Factor found in step 2: 126110244771031557278809682152871
Found probable prime factor of 33 digits: 126110244771031557278809682152871
Probable prime cofactor 974785733093042308010396782144898734663233985206820852016727149290684723767326775717208198754930119035872196205293376228506927605092858346962533362269673 has 153 digits

(82·10¹⁹⁴+71)/9 = 9(1)₁₉₃9_<195> = 157 · 35401 · 439303 · C183

C183 = P32 · P152

P32 = 22467877310459119267034990240771_<32>

P152 = 16608482289955078759929672168069305816166331355355992549338772775044676696047614498320631904769235512996939922475775859447478409033448005589419459522359_<152>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=93914341
Step 1 took 21998ms
Step 2 took 14025ms
********** Factor found in step 2: 22467877310459119267034990240771
Found probable prime factor of 32 digits: 22467877310459119267034990240771
Probable prime cofactor 16608482289955078759929672168069305816166331355355992549338772775044676696047614498320631904769235512996939922475775859447478409033448005589419459522359 has 152 digits

(4·10¹⁹⁵-7)/3 = 1(3)₁₉₄1_<196> = 11 · 1657 · 23283583928233049_<17> · C175

C175 = P34 · P142

P34 = 2194943961380131549337327265014227_<34>

P142 = 1431364613322065902729609803616244522630895563591548703486827349517993939479808043205791458209999060733306207315449033301346771404634709812211_<142>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3766808131
Step 1 took 22026ms
Step 2 took 10516ms
********** Factor found in step 2: 2194943961380131549337327265014227
Found probable prime factor of 34 digits: 2194943961380131549337327265014227
Probable prime cofactor 1431364613322065902729609803616244522630895563591548703486827349517993939479808043205791458209999060733306207315449033301346771404634709812211 has 142 digits

(8·10¹⁷²-71)/9 = (8)₁₇₁1_<172> = 179 · 286168242716791_<15> · C156

C156 = P42 · P47 · P67

P42 = 859892965727862593870368712758282269775693_<42>

P47 = 96055266805913240015249975071088706895776783497_<47>

P67 = 2100909916748059669934740832392497068778405503990060382377373126649_<67>

SNFS difficulty: 172 digits.
Divisors found:
 r1=859892965727862593870368712758282269775693
 r2=96055266805913240015249975071088706895776783497
 r3=2100909916748059669934740832392497068778405503990060382377373126649
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.738).
Factorization parameters were as follows:
n: 173529377939311546112233330859262908774776885502244844273521228100899743749862292880170396230641247365799626515772661387843469000681651927737996523449881229
m: 20000000000000000000000000000000000
c5: 25
c0: -71
skew: 1.23
type: snfs
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [4500000, 7800001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1228674 x 1228922
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,54,54,2.6,2.6,100000
total time: 80.00 hours.

Oct 22, 2008 (5th)

By Sinkiti Sibata / GMP-ECM

(25·10²⁰³-1)/3 = 8(3)₂₀₃_<204> = 900569 · 2432695777627_<13> · C186

C186 = P33 · C153

P33 = 486546315175897598205259424750039_<33>

C153 = [781789388846407183224231919023102419829059677554399166273755190513515221233686096508806523349056395051660115861262590344318823595148958539349778964632369_<153>]

Input number is 380376746386836391787720513595455266505544842024516623969328880579839730067674651069153627908565521628498123510335067429803810807786576517269219113340039622848742338852787297549353412391

Run 179 out of 904:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2772300172
Step 1 took 34118ms
Step 2 took 12776ms
Run 180 out of 904:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3515028684
Step 1 took 34117ms
Step 2 took 12761ms
********** Factor found in step 2: 486546315175897598205259424750039
Found probable prime factor of 33 digits: 486546315175897598205259424750039
Composite cofactor 781789388846407183224231919023102419829059677554399166273755190513515221233686096508806523349056395051660115861262590344318823595148958539349778964632369 has 153 digits

Oct 22, 2008 (4th)

By Serge Batalov / GMP-ECM 6.2.1

(25·10²¹⁷-1)/3 = 8(3)₂₁₇_<218> = 24083 · 50159 · 682397437 · C201

C201 = P32 · C169

P32 = 53312541175672655088375062336039_<32>

C169 = [1896236612999935992014192963454630164995472234248038672300325066098629976525511506392351915195618799007084787069826889009159795113041528626213108925327088233124191280523_<169>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4157420674
Step 1 took 25198ms
Step 2 took 15601ms
********** Factor found in step 2: 53312541175672655088375062336039
Found probable prime factor of 32 digits: 53312541175672655088375062336039
Composite cofactor 1896236612999935992014192963454630164995472234248038672300325066098629976525511506392351915195618799007084787069826889009159795113041528626213108925327088233124191280523 has 169 digits

3·10¹⁹⁵-7 = 2(9)₁₉₄3_<196> = 73 · 367 · 1013 · 919621 · C183

C183 = P37 · C146

P37 = 3410320049990177024859778486328134861_<37>

C146 = [35246732830663562403369748164068680908724548385265603739345073793139596507744308018070883299760651207926080099361321383824319522570619998407671491_<146>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3556153323
Step 1 took 29388ms
********** Factor found in step 1: 3410320049990177024859778486328134861
Found probable prime factor of 37 digits: 3410320049990177024859778486328134861
Composite cofactor 35246732830663562403369748164068680908724548385265603739345073793139596507744308018070883299760651207926080099361321383824319522570619998407671491 has 146 digits

Oct 22, 2008 (3rd)

Factorizations of 833...33 were extended to n=250. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Oct 22, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(26·10¹⁷⁵-17)/9 = 2(8)₁₇₄7_<176> = 3 · 368227817 · 45998168948410733_<17> · 4452792496021608493_<19> · C132

C132 = P42 · P90

P42 = 333421341979068916546519038846193733716819_<42>

P90 = 382936350699197296494228208288801846939571547135265957954115629647469996359944562538119167_<90>

Number: 28887_175
N=127679151942693728206021113439808513462081475775475615214415429600954901928788362016440862567483214318764393846123460096592454169773
  ( 132 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=333421341979068916546519038846193733716819 (pp42)
 r2=382936350699197296494228208288801846939571547135265957954115629647469996359944562538119167 (pp90)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 309.56 hours.
Scaled time: 312.35 units (timescale=1.009).
Factorization parameters were as follows:
name: 28887_175
n: 127679151942693728206021113439808513462081475775475615214415429600954901928788362016440862567483214318764393846123460096592454169773
m: 100000000000000000000000000000000000
c5: 26
c0: -17
skew: 0.92
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 15000001)
Primes: RFBsize:501962, AFBsize:501686, largePrimes:6831540 encountered
Relations: rels:7367937, finalFF:1178170
Max relations in full relation-set: 28
Initial matrix: 1003714 x 1178170 with sparse part having weight 96796142.
Pruned matrix : 860913 x 865995 with weight 75896054.
Total sieving time: 301.51 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 7.74 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 309.56 hours.
 --------- CPU info (if available) ----------

(22·10¹⁹⁵-31)/9 = 2(4)₁₉₄1_<196> = 18307 · 61409 · 226017649145596719973_<21> · C166

C166 = P32 · C135

P32 = 52333261226040013874068864421239_<32>

C135 = [183827640054939547309364653857658843651474314964103416379471945088898934302542172912689307063113308104017719598958720895076627555187681_<135>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1438106012
Step 1 took 21034ms
Step 2 took 12889ms
********** Factor found in step 2: 52333261226040013874068864421239
Found probable prime factor of 32 digits: 52333261226040013874068864421239
Composite cofactor 183827640054939547309364653857658843651474314964103416379471945088898934302542172912689307063113308104017719598958720895076627555187681 has 135 digits

(26·10¹⁷⁴-71)/9 = 2(8)₁₇₃1_<175> = 61 · 70388459 · C165

C165 = P38 · C128

P38 = 22644944916809299781937983566931675591_<38>

C128 = [29711753102043529863724139334764046191153540703972565269144764438568718925369069665849357714992411887439678409638011808886202809_<128>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=4142602450
Step 1 took 27291ms
Step 2 took 20090ms
********** Factor found in step 2: 22644944916809299781937983566931675591
Found probable prime factor of 38 digits: 22644944916809299781937983566931675591
Composite cofactor 29711753102043529863724139334764046191153540703972565269144764438568718925369069665849357714992411887439678409638011808886202809 has 128 digits

Oct 22, 2008

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38

5·10¹⁹⁷-9 = 4(9)₁₉₆1_<198> = 823 · 3257 · 34031 · 6940928766071_<13> · 76433656928038861510273_<23> · C152

C152 = P43 · P109

P43 = 2168632766838689918632576115783405377195649_<43>

P109 = 4764194222655886177034856326166901781481228840032171605198783310162696238849016167824739197316648246761058353_<109>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3644175409
Step 1 took 18528ms
Step 2 took 14609ms
********** Factor found in step 2: 2168632766838689918632576115783405377195649
Found probable prime factor of 43 digits: 2168632766838689918632576115783405377195649
Probable prime cofactor 4764194222655886177034856326166901781481228840032171605198783310162696238849016167824739197316648246761058353 has 109 digits

5·10¹⁹⁹+9 = 5(0)₁₉₈9_<200> = 17 · 163 · C197

C197 = P37 · C161

P37 = 1593430546178302621526623328857130497_<37>

C161 = [11324012502583584716566772960189801921788975775190511695521026198515623091804565348455568883549293387605458234997823194604094623522025069708549012210465528813107_<161>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1420271003
Step 1 took 29385ms
Step 2 took 17514ms
********** Factor found in step 2: 1593430546178302621526623328857130497
Found probable prime factor of 37 digits: 1593430546178302621526623328857130497
Composite cofactor 11324012502583584716566772960189801921788975775190511695521026198515623091804565348455568883549293387605458234997823194604094623522025069708549012210465528813107 has 161 digits

(7·10¹⁹⁶-61)/9 = (7)₁₉₅1_<196> = 131 · 1249 · 4051 · 127852841 · 1197242672028108617231_<22> · C158

C158 = P39 · P120

P39 = 484157287113548064449100693247493210791_<39>

P120 = 158336306549811414521395276193314134816000853211628844174230012646700094764773236328445359419394774791738633126133192019_<120>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1582530103
Step 1 took 24888ms
Step 2 took 16469ms
********** Factor found in step 2: 484157287113548064449100693247493210791
Found probable prime factor of 39 digits: 484157287113548064449100693247493210791
Probable prime cofactor 158336306549811414521395276193314134816000853211628844174230012646700094764773236328445359419394774791738633126133192019 has 120 digits

(4·10¹⁷⁷-13)/9 = (4)₁₇₆3_<177> = 19 · 14431 · 23473 · 628267 · C162

C162 = P57 · P105

P57 = 320789733615284478790758170913537296973917782547673504923_<57>

P105 = 342636910756108034586766060914046263261456091001097853168240096906715579872630546306091053981879958965759_<105>

SNFS difficulty: 177 digits.
Divisors found:
 r1=320789733615284478790758170913537296973917782547673504923
 r2=342636910756108034586766060914046263261456091001097853168240096906715579872630546306091053981879958965759
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.281).
Factorization parameters were as follows:
n: 109914403328215897583290904223367841286661632871483804427109630525156921629961980459222248722455169313801745457689541853647747810604369591678411685966649674931557
m: 200000000000000000000000000000000000
c5: 25
c0: -26
skew: 1.01
type: snfs
Factor base limits: 11400000/11400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [5700000, 10100001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1424965 x 1425213
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,177,5,0,0,0,0,0,0,0,0,11400000,11400000,27,27,54,54,2.6,2.6,100000
total time: 110.00 hours.

(34·10¹⁹³-7)/9 = 3(7)₁₉₃_<194> = 37 · 22901 · C188

C188 = P30 · P158

P30 = 946117454127035503341112357253_<30>

P158 = 47123244252065994014385015090264019377616545139384926670539844445909827517900655076093584087367694433369681889961469872752436905117920097107236907128765203957_<158>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3439099762
Step 1 took 28025ms
Step 2 took 19251ms
********** Factor found in step 2: 946117454127035503341112357253
Found probable prime factor of 30 digits: 946117454127035503341112357253
Probable prime cofactor 47123244252065994014385015090264019377616545139384926670539844445909827517900655076093584087367694433369681889961469872752436905117920097107236907128765203957 has 158 digits

(4·10¹⁹⁶+17)/3 = 1(3)₁₉₅9_<197> = 107 · C195

C195 = P30 · P165

P30 = 641296994832521105786533002959_<30>

P165 = 194310269507585008333310325816908802409995304643133352971273908773477838968564150543240097299719754825793275239136337188618271630275071223132887746105578377626129503_<165>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1275197237
Step 1 took 27673ms
Step 2 took 15717ms
********** Factor found in step 2: 641296994832521105786533002959
Found probable prime factor of 30 digits: 641296994832521105786533002959
Probable prime cofactor 194310269507585008333310325816908802409995304643133352971273908773477838968564150543240097299719754825793275239136337188618271630275071223132887746105578377626129503 has 165 digits

(5·10¹⁹³+13)/9 = (5)₁₉₂7_<193> = 7 · 47 · 15649 · 1023815540327_<13> · C175

C175 = P35 · C140

P35 = 96202913674607842378594019111136319_<35>

C140 = [10955572152743952498130226545991213873754319162826343738038102711428932017005877244725536758158221707727384194996333763864519351564276702309_<140>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1846112973
Step 1 took 28376ms
Step 2 took 18626ms
********** Factor found in step 2: 96202913674607842378594019111136319
Found probable prime factor of 35 digits: 96202913674607842378594019111136319
Composite cofactor 10955572152743952498130226545991213873754319162826343738038102711428932017005877244725536758158221707727384194996333763864519351564276702309 has 140 digits

(14·10¹⁹⁵+13)/9 = 1(5)₁₉₄7_<196> = 3 · C195

C195 = P31 · C165

P31 = 1415892518921261163610086153683_<31>

C165 = [366213191742524998189471571564403867788336481566277323078309497974979063250048045513244983636839391531554468834937850896594871724072212797942208215172448975244422093_<165>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1098833014
Step 1 took 35065ms
Step 2 took 20938ms
********** Factor found in step 2: 1415892518921261163610086153683
Found probable prime factor of 31 digits: 1415892518921261163610086153683
Composite cofactor 366213191742524998189471571564403867788336481566277323078309497974979063250048045513244983636839391531554468834937850896594871724072212797942208215172448975244422093 has 165 digits

(88·10¹⁹⁵-7)/9 = 9(7)₁₉₅_<196> = 3 · 1373153 · 23721061919_<11> · 998739769839937_<15> · 229945776953320669_<18> · C147

C147 = P32 · P116

P32 = 17709857971448705875752495584023_<32>

P116 = 24602145954927762256766162278883504969116012969682193397520906584714252423186238558577964843369251118649923063873823_<116>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3297299414
Step 1 took 15977ms
Step 2 took 10901ms
********** Factor found in step 2: 17709857971448705875752495584023
Found probable prime factor of 32 digits: 17709857971448705875752495584023
Probable prime cofactor 24602145954927762256766162278883504969116012969682193397520906584714252423186238558577964843369251118649923063873823 has 116 digits

Oct 21, 2008 (2nd)

By matsui /

9·10¹⁹⁵-7 = 8(9)₁₉₄3_<196> = 17 · 439 · 119183 · 1271399 · 242885213 · C173

C173 = P36 · C137

P36 = 461827684596426570878380861037770727_<36>

C137 = [70949910236655858413737617479417459261252133160753837106470160640665889525424116417039764845206841627192033768547036282598220368986487733_<137>]

32766632766919078662825942812534767317385600913749182215022623020157389542005326478182856310139863849914763447191777621051072856816588852757981045807466834521306007851991891
=
461827684596426570878380861037770727* 70949910236655858413737617479417459261252133160753837106470160640665889525424116417039764845206841627192033768547036282598220368986487733

Oct 21, 2008

By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1

(14·10¹⁷⁶+31)/9 = 1(5)₁₇₅9_<177> = 3 · 566207205049711_<15> · C161

C161 = P59 · P103

P59 = 56152629625366819992137469300041576546741213872597735252417_<59>

P103 = 1630867885921653385652101326198882104756613516393727742204108998674895216128979500226008716085217882819_<103>

SNFS difficulty: 177 digits.
Divisors found:
 r1=56152629625366819992137469300041576546741213872597735252417
 r2=1630867885921653385652101326198882104756613516393727742204108998674895216128979500226008716085217882819
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.310).
Factorization parameters were as follows:
n: 91577520366063589277240766947306748041354023568047146249685501908499620499316018448070354842587752733157064074686017179232354084676531620519553064437257292523523
Y1: 1
Y0: -100000000000000000000000000000000000
c5: 140
c0: 31
skew: 0.74
type: snfs
Factor base limits: 11400000/11400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [5700000, 10200001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1465262 x 1465510
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,177,5,0,0,0,0,0,0,0,0,11400000,11400000,27,27,54,54,2.6,2.6,100000
total time: 150.00 hours.

2·10¹⁸²+9 = 2(0)₁₈₁9_<183> = 11² · 19 · C179

C179 = P46 · P134

P46 = 4792421492537717215974620350584419014570035427_<46>

P134 = 18152482101795525258673725492310366645321546282550812322674378256610903698310179167802038160476302016480186262806948758018518330672633_<134>

SNFS difficulty: 182 digits.
Divisors found:
 r1=4792421492537717215974620350584419014570035427
 r2=18152482101795525258673725492310366645321546282550812322674378256610903698310179167802038160476302016480186262806948758018518330672633
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.314).
Factorization parameters were as follows:
n: 86994345367551109177903436276642018268812527185732927359721618094823836450630709003914745541539799913005654632448890822096563723357981731187472814267072640278381905176163549369291
m: 1000000000000000000000000000000000000
c5: 200
c0: 9
skew: 0.54
type: snfs
Factor base limits: 15000000/15000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 49/49
Sieved rational special-q in [7500000, 10300001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1054356 x 1054581
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,15000000,15000000,28,28,49,49,2.6,2.6,100000
total time: 220.00 hours.

(14·10²⁰⁰+13)/9 = 1(5)₁₉₉7_<201> = 149 · 82234460157247_<14> · 801797680026694996283_<21> · C164

C164 = P28 · P31 · P32 · P74

P28 = 6459280719655949148659797177_<28>

P31 = 3406177645914414016513634539813_<31>

P32 = 29650943696340059768408884079497_<32>

P74 = 24271166126560128989106147319544463210746453787159176905895443038471222169_<74>

# 3 ECM factors! Yes, 3!
#
Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3727128160
Step 1 took 19634ms
********** Factor found in step 1: 6459280719655949148659797177
Found probable prime factor of 28 digits: 6459280719655949148659797177
#
Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=520959377
Step 1 took 24794ms
Step 2 took 16513ms
********** Factor found in step 2: 3406177645914414016513634539813
Found probable prime factor of 31 digits: 3406177645914414016513634539813
#
Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=249960142
Step 1 took 24944ms
Step 2 took 16634ms
********** Factor found in step 2: 29650943696340059768408884079497
Found probable prime factor of 32 digits: 29650943696340059768408884079497

(19·10²⁰⁰+17)/9 = 2(1)₁₉₉3_<201> = 3 · 126544763 · 2943578385629665516163_<22> · C171

C171 = P27 · P144

P27 = 898447831098242238266148503_<27>

P144 = 210269939678342336529513921152874898053927458055258874398493904056791369753272627555998930381253413935650920678917164241827912150245681803371653_<144>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2082085495
Step 1 took 19441ms
Step 2 took 12897ms
********** Factor found in step 2: 898447831098242238266148503
Found probable prime factor of 27 digits: 898447831098242238266148503
Probable prime cofactor 210269939678342336529513921152874898053927458055258874398493904056791369753272627555998930381253413935650920678917164241827912150245681803371653 has 144 digits

2·10²⁰⁰-1 = 1(9)₂₀₀_<201> = 47 · 199 · 8832847 · 26986789362889673_<17> · C173

C173 = P32 · C142

P32 = 22887618087703883422612434497873_<32>

C142 = [3919462703564142473698047873878421629698357069094950750629640809045036371942703314337013367544634521328393484746001349161465007919976067433841_<142>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2533383244
Step 1 took 20761ms
Step 2 took 12781ms
********** Factor found in step 2: 22887618087703883422612434497873
Found probable prime factor of 32 digits: 22887618087703883422612434497873
Composite cofactor 3919462703564142473698047873878421629698357069094950750629640809045036371942703314337013367544634521328393484746001349161465007919976067433841 has 142 digits

8·10²⁰⁰+3 = 8(0)₁₉₉3_<201> = 11 · 607472219 · 147010366511382569644373_<24> · C168

C168 = P37 · C132

P37 = 7546527715304377195290179372975899421_<37>

C132 = [107913492600146389511828126361061001602717552095077467114432068529999855181951097623769940565256091764288088215600992621367406387499_<132>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4043050459
Step 1 took 24875ms
Step 2 took 17112ms
********** Factor found in step 2: 7546527715304377195290179372975899421
Found probable prime factor of 37 digits: 7546527715304377195290179372975899421
Composite cofactor 107913492600146389511828126361061001602717552095077467114432068529999855181951097623769940565256091764288088215600992621367406387499 has 132 digits

(82·10²⁰⁰-1)/9 = 9(1)₂₀₀_<201> = 402883508155939_<15> · C187

C187 = P33 · P155

P33 = 102407901890348689567844185695023_<33>

P155 = 22083015858137772409667015245738789158555690527213028648393927531768748273294785668401228006283649881036393732744822021725553670861667592092248276044786563_<155>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3874257449
Step 1 took 29631ms
Step 2 took 19525ms
********** Factor found in step 2: 102407901890348689567844185695023
Found probable prime factor of 33 digits: 102407901890348689567844185695023
Probable prime cofactor 22083015858137772409667015245738789158555690527213028648393927531768748273294785668401228006283649881036393732744822021725553670861667592092248276044786563 has 155 digits

6·10¹⁹⁸-7 = 5(9)₁₉₇3_<199> = 167 · 265447401151_<12> · C186

C186 = P31 · C155

P31 = 1599529266754550409912307759727_<31>

C155 = [84618263884039984680979205479242373328854046385994102543980925758836773562467373965067601568858438800912633777084401273137347795319481939335873583645268527_<155>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1986207576
Step 1 took 23769ms
********** Factor found in step 1: 1599529266754550409912307759727
Found probable prime factor of 31 digits: 1599529266754550409912307759727
Composite cofactor 84618263884039984680979205479242373328854046385994102543980925758836773562467373965067601568858438800912633777084401273137347795319481939335873583645268527 has 155 digits

(22·10¹⁹⁹+23)/9 = 2(4)₁₉₈7_<200> = 3² · 619 · 128173 · 742789 · 149620828199987785329497659_<27> · C159

C159 = P32 · P127

P32 = 43482312117488028224282836493909_<32>

P127 = 7084028770911422344248461958410720572198835237947535379552273443567806999719918274887993804124122573096734631865106103730841651_<127>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=329097599
Step 1 took 19390ms
Step 2 took 12444ms
********** Factor found in step 2: 43482312117488028224282836493909
Found probable prime factor of 32 digits: 43482312117488028224282836493909
Probable prime cofactor 7084028770911422344248461958410720572198835237947535379552273443567806999719918274887993804124122573096734631865106103730841651 has 127 digits

(4·10¹⁹⁸-7)/3 = 1(3)₁₉₇1_<199> = 35433614694519093943915021_<26> · C173

C173 = P29 · C144

P29 = 53080170921181623484835211569_<29>

C144 = [708909776366544417055494111166661177395346300454696028653520045734998051049191473489799475703118236101317585796307759176426123229836426451112719_<144>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1091327796
Step 1 took 20217ms
Step 2 took 12849ms
********** Factor found in step 2: 53080170921181623484835211569
Found probable prime factor of 29 digits: 53080170921181623484835211569
Composite cofactor 708909776366544417055494111166661177395346300454696028653520045734998051049191473489799475703118236101317585796307759176426123229836426451112719 has 144 digits

(8·10¹⁹⁸-71)/9 = (8)₁₉₇1_<198> = 7 · 181 · 246151 · 26571308869211899069_<20> · C171

C171 = P31 · C140

P31 = 2181736485124043717540785640249_<31>

C140 = [49164770484616078662130837495285105615980477313414831637996342826393591225258796960761072524813073625782737476138348702108473214785930571753_<140>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2812342345
Step 1 took 24849ms
Step 2 took 16942ms
********** Factor found in step 2: 2181736485124043717540785640249
Found probable prime factor of 31 digits: 2181736485124043717540785640249
Composite cofactor 49164770484616078662130837495285105615980477313414831637996342826393591225258796960761072524813073625782737476138348702108473214785930571753 has 140 digits

(14·10¹⁹⁹-41)/9 = 1(5)₁₉₈1_<200> = 11 · 9905209 · 49424550329263117_<17> · C175

C175 = P29 · C146

P29 = 93342682385042014936376105033_<29>

C146 = [30946119177002457256257679064752877429329252807104046662651498568475129246685538584195558365545659808057878297832367685917174350969470564322807409_<146>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3253425714
Step 1 took 28821ms
Step 2 took 18723ms
********** Factor found in step 2: 93342682385042014936376105033
Found probable prime factor of 29 digits: 93342682385042014936376105033
Composite cofactor 30946119177002457256257679064752877429329252807104046662651498568475129246685538584195558365545659808057878297832367685917174350969470564322807409 has 146 digits

(19·10¹⁹⁷+17)/9 = 2(1)₁₉₆3_<198> = 3 · 7 · 90017 · 189037603483_<12> · 1167987135194728007608387_<25> · C156

C156 = P33 · C124

P33 = 130987118004416341717932217759037_<33>

C124 = [3861467755350303484159223919449335539186556972805576020551599415949486879617583193229971628069176142786276497779467927144217_<124>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3671506003
Step 1 took 19437ms
Step 2 took 12449ms
********** Factor found in step 2: 130987118004416341717932217759037
Found probable prime factor of 33 digits: 130987118004416341717932217759037
Composite cofactor 3861467755350303484159223919449335539186556972805576020551599415949486879617583193229971628069176142786276497779467927144217 has 124 digits

(88·10¹⁹⁷-7)/9 = 9(7)₁₉₇_<198> = 47 · 61 · 12150092320841_<14> · 39579394802884247_<17> · C165

C165 = P36 · C130

P36 = 120780957158617319735656378500678509_<36>

C130 = [5871719163515225280922211088120438405575691242148159445644927132369821177548971534618963281375524980385790625213433048301365617017_<130>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3923837933
Step 1 took 21101ms
Step 2 took 12849ms
********** Factor found in step 2: 120780957158617319735656378500678509
Found probable prime factor of 36 digits: 120780957158617319735656378500678509
Composite cofactor 5871719163515225280922211088120438405575691242148159445644927132369821177548971534618963281375524980385790625213433048301365617017 has 130 digits

(25·10¹⁹⁷+11)/9 = 2(7)₁₉₆9_<198> = 3 · 29 · 31 · 131 · 167 · 11973221894137871_<17> · C174

C174 = P36 · P138

P36 = 859405617629884678518292762614354083_<36>

P138 = 457529990349271379357800820089302302513147819742197174361744364096811170650975745897790665507102867916025781272624748791884073929721978187_<138>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3634545673
Step 1 took 22749ms
Step 2 took 14193ms
********** Factor found in step 2: 859405617629884678518292762614354083
Found probable prime factor of 36 digits: 859405617629884678518292762614354083
Probable prime cofactor 457529990349271379357800820089302302513147819742197174361744364096811170650975745897790665507102867916025781272624748791884073929721978187 has 138 digits

3·10¹⁹⁷+7 = 3(0)₁₉₆7_<198> = 2357 · 8929 · 1802680774763383_<16> · C175

C175 = P29 · P146

P29 = 97148865973080265245073984193_<29>

P146 = 81395854489413446318803739695291383680562514323245286068600107617125030508665056235124237334794958273834035260731457900762605517868916643151494701_<146>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1336248685
Step 1 took 21957ms
Step 2 took 14189ms
********** Factor found in step 2: 97148865973080265245073984193
Found probable prime factor of 29 digits: 97148865973080265245073984193
Probable prime cofactor 81395854489413446318803739695291383680562514323245286068600107617125030508665056235124237334794958273834035260731457900762605517868916643151494701 has 146 digits

(19·10¹⁹⁷-1)/9 = 2(1)₁₉₇_<198> = 217409 · 148309607497483921_<18> · C175

C175 = P29 · C147

P29 = 39352703424498545120297305189_<29>

C147 = [166375630748703395463164557225749379129853263886867234344540086253317490155678563790257803512283631412627990637610456181042880430192706837121126091_<147>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2585434931
Step 1 took 22001ms
Step 2 took 2841ms
********** Factor found in step 2: 39352703424498545120297305189
Found probable prime factor of 29 digits: 39352703424498545120297305189
Composite cofactor 166375630748703395463164557225749379129853263886867234344540086253317490155678563790257803512283631412627990637610456181042880430192706837121126091 has 147 digits

(4·10¹⁹⁷+11)/3 = 1(3)₁₉₆7_<198> = 19 · 1511 · 19347313 · 434677339 · C177

C177 = P33 · C145

P33 = 145143707113728537226153436432311_<33>

C145 = [3804826017512159968793268569143505668827839952767829974171836729047124862981119444455807733568534433006902687070212949433801193366615213429833609_<145>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1442437893
Step 1 took 21958ms
Step 2 took 14017ms
********** Factor found in step 2: 145143707113728537226153436432311
Found probable prime factor of 33 digits: 145143707113728537226153436432311
Composite cofactor 3804826017512159968793268569143505668827839952767829974171836729047124862981119444455807733568534433006902687070212949433801193366615213429833609 has 145 digits

7·10¹⁹⁸-9 = 6(9)₁₉₇1_<199> = 113 · 557 · 14669 · 1011899197_<10> · C181

C181 = P33 · P149

P33 = 264988857469403991211956741757711_<33>

P149 = 28274766614610714157255420998775798591008627434112116606543963199796112209476723290238538742147137438714006318672046665431077283855690553184035469237_<149>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3404709547
Step 1 took 29350ms
Step 2 took 18701ms
********** Factor found in step 2: 264988857469403991211956741757711
Found probable prime factor of 33 digits: 264988857469403991211956741757711
Probable prime cofactor 28274766614610714157255420998775798591008627434112116606543963199796112209476723290238538742147137438714006318672046665431077283855690553184035469237 has 149 digits

Oct 20, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(26·10¹⁷²-17)/9 = 2(8)₁₇₁7_<173> = 3² · 41 · 83 · 131 · 527623 · 371470216724616829_<18> · 1322759690532757068064807_<25> · C119

C119 = P32 · P36 · P51

P32 = 79595740428624758405274066235447_<32>

P36 = 605333788407412819438944577230313913_<36>

P51 = 576423491058992736416957914655421765461285925809189_<51>

Number: 28887_172
N=27773231513010531676806997508834162293990971944311745383468612502175567406803821638563467475456350783538064197649005979
  ( 119 digits)
Divisors found:
 r1=79595740428624758405274066235447 (pp32)
 r2=605333788407412819438944577230313913 (pp36)
 r3=576423491058992736416957914655421765461285925809189 (pp51)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 94.00 hours.
Scaled time: 44.46 units (timescale=0.473).
Factorization parameters were as follows:
name: 28887_172
n: 27773231513010531676806997508834162293990971944311745383468612502175567406803821638563467475456350783538064197649005979
skew: 37008.98
# norm 3.26e+16
c5: 55440
c4: 3164058222
c3: 1264562398005151
c2: -4105551205117045627
c1: -550046594059784674117371
c0: -1001973857328021287339465895
# alpha -6.55
Y1: 524543343403
Y0: -54949100966099077885304
# Murphy_E 3.50e-10
# M 6977594599683708295921293182066515609590231586712473955854354315894030466074015681292072989429107770858219365562363712
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4170001)
Primes: RFBsize:315948, AFBsize:315849, largePrimes:7625017 encountered
Relations: rels:7651561, finalFF:714486
Max relations in full relation-set: 28
Initial matrix: 631882 x 714486 with sparse part having weight 61493390.
Pruned matrix : 563522 x 566745 with weight 43154206.
Total sieving time: 77.23 hours.
Total relation processing time: 0.94 hours.
Matrix solve time: 15.34 hours.
Time per square root: 0.48 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 94.00 hours.
 --------- CPU info (if available) ----------

Oct 20, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(86·10¹⁸⁷+31)/9 = 9(5)₁₈₆9_<188> = 3 · 11 · 17 · C186

C186 = P41 · P64 · P82

P41 = 82497070342294097847760872671048101547273_<41>

P64 = 1137506622062276258802403675541190635066970154120153739009283317_<64>

P82 = 1815100267956222784484327964833504354369950932271791040395824755849419204499493059_<82>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 170330758566052683699742523271935036640918993860170330758566052683699742523271935036640918993860170330758566052683699742523271935036640918993860170330758566052683699742523271935036640919 (186 digits)
Using B1=6498000, B2=14271500890, polynomial Dickson(12), sigma=3182954353
Step 1 took 110706ms
Step 2 took 38266ms
********** Factor found in step 2: 82497070342294097847760872671048101547273
Found probable prime factor of 41 digits: 82497070342294097847760872671048101547273
Composite cofactor 2064688574507215477497755904533791903970653712003879148874388035763738505270729759860310938616946784208098286504015093167178563384654221405996703 has 145 digits

Number: n
N=2064688574507215477497755904533791903970653712003879148874388035763738505270729759860310938616946784208098286504015093167178563384654221405996703
  ( 145 digits)
SNFS difficulty: 188 digits.
Divisors found:

Mon Oct 20 06:06:17 2008  prp64 factor: 1137506622062276258802403675541190635066970154120153739009283317
Mon Oct 20 06:06:17 2008  prp82 factor: 1815100267956222784484327964833504354369950932271791040395824755849419204499493059
Mon Oct 20 06:06:17 2008  elapsed time 14:04:55 (Msieve 1.38)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 73.18 hours.
Scaled time: 95.50 units (timescale=1.305).
Factorization parameters were as follows:
name: KA_9_5_186_9
n: 2064688574507215477497755904533791903970653712003879148874388035763738505270729759860310938616946784208098286504015093167178563384654221405996703

# n: 170330758566052683699742523271935036640918993860170330758566052683699742523271935036640918993860170330758566052683699742523271935036640918993860170330758566052683699742523271935036640919

type: snfs
skew: 0.32
deg: 5
c5: 8600
c0: 31
m: 10000000000000000000000000000000000000
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 4600001)
Primes: RFBsize:602489, AFBsize:602751, largePrimes:14634264 encountered
Relations: rels:14608986, finalFF:1232635
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 72.49 hours.
Total relation processing time: 0.69 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,188,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.5,2.5,100000
total time: 73.18 hours.
 --------- CPU info (if available) ----------

Oct 19, 2008 (2nd)

By Serge Batalov / Msieve-1.38

(5·10¹⁷⁵-11)/3 = 1(6)₁₇₄3_<176> = 13 · 79 · 2089896749_<10> · C163

C163 = P60 · P104

P60 = 144047157479044276664515263647763869136494387420848021424177_<60>

P104 = 53907449282249810484152355599174717398503110311207169164812814056689715236474601082663524167528740888753_<104>

SNFS difficulty: 175 digits.
Divisors found:
 r1=144047157479044276664515263647763869136494387420848021424177
 r2=53907449282249810484152355599174717398503110311207169164812814056689715236474601082663524167528740888753
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.289).
Factorization parameters were as follows:
n: 7765214836053830812275343365804816217160142233644828115751473920601722240369883569064895059784125043523570290124022191806025184608151076080284683874319931781581281
m: 100000000000000000000000000000000000
c5: 5
c0: -11
skew: 1.17
type: snfs
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [5000000, 8100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1275006 x 1275254
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,10000000,10000000,27,27,54,54,2.6,2.6,100000
total time: 60.00 hours.

Oct 19, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(67·10¹⁷²+23)/9 = 7(4)₁₇₁7_<173> = 97 · 113 · 1589431 · 1851763 · 15393406299013_<14> · 6244601986384031_<16> · C128

C128 = P48 · P80

P48 = 372451441498190701496064087171739015353189667169_<48>

P80 = 64453407041615178803320844206373593795836632906817191842652742276875476360294537_<80>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 24005764362119208380643126639474468236589502434740487688631317708317255847326760429726029271573224998580272635211810049838955753 (128 digits)
Using B1=7600000, B2=17126054410, polynomial Dickson(12), sigma=3670869563
Step 1 took 75402ms
Step 2 took 28669ms
********** Factor found in step 2: 372451441498190701496064087171739015353189667169
Found probable prime factor of 48 digits: 372451441498190701496064087171739015353189667169
Probable prime cofactor 64453407041615178803320844206373593795836632906817191842652742276875476360294537 has 80 digits

(26·10¹⁷⁵-53)/9 = 2(8)₁₇₄3_<176> = 19 · C175

C175 = P44 · P52 · P80

P44 = 19864097753703704521827520997023829831149889_<44>

P52 = 1054510268817082005325406588880925137752766424226059_<52>

P80 = 72586788244848406664760136158312476684344733516938432662645506456827825620239107_<80>

Number: n
N=1520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257
  ( 175 digits)
SNFS difficulty: 176 digits.
Divisors found:

Sun Oct 19 19:49:27 2008  prp44 factor: 19864097753703704521827520997023829831149889
Sun Oct 19 19:49:28 2008  prp52 factor: 1054510268817082005325406588880925137752766424226059
Sun Oct 19 19:49:28 2008  prp80 factor: 72586788244848406664760136158312476684344733516938432662645506456827825620239107
Sun Oct 19 19:49:28 2008  elapsed time 03:39:37 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 28.77 hours.
Scaled time: 58.83 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_2_8_174_3
n: 1520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257
type: snfs
skew: 1.15
deg: 5
c5: 26
c0: -53
m: 100000000000000000000000000000000000
rlim: 7500000
alim: 7500000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 7500000/7500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 5400001)
Primes: RFBsize:508261, AFBsize:507306, largePrimes:15130815 encountered
Relations: rels:15517541, finalFF:1644503
Max relations in full relation-set: 28
Initial matrix: 1015633 x 1644502 with sparse part having weight 201628258.
Pruned matrix : 
Total sieving time: 28.36 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,7500000,7500000,28,28,52,52,2.5,2.5,100000
total time: 28.77 hours.
 --------- CPU info (if available) ----------

Oct 18, 2008 (4th)

By Wataru Sakai / GGNFS

7·10¹⁸⁸+9 = 7(0)₁₈₇9_<189> = 29 · 281 · C185

C185 = P48 · P138

P48 = 390755155423951786421642709723832482956478913627_<48>

P138 = 219831035497922940488479509910463429809878109532808903912313282503371748866596450007079463861910551465289953658044366335149641788862040383_<138>

Number: 70009_188
N=85900110442999140998895570008590011044299914099889557000859001104429991409988955700085900110442999140998895570008590011044299914099889557000859001104429991409988955700085900110442999141
  ( 185 digits)
SNFS difficulty: 188 digits.
Divisors found:
 r1=390755155423951786421642709723832482956478913627 (pp48)
 r2=219831035497922940488479509910463429809878109532808903912313282503371748866596450007079463861910551465289953658044366335149641788862040383 (pp138)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 1450.14 hours.
Scaled time: 2891.58 units (timescale=1.994).
Factorization parameters were as follows:
n: 85900110442999140998895570008590011044299914099889557000859001104429991409988955700085900110442999140998895570008590011044299914099889557000859001104429991409988955700085900110442999141
m: 10000000000000000000000000000000000000
c5: 7000
c0: 9
skew: 0.26
type: snfsFactor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 24600001)
Primes: RFBsize:501962, AFBsize:501336, largePrimes:7487189 encountered
Relations: rels:8168947, finalFF:1186873
Max relations in full relation-set: 32
Initial matrix: 1003366 x 1186873 with sparse part having weight 161157006.
Pruned matrix : 876731 x 881811 with weight 145912668.
Total sieving time: 1436.68 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 12.95 hours.
Time per square root: 0.31 hours.
Prototype def-par.txt line would be:
snfs,188,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 1450.14 hours.
 --------- CPU info (if available) ----------

5·10¹⁹⁴-9 = 4(9)₁₉₃1_<195> = 311 · C193

C193 = P36 · P60 · P98

P36 = 568077914109210905300509346220531359_<36>

P60 = 132431729646308774647525574567728230397013165316585384835709_<60>

P98 = 21370252768992179896389372845940321522055761100150580614076984207751248231030310254841786517307851_<98>

Number: 49991_194
N=1607717041800643086816720257234726688102893890675241157556270096463022508038585209003215434083601286173633440514469453376205787781350482315112540192926045016077170418006430868167202572347266881
  ( 193 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=568077914109210905300509346220531359 (pp36)
 r2=132431729646308774647525574567728230397013165316585384835709 (pp60)
 r3=21370252768992179896389372845940321522055761100150580614076984207751248231030310254841786517307851 (pp98)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 2068.37 hours.
Scaled time: 4157.43 units (timescale=2.010).
Factorization parameters were as follows:
n: 1607717041800643086816720257234726688102893890675241157556270096463022508038585209003215434083601286173633440514469453376205787781350482315112540192926045016077170418006430868167202572347266881
m: 1000000000000000000000000000000000000000
c5: 1
c0: -18
skew: 1.78
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 3700000)
Primes: RFBsize:501962, AFBsize:502056, largePrimes:7770161 encountered
Relations: rels:8548694, finalFF:1151262
Max relations in full relation-set: 32
Initial matrix: 1004085 x 1151262 with sparse part having weight 177304272.
Pruned matrix : 910075 x 915159 with weight 160568505.
Total sieving time: 2049.99 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 17.74 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,195,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 2068.37 hours.
 --------- CPU info (if available) ----------

Oct 18, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(26·10¹⁷¹-53)/9 = 2(8)₁₇₀3_<172> = 3 · 211 · 122719 · C164

C164 = P75 · P90

P75 = 180794175688461612300191133500389304146671181730293708035199997373677168279_<75>

P90 = 205698386608080360118607066964350163888517864066216726017377451689667747458205138175489651_<90>

Number: 28883_171
N=37189070247254379933093515608867117606170787003243257385914198810335088069575624062314246404907190505731062435395522633044302883104269186116325126035940349949980629
  ( 164 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=180794175688461612300191133500389304146671181730293708035199997373677168279 (pp75)
 r2=205698386608080360118607066964350163888517864066216726017377451689667747458205138175489651 (pp90)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 221.55 hours.
Scaled time: 223.54 units (timescale=1.009).
Factorization parameters were as follows:
name: 28883_171
n: 37189070247254379933093515608867117606170787003243257385914198810335088069575624062314246404907190505731062435395522633044302883104269186116325126035940349949980629
m: 10000000000000000000000000000000000
c5: 260
c0: -53
skew: 0.73
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 11500001)
Primes: RFBsize:412849, AFBsize:413441, largePrimes:6524908 encountered
Relations: rels:6877907, finalFF:969004
Max relations in full relation-set: 28
Initial matrix: 826357 x 969004 with sparse part having weight 93418054.
Pruned matrix : 719756 x 723951 with weight 75272991.
Total sieving time: 215.51 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 5.74 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 221.55 hours.
 --------- CPU info (if available) ----------

Oct 18, 2008 (2nd)

By Serge Batalov / Msieve-1.38

(17·10¹⁶⁹+1)/9 = 1(8)₁₆₈9_<170> = 2286095969_<10> · 61583159712948473_<17> · C144

C144 = P40 · P50 · P54

P40 = 2904146275484962375815593435366057290811_<40>

P50 = 67503164136279247648768712027109846191861011687973_<50>

P54 = 684395851991037539017805425656538836579993071788064599_<54>

SNFS difficulty: 171 digits.
Divisors found:
 r1=2904146275484962375815593435366057290811
 r2=67503164136279247648768712027109846191861011687973
 r3=684395851991037539017805425656538836579993071788064599
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.313).
Factorization parameters were as follows:
n: 134168321346815434942285506994673592803638268962020611376419262011341845173814146151104444227872039130130466930338638784045925621136206412137697
m: 10000000000000000000000000000000000
c5: 17
c0: 10
skew: 0.9
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [3000000, 5200001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 959749 x 959997
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000
total time: 40.00 hours.

(13·10¹⁶⁷+23)/9 = 1(4)₁₆₆7_<168> = 3 · 571 · 1120864826830189595009_<22> · C143

C143 = P52 · P92

P52 = 2196722081660400619860435665895112903415321030329429_<52>

P92 = 34246415634863136312265358406712864250373833913675284562837241961141882980145948561830479379_<92>

SNFS difficulty: 168 digits.
Divisors found:
 r1=2196722081660400619860435665895112903415321030329429
 r2=34246415634863136312265358406712864250373833913675284562837241961141882980145948561830479379
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.310).
Factorization parameters were as follows:
n: 75229857442823839063327954585610815916921620664868103784648473223197175129674845956583458783493459542969045721078101701111280306855293361344591
m: 1000000000000000000000000000000000
c5: 1300
c0: 23
skew: 0.45
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [2750000, 5450001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 972189 x 972437
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,54,54,2.6,2.6,100000
total time: 40.00 hours.

Oct 18, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(8·10¹⁸⁶-71)/9 = (8)₁₈₅1_<186> = 7 · 6247 · C182

C182 = P45 · P49 · P89

P45 = 987895103890722668057692699475951929826842691_<45>

P49 = 1518369038049027997383307706026952156843005415743_<49>

P89 = 13551574573816468594611225834346709335102626184834964057831450659712303002693008791158453_<89>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 20327217381803583180243977426625097507120878339063067732829218342264604470463282693153030915156735550524569253559168718445171142465843922543138166637446291680324015845065949115893089 (182 digits)
Using B1=6016000, B2=14270867530, polynomial Dickson(12), sigma=513170549
Step 1 took 93488ms
Step 2 took 36334ms
********** Factor found in step 2: 987895103890722668057692699475951929826842691
Found probable prime factor of 45 digits: 987895103890722668057692699475951929826842691
Composite cofactor 20576291249695377971301832017847716213382725784697613948242181117163577126798867943121419615352806546244832708544699170564753533853725579 has 137 digits

Number: n
N=20576291249695377971301832017847716213382725784697613948242181117163577126798867943121419615352806546244832708544699170564753533853725579
  ( 137 digits)
SNFS difficulty: 187 digits.
Divisors found:

Sat Oct 18 02:11:00 2008  prp49 factor: 1518369038049027997383307706026952156843005415743
Sat Oct 18 02:11:00 2008  prp89 factor: 13551574573816468594611225834346709335102626184834964057831450659712303002693008791158453
Sat Oct 18 02:11:00 2008  elapsed time 07:20:02 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 82.38 hours.
Scaled time: 167.89 units (timescale=2.038).
Factorization parameters were as follows:
name: KA_8_185_1
n: 20576291249695377971301832017847716213382725784697613948242181117163577126798867943121419615352806546244832708544699170564753533853725579
type: snfs
skew: 1.95
deg: 5
c5: 5
c0: -142
m: 20000000000000000000000000000000000000
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 6500001)
Primes: RFBsize:602489, AFBsize:600661, largePrimes:14480275 encountered
Relations: rels:14249707, finalFF:1207021
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 81.94 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.5,2.5,100000
total time: 82.38 hours.
 --------- CPU info (if available) ----------

6·10¹⁷¹-7 = 5(9)₁₇₀3_<172> = 13 · 347 · 280561 · 3619261 · C157

C157 = P63 · P95

P63 = 104668478321136247869629778050319602787493232821426679133681787_<63>

P95 = 12514552052547785247649358827497335463132200483914345373302430877998388248495950980295389454969_<95>

Number: n
N=1309879120210828994066681132598393425452886882387371219479021676852192760494238995653573474587735850307389375209623160606880841799831258125095168152211949603
  ( 157 digits)
SNFS difficulty: 171 digits.
Divisors found:

Sat Oct 18 08:27:22 2008  prp63 factor: 104668478321136247869629778050319602787493232821426679133681787
Sat Oct 18 08:27:22 2008  prp95 factor: 12514552052547785247649358827497335463132200483914345373302430877998388248495950980295389454969
Sat Oct 18 08:27:23 2008  elapsed time 02:57:46 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.18 hours.
Scaled time: 14.01 units (timescale=1.951).
Factorization parameters were as follows:
name: KA_5_9_170_3
n: 1309879120210828994066681132598393425452886882387371219479021676852192760494238995653573474587735850307389375209623160606880841799831258125095168152211949603
type: snfs
skew: 0.65
deg: 5
c5: 60
c0: -7
m: 10000000000000000000000000000000000
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 2100001)
Primes: RFBsize:425648, AFBsize:426177, largePrimes:13318679 encountered
Relations: rels:12554588, finalFF:860203
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 6.87 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,52,52,2.5,2.5,100000
total time: 7.18 hours.
 --------- CPU info (if available) ----------

Oct 17, 2008 (6th)

By Tyler Cadigan / GGNFS, Msieve

(10¹⁸⁰+53)/9 = (1)₁₇₉7_<180> = 3 · 263 · 1847 · 62191 · 121590592499_<12> · 5868575487559_<13> · C145

C145 = P56 · P89

P56 = 81793764274037836798450374935577510454727483448973394983_<56>

P89 = 21005507864120051654894845196111841280466161257529202703568230197334018456832678768309963_<89>

Number: 11117_180
N=1718119558694283508664575042321785026498137677843135605871188922547889529147024841393023704163871626361079396990446562395410058599515961373115629
  ( 145 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=81793764274037836798450374935577510454727483448973394983
 r2=21005507864120051654894845196111841280466161257529202703568230197334018456832678768309963
Version: 
Total time: 370.11 hours.
Scaled time: 954.51 units (timescale=2.579).
Factorization parameters were as follows:
n: 1718119558694283508664575042321785026498137677843135605871188922547889529147024841393023704163871626361079396990446562395410058599515961373115629
m: 1000000000000000000000000000000000000
c5: 1
c0: 53
skew: 2.21
type: snfs
Y0: 1000000000000000000000000000000000000
Y1: -1
rlambda: 2.6
alambda: 2.6
rlim: 20000000
alim: 20000000
qintsize: 1000000Factor base limits: 20000000/20000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [10000000, 15000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1009060 x 1009286
Total sieving time: 370.11 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,20000000,20000000,27,27,48,48,2.6,2.6,100000
total time: 370.11 hours.
 --------- CPU info (if available) ----------

Oct 17, 2008 (5th)

By Sinkiti Sibata / GGNFS, Msieve

(26·10¹⁵⁷-17)/9 = 2(8)₁₅₆7_<158> = 3 · 41 · 82013 · 52965943 · 84856973371799_<14> · C129

C129 = P52 · P78

P52 = 3677069971699943402973240503427918915132808241897783_<52>

P78 = 173283371006799030478413179782103712024486470011088345019793475092290392389823_<78>

Number: 28887_157
N=637175080124041304185260340865104028285702638816685146476778755934657374983610403654286401198601947444535960325318924282255462409
  ( 129 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=3677069971699943402973240503427918915132808241897783 (pp52)
 r2=173283371006799030478413179782103712024486470011088345019793475092290392389823 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 58.34 hours.
Scaled time: 44.57 units (timescale=0.764).
Factorization parameters were as follows:
name: 28887_157
n: 637175080124041304185260340865104028285702638816685146476778755934657374983610403654286401198601947444535960325318924282255462409
m: 10000000000000000000000000000000
c5: 2600
c0: -17
skew: 0.37
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3700001)
Primes: RFBsize:283146, AFBsize:282132, largePrimes:5804981 encountered
Relations: rels:5920382, finalFF:725994
Max relations in full relation-set: 28
Initial matrix: 565345 x 725994 with sparse part having weight 47524292.
Pruned matrix : 442217 x 445107 with weight 31339304.
Total sieving time: 53.79 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 4.22 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 58.34 hours.
 --------- CPU info (if available) ----------

(26·10¹⁵⁹-17)/9 = 2(8)₁₅₈7_<160> = 8837 · 5635633 · 1139822240018422481622821_<25> · 145680615773863178153918657_<27> · C99

C99 = P48 · P51

P48 = 457172000486643298781203262917205228548147422071_<48>

P51 = 764125619267224024718139398079281672269351217374681_<51>

Fri Oct 17 07:48:19 2008  Msieve v. 1.38
Fri Oct 17 07:48:19 2008  random seeds: 0af0844d 10432bce
Fri Oct 17 07:48:19 2008  factoring 349336837983491953871872894642555708833828354422395239433937378913519331683566606179884934655984351 (99 digits)
Fri Oct 17 07:48:22 2008  searching for 15-digit factors
Fri Oct 17 07:48:25 2008  commencing quadratic sieve (99-digit input)
Fri Oct 17 07:48:26 2008  using multiplier of 5
Fri Oct 17 07:48:26 2008  using 32kb Intel Core sieve core
Fri Oct 17 07:48:26 2008  sieve interval: 36 blocks of size 32768
Fri Oct 17 07:48:26 2008  processing polynomials in batches of 6
Fri Oct 17 07:48:26 2008  using a sieve bound of 2605289 (95294 primes)
Fri Oct 17 07:48:26 2008  using large prime bound of 390793350 (28 bits)
Fri Oct 17 07:48:26 2008  using double large prime bound of 2920820370574650 (43-52 bits)
Fri Oct 17 07:48:26 2008  using trial factoring cutoff of 52 bits
Fri Oct 17 07:48:26 2008  polynomial 'A' values have 13 factors
Fri Oct 17 12:43:25 2008  15126 relations (9655 full + 5471 combined from 615376 partial), need 95390
Fri Oct 17 12:43:25 2008  elapsed time 04:55:06
Fri Oct 17 14:25:55 2008  
Fri Oct 17 14:25:55 2008  
Fri Oct 17 14:25:55 2008  Msieve v. 1.38
Fri Oct 17 14:25:55 2008  random seeds: 741f743b 867902a2
Fri Oct 17 14:25:55 2008  factoring 349336837983491953871872894642555708833828354422395239433937378913519331683566606179884934655984351 (99 digits)
Fri Oct 17 14:25:56 2008  searching for 15-digit factors
Fri Oct 17 14:25:58 2008  commencing quadratic sieve (99-digit input)
Fri Oct 17 14:25:58 2008  using multiplier of 5
Fri Oct 17 14:25:58 2008  using 32kb Intel Core sieve core
Fri Oct 17 14:25:58 2008  sieve interval: 36 blocks of size 32768
Fri Oct 17 14:25:58 2008  processing polynomials in batches of 6
Fri Oct 17 14:25:58 2008  using a sieve bound of 2605289 (95294 primes)
Fri Oct 17 14:25:58 2008  using large prime bound of 390793350 (28 bits)
Fri Oct 17 14:25:58 2008  using double large prime bound of 2920820370574650 (43-52 bits)
Fri Oct 17 14:25:58 2008  using trial factoring cutoff of 52 bits
Fri Oct 17 14:25:58 2008  polynomial 'A' values have 13 factors
Fri Oct 17 14:26:01 2008  restarting with 9655 full and 615376 partial relations
Fri Oct 17 19:59:18 2008  95480 relations (22688 full + 72792 combined from 1444752 partial), need 95390
Fri Oct 17 19:59:22 2008  begin with 1467440 relations
Fri Oct 17 19:59:23 2008  reduce to 252468 relations in 11 passes
Fri Oct 17 19:59:23 2008  attempting to read 252468 relations
Fri Oct 17 19:59:30 2008  recovered 252468 relations
Fri Oct 17 19:59:30 2008  recovered 242508 polynomials
Fri Oct 17 19:59:30 2008  attempting to build 95480 cycles
Fri Oct 17 19:59:30 2008  found 95480 cycles in 6 passes
Fri Oct 17 19:59:30 2008  distribution of cycle lengths:
Fri Oct 17 19:59:30 2008     length 1 : 22688
Fri Oct 17 19:59:30 2008     length 2 : 16361
Fri Oct 17 19:59:30 2008     length 3 : 15836
Fri Oct 17 19:59:30 2008     length 4 : 12998
Fri Oct 17 19:59:30 2008     length 5 : 9880
Fri Oct 17 19:59:30 2008     length 6 : 6778
Fri Oct 17 19:59:30 2008     length 7 : 4489
Fri Oct 17 19:59:30 2008     length 9+: 6450
Fri Oct 17 19:59:30 2008  largest cycle: 19 relations
Fri Oct 17 19:59:31 2008  matrix is 95294 x 95480 (25.1 MB) with weight 6205758 (65.00/col)
Fri Oct 17 19:59:31 2008  sparse part has weight 6205758 (65.00/col)
Fri Oct 17 19:59:31 2008  filtering completed in 3 passes
Fri Oct 17 19:59:31 2008  matrix is 91462 x 91526 (24.2 MB) with weight 5981686 (65.36/col)
Fri Oct 17 19:59:31 2008  sparse part has weight 5981686 (65.36/col)
Fri Oct 17 19:59:32 2008  saving the first 48 matrix rows for later
Fri Oct 17 19:59:32 2008  matrix is 91414 x 91526 (13.5 MB) with weight 4495303 (49.12/col)
Fri Oct 17 19:59:32 2008  sparse part has weight 2988757 (32.65/col)
Fri Oct 17 19:59:32 2008  matrix includes 64 packed rows
Fri Oct 17 19:59:32 2008  using block size 36610 for processor cache size 2048 kB
Fri Oct 17 19:59:33 2008  commencing Lanczos iteration
Fri Oct 17 19:59:33 2008  memory use: 14.1 MB
Fri Oct 17 20:00:21 2008  lanczos halted after 1448 iterations (dim = 91412)
Fri Oct 17 20:00:22 2008  recovered 17 nontrivial dependencies
Fri Oct 17 20:00:22 2008  prp48 factor: 457172000486643298781203262917205228548147422071
Fri Oct 17 20:00:22 2008  prp51 factor: 764125619267224024718139398079281672269351217374681
Fri Oct 17 20:00:22 2008  elapsed time 05:34:27

Oct 17, 2008 (4th)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38/gnfs

(26·10¹⁹⁶-17)/9 = 2(8)₁₉₅7_<197> = 3 · 287771327 · 810857563 · 185726128967846339_<18> · 671758004937985886076476237_<27> · C135

C135 = P32 · P104

P32 = 31939879173910580438400878878759_<32>

P104 = 10356150813844787900834823060533787167148150203266154500522047784924543502448871053345793359278564043017_<104>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=847032883
Step 1 took 10326ms
Step 2 took 4807ms
********** Factor found in step 2: 31939879173910580438400878878759
Found probable prime factor of 32 digits: 31939879173910580438400878878759
Probable prime cofactor 10356150813844787900834823060533787167148150203266154500522047784924543502448871053345793359278564043017 has 104 digits

(26·10¹⁹²-17)/9 = 2(8)₁₉₁7_<193> = 41 · 79272414103_<11> · 82042192357926772102610496389810561633_<38> · C143

C143 = P33 · P41 · P69

P33 = 646339692493393337747248290139367_<33>

P41 = 23347548471027891222391051218682713727291_<41>

P69 = 717935663614141323476198407218450614415097949778852880550482361549069_<69>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2198108180
Step 1 took 7098ms
Step 2 took 3284ms
********** Factor found in step 2: 646339692493393337747248290139367
Found probable prime factor of 33 digits: 646339692493393337747248290139367
Composite cofactor 16762037705310739694160961481530313246498654277376477496854405204777871932916995964594549612157158757580942079 has 110 digits

Number: 28883_192
N=16762037705310739694160961481530313246498654277376477496854405204777871932916995964594549612157158757580942079
  ( 110 digits)
Divisors found:
 r1=23347548471027891222391051218682713727291
 r2=717935663614141323476198407218450614415097949778852880550482361549069
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.729).
Factorization parameters were as follows:
name: 28883_192
n: 16762037705310739694160961481530313246498654277376477496854405204777871932916995964594549612157158757580942079
skew: 19634.27
# norm 1.15e+15
c5: 23760
c4: -732510172
c3: -74628572677882
c2: 291776264655235985
c1: 6237779486097660130452
c0: -18038503918973282230456943
# alpha -5.40
Y1: 313275396047
Y0: -932603358146879780640
# Murphy_E 1.05e-09
# M 5809571181138759701044419189937894699342167502695450717956767491143381064004365373882245868097473045576903676
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 3000001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 406475 x 406723
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 10.00 hours.

Oct 17, 2008 (3rd)

By Serge Batalov / PFGW

(86·10¹³⁷⁴¹+13)/9 = 9(5)₁₃₇₄₀7_<13742> is PRP.

Oct 17, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(26·10¹⁶⁸-17)/9 = 2(8)₁₆₇7_<169> = 1151 · 53189 · 3845297 · C155

C155 = P30 · P60 · P65

P30 = 691786150359227305260342651851_<30>

P60 = 946812596364691311451086016834132866784096017745846067579369_<60>

P65 = 18735613134758722493314686248856404802936412322699495052983347031_<65>

Number: 28887_168
N=12271673742223879146119302921287351987225723768693572415492792094221612528875452222509963796606702569982599797468379627090212002056147005375530500792715589
  ( 155 digits)
SNFS difficulty: 169 digits.
Divisors found:
 r1=691786150359227305260342651851 (pp30)
 r2=946812596364691311451086016834132866784096017745846067579369 (pp60)
 r3=18735613134758722493314686248856404802936412322699495052983347031 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 138.68 hours.
Scaled time: 139.93 units (timescale=1.009).
Factorization parameters were as follows:
name: 28887_168
n: 12271673742223879146119302921287351987225723768693572415492792094221612528875452222509963796606702569982599797468379627090212002056147005375530500792715589
m: 2000000000000000000000000000000000
c5: 1625
c0: -34
skew: 0.46
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 7900001)
Primes: RFBsize:412849, AFBsize:412476, largePrimes:6178678 encountered
Relations: rels:6457589, finalFF:939587
Max relations in full relation-set: 28
Initial matrix: 825391 x 939587 with sparse part having weight 63700451.
Pruned matrix : 733378 x 737568 with weight 48023686.
Total sieving time: 134.15 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 4.29 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 138.68 hours.
 --------- CPU info (if available) ----------

Oct 17, 2008

By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1

(26·10²⁰²-17)/9 = 2(8)₂₀₁7_<203> = 3 · 41 · 2333 · C198

C198 = P39 · C159

P39 = 129797485565316576138335938787553938939_<39>

C159 = [775612337868844507616271572284373761381973575256362313544270876107000293028543916178363902529711692579369109164356752919211141934170017178762799324790822743387_<159>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1776639700
Step 1 took 25697ms
Step 2 took 8377ms
********** Factor found in step 2: 129797485565316576138335938787553938939
Found probable prime factor of 39 digits: 129797485565316576138335938787553938939
Composite cofactor 775612337868844507616271572284373761381973575256362313544270876107000293028543916178363902529711692579369109164356752919211141934170017178762799324790822743387 has 159 digits

(26·10¹⁶¹-17)/9 = 2(8)₁₆₀7_<162> = 491 · 30557 · 12184547 · C148

C148 = P69 · P79

P69 = 265985593868700211361992135555305954314323409649102462483859930225459_<69>

P79 = 5941158371782505498596768539671106948764441091331681031338463367290089728487537_<79>

SNFS difficulty: 162 digits.
Divisors found:
 r1=265985593868700211361992135555305954314323409649102462483859930225459
 r2=5941158371782505498596768539671106948764441091331681031338463367290089728487537
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.315).
Factorization parameters were as follows:
n: 1580262537786569725372553727321669981525482758855547985590946005188563140610837578431188916339843319915956447890498719664890521061648998787481604483
m: 100000000000000000000000000000000
c5: 260
c0: -17
skew: 0.58
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [2250000, 3750001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 805162 x 805410
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,54,54,2.5,2.5,100000
total time: 20.00 hours.

(26·10¹⁷¹-17)/9 = 2(8)₁₇₀7_<172> = 71 · 2014690833579469_<16> · 1891416654878237659147193_<25> · C131

C131 = P35 · P96

P35 = 48109016865913520195095540051309093_<35>

P96 = 221947566920328070216344062694348500510850700259673035094854433728769797473984579418247370694137_<96>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2805974126
Step 1 took 5226ms
Step 2 took 3003ms
********** Factor found in step 2: 48109016865913520195095540051309093
Found probable prime factor of 35 digits: 48109016865913520195095540051309093
Probable prime cofactor 221947566920328070216344062694348500510850700259673035094854433728769797473984579418247370694137 has 96 digits

(26·10¹⁹²-17)/9 = 2(8)₁₉₁7_<193> = 41 · 79272414103_<11> · C180

C180 = P38 · C143

P38 = 82042192357926772102610496389810561633_<38>

C143 = [10833970296013207989084662536581651616879108714184793508692814128673265107095600617603313406072713756279265813854583416619917872689578064723993_<143>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=652635297
Step 1 took 9334ms
Step 2 took 4332ms
********** Factor found in step 2: 82042192357926772102610496389810561633
Found probable prime factor of 38 digits: 82042192357926772102610496389810561633
Composite cofactor 10833970296013207989084662536581651616879108714184793508692814128673265107095600617603313406072713756279265813854583416619917872689578064723993 has 143 digits

Oct 16, 2008 (7th)

By Serge Batalov / PFGW

(86·10¹⁰⁰⁰³+13)/9 = 9(5)₁₀₀₀₂7_<10004> is PRP.

Oct 16, 2008 (6th)

By Jo Yeong Uk / GGNFS

4·10¹⁷³+1 = 4(0)₁₇₂1_<174> = 7 · 19 · 19081 · 1380947158352491_<16> · C153

C153 = P49 · P49 · P56

P49 = 1031387844700915926546275570854626898299232457527_<49>

P49 = 4950984722498265333902822196208270860948138231881_<49>

P56 = 22352008973784616122462526641600512964655392476154917761_<56>

Number: 40001_173
N=114137973672119360672572150898106796661330101454417637896259526429919025856550052603359765770360708093834065329551585587198631771640340154306807238895407
  ( 153 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=1031387844700915926546275570854626898299232457527 (pp49)
 r2=4950984722498265333902822196208270860948138231881 (pp49)
 r3=22352008973784616122462526641600512964655392476154917761 (pp56)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 92.56 hours.
Scaled time: 220.01 units (timescale=2.377).
Factorization parameters were as follows:
n: 114137973672119360672572150898106796661330101454417637896259526429919025856550052603359765770360708093834065329551585587198631771640340154306807238895407
m: 100000000000000000000000000000000000
c5: 1
c0: 25
skew: 1.9
type: snfs
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [4000000, 5700001)
Primes: RFBsize:539777, AFBsize:538970, largePrimes:10773912 encountered
Relations: rels:10964419, finalFF:1364486
Max relations in full relation-set: 28
Initial matrix: 1078811 x 1364486 with sparse part having weight 86737254.
Pruned matrix : 813086 x 818544 with weight 49578617.
Total sieving time: 87.82 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 4.52 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,50,50,2.6,2.6,100000
total time: 92.56 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673800)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Calibrating delay using timer specific routine.. 5344.40 BogoMIPS (lpj=2672204)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)

Oct 16, 2008 (5th)

By Serge Batalov / Msieve-1.38

(26·10¹⁶⁶-17)/9 = 2(8)₁₆₅7_<167> = 3 · 293 · C164

C164 = P52 · P113

P52 = 1471197411837404676000587813206308006550640281066939_<52>

P113 = 22339374628322814429464629999793314774821231845019922359202585861305762667563370954938494467079355549589396537627_<113>

SNFS difficulty: 167 digits.
Divisors found:
 r1=1471197411837404676000587813206308006550640281066939
 r2=22339374628322814429464629999793314774821231845019922359202585861305762667563370954938494467079355549589396537627
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.953).
Factorization parameters were as follows:
n: 32865630135254708633548223991909998735937302490203514094299077234230817848565288838326380988497029452660851978258121602831500442421944128428770066995322968019213753
m: 1000000000000000000000000000000000
c5: 260
c0: -17
skew: 0.58
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [2750000, 4950001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 951798 x 952046
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,54,54,2.6,2.6,100000
total time: 40.00 hours.

Oct 16, 2008 (4th)

By Sinkiti Sibata / GGNFS, Msieve

(26·10¹²⁴-17)/9 = 2(8)₁₂₃7_<125> = 3 · 2089 · 67324333 · 83861369 · C105

C105 = P43 · P63

P43 = 1824903596618491254551411008086026120234261_<43>

P63 = 447401266840912389986722883683744380837849073077673223449077613_<63>

Number: 28887_124
N=816464180989650351224051488844692798792324458135191337497018777767584167746285873004029875623655930698993
  ( 105 digits)
Divisors found:
 r1=1824903596618491254551411008086026120234261 (pp43)
 r2=447401266840912389986722883683744380837849073077673223449077613 (pp63)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 16.15 hours.
Scaled time: 12.43 units (timescale=0.770).
Factorization parameters were as follows:
name: 28887_124
n: 816464180989650351224051488844692798792324458135191337497018777767584167746285873004029875623655930698993
skew: 5714.03
# norm 3.50e+14
c5: 401040
c4: 6493525469
c3: -27978259045032
c2: -159309783903663376
c1: 580710657569380116552
c0: -5182581195961543252333
# alpha -5.78
Y1: 154008731899
Y0: -72735580824209398380
# Murphy_E 1.78e-09
# M 447983274830461864379146476925871244975907299446442034552756791959963487336853989126526061321897454429511
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2300001)
Primes: RFBsize:183072, AFBsize:183110, largePrimes:4631329 encountered
Relations: rels:4993380, finalFF:682858
Max relations in full relation-set: 28
Initial matrix: 366260 x 682858 with sparse part having weight 52516455.
Pruned matrix : 195355 x 197250 with weight 26985107.
Total sieving time: 15.41 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 16.15 hours.
 --------- CPU info (if available) ----------

(26·10¹²⁵-17)/9 = 2(8)₁₂₄7_<126> = 367 · 829 · 107823286243_<12> · 7310071877663_<13> · C97

C97 = P31 · P66

P31 = 3042549675264553555477312649387_<31>

P66 = 395948183335808890825034372088476100294521230559806139712454179923_<66>

Wed Oct 15 16:15:04 2008  Msieve v. 1.38
Wed Oct 15 16:15:04 2008  random seeds: 96667591 d41288e4
Wed Oct 15 16:15:04 2008  factoring 1204692016629955256328089887937976301517969093592680868815711272508092143797499855243889513657201 (97 digits)
Wed Oct 15 16:15:06 2008  searching for 15-digit factors
Wed Oct 15 16:15:07 2008  commencing quadratic sieve (97-digit input)
Wed Oct 15 16:15:08 2008  using multiplier of 1
Wed Oct 15 16:15:08 2008  using 64kb Pentium 4 sieve core
Wed Oct 15 16:15:08 2008  sieve interval: 18 blocks of size 65536
Wed Oct 15 16:15:08 2008  processing polynomials in batches of 6
Wed Oct 15 16:15:08 2008  using a sieve bound of 2333549 (85882 primes)
Wed Oct 15 16:15:08 2008  using large prime bound of 350032350 (28 bits)
Wed Oct 15 16:15:08 2008  using double large prime bound of 2395491891430500 (43-52 bits)
Wed Oct 15 16:15:08 2008  using trial factoring cutoff of 52 bits
Wed Oct 15 16:15:08 2008  polynomial 'A' values have 12 factors
Wed Oct 15 23:33:55 2008  86273 relations (21010 full + 65263 combined from 1288906 partial), need 85978
Wed Oct 15 23:34:00 2008  begin with 1309916 relations
Wed Oct 15 23:34:02 2008  reduce to 225209 relations in 11 passes
Wed Oct 15 23:34:02 2008  attempting to read 225209 relations
Wed Oct 15 23:34:09 2008  recovered 225209 relations
Wed Oct 15 23:34:09 2008  recovered 208543 polynomials
Wed Oct 15 23:34:10 2008  attempting to build 86273 cycles
Wed Oct 15 23:34:10 2008  found 86273 cycles in 6 passes
Wed Oct 15 23:34:10 2008  distribution of cycle lengths:
Wed Oct 15 23:34:10 2008     length 1 : 21010
Wed Oct 15 23:34:10 2008     length 2 : 15212
Wed Oct 15 23:34:10 2008     length 3 : 14481
Wed Oct 15 23:34:10 2008     length 4 : 11709
Wed Oct 15 23:34:10 2008     length 5 : 8783
Wed Oct 15 23:34:10 2008     length 6 : 5987
Wed Oct 15 23:34:10 2008     length 7 : 3793
Wed Oct 15 23:34:10 2008     length 9+: 5298
Wed Oct 15 23:34:10 2008  largest cycle: 22 relations
Wed Oct 15 23:34:10 2008  matrix is 85882 x 86273 (23.5 MB) with weight 5811120 (67.36/col)
Wed Oct 15 23:34:10 2008  sparse part has weight 5811120 (67.36/col)
Wed Oct 15 23:34:12 2008  filtering completed in 4 passes
Wed Oct 15 23:34:12 2008  matrix is 81786 x 81850 (22.3 MB) with weight 5526947 (67.53/col)
Wed Oct 15 23:34:12 2008  sparse part has weight 5526947 (67.53/col)
Wed Oct 15 23:34:13 2008  saving the first 48 matrix rows for later
Wed Oct 15 23:34:13 2008  matrix is 81738 x 81850 (15.7 MB) with weight 4521233 (55.24/col)
Wed Oct 15 23:34:13 2008  sparse part has weight 3616544 (44.19/col)
Wed Oct 15 23:34:13 2008  matrix includes 64 packed rows
Wed Oct 15 23:34:13 2008  using block size 21845 for processor cache size 512 kB
Wed Oct 15 23:34:14 2008  commencing Lanczos iteration
Wed Oct 15 23:34:14 2008  memory use: 14.2 MB
Wed Oct 15 23:35:33 2008  lanczos halted after 1294 iterations (dim = 81736)
Wed Oct 15 23:35:34 2008  recovered 16 nontrivial dependencies
Wed Oct 15 23:35:35 2008  prp31 factor: 3042549675264553555477312649387
Wed Oct 15 23:35:35 2008  prp66 factor: 395948183335808890825034372088476100294521230559806139712454179923
Wed Oct 15 23:35:35 2008  elapsed time 07:20:31

Oct 16, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(34·10¹⁸⁶-43)/9 = 3(7)₁₈₅3_<187> = 2549 · C184

C184 = P72 · P112

P72 = 546343618539092922731973753936839243091501383544493873477842943394088769_<72>

P112 = 2712693316518363022366031105781560682107270534818253728649490721133162710749555853025070780629498066137114271833_<112>

Number: n
N=1482062682533455385554247853188614271391831219214506778257268645656248637810034436162329453816311407523647617802188221960681748833965389477354954012466762564840242360838673117998343577
  ( 184 digits)
SNFS difficulty: 187 digits.
Divisors found:

Thu Oct 16 05:34:52 2008  prp72 factor: 546343618539092922731973753936839243091501383544493873477842943394088769
Thu Oct 16 05:34:52 2008  prp112 factor: 2712693316518363022366031105781560682107270534818253728649490721133162710749555853025070780629498066137114271833
Thu Oct 16 05:34:52 2008  elapsed time 18:52:41 (Msieve 1.38)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 58.62 hours.
Scaled time: 76.43 units (timescale=1.304).
Factorization parameters were as follows:
name: KA_3_7_185_3
n: 1482062682533455385554247853188614271391831219214506778257268645656248637810034436162329453816311407523647617802188221960681748833965389477354954012466762564840242360838673117998343577
type: snfs
skew: 0.66
deg: 5
c5: 340
c0: -43
m: 10000000000000000000000000000000000000
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 5600001)
Primes: RFBsize:602489, AFBsize:603165, largePrimes:14394823 encountered
Relations: rels:14154498, finalFF:1206761
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 58.03 hours.
Total relation processing time: 0.58 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.5,2.5,100000
total time: 58.62 hours.
 --------- CPU info (if available) ----------

(5·10¹⁷¹-23)/9 = (5)₁₇₀3_<171> = 7 · 53 · 131 · C167

C167 = P82 · P85

P82 = 6027739170558698373176408401461180267513269261549301064477211046506440175172858341_<82>

P85 = 1896390793053781284969080421438636485505504937000715539338204658483363752598306704533_<85>

Number: n
N=11430949065977151819006924868944168958571954395085606377555102889972542860343522881330745366464796106161510165543004373481112642858285952049454858039043549629751559753
  ( 167 digits)
SNFS difficulty: 171 digits.
Divisors found:

Thu Oct 16 12:30:45 2008  prp82 factor: 6027739170558698373176408401461180267513269261549301064477211046506440175172858341
Thu Oct 16 12:30:45 2008  prp85 factor: 1896390793053781284969080421438636485505504937000715539338204658483363752598306704533
Thu Oct 16 12:30:45 2008  elapsed time 04:44:35 (Msieve 1.38)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 12.01 hours.
Scaled time: 15.58 units (timescale=1.297).
Factorization parameters were as follows:
name: KA_5_170_3
n: 11430949065977151819006924868944168958571954395085606377555102889972542860343522881330745366464796106161510165543004373481112642858285952049454858039043549629751559753
type: snfs
skew: 0.86
deg: 5
c5: 50
c0: -23
m: 10000000000000000000000000000000000
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 1100001)
Primes: RFBsize:425648, AFBsize:426017, largePrimes:13787792 encountered
Relations: rels:13296250, finalFF:939569
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 11.29 hours.
Total relation processing time: 0.72 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,52,52,2.5,2.5,100000
total time: 12.01 hours.
 --------- CPU info (if available) ----------

Oct 16, 2008 (2nd)

By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1

(26·10¹⁶²-17)/9 = 2(8)₁₆₁7_<163> = 29 · 41 · 61 · 995377 · C152

C152 = P40 · P47 · P66

P40 = 5501286498405655905342717694686972908197_<40>

P47 = 10125694884984205676521560253483207273265641799_<47>

P66 = 718360506293268421227792773673534536293455189801295656412695055613_<66>

SNFS difficulty: 163 digits.
Divisors found:
 r1=5501286498405655905342717694686972908197
 r2=10125694884984205676521560253483207273265641799
 r3=718360506293268421227792773673534536293455189801295656412695055613
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.927).
Factorization parameters were as follows:
n: 40015804032673956426793177377995556955910649250570011850509081244438492540540333850676610741645571858036088889078135323086736656603072425792048061050039
m: 100000000000000000000000000000000
c5: 2600
c0: -17
skew: 0.37
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [2250000, 3750001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 854525 x 854773
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,54,54,2.5,2.5,100000
total time: 20.00 hours.

(26·10¹⁵⁴-17)/9 = 2(8)₁₅₃7_<155> = 3² · 33349 · C149

C149 = P58 · P92

P58 = 1655806187784170081376129355024512400874595061215829462877_<58>

P92 = 58129423001915900497455256477363673668965485263795199277948640370085158428885797129195181391_<92>

SNFS difficulty: 156 digits.
Divisors found:
 r1=1655806187784170081376129355024512400874595061215829462877
 r2=58129423001915900497455256477363673668965485263795199277948640370085158428885797129195181391
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.315).
Factorization parameters were as follows:
n: 96251058298895815263122628660825708213435981385045324993549328112083616996308031521481200132234146247559943123028472914026703745535894425916115721907
m: 10000000000000000000000000000000
c5: 13
c0: -85
skew: 1.46
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [1500000, 2500001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 620058 x 620306
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,54,54,2.5,2.5,100000
total time: 15.00 hours.

(26·10¹⁶⁵-17)/9 = 2(8)₁₆₄7_<166> = 263957 · 4058137 · 7818152593406970277472416624103_<31> · C123

C123 = P32 · P92

P32 = 12764119228429224522971656618663_<32>

P92 = 27025638012775141945475448077100614364122822615878345459713349089216440618643727446116152387_<92>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=660598922
Step 1 took 12213ms
********** Factor found in step 1: 12764119228429224522971656618663
Found probable prime factor of 32 digits: 12764119228429224522971656618663
Probable prime cofactor 27025638012775141945475448077100614364122822615878345459713349089216440618643727446116152387 has 92 digits

(26·10¹⁸⁴-17)/9 = 2(8)₁₈₃7_<185> = 3 · 347 · 773 · C179

C179 = P37 · C143

P37 = 1320609859565989645500044320598167223_<37>

C143 = [27184796089295598978415391289548696133680825116303565800551982812921189048358167264993631889810511264157528029387662330821692327090836318455933_<143>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1909449008
Step 1 took 24466ms
Step 2 took 16501ms
********** Factor found in step 2: 1320609859565989645500044320598167223
Found probable prime factor of 37 digits: 1320609859565989645500044320598167223
Composite cofactor 27184796089295598978415391289548696133680825116303565800551982812921189048358167264993631889810511264157528029387662330821692327090836318455933 has 143 digits

Oct 16, 2008

By Serge Batalov / PFGW

(14·10¹³⁰²⁴-23)/9 = 1(5)₁₃₀₂₃3_<13025> is PRP.

Oct 15, 2008 (9th)

By Robert Backstrom / GGNFS, Msieve

4·10¹⁹³+9 = 4(0)₁₉₂9_<194> = 7 · 11437 · 13853895929_<11> · 284374155722383_<15> · 1455040861595700679822195920931_<31> · 40774884715492908428204364418823_<32> · C103

C103 = P46 · P57

P46 = 9456466122140544011470454984220083014832730601_<46>

P57 = 226042958165565708353120714503974059356275405880402226161_<57>

Number: n
N=2137567576041104372111455292736110616642012466158171115994587987948441933469530773750128809166787452761
  ( 103 digits)
Divisors found:

Wed Oct 15 22:27:48 2008  prp46 factor: 9456466122140544011470454984220083014832730601
Wed Oct 15 22:27:48 2008  prp57 factor: 226042958165565708353120714503974059356275405880402226161
Wed Oct 15 22:27:48 2008  elapsed time 00:36:40 (Msieve 1.38)

Version: GGNFS-0.77.1-20050930-k8
Total time: 5.56 hours.
Scaled time: 4.66 units (timescale=0.838).
Factorization parameters were as follows:
name: n
n: 2137567576041104372111455292736110616642012466158171115994587987948441933469530773750128809166787452761
skew: 9441.31
# norm 1.14e+14
c5: 44400
c4: -428088886
c3: -15435140099909
c2: 26020273585723447
c1: 570016691238045740745
c0: -1047976788238775541382005
# alpha -5.67
Y1: 15416468573
Y0: -34395985086804511558
# Murphy_E 2.49e-09
# M 454570796391432565790902417114729285898493548317986804335761562880391700012618568074746351559767174829
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved  special-q in [100000, 1950001)
Primes: RFBsize:169511, AFBsize:169709, largePrimes:4205201 encountered
Relations: rels:4098356, finalFF:370203
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 5.48 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 5.56 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

Oct 15, 2008 (8th)

By Serge Batalov / Msieve-1.38

(26·10¹⁴⁹-17)/9 = 2(8)₁₄₈7_<150> = C150

C150 = P69 · P82

P69 = 134971906566222676263728404267505511206402426126592403563178725170953_<69>

P82 = 2140363103985260191659544710319723616409514346738105611022769933803701494623081279_<82>

SNFS difficulty: 151 digits.
Divisors found:
 r1=134971906566222676263728404267505511206402426126592403563178725170953
 r2=2140363103985260191659544710319723616409514346738105611022769933803701494623081279
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.946).
Factorization parameters were as follows:
n: 288888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887
m: 1000000000000000000000000000000
c5: 13
c0: -85
skew: 1.46
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [1200000, 1900001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 506341 x 506589
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,54,54,2.5,2.5,100000
total time: 10.00 hours.

7·10¹⁷²-9 = 6(9)₁₇₁1_<173> = 10598698069_<11> · C163

C163 = P75 · P89

P75 = 223245829680143568677436140783698003000608237638667397220569703726322445019_<75>

P89 = 29584359061808698085356769885290337868193171920464425723391688951441403237695049377138881_<89>

SNFS difficulty: 172 digits.
Divisors found:
 r1=223245829680143568677436140783698003000608237638667397220569703726322445019
 r2=29584359061808698085356769885290337868193171920464425723391688951441403237695049377138881
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.731).
Factorization parameters were as follows:
n: 6604584784308756592809399333404107371973103803302616752748256819882053383173887637991171460740665429743736952188103699060096321723041245359586061437788090649683739
m: 10000000000000000000000000000000000
c5: 700
c0: -9
skew: 0.42
type: snfs
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [4500000, 7600001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1249370 x 1249618
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,54,54,2.6,2.6,100000
total time: 34.00 hours.

Oct 15, 2008 (7th)

By Sinkiti Sibata / GMP-ECM, Msieve, GGNFS

(26·10¹¹⁸-17)/9 = 2(8)₁₁₇7_<119> = 3² · 31 · 4817 · C113

C113 = P33 · P34 · P46

P33 = 339145835876930553447588298468823_<33>

P34 = 6925540496049346647691472035885723_<34>

P46 = 9151869670383651567843410263648963919135064821_<46>

Factor28887_118

Inputnumber is 21495620639334323620041094666134567380379144717364418646392658683358512145893753595865962238643222881393696673809

Run 216 out of 904:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=334309867
Step 1 took 15101ms
Step 2 took 7317ms
********** Factor found in step 2: 339145835876930553447588298468823
Found probable prime factor of 33 digits: 339145835876930553447588298468823
Composite cofactor 63381644016807764877796119529273285908378065539823990280799855167981847753450583 has 80 digits

Wed Oct 15 13:45:35 2008  
Wed Oct 15 13:45:35 2008  Msieve v. 1.38
Wed Oct 15 13:45:35 2008  random seeds: 6e94724d 3e8b164c
Wed Oct 15 13:45:35 2008  factoring 80 (2 digits)
Wed Oct 15 13:45:35 2008  p1 factor: 2
Wed Oct 15 13:45:35 2008  p1 factor: 2
Wed Oct 15 13:45:35 2008  p1 factor: 2
Wed Oct 15 13:45:35 2008  p1 factor: 2
Wed Oct 15 13:45:35 2008  p1 factor: 5
Wed Oct 15 13:45:35 2008  elapsed time 00:00:00
Wed Oct 15 13:51:54 2008  
Wed Oct 15 13:51:54 2008  
Wed Oct 15 13:51:54 2008  Msieve v. 1.38
Wed Oct 15 13:51:54 2008  random seeds: c1fb0222 03cd8c81
Wed Oct 15 13:51:54 2008  factoring 63381644016807764877796119529273285908378065539823990280799855167981847753450583 (80 digits)
Wed Oct 15 13:51:55 2008  searching for 15-digit factors
Wed Oct 15 13:51:57 2008  commencing quadratic sieve (80-digit input)
Wed Oct 15 13:51:57 2008  using multiplier of 47
Wed Oct 15 13:51:57 2008  using 32kb Intel Core sieve core
Wed Oct 15 13:51:57 2008  sieve interval: 12 blocks of size 32768
Wed Oct 15 13:51:57 2008  processing polynomials in batches of 17
Wed Oct 15 13:51:57 2008  using a sieve bound of 1301023 (49967 primes)
Wed Oct 15 13:51:57 2008  using large prime bound of 130102300 (26 bits)
Wed Oct 15 13:51:57 2008  using trial factoring cutoff of 27 bits
Wed Oct 15 13:51:57 2008  polynomial 'A' values have 10 factors
Wed Oct 15 14:04:14 2008  50098 relations (26281 full + 23817 combined from 265003 partial), need 50063
Wed Oct 15 14:04:15 2008  begin with 291284 relations
Wed Oct 15 14:04:15 2008  reduce to 70947 relations in 2 passes
Wed Oct 15 14:04:15 2008  attempting to read 70947 relations
Wed Oct 15 14:04:16 2008  recovered 70947 relations
Wed Oct 15 14:04:16 2008  recovered 58432 polynomials
Wed Oct 15 14:04:16 2008  attempting to build 50098 cycles
Wed Oct 15 14:04:16 2008  found 50098 cycles in 1 passes
Wed Oct 15 14:04:16 2008  distribution of cycle lengths:
Wed Oct 15 14:04:16 2008     length 1 : 26281
Wed Oct 15 14:04:16 2008     length 2 : 23817
Wed Oct 15 14:04:16 2008  largest cycle: 2 relations
Wed Oct 15 14:04:16 2008  matrix is 49967 x 50098 (6.6 MB) with weight 1541394 (30.77/col)
Wed Oct 15 14:04:16 2008  sparse part has weight 1541394 (30.77/col)
Wed Oct 15 14:04:17 2008  filtering completed in 3 passes
Wed Oct 15 14:04:17 2008  matrix is 34614 x 34677 (5.1 MB) with weight 1207990 (34.84/col)
Wed Oct 15 14:04:17 2008  sparse part has weight 1207990 (34.84/col)
Wed Oct 15 14:04:17 2008  saving the first 48 matrix rows for later
Wed Oct 15 14:04:17 2008  matrix is 34566 x 34677 (3.8 MB) with weight 961386 (27.72/col)
Wed Oct 15 14:04:17 2008  sparse part has weight 792580 (22.86/col)
Wed Oct 15 14:04:17 2008  matrix includes 64 packed rows
Wed Oct 15 14:04:17 2008  using block size 13870 for processor cache size 2048 kB
Wed Oct 15 14:04:17 2008  commencing Lanczos iteration
Wed Oct 15 14:04:17 2008  memory use: 4.1 MB
Wed Oct 15 14:04:23 2008  lanczos halted after 548 iterations (dim = 34564)
Wed Oct 15 14:04:23 2008  recovered 17 nontrivial dependencies
Wed Oct 15 14:04:23 2008  prp34 factor: 6925540496049346647691472035885723
Wed Oct 15 14:04:23 2008  prp46 factor: 9151869670383651567843410263648963919135064821
Wed Oct 15 14:04:23 2008  elapsed time 00:12:29

(26·10¹⁵³-17)/9 = 2(8)₁₅₂7_<154> = 191 · 13691 · 29404942766701_<14> · 2690568143184441439_<19> · 24008502534823630793_<20> · C96

C96 = P36 · P61

P36 = 144033299950349239793375411134290953_<36>

P61 = 4038034105758540631100193593028886436502038569222778774393017_<61>

Wed Oct 15 07:31:11 2008  Msieve v. 1.38
Wed Oct 15 07:31:11 2008  random seeds: 4a2e2996 99e36ae2
Wed Oct 15 07:31:11 2008  factoring 581611377564460147190254458089733717901553248586056816556993159064446199463882568826397249475201 (96 digits)
Wed Oct 15 07:31:13 2008  searching for 15-digit factors
Wed Oct 15 07:31:15 2008  commencing quadratic sieve (96-digit input)
Wed Oct 15 07:31:15 2008  using multiplier of 5
Wed Oct 15 07:31:15 2008  using 64kb Pentium 4 sieve core
Wed Oct 15 07:31:15 2008  sieve interval: 18 blocks of size 65536
Wed Oct 15 07:31:15 2008  processing polynomials in batches of 6
Wed Oct 15 07:31:15 2008  using a sieve bound of 2296873 (84706 primes)
Wed Oct 15 07:31:15 2008  using large prime bound of 344530950 (28 bits)
Wed Oct 15 07:31:15 2008  using double large prime bound of 2328149289953700 (43-52 bits)
Wed Oct 15 07:31:15 2008  using trial factoring cutoff of 52 bits
Wed Oct 15 07:31:15 2008  polynomial 'A' values have 12 factors
Wed Oct 15 16:02:07 2008  85039 relations (20512 full + 64527 combined from 1285560 partial), need 84802
Wed Oct 15 16:02:12 2008  begin with 1306072 relations
Wed Oct 15 16:02:14 2008  reduce to 223844 relations in 12 passes
Wed Oct 15 16:02:14 2008  attempting to read 223844 relations
Wed Oct 15 16:02:21 2008  recovered 223844 relations
Wed Oct 15 16:02:21 2008  recovered 210027 polynomials
Wed Oct 15 16:02:21 2008  attempting to build 85039 cycles
Wed Oct 15 16:02:21 2008  found 85039 cycles in 6 passes
Wed Oct 15 16:02:21 2008  distribution of cycle lengths:
Wed Oct 15 16:02:21 2008     length 1 : 20512
Wed Oct 15 16:02:21 2008     length 2 : 14602
Wed Oct 15 16:02:21 2008     length 3 : 13960
Wed Oct 15 16:02:21 2008     length 4 : 11605
Wed Oct 15 16:02:21 2008     length 5 : 8985
Wed Oct 15 16:02:21 2008     length 6 : 6035
Wed Oct 15 16:02:21 2008     length 7 : 3886
Wed Oct 15 16:02:21 2008     length 9+: 5454
Wed Oct 15 16:02:21 2008  largest cycle: 20 relations
Wed Oct 15 16:02:22 2008  matrix is 84706 x 85039 (23.8 MB) with weight 5898680 (69.36/col)
Wed Oct 15 16:02:22 2008  sparse part has weight 5898680 (69.36/col)
Wed Oct 15 16:02:24 2008  filtering completed in 3 passes
Wed Oct 15 16:02:24 2008  matrix is 80977 x 81040 (22.8 MB) with weight 5643742 (69.64/col)
Wed Oct 15 16:02:24 2008  sparse part has weight 5643742 (69.64/col)
Wed Oct 15 16:02:24 2008  saving the first 48 matrix rows for later
Wed Oct 15 16:02:25 2008  matrix is 80929 x 81040 (16.7 MB) with weight 4727767 (58.34/col)
Wed Oct 15 16:02:25 2008  sparse part has weight 3887127 (47.97/col)
Wed Oct 15 16:02:25 2008  matrix includes 64 packed rows
Wed Oct 15 16:02:25 2008  using block size 21845 for processor cache size 512 kB
Wed Oct 15 16:02:26 2008  commencing Lanczos iteration
Wed Oct 15 16:02:26 2008  memory use: 14.7 MB
Wed Oct 15 16:03:47 2008  lanczos halted after 1282 iterations (dim = 80929)
Wed Oct 15 16:03:47 2008  recovered 18 nontrivial dependencies
Wed Oct 15 16:03:50 2008  prp36 factor: 144033299950349239793375411134290953
Wed Oct 15 16:03:50 2008  prp61 factor: 4038034105758540631100193593028886436502038569222778774393017
Wed Oct 15 16:03:50 2008  elapsed time 08:32:39

(26·10¹⁴⁴-17)/9 = 2(8)₁₄₃7_<145> = 193 · C143

C143 = P37 · P41 · P66

P37 = 1782151055743702442344825007074171523_<37>

P41 = 16521095534080175058325500493943837954429_<41>

P66 = 508382011054035835676406114546052839485630855313152746851685502977_<66>

Number: 28887_144
N=14968336211859527921704087507196315486470926885434657455382843983880253310305123776626367299942429476108232584916522740356937248128957973517559
  ( 143 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=1782151055743702442344825007074171523 (pp37)
 r2=16521095534080175058325500493943837954429 (pp41)
 r3=508382011054035835676406114546052839485630855313152746851685502977 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 19.60 hours.
Scaled time: 19.78 units (timescale=1.009).
Factorization parameters were as follows:
name: 28887_144
n: 14968336211859527921704087507196315486470926885434657455382843983880253310305123776626367299942429476108232584916522740356937248128957973517559
m: 100000000000000000000000000000
c5: 13
c0: -85
skew: 1.46
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 3250001)
Primes: RFBsize:114155, AFBsize:114742, largePrimes:2972820 encountered
Relations: rels:2998620, finalFF:273682
Max relations in full relation-set: 28
Initial matrix: 228962 x 273682 with sparse part having weight 31732339.
Pruned matrix : 216250 x 217458 with weight 23641325.
Total sieving time: 19.18 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.32 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 19.60 hours.
 --------- CPU info (if available) ----------

Oct 15, 2008 (6th)

By Serge Batalov / PFGW

(67·10²⁶¹⁹⁴-13)/9 = 7(4)₂₆₁₉₃3_<26195> is PRP.

Oct 15, 2008 (5th)

By Sinkiti Sibata / Msieve, GGNFS

(26·10¹¹⁰-17)/9 = 2(8)₁₀₉7_<111> = 7 · 67 · 1367 · 43744265513290879_<17> · C89

C89 = P40 · P49

P40 = 6001131512745860146554482788707579097961_<40>

P49 = 1716466010916447043435880068391731173711732687851_<49>

Wed Oct 15 05:27:12 2008  Msieve v. 1.38
Wed Oct 15 05:27:12 2008  random seeds: dba802fa 24726388
Wed Oct 15 05:27:12 2008  factoring 10300738268667869941900222275951412419627031093089343147466513267202507820099968563571811 (89 digits)
Wed Oct 15 05:27:13 2008  searching for 15-digit factors
Wed Oct 15 05:27:15 2008  commencing quadratic sieve (89-digit input)
Wed Oct 15 05:27:15 2008  using multiplier of 11
Wed Oct 15 05:27:15 2008  using 64kb Pentium 4 sieve core
Wed Oct 15 05:27:15 2008  sieve interval: 14 blocks of size 65536
Wed Oct 15 05:27:15 2008  processing polynomials in batches of 8
Wed Oct 15 05:27:15 2008  using a sieve bound of 1537147 (58224 primes)
Wed Oct 15 05:27:15 2008  using large prime bound of 122971760 (26 bits)
Wed Oct 15 05:27:15 2008  using double large prime bound of 364459767191680 (42-49 bits)
Wed Oct 15 05:27:15 2008  using trial factoring cutoff of 49 bits
Wed Oct 15 05:27:15 2008  polynomial 'A' values have 11 factors
Wed Oct 15 06:57:24 2008  58395 relations (16414 full + 41981 combined from 610832 partial), need 58320
Wed Oct 15 06:57:26 2008  begin with 627246 relations
Wed Oct 15 06:57:27 2008  reduce to 139598 relations in 11 passes
Wed Oct 15 06:57:27 2008  attempting to read 139598 relations
Wed Oct 15 06:57:30 2008  recovered 139598 relations
Wed Oct 15 06:57:30 2008  recovered 115984 polynomials
Wed Oct 15 06:57:30 2008  attempting to build 58395 cycles
Wed Oct 15 06:57:31 2008  found 58395 cycles in 6 passes
Wed Oct 15 06:57:31 2008  distribution of cycle lengths:
Wed Oct 15 06:57:31 2008     length 1 : 16414
Wed Oct 15 06:57:31 2008     length 2 : 11404
Wed Oct 15 06:57:31 2008     length 3 : 10538
Wed Oct 15 06:57:31 2008     length 4 : 7465
Wed Oct 15 06:57:31 2008     length 5 : 5335
Wed Oct 15 06:57:31 2008     length 6 : 3216
Wed Oct 15 06:57:31 2008     length 7 : 1855
Wed Oct 15 06:57:31 2008     length 9+: 2168
Wed Oct 15 06:57:31 2008  largest cycle: 20 relations
Wed Oct 15 06:57:31 2008  matrix is 58224 x 58395 (14.0 MB) with weight 3437825 (58.87/col)
Wed Oct 15 06:57:31 2008  sparse part has weight 3437825 (58.87/col)
Wed Oct 15 06:57:32 2008  filtering completed in 3 passes
Wed Oct 15 06:57:32 2008  matrix is 53593 x 53657 (13.0 MB) with weight 3201131 (59.66/col)
Wed Oct 15 06:57:32 2008  sparse part has weight 3201131 (59.66/col)
Wed Oct 15 06:57:32 2008  saving the first 48 matrix rows for later
Wed Oct 15 06:57:32 2008  matrix is 53545 x 53657 (9.3 MB) with weight 2631124 (49.04/col)
Wed Oct 15 06:57:32 2008  sparse part has weight 2128145 (39.66/col)
Wed Oct 15 06:57:32 2008  matrix includes 64 packed rows
Wed Oct 15 06:57:32 2008  using block size 21462 for processor cache size 512 kB
Wed Oct 15 06:57:33 2008  commencing Lanczos iteration
Wed Oct 15 06:57:33 2008  memory use: 8.5 MB
Wed Oct 15 06:58:05 2008  lanczos halted after 848 iterations (dim = 53545)
Wed Oct 15 06:58:05 2008  recovered 18 nontrivial dependencies
Wed Oct 15 06:58:07 2008  prp40 factor: 6001131512745860146554482788707579097961
Wed Oct 15 06:58:07 2008  prp49 factor: 1716466010916447043435880068391731173711732687851
Wed Oct 15 06:58:07 2008  elapsed time 01:30:55

(26·10¹²⁷-17)/9 = 2(8)₁₂₆7_<128> = 3² · 41 · 2410931 · C119

C119 = P45 · P75

P45 = 176708995742868033725601335173947516522546743_<45>

P75 = 183764252538525370473390572332885210401984688084514695855899989508440764331_<75>

Number: 28887_127
N=32472796519521605950704707962779367391733293104734093089187017362312920723741833758460503464549450724888744205594623933
  ( 119 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=176708995742868033725601335173947516522546743 (pp45)
 r2=183764252538525370473390572332885210401984688084514695855899989508440764331 (pp75)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.81 hours.
Scaled time: 2.98 units (timescale=0.783).
Factorization parameters were as follows:
name: 28887_127
n: 32472796519521605950704707962779367391733293104734093089187017362312920723741833758460503464549450724888744205594623933
m: 10000000000000000000000000
c5: 2600
c0: -17
skew: 0.37
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:63951, AFBsize:63953, largePrimes:1446680 encountered
Relations: rels:1429455, finalFF:159869
Max relations in full relation-set: 28
Initial matrix: 127971 x 159869 with sparse part having weight 9961803.
Pruned matrix : 117646 x 118349 with weight 5787394.
Total sieving time: 3.68 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 3.81 hours.
 --------- CPU info (if available) ----------

(26·10¹³⁴-17)/9 = 2(8)₁₃₃7_<135> = 7 · 29 · 68113 · 3973247 · C121

C121 = P41 · P81

P41 = 15177348453623950838024813965176032894221_<41>

P81 = 346468154200169948635742296967949960762542906674809782261859479169727252266013559_<81>

Number: 28887_134
N=5258467904379893917425879319299797702544751262661304331982090981680291206386080564645724578974138223446115582384798742539
  ( 121 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=15177348453623950838024813965176032894221 (pp41)
 r2=346468154200169948635742296967949960762542906674809782261859479169727252266013559 (pp81)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 8.36 hours.
Scaled time: 8.38 units (timescale=1.002).
Factorization parameters were as follows:
name: 28887_134
n: 5258467904379893917425879319299797702544751262661304331982090981680291206386080564645724578974138223446115582384798742539
m: 1000000000000000000000000000
c5: 13
c0: -85
skew: 1.46
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1675001)
Primes: RFBsize:78498, AFBsize:64473, largePrimes:1753499 encountered
Relations: rels:1865992, finalFF:264471
Max relations in full relation-set: 28
Initial matrix: 143036 x 264471 with sparse part having weight 26412188.
Pruned matrix : 117853 x 118632 with weight 11238155.
Total sieving time: 8.22 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 8.36 hours.
 --------- CPU info (if available) ----------

(26·10¹³⁷-17)/9 = 2(8)₁₃₆7_<138> = 41 · 109 · C134

C134 = P36 · P37 · P62

P36 = 526294333620542813446146956660416129_<36>

P37 = 2734255542207168448248267232752481223_<37>

P62 = 44921338536578715635599211917927596126790380075342452322497069_<62>

Number: 28887_137
N=64642848263345018771288630317495835508813803734367618905546853633673951418413266701474354193083215235822082991472116556027945600556923
  ( 134 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=526294333620542813446146956660416129 (pp36)
 r2=2734255542207168448248267232752481223 (pp37)
 r3=44921338536578715635599211917927596126790380075342452322497069 (pp62)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 8.31 hours.
Scaled time: 8.41 units (timescale=1.011).
Factorization parameters were as follows:
name: 28887_137
n: 64642848263345018771288630317495835508813803734367618905546853633673951418413266701474354193083215235822082991472116556027945600556923
m: 1000000000000000000000000000
c5: 2600
c0: -17
skew: 0.37
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1675001)
Primes: RFBsize:78498, AFBsize:63953, largePrimes:1617804 encountered
Relations: rels:1626585, finalFF:164691
Max relations in full relation-set: 28
Initial matrix: 142518 x 164691 with sparse part having weight 17091487.
Pruned matrix : 136891 x 137667 with weight 12918139.
Total sieving time: 8.15 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 8.31 hours.
 --------- CPU info (if available) ----------

Oct 15, 2008 (4th)

By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1

(26·10¹¹¹-17)/9 = 2(8)₁₁₀7_<112> = C112

C112 = P35 · P77

P35 = 73754123201921790624647439007473229_<35>

P77 = 39169184900751608644593613969599919588169278840249296543982129934412148934803_<77>

SNFS difficulty: 113 digits.
Divisors found:
 r1=73754123201921790624647439007473229
 r2=39169184900751608644593613969599919588169278840249296543982129934412148934803
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.300).
Factorization parameters were as follows:
n: 2888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887
m: 10000000000000000000000000000
c4: 13
c0: -85
skew: 1.6
type: snfs
Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [225000, 345001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 48154 x 48371
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,113,4,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000
total time: 0.60 hours.

(26·10¹⁰³-17)/9 = 2(8)₁₀₂7_<104> = 3 · 31 · 463 · 115597 · C94

C94 = P31 · P64

P31 = 1972108063362367189451376248797_<31>

P64 = 2942995695171047624969249628590188180420693681219570640764638677_<64>

N=5803905540887558263985489078759725396885725234535263165222238080255654302916465210789360921569
  ( 94 digits)
SNFS difficulty: 105 digits.
Divisors found:
 r1=1972108063362367189451376248797
 r2=2942995695171047624969249628590188180420693681219570640764638677
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.316).
Factorization parameters were as follows:
n: 5803905540887558263985489078759725396885725234535263165222238080255654302916465210789360921569
m: 100000000000000000000000000
c4: 13
c0: -85
skew: 1.6
type: snfs
Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [225000, 285001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 37181 x 37410
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,105,4,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000
total time: 0.40 hours.

(26·10¹²⁰-17)/9 = 2(8)₁₁₉7_<121> = 5653 · 11949605451227_<14> · 4379004068674901_<16> · C88

C88 = P31 · P58

P31 = 3759727749368860911148358537753_<31>

P58 = 2597565697150329074823057784392058457450845003898821264709_<58>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=1986497679
Step 1 took 3732ms
Step 2 took 2901ms
********** Factor found in step 2: 3759727749368860911148358537753
Found probable prime factor of 31 digits: 3759727749368860911148358537753
Probable prime cofactor 2597565697150329074823057784392058457450845003898821264709 has 58 digits

(26·10¹⁶⁵-17)/9 = 2(8)₁₆₄7_<166> = 263957 · 4058137 · C154

C154 = P31 · C123

P31 = 7818152593406970277472416624103_<31>

C123 = [344958465819430965530710574646567760779022977241793408151628340601011887317136749920912630213301975588157023174300056198581_<123>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2782357100
Step 1 took 14693ms
Step 2 took 13021ms
********** Factor found in step 2: 7818152593406970277472416624103
Found probable prime factor of 31 digits: 7818152593406970277472416624103
Composite cofactor 344958465819430965530710574646567760779022977241793408151628340601011887317136749920912630213301975588157023174300056198581 has 123 digits

Oct 15, 2008 (3rd)

By Serge Batalov / PFGW

(38·10³⁹⁸⁵⁵+61)/9 = 4(2)₃₉₈₅₄9_<39856> is PRP.

(19·10²⁷²²²+53)/9 = 2(1)₂₇₂₂₁7_<27223> is PRP.

Oct 15, 2008 (2nd)

Factorizations of 288...887 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Oct 15, 2008

By matsui / GMP-ECM

4·10¹⁹²+9 = 4(0)₁₉₁9_<193> = 13 · 3084049 · 20054833 · 362793721871669762743297557966121_<33> · C146

C146 = P35 · P111

P35 = 34347828192180472650311406770836321_<35>

P111 = 399224581811496883777327450848889939055934413354952004388681194427258371965399996716709123759572132028042808069_<111>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
13712497346156392212676019147625431370510365650834689585981115102219563918727772856984851299023907414810459127022107546442249298162322016417074149
=
34347828192180472650311406770836321* 399224581811496883777327450848889939055934413354952004388681194427258371965399996716709123759572132028042808069

4·10¹⁹³+9 = 4(0)₁₉₂9_<194> = 7 · 11437 · 13853895929_<11> · 284374155722383_<15> · 40774884715492908428204364418823_<32> · C133

C133 = P31 · C103

P31 = 1455040861595700679822195920931_<31>

C103 = [2137567576041104372111455292736110616642012466158171115994587987948441933469530773750128809166787452761_<103>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
126820010468908806071880109357043266345981215766729369753337225868175064400665316164905372765852198104155866881930631191806135695255612601001613076169469586595362093
=
1455040861595700679822195920931* 87159071484651651948214084667005400934366096726356153793048130126152962818451986017052417673584656337918155219572308362365470331720303

Oct 14, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(25·10¹⁸⁶-43)/9 = 2(7)₁₈₅3_<187> = 131 · C185

C185 = P80 · P105

P80 = 31424022345942293721314643526777454557385387249420546118526109881135411541015663_<80>

P105 = 674783459735086705269541484554441010464640876312706928931469006792480841626496533516974299488863906180641_<105>

Number: n
N=21204410517387616624257845631891433418150975402883799830364715860899067005937234944868532654792196776929601357082273112807463952502120441051738761662425784563189143341815097540288379983
  ( 185 digits)
SNFS difficulty: 187 digits.
Divisors found:

Tue Oct 14 05:57:25 2008  prp80 factor: 31424022345942293721314643526777454557385387249420546118526109881135411541015663
Tue Oct 14 05:57:25 2008  prp105 factor: 674783459735086705269541484554441010464640876312706928931469006792480841626496533516974299488863906180641
Tue Oct 14 05:57:26 2008  elapsed time 06:56:43 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 73.50 hours.
Scaled time: 150.32 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_2_7_185_3
n: 21204410517387616624257845631891433418150975402883799830364715860899067005937234944868532654792196776929601357082273112807463952502120441051738761662425784563189143341815097540288379983
type: snfs
skew: 0.70
deg: 5
c5: 250
c0: -43
m: 10000000000000000000000000000000000000
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 6500001)
Primes: RFBsize:602489, AFBsize:602475, largePrimes:14280891 encountered
Relations: rels:14024050, finalFF:1214304
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 73.14 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.5,2.5,100000
total time: 73.50 hours.
 --------- CPU info (if available) ----------

Oct 14, 2008

By Serge Batalov / PFGW

(19·10¹⁷⁵²⁰+53)/9 = 2(1)₁₇₅₁₉7_<17521> is PRP.

(64·10¹⁷⁶⁶⁶+17)/9 = 7(1)₁₇₆₆₅3_<17667> is PRP.

(64·10²⁰⁸⁶⁴+17)/9 = 7(1)₂₀₈₆₃3_<20865> is PRP.

Oct 13, 2008 (3rd)

By Serge Batalov / PFGW

(35·10¹⁰¹⁷⁶-17)/9 = 3(8)₁₀₁₇₅7_<10177> is PRP.

(46·10¹²⁸⁰⁹+53)/9 = 5(1)₁₂₈₀₈7_<12810> is PRP.

(46·10¹⁵⁰⁷¹+53)/9 = 5(1)₁₅₀₇₀7_<15072> is PRP.

(58·10¹¹³⁹¹+41)/9 = 6(4)₁₁₃₉₀9_<11392> is PRP.

(58·10¹¹⁶⁷³+41)/9 = 6(4)₁₁₆₇₂9_<11674> is PRP.

Oct 13, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(26·10¹⁶⁷-53)/9 = 2(8)₁₆₆3_<168> = 7 · 2399 · 6323 · 127691 · 2938021 · 180397057763401_<15> · C134

C134 = P39 · P95

P39 = 641381666556496229620462884848095705753_<39>

P95 = 62678442074912406253135639578417547373032295596932760185025327623693360325589453770923938796959_<95>

Number: 28883_167
N=40200803635172132619878290809551400226863431975204543229129709070472743443263344426800924623027279256511540239797176634645520875205127
  ( 134 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=641381666556496229620462884848095705753 (pp39)
 r2=62678442074912406253135639578417547373032295596932760185025327623693360325589453770923938796959 (pp95)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 143.96 hours.
Scaled time: 145.25 units (timescale=1.009).
Factorization parameters were as follows:
name: 28883_167
n: 40200803635172132619878290809551400226863431975204543229129709070472743443263344426800924623027279256511540239797176634645520875205127
m: 1000000000000000000000000000000000
c5: 2600
c0: -53
skew: 0.46
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 8050001)
Primes: RFBsize:380800, AFBsize:380897, largePrimes:6325510 encountered
Relations: rels:6667158, finalFF:966762
Max relations in full relation-set: 28
Initial matrix: 761764 x 966762 with sparse part having weight 80074010.
Pruned matrix : 602881 x 606753 with weight 61848504.
Total sieving time: 139.97 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 3.75 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 143.96 hours.
 --------- CPU info (if available) ----------

Oct 13, 2008

By Serge Batalov / Msieve-1.38

(68·10¹⁷³+13)/9 = 7(5)₁₇₂7_<174> = 11² · 107 · 6606011 · C163

C163 = P43 · P57 · P64

P43 = 6610570985981893588217485599928065911900503_<43>

P57 = 580045643086614207620043405574822802210547317327758301137_<57>

P64 = 2303863904620842108302141414515874627622737561828500894022443411_<64>

SNFS difficulty: 174 digits.
Divisors found:
 r1=6610570985981893588217485599928065911900503
 r2=580045643086614207620043405574822802210547317327758301137
 r3=2303863904620842108302141414515874627622737561828500894022443411
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.596).
Factorization parameters were as follows:
n: 8834011550082961570244632107524709874248369610339476895245395710746521446283572650471917371886973695062656009852723821223435749028679163809470732622166742120828421
m: 20000000000000000000000000000000000
c5: 2125
c0: 13
skew: 0.36
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [3700000, 7200001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1243431 x 1243679
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 6.00 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,174,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,54,54,2.6,2.6,100000
total time: 61.00 hours.

Oct 12, 2008 (2nd)

By Jo Yeong Uk / GGNFS

(8·10¹⁶⁹+1)/9 = (8)₁₆₈9_<169> = 3 · 134838716741_<12> · 104450884973579663627_<21> · C138

C138 = P62 · P76

P62 = 67798627312166014383929640769882002342372388847421981172672289_<62>

P76 = 3102977219325565368707599249750650170581500768570091107590293404218912306981_<76>

Number: 88889_169
N=210377596051195229278114432178007432868301425550480627660077223627399086374121611283425294082727290932956598726259701763200994497679949509
  ( 138 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=67798627312166014383929640769882002342372388847421981172672289 (pp62)
 r2=3102977219325565368707599249750650170581500768570091107590293404218912306981 (pp76)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 57.72 hours.
Scaled time: 137.30 units (timescale=2.379).
Factorization parameters were as follows:
n: 210377596051195229278114432178007432868301425550480627660077223627399086374121611283425294082727290932956598726259701763200994497679949509
m: 10000000000000000000000000000000000
c5: 4
c0: 5
skew: 1.05
type: snfs
Factor base limits: 7000000/7000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [3500000, 6700001)
Primes: RFBsize:476648, AFBsize:476559, largePrimes:6565015 encountered
Relations: rels:7040243, finalFF:1111712
Max relations in full relation-set: 28
Initial matrix: 953271 x 1111712 with sparse part having weight 56167175.
Pruned matrix : 811416 x 816246 with weight 37322717.
Total sieving time: 53.99 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 3.57 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,7000000,7000000,27,27,49,49,2.5,2.5,100000
total time: 57.72 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673800)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Calibrating delay using timer specific routine.. 5344.40 BogoMIPS (lpj=2672204)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)

(52·10¹⁷⁵-7)/9 = 5(7)₁₇₅_<176> = 3 · 44119 · 505411 · 108654820435393_<15> · 107924410927665683001385431856290806743357967_<45> · C107

C107 = P53 · P55

P53 = 31288719349461934155851843896696720363661033230725719_<53>

P55 = 2354034136349944678676611987548074368673930574524031959_<55>

Number: 57777_175
N=73654713431306427074409733299667444457566434315864090073277343599353361668298394489931133898094003519253521
  ( 107 digits)
Divisors found:
 r1=31288719349461934155851843896696720363661033230725719 (pp53)
 r2=2354034136349944678676611987548074368673930574524031959 (pp55)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 8.93 hours.
Scaled time: 21.32 units (timescale=2.388).
Factorization parameters were as follows:
name: 57777_175
n: 73654713431306427074409733299667444457566434315864090073277343599353361668298394489931133898094003519253521
skew: 17886.39
# norm 2.10e+15
c5: 110160
c4: 5442417444
c3: -149713271052144
c2: -1264206659453831591
c1: 16575436908728770826116
c0: 83199602893546180382049300
# alpha -7.26
Y1: 24471492101
Y0: -231758072512480916699
# Murphy_E 1.55e-09
# M 38194101069741355399707275664143179168743790556414615227357162011118711033618235651356369089463785195133086
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved algebraic special-q in [900000, 1400001)
Primes: RFBsize:135072, AFBsize:134855, largePrimes:4986712 encountered
Relations: rels:5028126, finalFF:374807
Max relations in full relation-set: 28
Initial matrix: 270008 x 374807 with sparse part having weight 36527943.
Pruned matrix : 213572 x 214986 with weight 18438358.
Polynomial selection time: 0.55 hours.
Total sieving time: 8.04 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,50,50,2.6,2.6,50000
total time: 8.93 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673800)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Calibrating delay using timer specific routine.. 5344.40 BogoMIPS (lpj=2672204)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)

Oct 12, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(8·10¹⁶⁸-71)/9 = (8)₁₆₇1_<168> = 7 · 83 · 173 · 180380873 · 1899953897191177928067350987423_<31> · C125

C125 = P41 · P84

P41 = 30196695799267574612214510483582331213049_<41>

P84 = 854539752983938975409709010100505812475698391065616612344483235106134591693546624847_<84>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 25804276969237260916253285418344233476581942122469731457748077108761430322204665370889961476489935277885313096413193234028503 (125 digits)
Using B1=6486000, B2=14271342550, polynomial Dickson(12), sigma=3532503115
Step 1 took 57942ms
Step 2 took 23495ms
********** Factor found in step 2: 30196695799267574612214510483582331213049
Found probable prime factor of 41 digits: 30196695799267574612214510483582331213049
Probable prime cofactor 854539752983938975409709010100505812475698391065616612344483235106134591693546624847 has 84 digits

(26·10¹⁸⁵-53)/9 = 2(8)₁₈₄3_<186> = 7 · C185

C185 = P68 · P118

P68 = 11967880220222771535977473028528815286409995203134321966881379578399_<68>

P118 = 3448383549168999632700369166622141002514388314197364283079763510370070630825743226204284898075719770357515051628529131_<118>

Number: n
N=41269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269
  ( 185 digits)
SNFS difficulty: 186 digits.
Divisors found:

Sun Oct 12 22:19:14 2008  prp68 factor: 11967880220222771535977473028528815286409995203134321966881379578399
Sun Oct 12 22:19:14 2008  prp118 factor: 3448383549168999632700369166622141002514388314197364283079763510370070630825743226204284898075719770357515051628529131
Sun Oct 12 22:19:14 2008  elapsed time 16:31:56 (Msieve 1.38)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 64.71 hours.
Scaled time: 84.58 units (timescale=1.307).
Factorization parameters were as follows:
name: KA_2_8_184_3
n: 41269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269
type: snfs
skew: 1.15
deg: 5
c5: 26
c0: -53
m: 10000000000000000000000000000000000000
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 6100001)
Primes: RFBsize:602489, AFBsize:601295, largePrimes:14538080 encountered
Relations: rels:14376374, finalFF:1255184
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 64.04 hours.
Total relation processing time: 0.67 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.5,2.5,100000
total time: 64.71 hours.
 --------- CPU info (if available) ----------

Oct 11, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(26·10¹⁶⁶-53)/9 = 2(8)₁₆₅3_<167> = 521 · 1597 · 197787847 · C153

C153 = P54 · P99

P54 = 265118142137434755285925832970724934903901408844488191_<54>

P99 = 662138969195960498557622691000644669495559191169984336202123246282041767740138009213412163051256367_<99>

Number: 28883_166
N=175545053350029188479712622193807947858289238010646688835359710365749635407791235397932755833241463063172111251654787140131951630486754812817265645062097
  ( 153 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=265118142137434755285925832970724934903901408844488191 (pp54)
 r2=662138969195960498557622691000644669495559191169984336202123246282041767740138009213412163051256367 (pp99)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 133.61 hours.
Scaled time: 134.68 units (timescale=1.008).
Factorization parameters were as follows:
28883_166
n: 175545053350029188479712622193807947858289238010646688835359710365749635407791235397932755833241463063172111251654787140131951630486754812817265645062097
m: 1000000000000000000000000000000000
c5: 260
c0: -53
skew: 0.73
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 7650001)
Primes: RFBsize:380800, AFBsize:381462, largePrimes:6278885 encountered
Relations: rels:6593734, finalFF:945834
Max relations in full relation-set: 28
Initial matrix: 762329 x 945834 with sparse part having weight 74842668.
Pruned matrix : 619288 x 623163 with weight 56284364.
Total sieving time: 129.71 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 3.66 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 133.61 hours.
 --------- CPU info (if available) ----------

Oct 11, 2008

By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1

2·10¹⁷⁶-7 = 1(9)₁₇₅3_<177> = 31 · 167 · 84349 · 762539 · 5303471 · C156

C156 = P63 · P93

P63 = 337158791033264179423030381537184109066737553257391166972636621_<63>

P93 = 335903976890265082828384698860438605538743727883895495015727111914842671618296153307348566709_<93>

SNFS difficulty: 176 digits.
Divisors found:
 r1=337158791033264179423030381537184109066737553257391166972636621
 r2=335903976890265082828384698860438605538743727883895495015727111914842671618296153307348566709
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.735).
Factorization parameters were as follows:
n: 113252978751587285152120274127084084614582650358880557515891373662125548580378985430928277226131608413432226944828272335376297243741299360815777087034850289
Y1: 1
Y0: -100000000000000000000000000000000000
c5: 20
c0: -7
skew: 0.81
type: snfs
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [5000000, 7900001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1260259 x 1260507
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,10000000,10000000,27,27,54,54,2.6,2.6,100000
total time: 60.00 hours.

9·10¹⁷³+1 = 9(0)₁₇₂1_<174> = 263 · 659 · 719503 · C163

C163 = P48 · P53 · P64

P48 = 119042288029767638893284897945328190576465889847_<48>

P53 = 17758729179548142956399209216703776600136321973088783_<53>

P64 = 3413937667616485389431567664007791715409001756176675366899769851_<64>

SNFS difficulty: 173 digits.
Divisors found:
 r1=119042288029767638893284897945328190576465889847
 r2=17758729179548142956399209216703776600136321973088783
 r3=3413937667616485389431567664007791715409001756176675366899769851
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.924).
Factorization parameters were as follows:
n: 7217199947136759338491991713436421871033060911813262302390708730896124696133610146983344119522988647120966471514735115383937781143270879649291821299541605910126051
m: 10000000000000000000000000000000000
c5: 9000
c0: 1
skew: 0.16
type: snfs
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [4500000, 8000001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1277412 x 1277660
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,54,54,2.6,2.6,100000
total time: 50.00 hours.

(23·10¹⁷⁷+1)/3 = 7(6)₁₇₆7_<178> = 11 · 31 · 113 · 659 · 17107 · 26189 · 7423487 · C155

C155 = P37 · P119

P37 = 1222827647443896135605384277317373191_<37>

P119 = 74237334747024884434878158461319294495747514134705484811961053103278950707050742632109379197705733552024608749051925771_<119>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=486638099
Step 1 took 18977ms
Step 2 took 14697ms
********** Factor found in step 2: 1222827647443896135605384277317373191
Found probable prime factor of 37 digits: 1222827647443896135605384277317373191
Probable prime cofactor 74237334747024884434878158461319294495747514134705484811961053103278950707050742632109379197705733552024608749051925771 has 119 digits

(52·10¹⁷⁵-7)/9 = 5(7)₁₇₅_<176> = 3 · 44119 · 505411 · 108654820435393_<15> · C151

C151 = P45 · C107

P45 = 107924410927665683001385431856290806743357967_<45>

C107 = [73654713431306427074409733299667444457566434315864090073277343599353361668298394489931133898094003519253521_<107>]

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=4191283557
Step 1 took 61895ms
Step 2 took 34491ms
********** Factor found in step 2: 107924410927665683001385431856290806743357967
Found probable prime factor of 45 digits: 107924410927665683001385431856290806743357967
Composite cofactor 73654713431306427074409733299667444457566434315864090073277343599353361668298394489931133898094003519253521 has 107 digits

Oct 10, 2008 (4th)

By Wataru Sakai / GGNFS

(26·10¹⁸³-71)/9 = 2(8)₁₈₂1_<184> = C184

C184 = P54 · P130

P54 = 593003743193204034604146674734025028736359951238501379_<54>

P130 = 4871619988995031102117074254428860421831102448543408974537652092788862101145035929409514449229400537835795554628125214530032586939_<130>

Number: 28881_183
N=2888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888881
  ( 184 digits)
SNFS difficulty: 184 digits.
Divisors found:
 r1=593003743193204034604146674734025028736359951238501379 (pp54)
 r2=4871619988995031102117074254428860421831102448543408974537652092788862101145035929409514449229400537835795554628125214530032586939 (pp130)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 785.58 hours.
Scaled time: 1582.94 units (timescale=2.015).
Factorization parameters were as follows:
n: 2888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888881
m: 2000000000000000000000000000000000000
c5: 1625
c0: -142
skew: 0.61
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 14200001)
Primes: RFBsize:501962, AFBsize:500922, largePrimes:6904629 encountered
Relations: rels:7420737, finalFF:1166355
Max relations in full relation-set: 32
Initial matrix: 1002950 x 1166355 with sparse part having weight 109741467.
Pruned matrix : 875913 x 880991 with weight 88948169.
Total sieving time: 776.71 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 8.48 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,184,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 785.58 hours.
 --------- CPU info (if available) ----------

Oct 10, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(25·10¹⁸⁵+11)/9 = 2(7)₁₈₄9_<186> = 3 · C185

C185 = P67 · P119

P67 = 1823763826037021477970377431624932839442513244497272766446966241367_<67>

P119 = 50770056555948494869560884191142325298211888542444804452840248720103134991812471526266558180708741955889392180067993879_<119>

Number: n
N=92592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592593
  ( 185 digits)
SNFS difficulty: 186 digits.
Divisors found:

Fri Oct 10 06:51:11 2008  prp67 factor: 1823763826037021477970377431624932839442513244497272766446966241367
Fri Oct 10 06:51:11 2008  prp119 factor: 50770056555948494869560884191142325298211888542444804452840248720103134991812471526266558180708741955889392180067993879
Fri Oct 10 06:51:12 2008  elapsed time 04:57:15 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 48.26 hours.
Scaled time: 93.05 units (timescale=1.928).
Factorization parameters were as follows:
name: KA_2_7_184_9
n: 92592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592593
type: snfs
skew: 0.85
deg: 5
c5: 25
c0: 11
m: 10000000000000000000000000000000000000
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 5300001)
Primes: RFBsize:602489, AFBsize:601876, largePrimes:13793332 encountered
Relations: rels:13528674, finalFF:1248100
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 47.92 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.5,2.5,100000
total time: 48.26 hours.
 --------- CPU info (if available) ----------

(2·10¹⁶⁷-11)/9 = (2)₁₆₆1_<167> = 3³ · 211 · 345979 · 8190545575864479761627_<22> · C136

C136 = P44 · P92

P44 = 22483399937205086685698973749619580104633619_<44>

P92 = 61223296584507659608164240577076192938735095756775297725553210186474662678695824030849575959_<92>

Number: n
N=1376507862583607912194299306720179473657830314931095313323900204083253155343440552393400001707363124784549392207334549098635997205565621
  ( 136 digits)
SNFS difficulty: 167 digits.
Divisors found:

Fri Oct 10 19:46:59 2008  prp44 factor: 22483399937205086685698973749619580104633619
Fri Oct 10 19:47:00 2008  prp92 factor: 61223296584507659608164240577076192938735095756775297725553210186474662678695824030849575959
Fri Oct 10 19:47:00 2008  elapsed time 01:21:20 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 10.30 hours.
Scaled time: 21.06 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_2_166_1
n: 1376507862583607912194299306720179473657830314931095313323900204083253155343440552393400001707363124784549392207334549098635997205565621
type: snfs
skew: 0.56
deg: 5
c5: 200
c0: -11
m: 1000000000000000000000000000000000
rlim: 5400000
alim: 5400000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 1800001)
Primes: RFBsize:374362, AFBsize:375528, largePrimes:14838620 encountered
Relations: rels:15562665, finalFF:1959922
Max relations in full relation-set: 28
Initial matrix: 749955 x 1959922 with sparse part having weight 219154798.
Pruned matrix : 
Total sieving time: 9.93 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5400000,5400000,28,28,52,52,2.5,2.5,100000
total time: 10.30 hours.
 --------- CPU info (if available) ----------

(13·10¹⁷⁰-31)/9 = 1(4)₁₆₉1_<171> = 3 · 19 · 236119276660919_<15> · C155

C155 = P60 · P95

P60 = 109065844527518766065659152112671088120780239748152362904203_<60>

P95 = 98402419407674987943082172616752732098497131153709107438685468235316808878942400958071245812309_<95>

Number: n
N=10732342976249175501514261110742800869349996874710556532865562180039360327636609694024258570779685560647369177417833819967466747928851454103481701085234727
  ( 155 digits)
SNFS difficulty: 171 digits.
Divisors found:

Fri Oct 10 22:50:54 2008  prp60 factor: 109065844527518766065659152112671088120780239748152362904203
Fri Oct 10 22:50:54 2008  prp95 factor: 98402419407674987943082172616752732098497131153709107438685468235316808878942400958071245812309
Fri Oct 10 22:50:54 2008  elapsed time 03:40:28 (Msieve 1.38)

Version: GGNFS-0.77.1-20050930-k8
Total time: 29.13 hours.
Scaled time: 24.41 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_1_4_169_1
n: 10732342976249175501514261110742800869349996874710556532865562180039360327636609694024258570779685560647369177417833819967466747928851454103481701085234727
type: snfs
skew: 1.19
deg: 5
c5: 13
c0: -31
m: 10000000000000000000000000000000000
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 6100001)
Primes: RFBsize:425648, AFBsize:426143, largePrimes:14169683 encountered
Relations: rels:13493805, finalFF:875185
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 28.85 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,52,52,2.5,2.5,100000
total time: 29.13 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

Oct 10, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(26·10¹⁷²-71)/9 = 2(8)₁₇₁1_<173> = 3 · 1867 · 9980458761793547_<16> · 32389267017818243837131_<23> · C131

C131 = P61 · P70

P61 = 2449546433911624471161459374915594356652322414642886072105793_<61>

P70 = 6513703188268288072413620827782285132171359163786368510031938034560281_<70>

Number: 28881_172
N=15955618416381363719105020564561792442731148624050997442594452601010541512632742936245978681162464959750190451806002119796467807833
  ( 131 digits)
SNFS difficulty: 173 digits.
Divisors found:
 r1=2449546433911624471161459374915594356652322414642886072105793 (pp61)
 r2=6513703188268288072413620827782285132171359163786368510031938034560281 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 242.20 hours.
Scaled time: 244.38 units (timescale=1.009).
Factorization parameters were as follows:
name: 28881_172
n: 15955618416381363719105020564561792442731148624050997442594452601010541512632742936245978681162464959750190451806002119796467807833
m: 10000000000000000000000000000000000
c5: 2600
c0: -71
skew: 0.49
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 12200001)
Primes: RFBsize:501962, AFBsize:500812, largePrimes:6616660 encountered
Relations: rels:7076277, finalFF:1134545
Max relations in full relation-set: 28
Initial matrix: 1002841 x 1134545 with sparse part having weight 77981353.
Pruned matrix : 891612 x 896690 with weight 60315465.
Total sieving time: 235.01 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 6.90 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 242.20 hours.
 --------- CPU info (if available) ----------

Oct 10, 2008

By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1

(16·10¹⁶⁹-43)/9 = 1(7)₁₆₈3_<170> = 13 · 1337081204948276467921_<22> · C148

C148 = P47 · P101

P47 = 14960913929144985858253456596284691608551594667_<47>

P101 = 68362543450116714569706242160205915953260475026395859705760545962255010206177617289863648239322570803_<101>

SNFS difficulty: 170 digits.
Divisors found:
 r1=14960913929144985858253456596284691608551594667
 r2=68362543450116714569706242160205915953260475026395859705760545962255010206177617289863648239322570803
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 1022766128534630473716139749411132618557924540474766154578045443849993035831818663230810420705936920336800737164136824385552259626574190971664707601
m: 10000000000000000000000000000000000
c5: 8
c0: -215
skew: 1.93
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [3000000, 5600001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1095583 x 1095831
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000
total time: 30.00 hours.

(10¹⁷⁶+11)/3 = (3)₁₇₅7_<176> = 37 · 619 · 5807147 · 25654907 · C157

C157 = P70 · P88

P70 = 4086161435966825565731672088764901305281427456131784256360630460786921_<70>

P88 = 2390768841211409882313112507942100812266380438329776481094137736714719683197884863631231_<88>

SNFS difficulty: 176 digits.
Divisors found:
 r1=4086161435966825565731672088764901305281427456131784256360630460786921
 r2=2390768841211409882313112507942100812266380438329776481094137736714719683197884863631231
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.618).
Factorization parameters were as follows:
n: 9769067441269158180523604400486296984649389790765301062586030897703330125403155429472917988622131386228273403986649763681756430041630652919266860669811929751
Y1: 1
Y0: -100000000000000000000000000000000000
c5: 10
c0: 11
skew: 1.02
type: snfs
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [5000000, 8100001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1284153 x 1284401
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,10000000,10000000,27,27,54,54,2.6,2.6,100000
total time: 50.00 hours.

(22·10¹⁷⁷+41)/9 = 2(4)₁₇₆9_<178> = 173 · 1540115542109_<13> · C163

C163 = P31 · C133

P31 = 3988176640532111179738994803247_<31>

C133 = [2300415998333757249778490685464197237196599067392634238293373017266221785902267818855923626007378850090684685815884380328807466034631_<133>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1068787070
Step 1 took 18926ms
********** Factor found in step 1: 3988176640532111179738994803247
Found probable prime factor of 31 digits: 3988176640532111179738994803247
Composite cofactor 2300415998333757249778490685464197237196599067392634238293373017266221785902267818855923626007378850090684685815884380328807466034631 has 133 digits

(19·10¹⁷⁷+53)/9 = 2(1)₁₇₆7_<178> = 151 · 811 · 14901849676042845247_<20> · C154

C154 = P32 · P122

P32 = 34696836474803684531094725876141_<32>

P122 = 33341353998949281134084684490034526580396360733890803452497947844769267578107604119537306016289266699197332365783050679211_<122>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1881158939
Step 1 took 14161ms
Step 2 took 5968ms
********** Factor found in step 2: 34696836474803684531094725876141
Found probable prime factor of 32 digits: 34696836474803684531094725876141
Probable prime cofactor 33341353998949281134084684490034526580396360733890803452497947844769267578107604119537306016289266699197332365783050679211 has 122 digits

(4·10¹⁷³-31)/9 = (4)₁₇₂1_<173> = 16231087 · 354269821 · C157

C157 = P61 · P97

P61 = 4498230111620791750209610078468593245067235231274070330521039_<61>

P97 = 1718280454213440932277591880486530693988757269147198266364252508172991305884293618799254053566797_<97>

SNFS difficulty: 173 digits.
Divisors found:
 r1=4498230111620791750209610078468593245067235231274070330521039
 r2=1718280454213440932277591880486530693988757269147198266364252508172991305884293618799254053566797
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.726).
Factorization parameters were as follows:
n: 7729220879352351153013101378082592843337556829023539351665660507177539117223814006573982196897174293351721382439223285549015530353367195285541263649400342083
Y1: 1
Y0: -20000000000000000000000000000000000
c5: 125
c0: -31
skew: 0.76
type: snfs
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [4500000, 8000001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1312353 x 1312601
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,54,54,2.6,2.6,100000
total time: 30.00 hours.

Oct 9, 2008 (5th)

By Jo Yeong Uk / GGNFS

(67·10¹⁷⁵+23)/9 = 7(4)₁₇₄7_<176> = 7 · 11 · 42487 · C170

C170 = P83 · P87

P83 = 32537127495497706794954789158042722494748647843639292901724992978991735797029256711_<83>

P87 = 699368861975805845572995184055315621277581863012055140909431384666070068950015730613723_<87>

Number: 74447_175
N=22755453828487933037559982272482566690206674201778586649252970716006468118878973964058813542184926373030969731136841076351985571276177814648405652712852562218250546445053
  ( 170 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=32537127495497706794954789158042722494748647843639292901724992978991735797029256711 (pp83)
 r2=699368861975805845572995184055315621277581863012055140909431384666070068950015730613723 (pp87)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 114.12 hours.
Scaled time: 270.93 units (timescale=2.374).
Factorization parameters were as follows:
n: 22755453828487933037559982272482566690206674201778586649252970716006468118878973964058813542184926373030969731136841076351985571276177814648405652712852562218250546445053
m: 100000000000000000000000000000000000
c5: 67
c0: 23
skew: 0.81
type: snfs
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [4000000, 6100001)
Primes: RFBsize:539777, AFBsize:539305, largePrimes:10682829 encountered
Relations: rels:10758829, finalFF:1265217
Max relations in full relation-set: 28
Initial matrix: 1079147 x 1265217 with sparse part having weight 84046143.
Pruned matrix : 910123 x 915582 with weight 53529564.
Total sieving time: 108.12 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 5.77 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,50,50,2.6,2.6,100000
total time: 114.12 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673800)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Calibrating delay using timer specific routine.. 5344.40 BogoMIPS (lpj=2672204)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)

Oct 9, 2008 (4th)

By Sinkiti Sibata / GGNFS

(26·10¹⁶⁰-53)/9 = 2(8)₁₅₉3_<161> = 139 · 11833111840768866262117_<23> · C137

C137 = P41 · P43 · P54

P41 = 24699164607397616188571642243521836798253_<41>

P43 = 4778115508280883342643806899807566682589691_<43>

P54 = 148825777520226664598083038604252245390400654880786267_<54>

Number: 28883_160
N=17563742810030346118482219962830768316393397876574007624819397524539131637145339947227845276968833406707060393815181493162114024771700741
  ( 137 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=24699164607397616188571642243521836798253 (pp41)
 r2=4778115508280883342643806899807566682589691 (pp43)
 r3=148825777520226664598083038604252245390400654880786267 (pp54)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 75.15 hours.
Scaled time: 57.57 units (timescale=0.766).
Factorization parameters were as follows:
name: 28883_160
n: 17563742810030346118482219962830768316393397876574007624819397524539131637145339947227845276968833406707060393815181493162114024771700741
m: 100000000000000000000000000000000
c5: 26
c0: -53
skew: 1.15
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4500001)
Primes: RFBsize:283146, AFBsize:282797, largePrimes:5867428 encountered
Relations: rels:5950995, finalFF:678604
Max relations in full relation-set: 28
Initial matrix: 566009 x 678604 with sparse part having weight 55712005.
Pruned matrix : 491609 x 494503 with weight 40623709.
Total sieving time: 71.62 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 3.19 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 75.15 hours.
 --------- CPU info (if available) ----------

(26·10¹⁶⁴-53)/9 = 2(8)₁₆₃3_<165> = 17 · 61 · 173 · 1570859 · 3678654851_<10> · 5556478709_<10> · 88233409332539930388136681_<26> · C108

C108 = P41 · P68

P41 = 22070470776022600268261014908547019424559_<41>

P68 = 25753450207192235293374738897634290020737717214515574604202694188217_<68>

Number: 28883_164
N=568390770179589408939872195752617880907878497620541326109998551022184578078602427260979786896871916978221303
  ( 108 digits)
Divisors found:
 r1=22070470776022600268261014908547019424559 (pp41)
 r2=25753450207192235293374738897634290020737717214515574604202694188217 (pp68)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 23.43 hours.
Scaled time: 11.06 units (timescale=0.472).
Factorization parameters were as follows:
name: 28883_164
n: 568390770179589408939872195752617880907878497620541326109998551022184578078602427260979786896871916978221303
skew: 7666.01
# norm 2.95e+14
c5: 187200
c4: 843376632
c3: -3418951398874
c2: -175469085741270535
c1: -370049593689987005412
c0: 1943332529637999987863604
# alpha -5.56
Y1: 118808547149
Y0: -313666462701129548531
# Murphy_E 1.31e-09
# M 262874865414326697381161367861846653573701310987028493467367656403077279337065340473173389149331409696073463
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2600001)
Primes: RFBsize:183072, AFBsize:182839, largePrimes:4583538 encountered
Relations: rels:4786702, finalFF:525654
Max relations in full relation-set: 28
Initial matrix: 365992 x 525654 with sparse part having weight 44709387.
Pruned matrix : 260833 x 262726 with weight 24752832.
Polynomial selection time: 1.20 hours.
Total sieving time: 19.51 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 2.17 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 23.43 hours.
 --------- CPU info (if available) ----------

(26·10¹³⁰-53)/9 = 2(8)₁₂₉3_<131> = 2557961551_<10> · C122

C122 = P48 · P74

P48 = 236438277260853769814529260092665387318271835347_<48>

P74 = 47766018217713433955106464691584719775555236704971354158444251526906538639_<74>

Number: 28883_130
N=11293715059006721125218699148808624484633189425484405527285773064729262964941605914266882930520205027463639498969501472733
  ( 122 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=236438277260853769814529260092665387318271835347 (pp48)
 r2=47766018217713433955106464691584719775555236704971354158444251526906538639 (pp74)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.80 hours.
Scaled time: 4.54 units (timescale=0.783).
Factorization parameters were as follows:
name: 28883_130
n: 11293715059006721125218699148808624484633189425484405527285773064729262964941605914266882930520205027463639498969501472733
m: 100000000000000000000000000
c5: 26
c0: -53
skew: 1.15
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1150001)
Primes: RFBsize:63951, AFBsize:63973, largePrimes:1545334 encountered
Relations: rels:1548381, finalFF:166677
Max relations in full relation-set: 28
Initial matrix: 127990 x 166677 with sparse part having weight 14699325.
Pruned matrix : 118264 x 118967 with weight 8717232.
Total sieving time: 5.63 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.80 hours.
 --------- CPU info (if available) ----------

Oct 9, 2008 (3rd)

By Justin Card / msieve 1.38, ggnfs

(10¹⁷⁶+17)/9 = (1)₁₇₅3_<176> = 13 · 1879391 · 6718199 · 43731936268508244866927446133249317_<35> · C127

C127 = P48 · P79

P48 = 710124167792898446935804545868140581401807318057_<48>

P79 = 2179772311514524087931982060767986518870830842019718570624060123823472397032281_<79>

Msieve v. 1.38
Wed Oct  8 17:36:45 2008
random seeds: 52413acf cf6c524a
factoring 1547908998692254006817668407385442013503701471074265130054570365447559543406277463390309132007591482864040879451770914663198017 (127 digits)
no P-1/P+1/ECM available, skipping
commencing number field sieve (127-digit input)
R0: -100000000000000000000000000000
R1:  1
A0:  17
A1:  0
A2:  0
A3:  0
A4:  0
A5:  0
A6:  100
size score = 8.015950e-09, Murphy alpha = -1.265032, combined = 1.150603e-08

commencing relation filtering
commencing duplicate removal, pass 1
error -15 reading relation 30050
error -11 reading relation 57741
error -15 reading relation 3597789
error -15 reading relation 5167541
error -11 reading relation 9339118
found 958927 hash collisions in 10721948 relations
commencing duplicate removal, pass 2
found 835100 duplicates and 9886848 unique relations
memory use: 50.6 MB
reading rational ideals above 4915200
reading algebraic ideals above 4915200
commencing singleton removal, pass 1
relations with 0 large ideals: 137456
relations with 1 large ideals: 871545
relations with 2 large ideals: 2638586
relations with 3 large ideals: 3621314
relations with 4 large ideals: 1942464
relations with 5 large ideals: 82128
relations with 6 large ideals: 1244
relations with 7+ large ideals: 592111
9886848 relations and about 10243474 large ideals
commencing singleton removal, pass 2
found 3672509 singletons
current dataset: 6214339 relations and about 5185675 large ideals
commencing singleton removal, pass 3
found 1055209 singletons
current dataset: 5159130 relations and about 4059385 large ideals
commencing singleton removal, pass 4
found 268425 singletons
current dataset: 4890705 relations and about 3784822 large ideals
commencing singleton removal, final pass
memory use: 85.6 MB
commencing in-memory singleton removal
begin with 4890705 relations and 3998829 unique ideals
reduce to 4317250 relations and 3413986 ideals in 15 passes
max relations containing the same ideal: 55
reading rational ideals above 720000
reading algebraic ideals above 720000
commencing singleton removal, final pass
keeping 3681423 ideals with weight <= 20, new excess is 429104
memory use: 127.8 MB
commencing in-memory singleton removal
begin with 4318889 relations and 3681423 unique ideals
reduce to 4317135 relations and 3669929 ideals in 5 passes
max relations containing the same ideal: 20
removing 561927 relations and 487204 ideals in 74723 cliques
commencing in-memory singleton removal
begin with 3755208 relations and 3669929 unique ideals
reduce to 3697378 relations and 3123500 ideals in 8 passes
max relations containing the same ideal: 20
removing 423906 relations and 349183 ideals in 74723 cliques
commencing in-memory singleton removal
begin with 3273472 relations and 3123500 unique ideals
reduce to 3236125 relations and 2736235 ideals in 7 passes
max relations containing the same ideal: 20
relations with 0 large ideals: 38894
relations with 1 large ideals: 235104
relations with 2 large ideals: 678797
relations with 3 large ideals: 1034849
relations with 4 large ideals: 822119
relations with 5 large ideals: 323075
relations with 6 large ideals: 64340
relations with 7+ large ideals: 38947
commencing 2-way merge
reduce to 2013829 relation sets and 1513939 unique ideals
commencing full merge
memory use: 138.3 MB
found 969439 cycles, need 902139
weight of 902139 cycles is about 63203125 (70.06/cycle)
distribution of cycle lengths:
1 relations: 102303
2 relations: 96867
3 relations: 98547
4 relations: 92829
5 relations: 85292
6 relations: 77434
7 relations: 67639
8 relations: 58867
9 relations: 51014
10+ relations: 171347
heaviest cycle: 18 relations
commencing cycle optimization
start with 5307933 relations
pruned 150799 relations
memory use: 173.8 MB
distribution of cycle lengths:
1 relations: 102303
2 relations: 99276
3 relations: 102677
4 relations: 96095
5 relations: 88079
6 relations: 79370
7 relations: 68613
8 relations: 59191
9 relations: 51176
10+ relations: 155359
heaviest cycle: 18 relations
elapsed time 00:14:12
justin@riall:~/factoring_projects/11113_176$ ~/ggnfs/msieve -nc2 -nf 11113_176.fb -s 11113_176.dat -v -i 11113_176.ini 

Msieve v. 1.38
Wed Oct  8 18:53:11 2008
random seeds: 6da1b961 3bdc077b
factoring 1547908998692254006817668407385442013503701471074265130054570365447559543406277463390309132007591482864040879451770914663198017 (127 digits)
no P-1/P+1/ECM available, skipping
commencing number field sieve (127-digit input)
R0: -100000000000000000000000000000
R1:  1
A0:  17
A1:  0
A2:  0
A3:  0
A4:  0
A5:  0
A6:  100
size score = 8.015950e-09, Murphy alpha = -1.265032, combined = 1.150603e-08

commencing linear algebra
read 902139 cycles
cycles contain 2879140 unique relations
read 2879140 relations
using 32 quadratic characters above 134217324
building initial matrix
memory use: 356.1 MB
read 902139 cycles
matrix is 901831 x 902139 (268.9 MB) with weight 86502896 (95.89/col)
sparse part has weight 60564938 (67.13/col)
filtering completed in 3 passes
matrix is 895277 x 895477 (267.8 MB) with weight 86093846 (96.14/col)
sparse part has weight 60354117 (67.40/col)
read 895477 cycles
matrix is 895277 x 895477 (267.8 MB) with weight 86093846 (96.14/col)
sparse part has weight 60354117 (67.40/col)
saving the first 48 matrix rows for later
matrix is 895229 x 895477 (258.7 MB) with weight 67221065 (75.07/col)
sparse part has weight 58856479 (65.73/col)
matrix includes 64 packed rows
using block size 10922 for processor cache size 256 kB
commencing Lanczos iteration
memory use: 247.2 MB
linear algebra completed 894740 of 895477 dimensions (99.9%, ETA 0h 0m)    
lanczos halted after 14159 iterations (dim = 895225)
recovered 50 nontrivial dependencies
elapsed time 03:47:21
justin@riall:~/factoring_projects/11113_176$ ~/ggnfs/msieve -nc3 -nf 11113_176.fb -s 11113_176.dat -v -i 11113_176.ini 

Msieve v. 1.38
Wed Oct  8 23:20:44 2008
random seeds: ddd9cea2 c865422e
factoring 1547908998692254006817668407385442013503701471074265130054570365447559543406277463390309132007591482864040879451770914663198017 (127 digits)
no P-1/P+1/ECM available, skipping
commencing number field sieve (127-digit input)
R0: -100000000000000000000000000000
R1:  1
A0:  17
A1:  0
A2:  0
A3:  0
A4:  0
A5:  0
A6:  100
size score = 8.015950e-09, Murphy alpha = -1.265032, combined = 1.150603e-08

commencing square root phase
reading relations for dependency 1
read 447370 cycles
cycles contain 1763729 unique relations
read 1763729 relations
multiplying 1435668 relations
multiply complete, coefficients have about 41.54 million bits
initial square root is modulo 919693
reading relations for dependency 2
read 447432 cycles
cycles contain 1761594 unique relations
read 1761594 relations
multiplying 1433372 relations
multiply complete, coefficients have about 41.47 million bits
initial square root is modulo 899161
prp48 factor: 710124167792898446935804545868140581401807318057
prp79 factor: 2179772311514524087931982060767986518870830842019718570624060123823472397032281
elapsed time 00:26:34

Sieve time: 51.75 hours
Filtering: 0.25 hours
Block Lanczos: 3.78 hours
Square root: 0.5 hours

Had to manually restart the filtering/linalg/sqrt, so all I had were the newest run times and the time spent sieving

Oct 9, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(8·10¹⁸⁶-17)/9 = (8)₁₈₅7_<186> = 122041 · 600760122234227247339021404369_<30> · C152

C152 = P46 · P49 · P58

P46 = 3064396278824864704453221938558760266788976239_<46>

P49 = 2068999825167536250079312154581792851089121116323_<49>

P58 = 1912208492840357290420849493550726386987869589952298531099_<58>

Number: n
N=12123851911813520689442426339677939520762900296076844725658595042305449072115945719786865839939239072337205062999312826980398145833769450425203032477503
  ( 152 digits)
SNFS difficulty: 187 digits.
Divisors found:

Thu Oct 09 10:20:58 2008  prp46 factor: 3064396278824864704453221938558760266788976239
Thu Oct 09 10:20:58 2008  prp49 factor: 2068999825167536250079312154581792851089121116323
Thu Oct 09 10:20:58 2008  prp58 factor: 1912208492840357290420849493550726386987869589952298531099
Thu Oct 09 10:20:58 2008  elapsed time 12:57:42 (Msieve 1.38)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 60.70 hours.
Scaled time: 79.28 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_8_185_7
n: 12123851911813520689442426339677939520762900296076844725658595042305449072115945719786865839939239072337205062999312826980398145833769450425203032477503
type: snfs
skew: 1.47
deg: 5
c5: 5
c0: -34
m: 20000000000000000000000000000000000000
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 5600001)
Primes: RFBsize:602489, AFBsize:602555, largePrimes:14506280 encountered
Relations: rels:14387661, finalFF:1299453
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 60.15 hours.
Total relation processing time: 0.55 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.5,2.5,100000
total time: 60.70 hours.
 --------- CPU info (if available) ----------

Oct 9, 2008

By Serge Batalov / Msieve-1.38

(89·10¹⁷³+1)/9 = 9(8)₁₇₂9_<174> = 11² · 401 · 1972031 · C164

C164 = P44 · P59 · P62

P44 = 36508796972420217359188613859528017520402107_<44>

P59 = 26223045467053073103521145401907892655457523884058353664729_<59>

P62 = 10795017884319115590619497478062896384036042183481493808139013_<62>

SNFS difficulty: 174 digits.
Divisors found:
 r1=36508796972420217359188613859528017520402107
 r2=26223045467053073103521145401907892655457523884058353664729
 r3=10795017884319115590619497478062896384036042183481493808139013
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.927).
Factorization parameters were as follows:
n: 10334846166644773118947276370372213703596548275653083075970650843413193899166892826813873902967045814628347177312759151240329845214046927329358818292276154861809039
Y1: 1
Y0: -10000000000000000000000000000000000
c5: 89000
c0: 1
skew: 0.103
type: snfs
rlim: 9000000
alim: 9000000
lpbr: 27
lpba: 27
mfbr: 54
mfba: 54
rlambda: 2.6
alambda: 2.6
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [4500000, 7100001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1248890 x 1249138
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,174,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,54,54,2.6,2.6,100000
total time: 40.00 hours.

10¹⁷⁵+9 = 1(0)₁₇₄9_<176> = 3851 · 219533 · 85277080211_<11> · C156

C156 = P47 · P109

P47 = 16208367959129657766791547475962271323480435637_<47>

P109 = 8557660626492680468621533137816698825726336699568343271840514655920348964720598883835279448245250317366446089_<109>

SNFS difficulty: 175 digits.
Divisors found:
 r1=16208367959129657766791547475962271323480435637
 r2=8557660626492680468621533137816698825726336699568343271840514655920348964720598883835279448245250317366446089
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.735).
Factorization parameters were as follows:
n: 138705712303549395821421358642400204296070680855511012025776877011088224302623733204392953440147869792198011279515236944228094761620670597318606436194873693
Y1: 1
Y0: -100000000000000000000000000000000000
c5: 1
c0: 9
skew: 1.55
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [3700000, 6400001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1175765 x 1176013
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,54,54,2.6,2.6,100000
total time: 50.00 hours.

Oct 8, 2008 (4th)

By Tyler Cadigan / GGNFS + Msieve 1.38

(25·10¹⁹⁵-61)/9 = 2(7)₁₉₄1_<196> = 17 · C195

C195 = P96 · P100

P96 = 119509737931441137246596335232308772579390887315656085068081433412471176766596851200060667993821_<96>

P100 = 1367241662802357158967844931268345670438128299143736962843556968202636908577271893194737300367939703_<100>

Number: 15557_195
N=163398692810457516339869281045751633986928104575163398692810457516339869281045751633986928104575163398692810457516339869281045751633986928104575163398692810457516339869281045751633986928104575163
  ( 195 digits)
SNFS difficulty: 196 digits.
Divisors found:
 r1=119509737931441137246596335232308772579390887315656085068081433412471176766596851200060667993821
 r2=1367241662802357158967844931268345670438128299143736962843556968202636908577271893194737300367939703
Version: 
Total time: 1129.81 hours.
Scaled time: 2875.38 units (timescale=2.545).
Factorization parameters were as follows:
n: 163398692810457516339869281045751633986928104575163398692810457516339869281045751633986928104575163398692810457516339869281045751633986928104575163398692810457516339869281045751633986928104575163
m: 1000000000000000000000000000000000000000
c5: 25
c0: -61
skew: 1.2
type: snfs
Y0: 1000000000000000000000000000000000000000
Y1: -1
rlambda: 2.6
alambda: 2.6
rlim: 20000000
alim: 20000000
qintsize: 1000000Factor base limits: 20000000/20000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [10000000, 26000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1695139 x 1695356
Total sieving time: 1129.81 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,196,5,0,0,0,0,0,0,0,0,20000000,20000000,27,27,48,48,2.6,2.6,100000
total time: 1129.81 hours.
 --------- CPU info (if available) ----------

Oct 8, 2008 (3rd)

By Sinkiti Sibata / GGNFS, Msieve

(26·10¹⁴⁹-53)/9 = 2(8)₁₄₈3_<150> = 7 · 269 · 1531 · 4229 · 70639 · 12856007 · 4742624878308117767_<19> · C109

C109 = P35 · P74

P35 = 97788970591581258252270720835373003_<35>

P74 = 56261117004221928191795911695451058499504506266353625153621755380206925363_<74>

Number: 28883_149
N=5501716716175370397325516787455730544812029811212504821841017486779689125976143858501663582405137361886175089
  ( 109 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=97788970591581258252270720835373003 (pp35)
 r2=56261117004221928191795911695451058499504506266353625153621755380206925363 (pp74)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.19 hours.
Scaled time: 24.45 units (timescale=1.011).
Factorization parameters were as follows:
name: 28883_149
n: 5501716716175370397325516787455730544812029811212504821841017486779689125976143858501663582405137361886175089
m: 1000000000000000000000000000000
c5: 13
c0: -265
skew: 1.83
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176698, largePrimes:6417293 encountered
Relations: rels:7070190, finalFF:1144358
Max relations in full relation-set: 28
Initial matrix: 353065 x 1144358 with sparse part having weight 107679175.
Pruned matrix : 220217 x 222046 with weight 44610337.
Total sieving time: 23.50 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.54 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 24.19 hours.
 --------- CPU info (if available) ----------

(26·10¹³⁷-53)/9 = 2(8)₁₃₆3_<138> = 7 · 21563 · C133

C133 = P29 · P104

P29 = 41029142321912814750708583949_<29>

P104 = 46647801149261483258230864451435677225991269707280561420744207532823419482080864353602554573078146542987_<104>

Number: 28883_137
N=1913919272357337561622679648928315625899450042658316089656812190782417559767650200335819220019006690620102483015806764821280426715663
  ( 133 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=41029142321912814750708583949 (pp29)
 r2=46647801149261483258230864451435677225991269707280561420744207532823419482080864353602554573078146542987 (pp104)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.37 hours.
Scaled time: 11.46 units (timescale=1.008).
Factorization parameters were as follows:
name: 28883_137
n: 1913919272357337561622679648928315625899450042658316089656812190782417559767650200335819220019006690620102483015806764821280426715663
m: 1000000000000000000000000000
c5: 2600
c0: -53
skew: 0.46
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 2275001)
Primes: RFBsize:78498, AFBsize:64048, largePrimes:1748682 encountered
Relations: rels:1827123, finalFF:206065
Max relations in full relation-set: 28
Initial matrix: 142613 x 206065 with sparse part having weight 24284636.
Pruned matrix : 129253 x 130030 with weight 14132842.
Total sieving time: 11.20 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 11.37 hours.
 --------- CPU info (if available) ----------

(26·10¹⁴⁵-53)/9 = 2(8)₁₄₄3_<146> = 11239 · 216179 · 5232607 · 2857515761752823077296380205207103_<34> · C96

C96 = P43 · P54

P43 = 6321322749840508001653491196321933073104039_<43>

P54 = 125798350480661208614497151909486922156386678885355697_<54>

Tue Oct  7 22:38:21 2008  Msieve v. 1.38
Tue Oct  7 22:38:21 2008  random seeds: dcc069ef 6a45db20
Tue Oct  7 22:38:21 2008  factoring 795211974785813302750461673722896568366746906042605051709158919773319198321998699917820402360183 (96 digits)
Tue Oct  7 22:38:23 2008  searching for 15-digit factors
Tue Oct  7 22:38:25 2008  commencing quadratic sieve (96-digit input)
Tue Oct  7 22:38:25 2008  using multiplier of 7
Tue Oct  7 22:38:25 2008  using 64kb Pentium 4 sieve core
Tue Oct  7 22:38:25 2008  sieve interval: 18 blocks of size 65536
Tue Oct  7 22:38:25 2008  processing polynomials in batches of 6
Tue Oct  7 22:38:25 2008  using a sieve bound of 2298871 (84706 primes)
Tue Oct  7 22:38:25 2008  using large prime bound of 344830650 (28 bits)
Tue Oct  7 22:38:25 2008  using double large prime bound of 2331795890236200 (43-52 bits)
Tue Oct  7 22:38:25 2008  using trial factoring cutoff of 52 bits
Tue Oct  7 22:38:25 2008  polynomial 'A' values have 13 factors
Wed Oct  8 08:11:12 2008  85140 relations (20193 full + 64947 combined from 1290119 partial), need 84802
Wed Oct  8 08:11:17 2008  begin with 1310312 relations
Wed Oct  8 08:11:19 2008  reduce to 225183 relations in 10 passes
Wed Oct  8 08:11:19 2008  attempting to read 225183 relations
Wed Oct  8 08:11:26 2008  recovered 225183 relations
Wed Oct  8 08:11:26 2008  recovered 213287 polynomials
Wed Oct  8 08:11:27 2008  attempting to build 85140 cycles
Wed Oct  8 08:11:27 2008  found 85140 cycles in 5 passes
Wed Oct  8 08:11:27 2008  distribution of cycle lengths:
Wed Oct  8 08:11:27 2008     length 1 : 20193
Wed Oct  8 08:11:27 2008     length 2 : 14574
Wed Oct  8 08:11:27 2008     length 3 : 14166
Wed Oct  8 08:11:27 2008     length 4 : 11703
Wed Oct  8 08:11:27 2008     length 5 : 8966
Wed Oct  8 08:11:27 2008     length 6 : 6093
Wed Oct  8 08:11:27 2008     length 7 : 4011
Wed Oct  8 08:11:27 2008     length 9+: 5434
Wed Oct  8 08:11:27 2008  largest cycle: 20 relations
Wed Oct  8 08:11:27 2008  matrix is 84706 x 85140 (23.0 MB) with weight 5695354 (66.89/col)
Wed Oct  8 08:11:27 2008  sparse part has weight 5695354 (66.89/col)
Wed Oct  8 08:11:29 2008  filtering completed in 3 passes
Wed Oct  8 08:11:29 2008  matrix is 81132 x 81196 (22.0 MB) with weight 5438057 (66.97/col)
Wed Oct  8 08:11:29 2008  sparse part has weight 5438057 (66.97/col)
Wed Oct  8 08:11:30 2008  saving the first 48 matrix rows for later
Wed Oct  8 08:11:30 2008  matrix is 81084 x 81196 (13.8 MB) with weight 4318391 (53.18/col)
Wed Oct  8 08:11:30 2008  sparse part has weight 3130861 (38.56/col)
Wed Oct  8 08:11:30 2008  matrix includes 64 packed rows
Wed Oct  8 08:11:30 2008  using block size 21845 for processor cache size 512 kB
Wed Oct  8 08:11:31 2008  commencing Lanczos iteration
Wed Oct  8 08:11:31 2008  memory use: 13.3 MB
Wed Oct  8 08:12:42 2008  lanczos halted after 1284 iterations (dim = 81079)
Wed Oct  8 08:12:42 2008  recovered 14 nontrivial dependencies
Wed Oct  8 08:12:45 2008  prp43 factor: 6321322749840508001653491196321933073104039
Wed Oct  8 08:12:45 2008  prp54 factor: 125798350480661208614497151909486922156386678885355697
Wed Oct  8 08:12:45 2008  elapsed time 09:34:24

Oct 8, 2008 (2nd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38, Msieve-1.38+polyselect

(26·10¹⁵⁵-53)/9 = 2(8)₁₅₄3_<156> = 7 · 23 · 601751861 · C145

C145 = P36 · P109

P36 = 434606430250744155498232965602831581_<36>

P109 = 6861062456898643456131174629095768996957912069600254884539207471769541324001009925483131949479653797412862483_<109>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1810396645
Step 1 took 18717ms
Step 2 took 16371ms
********** Factor found in step 2: 434606430250744155498232965602831581
Found probable prime factor of 36 digits: 434606430250744155498232965602831581
Probable prime cofactor 6861062456898643456131174629095768996957912069600254884539207471769541324001009925483131949479653797412862483 has 109 digits

(26·10¹⁶¹-53)/9 = 2(8)₁₆₀3_<162> = 7² · 499 · 1787 · 69191 · C149

C149 = P73 · P77

P73 = 2820898047146817411392847106167872926575917073080403520030662745443696079_<73>

P77 = 33874481999243789182317500712459693487731094537714674684152288464812979533931_<77>

N=95556460119776824140681734005614945558557064412858747129162824146979553114842635616632409878886974756421559331683241340660947531973593588107432156549
  ( 149 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=2820898047146817411392847106167872926575917073080403520030662745443696079
 r2=33874481999243789182317500712459693487731094537714674684152288464812979533931
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 95556460119776824140681734005614945558557064412858747129162824146979553114842635616632409878886974756421559331683241340660947531973593588107432156549
Y1: 1
Y0: -100000000000000000000000000000000
c5: 260
c0: -53
skew: 0.73
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [2250000, 3950001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 812374 x 812622
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,54,54,2.5,2.5,100000
total time: 20.00 hours.

(26·10¹⁴⁷-53)/9 = 2(8)₁₄₆3_<148> = 3 · 56729549 · C140

C140 = P32 · P51 · P58

P32 = 29588801926945123689788161696051_<32>

P51 = 139196806868612644199754015153798471168262938060269_<51>

P58 = 4121388922514085391358255144517180551116771872537841893331_<58>

SNFS difficulty: 148 digits.
Divisors found:
 r1=29588801926945123689788161696051
 r2=139196806868612644199754015153798471168262938060269
 r3=4121388922514085391358255144517180551116771872537841893331
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.719).
Factorization parameters were as follows:
n: 16974627507843627717945773955702749601675186294235530815923866466186131022528717141096308785443772221121711419968506412116249381128747611989
Y1: 1
Y0: -100000000000000000000000000000
c5: 2600
c0: -53
skew: 0.46
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved rational special-q in [750000, 3750001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 291409 x 291640
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 11.00 hours.

9·10¹⁷³-1 = 8(9)₁₇₃_<174> = 1289 · 1997 · 34668071675443361_<17> · C152

C152 = P64 · P88

P64 = 3806940299291622726460350337947914704889277467532053374128676991_<64>

P88 = 2649145276309295977725794028033536754856664922424512618104600287851523960480215455939453_<88>

SNFS difficulty: 173 digits.
Divisors found:
 r1=3806940299291622726460350337947914704889277467532053374128676991
 r2=2649145276309295977725794028033536754856664922424512618104600287851523960480215455939453
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.729).
Factorization parameters were as follows:
n: 10085137911059899814189806692481744412911545555803075485333634280013678423569068540994799208916444935039759847996393359202808120784082348266403890225923
Y1: 1
Y0: -10000000000000000000000000000000000
c5: 9000
c0: -1
skew: 0.16
type: snfs
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [4500000, 8000001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1301900 x 1302148
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,54,54,2.6,2.6,100000
total time: 20.00 hours.

(26·10¹⁵⁹-53)/9 = 2(8)₁₅₈3_<160> = 3³ · 29 · 287107 · 23759322402380015305157_<23> · 10313704067523250659900937829730796309_<38> · C92

C92 = P44 · P49

P44 = 11921264837382755488951323168235476632314123_<44>

P49 = 4399002839960155168477804483921875138150723586357_<49>

Number: 28883_159
N=52441677875563878773945469819992980394894802790218697762200342387440721101475627254741219911
  ( 92 digits)
Divisors found:
 r1=11921264837382755488951323168235476632314123
 r2=4399002839960155168477804483921875138150723586357
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.943).
Factorization parameters were as follows:
name: 28883_159
n:  52441677875563878773945469819992980394894802790218697762200342387440721101475627254741219911
Y1: 1
Y0: -1064529985727826489681
deg: 4
c4: 40836168
c3: 202395460292
c2: 37363335780110865
c1: -807240905915521234
c0: -18833047913277457717700
skew: 1635.250
type: gnfs
# adj. I(F,S) = 52.156
# E(F1,F2) = 1.052910e-04
# GGNFS version 0.77.1-20060722-k8 polyselect.
# Options were:
# lcd=1, enumLCD=24, maxS1=58.00000000, seed=1223408207.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 700000
alim: 700000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.4
alambda: 2.4
qintsize: 40000
type: gnfs
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [350000, 790001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 122147 x 122395
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,91,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,700000,700000,25,25,44,44,2.4,2.4,40000
total time: 1.00 hours.

(26·10¹⁷⁰-53)/9 = 2(8)₁₆₉3_<171> = 7229 · C167

C167 = P83 · P85

P83 = 24035351007699908057581878367616649511683898296781394921019100136189478983771471809_<83>

P85 = 1662655008492786764992070871336132080310708411773454004559517256637120059624426981103_<85>

SNFS difficulty: 171 digits.
Divisors found:
 r1=24035351007699908057581878367616649511683898296781394921019100136189478983771471809
 r2=1662655008492786764992070871336132080310708411773454004559517256637120059624426981103
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.738).
Factorization parameters were as follows:
n: 39962496733834401561611410829836614869122823196692334885722629532285086303622754030832603249258388281766342355635480549023224358678778377215228785293801201948940225327
Y1: 1
Y0: -10000000000000000000000000000000000
c5: 26
c0: -53
skew: 1.15
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [3000000, 6200001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1134038 x 1134286
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000
total time: 30.00 hours.

Oct 8, 2008

By Robert Backstrom / GGNFS, Msieve

(26·10¹⁴²-53)/9 = 2(8)₁₄₁3_<143> = 53089 · 340047641 · 991880503657452655844894459_<27> · C103

C103 = P42 · P62

P42 = 132486450373648223508514208908735758773123_<42>

P62 = 12177431881605206398029290707267400696763668300063466828015931_<62>

Number: n
N=1613344724660769886649916619810211394771546044497351298684758158261984306026169867062528357836858622513
  ( 103 digits)
SNFS difficulty: 143 digits.
Divisors found:

Wed Oct 08 09:00:44 2008  prp42 factor: 132486450373648223508514208908735758773123
Wed Oct 08 09:00:44 2008  prp62 factor: 12177431881605206398029290707267400696763668300063466828015931
Wed Oct 08 09:00:44 2008  elapsed time 00:26:15 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.07 hours.
Scaled time: 11.10 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_8_141_3
n: 1613344724660769886649916619810211394771546044497351298684758158261984306026169867062528357836858622513
type: snfs
skew: 0.46
deg: 5
c5: 2600
c0: -53
m: 10000000000000000000000000000
rlim: 1300000
alim: 1300000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 1180001)
Primes: RFBsize:100021, AFBsize:100068, largePrimes:9478504 encountered
Relations: rels:8279703, finalFF:207932
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 5.87 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,28,28,52,52,2.5,2.5,100000
total time: 6.07 hours.
 --------- CPU info (if available) ----------

Oct 7, 2008 (7th)

By Robert Backstrom / GGNFS, Msieve

(22·10¹⁸²+41)/9 = 2(4)₁₈₁9_<183> = 3 · C182

C182 = P68 · P115

P68 = 11131817333645608134880826432818812343782233091922887565788360266449_<68>

P115 = 7319692646698933068447008380320554226838232071464676446580397185871101360352917608275605713660449939915296564240667_<115>

Number: n
N=81481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481483
  ( 182 digits)
SNFS difficulty: 183 digits.
Divisors found:

Wed Oct 08 01:16:41 2008  prp68 factor: 11131817333645608134880826432818812343782233091922887565788360266449
Wed Oct 08 01:16:41 2008  prp115 factor: 7319692646698933068447008380320554226838232071464676446580397185871101360352917608275605713660449939915296564240667
Wed Oct 08 01:16:42 2008  elapsed time 06:28:41 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 54.73 hours.
Scaled time: 111.92 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_2_4_181_9
n: 81481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481483
type: snfs
skew: 0.45
deg: 5
c5: 2200
c0: 41
m: 1000000000000000000000000000000000000
rlim: 8500000
alim: 8500000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8500000/8500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 4500001)
Primes: RFBsize:571119, AFBsize:570514, largePrimes:14085472 encountered
Relations: rels:13769297, finalFF:1174408
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 54.36 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,183,5,0,0,0,0,0,0,0,0,8500000,8500000,28,28,52,52,2.5,2.5,100000
total time: 54.73 hours.
 --------- CPU info (if available) ----------

Oct 7, 2008 (6th)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(26·10¹⁵⁸-53)/9 = 2(8)₁₅₇3_<159> = 130811 · 973426505769073_<15> · 34425015087386547163_<20> · 3241490273279072043571_<22> · C98

C98 = P41 · P58

P41 = 12344721383578441602570691129719532666583_<41>

P58 = 1646960755389981787462956664892649361997386854346581393679_<58>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 20331271654977211294393339555490793753127508716336082890964068276470475952992887907854903370728857 (98 digits)
Using B1=2008000, B2=2853999340, polynomial Dickson(6), sigma=809588647
Step 1 took 14062ms
********** Factor found in step 1: 12344721383578441602570691129719532666583
Found probable prime factor of 41 digits: 12344721383578441602570691129719532666583
Probable prime cofactor 1646960755389981787462956664892649361997386854346581393679 has 58 digits

(26·10¹²¹-53)/9 = 2(8)₁₂₀3_<122> = 19 · 173 · 991 · 67489 · C111

C111 = P43 · P68

P43 = 2007712048273207184446462298497217117810023_<43>

P68 = 65452021084529422210274885461837884035260977024336997039822115743117_<68>

Number: n
N=131408811315241709778882446115455544690473727820806141910612876582430405380071525155184407438686776994275861691
  ( 111 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=2007712048273207184446462298497217117810023 (pp43)
 r2=65452021084529422210274885461837884035260977024336997039822115743117 (pp68)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.61 hours.
Scaled time: 2.94 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_8_120_3
n: 131408811315241709778882446115455544690473727820806141910612876582430405380071525155184407438686776994275861691
type: snfs
skew: 0.73
deg: 5
c5: 260
c0: -53
m: 1000000000000000000000000
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved algebraic special-q in [100000, 320001)
Primes: RFBsize:41538, AFBsize:41737, largePrimes:4668741 encountered
Relations: rels:4058830, finalFF:149942
Max relations in full relation-set: 48
Initial matrix: 83342 x 149942 with sparse part having weight 20829512.
Pruned matrix : 73830 x 74310 with weight 6580037.
Total sieving time: 1.46 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.03 hours.
Total square root time: 0.04 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,500000,500000,28,28,52,52,2.5,2.5,50000
total time: 1.61 hours.
 --------- CPU info (if available) ----------

(26·10¹²⁸-53)/9 = 2(8)₁₂₇3_<129> = 3259 · 6329 · 10861 · 29861809811904979_<17> · C101

C101 = P46 · P56

P46 = 2131370352579613462233814865258221222956640337_<46>

P56 = 20261263429298435688151884603702447939050574911133385351_<56>

Number: n
N=43184256179012235031192687636333472190588881801215689091140993405776276872330744228362505736131503287
  ( 101 digits)
SNFS difficulty: 129 digits.
Divisors found:

Wed Oct 08 00:36:52 2008  prp46 factor: 2131370352579613462233814865258221222956640337
Wed Oct 08 00:36:52 2008  prp56 factor: 20261263429298435688151884603702447939050574911133385351
Wed Oct 08 00:36:52 2008  elapsed time 00:10:12 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.31 hours.
Scaled time: 4.22 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_8_127_3
n: 43184256179012235031192687636333472190588881801215689091140993405776276872330744228362505736131503287
type: snfs
skew: 0.58
deg: 5
c5: 1625
c0: -106
m: 20000000000000000000000000
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 440001)
Primes: RFBsize:63951, AFBsize:64263, largePrimes:5797517 encountered
Relations: rels:4914384, finalFF:132843
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 2.22 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,28,28,52,52,2.5,2.5,50000
total time: 2.31 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Oct 7, 2008 (5th)

By Sinkiti Sibata / Msieve, GGNFS

(26·10¹⁰¹-53)/9 = 2(8)₁₀₀3_<102> = 7 · 2054853599791_<13> · C89

C89 = P36 · P54

P36 = 121426997166013585257945094641811871_<36>

P54 = 165400438930491170714093139841463045980448069972087429_<54>

ue Oct  7 11:47:53 2008  Msieve v. 1.38
Tue Oct  7 11:47:53 2008  random seeds: 1d892829 4d448959
Tue Oct  7 11:47:53 2008  factoring 20084078629270154464915312484066295599082921065544328970184837510862039456747676582069659 (89 digits)
Tue Oct  7 11:47:55 2008  searching for 15-digit factors
Tue Oct  7 11:47:56 2008  commencing quadratic sieve (89-digit input)
Tue Oct  7 11:47:57 2008  using multiplier of 19
Tue Oct  7 11:47:57 2008  using 64kb Pentium 4 sieve core
Tue Oct  7 11:47:57 2008  sieve interval: 15 blocks of size 65536
Tue Oct  7 11:47:57 2008  processing polynomials in batches of 7
Tue Oct  7 11:47:57 2008  using a sieve bound of 1538939 (58667 primes)
Tue Oct  7 11:47:57 2008  using large prime bound of 123115120 (26 bits)
Tue Oct  7 11:47:57 2008  using double large prime bound of 365224943163840 (42-49 bits)
Tue Oct  7 11:47:57 2008  using trial factoring cutoff of 49 bits
Tue Oct  7 11:47:57 2008  polynomial 'A' values have 11 factors
Tue Oct  7 13:17:05 2008  59144 relations (16771 full + 42373 combined from 612311 partial), need 58763
Tue Oct  7 13:17:07 2008  begin with 629082 relations
Tue Oct  7 13:17:08 2008  reduce to 140845 relations in 10 passes
Tue Oct  7 13:17:08 2008  attempting to read 140845 relations
Tue Oct  7 13:17:12 2008  recovered 140845 relations
Tue Oct  7 13:17:12 2008  recovered 115844 polynomials
Tue Oct  7 13:17:12 2008  attempting to build 59144 cycles
Tue Oct  7 13:17:12 2008  found 59144 cycles in 5 passes
Tue Oct  7 13:17:12 2008  distribution of cycle lengths:
Tue Oct  7 13:17:12 2008     length 1 : 16771
Tue Oct  7 13:17:12 2008     length 2 : 11626
Tue Oct  7 13:17:12 2008     length 3 : 10380
Tue Oct  7 13:17:12 2008     length 4 : 7739
Tue Oct  7 13:17:12 2008     length 5 : 5283
Tue Oct  7 13:17:12 2008     length 6 : 3224
Tue Oct  7 13:17:12 2008     length 7 : 1938
Tue Oct  7 13:17:12 2008     length 9+: 2183
Tue Oct  7 13:17:12 2008  largest cycle: 18 relations
Tue Oct  7 13:17:12 2008  matrix is 58667 x 59144 (14.3 MB) with weight 3505818 (59.28/col)
Tue Oct  7 13:17:12 2008  sparse part has weight 3505818 (59.28/col)
Tue Oct  7 13:17:13 2008  filtering completed in 3 passes
Tue Oct  7 13:17:13 2008  matrix is 54053 x 54117 (13.1 MB) with weight 3220858 (59.52/col)
Tue Oct  7 13:17:13 2008  sparse part has weight 3220858 (59.52/col)
Tue Oct  7 13:17:14 2008  saving the first 48 matrix rows for later
Tue Oct  7 13:17:14 2008  matrix is 54005 x 54117 (9.9 MB) with weight 2692096 (49.75/col)
Tue Oct  7 13:17:14 2008  sparse part has weight 2262300 (41.80/col)
Tue Oct  7 13:17:14 2008  matrix includes 64 packed rows
Tue Oct  7 13:17:14 2008  using block size 21646 for processor cache size 512 kB
Tue Oct  7 13:17:15 2008  commencing Lanczos iteration
Tue Oct  7 13:17:15 2008  memory use: 8.8 MB
Tue Oct  7 13:17:48 2008  lanczos halted after 856 iterations (dim = 54005)
Tue Oct  7 13:17:48 2008  recovered 18 nontrivial dependencies
Tue Oct  7 13:17:49 2008  prp36 factor: 121426997166013585257945094641811871
Tue Oct  7 13:17:49 2008  prp54 factor: 165400438930491170714093139841463045980448069972087429
Tue Oct  7 13:17:49 2008  elapsed time 01:29:56

(26·10¹²⁷-53)/9 = 2(8)₁₂₆3_<128> = 71 · 223 · 1131379 · C118

C118 = P59 · P60

P59 = 15345026787558290531448963866298651876102210421274475955901_<59>

P60 = 105097373460091410047218511082896636270831228339123800626269_<60>

Number: 28883_127
N=1612722011047120431126093651159581582679062156542549515978111750383441311031911185410142095485998023922924326226163369
  ( 118 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=15345026787558290531448963866298651876102210421274475955901 (pp59)
 r2=105097373460091410047218511082896636270831228339123800626269 (pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.61 hours.
Scaled time: 3.60 units (timescale=0.780).
Factorization parameters were as follows:
name: 28883_127
n: 1612722011047120431126093651159581582679062156542549515978111750383441311031911185410142095485998023922924326226163369
m: 10000000000000000000000000
c5: 2600
c0: -53
skew: 0.46
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64048, largePrimes:1503692 encountered
Relations: rels:1505752, finalFF:174921
Max relations in full relation-set: 28
Initial matrix: 128066 x 174921 with sparse part having weight 12955403.
Pruned matrix : 114003 x 114707 with weight 6745759.
Total sieving time: 4.47 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.61 hours.
 --------- CPU info (if available) ----------

(26·10¹⁰⁴-53)/9 = 2(8)₁₀₃3_<105> = 61 · 1123 · 1470236641_<10> · C91

C91 = P40 · P51

P40 = 6918276745362442304529579011355599487433_<40>

P51 = 414606469566875297250530265767866835398335555183037_<51>

Tue Oct  7 13:26:14 2008  Msieve v. 1.38
Tue Oct  7 13:26:14 2008  random seeds: a8c52f61 feb94d20
Tue Oct  7 13:26:14 2008  factoring 2868362296881334515585997025651531016682339074705062742924681119186664562240834443696274021 (91 digits)
Tue Oct  7 13:26:16 2008  searching for 15-digit factors
Tue Oct  7 13:26:17 2008  commencing quadratic sieve (91-digit input)
Tue Oct  7 13:26:18 2008  using multiplier of 1
Tue Oct  7 13:26:18 2008  using 64kb Pentium 4 sieve core
Tue Oct  7 13:26:18 2008  sieve interval: 18 blocks of size 65536
Tue Oct  7 13:26:18 2008  processing polynomials in batches of 6
Tue Oct  7 13:26:18 2008  using a sieve bound of 1685869 (63499 primes)
Tue Oct  7 13:26:18 2008  using large prime bound of 155099948 (27 bits)
Tue Oct  7 13:26:18 2008  using double large prime bound of 553478662336492 (42-49 bits)
Tue Oct  7 13:26:18 2008  using trial factoring cutoff of 49 bits
Tue Oct  7 13:26:18 2008  polynomial 'A' values have 12 factors
Tue Oct  7 15:42:48 2008  63914 relations (16908 full + 47006 combined from 723821 partial), need 63595
Tue Oct  7 15:42:50 2008  begin with 740729 relations
Tue Oct  7 15:42:51 2008  reduce to 156965 relations in 10 passes
Tue Oct  7 15:42:51 2008  attempting to read 156965 relations
Tue Oct  7 15:42:55 2008  recovered 156965 relations
Tue Oct  7 15:42:55 2008  recovered 133565 polynomials
Tue Oct  7 15:42:55 2008  attempting to build 63914 cycles
Tue Oct  7 15:42:55 2008  found 63914 cycles in 6 passes
Tue Oct  7 15:42:55 2008  distribution of cycle lengths:
Tue Oct  7 15:42:55 2008     length 1 : 16908
Tue Oct  7 15:42:55 2008     length 2 : 12442
Tue Oct  7 15:42:55 2008     length 3 : 11234
Tue Oct  7 15:42:55 2008     length 4 : 8455
Tue Oct  7 15:42:55 2008     length 5 : 5982
Tue Oct  7 15:42:55 2008     length 6 : 3880
Tue Oct  7 15:42:55 2008     length 7 : 2258
Tue Oct  7 15:42:55 2008     length 9+: 2755
Tue Oct  7 15:42:55 2008  largest cycle: 19 relations
Tue Oct  7 15:42:56 2008  matrix is 63499 x 63914 (15.5 MB) with weight 3794539 (59.37/col)
Tue Oct  7 15:42:56 2008  sparse part has weight 3794539 (59.37/col)
Tue Oct  7 15:42:57 2008  filtering completed in 3 passes
Tue Oct  7 15:42:57 2008  matrix is 59321 x 59385 (14.4 MB) with weight 3538343 (59.58/col)
Tue Oct  7 15:42:57 2008  sparse part has weight 3538343 (59.58/col)
Tue Oct  7 15:42:57 2008  saving the first 48 matrix rows for later
Tue Oct  7 15:42:57 2008  matrix is 59273 x 59385 (9.0 MB) with weight 2762056 (46.51/col)
Tue Oct  7 15:42:57 2008  sparse part has weight 2003226 (33.73/col)
Tue Oct  7 15:42:57 2008  matrix includes 64 packed rows
Tue Oct  7 15:42:57 2008  using block size 21845 for processor cache size 512 kB
Tue Oct  7 15:42:58 2008  commencing Lanczos iteration
Tue Oct  7 15:42:58 2008  memory use: 8.9 MB
Tue Oct  7 15:43:33 2008  lanczos halted after 939 iterations (dim = 59273)
Tue Oct  7 15:43:34 2008  recovered 17 nontrivial dependencies
Tue Oct  7 15:43:35 2008  prp40 factor: 6918276745362442304529579011355599487433
Tue Oct  7 15:43:35 2008  prp51 factor: 414606469566875297250530265767866835398335555183037
Tue Oct  7 15:43:35 2008  elapsed time 02:17:21

(26·10¹²²-53)/9 = 2(8)₁₂₁3_<123> = 1396273 · C117

C117 = P32 · P86

P32 = 19402957166974971366426216788597_<32>

P86 = 10663323221080904571958089552579308973412592003811372507188170021888642482959500866743_<86>

Number: 28883_122
N=206900003716242374441738033241986981692612325017305991656996080916044991838192738016769563608899469436771239498929571
  ( 117 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=19402957166974971366426216788597 (pp32)
 r2=10663323221080904571958089552579308973412592003811372507188170021888642482959500866743 (pp86)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.76 hours.
Scaled time: 2.12 units (timescale=0.768).
Factorization parameters were as follows:
name: 28883_122
n: 206900003716242374441738033241986981692612325017305991656996080916044991838192738016769563608899469436771239498929571
m: 1000000000000000000000000
c5: 2600
c0: -53
skew: 0.46
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:64048, largePrimes:2190048 encountered
Relations: rels:2274759, finalFF:199026
Max relations in full relation-set: 28
Initial matrix: 113213 x 199026 with sparse part having weight 19677855.
Pruned matrix : 97348 x 97978 with weight 6954336.
Total sieving time: 2.63 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.76 hours.
 --------- CPU info (if available) ----------

(26·10¹⁰⁶-53)/9 = 2(8)₁₀₅3_<107> = 5198788583502427_<16> · C91

C91 = P39 · P53

P39 = 335500273381690253463142691283043816681_<39>

P53 = 16562878025476215601525675460299270300212300146053409_<53>

Tue Oct  7 15:52:28 2008  Msieve v. 1.38
Tue Oct  7 15:52:28 2008  random seeds: 16d200f0 5ed508d6
Tue Oct  7 15:52:28 2008  factoring 5556850105534860400941856415980529361598976848281810529616069149916703991904509622631115529 (91 digits)
Tue Oct  7 15:52:30 2008  searching for 15-digit factors
Tue Oct  7 15:52:31 2008  commencing quadratic sieve (91-digit input)
Tue Oct  7 15:52:31 2008  using multiplier of 1
Tue Oct  7 15:52:31 2008  using 64kb Pentium 4 sieve core
Tue Oct  7 15:52:31 2008  sieve interval: 18 blocks of size 65536
Tue Oct  7 15:52:31 2008  processing polynomials in batches of 6
Tue Oct  7 15:52:31 2008  using a sieve bound of 1718107 (64706 primes)
Tue Oct  7 15:52:31 2008  using large prime bound of 164938272 (27 bits)
Tue Oct  7 15:52:31 2008  using double large prime bound of 618270452838912 (42-50 bits)
Tue Oct  7 15:52:31 2008  using trial factoring cutoff of 50 bits
Tue Oct  7 15:52:31 2008  polynomial 'A' values have 12 factors
Tue Oct  7 18:39:51 2008  65214 relations (16974 full + 48240 combined from 766306 partial), need 64802
Tue Oct  7 18:39:54 2008  begin with 783280 relations
Tue Oct  7 18:39:55 2008  reduce to 162786 relations in 10 passes
Tue Oct  7 18:39:55 2008  attempting to read 162786 relations
Tue Oct  7 18:39:59 2008  recovered 162786 relations
Tue Oct  7 18:39:59 2008  recovered 142392 polynomials
Tue Oct  7 18:39:59 2008  attempting to build 65214 cycles
Tue Oct  7 18:39:59 2008  found 65213 cycles in 5 passes
Tue Oct  7 18:39:59 2008  distribution of cycle lengths:
Tue Oct  7 18:39:59 2008     length 1 : 16974
Tue Oct  7 18:39:59 2008     length 2 : 12127
Tue Oct  7 18:39:59 2008     length 3 : 11248
Tue Oct  7 18:39:59 2008     length 4 : 8709
Tue Oct  7 18:39:59 2008     length 5 : 6255
Tue Oct  7 18:39:59 2008     length 6 : 4176
Tue Oct  7 18:39:59 2008     length 7 : 2520
Tue Oct  7 18:39:59 2008     length 9+: 3204
Tue Oct  7 18:39:59 2008  largest cycle: 17 relations
Tue Oct  7 18:40:00 2008  matrix is 64706 x 65213 (16.0 MB) with weight 3920348 (60.12/col)
Tue Oct  7 18:40:00 2008  sparse part has weight 3920348 (60.12/col)
Tue Oct  7 18:40:01 2008  filtering completed in 3 passes
Tue Oct  7 18:40:01 2008  matrix is 60922 x 60986 (14.9 MB) with weight 3666150 (60.11/col)
Tue Oct  7 18:40:01 2008  sparse part has weight 3666150 (60.11/col)
Tue Oct  7 18:40:01 2008  saving the first 48 matrix rows for later
Tue Oct  7 18:40:02 2008  matrix is 60874 x 60986 (9.2 MB) with weight 2856674 (46.84/col)
Tue Oct  7 18:40:02 2008  sparse part has weight 2041678 (33.48/col)
Tue Oct  7 18:40:02 2008  matrix includes 64 packed rows
Tue Oct  7 18:40:02 2008  using block size 21845 for processor cache size 512 kB
Tue Oct  7 18:40:02 2008  commencing Lanczos iteration
Tue Oct  7 18:40:02 2008  memory use: 9.1 MB
Tue Oct  7 18:40:39 2008  lanczos halted after 963 iterations (dim = 60870)
Tue Oct  7 18:40:39 2008  recovered 15 nontrivial dependencies
Tue Oct  7 18:40:40 2008  prp39 factor: 335500273381690253463142691283043816681
Tue Oct  7 18:40:40 2008  prp53 factor: 16562878025476215601525675460299270300212300146053409
Tue Oct  7 18:40:40 2008  elapsed time 02:48:12

(26·10¹²⁶-53)/9 = 2(8)₁₂₅3_<127> = 3 · 1447 · 28935371 · C116

C116 = P39 · P78

P39 = 165228653254615932145236476570314596911_<39>

P78 = 139195961274715951475738988525401637958819321233452897120611300841286875640923_<78>

Number: 28883_126
N=22999161219902989050763756242254328115413953432130767044127223526570030118688305537411634697583777575015585520988853
  ( 116 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=165228653254615932145236476570314596911 (pp39)
 r2=139195961274715951475738988525401637958819321233452897120611300841286875640923 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.67 hours.
Scaled time: 3.57 units (timescale=0.765).
Factorization parameters were as follows:
name: 28883_126
n: 22999161219902989050763756242254328115413953432130767044127223526570030118688305537411634697583777575015585520988853
m: 10000000000000000000000000
c5: 260
c0: -53
skew: 0.73
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:49098, AFBsize:64238, largePrimes:2372758 encountered
Relations: rels:2620192, finalFF:260114
Max relations in full relation-set: 28
Initial matrix: 113403 x 260114 with sparse part having weight 29757285.
Pruned matrix : 95261 x 95892 with weight 9517273.
Total sieving time: 4.50 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 4.67 hours.
 --------- CPU info (if available) ----------

(26·10¹⁴³-53)/9 = 2(8)₁₄₂3_<144> = 7 · 283 · 577 · 639430311176401939_<18> · C120

C120 = P47 · P73

P47 = 72608421793173348599781043468017773823555749411_<47>

P73 = 5443651740505919077345587202768020121504697287012529543072932930028188871_<73>

Number: 28883_143
N=395254961669796004987946127703194385910388393704209881767151146015249881172862281036767220131736918647909394011455004981
  ( 120 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=72608421793173348599781043468017773823555749411 (pp47)
 r2=5443651740505919077345587202768020121504697287012529543072932930028188871 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 17.55 hours.
Scaled time: 17.69 units (timescale=1.008).
Factorization parameters were as follows:
name: 28883_143
n: 395254961669796004987946127703194385910388393704209881767151146015249881172862281036767220131736918647909394011455004981
m: 20000000000000000000000000000
c5: 1625
c0: -106
skew: 0.58
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 3150001)
Primes: RFBsize:100021, AFBsize:100028, largePrimes:3026076 encountered
Relations: rels:3108906, finalFF:263940
Max relations in full relation-set: 28
Initial matrix: 200115 x 263940 with sparse part having weight 33430537.
Pruned matrix : 184887 x 185951 with weight 22544896.
Total sieving time: 17.21 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.24 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 17.55 hours.
 --------- CPU info (if available) ----------

(26·10¹³³-53)/9 = 2(8)₁₃₂3_<134> = 23² · 97 · 135571 · 2876131 · 109545440891568721810547809_<27> · C92

C92 = P34 · P58

P34 = 5002428365042696296439157033787319_<34>

P58 = 2634831116987297229287109977599312699036948502466768118621_<58>

Tue Oct  7 18:56:25 2008  Msieve v. 1.38
Tue Oct  7 18:56:25 2008  random seeds: 83ca2303 33019c16
Tue Oct  7 18:56:25 2008  factoring 13180553916714386534909752569425608716853442786350982542867254483031175653902223819877567099 (92 digits)
Tue Oct  7 18:56:26 2008  searching for 15-digit factors
Tue Oct  7 18:56:28 2008  commencing quadratic sieve (92-digit input)
Tue Oct  7 18:56:28 2008  using multiplier of 11
Tue Oct  7 18:56:28 2008  using 64kb Pentium 4 sieve core
Tue Oct  7 18:56:28 2008  sieve interval: 18 blocks of size 65536
Tue Oct  7 18:56:28 2008  processing polynomials in batches of 6
Tue Oct  7 18:56:28 2008  using a sieve bound of 1753553 (65561 primes)
Tue Oct  7 18:56:28 2008  using large prime bound of 177108853 (27 bits)
Tue Oct  7 18:56:28 2008  using double large prime bound of 702801048059511 (42-50 bits)
Tue Oct  7 18:56:28 2008  using trial factoring cutoff of 50 bits
Tue Oct  7 18:56:28 2008  polynomial 'A' values have 12 factors
Tue Oct  7 22:29:52 2008  65765 relations (16425 full + 49340 combined from 804803 partial), need 65657
Tue Oct  7 22:29:55 2008  begin with 821228 relations
Tue Oct  7 22:29:56 2008  reduce to 167642 relations in 10 passes
Tue Oct  7 22:29:56 2008  attempting to read 167642 relations
Tue Oct  7 22:30:01 2008  recovered 167642 relations
Tue Oct  7 22:30:01 2008  recovered 150130 polynomials
Tue Oct  7 22:30:01 2008  attempting to build 65765 cycles
Tue Oct  7 22:30:01 2008  found 65765 cycles in 6 passes
Tue Oct  7 22:30:01 2008  distribution of cycle lengths:
Tue Oct  7 22:30:01 2008     length 1 : 16425
Tue Oct  7 22:30:01 2008     length 2 : 11908
Tue Oct  7 22:30:01 2008     length 3 : 11132
Tue Oct  7 22:30:01 2008     length 4 : 9002
Tue Oct  7 22:30:01 2008     length 5 : 6712
Tue Oct  7 22:30:01 2008     length 6 : 4291
Tue Oct  7 22:30:01 2008     length 7 : 2786
Tue Oct  7 22:30:01 2008     length 9+: 3509
Tue Oct  7 22:30:01 2008  largest cycle: 20 relations
Tue Oct  7 22:30:01 2008  matrix is 65561 x 65765 (16.2 MB) with weight 3995981 (60.76/col)
Tue Oct  7 22:30:01 2008  sparse part has weight 3995981 (60.76/col)
Tue Oct  7 22:30:02 2008  filtering completed in 3 passes
Tue Oct  7 22:30:02 2008  matrix is 62136 x 62200 (15.5 MB) with weight 3802683 (61.14/col)
Tue Oct  7 22:30:02 2008  sparse part has weight 3802683 (61.14/col)
Tue Oct  7 22:30:03 2008  saving the first 48 matrix rows for later
Tue Oct  7 22:30:03 2008  matrix is 62088 x 62200 (9.0 MB) with weight 2903630 (46.68/col)
Tue Oct  7 22:30:03 2008  sparse part has weight 1995181 (32.08/col)
Tue Oct  7 22:30:03 2008  matrix includes 64 packed rows
Tue Oct  7 22:30:03 2008  using block size 21845 for processor cache size 512 kB
Tue Oct  7 22:30:04 2008  commencing Lanczos iteration
Tue Oct  7 22:30:04 2008  memory use: 9.2 MB
Tue Oct  7 22:30:42 2008  lanczos halted after 983 iterations (dim = 62086)
Tue Oct  7 22:30:42 2008  recovered 17 nontrivial dependencies
Tue Oct  7 22:30:43 2008  prp34 factor: 5002428365042696296439157033787319
Tue Oct  7 22:30:43 2008  prp58 factor: 2634831116987297229287109977599312699036948502466768118621
Tue Oct  7 22:30:43 2008  elapsed time 03:34:18

(26·10¹²³-53)/9 = 2(8)₁₂₂3_<124> = 3² · 31 · 479 · 88657 · 10411764445779331_<17> · C98

C98 = P49 · P49

P49 = 4577386029919616907920358735921111593023502164133_<49>

P49 = 5116066918556820603101831088148502094912304324933_<49>

Number: 28883_123
N=23418213241135893111654536836037973463107834917996575496935072255016382759107548568754821130228089
  ( 98 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=4577386029919616907920358735921111593023502164133 (pp49)
 r2=5116066918556820603101831088148502094912304324933 (pp49)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.74 hours.
Scaled time: 2.09 units (timescale=0.762).
Factorization parameters were as follows:
name: 28883_123
n: 23418213241135893111654536836037973463107834917996575496935072255016382759107548568754821130228089
m: 2000000000000000000000000
c5: 1625
c0: -106
skew: 0.58
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:64263, largePrimes:2115498 encountered
Relations: rels:2111676, finalFF:135551
Max relations in full relation-set: 28
Initial matrix: 113427 x 135551 with sparse part having weight 12279235.
Pruned matrix : 108186 x 108817 with weight 8199310.
Total sieving time: 2.59 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.74 hours.
 --------- CPU info (if available) ----------

Oct 7, 2008 (4th)

By Serge Batalov / GMP-ECM 6.2.1; Msieve-1.38, Msieve v. 1.36

(26·10¹⁰⁵-53)/9 = 2(8)₁₀₄3_<106> = 3⁴ · 109 · 199 · C100

C100 = P30 · P34 · P37

P30 = 849624280316155038972453763277_<30>

P34 = 1577350554019897265169205252353313_<34>

P37 = 1226905483766051707687131862935370973_<37>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=2391236779
Step 1 took 3248ms
Step 2 took 3033ms
********** Factor found in step 2: 849624280316155038972453763277
Found probable prime factor of 30 digits: 849624280316155038972453763277

Mon Oct  6 19:24:09 2008  Msieve v. 1.36
Mon Oct  6 19:24:09 2008  random seeds: 06327895 4682e542
Mon Oct  6 19:24:09 2008  factoring 1935260044548431731260988683498011215653904307146361370089234920583549 (70 digits)
Mon Oct  6 19:24:10 2008  no P-1/P+1/ECM available, skipping
Mon Oct  6 19:24:10 2008  commencing quadratic sieve (70-digit input)
Mon Oct  6 19:24:10 2008  using multiplier of 5
Mon Oct  6 19:24:10 2008  using 64kb Opteron sieve core
Mon Oct  6 19:24:10 2008  sieve interval: 6 blocks of size 65536
Mon Oct  6 19:24:10 2008  processing polynomials in batches of 17
Mon Oct  6 19:24:10 2008  using a sieve bound of 215143 (9551 primes)
Mon Oct  6 19:24:10 2008  using large prime bound of 20438585 (24 bits)
Mon Oct  6 19:24:10 2008  using trial factoring cutoff of 24 bits
Mon Oct  6 19:24:10 2008  polynomial 'A' values have 9 factors
Mon Oct  6 19:25:37 2008  10205 relations (4704 full + 5501 combined from 55773 partial), need 9647
Mon Oct  6 19:25:37 2008  begin with 60477 relations
Mon Oct  6 19:25:37 2008  reduce to 14980 relations in 2 passes
Mon Oct  6 19:25:37 2008  attempting to read 14980 relations
Mon Oct  6 19:25:37 2008  recovered 14980 relations
Mon Oct  6 19:25:38 2008  recovered 12682 polynomials
Mon Oct  6 19:25:38 2008  attempting to build 10205 cycles
Mon Oct  6 19:25:38 2008  found 10205 cycles in 1 passes
Mon Oct  6 19:25:38 2008  distribution of cycle lengths:
Mon Oct  6 19:25:38 2008     length 1 : 4704
Mon Oct  6 19:25:38 2008     length 2 : 5501
Mon Oct  6 19:25:38 2008  largest cycle: 2 relations
Mon Oct  6 19:25:38 2008  matrix is 9551 x 10205 (1.4 MB) with weight 297849 (29.19/col)
Mon Oct  6 19:25:38 2008  sparse part has weight 297849 (29.19/col)
Mon Oct  6 19:25:38 2008  filtering completed in 4 passes
Mon Oct  6 19:25:38 2008  matrix is 8767 x 8831 (1.2 MB) with weight 249813 (28.29/col)
Mon Oct  6 19:25:38 2008  sparse part has weight 249813 (28.29/col)
Mon Oct  6 19:25:38 2008  commencing Lanczos iteration
Mon Oct  6 19:25:38 2008  memory use: 1.6 MB
Mon Oct  6 19:25:39 2008  lanczos halted after 140 iterations (dim = 8762)
Mon Oct  6 19:25:39 2008  recovered 63 nontrivial dependencies
Mon Oct  6 19:25:40 2008  prp34 factor: 1577350554019897265169205252353313
Mon Oct  6 19:25:40 2008  prp37 factor: 1226905483766051707687131862935370973
Mon Oct  6 19:25:40 2008  elapsed time 00:01:31

(26·10¹²⁵-53)/9 = 2(8)₁₂₄3_<126> = 7 · 6310145134591339_<16> · C109

C109 = P37 · P72

P37 = 7155330995836183377322672101607069373_<37>

P72 = 914036885595968065221316256368672623704512840186938586508794752515903627_<72>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=1904982041
Step 1 took 3273ms
Step 2 took 3168ms
********** Factor found in step 2: 7155330995836183377322672101607069373
Found probable prime factor of 37 digits: 7155330995836183377322672101607069373
Probable prime cofactor 914036885595968065221316256368672623704512840186938586508794752515903627 has 72 digits

(26·10¹⁹⁷-53)/9 = 2(8)₁₉₆3_<198> = 7 · 71 · 5827 · 33931 · 11178789730567_<14> · 160474133236419241_<18> · 56306547250849852600833678809_<29> · C128

C128 = P29 · P99

P29 = 75596565104432146039405528529_<29>

P99 = 385009979678762504086786747134199125917805790129411664760128132679332492042940092757602857005240341_<99>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3961827852
Step 1 took 4420ms
Step 2 took 3764ms
********** Factor found in step 2: 75596565104432146039405528529
Found probable prime factor of 29 digits: 75596565104432146039405528529
Probable prime cofactor 385009979678762504086786747134199125917805790129411664760128132679332492042940092757602857005240341 has 99 digits

(26·10¹⁰²-53)/9 = 2(8)₁₀₁3_<103> = 3 · 541 · 7056254953606319_<16> · C84

C84 = P42 · P43

P42 = 121810470780205711661897992036627074980747_<42>

P43 = 2070872842870751685650025646347946691354497_<43>

Mon Oct  6 19:27:00 2008  Msieve v. 1.36
Mon Oct  6 19:27:00 2008  random seeds: c8b1b998 262548ec
Mon Oct  6 19:27:00 2008  factoring 252253995916029232215594555960055997739757430421020264159842100261129995557626869259 (84 digits)
Mon Oct  6 19:27:01 2008  no P-1/P+1/ECM available, skipping
Mon Oct  6 19:27:01 2008  commencing quadratic sieve (84-digit input)
Mon Oct  6 19:27:01 2008  using multiplier of 35
Mon Oct  6 19:27:01 2008  using 64kb Opteron sieve core
Mon Oct  6 19:27:01 2008  sieve interval: 6 blocks of size 65536
Mon Oct  6 19:27:01 2008  processing polynomials in batches of 17
Mon Oct  6 19:27:01 2008  using a sieve bound of 1400453 (53488 primes)
Mon Oct  6 19:27:01 2008  using large prime bound of 120438958 (26 bits)
Mon Oct  6 19:27:01 2008  using double large prime bound of 351059328825056 (41-49 bits)
Mon Oct  6 19:27:01 2008  using trial factoring cutoff of 49 bits
Mon Oct  6 19:27:01 2008  polynomial 'A' values have 11 factors
Mon Oct  6 19:57:53 2008  53681 relations (16403 full + 37278 combined from 566333 partial), need 53584
Mon Oct  6 19:57:53 2008  begin with 582736 relations
Mon Oct  6 19:57:53 2008  reduce to 123581 relations in 9 passes
Mon Oct  6 19:57:53 2008  attempting to read 123581 relations
Mon Oct  6 19:57:54 2008  recovered 123581 relations
Mon Oct  6 19:57:54 2008  recovered 96905 polynomials
Mon Oct  6 19:57:55 2008  attempting to build 53681 cycles
Mon Oct  6 19:57:55 2008  found 53681 cycles in 5 passes
Mon Oct  6 19:57:55 2008  distribution of cycle lengths:
Mon Oct  6 19:57:55 2008     length 1 : 16403
Mon Oct  6 19:57:55 2008     length 2 : 11163
Mon Oct  6 19:57:55 2008     length 3 : 9472
Mon Oct  6 19:57:55 2008     length 4 : 6739
Mon Oct  6 19:57:55 2008     length 5 : 4402
Mon Oct  6 19:57:55 2008     length 6 : 2532
Mon Oct  6 19:57:55 2008     length 7 : 1382
Mon Oct  6 19:57:55 2008     length 9+: 1588
Mon Oct  6 19:57:55 2008  largest cycle: 17 relations
Mon Oct  6 19:57:55 2008  matrix is 53488 x 53681 (12.1 MB) with weight 2745542 (51.15/col)
Mon Oct  6 19:57:55 2008  sparse part has weight 2745542 (51.15/col)
Mon Oct  6 19:57:56 2008  filtering completed in 4 passes
Mon Oct  6 19:57:56 2008  matrix is 47610 x 47674 (10.9 MB) with weight 2470762 (51.83/col)
Mon Oct  6 19:57:56 2008  sparse part has weight 2470762 (51.83/col)
Mon Oct  6 19:57:56 2008  saving the first 48 matrix rows for later
Mon Oct  6 19:57:56 2008  matrix is 47562 x 47674 (6.3 MB) with weight 1818216 (38.14/col)
Mon Oct  6 19:57:56 2008  sparse part has weight 1182930 (24.81/col)
Mon Oct  6 19:57:56 2008  matrix includes 64 packed rows
Mon Oct  6 19:57:56 2008  using block size 19069 for processor cache size 1024 kB
Mon Oct  6 19:57:56 2008  commencing Lanczos iteration
Mon Oct  6 19:57:56 2008  memory use: 6.1 MB
Mon Oct  6 19:58:11 2008  lanczos halted after 754 iterations (dim = 47556)
Mon Oct  6 19:58:11 2008  recovered 14 nontrivial dependencies
Mon Oct  6 19:58:12 2008  prp42 factor: 121810470780205711661897992036627074980747
Mon Oct  6 19:58:12 2008  prp43 factor: 2070872842870751685650025646347946691354497
Mon Oct  6 19:58:12 2008  elapsed time 00:31:12

(26·10¹⁵⁶-53)/9 = 2(8)₁₅₅3_<157> = 3 · 331 · 587 · 9377 · 32537 · 82779547 · C135

C135 = P32 · P103

P32 = 29861311761897452258856672790427_<32>

P103 = 6571585131207911210838823149579888907845030427984588149967313321690114167689229511352163744579597243273_<103>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3981921852
Step 1 took 5012ms
Step 2 took 4817ms
********** Factor found in step 2: 29861311761897452258856672790427
Found probable prime factor of 32 digits: 29861311761897452258856672790427
Probable prime cofactor 6571585131207911210838823149579888907845030427984588149967313321690114167689229511352163744579597243273 has 103 digits

(26·10¹⁵⁷-53)/9 = 2(8)₁₅₆3_<158> = 19 · 313 · 34321501 · 1671089759_<10> · 21638934139807_<14> · 57074054446152619_<17> · 2220772121157679073_<19> · C89

C89 = P32 · P58

P32 = 18327578493929997273111231602653_<32>

P58 = 1684935087308557261733642836693608542354060512864471113923_<58>

Mon Oct  6 19:09:21 2008  Msieve v. 1.36
Mon Oct  6 19:09:21 2008  random seeds: 912b2852 0c5bdc26
Mon Oct  6 19:09:21 2008  factoring 30880780069824376361574877541433529546434253609647535122483720592782720577763879432037719 (89 digits)
Mon Oct  6 19:09:22 2008  no P-1/P+1/ECM available, skipping
Mon Oct  6 19:09:22 2008  commencing quadratic sieve (89-digit input)
Mon Oct  6 19:09:23 2008  using multiplier of 59
Mon Oct  6 19:09:23 2008  using 64kb Opteron sieve core
Mon Oct  6 19:09:23 2008  sieve interval: 15 blocks of size 65536
Mon Oct  6 19:09:23 2008  processing polynomials in batches of 7
Mon Oct  6 19:09:23 2008  using a sieve bound of 1545001 (58667 primes)
Mon Oct  6 19:09:23 2008  using large prime bound of 123600080 (26 bits)
Mon Oct  6 19:09:23 2008  using double large prime bound of 367818635270160 (42-49 bits)
Mon Oct  6 19:09:23 2008  using trial factoring cutoff of 49 bits
Mon Oct  6 19:09:23 2008  polynomial 'A' values have 12 factors
Mon Oct  6 20:22:39 2008  58782 relations (16284 full + 42498 combined from 616885 partial), need 58763
Mon Oct  6 20:22:39 2008  begin with 633169 relations
Mon Oct  6 20:22:40 2008  reduce to 141208 relations in 11 passes
Mon Oct  6 20:22:40 2008  attempting to read 141208 relations
Mon Oct  6 20:22:41 2008  recovered 141208 relations
Mon Oct  6 20:22:41 2008  recovered 121099 polynomials
Mon Oct  6 20:22:41 2008  attempting to build 58782 cycles
Mon Oct  6 20:22:41 2008  found 58782 cycles in 5 passes
Mon Oct  6 20:22:41 2008  distribution of cycle lengths:
Mon Oct  6 20:22:41 2008     length 1 : 16284
Mon Oct  6 20:22:41 2008     length 2 : 11594
Mon Oct  6 20:22:41 2008     length 3 : 10265
Mon Oct  6 20:22:41 2008     length 4 : 7688
Mon Oct  6 20:22:41 2008     length 5 : 5399
Mon Oct  6 20:22:41 2008     length 6 : 3363
Mon Oct  6 20:22:41 2008     length 7 : 1903
Mon Oct  6 20:22:41 2008     length 9+: 2286
Mon Oct  6 20:22:41 2008  largest cycle: 17 relations
Mon Oct  6 20:22:41 2008  matrix is 58667 x 58782 (14.9 MB) with weight 3437105 (58.47/col)
Mon Oct  6 20:22:41 2008  sparse part has weight 3437105 (58.47/col)
Mon Oct  6 20:22:42 2008  filtering completed in 3 passes
Mon Oct  6 20:22:42 2008  matrix is 54537 x 54601 (14.0 MB) with weight 3223743 (59.04/col)
Mon Oct  6 20:22:42 2008  sparse part has weight 3223743 (59.04/col)
Mon Oct  6 20:22:42 2008  saving the first 48 matrix rows for later
Mon Oct  6 20:22:42 2008  matrix is 54489 x 54601 (9.0 MB) with weight 2509159 (45.95/col)
Mon Oct  6 20:22:42 2008  sparse part has weight 1807075 (33.10/col)
Mon Oct  6 20:22:42 2008  matrix includes 64 packed rows
Mon Oct  6 20:22:42 2008  using block size 21840 for processor cache size 1024 kB
Mon Oct  6 20:22:43 2008  commencing Lanczos iteration
Mon Oct  6 20:22:43 2008  memory use: 8.0 MB
Mon Oct  6 20:23:04 2008  lanczos halted after 863 iterations (dim = 54485)
Mon Oct  6 20:23:04 2008  recovered 14 nontrivial dependencies
Mon Oct  6 20:23:05 2008  prp32 factor: 18327578493929997273111231602653
Mon Oct  6 20:23:05 2008  prp58 factor: 1684935087308557261733642836693608542354060512864471113923
Mon Oct  6 20:23:05 2008  elapsed time 01:13:44

(26·10¹²⁴-53)/9 = 2(8)₁₂₃3_<125> = C125

C125 = P58 · P67

P58 = 4702771018702305749095782377707818488983640114722149202591_<58>

P67 = 6142950352888021378812891699753388017001993925608663874220496607213_<67>

SNFS difficulty: 126 digits.
Divisors found:
 r1=4702771018702305749095782377707818488983640114722149202591
 r2=6142950352888021378812891699753388017001993925608663874220496607213
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.725).
Factorization parameters were as follows:
n: 28888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883
Y1: 1
Y0: -10000000000000000000000000
c5: 13
c0: -265
skew: 1.83
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 550001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 121605 x 121827
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.00 hours.

(26·10¹⁰³-53)/9 = 2(8)₁₀₂3_<104> = 19 · 29 · 227 · 5189 · C95

C95 = P41 · P54

P41 = 89692426478836592784300376550795841826967_<41>

P54 = 496265333259345156772057309654185119335498040025379133_<54>

SNFS difficulty: 105 digits.
Divisors found:
 r1=89692426478836592784300376550795841826967
 r2=496265333259345156772057309654185119335498040025379133
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 44511241917359155577106323878765321362023863046193398616907007659676149245603176570253558479611
Y1: 1
Y0: -100000000000000000000000000
c4: 13
c0: -265
skew: 2.5
type: snfs
Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [225000, 265001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 46343 x 46563
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,105,4,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000
total time: 0.20 hours.

(26·10¹⁷⁴-53)/9 = 2(8)₁₇₃3_<175> = 3 · 151 · 18917 · C168

C168 = P31 · C138

P31 = 2243086562866881513988079273467_<31>

C138 = [150291472292069767424055033263206434728976210392907193097679201540140532262561658836638110174056704378245409474091400576686840194702606449_<138>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1153297637
Step 1 took 19225ms
********** Factor found in step 1: 2243086562866881513988079273467
Found probable prime factor of 31 digits: 2243086562866881513988079273467
Composite cofactor 150291472292069767424055033263206434728976210392907193097679201540140532262561658836638110174056704378245409474091400576686840194702606449 has 138 digits

(26·10¹⁶⁹-53)/9 = 2(8)₁₆₈3_<170> = 599 · 564251 · 18224693 · 177056177 · 4722398199915096083_<19> · 4741302251973319790706989_<25> · C103

C103 = P35 · P68

P35 = 56575334809536652290971314862111609_<35>

P68 = 20910913013535396971131194830319308120739735863239243650630700492909_<68>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=67958517
Step 1 took 13433ms
Step 2 took 12543ms
********** Factor found in step 2: 56575334809536652290971314862111609
Found probable prime factor of 35 digits: 56575334809536652290971314862111609
Probable prime cofactor 20910913013535396971131194830319308120739735863239243650630700492909 has 68 digits

(26·10²⁰⁴-53)/9 = 2(8)₂₀₃3_<205> = 3² · 199 · 463 · 868884451118897_<15> · 156502951782418193_<18> · C167

C167 = P33 · P134

P33 = 694430743408346543317934266065283_<33>

P134 = 36892727464062353803746935998125110790437863065618259953712823593194923501179666721819922557179370336183877369556062715328482342983457_<134>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2172110407
Step 1 took 20453ms
Step 2 took 15109ms
********** Factor found in step 2: 694430743408346543317934266065283
Found probable prime factor of 33 digits: 694430743408346543317934266065283
Probable prime cofactor 36892727464062353803746935998125110790437863065618259953712823593194923501179666721819922557179370336183877369556062715328482342983457 has 134 digits

2·10¹⁷⁵-9 = 1(9)₁₇₄1_<176> = 11 · 2104936691786471_<16> · C159

C159 = P70 · P90

P70 = 2999235301404108672880852229001943743610905187225557697685545402923389_<70>

P90 = 287996846831064477423205097882532373558238456659108938210015914290084744018871680277303599_<90>

SNFS difficulty: 175 digits.
Divisors found:
 r1=2999235301404108672880852229001943743610905187225557697685545402923389
 r2=287996846831064477423205097882532373558238456659108938210015914290084744018871680277303599
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.739).
Factorization parameters were as follows:
n: 863770309708800587661565784926991363552067036251619250125149999067901342834852215125908090950700120597465563999602721827174720277628477497212972232080890977011
Y1: 1
Y0: -100000000000000000000000000000000000
c5: 2
c0: -9
skew: 1.35
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [3700000, 6400001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1083635 x 1083883
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,54,54,2.6,2.6,100000
total time: 35.00 hours.

(26·10¹⁶⁸-53)/9 = 2(8)₁₆₇3_<169> = 3² · 31 · 666737 · C161

C161 = P40 · P122

P40 = 1167093673337653327127830327069259661809_<40>

P122 = 13306577381392358475255309881615503665415368980360269644105388734553589493156498969747963330291726610161219478491166215269_<122>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=304196581
Step 1 took 18965ms
Step 2 took 14725ms
********** Factor found in step 2: 1167093673337653327127830327069259661809
Found probable prime factor of 40 digits: 1167093673337653327127830327069259661809
Probable prime cofactor 13306577381392358475255309881615503665415368980360269644105388734553589493156498969747963330291726610161219478491166215269 has 122 digits

(26·10¹⁵⁹-53)/9 = 2(8)₁₅₈3_<160> = 3³ · 29 · 287107 · 23759322402380015305157_<23> · C129

C129 = P38 · C92

P38 = 10313704067523250659900937829730796309_<38>

C92 = [52441677875563878773945469819992980394894802790218697762200342387440721101475627254741219911_<92>]

Input number is 540867946412947238983837576736402476646300389187376607989044293296034269709414547519382982732739649482451258823652599480116108499 (129 digits)
Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1193863371
Step 1 took 15386ms
Step 2 took 15370ms
********** Factor found in step 2: 10313704067523250659900937829730796309
Found probable prime factor of 38 digits: 10313704067523250659900937829730796309
Composite cofactor 52441677875563878773945469819992980394894802790218697762200342387440721101475627254741219911 has 92 digits

(26·10¹⁷⁴-53)/9 = 2(8)₁₇₃3_<175> = 3 · 151 · 18917 · 2243086562866881513988079273467_<31> · C138

C138 = P40 · P98

P40 = 9505588734014909843517432505768084428737_<40>

P98 = 15810853645946726698592400974520411575672816481225283858869417945537837498204945702733827218560177_<98>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=481747367
Step 1 took 25522ms
Step 2 took 19983ms
********** Factor found in step 2: 9505588734014909843517432505768084428737
Found probable prime factor of 40 digits: 9505588734014909843517432505768084428737

Oct 7, 2008 (3rd)

By matsui / GMP-ECM

(5·10¹⁸²-23)/9 = (5)₁₈₁3_<182> = 11587 · C178

C178 = P32 · C147

P32 = 22164089254899828504746140018019_<32>

C147 = [216324942791152081793580282576603715592327742295380183409321402881799332508862151634956890785529810487524741549747806557894880895635721994907999801_<147>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
4794645340084193972171878446151338185514417498537633171274320838487577073923841853418102662946021882761332144261288992453228234707478687801463325757793696000306857301765388414219
=22164089254899828504746140018019* 216324942791152081793580282576603715592327742295380183409321402881799332508862151634956890785529810487524741549747806557894880895635721994907999801

Oct 7, 2008 (2nd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38

(16·10²⁰⁰-7)/9 = 1(7)₂₀₀_<201> = 3 · 29 · 113 · 17239 · 183167 · C187

C187 = P35 · P152

P35 = 73650921956704125918421412553905053_<35>

P152 = 77757499705047821516199564486492518620219929342504211246580583218570399145822019564955875866277439662266095840431970859014732292772322991513398308879003_<152>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=437088288
Step 1 took 28010ms
Step 2 took 10289ms
********** Factor found in step 2: 73650921956704125918421412553905053
Found probable prime factor of 35 digits: 73650921956704125918421412553905053
Probable prime cofactor 77757499705047821516199564486492518620219929342504211246580583218570399145822019564955875866277439662266095840431970859014732292772322991513398308879003 has 152 digits

(55·10¹⁷⁴-1)/9 = 6(1)₁₇₄_<175> = 3² · 4597775143424143997_<19> · C156

C156 = P43 · P114

P43 = 1229252059113818413091149720294853232697801_<43>

P114 = 120140379125834124954583462842564535156416411241662126164981729522718127588795637427044066299014456569821516369507_<114>

SNFS difficulty: 176 digits.
Divisors found:
 r1=1229252059113818413091149720294853232697801
 r2=120140379125834124954583462842564535156416411241662126164981729522718127588795637427044066299014456569821516369507
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.854).
Factorization parameters were as follows:
n: 147682808423146405493156532543584238917034823309657064787055774798020076967093264949590809254482259992363365073823088990550667441301074161608069140782354107
Y1: 1
Y0: -100000000000000000000000000000000000
c5: 11
c0: -2
skew: 0.71
type: snfs
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [5000000, 7800001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1260653 x 1260901
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,10000000,10000000,27,27,54,54,2.6,2.6,100000
total time: 30.00 hours.

(23·10¹⁶⁸+31)/9 = 2(5)₁₆₇9_<169> = 3² · 236812287285483410929_<21> · C148

C148 = P43 · P105

P43 = 4399881371891076411517211881007444147724161_<43>

P105 = 272519521223774045867200767539451361177012007095888916737879651496577799389203378273684289426752607226079_<105>

SNFS difficulty: 169 digits.
Divisors found:
 r1=4399881371891076411517211881007444147724161
 r2=272519521223774045867200767539451361177012007095888916737879651496577799389203378273684289426752607226079
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.291).
Factorization parameters were as follows:
n: 1199053564909158263764865435863424465914489971376071052470965230844971018946176597623262002158130529740670738185026088323656292700989789111057594719
Y1: 1
Y0: -1000000000000000000000000000000000
c5: 23000
c0: 31
skew: 0.27
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [3000000, 6100001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1069246 x 1069494
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000
total time: 30.00 hours.

Oct 7, 2008

Factorizations of 288...883 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Oct 6, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(26·10¹⁷¹-71)/9 = 2(8)₁₇₀1_<172> = 43 · 1380617898681809_<16> · C155

C155 = P73 · P83

P73 = 3669494174838085730319346360886510108147157739379354571402691886612341441_<73>

P83 = 13261195602581412992450307530343836667060648761360730528724076800274659175677939043_<83>

Number: 28881_171
N=48661880015060933137981457416002802132480114106356745333892966732948461875636848914080280263954783190211344349331132472591262877557224150237206443500780963
  ( 155 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=3669494174838085730319346360886510108147157739379354571402691886612341441 (pp73)
 r2=13261195602581412992450307530343836667060648761360730528724076800274659175677939043 (pp83)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 221.80 hours.
Scaled time: 223.57 units (timescale=1.008).
Factorization parameters were as follows:
name: 28881_171
n: 48661880015060933137981457416002802132480114106356745333892966732948461875636848914080280263954783190211344349331132472591262877557224150237206443500780963
m: 10000000000000000000000000000000000
c5: 260
c0: -71
skew: 0.77
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 11500001)
Primes: RFBsize:412849, AFBsize:412212, largePrimes:6501610 encountered
Relations: rels:6831268, finalFF:949374
Max relations in full relation-set: 28
Initial matrix: 825128 x 949374 with sparse part having weight 91645762.
Pruned matrix : 732702 x 736891 with weight 74084923.
Total sieving time: 215.68 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 5.83 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 221.80 hours.
 --------- CPU info (if available) ----------

Oct 6, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(10¹⁸⁷+71)/9 = (1)₁₈₆9_<187> = 3 · 170759 · C181

C181 = P60 · P122

P60 = 118556060853532355684657119016905151082226412154225341230741_<60>

P122 = 18294850799511873801677071498271275076680523886468931501062534084271591363969148990966231170862572128613900878977069885767_<122>

Number: n
N=2168965444693224780950757326819496309830640671182018929429022015649953269639494084472094415933393673952004698846739383402165451720672821756805617099950048725808715033294704058763347
  ( 181 digits)
SNFS difficulty: 187 digits.
Divisors found:

Mon Oct 06 07:01:53 2008  prp60 factor: 118556060853532355684657119016905151082226412154225341230741
Mon Oct 06 07:01:53 2008  prp122 factor: 18294850799511873801677071498271275076680523886468931501062534084271591363969148990966231170862572128613900878977069885767
Mon Oct 06 07:01:53 2008  elapsed time 13:58:33 (Msieve 1.38)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 70.75 hours.
Scaled time: 91.41 units (timescale=1.292).
Factorization parameters were as follows:
name: KA_1_186_9
n: 2168965444693224780950757326819496309830640671182018929429022015649953269639494084472094415933393673952004698846739383402165451720672821756805617099950048725808715033294704058763347
type: snfs
skew: 0.93
deg: 5
c5: 100
c0: 71
m: 10000000000000000000000000000000000000
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 6100001)
Primes: RFBsize:602489, AFBsize:603001, largePrimes:14684678 encountered
Relations: rels:14609629, finalFF:1302685
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 70.18 hours.
Total relation processing time: 0.57 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.5,2.5,100000
total time: 70.75 hours.
 --------- CPU info (if available) ----------

Oct 6, 2008

By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1

(89·10¹⁷¹+1)/9 = 9(8)₁₇₀9_<172> = 11 · 29 · 31153 · C165

C165 = P65 · P101

P65 = 20859158360218646280250430937682237384800186664930597024627057321_<65>

P101 = 47704588922816156402622683680592959261170977885583403442268477509804178279463931489193875017204443487_<101>

SNFS difficulty: 172 digits.
Divisors found:
 r1=20859158360218646280250430937682237384800186664930597024627057321
 r2=47704588922816156402622683680592959261170977885583403442268477509804178279463931489193875017204443487
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.945).
Factorization parameters were as follows:
n: 995077574850154454487684142878694352676489781788767772295123953291595307585354484031425533710695819398473817099576283669917204961707234693618912994475429930254118327
Y1: 1
Y0: -10000000000000000000000000000000000
c5: 890
c0: 1
skew: 0.26
type: snfs
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [4500000, 7000001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1147835 x 1148083
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,54,54,2.6,2.6,100000
total time: 30.00 hours.

(86·10¹⁷⁰+31)/9 = 9(5)₁₆₉9_<171> = 7 · 137 · 2579 · 3582718889_<10> · C156

C156 = P50 · P106

P50 = 73044612100303015021615574110453666513439422703861_<50>

P106 = 1476335530587363807889463028248959534110527268122976885451689164688958624422893045288065598247542738990111_<106>

SNFS difficulty: 171 digits.
Divisors found:
 r1=73044612100303015021615574110453666513439422703861
 r2=1476335530587363807889463028248959534110527268122976885451689164688958624422893045288065598247542738990111
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.731).
Factorization parameters were as follows:
n: 107838356161649026351577516693291315248999841606208829510603234036113769212515591345037604034970771261765500380483485337838846613658594572419135364160518571
Y1: 1
Y0: -10000000000000000000000000000000000
c5: 86
c0: 31
skew: 0.82
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [3000000, 5500001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1061379 x 1061627
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000
total time: 30.00 hours.

(23·10¹⁷³-41)/9 = 2(5)₁₇₂1_<174> = 673 · 853 · 5591061403121_<13> · C155

C155 = P46 · P47 · P63

P46 = 7006809008629239360483702710486422780612342481_<46>

P47 = 25181631057758153981933321553668940225037068307_<47>

P63 = 451255837422041310778962833166372971071264336217045028875777297_<63>

SNFS difficulty: 174 digits.
Divisors found:
 r1=7006809008629239360483702710486422780612342481
 r2=25181631057758153981933321553668940225037068307
 r3=451255837422041310778962833166372971071264336217045028875777297
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 79620879277102236161350777737232714052888759619073923411143140991524898238688532735937210657700343773756579155877217308484407849335553097765189963046610099
Y1: 1
Y0: -10000000000000000000000000000000000
c5: 23000
c0: -41
skew: 0.28
type: snfs
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [4500000, 8800001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1366742 x 1366990
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,174,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,54,54,2.6,2.6,100000
total time: 30.00 hours.

(22·10¹⁷⁰+41)/9 = 2(4)₁₆₉9_<171> = 3 · 17 · 139 · 367 · 80993649263_<11> · C154

C154 = P49 · P105

P49 = 5658141762156826678442825564795456282008165567021_<49>

P105 = 205023828685265645027427152433093505046281741380993784990718808353878468660941885633315531455901334965301_<105>

SNFS difficulty: 171 digits.
Divisors found:
 r1=5658141762156826678442825564795456282008165567021
 r2=205023828685265645027427152433093505046281741380993784990718808353878468660941885633315531455901334965301
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.724).
Factorization parameters were as follows:
n: 1160053887321388306247894317985684521194560853620648242948063882893486761625576778027346877448599606173015566550740807961330613627642328527504536024938321
Y1: 1
Y0: -10000000000000000000000000000000000
c5: 22
c0: 41
skew: 1.13
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [3000000, 5900001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1117066 x 1117314
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000
total time: 30.00 hours.

(13·10¹⁷⁴+23)/9 = 1(4)₁₇₃7_<175> = 19 · 233584627 · 327017448697_<12> · C153

C153 = P49 · P105

P49 = 1508884939339678464343119204491325903774757813009_<49>

P105 = 659592843928901000722573606753947216311128546998729114026951853355308952821337342212632003472349819672303_<105>

SNFS difficulty: 176 digits.
Divisors found:
 r1=1508884939339678464343119204491325903774757813009
 r2=659592843928901000722573606753947216311128546998729114026951853355308952821337342212632003472349819672303
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.315).
Factorization parameters were as follows:
n: 995249708300545791129799221580502120491420761030163428196894321573713576560876946695413362256842523332134667375458489194130944953153275856117997330389727
Y1: 1
Y0: -100000000000000000000000000000000000
c5: 13
c0: 230
skew: 1.78
type: snfs
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [5000000, 8900001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1375609 x 1375857
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,10000000,10000000,27,27,54,54,2.6,2.6,100000
total time: 32.00 hours.

(5·10¹⁷⁰+13)/9 = (5)₁₆₉7_<170> = 3 · 503 · 207041 · 7023543563_<10> · C152

C152 = P64 · P88

P64 = 6757843255424349562422360600427818373615137317957647846931199517_<64>

P88 = 3746428975831510131769641735411669473409387191490552876044280413845098431855725258972543_<88>

SNFS difficulty: 170 digits.
Divisors found:
 r1=6757843255424349562422360600427818373615137317957647846931199517
 r2=3746428975831510131769641735411669473409387191490552876044280413845098431855725258972543
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.316).
Factorization parameters were as follows:
n: 25317779786249324256984188517325628223953057120399900583722505923834812071552989221685696863859315525075555386181217047735768127271487751932309957861731
Y1: 1
Y0: -10000000000000000000000000000000000
c5: 5
c0: 13
skew: 1.21
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [3000000, 5300001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 999105 x 999353
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000
total time: 30.00 hours.

(16·10¹⁸⁹-7)/9 = 1(7)₁₈₉_<190> = 97 · 565257584232221_<15> · 2894757784480057_<16> · C158

C158 = P33 · C125

P33 = 313874266742039388275321127723139_<33>

C125 = [35685468203316383629285285631630576483658593506329090236596327342634932358233727998968557498199790458256613246731307616845327_<125>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=349201591
Step 1 took 26185ms
Step 2 took 9028ms
********** Factor found in step 2: 313874266742039388275321127723139
Found probable prime factor of 33 digits: 313874266742039388275321127723139
Composite cofactor 35685468203316383629285285631630576483658593506329090236596327342634932358233727998968557498199790458256613246731307616845327 has 125 digits

Oct 5, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

4·10¹⁸⁸+3 = 4(0)₁₈₇3_<189> = 13 · 151 · 50311 · C181

C181 = P44 · P55 · P83

P44 = 24875180711963832920631823391799924802362043_<44>

P55 = 1752874383582602263485228831981881536452332411343350533_<55>

P83 = 92888019522893020037527962353614086664215590109173413876816904217403183939544249209_<83>

Number: n
N=4050202544047648688833499443952755480878371070909903214031140974559533638618025124682194528939826171179603163787365865012439741466256147587274599773413443774526317927554290357785071
  ( 181 digits)
SNFS difficulty: 188 digits.
Divisors found:

Sun Oct 05 10:57:16 2008  prp44 factor: 24875180711963832920631823391799924802362043
Sun Oct 05 10:57:16 2008  prp55 factor: 1752874383582602263485228831981881536452332411343350533
Sun Oct 05 10:57:16 2008  prp83 factor: 92888019522893020037527962353614086664215590109173413876816904217403183939544249209
Sun Oct 05 10:57:17 2008  elapsed time 06:48:28 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 69.83 hours.
Scaled time: 137.98 units (timescale=1.976).
Factorization parameters were as follows:
name: KA_4_0_187_3
n: 4050202544047648688833499443952755480878371070909903214031140974559533638618025124682194528939826171179603163787365865012439741466256147587274599773413443774526317927554290357785071
type: snfs
skew: 0.47
deg: 5
c5: 125
c0: 3
m: 20000000000000000000000000000000000000
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 6900001)
Primes: RFBsize:602489, AFBsize:601580, largePrimes:14186992 encountered
Relations: rels:13935264, finalFF:1227975
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 69.46 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,188,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.5,2.5,100000
total time: 69.83 hours.
 --------- CPU info (if available) ----------

(52·10¹⁹³-7)/9 = 5(7)₁₉₃_<194> = 3 · 1517945766670785449_<19> · 7229865440639606423_<19> · 36201349029514598526708460117_<29> · C128

C128 = P43 · P86

P43 = 1361633458879307976532980614815947376699811_<43>

P86 = 35601487205328491845602471971596039725155115291438663960324094921313571336527310320491_<86>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 48476176164638862053734691122979671227372039614455965680139465155443601982618066197127877857347079214807473440402864044309127201 (128 digits)
Using B1=6942000, B2=17125579390, polynomial Dickson(12), sigma=2494068609
Step 1 took 69080ms
Step 2 took 28676ms
********** Factor found in step 2: 1361633458879307976532980614815947376699811
Found probable prime factor of 43 digits: 1361633458879307976532980614815947376699811
Probable prime cofactor 35601487205328491845602471971596039725155115291438663960324094921313571336527310320491 has 86 digits

Oct 5, 2008

By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1

(26·10¹⁷⁰-71)/9 = 2(8)₁₆₉1_<171> = 281 · 1036151797_<10> · C159

C159 = P43 · P117

P43 = 8352757623297097696332618845370352702448983_<43>

P117 = 118787640151714003352535632523216976307927450058745101074936089603900745826743578588056704612356256078974602954505651_<117>

SNFS difficulty: 171 digits.
Divisors found:
 r1=8352757623297097696332618845370352702448983
 r2=118787640151714003352535632523216976307927450058745101074936089603900745826743578588056704612356256078974602954505651
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.943).
Factorization parameters were as follows:
n: 992204366830701552260601889495933995632772966000609277532605334444861061300128325310454559138001358509582850301327815420242221382563071698277700080441812702933
Y1: 1
Y0: -10000000000000000000000000000000000
c5: 26
c0: -71
skew: 1.22
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [3000000, 6100001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1163491 x 1163739
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 4.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000
total time: 30.00 hours.

(8·10¹⁷²-11)/3 = 2(6)₁₇₁3_<173> = 7 · 13 · 257 · 12729680113627_<14> · C155

C155 = P48 · P108

P48 = 379919932959707519722966083766347941284954305359_<48>

P108 = 235767884328121729344442224036858091022336279014513197183862800102339634118624490038634191101266307973040593_<108>

SNFS difficulty: 172 digits.
Divisors found:
 r1=379919932959707519722966083766347941284954305359
 r2=235767884328121729344442224036858091022336279014513197183862800102339634118624490038634191101266307973040593
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 89572918807992084599135765143735520891413934611338714495828143684100870450188258262831597166069426537504778163501521975640172727386960968697358477424437887
Y1: 1
Y0: -20000000000000000000000000000000000
c5: 25
c0: -11
skew: 0.85
type: snfs
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [4500000, 6700001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1208103 x 1208351
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,54,54,2.6,2.6,100000
total time: 30.00 hours.

6·10¹⁷²-1 = 5(9)₁₇₂_<173> = 71 · 5333 · C168

C168 = P32 · C137

P32 = 10527309174692505715358220955631_<32>

C137 = [15052337248182079245295376732473140587727231583696298965536998382697969877116207805028160665561308034389058830834673663504559791338218603_<137>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3257129926
Step 1 took 26700ms
********** Factor found in step 1: 10527309174692505715358220955631
Found probable prime factor of 32 digits: 10527309174692505715358220955631
Composite cofactor 15052337248182079245295376732473140587727231583696298965536998382697969877116207805028160665561308034389058830834673663504559791338218603 has 137 digits

(11·10¹⁶⁹+7)/9 = 1(2)₁₆₈3_<170> = 13 · 199 · 23117 · 21154360223_<11> · C151

C151 = P71 · P81

P71 = 56614438302582048814610056890653305828644096999449225595894307044593297_<71>

P81 = 170645631849406535892466311038242263821975056450557183563575141057584461818693727_<81>

SNFS difficulty: 171 digits.
Divisors found:
 r1=56614438302582048814610056890653305828644096999449225595894307044593297
 r2=170645631849406535892466311038242263821975056450557183563575141057584461818693727
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.722).
Factorization parameters were as follows:
n: 9661006595943356569335913717277784341104880983330214595309914724528045964926430879738402044162773517773405484364046472591892578927791104378358520147919
Y1: 1
Y0: -10000000000000000000000000000000000
c5: 11
c0: 70
skew: 1.45
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [3000000, 5500001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1040091 x 1040339
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000
total time: 30.00 hours.

(16·10¹⁷⁴+11)/9 = 1(7)₁₇₃9_<175> = 3 · 367 · 69677 · 229637 · C162

C162 = P33 · C129

P33 = 168059235324598838433859428519907_<33>

C129 = [600477118485275904046986059283468225318011819543399844819021644617823346316693276523484494374747561974398107937389166265935378453_<129>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=151457020
Step 1 took 26818ms
Step 2 took 16347ms
********** Factor found in step 2: 168059235324598838433859428519907
Found probable prime factor of 33 digits: 168059235324598838433859428519907
Composite cofactor 600477118485275904046986059283468225318011819543399844819021644617823346316693276523484494374747561974398107937389166265935378453 has 129 digits

Oct 4, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(26·10¹⁶⁶-71)/9 = 2(8)₁₆₅1_<167> = 3² · 251 · 331 · 5263090523549879_<16> · C145

C145 = P46 · P100

P46 = 1510502859597760806417065936942084544672808513_<46>

P100 = 4859865188787395072098314485948357294398599462740799180745466247719147971275211882335881557251224807_<100>

Number: 28881_166
N=7340840264922971933894794829417861112201031590340036998496018396191265355575127755600652658160478266119929479034056755293239804822403937826381991
  ( 145 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=1510502859597760806417065936942084544672808513 (pp46)
 r2=4859865188787395072098314485948357294398599462740799180745466247719147971275211882335881557251224807 (pp100)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 134.13 hours.
Scaled time: 135.34 units (timescale=1.009).
Factorization parameters were as follows:
name: 28881_166
n: 7340840264922971933894794829417861112201031590340036998496018396191265355575127755600652658160478266119929479034056755293239804822403937826381991
m: 1000000000000000000000000000000000
c5: 260
c0: -71
skew: 0.77
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 7650001)
Primes: RFBsize:380800, AFBsize:380063, largePrimes:6291023 encountered
Relations: rels:6618048, finalFF:955138
Max relations in full relation-set: 28
Initial matrix: 760930 x 955138 with sparse part having weight 75716287.
Pruned matrix : 609006 x 612874 with weight 57216633.
Total sieving time: 130.33 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 3.57 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 134.13 hours.
 --------- CPU info (if available) ----------

Oct 4, 2008 (2nd)

By Serge Batalov / Msieve-1.38

(26·10¹⁶⁷-71)/9 = 2(8)₁₆₆1_<168> = 47 · 3623 · 160163 · C158

C158 = P71 · P87

P71 = 62177173667916090994125727316510673911399562654031399314878446246681393_<71>

P87 = 170361507648356832458459057572079293694991001668148898771440660882317084143196327486739_<87>

SNFS difficulty: 168 digits.
Divisors found:
 r1=62177173667916090994125727316510673911399562654031399314878446246681393
 r2=170361507648356832458459057572079293694991001668148898771440660882317084143196327486739
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 10592597047379898181857972294175227389945639616830971048303006763410773656749525762983982387259612103870860289508693080736858983683550573934343464506965547427
Y1: 1
Y0: -1000000000000000000000000000000000
c5: 2600
c0: -71
skew: 0.49
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [2750000, 4450001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1039542 x 1039790
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 3.00 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,54,54,2.6,2.6,100000
total time: 30.00 hours.

Oct 4, 2008

By Jo Yeong Uk / GGNFS, GMP-ECM

(25·10¹⁹²+11)/9 = 2(7)₁₉₁9_<193> = 28850999 · 29654969 · 433264503167730948116363789_<27> · 21023680370390040093666753767791_<32> · C120

C120 = P54 · P66

P54 = 523283330570262509507095968646219549154589782060264537_<54>

P66 = 681146319566940643603387966607299632516460088185410724746611917543_<66>

Number: 27779_192
N=356432514708665067434889972034144550754335969029805940899612059115982464982373416977480490869176337160263355155411072591
  ( 120 digits)
Divisors found:
 r1=523283330570262509507095968646219549154589782060264537 (pp54)
 r2=681146319566940643603387966607299632516460088185410724746611917543 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 38.90 hours.
Scaled time: 92.46 units (timescale=2.377).
Factorization parameters were as follows:
name: 27779_192
n: 356432514708665067434889972034144550754335969029805940899612059115982464982373416977480490869176337160263355155411072591
skew: 45877.59
# norm 2.10e+16
c5: 59220
c4: 4268148652
c3: -54178355275093
c2: -32310008489240418903
c1: -452211177823445963143823
c0: -93973871227905947990253765
# alpha -5.48
Y1: 4244062156877
Y0: -90344452061388090682912
# Murphy_E 2.82e-10
# M 255242693196056850117205220883103512579840869547747893244572149774913258474069373072912491588421647886917861100495805716
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [2500000, 4600001)
Primes: RFBsize:348513, AFBsize:348452, largePrimes:8679735 encountered
Relations: rels:8845813, finalFF:843049
Max relations in full relation-set: 28
Initial matrix: 697049 x 843049 with sparse part having weight 74015787.
Pruned matrix : 573546 x 577095 with weight 47186435.
Polynomial selection time: 2.62 hours.
Total sieving time: 33.93 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 2.01 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,51,51,2.4,2.4,100000
total time: 38.90 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673800)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Calibrating delay using timer specific routine.. 5344.40 BogoMIPS (lpj=2672204)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)

(2·10¹⁷⁵+1)/3 = (6)₁₇₄7_<175> = 7 · 34429 · C170

C170 = P49 · P122

P49 = 1050191318423217125232464277698554503013130761249_<49>

P122 = 26340127233392236974087975009212418003633400562423119067589738496416129946457990774500568552310756834852983770264132755361_<122>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 27662172946671479884759387504166614800092391657641882742815096354263916493432308588136523888361002421823241481088063910684375989787125748088889626546834133461685815805889 (170 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1712934266
Step 1 took 16245ms
Step 2 took 7139ms
********** Factor found in step 2: 1050191318423217125232464277698554503013130761249
Found probable prime factor of 49 digits: 1050191318423217125232464277698554503013130761249
Probable prime cofactor 26340127233392236974087975009212418003633400562423119067589738496416129946457990774500568552310756834852983770264132755361 has 122 digits

Oct 3, 2008 (3rd)

By Wataru Sakai / GGNFS

(2·10¹⁹⁰+61)/9 = (2)₁₈₉9_<190> = 3² · C189

C189 = P68 · P122

P68 = 15037230780948987466386569695720830218543444409461952110026324979003_<68>

P122 = 16420149683393438216632983454542924702334404553643490266996276078158368227441725013767141314944794683769900016944611993527_<122>

Number: 22229_190
N=246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913581
  ( 189 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=15037230780948987466386569695720830218543444409461952110026324979003 (pp68)
 r2=16420149683393438216632983454542924702334404553643490266996276078158368227441725013767141314944794683769900016944611993527 (pp122)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 1316.55 hours.
Scaled time: 2589.65 units (timescale=1.967).
Factorization parameters were as follows:
n: 246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913581
m: 100000000000000000000000000000000000000
c5: 2
c0: 61
skew: 1.98
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 22700001)
Primes: RFBsize:501962, AFBsize:501692, largePrimes:7358473 encountered
Relations: rels:8000424, finalFF:1177185
Max relations in full relation-set: 32
Initial matrix: 1003721 x 1177185 with sparse part having weight 156407719.
Pruned matrix : 883064 x 888146 with weight 138266463.
Total sieving time: 1304.28 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 11.79 hours.
Time per square root: 0.31 hours.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 1316.55 hours.
 --------- CPU info (if available) ----------

Oct 3, 2008 (2nd)

By Jo Yeong Uk / GGNFS

3·10¹⁹⁶-1 = 2(9)₁₉₆_<197> = C197

C197 = P54 · P54 · P90

P54 = 122344767534061284667205826233542620221024729103782351_<54>

P54 = 349916959335497159053279727421119255555113601555011417_<54>

P90 = 700762515289784210874039143325825539548489780330736974377987653994531387998577206825482297_<90>

Number: 29999_196
N=29999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
  ( 197 digits)
SNFS difficulty: 196 digits.
Divisors found:
 r1=122344767534061284667205826233542620221024729103782351 (pp54)
 r2=349916959335497159053279727421119255555113601555011417 (pp54)
 r3=700762515289784210874039143325825539548489780330736974377987653994531387998577206825482297 (pp90)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 516.20 hours.
Scaled time: 1233.71 units (timescale=2.390).
Factorization parameters were as follows:
n: 29999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
m: 1000000000000000000000000000000000000000
c5: 30
c0: -1
skew: 0.51
type: snfs
Factor base limits: 20000000/20000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 53/53
Sieved algebraic special-q in [10000000, 18300001)
Primes: RFBsize:1270607, AFBsize:1269815, largePrimes:23687268 encountered
Relations: rels:24203236, finalFF:2931375
Max relations in full relation-set: 28
Initial matrix: 2540489 x 2931375 with sparse part having weight 208140655.
Pruned matrix : 2176346 x 2189112 with weight 145380897.
Total sieving time: 472.02 hours.
Total relation processing time: 1.03 hours.
Matrix solve time: 42.87 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,196,5,0,0,0,0,0,0,0,0,20000000,20000000,29,29,53,53,2.6,2.6,100000
total time: 516.20 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673800)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Calibrating delay using timer specific routine.. 5344.40 BogoMIPS (lpj=2672204)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)

Oct 3, 2008

By Robert Backstrom / GMP-ECM

6·10¹⁶⁷+1 = 6(0)₁₆₆1_<168> = 19 · 53 · 151888273037_<12> · 285222132532084029211_<21> · C134

C134 = P38 · P97

P38 = 11344553699289079283476154821341898793_<38>

P97 = 1212346876153485600056159157453359594304541020922218903516315067388636750613885280058055706162793_<97>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 13753534238688584322143339202854565292590236731829919256769931192382804504625818230345229409471072118823813652385708513638874588208849 (134 digits)
Using B1=5466000, B2=11416630690, polynomial Dickson(12), sigma=2706353897
Step 1 took 54142ms
Step 2 took 21534ms
********** Factor found in step 2: 11344553699289079283476154821341898793
Found probable prime factor of 38 digits: 11344553699289079283476154821341898793
Probable prime cofactor 1212346876153485600056159157453359594304541020922218903516315067388636750613885280058055706162793 has 97 digits

Oct 2, 2008 (4th)

By Serge Batalov / GMP-ECM 6.2.1

2·10¹⁷⁰+9 = 2(0)₁₆₉9_<171> = 11 · 20856546081214729_<17> · C153

C153 = P35 · P119

P35 = 31898045403876622590018206760962939_<35>

P119 = 27329447332447825571832005501356411557247380282440211338517340420235479911185535153515772085011975930967362685161689849_<119>

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=2478872043
Step 1 took 262323ms
Step 2 took 79158ms
********** Factor found in step 2: 31898045403876622590018206760962939
Found probable prime factor of 35 digits: 31898045403876622590018206760962939
Probable prime cofactor 27329447332447825571832005501356411557247380282440211338517340420235479911185535153515772085011975930967362685161689849 has 119 digits

Oct 2, 2008 (3rd)

By matsui / GMP-ECM

5·10¹⁸⁶-3 = 4(9)₁₈₅7_<187> = 67317521395141_<14> · 46615341719911308568542113_<26> · C148

C148 = P36 · P112

P36 = 440247862165415629914964024062743623_<36>

P112 = 3619226468217882437161494597428834606600520897650913186570957157465554197450093428407182748230547242163506739583_<112>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
1593356715325410319172868890988741940658975404678256641171322555945504876672202381871531579446721699351252766811856458978967108352978533218354929209
=440247862165415629914964024062743623* 3619226468217882437161494597428834606600520897650913186570957157465554197450093428407182748230547242163506739583

Oct 2, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(26·10¹⁶¹-71)/9 = 2(8)₁₆₀1_<162> = 19 · C161

C161 = P72 · P89

P72 = 632162252911445335796435973980354556377945502963326151746830745204115223_<72>

P89 = 24051860566725428718633081455487317525885368126175025927404218378326986147965349318982413_<89>

Number: 28881_161
N=15204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099
  ( 161 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=632162252911445335796435973980354556377945502963326151746830745204115223 (pp72)
 r2=24051860566725428718633081455487317525885368126175025927404218378326986147965349318982413 (pp89)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 77.65 hours.
Scaled time: 78.28 units (timescale=1.008).
Factorization parameters were as follows:
name: 28881_161
n: 15204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099
m: 100000000000000000000000000000000
c5: 260
c0: -71
skew: 0.77
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 5150001)
Primes: RFBsize:315948, AFBsize:315212, largePrimes:5888530 encountered
Relations: rels:5992989, finalFF:725848
Max relations in full relation-set: 28
Initial matrix: 631227 x 725848 with sparse part having weight 54679237.
Pruned matrix : 563033 x 566253 with weight 40813096.
Total sieving time: 74.92 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 2.54 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 77.65 hours.
 --------- CPU info (if available) ----------

Oct 2, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(17·10¹⁷⁰-53)/9 = 1(8)₁₆₉3_<171> = 3 · 31 · 2333 · 90168271 · C157

C157 = P33 · P34 · P92

P33 = 115142149344161629850376984688397_<33>

P34 = 1772963737984840369465746226474583_<34>

P92 = 47295606304386422476579305729270226175133053046692469208394133140258992145305451848568435167_<92>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 9655060123620669206025974738195444050561032290005483080386739714241489585777600926399707507460520910682304298115846620265195528870797762599462867740469931317 (157 digits)
Using B1=1252000, B2=1426326730, polynomial Dickson(6), sigma=374355149
Step 1 took 15984ms
Step 2 took 6844ms
********** Factor found in step 2: 115142149344161629850376984688397
Found probable prime factor of 33 digits: 115142149344161629850376984688397
Composite cofactor 83853394943684333473055241658152182035340424420224832510221965919173132871571422640806640872525599975611826059405083408860361 has 125 digits

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 83853394943684333473055241658152182035340424420224832510221965919173132871571422640806640872525599975611826059405083408860361 (125 digits)
Using B1=1372000, B2=1426564240, polynomial Dickson(6), sigma=495894633
Step 1 took 12015ms
Step 2 took 5141ms
********** Factor found in step 2: 1772963737984840369465746226474583
Found probable prime factor of 34 digits: 1772963737984840369465746226474583
Probable prime cofactor 47295606304386422476579305729270226175133053046692469208394133140258992145305451848568435167 has 92 digits

(5·10¹⁷⁰-23)/9 = (5)₁₆₉3_<170> = 31643 · 769507357 · C157

C157 = P56 · P101

P56 = 45001623418203325386019413691245428244292701406687273123_<56>

P101 = 50700108208826272869285692148550799344352074012722932660038293634721356836394536023755688749101133861_<101>

Number: n
N=2281587176875759054520890703509527182715102806806507622366468975418052184720131042409246726276126043931951476891864183073846751143457027596919608277490517903
  ( 157 digits)
SNFS difficulty: 170 digits.
Divisors found:

Thu Oct 02 03:06:19 2008  prp56 factor: 45001623418203325386019413691245428244292701406687273123
Thu Oct 02 03:06:19 2008  prp101 factor: 50700108208826272869285692148550799344352074012722932660038293634721356836394536023755688749101133861
Thu Oct 02 03:06:19 2008  elapsed time 04:09:19 (Msieve 1.38 **dep=7**)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 0.78 hours.
Scaled time: 1.02 units (timescale=1.299).
Factorization parameters were as follows:
name: KA_5_169_3
n: 2281587176875759054520890703509527182715102806806507622366468975418052184720131042409246726276126043931951476891864183073846751143457027596919608277490517903
type: snfs
skew: 1.36
deg: 5
c5: 5
c0: -23
m: 10000000000000000000000000000000000
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 200001)
Primes: RFBsize:425648, AFBsize:426252, largePrimes:14739769 encountered
Relations: rels:15116534, finalFF:1557464
Max relations in full relation-set: 28
Initial matrix: 851965 x 1557464 with sparse part having weight 149351625.
Pruned matrix : 
Total sieving time: 0.35 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,52,52,2.5,2.5,100000
total time: 0.78 hours.
 --------- CPU info (if available) ----------

(4·10¹⁷⁰+41)/9 = (4)₁₆₉9_<170> = 7² · 383 · 190938968767_<12> · C155

C155 = P32 · P124

P32 = 11076321807868186689085681697297_<32>

P124 = 1119779442197062735519303413885522946726562495949180557564827738640396690905680513942218528205584546242743238956698113861153_<124>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 12403037455609799575206813257751283380841275957391153538977388063043774573103258275233257298220454720621344967752277641859121318792311574674879151233403441 (155 digits)
Using B1=784000, B2=696767622, polynomial Dickson(3), sigma=1997601525
Step 1 took 9391ms
Step 2 took 3984ms
********** Factor found in step 2: 11076321807868186689085681697297
Found probable prime factor of 32 digits: 11076321807868186689085681697297
Probable prime cofactor 1119779442197062735519303413885522946726562495949180557564827738640396690905680513942218528205584546242743238956698113861153 has 124 digits

5·10¹⁷⁰-1 = 4(9)₁₇₀_<171> = 31 · 4688909 · 5962171 · C156

C156 = P36 · P121

P36 = 414098898368494463344506663169333769_<36>

P121 = 1393246636581073462780644946707410311348854022175587735092066569086144683145170283932792460440716222911271989247205306919_<121>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 576941897363832680247990659532154636533269260043447804982278645257355362380723176817840997220371791999561855565743580805836706271803510382912248634396047711 (156 digits)
Using B1=1114000, B2=1426247560, polynomial Dickson(6), sigma=3235219842
Step 1 took 14359ms
Step 2 took 6828ms
********** Factor found in step 2: 414098898368494463344506663169333769
Found probable prime factor of 36 digits: 414098898368494463344506663169333769
Probable prime cofactor 1393246636581073462780644946707410311348854022175587735092066569086144683145170283932792460440716222911271989247205306919 has 121 digits

3·10¹⁷¹-7 = 2(9)₁₇₀3_<172> = 73 · 26103770121167_<14> · C157

C157 = P71 · P86

P71 = 69185802781796879642077085597448791268734799821577537651715919383668229_<71>

P86 = 22755069893669253071145751833555900531496535657694741960060249774778750742959661038387_<86>

Number: n
N=1574327777949404635376174768673852196943179488710897574632998700132319413715457346172529249449492909562247276388632517481561461992754350763645351691241306623
  ( 157 digits)
SNFS difficulty: 171 digits.
Divisors found:

Thu Oct 02 04:55:00 2008  prp71 factor: 69185802781796879642077085597448791268734799821577537651715919383668229
Thu Oct 02 04:55:01 2008  prp86 factor: 22755069893669253071145751833555900531496535657694741960060249774778750742959661038387
Thu Oct 02 04:55:01 2008  elapsed time 02:13:30 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 16.58 hours.
Scaled time: 34.00 units (timescale=2.051).
Factorization parameters were as follows:
name: KA_2_9_170_3
n: 1574327777949404635376174768673852196943179488710897574632998700132319413715457346172529249449492909562247276388632517481561461992754350763645351691241306623
type: snfs
skew: 0.75
deg: 5
c5: 30
c0: -7
m: 10000000000000000000000000000000000
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 3800001)
Primes: RFBsize:425648, AFBsize:425482, largePrimes:13895280 encountered
Relations: rels:13425134, finalFF:1026037
Max relations in full relation-set: 28
Initial matrix: 851197 x 1026037 with sparse part having weight 114941916.
Pruned matrix : 
Total sieving time: 16.25 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,52,52,2.5,2.5,100000
total time: 16.58 hours.
 --------- CPU info (if available) ----------

Oct 1, 2008 (5th)

By Robert Backstrom / GGNFS, Msieve

(79·10¹⁶⁹-7)/9 = 8(7)₁₆₉_<170> = 3 · 19 · 29 · 1725943553750443_<16> · C152

C152 = P76 · P76

P76 = 3116549881367973389270395010859470666928419469489925409699923580919060881933_<76>

P76 = 9872134366631629882925427065540193668246546885604057444260571641728324014211_<76>

Number: n
N=30766999189174499224689468894868725545675655898997098145447140665073696881219316660229533882153414599964581869484884935996126880831097168266744485149863
  ( 152 digits)
SNFS difficulty: 171 digits.
Divisors found:

Wed Oct 01 10:57:02 2008  prp76 factor: 3116549881367973389270395010859470666928419469489925409699923580919060881933
Wed Oct 01 10:57:02 2008  prp76 factor: 9872134366631629882925427065540193668246546885604057444260571641728324014211
Wed Oct 01 10:57:02 2008  elapsed time 02:23:05 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 14.24 hours.
Scaled time: 27.78 units (timescale=1.951).
Factorization parameters were as follows:
name: KA_8_7_169
n: 30766999189174499224689468894868725545675655898997098145447140665073696881219316660229533882153414599964581869484884935996126880831097168266744485149863
type: snfs
skew: 0.98
deg: 5
c5: 79
c0: -70
m: 10000000000000000000000000000000000
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 3000001)
Primes: RFBsize:425648, AFBsize:426147, largePrimes:13749595 encountered
Relations: rels:13289628, finalFF:1055105
Max relations in full relation-set: 28
Initial matrix: 851860 x 1055105 with sparse part having weight 108793998.
Pruned matrix : 
Total sieving time: 13.93 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,52,52,2.5,2.5,100000
total time: 14.24 hours.
 --------- CPU info (if available) ----------

The two P76s are the largest "nice split" in our tables so far. Congratulations!

(13·10¹⁹³+23)/9 = 1(4)₁₉₂7_<194> = 17 · C192

C192 = P64 · P64 · P66

P64 = 1196455461628544734772941131559603494899791069387129434425021729_<64>

P64 = 5746234301488081463418161619215684930851366835539570351147091267_<64>

P66 = 123586790714944675816525046385603864129642170689196698566797580037_<66>

Number: n
N=849673202614379084967320261437908496732026143790849673202614379084967320261437908496732026143790849673202614379084967320261437908496732026143790849673202614379084967320261437908496732026143791
  ( 192 digits)
SNFS difficulty: 194 digits.
Divisors found:

Wed Oct 01 20:28:23 2008  prp64 factor: 1196455461628544734772941131559603494899791069387129434425021729
Wed Oct 01 20:28:23 2008  prp64 factor: 5746234301488081463418161619215684930851366835539570351147091267
Wed Oct 01 20:28:23 2008  prp66 factor: 123586790714944675816525046385603864129642170689196698566797580037
Wed Oct 01 20:28:23 2008  elapsed time 24:38:46 (Msieve 1.38)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 207.28 hours.
Scaled time: 266.77 units (timescale=1.287).
Factorization parameters were as follows:
name: KA_1_4_192_7
n: 849673202614379084967320261437908496732026143790849673202614379084967320261437908496732026143790849673202614379084967320261437908496732026143790849673202614379084967320261437908496732026143791
type: snfs
skew: 0.28
deg: 5
c5: 13000
c0: 23
m: 100000000000000000000000000000000000000
rlim: 9500000
alim: 9500000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9500000/9500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 17600001)
Primes: RFBsize:633578, AFBsize:634378, largePrimes:15782300 encountered
Relations: rels:16300207, finalFF:1288581
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 206.17 hours.
Total relation processing time: 1.11 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,194,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,52,52,2.5,2.5,100000
total time: 207.28 hours.
 --------- CPU info (if available) ----------

Oct 1, 2008 (4th)

By Jo Yeong Uk / GGNFS

(25·10¹⁷²+11)/9 = 2(7)₁₇₁9_<173> = 23981 · 53995615589_<11> · 7460424273338579899_<19> · 13239143598630449657_<20> · C120

C120 = P57 · P64

P57 = 109489131787240102633809097207760966409512000943817713697_<57>

P64 = 1983705886913857198927917859022711403667837530552000416457450961_<64>

Number: 27779_172
N=217194235279435322578068101831818127012956773396156707671960089661930773720951196887833399196951403371695218091515512817
  ( 120 digits)
Divisors found:
 r1=109489131787240102633809097207760966409512000943817713697 (pp57)
 r2=1983705886913857198927917859022711403667837530552000416457450961 (pp64)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 39.03 hours.
Scaled time: 88.36 units (timescale=2.264).
Factorization parameters were as follows:
name: 27779_172
n: 217194235279435322578068101831818127012956773396156707671960089661930773720951196887833399196951403371695218091515512817
skew: 120743.00
# norm 2.20e+16
c5: 12540
c4: -2801895919
c3: -707820581642247
c2: 37147529845475201007
c1: 3152016688089544702881334
c0: -61311511986314671396522758936
# alpha -5.67
Y1: 5015245439623
Y0: -111612034227956946874235
# Murphy_E 2.91e-10
# M 31924727766020902462974355133718177632421051733378130399990588470417387964299356643973755470171567151060421048341657594
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [2500000, 4600001)
Primes: RFBsize:348513, AFBsize:348407, largePrimes:8681924 encountered
Relations: rels:8873385, finalFF:860548
Max relations in full relation-set: 28
Initial matrix: 697004 x 860548 with sparse part having weight 75775813.
Pruned matrix : 560161 x 563710 with weight 47440428.
Polynomial selection time: 2.63 hours.
Total sieving time: 34.03 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 2.02 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,51,51,2.4,2.4,100000
total time: 39.03 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673800)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Calibrating delay using timer specific routine.. 5344.40 BogoMIPS (lpj=2672204)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)

Oct 1, 2008 (3rd)

By matsui / GMP-ECM

4·10¹⁹³+9 = 4(0)₁₉₂9_<194> = 7 · 11437 · 13853895929_<11> · 284374155722383_<15> · C165

C165 = P32 · C133

P32 = 40774884715492908428204364418823_<32>

C133 = [3110248167561881935201485645217781199329548107070074852028048966879022371455995745826435473920853302379411133812169289220566053640491_<133>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
126820010468908806071880109357043266345981215766729369753337225868175064400665316164905372765852198104155866881930631191806135695255612601001613076169469586595362093
=40774884715492908428204364418823* 3110248167561881935201485645217781199329548107070074852028048966879022371455995745826435473920853302379411133812169289220566053640491

Oct 1, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(26·10¹⁶⁰-71)/9 = 2(8)₁₅₉1_<161> = 3 · C160

C160 = P70 · P91

P70 = 1094998023968034643446213026625908789762145086429066485506433912988981_<70>

P91 = 8794198180133646807441422534325880565522933789319895295254625222992854439653169060283985967_<91>

Number: 28881_160
N=9629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629627
  ( 160 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=1094998023968034643446213026625908789762145086429066485506433912988981 (pp70)
 r2=8794198180133646807441422534325880565522933789319895295254625222992854439653169060283985967 (pp91)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 66.55 hours.
Scaled time: 67.29 units (timescale=1.011).
Factorization parameters were as follows:
name: 28881_160
n: 9629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629627
m: 100000000000000000000000000000000
c5: 26
c0: -71
skew: 1.22
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4500001)
Primes: RFBsize:283146, AFBsize:284453, largePrimes:6116457 encountered
Relations: rels:6399110, finalFF:847689
Max relations in full relation-set: 28
Initial matrix: 567665 x 847689 with sparse part having weight 74518698.
Pruned matrix : 396349 x 399251 with weight 60554454.
Total sieving time: 64.50 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.87 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 66.55 hours.
 --------- CPU info (if available) ----------

(26·10¹⁷⁶-71)/9 = 2(8)₁₇₅1_<177> = 107 · 613 · 5414231 · 10578209 · 230072970263_<12> · 4597194814998215328498307_<25> · C122

C122 = P41 · P82

P41 = 54750566371088487970140619870411787020199_<41>

P82 = 1327976953687722400410338375555843000971594563026585227832663573259827714155008331_<82>

Number: 28881_176
N=72707490342155548476515019381711751468610942138147232179566137303158185999391724808661810254764068692558145383814510277869
  ( 122 digits)
Divisors found:
 r1=54750566371088487970140619870411787020199 (pp41)
 r2=1327976953687722400410338375555843000971594563026585227832663573259827714155008331 (pp82)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 104.16 hours.
Scaled time: 79.47 units (timescale=0.763).
Factorization parameters were as follows:
name: 28881_176
n: 72707490342155548476515019381711751468610942138147232179566137303158185999391724808661810254764068692558145383814510277869
skew: 195914.61
# norm 6.01e+16
c5: 16920
c4: -2370698138
c3: -1945543577514837
c2: 94960906202510051988
c1: 32239981473917970843344652
c0: -350196706109857443759359141920
# alpha -6.48
Y1: 1223064843187
Y0: -336229491185560213282809
# Murphy_E 2.30e-10
# M 62554245738941506985845956102807922475403985619745266129749410940345544183912752389781863871923413333511066297556897473815
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 5560001)
Primes: RFBsize:348513, AFBsize:347798, largePrimes:7893977 encountered
Relations: rels:8200076, finalFF:872826
Max relations in full relation-set: 28
Initial matrix: 696394 x 872826 with sparse part having weight 85171281.
Pruned matrix : 554875 x 558420 with weight 58323465.
Total sieving time: 98.04 hours.
Total relation processing time: 0.62 hours.
Matrix solve time: 5.04 hours.
Time per square root: 0.45 hours.
Prototype def-par.txt line would be:
gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 104.16 hours.
 --------- CPU info (if available) ----------

Oct 1, 2008

By Serge Batalov / GMP-ECM 6.2.1

5·10¹⁹⁴-7 = 4(9)₁₉₃3_<195> = 17 · 1981997 · 128401228061807_<15> · C174

C174 = P33 · P141

P33 = 132786590634016095535035300329071_<33>

P141 = 870351520581469776388414556682719376942987278061824153278788586760800351254966171514056538147644847695340761111994287303596157877520893178381_<141>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=2621838758
Step 1 took 99259ms
Step 2 took 29938ms
********** Factor found in step 2: 132786590634016095535035300329071
Found probable prime factor of 33 digits: 132786590634016095535035300329071
Probable prime cofactor 870351520581469776388414556682719376942987278061824153278788586760800351254966171514056538147644847695340761111994287303596157877520893178381 has 141 digits

September 2008

Sep 30, 2008 (4th)

By Justin Card / ggnfs/msieve 1.38

(10¹⁸¹+17)/9 = (1)₁₈₀3_<181> = 3 · 157 · 1217 · 158606909 · 387812569 · 1081691731937760857100887471929643_<34> · C125

C125 = P46 · P79

P46 = 7385184232314750943068830580286922326162032853_<46>

P79 = 3944910724671705496959005657530034323166977886486088453196723251979037296752101_<79>

Number: 11113_181
N=29133892481734837183602135697334988973490703807163310757974571749978078052900604926957726939876253751243046373693076558774153
  ( 125 digits)
Divisors found:
 r1=7385184232314750943068830580286922326162032853
 r2=3944910724671705496959005657530034323166977886486088453196723251979037296752101
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.096).
Factorization parameters were as follows:
name: 11113_181
n: 29133892481734837183602135697334988973490703807163310757974571749978078052900604926957726939876253751243046373693076558774153
skew: 59306.55
# norm 1.20e+17
c5: 81240
c4: -26753789998
c3: 2671095956360131
c2: 181566292555311624899
c1: -2830291977228100294497705
c0: 6437501435799513345248142525
# alpha -5.47
Y1: 34134483791353
Y0: -814567199780845767882556
# Murphy_E 1.44e-10
# M 11523274213504150547440140399716556813368765874185185755558534481244351005830591973008858940401959649125501491092593456176972
type: gnfs
rlim: 8000000
alim: 8000000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [4000000, 8300001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 977398 x 977646
Total sieving time: 39.40 hours.
Total relation processing time: 1.00 hours.
Matrix solve time: 4.00 hours.
Time per square root: 0.16 hours.
total time: 44.73 hours.
 --------- CPU info (if available) ----------
[   27.172216] Memory: 3055428k/3111872k available (2523k kernel code, 56056k reserved, 1328k data, 328k init)
[   27.318604] Calibrating delay using timer specific routine.. 3982.80 BogoMIPS (lpj=19914039)
[   28.066173] Calibrating delay using timer specific routine.. 3979.59 BogoMIPS (lpj=19897994)

Sep 30, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(25·10¹⁸¹-43)/9 = 2(7)₁₈₀3_<182> = 199 · C180

C180 = P84 · P96

P84 = 737914540865569522516610635268562488832829093976632609420812249119634895894823895649_<84>

P96 = 189163941450691415519843770805049671097893785124964204776656846922107400108917180888501599597323_<96>

Number: n
N=139586823003908431044109436069235064209938581797878280290340591848129536571747627024008933556672250139586823003908431044109436069235064209938581797878280290340591848129536571747627
  ( 180 digits)
SNFS difficulty: 182 digits.
Divisors found:

Tue Sep 30 07:28:26 2008  prp84 factor: 737914540865569522516610635268562488832829093976632609420812249119634895894823895649
Tue Sep 30 07:28:27 2008  prp96 factor: 189163941450691415519843770805049671097893785124964204776656846922107400108917180888501599597323
Tue Sep 30 07:28:27 2008  elapsed time 04:32:32 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 43.65 hours.
Scaled time: 89.27 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_2_7_180_3
n: 139586823003908431044109436069235064209938581797878280290340591848129536571747627024008933556672250139586823003908431044109436069235064209938581797878280290340591848129536571747627
type: snfs
skew: 0.70
deg: 5
c5: 250
c0: -43
m: 1000000000000000000000000000000000000
rlim: 8000000
alim: 8000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 3700001)
Primes: RFBsize:539777, AFBsize:540260, largePrimes:13819945 encountered
Relations: rels:13443130, finalFF:1142439
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 43.32 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,52,52,2.5,2.5,100000
total time: 43.65 hours.
 --------- CPU info (if available) ----------

(8·10¹⁷⁰-71)/9 = (8)₁₆₉1_<170> = 3 · 10039 · 716789 · 2965043 · C154

C154 = P69 · P85

P69 = 443198506540851385333367717395890976633598570600406398617488535633577_<69>

P85 = 3133395045463270610737589355782572374210977477082636826967676595220533524174375587867_<85>

Number: n
N=1388716004551824663688127790977244167305559219887100242841409051448755631839236069068098714742279970502100643048354646251438202731220208003585966679010259
  ( 154 digits)
SNFS difficulty: 170 digits.
Divisors found:

Tue Sep 30 17:22:35 2008  prp69 factor: 443198506540851385333367717395890976633598570600406398617488535633577
Tue Sep 30 17:22:35 2008  prp85 factor: 3133395045463270610737589355782572374210977477082636826967676595220533524174375587867
Tue Sep 30 17:22:35 2008  elapsed time 01:58:27 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.00 hours.
Scaled time: 14.26 units (timescale=2.038).
Factorization parameters were as follows:
name: KA_8_169_1
n: 1388716004551824663688127790977244167305559219887100242841409051448755631839236069068098714742279970502100643048354646251438202731220208003585966679010259
type: snfs
skew: 1.55
deg: 5
c5: 8
c0: -71
m: 10000000000000000000000000000000000
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 1700001)
Primes: RFBsize:425648, AFBsize:425953, largePrimes:12556966 encountered
Relations: rels:11858449, finalFF:922632
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 6.74 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,52,52,2.5,2.5,100000
total time: 7.00 hours.
 --------- CPU info (if available) ----------

2·10¹⁷¹-7 = 1(9)₁₇₀3_<172> = 69542053866301_<14> · C158

C158 = P37 · P122

P37 = 2207526515260409521358128631916321637_<37>

P122 = 13027964122020918758541442567091441481729149610702735659626025690125388966404642417856907478360011684956625601358894013289_<122>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 28759576239222479445427457166769989217459420861873120828607886411638715838759733339575181195652664367341890322210548946242344000418152022255576564125476234093 (158 digits)
Using B1=990000, B2=1045563762, polynomial Dickson(6), sigma=38349962
Step 1 took 12640ms
Step 2 took 6438ms
********** Factor found in step 2: 2207526515260409521358128631916321637
Found probable prime factor of 37 digits: 2207526515260409521358128631916321637
Probable prime cofactor 13027964122020918758541442567091441481729149610702735659626025690125388966404642417856907478360011684956625601358894013289 has 122 digits

Sep 30, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(26·10¹⁶³-71)/9 = 2(8)₁₆₂1_<164> = 3 · 7 · 17482589 · 742458152998064175019_<21> · C135

C135 = P41 · P94

P41 = 82040906752589392506124571605912668180523_<41>

P94 = 1291824044130121762655087841332987925302619521194453123869004000921846867381372572710987124377_<94>

Number: 28881_163
N=105982415945232243895233769180678939994479004894602568437992066771945436505597759901254384722787348132133665169458489655421436489909171
  ( 135 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=82040906752589392506124571605912668180523 (pp41)
 r2=1291824044130121762655087841332987925302619521194453123869004000921846867381372572710987124377 (pp94)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 92.11 hours.
Scaled time: 92.66 units (timescale=1.006).
Factorization parameters were as follows:
name: 28881_163
n: 105982415945232243895233769180678939994479004894602568437992066771945436505597759901254384722787348132133665169458489655421436489909171
m: 200000000000000000000000000000000
c5: 1625
c0: -142
skew: 0.61
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 5800001)
Primes: RFBsize:348513, AFBsize:347822, largePrimes:6128209 encountered
Relations: rels:6437711, finalFF:928519
Max relations in full relation-set: 28
Initial matrix: 696401 x 928519 with sparse part having weight 64868998.
Pruned matrix : 512907 x 516453 with weight 47758086.
Total sieving time: 89.49 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 2.41 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 92.11 hours.
 --------- CPU info (if available) ----------

Sep 30, 2008

By matsui / GMP-ECM

4·10¹⁹⁸+3 = 4(0)₁₉₇3_<199> = 7³ · 499 · 6623605628946997_<16> · 1337219835698580307_<19> · C160

C160 = P38 · P123

P38 = 22355415272513896662048780081754279783_<38>

P123 = 118028070472771437685486920896484037107828428621451610964475648743976065340805709497284979806314122890506877033820039746847_<123>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
2638566529232341089643546066807989595166818810117536594989975833327270688254378755998477840372259078317921239139584373535543895418449639572065879395910130094201
=22355415272513896662048780081754279783* 118028070472771437685486920896484037107828428621451610964475648743976065340805709497284979806314122890506877033820039746847

Sep 29, 2008 (2nd)

By Wataru Sakai / GGNFS

(73·10¹⁹⁴-1)/9 = 8(1)₁₉₄_<195> = C195

C195 = P75 · P121

P75 = 306560981981481704619439698696478142677609707817262304366101661349418983307_<75>

P121 = 2645839355903771034479686515433710428643834762960463161678823519151880019097909680932155803208297225177206761675775557173_<121>

Number: 81111_194
N=811111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
  ( 195 digits)
SNFS difficulty: 196 digits.
Divisors found:
 r1=306560981981481704619439698696478142677609707817262304366101661349418983307 (pp75)
 r2=2645839355903771034479686515433710428643834762960463161678823519151880019097909680932155803208297225177206761675775557173 (pp121)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 4907.46 hours.
Scaled time: 9829.64 units (timescale=2.003).
Factorization parameters were as follows:
n: 811111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
m: 1000000000000000000000000000000000000000
c5: 73
c0: -10
skew: 0.67
type: snfsFactor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 86400001)
Primes: RFBsize:501962, AFBsize:502306, largePrimes:9714699 encountered
Relations: rels:11320200, finalFF:1140454
Max relations in full relation-set: 32
Initial matrix: 1004333 x 1140454 with sparse part having weight 216153670.
Pruned matrix : 939585 x 944670 with weight 198992522.
Total sieving time: 4888.56 hours.
Total relation processing time: 0.95 hours.
Matrix solve time: 17.53 hours.
Time per square root: 0.43 hours.
Prototype def-par.txt line would be:
snfs,196,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 4907.46 hours.
 --------- CPU info (if available) ----------

(16·10¹⁹⁰+11)/9 = 1(7)₁₈₉9_<191> = 163 · C189

C189 = P59 · P130

P59 = 15893897701210748826466356818360065080329541721568770733123_<59>

P130 = 6862138122843942847791922085053418154936259828171101678155392075764498344425374075168875066509622240658600914959115020089323939771_<130>

Number: 17779_190
N=109066121336059986366734832992501704158145875937286980231765507839127471029311520109066121336059986366734832992501704158145875937286980231765507839127471029311520109066121336059986366734833
  ( 189 digits)
SNFS difficulty: 191 digits.
Divisors found:
 r1=15893897701210748826466356818360065080329541721568770733123 (pp59)
 r2=6862138122843942847791922085053418154936259828171101678155392075764498344425374075168875066509622240658600914959115020089323939771 (pp130)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 1211.20 hours.
Scaled time: 2426.02 units (timescale=2.003).
Factorization parameters were as follows:
n: 109066121336059986366734832992501704158145875937286980231765507839127471029311520109066121336059986366734832992501704158145875937286980231765507839127471029311520109066121336059986366734833
m: 200000000000000000000000000000000000000
c5: 1
c0: 22
skew: 1.86
type: snfsFactor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 20600001)
Primes: RFBsize:501962, AFBsize:502487, largePrimes:7199292 encountered
Relations: rels:7802974, finalFF:1170083
Max relations in full relation-set: 32
Initial matrix: 1004513 x 1170083 with sparse part having weight 143400992.
Pruned matrix : 885927 x 891013 with weight 123578297.
Total sieving time: 1199.45 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 11.33 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 1211.20 hours.
 --------- CPU info (if available) ----------

Sep 29, 2008

By Sinkiti Sibata / GGNFS

(26·10¹⁶²-71)/9 = 2(8)₁₆₁1_<163> = 1605341 · C157

C157 = P44 · P56 · P57

P44 = 34840843885409601679480678418650111005563801_<44>

P56 = 65612945889179070840638882215639321183998522259344767579_<56>

P57 = 787200458193689081759211506325782501478201241604278678679_<57>

Number: 28881_162
N=1799548437926203148669901839477649227727248534042853754366760014781214015519997862690162955340260348978122958853532607021741106026002505940413213696584643941
  ( 157 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=34840843885409601679480678418650111005563801 (pp44)
 r2=65612945889179070840638882215639321183998522259344767579 (pp56)
 r3=787200458193689081759211506325782501478201241604278678679 (pp57)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 77.77 hours.
Scaled time: 78.40 units (timescale=1.008).
Factorization parameters were as follows:
name: 28881_162
n: 1799548437926203148669901839477649227727248534042853754366760014781214015519997862690162955340260348978122958853532607021741106026002505940413213696584643941
m: 100000000000000000000000000000000
c5: 2600
c0: -71
skew: 0.49
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 5150001)
Primes: RFBsize:315948, AFBsize:315767, largePrimes:5897191 encountered
Relations: rels:5994983, finalFF:717928
Max relations in full relation-set: 28
Initial matrix: 631782 x 717928 with sparse part having weight 56111003.
Pruned matrix : 571221 x 574443 with weight 42764962.
Total sieving time: 74.92 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 2.65 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 77.77 hours.
 --------- CPU info (if available) ----------

(26·10¹⁵⁵-71)/9 = 2(8)₁₅₄1_<156> = 761 · 54499 · 30564664990261253_<17> · C132

C132 = P47 · P85

P47 = 63836161460698741419691880404514945920853927423_<47>

P85 = 3570024888040223758946915583946688879184055497902878240186964550332918034067683819241_<85>

Number: 28881_155
N=227896685171648671109267995127880791600813825571543173727625987550571717872159185551505336201973631147175443328833813898063264945943
  ( 132 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=63836161460698741419691880404514945920853927423 (pp47)
 r2=3570024888040223758946915583946688879184055497902878240186964550332918034067683819241 (pp85)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 42.65 hours.
Scaled time: 33.26 units (timescale=0.780).
Factorization parameters were as follows:
name: 28881_155
n: 227896685171648671109267995127880791600813825571543173727625987550571717872159185551505336201973631147175443328833813898063264945943
m: 10000000000000000000000000000000
c5: 26
c0: -71
skew: 1.22
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3000001)
Primes: RFBsize:216816, AFBsize:218152, largePrimes:5706068 encountered
Relations: rels:5661084, finalFF:528212
Max relations in full relation-set: 28
Initial matrix: 435034 x 528212 with sparse part having weight 46997049.
Pruned matrix : 392905 x 395144 with weight 32227067.
Total sieving time: 40.43 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.94 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 42.65 hours.
 --------- CPU info (if available) ----------

(26·10¹³⁴-71)/9 = 2(8)₁₃₃1_<135> = 1801897 · 265450281363670856539_<21> · C108

C108 = P49 · P60

P49 = 2151771244658802648860981132723919893684815718567_<49>

P60 = 280686539850995217773316080340193459612811030104024615577821_<60>

Number: 28881_134
N=603973225214148590339598242124486865273569787328277014085649480739015184344731316431305397368734430023102507
  ( 108 digits)
Divisors found:
 r1=2151771244658802648860981132723919893684815718567 (pp49)
 r2=280686539850995217773316080340193459612811030104024615577821 (pp60)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 19.00 hours.
Scaled time: 8.97 units (timescale=0.472).
Factorization parameters were as follows:
name: 28881_134
n: 603973225214148590339598242124486865273569787328277014085649480739015184344731316431305397368734430023102507
skew: 9031.63
# norm 8.65e+14
c5: 132480
c4: -9655136832
c3: 3073901148074
c2: 788244391354358951
c1: 755654046763763982904
c0: -3914555308130336395968572
# alpha -6.44
Y1: 184659791063
Y0: -340233371806463795427
# Murphy_E 1.39e-09
# M 528174875071408094852850298995715238680787298333444263874278964954547222542074420587388804359136793122955655
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2300001)
Primes: RFBsize:183072, AFBsize:182771, largePrimes:4380791 encountered
Relations: rels:4391242, finalFF:413456
Max relations in full relation-set: 28
Initial matrix: 365923 x 413456 with sparse part having weight 29385875.
Pruned matrix : 328573 x 330466 with weight 19750900.
Total sieving time: 15.57 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 2.92 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 19.00 hours.
 --------- CPU info (if available) ----------

Sep 28, 2008 (5th)

By Serge Batalov / Msieve-1.38

(26·10¹⁴⁰-71)/9 = 2(8)₁₃₉1_<141> = 258551 · C136

C136 = P58 · P79

P58 = 1061457857440639884285723044526980992447605343813900560013_<58>

P79 = 1052644826720225490937098572168106297601845969296447812929710800726211325127987_<79>

SNFS difficulty: 141 digits.
Divisors found:
 r1=1061457857440639884285723044526980992447605343813900560013
 r2=1052644826720225490937098572168106297601845969296447812929710800726211325127987
Version: 
Total time: 5.70 hours.
Scaled time: 14.70 units (timescale=2.579).
Factorization parameters were as follows:
n: 1117338122416424182806830717687763299654183851112116715421285892875637258757030098080799876577112016154990268414699184643992438199383831
Y1: 1
Y0: -10000000000000000000000000000
c5: 26
c0: -71
skew: 1.22
type: snfs
lss: 1
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved rational special-q in [650000, 1950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 215541 x 215782
Total sieving time: 5.70 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 5.70 hours.

Sep 28, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve

5·10¹⁸¹-7 = 4(9)₁₈₀3_<182> = 107 · 167 · C178

C178 = P79 · P99

P79 = 5349247229374462217450139738261038814734050044867358474115901989701104007451021_<79>

P99 = 523090803940434651997243625173949810907397035980386998037130621336689305210083737010025418468122257_<99>

Number: n
N=2798142033689630085623146230902680620068274665622026974089204768034025407129665901841177458167776596340030219933963848004924729979293748950696737366388717891320163411494767474397
  ( 178 digits)
SNFS difficulty: 181 digits.
Divisors found:

Sun Sep 28 04:54:25 2008  prp79 factor: 5349247229374462217450139738261038814734050044867358474115901989701104007451021
Sun Sep 28 04:54:25 2008  prp99 factor: 523090803940434651997243625173949810907397035980386998037130621336689305210083737010025418468122257
Sun Sep 28 04:54:25 2008  elapsed time 05:08:16 (Msieve 1.38)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 42.26 hours.
Scaled time: 83.51 units (timescale=1.976).
Factorization parameters were as follows:
name: KA_4_9_180_3
n: 2798142033689630085623146230902680620068274665622026974089204768034025407129665901841177458167776596340030219933963848004924729979293748950696737366388717891320163411494767474397
type: snfs
skew: 0.67
deg: 5
c5: 50
c0: -7
m: 1000000000000000000000000000000000000
rlim: 8000000
alim: 8000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 4500001)
Primes: RFBsize:539777, AFBsize:540740, largePrimes:13860963 encountered
Relations: rels:13460271, finalFF:1117649
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 41.94 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,52,52,2.5,2.5,100000
total time: 42.26 hours.
 --------- CPU info (if available) ----------

Sep 28, 2008 (3rd)

By Justin Card / msieve 1.38

(26·10¹²⁶-71)/9 = 2(8)₁₂₅1_<127> = 401 · 3354622878026888455049_<22> · C103

C103 = P44 · P60

P44 = 16283299902589791600249813240195129893581187_<44>

P60 = 131886498973573202679378662889306990910980844571318172595187_<60>

Number: 28881_126
N=2147547415889293181059921809418318585188055202701289383214912889185222223648914042877205066401069946969
  ( 103 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=16283299902589791600249813240195129893581187
 r2=131886498973573202679378662889306990910980844571318172595187
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.090).
Factorization parameters were as follows:

n: 2147547415889293181059921809418318585188055202701289383214912889185222223648914042877205066401069946969
Y1: 1
Y0: -10000000000000000000000000
c5: 260
c0: -71
skew: 0.77
type: snfs

Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 800001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 131945 x 132185
Total sieving time: 1.22 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.

(26·10¹²⁴-71)/9 = 2(8)₁₂₃1_<125> = 3 · 163 · 57162358247_<11> · 4863987289960456051_<19> · C93

C93 = P44 · P49

P44 = 82711241811099317326869797485718892733761469_<44>

P49 = 2568945372540053678056380379294551958469473628953_<49>

Sat Sep 27 00:44:53 2008
Sat Sep 27 00:44:53 2008
Sat Sep 27 00:44:53 2008  Msieve v. 1.38
Sat Sep 27 00:44:53 2008  random seeds: 5731128c 633662a3
Sat Sep 27 00:44:53 2008  factoring 212480661907664999835916436228413132121070297399683627848151251731890808162658241713314211957 (93 digits)
Sat Sep 27 00:44:55 2008  no P-1/P+1/ECM available, skipping
Sat Sep 27 00:44:55 2008  commencing quadratic sieve (93-digit input)
Sat Sep 27 00:44:55 2008  using multiplier of 37
Sat Sep 27 00:44:55 2008  using 64kb Athlon XP sieve core
Sat Sep 27 00:44:55 2008  sieve interval: 18 blocks of size 65536
Sat Sep 27 00:44:55 2008  processing polynomials in batches of 6
Sat Sep 27 00:44:55 2008  using a sieve bound of 1883627 (70588 primes)
Sat Sep 27 00:44:55 2008  using large prime bound of 220384359 (27 bits)
Sat Sep 27 00:44:55 2008  using double large prime bound of 1041658353184527 (42-50 bits)
Sat Sep 27 00:44:55 2008  using trial factoring cutoff of 50 bits
Sat Sep 27 00:44:55 2008  polynomial 'A' values have 12 factors
Sat Sep 27 11:40:31 2008
Sat Sep 27 11:40:31 2008
Sat Sep 27 11:40:31 2008  Msieve v. 1.38
Sat Sep 27 11:40:31 2008  random seeds: 367b5676 c75d7466
Sat Sep 27 11:40:31 2008  factoring 212480661907664999835916436228413132121070297399683627848151251731890808162658241713314211957 (93 digits)
Sat Sep 27 11:40:32 2008  no P-1/P+1/ECM available, skipping
Sat Sep 27 11:40:32 2008  commencing quadratic sieve (93-digit input)
Sat Sep 27 11:40:33 2008  using multiplier of 37
Sat Sep 27 11:40:33 2008  using 64kb Athlon XP sieve core
Sat Sep 27 11:40:33 2008  sieve interval: 18 blocks of size 65536
Sat Sep 27 11:40:33 2008  processing polynomials in batches of 6
Sat Sep 27 11:40:33 2008  using a sieve bound of 1883627 (70588 primes)
Sat Sep 27 11:40:33 2008  using large prime bound of 220384359 (27 bits)
Sat Sep 27 11:40:33 2008  using double large prime bound of 1041658353184527 (42-50 bits)
Sat Sep 27 11:40:33 2008  using trial factoring cutoff of 50 bits
Sat Sep 27 11:40:33 2008  polynomial 'A' values have 12 factors
Sat Sep 27 11:40:37 2008  restarting with 12109 full and 628657 partial relations
Sat Sep 27 14:00:31 2008  71068 relations (17856 full + 53212 combined from 924337 partial), need 70684
Sat Sep 27 14:00:32 2008  begin with 942193 relations
Sat Sep 27 14:00:34 2008  reduce to 180710 relations in 10 passes
Sat Sep 27 14:00:34 2008  attempting to read 180710 relations
Sat Sep 27 14:00:39 2008  recovered 180710 relations
Sat Sep 27 14:00:39 2008  recovered 163046 polynomials
Sat Sep 27 14:00:40 2008  attempting to build 71068 cycles
Sat Sep 27 14:00:40 2008  found 71068 cycles in 6 passes
Sat Sep 27 14:00:40 2008  distribution of cycle lengths:
Sat Sep 27 14:00:40 2008     length 1 : 17856
Sat Sep 27 14:00:40 2008     length 2 : 13079
Sat Sep 27 14:00:40 2008     length 3 : 12068
Sat Sep 27 14:00:40 2008     length 4 : 9612
Sat Sep 27 14:00:40 2008     length 5 : 7147
Sat Sep 27 14:00:40 2008     length 6 : 4619
Sat Sep 27 14:00:40 2008     length 7 : 2916
Sat Sep 27 14:00:41 2008     length 9+: 3771
Sat Sep 27 14:00:41 2008  largest cycle: 18 relations
Sat Sep 27 14:00:41 2008  matrix is 70588 x 71068 (17.9 MB) with weight 4411696 (62.08/col)
Sat Sep 27 14:00:41 2008  sparse part has weight 4411696 (62.08/col)
Sat Sep 27 14:00:44 2008  filtering completed in 3 passes
Sat Sep 27 14:00:44 2008  matrix is 66723 x 66786 (16.9 MB) with weight 4156271 (62.23/col)
Sat Sep 27 14:00:44 2008  sparse part has weight 4156271 (62.23/col)
Sat Sep 27 14:00:46 2008  saving the first 48 matrix rows for later
Sat Sep 27 14:00:46 2008  matrix is 66675 x 66786 (10.3 MB) with weight 3184238 (47.68/col)
Sat Sep 27 14:00:46 2008  sparse part has weight 2309093 (34.57/col)
Sat Sep 27 14:00:46 2008  matrix includes 64 packed rows
Sat Sep 27 14:00:46 2008  using block size 10922 for processor cache size 256 kB
Sat Sep 27 14:00:47 2008  commencing Lanczos iteration
Sat Sep 27 14:00:47 2008  memory use: 10.3 MB
Sat Sep 27 14:25:49 2008
Sat Sep 27 14:25:49 2008
Sat Sep 27 14:25:49 2008  Msieve v. 1.38
Sat Sep 27 14:25:49 2008  random seeds: 6394e89c b1852f11
Sat Sep 27 14:25:49 2008  factoring 212480661907664999835916436228413132121070297399683627848151251731890808162658241713314211957 (93 digits)
Sat Sep 27 14:25:51 2008  no P-1/P+1/ECM available, skipping
Sat Sep 27 14:25:51 2008  commencing quadratic sieve (93-digit input)
Sat Sep 27 14:25:51 2008  using multiplier of 37
Sat Sep 27 14:25:51 2008  using 64kb Athlon XP sieve core
Sat Sep 27 14:25:51 2008  sieve interval: 18 blocks of size 65536
Sat Sep 27 14:25:51 2008  processing polynomials in batches of 6
Sat Sep 27 14:25:51 2008  using a sieve bound of 1883627 (70588 primes)
Sat Sep 27 14:25:51 2008  using large prime bound of 220384359 (27 bits)
Sat Sep 27 14:25:51 2008  using double large prime bound of 1041658353184527 (42-50 bits)
Sat Sep 27 14:25:51 2008  using trial factoring cutoff of 50 bits
Sat Sep 27 14:25:51 2008  polynomial 'A' values have 12 factors
Sat Sep 27 14:25:54 2008  restarting with 17856 full and 924337 partial relations
Sat Sep 27 14:25:54 2008  71068 relations (17856 full + 53212 combined from 924337 partial), need 70684
Sat Sep 27 14:25:55 2008  begin with 942193 relations
Sat Sep 27 14:25:58 2008  reduce to 180710 relations in 10 passes
Sat Sep 27 14:25:58 2008  attempting to read 180710 relations
Sat Sep 27 14:26:03 2008  recovered 180710 relations
Sat Sep 27 14:26:03 2008  recovered 163046 polynomials
Sat Sep 27 14:26:03 2008  attempting to build 71068 cycles
Sat Sep 27 14:26:04 2008  found 71068 cycles in 6 passes
Sat Sep 27 14:26:04 2008  distribution of cycle lengths:
Sat Sep 27 14:26:04 2008     length 1 : 17856
Sat Sep 27 14:26:04 2008     length 2 : 13079
Sat Sep 27 14:26:04 2008     length 3 : 12068
Sat Sep 27 14:26:04 2008     length 4 : 9612
Sat Sep 27 14:26:04 2008     length 5 : 7147
Sat Sep 27 14:26:04 2008     length 6 : 4619
Sat Sep 27 14:26:04 2008     length 7 : 2916
Sat Sep 27 14:26:04 2008     length 9+: 3771
Sat Sep 27 14:26:04 2008  largest cycle: 18 relations
Sat Sep 27 14:26:04 2008  matrix is 70588 x 71068 (17.9 MB) with weight 4411696 (62.08/col)
Sat Sep 27 14:26:04 2008  sparse part has weight 4411696 (62.08/col)
Sat Sep 27 14:26:08 2008  filtering completed in 3 passes
Sat Sep 27 14:26:08 2008  matrix is 66723 x 66786 (16.9 MB) with weight 4156271 (62.23/col)
Sat Sep 27 14:26:08 2008  sparse part has weight 4156271 (62.23/col)
Sat Sep 27 14:26:09 2008  saving the first 48 matrix rows for later
Sat Sep 27 14:26:09 2008  matrix is 66675 x 66786 (10.3 MB) with weight 3184238 (47.68/col)
Sat Sep 27 14:26:09 2008  sparse part has weight 2309093 (34.57/col)
Sat Sep 27 14:26:09 2008  matrix includes 64 packed rows
Sat Sep 27 14:26:09 2008  using block size 10922 for processor cache size 256 kB
Sat Sep 27 14:26:10 2008  commencing Lanczos iteration
Sat Sep 27 14:26:10 2008  memory use: 10.3 MB
Sat Sep 27 14:27:52 2008  lanczos halted after 1056 iterations (dim = 66674)
Sat Sep 27 14:27:53 2008  recovered 17 nontrivial dependencies
Sat Sep 27 14:27:54 2008  prp44 factor: 82711241811099317326869797485718892733761469
Sat Sep 27 14:27:54 2008  prp49 factor: 2568945372540053678056380379294551958469473628953
Sat Sep 27 14:27:54 2008  elapsed time 00:02:05

Sep 28, 2008 (2nd)

By Jo Yeong Uk / GMP-ECM, GGNFS

(26·10¹⁶⁵-71)/9 = 2(8)₁₆₄1_<166> = 17 · 13309 · 71671 · 101477581746372523_<18> · C139

C139 = P37 · P102

P37 = 1787383004449952594789773835754260083_<37>

P102 = 982212133326409521576440542949381649398350348153586585505016074608770961266853317136037014383074679043_<102>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 1755589273872155261233718370285448343873266326860841413940094147862817828579285028494983879753180712516018684386238936660834341115171540569 (139 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1501512258
Step 1 took 4703ms
Step 2 took 2604ms
********** Factor found in step 2: 1787383004449952594789773835754260083
Found probable prime factor of 37 digits: 1787383004449952594789773835754260083
Probable prime cofactor 982212133326409521576440542949381649398350348153586585505016074608770961266853317136037014383074679043 has 102 digits

(13·10¹⁷⁹+41)/9 = 1(4)₁₇₈9_<180> = 23 · 42015451969_<11> · 78770911838628725351_<20> · 46992713266751930707073011577_<29> · C119

C119 = P53 · P67

P53 = 30311897398836633926595718252104305336929992466250467_<53>

P67 = 1332154054820807868883060706294827597729163358841002375824024699203_<67>

Number: 14449_179
N=40380117029172520674769513188321069808478594187938313449637188262684915551986256553904977186681940701330222198933277801
  ( 119 digits)
Divisors found:
 r1=30311897398836633926595718252104305336929992466250467 (pp53)
 r2=1332154054820807868883060706294827597729163358841002375824024699203 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 34.61 hours.
Scaled time: 82.51 units (timescale=2.384).
Factorization parameters were as follows:
name: 14449_179
n: 40380117029172520674769513188321069808478594187938313449637188262684915551986256553904977186681940701330222198933277801
skew: 59519.84
# norm 5.30e+16
c5: 90180
c4: 37114906902
c3: -1064109571462834
c2: -114583571740201368031
c1: 1888116932644638843692268
c0: 14072364541878315912665194068
# alpha -6.66
Y1: 10050004274557
Y0: -53728508162727730627147
# Murphy_E 3.17e-10
# M 1546977283922582777487438798546142938538458754200649131652727350868351272901527820115965843604045265077433363727393309
type: gnfs
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2100000, 4050001)
Primes: RFBsize:296314, AFBsize:295837, largePrimes:7735710 encountered
Relations: rels:7843064, finalFF:755394
Max relations in full relation-set: 28
Initial matrix: 592232 x 755394 with sparse part having weight 67118714.
Pruned matrix : 463583 x 466608 with weight 42170854.
Polynomial selection time: 2.29 hours.
Total sieving time: 30.40 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.64 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4200000,4200000,27,27,50,50,2.4,2.4,75000
total time: 34.61 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)
Calibrating delay using timer specific routine.. 5344.63 BogoMIPS (lpj=2672318)
Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672355)

Sep 28, 2008

By Sinkiti Sibata / GGNFS

(26·10¹²⁷-71)/9 = 2(8)₁₂₆1_<128> = 3 · 7 · 4177 · C123

C123 = P33 · P91

P33 = 113230714718788553945893724491447_<33>

P91 = 2908592098095199284156292274582063675219090371694461454439845943319274746957258978219884619_<91>

Number: 28881_127
N=329341962092740163125607224242608489675762838319697309402839687733151941914211485674257998892904327426711913185458792353693
  ( 123 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=113230714718788553945893724491447 (pp33)
 r2=2908592098095199284156292274582063675219090371694461454439845943319274746957258978219884619 (pp91)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 5.33 hours.
Scaled time: 2.52 units (timescale=0.473).
Factorization parameters were as follows:
name: 28881_127
n: 329341962092740163125607224242608489675762838319697309402839687733151941914211485674257998892904327426711913185458792353693
m: 10000000000000000000000000
c5: 2600
c0: -71
skew: 0.49
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:63854, largePrimes:1453713 encountered
Relations: rels:1433520, finalFF:156420
Max relations in full relation-set: 28
Initial matrix: 127872 x 156420 with sparse part having weight 10645432.
Pruned matrix : 118915 x 119618 with weight 6495540.
Total sieving time: 5.06 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.33 hours.
 --------- CPU info (if available) ----------

(26·10¹⁴²-71)/9 = 2(8)₁₄₁1_<143> = 3 · 23 · 281 · 1277 · 351887 · 1043876039_<10> · C121

C121 = P54 · P67

P54 = 318812637521068164983566579422495812535445874888122847_<54>

P67 = 9963154172558509622279112283921622547309975069751848442172384313887_<67>

Number: 28881_142
N=3176379459782413951612104998475795623034111084218794263647507738095092102518673699145472039926316940831767873865464076289
  ( 121 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=318812637521068164983566579422495812535445874888122847 (pp54)
 r2=9963154172558509622279112283921622547309975069751848442172384313887 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 17.38 hours.
Scaled time: 13.48 units (timescale=0.776).
Factorization parameters were as follows:
name: 28881_142
n: 3176379459782413951612104998475795623034111084218794263647507738095092102518673699145472039926316940831767873865464076289
m: 10000000000000000000000000000
c5: 2600
c0: -71
skew: 0.49
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2550001)
Primes: RFBsize:100021, AFBsize:100034, largePrimes:2828558 encountered
Relations: rels:2813811, finalFF:228562
Max relations in full relation-set: 28
Initial matrix: 200122 x 228562 with sparse part having weight 25448559.
Pruned matrix : 192472 x 193536 with weight 20041376.
Total sieving time: 16.84 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.37 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 17.38 hours.
 --------- CPU info (if available) ----------

(26·10¹⁵¹-71)/9 = 2(8)₁₅₀1_<152> = 3 · 7 · 263 · 13679 · 3226777 · 17209986945207499_<17> · C121

C121 = P34 · P88

P34 = 2745596514435287531823283642891597_<34>

P88 = 2507928999895546296791005056224527982607687054515900884400907699433831261610761528623203_<88>

Number: 28881_151
N=6885761120564388500947561397500272791597190120780410367728327785360043793953985345335262886302990052218560958181187925191
  ( 121 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=2745596514435287531823283642891597 (pp34)
 r2=2507928999895546296791005056224527982607687054515900884400907699433831261610761528623203 (pp88)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 31.07 hours.
Scaled time: 31.35 units (timescale=1.009).
Factorization parameters were as follows:
name: 28881_151
n: 6885761120564388500947561397500272791597190120780410367728327785360043793953985345335262886302990052218560958181187925191
m: 1000000000000000000000000000000
c5: 260
c0: -71
skew: 0.77
type: snfs
 Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2500001)
Primes: RFBsize:176302, AFBsize:175109, largePrimes:6378422 encountered
Relations: rels:6891323, finalFF:940324
Max relations in full relation-set: 28
Initial matrix: 351478 x 940324 with sparse part having weight 106935468.
Pruned matrix : 239768 x 241589 with weight 53592392.
Total sieving time: 30.17 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.73 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 31.07 hours.
 --------- CPU info (if available) ----------

Sep 27, 2008 (7th)

By Sinkiti Sibata / GGNFS

(26·10¹²⁵-71)/9 = 2(8)₁₂₄1_<126> = 19 · 613 · 91823 · 153407 · C112

C112 = P41 · P72

P41 = 15699580490746648722017623746645943623109_<41>

P72 = 112158465934766181512722569942161506774982710985048339315616976232886227_<72>

Number: 28881_125
N=1760840863661527731242588303029745571382012232491529812649018974750700959809037491808401556805124013624565019743
  ( 112 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=15699580490746648722017623746645943623109 (pp41)
 r2=112158465934766181512722569942161506774982710985048339315616976232886227 (pp72)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 3.95 hours.
Scaled time: 1.87 units (timescale=0.473).
Factorization parameters were as follows:
name: 28881_125
n: 1760840863661527731242588303029745571382012232491529812649018974750700959809037491808401556805124013624565019743
m: 10000000000000000000000000
c5: 26
c0: -71
skew: 1.22
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:49098, AFBsize:64324, largePrimes:2208963 encountered
Relations: rels:2289393, finalFF:185176
Max relations in full relation-set: 28
Initial matrix: 113488 x 185176 with sparse part having weight 18384705.
Pruned matrix : 101189 x 101820 with weight 7567708.
Total sieving time: 3.68 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.95 hours.
 --------- CPU info (if available) ----------

Sep 27, 2008 (6th)

By Robert Backstrom / GGNFS, GMP-ECM

(26·10¹³³-71)/9 = 2(8)₁₃₂1_<134> = 3 · 7² · 17 · 151 · 1061 · 37783 · 99011812111_<11> · C110

C110 = P43 · P67

P43 = 1965547559984367689019258871317555515695451_<43>

P67 = 9813077914068196935358138454323876101771621519472202609560133578483_<67>

Number: n
N=19288071349933233074261710240111886312422696827531398603739748930210286351177246600319447391698166441034580833
  ( 110 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=1965547559984367689019258871317555515695451 (pp43)
 r2=9813077914068196935358138454323876101771621519472202609560133578483 (pp67)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.06 hours.
Scaled time: 5.58 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_2_8_132_1
n: 19288071349933233074261710240111886312422696827531398603739748930210286351177246600319447391698166441034580833
type: snfs
skew: 0.31
deg: 5
c5: 26000
c0: -71
m: 100000000000000000000000000
rlim: 900000
alim: 900000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved algebraic special-q in [100000, 540001)
Primes: RFBsize:71274, AFBsize:71446, largePrimes:6627165 encountered
Relations: rels:5704800, finalFF:179357
Max relations in full relation-set: 48
Initial matrix: 142787 x 179357 with sparse part having weight 22618482.
Pruned matrix : 132920 x 133697 with weight 12851718.
Total sieving time: 2.80 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.13 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,900000,900000,28,28,52,52,2.5,2.5,75000
total time: 3.06 hours.
 --------- CPU info (if available) ----------

(26·10¹³⁸-71)/9 = 2(8)₁₃₇1_<139> = 120949069 · 41467906931283023773_<20> · C111

C111 = P35 · P77

P35 = 35541916653799466686224456599258869_<35>

P77 = 16205981899812491349119706433005180738013612088106238598294885611831440295477_<77>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 575991657976118306505152747026865159701331253253282035051336670437456519531720961945340575972665515620572835513 (111 digits)
Using B1=962000, B2=871244232, polynomial Dickson(3), sigma=110969026
Step 1 took 7547ms
Step 2 took 3375ms
********** Factor found in step 2: 35541916653799466686224456599258869
Found probable prime factor of 35 digits: 35541916653799466686224456599258869
Probable prime cofactor 16205981899812491349119706433005180738013612088106238598294885611831440295477 has 77 digits

Sep 27, 2008 (5th)

By Sinkiti Sibata / GGNFS

(2·10¹⁶⁷+43)/9 = (2)₁₆₆7_<167> = 3 · 43577 · 6890591 · 114764843449205755577_<21> · C135

C135 = P53 · P83

P53 = 11279471825173337406649938800073870329587734408745733_<53>

P83 = 19057011588196652779014261179465989128269937645311151180852735600411117204477421907_<83>

Number: 22227_167
N=214953025281065940547395149502201290586118762475115084677179939782782050610010468173133158100944549423320604633635433583123437326972831
  ( 135 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=11279471825173337406649938800073870329587734408745733 (pp53)
 r2=19057011588196652779014261179465989128269937645311151180852735600411117204477421907 (pp83)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 115.79 hours.
Scaled time: 116.48 units (timescale=1.006).
Factorization parameters were as follows:
name: 22227_167
n: 214953025281065940547395149502201290586118762475115084677179939782782050610010468173133158100944549423320604633635433583123437326972831
m: 1000000000000000000000000000000000
c5: 200
c0: 43
skew: 0.74
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 6850001)
Primes: RFBsize:380800, AFBsize:380632, largePrimes:6097586 encountered
Relations: rels:6324207, finalFF:873305
Max relations in full relation-set: 28
Initial matrix: 761497 x 873305 with sparse part having weight 61105444.
Pruned matrix : 674396 x 678267 with weight 45815347.
Total sieving time: 111.93 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 3.64 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 115.79 hours.
 --------- CPU info (if available) ----------

(26·10¹³⁶-71)/9 = 2(8)₁₃₅1_<137> = 3 · 2741 · C133

C133 = P47 · P86

P47 = 92372285975211434631537057344098560567670446839_<47>

P86 = 38032848797379633248033194711881967676062087393154102007966129723213945990007458206473_<86>

Number: 28881_136
N=3513181185563527774399718945505154917778048022484359587606577756158201251232991473779507343899901360682097639412488007891145432188847
  ( 133 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=92372285975211434631537057344098560567670446839 (pp47)
 r2=38032848797379633248033194711881967676062087393154102007966129723213945990007458206473 (pp86)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 12.79 hours.
Scaled time: 10.05 units (timescale=0.786).
Factorization parameters were as follows:
name: 28881_136
n: 3513181185563527774399718945505154917778048022484359587606577756158201251232991473779507343899901360682097639412488007891145432188847
m: 1000000000000000000000000000
c5: 260
c0: -71
skew: 0.77
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 2125001)
Primes: RFBsize:78498, AFBsize:63419, largePrimes:1663569 encountered
Relations: rels:1683191, finalFF:159116
Max relations in full relation-set: 28
Initial matrix: 141984 x 159116 with sparse part having weight 17826188.
Pruned matrix : 137921 x 138694 with weight 14425970.
Total sieving time: 12.53 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 12.79 hours.
 --------- CPU info (if available) ----------

(26·10¹⁴⁶-71)/9 = 2(8)₁₄₅1_<147> = 17681 · 23242459 · C135

C135 = P56 · P80

P56 = 17943666279248153726359854426579738150064948201372651529_<56>

P80 = 39176962177511276591329105438819030419134508058060721100657357913796416293078491_<80>

Number: 28881_146
N=702978335147989415065882633006451840646443720183542402084529045134097378966611414274165384547692051817047065827290671468580902788162739
  ( 135 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=17943666279248153726359854426579738150064948201372651529 (pp56)
 r2=39176962177511276591329105438819030419134508058060721100657357913796416293078491 (pp80)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 28.94 hours.
Scaled time: 29.20 units (timescale=1.009).
Factorization parameters were as follows:
name: 28881_146
n: 702978335147989415065882633006451840646443720183542402084529045134097378966611414274165384547692051817047065827290671468580902788162739
m: 100000000000000000000000000000
c5: 260
c0: -71
skew: 0.77
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 4850001)
Primes: RFBsize:114155, AFBsize:113433, largePrimes:3262406 encountered
Relations: rels:3446743, finalFF:323228
Max relations in full relation-set: 28
Initial matrix: 227655 x 323228 with sparse part having weight 43074247.
Pruned matrix : 205449 x 206651 with weight 27908579.
Total sieving time: 28.49 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.33 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 28.94 hours.
 --------- CPU info (if available) ----------

Sep 27, 2008 (4th)

By Justin Card / msieve 1.38

(26·10¹¹⁰-71)/9 = 2(8)₁₀₉1_<111> = 127 · 1951 · 7886623688988353_<16> · C90

C90 = P37 · P53

P37 = 9671736314603461057887965599847505751_<37>

P53 = 15285311076956761976885931758180371769621907771691351_<53>

Fri Sep 26 23:47:52 2008  Msieve v. 1.38
Fri Sep 26 23:47:52 2008  random seeds: 7df286b6 f127304e
Fri Sep 26 23:47:52 2008  factoring 147835498223013253412349061166493597442944842892249770825188005060303286665934263969459601 (90 digits)
Fri Sep 26 23:47:52 2008  no P-1/P+1/ECM available, skipping
Fri Sep 26 23:47:52 2008  commencing quadratic sieve (90-digit input)
Fri Sep 26 23:47:52 2008  using multiplier of 1
Fri Sep 26 23:47:52 2008  using 64kb Opteron sieve core
Fri Sep 26 23:47:52 2008  sieve interval: 18 blocks of size 65536
Fri Sep 26 23:47:52 2008  processing polynomials in batches of 6
Fri Sep 26 23:47:52 2008  using a sieve bound of 1575281 (59491 primes)
Fri Sep 26 23:47:52 2008  using large prime bound of 126022480 (26 bits)
Fri Sep 26 23:47:52 2008  using double large prime bound of 380896014563600 (42-49 bits)
Fri Sep 26 23:47:52 2008  using trial factoring cutoff of 49 bits
Fri Sep 26 23:47:52 2008  polynomial 'A' values have 11 factors
Fri Sep 26 23:47:53 2008  restarting with 760 full and 30262 partial relations
Sat Sep 27 01:12:36 2008  59841 relations (15780 full + 44061 combined from 636896 partial), need 59587
Sat Sep 27 01:12:36 2008  begin with 652676 relations
Sat Sep 27 01:12:37 2008  reduce to 147025 relations in 10 passes
Sat Sep 27 01:12:37 2008  attempting to read 147025 relations
Sat Sep 27 01:12:38 2008  failed to read relation 88569
Sat Sep 27 01:12:38 2008  recovered 147024 relations
Sat Sep 27 01:12:38 2008  recovered 124630 polynomials
Sat Sep 27 01:12:38 2008  attempting to build 59840 cycles
Sat Sep 27 01:12:38 2008  found 59840 cycles in 5 passes
Sat Sep 27 01:12:38 2008  distribution of cycle lengths:
Sat Sep 27 01:12:38 2008     length 1 : 15780
Sat Sep 27 01:12:38 2008     length 2 : 11165
Sat Sep 27 01:12:38 2008     length 3 : 10262
Sat Sep 27 01:12:38 2008     length 4 : 8151
Sat Sep 27 01:12:38 2008     length 5 : 5865
Sat Sep 27 01:12:38 2008     length 6 : 3768
Sat Sep 27 01:12:38 2008     length 7 : 2170
Sat Sep 27 01:12:38 2008     length 9+: 2679
Sat Sep 27 01:12:38 2008  largest cycle: 17 relations
Sat Sep 27 01:12:39 2008  matrix is 59491 x 59840 (15.7 MB) with weight 3627865 (60.63/col)
Sat Sep 27 01:12:39 2008  sparse part has weight 3627865 (60.63/col)
Sat Sep 27 01:12:39 2008  filtering completed in 3 passes
Sat Sep 27 01:12:39 2008  matrix is 55644 x 55708 (14.7 MB) with weight 3402133 (61.07/col)
Sat Sep 27 01:12:39 2008  sparse part has weight 3402133 (61.07/col)
Sat Sep 27 01:12:40 2008  saving the first 48 matrix rows for later
Sat Sep 27 01:12:40 2008  matrix is 55596 x 55708 (11.1 MB) with weight 2851124 (51.18/col)
Sat Sep 27 01:12:40 2008  sparse part has weight 2355787 (42.29/col)
Sat Sep 27 01:12:40 2008  matrix includes 64 packed rows
Sat Sep 27 01:12:40 2008  using block size 10922 for processor cache size 256 kB
Sat Sep 27 01:12:40 2008  commencing Lanczos iteration
Sat Sep 27 01:12:40 2008  memory use: 9.3 MB
Sat Sep 27 01:13:00 2008  lanczos halted after 881 iterations (dim = 55592)
Sat Sep 27 01:13:00 2008  recovered 14 nontrivial dependencies
Sat Sep 27 01:13:00 2008  prp37 factor: 9671736314603461057887965599847505751
Sat Sep 27 01:13:00 2008  prp53 factor: 15285311076956761976885931758180371769621907771691351
Sat Sep 27 01:13:00 2008  elapsed time 01:25:08

Sep 27, 2008 (3rd)

By Serge Batalov / Msieve-1.36, Msieve-1.38

(26·10¹⁵⁰-71)/9 = 2(8)₁₄₉1_<151> = 43 · 59 · 39511 · 156236473309783_<15> · 306806534558417_<15> · 90996090683978972051700665489_<29> · C85

C85 = P42 · P44

P42 = 278892062287133994385679444936173651725679_<42>

P44 = 23691165618220695016170882191532431070649463_<44>

Fri Sep 26 20:08:09 2008  Msieve v. 1.36
Fri Sep 26 20:08:09 2008  random seeds: 3070926c edda5a26
Fri Sep 26 20:08:09 2008  factoring 6607278037251613419745403617730917584902354733438686568219298506923381764817244660377 (85 digits)
Fri Sep 26 20:08:09 2008  no P-1/P+1/ECM available, skipping
Fri Sep 26 20:08:09 2008  commencing quadratic sieve (85-digit input)
Fri Sep 26 20:08:09 2008  using multiplier of 17
Fri Sep 26 20:08:09 2008  using 64kb Opteron sieve core
Fri Sep 26 20:08:09 2008  sieve interval: 6 blocks of size 65536
Fri Sep 26 20:08:09 2008  processing polynomials in batches of 17
Fri Sep 26 20:08:09 2008  using a sieve bound of 1434229 (54704 primes)
Fri Sep 26 20:08:09 2008  using large prime bound of 116172549 (26 bits)
Fri Sep 26 20:08:09 2008  using double large prime bound of 328992642862119 (41-49 bits)
Fri Sep 26 20:08:09 2008  using trial factoring cutoff of 49 bits
Fri Sep 26 20:08:09 2008  polynomial 'A' values have 11 factors
Fri Sep 26 20:46:26 2008  54970 relations (16331 full + 38639 combined from 567574 partial), need 54800
Fri Sep 26 20:46:27 2008  begin with 583905 relations
Fri Sep 26 20:46:27 2008  reduce to 127831 relations in 10 passes
Fri Sep 26 20:46:27 2008  attempting to read 127831 relations
Fri Sep 26 20:46:28 2008  recovered 127831 relations
Fri Sep 26 20:46:28 2008  recovered 106406 polynomials
Fri Sep 26 20:46:29 2008  attempting to build 54970 cycles
Fri Sep 26 20:46:29 2008  found 54970 cycles in 5 passes
Fri Sep 26 20:46:29 2008  distribution of cycle lengths:
Fri Sep 26 20:46:29 2008     length 1 : 16331
Fri Sep 26 20:46:29 2008     length 2 : 11450
Fri Sep 26 20:46:29 2008     length 3 : 9750
Fri Sep 26 20:46:29 2008     length 4 : 6906
Fri Sep 26 20:46:29 2008     length 5 : 4543
Fri Sep 26 20:46:29 2008     length 6 : 2755
Fri Sep 26 20:46:29 2008     length 7 : 1559
Fri Sep 26 20:46:29 2008     length 9+: 1676
Fri Sep 26 20:46:29 2008  largest cycle: 18 relations
Fri Sep 26 20:46:29 2008  matrix is 54704 x 54970 (12.7 MB) with weight 2895459 (52.67/col)
Fri Sep 26 20:46:29 2008  sparse part has weight 2895459 (52.67/col)
Fri Sep 26 20:46:30 2008  filtering completed in 3 passes
Fri Sep 26 20:46:30 2008  matrix is 49166 x 49230 (11.5 MB) with weight 2617484 (53.17/col)
Fri Sep 26 20:46:30 2008  sparse part has weight 2617484 (53.17/col)
Fri Sep 26 20:46:30 2008  saving the first 48 matrix rows for later
Fri Sep 26 20:46:30 2008  matrix is 49118 x 49230 (7.0 MB) with weight 1976889 (40.16/col)
Fri Sep 26 20:46:30 2008  sparse part has weight 1351761 (27.46/col)
Fri Sep 26 20:46:30 2008  matrix includes 64 packed rows
Fri Sep 26 20:46:30 2008  using block size 19692 for processor cache size 1024 kB
Fri Sep 26 20:46:31 2008  commencing Lanczos iteration
Fri Sep 26 20:46:31 2008  memory use: 6.6 MB
Fri Sep 26 20:47:02 2008  lanczos halted after 778 iterations (dim = 49118)
Fri Sep 26 20:47:02 2008  recovered 18 nontrivial dependencies
Fri Sep 26 20:47:02 2008  prp42 factor: 278892062287133994385679444936173651725679
Fri Sep 26 20:47:02 2008  prp44 factor: 23691165618220695016170882191532431070649463
Fri Sep 26 20:47:02 2008  elapsed time 00:38:53

(26·10¹⁰²-71)/9 = 2(8)₁₀₁1_<103> = 67 · C101

C101 = P43 · P58

P43 = 4538946310673361934203419529586170464160589_<43>

P58 = 9499505316661328483693123081125976474462217351123397421287_<58>

SNFS difficulty: 103 digits.
Divisors found:
 r1=4538946310673361934203419529586170464160589
 r2=9499505316661328483693123081125976474462217351123397421287
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.944).
Factorization parameters were as follows:
n: 43117744610281923714759535655058043117744610281923714759535655058043117744610281923714759535655058043
Y1: 1
Y0: -100000000000000000000
c5: 2600
c0: -71
skew: 0.49
type: snfs
Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [225000, 305001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 43400 x 43627
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,103,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000
total time: 0.30 hours.

(26·10¹¹²-71)/9 = 2(8)₁₁₁1_<113> = 3² · 29147 · C108

C108 = P43 · P65

P43 = 4769177979227823799073881807117328228690591_<43>

P65 = 23091435821474135828457919814168101536665195947355131326279552917_<65>

SNFS difficulty: 113 digits.
Divisors found:
 r1=4769177979227823799073881807117328228690591
 r2=23091435821474135828457919814168101536665195947355131326279552917
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 110127167228527002546055393117983893478226800123850706529312675171025372875763424819359678293130563804503947
Y1: 1
Y0: -10000000000000000000000
c5: 2600
c0: -71
skew: 0.49
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 400001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 99584 x 99802
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 0.65 hours.

(26·10¹²¹-71)/9 = 2(8)₁₂₀1_<122> = 3² · 7 · 47 · 142543003 · C110

C110 = P54 · P57

P54 = 222364605027963289594960585610198951220800558531666759_<54>

P57 = 307808683726998816731583533019641595302396302718066515573_<57>

SNFS difficulty: 122 digits.
Divisors found:
 r1=222364605027963289594960585610198951220800558531666759
 r2=307808683726998816731583533019641595302396302718066515573
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.744).
Factorization parameters were as follows:
n: 68445756381131363080887663085460098626256994430630041422322275180521774617167939449170434442331404815119937907
Y1: 1
Y0: -1000000000000000000000000000000
c4: 260
c0: -71
skew: 0.77
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [500000, 725001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 91856 x 92076
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,122,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 1.20 hours.

Sep 27, 2008 (2nd)

By Robert Backstrom / GMP-ECM

(34·10¹⁹⁶-7)/9 = 3(7)₁₉₆_<197> = 37 · 47 · 6173 · 118373 · 31219384748723_<14> · 1473811541368567_<16> · 2242132689060816180407_<22> · C135

C135 = P43 · P92

P43 = 8818435865982917766354331139100370909728421_<43>

P92 = 32678997856966163491820964161711557583797401265091727332837787241185572405703184609703490221_<92>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 288177646766249323807994780014805681086201286651911030677961221351613989107380858450475712007537724154169055689087760689539206939271041 (135 digits)
Using B1=4866000, B2=11416155670, polynomial Dickson(12), sigma=1204317703
Step 1 took 48318ms
Step 2 took 21169ms
********** Factor found in step 2: 8818435865982917766354331139100370909728421
Found probable prime factor of 43 digits: 8818435865982917766354331139100370909728421
Probable prime cofactor 32678997856966163491820964161711557583797401265091727332837787241185572405703184609703490221 has 92 digits

Sep 27, 2008

Factorizations of 288...881 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Sep 26, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(13·10¹⁶⁶+41)/9 = 1(4)₁₆₅9_<167> = 431 · 659 · 67211 · 34187057 · 109318474575529_<15> · C135

C135 = P50 · P85

P50 = 34142122029434846349176131188868061554306868171903_<50>

P85 = 5929963384398578517109566018319591899379255541236213307569733895313595568330293252969_<85>

Number: 14449_166
N=202461533500216725433746524290492280498300806327822604511062313669686113177108949960264126600183931185734180294575384666460492157130007
  ( 135 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=34142122029434846349176131188868061554306868171903 (pp50)
 r2=5929963384398578517109566018319591899379255541236213307569733895313595568330293252969 (pp85)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 124.34 hours.
Scaled time: 125.46 units (timescale=1.009).
Factorization parameters were as follows:
name: 14449_166
n: 202461533500216725433746524290492280498300806327822604511062313669686113177108949960264126600183931185734180294575384666460492157130007
m: 1000000000000000000000000000000000
c5: 130
c0: 41
skew: 0.79
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 7250001)
Primes: RFBsize:380800, AFBsize:379893, largePrimes:6183848 encountered
Relations: rels:6450049, finalFF:907035
Max relations in full relation-set: 28
Initial matrix: 760760 x 907035 with sparse part having weight 68399919.
Pruned matrix : 645283 x 649150 with weight 50746737.
Total sieving time: 120.50 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 3.61 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 124.34 hours.
 --------- CPU info (if available) ----------

Sep 26, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(4·10¹⁸²-7)/3 = 1(3)₁₈₁1_<183> = 51473 · C178

C178 = P33 · P66 · P80

P33 = 111674969858577488476968435205091_<33>

P66 = 410923244146929474573211564906433238336504047888161145678797662857_<66>

P80 = 56447238927081583452010133015677952938829702727247218171506201584513543966479481_<80>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 2590354813850627189659303583108296258880060096231681334550800095843128112473206017394232575006961578562223560572209378379603546195740161508622643586605275257578406802271741171747 (178 digits)
Using B1=782000, B2=696767622, polynomial Dickson(3), sigma=2644948554
Step 1 took 12144ms
Step 2 took 4526ms
********** Factor found in step 2: 111674969858577488476968435205091
Found probable prime factor of 33 digits: 111674969858577488476968435205091
Composite cofactor 23195482543053206881421353751404610349519007646345770007549762402992329345957190547132777743367728994353508496397809803285168273674330253046337217 has 146 digits

Number: n
N=23195482543053206881421353751404610349519007646345770007549762402992329345957190547132777743367728994353508496397809803285168273674330253046337217
  ( 146 digits)
SNFS difficulty: 182 digits.
Divisors found:

Fri Sep 26 04:28:28 2008  prp66 factor: 410923244146929474573211564906433238336504047888161145678797662857
Fri Sep 26 04:28:28 2008  prp80 factor: 56447238927081583452010133015677952938829702727247218171506201584513543966479481
Fri Sep 26 04:28:29 2008  elapsed time 04:37:09 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 39.64 hours.
Scaled time: 81.07 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_1_3_181_1
n: 23195482543053206881421353751404610349519007646345770007549762402992329345957190547132777743367728994353508496397809803285168273674330253046337217
type: snfs
skew: 0.89
deg: 5
c5: 25
c0: -14
m: 2000000000000000000000000000000000000
rlim: 8000000
alim: 8000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 3700001)
Primes: RFBsize:539777, AFBsize:539275, largePrimes:13622239 encountered
Relations: rels:13313889, finalFF:1206082
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 39.33 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,52,52,2.5,2.5,100000
total time: 39.64 hours.
 --------- CPU info (if available) ----------

Sep 25, 2008

By Serge Batalov / **Msieve 1.38**

(5·10¹⁶⁹-41)/9 = (5)₁₆₈1_<169> = 5851 · 13267 · 1027853 · 73870523 · C147

C147 = P57 · P91

P57 = 696980304571246698535520900058861516042355649025352830041_<57>

P91 = 1352390091424003573905931189189861414444936573068295525332680772365816186487388077452104457_<91>

SNFS difficulty: 170 digits.
Divisors found:
 r1=696980304571246698535520900058861516042355649025352830041
 r2=1352390091424003573905931189189861414444936573068295525332680772365816186487388077452104457
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.724).
Factorization parameters were as follows:
n: 942589257819838178696155706168661683360821107017404276607244976674025274365182068018460893385781710775435724423885085318984473409680541616099592737
Y1: 1
Y0: -10000000000000000000000000000000000
c5: 1
c0: -82
skew: 2.41
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [3000000, 5100001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 988373 x 988621
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000
total time: 38.00 hours.

Sep 24, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve

9·10¹⁸⁰-7 = 8(9)₁₇₉3_<181> = 10891 · C177

C177 = P76 · P102

P76 = 5486819574558925029152624668200693996930258823313386814434120700542015883423_<76>

P102 = 150610091392044818382883472006373182746590680311053182451698963556980981251397542935784243994273255701_<102>

Number: n
N=826370397575980167110458176475989349003764576255623909650169865026168395923239371958497842255072996051785878248094757138922045725828665870902580112019098338077311541639886144523
  ( 177 digits)
SNFS difficulty: 180 digits.
Divisors found:

Wed Sep 24 11:08:36 2008  prp76 factor: 5486819574558925029152624668200693996930258823313386814434120700542015883423
Wed Sep 24 11:08:36 2008  prp102 factor: 150610091392044818382883472006373182746590680311053182451698963556980981251397542935784243994273255701
Wed Sep 24 11:08:37 2008  elapsed time 03:49:38 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 35.61 hours.
Scaled time: 60.78 units (timescale=1.707).
Factorization parameters were as follows:
name: KA_8_9_179_3
n: 826370397575980167110458176475989349003764576255623909650169865026168395923239371958497842255072996051785878248094757138922045725828665870902580112019098338077311541639886144523
type: snfs
skew: 0.95
deg: 5
c5: 9
c0: -7
m: 1000000000000000000000000000000000000
rlim: 8000000
alim: 8000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 3000001)
Primes: RFBsize:539777, AFBsize:539995, largePrimes:13973574 encountered
Relations: rels:13965082, finalFF:1414887
Max relations in full relation-set: 28
Initial matrix: 1079836 x 1414887 with sparse part having weight 138132887.
Pruned matrix : 
Total sieving time: 35.29 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,52,52,2.5,2.5,100000
total time: 35.61 hours.
 --------- CPU info (if available) ----------

Sep 24, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(5·10¹⁶⁶-23)/9 = (5)₁₆₅3_<166> = 3² · 334610021 · 733322295128893182421_<21> · C136

C136 = P36 · P100

P36 = 954966188692478370261835870373955259_<36>

P100 = 2634287420039296053564941005908420267092205878181191973670272490843357273239995457115579925801892643_<100>

Number: 55553_166
N=2515655417435468421906423529418482767298588603498122386763350799680220456382663824939484925376682675948872275090986001914951956003259537
  ( 136 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=954966188692478370261835870373955259 (pp36)
 r2=2634287420039296053564941005908420267092205878181191973670272490843357273239995457115579925801892643 (pp100)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 101.01 hours.
Scaled time: 101.82 units (timescale=1.008).
Factorization parameters were as follows:
name: 55553_166
n: 2515655417435468421906423529418482767298588603498122386763350799680220456382663824939484925376682675948872275090986001914951956003259537
m: 1000000000000000000000000000000000
c5: 50
c0: -23
skew: 0.86
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 6200001)
Primes: RFBsize:348513, AFBsize:348791, largePrimes:6077777 encountered
Relations: rels:6316953, finalFF:862311
Max relations in full relation-set: 28
Initial matrix: 697369 x 862311 with sparse part having weight 64492968.
Pruned matrix : 571242 x 574792 with weight 47124797.
Total sieving time: 97.95 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 2.86 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 101.01 hours.
 --------- CPU info (if available) ----------

(25·10¹⁶²+11)/9 = 2(7)₁₆₁9_<163> = 956996067485339718144137108196685667_<36> · C127

C127 = P44 · P83

P44 = 82764568509156828642850056701654905874238953_<44>

P83 = 35070575358147688261227157636411129948137439908546697720503815691536272272514529929_<83>

Number: 27779_162
N=2902601036884961627173699119809625917037467027349604362385456802139104947986390088924478788941052925770284265498185067416124337
  ( 127 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=82764568509156828642850056701654905874238953 (pp44)
 r2=35070575358147688261227157636411129948137439908546697720503815691536272272514529929 (pp83)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 61.07 hours.
Scaled time: 47.63 units (timescale=0.780).
Factorization parameters were as follows:
name: 27779_162
n: 2902601036884961627173699119809625917037467027349604362385456802139104947986390088924478788941052925770284265498185067416124337
m: 500000000000000000000000000000000
c5: 4
c0: 55
skew: 1.69
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4150001)
Primes: RFBsize:315948, AFBsize:315287, largePrimes:5705479 encountered
Relations: rels:5818145, finalFF:746133
Max relations in full relation-set: 28
Initial matrix: 631299 x 746133 with sparse part having weight 43557527.
Pruned matrix : 536894 x 540114 with weight 29054475.
Total sieving time: 58.07 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 2.71 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 61.07 hours.
 --------- CPU info (if available) ----------

Sep 24, 2008 (2nd)

By Justin Card / GGNFS

7·10¹⁶⁶+1 = 7(0)₁₆₅1_<167> = 23 · 53 · 31327 · 34726262056239405863392591_<26> · C134

C134 = P55 · P80

P55 = 1913290242196232539268012066652201280412112493917178819_<55>

P80 = 27589042770237067407217839796789774556735213612294539601853969868354417611828713_<80>

Number: 70001_166
N=52785846323829097015703542990556850979883528135952978084427866439294004697060090080086165672931785725911862903245367422061368419629947
  ( 134 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=1913290242196232539268012066652201280412112493917178819
 r2=27589042770237067407217839796789774556735213612294539601853969868354417611828713
Version:
Total time: 90.40 hours.
Scaled time: 189.48 units (timescale=2.096).
Factorization parameters were as follows:
n: 52785846323829097015703542990556850979883528135952978084427866439294004697060090080086165672931785725911862903245367422061368419629947
m: 1000000000000000000000000000000000
c5: 70
c4: 0
c3: 0
c2: 0
c1: 0
c0: 1
Y1: 1
Y0: -1000000000000000000000000000000000
skew: 0.43
type: snfs

Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 5700001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 603990 x 604208
Total sieving time: 90.40 hours.
Total relation processing time: 1.58 hours.
Matrix solve time: 1.25 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 93.42 hours.
 --------- CPU info (if available) ----------
[   27.172216] Memory: 3055428k/3111872k available (2523k kernel code, 56056k reserved, 1328k data, 328k init)
[   27.318604] Calibrating delay using timer specific routine.. 3982.80 BogoMIPS (lpj=19914039)
[   28.066173] Calibrating delay using timer specific routine.. 3979.59 BogoMIPS (lpj=19897994)

Sep 24, 2008

By Serge Batalov / Msieve-1.37 QS

(4·10¹⁷²+41)/9 = (4)₁₇₁9_<172> = 3² · 47 · 220793663 · 262458105583_<12> · 487196685878876428730725467376703_<33> · 398845555197803023949777099556339851_<36> · C81

C81 = P34 · P48

P34 = 2449842135058899424657127232517211_<34>

P48 = 380875764020883110409902511467730416896409998609_<48>

Tue Sep 23 11:56:13 2008  Msieve v. 1.37
Tue Sep 23 11:56:13 2008  random seeds: 53d42b0a 75560bf7
Tue Sep 23 11:56:13 2008  factoring 933085494921109827158710069754359573279758458138952040836991150992465132078559499 (81 digits)
Tue Sep 23 11:56:13 2008  searching for 15-digit factors
Tue Sep 23 11:56:14 2008  commencing quadratic sieve (81-digit input)
Tue Sep 23 11:56:14 2008  using multiplier of 1
Tue Sep 23 11:56:14 2008  using 64kb Opteron sieve core
Tue Sep 23 11:56:14 2008  sieve interval: 6 blocks of size 65536
Tue Sep 23 11:56:14 2008  processing polynomials in batches of 17
Tue Sep 23 11:56:14 2008  using a sieve bound of 1325923 (50864 primes)
Tue Sep 23 11:56:14 2008  using large prime bound of 127288608 (26 bits)
Tue Sep 23 11:56:14 2008  using trial factoring cutoff of 27 bits
Tue Sep 23 11:56:14 2008  polynomial 'A' values have 10 factors
Tue Sep 23 12:08:02 2008  51110 relations (26192 full + 24918 combined from 272885 partial), need 50960
Tue Sep 23 12:08:02 2008  begin with 299077 relations
Tue Sep 23 12:08:02 2008  reduce to 72955 relations in 2 passes
Tue Sep 23 12:08:02 2008  attempting to read 72955 relations
Tue Sep 23 12:08:03 2008  recovered 72955 relations
Tue Sep 23 12:08:03 2008  recovered 63005 polynomials
Tue Sep 23 12:08:03 2008  attempting to build 51110 cycles
Tue Sep 23 12:08:03 2008  found 51110 cycles in 1 passes
Tue Sep 23 12:08:03 2008  distribution of cycle lengths:
Tue Sep 23 12:08:03 2008     length 1 : 26192
Tue Sep 23 12:08:03 2008     length 2 : 24918
Tue Sep 23 12:08:03 2008  largest cycle: 2 relations
Tue Sep 23 12:08:03 2008  matrix is 50864 x 51110 (7.6 MB) with weight 1580108 (30.92/col)
Tue Sep 23 12:08:03 2008  sparse part has weight 1580108 (30.92/col)
Tue Sep 23 12:08:03 2008  filtering completed in 3 passes
Tue Sep 23 12:08:03 2008  matrix is 36125 x 36188 (5.9 MB) with weight 1256316 (34.72/col)
Tue Sep 23 12:08:03 2008  sparse part has weight 1256316 (34.72/col)
Tue Sep 23 12:08:03 2008  saving the first 48 matrix rows for later
Tue Sep 23 12:08:03 2008  matrix is 36077 x 36188 (4.5 MB) with weight 995457 (27.51/col)
Tue Sep 23 12:08:03 2008  sparse part has weight 804953 (22.24/col)
Tue Sep 23 12:08:03 2008  matrix includes 64 packed rows
Tue Sep 23 12:08:03 2008  using block size 14475 for processor cache size 1024 kB
Tue Sep 23 12:08:04 2008  commencing Lanczos iteration
Tue Sep 23 12:08:04 2008  memory use: 4.2 MB
Tue Sep 23 12:08:08 2008  lanczos halted after 572 iterations (dim = 36076)
Tue Sep 23 12:08:08 2008  recovered 17 nontrivial dependencies
Tue Sep 23 12:08:08 2008  prp34 factor: 2449842135058899424657127232517211
Tue Sep 23 12:08:08 2008  prp48 factor: 380875764020883110409902511467730416896409998609
Tue Sep 23 12:08:08 2008  elapsed time 00:11:55

Sep 23, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(25·10¹⁶⁵+11)/9 = 2(7)₁₆₄9_<166> = 7² · 71 · 1229 · 156799 · 86859680114923_<14> · 141208653207553585741_<21> · C120

C120 = P59 · P62

P59 = 16074984290793976464998006648109533726617375552718845662617_<59>

P62 = 21014439226186271746727555583827699417119049826464020217738801_<62>

Number: 27779_165
N=337806780440789045113039137220969559081629068252855899137979087861381973412324924977923686904046145934723285022276102217
  ( 120 digits)
Divisors found:
 r1=16074984290793976464998006648109533726617375552718845662617 (pp59)
 r2=21014439226186271746727555583827699417119049826464020217738801 (pp62)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 64.36 hours.
Scaled time: 49.49 units (timescale=0.769).
Factorization parameters were as follows:
name: 27779_165
n: 337806780440789045113039137220969559081629068252855899137979087861381973412324924977923686904046145934723285022276102217
skew: 95898.23
# norm 1.67e+16
c5: 30060
c4: -74717654
c3: -705030454434139
c2: 8050922963625462632
c1: 3155243119129826402614188
c0: -64504785277031888812155507520
# alpha -5.98
Y1: 7426006963723
Y0: -102361323587563003671847
# Murphy_E 3.18e-10
# M 285492000409818898872953286248517410567252442636728159563327865228391630836454600444674685956951115206410069923986873559
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4110001)
Primes: RFBsize:315948, AFBsize:316989, largePrimes:7774050 encountered
Relations: rels:7972494, finalFF:848401
Max relations in full relation-set: 28
Initial matrix: 633016 x 848401 with sparse part having weight 71702901.
Pruned matrix : 457851 x 461080 with weight 42942460.
Total sieving time: 60.49 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 3.08 hours.
Time per square root: 0.36 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 64.36 hours.
 --------- CPU info (if available) ----------

Sep 23, 2008

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.37

(4·10¹⁷²+41)/9 = (4)₁₇₁9_<172> = 3² · 47 · 220793663 · 262458105583_<12> · C150

C150 = P33 · P36 · C81

P33 = 487196685878876428730725467376703_<33>

P36 = 398845555197803023949777099556339851_<36>

C81 = [933085494921109827158710069754359573279758458138952040836991150992465132078559499_<81>]

# two ECM factors:
#
Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3260962697
Step 1 took 14297ms
Step 2 took 12741ms
********** Factor found in step 2: 398845555197803023949777099556339851
Found probable prime factor of 36 digits: 398845555197803023949777099556339851

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2979693243
Step 1 took 16485ms
Step 2 took 12965ms
********** Factor found in step 2: 487196685878876428730725467376703
Found probable prime factor of 33 digits: 487196685878876428730725467376703

(13·10¹⁷⁹+41)/9 = 1(4)₁₇₈9_<180> = 23 · 42015451969_<11> · 78770911838628725351_<20> · C148

C148 = P29 · C119

P29 = 46992713266751930707073011577_<29>

C119 = [40380117029172520674769513188321069808478594187938313449637188262684915551986256553904977186681940701330222198933277801_<119>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=843826318
Step 1 took 14245ms
Step 2 took 12917ms
********** Factor found in step 2: 46992713266751930707073011577
Found probable prime factor of 29 digits: 46992713266751930707073011577
Composite cofactor 40380117029172520674769513188321069808478594187938313449637188262684915551986256553904977186681940701330222198933277801 has 119 digits

4·10¹⁹⁵-9 = 3(9)₁₉₄1_<196> = 13 · 107 · 317 · 683 · 4813 · 34945726168123_<14> · 235346907565680687670001_<24> · C147

C147 = P35 · P112

P35 = 84023102213882289455105713911646201_<35>

P112 = 3993335105848129845498334339702023428427294782244533437466867913637243996141634999335678685464308070534367797009_<112>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3729024413
Step 1 took 18539ms
Step 2 took 16998ms
********** Factor found in step 2: 84023102213882289455105713911646201
Found probable prime factor of 35 digits: 84023102213882289455105713911646201
Probable prime cofactor 3993335105848129845498334339702023428427294782244533437466867913637243996141634999335678685464308070534367797009 has 112 digits

(8·10¹⁹⁸-53)/9 = (8)₁₉₇3_<198> = 443² · 509 · 54001 · 781721 · 23743506773317561028947_<23> · 2580754674706962971246952203_<28> · C130

C130 = P29 · P102

P29 = 32368523515701041820822572173_<29>

P102 = 106280646441674238900428385238379104570468681385301477094082044361402629538958719229812675579724825371_<102>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3529257140
Step 1 took 12445ms
Step 2 took 11241ms
********** Factor found in step 2: 32368523515701041820822572173
Found probable prime factor of 29 digits: 32368523515701041820822572173
Probable prime cofactor 106280646441674238900428385238379104570468681385301477094082044361402629538958719229812675579724825371 has 102 digits

(13·10¹⁶⁷+41)/9 = 1(4)₁₆₆9_<168> = 480185983 · 28444017767816011987_<20> · C140

C140 = P60 · P80

P60 = 255495494090934243398138407064825919513157133359958105353597_<60>

P80 = 41392073043566976748716370443946057031311344967750540425260269537821998787807977_<80>

SNFS difficulty: 168 digits.
Divisors found:
 r1=255495494090934243398138407064825919513157133359958105353597
 r2=41392073043566976748716370443946057031311344967750540425260269537821998787807977
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.729).
Factorization parameters were as follows:
n: 10575488153714185091397046009582798434739843055341525642692804920734214201457798874370694763287755300109417664211267870586842810176122243269
Y1: 1
Y0: -1000000000000000000000000000000000
c5: 1300
c0: 41
skew: 0.5
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [2750000, 5050001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1009651 x 1009899
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 4.00 hours.
Time per square root: 0.30 hours * 3
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,54,54,2.6,2.6,100000
total time: 39.00 hours.

8·10¹⁸⁹-7 = 7(9)₁₈₈3_<190> = 1403785393_<10> · 1947272813871401270971_<22> · C160

C160 = P30 · P131

P30 = 259434316310048883009749966749_<30>

P131 = 11280673929515482410186744031856075693766227254925575504050922917780974235338007459650081318927619624208279244239261693510134938119_<131>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1724537978
Step 1 took 20561ms
Step 2 took 2944ms
********** Factor found in step 2: 259434316310048883009749966749
Found probable prime factor of 30 digits: 259434316310048883009749966749
Probable prime cofactor 11280673929515482410186744031856075693766227254925575504050922917780974235338007459650081318927619624208279244239261693510134938119 has 131 digits

Sep 23, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve

7·10¹⁷⁸-9 = 6(9)₁₇₇1_<179> = 19 · 2539 · C175

C175 = P65 · P111

P65 = 12897341641762311482225721924377786620072960817038184469508152023_<65>

P111 = 112507515436489482196909605851330785043044214218396095102143177575566128872215934971677861051720757848691700337_<111>

Number: n
N=1451047863850251860450654008001492506374245973342177815551087249435127795858294811467423975456561845732882817520366493231898177898468108040878091250181380982981281482556331751
  ( 175 digits)
SNFS difficulty: 178 digits.
Divisors found:

Mon Sep 22 18:53:36 2008  prp65 factor: 12897341641762311482225721924377786620072960817038184469508152023
Mon Sep 22 18:53:36 2008  prp111 factor: 112507515436489482196909605851330785043044214218396095102143177575566128872215934971677861051720757848691700337
Mon Sep 22 18:53:36 2008  elapsed time 05:54:33 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 57.99 hours.
Scaled time: 118.94 units (timescale=2.051).
Factorization parameters were as follows:
name: KA_6_9_177_1
n: 1451047863850251860450654008001492506374245973342177815551087249435127795858294811467423975456561845732882817520366493231898177898468108040878091250181380982981281482556331751
type: snfs
skew: 0.26
deg: 5
c5: 7000
c0: -9
m: 100000000000000000000000000000000000
rlim: 8000000
alim: 8000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 11400001)
Primes: RFBsize:539777, AFBsize:539075, largePrimes:15392040 encountered
Relations: rels:15911037, finalFF:1641017
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 57.50 hours.
Total relation processing time: 0.49 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,178,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,52,52,2.5,2.5,100000
total time: 57.99 hours.
 --------- CPU info (if available) ----------

Sep 23, 2008 (3rd)

By Serge Batalov / GMP-ECM 6.2.1

(8·10¹⁹⁸-53)/9 = (8)₁₉₇3_<198> = 443² · 509 · 54001 · 781721 · 23743506773317561028947_<23> · C157

C157 = P28 · C130

P28 = 2580754674706962971246952203_<28>

C130 = [3440147603611240855717915265739196737191480416785639942379705043877609846496446141839893018288901405432125844676826299567469001183_<130>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1884473842
Step 1 took 24308ms
********** Factor found in step 1: 2580754674706962971246952203
Found probable prime factor of 28 digits: 2580754674706962971246952203
Composite cofactor 3440147603611240855717915265739196737191480416785639942379705043877609846496446141839893018288901405432125844676826299567469001183 has 130 digits

Sep 22, 2008 (2nd)

By matsui / GMP-ECM

4·10¹⁸²+9 = 4(0)₁₈₁9_<183> = 593 · 1328642261_<10> · 23666791403837444777_<20> · C152

C152 = P38 · P114

P38 = 30538114624651788954583755347034152657_<38>

P114 = 702450347822345188677038220687379849426066288977031773444331177142414305322712815983768134833633739828814217175997_<114>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
21451509239925295538168421795102247653439573588875108420209533505822891969985296592779292726269424313705399400454705326894779927663246219481894334174029
=30538114624651788954583755347034152657* 702450347822345188677038220687379849426066288977031773444331177142414305322712815983768134833633739828814217175997

Sep 22, 2008

By Sinkiti Sibata / GGNFS

(25·10¹⁵⁷+11)/9 = 2(7)₁₅₆9_<158> = 9542909 · 2914206752057_<13> · 9138747720366349_<16> · C123

C123 = P58 · P65

P58 = 1324246518820340916190100054706676378801923457295730611749_<58>

P65 = 82535507900081281232126800634121927761333411590662336194211534983_<65>

Number: 27779_157
N=109297359015751382757590584761681435097761745318418345552443725745543683153018309251137026627824848955651477944234904315267
  ( 123 digits)
Divisors found:
 r1=1324246518820340916190100054706676378801923457295730611749 (pp58)
 r2=82535507900081281232126800634121927761333411590662336194211534983 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 82.43 hours.
Scaled time: 83.18 units (timescale=1.009).
Factorization parameters were as follows:
name: 27779_157
n: 109297359015751382757590584761681435097761745318418345552443725745543683153018309251137026627824848955651477944234904315267
skew: 62000.91
# norm 9.42e+15
c5: 1560
c4: 1495301999
c3: -237801306897353
c2: -6516794873467408648
c1: 46696468715858655525789
c0: 428876002410578610703489620
# alpha -4.43
Y1: 11440970936461
Y0: -587618408973170623261291
# Murphy_E 2.39e-10
# M 100730276207215881327981099032047925236957950976150459045887497600095574624645597788010714685658071890436466215979834840367
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 5440001)
Primes: RFBsize:348513, AFBsize:348010, largePrimes:7962731 encountered
Relations: rels:8330423, finalFF:925608
Max relations in full relation-set: 28
Initial matrix: 696602 x 925608 with sparse part having weight 90657732.
Pruned matrix : 519652 x 523199 with weight 62536167.
Total sieving time: 79.00 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 2.92 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
gnfs,122,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 82.43 hours.
 --------- CPU info (if available) ----------

Sep 21, 2008 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(43·10¹⁸⁰-7)/9 = 4(7)₁₈₀_<181> = 7717 · C177

C177 = P37 · P140

P37 = 7974850129236699611743439999799043481_<37>

P140 = 77634527787228389847918815078532026524742425012288827865479837265962584100748133165695301835012008917167725311213692593828248802988299673701_<140>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 619123723957208471916259916778252919240349588930643744690654111413473860020445481116726419305141606554072538263285963169337537615365786935049601889047269376412825939844211193181 (177 digits)
Using B1=3834000, B2=8561443810, polynomial Dickson(6), sigma=936150032
Step 1 took 59850ms
Step 2 took 21227ms
********** Factor found in step 2: 7974850129236699611743439999799043481
Found probable prime factor of 37 digits: 7974850129236699611743439999799043481
Probable prime cofactor 77634527787228389847918815078532026524742425012288827865479837265962584100748133165695301835012008917167725311213692593828248802988299673701 has 140 digits

(22·10¹⁹⁵+41)/9 = 2(4)₁₉₄9_<196> = C196

C196 = P48 · P149

P48 = 133847907008974165416726785238473125656386676331_<48>

P149 = 18262851463792785302404893664396092758157756934387695704742235137911239465916250049387416609237886485726480277100893540116149440927005054900514665379_<149>

Number: n
N=2444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449
  ( 196 digits)
SNFS difficulty: 196 digits.
Divisors found:

Sun Sep 21 23:31:43 2008  prp48 factor: 133847907008974165416726785238473125656386676331
Sun Sep 21 23:31:43 2008  prp149 factor: 18262851463792785302404893664396092758157756934387695704742235137911239465916250049387416609237886485726480277100893540116149440927005054900514665379
Sun Sep 21 23:31:43 2008  elapsed time 24:58:19 (Msieve 1.37)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 183.83 hours.
Scaled time: 236.96 units (timescale=1.289).
Factorization parameters were as follows:
name: KA_2_4_194_9
n: 2444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449
type: snfs
skew: 1.13
deg: 5
c5: 22
c0: 41
m: 1000000000000000000000000000000000000000
rlim: 9600000
alim: 9600000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9600000/9600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 16100001)
Primes: RFBsize:639851, AFBsize:639690, largePrimes:15700927 encountered
Relations: rels:16181449, finalFF:1303141
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 182.76 hours.
Total relation processing time: 1.08 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,196,5,0,0,0,0,0,0,0,0,9600000,9600000,28,28,52,52,2.5,2.5,100000
total time: 183.83 hours.
 --------- CPU info (if available) ----------

Sep 21, 2008 (2nd)

By Serge Batalov / Msieve-1.37

(25·10¹⁵⁸+11)/9 = 2(7)₁₅₇9_<159> = 3 · 163 · 448801 · C151

C151 = P39 · P112

P39 = 137389628695179787605418180755763657877_<39>

P112 = 9212571560698381077396463062817283198373662941165977110800670318580503998459757629198423949102641490029724479343_<112>

SNFS difficulty: 159 digits.
Divisors found:
 r1=137389628695179787605418180755763657877
 r2=9212571560698381077396463062817283198373662941165977110800670318580503998459757629198423949102641490029724479343
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.720).
Factorization parameters were as follows:
n: 1265711786052123537291755711705811059148731331941557665959847133426148586146192857342235679715462077090018193295647088925848584354096853706755005734811
Y1: 1
Y0: -50000000000000000000000000000000
c5: 8
c0: 11
skew: 1.07
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [2000000, 2800001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 648365 x 648613
Total sieving time: 12.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 1.50 hours.
Time per square root: 0.50 hours.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,54,54,2.5,2.5,100000
total time: 14.00 hours.

(25·10¹⁵⁹+11)/9 = 2(7)₁₅₈9_<160> = 7 · C159

C159 = P43 · P117

P43 = 2657780922364980442038543388644686126602807_<43>

P117 = 149307037869881540490495888397203652439490230060489375653475306412910625822390022203824618445561134554266447970512371_<117>

SNFS difficulty: 160 digits.
Divisors found:
 r1=2657780922364980442038543388644686126602807
 r2=149307037869881540490495888397203652439490230060489375653475306412910625822390022203824618445561134554266447970512371
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.703).
Factorization parameters were as follows:
n: 396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825397
Y1: 1
Y0: -100000000000000000000000000000000
c5: 5
c0: 22
skew: 1.34
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [2000000, 3200001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 715410 x 715658
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,54,54,2.5,2.5,100000
total time: 19.00 hours.

Sep 21, 2008

By Sinkiti Sibata / GGNFS, Msieve

(25·10¹⁶⁸+11)/9 = 2(7)₁₆₇9_<169> = 60737823877_<11> · 2391245651153087_<16> · 88327195955309617_<17> · 11269454630239385869_<20> · C107

C107 = P44 · P63

P44 = 99636796677422281629691745530908874418949017_<44>

P63 = 192839935983067964860238605035402472643939209453310925694585381_<63>

Number: 27779_168
N=19213953492832071691888356432134441574295306649176679790741819525345351703318048554011557238677581592520477
  ( 107 digits)
Divisors found:
 r1=99636796677422281629691745530908874418949017 (pp44)
 r2=192839935983067964860238605035402472643939209453310925694585381 (pp63)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 19.68 hours.
Scaled time: 15.17 units (timescale=0.771).
Factorization parameters were as follows:
name: 27779_168
n: 19213953492832071691888356432134441574295306649176679790741819525345351703318048554011557238677581592520477
skew: 9817.78
# norm 1.43e+14
c5: 6840
c4: -1293420660
c3: 965728069439
c2: 125523965749091149
c1: 284947326891434748589
c0: -4579311507562674711556
# alpha -4.62
Y1: 7631626717
Y0: -308825058652731342747
# Murphy_E 1.46e-09
# M 17111148031494828095272157669907087589765217394301232366704600631807007446817858694000563667479322053158049
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2600001)
Primes: RFBsize:183072, AFBsize:183200, largePrimes:4619239 encountered
Relations: rels:4875921, finalFF:565343
Max relations in full relation-set: 28
Initial matrix: 366351 x 565343 with sparse part having weight 48074444.
Pruned matrix : 245460 x 247355 with weight 26390764.
Total sieving time: 18.67 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.68 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 19.68 hours.
 --------- CPU info (if available) ----------

(25·10¹³⁵+11)/9 = 2(7)₁₃₄9_<136> = 7 · 17 · 24618943 · 829455593933613949664672311_<27> · C100

C100 = P33 · P68

P33 = 101760642791834943232640563376777_<33>

P68 = 11233320577193988996054868802362165629420963942890486212300213105621_<68>

Sat Sep 20 16:03:00 2008  Msieve v. 1.36
Sat Sep 20 16:03:00 2008  random seeds: a78bf2a4 352f1807
Sat Sep 20 16:03:00 2008  factoring 1143109922622006640335934320858230741322564114655730564054913482556917003342965340126485297919563517 (100 digits)
Sat Sep 20 16:03:02 2008  no P-1/P+1/ECM available, skipping
Sat Sep 20 16:03:02 2008  commencing quadratic sieve (100-digit input)
Sat Sep 20 16:03:02 2008  using multiplier of 3
Sat Sep 20 16:03:02 2008  using 64kb Pentium 4 sieve core
Sat Sep 20 16:03:02 2008  sieve interval: 18 blocks of size 65536
Sat Sep 20 16:03:02 2008  processing polynomials in batches of 6
Sat Sep 20 16:03:02 2008  using a sieve bound of 2681729 (97571 primes)
Sat Sep 20 16:03:02 2008  using large prime bound of 402259350 (28 bits)
Sat Sep 20 16:03:02 2008  using double large prime bound of 3076883377187400 (43-52 bits)
Sat Sep 20 16:03:02 2008  using trial factoring cutoff of 52 bits
Sat Sep 20 16:03:02 2008  polynomial 'A' values have 13 factors
Sat Sep 20 16:03:06 2008  restarting with 8177 full and 518198 partial relations
Sun Sep 21 03:25:34 2008  97777 relations (23198 full + 74579 combined from 1477182 partial), need 97667
Sun Sep 21 03:25:39 2008  begin with 1500380 relations
Sun Sep 21 03:25:41 2008  reduce to 258871 relations in 12 passes
Sun Sep 21 03:25:41 2008  attempting to read 258871 relations
Sun Sep 21 03:25:50 2008  recovered 258871 relations
Sun Sep 21 03:25:50 2008  recovered 249493 polynomials
Sun Sep 21 03:25:50 2008  attempting to build 97777 cycles
Sun Sep 21 03:25:51 2008  found 97777 cycles in 6 passes
Sun Sep 21 03:25:51 2008  distribution of cycle lengths:
Sun Sep 21 03:25:51 2008     length 1 : 23198
Sun Sep 21 03:25:51 2008     length 2 : 16628
Sun Sep 21 03:25:51 2008     length 3 : 16331
Sun Sep 21 03:25:51 2008     length 4 : 13312
Sun Sep 21 03:25:51 2008     length 5 : 10105
Sun Sep 21 03:25:51 2008     length 6 : 7105
Sun Sep 21 03:25:51 2008     length 7 : 4567
Sun Sep 21 03:25:51 2008     length 9+: 6531
Sun Sep 21 03:25:51 2008  largest cycle: 22 relations
Sun Sep 21 03:25:51 2008  matrix is 97571 x 97777 (26.0 MB) with weight 6414114 (65.60/col)
Sun Sep 21 03:25:51 2008  sparse part has weight 6414114 (65.60/col)
Sun Sep 21 03:25:53 2008  filtering completed in 3 passes
Sun Sep 21 03:25:53 2008  matrix is 93701 x 93765 (25.0 MB) with weight 6179719 (65.91/col)
Sun Sep 21 03:25:53 2008  sparse part has weight 6179719 (65.91/col)
Sun Sep 21 03:25:54 2008  saving the first 48 matrix rows for later
Sun Sep 21 03:25:54 2008  matrix is 93653 x 93765 (13.8 MB) with weight 4676238 (49.87/col)
Sun Sep 21 03:25:54 2008  sparse part has weight 3067094 (32.71/col)
Sun Sep 21 03:25:54 2008  matrix includes 64 packed rows
Sun Sep 21 03:25:54 2008  using block size 21845 for processor cache size 512 kB
Sun Sep 21 03:25:55 2008  commencing Lanczos iteration
Sun Sep 21 03:25:55 2008  memory use: 14.5 MB
Sun Sep 21 03:27:25 2008  lanczos halted after 1482 iterations (dim = 93647)
Sun Sep 21 03:27:25 2008  recovered 15 nontrivial dependencies
Sun Sep 21 03:27:28 2008  prp33 factor: 101760642791834943232640563376777
Sun Sep 21 03:27:28 2008  prp68 factor: 11233320577193988996054868802362165629420963942890486212300213105621
Sun Sep 21 03:27:28 2008  elapsed time 11:24:28

Sep 20, 2008 (6th)

By Jo Yeong Uk / GGNFS

(25·10¹⁷⁷+11)/9 = 2(7)₁₇₆9_<178> = 7 · 401 · 2677468327_<10> · 845137723820723_<15> · 545382280341452033_<18> · 384200698398579815600737_<24> · C109

C109 = P46 · P63

P46 = 6157197430675453532424056643451057039223485303_<46>

P63 = 338969797703252851359735909773659729555343992931588939572392839_<63>

Number: 27779_177
N=2087103967495046706276067970122419419022511455953998279647936986802817671321789654961798929535928625058945217
  ( 109 digits)
Divisors found:
 r1=6157197430675453532424056643451057039223485303 (pp46)
 r2=338969797703252851359735909773659729555343992931588939572392839 (pp63)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.74 hours.
Scaled time: 27.28 units (timescale=2.323).
Factorization parameters were as follows:
name: 27779_177
n: 2087103967495046706276067970122419419022511455953998279647936986802817671321789654961798929535928625058945217
skew: 32823.13
# norm 4.71e+14
c5: 4140
c4: -71364416
c3: -11634601779911
c2: -437449399023178436
c1: 2192614406917375491624
c0: 51523026074077021222366080
# alpha -5.51
Y1: 53450399057
Y0: -871984650797901441577
# Murphy_E 1.24e-09
# M 1324511941542110147642404859276676481618277862522208959679582391092161274809532009101863003961825845040641987
type: gnfs
rlim: 2000000
alim: 2000000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved algebraic special-q in [1000000, 1700001)
Primes: RFBsize:148933, AFBsize:148689, largePrimes:5135535 encountered
Relations: rels:5333563, finalFF:456369
Max relations in full relation-set: 28
Initial matrix: 297703 x 456369 with sparse part having weight 47715445.
Pruned matrix : 224563 x 226115 with weight 22753216.
Polynomial selection time: 0.68 hours.
Total sieving time: 10.69 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.22 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,26,26,50,50,2.6,2.6,50000
total time: 11.74 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)
Calibrating delay using timer specific routine.. 5344.63 BogoMIPS (lpj=2672318)
Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672355)

Sep 20, 2008 (5th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(14·10¹⁷⁸-23)/9 = 1(5)₁₇₇3_<179> = 17 · C177

C177 = P43 · P135

P43 = 2225841655194472268016781853809366714396313_<43>

P135 = 411095136800562521541539475829738868608002274427477071385840597838998349260485047470252329367328208883411589540139084008392762907660793_<135>

Number: n
N=915032679738562091503267973856209150326797385620915032679738562091503267973856209150326797385620915032679738562091503267973856209150326797385620915032679738562091503267973856209
  ( 177 digits)
SNFS difficulty: 179 digits.
Divisors found:

Sat Sep 20 16:52:55 2008  prp43 factor: 2225841655194472268016781853809366714396313
Sat Sep 20 16:52:55 2008  prp135 factor: 411095136800562521541539475829738868608002274427477071385840597838998349260485047470252329367328208883411589540139084008392762907660793
Sat Sep 20 16:52:55 2008  elapsed time 06:44:14 (Msieve 1.36)

Version: GGNFS-0.77.1-20050930-k8
Total time: 103.73 hours.
Scaled time: 87.34 units (timescale=0.842).
Factorization parameters were as follows:
name: KA_1_5_177_3
n: 915032679738562091503267973856209150326797385620915032679738562091503267973856209150326797385620915032679738562091503267973856209150326797385620915032679738562091503267973856209
type: snfs
skew: 0.55
deg: 5
c5: 875
c0: -46
m: 200000000000000000000000000000000000
rlim: 8000000
alim: 8000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 13800001)
Primes: RFBsize:539777, AFBsize:540340, largePrimes:15352877 encountered
Relations: rels:15599595, finalFF:1126756
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 103.04 hours.
Total relation processing time: 0.69 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,179,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,52,52,2.5,2.5,100000
total time: 103.73 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(79·10¹⁷¹-7)/9 = 8(7)₁₇₁_<172> = 455849 · 5458373 · 67309522537_<11> · 1478323965043_<13> · 21868648504691_<14> · C124

C124 = P39 · P85

P39 = 205933584244552585437467949053421910141_<39>

P85 = 7872363074833719679020067199964325911944706977770586747781253428175946317375962633481_<85>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 1621183944474974841004973167630623544618770286330625649993113352858042939934854174924508403146115135259070343188195700030821 (124 digits)
Using B1=5472000, B2=11416630690, polynomial Dickson(12), sigma=1768681715
Step 1 took 48726ms
Step 2 took 20109ms
********** Factor found in step 2: 205933584244552585437467949053421910141
Found probable prime factor of 39 digits: 205933584244552585437467949053421910141
Probable prime cofactor 7872363074833719679020067199964325911944706977770586747781253428175946317375962633481 has 85 digits

Sep 20, 2008 (4th)

By Serge Batalov / Msieve 1.37, GMP-ECM 6.2.1, Msieve-1.37

(25·10¹⁴⁵+11)/9 = 2(7)₁₄₄9_<146> = 39119 · C141

C141 = P65 · P77

P65 = 22018123084442256945601181842870458576967444925337048195952914377_<65>

P77 = 32249980746513672256233897182103678492771023523845280466382534623925440318133_<77>

Number: 27779_145
N=710084045547631017607243993399058712589222060323059837362350207770591727236835751879592468564579303606374850527308412223670793675139389498141
  ( 141 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=22018123084442256945601181842870458576967444925337048195952914377
 r2=32249980746513672256233897182103678492771023523845280466382534623925440318133
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.723).
Factorization parameters were as follows:
n: 710084045547631017607243993399058712589222060323059837362350207770591727236835751879592468564579303606374850527308412223670793675139389498141
Y1: 1
Y0: -100000000000000000000000000000
c5: 25
c0: 11
skew: 0.85
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved rational special-q in [750000, 1950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 217022 x 217241
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 4.90 hours.

(25·10¹⁸¹+11)/9 = 2(7)₁₈₀9_<182> = 489343 · 210435473 · 429402721073_<12> · 182964771137591_<15> · 43944186772223093519_<20> · C122

C122 = P32 · P91

P32 = 23598479575400327060190027268979_<32>

P91 = 3310910530014099084884003286660786026675819476626077776496236615555080721288380919172566327_<91>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1615171658
Step 1 took 4421ms
Step 2 took 2396ms
********** Factor found in step 2: 23598479575400327060190027268979
Found probable prime factor of 32 digits: 23598479575400327060190027268979
Probable prime cofactor 3310910530014099084884003286660786026675819476626077776496236615555080721288380919172566327 has 91 digits

(25·10¹⁴⁹+11)/9 = 2(7)₁₄₈9_<150> = 3 · C149

C149 = P44 · P48 · P58

P44 = 89422569745722268375593254754751733693202109_<44>

P48 = 284115817265519624811828721956934316858888334641_<48>

P58 = 3644464179724676150814281014736489200665629737281618159797_<58>

SNFS difficulty: 150 digits.
Divisors found:
 r1=89422569745722268375593254754751733693202109
 r2=284115817265519624811828721956934316858888334641
 r3=3644464179724676150814281014736489200665629737281618159797
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.726).
Factorization parameters were as follows:
n: 92592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592593
Y1: 1
Y0: -1000000000000000000000000000000
c5: 5
c0: 22
skew: 1.34
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [1200000, 1800001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 451014 x 451254
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,54,54,2.5,2.5,100000
total time: 9.50 hours.

Sep 20, 2008 (3rd)

By Sinkiti Sibata / GGNFS, Msieve

(25·10¹⁴⁴+11)/9 = 2(7)₁₄₃9_<145> = 2179652333_<10> · 555525169807_<12> · C124

C124 = P34 · P41 · P49

P34 = 6555616797040220553503787469828621_<34>

P41 = 73975542567038708308894989343115810707013_<41>

P49 = 4730475671659868972131894097385159232743234787633_<49>

Number: 27779_144
N=2294069293066095745670137846707089174646054183142057512760829022119782349751523968362806955211662464140409618998272826924209
  ( 124 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=6555616797040220553503787469828621 (pp34)
 r2=73975542567038708308894989343115810707013 (pp41)
 r3=4730475671659868972131894097385159232743234787633 (pp49)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 16.88 hours.
Scaled time: 17.02 units (timescale=1.008).
Factorization parameters were as follows:
name: 27779_144
n: 2294069293066095745670137846707089174646054183142057512760829022119782349751523968362806955211662464140409618998272826924209
m: 100000000000000000000000000000
c5: 5
c0: 22
skew: 1.34
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 3150001)
Primes: RFBsize:100021, AFBsize:100104, largePrimes:3076799 encountered
Relations: rels:3208992, finalFF:311014
Max relations in full relation-set: 28
Initial matrix: 200190 x 311014 with sparse part having weight 39232556.
Pruned matrix : 176682 x 177746 with weight 22487174.
Total sieving time: 16.56 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.22 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 16.88 hours.
 --------- CPU info (if available) ----------

(25·10¹⁰⁹+11)/9 = 2(7)₁₀₈9_<110> = 621059 · 60520133 · C96

C96 = P37 · P59

P37 = 8518541216079366642207800998712558843_<37>

P59 = 86756003328650734930201809343394393921066217104696711721799_<59>

Fri Sep 19 21:48:34 2008  Msieve v. 1.36
Fri Sep 19 21:48:34 2008  random seeds: 6141f597 886cea6a
Fri Sep 19 21:48:34 2008  factoring 739034590097430011847178811447724966016948771754630731479696239768907048998575629325791633318557 (96 digits)
Fri Sep 19 21:48:36 2008  no P-1/P+1/ECM available, skipping
Fri Sep 19 21:48:36 2008  commencing quadratic sieve (96-digit input)
Fri Sep 19 21:48:36 2008  using multiplier of 5
Fri Sep 19 21:48:36 2008  using 64kb Pentium 4 sieve core
Fri Sep 19 21:48:36 2008  sieve interval: 18 blocks of size 65536
Fri Sep 19 21:48:36 2008  processing polynomials in batches of 6
Fri Sep 19 21:48:36 2008  using a sieve bound of 2298889 (84706 primes)
Fri Sep 19 21:48:36 2008  using large prime bound of 344833350 (28 bits)
Fri Sep 19 21:48:36 2008  using double large prime bound of 2331828631036500 (43-52 bits)
Fri Sep 19 21:48:36 2008  using trial factoring cutoff of 52 bits
Fri Sep 19 21:48:36 2008  polynomial 'A' values have 12 factors
Sat Sep 20 05:02:55 2008  84910 relations (21169 full + 63741 combined from 1268574 partial), need 84802
Sat Sep 20 05:03:00 2008  begin with 1289743 relations
Sat Sep 20 05:03:01 2008  reduce to 219896 relations in 10 passes
Sat Sep 20 05:03:01 2008  attempting to read 219896 relations
Sat Sep 20 05:03:09 2008  recovered 219896 relations
Sat Sep 20 05:03:09 2008  recovered 203990 polynomials
Sat Sep 20 05:03:09 2008  attempting to build 84910 cycles
Sat Sep 20 05:03:09 2008  found 84910 cycles in 6 passes
Sat Sep 20 05:03:09 2008  distribution of cycle lengths:
Sat Sep 20 05:03:09 2008     length 1 : 21169
Sat Sep 20 05:03:09 2008     length 2 : 14932
Sat Sep 20 05:03:09 2008     length 3 : 14313
Sat Sep 20 05:03:09 2008     length 4 : 11452
Sat Sep 20 05:03:09 2008     length 5 : 8668
Sat Sep 20 05:03:09 2008     length 6 : 5678
Sat Sep 20 05:03:09 2008     length 7 : 3710
Sat Sep 20 05:03:09 2008     length 9+: 4988
Sat Sep 20 05:03:09 2008  largest cycle: 21 relations
Sat Sep 20 05:03:10 2008  matrix is 84706 x 84910 (23.5 MB) with weight 5816551 (68.50/col)
Sat Sep 20 05:03:10 2008  sparse part has weight 5816551 (68.50/col)
Sat Sep 20 05:03:11 2008  filtering completed in 3 passes
Sat Sep 20 05:03:11 2008  matrix is 80313 x 80375 (22.4 MB) with weight 5547279 (69.02/col)
Sat Sep 20 05:03:11 2008  sparse part has weight 5547279 (69.02/col)
Sat Sep 20 05:03:12 2008  saving the first 48 matrix rows for later
Sat Sep 20 05:03:12 2008  matrix is 80265 x 80375 (16.9 MB) with weight 4712491 (58.63/col)
Sat Sep 20 05:03:12 2008  sparse part has weight 3959309 (49.26/col)
Sat Sep 20 05:03:12 2008  matrix includes 64 packed rows
Sat Sep 20 05:03:12 2008  using block size 21845 for processor cache size 512 kB
Sat Sep 20 05:03:13 2008  commencing Lanczos iteration
Sat Sep 20 05:03:13 2008  memory use: 14.7 MB
Sat Sep 20 05:04:34 2008  lanczos halted after 1270 iterations (dim = 80265)
Sat Sep 20 05:04:34 2008  recovered 18 nontrivial dependencies
Sat Sep 20 05:04:36 2008  prp37 factor: 8518541216079366642207800998712558843
Sat Sep 20 05:04:36 2008  prp59 factor: 86756003328650734930201809343394393921066217104696711721799
Sat Sep 20 05:04:36 2008  elapsed time 07:16:02

(25·10¹⁴⁶+11)/9 = 2(7)₁₄₅9_<147> = 3² · 311 · 815280920042379045817_<21> · C123

C123 = P36 · P87

P36 = 217157733583248726770838103900749061_<36>

P87 = 560546985914951290774332227279129798735530007314797011598600521856481772063274777635233_<87>

Number: 27779_146
N=121727113028212068940104061530922353894609120636416006266835333908723404409672394991179681058140998472858620222918925266213
  ( 123 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=217157733583248726770838103900749061 (pp36)
 r2=560546985914951290774332227279129798735530007314797011598600521856481772063274777635233 (pp87)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 15.59 hours.
Scaled time: 15.71 units (timescale=1.008).
Factorization parameters were as follows:
name: 27779_146
n: 121727113028212068940104061530922353894609120636416006266835333908723404409672394991179681058140998472858620222918925266213
m: 100000000000000000000000000000
c5: 250
c0: 11
skew: 0.54
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2850001)
Primes: RFBsize:114155, AFBsize:114243, largePrimes:2880134 encountered
Relations: rels:2875007, finalFF:270616
Max relations in full relation-set: 28
Initial matrix: 228464 x 270616 with sparse part having weight 29150397.
Pruned matrix : 215839 x 217045 with weight 21581657.
Total sieving time: 15.19 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 15.59 hours.
 --------- CPU info (if available) ----------

(25·10¹⁵³+11)/9 = 2(7)₁₅₂9_<154> = 7 · 1619 · 26249 · 121001 · 9629191476013162601_<19> · C121

C121 = P47 · P75

P47 = 17089294561179909609497895907997512028577048257_<47>

P75 = 468961218759818144911743241615271591080346751331129510155707954444981636591_<75>

Number: 27779_153
N=8014216405156462018926099823156586249159542824660379557516458721325017323013340800025073267558580653489159472339843971887
  ( 121 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=17089294561179909609497895907997512028577048257 (pp47)
 r2=468961218759818144911743241615271591080346751331129510155707954444981636591 (pp75)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 25.53 hours.
Scaled time: 19.99 units (timescale=0.783).
Factorization parameters were as follows:
name: 27779_153
n: 8014216405156462018926099823156586249159542824660379557516458721325017323013340800025073267558580653489159472339843971887
m: 5000000000000000000000000000000
c5: 8
c0: 11
skew: 1.07
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:175424, largePrimes:5471494 encountered
Relations: rels:5387090, finalFF:488774
Max relations in full relation-set: 28
Initial matrix: 351791 x 488774 with sparse part having weight 42592876.
Pruned matrix : 290759 x 292581 with weight 23002981.
Total sieving time: 24.47 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.86 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 25.53 hours.
 --------- CPU info (if available) ----------

Sep 20, 2008 (2nd)

By Jo Yeong Uk / GGNFS, GMP-ECM

(25·10¹⁴²+11)/9 = 2(7)₁₄₁9_<143> = 18679 · 2324149 · 21883871 · 2721872386127978805349_<22> · C104

C104 = P32 · P72

P32 = 17100579543785749444125700728983_<32>

P72 = 628169976582331219460679003133833163982380481247619650573495514275530357_<72>

Number: 27779_142
N=10742070651564186516675552053776763874950710443051540573202381782044493421278783011980786156993846236931
  ( 104 digits)
Divisors found:
 r1=17100579543785749444125700728983 (pp32)
 r2=628169976582331219460679003133833163982380481247619650573495514275530357 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.95 hours.
Scaled time: 11.79 units (timescale=2.380).
Factorization parameters were as follows:
name: 27779_142
n: 10742070651564186516675552053776763874950710443051540573202381782044493421278783011980786156993846236931
skew: 25644.16
# norm 4.05e+14
c5: 4200
c4: 237417580
c3: -22938014228706
c2: -99292987080815543
c1: 3491001841126376848650
c0: -7512869258041779422968325
# alpha -6.19
Y1: 6826139641
Y0: -76132011157515595038
# Murphy_E 2.31e-09
# M 2345490416613929445046528387112026856772247017840236364780300929704505961959466593458521683729229215729
type: gnfs
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [800000, 1550001)
Primes: RFBsize:121127, AFBsize:120508, largePrimes:4424323 encountered
Relations: rels:4365416, finalFF:305834
Max relations in full relation-set: 28
Initial matrix: 241714 x 305834 with sparse part having weight 26506673.
Pruned matrix : 208289 x 209561 with weight 15361234.
Polynomial selection time: 0.39 hours.
Total sieving time: 4.29 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1600000,1600000,26,26,49,49,2.6,2.6,50000
total time: 4.95 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)
Calibrating delay using timer specific routine.. 5344.63 BogoMIPS (lpj=2672318)
Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672355)

(25·10¹⁷¹+11)/9 = 2(7)₁₇₀9_<172> = 7 · 139 · 160019 · 16845041 · 26144659 · 65978131 · 31757213781199_<14> · 470300919484222862311_<21> · C107

C107 = P44 · P63

P44 = 47874100857762290609637818483054673407660177_<44>

P63 = 858695511971689614580328938461510753245623133163645463110819701_<63>

Number: 27779_171
N=41109275546240495062432283264051165658091623196993437906976151352389340190469170320769270885516502924747077
  ( 107 digits)
Divisors found:
 r1=47874100857762290609637818483054673407660177 (pp44)
 r2=858695511971689614580328938461510753245623133163645463110819701 (pp63)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 9.77 hours.
Scaled time: 22.77 units (timescale=2.331).
Factorization parameters were as follows:
name: 27779_171
n: 41109275546240495062432283264051165658091623196993437906976151352389340190469170320769270885516502924747077
skew: 12398.44
# norm 1.37e+15
c5: 159840
c4: -1028441856
c3: -137128844967686
c2: 134334849458104183
c1: 5984236747583308367232
c0: 6813532622585497995327780
# alpha -6.31
Y1: 102254484497
Y0: -191448147793948031093
# Murphy_E 1.43e-09
# M 17913856090839271483351743511826600163139299801714024344774155683648315054779271422721430516648895900507594
type: gnfs
rlim: 2000000
alim: 2000000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved algebraic special-q in [1000000, 1550001)
Primes: RFBsize:148933, AFBsize:148910, largePrimes:4994109 encountered
Relations: rels:5074616, finalFF:422065
Max relations in full relation-set: 28
Initial matrix: 297927 x 422065 with sparse part having weight 40159545.
Pruned matrix : 222425 x 223978 with weight 20465865.
Polynomial selection time: 0.54 hours.
Total sieving time: 8.84 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.24 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,26,26,50,50,2.6,2.6,50000
total time: 9.77 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)
Calibrating delay using timer specific routine.. 5344.63 BogoMIPS (lpj=2672318)
Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672355)

(25·10¹⁸⁷+11)/9 = 2(7)₁₈₆9_<188> = C188

C188 = P37 · C151

P37 = 3467294206652453951666199350752110791_<37>

C151 = [8011370285360413276920870842742682043675772489490261688319864518192193944560646037656706933240715383931249954780125806286441085989770305439253452225269_<151>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 (188 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3112568619
Step 1 took 18665ms
Step 2 took 7928ms
********** Factor found in step 2: 3467294206652453951666199350752110791
Found probable prime factor of 37 digits: 3467294206652453951666199350752110791
Composite cofactor 8011370285360413276920870842742682043675772489490261688319864518192193944560646037656706933240715383931249954780125806286441085989770305439253452225269 has 151 digits

Sep 20, 2008

By Thomas Womack / ggnfs lattice siever, msieve

(16·10¹⁷⁹-1)/3 = 5(3)₁₇₉_<180> = 59431787 · C172

C172 = P58 · P115

P58 = 1226638090264928115723655327333228728490191370449664758311_<58>

P115 = 7315828104216888973836157895081638072697654891738449634905084897704701381178005284947042277396339224057301618595369_<115>

prp58 factor: 1226638090264928115723655327333228728490191370449664758311
prp115 factor: 7315828104216888973836157895081638072697654891738449634905084897704701381178005284947042277396339224057301618595369
elapsed time 06:07:08

(that's the processing time, sieving was ~101 CPU-hours)

Sep 19, 2008 (8th)

By Robert Backstrom / GGNFS, Msieve

(13·10¹⁷⁸+23)/9 = 1(4)₁₇₇7_<179> = 277 · C176

C176 = P64 · P113

P64 = 4761758900615140831294272937064147828242820480788864164772892249_<64>

P113 = 10950997291772328108097594654307473313103101691401224343725196196487050663817487869687697193902016189467940704539_<113>

Number: n
N=52146008824709185720016044925792218210990774167669474528680304853590052146008824709185720016044925792218210990774167669474528680304853590052146008824709185720016044925792218211
  ( 176 digits)
SNFS difficulty: 179 digits.
Divisors found:

Sat Sep 20 00:18:31 2008  prp64 factor: 4761758900615140831294272937064147828242820480788864164772892249
Sat Sep 20 00:18:31 2008  prp113 factor: 10950997291772328108097594654307473313103101691401224343725196196487050663817487869687697193902016189467940704539
Sat Sep 20 00:18:31 2008  elapsed time 04:43:43 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 55.55 hours.
Scaled time: 113.93 units (timescale=2.051).
Factorization parameters were as follows:
name: KA_1_4_177_7
n: 52146008824709185720016044925792218210990774167669474528680304853590052146008824709185720016044925792218210990774167669474528680304853590052146008824709185720016044925792218211
type: snfs
skew: 0.28
deg: 5
c5: 13000
c0: 23
m: 100000000000000000000000000000000000
rlim: 8000000
alim: 8000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 11400001)
Primes: RFBsize:539777, AFBsize:540425, largePrimes:15635665 encountered
Relations: rels:16290338, finalFF:1677740
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 54.95 hours.
Total relation processing time: 0.60 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,179,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,52,52,2.5,2.5,100000
total time: 55.55 hours.
 --------- CPU info (if available) ----------

Sep 19, 2008 (7th)

By Sinkiti Sibata / Msieve, GGNFS

(25·10¹⁰⁴+11)/9 = 2(7)₁₀₃9_<105> = 3 · 157 · 491248811 · C94

C94 = P45 · P49

P45 = 252854036142891231851223614578087693577960987_<45>

P49 = 4747939643331217537545944530363101682879932936157_<49>

Fri Sep 19 16:36:13 2008  Msieve v. 1.36
Fri Sep 19 16:36:13 2008  random seeds: 58339ecb c2f9e10e
Fri Sep 19 16:36:13 2008  factoring 1200535702179137783553330569598159007986633480577939579822794144056580555474363458076107706959 (94 digits)
Fri Sep 19 16:36:14 2008  no P-1/P+1/ECM available, skipping
Fri Sep 19 16:36:14 2008  commencing quadratic sieve (94-digit input)
Fri Sep 19 16:36:14 2008  using multiplier of 5
Fri Sep 19 16:36:14 2008  using 64kb Pentium 4 sieve core
Fri Sep 19 16:36:14 2008  sieve interval: 18 blocks of size 65536
Fri Sep 19 16:36:14 2008  processing polynomials in batches of 6
Fri Sep 19 16:36:14 2008  using a sieve bound of 1991609 (73803 primes)
Fri Sep 19 16:36:14 2008  using large prime bound of 256917561 (27 bits)
Fri Sep 19 16:36:14 2008  using double large prime bound of 1372868018887893 (42-51 bits)
Fri Sep 19 16:36:14 2008  using trial factoring cutoff of 51 bits
Fri Sep 19 16:36:14 2008  polynomial 'A' values have 12 factors
Fri Sep 19 21:37:50 2008  74067 relations (18463 full + 55604 combined from 1027184 partial), need 73899
Fri Sep 19 21:37:54 2008  begin with 1045647 relations
Fri Sep 19 21:37:55 2008  reduce to 190511 relations in 10 passes
Fri Sep 19 21:37:55 2008  attempting to read 190511 relations
Fri Sep 19 21:38:01 2008  recovered 190511 relations
Fri Sep 19 21:38:01 2008  recovered 173085 polynomials
Fri Sep 19 21:38:01 2008  attempting to build 74067 cycles
Fri Sep 19 21:38:01 2008  found 74067 cycles in 5 passes
Fri Sep 19 21:38:01 2008  distribution of cycle lengths:
Fri Sep 19 21:38:01 2008     length 1 : 18463
Fri Sep 19 21:38:01 2008     length 2 : 13069
Fri Sep 19 21:38:01 2008     length 3 : 12697
Fri Sep 19 21:38:01 2008     length 4 : 10086
Fri Sep 19 21:38:01 2008     length 5 : 7424
Fri Sep 19 21:38:01 2008     length 6 : 5078
Fri Sep 19 21:38:01 2008     length 7 : 3085
Fri Sep 19 21:38:01 2008     length 9+: 4165
Fri Sep 19 21:38:01 2008  largest cycle: 19 relations
Fri Sep 19 21:38:02 2008  matrix is 73803 x 74067 (19.5 MB) with weight 4812420 (64.97/col)
Fri Sep 19 21:38:02 2008  sparse part has weight 4812420 (64.97/col)
Fri Sep 19 21:38:03 2008  filtering completed in 3 passes
Fri Sep 19 21:38:03 2008  matrix is 69969 x 70033 (18.5 MB) with weight 4577242 (65.36/col)
Fri Sep 19 21:38:03 2008  sparse part has weight 4577242 (65.36/col)
Fri Sep 19 21:38:04 2008  saving the first 48 matrix rows for later
Fri Sep 19 21:38:04 2008  matrix is 69921 x 70033 (11.8 MB) with weight 3620447 (51.70/col)
Fri Sep 19 21:38:04 2008  sparse part has weight 2665595 (38.06/col)
Fri Sep 19 21:38:04 2008  matrix includes 64 packed rows
Fri Sep 19 21:38:04 2008  using block size 21845 for processor cache size 512 kB
Fri Sep 19 21:38:05 2008  commencing Lanczos iteration
Fri Sep 19 21:38:05 2008  memory use: 11.2 MB
Fri Sep 19 21:38:59 2008  lanczos halted after 1107 iterations (dim = 69913)
Fri Sep 19 21:38:59 2008  recovered 12 nontrivial dependencies
Fri Sep 19 21:39:01 2008  prp45 factor: 252854036142891231851223614578087693577960987
Fri Sep 19 21:39:01 2008  prp49 factor: 4747939643331217537545944530363101682879932936157
Fri Sep 19 21:39:01 2008  elapsed time 05:02:48

(25·10¹³¹+11)/9 = 2(7)₁₃₀9_<132> = 3 · 474917 · 916760665887089_<15> · C111

C111 = P35 · P76

P35 = 94380226647732964091537890550890669_<35>

P76 = 2253313099465234579424830713654498806792655361016665349309311724347507836769_<76>

Number: 27779_131
N=212668201035834491692037209728328759241937969007540092694188106330944785211386193946770471207640858090417208461
  ( 111 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=94380226647732964091537890550890669 (pp35)
 r2=2253313099465234579424830713654498806792655361016665349309311724347507836769 (pp76)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.15 hours.
Scaled time: 4.02 units (timescale=0.781).
Factorization parameters were as follows:
name: 27779_131
n: 212668201035834491692037209728328759241937969007540092694188106330944785211386193946770471207640858090417208461
m: 100000000000000000000000000
c5: 250
c0: 11
skew: 0.54
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1050001)
Primes: RFBsize:63951, AFBsize:64024, largePrimes:1524370 encountered
Relations: rels:1534771, finalFF:177835
Max relations in full relation-set: 28
Initial matrix: 128041 x 177835 with sparse part having weight 14394177.
Pruned matrix : 114549 x 115253 with weight 7529044.
Total sieving time: 5.01 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.15 hours.
 --------- CPU info (if available) ----------

Sep 19, 2008 (6th)

By Jo Yeong Uk / GGNFS

(25·10¹²⁶+11)/9 = 2(7)₁₂₅9_<127> = 4079 · 80877693697_<11> · C112

C112 = P34 · P79

P34 = 5921234966250715563066349802636897_<34>

P79 = 1422010294334862352761456402011079915700506602156564668923988341467060275943389_<79>

Number: 27779_126
N=8420057077184058787598473132349406192030301923297927628502389558208977776558965593828185370809262511926494623933
  ( 112 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=5921234966250715563066349802636897 (pp34)
 r2=1422010294334862352761456402011079915700506602156564668923988341467060275943389 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.76 hours.
Scaled time: 4.04 units (timescale=2.292).
Factorization parameters were as follows:
n: 8420057077184058787598473132349406192030301923297927628502389558208977776558965593828185370809262511926494623933
m: 50000000000000000000000000
c5: 2
c0: 275
skew: 2.68
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 900001)
Primes: RFBsize:78498, AFBsize:78707, largePrimes:1558651 encountered
Relations: rels:1609975, finalFF:224099
Max relations in full relation-set: 28
Initial matrix: 157270 x 224099 with sparse part having weight 11295137.
Pruned matrix : 125906 x 126756 with weight 5116173.
Total sieving time: 1.70 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 1.76 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.62 BogoMIPS (lpj=2673813)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.29 BogoMIPS (lpj=2672145)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(25·10¹²⁸+11)/9 = 2(7)₁₂₇9_<129> = 3³ · 463 · 3053293 · 106459341671_<12> · C107

C107 = P41 · P66

P41 = 88835349405043160784533804171443167335437_<41>

P66 = 769510713970792550300555952851855989341577812582377543694990208889_<66>

Number: 27779_128
N=68359753146519583856843073026007483494688797670717179829285121834152207820493624762386763326338142162099493
  ( 107 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=88835349405043160784533804171443167335437 (pp41)
 r2=769510713970792550300555952851855989341577812582377543694990208889 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.51 hours.
Scaled time: 3.57 units (timescale=2.354).
Factorization parameters were as follows:
n: 68359753146519583856843073026007483494688797670717179829285121834152207820493624762386763326338142162099493
m: 100000000000000000000000000
c5: 1
c0: 44
skew: 2.13
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 850001)
Primes: RFBsize:78498, AFBsize:78087, largePrimes:1507905 encountered
Relations: rels:1540170, finalFF:207011
Max relations in full relation-set: 28
Initial matrix: 156649 x 207011 with sparse part having weight 9809048.
Pruned matrix : 130030 x 130877 with weight 4819028.
Total sieving time: 1.46 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 1.51 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.62 BogoMIPS (lpj=2673813)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.29 BogoMIPS (lpj=2672145)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Sep 19, 2008 (5th)

By anonymous / GMP-ECM

(25·10¹⁶⁴+11)/9 = 2(7)₁₆₃9_<165> = 3² · 2729 · 2336093 · 21024053473_<11> · C144

C144 = P31 · P113

P31 = 2530290505519396636552217573611_<31>

P113 = 91006934911632667105331373545676803276176580669962007769491107333139904850733355058121735195657525624018987256541_<113>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 230273983343325847520474402702127170340777004798958820095817677549008342383184157970938223756549950521498102500948013368207088201076600608739551 (144 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=808694177
Step 1 took 4610ms
Step 2 took 2619ms
********** Factor found in step 2: 2530290505519396636552217573611
Found probable prime factor of 31 digits: 2530290505519396636552217573611
Probable prime cofactor 91006934911632667105331373545676803276176580669962007769491107333139904850733355058121735195657525624018987256541 has 113 digits

Sep 19, 2008 (4th)

By Serge Batalov / Msieve-1.37 QS, GMP-ECM 6.2.1, GMP-ECM 6.2.1 [P-1!]

(25·10¹³⁴+11)/9 = 2(7)₁₃₃9_<135> = 3 · 5569 · 6501367 · 325527911 · 1641755237_<10> · 35864341695964682465531767_<26> · C81

C81 = P37 · P44

P37 = 7464496412545245228296694969557118343_<37>

P44 = 17874517414703582293209008808015497997711773_<44>

Thu Sep 18 21:24:45 2008  Msieve v. 1.37
Thu Sep 18 21:24:45 2008  random seeds: 8396dfb3 39287007
Thu Sep 18 21:24:45 2008  factoring 133424271118032401399678682893589251520170031584126003417413899923975037765352139 (81 digits)
Thu Sep 18 21:24:46 2008  searching for 15-digit factors
Thu Sep 18 21:24:46 2008  commencing quadratic sieve (81-digit input)
Thu Sep 18 21:24:46 2008  using multiplier of 3
Thu Sep 18 21:24:46 2008  using 64kb Opteron sieve core
Thu Sep 18 21:24:46 2008  sieve interval: 6 blocks of size 65536
Thu Sep 18 21:24:46 2008  processing polynomials in batches of 17
Thu Sep 18 21:24:46 2008  using a sieve bound of 1309421 (50122 primes)
Thu Sep 18 21:24:46 2008  using large prime bound of 129632679 (26 bits)
Thu Sep 18 21:24:46 2008  using trial factoring cutoff of 27 bits
Thu Sep 18 21:24:46 2008  polynomial 'A' values have 10 factors
Thu Sep 18 21:36:25 2008  50241 relations (25847 full + 24394 combined from 272444 partial), need 50218
Thu Sep 18 21:36:25 2008  begin with 298291 relations
Thu Sep 18 21:36:25 2008  reduce to 71651 relations in 2 passes
Thu Sep 18 21:36:25 2008  attempting to read 71651 relations
Thu Sep 18 21:36:26 2008  recovered 71651 relations
Thu Sep 18 21:36:26 2008  recovered 61361 polynomials
Thu Sep 18 21:36:26 2008  attempting to build 50241 cycles
Thu Sep 18 21:36:26 2008  found 50241 cycles in 1 passes
Thu Sep 18 21:36:26 2008  distribution of cycle lengths:
Thu Sep 18 21:36:26 2008     length 1 : 25847
Thu Sep 18 21:36:26 2008     length 2 : 24394
Thu Sep 18 21:36:26 2008  largest cycle: 2 relations
Thu Sep 18 21:36:26 2008  matrix is 50122 x 50241 (7.4 MB) with weight 1528596 (30.43/col)
Thu Sep 18 21:36:26 2008  sparse part has weight 1528596 (30.43/col)
Thu Sep 18 21:36:26 2008  filtering completed in 3 passes
Thu Sep 18 21:36:26 2008  matrix is 35603 x 35667 (5.7 MB) with weight 1215903 (34.09/col)
Thu Sep 18 21:36:26 2008  sparse part has weight 1215903 (34.09/col)
Thu Sep 18 21:36:26 2008  saving the first 48 matrix rows for later
Thu Sep 18 21:36:26 2008  matrix is 35555 x 35667 (4.1 MB) with weight 931931 (26.13/col)
Thu Sep 18 21:36:26 2008  sparse part has weight 707670 (19.84/col)
Thu Sep 18 21:36:26 2008  matrix includes 64 packed rows
Thu Sep 18 21:36:26 2008  using block size 14266 for processor cache size 1024 kB
Thu Sep 18 21:36:27 2008  commencing Lanczos iteration
Thu Sep 18 21:36:27 2008  memory use: 4.0 MB
Thu Sep 18 21:36:31 2008  lanczos halted after 564 iterations (dim = 35553)
Thu Sep 18 21:36:31 2008  recovered 16 nontrivial dependencies
Thu Sep 18 21:36:31 2008  prp37 factor: 7464496412545245228296694969557118343
Thu Sep 18 21:36:31 2008  prp44 factor: 17874517414703582293209008808015497997711773
Thu Sep 18 21:36:31 2008  elapsed time 00:11:46

(25·10¹⁶²+11)/9 = 2(7)₁₆₁9_<163> = C163

C163 = P36 · C127

P36 = 956996067485339718144137108196685667_<36>

C127 = [2902601036884961627173699119809625917037467027349604362385456802139104947986390088924478788941052925770284265498185067416124337_<127>]

Using B1=3000000, B2=23415979870, polynomial Dickson(12), sigma=3570635795
Step 1 took 21809ms
Step 2 took 19409ms
********** Factor found in step 2: 956996067485339718144137108196685667
Found probable prime factor of 36 digits: 956996067485339718144137108196685667
Composite cofactor 2902601036884961627173699119809625917037467027349604362385456802139104947986390088924478788941052925770284265498185067416124337 has 127 digits

(25·10¹²¹+11)/9 = 2(7)₁₂₀9_<122> = C122

C122 = P41 · P81

P41 = 28281986806699176262127343626160011389591_<41>

P81 = 982172078914838963908547772788255008357011466169123485822865552044233331522856069_<81>

Number: 27779_121
N=27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
  ( 122 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=28281986806699176262127343626160011389591
 r2=982172078914838963908547772788255008357011466169123485822865552044233331522856069
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.728).
Factorization parameters were as follows:
n: 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
Y1: 1
Y0: -1000000000000000000000000
c5: 250
c0: 11
skew: 0.54
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 500001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 121099 x 121346
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 0.80 hours.

(25·10¹²⁴+11)/9 = 2(7)₁₂₃9_<125> = C125

C125 = P47 · P78

P47 = 27794149819268048962266606788818980074038015727_<47>

P78 = 999410953686414922780705848621382863777285842485662131420022280753390278988477_<78>

Number: 27779_124
N=27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
  ( 125 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=27794149819268048962266606788818980074038015727
 r2=999410953686414922780705848621382863777285842485662131420022280753390278988477
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.180).
Factorization parameters were as follows:
n: 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
Y1: 1
Y0: -10000000000000000000000000
c5: 5
c0: 22
skew: 1.34
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 550001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 127050 x 127270
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.20 hours.

(25·10¹⁹¹+11)/9 = 2(7)₁₉₀9_<192> = 3² · 19 · 33419237 · 25138963259580059_<17> · 3389122341921446988947_<22> · C144

C144 = P31 · P114

P31 = 2526416268926009103666694532857_<31>

P114 = 225821526905109989428395988313810618602302745969461692647476062511113200159315648162004578240008559799312133924557_<114>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [P-1]
Input number is 570519179446782359339252890837934249143440005001801732527646024358610926299288672350376351755659176142334448475296192648854650039135351195669349 (144 digits)
Using B1=30000000, B2=756268978042, polynomial x^1, x0=3676457812
Step 1 took 18456ms
********** Factor found in step 1: 2526416268926009103666694532857
Found probable prime factor of 31 digits: 2526416268926009103666694532857
Probable prime cofactor 225821526905109989428395988313810618602302745969461692647476062511113200159315648162004578240008559799312133924557 has 114 digits

(25·10¹³⁶+11)/9 = 2(7)₁₃₅9_<137> = C137

C137 = P68 · P69

P68 = 49939563665725420108333887821126316151365501830209825661485480290103_<68>

P69 = 556227883041001713698169637988173699800671023277860382280971907619493_<69>

Number: 27779_136
N=27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
  ( 137 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=49939563665725420108333887821126316151365501830209825661485480290103
 r2=556227883041001713698169637988173699800671023277860382280971907619493
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.731).
Factorization parameters were as follows:
n: 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
Y1: 1
Y0: -1000000000000000000000000000
c5: 250
c0: 11
skew: 0.54
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [500000, 1550001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 142483 x 142700
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 4.00 hours.

Sep 19, 2008 (3rd)

By Sinkiti Sibata / GGNFS, Msieve

(25·10¹⁷³-43)/9 = 2(7)₁₇₂3_<174> = 3 · 33037 · C169

C169 = P77 · P92

P77 = 46558850779493096424492483442855753081279943870049563681536791783611326923121_<77>

P92 = 60196797774643852813248874227286977777238841940686534272161886935039204136300928460553097083_<92>

Number: 27773_173
N=2802693724992965238750267657250736828180300650561267445367091218712128601041032557211387008281399418609213687459290873644477179907152362278433047570681133050597590356043
  ( 169 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=46558850779493096424492483442855753081279943870049563681536791783611326923121 (pp77)
 r2=60196797774643852813248874227286977777238841940686534272161886935039204136300928460553097083 (pp92)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 262.57 hours.
Scaled time: 265.45 units (timescale=1.011).
Factorization parameters were as follows:
name: 27773_173
n: 2802693724992965238750267657250736828180300650561267445367091218712128601041032557211387008281399418609213687459290873644477179907152362278433047570681133050597590356043
m: 50000000000000000000000000000000000
c5: 8
c0: -43
skew: 1.4
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 11000001)
Primes: RFBsize:501962, AFBsize:502386, largePrimes:6593939 encountered
Relations: rels:7149050, finalFF:1223519
Max relations in full relation-set: 28
Initial matrix: 1004413 x 1223519 with sparse part having weight 75368111.
Pruned matrix : 812967 x 818053 with weight 54796900.
Total sieving time: 255.78 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 6.48 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,174,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 262.57 hours.
 --------- CPU info (if available) ----------

(25·10¹⁰⁸+11)/9 = 2(7)₁₀₇9_<109> = 47 · 97² · 1489717 · 22665857 · C90

C90 = P33 · P57

P33 = 853359707941802590369203380773573_<33>

P57 = 217995797342499960244508687999226483457599274315394828629_<57>

Fri Sep 19 14:38:44 2008  Msieve v. 1.36
Fri Sep 19 14:38:44 2008  random seeds: e11317bc 9b0d859a
Fri Sep 19 14:38:44 2008  factoring 186028829952736151348531947356431309694958639565062282660203345428934749304330489787021417 (90 digits)
Fri Sep 19 14:38:45 2008  no P-1/P+1/ECM available, skipping
Fri Sep 19 14:38:45 2008  commencing quadratic sieve (90-digit input)
Fri Sep 19 14:38:46 2008  using multiplier of 1
Fri Sep 19 14:38:46 2008  using 64kb Pentium 4 sieve core
Fri Sep 19 14:38:46 2008  sieve interval: 18 blocks of size 65536
Fri Sep 19 14:38:46 2008  processing polynomials in batches of 6
Fri Sep 19 14:38:46 2008  using a sieve bound of 1572443 (59667 primes)
Fri Sep 19 14:38:46 2008  using large prime bound of 125795440 (26 bits)
Fri Sep 19 14:38:46 2008  using double large prime bound of 379661707918720 (42-49 bits)
Fri Sep 19 14:38:46 2008  using trial factoring cutoff of 49 bits
Fri Sep 19 14:38:46 2008  polynomial 'A' values have 11 factors
Fri Sep 19 16:27:20 2008  59783 relations (16226 full + 43557 combined from 632833 partial), need 59763
Fri Sep 19 16:27:22 2008  begin with 649059 relations
Fri Sep 19 16:27:23 2008  reduce to 145005 relations in 9 passes
Fri Sep 19 16:27:23 2008  attempting to read 145005 relations
Fri Sep 19 16:27:26 2008  recovered 145005 relations
Fri Sep 19 16:27:26 2008  recovered 120201 polynomials
Fri Sep 19 16:27:27 2008  attempting to build 59783 cycles
Fri Sep 19 16:27:27 2008  found 59783 cycles in 5 passes
Fri Sep 19 16:27:27 2008  distribution of cycle lengths:
Fri Sep 19 16:27:27 2008     length 1 : 16226
Fri Sep 19 16:27:27 2008     length 2 : 11495
Fri Sep 19 16:27:27 2008     length 3 : 10335
Fri Sep 19 16:27:27 2008     length 4 : 7992
Fri Sep 19 16:27:27 2008     length 5 : 5624
Fri Sep 19 16:27:27 2008     length 6 : 3481
Fri Sep 19 16:27:27 2008     length 7 : 2186
Fri Sep 19 16:27:27 2008     length 9+: 2444
Fri Sep 19 16:27:27 2008  largest cycle: 18 relations
Fri Sep 19 16:27:27 2008  matrix is 59667 x 59783 (14.6 MB) with weight 3583703 (59.95/col)
Fri Sep 19 16:27:27 2008  sparse part has weight 3583703 (59.95/col)
Fri Sep 19 16:27:28 2008  filtering completed in 3 passes
Fri Sep 19 16:27:28 2008  matrix is 55554 x 55618 (13.7 MB) with weight 3369862 (60.59/col)
Fri Sep 19 16:27:28 2008  sparse part has weight 3369862 (60.59/col)
Fri Sep 19 16:27:28 2008  saving the first 48 matrix rows for later
Fri Sep 19 16:27:29 2008  matrix is 55506 x 55618 (10.1 MB) with weight 2804439 (50.42/col)
Fri Sep 19 16:27:29 2008  sparse part has weight 2310918 (41.55/col)
Fri Sep 19 16:27:29 2008  matrix includes 64 packed rows
Fri Sep 19 16:27:29 2008  using block size 21845 for processor cache size 512 kB
Fri Sep 19 16:27:29 2008  commencing Lanczos iteration
Fri Sep 19 16:27:29 2008  memory use: 9.1 MB
Fri Sep 19 16:28:04 2008  lanczos halted after 879 iterations (dim = 55506)
Fri Sep 19 16:28:05 2008  recovered 17 nontrivial dependencies
Fri Sep 19 16:28:06 2008  prp33 factor: 853359707941802590369203380773573
Fri Sep 19 16:28:06 2008  prp57 factor: 217995797342499960244508687999226483457599274315394828629
Fri Sep 19 16:28:06 2008  elapsed time 01:49:22

(25·10¹³⁷+11)/9 = 2(7)₁₃₆9_<138> = 3² · 19 · 31 · C134

C134 = P45 · P90

P45 = 161921640164388497483372857632347906673665639_<45>

P90 = 323619588033082331955512247873525202849766126106862528717344406156559958159975949812820961_<90>

Number: 27779_137
N=52401014483640403278207466096543629084659078999769435536271982225575887149175208032027500052401014483640403278207466096543629084659079
  ( 134 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=161921640164388497483372857632347906673665639 (pp45)
 r2=323619588033082331955512247873525202849766126106862528717344406156559958159975949812820961 (pp90)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.21 hours.
Scaled time: 5.25 units (timescale=1.008).
Factorization parameters were as follows:
name: 27779_137
n: 52401014483640403278207466096543629084659078999769435536271982225575887149175208032027500052401014483640403278207466096543629084659079
m: 5000000000000000000000000000
c5: 4
c0: 55
skew: 1.69
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:63994, largePrimes:1557289 encountered
Relations: rels:1578648, finalFF:193359
Max relations in full relation-set: 28
Initial matrix: 142556 x 193359 with sparse part having weight 14877974.
Pruned matrix : 126678 x 127454 with weight 8126953.
Total sieving time: 5.09 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.21 hours.
 --------- CPU info (if available) ----------

(25·10¹³⁹+11)/9 = 2(7)₁₃₈9_<140> = 1579 · 23677 · C132

C132 = P30 · P103

P30 = 209083018584969192252595113529_<30>

P103 = 3553611393113190589659808998064869756016200551109239594585632907970680199445429803699384634763303281397_<103>

Number: 27779_139
N=742999796950043490304314795675635378579661200235868554740897886188462070872331423725779198524157510524138893921226513631533448720013
  ( 132 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=209083018584969192252595113529 (pp30)
 r2=3553611393113190589659808998064869756016200551109239594585632907970680199445429803699384634763303281397 (pp103)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.10 hours.
Scaled time: 10.19 units (timescale=1.009).
Factorization parameters were as follows:
name: 27779_137
n: 742999796950043490304314795675635378579661200235868554740897886188462070872331423725779198524157510524138893921226513631533448720013
m: 10000000000000000000000000000
c5: 5
c0: 22
skew: 1.34
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1950001)
Primes: RFBsize:100021, AFBsize:100104, largePrimes:2894835 encountered
Relations: rels:2976696, finalFF:348480
Max relations in full relation-set: 28
Initial matrix: 200190 x 348480 with sparse part having weight 35375015.
Pruned matrix : 163148 x 164212 with weight 16176754.
Total sieving time: 9.88 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 10.10 hours.
 --------- CPU info (if available) ----------

(25·10¹⁵⁵+11)/9 = 2(7)₁₅₄9_<156> = 3³ · 19 · 862257989 · 822143730045749087393_<21> · 182026023701860412223553_<24> · C100

C100 = P41 · P60

P41 = 18085812322923420183023124569529108930833_<41>

P60 = 232019056365966092443217013695946993609084795707320945808071_<60>

Number: 27779_155
N=4196253108776653175638038416478924297372907360500066045972590132987812392925813812223693780032153143
  ( 100 digits)
Divisors found:
 r1=18085812322923420183023124569529108930833 (pp41)
 r2=232019056365966092443217013695946993609084795707320945808071 (pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 7.29 hours.
Scaled time: 5.71 units (timescale=0.784).
Factorization parameters were as follows:
name: 27779_155
n: 4196253108776653175638038416478924297372907360500066045972590132987812392925813812223693780032153143
skew: 2549.76
# norm 8.24e+13
c5: 708000
c4: 19166104
c3: -4074259275762
c2: -16901136602923433
c1: 32379437717701640298
c0: 46739428509995733823168
# alpha -6.81
Y1: 50409368801
Y0: -5682843064049718825
# Murphy_E 3.68e-09
# M 1027250211033138229216287220548871958441136017879058543953306680295155783875246280193616482926558222
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1400001)
Primes: RFBsize:135072, AFBsize:135060, largePrimes:4208119 encountered
Relations: rels:4572216, finalFF:675038
Max relations in full relation-set: 28
Initial matrix: 270217 x 675038 with sparse part having weight 54174360.
Pruned matrix : 135288 x 136703 with weight 15301062.
Total sieving time: 6.89 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 7.29 hours.
 --------- CPU info (if available) ----------

Sep 19, 2008 (2nd)

Factorizations of 277...779 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Sep 19, 2008

By Serge Batalov / GMP-ECM 6.2.1

(7·10¹⁸⁹-61)/9 = (7)₁₈₈1_<189> = 3 · 1291 · 355909522613_<12> · C174

C174 = P40 · C134

P40 = 6586408395714765506229052421915313517957_<40>

C134 = [85668225182877184644786666541917164742621853107779269580528230063969136871950475692301384534838463105695144272049997293525583827839347_<134>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=272832663
Step 1 took 28102ms
Step 2 took 18633ms
********** Factor found in step 2: 6586408395714765506229052421915313517957
Found probable prime factor of 40 digits: 6586408395714765506229052421915313517957
Composite cofactor 85668225182877184644786666541917164742621853107779269580528230063969136871950475692301384534838463105695144272049997293525583827839347 has 134 digits

Sep 18, 2008

By Serge Batalov / GMP-ECM 6.2.1

(5·10¹⁸⁰-23)/9 = (5)₁₇₉3_<180> = 617 · 19195003 · 108827351 · 1035425066346613909_<19> · C144

C144 = P42 · P102

P42 = 687803100970957788662415682330278575034733_<42>

P102 = 605247890592415863871110605761674126376482105290280241337087884763077147497213529971623886197755952749_<102>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=1426785098
Step 1 took 67428ms
Step 2 took 43125ms
********** Factor found in step 2: 687803100970957788662415682330278575034733
Found probable prime factor of 42 digits: 687803100970957788662415682330278575034733
Probable prime cofactor 605247890592415863871110605761674126376482105290280241337087884763077147497213529971623886197755952749 has 102 digits

3·10¹⁸⁹-7 = 2(9)₁₈₈3_<190> = 29 · 4139 · 116881 · 184949 · C175

C175 = P33 · P142

P33 = 349757439117349435285448300528377_<33>

P142 = 3305711616124445048311225343825846971474411661265757514018027000415495130450466308113753852376938088222883119475153546917208332615074442720531_<142>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3188158830
Step 1 took 29325ms
Step 2 took 18759ms
********** Factor found in step 2: 349757439117349435285448300528377
Found probable prime factor of 33 digits: 349757439117349435285448300528377
Probable prime cofactor 3305711616124445048311225343825846971474411661265757514018027000415495130450466308113753852376938088222883119475153546917208332615074442720531 has 142 digits

(5·10¹⁸⁸-23)/9 = (5)₁₈₇3_<188> = 329994138355223_<15> · C174

C174 = P28 · C146

P28 = 6949099976695798019485329959_<28>

C146 = [24226613417251399107633278235282534498979801691191248382376457126126295340750015734646309207992878830271994380586380451824139683183787774912460129_<146>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2395590199
Step 1 took 25942ms
********** Factor found in step 1: 6949099976695798019485329959
Found probable prime factor of 28 digits: 6949099976695798019485329959
Composite cofactor 24226613417251399107633278235282534498979801691191248382376457126126295340750015734646309207992878830271994380586380451824139683183787774912460129 has 146 digits

(8·10¹⁸¹-17)/9 = (8)₁₈₀7_<181> = 7 · 1709 · 4253 · C174

C174 = P28 · C146

P28 = 3983165093026307702402046217_<28>

C146 = [43861520701364732252769870687031534361057141753068471924374557286056504583720673640378144134184647090935167172927062385446263634692674481022068849_<146>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2914738981
Step 1 took 25105ms
Step 2 took 16411ms
********** Factor found in step 2: 3983165093026307702402046217
Found probable prime factor of 28 digits: 3983165093026307702402046217
Composite cofactor 43861520701364732252769870687031534361057141753068471924374557286056504583720673640378144134184647090935167172927062385446263634692674481022068849 has 146 digits

Sep 17, 2008 (2nd)

By matsui / GMP-ECM

4·10¹⁸⁸+9 = 4(0)₁₈₇9_<189> = 337 · 1201 · 58693 · 876529 · C173

C173 = P37 · P136

P37 = 2430640727175969638994585027337101361_<37>

P136 = 7903395490385727731463723829241886338897947794113256415232279926080628572269461573229661036837524536596561491729907318379745124431713621_<136>

Input number is 19210314961910444414903654271569167794536732506063457824599929055888256292329337954197463698980821541562015442076418326664270192429185687422314470872745845677597780201338181 (173 digits)

Using B1=88000000, B2=582207787990, polynomial Dickson(30), sigma=101061817

Step 1 took 1763944ms

Step 2 took 402772ms

********** Factor found in step 2: 2430640727175969638994585027337101361

Found probable prime factor of 37 digits: 2430640727175969638994585027337101361
Probable prime cofactor 7903395490385727731463723829241886338897947794113256415232279926080628572269461573229661036837524536596561491729907318379745124431713621 has 136 digits

4·10¹⁹⁰+9 = 4(0)₁₈₉9_<191> = 2789 · 17155258129_<11> · C177

C177 = P34 · C144

P34 = 1411411376393248424585966404607993_<34>

C144 = [592325740845773596110618934810993533587964947739141920784957245331142523666993635952898907996987364689434079735407153529578722036865973825841773_<144>]

Input number is 836015289160283879500272797444715885812605958351520507116372858766515218453575577239195951346683064794135993251110322481581764211436292340215488177214241765662632022089309091589 (177 digits)

Using B1=88000000, B2=582207787990, polynomial Dickson(30), sigma=2898798771

Step 1 took 1923663ms

********** Factor found in step 1: 1411411376393248424585966404607993

Found probable prime factor of 34 digits: 1411411376393248424585966404607993

Composite cofactor 592325740845773596110618934810993533587964947739141920784957245331142523666993635952898907996987364689434079735407153529578722036865973825841773 has 144 digits

4·10¹⁹²+9 = 4(0)₁₉₁9_<193> = 13 · 3084049 · 20054833 · C178

C178 = P33 · C146

P33 = 362793721871669762743297557966121_<33>

C146 = [13712497346156392212676019147625431370510365650834689585981115102219563918727772856984851299023907414810459127022107546442249298162322016417074149_<146>]

Input number is 4974807948367471887114396159851198874837557117234981819868633168970552843782088694722828194509779833777082181924438616285128530903647465329505197651600423635188354862434086906029 (178 digits)

Using B1=88000000, B2=582207787990, polynomial Dickson(30), sigma=2110858031

Step 1 took 1929223ms

Step 2 took 431804ms

********** Factor found in step 2: 362793721871669762743297557966121

Found probable prime factor of 33 digits: 362793721871669762743297557966121

Composite cofactor 13712497346156392212676019147625431370510365650834689585981115102219563918727772856984851299023907414810459127022107546442249298162322016417074149 has 146 digits

Sep 17, 2008

By Robert Backstrom / GGNFS, Msieve

9·10¹⁹³-1 = 8(9)₁₉₃_<194> = 43 · C193

C193 = P43 · P66 · P85

P43 = 1821585162697457488304296102273254935173081_<43>

P66 = 577907847913674910737796883693373565504125011795363899114213268519_<66>

P85 = 1988227065562338941228938824773608620242017418041162968604820660552549013425070142387_<85>

Number: n
N=2093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093
  ( 193 digits)
SNFS difficulty: 193 digits.
Divisors found:

Wed Sep 17 08:14:24 2008  prp43 factor: 1821585162697457488304296102273254935173081
Wed Sep 17 08:14:24 2008  prp66 factor: 577907847913674910737796883693373565504125011795363899114213268519
Wed Sep 17 08:14:24 2008  prp85 factor: 1988227065562338941228938824773608620242017418041162968604820660552549013425070142387
Wed Sep 17 08:14:25 2008  elapsed time 09:59:33 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 161.42 hours.
Scaled time: 330.10 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_8_9_193
n: 2093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093
type: snfs
skew: 0.16
deg: 5
c5: 9000
c0: -1
m: 100000000000000000000000000000000000000
rlim: 9500000
alim: 9500000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9500000/9500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 12100001)
Primes: RFBsize:633578, AFBsize:634548, largePrimes:15156746 encountered
Relations: rels:15251348, finalFF:1305201
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 160.82 hours.
Total relation processing time: 0.59 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,193,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,52,52,2.5,2.5,100000
total time: 161.42 hours.
 --------- CPU info (if available) ----------

Sep 16, 2008

By Sinkiti Sibata / GGNFS

(25·10¹⁷⁰-43)/9 = 2(7)₁₆₉3_<171> = 3² · 7 · 13 · 331 · 78778604771093191_<17> · C149

C149 = P44 · P105

P44 = 17619764491236916651312474862954886430331357_<44>

P105 = 738205403106764575938062723471690111389545121101186209390350592296561164036335958186089930067485740613911_<105>

Number: 27773_170
N=13007005348899804709094980881302261626646867240510572909883953359395253502607313995996074802578303581068987576332763598695119953893377355680333707227
  ( 149 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=17619764491236916651312474862954886430331357 (pp44)
 r2=738205403106764575938062723471690111389545121101186209390350592296561164036335958186089930067485740613911 (pp105)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 183.30 hours.
Scaled time: 184.95 units (timescale=1.009).
Factorization parameters were as follows:
name: 27773_170
n: 13007005348899804709094980881302261626646867240510572909883953359395253502607313995996074802578303581068987576332763598695119953893377355680333707227
m: 10000000000000000000000000000000000
c5: 25
c0: -43
skew: 1.11
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 8700001)
Primes: RFBsize:412849, AFBsize:411971, largePrimes:6323654 encountered
Relations: rels:6647667, finalFF:972289
Max relations in full relation-set: 28
Initial matrix: 824884 x 972289 with sparse part having weight 73248063.
Pruned matrix : 707814 x 712002 with weight 55447414.
Total sieving time: 178.63 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 4.40 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 183.30 hours.
 --------- CPU info (if available) ----------

Sep 15, 2008 (4th)

By Chris Monico / GGNFS-0.91.4

(16·10¹⁶⁹-1)/3 = 5(3)₁₆₉_<170> = 2477 · 2837 · 4254557 · 4055471607565486774482757_<25> · C132

C132 = P49 · P84

P49 = 2359339499068883240543885710901550432466257806573_<49>

P84 = 186434909099572698920884170268392055319140036876977757831249406175990968275589112521_<84>

N=439863245043938633275360032107760843619767204363929593692974356134399238277245461761858058337741355248435942840638766855441150400533
r1=2359339499068883240543885710901550432466257806573 (pp49)
r2=186434909099572698920884170268392055319140036876977757831249406175990968275589112521 (pp84)
Version: GGNFS-0.91.4

Sep 15, 2008 (3rd)

By Sinkiti Sibata / Msieve

(25·10¹⁰⁸-43)/9 = 2(7)₁₀₇3_<109> = C109

C109 = P47 · P62

P47 = 98977571642142365276984929935548439173343598577_<47>

P62 = 28064719427760380820022102182615812657550236296462577237567549_<62>

Fri Sep 12 05:02:50 2008  Msieve v. 1.36
Fri Sep 12 05:02:50 2008  random seeds: 9881df76 48087ea0
Fri Sep 12 05:02:50 2008  factoring 2777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773 (109 digits)
Fri Sep 12 05:02:52 2008  no P-1/P+1/ECM available, skipping
Fri Sep 12 05:02:52 2008  commencing quadratic sieve (109-digit input)
Fri Sep 12 05:02:52 2008  using multiplier of 5
Fri Sep 12 05:02:52 2008  using 32kb Intel Core sieve core
Fri Sep 12 05:02:52 2008  sieve interval: 50 blocks of size 32768
Fri Sep 12 05:02:52 2008  processing polynomials in batches of 5
Fri Sep 12 05:02:52 2008  using a sieve bound of 5812619 (200667 primes)
Fri Sep 12 05:02:52 2008  using large prime bound of 871892850 (29 bits)
Fri Sep 12 05:02:52 2008  using double large prime bound of 12383220374195100 (45-54 bits)
Fri Sep 12 05:02:52 2008  using trial factoring cutoff of 54 bits
Fri Sep 12 05:02:52 2008  polynomial 'A' values have 14 factors
Mon Sep 15 10:59:05 2008  201065 relations (48104 full + 152961 combined from 2940810 partial), need 200763
Mon Sep 15 10:59:18 2008  begin with 2988914 relations
Mon Sep 15 10:59:21 2008  reduce to 528487 relations in 12 passes
Mon Sep 15 10:59:21 2008  attempting to read 528487 relations
Mon Sep 15 10:59:38 2008  recovered 528487 relations
Mon Sep 15 10:59:38 2008  recovered 519328 polynomials
Mon Sep 15 10:59:39 2008  attempting to build 201065 cycles
Mon Sep 15 10:59:39 2008  found 201065 cycles in 7 passes
Mon Sep 15 10:59:39 2008  distribution of cycle lengths:
Mon Sep 15 10:59:39 2008     length 1 : 48104
Mon Sep 15 10:59:39 2008     length 2 : 34121
Mon Sep 15 10:59:39 2008     length 3 : 33987
Mon Sep 15 10:59:39 2008     length 4 : 27116
Mon Sep 15 10:59:39 2008     length 5 : 21113
Mon Sep 15 10:59:39 2008     length 6 : 14366
Mon Sep 15 10:59:39 2008     length 7 : 9281
Mon Sep 15 10:59:39 2008     length 9+: 12977
Mon Sep 15 10:59:39 2008  largest cycle: 21 relations
Mon Sep 15 10:59:40 2008  matrix is 200667 x 201065 (61.2 MB) with weight 15238112 (75.79/col)
Mon Sep 15 10:59:40 2008  sparse part has weight 15238112 (75.79/col)
Mon Sep 15 10:59:42 2008  filtering completed in 3 passes
Mon Sep 15 10:59:42 2008  matrix is 192791 x 192855 (59.0 MB) with weight 14697710 (76.21/col)
Mon Sep 15 10:59:42 2008  sparse part has weight 14697710 (76.21/col)
Mon Sep 15 10:59:44 2008  saving the first 48 matrix rows for later
Mon Sep 15 10:59:44 2008  matrix is 192743 x 192855 (40.9 MB) with weight 12213594 (63.33/col)
Mon Sep 15 10:59:44 2008  sparse part has weight 9571959 (49.63/col)
Mon Sep 15 10:59:44 2008  matrix includes 64 packed rows
Mon Sep 15 10:59:44 2008  using block size 65536 for processor cache size 2048 kB
Mon Sep 15 10:59:46 2008  commencing Lanczos iteration
Mon Sep 15 10:59:46 2008  memory use: 36.9 MB
Mon Sep 15 11:04:34 2008  lanczos halted after 3049 iterations (dim = 192738)
Mon Sep 15 11:04:35 2008  recovered 15 nontrivial dependencies
Mon Sep 15 11:04:38 2008  prp47 factor: 98977571642142365276984929935548439173343598577
Mon Sep 15 11:04:38 2008  prp62 factor: 28064719427760380820022102182615812657550236296462577237567549
Mon Sep 15 11:04:38 2008  elapsed time 78:01:48

Sep 15, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(16·10¹⁶⁶-7)/9 = 1(7)₁₆₆_<167> = 73867 · 261427 · 45020051 · 2159829807661_<13> · C136

C136 = P65 · P72

P65 = 11534998653303754286376078599436060408108912634496357909792199251_<65>

P72 = 820792749689864725133726681975155104671578537741228360509241468320423773_<72>

Number: n
N=9467843262314075088114456690203792146385655753244537824265820827096598765879588060136679376473184972544225902520642437741750597973194023
  ( 136 digits)
SNFS difficulty: 167 digits.
Divisors found:

Mon Sep 15 00:12:37 2008  prp65 factor: 11534998653303754286376078599436060408108912634496357909792199251
Mon Sep 15 00:12:37 2008  prp72 factor: 820792749689864725133726681975155104671578537741228360509241468320423773
Mon Sep 15 00:12:37 2008  elapsed time 03:35:17 (Msieve 1.36)

Version: GGNFS-0.77.1-20050930-k8
Total time: 40.54 hours.
Scaled time: 34.09 units (timescale=0.841).
Factorization parameters were as follows:
name: KA_1_7_166
n: 9467843262314075088114456690203792146385655753244537824265820827096598765879588060136679376473184972544225902520642437741750597973194023
type: snfs
skew: 1.07
deg: 5
c5: 5
c0: -7
m: 2000000000000000000000000000000000
rlim: 5400000
alim: 5400000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 4700001)
Primes: RFBsize:374362, AFBsize:373867, largePrimes:14071031 encountered
Relations: rels:13318773, finalFF:814933
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 40.16 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5400000,5400000,28,28,52,52,2.5,2.5,100000
total time: 40.54 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(29·10¹⁶⁶+7)/9 = 3(2)₁₆₅3_<167> = 3 · 2309 · 63281501 · 412394155289780003_<18> · C138

C138 = P53 · P85

P53 = 79353768896243354879317921547141159657539357186424707_<53>

P85 = 2246226099411522565081310175327100561059317639528459166402607843175730179074495466669_<85>

Number: n
N=178246506781412113310294463823584874541396179184968819439212220708712747355434245310443530401773459134403743276598581768969540379596590983
  ( 138 digits)
SNFS difficulty: 167 digits.
Divisors found:

Mon Sep 15 03:08:09 2008  prp53 factor: 79353768896243354879317921547141159657539357186424707
Mon Sep 15 03:08:09 2008  prp85 factor: 2246226099411522565081310175327100561059317639528459166402607843175730179074495466669
Mon Sep 15 03:08:09 2008  elapsed time 03:50:18 (Msieve 1.36)

Version: GGNFS-0.77.1-20050930-k8
Total time: 43.04 hours.
Scaled time: 36.20 units (timescale=0.841).
Factorization parameters were as follows:
name: KA_3_2_165_3
n: 178246506781412113310294463823584874541396179184968819439212220708712747355434245310443530401773459134403743276598581768969540379596590983
type: snfs
skew: 0.47
deg: 5
c5: 290
c0: 7
m: 1000000000000000000000000000000000
rlim: 5400000
alim: 5400000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 4900001)
Primes: RFBsize:374362, AFBsize:374497, largePrimes:14043887 encountered
Relations: rels:13214911, finalFF:755528
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 42.60 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5400000,5400000,28,28,52,52,2.5,2.5,100000
total time: 43.04 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

Sep 15, 2008

By Serge Batalov / Msieve-1.37

(25·10¹⁶⁹-43)/9 = 2(7)₁₆₈3_<170> = 6761 · C166

C166 = P79 · P88

P79 = 3080145577490737926404037860940972976068672736877912330103917098426035030034777_<79>

P88 = 1333875575134097511706641124139988902844113672229182918543377260872116052419579028419309_<88>

Number: 27773_169
N=4108530953672204966392216798961363374911666584496047593222567338822330687439399168433334976745714802215319890220052917878683297999967131752370622360268862265608309093
  ( 166 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=3080145577490737926404037860940972976068672736877912330103917098426035030034777
 r2=1333875575134097511706641124139988902844113672229182918543377260872116052419579028419309
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.727).
Factorization parameters were as follows:
n: 4108530953672204966392216798961363374911666584496047593222567338822330687439399168433334976745714802215319890220052917878683297999967131752370622360268862265608309093
Y1: 1
Y0: -10000000000000000000000000000000000
c5: 5
c0: -86
skew: 1.77
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [3000000, 5500001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 996680 x 996928
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000
total time: 42.50 hours.

Sep 14, 2008 (2nd)

By Wataru Sakai / GGNFS

(25·10¹⁸⁴-61)/9 = 2(7)₁₈₃1_<185> = 3 · 269 · C182

C182 = P75 · P107

P75 = 509575232245114400105218066214409542599718583695395748663216501642189269183_<75>

P107 = 67548491293142657192636214891586037775613013390913300305025073464846830376816916705229553974495985164761891_<107>

Number: 27771_184
N=34421038138510257469365276056725870852264904309513974941484235164532562302079030703566019551149662673826242599476800220294644086465647803937766763045573454495387580889439625499105053
  ( 182 digits)
SNFS difficulty: 185 digits.
Divisors found:
 r1=509575232245114400105218066214409542599718583695395748663216501642189269183 (pp75)
 r2=67548491293142657192636214891586037775613013390913300305025073464846830376816916705229553974495985164761891 (pp107)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 835.22 hours.
Scaled time: 1672.94 units (timescale=2.003).
Factorization parameters were as follows:
n: 34421038138510257469365276056725870852264904309513974941484235164532562302079030703566019551149662673826242599476800220294644086465647803937766763045573454495387580889439625499105053
m: 10000000000000000000000000000000000000
c5: 5
c0: -122
skew: 1.89
type: snfsFactor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 15000001)
Primes: RFBsize:501962, AFBsize:500647, largePrimes:6989854 encountered
Relations: rels:7537555, finalFF:1185130
Max relations in full relation-set: 32
Initial matrix: 1002674 x 1185130 with sparse part having weight 117077372.
Pruned matrix : 861922 x 866999 with weight 96601519.
Total sieving time: 826.03 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 8.80 hours.
Time per square root: 0.26 hours.
Prototype def-par.txt line would be:
snfs,185,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 835.22 hours.
 --------- CPU info (if available) ----------

Sep 14, 2008

By Sinkiti Sibata / GMP-ECM

(25·10¹⁶⁸-43)/9 = 2(7)₁₆₇3_<169> = 17 · 8971 · 10337 · 8615692218787_<13> · C147

C147 = P40 · P108

P40 = 1985140693063465171692545141141610284639_<40>

P108 = 103022417519537981589629426097797637160177611134278915004628187551244055578499294100173927259247731956871779_<108>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 204513993315809305228716749061373306143831113687280897005385595482580547491319916444125287840919440008825849540473546379899733573903628096216302781

Run 377 out of 2350:
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3964083566
Step 1 took 54756ms
Step 2 took 18455ms
********** Factor found in step 2: 1985140693063465171692545141141610284639
Found probable prime factor of 40 digits: 1985140693063465171692545141141610284639
Probable prime cofactor 103022417519537981589629426097797637160177611134278915004628187551244055578499294100173927259247731956871779 has 108 digits

Sep 13, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(25·10¹⁶⁶-43)/9 = 2(7)₁₆₅3_<167> = 503 · 706751 · 2776343 · 2440785247913_<13> · C140

C140 = P47 · P93

P47 = 64438863979153398772474615309331228867392153447_<47>

P93 = 178942095075642967256744351697024985709989506953109244293032020741491038953890828802470902717_<93>

Number: 27773_166
N=11530825324724092380753939585475456118157613190482884095671427620741334156187743828513545625362299892188371422291850861036994978256673215499
  ( 140 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=64438863979153398772474615309331228867392153447 (pp47)
 r2=178942095075642967256744351697024985709989506953109244293032020741491038953890828802470902717 (pp93)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 106.94 hours.
Scaled time: 107.80 units (timescale=1.008).
Factorization parameters were as follows:
name: 27773_166
n: 11530825324724092380753939585475456118157613190482884095671427620741334156187743828513545625362299892188371422291850861036994978256673215499
m: 1000000000000000000000000000000000
c5: 250
c0: -43
skew: 0.7
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 6450001)
Primes: RFBsize:380800, AFBsize:381622, largePrimes:6131252 encountered
Relations: rels:6442154, finalFF:949844
Max relations in full relation-set: 28
Initial matrix: 762488 x 949844 with sparse part having weight 61604041.
Pruned matrix : 608545 x 612421 with weight 43738158.
Total sieving time: 103.72 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 3.01 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 106.94 hours.
 --------- CPU info (if available) ----------

Sep 13, 2008

By Robert Backstrom / GGNFS

(25·10¹⁵⁰-43)/9 = 2(7)₁₄₉3_<151> = 4024156931_<10> · C141

C141 = P55 · P86

P55 = 7093738736322567193255076634889767778935410319128407547_<55>

P86 = 97307743410819327218171555923430401617608483828797046105780850465138527911441189609789_<86>

Number: n
N=690275708777466108659015857296291355238347134374660344919281622761788307051929376602579065219307615957827509927638499885773410405245892677583
  ( 141 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=7093738736322567193255076634889767778935410319128407547 (pp55)
 r2=97307743410819327218171555923430401617608483828797046105780850465138527911441189609789 (pp86)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 14.80 hours.
Scaled time: 26.61 units (timescale=1.798).
Factorization parameters were as follows:
name: KA_2_7_149_3
n: 690275708777466108659015857296291355238347134374660344919281622761788307051929376602579065219307615957827509927638499885773410405245892677583
type: snfs
skew: 1.11
deg: 5
c5: 25
c0: -43
m: 1000000000000000000000000000000
rlim: 1600000
alim: 1600000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved algebraic special-q in [100000, 960001)
Primes: RFBsize:121127, AFBsize:120625, largePrimes:10273485 encountered
Relations: rels:9213877, finalFF:294423
Max relations in full relation-set: 48
Initial matrix: 241816 x 294423 with sparse part having weight 47230275.
Pruned matrix : 227056 x 228329 with weight 31481125.
Total sieving time: 13.74 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.78 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,1600000,1600000,28,28,52,52,2.5,2.5,100000
total time: 14.80 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Sep 12, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve

(13·10¹⁹³+41)/9 = 1(4)₁₉₂9_<194> = C194

C194 = P49 · P145

P49 = 1901287922333370738124450534127671428882960582469_<49>

P145 = 7597189397131069455903065721394056844398540195601305071590900567978034358366761385835754036511022197005546476527689112466320193426394369847525421_<145>

Number: n
N=14444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449
  ( 194 digits)
SNFS difficulty: 194 digits.
Divisors found:

Fri Sep 12 22:18:39 2008  prp49 factor: 1901287922333370738124450534127671428882960582469
Fri Sep 12 22:18:39 2008  prp145 factor: 7597189397131069455903065721394056844398540195601305071590900567978034358366761385835754036511022197005546476527689112466320193426394369847525421
Fri Sep 12 22:18:39 2008  elapsed time 24:07:01 (Msieve 1.37)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 249.78 hours.
Scaled time: 320.72 units (timescale=1.284).
Factorization parameters were as follows:
name: KA_1_4_192_9
n: 14444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449
type: snfs
skew: 0.32
deg: 5
c5: 13000
c0: 41
m: 100000000000000000000000000000000000000
rlim: 9500000
alim: 9500000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9500000/9500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 20100001)
Primes: RFBsize:633578, AFBsize:632714, largePrimes:15887207 encountered
Relations: rels:16490078, finalFF:1303499
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 248.58 hours.
Total relation processing time: 1.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,194,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,52,52,2.5,2.5,100000
total time: 249.78 hours.
 --------- CPU info (if available) ----------

Sep 12, 2008 (3rd)

By Jo Yeong Uk / GGNFS, GMP-ECM

(25·10¹⁵⁶-43)/9 = 2(7)₁₅₅3_<157> = C157

C157 = P39 · P50 · P69

P39 = 372185119464374581000505742262872837559_<39>

P50 = 27261215972898031404791163916223415134863840191709_<50>

P69 = 273774673963716145379187767741510557645709906000665535557462756307383_<69>

Number: 27773_156
N=2777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773
  ( 157 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=372185119464374581000505742262872837559 (pp39)
 r2=27261215972898031404791163916223415134863840191709 (pp50)
 r3=273774673963716145379187767741510557645709906000665535557462756307383 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.15 hours.
Scaled time: 57.46 units (timescale=2.379).
Factorization parameters were as follows:
n: 2777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773
m: 50000000000000000000000000000000
c5: 2
c0: -1075
skew: 3.52
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:283717, largePrimes:5772871 encountered
Relations: rels:5900578, finalFF:739057
Max relations in full relation-set: 28
Initial matrix: 566928 x 739057 with sparse part having weight 46097498.
Pruned matrix : 429064 x 431962 with weight 29205104.
Total sieving time: 23.11 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.93 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 24.15 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.05 BogoMIPS (lpj=2672026)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(25·10¹⁸⁵-43)/9 = 2(7)₁₈₄3_<186> = 3 · 1106257 · 527014997 · 6161874197_<10> · 7380221741_<10> · 645660194219364791_<18> · 773333185615761311050817_<24> · C109

C109 = P36 · P74

P36 = 207427746518315298219866961491334487_<36>

P74 = 33719217843231569076697258173474898117809420616890018677139524636324971843_<74>

Number: 27773_185
N=6994301371581692181777843367355613443324859575717902716265870548989008052704863600572322946143570728769849541
  ( 109 digits)
Divisors found:
 r1=207427746518315298219866961491334487 (pp36)
 r2=33719217843231569076697258173474898117809420616890018677139524636324971843 (pp74)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.43 hours.
Scaled time: 27.16 units (timescale=2.377).
Factorization parameters were as follows:
name: 27773_185
n: 6994301371581692181777843367355613443324859575717902716265870548989008052704863600572322946143570728769849541
skew: 21151.42
# norm 1.25e+15
c5: 16560
c4: -2088178530
c3: -65952207601223
c2: 745789390304980316
c1: 6183343412064671125560
c0: -39578050847778957024291000
# alpha -6.06
Y1: 210305389327
Y0: -841665524867103496247
# Murphy_E 1.19e-09
# M 3656899472026595564392796563244510379395325061944130045086403262223357093135654178911921285543656665588495754
type: gnfs
rlim: 2000000
alim: 2000000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved algebraic special-q in [1000000, 1650001)
Primes: RFBsize:148933, AFBsize:148957, largePrimes:4996228 encountered
Relations: rels:5005800, finalFF:346194
Max relations in full relation-set: 28
Initial matrix: 297968 x 346194 with sparse part having weight 32876209.
Pruned matrix : 268177 x 269730 with weight 22653877.
Polynomial selection time: 0.68 hours.
Total sieving time: 10.27 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.33 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,26,26,50,50,2.6,2.6,50000
total time: 11.43 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.05 BogoMIPS (lpj=2672026)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(23·10¹⁶⁷+31)/9 = 2(5)₁₆₆9_<168> = 37 · 89 · 42499349 · 111504861389_<12> · 186436563074621_<15> · C131

C131 = P38 · P94

P38 = 55483666228939118598781075378752414371_<38>

P94 = 1583147127896190823350447145282876632629418105166606868157240854518223554213826164611612094613_<94>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 87838806835495842387786872741538203556807416279684160572753784510959133212549527350596610907585322642508289465712809312178232883423 (131 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3374304280
Step 1 took 3886ms
Step 2 took 2369ms
********** Factor found in step 2: 55483666228939118598781075378752414371
Found probable prime factor of 38 digits: 55483666228939118598781075378752414371
Probable prime cofactor 1583147127896190823350447145282876632629418105166606868157240854518223554213826164611612094613 has 94 digits

Sep 12, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(25·10¹³⁸-43)/9 = 2(7)₁₃₇3_<139> = 3461369355503102471_<19> · C120

C120 = P48 · P73

P48 = 790851346784577684398460172607720171516872020779_<48>

P73 = 1014739803995546828170875314780552789730502310354605465076404664637362497_<73>

Number: 27773_138
N=802508340625796592750740934904214903221912043435135793932312557736238617400120237419203039842903464308882342049139325163
  ( 120 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=790851346784577684398460172607720171516872020779 (pp48)
 r2=1014739803995546828170875314780552789730502310354605465076404664637362497 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.93 hours.
Scaled time: 8.46 units (timescale=0.774).
Factorization parameters were as follows:
name: 27773_142
n: 802508340625796592750740934904214903221912043435135793932312557736238617400120237419203039842903464308882342049139325163
m: 5000000000000000000000000000
c5: 8
c0: -43
skew: 1.4
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1825001)
Primes: RFBsize:78498, AFBsize:64453, largePrimes:1658794 encountered
Relations: rels:1698186, finalFF:193639
Max relations in full relation-set: 28
Initial matrix: 143016 x 193639 with sparse part having weight 20004298.
Pruned matrix : 130828 x 131607 with weight 12027837.
Total sieving time: 10.71 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 10.93 hours.
 --------- CPU info (if available) ----------

(25·10¹⁵⁸-43)/9 = 2(7)₁₅₇3_<159> = 3 · 7 · 13 · 18731 · 43991 · 3802871 · 1406979953_<10> · 31936685952781180337671_<23> · C109

C109 = P52 · P58

P52 = 1060954734369655295158543412841251294725874914494979_<52>

P58 = 6811203372630868140845047043796262908156716759170685398043_<58>

Number: 27773_158
N=7226378464947282981654061338531266785619495339921092659976461093024228582184017894788462297005065080939926097
  ( 109 digits)
Divisors found:
 r1=1060954734369655295158543412841251294725874914494979 (pp52)
 r2=6811203372630868140845047043796262908156716759170685398043 (pp58)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 21.60 hours.
Scaled time: 21.65 units (timescale=1.002).
Factorization parameters were as follows:
name: 27773_158
n: 7226378464947282981654061338531266785619495339921092659976461093024228582184017894788462297005065080939926097
skew: 13387.42
# norm 4.83e+14
c5: 114000
c4: 25870285
c3: -58382673621146
c2: 61359297300806952
c1: 4190972551164436333248
c0: -10579597973151794333285760
# alpha -5.46
Y1: 423910963663
Y0: -575974366622446883713
# Murphy_E 1.16e-09
# M 4576898731503046020234271183227462729024026786633249131730637009994011599613654968105344173860276081349930103
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2900001)
Primes: RFBsize:230209, AFBsize:230748, largePrimes:8157077 encountered
Relations: rels:8862586, finalFF:1267055
Max relations in full relation-set: 28
Initial matrix: 461037 x 1267055 with sparse part having weight 112957061.
Pruned matrix : 231027 x 233396 with weight 44419779.
Total sieving time: 20.70 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.55 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 21.60 hours.
 --------- CPU info (if available) ----------

(25·10¹⁵²-43)/9 = 2(7)₁₅₁3_<153> = 3³ · 7 · 13 · 17² · 71593 · 19123127327388755233_<20> · C123

C123 = P43 · P81

P43 = 1979428177393314368570122123308590554452839_<43>

P81 = 144352820453911733686418927078964022953285009748700229868308507688975473906555211_<81>

Number: 27773_152
N=285736040292670853957964209651635759654923438991468283221845678871226287254773670813818454574097166010637334422447449194029
  ( 123 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=1979428177393314368570122123308590554452839 (pp43)
 r2=144352820453911733686418927078964022953285009748700229868308507688975473906555211 (pp81)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 31.41 hours.
Scaled time: 31.60 units (timescale=1.006).
Factorization parameters were as follows:
name: 27773_152
n: 285736040292670853957964209651635759654923438991468283221845678871226287254773670813818454574097166010637334422447449194029
m: 5000000000000000000000000000000
c5: 4
c0: -215
skew: 2.22
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2500001)
Primes: RFBsize:176302, AFBsize:176203, largePrimes:6287534 encountered
Relations: rels:6809416, finalFF:1013312
Max relations in full relation-set: 28
Initial matrix: 352569 x 1013312 with sparse part having weight 97004807.
Pruned matrix : 226092 x 227918 with weight 43662774.
Total sieving time: 30.70 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.56 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 31.41 hours.
 --------- CPU info (if available) ----------

Sep 12, 2008

By Serge Batalov / GMP-ECM 6.2.1, Msieve 1.37

(25·10¹⁹⁷-43)/9 = 2(7)₁₉₆3_<198> = 3² · 557 · 69708090293108587957264033909_<29> · C165

C165 = P39 · C127

P39 = 295129451897746307965079731115042417503_<39>

C127 = [2693419861220489027602411855507083936235406613469644223236807794490616222429689028593525007468377268250369054863714727544458923_<127>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3572283450
Step 1 took 24483ms
Step 2 took 20195ms
********** Factor found in step 2: 295129451897746307965079731115042417503
Found probable prime factor of 39 digits: 295129451897746307965079731115042417503
Composite cofactor 2693419861220489027602411855507083936235406613469644223236807794490616222429689028593525007468377268250369054863714727544458923 has 127 digits

(25·10¹⁵⁹-43)/9 = 2(7)₁₅₈3_<160> = 14804843 · C153

C153 = P52 · P101

P52 = 7089429201080214479664670394561412242126294491529591_<52>

P101 = 26465641374720917002970020698949335866709819281304228891957159307035545316434566546736730357665451121_<101>

Number: 27773_159
N=187626290787263179878218078893357921983892553117772189666434002561038828833090481120115747109089760545098504440592701846130876077360481146458478335621511
  ( 153 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=7089429201080214479664670394561412242126294491529591
 r2=26465641374720917002970020698949335866709819281304228891957159307035545316434566546736730357665451121
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.726).
Factorization parameters were as follows:
n: 187626290787263179878218078893357921983892553117772189666434002561038828833090481120115747109089760545098504440592701846130876077360481146458478335621511
Y1: 1
Y0: -100000000000000000000000000000000
c5: 5
c0: -86
skew: 1.77
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2000000, 3200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 653896 x 654144
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,52,52,2.5,2.5,100000
total time: 18.00 hours.

Sep 11, 2008 (4th)

By Robert Backstrom / GGNFS

(25·10¹²²-43)/9 = 2(7)₁₂₁3_<123> = 3 · 7² · 13 · 53 · 163 · 15187 · C112

C112 = P41 · P71

P41 = 12296099279101296181724216494604921968343_<41>

P71 = 90101907275351747216622783339526222453849108310187602759487276953447057_<71>

Number: n
N=1107901997094104452594768197905015821872713125836258972221023391495310813044300088873487367827302532099280516551
  ( 112 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=12296099279101296181724216494604921968343 (pp41)
 r2=90101907275351747216622783339526222453849108310187602759487276953447057 (pp71)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.58 hours.
Scaled time: 2.87 units (timescale=1.813).
Factorization parameters were as follows:
name: KA_2_7_121_3
n: 1107901997094104452594768197905015821872713125836258972221023391495310813044300088873487367827302532099280516551
type: snfs
skew: 2.22
deg: 5
c5: 4
c0: -215
m: 5000000000000000000000000
rlim: 600000
alim: 600000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved algebraic special-q in [100000, 260001)
Primes: RFBsize:49098, AFBsize:49151, largePrimes:4627065 encountered
Relations: rels:3986750, finalFF:176484
Max relations in full relation-set: 48
Initial matrix: 98313 x 176484 with sparse part having weight 18651096.
Pruned matrix : 80127 x 80682 with weight 4849535.
Total sieving time: 1.44 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.03 hours.
Total square root time: 0.05 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,600000,600000,28,28,52,52,2.5,2.5,50000
total time: 1.58 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Sep 11, 2008 (3rd)

By Sinkiti Sibata / Msieve, GGNFS

(25·10¹¹¹-43)/9 = 2(7)₁₁₀3_<112> = 23 · 595207 · 4435129 · 6200659 · C91

C91 = P32 · P59

P32 = 80335719249839503097507848265209_<32>

P59 = 91843588104175473506416389257508387935075613929940942541007_<59>

Wed Sep 10 21:25:51 2008  Msieve v. 1.36
Wed Sep 10 21:25:51 2008  random seeds: e69762f8 0dfdb476
Wed Sep 10 21:25:51 2008  factoring 7378320708834939980942794923012846889957608886051853826338735120290578568531951753293925463 (91 digits)
Wed Sep 10 21:25:53 2008  no P-1/P+1/ECM available, skipping
Wed Sep 10 21:25:53 2008  commencing quadratic sieve (91-digit input)
Wed Sep 10 21:25:53 2008  using multiplier of 15
Wed Sep 10 21:25:53 2008  using 64kb Pentium 4 sieve core
Wed Sep 10 21:25:53 2008  sieve interval: 18 blocks of size 65536
Wed Sep 10 21:25:53 2008  processing polynomials in batches of 6
Wed Sep 10 21:25:53 2008  using a sieve bound of 1719863 (64695 primes)
Wed Sep 10 21:25:53 2008  using large prime bound of 165106848 (27 bits)
Wed Sep 10 21:25:53 2008  using double large prime bound of 619408411789728 (42-50 bits)
Wed Sep 10 21:25:53 2008  using trial factoring cutoff of 50 bits
Wed Sep 10 21:25:53 2008  polynomial 'A' values have 12 factors
Thu Sep 11 00:35:10 2008  64893 relations (16878 full + 48015 combined from 766514 partial), need 64791
Thu Sep 11 00:35:13 2008  begin with 783392 relations
Thu Sep 11 00:35:13 2008  reduce to 162113 relations in 11 passes
Thu Sep 11 00:35:13 2008  attempting to read 162113 relations
Thu Sep 11 00:35:18 2008  recovered 162113 relations
Thu Sep 11 00:35:18 2008  recovered 143629 polynomials
Thu Sep 11 00:35:18 2008  attempting to build 64893 cycles
Thu Sep 11 00:35:18 2008  found 64893 cycles in 6 passes
Thu Sep 11 00:35:18 2008  distribution of cycle lengths:
Thu Sep 11 00:35:18 2008     length 1 : 16878
Thu Sep 11 00:35:18 2008     length 2 : 12100
Thu Sep 11 00:35:18 2008     length 3 : 11142
Thu Sep 11 00:35:18 2008     length 4 : 8604
Thu Sep 11 00:35:18 2008     length 5 : 6293
Thu Sep 11 00:35:18 2008     length 6 : 4176
Thu Sep 11 00:35:18 2008     length 7 : 2556
Thu Sep 11 00:35:18 2008     length 9+: 3144
Thu Sep 11 00:35:18 2008  largest cycle: 20 relations
Thu Sep 11 00:35:19 2008  matrix is 64695 x 64893 (16.0 MB) with weight 3929052 (60.55/col)
Thu Sep 11 00:35:19 2008  sparse part has weight 3929052 (60.55/col)
Thu Sep 11 00:35:20 2008  filtering completed in 3 passes
Thu Sep 11 00:35:20 2008  matrix is 60904 x 60968 (15.1 MB) with weight 3714849 (60.93/col)
Thu Sep 11 00:35:20 2008  sparse part has weight 3714849 (60.93/col)
Thu Sep 11 00:35:20 2008  saving the first 48 matrix rows for later
Thu Sep 11 00:35:20 2008  matrix is 60856 x 60968 (8.8 MB) with weight 2835309 (46.50/col)
Thu Sep 11 00:35:20 2008  sparse part has weight 1949848 (31.98/col)
Thu Sep 11 00:35:20 2008  matrix includes 64 packed rows
Thu Sep 11 00:35:20 2008  using block size 21845 for processor cache size 512 kB
Thu Sep 11 00:35:21 2008  commencing Lanczos iteration
Thu Sep 11 00:35:21 2008  memory use: 9.0 MB
Thu Sep 11 00:35:58 2008  lanczos halted after 964 iterations (dim = 60856)
Thu Sep 11 00:35:58 2008  recovered 19 nontrivial dependencies
Thu Sep 11 00:35:59 2008  prp32 factor: 80335719249839503097507848265209
Thu Sep 11 00:35:59 2008  prp59 factor: 91843588104175473506416389257508387935075613929940942541007
Thu Sep 11 00:35:59 2008  elapsed time 03:10:08

(5·10¹⁶⁵+31)/9 = (5)₁₆₄9_<165> = 13² · 197 · 509 · 90527 · 272351681066590730815104119_<27> · C127

C127 = P60 · P67

P60 = 370716149467693053462676008244862500592389799729429922243563_<60>

P67 = 3586799392723596076389074822312062821586305721304049998960779310453_<67>

Number: 55559_165
N=1329684459783551319011438303306065173410835619674644634108352388375150231496077427760368587873116286526650932326829865857864039
  ( 127 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=370716149467693053462676008244862500592389799729429922243563 (pp60)
 r2=3586799392723596076389074822312062821586305721304049998960779310453 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 88.75 hours.
Scaled time: 89.55 units (timescale=1.009).
Factorization parameters were as follows:
name: 55559_165
n: 1329684459783551319011438303306065173410835619674644634108352388375150231496077427760368587873116286526650932326829865857864039
m: 1000000000000000000000000000000000
c5: 5
c0: 31
skew: 1.44
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 5400001)
Primes: RFBsize:348513, AFBsize:348707, largePrimes:5990856 encountered
Relations: rels:6232115, finalFF:871113
Max relations in full relation-set: 28
Initial matrix: 697285 x 871113 with sparse part having weight 55986264.
Pruned matrix : 558153 x 561703 with weight 38940973.
Total sieving time: 86.17 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 2.38 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 88.75 hours.
 --------- CPU info (if available) ----------

(25·10¹²³-43)/9 = 2(7)₁₂₂3_<124> = 9187 · 23567851 · 2954627142542967631_<19> · C94

C94 = P36 · P59

P36 = 197767387776465112016466741177603017_<36>

P59 = 21955657065213338757728221623461856918053744589286504372427_<59>

Thu Sep 11 05:57:41 2008  Msieve v. 1.36
Thu Sep 11 05:57:41 2008  random seeds: 19311b63 c69426e7
Thu Sep 11 05:57:41 2008  factoring 4342112944703132326197740951319412899341521838472865926258815265174619316324832004333726812259 (94 digits)
Thu Sep 11 05:57:43 2008  no P-1/P+1/ECM available, skipping
Thu Sep 11 05:57:43 2008  commencing quadratic sieve (94-digit input)
Thu Sep 11 05:57:43 2008  using multiplier of 19
Thu Sep 11 05:57:43 2008  using 64kb Pentium 4 sieve core
Thu Sep 11 05:57:43 2008  sieve interval: 18 blocks of size 65536
Thu Sep 11 05:57:43 2008  processing polynomials in batches of 6
Thu Sep 11 05:57:43 2008  using a sieve bound of 2058671 (76471 primes)
Thu Sep 11 05:57:43 2008  using large prime bound of 284096598 (28 bits)
Thu Sep 11 05:57:43 2008  using double large prime bound of 1645276127747088 (42-51 bits)
Thu Sep 11 05:57:43 2008  using trial factoring cutoff of 51 bits
Thu Sep 11 05:57:43 2008  polynomial 'A' values have 12 factors
Thu Sep 11 10:30:36 2008  76676 relations (19493 full + 57183 combined from 1084674 partial), need 76567
Thu Sep 11 10:30:40 2008  begin with 1104167 relations
Thu Sep 11 10:30:41 2008  reduce to 195866 relations in 10 passes
Thu Sep 11 10:30:41 2008  attempting to read 195866 relations
Thu Sep 11 10:30:47 2008  recovered 195866 relations
Thu Sep 11 10:30:47 2008  recovered 176093 polynomials
Thu Sep 11 10:30:48 2008  attempting to build 76676 cycles
Thu Sep 11 10:30:48 2008  found 76676 cycles in 5 passes
Thu Sep 11 10:30:48 2008  distribution of cycle lengths:
Thu Sep 11 10:30:48 2008     length 1 : 19493
Thu Sep 11 10:30:48 2008     length 2 : 13874
Thu Sep 11 10:30:48 2008     length 3 : 13105
Thu Sep 11 10:30:48 2008     length 4 : 10291
Thu Sep 11 10:30:48 2008     length 5 : 7656
Thu Sep 11 10:30:48 2008     length 6 : 5026
Thu Sep 11 10:30:48 2008     length 7 : 3090
Thu Sep 11 10:30:48 2008     length 9+: 4141
Thu Sep 11 10:30:48 2008  largest cycle: 20 relations
Thu Sep 11 10:30:48 2008  matrix is 76471 x 76676 (20.2 MB) with weight 4983164 (64.99/col)
Thu Sep 11 10:30:48 2008  sparse part has weight 4983164 (64.99/col)
Thu Sep 11 10:30:50 2008  filtering completed in 3 passes
Thu Sep 11 10:30:50 2008  matrix is 72258 x 72322 (19.2 MB) with weight 4734465 (65.46/col)
Thu Sep 11 10:30:50 2008  sparse part has weight 4734465 (65.46/col)
Thu Sep 11 10:30:50 2008  saving the first 48 matrix rows for later
Thu Sep 11 10:30:51 2008  matrix is 72210 x 72322 (12.7 MB) with weight 3804435 (52.60/col)
Thu Sep 11 10:30:51 2008  sparse part has weight 2885271 (39.89/col)
Thu Sep 11 10:30:51 2008  matrix includes 64 packed rows
Thu Sep 11 10:30:51 2008  using block size 21845 for processor cache size 512 kB
Thu Sep 11 10:30:51 2008  commencing Lanczos iteration
Thu Sep 11 10:30:51 2008  memory use: 11.8 MB
Thu Sep 11 10:31:50 2008  lanczos halted after 1143 iterations (dim = 72210)
Thu Sep 11 10:31:50 2008  recovered 18 nontrivial dependencies
Thu Sep 11 10:31:51 2008  prp36 factor: 197767387776465112016466741177603017
Thu Sep 11 10:31:51 2008  prp59 factor: 21955657065213338757728221623461856918053744589286504372427
Thu Sep 11 10:31:51 2008  elapsed time 04:34:10

(25·10¹³⁷-43)/9 = 2(7)₁₃₆3_<138> = 3 · 183078069497_<12> · C126

C126 = P37 · P41 · P49

P37 = 3450507775979522920422222278082125473_<37>

P41 = 18317658128532632830435818365348120635739_<41>

P49 = 8001786516984967398026373100632236071167857872549_<49>

Number: 27773_137
N=505754691684193538361759780341565552359166040090181804723821047319728569316991723580215967720444203699416467812879368361655303
  ( 126 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=3450507775979522920422222278082125473 (pp37)
 r2=18317658128532632830435818365348120635739 (pp41)
 r3=8001786516984967398026373100632236071167857872549 (pp49)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 8.32 hours.
Scaled time: 8.37 units (timescale=1.005).
Factorization parameters were as follows:
name: 27773_137
n: 505754691684193538361759780341565552359166040090181804723821047319728569316991723580215967720444203699416467812879368361655303
m: 5000000000000000000000000000
c5: 4
c0: -215
skew: 2.22
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1675001)
Primes: RFBsize:78498, AFBsize:64043, largePrimes:1675641 encountered
Relations: rels:1732833, finalFF:212605
Max relations in full relation-set: 28
Initial matrix: 142605 x 212605 with sparse part having weight 21652651.
Pruned matrix : 126227 x 127004 with weight 11457432.
Total sieving time: 8.18 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 8.32 hours.
 --------- CPU info (if available) ----------

(25·10¹⁴⁵-43)/9 = 2(7)₁₄₄3_<146> = 47237 · 52957 · 4493917383401_<13> · C124

C124 = P61 · P63

P61 = 9361636002439421548832013290405714726713563748317735359487143_<61>

P63 = 263945937385059899912750880407649594646514339637183924419826979_<63>

Number: 27773_145
N=2470965790121598028563385922026799376277420920856636335118189769521140183570701413099038001314908717575196572384098235030997
  ( 124 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=9361636002439421548832013290405714726713563748317735359487143 (pp61)
 r2=263945937385059899912750880407649594646514339637183924419826979 (pp63)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.36 hours.
Scaled time: 18.96 units (timescale=0.778).
Factorization parameters were as follows:
name: 27773_145
n: 2470965790121598028563385922026799376277420920856636335118189769521140183570701413099038001314908717575196572384098235030997
m: 100000000000000000000000000000
c5: 25
c0: -43
skew: 1.11
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 3450001)
Primes: RFBsize:114155, AFBsize:113677, largePrimes:2999915 encountered
Relations: rels:3045828, finalFF:292596
Max relations in full relation-set: 28
Initial matrix: 227896 x 292596 with sparse part having weight 34011955.
Pruned matrix : 209927 x 211130 with weight 23189695.
Total sieving time: 23.70 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.48 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 24.36 hours.
 --------- CPU info (if available) ----------

(25·10¹⁴²-43)/9 = 2(7)₁₄₁3_<143> = 19 · 109 · 59026157 · 18399994554796203751_<20> · C113

C113 = P34 · P79

P34 = 5428210099470840332597507186448961_<34>

P79 = 2275089826819532792479137350314839096344705558799489784040259764474500966858369_<79>

Number: 27773_142
N=12349665575145153005345838457224467517841859428044691619956472747422827816639099804751127362518567750321334204609
  ( 113 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=5428210099470840332597507186448961 (pp34)
 r2=2275089826819532792479137350314839096344705558799489784040259764474500966858369 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.10 hours.
Scaled time: 10.21 units (timescale=1.011).
Factorization parameters were as follows:
name: 27773_142
n: 12349665575145153005345838457224467517841859428044691619956472747422827816639099804751127362518567750321334204609
m: 50000000000000000000000000000
c5: 4
c0: -215
skew: 2.22
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1950001)
Primes: RFBsize:100021, AFBsize:100053, largePrimes:2707861 encountered
Relations: rels:2659320, finalFF:231209
Max relations in full relation-set: 28
Initial matrix: 200138 x 231209 with sparse part having weight 23015066.
Pruned matrix : 191293 x 192357 with weight 17221770.
Total sieving time: 9.82 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 10.10 hours.
 --------- CPU info (if available) ----------

(25·10¹³⁵-43)/9 = 2(7)₁₃₄3_<136> = 29 · 53 · 238020656130017_<15> · C118

C118 = P43 · P76

P43 = 1364825535132809236399287376342620506894869_<43>

P76 = 5563291859982587204588404791822161196008037539326329882180989274171637224473_<76>

Number: 27773_135
N=7592922789900736215977182615340711041741161887250275039784231201917045291412141943209741657646425920334073674764929037
  ( 118 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=1364825535132809236399287376342620506894869 (pp43)
 r2=5563291859982587204588404791822161196008037539326329882180989274171637224473 (pp76)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 8.93 hours.
Scaled time: 6.95 units (timescale=0.778).
Factorization parameters were as follows:
name: 27773_135
n: 7592922789900736215977182615340711041741161887250275039784231201917045291412141943209741657646425920334073674764929037
m: 1000000000000000000000000000
c5: 25
c0: -43
skew: 1.11
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1525001)
Primes: RFBsize:78498, AFBsize:63718, largePrimes:1599745 encountered
Relations: rels:1612334, finalFF:178104
Max relations in full relation-set: 28
Initial matrix: 142280 x 178104 with sparse part having weight 16706176.
Pruned matrix : 132155 x 132930 with weight 10824903.
Total sieving time: 8.73 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 8.93 hours.
 --------- CPU info (if available) ----------

(25·10¹¹⁷-43)/9 = 2(7)₁₁₆3_<118> = 24535543 · C111

C111 = P54 · P57

P54 = 332379232893091453153280727133385117857511762001897881_<54>

P57 = 340618274207022680190491805403099427972738440448723209331_<57>

Number: 27773_117
N=113214440690298876930409804982827475135878499928767738206477752612924758900904609194007965414817914475248327611
  ( 111 digits)
SNFS difficulty: 119 digits.
Divisors found:
 r1=332379232893091453153280727133385117857511762001897881 (pp54)
 r2=340618274207022680190491805403099427972738440448723209331 (pp57)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 2.08 hours.
Scaled time: 0.98 units (timescale=0.473).
Factorization parameters were as follows:
name: 27773_117
n: 113214440690298876930409804982827475135878499928767738206477752612924758900904609194007965414817914475248327611
m: 500000000000000000000000
c5: 4
c0: -215
skew: 2.22
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64043, largePrimes:2098489 encountered
Relations: rels:2176365, finalFF:225353
Max relations in full relation-set: 28
Initial matrix: 113205 x 225353 with sparse part having weight 18857668.
Pruned matrix : 86361 x 86991 with weight 4764692.
Total sieving time: 1.91 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,119,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.08 hours.
 --------- CPU info (if available) ----------

Sep 11, 2008 (2nd)

By Serge Batalov / Msieve 1.37, GMP-ECM 6.2.1

(25·10¹²⁵-43)/9 = 2(7)₁₂₄3_<126> = 3³ · 1873255141_<10> · 71896123627953440059_<20> · C95

C95 = P33 · P63

P33 = 381306168368381458964149411069297_<33>

P63 = 200335306845756080003950949178160433159808858651862484975520193_<63>

Number: 27773_125
N=76389088242259230546878135267029828620090034029365369180195758708686390425923652120904945814321
  ( 95 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=381306168368381458964149411069297
 r2=200335306845756080003950949178160433159808858651862484975520193
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.315).
Factorization parameters were as follows:
n: 76389088242259230546878135267029828620090034029365369180195758708686390425923652120904945814321
Y1: 1
Y0: -10000000000000000000000000
c5: 25
c0: -43
skew: 1.11
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 600001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 113348 x 113566
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.60 hours.

(25·10¹⁴³-43)/9 = 2(7)₁₄₂3_<144> = 3² · 1482743516013854857834034989178053_<34> · C110

C110 = P31 · P79

P31 = 8226588327582747533833817658727_<31>

P79 = 2530283545192651715467543393327713035545251849149594450020225834649504085392087_<79>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3216840893
Step 1 took 4375ms
Step 2 took 4197ms
********** Factor found in step 2: 8226588327582747533833817658727
Found probable prime factor of 31 digits: 8226588327582747533833817658727
Probable prime cofactor 2530283545192651715467543393327713035545251849149594450020225834649504085392087 has 79 digits

(25·10¹⁸⁷-43)/9 = 2(7)₁₈₆3_<188> = 47 · 53 · 191 · 730757 · C176

C176 = P36 · C141

P36 = 408695703662735190084599512114819513_<36>

C141 = [195486759675827484517045324269925956580801061150249953622950500225372551296385452583893098093930134597595406548846078045518688710538357715613_<141>]

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=634280738
Step 1 took 9559ms
Step 2 took 7056ms
********** Factor found in step 2: 408695703662735190084599512114819513
Found probable prime factor of 36 digits: 408695703662735190084599512114819513
Composite cofactor 195486759675827484517045324269925956580801061150249953622950500225372551296385452583893098093930134597595406548846078045518688710538357715613 has 141 digits

(25·10¹⁵⁵-43)/9 = 2(7)₁₅₄3_<156> = 3 · 23 · 548425147 · C145

C145 = P32 · P114

P32 = 34510830591104725201050200123389_<32>

P114 = 212703989838578957956596911663076383197629838071552664368933220525486296004406576502241258446128246382524518156199_<114>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=4161596758
Step 1 took 6051ms
Step 2 took 5277ms
********** Factor found in step 2: 34510830591104725201050200123389
Found probable prime factor of 32 digits: 34510830591104725201050200123389
Probable prime cofactor 212703989838578957956596911663076383197629838071552664368933220525486296004406576502241258446128246382524518156199 has 114 digits

(25·10¹⁷¹-43)/9 = 2(7)₁₇₀3_<172> = 233 · C170

C170 = P39 · P131

P39 = 308225110411339886828989718831887891927_<39>

P131 = 38678850732708674890175184503305789832974358219544817519426484893378186338847858514538120983978402786856331024910705786603696208803_<131>

Run 731 out of 940:
Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=1398058429
Step 1 took 9015ms
Step 2 took 5397ms
********** Factor found in step 2: 308225110411339886828989718831887891927
Found probable prime factor of 39 digits: 308225110411339886828989718831887891927
Probable prime cofactor 38678850732708674890175184503305789832974358219544817519426484893378186338847858514538120983978402786856331024910705786603696208803 has 131 digits

(25·10¹⁸⁸-43)/9 = 2(7)₁₈₇3_<189> = 3² · 7 · 13 · 2501779210016117_<16> · C171

C171 = P32 · C139

P32 = 75595202411944051335860944001329_<32>

C139 = [1793371996900593249505181161038180873846675034251124827702447409512594054767965061858759389454185358822624969674213962033030690382324261619_<139>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1655319311
Step 1 took 24426ms
Step 2 took 19927ms
********** Factor found in step 2: 75595202411944051335860944001329
Found probable prime factor of 32 digits: 75595202411944051335860944001329
Composite cofactor 1793371996900593249505181161038180873846675034251124827702447409512594054767965061858759389454185358822624969674213962033030690382324261619 has 139 digits

(25·10¹⁷⁹-43)/9 = 2(7)₁₇₈3_<180> = 3⁷ · 1321 · 2309 · 16398814309_<11> · C160

C160 = P36 · P125

P36 = 129908366675717436134275154951566843_<36>

P125 = 19546652628421566148393564324629980588172892836991090912732311730703259332008780061652120853995535520635416749547652215263653_<125>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2302857862
Step 1 took 24350ms
Step 2 took 19295ms
********** Factor found in step 2: 129908366675717436134275154951566843
Found probable prime factor of 36 digits: 129908366675717436134275154951566843
Probable prime cofactor 19546652628421566148393564324629980588172892836991090912732311730703259332008780061652120853995535520635416749547652215263653 has 125 digits

(25·10¹⁶³-43)/9 = 2(7)₁₆₂3_<164> = 29 · 9689 · 2518933 · C152

C152 = P38 · P115

P38 = 25131004094841299841358281520343734889_<38>

P115 = 1561687335706147372245163522601054060771060260107529473974744099616485815066706249125187406434716123100749765802509_<115>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=4270192938
Step 1 took 20946ms
********** Factor found in step 1: 25131004094841299841358281520343734889
Found probable prime factor of 38 digits: 25131004094841299841358281520343734889
Probable prime cofactor 1561687335706147372245163522601054060771060260107529473974744099616485815066706249125187406434716123100749765802509 has 115 digits

Sep 11, 2008

By Jo Yeong Uk / GGNFS, Msieve v1.32 for x86_64

(25·10¹³²-43)/9 = 2(7)₁₃₁3_<133> = C133

C133 = P50 · P83

P50 = 91185321297776872404938800679692229995674932806297_<50>

P83 = 30462992708076369935379615201255241888123967336490277389467361391384334239604056309_<83>

Number: 27773_132
N=2777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773
  ( 133 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=91185321297776872404938800679692229995674932806297 (pp50)
 r2=30462992708076369935379615201255241888123967336490277389467361391384334239604056309 (pp83)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.65 hours.
Scaled time: 6.31 units (timescale=2.382).
Factorization parameters were as follows:
n: 2777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773
m: 500000000000000000000000000
c5: 4
c0: -215
skew: 2.22
type: snfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved algebraic special-q in [600000, 1200001)
Primes: RFBsize:92938, AFBsize:93049, largePrimes:2380853 encountered
Relations: rels:2288460, finalFF:236025
Max relations in full relation-set: 28
Initial matrix: 186051 x 236025 with sparse part having weight 12189200.
Pruned matrix : 164924 x 165918 with weight 6809779.
Total sieving time: 2.54 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,46,46,2.2,2.2,50000
total time: 2.65 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.05 BogoMIPS (lpj=2672026)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(25·10¹⁵³-43)/9 = 2(7)₁₅₂3_<154> = 881 · 71577134882299548903547_<23> · 84565353734169392574360041_<26> · C102

C102 = P41 · P61

P41 = 80602305649128280728158724072025600598519_<41>

P61 = 6462601031553857846813389871404198724474243802915238445011241_<61>

Wed Sep 10 22:58:26 2008  
Wed Sep 10 22:58:26 2008  
Wed Sep 10 22:58:26 2008  Msieve v. 1.32
Wed Sep 10 22:58:26 2008  random seeds: 3e19a540 473eeb8a
Wed Sep 10 22:58:26 2008  factoring 520900543633675770740076921288124839804013151855325091973855979598655668095461137038511238639282952079 (102 digits)
Wed Sep 10 22:58:27 2008  no P-1/P+1/ECM available, skipping
Wed Sep 10 22:58:27 2008  commencing quadratic sieve (102-digit input)
Wed Sep 10 22:58:27 2008  using multiplier of 7
Wed Sep 10 22:58:27 2008  using VC8 32kb sieve core
Wed Sep 10 22:58:27 2008  sieve interval: 36 blocks of size 32768
Wed Sep 10 22:58:27 2008  processing polynomials in batches of 6
Wed Sep 10 22:58:27 2008  using a sieve bound of 3198409 (114644 primes)
Wed Sep 10 22:58:27 2008  using large prime bound of 479761350 (28 bits)
Wed Sep 10 22:58:27 2008  using double large prime bound of 4225182407156700 (44-52 bits)
Wed Sep 10 22:58:27 2008  using trial factoring cutoff of 52 bits
Wed Sep 10 22:58:27 2008  polynomial 'A' values have 13 factors
Thu Sep 11 15:38:50 2008  114820 relations (26751 full + 88069 combined from 1732378 partial), need 114740
Thu Sep 11 15:39:08 2008  begin with 1759129 relations
Thu Sep 11 15:39:09 2008  reduce to 306160 relations in 10 passes
Thu Sep 11 15:39:09 2008  attempting to read 306160 relations
Thu Sep 11 15:39:14 2008  recovered 306160 relations
Thu Sep 11 15:39:14 2008  recovered 298979 polynomials
Thu Sep 11 15:39:14 2008  attempting to build 114820 cycles
Thu Sep 11 15:39:14 2008  found 114820 cycles in 7 passes
Thu Sep 11 15:39:14 2008  distribution of cycle lengths:
Thu Sep 11 15:39:14 2008     length 1 : 26751
Thu Sep 11 15:39:14 2008     length 2 : 19192
Thu Sep 11 15:39:14 2008     length 3 : 19098
Thu Sep 11 15:39:14 2008     length 4 : 15690
Thu Sep 11 15:39:14 2008     length 5 : 12104
Thu Sep 11 15:39:14 2008     length 6 : 8269
Thu Sep 11 15:39:14 2008     length 7 : 5581
Thu Sep 11 15:39:14 2008     length 9+: 8135
Thu Sep 11 15:39:14 2008  largest cycle: 25 relations
Thu Sep 11 15:39:15 2008  matrix is 114644 x 114820 with weight 8535738 (avg 74.34/col)
Thu Sep 11 15:39:15 2008  filtering completed in 3 passes
Thu Sep 11 15:39:15 2008  matrix is 110340 x 110404 with weight 8259057 (avg 74.81/col)
Thu Sep 11 15:39:16 2008  saving the first 48 matrix rows for later
Thu Sep 11 15:39:16 2008  matrix is 110292 x 110404 with weight 7008939 (avg 63.48/col)
Thu Sep 11 15:39:16 2008  matrix includes 64 packed rows
Thu Sep 11 15:39:16 2008  using block size 44161 for processor cache size 4096 kB
Thu Sep 11 15:39:17 2008  commencing Lanczos iteration
Thu Sep 11 15:40:34 2008  lanczos halted after 1746 iterations (dim = 110292)
Thu Sep 11 15:40:34 2008  recovered 18 nontrivial dependencies
Thu Sep 11 15:40:36 2008  prp41 factor: 80602305649128280728158724072025600598519
Thu Sep 11 15:40:36 2008  prp61 factor: 6462601031553857846813389871404198724474243802915238445011241
Thu Sep 11 15:40:36 2008  elapsed time 16:42:10

Sep 10, 2008 (4th)

Factorizations of 277...773 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Sep 10, 2008 (3rd)

By Serge Batalov / GMP-ECM 6.2.1

(22·10¹⁹⁹+41)/9 = 2(4)₁₉₈9_<200> = 41061733 · C192

C192 = P31 · C162

P31 = 1897620275559982337516555558951_<31>

C162 = [313713772035430533818551391590458721020856491086140653105242080969835209074220644870655195685240555478883046828465009236909425448182270062487091452141001532415403_<162>]

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=614666195
Step 1 took 7800ms
Step 2 took 5917ms
********** Factor found in step 2: 1897620275559982337516555558951
Found probable prime factor of 31 digits: 1897620275559982337516555558951
Composite cofactor 313713772035430533818551391590458721020856491086140653105242080969835209074220644870655195685240555478883046828465009236909425448182270062487091452141001532415403 has 162 digits

(4·10²⁰⁰+17)/3 = 1(3)₁₉₉9_<201> = 4877 · 1293587 · C191

C191 = P33 · P158

P33 = 310858393336630686720841637998697_<33>

P158 = 67987291591061721286953508434298743969287676084869733019950591260403028836697158046529832913321391635730918226951318222021514833120320272626786443796812828213_<158>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=4007235084
Step 1 took 7252ms
Step 2 took 5488ms
********** Factor found in step 2: 310858393336630686720841637998697
Found probable prime factor of 33 digits: 310858393336630686720841637998697
Probable prime cofactor 67987291591061721286953508434298743969287676084869733019950591260403028836697158046529832913321391635730918226951318222021514833120320272626786443796812828213 has 158 digits

(23·10¹⁹⁹+1)/3 = 7(6)₁₉₈7_<200> = 7³ · 11 · 1733 · 10429 · C190

C190 = P29 · C161

P29 = 34568930457523287016666104607_<29>

C161 = [32523150062698802917720624652745100514767773266788406670334720522108075012188621040006096086302630721307928762888386196012800664896540679247928777489412633566121_<161>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=567802524
Step 1 took 29554ms
Step 2 took 22544ms
********** Factor found in step 2: 34568930457523287016666104607
Found probable prime factor of 29 digits: 34568930457523287016666104607
Composite cofactor 32523150062698802917720624652745100514767773266788406670334720522108075012188621040006096086302630721307928762888386196012800664896540679247928777489412633566121 has 161 digits

7·10²⁰⁰-9 = 6(9)₁₉₉1_<201> = 15764641 · C194

C194 = P32 · P163

P32 = 11284635217137977617526487653933_<32>

P163 = 3934834132347528894029161821328170864341780603433105197044385991837432909415350859571119308115656096581344079723625343143220426630178141030835445756037523722590547_<163>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=13078247
Step 1 took 8353ms
********** Factor found in step 1: 11284635217137977617526487653933
Found probable prime factor of 32 digits: 11284635217137977617526487653933
Probable prime cofactor 3934834132347528894029161821328170864341780603433105197044385991837432909415350859571119308115656096581344079723625343143220426630178141030835445756037523722590547 has 163 digits

Sep 10, 2008 (2nd)

By Serge Batalov / Msieve v. 1.37

(22·10²⁰³+41)/9 = 2(4)₂₀₂9_<204> = 3³ · C202

C202 = P80 · P123

P80 = 20334617025001623036456051797874969977087099512082033181887892745732650713921249_<80>

P123 = 445225888997833666251265091330295968315737344718479488559782320485075276157873543888006881723934397805015254789157876721363_<123>

Number: 24449_203
N=905349...53497942387 ( 202 digits)
SNFS difficulty: 205 digits.
Divisors found:
 r1=20334617025001623036456051797874969977087099512082033181887892745732650713921249
 r2=445225888997833666251265091330295968315737344718479488559782320485075276157873543888006881723934397805015254789157876721363
Version: Msieve v. 1.37
Scaled time: 0.00 units (timescale=2.512).
Factorization parameters were as follows:
Y0: -10000000000000000000000000000000000
Y1: 1
c0: 205
c6: 11
skew: 1.6
type: snfs
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
rlim: 15000000
alim: 15000000
Factor base limits: 15000000/15000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [7500000, 15100001)
Primes: rational ideals reading, algebraic ideals reading, 
found 4443154 hash collisions in 25,677,752 relations
found 4233772 duplicates and 22662229 unique relations
Relations: 22,662,229 relations and about 20,667,937 large ideals 
Max relations in full relation-set: 19
found 2671198 cycles, need 2587737
building initial matrix
memory use: 997.0 MB
Pruned matrix : 2578133 x 2578381
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 17.90 hours.
Time per square root: 3.50 hours.
Prototype def-par.txt line would be:
snfs,205,6,0,0,0,0,0,0,0,0,15000000,15000000,28,28,56,56,2.5,2.5,100000

total time: 24 CPU-days.

Sep 10, 2008

By Sinkiti Sibata / GGNFS

(23·10¹⁸⁴+13)/9 = 2(5)₁₈₃7_<185> = 3 · 7 · C184

C184 = P60 · P62 · P62

P60 = 142386499451271609105675459975554447296326441982772562419531_<60>

P62 = 89036746517664876241810609616253040552772136863324747726467631_<62>

P62 = 95990429887620748854364521660144618194288049254915390847010397_<62>

Number: 25557_184
N=1216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931217
  ( 184 digits)
SNFS difficulty: 186 digits.
Divisors found:
 r1=142386499451271609105675459975554447296326441982772562419531 (pp60)
 r2=89036746517664876241810609616253040552772136863324747726467631 (pp62)
 r3=95990429887620748854364521660144618194288049254915390847010397 (pp62)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1200.97 hours.
Scaled time: 922.35 units (timescale=0.768).
Factorization parameters were as follows:
name: 25557_184
n: 1216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931217
m: 10000000000000000000000000000000000000
c5: 23
c0: 130
skew: 1.41
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 17400001)
Primes: RFBsize:501962, AFBsize:502146, largePrimes:7061627 encountered
Relations: rels:7610234, finalFF:1155388
Max relations in full relation-set: 28
Initial matrix: 1004173 x 1155388 with sparse part having weight 119681935.
Pruned matrix : 890697 x 895781 with weight 101009017.
Total sieving time: 1183.49 hours.
Total relation processing time: 1.03 hours.
Matrix solve time: 16.19 hours.
Time per square root: 0.26 hours.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 1200.97 hours.
 --------- CPU info (if available) ----------

Sep 9, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(64·10¹⁷⁷+53)/9 = 7(1)₁₇₆7_<178> = 11 · 239 · C175

C175 = P79 · P96

P79 = 2746163758092184047690455322356302856116462038401676834020608038326185212384119_<79>

P96 = 984964203168698675125288342788491918288490272600571711870157920520614551405691698408931673803167_<96>

Number: n
N=2704872997760027048729977600270487299776002704872997760027048729977600270487299776002704872997760027048729977600270487299776002704872997760027048729977600270487299776002704873
  ( 175 digits)
SNFS difficulty: 178 digits.
Divisors found:

Tue Sep 09 18:31:04 2008  prp79 factor: 2746163758092184047690455322356302856116462038401676834020608038326185212384119
Tue Sep 09 18:31:04 2008  prp96 factor: 984964203168698675125288342788491918288490272600571711870157920520614551405691698408931673803167
Tue Sep 09 18:31:05 2008  elapsed time 04:42:39 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 24.10 hours.
Scaled time: 49.11 units (timescale=2.038).
Factorization parameters were as follows:
name: KA_7_1_176_7
n: 2704872997760027048729977600270487299776002704872997760027048729977600270487299776002704872997760027048729977600270487299776002704872997760027048729977600270487299776002704873
type: snfs
skew: 0.77
deg: 5
c5: 200
c0: 53
m: 200000000000000000000000000000000000
rlim: 8000000
alim: 8000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 6100001)
Primes: RFBsize:539777, AFBsize:539400, largePrimes:13853455 encountered
Relations: rels:13478199, finalFF:1170101
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 23.78 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,178,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,52,52,2.5,2.5,100000
total time: 24.10 hours.
 --------- CPU info (if available) ----------

Sep 9, 2008

By Robert Backstrom / GGNFS, Msieve

(16·10¹⁷⁷+11)/9 = 1(7)₁₇₆9_<178> = 3³ · C176

C176 = P82 · P95

P82 = 2621531707625220519663585478246951504563621768505547944917351252820632944202250639_<82>

P95 = 25116469584425904701377272005029275086064055491074195222257361498430466934150973115235367370343_<95>

Number: n
N=65843621399176954732510288065843621399176954732510288065843621399176954732510288065843621399176954732510288065843621399176954732510288065843621399176954732510288065843621399177
  ( 176 digits)
SNFS difficulty: 178 digits.
Divisors found:

Tue Sep  9 00:56:01 2008  prp82 factor: 2621531707625220519663585478246951504563621768505547944917351252820632944202250639
Tue Sep  9 00:56:01 2008  prp95 factor: 25116469584425904701377272005029275086064055491074195222257361498430466934150973115235367370343
Tue Sep  9 00:56:01 2008  elapsed time 06:39:00 (Msieve 1.36)

Version: GGNFS-0.77.1-20050930-k8
Total time: 69.76 hours.
Scaled time: 58.46 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_1_7_176_9
n: 65843621399176954732510288065843621399176954732510288065843621399176954732510288065843621399176954732510288065843621399176954732510288065843621399176954732510288065843621399177
type: snfs
skew: 0.74
deg: 5
c5: 50
c0: 11
m: 200000000000000000000000000000000000
rlim: 8500000
alim: 8500000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8500000/8500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 11050001)
Primes: RFBsize:571119, AFBsize:570218, largePrimes:14534848 encountered
Relations: rels:14277297, finalFF:1165292
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 69.27 hours.
Total relation processing time: 0.49 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,178,5,0,0,0,0,0,0,0,0,8500000,8500000,28,28,52,52,2.5,2.5,100000
total time: 69.76 hours.
 --------- CPU info (if available) ----------

Sep 8, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(82·10¹⁹³-1)/9 = 9(1)₁₉₃_<194> = 7 · 13 · 569 · C190

C190 = P53 · P137

P53 = 39594545141939885526894322438648642768790356810813157_<53>

P137 = 44440846840731324443581573454499877887493864000996240378981166983107524169324621440113544908284126532200838021972350456511361678763879337_<137>

Number: n
N=1759615116381372971882637963481548718807066785977155045696346223586996873464360283340951179264008789492093534272796135713534659053112480177506539545203868578209527242919158560634834800036909
  ( 190 digits)
SNFS difficulty: 195 digits.
Divisors found:

Mon Sep 08 12:03:07 2008  prp53 factor: 39594545141939885526894322438648642768790356810813157
Mon Sep 08 12:03:07 2008  prp137 factor: 44440846840731324443581573454499877887493864000996240378981166983107524169324621440113544908284126532200838021972350456511361678763879337
Mon Sep 08 12:03:07 2008  elapsed time 07:55:00 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 147.85 hours.
Scaled time: 303.24 units (timescale=2.051).
Factorization parameters were as follows:
name: KA_9_1_193
n: 1759615116381372971882637963481548718807066785977155045696346223586996873464360283340951179264008789492093534272796135713534659053112480177506539545203868578209527242919158560634834800036909
type: snfs
skew: 0.21
deg: 5
c5: 5125
c0: -2
m: 200000000000000000000000000000000000000
rlim: 9500000
alim: 9500000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9500000/9500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 12100001)
Primes: RFBsize:633578, AFBsize:633804, largePrimes:14961201 encountered
Relations: rels:14978001, finalFF:1305987
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 147.24 hours.
Total relation processing time: 0.61 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,195,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,52,52,2.5,2.5,100000
total time: 147.85 hours.
 --------- CPU info (if available) ----------

Sep 8, 2008 (2nd)

By Jo Yeong Uk / GGNFS

(65·10¹⁶⁵+43)/9 = 7(2)₁₆₄7_<166> = 3² · 11 · 29 · 7639 · 2252567 · 12425239 · 72706584488576609_<17> · C129

C129 = P49 · P80

P49 = 2844021580936529047321181522766000025422187626149_<49>

P80 = 56899971005532573858733054130402004114671676641026019412601626011729833138572151_<80>

Number: 72227_165
N=161824745494397415085594949862446015318804831340450950581977528424876612513918227943180593176597511704495626812201425598050776499
  ( 129 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=2844021580936529047321181522766000025422187626149 (pp49)
 r2=56899971005532573858733054130402004114671676641026019412601626011729833138572151 (pp80)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 45.38 hours.
Scaled time: 108.18 units (timescale=2.384).
Factorization parameters were as follows:
n: 161824745494397415085594949862446015318804831340450950581977528424876612513918227943180593176597511704495626812201425598050776499
m: 1000000000000000000000000000000000
c5: 65
c0: 43
skew: 0.92
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [3000000, 5500001)
Primes: RFBsize:412849, AFBsize:413366, largePrimes:6535631 encountered
Relations: rels:6859270, finalFF:962155
Max relations in full relation-set: 28
Initial matrix: 826281 x 962155 with sparse part having weight 57220973.
Pruned matrix : 707273 x 711468 with weight 37824375.
Total sieving time: 42.55 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 2.66 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,49,49,2.6,2.6,100000
total time: 45.38 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.05 BogoMIPS (lpj=2672026)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Sep 8, 2008

By Serge Batalov / Msieve-1.37

3·10¹⁹⁸+1 = 3(0)₁₉₇1_<199> = C199

C199 = P82 · P118

P82 = 1833911383348466522566074446250134380140228731863510782284501695384966021186952971_<82>

P118 = 1635847853521917851052479217771526282232255683407487990801439756907074080101789715314755512178980013517705612191904931_<118>

Number: 30001_198
N=3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
  ( 199 digits)
SNFS difficulty: 198 digits.
Divisors found:
 r1=1833911383348466522566074446250134380140228731863510782284501695384966021186952971
 r2=1635847853521917851052479217771526282232255683407487990801439756907074080101789715314755512178980013517705612191904931
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
n: 3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
Y1: 1
Y0: -1000000000000000000000000000000000000000
c5: 3000
c0: 1
skew: 0.2
type: snfs
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
rlim: 10000000
alim: 10000000
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [5000000, 10100001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1857143 x 1857391
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 11.00 hours. (4 threads)
Time per square root: 0.55 hours.
Prototype def-par.txt line would be:
snfs,198,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,56,56,2.5,2.5,100000
total time: 20 CPU-days.

Sep 7, 2008 (2nd)

By Wataru Sakai / GGNFS

(4·10¹⁸⁶+17)/3 = 1(3)₁₈₅9_<187> = 7 · 139 · C184

C184 = P70 · P114

P70 = 4683752657040481930352270796090095702982198572437623038900544234035807_<70>

P114 = 292571449844658244129724130403038430010264115229371023800613342811197195422433644669612330433068714444752149233049_<114>

Number: 13339_186
N=1370332305584104145255224391915039397053785542994176087701267557382665296334361082562521411442274751627269612881123672490578965399109284001370332305584104145255224391915039397053785543
  ( 184 digits)
SNFS difficulty: 186 digits.
Divisors found:
 r1=4683752657040481930352270796090095702982198572437623038900544234035807 (pp70)
 r2=292571449844658244129724130403038430010264115229371023800613342811197195422433644669612330433068714444752149233049 (pp114)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 739.89 hours.
Scaled time: 1489.40 units (timescale=2.013).
Factorization parameters were as follows:
n: 1370332305584104145255224391915039397053785542994176087701267557382665296334361082562521411442274751627269612881123672490578965399109284001370332305584104145255224391915039397053785543
m: 10000000000000000000000000000000000000
c5: 40
c0: 17
skew: 0.84
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 13600001)
Primes: RFBsize:501962, AFBsize:502686, largePrimes:6810292 encountered
Relations: rels:7291905, finalFF:1137529
Max relations in full relation-set: 32
Initial matrix: 1004714 x 1137529 with sparse part having weight 102564823.
Pruned matrix : 901497 x 906584 with weight 83116476.
Total sieving time: 730.37 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 9.13 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 739.89 hours.
 --------- CPU info (if available) ----------

Sep 7, 2008

By Robert Backstrom / GMP-ECM, Msieve

(4·10¹⁶²+17)/3 = 1(3)₁₆₁9_<163> = 7 · 631789 · 1255021 · 4123529 · 219455932845923_<15> · C129

C129 = P39 · P41 · P51

P39 = 175477359310145651369576592622195539679_<39>

P41 = 11017383187107043445598825146216819497967_<41>

P51 = 137309858416434405546180978438036203884533672564143_<51>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 265461328902714720449135413796276012856770681128783935438114532587303104386318078788477129357372613085202661101773298430470012799 (129 digits)
Using B1=2842000, B2=4281592780, polynomial Dickson(6), sigma=4034181669
Step 1 took 27125ms
Step 2 took 11531ms
********** Factor found in step 2: 11017383187107043445598825146216819497967
Found probable prime factor of 41 digits: 11017383187107043445598825146216819497967
Composite cofactor 24094771362165887160008178046242774179489161331528524488085284544470775942950829629130097 has 89 digits

Sun Sep 07 03:19:16 2008  
Sun Sep 07 03:19:16 2008  
Sun Sep 07 03:19:16 2008  Msieve v. 1.37
Sun Sep 07 03:19:16 2008  random seeds: f938b800 08bc6fd4
Sun Sep 07 03:19:16 2008  factoring 24094771362165887160008178046242774179489161331528524488085284544470775942950829629130097 (89 digits)
Sun Sep 07 03:19:16 2008  searching for 15-digit factors
Sun Sep 07 03:19:17 2008  commencing quadratic sieve (89-digit input)
Sun Sep 07 03:19:17 2008  using multiplier of 17
Sun Sep 07 03:19:17 2008  using 64kb Opteron sieve core
Sun Sep 07 03:19:17 2008  sieve interval: 15 blocks of size 65536
Sun Sep 07 03:19:17 2008  processing polynomials in batches of 7
Sun Sep 07 03:19:17 2008  using a sieve bound of 1546837 (58635 primes)
Sun Sep 07 03:19:17 2008  using large prime bound of 123746960 (26 bits)
Sun Sep 07 03:19:17 2008  using double large prime bound of 368605688486800 (42-49 bits)
Sun Sep 07 03:19:17 2008  using trial factoring cutoff of 49 bits
Sun Sep 07 03:19:17 2008  polynomial 'A' values have 11 factors
Sun Sep 07 04:22:05 2008  58762 relations (16144 full + 42618 combined from 616952 partial), need 58731
Sun Sep 07 04:22:07 2008  begin with 633096 relations
Sun Sep 07 04:22:07 2008  reduce to 141733 relations in 11 passes
Sun Sep 07 04:22:07 2008  attempting to read 141733 relations
Sun Sep 07 04:22:10 2008  recovered 141733 relations
Sun Sep 07 04:22:10 2008  recovered 119607 polynomials
Sun Sep 07 04:22:10 2008  attempting to build 58762 cycles
Sun Sep 07 04:22:10 2008  found 58762 cycles in 5 passes
Sun Sep 07 04:22:11 2008  distribution of cycle lengths:
Sun Sep 07 04:22:11 2008     length 1 : 16144
Sun Sep 07 04:22:11 2008     length 2 : 11470
Sun Sep 07 04:22:11 2008     length 3 : 10451
Sun Sep 07 04:22:11 2008     length 4 : 7660
Sun Sep 07 04:22:11 2008     length 5 : 5338
Sun Sep 07 04:22:11 2008     length 6 : 3372
Sun Sep 07 04:22:11 2008     length 7 : 1977
Sun Sep 07 04:22:11 2008     length 9+: 2350
Sun Sep 07 04:22:11 2008  largest cycle: 19 relations
Sun Sep 07 04:22:11 2008  matrix is 58635 x 58762 (14.3 MB) with weight 3516020 (59.83/col)
Sun Sep 07 04:22:11 2008  sparse part has weight 3516020 (59.83/col)
Sun Sep 07 04:22:12 2008  filtering completed in 4 passes
Sun Sep 07 04:22:12 2008  matrix is 54458 x 54522 (13.4 MB) with weight 3300382 (60.53/col)
Sun Sep 07 04:22:12 2008  sparse part has weight 3300382 (60.53/col)
Sun Sep 07 04:22:13 2008  saving the first 48 matrix rows for later
Sun Sep 07 04:22:13 2008  matrix is 54410 x 54522 (10.1 MB) with weight 2767191 (50.75/col)
Sun Sep 07 04:22:13 2008  sparse part has weight 2308672 (42.34/col)
Sun Sep 07 04:22:13 2008  matrix includes 64 packed rows
Sun Sep 07 04:22:13 2008  using block size 21808 for processor cache size 1024 kB
Sun Sep 07 04:22:14 2008  commencing Lanczos iteration
Sun Sep 07 04:22:14 2008  memory use: 9.0 MB
Sun Sep 07 04:22:56 2008  lanczos halted after 862 iterations (dim = 54409)
Sun Sep 07 04:22:56 2008  recovered 17 nontrivial dependencies
Sun Sep 07 04:22:56 2008  prp39 factor: 175477359310145651369576592622195539679
Sun Sep 07 04:22:56 2008  prp51 factor: 137309858416434405546180978438036203884533672564143
Sun Sep 07 04:22:56 2008  elapsed time 01:03:40

Sep 6, 2008 (5th)

By Serge Batalov / GMP-ECM 6.2.1

(4·10²²⁹-1)/3 = 1(3)₂₂₉_<230> = 13 · 347 · C226

C226 = P49 · C177

P49 = 4246645545363041585151546344082603927473277793231_<49>

C177 = [696017078534428470457529048170257815534293367782109964021146339362857748163339563659802340252478769639355612562186287999935138147155138236220734436267484891688123677205851655813_<177>]

# ...and another nice factor; my personal 2nd best (my best is 56-digit)
#
Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=2062470196
Step 1 took 111731ms
Step 2 took 57919ms
********** Factor found in step 2: 4246645545363041585151546344082603927473277793231
Found probable prime factor of 49 digits: 4246645545363041585151546344082603927473277793231
Composite cofactor 696017078534428470457529048170257815534293367782109964021146339362857748163339563659802340252478769639355612562186287999935138147155138236220734436267484891688123677205851655813 has 177 digits

Sep 6, 2008 (4th)

By nuggetprime / GMP-ECM

(4·10¹⁶³+17)/3 = 1(3)₁₆₂9_<164> = 19 · 2797 · 5791 · 69661 · 720611 · 1560371 · 14857397 · 3514121576753_<13> · C119

C119 = P51 · P68

P51 = 495436223298434385356722609135189152207142936793249_<51>

P68 = 21383233343940664218943433891745463379743409952464040968535330972587_<68>

This is a nuggetprime's result posted on 21 Aug 2008 at:
https://www.mersenneforum.org/showthread.php?p=139605#post139605

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 10594028369831114716682888330845541566105401124620505895213725128397891350870967330967394277735211887867089454105665163 (119 digits)
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=861666340
Step 1 took 46698ms
Step 2 took 25614ms
********** Factor found in step 2: 495436223298434385356722609135189152207142936793249
Found probable prime factor of 51 digits: 495436223298434385356722609135189152207142936793249
Probable prime cofactor 21383233343940664218943433891745463379743409952464040968535330972587 has 68 digits

Makoto Kamada posted.

Sep 6, 2008 (3rd)

By Serge Batalov / Msieve-1.37, GMP-ECM 6.2.1

8·10¹⁷²-7 = 7(9)₁₇₁3_<173> = 190313 · C168

C168 = P60 · P109

P60 = 138161571992322355518249925361034781278945385532571294634897_<60>

P109 = 3042525772479980573421781698654833894292124178776206300829682839392738230075715174164879797011327208823658113_<109>

Number: 79993_172
N=420360143552989023345751472574127884064672408085627361241743864055529574963349849983973769527042293484943225108111374420034364441735456852658515182882934954522286969361
  ( 168 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=138161571992322355518249925361034781278945385532571294634897
 r2=3042525772479980573421781698654833894292124178776206300829682839392738230075715174164879797011327208823658113
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.728).
Factorization parameters were as follows:
n: 420360143552989023345751472574127884064672408085627361241743864055529574963349849983973769527042293484943225108111374420034364441735456852658515182882934954522286969361
Y1: 1
Y0: -20000000000000000000000000000000000
c5: 25
c0: -7
skew: 0.78
type: snfs
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [4500000, 6800001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1139892 x 1140140
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,52,52,2.6,2.6,100000
total time: 45.00 hours.

8·10²²⁹-1 = 7(9)₂₂₉_<230> = 4365541 · C224

C224 = P35 · P189

P35 = 22899378996803067916894382980974701_<35>

P189 = 800254657956886391196780894633531374565554844629496936038376921729764352514694201229462957643423367969876748771951592669068650319491433270363334538454741598932512755263816205496476120544639_<189>

# there goes a big number
#
Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=754930536
Step 1 took 37320ms
Step 2 took 27701ms
********** Factor found in step 2: 22899378996803067916894382980974701
Found probable prime factor of 35 digits: 22899378996803067916894382980974701
Probable prime cofactor 800254657956886391196780894633531374565554844629496936038376921729764352514694201229462957643423367969876748771951592669068650319491433270363334538454741598932512755263816205496476120544639 has 189 digits

Sep 6, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(25·10¹⁷⁰-61)/9 = 2(7)₁₆₉1_<171> = 131909045573_<12> · 123310363949659_<15> · C146

C146 = P71 · P75

P71 = 51349565953817840490156245892197350453929733234153814020952530482561583_<71>

P75 = 332572675808658297792850706653907384324838226345820816882845634793838252691_<75>

Number: 27771_170
N=17077462550874378271150629056169128122565987071157482103253108951984884573035699470470382216719112388277895264154420547419468349410224094522969853
  ( 146 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=51349565953817840490156245892197350453929733234153814020952530482561583 (pp71)
 r2=332572675808658297792850706653907384324838226345820816882845634793838252691 (pp75)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 170.65 hours.
Scaled time: 172.53 units (timescale=1.011).
Factorization parameters were as follows:
name: 27771_170
n: 17077462550874378271150629056169128122565987071157482103253108951984884573035699470470382216719112388277895264154420547419468349410224094522969853
m: 10000000000000000000000000000000000
c5: 25
c0: -61
skew: 1.2
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 7900001)
Primes: RFBsize:412849, AFBsize:412112, largePrimes:6360126 encountered
Relations: rels:6833798, finalFF:1111408
Max relations in full relation-set: 28
Initial matrix: 825025 x 1111408 with sparse part having weight 72010060.
Pruned matrix : 587573 x 591762 with weight 55353352.
Total sieving time: 166.78 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.59 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 170.65 hours.
 --------- CPU info (if available) ----------

Sep 6, 2008

By Jo Yeong Uk / GMP-ECM, GGNFS

(43·10¹⁶⁵-7)/9 = 4(7)₁₆₅_<166> = 1344190880737392833_<19> · 2301204226992762281_<19> · C130

C130 = P42 · P88

P42 = 385071591629280252011363710960963257145127_<42>

P88 = 4011144968271534743653930349805245289947412403901164321780638693543548253701599315974287_<88>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 1544577977188098720238620993157952890934508035999346072911447051418801275216503660329923388280907102934899877127344967702159349449 (130 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3941855257
Step 1 took 11715ms
Step 2 took 5580ms
********** Factor found in step 2: 385071591629280252011363710960963257145127
Found probable prime factor of 42 digits: 385071591629280252011363710960963257145127
Probable prime cofactor 4011144968271534743653930349805245289947412403901164321780638693543548253701599315974287 has 88 digits

5·10¹⁹⁴+9 = 5(0)₁₉₃9_<195> = C195

C195 = P88 · P108

P88 = 3403248951366474932718274863522798490198007146565255920384348350563174584990964183684189_<88>

P108 = 146918432105661751654501039168244531252281316834293602197361365522821831096719447512829008767795879133716381_<108>

Number: 50009_194
N=500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 195 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=3403248951366474932718274863522798490198007146565255920384348350563174584990964183684189 (pp88)
 r2=146918432105661751654501039168244531252281316834293602197361365522821831096719447512829008767795879133716381 (pp108)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 482.37 hours.
Scaled time: 1149.02 units (timescale=2.382).
Factorization parameters were as follows:
n: 500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
m: 1000000000000000000000000000000000000000
c5: 1
c0: 18
skew: 1.78
type: snfs
Factor base limits: 20000000/20000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 53/53
Sieved algebraic special-q in [10000000, 17700001)
Primes: RFBsize:1270607, AFBsize:1269885, largePrimes:23603955 encountered
Relations: rels:24083724, finalFF:2909883
Max relations in full relation-set: 28
Initial matrix: 2540559 x 2909883 with sparse part having weight 199159428.
Pruned matrix : 2192610 x 2205376 with weight 135726398.
Total sieving time: 435.38 hours.
Total relation processing time: 0.62 hours.
Matrix solve time: 46.13 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,195,5,0,0,0,0,0,0,0,0,20000000,20000000,29,29,53,53,2.6,2.6,100000
total time: 482.37 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.05 BogoMIPS (lpj=2672026)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Sep 5, 2008 (2nd)

By Robert Backstrom / GMP-ECM

(73·10¹⁸⁷-1)/9 = 8(1)₁₈₇_<188> = 3 · C188

C188 = P43 · P146

P43 = 2013417203339758754699697149093409802311811_<43>

P146 = 13428432513733026611376469936844319340401408181621142465772463805980046207426301273004696887406182311284638034277950590963617673065257314162498767_<146>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 27037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037 (188 digits)
Using B1=5764000, B2=11416947370, polynomial Dickson(12), sigma=2302872240
Step 1 took 98185ms
Step 2 took 33267ms
********** Factor found in step 2: 2013417203339758754699697149093409802311811
Found probable prime factor of 43 digits: 2013417203339758754699697149093409802311811
Probable prime cofactor 13428432513733026611376469936844319340401408181621142465772463805980046207426301273004696887406182311284638034277950590963617673065257314162498767 has 146 digits

Sep 5, 2008

By Serge Batalov / GMP-ECM 6.2.1

(25·10¹⁹⁹-61)/9 = 2(7)₁₉₈1_<200> = 3 · 7 · 283 · 1391259626479767819093311_<25> · 4950310741210515424439214523_<28> · 21631834288992712007555427246085799_<35> · C110

C110 = P34 · P76

P34 = 8137130775905265500667125642011561_<34>

P76 = 3855551265441025333983640384610406523731030541038891638539125959121664278391_<76>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=2054967644
Step 1 took 37534ms
Step 2 took 21049ms
********** Factor found in step 2: 8137130775905265500667125642011561
Found probable prime factor of 34 digits: 8137130775905265500667125642011561
Probable prime cofactor 3855551265441025333983640384610406523731030541038891638539125959121664278391 has 76 digits

(25·10¹⁷⁷-61)/9 = 2(7)₁₇₆1_<178> = 271 · 419 · 66821 · 141356306265971_<15> · 127353589502138899_<18> · C137

C137 = P35 · P102

P35 = 71134251631905636534346663289671327_<35>

P102 = 285888094063953311988136712438838290992815309587898590647604791112176558836528871352247718253340599053_<102>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=1489180364
Step 1 took 60415ms
Step 2 took 11865ms
********** Factor found in step 2: 71134251631905636534346663289671327
Found probable prime factor of 35 digits: 71134251631905636534346663289671327
Probable prime cofactor 285888094063953311988136712438838290992815309587898590647604791112176558836528871352247718253340599053 has 102 digits

Sep 4, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(25·10¹⁶¹-61)/9 = 2(7)₁₆₀1_<162> = 13 · 984211 · 17915596918681641487769_<23> · C133

C133 = P66 · P67

P66 = 253653749852508153250333883090711675749451709540031375104589078333_<66>

P67 = 4777419331469809285428949137256054363568169465244600000364285743961_<67>

Number: n
N=1211810328045179737137835843378066173006313450989972138219571769921632974435429855162342174929531805158519800996508886585732210697013
  ( 133 digits)
SNFS difficulty: 162 digits.
Divisors found:

Thu Sep  4 16:02:43 2008  prp66 factor: 253653749852508153250333883090711675749451709540031375104589078333
Thu Sep  4 16:02:43 2008  prp67 factor: 4777419331469809285428949137256054363568169465244600000364285743961
Thu Sep  4 16:02:43 2008  elapsed time 01:45:45 (Msieve 1.36)

Version: GGNFS-0.77.1-20050930-k8
Total time: 15.24 hours.
Scaled time: 12.77 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_2_7_160_1
n: 1211810328045179737137835843378066173006313450989972138219571769921632974435429855162342174929531805158519800996508886585732210697013
type: snfs
skew: 0.75
deg: 5
c5: 250
c0: -61
m: 100000000000000000000000000000000
rlim: 4400000
alim: 4400000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 2100001)
Primes: RFBsize:309335, AFBsize:309449, largePrimes:12410612 encountered
Relations: rels:11542233, finalFF:649714
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 14.97 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4400000,4400000,28,28,52,52,2.5,2.5,100000
total time: 15.24 hours.
 --------- CPU info (if available) ----------

Sep 4, 2008 (2nd)

By Serge Batalov / GMP-ECM 6.2.1

(25·10¹⁷¹-61)/9 = 2(7)₁₇₀1_<172> = 1777 · 11110598531288144356616827185083_<32> · C138

C138 = P47 · P91

P47 = 44512398379504795249333730316447728566719025499_<47>

P91 = 3160760731055610510155798731208531392799859145056964147663316803202246756868891237027738419_<91>

# what a nice catch for B1=3e6! :-) Wow.
#
Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3132305148
Step 1 took 18363ms
Step 2 took 16355ms
********** Factor found in step 2: 44512398379504795249333730316447728566719025499
Found probable prime factor of 47 digits: 44512398379504795249333730316447728566719025499
Probable prime cofactor 3160760731055610510155798731208531392799859145056964147663316803202246756868891237027738419 has 91 digits

(25·10¹⁹³-61)/9 = 2(7)₁₉₂1_<194> = 3 · 7 · 73883 · 26925317 · 19159973142181_<14> · 284017799510891_<15> · C153

C153 = P29 · C124

P29 = 80485311297327121853982640517_<29>

C124 = [1518153815704622240936737904859078621016147552740776785285576396386699185397561525934124104891750356941221401004594467058163_<124>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1712037598
Step 1 took 18241ms
Step 2 took 16894ms
********** Factor found in step 2: 80485311297327121853982640517
Found probable prime factor of 29 digits: 80485311297327121853982640517
Composite cofactor 1518153815704622240936737904859078621016147552740776785285576396386699185397561525934124104891750356941221401004594467058163 has 124 digits

(25·10¹⁹⁹-61)/9 = 2(7)₁₉₈1_<200> = 3 · 7 · 283 · 1391259626479767819093311_<25> · 4950310741210515424439214523_<28> · C144

C144 = P35 · C110

P35 = 21631834288992712007555427246085799_<35>

C110 = [31373124860100658739370173152893372981358932607827628090607273537011259875274623530665824683543468162744478351_<110>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1435650970
Step 1 took 20513ms
Step 2 took 16641ms
********** Factor found in step 2: 21631834288992712007555427246085799
Found probable prime factor of 35 digits: 21631834288992712007555427246085799
Composite cofactor 31373124860100658739370173152893372981358932607827628090607273537011259875274623530665824683543468162744478351 has 110 digits

(25·10¹⁸⁹-61)/9 = 2(7)₁₈₈1_<190> = 59 · 1447 · 1549 · 55837 · 18626559023_<11> · 1680493671035288368696859_<25> · C143

C143 = P40 · P103

P40 = 2016363122734122769308758804969621922733_<40>

P103 = 5960259958234267822953007523507500830294029263387822644819553059732204123759026007056155922498545778959_<103>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2931673241
Step 1 took 18370ms
Step 2 took 16498ms
********** Factor found in step 2: 2016363122734122769308758804969621922733
Found probable prime factor of 40 digits: 2016363122734122769308758804969621922733
Probable prime cofactor 5960259958234267822953007523507500830294029263387822644819553059732204123759026007056155922498545778959 has 103 digits

Sep 4, 2008

By Sinkiti Sibata / Msieve, GGNFS

(25·10¹⁷²-61)/9 = 2(7)₁₇₁1_<173> = 3 · 47 · 271 · 57935341 · 12956265741884479104103362197_<29> · 323491665334534849464472655197_<30> · C103

C103 = P46 · P58

P46 = 1419307810265852610333835137969799236391677581_<46>

P58 = 2109337107130584539479018932845314440549663990721314805649_<58>

Msieve v. 1.36
Tue Sep  2 13:53:04 2008
random seeds: 331ffe7b d5a5e8c8
factoring 2993798630634018102752511257355121413329191653523966592393572962544732
016371065178595419712380085455069 (103 digits)
no P-1/P+1/ECM available, skipping
commencing quadratic sieve (103-digit input)
using multiplier of 1
using 64kb Pentium 4 sieve core
sieve interval: 18 blocks of size 65536
processing polynomials in batches of 6
using a sieve bound of 3418799 (122500 primes)
using large prime bound of 512819850 (28 bits)
using double large prime bound of 4763615381480700 (44-53 bits)
using trial factoring cutoff of 53 bits
polynomial 'A' values have 13 factors

sieving in progress (press Ctrl-C to pause)
100039 relations (27689 full + 72350 combined from 1685255 partial), need 122596
100275 relations (27714 full + 72561 combined from 1686837 partial), need 122596
100506 relations (27736 full + 72770 combined from 1688414 partial), need 122596
100749 relations (27755 full + 72994 combined from 1690053 partial), need 122596
101012 relations (27781 full + 73231 combined from 1691734 partial), need 122596
101272 relations (27809 full + 73463 combined from 1693393 partial), need 122596
101524 relations (27834 full + 73690 combined from 1695033 partial), need 122596
101785 relations (27857 full + 73928 combined from 1696615 partial), need 122596
102024 relations (27882 full + 74142 combined from 1698192 partial), need 122596
102312 relations (27902 full + 74410 combined from 1699740 partial), need 122596
102557 relations (27936 full + 74621 combined from 1701299 partial), need 122596
102792 relations (27961 full + 74831 combined from 1702802 partial), need 122596
103045 relations (27997 full + 75048 combined from 1704372 partial), need 122596
103324 relations (28032 full + 75292 combined from 1706045 partial), need 122596
103582 relations (28060 full + 75522 combined from 1707634 partial), need 122596
103834 relations (28093 full + 75741 combined from 1709201 partial), need 122596
104069 relations (28118 full + 75951 combined from 1710735 partial), need 122596
104304 relations (28156 full + 76148 combined from 1712299 partial), need 122596
104536 relations (28183 full + 76353 combined from 1713828 partial), need 122596
104784 relations (28212 full + 76572 combined from 1715370 partial), need 122596
105055 relations (28236 full + 76819 combined from 1716949 partial), need 122596
105312 relations (28269 full + 77043 combined from 1718490 partial), need 122596
105545 relations (28303 full + 77242 combined from 1720109 partial), need 122596
105798 relations (28327 full + 77471 combined from 1721726 partial), need 122596
106066 relations (28358 full + 77708 combined from 1723336 partial), need 122596
106315 relations (28382 full + 77933 combined from 1724913 partial), need 122596
106540 relations (28405 full + 78135 combined from 1726523 partial), need 122596
106795 relations (28430 full + 78365 combined from 1728052 partial), need 122596
107071 relations (28456 full + 78615 combined from 1729635 partial), need 122596
107349 relations (28486 full + 78863 combined from 1731297 partial), need 122596
107612 relations (28505 full + 79107 combined from 1732891 partial), need 122596
107878 relations (28531 full + 79347 combined from 1734576 partial), need 122596
108119 relations (28560 full + 79559 combined from 1736178 partial), need 122596
108348 relations (28582 full + 79766 combined from 1737692 partial), need 122596
108579 relations (28603 full + 79976 combined from 1739206 partial), need 122596
108835 relations (28630 full + 80205 combined from 1740789 partial), need 122596
109089 relations (28658 full + 80431 combined from 1742365 partial), need 122596
109343 relations (28687 full + 80656 combined from 1743914 partial), need 122596
109578 relations (28712 full + 80866 combined from 1745500 partial), need 122596
109836 relations (28739 full + 81097 combined from 1747133 partial), need 122596
110093 relations (28764 full + 81329 combined from 1748667 partial), need 122596
110348 relations (28789 full + 81559 combined from 1750171 partial), need 122596
110618 relations (28818 full + 81800 combined from 1751812 partial), need 122596
110880 relations (28833 full + 82047 combined from 1753432 partial), need 122596
111115 relations (28862 full + 82253 combined from 1754973 partial), need 122596
111382 relations (28887 full + 82495 combined from 1756580 partial), need 122596
111634 relations (28915 full + 82719 combined from 1758168 partial), need 122596
111902 relations (28944 full + 82958 combined from 1759681 partial), need 122596
112141 relations (28969 full + 83172 combined from 1761279 partial), need 122596
112406 relations (28996 full + 83410 combined from 1762883 partial), need 122596
112641 relations (29019 full + 83622 combined from 1764483 partial), need 122596
112900 relations (29044 full + 83856 combined from 1765994 partial), need 122596
113157 relations (29063 full + 84094 combined from 1767612 partial), need 122596
113431 relations (29094 full + 84337 combined from 1769187 partial), need 122596
113699 relations (29115 full + 84584 combined from 1770789 partial), need 122596
113976 relations (29152 full + 84824 combined from 1772445 partial), need 122596
114260 relations (29181 full + 85079 combined from 1774007 partial), need 122596
114504 relations (29203 full + 85301 combined from 1775586 partial), need 122596
114784 relations (29225 full + 85559 combined from 1777186 partial), need 122596
115057 relations (29259 full + 85798 combined from 1778770 partial), need 122596
115325 relations (29282 full + 86043 combined from 1780307 partial), need 122596
115605 relations (29305 full + 86300 combined from 1781882 partial), need 122596
115862 relations (29330 full + 86532 combined from 1783480 partial), need 122596
116094 relations (29347 full + 86747 combined from 1785041 partial), need 122596
116349 relations (29365 full + 86984 combined from 1786621 partial), need 122596
116608 relations (29392 full + 87216 combined from 1788221 partial), need 122596
116875 relations (29411 full + 87464 combined from 1789818 partial), need 122596
117163 relations (29438 full + 87725 combined from 1791426 partial), need 122596
117465 relations (29464 full + 88001 combined from 1793037 partial), need 122596
117754 relations (29493 full + 88261 combined from 1794667 partial), need 122596
118013 relations (29511 full + 88502 combined from 1796239 partial), need 122596
118293 relations (29539 full + 88754 combined from 1797859 partial), need 122596
118590 relations (29576 full + 89014 combined from 1799475 partial), need 122596
118867 relations (29595 full + 89272 combined from 1801040 partial), need 122596
119128 relations (29618 full + 89510 combined from 1802617 partial), need 122596
119375 relations (29645 full + 89730 combined from 1804194 partial), need 122596
119642 relations (29675 full + 89967 combined from 1805758 partial), need 122596
119923 relations (29704 full + 90219 combined from 1807401 partial), need 122596
120225 relations (29745 full + 90480 combined from 1809005 partial), need 122596
120505 relations (29768 full + 90737 combined from 1810656 partial), need 122596
120771 relations (29787 full + 90984 combined from 1812243 partial), need 122596
121035 relations (29810 full + 91225 combined from 1813821 partial), need 122596
121305 relations (29831 full + 91474 combined from 1815435 partial), need 122596
121600 relations (29860 full + 91740 combined from 1816956 partial), need 122596
121881 relations (29884 full + 91997 combined from 1818562 partial), need 122596
122151 relations (29908 full + 92243 combined from 1820182 partial), need 122596
122423 relations (29927 full + 92496 combined from 1821756 partial), need 122596
122710 relations (29950 full + 92760 combined from 1823402 partial), need 122596

122710 relations (29950 full + 92760 combined from 1823402 partial), need 122596

sieving complete, commencing postprocessing
begin with 1853352 relations
reduce to 320739 relations in 10 passes
attempting to read 320739 relations
recovered 320739 relations
recovered 310067 polynomials
attempting to build 122710 cycles
found 122709 cycles in 5 passes
distribution of cycle lengths:
   length 1 : 29950
   length 2 : 21063
   length 3 : 20688
   length 4 : 16492
   length 5 : 12620
   length 6 : 8658
   length 7 : 5521
   length 9+: 7717
largest cycle: 19 relations
matrix is 122500 x 122709 (35.8 MB) with weight 8892811 (72.47/col)
sparse part has weight 8892811 (72.47/col)
filtering completed in 3 passes
matrix is 116994 x 117058 (34.4 MB) with weight 8538750 (72.94/col)
sparse part has weight 8538750 (72.94/col)
saving the first 48 matrix rows for later
matrix is 116946 x 117058 (24.7 MB) with weight 7163227 (61.19/col)
sparse part has weight 5785677 (49.43/col)
matrix includes 64 packed rows
using block size 21845 for processor cache size 512 kB
commencing Lanczos iteration
memory use: 21.9 MB
linear algebra completed 115406 out of 117058 dimensions (98.6%)
lanczos halted after 1850 iterations (dim = 116945)
recovered 16 nontrivial dependencies
prp46 factor: 1419307810265852610333835137969799236391677581
prp58 factor: 2109337107130584539479018932845314440549663990721314805649
elapsed time 34:58:42

(25·10¹⁵⁷-61)/9 = 2(7)₁₅₆1_<158> = 3 · 7 · 271 · 3096349 · 23837571371_<11> · 53476976743_<11> · C127

C127 = P42 · P85

P42 = 251111527431617622010853018800610054904163_<42>

P85 = 4924515457609151256111451286897140203112085825934235152907008026879826815789247413971_<85>

Number: 27771_157
N=1236602598420845392465064144285320486196111595543875173246683943577905648456176531599471021910006680459702992441135973992261273
  ( 127 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=251111527431617622010853018800610054904163 (pp42)
 r2=4924515457609151256111451286897140203112085825934235152907008026879826815789247413971 (pp85)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 43.89 hours.
Scaled time: 44.02 units (timescale=1.003).
Factorization parameters were as follows:
name: 27771_157
n: 1236602598420845392465064144285320486196111595543875173246683943577905648456176531599471021910006680459702992441135973992261273
m: 50000000000000000000000000000000
c5: 4
c0: -305
skew: 2.38
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3700001)
Primes: RFBsize:283146, AFBsize:282638, largePrimes:6156179 encountered
Relations: rels:6587926, finalFF:1001963
Max relations in full relation-set: 28
Initial matrix: 565848 x 1001963 with sparse part having weight 66147813.
Pruned matrix : 326559 x 329452 with weight 53505394.
Total sieving time: 42.50 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.22 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 43.89 hours.
 --------- CPU info (if available) ----------

Sep 3, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(25·10¹⁴⁹-61)/9 = 2(7)₁₄₈1_<150> = 13 · 181 · 197 · 1690007339_<10> · C135

C135 = P39 · P96

P39 = 470636525232146442959347571682077326597_<39>

P96 = 753416498702436697593695957452689801144133736876627078063382917767291118360831661478156933806457_<96>

Number: 27771_149
N=354585323001884776628629511894083866932645350523269087652602074338492850583139742796679407422397312103865993638601297787473881576436829
  ( 135 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=470636525232146442959347571682077326597 (pp39)
 r2=753416498702436697593695957452689801144133736876627078063382917767291118360831661478156933806457 (pp96)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 29.16 hours.
Scaled time: 29.54 units (timescale=1.013).
Factorization parameters were as follows:
name: 27771_149
n: 354585323001884776628629511894083866932645350523269087652602074338492850583139742796679407422397312103865993638601297787473881576436829
m: 1000000000000000000000000000000
c5: 5
c0: -122
skew: 1.89
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:175719, largePrimes:5507544 encountered
Relations: rels:5398019, finalFF:462635
Max relations in full relation-set: 28
Initial matrix: 352086 x 462635 with sparse part having weight 40929944.
Pruned matrix : 302640 x 304464 with weight 23597003.
Total sieving time: 28.49 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.52 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 29.16 hours.
 --------- CPU info (if available) ----------

(25·10¹³⁰-61)/9 = 2(7)₁₂₉1_<131> = 3 · 58495944249857_<14> · C117

C117 = P38 · P79

P38 = 72325146532934744296452924098623296259_<38>

P79 = 2188573651977845386131277387482593882061834489364029224669677420951255801033939_<79>

Number: 27771_130
N=158288910077417795908138195479665635472032771658895991675636236713434628266715780232941527665528194251098524510734201
  ( 117 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=72325146532934744296452924098623296259 (pp38)
 r2=2188573651977845386131277387482593882061834489364029224669677420951255801033939 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.74 hours.
Scaled time: 2.93 units (timescale=0.783).
Factorization parameters were as follows:
name: 27771_130
n: 158288910077417795908138195479665635472032771658895991675636236713434628266715780232941527665528194251098524510734201
m: 100000000000000000000000000
c5: 25
c0: -61
skew: 1.2
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:63951, AFBsize:63799, largePrimes:1454614 encountered
Relations: rels:1449393, finalFF:168881
Max relations in full relation-set: 28
Initial matrix: 127814 x 168881 with sparse part having weight 10444584.
Pruned matrix : 114673 x 115376 with weight 5503834.
Total sieving time: 3.62 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 3.74 hours.
 --------- CPU info (if available) ----------

(25·10¹⁵⁴-61)/9 = 2(7)₁₅₃1_<155> = 3 · 293 · 26557 · 49256293730178799051846621_<26> · C122

C122 = P40 · P82

P40 = 5301064110976528276021825235523818767679_<40>

P82 = 4557270671561061255123982087138571971565022174347192982395270017827900110497448323_<82>

Number: 27771_154
N=24158384001018243165313643924362406754822830761328446656124480605992670616305009456597905435143480920734912217227845152317
  ( 122 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=5301064110976528276021825235523818767679 (pp40)
 r2=4557270671561061255123982087138571971565022174347192982395270017827900110497448323 (pp82)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 32.40 hours.
Scaled time: 32.60 units (timescale=1.006).
Factorization parameters were as follows:
name: 27771_154
n: 24158384001018243165313643924362406754822830761328446656124480605992670616305009456597905435143480920734912217227845152317
m: 10000000000000000000000000000000
c5: 5
c0: -122
skew: 1.89
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2800001)
Primes: RFBsize:216816, AFBsize:216067, largePrimes:6039660 encountered
Relations: rels:6273316, finalFF:769405
Max relations in full relation-set: 28
Initial matrix: 432948 x 769405 with sparse part having weight 68934654.
Pruned matrix : 305773 x 308001 with weight 39508435.
Total sieving time: 31.36 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.88 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 32.40 hours.
 --------- CPU info (if available) ----------

(25·10¹⁵²-61)/9 = 2(7)₁₅₁1_<153> = 271 · 251197 · 23650616473873_<14> · C132

C132 = P37 · P41 · P55

P37 = 1649194932995458194552098353071508753_<37>

P41 = 40462912832676719001557694003003432413533_<41>

P55 = 2585485814085485481752663875511265877142630193494391229_<55>

Number: 27771_152
N=172532650636111904860054938051259144514788546119627239692446419141078903561074468627544423576489365555172803898817679618101016804921
  ( 132 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=1649194932995458194552098353071508753 (pp37)
 r2=40462912832676719001557694003003432413533 (pp41)
 r3=2585485814085485481752663875511265877142630193494391229 (pp55)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 30.42 hours.
Scaled time: 23.91 units (timescale=0.786).
Factorization parameters were as follows:
name: 27771_152
n: 172532650636111904860054938051259144514788546119627239692446419141078903561074468627544423576489365555172803898817679618101016804921
m: 5000000000000000000000000000000
c5: 4
c0: -305
skew: 2.38
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2300001)
Primes: RFBsize:176302, AFBsize:175969, largePrimes:5737118 encountered
Relations: rels:5759844, finalFF:564149
Max relations in full relation-set: 28
Initial matrix: 352335 x 564149 with sparse part having weight 53178188.
Pruned matrix : 277777 x 279602 with weight 28211723.
Total sieving time: 29.27 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.94 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 30.42 hours.
 --------- CPU info (if available) ----------

Sep 3, 2008

By Serge Batalov / Msieve 1.37, GMP-ECM 6.2.1+Msieve 1.37/QS

(25·10¹⁵³-61)/9 = 2(7)₁₅₂1_<154> = C154

C154 = P51 · P104

P51 = 109597476817915399648783767470638342286678753105441_<51>

P104 = 25345271245548484326118620469718080997667197757537826608184756610171014468393711341782508146039235365131_<104>

Number: 27771_153
N=2777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777771
  ( 154 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=109597476817915399648783767470638342286678753105441
 r2=25345271245548484326118620469718080997667197757537826608184756610171014468393711341782508146039235365131
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.716).
Factorization parameters were as follows:
n: 2777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777771
Y1: 1
Y0: -5000000000000000000000000000000
c5: 8
c0: -61
skew: 1.5
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1200000, 2000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 472490 x 472732
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,52,52,2.5,2.5,100000
total time: 11.50 hours.

(25·10¹⁶⁵-61)/9 = 2(7)₁₆₄1_<166> = 139 · 163 · 1399 · 17783920837_<11> · 5046891031387_<13> · 28368734240391359_<17> · C119

C119 = P32 · P37 · P51

P32 = 80362373512148298738695020240543_<32>

P37 = 1311733054597632858229417944775231493_<37>

P51 = 326503438371259342587167097723316440052457045232143_<51>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=4222096588
Step 1 took 3912ms
********** Factor found in step 1: 80362373512148298738695020240543
Found probable prime factor of 32 digits: 80362373512148298738695020240543
Composite cofactor 428285352551361986373445292067672882719692682241289020565800346753478523267674749479499 has 87 digits

Tue Sep  2 09:21:10 2008  Msieve v. 1.37
Tue Sep  2 09:21:10 2008  random seeds: a88b20fd 0f1ad02c
Tue Sep  2 09:21:10 2008  factoring 428285352551361986373445292067672882719692682241289020565800346753478523267674749479499 (87 digits)
Tue Sep  2 09:21:11 2008  no P-1/P+1/ECM available, skipping
Tue Sep  2 09:21:11 2008  commencing quadratic sieve (87-digit input)
Tue Sep  2 09:21:11 2008  using multiplier of 3
Tue Sep  2 09:21:11 2008  using 64kb Opteron sieve core
Tue Sep  2 09:21:11 2008  sieve interval: 10 blocks of size 65536
Tue Sep  2 09:21:11 2008  processing polynomials in batches of 11
Tue Sep  2 09:21:11 2008  using a sieve bound of 1484177 (56667 primes)
Tue Sep  2 09:21:11 2008  using large prime bound of 118734160 (26 bits)
Tue Sep  2 09:21:11 2008  using double large prime bound of 342165490136480 (42-49 bits)
Tue Sep  2 09:21:11 2008  using trial factoring cutoff of 49 bits
Tue Sep  2 09:21:11 2008  polynomial 'A' values have 11 factors
Tue Sep  2 10:02:32 2008  56852 relations (15434 full + 41418 combined from 599869 partial), need 56763
Tue Sep  2 10:02:33 2008  begin with 615303 relations
Tue Sep  2 10:02:33 2008  reduce to 138044 relations in 11 passes
Tue Sep  2 10:02:33 2008  attempting to read 138044 relations
Tue Sep  2 10:02:34 2008  recovered 138044 relations
Tue Sep  2 10:02:34 2008  recovered 118769 polynomials
Tue Sep  2 10:02:34 2008  attempting to build 56852 cycles
Tue Sep  2 10:02:34 2008  found 56852 cycles in 5 passes
Tue Sep  2 10:02:34 2008  distribution of cycle lengths:
Tue Sep  2 10:02:34 2008     length 1 : 15434
Tue Sep  2 10:02:34 2008     length 2 : 11111
Tue Sep  2 10:02:34 2008     length 3 : 10050
Tue Sep  2 10:02:34 2008     length 4 : 7450
Tue Sep  2 10:02:34 2008     length 5 : 5195
Tue Sep  2 10:02:34 2008     length 6 : 3284
Tue Sep  2 10:02:34 2008     length 7 : 2019
Tue Sep  2 10:02:34 2008     length 9+: 2309
Tue Sep  2 10:02:34 2008  largest cycle: 17 relations
Tue Sep  2 10:02:34 2008  matrix is 56667 x 56852 (14.0 MB) with weight 3220880 (56.65/col)
Tue Sep  2 10:02:34 2008  sparse part has weight 3220880 (56.65/col)
Tue Sep  2 10:02:35 2008  filtering completed in 3 passes
Tue Sep  2 10:02:35 2008  matrix is 52655 x 52719 (13.1 MB) with weight 3016772 (57.22/col)
Tue Sep  2 10:02:35 2008  sparse part has weight 3016772 (57.22/col)
Tue Sep  2 10:02:35 2008  saving the first 48 matrix rows for later
Tue Sep  2 10:02:35 2008  matrix is 52607 x 52719 (8.5 MB) with weight 2347485 (44.53/col)
Tue Sep  2 10:02:35 2008  sparse part has weight 1706392 (32.37/col)
Tue Sep  2 10:02:35 2008  matrix includes 64 packed rows
Tue Sep  2 10:02:35 2008  using block size 21087 for processor cache size 1024 kB
Tue Sep  2 10:02:35 2008  commencing Lanczos iteration
Tue Sep  2 10:02:35 2008  memory use: 7.7 MB
Tue Sep  2 10:02:50 2008  lanczos halted after 834 iterations (dim = 52604)
Tue Sep  2 10:02:50 2008  recovered 15 nontrivial dependencies
Tue Sep  2 10:02:50 2008  prp37 factor: 1311733054597632858229417944775231493
Tue Sep  2 10:02:50 2008  prp51 factor: 326503438371259342587167097723316440052457045232143
Tue Sep  2 10:02:50 2008  elapsed time 00:41:40

(25·10¹⁶⁴-61)/9 = 2(7)₁₆₃1_<165> = 3299 · C161

C161 = P33 · P48 · P81

P33 = 659829942255417221379291150281179_<33>

P48 = 248570702244139474826035756339690768851787296439_<48>

P81 = 513373237714119628900245111388942430675374787557277953916106237311225424401827709_<81>

Number: 27771_164
N=84200599508268498871711966589202115119059647704691657404600720757131790778350341854434003570105419150584352160587383382169681048129062678926273955070560102387929
  ( 161 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=659829942255417221379291150281179
 r2=248570702244139474826035756339690768851787296439
 r3=513373237714119628900245111388942430675374787557277953916106237311225424401827709
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.725).
Factorization parameters were as follows:
n: 84200599508268498871711966589202115119059647704691657404600720757131790778350341854434003570105419150584352160587383382169681048129062678926273955070560102387929
Y1: 1
Y0: -1000000000000000000000000000000000
c5: 5
c0: -122
skew: 1.89
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 4500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 827994 x 828242
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.5,2.5,100000
total time: 31.00 hours.

# I knew about 3 factors, because of ECM results (but GNFS was still useless):

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3546418022
Step 1 took 19842ms
Step 2 took 14809ms
********** Factor found in step 2: 659829942255417221379291150281179
Found probable prime factor of 33 digits: 659829942255417221379291150281179
Composite cofactor 127609546211946264112980194582537324356226142070695470718473719517438302591875232733472700792167849318979451951203715019387228251 has 129 digits

Sep 2, 2008 (5th)

By Wataru Sakai / GGNFS

(8·10¹⁷⁹-11)/3 = 2(6)₁₇₈3_<180> = C180

C180 = P40 · P140

P40 = 4682209735745219226761500789554699502777_<40>

P140 = 56953165645456519175499917759107331724155107752653509943265611671232250463973830108138400277147620488064312051591440159053383107906533210719_<140>

Number: 26663_179
N=266666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
  ( 180 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=4682209735745219226761500789554699502777 (pp40)
 r2=56953165645456519175499917759107331724155107752653509943265611671232250463973830108138400277147620488064312051591440159053383107906533210719 (pp140)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 340.53 hours.
Scaled time: 686.16 units (timescale=2.015).
Factorization parameters were as follows:
n: 266666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
m: 1000000000000000000000000000000000000
c5: 4
c0: -55
skew: 1.69
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 7800001)
Primes: RFBsize:501962, AFBsize:500697, largePrimes:6409304 encountered
Relations: rels:6929357, finalFF:1194527
Max relations in full relation-set: 32
Initial matrix: 1002723 x 1194527 with sparse part having weight 57740419.
Pruned matrix : 833652 x 838729 with weight 41052163.
Total sieving time: 336.37 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 3.89 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 340.53 hours.
 --------- CPU info (if available) ----------

Sep 2, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(8·10¹⁶⁶-11)/3 = 2(6)₁₆₅3_<167> = 7 · 13² · 3343 · C160

C160 = P78 · P83

P78 = 651701029217118246663040446269232348044819826548758806571194117322481623985581_<78>

P83 = 10346636798875123657678542081026145261494185181631514140254760838629797607664649267_<83>

Number: n
N=6742913850762627770842409927524633339309240733571712195242419131602039630296147933461263266366927288715640955683294439363377903151022642957570130307653030219127
  ( 160 digits)
SNFS difficulty: 167 digits.
Divisors found:

Tue Sep  2 13:14:52 2008  prp78 factor: 651701029217118246663040446269232348044819826548758806571194117322481623985581
Tue Sep  2 13:14:52 2008  prp83 factor: 10346636798875123657678542081026145261494185181631514140254760838629797607664649267
Tue Sep  2 13:14:52 2008  elapsed time 01:26:16 (Msieve 1.36)

Version: GGNFS-0.77.1-20050930-k8
Total time: 22.59 hours.
Scaled time: 18.93 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_2_6_165_3
n: 6742913850762627770842409927524633339309240733571712195242419131602039630296147933461263266366927288715640955683294439363377903151022642957570130307653030219127
type: snfs
skew: 1.34
deg: 5
c5: 5
c0: -22
m: 2000000000000000000000000000000000
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 2600001)
Primes: RFBsize:348513, AFBsize:348587, largePrimes:13964706 encountered
Relations: rels:13838473, finalFF:1133567
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Loading matrix into RAM...
Matrix scanned: it should be 697165 x 1133567.
Found 6 dense blocks. Re-reading matrix...
The dense blocks consist of the following sets of rows:
[697101, 697164]
[0, 63]
[64, 127]
[128, 191]
[348513, 348576]
[348577, 348640]
Matrix loaded: it is 697165 x 1133567.
Warning: column 121076 is all zero!
checkMat() did not like something about the matrix:
This is probably a sign that something has gone horribly wrong
in the matrix construction (matbuild).
However, the number of bad columns is only 1,
so we will delete them and attempt to continue.
checkMat() returned some error! Terminating...
Return value 65280. Terminating...

Total sieving time: 22.25 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,52,52,2.5,2.5,100000
total time: 22.59 hours.
 --------- CPU info (if available) ----------

(52·10¹⁶⁷-7)/9 = 5(7)₁₆₇_<168> = 6469 · 14737 · 59029 · 158560488000179_<15> · C141

C141 = P39 · P50 · P53

P39 = 134423132005673053281516895507169533951_<39>

P50 = 92767036161728595441434580385004989605003143823259_<50>

P53 = 51926195999481557111023152924214215900076403618583911_<53>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 647521509972609978778474895181437790066412069595365135629283038763004668109673455943367523705566963333241654425358525680208523021452673454499 (141 digits)
Using B1=4860000, B2=11416155670, polynomial Dickson(12), sigma=3081001015
Step 1 took 51375ms
Step 2 took 24656ms
********** Factor found in step 2: 134423132005673053281516895507169533951
Found probable prime factor of 39 digits: 134423132005673053281516895507169533951
Composite cofactor 4817039302024912335467132326152784905075738362859412701896443731750706099437308147192818330864044985949 has 103 digits

Number: n
N=4817039302024912335467132326152784905075738362859412701896443731750706099437308147192818330864044985949
  ( 103 digits)
Divisors found:
 r1=92767036161728595441434580385004989605003143823259 (pp50)
 r2=51926195999481557111023152924214215900076403618583911 (pp53)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.65 hours.
Scaled time: 12.17 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_5_7_167
n: 4817039302024912335467132326152784905075738362859412701896443731750706099437308147192818330864044985949
skew: 3985.52
# norm 3.59e+13
c5: 93600
c4: -601932860
c3: -2428712294883
c2: 21750733387237273
c1: 13248076622685588363
c0: -19810988854558364477813
# alpha -4.55
Y1: 81379529627
Y0: -34857976460207414076
# Murphy_E 2.31e-09
# M 4281574460791113755516230351221977994129597477696987288901441868558155807652878845341700823494448725006
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [100000, 1000001)
Primes: RFBsize:169511, AFBsize:169363, largePrimes:4077544 encountered
Relations: rels:4035675, finalFF:430083
Max relations in full relation-set: 48
Initial matrix: 338952 x 430083 with sparse part having weight 26429719.
Pruned matrix : 252628 x 254386 with weight 10673012.
Total sieving time: 6.20 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.28 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 6.65 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Sep 2, 2008 (3rd)

By Sinkiti Sibata / GGNFS, GMP-ECM, Msieve

(25·10¹²⁹-61)/9 = 2(7)₁₂₈1_<130> = 153151 · 4673772755787217_<16> · C109

C109 = P38 · P72

P38 = 20453259670836204190673329947267817129_<38>

P72 = 189735037545599924396551452154414396763586188577807393187978065955851197_<72>

Number: 27771_129
N=3880699991576011953128227159099334239837445535573922171440035776758693606702134517293709663755165267331753413
  ( 109 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=20453259670836204190673329947267817129 (pp38)
 r2=189735037545599924396551452154414396763586188577807393187978065955851197 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.11 hours.
Scaled time: 4.01 units (timescale=0.785).
Factorization parameters were as follows:
name: 27771_129
n: 3880699991576011953128227159099334239837445535573922171440035776758693606702134517293709663755165267331753413
m: 100000000000000000000000000
c5: 5
c0: -122
skew: 1.89
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1050001)
Primes: RFBsize:63951, AFBsize:63784, largePrimes:1545512 encountered
Relations: rels:1563329, finalFF:183787
Max relations in full relation-set: 28
Initial matrix: 127800 x 183787 with sparse part having weight 14621739.
Pruned matrix : 113248 x 113951 with weight 7290682.
Total sieving time: 4.97 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.11 hours.
 --------- CPU info (if available) ----------

(25·10¹⁴⁷-61)/9 = 2(7)₁₄₆1_<148> = 17 · 271 · 3309855891091_<13> · C132

C132 = P34 · P98

P34 = 9229490189668026616203266998176737_<34>

P98 = 19737515731549627398346041144166461110062712518326895924348032317964415590287193972630324247892759_<98>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 182167207812755629686046229168270893227835379964737052055815747768780391916854905259389815243129008035784843900450078564467304547383

Run 334 out of 904:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4055225039
Step 1 took 14680ms
Step 2 took 6957ms
********** Factor found in step 2: 9229490189668026616203266998176737
Found probable prime factor of 34 digits: 9229490189668026616203266998176737
Probable prime cofactor 19737515731549627398346041144166461110062712518326895924348032317964415590287193972630324247892759 has 98 digits

(25·10¹²⁴-61)/9 = 2(7)₁₂₃1_<125> = 3² · 502027579 · 7574678889386110163953_<22> · C93

C93 = P41 · P53

P41 = 70362686316521436307034813012932569418787_<41>

P53 = 11535084375410612732158710144999540847723947258858451_<53>

Msieve v. 1.36
Tue Sep  2 06:30:15 2008
random seeds: fac47258 aa7b8a3d
factoring 8116395235416245391682881300129730356859284926250012455520665659765342
50127979479486173118937 (93 digits)
no P-1/P+1/ECM available, skipping
commencing quadratic sieve (93-digit input)
using multiplier of 57
using 64kb Pentium 4 sieve core
sieve interval: 18 blocks of size 65536
processing polynomials in batches of 6
using a sieve bound of 1956883 (72856 primes)
using large prime bound of 244610375 (27 bits)
using double large prime bound of 1256766767596625 (42-51 bits)
using trial factoring cutoff of 51 bits
polynomial 'A' values have 12 factors

sieving in progress (press Ctrl-C to pause)
73048 relations (18356 full + 54692 combined from 993590 partial), need 72952
73048 relations (18356 full + 54692 combined from 993590 partial), need 72952
sieving complete, commencing postprocessing
begin with 1011946 relations
reduce to 187410 relations in 10 passes
attempting to read 187410 relations
recovered 187410 relations
recovered 170694 polynomials
attempting to build 73048 cycles
found 73048 cycles in 6 passes
distribution of cycle lengths:
   length 1 : 18356
   length 2 : 12889
   length 3 : 12517
   length 4 : 9860
   length 5 : 7391
   length 6 : 4737
   length 7 : 3122
   length 9+: 4176
largest cycle: 23 relations
matrix is 72856 x 73048 (19.3 MB) with weight 4773964 (65.35/col)
sparse part has weight 4773964 (65.35/col)
filtering completed in 3 passes
matrix is 69230 x 69294 (18.5 MB) with weight 4561561 (65.83/col)
sparse part has weight 4561561 (65.83/col)
saving the first 48 matrix rows for later
matrix is 69182 x 69294 (11.9 MB) with weight 3618831 (52.22/col)
sparse part has weight 2700647 (38.97/col)
matrix includes 64 packed rows
using block size 21845 for processor cache size 512 kB
commencing Lanczos iteration
memory use: 11.2 MB
linear algebra completed 64229 out of 69294 dimensions (92.7%)
lanczos halted after 1096 iterations (dim = 69181)
recovered 18 nontrivial dependencies
prp41 factor: 70362686316521436307034813012932569418787
prp53 factor: 11535084375410612732158710144999540847723947258858451
elapsed time 04:50:14

(25·10¹⁴³-61)/9 = 2(7)₁₄₂1_<144> = 13 · 2171111317_<10> · 9299223345239532250199_<22> · C112

C112 = P34 · P39 · P40

P34 = 1309143485309777583241846470683317_<34>

P39 = 484378549302141911629687706665230167387_<39>

P40 = 1668988046339800108673532942790290417931_<40>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 1058340406055840797247159275511465608167592959514093349104328096492970348022598919601596788146797957174561417149

Run 100 out of 904:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2624782773
Step 1 took 11606ms
Step 2 took 5928ms
********** Factor found in step 2: 1309143485309777583241846470683317
Found probable prime factor of 34 digits: 1309143485309777583241846470683317
Composite cofactor 808422008688688376397533217076481426744848381871723328550796245844581316216297 has 78 digits

Tue Sep  2 11:39:26 2008  Msieve v. 1.36
Tue Sep  2 11:39:26 2008  random seeds: 5ccc56ec cd254687
Tue Sep  2 11:39:26 2008  factoring 808422008688688376397533217076481426744848381871723328550796245844581316216297 (78 digits)
Tue Sep  2 11:39:27 2008  no P-1/P+1/ECM available, skipping
Tue Sep  2 11:39:27 2008  commencing quadratic sieve (78-digit input)
Tue Sep  2 11:39:27 2008  using multiplier of 5
Tue Sep  2 11:39:27 2008  using 32kb Intel Core sieve core
Tue Sep  2 11:39:27 2008  sieve interval: 12 blocks of size 32768
Tue Sep  2 11:39:27 2008  processing polynomials in batches of 17
Tue Sep  2 11:39:27 2008  using a sieve bound of 1032511 (40529 primes)
Tue Sep  2 11:39:27 2008  using large prime bound of 103251100 (26 bits)
Tue Sep  2 11:39:27 2008  using trial factoring cutoff of 27 bits
Tue Sep  2 11:39:27 2008  polynomial 'A' values have 10 factors
Tue Sep  2 11:46:12 2008  40779 relations (20784 full + 19995 combined from 222822 partial), need 40625
Tue Sep  2 11:46:12 2008  begin with 243606 relations
Tue Sep  2 11:46:12 2008  reduce to 58257 relations in 2 passes
Tue Sep  2 11:46:12 2008  attempting to read 58257 relations
Tue Sep  2 11:46:12 2008  recovered 58257 relations
Tue Sep  2 11:46:12 2008  recovered 47947 polynomials
Tue Sep  2 11:46:13 2008  attempting to build 40779 cycles
Tue Sep  2 11:46:13 2008  found 40779 cycles in 1 passes
Tue Sep  2 11:46:13 2008  distribution of cycle lengths:
Tue Sep  2 11:46:13 2008     length 1 : 20784
Tue Sep  2 11:46:13 2008     length 2 : 19995
Tue Sep  2 11:46:13 2008  largest cycle: 2 relations
Tue Sep  2 11:46:13 2008  matrix is 40529 x 40779 (5.3 MB) with weight 1219217 (29.90/col)
Tue Sep  2 11:46:13 2008  sparse part has weight 1219217 (29.90/col)
Tue Sep  2 11:46:13 2008  filtering completed in 3 passes
Tue Sep  2 11:46:13 2008  matrix is 29746 x 29810 (4.1 MB) with weight 967944 (32.47/col)
Tue Sep  2 11:46:13 2008  sparse part has weight 967944 (32.47/col)
Tue Sep  2 11:46:13 2008  saving the first 48 matrix rows for later
Tue Sep  2 11:46:13 2008  matrix is 29698 x 29810 (2.3 MB) with weight 682503 (22.90/col)
Tue Sep  2 11:46:13 2008  sparse part has weight 436808 (14.65/col)
Tue Sep  2 11:46:13 2008  matrix includes 64 packed rows
Tue Sep  2 11:46:13 2008  commencing Lanczos iteration
Tue Sep  2 11:46:13 2008  memory use: 3.5 MB
Tue Sep  2 11:46:25 2008  lanczos halted after 471 iterations (dim = 29698)
Tue Sep  2 11:46:25 2008  recovered 18 nontrivial dependencies
Tue Sep  2 11:46:25 2008  prp39 factor: 484378549302141911629687706665230167387
Tue Sep  2 11:46:25 2008  prp40 factor: 1668988046339800108673532942790290417931
Tue Sep  2 11:46:25 2008  elapsed time 00:06:59

(25·10¹²¹-61)/9 = 2(7)₁₂₀1_<122> = 3 · 7 · 49627 · C116

C116 = P51 · P66

P51 = 151751901518049889837708613154968992021300406120197_<51>

P66 = 175641056329064573758109081077588831777126235148165732731308152329_<66>

Number: 27771_121
N=26653864282574460501798442838602429147898348132091860304325293141864766182174044829454183233376011500822591559488813
  ( 116 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=151751901518049889837708613154968992021300406120197 (pp51)
 r2=175641056329064573758109081077588831777126235148165732731308152329 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.43 hours.
Scaled time: 1.90 units (timescale=0.781).
Factorization parameters were as follows:
name: 27771_121
n: 26653864282574460501798442838602429147898348132091860304325293141864766182174044829454183233376011500822591559488813
m: 1000000000000000000000000
c5: 250
c0: -61
skew: 0.75
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:64054, largePrimes:2215166 encountered
Relations: rels:2352484, finalFF:253562
Max relations in full relation-set: 28
Initial matrix: 113218 x 253562 with sparse part having weight 24450133.
Pruned matrix : 87484 x 88114 with weight 6169356.
Total sieving time: 2.31 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.43 hours.
 --------- CPU info (if available) ----------

(25·10¹²⁰-61)/9 = 2(7)₁₁₉1_<121> = 19 · 731683 · 1060777 · C108

C108 = P34 · P74

P34 = 2077909526098467227127095357094899_<34>

P74 = 90650500191125839001849566503209300133757025311439466547532183753689765801_<74>

Number: 27771_120
N=188363537892731304918189934923172037561952148759302117343469768319278002963865656881762961384765891041749099
  ( 108 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=2077909526098467227127095357094899 (pp34)
 r2=90650500191125839001849566503209300133757025311439466547532183753689765801 (pp74)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 2.05 hours.
Scaled time: 0.97 units (timescale=0.473).
Factorization parameters were as follows:
name: 27771_120
n: 188363537892731304918189934923172037561952148759302117343469768319278002963865656881762961384765891041749099
m: 1000000000000000000000000
c5: 25
c0: -61
skew: 1.2
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63799, largePrimes:2043190 encountered
Relations: rels:2063781, finalFF:182037
Max relations in full relation-set: 28
Initial matrix: 112961 x 182037 with sparse part having weight 14502213.
Pruned matrix : 92717 x 93345 with weight 4989049.
Total sieving time: 1.87 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.05 hours.
 --------- CPU info (if available) ----------

(25·10¹⁴²-61)/9 = 2(7)₁₄₁1_<143> = 3² · 271 · 13907 · 8197537 · 4493806896529693_<16> · C113

C113 = P46 · P67

P46 = 2901173421641272627502030357866773367220862841_<46>

P67 = 7662681283468009442196894266756698463559266727460022585926879778867_<67>

Number: 27771_142
N=22230767278105423457838826207878695530231315713506366491222875197108426865608784560893162769503742321415017381147
  ( 113 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=2901173421641272627502030357866773367220862841 (pp46)
 r2=7662681283468009442196894266756698463559266727460022585926879778867 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 16.27 hours.
Scaled time: 16.45 units (timescale=1.011).
Factorization parameters were as follows:
name: 27771_142
n: 22230767278105423457838826207878695530231315713506366491222875197108426865608784560893162769503742321415017381147
m: 50000000000000000000000000000
c5: 4
c0: -305
skew: 2.38
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2350001)
Primes: RFBsize:100021, AFBsize:99834, largePrimes:3010808 encountered
Relations: rels:3140551, finalFF:366900
Max relations in full relation-set: 28
Initial matrix: 199919 x 366900 with sparse part having weight 41430559.
Pruned matrix : 163905 x 164968 with weight 19507651.
Total sieving time: 15.88 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.27 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 16.27 hours.
 --------- CPU info (if available) ----------

(25·10¹³⁹-61)/9 = 2(7)₁₃₈1_<140> = 3 · 7 · 80084639981_<11> · C128

C128 = P52 · P76

P52 = 6190455589244173649468957716997216405600058094976893_<52>

P76 = 2668126182700760482119033930880089627186177930718096494876239686787844595447_<76>

Number: 27771_139
N=16516916640508643948357831885991140837451264045925620296168380208470962412813488436668742365820180095732542134692365768398006171
  ( 128 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=6190455589244173649468957716997216405600058094976893 (pp52)
 r2=2668126182700760482119033930880089627186177930718096494876239686787844595447 (pp76)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 16.63 hours.
Scaled time: 13.07 units (timescale=0.786).
Factorization parameters were as follows:
name: 27771_139
n: 16516916640508643948357831885991140837451264045925620296168380208470962412813488436668742365820180095732542134692365768398006171
m: 10000000000000000000000000000
c5: 5
c0: -122
skew: 1.89
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1950001)
Primes: RFBsize:100021, AFBsize:99699, largePrimes:2732880 encountered
Relations: rels:2707703, finalFF:256474
Max relations in full relation-set: 28
Initial matrix: 199785 x 256474 with sparse part having weight 24432411.
Pruned matrix : 182795 x 183857 with weight 15345607.
Total sieving time: 16.20 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 16.63 hours.
 --------- CPU info (if available) ----------

Sep 2, 2008 (2nd)

By Serge Batalov / Msieve v. 1.36/QS, Msieve v. 1.37/QS, Msieve-1.37 snfs, GMP-ECM 6.2.1, Msieve-1.37; 64-bit sievers (Childers)

(25·10¹³⁴-61)/9 = 2(7)₁₃₃1_<135> = 154682376054408611_<18> · 4819569705512101509596789_<25> · C93

C93 = P34 · P60

P34 = 2285341270841103220316892131357527_<34>

P60 = 163041189884638045718398236420560827643537175317697019375987_<60>

Mon Sep  1 10:51:50 2008  Msieve v. 1.36
Mon Sep  1 10:51:50 2008  random seeds: 6c6c726c 4abd9356
Mon Sep  1 10:51:50 2008  factoring 372604760090404334748669246936986927822050971487117589245170278954091582540355072904735504149 (93 digits)
Mon Sep  1 10:51:50 2008  no P-1/P+1/ECM available, skipping
Mon Sep  1 10:51:50 2008  commencing quadratic sieve (93-digit input)
Mon Sep  1 10:51:51 2008  using multiplier of 1
Mon Sep  1 10:51:51 2008  using 64kb Opteron sieve core
Mon Sep  1 10:51:51 2008  sieve interval: 18 blocks of size 65536
Mon Sep  1 10:51:51 2008  processing polynomials in batches of 6
Mon Sep  1 10:51:51 2008  using a sieve bound of 1923133 (71747 primes)
Mon Sep  1 10:51:51 2008  using large prime bound of 232699093 (27 bits)
Mon Sep  1 10:51:51 2008  using double large prime bound of 1148762820023984 (42-51 bits)
Mon Sep  1 10:51:51 2008  using trial factoring cutoff of 51 bits
Mon Sep  1 10:51:51 2008  polynomial 'A' values have 12 factors
Mon Sep  1 13:09:44 2008  72146 relations (17299 full + 54847 combined from 977711 partial), need 71843
Mon Sep  1 13:09:45 2008  begin with 995010 relations
Mon Sep  1 13:09:45 2008  reduce to 187321 relations in 9 passes
Mon Sep  1 13:09:45 2008  attempting to read 187321 relations
Mon Sep  1 13:09:47 2008  recovered 187321 relations
Mon Sep  1 13:09:47 2008  recovered 171042 polynomials
Mon Sep  1 13:09:47 2008  attempting to build 72146 cycles
Mon Sep  1 13:09:47 2008  found 72146 cycles in 6 passes
Mon Sep  1 13:09:47 2008  distribution of cycle lengths:
Mon Sep  1 13:09:47 2008     length 1 : 17299
Mon Sep  1 13:09:47 2008     length 2 : 12778
Mon Sep  1 13:09:47 2008     length 3 : 12307
Mon Sep  1 13:09:47 2008     length 4 : 9774
Mon Sep  1 13:09:47 2008     length 5 : 7552
Mon Sep  1 13:09:47 2008     length 6 : 4913
Mon Sep  1 13:09:47 2008     length 7 : 3199
Mon Sep  1 13:09:47 2008     length 9+: 4324
Mon Sep  1 13:09:47 2008  largest cycle: 20 relations
Mon Sep  1 13:09:47 2008  matrix is 71747 x 72146 (18.8 MB) with weight 4351494 (60.32/col)
Mon Sep  1 13:09:47 2008  sparse part has weight 4351494 (60.32/col)
Mon Sep  1 13:09:48 2008  filtering completed in 3 passes
Mon Sep  1 13:09:48 2008  matrix is 68402 x 68465 (17.9 MB) with weight 4139994 (60.47/col)
Mon Sep  1 13:09:48 2008  sparse part has weight 4139994 (60.47/col)
Mon Sep  1 13:09:48 2008  saving the first 48 matrix rows for later
Mon Sep  1 13:09:48 2008  matrix is 68354 x 68465 (10.6 MB) with weight 3144332 (45.93/col)
Mon Sep  1 13:09:48 2008  sparse part has weight 2085056 (30.45/col)
Mon Sep  1 13:09:48 2008  matrix includes 64 packed rows
Mon Sep  1 13:09:48 2008  using block size 27386 for processor cache size 1024 kB
Mon Sep  1 13:09:48 2008  commencing Lanczos iteration
Mon Sep  1 13:09:48 2008  memory use: 10.0 MB
Mon Sep  1 13:10:13 2008  lanczos halted after 1082 iterations (dim = 68350)
Mon Sep  1 13:10:13 2008  recovered 13 nontrivial dependencies
Mon Sep  1 13:10:14 2008  prp34 factor: 2285341270841103220316892131357527
Mon Sep  1 13:10:14 2008  prp60 factor: 163041189884638045718398236420560827643537175317697019375987
Mon Sep  1 13:10:14 2008  elapsed time 02:18:24

(25·10¹¹⁷-61)/9 = 2(7)₁₁₆1_<118> = 271 · 39064037 · 35586743578678280759909_<23> · C85

C85 = P42 · P44

P42 = 619747506717711772232144970127654889620759_<42>

P44 = 11897290019020184431574871639392025782656283_<44>

Mon Sep  1 11:02:19 2008  Msieve v. 1.37
Mon Sep  1 11:02:19 2008  random seeds: 714daeb2 a296f0bc
Mon Sep  1 11:02:19 2008  factoring 7373315825985276969439340659001240598496120288389807384293268160113990464333518578797 (85 digits)
Mon Sep  1 11:02:20 2008  no P-1/P+1/ECM available, skipping
Mon Sep  1 11:02:20 2008  commencing quadratic sieve (85-digit input)
Mon Sep  1 11:02:20 2008  using multiplier of 2
Mon Sep  1 11:02:20 2008  using 64kb Opteron sieve core
Mon Sep  1 11:02:20 2008  sieve interval: 6 blocks of size 65536
Mon Sep  1 11:02:20 2008  processing polynomials in batches of 17
Mon Sep  1 11:02:20 2008  using a sieve bound of 1434241 (54705 primes)
Mon Sep  1 11:02:20 2008  using large prime bound of 116173521 (26 bits)
Mon Sep  1 11:02:20 2008  using double large prime bound of 328997602795950 (41-49 bits)
Mon Sep  1 11:02:20 2008  using trial factoring cutoff of 49 bits
Mon Sep  1 11:02:20 2008  polynomial 'A' values have 11 factors
Mon Sep  1 11:31:50 2008  54866 relations (16358 full + 38508 combined from 570198 partial), need 54801
Mon Sep  1 11:31:50 2008  begin with 586556 relations
Mon Sep  1 11:31:51 2008  reduce to 128079 relations in 8 passes
Mon Sep  1 11:31:51 2008  attempting to read 128079 relations
Mon Sep  1 11:31:51 2008  recovered 128079 relations
Mon Sep  1 11:31:51 2008  recovered 107644 polynomials
Mon Sep  1 11:31:52 2008  attempting to build 54866 cycles
Mon Sep  1 11:31:52 2008  found 54866 cycles in 5 passes
Mon Sep  1 11:31:52 2008  distribution of cycle lengths:
Mon Sep  1 11:31:52 2008     length 1 : 16358
Mon Sep  1 11:31:52 2008     length 2 : 11052
Mon Sep  1 11:31:52 2008     length 3 : 9697
Mon Sep  1 11:31:52 2008     length 4 : 7070
Mon Sep  1 11:31:52 2008     length 5 : 4547
Mon Sep  1 11:31:52 2008     length 6 : 2753
Mon Sep  1 11:31:52 2008     length 7 : 1601
Mon Sep  1 11:31:52 2008     length 9+: 1788
Mon Sep  1 11:31:52 2008  largest cycle: 18 relations
Mon Sep  1 11:31:52 2008  matrix is 54705 x 54866 (12.5 MB) with weight 2844525 (51.84/col)
Mon Sep  1 11:31:52 2008  sparse part has weight 2844525 (51.84/col)
Mon Sep  1 11:31:52 2008  filtering completed in 4 passes
Mon Sep  1 11:31:52 2008  matrix is 49391 x 49455 (11.4 MB) with weight 2593007 (52.43/col)
Mon Sep  1 11:31:52 2008  sparse part has weight 2593007 (52.43/col)
Mon Sep  1 11:31:52 2008  saving the first 48 matrix rows for later
Mon Sep  1 11:31:52 2008  matrix is 49343 x 49455 (6.7 MB) with weight 1918802 (38.80/col)
Mon Sep  1 11:31:52 2008  sparse part has weight 1248764 (25.25/col)
Mon Sep  1 11:31:52 2008  matrix includes 64 packed rows
Mon Sep  1 11:31:52 2008  using block size 19782 for processor cache size 1024 kB
Mon Sep  1 11:31:53 2008  commencing Lanczos iteration
Mon Sep  1 11:31:53 2008  memory use: 6.4 MB
Mon Sep  1 11:32:03 2008  lanczos halted after 781 iterations (dim = 49337)
Mon Sep  1 11:32:03 2008  recovered 14 nontrivial dependencies
Mon Sep  1 11:32:04 2008  prp42 factor: 619747506717711772232144970127654889620759
Mon Sep  1 11:32:04 2008  prp44 factor: 11897290019020184431574871639392025782656283
Mon Sep  1 11:32:04 2008  elapsed time 00:29:45

(25·10¹⁶²-61)/9 = 2(7)₁₆₁1_<163> = 271 · 563 · 1879 · 1373431 · 1359263813985643_<16> · 151483474336947757_<18> · 23620461886232346133505839_<26> · C91

C91 = P30 · P61

P30 = 518359647652198152916575830119_<30>

P61 = 2798321461530763710270557913472221025759214843794041462439153_<61>

Mon Sep  1 10:49:29 2008  Msieve v. 1.37
Mon Sep  1 10:49:29 2008  random seeds: dc3a699f 068f696d
Mon Sep  1 10:49:29 2008  factoring 1450536926816670844973433674050011398591359995388009351598663646137374467946327419502249207 (91 digits)
Mon Sep  1 10:49:29 2008  no P-1/P+1/ECM available, skipping
Mon Sep  1 10:49:29 2008  commencing quadratic sieve (91-digit input)
Mon Sep  1 10:49:29 2008  using multiplier of 7
Mon Sep  1 10:49:30 2008  using 64kb Opteron sieve core
Mon Sep  1 10:49:30 2008  sieve interval: 18 blocks of size 65536
Mon Sep  1 10:49:30 2008  processing polynomials in batches of 6
Mon Sep  1 10:49:30 2008  using a sieve bound of 1648379 (62353 primes)
Mon Sep  1 10:49:30 2008  using large prime bound of 145057352 (27 bits)
Mon Sep  1 10:49:30 2008  using double large prime bound of 490649675444456 (42-49 bits)
Mon Sep  1 10:49:30 2008  using trial factoring cutoff of 49 bits
Mon Sep  1 10:49:30 2008  polynomial 'A' values have 12 factors
Mon Sep  1 12:30:08 2008  62716 relations (16467 full + 46249 combined from 697522 partial), need 62449
Mon Sep  1 12:30:08 2008  begin with 713989 relations
Mon Sep  1 12:30:09 2008  reduce to 154131 relations in 12 passes
Mon Sep  1 12:30:09 2008  attempting to read 154131 relations
Mon Sep  1 12:30:11 2008  recovered 154131 relations
Mon Sep  1 12:30:11 2008  recovered 134673 polynomials
Mon Sep  1 12:30:11 2008  attempting to build 62716 cycles
Mon Sep  1 12:30:11 2008  found 62716 cycles in 6 passes
Mon Sep  1 12:30:11 2008  distribution of cycle lengths:
Mon Sep  1 12:30:11 2008     length 1 : 16467
Mon Sep  1 12:30:11 2008     length 2 : 11946
Mon Sep  1 12:30:11 2008     length 3 : 11000
Mon Sep  1 12:30:11 2008     length 4 : 8364
Mon Sep  1 12:30:11 2008     length 5 : 5902
Mon Sep  1 12:30:11 2008     length 6 : 3907
Mon Sep  1 12:30:11 2008     length 7 : 2351
Mon Sep  1 12:30:11 2008     length 9+: 2779
Mon Sep  1 12:30:11 2008  largest cycle: 19 relations
Mon Sep  1 12:30:11 2008  matrix is 62353 x 62716 (16.4 MB) with weight 3807249 (60.71/col)
Mon Sep  1 12:30:11 2008  sparse part has weight 3807249 (60.71/col)
Mon Sep  1 12:30:12 2008  filtering completed in 3 passes
Mon Sep  1 12:30:12 2008  matrix is 58563 x 58627 (15.4 MB) with weight 3568812 (60.87/col)
Mon Sep  1 12:30:12 2008  sparse part has weight 3568812 (60.87/col)
Mon Sep  1 12:30:12 2008  saving the first 48 matrix rows for later
Mon Sep  1 12:30:12 2008  matrix is 58515 x 58627 (10.2 MB) with weight 2824552 (48.18/col)
Mon Sep  1 12:30:12 2008  sparse part has weight 2093163 (35.70/col)
Mon Sep  1 12:30:12 2008  matrix includes 64 packed rows
Mon Sep  1 12:30:12 2008  using block size 23450 for processor cache size 1024 kB
Mon Sep  1 12:30:13 2008  commencing Lanczos iteration
Mon Sep  1 12:30:13 2008  memory use: 9.0 MB
Mon Sep  1 12:30:39 2008  lanczos halted after 927 iterations (dim = 58513)
Mon Sep  1 12:30:40 2008  recovered 17 nontrivial dependencies
Mon Sep  1 12:30:40 2008  prp30 factor: 518359647652198152916575830119
Mon Sep  1 12:30:40 2008  prp61 factor: 2798321461530763710270557913472221025759214843794041462439153
Mon Sep  1 12:30:40 2008  elapsed time 01:41:11

(25·10¹⁰¹-61)/9 = 2(7)₁₀₀1_<102> = 13 · 317 · 517601989 · C90

C90 = P40 · P51

P40 = 1220440232504536752439016607144455724019_<40>

P51 = 106704425575836651096236897680730256801192448458461_<51>

Number: 27771_101
N=130226373959037120408897782242685193121360604141675290599021813285783982746449324201474759
  ( 90 digits)
SNFS difficulty: 102 digits.
Divisors found:
 r1=1220440232504536752439016607144455724019
 r2=106704425575836651096236897680730256801192448458461
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.944).
Factorization parameters were as follows:
n: 130226373959037120408897782242685193121360604141675290599021813285783982746449324201474759
Y1: 1
Y0: -100000000000000000000
c5: 250
c0: -61
skew: 0.75
type: snfs
Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [225000, 285001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 42339 x 42554
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,102,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000
total time: 0.30 hours.

(25·10¹⁹⁰-61)/9 = 2(7)₁₈₉1_<191> = 3 · 619 · 2858827 · 3617101 · 220477529829865223482993_<24> · 26459747372041207956272582179_<29> · C123

C123 = P37 · P86

P37 = 2976504347692375718574208936493265731_<37>

P86 = 83306815908902703939279567118759249527571709871356299315811741626793814308282721962477_<86>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2641304095
Step 1 took 5033ms
Step 2 took 2858ms
********** Factor found in step 2: 2976504347692375718574208936493265731
Found probable prime factor of 37 digits: 2976504347692375718574208936493265731
Probable prime cofactor 83306815908902703939279567118759249527571709871356299315811741626793814308282721962477 has 86 digits

(25·10¹⁴⁵-61)/9 = 2(7)₁₄₄1_<146> = 3 · 7² · C144

C144 = P40 · P47 · P57

P40 = 9828296418549422058299450666557398619289_<40>

P47 = 87046340760163089105257888142997578027021705923_<47>

P57 = 220877459896081835011433334820685258323697425657910538619_<57>

Number: 27771_145
N=188964474678760393046107331821617535903250188964474678760393046107331821617535903250188964474678760393046107331821617535903250188964474678760393
  ( 144 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=9828296418549422058299450666557398619289
 r2=87046340760163089105257888142997578027021705923
 r3=220877459896081835011433334820685258323697425657910538619
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.731).
Factorization parameters were as follows:
n: 188964474678760393046107331821617535903250188964474678760393046107331821617535903250188964474678760393046107331821617535903250188964474678760393
Y1: 1
Y0: -100000000000000000000000000000
c5: 25
c0: -61
skew: 1.2
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved rational special-q in [750000, 1950001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 224466 x 224712
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 5.00 hours.

(25·10¹³⁶-61)/9 = 2(7)₁₃₅1_<137> = 3 · C136

C136 = P40 · P97

P40 = 1901077818633176986641273760618004825731_<40>

P97 = 4870531426176132915928552436849317829157610124238343115163233836263288860176292922476799468932947_<97>

Number: 27771_136
N=9259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259257
  ( 136 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=1901077818633176986641273760618004825731
 r2=4870531426176132915928552436849317829157610124238343115163233836263288860176292922476799468932947
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.291).
Factorization parameters were as follows:
n: 9259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259257
Y1: 1
Y0: -1000000000000000000000000000
c5: 250
c0: -61
skew: 0.75
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [500000, 1850001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 154199 x 154447
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.10 hours.

(25·10¹⁵⁹-61)/9 = 2(7)₁₅₈1_<160> = 23 · 29 · 1448387 · 439692763 · 961430228377_<12> · C130

C130 = P35 · P96

P35 = 40938435274311943365251489605994903_<35>

P96 = 166145551502820974033100434453141488073658394935290823556214125540250731272635492119584942449183_<96>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=232563863
Step 1 took 4581ms
Step 2 took 3756ms
********** Factor found in step 2: 40938435274311943365251489605994903
Found probable prime factor of 35 digits: 40938435274311943365251489605994903
Probable prime cofactor 166145551502820974033100434453141488073658394935290823556214125540250731272635492119584942449183 has 96 digits

(25·10¹⁶³-61)/9 = 2(7)₁₆₂1_<164> = 3 · 7 · 17 · 739 · 11492161 · 4402226051_<10> · C142

C142 = P33 · P109

P33 = 343669074489795639277832878263307_<33>

P109 = 6055783638574069034440712866051481024164387943862544584024154281615135516630551624273818820529570512643159301_<109>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=1462551368
Step 1 took 5520ms
Step 2 took 4013ms
********** Factor found in step 2: 343669074489795639277832878263307
Found probable prime factor of 33 digits: 343669074489795639277832878263307
Probable prime cofactor 6055783638574069034440712866051481024164387943862544584024154281615135516630551624273818820529570512643159301 has 109 digits

10¹⁹³-9 = (9)₁₉₂1_<193> = 31 · 71 · 397 · 31039 · 7333825763352817867_<19> · C164

C164 = P66 · P99

P66 = 114623516402068263048374107148074526153902078826891749923032115067_<66>

P99 = 438608874285502256844751510885066987832289149361752461518587566928513572528389208388687896598390093_<99>

# the Labor day weekend (idle computers) motivated me to finish the 99991 series.
# 1 day on 20cpu + 7 hrs Lanczos
#
Number: 99991_193
N=50274891495756964747055055496890986637122321939508209584006709525221053605515373965266365474014162871727873923935469195773083682555289322275596819198059208928831231
  ( 164 digits)
SNFS difficulty: 193 digits.
Divisors found:
 r1=114623516402068263048374107148074526153902078826891749923032115067
 r2=438608874285502256844751510885066987832289149361752461518587566928513572528389208388687896598390093
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 50274891495756964747055055496890986637122321939508209584006709525221053605515373965266365474014162871727873923935469195773083682555289322275596819198059208928831231
Y1: 1
Y0: -100000000000000000000000000000000000000
c5: 1000
c0: -9
skew: 0.39
type: snfs
rlim: 15000000
alim: 15000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
#qintsize: 100000
Factor base limits: 15000000/15000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved rational special-q in [7500000, 15100001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: 63000000 relations (had to throw away 10000000) => 53000000
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1729622 x 1729870
Total sieving time: 380.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 7.30 hours.
Time per square root: 0.40 hours * (4 sqrts)
Prototype def-par.txt line would be:
snfs,193,5,0,0,0,0,0,0,0,0,15000000,15000000,29,29,58,58,2.5,2.5,100000
total time: 389.00 hours.

Sep 2, 2008

Factorizations of 277...771 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Sep 1, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve

(68·10¹⁹²+13)/9 = 7(5)₁₉₁7_<193> = 3 · C193

C193 = P92 · P102

P92 = 10084827411252959360121233502972739996691984935274651940807752390233804581909806438612395447_<92>

P102 = 249733427833209956994171060959372869772921006108776325921841891154070929004420634528685716659200605377_<102>

Number: n
N=2518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518519
  ( 193 digits)
SNFS difficulty: 194 digits.
Divisors found:

Mon Sep 01 20:42:16 2008  prp92 factor: 10084827411252959360121233502972739996691984935274651940807752390233804581909806438612395447
Mon Sep 01 20:42:16 2008  prp102 factor: 249733427833209956994171060959372869772921006108776325921841891154070929004420634528685716659200605377
Mon Sep 01 20:42:17 2008  elapsed time 06:18:29 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 160.26 hours.
Scaled time: 327.72 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_7_5_191_7
n: 2518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518519
type: snfs
skew: 0.57
deg: 5
c5: 425
c0: 26
m: 200000000000000000000000000000000000000
rlim: 9500000
alim: 9500000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9500000/9500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 12500001)
Primes: RFBsize:633578, AFBsize:634283, largePrimes:11118249 encountered
Relations: rels:11173345, finalFF:1300777
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 159.88 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,194,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,50,50,2.5,2.5,100000
total time: 160.26 hours.
 --------- CPU info (if available) ----------

Sep 1, 2008 (3rd)

By suberi / GMP-ECM 6.2.1

4·10¹⁶⁷+3 = 4(0)₁₆₆3_<168> = 31 · 28775130387762169_<17> · 6041416682842093129_<19> · C131

C131 = P40 · P91

P40 = 9040172761574724472563661611963885082577_<40>

P91 = 8210421944564469678826128815336450569971653908303104793893829949559207978039441352980000269_<91>

Run 691 out of 904:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4208089882
Step 1 took 18313ms
Step 2 took 9062ms
********** Factor found in step 2: 9040172761574724472563661611963885082577
Found probable prime factor of 40 digits: 9040172761574724472563661611963885082577
Probable prime cofactor 8210421944564469678826128815336450569971653908303104793893829949559207978039441352980000269 has 91 digits

Sep 1, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(8·10¹⁶⁸-11)/3 = 2(6)₁₆₇3_<169> = 10147737487_<11> · 16342775944014823_<17> · 7182282825305090787823969_<25> · C118

C118 = P52 · P66

P52 = 8673076109373383322045834079530356383323130570903067_<52>

P66 = 258129726574229822024593324520497107330628067659816506194390087581_<66>

Number: 26663_168
N=2238778764670036419303891122295571160842294590325316161112993170253842339716470732568621665558861692124847724391510927
  ( 118 digits)
Divisors found:
 r1=8673076109373383322045834079530356383323130570903067 (pp52)
 r2=258129726574229822024593324520497107330628067659816506194390087581 (pp66)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 82.55 hours.
Scaled time: 38.96 units (timescale=0.472).
Factorization parameters were as follows:
name: 26663_168
n: 2238778764670036419303891122295571160842294590325316161112993170253842339716470732568621665558861692124847724391510927
skew: 87948.71
# norm 6.50e+15
c5: 3300
c4: -2150396930
c3: -27162499434620
c2: 11425700944262902017
c1: -153744611732049114131170
c0: -9212687014339136827415685337
# alpha -5.65
Y1: 3149785904737
Y0: -58385163583490247768414
# Murphy_E 4.08e-10
# M 75257000721508686292250693276166591660463930381830897805141574721611218468907349199283468006029506246273595166527328
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 3810001)
Primes: RFBsize:315948, AFBsize:315291, largePrimes:7527907 encountered
Relations: rels:7516576, finalFF:709664
Max relations in full relation-set: 28
Initial matrix: 631318 x 709664 with sparse part having weight 55983557.
Pruned matrix : 563555 x 566775 with weight 38359589.
Polynomial selection time: 3.98 hours.
Total sieving time: 63.38 hours.
Total relation processing time: 0.72 hours.
Matrix solve time: 14.05 hours.
Time per square root: 0.42 hours.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 82.55 hours.
 --------- CPU info (if available) ----------

Sep 1, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

3·10¹⁹²+1 = 3(0)₁₉₁1_<193> = 151 · C191

C191 = P48 · P71 · P72

P48 = 791442937966190685229637395742267041720820331589_<48>

P71 = 95011290548333356448178869786693410025075222062601524884381341878748749_<71>

P72 = 264210140483694895177251228728197166603387493603667452462313902636578791_<72>

Number: n
N=19867549668874172185430463576158940397350993377483443708609271523178807947019867549668874172185430463576158940397350993377483443708609271523178807947019867549668874172185430463576158940397351
  ( 191 digits)
SNFS difficulty: 192 digits.
Divisors found:

Mon Sep 01 05:42:01 2008  prp48 factor: 791442937966190685229637395742267041720820331589
Mon Sep 01 05:42:01 2008  prp71 factor: 95011290548333356448178869786693410025075222062601524884381341878748749
Mon Sep 01 05:42:01 2008  prp72 factor: 264210140483694895177251228728197166603387493603667452462313902636578791
Mon Sep 01 05:42:01 2008  elapsed time 14:25:58 (Msieve 1.36)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 179.21 hours.
Scaled time: 103.23 units (timescale=0.576).
Factorization parameters were as follows:
name: KA_3_0_191_1
n: 19867549668874172185430463576158940397350993377483443708609271523178807947019867549668874172185430463576158940397350993377483443708609271523178807947019867549668874172185430463576158940397351
type: snfs
skew: 0.32
deg: 5
c5: 300
c0: 1
m: 100000000000000000000000000000000000000
rlim: 9500000
alim: 9500000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9500000/9500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 14600001)
Primes: RFBsize:633578, AFBsize:633363, largePrimes:11219211 encountered
Relations: rels:11288392, finalFF:1313629
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 178.52 hours.
Total relation processing time: 0.69 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,192,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,50,50,2.5,2.5,100000
total time: 179.21 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(8·10¹⁶⁵-11)/3 = 2(6)₁₆₄3_<166> = 1553 · 1190821 · C157

C157 = P33 · P57 · P67

P33 = 892943739843446667190715388245117_<33>

P57 = 392527646794798165127898569877809173341146158091463648461_<57>

P67 = 4113925703226251734064538448395755445011135196921757070023860615523_<67>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 1441951960246082360764268417591729632910128417810088023130093284906523100277052882542186121907079037104833973273686096487538783909255696393232530195633467051 (157 digits)
Using B1=2610000, B2=3568033570, polynomial Dickson(6), sigma=2799032758
Step 1 took 31469ms
Step 2 took 12031ms
********** Factor found in step 2: 892943739843446667190715388245117
Found probable prime factor of 33 digits: 892943739843446667190715388245117
Composite cofactor 1614829575376035798972495961314039512335349400212716937196026101586056506417632008295855000696288207767290358854258751660103 has 124 digits

Number: n
N=1614829575376035798972495961314039512335349400212716937196026101586056506417632008295855000696288207767290358854258751660103
  ( 124 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Sep  1 12:19:26 2008  prp57 factor: 392527646794798165127898569877809173341146158091463648461
Mon Sep  1 12:19:26 2008  prp67 factor: 4113925703226251734064538448395755445011135196921757070023860615523
Mon Sep  1 12:19:26 2008  elapsed time 01:21:42 (Msieve 1.36)

Version: GGNFS-0.77.1-20050930-k8
Total time: 12.27 hours.
Scaled time: 10.29 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_2_6_164_3
n: 1614829575376035798972495961314039512335349400212716937196026101586056506417632008295855000696288207767290358854258751660103
type: snfs
skew: 2.13
deg: 5
c5: 1
c0: -44
m: 2000000000000000000000000000000000
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved  special-q in [100000, 1400001)
Primes: RFBsize:348513, AFBsize:347567, largePrimes:11994991 encountered
Relations: rels:11300458, finalFF:810381
Max relations in full relation-set: 28
Initial matrix: 696143 x 810381 with sparse part having weight 59295126.
Pruned matrix : 
Total sieving time: 12.01 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,52,52,2.5,2.5,100000
total time: 12.27 hours.
 --------- CPU info (if available) ----------

August 2008

Aug 31, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(5·10¹⁸⁸+7)/3 = 1(6)₁₈₇9_<189> = 13 · 4508291 · C181

C181 = P64 · P117

P64 = 5572625206496682509937965003069828168574001110247054129799055991_<64>

P117 = 510309462344547784599419974697282044175752543112956276456061023653909400195521795522887826526858682926321882006053773_<117>

Number: n
N=2843763372974996625732569796517753737019307941859303339740161586843622231311269130700041437613612967865832199567532978796803603143744008652684689790546533156981329027011082583804043
  ( 181 digits)
SNFS difficulty: 190 digits.
Divisors found:

Sun Aug 31 21:55:16 2008  prp64 factor: 5572625206496682509937965003069828168574001110247054129799055991
Sun Aug 31 21:55:16 2008  prp117 factor: 510309462344547784599419974697282044175752543112956276456061023653909400195521795522887826526858682926321882006053773
Sun Aug 31 21:55:16 2008  elapsed time 05:08:39 (Msieve 1.36)

Version: GGNFS-0.77.1-20050930-k8
Total time: 214.52 hours.
Scaled time: 179.76 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_1_6_187_9
n: 2843763372974996625732569796517753737019307941859303339740161586843622231311269130700041437613612967865832199567532978796803603143744008652684689790546533156981329027011082583804043
type: snfs
skew: 2.69
deg: 5
c5: 1
c0: 140
m: 100000000000000000000000000000000000000
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 8900001)
Primes: RFBsize:602489, AFBsize:603790, largePrimes:10824329 encountered
Relations: rels:10821915, finalFF:1236646
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 214.11 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,50,50,2.5,2.5,100000
total time: 214.52 hours.
 --------- CPU info (if available) ----------

Aug 31, 2008 (2nd)

By Wataru Sakai / GGNFS

(2·10¹⁹⁹-17)/3 = (6)₁₉₈1_<199> = C199

C199 = P61 · P138

P61 = 7746198155672718412194373416422042294291282224078057676781559_<61>

P138 = 860637248452586240793411305547124642667894480293199002512800099070390305673067846165291277474909445333699703778303587085959036214662816579_<138>

Number: 66661_199
N=6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661
  ( 199 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=7746198155672718412194373416422042294291282224078057676781559 (pp61)
 r2=860637248452586240793411305547124642667894480293199002512800099070390305673067846165291277474909445333699703778303587085959036214662816579 (pp138)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 6373.94 hours.
Scaled time: 11944.77 units (timescale=1.874).
Factorization parameters were as follows:
n: 6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661
m: 10000000000000000000000000000000000000000
c5: 1
c0: -85
skew: 2.43
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 107400001)
Primes: RFBsize:501962, AFBsize:502501, largePrimes:10315349 encountered
Relations: rels:12144748, finalFF:1129224
Max relations in full relation-set: 32
Initial matrix: 1004527 x 1129224 with sparse part having weight 218619771.
Pruned matrix : 945193 x 950279 with weight 202057474.
Total sieving time: 6350.64 hours.
Total relation processing time: 1.31 hours.
Matrix solve time: 21.57 hours.
Time per square root: 0.43 hours.
Prototype def-par.txt line would be:
snfs,200,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 6373.94 hours.
 --------- CPU info (if available) ----------

Aug 31, 2008

By Sinkiti Sibata / GMP-ECM

(8·10¹⁷⁰-11)/3 = 2(6)₁₆₉3_<171> = 733 · 433336074385189_<15> · 4848705026009567_<16> · C138

C138 = P41 · P97

P41 = 21444720061961923459119388271642272065257_<41>

P97 = 8074093367579318645109991039242689165888372857971148977391463264840925662722940362463996964183521_<97>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 173146672021881921378896373090978957549911838084851329459712681790545591628898153652066417156764183279951056853213653990375319291436029897

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1148971329
Step 1 took 48953ms
Step 2 took 16973ms
********** Factor found in step 2: 21444720061961923459119388271642272065257
Found probable prime factor of 41 digits: 21444720061961923459119388271642272065257
Probable prime cofactor 8074093367579318645109991039242689165888372857971148977391463264840925662722940362463996964183521 has 97 digits

Aug 30, 2008 (2nd)

By Tyler Cadigan / GGNFS, Msieve

(25·10¹⁹⁵-1)/3 = 8(3)₁₉₅_<196> = 13 · 191 · 641 · 2521 · 70360703591_<11> · C176

C176 = P45 · P131

P45 = 347475803459299610733739361332835589747500711_<45>

P131 = 84948637535002693046809344987987788506145903659602270746463195239782274901028606636613753795353452586876315488810371234015435431391_<131>

Number: 83333_195
N=29517596080247877525790851053981747064359792547947739805692098981033869953189081994166555707582584397071309454538456953939153374792078239873193031003841009649977944238364219001
  ( 176 digits)
SNFS difficulty: 196 digits.
Divisors found:
 r1=347475803459299610733739361332835589747500711
 r2=84948637535002693046809344987987788506145903659602270746463195239782274901028606636613753795353452586876315488810371234015435431391
Version: 
Total time: 436.75 hours.
Scaled time: 1128.56 units (timescale=2.584).
Factorization parameters were as follows:
n: 29517596080247877525790851053981747064359792547947739805692098981033869953189081994166555707582584397071309454538456953939153374792078239873193031003841009649977944238364219001
m: 1000000000000000000000000000000000000000
c5: 25
c0: -1
skew: 0.53
Y0: 1000000000000000000000000000000000000000
Y1: -1
type: snfs
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
rlim: 20000000
alim: 20000000
qintsize: 1000000Factor base limits: 20000000/20000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved algebraic special-q in [10000000, 16000001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2686515 x 2686763
Total sieving time: 436.75 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,196,5,0,0,0,0,0,0,0,0,20000000,20000000,29,29,58,58,2.6,2.6,100000
total time: 436.75 hours.
 --------- CPU info (if available) ----------

Factorizations of 833...33 have been completed up to n=200.

Aug 30, 2008

By Jo Yeong Uk / GGNFS

8·10¹⁷⁴-9 = 7(9)₁₇₃1_<175> = 41 · 173743074481_<12> · 19106912458400837994080317241_<29> · 451656251742733916273683704772193_<33> · C102

C102 = P45 · P57

P45 = 592251998082554341409369753785202370375115807_<45>

P57 = 219732123875349514938455918437129730022904144914165154681_<57>

Number: 79991_174
N=130136789408099093943642895529280422128901086592792253560350069883955602104627506623059801699443142567
  ( 102 digits)
Divisors found:
 r1=592251998082554341409369753785202370375115807 (pp45)
 r2=219732123875349514938455918437129730022904144914165154681 (pp57)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.00 hours.
Scaled time: 9.56 units (timescale=2.392).
Factorization parameters were as follows:
name: 79991_174
n: 130136789408099093943642895529280422128901086592792253560350069883955602104627506623059801699443142567
skew: 10873.83
# norm 5.58e+13
c5: 8280
c4: -265261398
c3: -736553682108
c2: 6989101037039633
c1: -128237153725381623216
c0: 63440594100681936495345
# alpha -5.23
Y1: 31466063483
Y0: -27496482160245593002
# Murphy_E 2.83e-09
# M 12646438619583911536750972380335684031448376564007326365424264391297480438938008412765721828969481049
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [750000, 1350001)
Primes: RFBsize:114155, AFBsize:113556, largePrimes:4385038 encountered
Relations: rels:4331759, finalFF:321559
Max relations in full relation-set: 28
Initial matrix: 227790 x 321559 with sparse part having weight 27654118.
Pruned matrix : 180096 x 181298 with weight 12977876.
Polynomial selection time: 0.31 hours.
Total sieving time: 3.46 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,49,49,2.6,2.6,50000
total time: 4.00 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673799)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Calibrating delay using timer specific routine.. 5344.51 BogoMIPS (lpj=2672259)
Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672350)

Aug 29, 2008

By Serge Batalov / GMP-ECM 6.2.1, pol51+Msieve 1.37

(14·10¹⁷¹+31)/9 = 1(5)₁₇₀9_<172> = 53 · 496681 · 410603139824071_<15> · 2475177024694321515444421_<25> · C125

C125 = P34 · P92

P34 = 5813483701575740349680035428752387_<34>

P92 = 10001545600677817037581209402111644839880337297632163971294502938355625025052962872656161339_<92>

Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=783124874
Step 1 took 11510ms
Step 2 took 6852ms
********** Factor found in step 2: 5813483701575740349680035428752387
Found probable prime factor of 34 digits: 5813483701575740349680035428752387
Probable prime cofactor 10001545600677817037581209402111644839880337297632163971294502938355625025052962872656161339 has 92 digits

8·10¹⁷⁴-9 = 7(9)₁₇₃1_<175> = 41 · 173743074481_<12> · 19106912458400837994080317241_<29> · C134

C134 = P33 · C102

P33 = 451656251742733916273683704772193_<33>

C102 = [130136789408099093943642895529280422128901086592792253560350069883955602104627506623059801699443142567_<102>]

Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=1366989160
Step 1 took 10130ms
Step 2 took 6967ms
********** Factor found in step 2: 451656251742733916273683704772193
Found probable prime factor of 33 digits: 451656251742733916273683704772193
Composite cofactor 130136789408099093943642895529280422128901086592792253560350069883955602104627506623059801699443142567 has 102 digits

(4·10¹⁷⁶+11)/3 = 1(3)₁₇₅7_<177> = 654817399 · 2654433511_<10> · 651698912539_<12> · 137745684013733_<15> · C132

C132 = P34 · P34 · P66

P34 = 1089318090564868475456017418176427_<34>

P34 = 1231627716604690046697182424513253_<34>

P66 = 636923845516948278854619576438453364025839828712022887610324552089_<66>

#ECM, then gnfs/Msieve
#
Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=3838364986
Step 1 took 11629ms
Step 2 took 7041ms
********** Factor found in step 2: 1089318090564868475456017418176427
Found probable prime factor of 34 digits: 1089318090564868475456017418176427
Composite cofactor 784453061505117357864038664345811078914332428946244066627988881633785366535204327880785191069335517 has 99 digits

Number: 13337_176
N=784453061505117357864038664345811078914332428946244066627988881633785366535204327880785191069335517
  ( 99 digits)
Divisors found:
 r1=1231627716604690046697182424513253
 r2=636923845516948278854619576438453364025839828712022887610324552089
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
name: 13337_176
n: 784453061505117357864038664345811078914332428946244066627988881633785366535204327880785191069335517
skew: 2513.29
# norm 1.16e+13
c5: 20580
c4: 508307051
c3: 557345214445
c2: -470168275690464
c1: -2589049590718293107
c0: -52486279407165116565
# alpha -4.66
Y1: 5234753843
Y0: -8245613164455536492
# Murphy_E 3.94e-09
# M 675691405801972959220472988772094584688379672974200505104477011633136745725111786358588561469188675
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 165902 x 166133
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,98,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000

total time: 2.50 hours.

Aug 28, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(8·10¹⁵⁵-11)/3 = 2(6)₁₅₄3_<156> = 23 · 383 · 7853 · 140143 · 89728591 · 1561361513_<10> · C126

C126 = P46 · P80

P46 = 8627089357765378991076246682719777963998610241_<46>

P80 = 22758126142966332417669133587283570000761657492867169951767849493683399601751411_<80>

Number: 26663_155
N=196336387850666898435886985994390947515578847455806385406582232661469625771635883806609574286096836768770851495960073560800051
  ( 126 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=8627089357765378991076246682719777963998610241 (pp46)
 r2=22758126142966332417669133587283570000761657492867169951767849493683399601751411 (pp80)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 38.18 hours.
Scaled time: 18.02 units (timescale=0.472).
Factorization parameters were as follows:
name: 26663_155
n: 196336387850666898435886985994390947515578847455806385406582232661469625771635883806609574286096836768770851495960073560800051
m: 10000000000000000000000000000000
c5: 8
c0: -11
skew: 1.07
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2500001)
Primes: RFBsize:216816, AFBsize:216082, largePrimes:5574642 encountered
Relations: rels:5553841, finalFF:573445
Max relations in full relation-set: 28
Initial matrix: 432963 x 573445 with sparse part having weight 42953283.
Pruned matrix : 333445 x 335673 with weight 26446379.
Total sieving time: 34.16 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 3.70 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 38.18 hours.
 --------- CPU info (if available) ----------

Aug 28, 2008 (2nd)

By Serge Batalov / GMP-ECM 6.2.1, ***Msieve-1.37***

(19·10¹⁷⁶+17)/9 = 2(1)₁₇₅3_<177> = 3² · 167 · 1543 · 53611 · 2401409 · 974819639393790407634579313_<27> · C132

C132 = P31 · P102

P31 = 4956648204881915050768672150327_<31>

P102 = 146336874948973085318917842213648178095098263874900615495508640162228819919842162403788352528350133653_<102>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2131237211
Step 1 took 16750ms
Step 2 took 6958ms
********** Factor found in step 2: 4956648204881915050768672150327
Found probable prime factor of 31 digits: 4956648204881915050768672150327
Probable prime cofactor 146336874948973085318917842213648178095098263874900615495508640162228819919842162403788352528350133653 has 102 digits

(8·10¹⁶³-11)/3 = 2(6)₁₆₂3_<164> = 814320350738108743_<18> · 2763870653886852635716885631_<28> · C119

C119 = P42 · P77

P42 = 301147670230833087243353381876753817878047_<42>

P77 = 39343792552349727779693072074780867921299727848712907400115696799639680859713_<77>

Number: 26663_163
N=11848291465185322644709783710930277954304746404731360294607998144533448422134791685213367257651306885901437134349420511
  ( 119 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=301147670230833087243353381876753817878047
 r2=39343792552349727779693072074780867921299727848712907400115696799639680859713
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 11848291465185322644709783710930277954304746404731360294607998144533448422134791685213367257651306885901437134349420511
Y1: 1
Y0: -200000000000000000000000000000000
c5: 250
c0: -11
skew: 0.54
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2250000, 2850001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 741400 x 741648
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 2.10 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,52,52,2.5,2.5,100000
total time: 14.00 hours.

Aug 28, 2008

Msieve 1.37 has been released.

HOW TO for Japanese users

Aug 27, 2008 (3rd)

By Wataru Sakai / GGNFS

6·10¹⁸⁷+1 = 6(0)₁₈₆1_<188> = 4547 · C185

C185 = P67 · P118

P67 = 6536834037833420095985946925674276836560136508795702561667702266167_<67>

P118 = 2018639826103785865286631933082975605890545795355024440916114945745465813061205948102752034943266139296166842862791149_<118>

Number: 60001_187
N=13195513525401363536397624807565427754563448427534638223004178579283043765119859247855729052122278425335385968770617989883439630525621288761820980866505388168022872223444029030129755883
  ( 185 digits)
SNFS difficulty: 187 digits.
Divisors found:
 r1=6536834037833420095985946925674276836560136508795702561667702266167 (pp67)
 r2=2018639826103785865286631933082975605890545795355024440916114945745465813061205948102752034943266139296166842862791149 (pp118)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 777.86 hours.
Scaled time: 1561.95 units (timescale=2.008).
Factorization parameters were as follows:
n: 13195513525401363536397624807565427754563448427534638223004178579283043765119859247855729052122278425335385968770617989883439630525621288761820980866505388168022872223444029030129755883
m: 10000000000000000000000000000000000000
c5: 600
c0: 1
skew: 0.28
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 15700001)
Primes: RFBsize:501962, AFBsize:501791, largePrimes:6891187 encountered
Relations: rels:7436758, finalFF:1180022
Max relations in full relation-set: 32
Initial matrix: 1003819 x 1180022 with sparse part having weight 115293725.
Pruned matrix : 865389 x 870472 with weight 93704423.
Total sieving time: 768.45 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 9.03 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 777.86 hours.
 --------- CPU info (if available) ----------

Aug 27, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(8·10¹⁶²-11)/3 = 2(6)₁₆₁3_<163> = 359 · 4507487 · 27059729 · 6315921853_<10> · 103496669775133_<15> · C122

C122 = P40 · P83

P40 = 4696433042047289514966970256674200476261_<40>

P83 = 19837415944333569454521178385670584763249729870811764701051961027139351921162624331_<83>

Number: 26663_162
N=93165095709803910034220755200074213920442816991906500418090991135299650476503556714014354208663641612641625384792826506391
  ( 122 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=4696433042047289514966970256674200476261 (pp40)
 r2=19837415944333569454521178385670584763249729870811764701051961027139351921162624331 (pp83)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 53.91 hours.
Scaled time: 54.39 units (timescale=1.009).
Factorization parameters were as follows:
name: 26663_162
n: 93165095709803910034220755200074213920442816991906500418090991135299650476503556714014354208663641612641625384792826506391
m: 200000000000000000000000000000000
c5: 25
c0: -11
skew: 0.85
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4350001)
Primes: RFBsize:315948, AFBsize:315742, largePrimes:5978765 encountered
Relations: rels:6297572, finalFF:922018
Max relations in full relation-set: 28
Initial matrix: 631754 x 922018 with sparse part having weight 52727144.
Pruned matrix : 405565 x 408787 with weight 39479532.
Total sieving time: 52.40 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.34 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 53.91 hours.
 --------- CPU info (if available) ----------

Aug 27, 2008

By Serge Batalov / Msieve 1.36, GMP-ECM 6.2.1

(8·10¹⁵⁷-11)/3 = 2(6)₁₅₆3_<158> = 11069 · C154

C154 = P40 · P115

P40 = 1105327928036418569669147130317306733637_<40>

P115 = 2179561869275003655805053554544359944708001505318774837743094477875371215017299055737728009643796884495907468594071_<115>

Number: 26663_157
N=2409130604992923178847833288162134489716023729936459180293311651157888397024723702833739874122925889119763905200710693528472912337760110820007829674466227
  ( 154 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=1105327928036418569669147130317306733637
 r2=2179561869275003655805053554544359944708001505318774837743094477875371215017299055737728009643796884495907468594071
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.313).
Factorization parameters were as follows:
n: 2409130604992923178847833288162134489716023729936459180293311651157888397024723702833739874122925889119763905200710693528472912337760110820007829674466227
Y1: 1
Y0: -20000000000000000000000000000000
c5: 25
c0: -11
skew: 0.85
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1500000, 2300001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 496232 x 496474
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,52,52,2.5,2.5,100000
total time: 15.20 hours.

(8·10¹⁶⁴-11)/3 = 2(6)₁₆₃3_<165> = 179 · 77450201 · 386822927 · C146

C146 = P35 · P112

P35 = 10865659052292619388679044078475137_<35>

P112 = 4576409430557803066039585822705526398937317357435248022811589980525323757752016816620470019755082138495042370603_<112>

Using B1=25000000, B2=96190324246, polynomial Dickson(12), sigma=2919656688
Step 1 took 173974ms
Step 2 took 45112ms
********** Factor found in step 2: 10865659052292619388679044078475137
Found probable prime factor of 35 digits: 10865659052292619388679044078475137
Probable prime cofactor 4576409430557803066039585822705526398937317357435248022811589980525323757752016816620470019755082138495042370603 has 112 digits

Aug 26, 2008 (3rd)

By Hugo Platzer / Msieve-1.36 optimized 64-bit linux lattice siever from Greg Childers

6·10¹⁸⁰-7 = 5(9)₁₇₉3_<181> = 17 · 5791 · C176

C176 = P61 · P116

P61 = 4830487850130825355136992625082278853531328717363811995759451_<61>

P116 = 12617048427077972576764760920138324767170820384685368004188695290274577720048489648872812603297601032348850349016469_<116>

Tue Aug 26 11:38:06 2008  
Tue Aug 26 11:38:06 2008  
Tue Aug 26 11:38:06 2008  Msieve v. 1.36
Tue Aug 26 11:38:06 2008  random seeds: d67440d2 74216d9f
Tue Aug 26 11:38:06 2008  factoring 60946499131512387375948479892734161528538198218330675388787875709772771135738011315733338750799922801101100084309323798592135870062063851615590114477840868690767621156561398519 (176 digits)
Tue Aug 26 11:38:08 2008  no P-1/P+1/ECM available, skipping
Tue Aug 26 11:38:08 2008  commencing number field sieve (176-digit input)
Tue Aug 26 11:38:08 2008  R0: -1000000000000000000000000000000000000
Tue Aug 26 11:38:08 2008  R1:  1
Tue Aug 26 11:38:08 2008  A0: -7
Tue Aug 26 11:38:08 2008  A1:  0
Tue Aug 26 11:38:08 2008  A2:  0
Tue Aug 26 11:38:08 2008  A3:  0
Tue Aug 26 11:38:08 2008  A4:  0
Tue Aug 26 11:38:08 2008  A5:  6
Tue Aug 26 11:38:08 2008  size score = 2.794913e-12, Murphy alpha = 1.791017, combined = 1.538481e-12
Tue Aug 26 11:38:08 2008  generating factor base
Tue Aug 26 11:38:11 2008  factor base complete:
Tue Aug 26 11:38:11 2008  539777 rational roots (max prime = 7999993)
Tue Aug 26 11:38:11 2008  539975 algebraic roots (max prime = 7999993)
Tue Aug 26 11:38:12 2008  a range: [-60000000, 60000000]
Tue Aug 26 11:38:12 2008  b range: [1, 4294967295]
Tue Aug 26 11:38:12 2008  number of hash buckets: 123
Tue Aug 26 11:38:12 2008  sieve block size: 65536
Tue Aug 26 11:38:12 2008  
Tue Aug 26 11:38:12 2008  maximum RFB prime: 7999993
Tue Aug 26 11:38:12 2008  RFB entries: 539777
Tue Aug 26 11:38:12 2008  medium RFB entries: 6542
Tue Aug 26 11:38:12 2008  resieved RFB entries: 6374
Tue Aug 26 11:38:12 2008  small RFB prime powers: 28
Tue Aug 26 11:38:12 2008  projective RFB roots: 0
Tue Aug 26 11:38:12 2008  RFB trial factoring cutoff: 60 or 89 bits
Tue Aug 26 11:38:12 2008  single large prime RFB range: 23 - 27 bits
Tue Aug 26 11:38:12 2008  double large prime RFB range: 46 - 52 bits
Tue Aug 26 11:38:12 2008  triple large prime RFB range: 72 - 79 bits
Tue Aug 26 11:38:12 2008  
Tue Aug 26 11:38:12 2008  maximum AFB prime: 7999993
Tue Aug 26 11:38:12 2008  AFB entries: 539975
Tue Aug 26 11:38:12 2008  medium AFB entries: 6517
Tue Aug 26 11:38:12 2008  resieved AFB entries: 6364
Tue Aug 26 11:38:12 2008  small AFB prime powers: 6
Tue Aug 26 11:38:12 2008  projective AFB roots: 2
Tue Aug 26 11:38:12 2008  AFB trial factoring cutoff: 60 or 89 bits
Tue Aug 26 11:38:12 2008  single large prime AFB range: 23 - 27 bits
Tue Aug 26 11:38:12 2008  double large prime AFB range: 46 - 52 bits
Tue Aug 26 11:38:12 2008  triple large prime AFB range: 72 - 79 bits
Tue Aug 26 11:38:12 2008  
Tue Aug 26 11:38:12 2008  multiplying 1523913 primes from 7999993 to 33554432
Tue Aug 26 11:38:16 2008  multiply complete, product has 36865603 bits
Tue Aug 26 11:38:44 2008  completed b = 3, found 172 relations
Tue Aug 26 11:38:44 2008  elapsed time 00:00:38
Tue Aug 26 11:43:18 2008  
Tue Aug 26 11:43:18 2008  
Tue Aug 26 11:43:18 2008  Msieve v. 1.36
Tue Aug 26 11:43:18 2008  random seeds: 0d302a09 c30c0b1f
Tue Aug 26 11:43:18 2008  factoring 60946499131512387375948479892734161528538198218330675388787875709772771135738011315733338750799922801101100084309323798592135870062063851615590114477840868690767621156561398519 (176 digits)
Tue Aug 26 11:43:20 2008  no P-1/P+1/ECM available, skipping
Tue Aug 26 11:43:20 2008  commencing number field sieve (176-digit input)
Tue Aug 26 11:43:20 2008  R0: -1000000000000000000000000000000000000
Tue Aug 26 11:43:20 2008  R1:  1
Tue Aug 26 11:43:20 2008  A0: -7
Tue Aug 26 11:43:20 2008  A1:  0
Tue Aug 26 11:43:20 2008  A2:  0
Tue Aug 26 11:43:20 2008  A3:  0
Tue Aug 26 11:43:20 2008  A4:  0
Tue Aug 26 11:43:20 2008  A5:  6
Tue Aug 26 11:43:20 2008  size score = 2.794913e-12, Murphy alpha = 1.791017, combined = 1.538481e-12
Tue Aug 26 11:43:46 2008  restarting with 11607220 relations
Tue Aug 26 11:43:48 2008  added 27651 free relations
Tue Aug 26 11:43:48 2008  
Tue Aug 26 11:43:48 2008  commencing relation filtering
Tue Aug 26 11:43:48 2008  commencing duplicate removal, pass 1
Tue Aug 26 11:44:34 2008  error -9 reading relation 6604032
Tue Aug 26 11:44:41 2008  error -11 reading relation 7631047
Tue Aug 26 11:44:48 2008  error -9 reading relation 8631315
Tue Aug 26 11:44:55 2008  error -5 reading relation 9591341
Tue Aug 26 11:44:58 2008  error -11 reading relation 10123854
Tue Aug 26 11:45:02 2008  error -9 reading relation 10634976
Tue Aug 26 11:45:05 2008  error -15 reading relation 11125754
Tue Aug 26 11:45:09 2008  error -11 reading relation 11607220
Tue Aug 26 11:45:09 2008  found 1494552 hash collisions in 11634863 relations
Tue Aug 26 11:45:09 2008  commencing duplicate removal, pass 2
Tue Aug 26 11:45:18 2008  found 1523897 duplicates and 10110966 unique relations
Tue Aug 26 11:45:18 2008  memory use: 65.3 MB
Tue Aug 26 11:45:20 2008  ignoring smallest 592937 rational and 593231 algebraic ideals
Tue Aug 26 11:45:20 2008  filtering rational ideals above 8847360
Tue Aug 26 11:45:20 2008  filtering algebraic ideals above 8847360
Tue Aug 26 11:45:20 2008  need 1779252 more relations than ideals
Tue Aug 26 11:45:20 2008  commencing singleton removal, pass 1
Tue Aug 26 11:46:32 2008  relations with 0 large ideals: 97035
Tue Aug 26 11:46:32 2008  relations with 1 large ideals: 975911
Tue Aug 26 11:46:32 2008  relations with 2 large ideals: 3729723
Tue Aug 26 11:46:32 2008  relations with 3 large ideals: 4605398
Tue Aug 26 11:46:32 2008  relations with 4 large ideals: 676207
Tue Aug 26 11:46:32 2008  relations with 5 large ideals: 26692
Tue Aug 26 11:46:32 2008  relations with 6 large ideals: 0
Tue Aug 26 11:46:32 2008  relations with 7+ large ideals: 0
Tue Aug 26 11:46:32 2008  10110966 relations and about 7977776 large ideals
Tue Aug 26 11:46:32 2008  commencing singleton removal, pass 2
Tue Aug 26 11:47:43 2008  found 3829552 singletons
Tue Aug 26 11:47:43 2008  current dataset: 6281414 relations and about 3704726 large ideals
Tue Aug 26 11:47:43 2008  commencing singleton removal, pass 3
Tue Aug 26 11:48:29 2008  found 415704 singletons
Tue Aug 26 11:48:29 2008  current dataset: 5865710 relations and about 3281204 large ideals
Tue Aug 26 11:48:29 2008  commencing singleton removal, final pass
Tue Aug 26 11:49:15 2008  memory use: 97.1 MB
Tue Aug 26 11:49:15 2008  commencing in-memory singleton removal
Tue Aug 26 11:49:15 2008  begin with 5865710 relations and 3465322 unique ideals
Tue Aug 26 11:49:18 2008  reduce to 5552191 relations and 3148643 ideals in 7 passes
Tue Aug 26 11:49:18 2008  max relations containing the same ideal: 27
Tue Aug 26 11:49:20 2008  removing 981791 relations and 669643 ideals in 312148 cliques
Tue Aug 26 11:49:21 2008  commencing in-memory singleton removal
Tue Aug 26 11:49:21 2008  begin with 4570400 relations and 3148643 unique ideals
Tue Aug 26 11:49:23 2008  reduce to 4538232 relations and 2445242 ideals in 5 passes
Tue Aug 26 11:49:23 2008  max relations containing the same ideal: 23
Tue Aug 26 11:49:24 2008  removing 695031 relations and 382883 ideals in 312148 cliques
Tue Aug 26 11:49:25 2008  commencing in-memory singleton removal
Tue Aug 26 11:49:25 2008  begin with 3843201 relations and 2445242 unique ideals
Tue Aug 26 11:49:26 2008  reduce to 3788806 relations and 2003161 ideals in 5 passes
Tue Aug 26 11:49:26 2008  max relations containing the same ideal: 21
Tue Aug 26 11:49:28 2008  filtering rational ideals above 720000
Tue Aug 26 11:49:28 2008  filtering algebraic ideals above 720000
Tue Aug 26 11:49:28 2008  need 116061 more relations than ideals
Tue Aug 26 11:49:28 2008  commencing singleton removal, final pass
Tue Aug 26 11:50:21 2008  keeping 3928915 ideals with weight <= 20, new excess is 405849
Tue Aug 26 11:50:25 2008  memory use: 173.7 MB
Tue Aug 26 11:50:25 2008  commencing in-memory singleton removal
Tue Aug 26 11:50:26 2008  begin with 5552191 relations and 3928915 unique ideals
Tue Aug 26 11:50:29 2008  reduce to 5551567 relations and 3928291 ideals in 4 passes
Tue Aug 26 11:50:29 2008  max relations containing the same ideal: 20
Tue Aug 26 11:50:32 2008  removing 1158851 relations and 758851 ideals in 400000 cliques
Tue Aug 26 11:50:33 2008  commencing in-memory singleton removal
Tue Aug 26 11:50:33 2008  begin with 4392716 relations and 3928291 unique ideals
Tue Aug 26 11:50:37 2008  reduce to 4330937 relations and 3103156 ideals in 6 passes
Tue Aug 26 11:50:37 2008  max relations containing the same ideal: 20
Tue Aug 26 11:50:39 2008  removing 880038 relations and 480038 ideals in 400000 cliques
Tue Aug 26 11:50:40 2008  commencing in-memory singleton removal
Tue Aug 26 11:50:40 2008  begin with 3450899 relations and 3103156 unique ideals
Tue Aug 26 11:50:42 2008  reduce to 3381301 relations and 2546450 ideals in 5 passes
Tue Aug 26 11:50:42 2008  max relations containing the same ideal: 20
Tue Aug 26 11:50:44 2008  removing 775867 relations and 411801 ideals in 364066 cliques
Tue Aug 26 11:50:45 2008  commencing in-memory singleton removal
Tue Aug 26 11:50:45 2008  begin with 2605434 relations and 2546450 unique ideals
Tue Aug 26 11:50:47 2008  reduce to 2540585 relations and 2063741 ideals in 6 passes
Tue Aug 26 11:50:47 2008  max relations containing the same ideal: 19
Tue Aug 26 11:50:48 2008  relations with 0 large ideals: 7566
Tue Aug 26 11:50:48 2008  relations with 1 large ideals: 73927
Tue Aug 26 11:50:48 2008  relations with 2 large ideals: 377040
Tue Aug 26 11:50:48 2008  relations with 3 large ideals: 723326
Tue Aug 26 11:50:48 2008  relations with 4 large ideals: 726199
Tue Aug 26 11:50:48 2008  relations with 5 large ideals: 427856
Tue Aug 26 11:50:48 2008  relations with 6 large ideals: 164504
Tue Aug 26 11:50:48 2008  relations with 7+ large ideals: 40167
Tue Aug 26 11:50:48 2008  commencing 2-way merge
Tue Aug 26 11:50:50 2008  reduce to 2074143 relation sets and 1597299 unique ideals
Tue Aug 26 11:50:50 2008  commencing full merge
Tue Aug 26 11:51:16 2008  memory use: 159.8 MB
Tue Aug 26 11:51:16 2008  found 1023946 cycles, need 953499
Tue Aug 26 11:51:16 2008  weight of 953499 cycles is about 67027131 (70.30/cycle)
Tue Aug 26 11:51:16 2008  distribution of cycle lengths:
Tue Aug 26 11:51:16 2008  1 relations: 27101
Tue Aug 26 11:51:16 2008  2 relations: 92836
Tue Aug 26 11:51:16 2008  3 relations: 126795
Tue Aug 26 11:51:16 2008  4 relations: 136910
Tue Aug 26 11:51:16 2008  5 relations: 133726
Tue Aug 26 11:51:16 2008  6 relations: 116981
Tue Aug 26 11:51:16 2008  7 relations: 97766
Tue Aug 26 11:51:16 2008  8 relations: 76828
Tue Aug 26 11:51:16 2008  9 relations: 58371
Tue Aug 26 11:51:16 2008  10+ relations: 86185
Tue Aug 26 11:51:16 2008  heaviest cycle: 15 relations
Tue Aug 26 11:51:16 2008  commencing cycle optimization
Tue Aug 26 11:51:17 2008  start with 5257576 relations
Tue Aug 26 11:51:28 2008  pruned 115780 relations
Tue Aug 26 11:51:28 2008  memory use: 158.4 MB
Tue Aug 26 11:51:28 2008  distribution of cycle lengths:
Tue Aug 26 11:51:28 2008  1 relations: 27101
Tue Aug 26 11:51:28 2008  2 relations: 94079
Tue Aug 26 11:51:28 2008  3 relations: 130300
Tue Aug 26 11:51:28 2008  4 relations: 140494
Tue Aug 26 11:51:28 2008  5 relations: 138881
Tue Aug 26 11:51:28 2008  6 relations: 120218
Tue Aug 26 11:51:28 2008  7 relations: 100012
Tue Aug 26 11:51:28 2008  8 relations: 76349
Tue Aug 26 11:51:28 2008  9 relations: 56039
Tue Aug 26 11:51:28 2008  10+ relations: 70026
Tue Aug 26 11:51:28 2008  heaviest cycle: 15 relations
Tue Aug 26 11:51:29 2008  
Tue Aug 26 11:51:29 2008  commencing linear algebra
Tue Aug 26 11:51:30 2008  read 953499 cycles
Tue Aug 26 11:51:31 2008  cycles contain 2367107 unique relations
Tue Aug 26 11:51:56 2008  read 2367107 relations
Tue Aug 26 11:52:00 2008  using 32 quadratic characters above 134213508
Tue Aug 26 11:52:21 2008  building initial matrix
Tue Aug 26 11:52:40 2008  
Tue Aug 26 11:52:40 2008  
Tue Aug 26 11:52:40 2008  Msieve v. 1.36
Tue Aug 26 11:52:40 2008  random seeds: 091c43c1 ad0d2b3e
Tue Aug 26 11:52:40 2008  factoring 60946499131512387375948479892734161528538198218330675388787875709772771135738011315733338750799922801101100084309323798592135870062063851615590114477840868690767621156561398519 (176 digits)
Tue Aug 26 11:52:42 2008  no P-1/P+1/ECM available, skipping
Tue Aug 26 11:52:42 2008  commencing number field sieve (176-digit input)
Tue Aug 26 11:52:42 2008  R0: -1000000000000000000000000000000000000
Tue Aug 26 11:52:42 2008  R1:  1
Tue Aug 26 11:52:42 2008  A0: -7
Tue Aug 26 11:52:42 2008  A1:  0
Tue Aug 26 11:52:42 2008  A2:  0
Tue Aug 26 11:52:42 2008  A3:  0
Tue Aug 26 11:52:42 2008  A4:  0
Tue Aug 26 11:52:42 2008  A5:  6
Tue Aug 26 11:52:42 2008  size score = 2.794913e-12, Murphy alpha = 1.791017, combined = 1.538481e-12
Tue Aug 26 11:52:42 2008  
Tue Aug 26 11:52:42 2008  commencing linear algebra
Tue Aug 26 11:52:42 2008  read 953499 cycles
Tue Aug 26 11:52:44 2008  cycles contain 2367107 unique relations
Tue Aug 26 11:53:13 2008  read 2367107 relations
Tue Aug 26 11:53:17 2008  using 32 quadratic characters above 134213508
Tue Aug 26 11:53:38 2008  building initial matrix
Tue Aug 26 11:54:12 2008  memory use: 311.7 MB
Tue Aug 26 11:54:14 2008  read 953499 cycles
Tue Aug 26 11:54:16 2008  matrix is 953311 x 953499 (283.2 MB) with weight 89798014 (94.18/col)
Tue Aug 26 11:54:16 2008  sparse part has weight 63743099 (66.85/col)
Tue Aug 26 11:54:24 2008  filtering completed in 2 passes
Tue Aug 26 11:54:24 2008  matrix is 952824 x 953012 (283.1 MB) with weight 89772381 (94.20/col)
Tue Aug 26 11:54:24 2008  sparse part has weight 63730580 (66.87/col)
Tue Aug 26 11:54:34 2008  read 953012 cycles
Tue Aug 26 11:54:34 2008  matrix is 952824 x 953012 (283.1 MB) with weight 89772381 (94.20/col)
Tue Aug 26 11:54:34 2008  sparse part has weight 63730580 (66.87/col)
Tue Aug 26 11:54:35 2008  saving the first 48 matrix rows for later
Tue Aug 26 11:54:35 2008  matrix is 952776 x 953012 (270.1 MB) with weight 68365485 (71.74/col)
Tue Aug 26 11:54:35 2008  sparse part has weight 61268317 (64.29/col)
Tue Aug 26 11:54:35 2008  matrix includes 64 packed rows
Tue Aug 26 11:54:35 2008  using block size 65536 for processor cache size 4096 kB
Tue Aug 26 11:54:40 2008  commencing Lanczos iteration (4 threads)
Tue Aug 26 11:54:40 2008  memory use: 279.2 MB
Tue Aug 26 13:05:42 2008  lanczos halted after 15067 iterations (dim = 952776)
Tue Aug 26 13:05:44 2008  recovered 49 nontrivial dependencies
Tue Aug 26 13:05:44 2008  elapsed time 01:13:04
Tue Aug 26 13:16:40 2008  
Tue Aug 26 13:16:40 2008  
Tue Aug 26 13:16:40 2008  Msieve v. 1.36
Tue Aug 26 13:16:40 2008  random seeds: d1ae08a7 def52c6a
Tue Aug 26 13:16:40 2008  factoring 60946499131512387375948479892734161528538198218330675388787875709772771135738011315733338750799922801101100084309323798592135870062063851615590114477840868690767621156561398519 (176 digits)
Tue Aug 26 13:16:42 2008  no P-1/P+1/ECM available, skipping
Tue Aug 26 13:16:42 2008  commencing number field sieve (176-digit input)
Tue Aug 26 13:16:42 2008  R0: -1000000000000000000000000000000000000
Tue Aug 26 13:16:42 2008  R1:  1
Tue Aug 26 13:16:42 2008  A0: -7
Tue Aug 26 13:16:42 2008  A1:  0
Tue Aug 26 13:16:42 2008  A2:  0
Tue Aug 26 13:16:42 2008  A3:  0
Tue Aug 26 13:16:42 2008  A4:  0
Tue Aug 26 13:16:42 2008  A5:  6
Tue Aug 26 13:16:42 2008  size score = 2.794913e-12, Murphy alpha = 1.791017, combined = 1.538481e-12
Tue Aug 26 13:16:42 2008  
Tue Aug 26 13:16:42 2008  commencing square root phase
Tue Aug 26 13:16:42 2008  reading relations for dependency 1
Tue Aug 26 13:16:42 2008  read 476023 cycles
Tue Aug 26 13:16:43 2008  cycles contain 1540727 unique relations
Tue Aug 26 13:17:11 2008  read 1540727 relations
Tue Aug 26 13:17:20 2008  multiplying 2569832 relations
Tue Aug 26 13:20:01 2008  multiply complete, coefficients have about 64.69 million bits
Tue Aug 26 13:20:03 2008  initial square root is modulo 1936936291
Tue Aug 26 13:25:03 2008  reading relations for dependency 2
Tue Aug 26 13:25:03 2008  read 476612 cycles
Tue Aug 26 13:25:04 2008  cycles contain 1542603 unique relations
Tue Aug 26 13:25:25 2008  read 1542603 relations
Tue Aug 26 13:25:34 2008  multiplying 2570336 relations
Tue Aug 26 13:28:16 2008  multiply complete, coefficients have about 64.70 million bits
Tue Aug 26 13:28:17 2008  initial square root is modulo 1946412371
Tue Aug 26 13:33:19 2008  reading relations for dependency 3
Tue Aug 26 13:33:19 2008  read 476357 cycles
Tue Aug 26 13:33:20 2008  cycles contain 1541319 unique relations
Tue Aug 26 13:33:33 2008  read 1541319 relations
Tue Aug 26 13:33:41 2008  multiplying 2568952 relations
Tue Aug 26 13:36:23 2008  multiply complete, coefficients have about 64.67 million bits
Tue Aug 26 13:36:24 2008  initial square root is modulo 1924029001
Tue Aug 26 13:41:25 2008  prp61 factor: 4830487850130825355136992625082278853531328717363811995759451
Tue Aug 26 13:41:25 2008  prp116 factor: 12617048427077972576764760920138324767170820384685368004188695290274577720048489648872812603297601032348850349016469
Tue Aug 26 13:41:25 2008  elapsed time 00:24:45

Aug 26, 2008 (2nd)

By Sinkiti Sibata / GGNFS, Msieve

(8·10¹⁴⁸-11)/3 = 2(6)₁₄₇3_<149> = 7 · 13 · C147

C147 = P36 · P36 · P75

P36 = 631170595247677325494007511276201721_<36>

P36 = 737524339058375728078988025299221609_<36>

P75 = 629512306969773167184550234503027158972717529174606520898597164110023596037_<75>

Number: 26663_148
N=293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293
  ( 147 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=631170595247677325494007511276201721 (pp36)
 r2=737524339058375728078988025299221609 (pp36)
 r3=629512306969773167184550234503027158972717529174606520898597164110023596037 (pp75)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 20.94 hours.
Scaled time: 21.21 units (timescale=1.013).
Factorization parameters were as follows:
name: 26663_148
n: 293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293
m: 200000000000000000000000000000
c5: 250
c0: -11
skew: 0.54
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 3650001)
Primes: RFBsize:114155, AFBsize:114243, largePrimes:3091916 encountered
Relations: rels:3208626, finalFF:346994
Max relations in full relation-set: 28
Initial matrix: 228464 x 346994 with sparse part having weight 42238202.
Pruned matrix : 199407 x 200613 with weight 24522224.
Total sieving time: 20.55 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 20.94 hours.
 --------- CPU info (if available) ----------

(8·10¹⁴¹-11)/3 = 2(6)₁₄₀3_<142> = 5483 · C138

C138 = P65 · P74

P65 = 42566066342315420407961503276609805239725144032539524413928807061_<65>

P74 = 11425809234867554634313801966008971003354585779235506262097186026891882401_<74>

Number: 26663_141
N=486351753906012523557663079822481609824305428901452975864794212414128518450969663809350112468843090765396072709587208948872271870630433461
  ( 138 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=42566066342315420407961503276609805239725144032539524413928807061 (pp65)
 r2=11425809234867554634313801966008971003354585779235506262097186026891882401 (pp74)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 14.88 hours.
Scaled time: 15.04 units (timescale=1.011).
Factorization parameters were as follows:
name: 26663_141
n: 486351753906012523557663079822481609824305428901452975864794212414128518450969663809350112468843090765396072709587208948872271870630433461
m: 20000000000000000000000000000
c5: 5
c0: -22
skew: 1.34
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2350001)
Primes: RFBsize:100021, AFBsize:100104, largePrimes:3163162 encountered
Relations: rels:3417143, finalFF:483950
Max relations in full relation-set: 28
Initial matrix: 200190 x 483950 with sparse part having weight 54374487.
Pruned matrix : 151850 x 152914 with weight 22718147.
Total sieving time: 14.49 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 14.88 hours.
 --------- CPU info (if available) ----------

(8·10¹¹⁰-11)/3 = 2(6)₁₀₉3_<111> = 422270161 · C102

C102 = P50 · P53

P50 = 16332279646114817898481597976376858514229176394471_<50>

P53 = 38666203384806306112733511010467776636962683473769073_<53>

Mon Aug 25 15:02:36 2008  Msieve v. 1.36
Mon Aug 25 15:02:36 2008  random seeds: fad24d48 84aab7b6
Mon Aug 25 15:02:36 2008  factoring 631507246534207911192348413807687128209531875179469919179694694711489848004360096537028735655007995383 (102 digits)
Mon Aug 25 15:02:37 2008  no P-1/P+1/ECM available, skipping
Mon Aug 25 15:02:38 2008  commencing quadratic sieve (102-digit input)
Mon Aug 25 15:02:38 2008  using multiplier of 3
Mon Aug 25 15:02:38 2008  using 32kb Intel Core sieve core
Mon Aug 25 15:02:38 2008  sieve interval: 36 blocks of size 32768
Mon Aug 25 15:02:38 2008  processing polynomials in batches of 6
Mon Aug 25 15:02:38 2008  using a sieve bound of 3264419 (117500 primes)
Mon Aug 25 15:02:38 2008  using large prime bound of 489662850 (28 bits)
Mon Aug 25 15:02:38 2008  using double large prime bound of 4383437839720350 (44-52 bits)
Mon Aug 25 15:02:38 2008  using trial factoring cutoff of 52 bits
Mon Aug 25 15:02:38 2008  polynomial 'A' values have 13 factors
Tue Aug 26 11:57:29 2008  117764 relations (27401 full + 90363 combined from 1765490 partial), need 117596
Tue Aug 26 11:57:34 2008  begin with 1792891 relations
Tue Aug 26 11:57:36 2008  reduce to 313570 relations in 12 passes
Tue Aug 26 11:57:36 2008  attempting to read 313570 relations
Tue Aug 26 11:57:44 2008  recovered 313570 relations
Tue Aug 26 11:57:44 2008  recovered 305981 polynomials
Tue Aug 26 11:57:44 2008  attempting to build 117764 cycles
Tue Aug 26 11:57:44 2008  found 117764 cycles in 6 passes
Tue Aug 26 11:57:44 2008  distribution of cycle lengths:
Tue Aug 26 11:57:44 2008     length 1 : 27401
Tue Aug 26 11:57:44 2008     length 2 : 19789
Tue Aug 26 11:57:44 2008     length 3 : 19479
Tue Aug 26 11:57:44 2008     length 4 : 16071
Tue Aug 26 11:57:44 2008     length 5 : 12409
Tue Aug 26 11:57:44 2008     length 6 : 8719
Tue Aug 26 11:57:44 2008     length 7 : 5710
Tue Aug 26 11:57:44 2008     length 9+: 8186
Tue Aug 26 11:57:44 2008  largest cycle: 24 relations
Tue Aug 26 11:57:45 2008  matrix is 117500 x 117764 (34.8 MB) with weight 8659607 (73.53/col)
Tue Aug 26 11:57:45 2008  sparse part has weight 8659607 (73.53/col)
Tue Aug 26 11:57:46 2008  filtering completed in 3 passes
Tue Aug 26 11:57:46 2008  matrix is 113226 x 113290 (33.6 MB) with weight 8365111 (73.84/col)
Tue Aug 26 11:57:46 2008  sparse part has weight 8365111 (73.84/col)
Tue Aug 26 11:57:47 2008  saving the first 48 matrix rows for later
Tue Aug 26 11:57:47 2008  matrix is 113178 x 113290 (23.7 MB) with weight 6978451 (61.60/col)
Tue Aug 26 11:57:47 2008  sparse part has weight 5540716 (48.91/col)
Tue Aug 26 11:57:47 2008  matrix includes 64 packed rows
Tue Aug 26 11:57:47 2008  using block size 45316 for processor cache size 2048 kB
Tue Aug 26 11:57:48 2008  commencing Lanczos iteration
Tue Aug 26 11:57:48 2008  memory use: 21.2 MB
Tue Aug 26 11:59:27 2008  lanczos halted after 1792 iterations (dim = 113178)
Tue Aug 26 11:59:27 2008  recovered 18 nontrivial dependencies
Tue Aug 26 11:59:29 2008  prp50 factor: 16332279646114817898481597976376858514229176394471
Tue Aug 26 11:59:29 2008  prp53 factor: 38666203384806306112733511010467776636962683473769073
Tue Aug 26 11:59:29 2008  elapsed time 20:56:53

(8·10¹⁵³-11)/3 = 2(6)₁₅₂3_<154> = 19 · 403653373 · C144

C144 = P67 · P77

P67 = 9584647896404527490150217237474587315829821200029362091271254431753_<67>

P77 = 36276917910572708977019726585543332934889029681264749296841149667688620319833_<77>

Number: 26663_153
N=347701484939610441804361875586216038235238225528174779157242115236783754412850842678285896895876743219937012988495149260111487140603869530857249
  ( 144 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=9584647896404527490150217237474587315829821200029362091271254431753 (pp67)
 r2=36276917910572708977019726585543332934889029681264749296841149667688620319833 (pp77)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.00 hours.
Scaled time: 24.07 units (timescale=1.003).
Factorization parameters were as follows:
name: 26663_153
n: 347701484939610441804361875586216038235238225528174779157242115236783754412850842678285896895876743219937012988495149260111487140603869530857249
m: 2000000000000000000000000000000
c5: 250
c0: -11
skew: 0.54
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176244, largePrimes:5838800 encountered
Relations: rels:5925527, finalFF:616857
Max relations in full relation-set: 28
Initial matrix: 352612 x 616857 with sparse part having weight 59940685.
Pruned matrix : 264646 x 266473 with weight 31491438.
Total sieving time: 23.08 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.76 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 24.00 hours.
 --------- CPU info (if available) ----------

Aug 26, 2008

By Serge Batalov / GMP-ECM 6.2.1, pol51, Msieve 1.36

(8·10¹⁹⁷-11)/3 = 2(6)₁₉₆3_<198> = 111733 · 5397377 · 30795825067283_<14> · 255721698337823_<15> · 1123975172813840253229_<22> · C137

C137 = P30 · P107

P30 = 584631897521184211264327771703_<30>

P107 = 85448780591496185069139272511079480379794034535247604377701836586510272565252157696362447303206979984172421_<107>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=4075465090
Step 1 took 7029ms
Step 2 took 5423ms
********** Factor found in step 2: 584631897521184211264327771703
Found probable prime factor of 30 digits: 584631897521184211264327771703
Probable prime cofactor 85448780591496185069139272511079480379794034535247604377701836586510272565252157696362447303206979984172421 has 107 digits

(8·10¹⁷⁸-11)/3 = 2(6)₁₇₇3_<179> = 7² · 13 · 68889803 · C168

C168 = P32 · C137

P32 = 24902290071539505232947157370809_<32>

C137 = [24402542030292362032996350257126313176584682115300957283898560700731379335812856761997377266656064229543530545017001142017298689072691137_<137>]

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=2294159883
Step 1 took 8351ms
Step 2 took 6372ms
********** Factor found in step 2: 24902290071539505232947157370809
Found probable prime factor of 32 digits: 24902290071539505232947157370809
Composite cofactor 24402542030292362032996350257126313176584682115300957283898560700731379335812856761997377266656064229543530545017001142017298689072691137 has 137 digits

(8·10¹⁹⁴-11)/3 = 2(6)₁₉₃3_<195> = 173 · 1489 · C190

C190 = P32 · C158

P32 = 13268292354555506055377112473833_<32>

C158 = [78021249133662649201010056260756443212459081834801215517983657063217652246078341944261089148602713232013125543543274882835988069853193682190413043480015720763_<158>]

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=2757967481
Step 1 took 9391ms
Step 2 took 7236ms
********** Factor found in step 2: 13268292354555506055377112473833
Found probable prime factor of 32 digits: 13268292354555506055377112473833
Composite cofactor 78021249133662649201010056260756443212459081834801215517983657063217652246078341944261089148602713232013125543543274882835988069853193682190413043480015720763 has 158 digits

(8·10¹⁸⁰-11)/3 = 2(6)₁₇₉3_<181> = 3397753236583_<13> · 392394707280681851533_<21> · 205355556215967421129829_<24> · C124

C124 = P28 · P41 · P56

P28 = 3400747871425819708132739489_<28>

P41 = 38816920840993351478857495860128753476187_<41>

P56 = 73782230785092535333770078843852428216528975329015286611_<56>

#ECM, then gnfs/Msieve
#
Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=1157696711
Step 1 took 5689ms
Step 2 took 3166ms
********** Factor found in step 2: 3400747871425819708132739489
Found probable prime factor of 28 digits: 3400747871425819708132739489
Composite cofactor 2863999011856839684189632857032227275314528666558642362791977590502022197508465810654828368432257 has 97 digits

Number: 26663_180
N=2863999011856839684189632857032227275314528666558642362791977590502022197508465810654828368432257
  ( 97 digits)
Divisors found:
 r1=38816920840993351478857495860128753476187
 r2=73782230785092535333770078843852428216528975329015286611
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.953).
Factorization parameters were as follows:
name: 26663_180
n: 2863999011856839684189632857032227275314528666558642362791977590502022197508465810654828368432257
skew: 4520.93
# norm 1.38e+13
c5: 32880
c4: 2367442
c3: -1766456187165
c2: 3692732179295755
c1: 21831126546193430705
c0: 6433261978193336300543
# alpha -5.40
Y1: 10108298959
Y0: -2443476604716635280
# Murphy_E 4.95e-09
# M 1500633408794892675967970158936107201052746886196142694054793555285370286000876464460094243978359
type: gnfs
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1020001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 123265 x 123498
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,96,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 1.70 hours.

(8·10¹⁵⁸-11)/3 = 2(6)₁₅₇3_<159> = 29 · 89 · C156

C156 = P41 · P115

P41 = 85645030255583612491797176677799392292263_<41>

P115 = 1206364533295746858405918018055464413960376241979912931904257349702717955872012065492560876276627423631920046146621_<115>

Number: 26663_158
N=103319126953377243962288518662017305953764690688363683326875887898747255585690300916957251711223040165310603125403590339661629859227689526023505101381893323
  ( 156 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=85645030255583612491797176677799392292263
 r2=1206364533295746858405918018055464413960376241979912931904257349702717955872012065492560876276627423631920046146621
Version: 
Total time: 22.37 hours.
Scaled time: 76.54 units (timescale=3.422).
Factorization parameters were as follows:
n: 103319126953377243962288518662017305953764690688363683326875887898747255585690300916957251711223040165310603125403590339661629859227689526023505101381893323
Y1: 1
Y0: -20000000000000000000000000000000
c5: 250
c0: -11
skew: 0.54
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3500001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 490121 x 490369
Total sieving time: 22.37 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.70 hours.
Time per square root: 0.50 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 22.37 hours.

Aug 25, 2008 (5th)

By Jo Yeong Uk / GMP-ECM

(8·10²⁰¹-11)/3 = 2(6)₂₀₀3_<202> = C202

C202 = P30 · C172

P30 = 451812655504187553833642493151_<30>

C172 = [5902151332372209503609296911272406487211881024719526726349392490909514083822506333934172090530872360967046140330267742066517371414348495611729173874621014004093969936550713_<172>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 2666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 (202 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2863822186
Step 1 took 7248ms
********** Factor found in step 1: 451812655504187553833642493151
Found probable prime factor of 30 digits: 451812655504187553833642493151
Composite cofactor 5902151332372209503609296911272406487211881024719526726349392490909514083822506333934172090530872360967046140330267742066517371414348495611729173874621014004093969936550713 has 172 digits

Aug 25, 2008 (4th)

By Sinkiti Sibata / Msieve, GGNFS

(8·10¹¹⁵-11)/3 = 2(6)₁₁₄3_<116> = 27327373 · 744960989 · 159825498529_<12> · C88

C88 = P38 · P51

P38 = 36394744129187324330831066302113920077_<38>

P51 = 225191803222073042077948412162190617679629996439163_<51>

Msieve v. 1.36
Mon Aug 25 09:12:26 2008
random seeds: 022eeabf 0fc3ee48
factoring 8195798058257650035222798926893206468073882016281189047624546008259499
372911085174775551 (88 digits)
no P-1/P+1/ECM available, skipping
commencing quadratic sieve (88-digit input)
using multiplier of 15
using 32kb Intel Core sieve core
sieve interval: 28 blocks of size 32768
processing polynomials in batches of 8
using a sieve bound of 1533799 (58333 primes)
using large prime bound of 122703920 (26 bits)
using double large prime bound of 363032185823760 (42-49 bits)
using trial factoring cutoff of 49 bits
polynomial 'A' values have 11 factors

sieving in progress (press Ctrl-C to pause)
58733 relations (16463 full + 42270 combined from 612585 partial), need 58429
58733 relations (16463 full + 42270 combined from 612585 partial), need 58429
sieving complete, commencing postprocessing
begin with 629048 relations
reduce to 140284 relations in 10 passes
attempting to read 140284 relations
recovered 140284 relations
recovered 117682 polynomials
attempting to build 58733 cycles
found 58733 cycles in 5 passes
distribution of cycle lengths:
   length 1 : 16463
   length 2 : 11455
   length 3 : 10354
   length 4 : 7733
   length 5 : 5344
   length 6 : 3310
   length 7 : 1921
   length 9+: 2153
largest cycle: 18 relations
matrix is 58333 x 58733 (14.2 MB) with weight 3477966 (59.22/col)
sparse part has weight 3477966 (59.22/col)
filtering completed in 3 passes
matrix is 53756 x 53820 (13.0 MB) with weight 3201859 (59.49/col)
sparse part has weight 3201859 (59.49/col)
saving the first 48 matrix rows for later
matrix is 53708 x 53820 (9.4 MB) with weight 2620040 (48.68/col)
sparse part has weight 2132255 (39.62/col)
matrix includes 64 packed rows
using block size 21528 for processor cache size 4096 kB
commencing Lanczos iteration
memory use: 8.6 MB
lanczos halted after 851 iterations (dim = 53706)
recovered 17 nontrivial dependencies
prp38 factor: 36394744129187324330831066302113920077
prp51 factor: 225191803222073042077948412162190617679629996439163
elapsed time 00:54:52

(8·10¹³⁸-11)/3 = 2(6)₁₃₇3_<139> = 8419 · 185873959 · 1807965893376375389_<19> · C108

C108 = P31 · P78

P31 = 4022953384627041789849995127289_<31>

P78 = 234290370863190928348570573401696087817693212086985056963495641872571535390143_<78>

Number: 26663_138
N=942539240449598799728657907393877165710658736278448078722000554709399106887259501615297280227529767560912327
  ( 108 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=4022953384627041789849995127289 (pp31)
 r2=234290370863190928348570573401696087817693212086985056963495641872571535390143 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.64 hours.
Scaled time: 9.25 units (timescale=0.869).
Factorization parameters were as follows:
name: 26663_138
n: 942539240449598799728657907393877165710658736278448078722000554709399106887259501615297280227529767560912327
m: 2000000000000000000000000000
c5: 250
c0: -11
skew: 0.54
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1675001)
Primes: RFBsize:78498, AFBsize:64024, largePrimes:1644943 encountered
Relations: rels:1676321, finalFF:186319
Max relations in full relation-set: 28
Initial matrix: 142588 x 186319 with sparse part having weight 19451277.
Pruned matrix : 131689 x 132465 with weight 12236740.
Total sieving time: 10.38 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 10.64 hours.
 --------- CPU info (if available) ----------

(8·10¹²⁶-11)/3 = 2(6)₁₂₅3_<127> = 349 · C124

C124 = P34 · P91

P34 = 1077539553478360533230464619964479_<34>

P91 = 7091042436804680319855247362684038701737502682164360896283654857951232009654026676364876653_<91>

Number: 26663_126
N=7640878701050620821394460362941738299904489016236867239732569245463228271251193887297039159503342884431709646609360076408787
  ( 124 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=1077539553478360533230464619964479 (pp34)
 r2=7091042436804680319855247362684038701737502682164360896283654857951232009654026676364876653 (pp91)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.46 hours.
Scaled time: 2.70 units (timescale=0.780).
Factorization parameters were as follows:
name: 26663_126
n: 7640878701050620821394460362941738299904489016236867239732569245463228271251193887297039159503342884431709646609360076408787
m: 20000000000000000000000000
c5: 5
c0: -22
skew: 1.34
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:49098, AFBsize:63744, largePrimes:2346493 encountered
Relations: rels:2596068, finalFF:320129
Max relations in full relation-set: 28
Initial matrix: 112907 x 320129 with sparse part having weight 33834564.
Pruned matrix : 89415 x 90043 with weight 8750419.
Total sieving time: 3.31 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.46 hours.
 --------- CPU info (if available) ----------

(8·10¹³⁶-11)/3 = 2(6)₁₃₅3_<137> = 7² · 13 · 2477 · 958183397433934124845303_<24> · C107

C107 = P43 · P65

P43 = 1571318684431170472268584011635077965756373_<43>

P65 = 11225104096442483874271543011120612457408910397229839548437445173_<65>

Number: 26663_136
N=17638215801424946277538705205049357412849843641681158464695470568727377018710107384739025942038188662837529
  ( 107 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=1571318684431170472268584011635077965756373 (pp43)
 r2=11225104096442483874271543011120612457408910397229839548437445173 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.52 hours.
Scaled time: 6.91 units (timescale=0.657).
Factorization parameters were as follows:
name: 26663_136
n: 17638215801424946277538705205049357412849843641681158464695470568727377018710107384739025942038188662837529
m: 2000000000000000000000000000
c5: 5
c0: -22
skew: 1.34
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1675001)
Primes: RFBsize:78498, AFBsize:63744, largePrimes:1792261 encountered
Relations: rels:1939159, finalFF:299448
Max relations in full relation-set: 28
Initial matrix: 142307 x 299448 with sparse part having weight 29445787.
Pruned matrix : 112486 x 113261 with weight 11386504.
Total sieving time: 10.31 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 10.52 hours.
 --------- CPU info (if available) ----------

(8·10¹⁰⁸-11)/3 = 2(6)₁₀₇3_<109> = 173 · 1396985297_<10> · C98

C98 = P46 · P52

P46 = 9478218721635962950063775331955797995694998263_<46>

P52 = 1164136932415231088051595778237945031400502778838821_<52>

Msieve v. 1.36
Mon Aug 25 10:36:30 2008
random seeds: 38e93f28 18cf46c6
factoring 1103394446736590300212881872621524333132390980448938746594859925015513
3200443654428583548751967923 (98 digits)
no P-1/P+1/ECM available, skipping
commencing quadratic sieve (98-digit input)
using multiplier of 3
using 32kb Intel Core sieve core
sieve interval: 36 blocks of size 32768
processing polynomials in batches of 6
using a sieve bound of 2439067 (89109 primes)
using large prime bound of 365860050 (28 bits)
using double large prime bound of 2593981779484650 (43-52 bits)
using trial factoring cutoff of 52 bits
polynomial 'A' values have 13 factors

sieving in progress (press Ctrl-C to pause)
89224 relations (20824 full + 68400 combined from 1362659 partial), need 89205
89224 relations (20824 full + 68400 combined from 1362659 partial), need 89205
sieving complete, commencing postprocessing
begin with 1383483 relations
reduce to 237176 relations in 10 passes
attempting to read 237176 relations
recovered 237176 relations
recovered 226560 polynomials
attempting to build 89224 cycles
found 89224 cycles in 6 passes
distribution of cycle lengths:
   length 1 : 20824
   length 2 : 15190
   length 3 : 14918
   length 4 : 12146
   length 5 : 9457
   length 6 : 6438
   length 7 : 4306
   length 9+: 5945
largest cycle: 21 relations
matrix is 89109 x 89224 (24.4 MB) with weight 6042868 (67.73/col)
sparse part has weight 6042868 (67.73/col)
filtering completed in 3 passes
matrix is 85635 x 85699 (23.6 MB) with weight 5842727 (68.18/col)
sparse part has weight 5842727 (68.18/col)
saving the first 48 matrix rows for later
matrix is 85587 x 85699 (14.7 MB) with weight 4635880 (54.09/col)
sparse part has weight 3342133 (39.00/col)
matrix includes 64 packed rows
using block size 34279 for processor cache size 4096 kB
commencing Lanczos iteration
memory use: 14.2 MB
linear algebra completed 80326 out of 85699 dimensions (93.7%)
lanczos halted after 1355 iterations (dim = 85586)
recovered 17 nontrivial dependencies
prp46 factor: 9478218721635962950063775331955797995694998263
prp52 factor: 1164136932415231088051595778237945031400502778838821
elapsed time 06:57:03

(8·10¹⁴³-11)/3 = 2(6)₁₄₂3_<144> = 17 · 7146336199_<10> · C133

C133 = P35 · P45 · P53

P35 = 74131706740520134432488133381283627_<35>

P45 = 473918783322639150993506355219846282948081391_<45>

P53 = 62478190973515905091229270530795437441876297718914173_<53>

Number: 26663_143
N=2195009312883842615956312494274824259880177803431059411666199434226845762617106919694017756641960595544954965800031013549434101030161
  ( 133 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=74131706740520134432488133381283627 (pp35)
 r2=473918783322639150993506355219846282948081391 (pp45)
 r3=62478190973515905091229270530795437441876297718914173 (pp53)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 12.89 hours.
Scaled time: 12.93 units (timescale=1.003).
Factorization parameters were as follows:
name: 26663_143
n: 2195009312883842615956312494274824259880177803431059411666199434226845762617106919694017756641960595544954965800031013549434101030161
m: 20000000000000000000000000000
c5: 250
c0: -11
skew: 0.54
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2350001)
Primes: RFBsize:100021, AFBsize:100179, largePrimes:2890914 encountered
Relations: rels:2943556, finalFF:305165
Max relations in full relation-set: 28
Initial matrix: 200266 x 305165 with sparse part having weight 33397507.
Pruned matrix : 173998 x 175063 with weight 17976771.
Total sieving time: 12.62 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 12.89 hours.
 --------- CPU info (if available) ----------

Aug 25, 2008 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(8·10¹⁰³-11)/3 = 2(6)₁₀₂3_<104> = 42640406154121325305813_<23> · C81

C81 = P29 · P53

P29 = 32310722809845102049503136009_<29>

P53 = 19355336495052044162304280966510001150870536267517939_<53>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 625384912382905433497831556663133629465431712905651150435013281886485743164365451 (81 digits)
Using B1=716000, B2=696728352, polynomial Dickson(3), sigma=3553693662
Step 1 took 3813ms
Step 2 took 2156ms
********** Factor found in step 2: 32310722809845102049503136009
Found probable prime factor of 29 digits: 32310722809845102049503136009
Probable prime cofactor 19355336495052044162304280966510001150870536267517939 has 53 digits

(8·10¹¹⁴-11)/3 = 2(6)₁₁₃3_<115> = 89 · C113

C113 = P34 · P80

P34 = 2259115997850597640784499152946323_<34>

P80 = 13262951900206461666213310460070950876252932275320620693018204736411989385181029_<80>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 29962546816479400749063670411985018726591760299625468164794007490636704119850187265917602996254681647940074906367 (113 digits)
Using B1=1054000, B2=1045563762, polynomial Dickson(6), sigma=3402612825
Step 1 took 8203ms
Step 2 took 4407ms
********** Factor found in step 2: 2259115997850597640784499152946323
Found probable prime factor of 34 digits: 2259115997850597640784499152946323
Probable prime cofactor 13262951900206461666213310460070950876252932275320620693018204736411989385181029 has 80 digits

(8·10¹²⁸-11)/3 = 2(6)₁₂₇3_<129> = C129

C129 = P36 · P93

P36 = 497804025886962506207714390938400623_<36>

P93 = 535686038680649951068585178875042757472954243229661921056248994248736475025875054178317329481_<93>

Number: n
N=266666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
  ( 129 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=497804025886962506207714390938400623 (pp36)
 r2=535686038680649951068585178875042757472954243229661921056248994248736475025875054178317329481 (pp93)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.27 hours.
Scaled time: 2.96 units (timescale=0.905).
Factorization parameters were as follows:
name: KA_2_6_127_3
n: 266666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
type: snfs
skew: 0.54
deg: 5
c5: 250
c0: -11
m: 20000000000000000000000000
rlim: 700000
alim: 700000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [100000, 360001)
Primes: RFBsize:56543, AFBsize:56529, largePrimes:5287037 encountered
Relations: rels:4505640, finalFF:143302
Max relations in full relation-set: 48
Initial matrix: 113138 x 143302 with sparse part having weight 17608215.
Pruned matrix : 105459 x 106088 with weight 9691679.
Total sieving time: 2.98 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.12 hours.
Total square root time: 0.03 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,700000,700000,28,28,50,50,2.5,2.5,50000
total time: 3.27 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(17·10¹⁹²+1)/9 = 1(8)₁₉₁9_<193> = 23 · C191

C191 = P94 · P98

P94 = 1948662034201098323710903730958276574627075333548724371561250262056978094886490485343891106957_<94>

P98 = 42144611237527240110223119654035423284203139603203167827807897848137401763143004307433958811849899_<98>

Number: n
N=82125603864734299516908212560386473429951690821256038647342995169082125603864734299516908212560386473429951690821256038647342995169082125603864734299516908212560386473429951690821256038647343
  ( 191 digits)
SNFS difficulty: 193 digits.
Divisors found:

Mon Aug 25 19:56:31 2008  prp94 factor: 1948662034201098323710903730958276574627075333548724371561250262056978094886490485343891106957
Mon Aug 25 19:56:31 2008  prp98 factor: 42144611237527240110223119654035423284203139603203167827807897848137401763143004307433958811849899
Mon Aug 25 19:56:31 2008  elapsed time 07:59:02 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 177.74 hours.
Scaled time: 364.55 units (timescale=2.051).
Factorization parameters were as follows:
name: KA_1_8_191_9
n: 82125603864734299516908212560386473429951690821256038647342995169082125603864734299516908212560386473429951690821256038647342995169082125603864734299516908212560386473429951690821256038647343
type: snfs
skew: 0.23
deg: 5
c5: 1700
c0: 1
m: 100000000000000000000000000000000000000
rlim: 9500000
alim: 9500000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9500000/9500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 13700001)
Primes: RFBsize:633578, AFBsize:634678, largePrimes:11237680 encountered
Relations: rels:11302726, finalFF:1311085
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 177.34 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,193,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,50,50,2.5,2.5,100000
total time: 177.74 hours.
 --------- CPU info (if available) ----------

(8·10¹³⁹-11)/3 = 2(6)₁₃₈3_<140> = C140

C140 = P33 · P107

P33 = 959282682025957797850608113019113_<33>

P107 = 27798549026599729182324561097530178917531373289574911508549281342744062452451420379597840926261692683566351_<107>

Number: n
N=26666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
  ( 140 digits)
SNFS difficulty: 140 digits.
Divisors found:

Mon Aug 25 20:32:13 2008  prp33 factor: 959282682025957797850608113019113
Mon Aug 25 20:32:13 2008  prp107 factor: 27798549026599729182324561097530178917531373289574911508549281342744062452451420379597840926261692683566351
Mon Aug 25 20:32:13 2008  elapsed time 00:17:59 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 5.66 hours.
Scaled time: 10.35 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_6_138_3
n: 26666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
type: snfs
skew: 1.69
deg: 5
c5: 4
c0: -55
m: 10000000000000000000000000000
rlim: 1200000
alim: 1200000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 560001)
Primes: RFBsize:92938, AFBsize:92975, largePrimes:7002152 encountered
Relations: rels:6006723, finalFF:211320
Max relations in full relation-set: 28
Initial matrix: 185977 x 211320 with sparse part having weight 22376445.
Pruned matrix : 
Total sieving time: 4.96 hours.
Total relation processing time: 0.69 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,50,50,2.5,2.5,100000
total time: 5.66 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(8·10¹²³-11)/3 = 2(6)₁₂₂3_<124> = 193 · 3323 · C118

C118 = P45 · P73

P45 = 642613838830751806249659095006571736039311649_<45>

P73 = 6470398189326729013605156656933550973595555578999795769319970345586959333_<73>

Number: n
N=4157967419206794950356467744307872539587747925304194297659532114321235207381223762575902395872801539695335332276170117
  ( 118 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=642613838830751806249659095006571736039311649 (pp45)
 r2=6470398189326729013605156656933550973595555578999795769319970345586959333 (pp73)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.50 hours.
Scaled time: 2.74 units (timescale=1.827).
Factorization parameters were as follows:
name: KA_2_6_122_3
n: 4157967419206794950356467744307872539587747925304194297659532114321235207381223762575902395872801539695335332276170117
type: snfs
skew: 0.54
deg: 5
c5: 250
c0: -11
m: 2000000000000000000000000
rlim: 700000
alim: 700000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [100000, 260001)
Primes: RFBsize:56543, AFBsize:56529, largePrimes:4753006 encountered
Relations: rels:3997616, finalFF:139366
Max relations in full relation-set: 48
Initial matrix: 113138 x 139366 with sparse part having weight 13526645.
Pruned matrix : 104170 x 104799 with weight 7166986.
Total sieving time: 1.29 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.05 hours.
Total square root time: 0.09 hours, sqrts: 6.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,700000,700000,28,28,50,50,2.5,2.5,50000
total time: 1.50 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Aug 25, 2008 (2nd)

By Serge Batalov / Msieve

(8·10¹³²-11)/3 = 2(6)₁₃₁3_<133> = 15536946350327_<14> · 57716815808783_<14> · 97764490225841183_<17> · C89

C89 = P31 · P59

P31 = 2878173973878396344472623824273_<31>

P59 = 10568236438025805805146214006943933895776577890265004772977_<59>

Sun Aug 24 12:23:27 2008  Msieve v. 1.36
Sun Aug 24 12:23:27 2008  random seeds: 91c7b3f0 39fd5771
Sun Aug 24 12:23:27 2008  factoring 30417223065719202025408393332329506476088430781684930885264026157024451489312987907070721 (89 digits)
Sun Aug 24 12:23:27 2008  searching for 15-digit factors
Sun Aug 24 12:23:28 2008  commencing quadratic sieve (89-digit input)
Sun Aug 24 12:23:28 2008  using multiplier of 1
Sun Aug 24 12:23:28 2008  using 32kb Intel Core sieve core
Sun Aug 24 12:23:28 2008  sieve interval: 30 blocks of size 32768
Sun Aug 24 12:23:28 2008  processing polynomials in batches of 7
Sun Aug 24 12:23:28 2008  using a sieve bound of 1546697 (58666 primes)
Sun Aug 24 12:23:28 2008  using large prime bound of 123735760 (26 bits)
Sun Aug 24 12:23:28 2008  using double large prime bound of 368545723802400 (42-49 bits)
Sun Aug 24 12:23:28 2008  using trial factoring cutoff of 49 bits
Sun Aug 24 12:23:28 2008  polynomial 'A' values have 11 factors
Sun Aug 24 12:49:33 2008  59095 relations (17383 full + 41712 combined from 602353 partial), need 58762
Sun Aug 24 12:49:34 2008  begin with 619735 relations
Sun Aug 24 12:49:34 2008  reduce to 137172 relations in 9 passes
Sun Aug 24 12:49:34 2008  attempting to read 137172 relations
Sun Aug 24 12:49:35 2008  recovered 137172 relations
Sun Aug 24 12:49:35 2008  recovered 103123 polynomials
Sun Aug 24 12:49:35 2008  attempting to build 59095 cycles
Sun Aug 24 12:49:35 2008  found 59095 cycles in 5 passes
Sun Aug 24 12:49:35 2008  distribution of cycle lengths:
Sun Aug 24 12:49:35 2008     length 1 : 17383
Sun Aug 24 12:49:35 2008     length 2 : 12291
Sun Aug 24 12:49:35 2008     length 3 : 10403
Sun Aug 24 12:49:35 2008     length 4 : 7514
Sun Aug 24 12:49:35 2008     length 5 : 5032
Sun Aug 24 12:49:35 2008     length 6 : 2924
Sun Aug 24 12:49:35 2008     length 7 : 1676
Sun Aug 24 12:49:35 2008     length 9+: 1872
Sun Aug 24 12:49:35 2008  largest cycle: 16 relations
Sun Aug 24 12:49:36 2008  matrix is 58666 x 59095 (13.6 MB) with weight 3325898 (56.28/col)
Sun Aug 24 12:49:36 2008  sparse part has weight 3325898 (56.28/col)
Sun Aug 24 12:49:36 2008  filtering completed in 4 passes
Sun Aug 24 12:49:36 2008  matrix is 53129 x 53193 (12.3 MB) with weight 3012466 (56.63/col)
Sun Aug 24 12:49:36 2008  sparse part has weight 3012466 (56.63/col)
Sun Aug 24 12:49:36 2008  saving the first 48 matrix rows for later
Sun Aug 24 12:49:36 2008  matrix is 53081 x 53193 (8.4 MB) with weight 2389276 (44.92/col)
Sun Aug 24 12:49:36 2008  sparse part has weight 1875750 (35.26/col)
Sun Aug 24 12:49:36 2008  matrix includes 64 packed rows
Sun Aug 24 12:49:36 2008  using block size 21277 for processor cache size 4096 kB
Sun Aug 24 12:49:37 2008  commencing Lanczos iteration
Sun Aug 24 12:49:37 2008  memory use: 7.9 MB
Sun Aug 24 12:49:50 2008  lanczos halted after 841 iterations (dim = 53079)
Sun Aug 24 12:49:50 2008  recovered 16 nontrivial dependencies
Sun Aug 24 12:49:50 2008  prp31 factor: 2878173973878396344472623824273
Sun Aug 24 12:49:50 2008  prp59 factor: 10568236438025805805146214006943933895776577890265004772977
Sun Aug 24 12:49:50 2008  elapsed time 00:26:23

(8·10¹¹³-11)/3 = 2(6)₁₁₂3_<114> = 2341 · 30810511543917882721369333_<26> · C85

C85 = P28 · P57

P28 = 6149421791025899547499894967_<28>

P57 = 601220980001406340971556885053700885153827701171358855913_<57>

Sun Aug 24 12:53:43 2008  Msieve v. 1.36
Sun Aug 24 12:53:43 2008  random seeds: 7f72a470 3623d00f
Sun Aug 24 12:53:43 2008  factoring 3697161395642594715145547845696911974342125553234116133620464452526327268032786889871 (85 digits)
Sun Aug 24 12:53:43 2008  searching for 15-digit factors
Sun Aug 24 12:53:44 2008  commencing quadratic sieve (85-digit input)
Sun Aug 24 12:53:44 2008  using multiplier of 47
Sun Aug 24 12:53:44 2008  using 32kb Intel Core sieve core
Sun Aug 24 12:53:44 2008  sieve interval: 12 blocks of size 32768
Sun Aug 24 12:53:44 2008  processing polynomials in batches of 17
Sun Aug 24 12:53:44 2008  using a sieve bound of 1422583 (54412 primes)
Sun Aug 24 12:53:44 2008  using large prime bound of 116651806 (26 bits)
Sun Aug 24 12:53:44 2008  using double large prime bound of 331439743440844 (41-49 bits)
Sun Aug 24 12:53:44 2008  using trial factoring cutoff of 49 bits
Sun Aug 24 12:53:44 2008  polynomial 'A' values have 11 factors
Sun Aug 24 13:17:41 2008  54639 relations (16031 full + 38608 combined from 572576 partial), need 54508
Sun Aug 24 13:17:42 2008  begin with 588606 relations
Sun Aug 24 13:17:43 2008  reduce to 127985 relations in 11 passes
Sun Aug 24 13:17:43 2008  attempting to read 127985 relations
Sun Aug 24 13:17:44 2008  recovered 127985 relations
Sun Aug 24 13:17:44 2008  recovered 109198 polynomials
Sun Aug 24 13:17:44 2008  attempting to build 54639 cycles
Sun Aug 24 13:17:44 2008  found 54639 cycles in 6 passes
Sun Aug 24 13:17:44 2008  distribution of cycle lengths:
Sun Aug 24 13:17:44 2008     length 1 : 16031
Sun Aug 24 13:17:44 2008     length 2 : 11091
Sun Aug 24 13:17:44 2008     length 3 : 9819
Sun Aug 24 13:17:44 2008     length 4 : 6949
Sun Aug 24 13:17:44 2008     length 5 : 4532
Sun Aug 24 13:17:44 2008     length 6 : 2756
Sun Aug 24 13:17:44 2008     length 7 : 1649
Sun Aug 24 13:17:44 2008     length 9+: 1812
Sun Aug 24 13:17:44 2008  largest cycle: 19 relations
Sun Aug 24 13:17:44 2008  matrix is 54412 x 54639 (12.2 MB) with weight 2973852 (54.43/col)
Sun Aug 24 13:17:44 2008  sparse part has weight 2973852 (54.43/col)
Sun Aug 24 13:17:44 2008  filtering completed in 3 passes
Sun Aug 24 13:17:44 2008  matrix is 49179 x 49239 (11.1 MB) with weight 2708823 (55.01/col)
Sun Aug 24 13:17:44 2008  sparse part has weight 2708823 (55.01/col)
Sun Aug 24 13:17:44 2008  saving the first 48 matrix rows for later
Sun Aug 24 13:17:45 2008  matrix is 49131 x 49239 (7.1 MB) with weight 2122297 (43.10/col)
Sun Aug 24 13:17:45 2008  sparse part has weight 1554725 (31.58/col)
Sun Aug 24 13:17:45 2008  matrix includes 64 packed rows
Sun Aug 24 13:17:45 2008  using block size 19695 for processor cache size 4096 kB
Sun Aug 24 13:17:45 2008  commencing Lanczos iteration
Sun Aug 24 13:17:45 2008  memory use: 7.0 MB
Sun Aug 24 13:17:55 2008  lanczos halted after 779 iterations (dim = 49130)
Sun Aug 24 13:17:55 2008  recovered 17 nontrivial dependencies
Sun Aug 24 13:17:57 2008  prp28 factor: 6149421791025899547499894967
Sun Aug 24 13:17:57 2008  prp57 factor: 601220980001406340971556885053700885153827701171358855913
Sun Aug 24 13:17:57 2008  elapsed time 00:24:14

(8·10¹³⁵-11)/3 = 2(6)₁₃₄3_<136> = 19 · 1399 · 28360288684575581731_<20> · 6005110147387091815727_<22> · C90

C90 = P39 · P51

P39 = 760367035665068717323133747416114223399_<39>

P51 = 774715974656339115136575138199572212734645113395921_<51>

Sun Aug 24 13:20:02 2008  Msieve v. 1.36
Sun Aug 24 13:20:02 2008  random seeds: fbaa4548 d5ff5a09
Sun Aug 24 13:20:02 2008  factoring 589068489131815076485354105182151500327586386083290131231332775086317716668600958529355479 (90 digits)
Sun Aug 24 13:20:03 2008  searching for 15-digit factors
Sun Aug 24 13:20:04 2008  commencing quadratic sieve (90-digit input)
Sun Aug 24 13:20:04 2008  using multiplier of 31
Sun Aug 24 13:20:04 2008  using 32kb Intel Core sieve core
Sun Aug 24 13:20:04 2008  sieve interval: 36 blocks of size 32768
Sun Aug 24 13:20:04 2008  processing polynomials in batches of 6
Sun Aug 24 13:20:04 2008  using a sieve bound of 1615223 (61176 primes)
Sun Aug 24 13:20:04 2008  using large prime bound of 135678732 (27 bits)
Sun Aug 24 13:20:04 2008  using double large prime bound of 435031874203416 (42-49 bits)
Sun Aug 24 13:20:04 2008  using trial factoring cutoff of 49 bits
Sun Aug 24 13:20:04 2008  polynomial 'A' values have 12 factors
Sun Aug 24 14:23:42 2008  61374 relations (16026 full + 45348 combined from 666990 partial), need 61272
Sun Aug 24 14:23:44 2008  begin with 683015 relations
Sun Aug 24 14:23:44 2008  reduce to 150768 relations in 11 passes
Sun Aug 24 14:23:44 2008  attempting to read 150768 relations
Sun Aug 24 14:23:45 2008  recovered 150768 relations
Sun Aug 24 14:23:45 2008  recovered 132163 polynomials
Sun Aug 24 14:23:46 2008  attempting to build 61374 cycles
Sun Aug 24 14:23:46 2008  found 61374 cycles in 5 passes
Sun Aug 24 14:23:46 2008  distribution of cycle lengths:
Sun Aug 24 14:23:46 2008     length 1 : 16026
Sun Aug 24 14:23:46 2008     length 2 : 11796
Sun Aug 24 14:23:46 2008     length 3 : 10722
Sun Aug 24 14:23:46 2008     length 4 : 8278
Sun Aug 24 14:23:46 2008     length 5 : 5853
Sun Aug 24 14:23:46 2008     length 6 : 3771
Sun Aug 24 14:23:46 2008     length 7 : 2257
Sun Aug 24 14:23:46 2008     length 9+: 2671
Sun Aug 24 14:23:46 2008  largest cycle: 20 relations
Sun Aug 24 14:23:46 2008  matrix is 61176 x 61374 (15.1 MB) with weight 3710603 (60.46/col)
Sun Aug 24 14:23:46 2008  sparse part has weight 3710603 (60.46/col)
Sun Aug 24 14:23:46 2008  filtering completed in 4 passes
Sun Aug 24 14:23:46 2008  matrix is 57514 x 57578 (14.3 MB) with weight 3511473 (60.99/col)
Sun Aug 24 14:23:46 2008  sparse part has weight 3511473 (60.99/col)
Sun Aug 24 14:23:46 2008  saving the first 48 matrix rows for later
Sun Aug 24 14:23:46 2008  matrix is 57466 x 57578 (9.1 MB) with weight 2779570 (48.27/col)
Sun Aug 24 14:23:46 2008  sparse part has weight 2038144 (35.40/col)
Sun Aug 24 14:23:46 2008  matrix includes 64 packed rows
Sun Aug 24 14:23:46 2008  using block size 23031 for processor cache size 4096 kB
Sun Aug 24 14:23:47 2008  commencing Lanczos iteration
Sun Aug 24 14:23:47 2008  memory use: 8.8 MB
Sun Aug 24 14:24:02 2008  lanczos halted after 911 iterations (dim = 57464)
Sun Aug 24 14:24:02 2008  recovered 16 nontrivial dependencies
Sun Aug 24 14:24:03 2008  prp39 factor: 760367035665068717323133747416114223399
Sun Aug 24 14:24:03 2008  prp51 factor: 774715974656339115136575138199572212734645113395921
Sun Aug 24 14:24:03 2008  elapsed time 01:04:01

(8·10¹⁰²-11)/3 = 2(6)₁₀₁3_<103> = 29 · 70516981 · C94

C94 = P45 · P49

P45 = 919296806573087122167025368337737943218105509_<45>

P49 = 1418473648139463334070630967104623852741892124443_<49>

Number: 26663_102
N=1303998294942685466447248806768902972446460444933734162001625398992691667717090268173731856487
  ( 94 digits)
SNFS difficulty: 102 digits.
Divisors found:
 r1=919296806573087122167025368337737943218105509 (pp45)
 r2=1418473648139463334070630967104623852741892124443 (pp49)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 0.29 hours.
Scaled time: 0.99 units (timescale=3.423).
Factorization parameters were as follows:
n: 1303998294942685466447248806768902972446460444933734162001625398992691667717090268173731856487
Y1: 1
Y0: -200000000000000000000
c5: 25
c0: -11
skew: 0.85
type: snfs
Factor base limits: 300000/350000
Large primes per side: 3
Large prime bits: 25/25
Sieved special-q in [175000, 235001)
Relations: rels:882623, finalFF:80529
Initial matrix: 55859 x 80529 with sparse part having weight 2078125.
Pruned matrix : 44104 x 44447 with weight 826916.
Total sieving time: 0.27 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,102,5,0,0,0,0,0,0,0,0,300000,350000,25,25,43,43,2.1,2.1,10000
total time: 0.29 hours.

Aug 25, 2008

Factorizations of 266...663 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Aug 24, 2008

By Robert Backstrom / GGNFS, Msieve

(28·10¹⁹²+17)/9 = 3(1)₁₉₁3_<193> = 521 · C190

C190 = P73 · P118

P73 = 1458937323972688141163556335746502776674397881172224762818763944697215069_<73>

P118 = 4092994524178830122862088646214472282038812569865140154265414739307172089165984897534485615008489229532328512174074037_<118>

Number: n
N=5971422478140328428236297718063552996374493495414800597142247814032842823629771806355299637449349541480059714224781403284282362977180635529963744934954148005971422478140328428236297718063553
  ( 190 digits)
SNFS difficulty: 193 digits.
Divisors found:

Sun Aug 24 01:06:20 2008  prp73 factor: 1458937323972688141163556335746502776674397881172224762818763944697215069
Sun Aug 24 01:06:20 2008  prp118 factor: 4092994524178830122862088646214472282038812569865140154265414739307172089165984897534485615008489229532328512174074037
Sun Aug 24 01:06:20 2008  elapsed time 13:52:38 (Msieve 1.36)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 205.33 hours.
Scaled time: 269.80 units (timescale=1.314).
Factorization parameters were as follows:
name: KA_3_1_191_3
n: 5971422478140328428236297718063552996374493495414800597142247814032842823629771806355299637449349541480059714224781403284282362977180635529963744934954148005971422478140328428236297718063553
type: snfs
skew: 0.66
deg: 5
c5: 175
c0: 34
m: 200000000000000000000000000000000000000
rlim: 9500000
alim: 9500000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9500000/9500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 19100001)
Primes: RFBsize:633578, AFBsize:634408, largePrimes:11259898 encountered
Relations: rels:11316728, finalFF:1301584
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 204.60 hours.
Total relation processing time: 0.73 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,193,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,50,50,2.5,2.5,100000
total time: 205.33 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Aug 23, 2008

By Serge Batalov / Msieve

(5·10¹⁶⁶+1)/3 = 1(6)₁₆₅7_<167> = 7 · 2412311810963_<13> · 21681484588402783327_<20> · C134

C134 = P60 · P75

P60 = 120290653074033155377693119077932432451849157820371719000141_<60>

P75 = 378439419381373063595334977207576433701637494219631261758036807264278082741_<75>

Number: 16667_166
N=45522724906343286192598532980210324781874447309646171866952716995837515000348028814367639145587478869903469660672480559082664988666481
  ( 134 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=120290653074033155377693119077932432451849157820371719000141
 r2=378439419381373063595334977207576433701637494219631261758036807264278082741
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.719).
Factorization parameters were as follows:
n: 45522724906343286192598532980210324781874447309646171866952716995837515000348028814367639145587478869903469660672480559082664988666481
Y1: 1
Y0: -1000000000000000000000000000000000
c5: 50
c0: 1
skew: 0.46
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 4000001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 714390 x 714638
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 1.90 hours.
Time per square root: 0.60 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.5,2.5,100000
total time: 24.00 hours.

Aug 22, 2008 (2nd)

By Serge Batalov / Msieve

4·10¹⁶⁶+1 = 4(0)₁₆₅1_<167> = 13 · 41 · 4517 · 152421337841_<12> · 941160476969540120952877_<24> · C126

C126 = P51 · P75

P51 = 338717486802811900673981008844119653096357974239957_<51>

P75 = 341928753479598700237304527485927308118819144008567869244980664981674968409_<75>

Number: 40001_166
N=115817248044227896509289122964484316966630639321189981212930837312203257669785275747098638613513868711415814586413023760518413
  ( 126 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=338717486802811900673981008844119653096357974239957
 r2=341928753479598700237304527485927308118819144008567869244980664981674968409
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.694).
Factorization parameters were as follows:
n: 115817248044227896509289122964484316966630639321189981212930837312203257669785275747098638613513868711415814586413023760518413
Y1: 1
Y0: -1000000000000000000000000000000000
c5: 40
c0: 1
skew: 0.48
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 3900001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 741740 x 741988
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 2.20 hours.
Time per square root: 0.40 hours. * 2
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.5,2.5,100000
total time: 23.50 hours.

(7·10¹⁷¹-1)/3 = 2(3)₁₇₁_<172> = 1138853 · C166

C166 = P56 · P110

P56 = 52466933536616764762455731674465527913345675902479976653_<56>

P110 = 39050215312850715281346300573082614025282121181643881618463088046577029592640409813713876589831290571574330037_<110>

Number: 23333_171
N=2048845051409912722127731439732198390251712322251715834557518251550756184804652868573321871508731445878733544481450488634910153754113422305893151559800372245876626161
  ( 166 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=52466933536616764762455731674465527913345675902479976653
 r2=39050215312850715281346300573082614025282121181643881618463088046577029592640409813713876589831290571574330037
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.726).
Factorization parameters were as follows:
n: 2048845051409912722127731439732198390251712322251715834557518251550756184804652868573321871508731445878733544481450488634910153754113422305893151559800372245876626161
Y1: 1
Y0: -10000000000000000000000000000000000
c5: 70
c0: -1
skew: 0.43
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 5700001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1012135 x 1012383
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 4.20 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.6,2.6,100000

total time: 44.50 hours.

Aug 22, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(5·10¹⁹⁸-23)/9 = (5)₁₉₇3_<198> = 79 · 1787 · 92166227 · 62964716122813547478189355909_<29> · 119356565544646731891786102577789_<33> · C124

C124 = P42 · P83

P42 = 396488530126012349110486416962263561871273_<42>

P83 = 14329460853556106742975766217842853536031643858403149301167495308116549583366771591_<83>

(22·10¹⁷⁴+23)/9 = 2(4)₁₇₃7_<175> = 947 · C172

C172 = P44 · P45 · P85

P44 = 13793496764933613173998444708639348503342167_<44>

P45 = 110540140507371818048930699460533646011671649_<45>

P85 = 1692917532546119710378264581159890068911580941102272929764210993817970269701152940547_<85>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 2581250733309867417575970902264460870585474598146192655168367945559075442919159920215886424967734365833626657280300363721694239117681567523172591810395400680511556963510501 (172 digits)
Using B1=4606000, B2=8562235510, polynomial Dickson(6), sigma=970024370
Step 1 took 65031ms
Step 2 took 21375ms
********** Factor found in step 2: 13793496764933613173998444708639348503342167
Found probable prime factor of 44 digits: 13793496764933613173998444708639348503342167
Composite cofactor 187135341915041275536807385055191549657231130756477371436302859011515528532617086139748716813756071039729965347118336379382452003 has 129 digits

Number: n
N=187135341915041275536807385055191549657231130756477371436302859011515528532617086139748716813756071039729965347118336379382452003
  ( 129 digits)
SNFS difficulty: 176 digits.
Divisors found:

Fri Aug 22 16:47:46 2008  prp45 factor: 110540140507371818048930699460533646011671649
Fri Aug 22 16:47:46 2008  prp85 factor: 1692917532546119710378264581159890068911580941102272929764210993817970269701152940547
Fri Aug 22 16:47:46 2008  elapsed time 02:52:14 (Msieve 1.36)

Version: GGNFS-0.77.1-20050930-k8
Total time: 48.99 hours.
Scaled time: 41.06 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_2_4_173_7
n: 187135341915041275536807385055191549657231130756477371436302859011515528532617086139748716813756071039729965347118336379382452003
type: snfs
skew: 1.60
deg: 5
c5: 11
c0: 115
m: 100000000000000000000000000000000000
rlim: 7400000
alim: 7400000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 5300001)
Primes: RFBsize:501962, AFBsize:502147, largePrimes:10305780 encountered
Relations: rels:10097030, finalFF:1048955
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 48.70 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,7400000,7400000,28,28,50,50,2.5,2.5,100000
total time: 48.99 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

Aug 21, 2008

By Serge Batalov / Msieve

9·10¹⁷⁷-1 = 8(9)₁₇₇_<178> = 89 · 757 · C174

C174 = P76 · P98

P76 = 2795376519729848150784923706882701877318922481507609115407740172075186231071_<76>

P98 = 47787719999108578060151819968036562451065721814882830579492456551763376466710619837746260674550853_<98>

Number: 89999_177
N=133584670416932599112404078785270063675359565404538910245944220978730351921392842830213883900078666528134415863921749068617992370831045077404895136033722707909696762798153563
  ( 174 digits)
SNFS difficulty: 177 digits.
Divisors found:
 r1=2795376519729848150784923706882701877318922481507609115407740172075186231071
 r2=47787719999108578060151819968036562451065721814882830579492456551763376466710619837746260674550853
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.651).
Factorization parameters were as follows:
n: 133584670416932599112404078785270063675359565404538910245944220978730351921392842830213883900078666528134415863921749068617992370831045077404895136033722707909696762798153563
Y1: 1
Y0: -100000000000000000000000000000000000
c5: 900
c0: -1
skew: 0.26
type: snfs
Factor base limits: 11400000/11400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [5700000, 9700001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1301455 x 1301703
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 7.00 hours.
Time per square root: 0.40 hours.
Prototype def-par.txt line would be:
snfs,177,5,0,0,0,0,0,0,0,0,11400000,11400000,27,27,52,52,2.6,2.6,100000

total time: 76.00 hours.

Aug 20, 2008 (2nd)

By matsui / GGNFS

10¹⁹¹+9 = 1(0)₁₉₀9_<192> = 7 · 13 · 103 · C188

C188 = P39 · P149

P39 = 558512525126795884293354955450279221529_<39>

P149 = 19102423361688353491586596941283273631279087307124210159959098992316128275614458548628339728160988510023049614103059197070847250912364210612167195877_<149>

N=10668942707777659233969913581564067000960204843699989331057292222340766030086418435932999039795156300010668942707777659233969913581564067000960204843699989331057292222340766030086418435933
  ( 188 digits)
SNFS difficulty: 191 digits.
Divisors found:
 r1=558512525126795884293354955450279221529 (pp39)
 r2=19102423361688353491586596941283273631279087307124210159959098992316128275614458548628339728160988510023049614103059197070847250912364210612167195877 (pp149)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 477.36 hours.
Scaled time: 915.57 units (timescale=1.918).
Factorization parameters were as follows:
n: 10668942707777659233969913581564067000960204843699989331057292222340766030086418435932999039795156300010668942707777659233969913581564067000960204843699989331057292222340766030086418435933
m: 100000000000000000000000000000000000000
c5: 10
c0: 9
skew: 0.98
type: snfs
rlim: 10000000
alim: 10000000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000

Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [5000000, 14500001)
Primes: RFBsize:664579, AFBsize:664685, largePrimes:11579378 encountered
Relations: rels:11937015, finalFF:1530165
Max relations in full relation-set: 28
Initial matrix: 1329331 x 1530165 with sparse part having weight 146036484.
Pruned matrix : 1164732 x 1171442 with weight 119352904.
Total sieving time: 456.55 hours.
Total relation processing time: 0.53 hours.
Matrix solve time: 19.77 hours.
Time per square root: 0.50 hours.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000
total time: 477.36 hours.

Aug 20, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(5·10¹⁷⁴-23)/9 = (5)₁₇₃3_<174> = 17 · 29 · C172

C172 = P63 · P109

P63 = 359886655710553109256565370413038399176555884657330308072113227_<63>

P109 = 3131229009864065205534482597030840703301171760518459388457299185286436731474229584526926422614873427573448623_<109>

Number: n
N=1126887536623844940274960558936218165427090376380437232364210051836826684696867252648185711066035609646157313500112688753662384494027496055893621816542709037638043723236421
  ( 172 digits)
SNFS difficulty: 175 digits.
Divisors found:

Wed Aug 20 12:24:15 2008  prp63 factor: 359886655710553109256565370413038399176555884657330308072113227
Wed Aug 20 12:24:15 2008  prp109 factor: 3131229009864065205534482597030840703301171760518459388457299185286436731474229584526926422614873427573448623
Wed Aug 20 12:24:15 2008  elapsed time 02:54:01 (Msieve 1.36)

Version: GGNFS-0.77.1-20050930-k8
Total time: 43.83 hours.
Scaled time: 36.90 units (timescale=0.842).
Factorization parameters were as follows:
name: KA_5_173_3
n: 1126887536623844940274960558936218165427090376380437232364210051836826684696867252648185711066035609646157313500112688753662384494027496055893621816542709037638043723236421
type: snfs
skew: 2.15
deg: 5
c5: 1
c0: -46
m: 100000000000000000000000000000000000
rlim: 7400000
alim: 7400000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 4700001)
Primes: RFBsize:501962, AFBsize:502151, largePrimes:10263667 encountered
Relations: rels:10063226, finalFF:1058780
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 43.56 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,28,28,50,50,2.5,2.5,100000
total time: 43.83 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

(67·10¹⁷⁰+23)/9 = 7(4)₁₆₉7_<171> = 3 · 2340797939300562583_<19> · 702139207668471108691_<21> · C132

C132 = P42 · P90

P42 = 391473357601478428260308573141911055833729_<42>

P90 = 385675167227586804576204636749049134730109858952723259341925218373142706418135301504058177_<90>

Aug 19, 2008 (2nd)

By Wataru Sakai / GGNFS

(5·10¹⁸⁹+1)/3 = 1(6)₁₈₈7_<190> = 89 · C188

C188 = P69 · P120

P69 = 155220716217629705641047956974028903638974953850976713020609050449043_<69>

P120 = 120644925604155219989104828180435891279930064771908342549722918494534590742040930991869791304135720103379793852604543921_<120>

Number: 16667_189
N=18726591760299625468164794007490636704119850187265917602996254681647940074906367041198501872659176029962546816479400749063670411985018726591760299625468164794007490636704119850187265917603
  ( 188 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=155220716217629705641047956974028903638974953850976713020609050449043 (pp69)
 r2=120644925604155219989104828180435891279930064771908342549722918494534590742040930991869791304135720103379793852604543921 (pp120)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 878.82 hours.
Scaled time: 1761.16 units (timescale=2.004).
Factorization parameters were as follows:
n: 18726591760299625468164794007490636704119850187265917602996254681647940074906367041198501872659176029962546816479400749063670411985018726591760299625468164794007490636704119850187265917603
m: 100000000000000000000000000000000000000
c5: 1
c0: 2
skew: 1.15
type: snfsFactor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 15700001)
Primes: RFBsize:501962, AFBsize:501936, largePrimes:6977777 encountered
Relations: rels:7567375, finalFF:1214697
Max relations in full relation-set: 32
Initial matrix: 1003962 x 1214697 with sparse part having weight 117983597.
Pruned matrix : 840086 x 845169 with weight 98678495.
Total sieving time: 869.86 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 8.60 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 878.82 hours.
 --------- CPU info (if available) ----------

10¹⁸⁸+7 = 1(0)₁₈₇7_<189> = 919 · C186

C186 = P48 · P138

P48 = 546994870962230793373065729931284587933779712219_<48>

P138 = 198930436022901655488560388986742823483843042807587457103337590796061445066460085353325337124807905412409771088506395458055122523822016387_<138>

Number: 10007_188
N=108813928182807399347116430903155603917301414581066376496191512513601741022850924918389553862894450489662676822633297062023939064200217627856365614798694232861806311207834602829162132753
  ( 186 digits)
SNFS difficulty: 188 digits.
Divisors found:
 r1=546994870962230793373065729931284587933779712219 (pp48)
 r2=198930436022901655488560388986742823483843042807587457103337590796061445066460085353325337124807905412409771088506395458055122523822016387 (pp138)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 842.87 hours.
Scaled time: 1690.80 units (timescale=2.006).
Factorization parameters were as follows:
n: 108813928182807399347116430903155603917301414581066376496191512513601741022850924918389553862894450489662676822633297062023939064200217627856365614798694232861806311207834602829162132753
m: 10000000000000000000000000000000000000
c5: 1000
c0: 7
skew: 0.37
type: snfsFactor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 15000001)
Primes: RFBsize:501962, AFBsize:501101, largePrimes:6954314 encountered
Relations: rels:7527639, finalFF:1210235
Max relations in full relation-set: 32
Initial matrix: 1003129 x 1210235 with sparse part having weight 117655184.
Pruned matrix : 840397 x 845476 with weight 97173257.
Total sieving time: 833.71 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 8.78 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,188,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 842.87 hours.
 --------- CPU info (if available) ----------

Aug 19, 2008

By Serge Batalov / Msieve

(23·10¹⁷¹+31)/9 = 2(5)₁₇₀9_<172> = 3 · 347 · C169

C169 = P46 · P123

P46 = 2507406786358400630053956114754671784954141033_<46>

P123 = 979061110287926914452686823674334926754673406716505690256590865236353645010621985257918365427531665179753798361452391361503_<123>

Number: 25559_171
N=2454904472195538477959227238766143665279111964990927526950581705624933290639342512541359803607642224356921763261820898708506777671042800725797843953463550005336748852599
  ( 169 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=2507406786358400630053956114754671784954141033
 r2=979061110287926914452686823674334926754673406716505690256590865236353645010621985257918365427531665179753798361452391361503
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.721).
Factorization parameters were as follows:
n: 2454904472195538477959227238766143665279111964990927526950581705624933290639342512541359803607642224356921763261820898708506777671042800725797843953463550005336748852599
Y1: 1
Y0: -10000000000000000000000000000000000
c5: 230
c0: 31
skew: 0.67
type: snfs
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [4500000, 10000001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1302887 x 1303135
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 7.15 hours.
Time per square root: 2.70 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,52,52,2.6,2.6,100000
total time: 84.00 hours.

Aug 18, 2008 (2nd)

By Sinkiti Sibata / GMP-ECM

(22·10¹⁷⁹-13)/9 = 2(4)₁₇₈3_<180> = 3 · 167 · 630373842617_<12> · 2216727877196124340330489_<25> · C141

C141 = P47 · P95

P47 = 24726223009098487467636225633358624031335131751_<47>

P95 = 14121281057022318743169320232071258885317897178039011226565812763366085713013565900617484617961_<95>

factor24443_179
GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 349165944590091867944970739224950115657298071576715071521804379303095232821001110672336976242671808298508474956698907944114498422023835979711

Run 1472 out of 2350:
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1048915276
Step 1 took 49375ms
Step 2 took 17269ms
********** Factor found in step 2: 24726223009098487467636225633358624031335131751
Found probable prime factor of 47 digits: 24726223009098487467636225633358624031335131751
Probable prime cofactor 14121281057022318743169320232071258885317897178039011226565812763366085713013565900617484617961 has 95 digits

Aug 18, 2008

By Robert Backstrom / GGNFS, Msieve

9·10¹⁹²+1 = 9(0)₁₉₁1_<193> = 1109 · C190

C190 = P62 · P129

P62 = 14734116298400713270539985713991888026642775154005017603856013_<62>

P129 = 550791043881235942395862556041076669468450897765276463896412425335034457457595786628772946981138862497150863003489314800842696753_<129>

Number: n
N=8115419296663660955816050495942290351668169522091974752028854824165915238954012623985572587917042380522993688007213706041478809738503155996393146979260595130748422001803426510369702434625789
  ( 190 digits)
SNFS difficulty: 192 digits.
Divisors found:

Mon Aug 18 06:37:29 2008  prp62 factor: 14734116298400713270539985713991888026642775154005017603856013
Mon Aug 18 06:37:30 2008  prp129 factor: 550791043881235942395862556041076669468450897765276463896412425335034457457595786628772946981138862497150863003489314800842696753
Mon Aug 18 06:37:30 2008  elapsed time 06:34:54 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 151.51 hours.
Scaled time: 309.84 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_9_0_191_1
n: 8115419296663660955816050495942290351668169522091974752028854824165915238954012623985572587917042380522993688007213706041478809738503155996393146979260595130748422001803426510369702434625789
type: snfs
skew: 0.26
deg: 5
c5: 900
c0: 1
m: 100000000000000000000000000000000000000
rlim: 9500000
alim: 9500000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9500000/9500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 12100001)
Primes: RFBsize:633578, AFBsize:632398, largePrimes:11067961 encountered
Relations: rels:11117802, finalFF:1296478
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 151.11 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,192,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,50,50,2.5,2.5,100000
total time: 151.51 hours.
 --------- CPU info (if available) ----------

(23·10¹⁶⁶+31)/9 = 2(5)₁₆₅9_<167> = 17² · 107 · C162

C162 = P56 · P107

P56 = 18196127155026565765210313040636762315634917977595426793_<56>

P107 = 45417658774727419799492427840630036712482623752503343649034406587180499821842694832789683367090599801389581_<107>

Number: n
N=826425494148548185996040343936731738691445058873833572278095771935308849579780601997075172381578616419996622434936958107413755313376954226807087137585472158443733
  ( 162 digits)
SNFS difficulty: 167 digits.
Divisors found:

Mon Aug 18 12:45:53 2008  prp56 factor: 18196127155026565765210313040636762315634917977595426793
Mon Aug 18 12:45:57 2008  prp107 factor: 45417658774727419799492427840630036712482623752503343649034406587180499821842694832789683367090599801389581
Mon Aug 18 12:45:57 2008  elapsed time 01:29:48 (Msieve 1.36)

Version: GGNFS-0.77.1-20050930-k8
Total time: 49.69 hours.
Scaled time: 41.59 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_2_5_165_9
n: 826425494148548185996040343936731738691445058873833572278095771935308849579780601997075172381578616419996622434936958107413755313376954226807087137585472158443733
type: snfs
deg: 5
c5: 230
c0: 31
skew: 0.28
m: 1000000000000000000000000000000000
rlim: 6000000
alim: 6000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5700001)
Primes: RFBsize:412849, AFBsize:413297, largePrimes:5940623 encountered
Relations: rels:6154327, finalFF:881975
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 49.48 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.5,2.5,100000
total time: 49.69 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

Aug 16, 2008 (5th)

By Jo Yeong Uk / GGNFS

(23·10¹⁷⁰+31)/9 = 2(5)₁₆₉9_<171> = 7 · 37 · 26671840033_<11> · 161421299558369246533_<21> · 297906976876056499602031_<24> · C114

C114 = P50 · P65

P50 = 36980604693757519861771088341660957144857651838787_<50>

P65 = 20802573382540544081050343846624872121634029784960968772855844397_<65>

Number: 25559_170
N=769291742872614091219688752614724603405832009110180438834256123590702076321274183344961360080414224048366601226439
  ( 114 digits)
Divisors found:
 r1=36980604693757519861771088341660957144857651838787 (pp50)
 r2=20802573382540544081050343846624872121634029784960968772855844397 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 19.66 hours.
Scaled time: 46.86 units (timescale=2.383).
Factorization parameters were as follows:
name: 25559_170
n: 769291742872614091219688752614724603405832009110180438834256123590702076321274183344961360080414224048366601226439
skew: 46401.47
# norm 1.16e+16
c5: 59280
c4: -555799160
c3: -633544502641438
c2: 2986793278184410387
c1: 397242036976346980316280
c0: -1036910798119627579106192689
# alpha -6.47
Y1: 467621825129
Y0: -6647167652001661320280
# Murphy_E 5.90e-10
# M 68984389221729131535103752351912674335008154275451042128487769092207973153624902851094592364583691152142341444552
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 70000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2870001)
Primes: RFBsize:250150, AFBsize:249788, largePrimes:7423751 encountered
Relations: rels:7272702, finalFF:578183
Max relations in full relation-set: 28
Initial matrix: 500021 x 578183 with sparse part having weight 47872572.
Pruned matrix : 436944 x 439508 with weight 31525107.
Polynomial selection time: 1.19 hours.
Total sieving time: 17.17 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 1.05 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.4,2.4,70000
total time: 19.66 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2459k kernel code, 339200k reserved, 1247k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.73 BogoMIPS (lpj=2672366)
Calibrating delay using timer specific routine.. 5343.99 BogoMIPS (lpj=2671997)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Aug 16, 2008 (4th)

By Serge Batalov / Msieve

(23·10¹⁶⁵+31)/9 = 2(5)₁₆₄9_<166> = 3 · C165

C165 = P57 · P109

P57 = 352723018532378683493559904773387908384026434468579905407_<57>

P109 = 2415073037751447362227275468798835152491591313608019272430734224422879445896978821428462796498802433657712179_<109>

Number: 25559_165
N=851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851853
  ( 165 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=352723018532378683493559904773387908384026434468579905407
 r2=2415073037751447362227275468798835152491591313608019272430734224422879445896978821428462796498802433657712179
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.740).
Factorization parameters were as follows:
n: 851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851853
Y1: 1
Y0: -1000000000000000000000000000000000
c5: 23
c0: 31
skew: 1.06
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 4600001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 874652 x 874900
Total sieving time: 0.00 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 3.00 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.5,2.5,100000

total time: 32.00 hours.

Aug 16, 2008 (3rd)

By Sinkiti Sibata / GGNFS, GMP-ECM

(22·10¹⁶⁵-31)/9 = 2(4)₁₆₄1_<166> = 1697 · 111127 · 3102605993391224233_<19> · C139

C139 = P43 · P96

P43 = 9181028417573967427804067865162623442511111_<43>

P96 = 455051740794629015966935014142950094789983481286596107420482412029657149588773814025318977528753_<96>

Number: 24441_165
N=4177842963701992033746833730712078164567800348143405756245054797703306366232238457460680059458300800412620841713791420956286274751524474583
  ( 139 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=9181028417573967427804067865162623442511111 (pp43)
 r2=455051740794629015966935014142950094789983481286596107420482412029657149588773814025318977528753 (pp96)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 92.09 hours.
Scaled time: 92.92 units (timescale=1.009).
Factorization parameters were as follows:
name: 24441_165
n: 4177842963701992033746833730712078164567800348143405756245054797703306366232238457460680059458300800412620841713791420956286274751524474583
m: 1000000000000000000000000000000000
c5: 22
c0: -31
skew: 1.07
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 5800001)
Primes: RFBsize:348513, AFBsize:349063, largePrimes:6054324 encountered
Relations: rels:6306720, finalFF:875688
Max relations in full relation-set: 28
Initial matrix: 697642 x 875688 with sparse part having weight 62365519.
Pruned matrix : 559325 x 562877 with weight 44759532.
Total sieving time: 89.22 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 2.66 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 92.09 hours.
 --------- CPU info (if available) ----------

(23·10¹⁶⁴+31)/9 = 2(5)₁₆₃9_<165> = 7³ · 37 · 53 · 724604863 · 2644339927_<10> · 149558255498137_<15> · 31384734606290870461_<20> · C107

C107 = P44 · P64

P44 = 20314652098684047620712717838258567099838687_<44>

P64 = 2079490044692460090839907111629368942340721746105913902433258787_<64>

Number: 25559_164
N=42244116800604268366529850193804123484513381418170860149158312723787899125249545685537409884760891425292669
  ( 107 digits)
Divisors found:
 r1=20314652098684047620712717838258567099838687 (pp44)
 r2=2079490044692460090839907111629368942340721746105913902433258787 (pp64)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 18.02 hours.
Scaled time: 13.97 units (timescale=0.775).
Factorization parameters were as follows:
name: 25559_164
n: 42244116800604268366529850193804123484513381418170860149158312723787899125249545685537409884760891425292669
skew: 16965.36
# norm 7.81e+14
c5: 37380
c4: -2072117878
c3: 459849219343
c2: 650402933349225612
c1: 3693541153055369233838
c0: -99725642052992786755340
# alpha -6.01
Y1: 244617478073
Y0: -257412696036039939867
# Murphy_E 1.59e-09
# M 14173624692086331959785602197541481713292728257386366262229978088003544278931180429090516706414989995363285
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2600001)
Primes: RFBsize:183072, AFBsize:182751, largePrimes:4603461 encountered
Relations: rels:4871820, finalFF:586406
Max relations in full relation-set: 28
Initial matrix: 365902 x 586406 with sparse part having weight 48127292.
Pruned matrix : 228725 x 230618 with weight 25556880.
Total sieving time: 17.12 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.56 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 18.02 hours.
 --------- CPU info (if available) ----------

(22·10¹⁷⁵-13)/9 = 2(4)₁₇₄3_<176> = 499 · 665179 · C167

C167 = P39 · C129

P39 = 108255761415671706622622739225515636293_<39>

C129 = [680283718429769696056120418073040544541397423248695726710441763806401518016805452458069590962210373264962514288556879937951373631_<129>]

Aug 16, 2008 (2nd)

Factorizations of 244...443 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Aug 16, 2008

By Tyler Cadigan / GGNFS, Msieve

10¹⁹¹-9 = (9)₁₉₀1_<191> = 25890181282711_<14> · 19215578593700683_<17> · C162

C162 = P55 · P108

P55 = 1107810740439824418721011542356263180679141608975450841_<55>

P108 = 181445361934394941929618652274442590996558678743985524419560737457231701804057845993063138605270872862639227_<108>

Number: 99991_191
N=201007120753913992913726676871999752197866484593647274473058062430107124951627993332234694165639979396161961186666496539291615060870044793869267715322527456739907
  ( 162 digits)
SNFS difficulty: 191 digits.
Divisors found:
 r1=1107810740439824418721011542356263180679141608975450841
 r2=181445361934394941929618652274442590996558678743985524419560737457231701804057845993063138605270872862639227
Version: 
Total time: 363.74 hours.
Scaled time: 939.54 units (timescale=2.583).
Factorization parameters were as follows:
n: 201007120753913992913726676871999752197866484593647274473058062430107124951627993332234694165639979396161961186666496539291615060870044793869267715322527456739907
m: 100000000000000000000000000000000000000
Y0: -100000000000000000000000000000000000000
Y1: 1
c5: 10
c0: -9
skew: 0.98
type: snfs
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
rlim: 20000000
alim: 20000000
qintsize: 1000000Factor base limits: 20000000/20000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved algebraic special-q in [10000000, 15000001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2351993 x 2352241
Total sieving time: 363.74 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,20000000,20000000,29,29,58,58,2.6,2.6,100000
total time: 363.74 hours.
 --------- CPU info (if available) ----------

Aug 15, 2008 (3rd)

By Jo Yeong Uk / GGNFS

(5·10¹⁷²+31)/9 = (5)₁₇₁9_<172> = 3³ · 19 · 367 · 43714416961213_<14> · 1653798301727248021218700562722037_<34> · C120

C120 = P44 · P76

P44 = 72241579725298286703752721169908212029424891_<44>

P76 = 5650014980209093403988213136282838275204663201213283605113623503379000966699_<76>

Number: 55559_172
N=408166007641904842658786198853065554777699197980622797915618429703920585969239307313834166622909064779063867322012704809
  ( 120 digits)
Divisors found:
 r1=72241579725298286703752721169908212029424891 (pp44)
 r2=5650014980209093403988213136282838275204663201213283605113623503379000966699 (pp76)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 42.61 hours.
Scaled time: 99.58 units (timescale=2.337).
Factorization parameters were as follows:
name: 55559_172
n: 408166007641904842658786198853065554777699197980622797915618429703920585969239307313834166622909064779063867322012704809
skew: 54464.11
# norm 3.98e+16
c5: 40560
c4: 6211959848
c3: 1146515758710458
c2: -11049075575316808459
c1: -1084310473612104839818758
c0: 92932460856167809044240576
# alpha -6.32
Y1: 5874725186849
Y0: -100126030045029031070743
# Murphy_E 2.99e-10
# M 258527015088446783614594124384726963336972174365477566922540598905648026740976070805859456854511819187120769710896024535
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4650001)
Primes: RFBsize:315948, AFBsize:316780, largePrimes:7744450 encountered
Relations: rels:7832498, finalFF:721672
Max relations in full relation-set: 28
Initial matrix: 632807 x 721672 with sparse part having weight 65602018.
Pruned matrix : 562992 x 566220 with weight 47467813.
Polynomial selection time: 2.63 hours.
Total sieving time: 37.39 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 2.29 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000
total time: 42.61 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2459k kernel code, 339200k reserved, 1247k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.73 BogoMIPS (lpj=2672366)
Calibrating delay using timer specific routine.. 5343.99 BogoMIPS (lpj=2671997)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Aug 15, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(23·10¹⁴⁹+31)/9 = 2(5)₁₄₈9_<150> = 37 · 191 · 15679 · 37011751151_<11> · C131

C131 = P34 · P98

P34 = 3361584197264652895273596117265271_<34>

P98 = 18537375539177608834436534677836482023113574981058078117740700688664556806167695348972239081086803_<98>

Number: 25559_149
N=62314948671259774341306738441476012012330414940443595705313775103277218363502467421308755586346875644340628426542897274022928318613
  ( 131 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=3361584197264652895273596117265271 (pp34)
 r2=18537375539177608834436534677836482023113574981058078117740700688664556806167695348972239081086803 (pp98)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.35 hours.
Scaled time: 24.57 units (timescale=1.009).
Factorization parameters were as follows:
name: 25559_149
n: 62314948671259774341306738441476012012330414940443595705313775103277218363502467421308755586346875644340628426542897274022928318613
m: 1000000000000000000000000000000
c5: 23
c0: 310
skew: 1.68
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176064, largePrimes:5968072 encountered
Relations: rels:6262049, finalFF:824133
Max relations in full relation-set: 28
Initial matrix: 352431 x 824133 with sparse part having weight 71719533.
Pruned matrix : 215298 x 217124 with weight 31813327.
Total sieving time: 23.81 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.40 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 24.35 hours.
 --------- CPU info (if available) ----------

(23·10¹⁴²+31)/9 = 2(5)₁₄₁9_<143> = 48904153 · C135

C135 = P30 · P106

P30 = 444194718344280895043997630773_<30>

P106 = 1176430281451362767142572801287387880687088852707840173878701242816842277224993751011294270542540793205411_<106>

Number: 25559_142
N=522564117520971185321532008857316382834716625304921558616004566228875399509639918629314683265356943316359155746047898131587220323712703
  ( 135 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=444194718344280895043997630773 (pp30)
 r2=1176430281451362767142572801287387880687088852707840173878701242816842277224993751011294270542540793205411 (pp106)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 16.94 hours.
Scaled time: 16.94 units (timescale=1.000).
Factorization parameters were as follows:
name: 25559_142
n: 522564117520971185321532008857316382834716625304921558616004566228875399509639918629314683265356943316359155746047898131587220323712703
m: 10000000000000000000000000000
c5: 2300
c0: 31
skew: 0.42
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 3150001)
Primes: RFBsize:100021, AFBsize:100199, largePrimes:3033286 encountered
Relations: rels:3111625, finalFF:248898
Max relations in full relation-set: 28
Initial matrix: 200287 x 248898 with sparse part having weight 31797235.
Pruned matrix : 188622 x 189687 with weight 23055159.
Total sieving time: 16.58 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.25 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 16.94 hours.
 --------- CPU info (if available) ----------

(23·10¹⁴⁷+31)/9 = 2(5)₁₄₆9_<148> = 3 · 607 · 613 · 11814950847142514192592437550491_<32> · C111

C111 = P44 · P67

P44 = 75103645093403353316146749218224397401074883_<44>

P67 = 2580013458340758255133834372880389552639163595586137327515941451111_<67>

Number: 25559_147
N=193768415111428505634206429615235537385350691524879778259506099811343404692477670800012264250391853206194545013
  ( 111 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=75103645093403353316146749218224397401074883 (pp44)
 r2=2580013458340758255133834372880389552639163595586137327515941451111 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 37.50 hours.
Scaled time: 37.92 units (timescale=1.011).
Factorization parameters were as follows:
name: 25559_147
n: 193768415111428505634206429615235537385350691524879778259506099811343404692477670800012264250391853206194545013
m: 100000000000000000000000000000
c5: 2300
c0: 31
skew: 0.42
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 6050001)
Primes: RFBsize:114155, AFBsize:114273, largePrimes:3381300 encountered
Relations: rels:3629815, finalFF:298783
Max relations in full relation-set: 28
Initial matrix: 228495 x 298783 with sparse part having weight 41916253.
Pruned matrix : 212196 x 213402 with weight 29855920.
Total sieving time: 36.99 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.37 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 37.50 hours.
 --------- CPU info (if available) ----------

(23·10¹⁵⁶+31)/9 = 2(5)₁₅₅9_<157> = 3 · 103 · 30103 · 356309378983_<12> · 1282946082595495938311_<22> · C117

C117 = P37 · P81

P37 = 2246093478334450292669536908800692657_<37>

P81 = 267579958753199187375886538609657583415035345954915647058260946016914480850748237_<81>

Number: 25559_156
N=601009600288561901917388771431808879676434281891754853211007016430854322163937732912532470157987210701592422321595709
  ( 117 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=2246093478334450292669536908800692657 (pp37)
 r2=267579958753199187375886538609657583415035345954915647058260946016914480850748237 (pp81)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 60.72 hours.
Scaled time: 46.39 units (timescale=0.764).
Factorization parameters were as follows:
name: 25559_156
n: 601009600288561901917388771431808879676434281891754853211007016430854322163937732912532470157987210701592422321595709
m: 10000000000000000000000000000000
c5: 230
c0: 31
skew: 0.67
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3600001)
Primes: RFBsize:216816, AFBsize:217007, largePrimes:5989157 encountered
Relations: rels:6100315, finalFF:603185
Max relations in full relation-set: 28
Initial matrix: 433890 x 603185 with sparse part having weight 65102898.
Pruned matrix : 365549 x 367782 with weight 42219288.
Total sieving time: 58.23 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 2.14 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 60.72 hours.
 --------- CPU info (if available) ----------

Aug 15, 2008

By Serge Batalov / Msieve

(23·10¹⁵⁴+31)/9 = 2(5)₁₅₃9_<155> = C155

C155 = P68 · P88

P68 = 24004480982001907880256277793174862134905775836273857482990834610803_<68>

P88 = 1064616042926177540280830726352520704884408223688229599012984589433059561384926047461053_<88>

Number: 25559_154
N=25555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555559
  ( 155 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=24004480982001907880256277793174862134905775836273857482990834610803
 r2=1064616042926177540280830726352520704884408223688229599012984589433059561384926047461053
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 25555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555559
Y1: 1
Y0: -10000000000000000000000000000000
c5: 23
c0: 310
skew: 1.68
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1500000, 2200001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 536384 x 536632
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,52,52,2.5,2.5,100000
total time: 12.00 hours.

(23·10¹⁵⁹+31)/9 = 2(5)₁₅₈9_<160> = 3² · 151 · 173 · C155

C155 = P68 · P87

P68 = 89402830646845862862212588779611774210792761685868432636233023487881_<68>

P87 = 121581779965533991572064099812148849337116961553860068777860822932046094064865597027077_<87>

Number: 25559_159
N=10869755284000712677868185785857314140181090123031451873213283975192382853575416961449703988207733311026705098340566446577752068443540836961704906938353837
  ( 155 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=89402830646845862862212588779611774210792761685868432636233023487881
 r2=121581779965533991572064099812148849337116961553860068777860822932046094064865597027077
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.725).
Factorization parameters were as follows:
n: 10869755284000712677868185785857314140181090123031451873213283975192382853575416961449703988207733311026705098340566446577752068443540836961704906938353837
Y1: 1
Y0: -100000000000000000000000000000000
c5: 23
c0: 310
skew: 1.68
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2000000, 3100001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 612972 x 613220
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,52,52,2.5,2.5,100000
total time: 17.20 hours.

(23·10¹⁵⁷+31)/9 = 2(5)₁₅₆9_<158> = C158

C158 = P50 · P108

P50 = 49305565416638237546855293608378285511055783935823_<50>

P108 = 518309755493277331341705329873406123057615376398129738348359754423513248803380888816255348102631292457305833_<108>

Number: 25559_157
N=25555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555559
  ( 158 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=49305565416638237546855293608378285511055783935823
 r2=518309755493277331341705329873406123057615376398129738348359754423513248803380888816255348102631292457305833
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.707).
Factorization parameters were as follows:
n: 25555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555559
Y1: 1
Y0: -10000000000000000000000000000000
c5: 2300
c0: 31
skew: 0.42
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2000000, 5300001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 775626 x 775874
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,52,52,2.5,2.5,100000
total time: 23.00 hours.

(23·10¹⁶³+31)/9 = 2(5)₁₆₂9_<164> = 11197 · 600135654958518913015121_<24> · 15917843362328931372400174231396061_<35> · C102

C102 = P46 · P56

P46 = 4777261969155687481306587205398516207932071267_<46>

P56 = 50011621397949403287827699425161427247300887932441419861_<56>

N=238918616920236482284688193493767802557297554431710259935973434002654087902904166343115871840121233887
  ( 102 digits)
Divisors found:
 r1=4777261969155687481306587205398516207932071267
 r2=50011621397949403287827699425161427247300887932441419861
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.718).
Factorization parameters were as follows:
name: 25559_163
n: 238918616920236482284688193493767802557297554431710259935973434002654087902904166343115871840121233887
skew: 26690.28
# norm 3.49e+14
c5: 11340
c4: 172695024
c3: -21952003729623
c2: -183405417277364978
c1: 2326716827805210224682
c0: 34516205836374053444042628
# alpha -7.10
Y1: 46579288979
Y0: -29155820963474000399
# Murphy_E 2.89e-09
# M 60712994758916835332065667762407420644104045750246852901951305449959008087828470303990127529380791560
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1750001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 215230 x 215478
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000

total time: 4.50 hours.

Aug 14, 2008 (5th)

By Sinkiti Sibata / GGNFS

(23·10¹³⁶+31)/9 = 2(5)₁₃₅9_<137> = 227 · 397 · 727 · 773 · C126

C126 = P37 · P42 · P48

P37 = 4294379808444677906913969409355254559_<37>

P42 = 377963583243089172487553781282255778332803_<42>

P48 = 310888493269623289140455555332340572349264972183_<48>

Number: 25559_136
N=504609076331431584228366233423443440822540269199705375616028388572415036563660999834170097655998553802901539210099104791238491
  ( 126 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=4294379808444677906913969409355254559 (pp37)
 r2=377963583243089172487553781282255778332803 (pp42)
 r3=310888493269623289140455555332340572349264972183 (pp48)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.32 hours.
Scaled time: 11.19 units (timescale=0.988).
Factorization parameters were as follows:
name: 25559_136
n: 504609076331431584228366233423443440822540269199705375616028388572415036563660999834170097655998553802901539210099104791238491
m: 1000000000000000000000000000
c5: 230
c0: 31
skew: 0.67
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 2275001)
Primes: RFBsize:78498, AFBsize:63729, largePrimes:1760780 encountered
Relations: rels:1843501, finalFF:205262
Max relations in full relation-set: 28
Initial matrix: 142294 x 205262 with sparse part having weight 24445222.
Pruned matrix : 129188 x 129963 with weight 14345545.
Total sieving time: 11.15 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 11.32 hours.
 --------- CPU info (if available) ----------

(23·10¹⁴¹+31)/9 = 2(5)₁₄₀9_<142> = 3² · 29 · 10607 · 372078052816479538519637_<24> · C112

C112 = P35 · P77

P35 = 76194565446367493174455763880460463_<35>

P77 = 32560735029065341214128814187400511581285961062243794359923482842555071079407_<77>

Number: 25559_141
N=2480951056153949701228703243919926546283721927193703106236404703317962887038008437037078659456775758113596985441
  ( 112 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=76194565446367493174455763880460463 (pp35)
 r2=32560735029065341214128814187400511581285961062243794359923482842555071079407 (pp77)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 14.76 hours.
Scaled time: 14.76 units (timescale=1.000).
Factorization parameters were as follows:
name: 25559_141
n: 2480951056153949701228703243919926546283721927193703106236404703317962887038008437037078659456775758113596985441
m: 10000000000000000000000000000
c5: 230
c0: 31
skew: 0.67
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2750001)
Primes: RFBsize:100021, AFBsize:99799, largePrimes:3038180 encountered
Relations: rels:3144558, finalFF:307864
Max relations in full relation-set: 28
Initial matrix: 199887 x 307864 with sparse part having weight 38526056.
Pruned matrix : 175685 x 176748 with weight 21820711.
Total sieving time: 14.44 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 14.76 hours.
 --------- CPU info (if available) ----------

(23·10¹³⁷+31)/9 = 2(5)₁₃₆9_<138> = 37 · 308555744497093_<15> · C122

C122 = P42 · P80

P42 = 305762271390977651319812135780994171599831_<42>

P80 = 73209268986643556707742394636801129517180084446760232905412721334096208230335929_<80>

Number: 25559_137
N=22384632372229190609714858716588723245099169836977091812409926831894009881923370879370091085934184452345263599880489627999
  ( 122 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=305762271390977651319812135780994171599831 (pp42)
 r2=73209268986643556707742394636801129517180084446760232905412721334096208230335929 (pp80)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 17.38 hours.
Scaled time: 13.37 units (timescale=0.769).
Factorization parameters were as follows:
name: 25559_137
n: 22384632372229190609714858716588723245099169836977091812409926831894009881923370879370091085934184452345263599880489627999
m: 1000000000000000000000000000
c5: 2300
c0: 31
skew: 0.42
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 2725001)
Primes: RFBsize:78498, AFBsize:64019, largePrimes:1757390 encountered
Relations: rels:1826972, finalFF:174401
Max relations in full relation-set: 28
Initial matrix: 142584 x 174401 with sparse part having weight 21121949.
Pruned matrix : 135557 x 136333 with weight 15350591.
Total sieving time: 17.08 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 17.38 hours.
 --------- CPU info (if available) ----------

(23·10¹³⁸+31)/9 = 2(5)₁₃₇9_<139> = 3 · 53 · 389 · 1433539 · C128

C128 = P64 · P65

P64 = 1279333927545199012128258534852861478951245004473500538855514499_<64>

P65 = 22529168901137974895314002117395908892469523921646148358021532669_<65>

Number: 25559_138
N=28822330134622000820620584010253028421676120212058138406067842081365878773742408071645154741613441781555667878148540074531667831
  ( 128 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=1279333927545199012128258534852861478951245004473500538855514499 (pp64)
 r2=22529168901137974895314002117395908892469523921646148358021532669 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 14.19 hours.
Scaled time: 14.19 units (timescale=1.000).
Factorization parameters were as follows:
name: 25559_138
n: 28822330134622000820620584010253028421676120212058138406067842081365878773742408071645154741613441781555667878148540074531667831
m: 1000000000000000000000000000
c5: 23000
c0: 31
skew: 0.27
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 2875001)
Primes: RFBsize:78498, AFBsize:63914, largePrimes:1802628 encountered
Relations: rels:1904248, finalFF:193118
Max relations in full relation-set: 28
Initial matrix: 142479 x 193118 with sparse part having weight 24230890.
Pruned matrix : 132213 x 132989 with weight 15653467.
Total sieving time: 14.00 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 14.19 hours.
 --------- CPU info (if available) ----------

Aug 14, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve

(23·10¹⁰²+31)/9 = 2(5)₁₀₁9_<103> = 3 · 17 · 336761 · 14684161 · C89

C89 = P38 · P51

P38 = 36174622317116628604747601318347875179_<38>

P51 = 280117484022614210615310757466475649891967034175151_<51>

Number: n
N=10133144188939020667332924829099166344145459417174872384023152068186407293124797771477029
  ( 89 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=36174622317116628604747601318347875179 (pp38)
 r2=280117484022614210615310757466475649891967034175151 (pp51)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.75 hours.
Scaled time: 1.09 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_2_5_101_9
n: 10133144188939020667332924829099166344145459417174872384023152068186407293124797771477029
type: snfs
skew: 0.42
deg: 5
c5: 2300
c0: 31
m: 100000000000000000000
rlim: 300000
alim: 300000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 300000/300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [100000, 160001)
Primes: RFBsize:25997, AFBsize:25925, largePrimes:3193322 encountered
Relations: rels:2812979, finalFF:136783
Max relations in full relation-set: 28
Initial matrix: 51989 x 136783 with sparse part having weight 12094637.
Pruned matrix : 40477 x 40800 with weight 2131424.
Total sieving time: 0.67 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.01 hours.
Total square root time: 0.02 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,103,5,0,0,0,0,0,0,0,0,300000,300000,28,28,50,50,2.5,2.5,20000
total time: 0.75 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(23·10¹²⁷+31)/9 = 2(5)₁₂₆9_<128> = 47 · 67 · 19474127 · C117

C117 = P50 · P68

P50 = 37482453682442295251317733556828300327910374081709_<50>

P68 = 11117999624135567706071487447289819238425678281178420561049303069537_<68>

Number: n
N=416729905953072264269507026565861748886593163661877469648194994869817747460538910312526637595843864694003181346798733
  ( 117 digits)
SNFS difficulty: 128 digits.
Divisors found:

Thu Aug 14 14:30:21 2008  prp50 factor: 37482453682442295251317733556828300327910374081709
Thu Aug 14 14:30:21 2008  prp68 factor: 11117999624135567706071487447289819238425678281178420561049303069537
Thu Aug 14 14:30:21 2008  elapsed time 00:25:45 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.18 hours.
Scaled time: 4.59 units (timescale=1.444).
Factorization parameters were as follows:
name: KA_2_5_126_9
n: 416729905953072264269507026565861748886593163661877469648194994869817747460538910312526637595843864694003181346798733
type: snfs
skew: 0.42
deg: 5
c5: 2300
c0: 31
m: 10000000000000000000000000
rlim: 700000
alim: 700000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 460001)
Primes: RFBsize:56543, AFBsize:56539, largePrimes:5776983 encountered
Relations: rels:4980603, finalFF:104656
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 3.05 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,700000,700000,28,28,50,50,2.5,2.5,50000
total time: 3.18 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

7·10¹⁹¹+9 = 7(0)₁₉₀9_<192> = 97 · C190

C190 = P57 · P65 · P69

P57 = 234464897294589778294207283924185372179122521034823214261_<57>

P65 = 37245591958990518315896750106678790768293832822047005717210831897_<65>

P69 = 826368192949751598558367932833322291039122696920944478534061838111341_<69>

Number: n
N=7216494845360824742268041237113402061855670103092783505154639175257731958762886597938144329896907216494845360824742268041237113402061855670103092783505154639175257731958762886597938144329897
  ( 190 digits)
SNFS difficulty: 191 digits.
Divisors found:

Thu Aug 14 17:44:30 2008  prp57 factor: 234464897294589778294207283924185372179122521034823214261
Thu Aug 14 17:44:30 2008  prp65 factor: 37245591958990518315896750106678790768293832822047005717210831897
Thu Aug 14 17:44:30 2008  prp69 factor: 826368192949751598558367932833322291039122696920944478534061838111341
Thu Aug 14 17:44:30 2008  elapsed time 12:59:34 (Msieve 1.36)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 167.63 hours.
Scaled time: 218.25 units (timescale=1.302).
Factorization parameters were as follows:
name: KA_7_0_190_9
n: 7216494845360824742268041237113402061855670103092783505154639175257731958762886597938144329896907216494845360824742268041237113402061855670103092783505154639175257731958762886597938144329897
type: snfs
skew: 0.66
deg: 5
c5: 70
c0: 9
m: 100000000000000000000000000000000000000
rlim: 9500000
alim: 9500000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9500000/9500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 14600001)
Primes: RFBsize:633578, AFBsize:635068, largePrimes:11104373 encountered
Relations: rels:11157968, finalFF:1297829
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 166.97 hours.
Total relation processing time: 0.66 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,50,50,2.5,2.5,100000
total time: 167.63 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(23·10¹³⁰+31)/9 = 2(5)₁₂₉9_<131> = 233 · 6949 · 15443 · 12049469 · 67386721 · C106

C106 = P44 · P62

P44 = 14880480537836991036560178301181133024307979_<44>

P62 = 84589456232401803618572893875810928263984685426113509528121359_<62>

Number: n
N=1258731757172469004163889939303851535943090531086634050129863780310728667440482666587361506345620904023461
  ( 106 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=14880480537836991036560178301181133024307979 (pp44)
 r2=84589456232401803618572893875810928263984685426113509528121359 (pp62)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.43 hours.
Scaled time: 4.98 units (timescale=1.450).
Factorization parameters were as follows:
name: KA_2_5_129_9
n: 1258731757172469004163889939303851535943090531086634050129863780310728667440482666587361506345620904023461
type: snfs
skew: 1.06
deg: 5
c5: 23
c0: 31
m: 100000000000000000000000000
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [100000, 480001)
Primes: RFBsize:63951, AFBsize:63869, largePrimes:6329489 encountered
Relations: rels:5532637, finalFF:154928
Max relations in full relation-set: 28
Initial matrix: 127885 x 154928 with sparse part having weight 14763138.
Pruned matrix : 119834 x 120537 with weight 9726166.
Total sieving time: 2.95 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.27 hours.
Total square root time: 0.08 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,28,28,50,50,2.5,2.5,50000
total time: 3.43 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Aug 14, 2008 (3rd)

By Serge Batalov / Msieve, GMP-ECM, pol51

(23·10¹⁰⁸+31)/9 = 2(5)₁₀₇9_<109> = 3 · C108

C108 = P32 · P76

P32 = 87457626883402500347090286707579_<32>

P76 = 9740166549311141470879840695000672432811606088405464382425229128401576277207_<76>

Number: 25559_108
N=851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851853
  ( 108 digits)
SNFS difficulty: 109 digits.
Divisors found:
 r1=87457626883402500347090286707579
 r2=9740166549311141470879840695000672432811606088405464382425229128401576277207
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=1.875).
Factorization parameters were as follows:
n: 851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851853
Y1: 1
Y0: -1000000000000000000000
c5: 23000
c0: 31
skew: 0.27
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 400001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 73371 x 73604
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,109,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 0.90 hours.

(23·10¹³²+31)/9 = 2(5)₁₃₁9_<133> = 3² · 415729 · 11552413 · 38085356615361651136669097_<26> · C94

C94 = P43 · P51

P43 = 1655570577258704683443960244245536278805161_<43>

P51 = 937678728208859008823339976946357714452296342866939_<51>

Wed Aug 13 10:45:30 2008  Msieve v. 1.36
Wed Aug 13 10:45:30 2008  random seeds: 9f5c825b c4951560
Wed Aug 13 10:45:30 2008  factoring 1552393313343948764302713161569033385259291635053878410148001293956160874279801427032129472179 (94 digits)
Wed Aug 13 10:45:31 2008  no P-1/P+1/ECM available, skipping
Wed Aug 13 10:45:31 2008  commencing quadratic sieve (94-digit input)
Wed Aug 13 10:45:31 2008  using multiplier of 1
Wed Aug 13 10:45:31 2008  using 64kb Opteron sieve core
Wed Aug 13 10:45:31 2008  sieve interval: 18 blocks of size 65536
Wed Aug 13 10:45:31 2008  processing polynomials in batches of 6
Wed Aug 13 10:45:31 2008  using a sieve bound of 1984859 (74118 primes)
Wed Aug 13 10:45:31 2008  using large prime bound of 256046811 (27 bits)
Wed Aug 13 10:45:31 2008  using double large prime bound of 1364503925389509 (42-51 bits)
Wed Aug 13 10:45:31 2008  using trial factoring cutoff of 51 bits
Wed Aug 13 10:45:31 2008  polynomial 'A' values have 12 factors
Wed Aug 13 14:12:07 2008  74570 relations (18435 full + 56135 combined from 1036730 partial), need 74214
Wed Aug 13 14:12:07 2008  begin with 1055165 relations
Wed Aug 13 14:12:08 2008  reduce to 193738 relations in 11 passes
Wed Aug 13 14:12:08 2008  attempting to read 193738 relations
Wed Aug 13 14:12:10 2008  recovered 193738 relations
Wed Aug 13 14:12:10 2008  recovered 177248 polynomials
Wed Aug 13 14:12:10 2008  attempting to build 74570 cycles
Wed Aug 13 14:12:10 2008  found 74570 cycles in 5 passes
Wed Aug 13 14:12:10 2008  distribution of cycle lengths:
Wed Aug 13 14:12:10 2008     length 1 : 18435
Wed Aug 13 14:12:10 2008     length 2 : 13018
Wed Aug 13 14:12:10 2008     length 3 : 12408
Wed Aug 13 14:12:10 2008     length 4 : 10058
Wed Aug 13 14:12:10 2008     length 5 : 7624
Wed Aug 13 14:12:10 2008     length 6 : 5079
Wed Aug 13 14:12:10 2008     length 7 : 3422
Wed Aug 13 14:12:10 2008     length 9+: 4526
Wed Aug 13 14:12:10 2008  largest cycle: 21 relations
Wed Aug 13 14:12:11 2008  matrix is 74118 x 74570 (20.0 MB) with weight 4654747 (62.42/col)
Wed Aug 13 14:12:11 2008  sparse part has weight 4654747 (62.42/col)
Wed Aug 13 14:12:12 2008  filtering completed in 3 passes
Wed Aug 13 14:12:12 2008  matrix is 70647 x 70711 (19.0 MB) with weight 4418943 (62.49/col)
Wed Aug 13 14:12:12 2008  sparse part has weight 4418943 (62.49/col)
Wed Aug 13 14:12:13 2008  saving the first 48 matrix rows for later
Wed Aug 13 14:12:13 2008  matrix is 70599 x 70711 (11.6 MB) with weight 3378476 (47.78/col)
Wed Aug 13 14:12:13 2008  sparse part has weight 2338269 (33.07/col)
Wed Aug 13 14:12:13 2008  matrix includes 64 packed rows
Wed Aug 13 14:12:13 2008  using block size 28284 for processor cache size 1024 kB
Wed Aug 13 14:12:13 2008  commencing Lanczos iteration
Wed Aug 13 14:12:13 2008  memory use: 10.7 MB
Wed Aug 13 14:12:53 2008  lanczos halted after 1118 iterations (dim = 70597)
Wed Aug 13 14:12:54 2008  recovered 16 nontrivial dependencies
Wed Aug 13 14:12:54 2008  prp43 factor: 1655570577258704683443960244245536278805161
Wed Aug 13 14:12:54 2008  prp51 factor: 937678728208859008823339976946357714452296342866939
Wed Aug 13 14:12:54 2008  elapsed time 03:27:24

(23·10¹¹⁶+31)/9 = 2(5)₁₁₅9_<117> = 7 · 37 · 173 · 6650044967_<10> · C102

C102 = P44 · P59

P44 = 54931236506670937151390207759795749240532083_<44>

P59 = 15613328680502956072470938717289086244068747139245028532717_<59>

Number: 25559_116
N=857659450405096353317645695092954648720447466263198250149873858089122806724718795563981780401853659511
  ( 102 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=54931236506670937151390207759795749240532083
 r2=15613328680502956072470938717289086244068747139245028532717
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.315).
Factorization parameters were as follows:
n: 857659450405096353317645695092954648720447466263198250149873858089122806724718795563981780401853659511
Y1: 1
Y0: -100000000000000000000000
c5: 230
c0: 31
skew: 0.67
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 450001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 107451 x 107666
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.00 hours.

(23·10¹²³+31)/9 = 2(5)₁₂₂9_<124> = 3³ · 89 · 426530711 · 346377283131541_<15> · C97

C97 = P33 · P65

P33 = 714725418909421255436482397289613_<33>

P65 = 10071464350712919091136784607863782767507181435730410139468751531_<65>

(23·10¹⁵¹+31)/9 = 2(5)₁₅₀9_<152> = 53 · 3631 · 6833 · C143

C143 = P35 · P108

P35 = 28491347801258535159984087380636957_<35>

P108 = 682116873892988320832073056144143663626338689069642201544762686263040341183467097296639486409774086795960473_<108>

(23·10¹⁶³+31)/9 = 2(5)₁₆₂9_<164> = 11197 · 600135654958518913015121_<24> · C136

C136 = P35 · C102

P35 = 15917843362328931372400174231396061_<35>

C102 = [238918616920236482284688193493767802557297554431710259935973434002654087902904166343115871840121233887_<102>]

(23·10¹⁵³+31)/9 = 2(5)₁₅₂9_<154> = 3 · 14207 · 542856502895113009_<18> · C132

C132 = P30 · P33 · P69

P30 = 148492579562995654158351194371_<30>

P33 = 751293507943332722148018478605683_<33>

P69 = 990061696833602124338231060672328983775827259228387769290559186187867_<69>

#ECM, then gnfs/Msieve
#
Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3707587740
Step 1 took 5072ms
Step 2 took 4844ms
********** Factor found in step 2: 148492579562995654158351194371
Found probable prime factor of 30 digits: 148492579562995654158351194371
Composite cofactor 743826925294445331005247766856880519633040968045235123810908647040711559143705680259634454974251848161 has 102 digits

Number: 25559_153
N=743826925294445331005247766856880519633040968045235123810908647040711559143705680259634454974251848161
  ( 102 digits)
Divisors found:
 r1=751293507943332722148018478605683
 r2=990061696833602124338231060672328983775827259228387769290559186187867
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.948).
Factorization parameters were as follows:
name: 25559_153
n: 743826925294445331005247766856880519633040968045235123810908647040711559143705680259634454974251848161
skew: 7667.78
# norm 1.63e+14
c5: 79380
c4: -1220023119
c3: -11990119136399
c2: 43162577465978701
c1: -50323790623128607716
c0: 595649923520302040373
# alpha -5.39
Y1: 40114117769
Y0: -24794440917443004098
# Murphy_E 2.51e-09
# M 108954050070074233826012025933116688514356381169118919916758488143137004054206742903805050301638526229
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1950001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 269347 x 269595
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000

total time: 5.10 hours.

Aug 14, 2008 (2nd)

Factorizations of 255...559 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Aug 14, 2008

By Jo Yeong Uk / GGNFS, GMP-ECM

(67·10¹⁸⁶+23)/9 = 7(4)₁₈₅7_<187> = 19 · 195493 · 9573671 · 15879889 · 867874901 · 21647287940191_<14> · 89421769771573038016990490819_<29> · C115

C115 = P37 · P79

P37 = 1746382501984432932253147027099413497_<37>

P79 = 4493432943695280633611271672078629570872945669670928390073563152978895513171103_<79>

Number: 74447_186
N=7847252666709839743467752504350917467823681102493087715558574118900695078873620596188423137154878036922729908577191
  ( 115 digits)
Divisors found:
 r1=1746382501984432932253147027099413497 (pp37)
 r2=4493432943695280633611271672078629570872945669670928390073563152978895513171103 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 22.87 hours.
Scaled time: 54.46 units (timescale=2.381).
Factorization parameters were as follows:
name: 74447_186
n: 7847252666709839743467752504350917467823681102493087715558574118900695078873620596188423137154878036922729908577191
skew: 51581.35
# norm 1.74e+16
c5: 44400
c4: 11244086600
c3: -438029123632375
c2: -16066004853798946614
c1: 595416047125765423448296
c0: 2879863880296498472471170048
# alpha -6.95
Y1: 2243360191787
Y0: -11206307361932270455113
# Murphy_E 5.39e-10
# M 2501025341128000393248592538385081061341254539000833808236602444299295780685350436595419391261914916678877912287855
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 70000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 3080001)
Primes: RFBsize:250150, AFBsize:250380, largePrimes:7570818 encountered
Relations: rels:7503217, finalFF:612787
Max relations in full relation-set: 28
Initial matrix: 500610 x 612787 with sparse part having weight 54051584.
Pruned matrix : 411617 x 414184 with weight 34251677.
Polynomial selection time: 1.33 hours.
Total sieving time: 20.21 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 1.07 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.4,2.4,70000
total time: 22.87 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2459k kernel code, 339200k reserved, 1247k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.73 BogoMIPS (lpj=2672366)
Calibrating delay using timer specific routine.. 5343.99 BogoMIPS (lpj=2671997)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(55·10¹⁸⁴-1)/9 = 6(1)₁₈₄_<185> = 113113526204811467_<18> · 902962100831388890356903_<24> · 30298080812156225043145231_<26> · C119

C119 = P33 · P86

P33 = 299222870320790868968071687171273_<33>

P86 = 65997306601865480874354633900283209180626121298931610636261094645539057137062347684197_<86>

Aug 13, 2008 (3rd)

By Sinkiti Sibata / GGNFS

6·10¹⁶⁵+1 = 6(0)₁₆₄1_<166> = 108649 · 1383530154323_<13> · 10418259026881_<14> · C136

C136 = P59 · P78

P59 = 12198214958645406697515956553865609339286480946779228031841_<59>

P78 = 314083740589948806536874133179020940182628645393194584520163117078481245780803_<78>

Number: 60001_165
N=3831260982731617026109963484953683259170695517683951964059413219775587940296031765586309929215323885262414918355104547162842906990548323
  ( 136 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=12198214958645406697515956553865609339286480946779228031841 (pp59)
 r2=314083740589948806536874133179020940182628645393194584520163117078481245780803 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 73.33 hours.
Scaled time: 73.92 units (timescale=1.008).
Factorization parameters were as follows:
name: 60001_165
n: 3831260982731617026109963484953683259170695517683951964059413219775587940296031765586309929215323885262414918355104547162842906990548323
m: 1000000000000000000000000000000000
c5: 6
c0: 1
skew: 0.7
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 5000001)
Primes: RFBsize:348513, AFBsize:348726, largePrimes:6213178 encountered
Relations: rels:6700823, finalFF:1088127
Max relations in full relation-set: 28
Initial matrix: 697305 x 1088127 with sparse part having weight 65822247.
Pruned matrix : 402300 x 405850 with weight 63363491.
Total sieving time: 71.21 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.94 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 73.33 hours.
 --------- CPU info (if available) ----------

Aug 13, 2008 (2nd)

By Serge Batalov / pol51, Franke/Childers-64bit-assembly-sievers, Msieve

(19·10¹⁷⁶+53)/9 = 2(1)₁₇₅7_<177> = 7 · 288499 · 2637468153113_<13> · 246110466160057_<15> · 7544750677235511008287_<22> · C122

C122 = P45 · P77

P45 = 664699855687740871426245760733544298057358189_<45>

P77 = 32113005584426118305653746784676287558964283770905370659367037921112708262563_<77>

Number: 21117_176
N=21345510177667657540730006301434663701471756955685409885592596413899469145549610473198894598984475625669925326599950178407
  ( 122 digits)
Divisors found:
 r1=664699855687740871426245760733544298057358189
 r2=32113005584426118305653746784676287558964283770905370659367037921112708262563
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.719).
Factorization parameters were as follows:
name: 21117_176
n: 21345510177667657540730006301434663701471756955685409885592596413899469145549610473198894598984475625669925326599950178407
skew: 170756.40
# norm 7.43e+16
c5: 3960
c4: -2169820698
c3: 1300114549842949
c2: 51004422752112391841
c1: -13720078057851879793267805
c0: -306179776140910730398882578519
# alpha -6.28
Y1: 9129774563993
Y0: -351822415252155645580046
# Murphy_E 2.29e-10
# M 19568358484057287237196273449831904887169580518105982422756745467726799115462603151064661311112921045638463225213236455353
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 9100001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 815845 x 816093
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 3.00 hours.
Time per square root: 0.35 hours.
Prototype def-par.txt line would be:
gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.5,2.5,100000

total time: 51 hours.

(64·10²³²+53)/9 = 7(1)₂₃₁7_<233> = 29 · 31 · 25544394638150569_<17> · 21891861055037187204902189298063661_<35> · 1156244055915277149927645527883080159_<37> · C144

C144 = P70 · P74

P70 = 5629056896456130761115640768115712949562588093167473845957065096607951_<70>

P74 = 21732731937076769089333819026656467057955775638915262225760919560406955043_<74>

Number: 71117_232
N=122334784589234392683295194652612149338189319179115868523072772347572950426690801931827228533310815015647306731512386262336087369965447853346893
  ( 144 digits)
Divisors found:
 r1=5629056896456130761115640768115712949562588093167473845957065096607951
 r2=21732731937076769089333819026656467057955775638915262225760919560406955043
Version: 
Total time: 22 CPU-days.
Scaled time: ? units (timescale=2.739).
Factorization parameters were as follows:
name: 71117_232
n: 122334784589234392683295194652612149338189319179115868523072772347572950426690801931827228533310815015647306731512386262336087369965447853346893
skew: 690006.04
# norm 1.16e+20
c5: 366240
c4: -200755493198
c3: -1264280431194248789
c2: 30690227552865176460280
c1: 116115356677156443273022507812
c0: 1643772806174680731101452821850125
# alpha -6.86
Y1: 12549580773819617
Y0: -3197105916158047746993222154
# Murphy_E 1.41e-11
# M 5734946885270096719071646003056964635381291967622973864385956607094834583149950289638574241818695561052754902888430269917445698295408593930669
type: gnfs
rlim: 20000000
alim: 20000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 20000000/20000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [10000000, 11400001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: 24,475,000 relations (22,067,313 unique) vs. 19,071,047 large primes
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2595393 x 2595641
Total sieving time: 20 CPU-days. (with 8cpus * a 2.5-day weekend)
Total relation processing time: 0.50 hours.
Top memory use in filtering: 1.5 Gb
Matrix solve time: 37.35 hours.
Time per square root: 1.90 hours.
Prototype def-par.txt line would be:
gnfs,144,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,20000000,20000000,28,28,56,56,2.6,2.6,100000
#use this line, sieve algebraic (or better yet, always do test runs)

total time: 22 CPU-days.

# Note: my estimate of a general case GNFS:SNFS break-even ratio is 72:100
# this is GNFS-144 ~= complexity of SNFS-200
# GNFS is absolutely better for this particular number

Note: C144 is the largest composite number factored by GNFS so far in our tables.

Aug 13, 2008

By Robert Backstrom / GMP-ECM

7·10¹⁷¹+1 = 7(0)₁₇₀1_<172> = 191 · 11351 · 200087 · 199743193690849_<15> · 503783621180657_<15> · C132

C132 = P42 · P90

P42 = 640757244242093195737825269513973688101421_<42>

P90 = 250266153200200437607062854749076319929624557778915248618363969037755267406743304872865851_<90>

Aug 12, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(23·10¹⁶⁵-41)/9 = 2(5)₁₆₄1_<166> = 29 · 71 · 132745428289_<12> · 1240062004353599171_<19> · C133

C133 = P66 · P68

P66 = 620307761470091015755690541703303810222293530677225354864980633273_<66>

P68 = 12155107128456035886009851568901921324819251306725762561321071641847_<68>

Number: 25551_165
N=7539907293281709664021555033543314880138720337710856966983086890475334408273968539560151442899749274783057664654530833081819907375231
  ( 133 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=620307761470091015755690541703303810222293530677225354864980633273 (pp66)
 r2=12155107128456035886009851568901921324819251306725762561321071641847 (pp68)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 101.57 hours.
Scaled time: 102.39 units (timescale=1.008).
Factorization parameters were as follows:
name: 25551_165
n: 7539907293281709664021555033543314880138720337710856966983086890475334408273968539560151442899749274783057664654530833081819907375231
m: 1000000000000000000000000000000000
c5: 23
c0: -41
skew: 1.12
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 6200001)
Primes: RFBsize:348513, AFBsize:348762, largePrimes:6205595 encountered
Relations: rels:6582900, finalFF:985608
Max relations in full relation-set: 28
Initial matrix: 697340 x 985608 with sparse part having weight 70810848.
Pruned matrix : 477437 x 480987 with weight 57774851.
Total sieving time: 98.88 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 2.49 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 101.57 hours.
 --------- CPU info (if available) ----------

Aug 12, 2008 (2nd)

By Jo Yeong Uk / GGNFS

(4·10¹⁹³-31)/9 = (4)₁₉₂1_<193> = C193

C193 = P57 · P136

P57 = 646181061524363199600970571839514279881175613475434692033_<57>

P136 = 6878017182923696594530988282380362877712659016819970541769693419701317790915722248377653237079002311402940729245426422513461529454956377_<136>

Number: 44441_193
N=4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441
  ( 193 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=646181061524363199600970571839514279881175613475434692033 (pp57)
 r2=6878017182923696594530988282380362877712659016819970541769693419701317790915722248377653237079002311402940729245426422513461529454956377 (pp136)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 633.40 hours.
Scaled time: 1503.05 units (timescale=2.373).
Factorization parameters were as follows:
n: 4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441
m: 1000000000000000000000000000000000000000
c5: 1
c0: -775
skew: 3.78
type: snfs
Factor base limits: 20000000/20000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 52/52
Sieved algebraic special-q in [10000000, 20400001)
Primes: RFBsize:1270607, AFBsize:1272451, largePrimes:21030425 encountered
Relations: rels:21534447, finalFF:2888534
Max relations in full relation-set: 28
Initial matrix: 2543122 x 2888533 with sparse part having weight 170079893.
Pruned matrix : 2224800 x 2237579 with weight 124339102.
Total sieving time: 591.27 hours.
Total relation processing time: 0.69 hours.
Matrix solve time: 41.22 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,195,5,0,0,0,0,0,0,0,0,20000000,20000000,29,29,52,52,2.6,2.6,100000
total time: 633.40 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047092k/8912896k available (2459k kernel code, 339200k reserved, 1247k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.73 BogoMIPS (lpj=2672366)
Calibrating delay using timer specific routine.. 5343.99 BogoMIPS (lpj=2671997)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Aug 12, 2008

By Serge Batalov / Msieve

(85·10¹⁸⁵+41)/9 = 9(4)₁₈₄9_<186> = 11 · 97 · 859 · 994769 · 725406797 · 1283920045522639113163_<22> · 49703136401507545869061_<23> · C122

C122 = P55 · P67

P55 = 5945312755539665917551963829023944543338834374958932437_<55>

P67 = 3763730250037354798169122734936464412007531853274549949355322112591_<67>

Number: 94449_185
N=22376553463957581646819827364810402074663641841688814278996265692919457557189900085368580368180018925514654615380876014267
  ( 122 digits)
Divisors found:
 r1=5945312755539665917551963829023944543338834374958932437
 r2=3763730250037354798169122734936464412007531853274549949355322112591
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.719).
Factorization parameters were as follows:
name: 94449_185
n: 22376553463957581646819827364810402074663641841688814278996265692919457557189900085368580368180018925514654615380876014267
skew: 395089.16
# norm 8.53e+16
c5: 1920
c4: -2122639568
c3: -1001519971436916
c2: 252010646313405784356
c1: 17053914602620055702421409
c0: -5102205586876697697049786391166
# alpha -6.67
Y1: 14417436812383
Y0: -410489229162219968921845
# Murphy_E 2.43e-10
# M 13327227797342778556781154439976826870101708204128832160162315240816752369766045276700781494476592724195508665899854601153
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 5800001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 693877 x 694113
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 1.80 hours.
Time per square root: 1.80 hours / 6deps.
Prototype def-par.txt line would be:
gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.5,2.5,100000
total time: 41.00 hours.

(8·10¹⁷⁸-53)/9 = (8)₁₇₇3_<178> = 3 · 7 · 580033 · 4121233246377533370895087_<25> · 11414389645507504885866557_<26> · C122

C122 = P61 · P61

P61 = 2084319019311817485408263671504067644597211773621536836338031_<61>

P61 = 7442715191706727951117023466133424089625836289964455009349139_<61>

# Nice split, again, P61.P61 :-)    ...guys, don't shy away from gnfs-122
#
Number: 88883_178
N=15512992829395332874459989302553000844308438535363267904145402644391992053787434208266071942229443864121635964649502805309
  ( 122 digits)
Divisors found:
 r1=2084319019311817485408263671504067644597211773621536836338031
 r2=7442715191706727951117023466133424089625836289964455009349139
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.740).
Factorization parameters were as follows:
name: 88883_178
n: 15512992829395332874459989302553000844308438535363267904145402644391992053787434208266071942229443864121635964649502805309
skew: 98981.13
# norm 3.36e+16
c5: 1320
c4: -10396789456
c3: -66076991548644
c2: 78186712031832272171
c1: 200139365179873413081944
c0: -88020638544471412575938322460
# alpha -5.65
Y1: 1247076274951
Y0: -411174721634384235437837
# Murphy_E 2.21e-10
# M 12429707818737800271460182262993084301376975976751266457817355689134402992212562892000794069795686993932653381134042300059
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 5300001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 727897 x 728145
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 2.50 hours.
Time per square root: 0.40 hours.
Prototype def-par.txt line would be:
gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.5,2.5,100000

total time: 43.00 hours.

(23·10¹⁶⁹+13)/9 = 2(5)₁₆₈7_<170> = 3 · 83 · 311 · 28517 · 199813 · C155

C155 = P64 · P91

P64 = 7124994157222814707790131826005124154401833141434559408862786761_<64>

P91 = 8128557869000804133044033360884580345414021448333631032282453920166787798539408237113453723_<91>

Number: 25557_169
N=57915927323278263122576779147506228774571092503906587992363346778093393164170615259694974150158339232963013238210915096456461157537716585458112711190561203
  ( 155 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=7124994157222814707790131826005124154401833141434559408862786761
 r2=8128557869000804133044033360884580345414021448333631032282453920166787798539408237113453723
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.649).
Factorization parameters were as follows:
n: 57915927323278263122576779147506228774571092503906587992363346778093393164170615259694974150158339232963013238210915096456461157537716585458112711190561203
Y1: 1
Y0: -10000000000000000000000000000000000
c5: 23
c0: 130
skew: 1.41
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 11500001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1186790 x 1187021
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 5.75 hours.
Time per square root: 0.6 hours. * 2
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.6,2.6,100000

total time: 81 hours.

Aug 11, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(55·10¹⁹⁰-1)/9 = 6(1)₁₉₀_<191> = 19 · C190

C190 = P70 · P120

P70 = 4021755757979865444475768755543444537089434622309462148175034259090497_<70>

P120 = 799743809062497136193595600318187981540855191647234243172296174585420358670139789796095969053096762864603044328884198077_<120>

Number: n
N=3216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269
  ( 190 digits)
SNFS difficulty: 191 digits.
Divisors found:

Mon Aug 11 14:32:35 2008  prp70 factor: 4021755757979865444475768755543444537089434622309462148175034259090497
Mon Aug 11 14:32:35 2008  prp120 factor: 799743809062497136193595600318187981540855191647234243172296174585420358670139789796095969053096762864603044328884198077
Mon Aug 11 14:32:36 2008  elapsed time 05:04:45 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 112.32 hours.
Scaled time: 230.37 units (timescale=2.051).
Factorization parameters were as follows:
name: KA_6_1_190
n: 3216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269
type: snfs
skew: 0.45
deg: 5
c5: 55
c0: -1
m: 100000000000000000000000000000000000000
rlim: 9500000
alim: 9500000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9500000/9500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 10100001)
Primes: RFBsize:633578, AFBsize:632819, largePrimes:10786354 encountered
Relations: rels:10836389, finalFF:1293401
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 111.99 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,50,50,2.5,2.5,100000
total time: 112.32 hours.
 --------- CPU info (if available) ----------

5·10¹⁹²+9 = 5(0)₁₉₁9_<193> = 7 · C192

C192 = P33 · P160

P33 = 185946012230334004175737692114361_<33>

P160 = 3841360756911088155477151257427655759049773811262830812715564417935995018641284052166995975037217217287976245074877594743197862509898796882391887621294514456167_<160>

Aug 11, 2008

By Serge Batalov / Msieve

(8·10¹⁷⁰+1)/9 = (8)₁₆₉9_<170> = 17 · 5099 · 31249 · C161

C161 = P47 · P114

P47 = 40186975583101099592439039411422087973769840987_<47>

P114 = 816567512176293048559848164336180107760931586096734124270214265473016206624606162885231652725468625601857209063441_<114>

N=32815378673782298576607235073579556585939084838902199304862538597260220415657115437029661430649398611754093077143742580179076977702588819453143262953557765056267
  ( 161 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=40186975583101099592439039411422087973769840987
 r2=816567512176293048559848164336180107760931586096734124270214265473016206624606162885231652725468625601857209063441
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.384).
Factorization parameters were as follows:
n: 32815378673782298576607235073579556585939084838902199304862538597260220415657115437029661430649398611754093077143742580179076977702588819453143262953557765056267
Y1: 1
Y0: -10000000000000000000000000000000000
c5: 8
c0: 1
skew: 0.66
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 7700001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1009103 x 1009351
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 4.00 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.6,2.6,100000
total time: 41 hours.

(14·10¹⁷⁶-41)/9 = 1(5)₁₇₅1_<177> = 2259105661271087_<16> · 80720351480358203_<17> · 6253487942641704767889353221_<28> · C117

C117 = P46 · P72

P46 = 1019051608417910918330923759093085376287866529_<46>

P72 = 133858958754694373843982955055938024720353027482661337116522058059690599_<72>

Number: 15551_176
N=136409187220118099594259543876309212197184154651522471682143115643170104578299575205818479783053844257159831548060871
  ( 117 digits)
Divisors found:
 r1=1019051608417910918330923759093085376287866529
 r2=133858958754694373843982955055938024720353027482661337116522058059690599
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.314).
Factorization parameters were as follows:
name: 15551_176
n: 136409187220118099594259543876309212197184154651522471682143115643170104578299575205818479783053844257159831548060871
skew: 49132.51
# norm 2.08e+16
c5: 6660
c4: 447743516
c3: -609459037292731
c2: -187213174297973853
c1: 85240638334503841045441
c0: 142345279227926981946484747
# alpha -5.80
Y1: 173069743693
Y0: -28991710782521877328584
# Murphy_E 4.58e-10
# M 111726850663256429068149510231893237790161040770684032330899062146596737783001767146726624576283412255547250616765441
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 5550001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 624752 x 624980
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 1.9 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.5,2.5,100000

total time: 31 hours.

(55·10¹⁷⁰-1)/9 = 6(1)₁₇₀_<171> = 13 · 4669558519_<10> · C161

C161 = P39 · P122

P39 = 153955579103572816331228445297936006451_<39>

P122 = 65389132198097929317384532477022329243907106763690774891859053196341390466253053476569510421739623931334520824845665359863_<122>

Number: 61111_170
N=10067021714638245985971023443671936676077995417139563755622043422676508607003185306595149781655096762809625375423750419979908286273807163855998898770530004476213
  ( 161 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=153955579103572816331228445297936006451
 r2=65389132198097929317384532477022329243907106763690774891859053196341390466253053476569510421739623931334520824845665359863
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.728).
Factorization parameters were as follows:
n: 10067021714638245985971023443671936676077995417139563755622043422676508607003185306595149781655096762809625375423750419979908286273807163855998898770530004476213
Y1: 1
Y0: -10000000000000000000000000000000000
c5: 55
c0: -1
skew: 0.45
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 8300001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1037714 x 1037962
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 4.00 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.6,2.6,100000

total time: 46.00 hours.

(2·10¹⁷⁰-11)/9 = (2)₁₆₉1_<170> = 3 · 7 · 521 · 19415939 · C159

C159 = P69 · P90

P69 = 210932730451696181940250897337150581037995111538975826259659355381171_<69>

P90 = 495938809108537651024325469852249119314303434921038892150321898130866669026706293313313849_<90>

Number: 22221_170
N=104609727142226379588669649515486510594483116351492265894829942358267978639698604872885143129569104911079270956508881509938720071447460557768825472436548137179
  ( 159 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=210932730451696181940250897337150581037995111538975826259659355381171
 r2=495938809108537651024325469852249119314303434921038892150321898130866669026706293313313849
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.315).
Factorization parameters were as follows:
n: 104609727142226379588669649515486510594483116351492265894829942358267978639698604872885143129569104911079270956508881509938720071447460557768825472436548137179
Y1: 1
Y0: -10000000000000000000000000000000000
c5: 2
c0: -11
skew: 1.41
type: snfsFactor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 7300001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 973133 x 973381
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 5.00 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.6,2.6,100000

total time: 47.00 hours.

Aug 10, 2008

By Serge Batalov / GMP-ECM, Msieve

(5·10¹⁸⁵-23)/9 = (5)₁₈₄3_<185> = 79 · 76231583 · 1164328700579194207_<19> · 44029950759275554233180522078377_<32> · C126

C126 = P55 · P71

P55 = 4447157373848506897595629163234478692497222248038378089_<55>

P71 = 40463101119128220174838353390558913450445769536584152739988540703367199_<71>

Number: 55553_185
N=179945778510708836080589448871146949371246104317066383335530794551793683889740159757425063640639714889836321930337300962902711
  ( 126 digits)
Divisors found:
 r1=4447157373848506897595629163234478692497222248038378089
 r2=40463101119128220174838353390558913450445769536584152739988540703367199
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.737).
Factorization parameters were as follows:
name: 55553_185
n: 179945778510708836080589448871146949371246104317066383335530794551793683889740159757425063640639714889836321930337300962902711
skew: 78436.96
# norm 4.47e+17
c5: 141120
c4: 210798550396
c3: -2311548511262600
c2: -1331340454492406883599
c1: -12898272503990683384020858
c0: 342428524648698367377122484465
# alpha -6.86
Y1: 28117900703519
Y0: -1049801391123476444878468
# Murphy_E 1.33e-10
# M 159496249529484995713156133406394224529425016161226558234898604187480904861637765732940295828492291561597036179686238567469420
type: gnfs
rlim: 8000000
alim: 8000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [4000000, 7800001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 994198 x 994446
Poly selection time: 4.00 hours
Total sieving time: 60.00 hours.
Total relation processing time: 0.50 hours.
Matrix solve time: 4.00 hours.
Time per square root: 0.50 hours.
Prototype def-par.txt line would be:
gnfs,125,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,8000000,8000000,27,27,52,52,2.5,2.5,100000

total time: 69 hours.

(37·10¹⁷⁹-1)/9 = 4(1)₁₇₉_<180> = 3 · 1097 · 13591 · 75541 · 45882114659_<11> · 7184177864869_<13> · C144

C144 = P31 · P36 · P78

P31 = 1722998328122894393200632853951_<31>

P36 = 692868277288158536240177021151239891_<36>

P78 = 309201188459405009925071126374392611866926465706986114595332287804513277197981_<78>

#ECM, then gnfs-114
#
Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=3638089732
Step 1 took 70571ms
Step 2 took 43411ms
********** Factor found in step 2: 1722998328122894393200632853951
Found probable prime factor of 31 digits: 1722998328122894393200632853951
Composite cofactor 214235694783319195542137193905151660133632944476526636783089769017222260753479030798583580704509521146076431860071 has 114 digits

Number: 41111_179
N=214235694783319195542137193905151660133632944476526636783089769017222260753479030798583580704509521146076431860071
  ( 114 digits)
Divisors found:
 r1=692868277288158536240177021151239891
 r2=309201188459405009925071126374392611866926465706986114595332287804513277197981
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.650).
Factorization parameters were as follows:
name: 41111_179
n: 214235694783319195542137193905151660133632944476526636783089769017222260753479030798583580704509521146076431860071
skew: 51889.37
# norm 2.73e+15
c5: 22320
c4: -30532338
c3: -142817595591249
c2: 809069780721612917
c1: 203983597776382398282865
c0: -2359341539772994802155635507
# alpha -5.57
Y1: 1833293458381
Y0: -6258057702735141305522
# Murphy_E 6.49e-10
# M 162728657052454355033301763797280575233678834117861705307163381743582580557743703942799163215917912548867785628741
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 3950001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 492737 x 492977
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.90 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000

total time: 16.00 hours.

Aug 9, 2008

By Serge Batalov / GMP-ECM, pol51, Msieve

(67·10¹⁸⁶+23)/9 = 7(4)₁₈₅7_<187> = 19 · 195493 · 9573671 · 15879889 · 867874901 · 21647287940191_<14> · C144

C144 = P29 · C115

P29 = 89421769771573038016990490819_<29>

C115 = [7847252666709839743467752504350917467823681102493087715558574118900695078873620596188423137154878036922729908577191_<115>]

(46·10¹⁹³-1)/9 = 5(1)₁₉₃_<194> = 3³ · 17 · 2721767 · 3878672933_<10> · 18833673139_<11> · 253531733109664214357_<21> · C145

C145 = P30 · P116

P30 = 219941831910466951808401970081_<30>

P116 = 10043690953294073007230012497539826164684415783776924661750095830636397234524639892390514224691823099504978786649353_<116>

(10¹⁸⁰+71)/9 = (1)₁₇₉9_<180> = 10627 · 7936631 · 699357776561_<12> · 9775791858109_<13> · C144

C144 = P34 · P34 · P77

P34 = 1226535304270133824209889298575081_<34>

P34 = 9646827652244259591998878269506813_<34>

P77 = 16285259880623894915342400241019541187822058715291361864722782960855927435971_<77>

#ECM, then gnfs/Msieve
#
Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=3029909724
Step 1 took 70033ms
Step 2 took 4611ms
********** Factor found in step 2: 9646827652244259591998878269506813
Found probable prime factor of 34 digits: 9646827652244259591998878269506813
Composite cofactor 19974446182799232189458363156421231710407036132090260102835765147805964274317792564316416219690880744163638651 has 110 digits

Number: 11119_180
N=19974446182799232189458363156421231710407036132090260102835765147805964274317792564316416219690880744163638651
  ( 110 digits)
Divisors found:
 r1=1226535304270133824209889298575081
 r2=16285259880623894915342400241019541187822058715291361864722782960855927435971
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.718).
Factorization parameters were as follows:
name: 11119_180
n: 19974446182799232189458363156421231710407036132090260102835765147805964274317792564316416219690880744163638651
skew: 33063.44
# norm 4.01e+15
c5: 22800
c4: 3094334570
c3: -43841089883993
c2: 652837658814255144
c1: -1748227893997554020746
c0: -332389422893059106735269160
# alpha -6.55
Y1: 199871801533
Y0: -973880254752302195949
# Murphy_E 1.01e-09
# M 3541451005798240763734180262500322055167427459870109414796898368049994906448361437203335532088229954682971890
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 3000001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 400903 x 401151
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000

total time: 10.1 hours.

(82·10¹⁹⁰-1)/9 = 9(1)₁₉₀_<191> = 3677 · 27737 · 428987020794740431_<18> · 139985185084079890573_<21> · C146

C146 = P32 · P40 · P75

P32 = 44235066145162170816345276923453_<32>

P40 = 1525202975164716560489995462930009247117_<40>

P75 = 220494455529149193117835135530917883959908968067515100876835257557187880353_<75>

#ECM, then gnfs/Msieve
#
Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=3120628407
Step 1 took 4820ms
Step 2 took 3349ms
********** Factor found in step 2: 44235066145162170816345276923453
Found probable prime factor of 32 digits: 44235066145162170816345276923453
Composite cofactor 336298799580382636884047391898935435196982232927500031943041760199290494110321251616554876960770043264810606192301 has 114 digits

Number: 91111_190
N=336298799580382636884047391898935435196982232927500031943041760199290494110321251616554876960770043264810606192301
  ( 114 digits)
Divisors found:
 r1=1525202975164716560489995462930009247117
 r2=220494455529149193117835135530917883959908968067515100876835257557187880353
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.739).
Factorization parameters were as follows:
name: 91111_190
n: 336298799580382636884047391898935435196982232927500031943041760199290494110321251616554876960770043264810606192301
skew: 32758.65
# norm 6.57e+15
c5: 50880
c4: -4540729432
c3: -272586044989870
c2: 3297416222680395891
c1: 23148281183123748940654
c0: -388365960665666774880376595
# alpha -6.25
Y1: 1469988935897
Y0: -5808147070876337435082
# Murphy_E 6.48e-10
# M 229552349424334768180847434863489988993809348628602001900164640068452475773800216940633862159662059995974114158504
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 3950001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 504464 x 504706
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000

total time: 15.5 hours.

(16·10¹⁷⁶+11)/9 = 1(7)₁₇₅9_<177> = 4061677 · 1714060249079230343915479_<25> · C146

C146 = P30 · P39 · P78

P30 = 496354928791903362317826467779_<30>

P39 = 387669240746989213840155332047740229877_<39>

P78 = 132706539281050231573399714574367502225844538391956406948964649195004351055911_<78>

#ECM, then gnfs/Msieve
#
Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=4163435521
Step 1 took 4756ms
Step 2 took 3461ms
********** Factor found in step 2: 496354928791903362317826467779
Found probable prime factor of 30 digits: 496354928791903362317826467779
Composite cofactor 51446243325245243124883276436320816900607858949251075683543295198629791680567051300669622750582627486876398819652947 has 116 digits

Number: 17779_176
N=51446243325245243124883276436320816900607858949251075683543295198629791680567051300669622750582627486876398819652947
  ( 116 digits)
Divisors found:
 r1=387669240746989213840155332047740229877
 r2=132706539281050231573399714574367502225844538391956406948964649195004351055911
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.725).
Factorization parameters were as follows:
name: 17779_176
n: 51446243325245243124883276436320816900607858949251075683543295198629791680567051300669622750582627486876398819652947
skew: 49622.16
# norm 1.82e+16
c5: 35640
c4: 4885507446
c3: 532420277871665
c2: -13094255266500546523
c1: -567963476960577454726385
c0: 9529471883982232144532871901
# alpha -6.81
Y1: 446283389723
Y0: -17056223681646455534652
# Murphy_E 4.89e-10
# M 44535924776312533812638796895673595643407947395099259882857573980766606301104420581431481670434365857616130626039851
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 5150001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 602954 x 603191
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.5,2.5,100000

total time: 22.5 hours.

(11·10¹⁷³+61)/9 = 1(2)₁₇₂9_<174> = 3 · 167 · 9393214717_<10> · 3991464716169220319_<19> · C142

C142 = P36 · P39 · P69

P36 = 370213993053058810577180008052464963_<36>

P39 = 135581314979100013821605633469943622819_<39>

P69 = 129632302176827106237494463843268187181151032935432367315492954199859_<69>

#ECM, then gnfs/Msieve
#
Using B1=2000000, B2=11413147210, polynomial Dickson(12), sigma=774383078
Step 1 took 13440ms
Step 2 took 13985ms
********** Factor found in step 2: 370213993053058810577180008052464963
Found probable prime factor of 36 digits: 370213993053058810577180008052464963
Composite cofactor 17575717992902268267555073239638187779950682665186919490503984459819118518231525646978446649297579838982521 has 107 digits

Number: 12229_173
N=17575717992902268267555073239638187779950682665186919490503984459819118518231525646978446649297579838982521
  ( 107 digits)
Divisors found:
 r1=135581314979100013821605633469943622819
 r2=129632302176827106237494463843268187181151032935432367315492954199859
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.719).
Factorization parameters were as follows:
name: 12229_173
n: 17575717992902268267555073239638187779950682665186919490503984459819118518231525646978446649297579838982521
skew: 12412.40
# norm 3.95e+14
c5: 23880
c4: -801144701
c3: -28651090013206
c2: 233589483730740904
c1: 1012470718482202241190
c0: 858705876167084202647853
# alpha -5.24
Y1: 60738216517
Y0: -236252547292224089980
# Murphy_E 1.52e-09
# M 17395019518137050286633518025364420683886479604045755806861763608633749627030105245197574996886503717697083
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2450001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 298764 x 299012
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000

total time: 8.50 hours.

(16·10¹⁹⁵+11)/9 = 1(7)₁₉₄9_<196> = 3² · 740087 · 230743222131950995499_<21> · 162777255677946980081591009_<27> · C142

C142 = P32 · P44 · P67

P32 = 73424827831293500485868707674581_<32>

P44 = 20303773842269115123939467873342342848136567_<44>

P67 = 4766612074547657425113602299458810889222950655299003162801405514909_<67>

#ECM, then Msieve-1.36/gnfs
#
Using B1=2000000, B2=11413147210, polynomial Dickson(12), sigma=3622984911
Step 1 took 13465ms
Step 2 took 14018ms
********** Factor found in step 2: 73424827831293500485868707674581
Found probable prime factor of 32 digits: 73424827831293500485868707674581
Composite cofactor 96780213555444848209611889152187386372688573948470598229105258151036484021479960765765687805868153067786577403 has 110 digits

Number: 17779_195
N=96780213555444848209611889152187386372688573948470598229105258151036484021479960765765687805868153067786577403
  ( 110 digits)
Divisors found:
 r1=20303773842269115123939467873342342848136567
 r2=4766612074547657425113602299458810889222950655299003162801405514909
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.734).
Factorization parameters were as follows:
name: 17779_195
n: 96780213555444848209611889152187386372688573948470598229105258151036484021479960765765687805868153067786577403
skew: 39343.05
# norm 4.40e+15
c5: 29700
c4: -2720680614
c3: -229660812986110
c2: 3755159898497477197
c1: 103107695126468227504850
c0: -1036926091866752413602699423
# alpha -6.52
Y1: 416125022923
Y0: -1266510048212425943194
# Murphy_E 9.33e-10
# M 38482898344273848443470793235030589679953893757120088997777761815782974719049996096666657288907626213621790808
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 3100001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 401501 x 401746
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000

total time: 12.00 hours.

Aug 8, 2008 (5th)

By Wataru Sakai / GGNFS

(67·10¹⁸⁹+23)/9 = 7(4)₁₈₈7_<190> = 11 · C189

C189 = P41 · P41 · P109

P41 = 12302291030660287515731443085247910553801_<41>

P41 = 33535040497930633918581716583415099870073_<41>

P109 = 1640418944811902951085590868766787391959788474209885459585076912235664555929048919674251980667635272532335549_<109>

Number: 74447_189
N=676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767677
  ( 189 digits)
SNFS difficulty: 191 digits.
Divisors found:
 r1=12302291030660287515731443085247910553801 (pp41)
 r2=33535040497930633918581716583415099870073 (pp41)
 r3=1640418944811902951085590868766787391959788474209885459585076912235664555929048919674251980667635272532335549 (pp109)

Version: GGNFS-0.77.1-20060722-nocona
Total time: 1521.52 hours.
Scaled time: 2985.23 units (timescale=1.962).
Factorization parameters were as follows:
n: 676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767677
m: 100000000000000000000000000000000000000
c5: 67
c0: 230
skew: 1.28
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 3700000)
Primes: RFBsize:501962, AFBsize:501696, largePrimes:7422129 encountered
Relations: rels:8069778, finalFF:1154154
Max relations in full relation-set: 32
Initial matrix: 1003723 x 1154154 with sparse part having weight 155775130.
Pruned matrix : 901456 x 906538 with weight 137484835.
Total sieving time: 1508.35 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 12.67 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 1521.52 hours.
 --------- CPU info (if available) ----------

Aug 8, 2008 (4th)

By Serge Batalov / GMP-ECM

(17·10¹⁷³-53)/9 = 1(8)₁₇₂3_<174> = 3 · 33538283375647_<14> · 344480854549100429_<18> · C142

C142 = P31 · P112

P31 = 5082667344375497681419535599351_<31>

P112 = 1072229004522264389297731966081077378110519279231987469943729528228287736187297292244073007381734462645151035597_<112>

Aug 8, 2008 (3rd)

By Sinkiti Sibata / GMP-ECM, GGNFS

(5·10¹⁷²+31)/9 = (5)₁₇₁9_<172> = 3³ · 19 · 367 · 43714416961213_<14> · C153

C153 = P34 · C120

P34 = 1653798301727248021218700562722037_<34>

C120 = [408166007641904842658786198853065554777699197980622797915618429703920585969239307313834166622909064779063867322012704809_<120>]

(23·10¹⁶¹+13)/9 = 2(5)₁₆₀7_<162> = 599 · 15607 · C155

C155 = P41 · P115

P41 = 19719319340366401075426222484741876988119_<41>

P115 = 1386267857558319169729300035985642690747006048187548119187725566550353932206640751237137083635630032062262815957971_<115>

Number: 25557_161
N=27336258574478058415373902314022608060438138183527249026196300935932878408072268795481368753089962901963488575826924496077169639918601179402671135170346549
  ( 155 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=19719319340366401075426222484741876988119 (pp41)
 r2=1386267857558319169729300035985642690747006048187548119187725566550353932206640751237137083635630032062262815957971 (pp115)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 80.39 hours.
Scaled time: 81.11 units (timescale=1.009).
Factorization parameters were as follows:
name: 25557_161
n: 27336258574478058415373902314022608060438138183527249026196300935932878408072268795481368753089962901963488575826924496077169639918601179402671135170346549
m: 100000000000000000000000000000000
c5: 230
c0: 13
skew: 0.56
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4750001)
Primes: RFBsize:315948, AFBsize:315406, largePrimes:5864181 encountered
Relations: rels:5997416, finalFF:758540
Max relations in full relation-set: 28
Initial matrix: 631421 x 758540 with sparse part having weight 49501404.
Pruned matrix : 535315 x 538536 with weight 34463912.
Total sieving time: 78.17 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.97 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 80.39 hours.
 --------- CPU info (if available) ----------

(23·10¹⁶⁸+13)/9 = 2(5)₁₆₇7_<169> = 19 · 324341 · 532000939 · 216482375323_<12> · 425109585038514342899997341_<27> · C115

C115 = P57 · P59

P57 = 752167598816115129543711951071928819636012261007143013921_<57>

P59 = 11261063627173626179935047244183866914533647947005762221199_<59>

Number: 25557_168
N=8470207188566678333602446992785470861350447681497005619521829651930901627167738151021929008822533350752240338311279
  ( 115 digits)
Divisors found:
 r1=752167598816115129543711951071928819636012261007143013921 (pp57)
 r2=11261063627173626179935047244183866914533647947005762221199 (pp59)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 68.17 hours.
Scaled time: 32.18 units (timescale=0.472).
Factorization parameters were as follows:
name: 25557_168
n: 8470207188566678333602446992785470861350447681497005619521829651930901627167738151021929008822533350752240338311279
skew: 27936.96
# norm 2.58e+16
c5: 124740
c4: 8884344672
c3: -720747713544096
c2: 14872117333479277883
c1: 141746735268279867872576
c0: 287065501993506415599337280
# alpha -6.37
Y1: 2338220458913
Y0: -9254993027360638988041
# Murphy_E 4.89e-10
# M 2062918138089881151250020832567888086452521627216082223859635173810679776500422403196605929108393081923762769012169
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 3150001)
Primes: RFBsize:250150, AFBsize:250255, largePrimes:7732143 encountered
Relations: rels:7764575, finalFF:677928
Max relations in full relation-set: 28
Initial matrix: 500489 x 677928 with sparse part having weight 63776725.
Pruned matrix : 367416 x 369982 with weight 38952604.
Polynomial selection time: 2.60 hours.
Total sieving time: 58.12 hours.
Total relation processing time: 0.68 hours.
Matrix solve time: 6.40 hours.
Time per square root: 0.36 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 68.17 hours.
 --------- CPU info (if available) ----------

Aug 8, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(23·10¹⁵⁵+13)/9 = 2(5)₁₅₄7_<156> = 27733 · 298395011 · C143

C143 = P64 · P80

P64 = 1536858237752765680135546884026991837272131624810560183412405141_<64>

P80 = 20093847776981569795021169228096774173833895240522025864774809260371178027213679_<80>

Number: 25557_155
N=30881395484204223525048363706070578871079743618026477135015191321940299122219049311869646894913492403479134345321756517220076016992416125123739
  ( 143 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=1536858237752765680135546884026991837272131624810560183412405141 (pp64)
 r2=20093847776981569795021169228096774173833895240522025864774809260371178027213679 (pp80)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 36.57 hours.
Scaled time: 28.09 units (timescale=0.768).
Factorization parameters were as follows:
name: 25557_155
n: 30881395484204223525048363706070578871079743618026477135015191321940299122219049311869646894913492403479134345321756517220076016992416125123739
m: 10000000000000000000000000000000
c5: 23
c0: 13
skew: 0.89
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:215956, largePrimes:5538932 encountered
Relations: rels:5466993, finalFF:530339
Max relations in full relation-set: 28
Initial matrix: 432837 x 530339 with sparse part having weight 40290796.
Pruned matrix : 366783 x 369011 with weight 26137725.
Total sieving time: 34.89 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.44 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 36.57 hours.
 --------- CPU info (if available) ----------

Aug 8, 2008

By Serge Batalov / GMP-ECM, pol51, Msieve

8·10¹⁷³-9 = 7(9)₁₇₂1_<174> = 762946411 · 25759368564863328438503015111_<29> · C137

C137 = P41 · P97

P41 = 23660900021573994987453189462396384397709_<41>

P97 = 1720400179231385795985452436310629205021018478432220686288060649998543845046452046194341069059519_<97>

(22·10¹⁷⁶-13)/9 = 2(4)₁₇₅3_<177> = 3 · 47 · 11795329101796117_<17> · 9398668257774823337_<19> · C140

C140 = P37 · P103

P37 = 3402062619689460830934510402880048421_<37>

P103 = 4596659900995630289638965548262792933809828494069495661471865826071626866018519050235823880497506667447_<103>

(46·10¹⁷⁴-1)/9 = 5(1)₁₇₄_<175> = 35159 · 58943237 · 1746625507597_<13> · 248922781670497343680620477691_<30> · C121

C121 = P61 · P61

P61 = 1067893823990919847935504982633835567161445887859246435573567_<61>

P61 = 5311929554816100268964112016368816505627228318873420984890013_<61>

# Nice split = P61 . P61
#
Number: 51111_174
N=5672576765062949804877898588549304541456787458112679112216952341251445580533290906546230462728475408918734991394065086371
  ( 121 digits)
Divisors found:
 r1=1067893823990919847935504982633835567161445887859246435573567
 r2=5311929554816100268964112016368816505627228318873420984890013
Version: Msieve 1.36
Total time: 42.5 hours.
Scaled time: 0.00 units (timescale=2.731).
Factorization parameters were as follows:
name: 51111_174
n: 5672576765062949804877898588549304541456787458112679112216952341251445580533290906546230462728475408918734991394065086371
skew: 102014.76
# norm 3.35e+16
c5: 19140
c4: -9372030763
c3: -731870746623170
c2: 92837430175095225840
c1: 5337914859676003650431006
c0: 58938389159516231169474581275
# alpha -6.11
Y1: 216595974521
Y0: -196955329213367588586144
# Murphy_E 2.63e-10
# M 5469059722226539692538946386706739042829288291660310148684440958350372775671721201637447869734866081337144509489415174153
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 7900001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 749432 x 749653
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 2.10 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.5,2.5,100000

total time: 42.5 hours.

7·10¹⁷¹-9 = 6(9)₁₇₀1_<172> = 1951 · 32173 · 42839 · 191392620057115592363_<21> · C140

C140 = P30 · P44 · P67

P30 = 121675574481606991533348359183_<30>

P44 = 37422933325867189106477419970456951426047763_<44>

P67 = 2987056712446451498387325795625445621950302093418101807281997373189_<67>

#ECM, then gnfs/Msieve
#
Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3791932801
Step 1 took 4752ms
Step 2 took 4028ms
********** Factor found in step 2: 121675574481606991533348359183
Found probable prime factor of 30 digits: 121675574481606991533348359183
Composite cofactor 111784424190467595098459056149911917007502961485656473196420609707893662179624033360420585864758177758049626207 has 111 digits

Number: 69991_171
N=111784424190467595098459056149911917007502961485656473196420609707893662179624033360420585864758177758049626207
  ( 111 digits)
Divisors found:
 r1=37422933325867189106477419970456951426047763
 r2=2987056712446451498387325795625445621950302093418101807281997373189
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.731).
Factorization parameters were as follows:
name: 69991_171
n: 111784424190467595098459056149911917007502961485656473196420609707893662179624033360420585864758177758049626207
skew: 16193.65
# norm 1.24e+15
c5: 11520
c4: 3427171552
c3: -6558936108298
c2: -63252626562105279
c1: 1972660268393096151002
c0: -13877734259057275740107961
# alpha -5.84
Y1: 104053675033
Y0: -1575375388115067456790
# Murphy_E 9.89e-10
# M 37041568271832547269366268052856747176849485994032370674464185504456218729408930988297991607542039622190059088
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 3100001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 416881 x 417129
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.60 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000

total time: 12.00 hours.

(7·10¹⁷³+11)/9 = (7)₁₇₂9_<173> = 13 · 41 · 97 · 1187 · 4283 · 20123 · 2542985731006770567379_<22> · C136

C136 = P33 · P44 · P61

P33 = 148374117022910019762569059285381_<33>

P44 = 12742154383891239743677658168449128630353237_<44>

P61 = 3058582034683493208292511149822611160088020815388316641196351_<61>

#ECM, then gnfs/Msieve
#
Using B1=6000000, B2=46838457130, polynomial Dickson(12), sigma=3016012969
Step 1 took 41693ms
Step 2 took 28838ms
********** Factor found in step 2: 148374117022910019762569059285381
Found probable prime factor of 33 digits: 148374117022910019762569059285381
Composite cofactor 38972924481733260870403559566764442799445187208849829731616034785643738108037675326777009491015405438187 has 104 digits

Number: 77779_173
N=38972924481733260870403559566764442799445187208849829731616034785643738108037675326777009491015405438187
  ( 104 digits)
Divisors found:
 r1=12742154383891239743677658168449128630353237
 r2=3058582034683493208292511149822611160088020815388316641196351
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
name: 77779_173
n: 38972924481733260870403559566764442799445187208849829731616034785643738108037675326777009491015405438187
skew: 9933.83
# norm 1.97e+14
c5: 34860
c4: 901297777
c3: -21180099304087
c2: -78583700990596635
c1: 703469453536820960998
c0: -394872940644774252554872
# alpha -5.56
Y1: 92456260217
Y0: -64518446932467432327
# Murphy_E 2.08e-09
# M 30218089768888548155266849306367562088407850169320702880711957874078613122326425973957506041161891019394
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1950001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 246221 x 246469
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000

total time: 5.00 hours.

(22·10²⁰¹+41)/9 = 2(4)₂₀₀9_<202> = 3797 · 3739573 · 9224921 · 103799099 · 1624797562127_<13> · 1003362284833326692245409_<25> · C141

C141 = P36 · P41 · P64

P36 = 330339604811711267297717657513076361_<36>

P41 = 98925041246554540448114569641042954062293_<41>

P64 = 3374717342088131963785890619806166620582933081953540929990793009_<64>

#ECM, then gnfs/Msieve
#
Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3739902623
Step 1 took 19269ms
Step 2 took 16557ms
********** Factor found in step 2: 330339604811711267297717657513076361
Found probable prime factor of 36 digits: 330339604811711267297717657513076361
Composite cofactor 333844052261531363551751769986354954315086292507097564052612942432609377571688862191585189443825054909637 has 105 digits

Number: 24449_201
N=333844052261531363551751769986354954315086292507097564052612942432609377571688862191585189443825054909637
  ( 105 digits)
Divisors found:
 r1=98925041246554540448114569641042954062293
 r2=3374717342088131963785890619806166620582933081953540929990793009
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.640).
Factorization parameters were as follows:
name: 24449_201
n: 333844052261531363551751769986354954315086292507097564052612942432609377571688862191585189443825054909637
skew: 13311.19
# norm 3.73e+14
c5: 12600
c4: 1440916962
c3: -12014813041711
c2: -50543851810534588
c1: 1101519325379670022132
c0: 88313820922993320076000
# alpha -6.41
Y1: 81213642653
Y0: -121514465581815833139
# Murphy_E 2.04e-09
# M 101610898617811713987352624168799700761878918485444785286881499599136886363679267953692098842357271862008
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2000001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 305904 x 306152
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000

total time: 5.00 hours.

(14·10¹⁷⁶-41)/9 = 1(5)₁₇₅1_<177> = 2259105661271087_<16> · 80720351480358203_<17> · C144

C144 = P28 · C117

P28 = 6253487942641704767889353221_<28>

C117 = [136409187220118099594259543876309212197184154651522471682143115643170104578299575205818479783053844257159831548060871_<117>]

(55·10¹⁸⁴-1)/9 = 6(1)₁₈₄_<185> = 113113526204811467_<18> · 902962100831388890356903_<24> · C144

C144 = P26 · C119

P26 = 30298080812156225043145231_<26>

C119 = [19747903514851469875519184933191367723255404512820964004527952705940791479122740524381113999412093592853212505254472781_<119>]

2·10¹⁷⁹-1 = 1(9)₁₇₉_<180> = 149 · 19645014971_<11> · 838639710091_<12> · 13513905648601_<14> · C142

C142 = P34 · P108

P34 = 7736164186569272400196540924681661_<34>

P108 = 779308440001156560248963164065011218680470960978737478778245389819252290693403741828408530381050760178412831_<108>

(7·10¹⁸⁴-61)/9 = (7)₁₈₃1_<184> = 17 · 19 · 12973 · 154681 · 1214431 · 8563859219_<10> · 125889320445307_<15> · C142

C142 = P33 · P110

P33 = 129094206503327431146389777618501_<33>

P110 = 70996610207680637642204608399521543078046698423883298589248821326163661299941720117124087158672108046378173023_<110>

(7·10¹⁷⁵-43)/9 = (7)₁₇₄3_<175> = 3 · 382871 · 4421693 · 17287094566914421_<17> · C146

C146 = P37 · P110

P37 = 1684109493826672636928080591712280253_<37>

P110 = 52601833872567659626851043826581619661581030085497192629117169385792946029809296953983334314216888134146219869_<110>

(88·10¹⁹²-7)/9 = 9(7)₁₉₂_<193> = 3 · 23 · 7288271 · 64712835717378481819_<20> · 464852779560926987089_<21> · C144

C144 = P32 · P113

P32 = 18366535073149532144552799837541_<32>

P113 = 35191150359072223380378605356328279445463560817952105212736869086800146064986873859220813359328377257541095219333_<113>

Aug 7, 2008 (6th)

By Sinkiti Sibata / GGNFS

(23·10¹⁵⁶+13)/9 = 2(5)₁₅₅7_<157> = 17657 · 44971 · C148

C148 = P54 · P94

P54 = 781907070859593547152702692114831874677192073746363363_<54>

P94 = 4116050781119597221247693666790093823786502395231349904415402687602576392453281676423041883437_<94>

Number: 25557_156
N=3218369209774566274049173141039366428490259800717741754764314923643946321825760512611705672009243932137381206086696326505234361349905745712893318631
  ( 148 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=781907070859593547152702692114831874677192073746363363 (pp54)
 r2=4116050781119597221247693666790093823786502395231349904415402687602576392453281676423041883437 (pp94)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 40.68 hours.
Scaled time: 40.56 units (timescale=0.997).
Factorization parameters were as follows:
name: 25557_156
n: 3218369209774566274049173141039366428490259800717741754764314923643946321825760512611705672009243932137381206086696326505234361349905745712893318631
m: 10000000000000000000000000000000
c5: 230
c0: 13
skew: 0.56
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3200001)
Primes: RFBsize:216816, AFBsize:216366, largePrimes:6056710 encountered
Relations: rels:6288634, finalFF:749664
Max relations in full relation-set: 28
Initial matrix: 433249 x 749664 with sparse part having weight 72754471.
Pruned matrix : 315959 x 318189 with weight 42689934.
Total sieving time: 39.53 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.98 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 40.68 hours.
 --------- CPU info (if available) ----------

Aug 7, 2008 (5th)

By Serge Batalov / GMP-ECM

3·10¹⁷⁴-7 = 2(9)₁₇₃3_<175> = 17 · 13707838783_<11> · 37843367550258766630487_<23> · C141

C141 = P34 · P108

P34 = 2335652610416605452519508897978433_<34>

P108 = 145648266590335890831386445560195486299154390924262334577765318323875048848015754190501837612604655871004353_<108>

Aug 7, 2008 (4th)

By Serge Batalov / GMP-ECM, pol51, Msieve

7·10¹⁷³+1 = 7(0)₁₇₂1_<174> = 62473 · 1835807801_<10> · 3510906612731053298436347_<25> · C136

C136 = P33 · P34 · P70

P33 = 992595949608553727415223604789713_<33>

P34 = 1626878119033344343859043164870647_<34>

P70 = 1076543722683910823425060595208148712881299436943475382391159481127061_<70>

#ECM, then gnfs/Msieve
#
Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3918156657
Step 1 took 4876ms
Step 2 took 3917ms
********** Factor found in step 2: 1626878119033344343859043164870647
Found probable prime factor of 34 digits: 1626878119033344343859043164870647
Composite cofactor 1068572938712563985973724191660647332399339731320429804051791387573023191775826284252964977667138723493 has 103 digits

Number: 70001_173
N=1068572938712563985973724191660647332399339731320429804051791387573023191775826284252964977667138723493
  ( 103 digits)
Divisors found:
 r1=992595949608553727415223604789713
 r2=1076543722683910823425060595208148712881299436943475382391159481127061
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.735).
Factorization parameters were as follows:
name: 70001_173
n: 1068572938712563985973724191660647332399339731320429804051791387573023191775826284252964977667138723493
skew: 15552.49
# norm 5.16e+13
c5: 2940
c4: 129072552
c3: 676512448813
c2: -10144897000555416
c1: -183754969317295252134
c0: 1149836521829367843055935
# alpha -4.98
Y1: 2140818119
Y0: -51533686343477739386
# Murphy_E 2.69e-09
# M 737117335365418159696785999293603511904503343401603691135378419973771783304690523634342544985619791933
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1850001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 273072 x 273320
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 4.00 hours.

Aug 7, 2008 (3rd)

By Serge Batalov / GMP-ECM, pol51, Msieve

5·10¹⁸⁸-7 = 4(9)₁₈₇3_<189> = 1013 · 5167 · 304746299542785906368113_<24> · 305640055064400234524887_<24> · C136

C136 = P31 · P52 · P54

P31 = 1125757121291323820335846959911_<31>

P52 = 7781904029500380045551718378173661286980891261937589_<52>

P54 = 117069244032165610046166201324768623892290569937890367_<54>

#ECM, then gnfs/Msieve
#
Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=1218311065
Step 1 took 6562ms
Step 2 took 5173ms
********** Factor found in step 2: 1125757121291323820335846959911
Found probable prime factor of 31 digits: 1125757121291323820335846959911
Composite cofactor 911021621864472880075023900946638173443125657307892780789019050463547543440983821891566758943879478305163 has 105 digits
#
Number: 49993_188
N=911021621864472880075023900946638173443125657307892780789019050463547543440983821891566758943879478305163
  ( 105 digits)
Divisors found:
 r1=7781904029500380045551718378173661286980891261937589
 r2=117069244032165610046166201324768623892290569937890367
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.734).
Factorization parameters were as follows:
name: 49993_188
n: 911021621864472880075023900946638173443125657307892780789019050463547543440983821891566758943879478305163
skew: 25126.52
# norm 1.03e+14
c5: 3000
c4: -184008800
c3: -4855436126528
c2: 67822196941694137
c1: 1629442699164998766054
c0: -1737491899063811738070735
# alpha -5.76
Y1: 37648389859
Y0: -197916726587171231828
# Murphy_E 2.09e-09
# M 765710024518842781312326828781050795290290399363406343051939875665884698804336614622533704295513648569450
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2000001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 254568 x 254816
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 5.1 hours.

(8·10¹⁷⁴-71)/9 = (8)₁₇₃1_<174> = 7 · 53 · 12101 · 1939607078801257064760060301_<28> · C141

C141 = P33 · P41 · P67

P33 = 850114323448304243508033259581857_<33>

P41 = 78519989734889223718360727461925074539577_<41>

P67 = 1529258766563958643337276955202978587578375066092351071414778732099_<67>

#ECM, then gnfs/Msieve
#
Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=2137109807
Step 1 took 6074ms
Step 2 took 5382ms
********** Factor found in step 2: 850114323448304243508033259581857
Found probable prime factor of 33 digits: 850114323448304243508033259581857
Composite cofactor 120077382652591388295983297045168552769870447621305691159671304298960005415149680145939340552228814255782123 has 108 digits

Number: 88881_174
N=120077382652591388295983297045168552769870447621305691159671304298960005415149680145939340552228814255782123
  ( 108 digits)
Divisors found:
 r1=78519989734889223718360727461925074539577
 r2=1529258766563958643337276955202978587578375066092351071414778732099
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.737).
Factorization parameters were as follows:
name: 88881_174
n: 120077382652591388295983297045168552769870447621305691159671304298960005415149680145939340552228814255782123
skew: 15539.87
# norm 5.21e+14
c5: 10620
c4: 2345195624
c3: -9769755854673
c2: -757793244395768101
c1: -346626392993315128485
c0: 663410832095626035419180
# alpha -5.61
Y1: 214905875723
Y0: -407997250730317195257
# Murphy_E 1.32e-09
# M 45879032032193932672059950995837741871759094187743379265860171579020205688976944665220708460720323858425038
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1600000, 2900001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 335656 x 335899
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,26,26,49,49,2.6,2.6,100000
total time: 8.5 hours.

(8·10¹⁷⁷-71)/9 = (8)₁₇₆1_<177> = 2521 · 12347 · 508009 · 2364600556759857195209813_<25> · C140

C140 = P39 · P42 · P60

P39 = 652164356657968751849283918254856440873_<39>

P42 = 286392555317369108538464512499833719018257_<42>

P60 = 127281476955854375844191574769583701186317121525016829505199_<60>

#ECM, then gnfs/Msieve
#
Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=2437338572
Step 1 took 6152ms
Step 2 took 5294ms
********** Factor found in step 2: 652164356657968751849283918254856440873
Found probable prime factor of 39 digits: 652164356657968751849283918254856440873
Composite cofactor 36452467429955965780886924086595385555832450018859545691294583204020859281578886114742778261357418143 has 101 digits

Number: 88881_177
N=36452467429955965780886924086595385555832450018859545691294583204020859281578886114742778261357418143
  ( 101 digits)
Divisors found:
 r1=286392555317369108538464512499833719018257
 r2=127281476955854375844191574769583701186317121525016829505199
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.313).
Factorization parameters were as follows:
name: 88881_177
n: 36452467429955965780886924086595385555832450018859545691294583204020859281578886114742778261357418143
skew: 12368.22
# norm 1.12e+14
c5: 15120
c4: 150264694
c3: -11598943337685
c2: -17156313923209009
c1: 524819569682653239745
c0: 949953813586943591715135
# alpha -5.76
Y1: 139498271
Y0: -18898834485199271362
# Murphy_E 3.00e-09
# M 26093282328691552134264344581641201739610238309972482507984177247986435870294398991833476024748170828
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1500001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 196349 x 196597
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 5.2 hours.

(29·10¹⁸⁵+7)/9 = 3(2)₁₈₄3_<186> = 11 · 59 · 685249 · 171202729 · 734289631 · 411680179561846754678303_<24> · C137

C137 = P36 · P42 · P59

P36 = 998491758420129256214012778643327061_<36>

P42 = 191014929503817134873863510492700758731779_<42>

P59 = 73402786568103797704687105151174128789470935649299173949761_<59>

#ECM, then gnfs/Msieve
#
Using B1=2000000, B2=8559543730, polynomial Dickson(6), sigma=2737868976
Step 1 took 9609ms
Step 2 took 7188ms
********** Factor found in step 2: 998491758420129256214012778643327061
Found probable prime factor of 36 digits: 998491758420129256214012778643327061
Composite cofactor 14021028101690082203690938282107943503058227685215117433407131744368757397621888113439598832620154819 has 101 digits

Number: 32223_185
N=14021028101690082203690938282107943503058227685215117433407131744368757397621888113439598832620154819
  ( 101 digits)
Divisors found:
 r1=191014929503817134873863510492700758731779
 r2=73402786568103797704687105151174128789470935649299173949761
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.738).
Factorization parameters were as follows:
name: 32223_185
n: 14021028101690082203690938282107943503058227685215117433407131744368757397621888113439598832620154819
skew: 5770.54
# norm 1.14e+14
c5: 48600
c4: 1184294521
c3: -12491219393246
c2: -27607875436124762
c1: 101137989921524038740
c0: 155838742740402087911160
# alpha -5.97
Y1: 29392050083
Y0: -12360148402989801913
# Murphy_E 3.32e-09
# M 10280378046388752780938709639775952386580967738344090357039117454518361154218840421540055381266736973
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1400001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 201675 x 201913
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 3.4 hours.

(2·10¹⁸³+7)/9 = (2)₁₈₂3_<183> = 17 · 361822305232022329_<18> · 152872903897698185022599_<24> · C141

C141 = P41 · P42 · P59

P41 = 56504766697054018996849756720133510657753_<41>

P42 = 129327126139044059461605326059944584322779_<42>

P59 = 32339849927200696698255186332877160637861959050438843478747_<59>

#ECM, then gnfs/Msieve
#
Using B1=2000000, B2=8559543730, polynomial Dickson(6), sigma=1270233868
Step 1 took 9533ms
Step 2 took 7464ms
********** Factor found in step 2: 129327126139044059461605326059944584322779
Found probable prime factor of 42 digits: 129327126139044059461605326059944584322779
Composite cofactor 1827355675154214767482106570239375220163114678088840958328885624433969277661546681725988126646275491 has 100 digits

Number: 22223_183
N=1827355675154214767482106570239375220163114678088840958328885624433969277661546681725988126646275491
  ( 100 digits)
Divisors found:
 r1=56504766697054018996849756720133510657753
 r2=32339849927200696698255186332877160637861959050438843478747
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.314).
Factorization parameters were as follows:
name: 22223_183
n: 1827355675154214767482106570239375220163114678088840958328885624433969277661546681725988126646275491
skew: 3575.19
# norm 2.82e+13
c5: 102900
c4: -1062787720
c3: -2272158754673
c2: 10216394129434064
c1: 16004713462425507864
c0: 8663053915124755834480
# alpha -5.13
Y1: 3656686517
Y0: -7077534675564246313
# Murphy_E 3.52e-09
# M 940969014475266382158432414369008942926809560248257615283982847759757507643575631266244431986526342
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1400001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 178248 x 178496
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 3.9 hours.

4·10¹⁸²+7 = 4(0)₁₈₁7_<183> = 11 · 37 · 5902703 · 37760843933_<11> · 1674936332852367533987873251_<28> · C136

C136 = P37 · P41 · P59

P37 = 2330176577666875374606105976962270839_<37>

P41 = 47627606812357868080621344383726803782953_<41>

P59 = 23720676061967159486831460421686709294636997657176676784247_<59>

#ECM, then gnfs/Msieve
#
Using B1=2000000, B2=8559543730, polynomial Dickson(6), sigma=55071172
Step 1 took 10844ms
Step 2 took 7141ms
********** Factor found in step 2: 2330176577666875374606105976962270839
Found probable prime factor of 37 digits: 2330176577666875374606105976962270839
Composite cofactor 1129759032802681292108641345913746599729470090263548664373455174466738092066408583230872690597541391 has 100 digits

Number: 40007_182
N=1129759032802681292108641345913746599729470090263548664373455174466738092066408583230872690597541391
  ( 100 digits)
Divisors found:
 r1=47627606812357868080621344383726803782953
 r2=23720676061967159486831460421686709294636997657176676784247
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.313).
Factorization parameters were as follows:
name: 40007_182
n: 1129759032802681292108641345913746599729470090263548664373455174466738092066408583230872690597541391
skew: 5286.20
# norm 4.88e+13
c5: 58800
c4: -906758215
c3: -6836595460751
c2: 23281841126672733
c1: 66931458270165345836
c0: -88859584402032996519968
# alpha -5.55
Y1: 15480297767
Y0: -7189928693554233609
# Murphy_E 3.55e-09
# M 947782540688762278453606516086462947233300208592534816796037426704101353095513118854962769689206778
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1400001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 180923 x 181171
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 4.3 hours.

(19·10¹⁹³-1)/9 = 2(1)₁₉₃_<194> = 3 · 7 · 23 · 613 · 2833 · 416490302317_<12> · 33136289468939_<14> · 6387850378064999378621_<22> · C138

C138 = P34 · P36 · P69

P34 = 3585254944930175016436306851443401_<34>

P36 = 105774509586365818991279929828972043_<36>

P69 = 752822071840582304755740077449928254967150719264138691792961720686657_<69>

#ECM, then gnfs/Msieve
#
Using B1=2000000, B2=8559543730, polynomial Dickson(6), sigma=1729672148
Step 1 took 9573ms
Step 2 took 7300ms
********** Factor found in step 2: 3585254944930175016436306851443401
Found probable prime factor of 34 digits: 3585254944930175016436306851443401
Composite cofactor 79629385454729450269141990896146731249794383524320855682484215788054337303524638643371992825766416130251 has 104 digits

Number: 21111_193
N=79629385454729450269141990896146731249794383524320855682484215788054337303524638643371992825766416130251
  ( 104 digits)
Divisors found:
 r1=105774509586365818991279929828972043
 r2=752822071840582304755740077449928254967150719264138691792961720686657
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.737).
Factorization parameters were as follows:
name: 21111_193
n: 79629385454729450269141990896146731249794383524320855682484215788054337303524638643371992825766416130251
skew: 11440.70
# norm 3.65e+14
c5: 49560
c4: 954446464
c3: -11673185859318
c2: 99159039807627574
c1: 85142343816020421663
c0: -3137015993006215705337408
# alpha -5.99
Y1: 67495019713
Y0: -69372410581475242965
# Murphy_E 1.98e-09
# M 71658718969377613232222706448506061496258100849620301512030428716481435024437065551927822137618899207361
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1950001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 281490 x 281734
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 4.9 hours.

Aug 7, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(23·10¹⁵⁸+13)/9 = 2(5)₁₅₇7_<159> = 179 · 857 · 5853319 · 10428049068221_<14> · 396542762668729543_<18> · C116

C116 = P38 · P79

P38 = 28481733151018451194381169971516170137_<38>

P79 = 2416516546246403734291325726758822978398144770574446242022023119207272957248691_<79>

Number: 25557_158
N=68826579425210809470015553353770765456077504207060256500230860436840512081806665744753698910449007201997412976540667
  ( 116 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=28481733151018451194381169971516170137 (pp38)
 r2=2416516546246403734291325726758822978398144770574446242022023119207272957248691 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 58.23 hours.
Scaled time: 58.75 units (timescale=1.009).
Factorization parameters were as follows:
name: 25557_158
n: 68826579425210809470015553353770765456077504207060256500230860436840512081806665744753698910449007201997412976540667
m: 10000000000000000000000000000000
c5: 23000
c0: 13
skew: 0.22
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4100001)
Primes: RFBsize:283146, AFBsize:282137, largePrimes:5923659 encountered
Relations: rels:6064985, finalFF:735082
Max relations in full relation-set: 28
Initial matrix: 565350 x 735082 with sparse part having weight 58078754.
Pruned matrix : 446248 x 449138 with weight 41455549.
Total sieving time: 56.27 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 1.76 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 58.23 hours.
 --------- CPU info (if available) ----------

(23·10¹⁴⁹+13)/9 = 2(5)₁₄₈7_<150> = 64772479953469503305191_<23> · C127

C127 = P45 · P82

P45 = 566133521560795325889304563432237670928480249_<45>

P82 = 6969087711214779205512251281730735486566945920175972509570822329865906521478641323_<82>

Number: 25557_149
N=3945434168016085953016073180664300665240976809696498373238898533666905590653549512885830295321311057834646752892450153760729427
  ( 127 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=566133521560795325889304563432237670928480249 (pp45)
 r2=6969087711214779205512251281730735486566945920175972509570822329865906521478641323 (pp82)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 30.98 hours.
Scaled time: 24.11 units (timescale=0.778).
Factorization parameters were as follows:
name: 25557_149
n: 3945434168016085953016073180664300665240976809696498373238898533666905590653549512885830295321311057834646752892450153760729427
m: 1000000000000000000000000000000
c5: 23
c0: 130
skew: 1.41
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2300001)
Primes: RFBsize:176302, AFBsize:176533, largePrimes:5965007 encountered
Relations: rels:6142480, finalFF:692622
Max relations in full relation-set: 28
Initial matrix: 352900 x 692622 with sparse part having weight 67465135.
Pruned matrix : 251696 x 253524 with weight 35454550.
Total sieving time: 29.81 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.93 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 30.98 hours.
 --------- CPU info (if available) ----------

Aug 7, 2008

By Robert Backstrom / GGNFS, Msieve

(19·10¹⁸⁷-1)/9 = 2(1)₁₈₇_<188> = 3² · 7 · C186

C186 = P48 · P59 · P80

P48 = 329022937768969847915045880276123722387918253629_<48>

P59 = 94329378756867316059517725551482756560238888705578834764291_<59>

P80 = 10796858061879096975942872469334528421951068133497198680481477155854888637343823_<80>

Number: n
N=335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097
  ( 186 digits)
SNFS difficulty: 188 digits.
Divisors found:

Thu Aug 07 03:14:08 2008  prp48 factor: 329022937768969847915045880276123722387918253629
Thu Aug 07 03:14:08 2008  prp59 factor: 94329378756867316059517725551482756560238888705578834764291
Thu Aug 07 03:14:08 2008  prp80 factor: 10796858061879096975942872469334528421951068133497198680481477155854888637343823
Thu Aug 07 03:14:08 2008  elapsed time 10:51:17 (Msieve 1.36)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 128.02 hours.
Scaled time: 167.58 units (timescale=1.309).
Factorization parameters were as follows:
name: KA_2_1_187
n: 335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097
type: snfs
skew: 0.22
deg: 5
c5: 1900
c0: -1
m: 10000000000000000000000000000000000000
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 10350001)
Primes: RFBsize:602489, AFBsize:602920, largePrimes:11018733 encountered
Relations: rels:11102338, finalFF:1302917
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 127.32 hours.
Total relation processing time: 0.71 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,188,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,50,50,2.5,2.5,100000
total time: 128.02 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Aug 6, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(16·10¹⁸⁷-7)/9 = 1(7)₁₈₇_<188> = 23 · C186

C186 = P61 · P125

P61 = 8413570336737408496831483163541109031813882697182810158716967_<61>

P125 = 91869067348061522362678558846592350747618316691107208817401001795528904555531717670493313920079035651924077479602838554208497_<125>

Number: n
N=772946859903381642512077294685990338164251207729468599033816425120772946859903381642512077294685990338164251207729468599033816425120772946859903381642512077294685990338164251207729468599
  ( 186 digits)
SNFS difficulty: 188 digits.
Divisors found:

Wed Aug 06 14:01:52 2008  prp61 factor: 8413570336737408496831483163541109031813882697182810158716967
Wed Aug 06 14:01:52 2008  prp125 factor: 91869067348061522362678558846592350747618316691107208817401001795528904555531717670493313920079035651924077479602838554208497
Wed Aug 06 14:01:52 2008  elapsed time 04:55:33 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 104.83 hours.
Scaled time: 215.00 units (timescale=2.051).
Factorization parameters were as follows:
name: KA_1_7_187
n: 772946859903381642512077294685990338164251207729468599033816425120772946859903381642512077294685990338164251207729468599033816425120772946859903381642512077294685990338164251207729468599
type: snfs
skew: 0.67
deg: 5
c5: 50
c0: -7
m: 20000000000000000000000000000000000000
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 7700001)
Primes: RFBsize:602489, AFBsize:603650, largePrimes:10820302 encountered
Relations: rels:10822304, finalFF:1234763
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 104.47 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,188,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,50,50,2.5,2.5,100000
total time: 104.83 hours.
 --------- CPU info (if available) ----------

Aug 6, 2008 (2nd)

By Sinkiti Sibata / GGNFS, GMP-ECM

(23·10¹⁴⁴+13)/9 = 2(5)₁₄₃7_<145> = 457 · 17183 · 4178794657_<10> · 343786229129288649902671981_<27> · C102

C102 = P40 · P62

P40 = 4114335642866747764693039576228582994911_<40>

P62 = 55059328596536920501386029149429591370549677520488608295796081_<62>

Number: 25557_144
N=226532558117044239774320977876345460092466644275246353722984829588615428664800021207013083965916743791
  ( 102 digits)
Divisors found:
 r1=4114335642866747764693039576228582994911 (pp40)
 r2=55059328596536920501386029149429591370549677520488608295796081 (pp62)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 9.89 hours.
Scaled time: 7.61 units (timescale=0.769).
Factorization parameters were as follows:
name: 25557_144
n: 226532558117044239774320977876345460092466644275246353722984829588615428664800021207013083965916743791
skew: 7988.34
# norm 3.60e+14
c5: 71400
c4: -774575110
c3: 15524586669067
c2: -87782106422671083
c1: -780942194720821060323
c0: -750391296517424150053023
# alpha -6.72
Y1: 23670384947
Y0: -19965840648434549932
# Murphy_E 2.77e-09
# M 83675160995847320103734812275915734706169745801809051083627009931664545162604386774762890030652613951
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1650001)
Primes: RFBsize:169511, AFBsize:169027, largePrimes:4335727 encountered
Relations: rels:4400992, finalFF:476262
Max relations in full relation-set: 28
Initial matrix: 338623 x 476262 with sparse part having weight 33631253.
Pruned matrix : 223554 x 225311 with weight 14342686.
Total sieving time: 9.27 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.34 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 9.89 hours.
 --------- CPU info (if available) ----------

(23·10¹⁶⁴+13)/9 = 2(5)₁₆₃7_<165> = 173 · 2459 · 69821287 · C151

C151 = P35 · P116

P35 = 97996674633214703904333152367330721_<35>

P116 = 87797369882483358127297218980473387849967031598734392845350193043538916210511016929393258070159166263052725101579213_<116>

(23·10¹⁴⁶+13)/9 = 2(5)₁₄₅7_<147> = 15881 · 92333 · 217691 · 522492712207777_<15> · C118

C118 = P41 · P77

P41 = 30395386576514997938657854711907051494819_<41>

P77 = 50410633075491711788515806989680923366586844061809091392422973274639746710273_<77>

Number: 25557_146
N=1532250679896423743216230013144060122627556389523592324124708922006937367233119275394131176657352314823367662353575587
  ( 118 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=30395386576514997938657854711907051494819 (pp41)
 r2=50410633075491711788515806989680923366586844061809091392422973274639746710273 (pp77)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.21 hours.
Scaled time: 18.60 units (timescale=0.768).
Factorization parameters were as follows:
name: 25557_146
n: 1532250679896423743216230013144060122627556389523592324124708922006937367233119275394131176657352314823367662353575587
m: 100000000000000000000000000000
c5: 230
c0: 13
skew: 0.56
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 3450001)
Primes: RFBsize:114155, AFBsize:113437, largePrimes:2959727 encountered
Relations: rels:2981079, finalFF:268285
Max relations in full relation-set: 28
Initial matrix: 227659 x 268285 with sparse part having weight 31407304.
Pruned matrix : 216257 x 217459 with weight 23868475.
Total sieving time: 23.52 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.49 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 24.21 hours.
 --------- CPU info (if available) ----------

Aug 6, 2008

By Serge Batalov / GMP-ECM, pol51, Msieve

(23·10¹⁴²+13)/9 = 2(5)₁₄₁7_<143> = 3 · 7 · 489601939 · 1872029835859049_<16> · C118

C118 = P55 · P63

P55 = 6625098495942842425461341162814530427168462082503703937_<55>

P63 = 200409265926613305929760532852100392767304804014811227076778131_<63>

Number: 25557_142
N=1327731126263414951933406087090320904441165906586586461502979533450403825686008579656045087639294576190702887860201747
  ( 118 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=6625098495942842425461341162814530427168462082503703937
 r2=200409265926613305929760532852100392767304804014811227076778131
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.316).
Factorization parameters were as follows:
n: 1327731126263414951933406087090320904441165906586586461502979533450403825686008579656045087639294576190702887860201747
Y1: 1
Y0: -10000000000000000000000000000
c5: 2300
c0: 13
skew: 0.36
type: snfsFactor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved rational special-q in [650000, 2550001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 232957 x 233174
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000

total time: 8.8 hours.

(23·10¹⁴³+13)/9 = 2(5)₁₄₂7_<144> = 17 · 61744519 · 101301403166701741_<18> · C118

C118 = P53 · P65

P53 = 65859675644733747744876500166006837201688502506803137_<53>

P65 = 36492443555669713830870958080651283618116301983410638260983585327_<65>

Number: 25557_143
N=2403380496060161658259467596978281135018814158374470115183024859384918654165882944235953366808378500030515903230770799
  ( 118 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=65859675644733747744876500166006837201688502506803137
 r2=36492443555669713830870958080651283618116301983410638260983585327
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.314).
Factorization parameters were as follows:
n: 2403380496060161658259467596978281135018814158374470115183024859384918654165882944235953366808378500030515903230770799
Y1: 1
Y0: -10000000000000000000000000000
c5: 23000
c0: 13
skew: 0.22
type: snfsFactor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved rational special-q in [650000, 2750001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 239842 x 240061
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000

total time: 9.50 hours.

(23·10¹⁶¹-41)/9 = 2(5)₁₆₀1_<162> = 34239449 · 2926008353_<10> · C145

C145 = P37 · P108

P37 = 3265797762225884596670732499419492287_<37>

P108 = 781076750339822130193637764085753788800316293642129828413036710971415513493721659905790281056519495473703209_<108>

Number: 25551_161
N=2550838703386457058983851982174471636580809444581382140772962847792680968368041877385417491833370434666366908243887386972936845573239198502648983
  ( 145 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=3265797762225884596670732499419492287
 r2=781076750339822130193637764085753788800316293642129828413036710971415513493721659905790281056519495473703209
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.735).
Factorization parameters were as follows:
n: 2550838703386457058983851982174471636580809444581382140772962847792680968368041877385417491833370434666366908243887386972936845573239198502648983
Y1: 1
Y0: -100000000000000000000000000000000
c5: 230
c0: -41
skew: 0.71
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2250000, 5850001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 847882 x 848130
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,52,52,2.5,2.5,100000

total time: 31.00 hours.

(89·10¹⁸³+1)/9 = 9(8)₁₈₂9_<184> = 11 · 31 · 230939 · 6528699292836557_<16> · 45042607302532677661259_<23> · C138

C138 = P30 · P48 · P61

P30 = 855468002423990818667567862479_<30>

P48 = 275723309612424883809954589539130241126436024793_<48>

P61 = 1810374387839617565875816723065884562933961409570318045244551_<61>

# by ECM -
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3594520275
Step 1 took 4753ms
Step 2 took 2516ms
********** Factor found in step 2: 855468002423990818667567862479
Found probable prime factor of 30 digits: 855468002423990818667567862479
Composite cofactor 499162417852707040683001124722295789588462930665489693937531449950777948895806297476020644412226345984152943 has 108 digits
# 
# then gnfs-108
#
Number: 98889_183
N=499162417852707040683001124722295789588462930665489693937531449950777948895806297476020644412226345984152943
  ( 108 digits)
Divisors found:
 r1=275723309612424883809954589539130241126436024793
 r2=1810374387839617565875816723065884562933961409570318045244551
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.731).
Factorization parameters were as follows:
name: 98889_183
n: 499162417852707040683001124722295789588462930665489693937531449950777948895806297476020644412226345984152943
skew: 6367.74
# norm 1.99e+14
c5: 98280
c4: -3932189772
c3: -14195911115856
c2: 168247492708970018
c1: 394303928144318474569
c0: 11250118535848240977980
# alpha -4.82
Y1: 146536788547
Y0: -347661669355558617337
# Murphy_E 1.26e-09
# M 234099490853764417282034601725069136841311422359331376023196173334057189716504940742691805709108107303510010
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1600000, 2900001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 363455 x 363690
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,26,26,49,49,2.6,2.6,100000

total time: 9.00 hours.

(23·10¹⁷⁸+13)/9 = 2(5)₁₇₇7_<179> = 3 · 7 · 3089 · 30965694031_<11> · 105798861707767097_<18> · C147

C147 = P34 · P113

P34 = 9190189260448802869426553982826697_<34>

P113 = 13084642307823470911065057058071680416067637028123994347405023218259557598814694113241703703772546244245296570607_<113>

(23·10¹⁹⁷+13)/9 = 2(5)₁₉₆7_<198> = 53714423800700912989_<20> · 1014976496456936546473_<22> · C157

C157 = P34 · P124

P34 = 2580874998888541245310406445060083_<34>

P124 = 1816232526436507979241205514927769365658211492022209623151229839650671428819401905149150226796372100647466485902499391480507_<124>

(23·10¹⁹⁶+13)/9 = 2(5)₁₉₅7_<197> = 3 · 7 · 4871 · 961159 · 131819032819_<12> · 1698569523257_<13> · C163

C163 = P35 · C128

P35 = 53004070707953670657090858563081161_<35>

C128 = [21901910122835344256061530624500431703779582143146602139059801748063458973892397511598243950760773344980568496721822880202328731_<128>]

(23·10¹⁷⁰+13)/9 = 2(5)₁₆₉7_<171> = 131 · C169

C169 = P37 · P133

P37 = 1044017213865280636808570384948699591_<37>

P133 = 1868557090526470524991054799255390917927347831803388988191607353986471639712766833299263075001398831704077334177755758059926799038417_<133>

(23·10¹⁸⁶+13)/9 = 2(5)₁₈₅7_<187> = 19 · 98830288759_<11> · 13923449887211_<14> · 7114090681306556579_<19> · 88088266222011349289720093_<26> · C117

C117 = P44 · P73

P44 = 27296107544757600811971553165015267535987419_<44>

P73 = 5714215643994044486498201355639702225760874868392820299955666521320942079_<73>

(23·10¹⁵⁷+13)/9 = 2(5)₁₅₆7_<158> = 3 · C157

C157 = P60 · P98

P60 = 126011477037647694969872702702861906404388540860818011857969_<60>

P98 = 67601132204596663156815669683198816877432469167676276619995009811867251792268967419820117585110951_<98>

Number: 25557_157
N=8518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518519
  ( 157 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=126011477037647694969872702702861906404388540860818011857969
 r2=67601132204596663156815669683198816877432469167676276619995009811867251792268967419820117585110951
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.735).
Factorization parameters were as follows:
n: 8518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518519
Y1: 1
Y0: -10000000000000000000000000000000
c5: 2300
c0: 13
skew: 0.36
type: snfsFactor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2000000, 3300001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 759044 x 759292
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 2.10 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,52,52,2.5,2.5,100000

total time: 20 hours.

2·10¹⁷⁵-7 = 1(9)₁₇₄3_<176> = 13 · 17 · 19 · 263 · 1061 · 2381 · 13441 · 4860859 · 226155589725368669_<18> · C135

C135 = P32 · P36 · P68

P32 = 39446498300985945769793398333109_<32>

P36 = 938415519872263667316969095279317859_<36>

P68 = 13106840786581520901091016381324397299535250533490063320445846306169_<68>

(5·10¹⁸³-17)/3 = 1(6)₁₈₂1_<184> = 11³ · 12379 · 1256764309_<10> · 125559628324721_<15> · 10322887976088217_<17> · C137

C137 = P31 · P107

P31 = 4829132631888808394893101232471_<31>

P107 = 12859110351779873791714693881189925990159509826139111805995342132170989852683935783801451769837720188516543_<107>

5·10¹⁷⁹+9 = 5(0)₁₇₈9_<180> = 19 · 24379 · 343338641215057_<15> · 14527279412530452112203563_<26> · C135

C135 = P35 · P37 · P65

P35 = 12944269695080218973540346309891121_<35>

P37 = 1416113441407550287859867356704288481_<37>

P65 = 11806412269556885461858705275762974929092425790557887195787409499_<65>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3581677858
Step 1 took 3904ms
Step 2 took 3752ms
********** Factor found in step 2: 12944269695080218973540346309891121
Found probable prime factor of 35 digits: 12944269695080218973540346309891121
Composite cofactor 16719219109718527335685783927057161772888685825706508837251201359866567487929188872684878878975681019 has 101 digits
#
# then gnfs-101
#
Number: 50009_179
N=16719219109718527335685783927057161772888685825706508837251201359866567487929188872684878878975681019
  ( 101 digits)
Divisors found:
 r1=1416113441407550287859867356704288481
 r2=11806412269556885461858705275762974929092425790557887195787409499
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.736).
Factorization parameters were as follows:
name: 50009_179
n: 16719219109718527335685783927057161772888685825706508837251201359866567487929188872684878878975681019
skew: 6884.51
# norm 1.80e+14
c5: 59040
c4: 1540165672
c3: 1429662248062
c2: -5353850835984479
c1: -182843902268221600200
c0: 165393405335782266813485
# alpha -6.13
Y1: 32528906267
Y0: -12314249336339487954
# Murphy_E 3.05e-09
# M 2698677695487388832340123883243887723436621037793473171541586333935792498476842577280377936006176964
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1500001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 220160 x 220404
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 3.10 hours.

7·10¹⁷⁵-3 = 6(9)₁₇₄7_<176> = 23 · 29 · 1945849999_<10> · 2698778453724854253232121_<25> · C140

C140 = P29 · P111

P29 = 35295282339376795682867577001_<29>

P111 = 566211848432648253496266298077169810224298129799525026373713085611725821142446735214380281508918974507036807529_<111>

(2·10¹⁹⁶+43)/9 = (2)₁₉₅7_<196> = 17 · 110603 · 230233 · 3753551 · 6394253894512031_<16> · 27649217431563171213901_<23> · C139

C139 = P32 · P107

P32 = 81138414297630889430251145739989_<32>

P107 = 95337229664362344632451111019572229885524724831347194268019251865868739229410557616425622800014970494708241_<107>

(82·10¹⁸³+71)/9 = 9(1)₁₈₂9_<184> = 11 · 23 · 163 · 197 · 3274339280356427_<16> · 3335041541237212183843_<22> · C141

C141 = P38 · P103

P38 = 41480030672124309263512074376549364243_<38>

P103 = 2475899410245908517561043105208184696388776127548286273247484238023102962064108404636745176885425655191_<103>

(4·10¹⁷⁹+23)/9 = (4)₁₇₈7_<179> = 13 · 1129 · 1068209353_<10> · 4580453449268690402279557_<25> · C141

C141 = P37 · P105

P37 = 4350096229342528260116893990630301077_<37>

P105 = 142271029265416575875338086225461356162340830827056279182201282910066824179702907590984231521837085273683_<105>

(4·10¹⁷⁷+11)/3 = 1(3)₁₇₆7_<178> = 7 · 17 · 2441851757_<10> · 344843269369_<12> · 17322469213591_<14> · C141

C141 = P31 · P111

P31 = 1310834231603013835472766122929_<31>

P111 = 585993979754822263932541066661484381757424330937782473588984197513512092586728761605870328163008363244704467429_<111>

7·10¹⁷⁶+1 = 7(0)₁₇₅1_<177> = 71 · 8573471 · 805581827 · 284095648103_<12> · 8413635332369_<13> · C135

C135 = P34 · P37 · P65

P34 = 1772201439222433182847040694601969_<34>

P37 = 5991250959750702185019813412247610703_<37>

P65 = 56246368184668911475605266297942702738852214410521358324628735307_<65>

Aug 5, 2008 (6th)

By Sinkiti Sibata / GGNFS

(23·10¹³¹+13)/9 = 2(5)₁₃₀7_<132> = 61 · 419 · 1365289 · 9462091313_<10> · C111

C111 = P50 · P62

P50 = 29649551865195893964260815165749888504612732839393_<50>

P62 = 26104273375312135035055511375576115903150531981672897300414523_<62>

Number: 25557_131
N=773980007344569427881399921940724281760206790024553518841461247679190814482147572814023669633379467193683704539
  ( 111 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=29649551865195893964260815165749888504612732839393 (pp50)
 r2=26104273375312135035055511375576115903150531981672897300414523 (pp62)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 6.72 hours.
Scaled time: 3.17 units (timescale=0.472).
Factorization parameters were as follows:
name: 25557_131
n: 773980007344569427881399921940724281760206790024553518841461247679190814482147572814023669633379467193683704539
m: 100000000000000000000000000
c5: 230
c0: 13
skew: 0.56
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1100001)
Primes: RFBsize:63951, AFBsize:63408, largePrimes:1478490 encountered
Relations: rels:1453525, finalFF:144533
Max relations in full relation-set: 28
Initial matrix: 127426 x 144533 with sparse part having weight 11750424.
Pruned matrix : 123058 x 123759 with weight 8687465.
Total sieving time: 6.39 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 6.72 hours.
 --------- CPU info (if available) ----------

Aug 5, 2008 (5th)

By Sinkiti Sibata / GGNFS

(23·10¹²⁷+13)/9 = 2(5)₁₂₆7_<128> = 3² · 17 · 89 · 550127 · 15161969 · C111

C111 = P35 · P77

P35 = 13962671799159788912176788641978303_<35>

P77 = 16114498505559821766333917333370677084205143841791033427451207993209327515189_<77>

Number: 25557_127
N=225001453841182686270734845345767763482321035145545368687777587106504220899885180817018327157682834904240944267
  ( 111 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=13962671799159788912176788641978303 (pp35)
 r2=16114498505559821766333917333370677084205143841791033427451207993209327515189 (pp77)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.50 hours.
Scaled time: 3.52 units (timescale=0.782).
Factorization parameters were as follows:
name: 25557_127
n: 225001453841182686270734845345767763482321035145545368687777587106504220899885180817018327157682834904240944267
m: 10000000000000000000000000
c5: 2300
c0: 13
skew: 0.36
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64288, largePrimes:1480412 encountered
Relations: rels:1464229, finalFF:157594
Max relations in full relation-set: 28
Initial matrix: 128306 x 157594 with sparse part having weight 11631696.
Pruned matrix : 119660 x 120365 with weight 7163626.
Total sieving time: 4.35 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.50 hours.
 --------- CPU info (if available) ----------

(23·10¹¹⁹+13)/9 = 2(5)₁₁₈7_<120> = 280032133 · 16397289482959744157_<20> · C92

C92 = P44 · P48

P44 = 96993982263781813971167216661363091550858813_<44>

P48 = 573800079124972352177927819974219178800933411769_<48>

Number: 25557_119
N=55655154697604169806028078164116264032438483353137260828203497020024427432838560478111570197
  ( 92 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=96993982263781813971167216661363091550858813 (pp44)
 r2=573800079124972352177927819974219178800933411769 (pp48)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 3.02 hours.
Scaled time: 1.43 units (timescale=0.472).
Factorization parameters were as follows:
name: 25557_119
n: 55655154697604169806028078164116264032438483353137260828203497020024427432838560478111570197
m: 1000000000000000000000000
c5: 23
c0: 130
skew: 1.41
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:63533, largePrimes:2228706 encountered
Relations: rels:2377123, finalFF:258771
Max relations in full relation-set: 28
Initial matrix: 112696 x 258771 with sparse part having weight 25229340.
Pruned matrix : 86971 x 87598 with weight 6306762.
Total sieving time: 2.82 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.02 hours.
 --------- CPU info (if available) ----------

(23·10¹²⁸+13)/9 = 2(5)₁₂₇7_<129> = 83 · 920849 · 1030201 · 24436253 · C108

C108 = P34 · P74

P34 = 7593900515955794514613493406731977_<34>

P74 = 17490302870130540569518879363200396131415419419892069960190397320321006691_<74>

Number: 25557_128
N=132819619989707425690297221931201401167919173092980715094496396268807687443328293733002387041546989060658107
  ( 108 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=7593900515955794514613493406731977 (pp34)
 r2=17490302870130540569518879363200396131415419419892069960190397320321006691 (pp74)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.15 hours.
Scaled time: 4.00 units (timescale=0.778).
Factorization parameters were as follows:
name: 25557_128
n: 132819619989707425690297221931201401167919173092980715094496396268807687443328293733002387041546989060658107
m: 10000000000000000000000000
c5: 23000
c0: 13
skew: 0.22
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1050001)
Primes: RFBsize:63951, AFBsize:63628, largePrimes:1510729 encountered
Relations: rels:1505111, finalFF:164740
Max relations in full relation-set: 28
Initial matrix: 127646 x 164740 with sparse part having weight 12961919.
Pruned matrix : 117224 x 117926 with weight 7554883.
Total sieving time: 4.99 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.15 hours.
 --------- CPU info (if available) ----------

Aug 5, 2008 (4th)

By Serge Batalov / GMP-ECM, Msieve

(23·10¹¹⁵+13)/9 = 2(5)₁₁₄7_<116> = 3 · 1590765569_<10> · C106

C106 = P41 · P66

P41 = 25989819434052094099886238319121888616577_<41>

P66 = 206041464084329287564612835952629247644214995705639504013510860663_<66>

Number: 25557_115
N=5354980447479447877412865049581996904861673252948384953709366158979594131835599541140507623419977679010551
  ( 106 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=25989819434052094099886238319121888616577
 r2=206041464084329287564612835952629247644214995705639504013510860663
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.204).
Factorization parameters were as follows:
n: 5354980447479447877412865049581996904861673252948384953709366158979594131835599541140507623419977679010551
Y1: 1
Y0: -100000000000000000000000
c5: 23
c0: 13
skew: 0.89
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 400001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 72538 x 72764
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000

total time: 0.75 hours.

(23·10¹⁷⁶+13)/9 = 2(5)₁₇₅7_<177> = 4567 · C173

C173 = P31 · C143

P31 = 1370850223332403243997479287923_<31>

C143 = [40819182982692297903201245645427546973252118080333946991250896508476928198768851369315568750971333405347653894783379624671217671886324833679377_<143>]

(23·10¹¹⁷+13)/9 = 2(5)₁₁₆7_<118> = 67 · 1069 · C113

C113 = P37 · P77

P37 = 1088529921713480335664455585324748987_<37>

P77 = 32778754467867428138643680913471158736943850231412323569027407329166201609257_<77>

Number: 25557_117
N=35680655034773125330627808882000971134350076868541607522102614461214352310787813349839514618984900877588980572659
  ( 113 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=1088529921713480335664455585324748987
 r2=32778754467867428138643680913471158736943850231412323569027407329166201609257
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.287).
Factorization parameters were as follows:
n: 35680655034773125330627808882000971134350076868541607522102614461214352310787813349839514618984900877588980572659
Y1: 1
Y0: -100000000000000000000000
c5: 2300
c0: 13
skew: 0.36
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 500001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 115127 x 115347
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,118,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000

total time: 1.00 hours.

(23·10¹⁴⁰+13)/9 = 2(5)₁₃₉7_<141> = 383 · 37571 · 60029 · 323957 · 543259 · 1169334002020951974997922683_<28> · C91

C91 = P41 · P50

P41 = 97007064866694932760814312825637589612503_<41>

P50 = 14819598862760793777831985088043035801154127559863_<50>

Mon Aug  4 20:04:31 2008  Msieve v. 1.36
Mon Aug  4 20:04:31 2008  random seeds: 3716472c 5ff7c185
Mon Aug  4 20:04:31 2008  factoring 1437605788178234778599655579349905454752457659865333975172464249220608012494047083105767089 (91 digits)
Mon Aug  4 20:04:32 2008  no P-1/P+1/ECM available, skipping
Mon Aug  4 20:04:32 2008  commencing quadratic sieve (91-digit input)
Mon Aug  4 20:04:32 2008  using multiplier of 1
Mon Aug  4 20:04:32 2008  using 64kb Opteron sieve core
Mon Aug  4 20:04:32 2008  sieve interval: 18 blocks of size 65536
Mon Aug  4 20:04:32 2008  processing polynomials in batches of 6
Mon Aug  4 20:04:32 2008  using a sieve bound of 1650079 (62353 primes)
Mon Aug  4 20:04:32 2008  using large prime bound of 145206952 (27 bits)
Mon Aug  4 20:04:32 2008  using double large prime bound of 491560817809336 (42-49 bits)
Mon Aug  4 20:04:32 2008  using trial factoring cutoff of 49 bits
Mon Aug  4 20:04:32 2008  polynomial 'A' values have 12 factors
Mon Aug  4 21:17:32 2008  62761 relations (17292 full + 45469 combined from 684074 partial), need 62449
Mon Aug  4 21:17:33 2008  begin with 701366 relations
Mon Aug  4 21:17:33 2008  reduce to 151346 relations in 10 passes
Mon Aug  4 21:17:33 2008  attempting to read 151346 relations
Mon Aug  4 21:17:35 2008  recovered 151346 relations
Mon Aug  4 21:17:35 2008  recovered 125083 polynomials
Mon Aug  4 21:17:35 2008  attempting to build 62761 cycles
Mon Aug  4 21:17:35 2008  found 62761 cycles in 6 passes
Mon Aug  4 21:17:35 2008  distribution of cycle lengths:
Mon Aug  4 21:17:35 2008     length 1 : 17292
Mon Aug  4 21:17:35 2008     length 2 : 12526
Mon Aug  4 21:17:35 2008     length 3 : 11168
Mon Aug  4 21:17:35 2008     length 4 : 8120
Mon Aug  4 21:17:35 2008     length 5 : 5621
Mon Aug  4 21:17:35 2008     length 6 : 3514
Mon Aug  4 21:17:35 2008     length 7 : 2067
Mon Aug  4 21:17:35 2008     length 9+: 2453
Mon Aug  4 21:17:35 2008  largest cycle: 20 relations
Mon Aug  4 21:17:35 2008  matrix is 62353 x 62761 (15.8 MB) with weight 3643919 (58.06/col)
Mon Aug  4 21:17:35 2008  sparse part has weight 3643919 (58.06/col)
Mon Aug  4 21:17:36 2008  filtering completed in 3 passes
Mon Aug  4 21:17:36 2008  matrix is 57751 x 57815 (14.6 MB) with weight 3369339 (58.28/col)
Mon Aug  4 21:17:36 2008  sparse part has weight 3369339 (58.28/col)
Mon Aug  4 21:17:36 2008  saving the first 48 matrix rows for later
Mon Aug  4 21:17:37 2008  matrix is 57703 x 57815 (9.2 MB) with weight 2595919 (44.90/col)
Mon Aug  4 21:17:37 2008  sparse part has weight 1846004 (31.93/col)
Mon Aug  4 21:17:37 2008  matrix includes 64 packed rows
Mon Aug  4 21:17:37 2008  using block size 23126 for processor cache size 1024 kB
Mon Aug  4 21:17:37 2008  commencing Lanczos iteration
Mon Aug  4 21:17:37 2008  memory use: 8.4 MB
Mon Aug  4 21:18:00 2008  lanczos halted after 914 iterations (dim = 57701)
Mon Aug  4 21:18:00 2008  recovered 16 nontrivial dependencies
Mon Aug  4 21:18:01 2008  prp41 factor: 97007064866694932760814312825637589612503
Mon Aug  4 21:18:01 2008  prp50 factor: 14819598862760793777831985088043035801154127559863

Mon Aug  4 21:18:01 2008  elapsed time 01:13:30

(23·10¹³⁰+13)/9 = 2(5)₁₂₉7_<131> = 3 · 7 · 1911853405367337457_<19> · C111

C111 = P45 · P67

P45 = 273621240879818118935599372820806523689400881_<45>

P67 = 2326278114029065603348744181689416700387279243410338996591662514801_<67>

Number: 25557_130
N=636519104192195960835737776365832516184927682124212998818556622451324575858446919445568813294192981881484939681
  ( 111 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=273621240879818118935599372820806523689400881
 r2=2326278114029065603348744181689416700387279243410338996591662514801
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.313).
Factorization parameters were as follows:
n: 636519104192195960835737776365832516184927682124212998818556622451324575858446919445568813294192981881484939681
Y1: 1
Y0: -100000000000000000000000000
c5: 23
c0: 13
skew: 0.89
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [400000, 800001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 103517 x 103765
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 1.75 hours.

(23·10¹³⁸+13)/9 = 2(5)₁₃₇7_<139> = 12307410569462018609_<20> · C120

C120 = P30 · P34 · P57

P30 = 507750308517183330272789653297_<30>

P34 = 3474089539882015715274674665350059_<34>

P57 = 117713814807586006583552288564604273462593769995433243151_<57>

#by ECM
Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3165820906
Step 1 took 11745ms
Step 2 took 11152ms
********** Factor found in step 2: 507750308517183330272789653297
Found probable prime factor of 30 digits: 507750308517183330272789653297
Composite cofactor 408948332722643277879927696871940117264041855347969617854343237250222908088195835079195909 has 90 digits
#
# then stopped the running snfs-138, and did QS-90 (with Msieve-1.36)
#
Mon Aug  4 22:13:03 2008  Msieve v. 1.36
Mon Aug  4 22:13:03 2008  random seeds: bac18a9e 3a47e97e
Mon Aug  4 22:13:03 2008  factoring 408948332722643277879927696871940117264041855347969617854343237250222908088195835079195909 (90 digits)
Mon Aug  4 22:13:04 2008  no P-1/P+1/ECM available, skipping
Mon Aug  4 22:13:04 2008  commencing quadratic sieve (90-digit input)
Mon Aug  4 22:13:04 2008  using multiplier of 11
Mon Aug  4 22:13:04 2008  using 64kb Opteron sieve core
Mon Aug  4 22:13:04 2008  sieve interval: 18 blocks of size 65536
Mon Aug  4 22:13:04 2008  processing polynomials in batches of 6
Mon Aug  4 22:13:04 2008  using a sieve bound of 1578193 (60000 primes)
Mon Aug  4 22:13:04 2008  using large prime bound of 126255440 (26 bits)
Mon Aug  4 22:13:04 2008  using double large prime bound of 382164232656720 (42-49 bits)
Mon Aug  4 22:13:04 2008  using trial factoring cutoff of 49 bits
Mon Aug  4 22:13:04 2008  polynomial 'A' values have 12 factors
Mon Aug  4 23:37:53 2008  60097 relations (15999 full + 44098 combined from 632948 partial), need 60096
Mon Aug  4 23:37:53 2008  begin with 648947 relations
Mon Aug  4 23:37:54 2008  reduce to 146281 relations in 10 passes
Mon Aug  4 23:37:54 2008  attempting to read 146281 relations
Mon Aug  4 23:37:55 2008  recovered 146281 relations
Mon Aug  4 23:37:55 2008  recovered 125898 polynomials
Mon Aug  4 23:37:55 2008  attempting to build 60097 cycles
Mon Aug  4 23:37:55 2008  found 60097 cycles in 6 passes
Mon Aug  4 23:37:55 2008  distribution of cycle lengths:
Mon Aug  4 23:37:55 2008     length 1 : 15999
Mon Aug  4 23:37:55 2008     length 2 : 11696
Mon Aug  4 23:37:55 2008     length 3 : 10617
Mon Aug  4 23:37:55 2008     length 4 : 7985
Mon Aug  4 23:37:55 2008     length 5 : 5632
Mon Aug  4 23:37:55 2008     length 6 : 3524
Mon Aug  4 23:37:55 2008     length 7 : 2118
Mon Aug  4 23:37:55 2008     length 9+: 2526
Mon Aug  4 23:37:55 2008  largest cycle: 23 relations
Mon Aug  4 23:37:56 2008  matrix is 60000 x 60097 (15.8 MB) with weight 3662551 (60.94/col)
Mon Aug  4 23:37:56 2008  sparse part has weight 3662551 (60.94/col)
Mon Aug  4 23:37:56 2008  filtering completed in 3 passes
Mon Aug  4 23:37:56 2008  matrix is 56117 x 56181 (14.9 MB) with weight 3461219 (61.61/col)
Mon Aug  4 23:37:56 2008  sparse part has weight 3461219 (61.61/col)
Mon Aug  4 23:37:57 2008  saving the first 48 matrix rows for later
Mon Aug  4 23:37:57 2008  matrix is 56069 x 56181 (9.9 MB) with weight 2726773 (48.54/col)
Mon Aug  4 23:37:57 2008  sparse part has weight 2024982 (36.04/col)
Mon Aug  4 23:37:57 2008  matrix includes 64 packed rows
Mon Aug  4 23:37:57 2008  using block size 22472 for processor cache size 1024 kB
Mon Aug  4 23:37:57 2008  commencing Lanczos iteration
Mon Aug  4 23:37:57 2008  memory use: 8.6 MB
Mon Aug  4 23:38:21 2008  lanczos halted after 888 iterations (dim = 56069)
Mon Aug  4 23:38:21 2008  recovered 19 nontrivial dependencies
Mon Aug  4 23:38:22 2008  prp34 factor: 3474089539882015715274674665350059
Mon Aug  4 23:38:22 2008  prp57 factor: 117713814807586006583552288564604273462593769995433243151

elapsed time 01:25:19

(23·10¹³⁶+13)/9 = 2(5)₁₃₅7_<137> = 3³ · 7 · 260511659 · C126

C126 = P35 · P92

P35 = 35617088186151596018674980636783041_<35>

P92 = 14572630267115638925813556562718250466819225757428431015167830009407651750016178741452169627_<92>

Number: 25557_136
N=519034657328039600210553006352615630158346372995501019534847688559781900082053191302111498978559137446093228922297791128895707
  ( 126 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=35617088186151596018674980636783041
 r2=14572630267115638925813556562718250466819225757428431015167830009407651750016178741452169627
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
n: 519034657328039600210553006352615630158346372995501019534847688559781900082053191302111498978559137446093228922297791128895707
Y1: 1
Y0: -1000000000000000000000000000
c5: 230
c0: 13
skew: 0.56
type: snfsFactor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [500000, 1625001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 146625 x 146858
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000

total time: 3.00 hours.

(17·10¹⁸⁹+1)/9 = 1(8)₁₈₈9_<190> = 59 · 71 · 1617391 · 12524207 · 3607698986231981_<16> · 370127884625109553441_<21> · C137

C137 = P31 · P36 · P71

P31 = 1756706333511604963524042522871_<31>

P36 = 668814360582016023721300568011912207_<36>

P71 = 14188743452434643875801927553951755349395681019380535143529908397628329_<71>

(23·10¹⁷¹+13)/9 = 2(5)₁₇₀7_<172> = 47 · 89 · 224293807 · C160

C160 = P30 · P130

P30 = 420665653593367124551131807829_<30>

P130 = 6475049984190779352600188491788559885012137408499137509465838676005670925080692961463905247359951019310758928110457579498055421593_<130>

(23·10¹³⁷+13)/9 = 2(5)₁₃₆7_<138> = 1193 · C135

C135 = P53 · P82

P53 = 24825801948309814186567834093884243731110843768686833_<53>

P82 = 8628625030368435551953354953972853797741901598228835301547475858040231276993102253_<82>

Number: 25557_137
N=214212536090155536928378504237682779174816056626618236006333240197448076743969451429635838688646735587221756542795939275402812703734749
  ( 135 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=24825801948309814186567834093884243731110843768686833
 r2=8628625030368435551953354953972853797741901598228835301547475858040231276993102253
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.946).
Factorization parameters were as follows:
n: 214212536090155536928378504237682779174816056626618236006333240197448076743969451429635838688646735587221756542795939275402812703734749
Y1: 1
Y0: -1000000000000000000000000000
c5: 2300
c0: 13
skew: 0.36
type: snfsFactor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [500000, 2450001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 172185 x 172417
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.25 hours.

(23·10¹⁹¹+13)/9 = 2(5)₁₉₀7_<192> = 17 · 61 · 600577511 · C180

C180 = P33 · P147

P33 = 581223556439835774287202811285249_<33>

P147 = 705983086990766454288312162598464346964091589028038512031272672754584909109068532226533435641467045849482264569501155389959859487896366390090168799_<147>

Aug 5, 2008 (3rd)

Factorizations of 255...557 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Aug 5, 2008 (2nd)

By Serge Batalov / GMP-ECM

(8·10¹⁷⁹-17)/9 = (8)₁₇₈7_<179> = 3² · 193 · 15809 · 552241 · 1674912378443233_<16> · 3436763031126603253_<19> · C133

C133 = P30 · P103

P30 = 681730178728744701011924498497_<30>

P103 = 1493689791486146713478996194570842049379770863848290072870963693810359525801102136426038074592658672243_<103>

(43·10¹⁸⁷-7)/9 = 4(7)₁₈₇_<188> = 157 · 167 · 857 · 398681 · 15621247 · 153367745358551_<15> · 38912178926543071_<17> · C137

C137 = P33 · P105

P33 = 563109820432391065038572286966239_<33>

P105 = 101595641665225801482855126843463077933095944176748411552258185690480521896642701682667226673118857591243_<105>

(67·10¹⁷⁹+23)/9 = 7(4)₁₇₈7_<180> = 3 · 11 · 127721089 · 12689264677_<11> · 11278525964270232939888763_<26> · C136

C136 = P31 · P105

P31 = 1503577311371110536299145909067_<31>

P105 = 820807237203065576049616360230827773873672515282532295733748443458210584183593438540403638917367057872443_<105>

(10¹⁸¹+11)/3 = (3)₁₈₀7_<181> = 7 · 17 · 37426643 · 314567063 · 5853728102221_<13> · 954343568843543_<15> · C135

C135 = P30 · P33 · P74

P30 = 105981447101665873606353102413_<30>

P33 = 173528881158073536221773584328933_<33>

P74 = 23157877513186904238703485740025834562034755077344962107936455349631017881_<74>

Aug 5, 2008

By matsui / GGNFS

(2·10¹⁸⁵+1)/3 = (6)₁₈₄7_<185> = 21143 · C181

C181 = P81 · P100

P81 = 900453601285265582520047067012732576071069650788340131680486043607858213615331267_<81>

P100 = 3501714962000928317461759364309288753778079923142299914269367242522743703784043573496181765706887407_<100>

N=3153131848208232827255671695911964558798026139463021646250137949518359110186192435636696148449447413643601507197023443535291428211070645919059105456494663324346907565939869775654669
  ( 181 digits)
SNFS difficulty: 185 digits.
Divisors found:
 r1=900453601285265582520047067012732576071069650788340131680486043607858213615331267 (pp81)
 r2=3501714962000928317461759364309288753778079923142299914269367242522743703784043573496181765706887407 (pp100)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 298.03 hours.
Scaled time: 848.78 units (timescale=2.848).
Factorization parameters were as follows:
n: 3153131848208232827255671695911964558798026139463021646250137949518359110186192435636696148449447413643601507197023443535291428211070645919059105456494663324346907565939869775654669
m: 10000000000000000000000000000000000000
c5: 2
c0: 1
skew: 0.87
type: snfs

Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 10800001)
Primes: RFBsize:501962, AFBsize:501936, largePrimes:6574782 encountered
Relations: rels:7037035, finalFF:1136338
Max relations in full relation-set: 28
Initial matrix: 1003963 x 1136338 with sparse part having weight 79195228.
Pruned matrix : 896127 x 901210 with weight 62006881.
Total sieving time: 291.34 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 6.33 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,185,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 298.03 hours.

Aug 4, 2008 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(23·10¹⁶⁴-41)/9 = 2(5)₁₆₃1_<165> = 17 · 14783 · 6954611 · C153

C153 = P39 · P40 · P75

P39 = 127092897952617830861128387381793123491_<39>

P40 = 5984338350534202483602163442377911766177_<40>

P75 = 192248766671982198740268835298401979782919136451461142361013167032834159033_<75>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 146218049130642441234495363713913754675210966706539923532522558284754745799883843367386080454093351306607004960263989647786921657401273701595788872021931 (153 digits)
Using B1=4366000, B2=8561918830, polynomial Dickson(6), sigma=1627898278
Step 1 took 52484ms
Step 2 took 17660ms
********** Factor found in step 2: 5984338350534202483602163442377911766177
Found probable prime factor of 40 digits: 5984338350534202483602163442377911766177
Composite cofactor 24433452884158869463121391219856044588647399397141519895148690044715795722505127594463645181432631902409302144203 has 113 digits

Number: n
N=24433452884158869463121391219856044588647399397141519895148690044715795722505127594463645181432631902409302144203
  ( 113 digits)
Divisors found:

Mon Aug  4 22:19:36 2008  prp39 factor: 127092897952617830861128387381793123491
Mon Aug  4 22:19:36 2008  prp75 factor: 192248766671982198740268835298401979782919136451461142361013167032834159033
Mon Aug  4 22:19:36 2008  elapsed time 00:39:09 (Msieve 1.36)

Version: GGNFS-0.77.1-20050930-k8
Total time: 21.39 hours.
Scaled time: 17.93 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_2_5_163_1
n: 24433452884158869463121391219856044588647399397141519895148690044715795722505127594463645181432631902409302144203
skew: 22181.66
# norm 3.00e+15
c5: 92520
c4: -6744153222
c3: -45832076939516
c2: 3355354381773925699
c1: 26376496291199123709754
c0: 55897100324407256183969376
# alpha -5.88
Y1: 32923335533
Y0: -3050351678222518898863
# Murphy_E 7.42e-10
# M 24431814637208274680734783426277441947002447691196750391363360992421760360967572735589642666701638520266722683606
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1500001)
Primes: RFBsize:250150, AFBsize:249815, largePrimes:6780508 encountered
Relations: rels:6430342, finalFF:544879
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 21.19 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 21.39 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

(2·10¹⁹¹+61)/9 = (2)₁₉₀9_<191> = 17 · C190

C190 = P35 · C156

P35 = 10852771508056059135206234116514171_<35>

C156 = [120447531905866413108914601272250048343140105606651999784883636087529705448811959016585189877632383393661040361642471439530256902961775524681574643452982847_<156>]

Aug 4, 2008 (2nd)

By Serge Batalov / GMP-ECM, pol51, Msieve

(43·10¹⁹³-7)/9 = 4(7)₁₉₃_<194> = 919 · 445461301538551_<15> · 893558958002816352193_<21> · 4284288203992414224517391893_<28> · C128

C128 = P33 · P96

P33 = 150826515975256399552220025155339_<33>

P96 = 202125386244925252749734893061275680905056146225460546218343135651883483612166284107990237484503_<96>

(10¹⁸⁴+71)/9 = (1)₁₈₃9_<184> = 3 · 29 · 199 · 1697 · 919179139 · 1299592780666421554668910151_<28> · 9343168720031962523222369884197334253_<37> · C103

C103 = P40 · P64

P40 = 1586931314118813407557567732512708559877_<40>

P64 = 2135224521200188890616493683567821754642212756737532735710790131_<64>

Number: 11119_184
N=3388454655366929914498505057165802657142065274822407340167831244985945664751645516070076150034794173887
  ( 103 digits)
Divisors found:
 r1=1586931314118813407557567732512708559877
 r2=2135224521200188890616493683567821754642212756737532735710790131
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.316).
Factorization parameters were as follows:
name: 11119_184
n: 3388454655366929914498505057165802657142065274822407340167831244985945664751645516070076150034794173887
skew: 31960.24
# norm 9.10e+13
c5: 480
c4: -138581412
c3: -2970890933000
c2: 125334112112828449
c1: 728602337992886243758
c0: -14786800388206937397895095
# alpha -5.22
Y1: 7082309663
Y0: -93272580525981859492
# Murphy_E 2.34e-09
# M 3088295724384864144699871818544359448147530931965530510173465076385594779988601548584947108074515787463
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1850001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 273090 x 273338
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000

total time: 5.90 hours.

(16·10¹⁹⁹-43)/9 = 1(7)₁₉₈3_<200> = 13² · 197 · 41046419 · 3191682259_<10> · 200516406221467309_<18> · C161

C161 = P40 · P56 · P66

P40 = 4390892260316240532684572528091436747139_<40>

P56 = 23900525030689996426582940228851626653088952483784974829_<56>

P66 = 193695479051958499150090176237277153417415656132662983103787245979_<66>

# first ECM
#
Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1416775493
Step 1 took 24354ms
Step 2 took 19253ms
********** Factor found in step 2: 4390892260316240532684572528091436747139
Found probable prime factor of 40 digits: 4390892260316240532684572528091436747139
Composite cofactor 4629423645412823967849086103516114227366096388384060554523226454110605387301721011151681397173112326997089098521746462591 has 121 digits
#
# then Msieve-1.36/gnfs-121
#
Number: 17773_199
N=4629423645412823967849086103516114227366096388384060554523226454110605387301721011151681397173112326997089098521746462591
  ( 121 digits)
Divisors found:
 r1=23900525030689996426582940228851626653088952483784974829
 r2=193695479051958499150090176237277153417415656132662983103787245979
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.299).
Factorization parameters were as follows:
name: 17773_199
n: 4629423645412823967849086103516114227366096388384060554523226454110605387301721011151681397173112326997089098521746462591
skew: 43909.78
# norm 6.12e+16
c5: 13800
c4: 29054540302
c3: -1619554790749659
c2: -70244931498683416923
c1: 55355974140314250897651
c0: 1392762997799671933665557405
# alpha -5.70
Y1: 9197936842171
Y0: -201892988572876655833536
# Murphy_E 2.30e-10
# M 4486796550059614013416217299982389050995435682256387198880252966082610771759153383949597551122257473790454129900955193894
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 9500001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 830699 x 830947
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.5,2.5,100000

total time: 2.5 days

(16·10²¹⁴-61)/9 = 1(7)₂₁₃1_<215> = 13 · 863 · 18661 · 369819256019_<12> · 584833068852155422531_<21> · 4516565897012282883697690057920883_<34> · C140

C140 = P53 · P88

P53 = 16814750565378686502204377710527501824320586545945603_<53>

P88 = 5169733908173540534007921788791377675334362229095173255753307146459503895142109161685829_<88>

# gnfs,140
# pol51 polynomial selection time: 2 or 3 days (while ECM was run for a week or two)
#
Number: 17771_214
N=86927786155318407263273710266523202940690097929584601977940218641236715258445415008714444666356629075405450626239173034367866144188409959887
  ( 140 digits)
Divisors found:
 r1=16814750565378686502204377710527501824320586545945603
 r2=5169733908173540534007921788791377675334362229095173255753307146459503895142109161685829
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.735).
Factorization parameters were as follows:
name: 17771_214
n: 86927786155318407263273710266523202940690097929584601977940218641236715258445415008714444666356629075405450626239173034367866144188409959887
skew: 267143.89
# norm 1.97e+19
c5: 698880
c4: -1489690686532
c3: -176616113976832028
c2: 103006324549653347616719
c1: 3712851734270791622017222272
c0: -432658741100514020527612440105864
# alpha -6.29
Y1: 13968147388773457
Y0: -659105787539946137530863055
# Murphy_E 1.94e-11
# M 49579079600743972072443184556436418407617530021357634358500716158197635856463288739352084719618552259657530257163309696054721363836328031333
type: gnfs
rlim: 12000000
alim: 12000000
lpbr: 27
lpba: 27
mfbr: 54
mfba: 54
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 12000000/12000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved rational special-q in [6000000, 37700001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: 16715895 relations 
#### (beware of huge redundancy! up to 25-30% in the end)
12175171 unique relations and about 10717437 large ideals
Max relations in full relation-set: 20
Initial matrix:
Pruned matrix : 2296340 x 2296588 (this one, Lanczos = 31hrs)
Pruned matrix : 1881104 x 1881352 (with most oversieving, Lanczos = 15hrs, -> 
...Sun Aug  3 03:17:51 2008  lanczos error: only trivial dependencies found !! tried twice)
Pruned matrix : 2052464 x 2052685 (alternative run with oversieving and pruning, Lanczos = 19hrs, still running for studying purposes)

Total sieving time: 17 days
Total relation processing time: 2.00 hours.
Matrix solve time: 31.00 hours.
Time per square root: 1.60 hours. * 3 deps
Prototype def-par.txt line would be:
gnfs,139,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,12000000,12000000,27,27,54,54,2.6,2.6,100000

total time: 19 days

# in retrospect, obervations - rlim/alim should be higher still 
# 28 bit would have been probably better in terms of redundancy of sieving

Note: C140 is the largest composite number factored by GNFS so far in our tables.

Aug 4, 2008

By Tyler Cadigan / Msieve, GGNFS

(5·10¹⁹⁸-11)/3 = 1(6)₁₉₇3_<199> = 17 · 73 · 14417612748337_<14> · 15591863092514077_<17> · 2050925281672230869_<19> · 798492457907659976598191_<24> · C124

C124 = P59 · P65

P59 = 58029655586752866277654340982152770761209260744213665747727_<59>

P65 = 62865872733823391060391929387855942847658010265702276841724324879_<65>

Number: 16663_198
N=3648084942904409231781740133863005618024633980723139006909650256997407933041732927137820715390571584310230633883275803800033
  ( 124 digits)
Divisors found:
 r1=58029655586752866277654340982152770761209260744213665747727
 r2=62865872733823391060391929387855942847658010265702276841724324879
Version: 
Total time: 82.43 hours.
Scaled time: 205.57 units (timescale=2.494).
Factorization parameters were as follows:
name: 16663_198
n: 3648084942904409231781740133863005618024633980723139006909650256997407933041732927137820715390571584310230633883275803800033
skew: 212888.11
# norm 1.22e+017
c5: 10740
c4: 7370305606
c3: -2467585952064540
c2: -248933528645380281069
c1: 34811739326102006425315528
c0: 1611754352640371786855945807871
# alpha -5.96
Y1: 22584968622799
Y0: -805768826493317965725508
# Murphy_E 1.69e-010
# M 2314935598007029659498302023408434039733754485237880886588822343019923669131832398564903343895745163314827211213456861106685
type: gnfs
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.5
alambda: 2.5
qintsize: 1000000Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [2700000, 6700001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 715840 x 716088
Total sieving time: 82.43 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5400000,5400000,27,27,51,51,2.5,2.5,
total time: 82.43 hours.
 --------- CPU info (if available) ----------

Aug 3, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(23·10¹⁶⁶-41)/9 = 2(5)₁₆₅1_<167> = 3² · C166

C166 = P72 · P94

P72 = 643496646045034314863036088356290602835699348302317420935391877062800651_<72>

P94 = 4412620003991111484688047460906035814232134281081696744784440167395589300355555901131709979989_<94>

Number: n
N=2839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839
  ( 166 digits)
SNFS difficulty: 167 digits.
Divisors found:

Sun Aug  3 15:17:18 2008  prp72 factor: 643496646045034314863036088356290602835699348302317420935391877062800651
Sun Aug  3 15:17:18 2008  prp94 factor: 4412620003991111484688047460906035814232134281081696744784440167395589300355555901131709979989
Sun Aug  3 15:17:18 2008  elapsed time 01:27:42 (Msieve 1.36)

Version: GGNFS-0.77.1-20050930-k8
Total time: 88.42 hours.
Scaled time: 74.18 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_2_5_165_1
n: 2839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839
type: snfs
deg: 5
c5: 230
c0: -41
skew: 0.71
m: 1000000000000000000000000000000000
rlim: 5800000
alim: 5800000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4600001)
Primes: RFBsize:399993, AFBsize:399420, largePrimes:5834136 encountered
Relations: rels:5996928, finalFF:828084
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 88.21 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5800000,5800000,27,27,48,48,2.5,2.5,100000
total time: 88.42 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

Aug 3, 2008 (2nd)

By suberi / GMP-ECM

(46·10¹⁶⁷-1)/9 = 5(1)₁₆₇_<168> = 70626533 · 213771611 · 38387318408683_<14> · C138

C138 = P41 · P98

P41 = 10652708041146778174216248100844005311463_<41>

P98 = 82784609590842840754482542867744143167470530984746443938052838133532893663609041186948295276030693_<98>

(46·10¹⁷⁴-1)/9 = 5(1)₁₇₄_<175> = 35159 · 58943237 · 1746625507597_<13> · C151

C151 = P30 · C121

P30 = 248922781670497343680620477691_<30>

C121 = [5672576765062949804877898588549304541456787458112679112216952341251445580533290906546230462728475408918734991394065086371_<121>]

Aug 3, 2008

By Serge Batalov / GMP-ECM, Msieve, pol51

(4·10¹⁹⁰+23)/9 = (4)₁₈₉7_<190> = 9569335559270336914133_<22> · 2204456588025119545885777787_<28> · C141

C141 = P33 · P108

P33 = 914614705542996095283314411688089_<33>

P108 = 230354111071823462818299073248460216708575614431593821351666507826249002338559777821243718681313328757074913_<108>

3·10¹⁸¹-7 = 2(9)₁₈₀3_<182> = 1936760724982998289_<19> · 68808646991249141025719_<23> · C141

C141 = P37 · P105

P37 = 1724512309637715528857993530467193207_<37>

P105 = 130537703533059377398780785440600547165396660129485394210598345885209061956376547057033455498259978403289_<105>

(16·10¹⁹⁶+11)/9 = 1(7)₁₉₅9_<197> = 10099 · 160006301767452572991787889_<27> · 888035983002108169065398017_<27> · C140

C140 = P31 · P53 · P57

P31 = 4803801617306383518347006989561_<31>

P53 = 14715761835396161314812187666323650894319358275041849_<53>

P57 = 175252263317018383575140193534337967914768654073004843553_<57>

(22·10¹⁸¹+41)/9 = 2(4)₁₈₀9_<182> = 23897095845197_<14> · 776272617318286786491553225607_<30> · C139

C139 = P34 · P36 · P69

P34 = 1769770208978296859658331890070637_<34>

P36 = 894919377524823262965410505209487619_<36>

P69 = 831993602705134771540965249704583123198561362548116161848843063999477_<69>

#ecm:
#
Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1689418823
Step 1 took 18414ms
Step 2 took 16307ms
********** Factor found in step 2: 894919377524823262965410505209487619
Found probable prime factor of 36 digits: 894919377524823262965410505209487619
Composite cofactor 1472437492128072456080341721656210925078116385346784875563765316598223832211646356703426379933261056849 has 103 digits
#
#then pol51, and Msieve/gnfs-103
#
Number: 24449_181
N=1472437492128072456080341721656210925078116385346784875563765316598223832211646356703426379933261056849
  ( 103 digits)
Divisors found:
 r1=1769770208978296859658331890070637
 r2=831993602705134771540965249704583123198561362548116161848843063999477
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.725).
Factorization parameters were as follows:
name: 24449_181
n: 1472437492128072456080341721656210925078116385346784875563765316598223832211646356703426379933261056849
skew: 12109.92
# norm 1.11e+14
c5: 13800
c4: 229021120
c3: -5546394553982
c2: 39015717440707647
c1: 265001117184500868642
c0: -1409292541606116852827712
# alpha -5.56
Y1: 57257448043
Y0: -40330119583764690079
# Murphy_E 2.48e-09
# M 555219686948494539915267439001639650635907604410780913489476571794940846402885098730478554425179319560
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1850001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 231148 x 231396
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000

total time: 4.50 hours.

(23·10¹⁸⁵+1)/3 = 7(6)₁₈₄7_<186> = 11 · 409 · 3919 · 9019884346492579823_<19> · 81540614634217442591_<20> · C140

C140 = P33 · P108

P33 = 334871162855198257095061908037933_<33>

P108 = 176547927865901998870134175492592669582800548196356188701886100127196219234273530578226419288591470033352403_<108>

(10¹⁸⁴+71)/9 = (1)₁₈₃9_<184> = 3 · 29 · 199 · 1697 · 919179139 · 1299592780666421554668910151_<28> · C140

C140 = P37 · C103

P37 = 9343168720031962523222369884197334253_<37>

C103 = [3388454655366929914498505057165802657142065274822407340167831244985945664751645516070076150034794173887_<103>]

6·10¹⁸⁹+1 = 6(0)₁₈₈1_<190> = 42589 · 5780291335866737_<16> · 107788304148617970061487122159_<30> · C141

C141 = P30 · P41 · P71

P30 = 174013302696433020274845304681_<30>

P41 = 18309085696764041534162136664724986762411_<41>

P71 = 70971393580825121102733841341176453634821357709829428898091709401554553_<71>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2803236752
Step 1 took 20722ms
Step 2 took 16429ms
********** Factor found in step 2: 174013302696433020274845304681
Found probable prime factor of 30 digits: 174013302696433020274845304681
Composite cofactor 1299421327090096537092650364554015119148292501873377738981166234391431318448786187635106425292624877709866307283 has 112 digits
#
# then Msieve/gnfs-112
#
Number: 60001_189
N=1299421327090096537092650364554015119148292501873377738981166234391431318448786187635106425292624877709866307283
  ( 112 digits)
Divisors found:
 r1=18309085696764041534162136664724986762411
 r2=70971393580825121102733841341176453634821357709829428898091709401554553
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.188).
Factorization parameters were as follows:
name: 60001_189
n: 1299421327090096537092650364554015119148292501873377738981166234391431318448786187635106425292624877709866307283
skew: 52578.04
# norm 2.72e+15
c5: 16440
c4: 1619746172
c3: -135511103262470
c2: -4014692173401370183
c1: 183805157963031787936530
c0: 1031049847200277256970651600
# alpha -5.96
Y1: 828435965947
Y0: -2396440646982282764377
# Murphy_E 7.97e-10
# M 1136488550539358265641494014969627028960530201153737973603644946454438107607609201185415837558953909792296923205
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 3550001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 437477 x 437725
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000

total time: 16.0 hours.

Aug 2, 2008 (3rd)

By Serge Batalov / GMP-ECM

(23·10¹⁹⁴+1)/3 = 7(6)₁₉₃7_<195> = 13 · 139 · 78459255911_<11> · 234102535388474561689151_<24> · C158

C158 = P32 · C126

P32 = 28755254470177769678351594744207_<32>

C126 = [803305815778793560119943241710039446370201891384089344299540163842961294333911367771016525950573017814190338673989871897500803_<126>]

(5·10¹⁹⁸-23)/9 = (5)₁₉₇3_<198> = 79 · 1787 · 92166227 · 62964716122813547478189355909_<29> · C156

C156 = P33 · C124

P33 = 119356565544646731891786102577789_<33>

C124 = [5681466871324695058688910174023721450274408912155790860885985665340075745372042729625565314195995410292414361378012735405343_<124>]

(43·10¹⁹³-7)/9 = 4(7)₁₉₃_<194> = 919 · 445461301538551_<15> · 893558958002816352193_<21> · C156

C156 = P28 · C128

P28 = 4284288203992414224517391893_<28>

C128 = [30485867797475088755064300991906426987241836546815788111296849337158228409230973644957546968604924308437984135196279273180211517_<128>]

Aug 2, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(23·10¹⁵⁴-41)/9 = 2(5)₁₅₃1_<155> = 3 · 91411 · 125717 · 99479243282099_<14> · C130

C130 = P33 · P47 · P51

P33 = 340181494077011694290357817506041_<33>

P47 = 69952169448817622365476237996541279017803003027_<47>

P51 = 313131860083472179775867830221927950460921636582587_<51>

Number: 25551_154
N=7451421490539368400745666140791923586210703006310976378376855205625717878891916365540177939686299220679430926588394932343158718809
  ( 130 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=340181494077011694290357817506041 (pp33)
 r2=69952169448817622365476237996541279017803003027 (pp47)
 r3=313131860083472179775867830221927950460921636582587 (pp51)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 57.77 hours.
Scaled time: 27.27 units (timescale=0.472).
Factorization parameters were as follows:
name: 25551_154
n: 7451421490539368400745666140791923586210703006310976378376855205625717878891916365540177939686299220679430926588394932343158718809
m: 10000000000000000000000000000000
c5: 23
c0: -410
skew: 1.78
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3000001)
Primes: RFBsize:216816, AFBsize:216777, largePrimes:5650674 encountered
Relations: rels:5572838, finalFF:509244
Max relations in full relation-set: 28
Initial matrix: 433658 x 509244 with sparse part having weight 42472284.
Pruned matrix : 400314 x 402546 with weight 29842667.
Total sieving time: 51.37 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 5.99 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 57.77 hours.
 --------- CPU info (if available) ----------

(23·10¹⁷⁹-41)/9 = 2(5)₁₇₈1_<180> = 311 · 605993 · 9486007 · 14509530323_<11> · 29282668291_<11> · 62155026673_<11> · 348398479188686501_<18> · C116

C116 = P55 · P61

P55 = 4498980788192811699189568905957540794386101261910526893_<55>

P61 = 3453371022627095076155775850110344684731257028691845350307583_<61>

Number: 25551_179
N=15536649885301064370678981856573830216220820743461352404945988973856041528897128938405796842530844335414223143329619
  ( 116 digits)
Divisors found:
 r1=4498980788192811699189568905957540794386101261910526893 (pp55)
 r2=3453371022627095076155775850110344684731257028691845350307583 (pp61)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 47.90 hours.
Scaled time: 36.41 units (timescale=0.760).
Factorization parameters were as follows:
name: 25551_179
n: 15536649885301064370678981856573830216220820743461352404945988973856041528897128938405796842530844335414223143329619
skew: 29412.77
# norm 3.98e+15
c5: 13440
c4: 7304861420
c3: -37829521335628
c2: -4586753777585773893
c1: 32509909704735860085894
c0: 381949982671101480999382968
# alpha -5.47
Y1: 523520788439
Y0: -16315113794246774390069
# Murphy_E 4.96e-10
# M 2833285247338597467203869810197414061555862670509082923762924242923193033919568095952457100773799659651415061182693
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 3630001)
Primes: RFBsize:315948, AFBsize:316793, largePrimes:7713552 encountered
Relations: rels:7941927, finalFF:902430
Max relations in full relation-set: 28
Initial matrix: 632821 x 902430 with sparse part having weight 72590726.
Pruned matrix : 404955 x 408183 with weight 39044189.
Total sieving time: 45.03 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 2.20 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 47.90 hours.
 --------- CPU info (if available) ----------

Aug 2, 2008

By Robert Backstrom / GMP-ECM

(23·10¹⁶⁹-41)/9 = 2(5)₁₆₈1_<170> = 3 · 7 · 19 · C167

C167 = P38 · P129

P38 = 99115019415880121677092502404222247027_<38>

P129 = 646208937806761842825739606924013230081780096425955573149216008366271383509656353669041781599017902484058310271913115315734810187_<129>

Aug 1, 2008 (6th)

By Robert Backstrom / GGNFS, Msieve

(82·10¹⁸⁷-1)/9 = 9(1)₁₈₇_<188> = 7 · 13 · C187

C187 = P73 · P114

P73 = 3026480116245698243462872523183807295562073549268169183952528712774717527_<73>

P114 = 330820280578284578811104218819679244326107204280567814363792995482310812487533307731049138903576211787733292120323_<114>

Number: n
N=1001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221
  ( 187 digits)
SNFS difficulty: 188 digits.
Divisors found:

Fri Aug 01 22:10:03 2008  prp73 factor: 3026480116245698243462872523183807295562073549268169183952528712774717527
Fri Aug 01 22:10:03 2008  prp114 factor: 330820280578284578811104218819679244326107204280567814363792995482310812487533307731049138903576211787733292120323
Fri Aug 01 22:10:03 2008  elapsed time 06:58:34 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 125.80 hours.
Scaled time: 258.01 units (timescale=2.051).
Factorization parameters were as follows:
name: KA_9_1_187
n: 1001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221
type: snfs
skew: 0.16
deg: 5
c5: 8200
c0: -1
m: 10000000000000000000000000000000000000
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 9300001)
Primes: RFBsize:602489, AFBsize:603036, largePrimes:10948587 encountered
Relations: rels:10948800, finalFF:1233699
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 125.35 hours.
Total relation processing time: 0.45 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,188,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,50,50,2.5,2.5,100000
total time: 125.80 hours.
 --------- CPU info (if available) ----------

Aug 1, 2008 (5th)

By Serge Batalov / Msieve

(22·10²⁰⁰-31)/9 = 2(4)₁₉₉1_<201> = C201

C201 = P53 · P70 · P79

P53 = 47713862744287860379304252114030623412334743979315223_<53>

P70 = 2395392072792774623211423837351600973074529935809359597689484971362983_<70>

P79 = 2138744897728437264421864974178897354836969223259709418858727405909337720973849_<79>

# ok, dudes! If there's a thing called a nice split, 
# there must be a thing called an ugly split. Well, it's OK. 
# Doing a full 43M ECM wouldn't have helped -- 
# SNFS-201 is easier than GNFS-149
#
# C201 = P53 . P70 . P79   (no smaller factors!)
#
# plain SNFS, 29-bit LPs, 1 CPU, 2Gb of memory, 23 days
#
Number: 24441_200
N=244444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441
  ( 201 digits)
SNFS difficulty: 201 digits.
Divisors found:
 r1=47713862744287860379304252114030623412334743979315223
 r2=2395392072792774623211423837351600973074529935809359597689484971362983
 r3=2138744897728437264421864974178897354836969223259709418858727405909337720973849
Version: Msieve 1.36
Total time: 23 days
Scaled time: ? units (timescale=2.738).
Factorization parameters were as follows:
n: 244444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441
name: 24441_200
#res: 1872
Y0: -10000000000000000000000000000000000000000
Y1: 1
c5: 22
c0: -31
skew: 1.07
type: snfs
lpbr: 29
lpba: 29
mfbr: 57
mfba: 57
rlambda: 2.5
alambda: 2.5
rlim: 16000000
alim: 16000000
Factor base limits: 16000000/16000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 57/57
Sieved rational special-q in [8000000, 16900001)
Relations: 40323955 relations
37001703 unique relations and about 33452936 large ideals
Max relations in full relation-set: 20
Initial matrix: 3454542 x 3455788 (1045.7 MB) with weight 328806948 (95.15/col)
  sparse part has weight 236099120 (68.32/col)
Pruned matrix : 3395676 x 3395924 (991.3 MB) with weight 250430313 (73.74/col)
  sparse part has weight 225898752 (66.52/col)
Total sieving time: exactly 20 days on 1cpu.
Total relation processing time: 2.00 hours.
Matrix solve time: 67.50 hours. (a bit under 3 days)
Time per square root: 1.11 hours. Times 5. (One Newton failed to converge.) elapsed time 05:35:31
Prototype def-par.txt line would be:
snfs,201,5,0,0,0,0,0,0,0,0,16000000,16000000,29,29,57,57,2.5,2.5,100000

total time: 23 days.

Aug 1, 2008 (4th)

By Serge Batalov / GMP-ECM

(5·10¹⁹⁸-23)/9 = (5)₁₉₇3_<198> = 79 · 1787 · 92166227 · C185

C185 = P29 · C156

P29 = 62964716122813547478189355909_<29>

C156 = [678120373017004965696027723355266137898901427492400737189655707913532453650073593892558088509716301805095025038393270924775790361244152143461824320103726627_<156>]

(8·10²⁰⁰+7)/3 = 2(6)₁₉₉9_<201> = 10181399 · 126355837 · 36206518457_<11> · 28184782664921_<14> · C162

C162 = P30 · P132

P30 = 697368348053808161867372475367_<30>

P132 = 291274374180553751645366386448159892837438428245940571965196990275330307174828818699791027080461993416672152709678515211741667562337_<132>

Aug 1, 2008 (3rd)

By Sinkiti Sibata / GGNFS, GMP-ECM

(23·10¹⁵⁶-41)/9 = 2(5)₁₅₅1_<157> = 109 · 1949 · 615887 · 79671967 · C138

C138 = P60 · P78

P60 = 568072473549876077847951681943235841700911865100362592901083_<60>

P78 = 431555511214783572160697906549520112228842379475734051031125209152188991775173_<78>

Number: 25551_156
N=245154806729863389877554529829728473478831042552701224896737949891351647068415901547655165076105391748463107205434374654549956804164212359
  ( 138 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=568072473549876077847951681943235841700911865100362592901083 (pp60)
 r2=431555511214783572160697906549520112228842379475734051031125209152188991775173 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 60.42 hours.
Scaled time: 46.29 units (timescale=0.766).
Factorization parameters were as follows:
name: 25551_156
n: 245154806729863389877554529829728473478831042552701224896737949891351647068415901547655165076105391748463107205434374654549956804164212359
m: 10000000000000000000000000000000
c5: 230
c0: -41
skew: 0.71
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3600001)
Primes: RFBsize:216816, AFBsize:216312, largePrimes:5870783 encountered
Relations: rels:5897251, finalFF:541008
Max relations in full relation-set: 28
Initial matrix: 433195 x 541008 with sparse part having weight 56507710.
Pruned matrix : 387613 x 389842 with weight 39426318.
Total sieving time: 57.85 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 2.25 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 60.42 hours.
 --------- CPU info (if available) ----------

8·10²⁰⁶-1 = 7(9)₂₀₆_<207> = 2844937 · 95500513 · 69076890761242761822409_<23> · C170

C170 = P47 · P124

P47 = 41135749498277498847659154913591669404231513839_<47>

P124 = 1036237806348703114978686943063529149880910428973216429428407074021642801060804673132690587919795720559017683362400311580929_<124>

Factor79991_206
Input number is 42626418822604840172098173334880818320537225294947181741042961592958391680695314798229314971658518580998472053287968986315776968375378540443044665760795283585213031976431

Run 1845 out of 2350:
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1065804300
Step 1 took 66862ms
Step 2 took 21278ms
********** Factor found in step 2: 41135749498277498847659154913591669404231513839
Found probable prime factor of 47 digits: 41135749498277498847659154913591669404231513839
Probable prime cofactor 1036237806348703114978686943063529149880910428973216429428407074021642801060804673132690587919795720559017683362400311580929 has 124 digits

Aug 1, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(8·10¹⁸⁶+7)/3 = 2(6)₁₈₅9_<187> = 19 · C186

C186 = P64 · P122

P64 = 9461561365491417751494369249651340254835341510781699493399324537_<64>

P122 = 14833796640042493150323341558774456583384342378431564682298156460186483076837772252833910763261999400743782662308014748023_<122>

Number: n
N=140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140351
  ( 186 digits)
SNFS difficulty: 186 digits.
Divisors found:

Fri Aug 01 04:57:51 2008  prp64 factor: 9461561365491417751494369249651340254835341510781699493399324537
Fri Aug 01 04:57:51 2008  prp122 factor: 14833796640042493150323341558774456583384342378431564682298156460186483076837772252833910763261999400743782662308014748023
Fri Aug 01 04:57:51 2008  elapsed time 08:20:34 (Msieve 1.36)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 75.43 hours.
Scaled time: 98.52 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_2_6_185_9
n: 140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140351
type: snfs
skew: 0.61
deg: 5
c5: 80
c0: 7
m: 10000000000000000000000000000000000000
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 6350001)
Primes: RFBsize:602489, AFBsize:603715, largePrimes:10590638 encountered
Relations: rels:10590627, finalFF:1235224
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 74.89 hours.
Total relation processing time: 0.54 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,50,50,2.5,2.5,100000
total time: 75.43 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(23·10¹⁵⁸-41)/9 = 2(5)₁₅₇1_<159> = 203982161 · C151

C151 = P66 · P85

P66 = 171689635527179533850177211158120096687991880816145824295203094123_<66>

P85 = 7297079191886613832743568747111087572188527660082593836965018158316475096972563946317_<85>

Number: n
N=1252832866867978497176307273044114654494495504219879088130434874427845460248632014225771221021408610116428541785845457120907526592757077201253670194991
  ( 151 digits)
SNFS difficulty: 159 digits.
Divisors found:

Fri Aug  1 10:14:11 2008  prp66 factor: 171689635527179533850177211158120096687991880816145824295203094123
Fri Aug  1 10:14:11 2008  prp85 factor: 7297079191886613832743568747111087572188527660082593836965018158316475096972563946317
Fri Aug  1 10:14:11 2008  elapsed time 00:58:14 (Msieve 1.36)

Version: GGNFS-0.77.1-20050930-k8
Total time: 35.26 hours.
Scaled time: 29.51 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_2_5_157_1
n: 1252832866867978497176307273044114654494495504219879088130434874427845460248632014225771221021408610116428541785845457120907526592757077201253670194991
type: snfs
deg: 5
c5: 23000
c0: -41
skew: 0.28
m: 10000000000000000000000000000000
rlim: 5500000
alim: 5500000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100001)
Primes: RFBsize:380800, AFBsize:381098, largePrimes:5429667 encountered
Relations: rels:5543974, finalFF:780100
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 35.09 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.5,2.5,100000
total time: 35.26 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

Aug 1, 2008

By Tyler Cadigan / Msieve, GGNFS

(10¹⁹⁸+53)/9 = (1)₁₉₇7_<198> = 3 · 11618966467_<11> · 272033009875993867_<18> · 30874217309083734095351287845727_<32> · C138

C138 = P49 · P89

P49 = 9453997590293827952520076434647256044623334210059_<49>

P89 = 40145390515984245549625564941684431539990421548183675478964571944721581807941671195434707_<89>

Number: 11117_198
N=379534425199519751802558862062259553534112280564965144585212678040651849592463853984445240166695146589693057988042923980473715294957117713
  ( 138 digits)
Divisors found:
 r1=9453997590293827952520076434647256044623334210059
 r2=40145390515984245549625564941684431539990421548183675478964571944721581807941671195434707
Version: 
Total time: 621.18 hours.
Scaled time: 1600.17 units (timescale=2.576).
Factorization parameters were as follows:
name: 11117_198
n: 379534425199519751802558862062259553534112280564965144585212678040651849592463853984445240166695146589693057988042923980473715294957117713
skew: 113421.69
# norm 6.07e+018
c5: 4597020
c4: 112946341846
c3: -142581740199761914
c2: 9306396615802705483023
c1: 924174800200196017988522392
c0: -13806708124835709986443831217980
# alpha -5.94
Y1: 6237782020208299
Y0: -152529859043766825334703079
# Murphy_E 2.62e-011
# M 105204987891615758404166717436433383277087204802518042147842137078868339598661102665100403548164843043068382038692909504027948782527384386
type: gnfs
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.5
alambda: 2.5
qintsize: 1000000Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [2700000, 13700001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1309332 x 1309580
Total sieving time: 621.18 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,137,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5400000,5400000,27,27,51,51,2.5,2.5,
total time: 621.18 hours.
 --------- CPU info (if available) ----------

July 2008

Jul 31, 2008

By Serge Batalov / pol51, Msieve

(23·10¹⁸⁸-41)/9 = 2(5)₁₈₇1_<189> = 43 · 683 · 1123 · 11003 · 129491 · 13776430890486919_<17> · 1998967854737700046309_<22> · 4118359186990383026851_<22> · C113

C113 = P44 · P69

P44 = 65615481280730819870909029109781563549335597_<44>

P69 = 730790082739108945520358150329693309160286713343015176689118525792073_<69>

Number: 25551_188
N=47951142994111730052600594373683969756210565578842353767390601851826733211778758756378457047403995719847319322581
  ( 113 digits)
Divisors found:
 r1=65615481280730819870909029109781563549335597
 r2=730790082739108945520358150329693309160286713343015176689118525792073
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.315).
Factorization parameters were as follows:
name: 25551_188
n: 47951142994111730052600594373683969756210565578842353767390601851826733211778758756378457047403995719847319322581
skew: 39942.85
# norm 4.55e+15
c5: 34440
c4: 33787766
c3: -289153465319201
c2: 86740494851837328
c1: 170200457961466906677222
c0: 1225255008348063687936417840
# alpha -6.30
Y1: 624020572153
Y0: -4253506998509198027219
# Murphy_E 7.21e-10
# M 13308855079719020252483670510147535496065937586070006992997317244223463936867911346371720820664892712291005385604
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 3650001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: 7790604 relations (7008594 unique relations and about 7083638 large ideals)
Max relations in full relation-set: 20
Initial matrix: 486909 x 487115 (149.7 MB) with weight 49914063 (102.47/col)
Pruned matrix : 484228 x 484476
Total sieving time: 12.00 hours.
Total relation processing time: 00:06:58
Matrix solve time: 01:06:27
Time per square root: 00:14:26 
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000

total time: 13.6 hours.

Jul 30, 2008

By Sinkiti Sibata / GMP-ECM, GGNFS

8·10²⁰³-1 = 7(9)₂₀₃_<204> = 139 · 661 · 691 · 221101 · 7609211 · 8030409029_<10> · 58953836021010431_<17> · C158

C158 = P35 · P123

P35 = 15964735925805978713074497549589901_<35>

P123 = 990954857884280807155141937143358514822699724692261377137730212333798710863533568558966350673543013087657806107656416640019_<123>

(23·10¹⁶⁰-41)/9 = 2(5)₁₅₉1_<161> = 3 · 421 · 1303290019_<10> · 16757517846851_<14> · 33410740941589932192257971_<26> · C110

C110 = P51 · P60

P51 = 141201378282839605551482507237147623978827958693229_<51>

P60 = 196384032376405294052137230651200422806370915812525870825887_<60>

Number: 25551_160
N=27729696044290224460609024058949846655012187821821005718326741022823024412724637968075461477077242655504819123
  ( 110 digits)
Divisors found:
 r1=141201378282839605551482507237147623978827958693229 (pp51)
 r2=196384032376405294052137230651200422806370915812525870825887 (pp60)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 34.78 hours.
Scaled time: 16.45 units (timescale=0.473).
Factorization parameters were as follows:
name: 25551_160
n: 27729696044290224460609024058949846655012187821821005718326741022823024412724637968075461477077242655504819123
skew: 19703.02
# norm 2.58e+15
c5: 97200
c4: 2699482653
c3: -193815028071876
c2: -1584280404140977288
c1: 22126732270643781438316
c0: -44916850879699875155644045
# alpha -6.32
Y1: 17675023289
Y0: -778136368901680828542
# Murphy_E 1.04e-09
# M 5474228949482118542256893329492702222648847949467955749282916956767404137793286945529386778071697693401222665
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2300001)
Primes: RFBsize:230209, AFBsize:230705, largePrimes:7471164 encountered
Relations: rels:7388085, finalFF:642533
Max relations in full relation-set: 28
Initial matrix: 460991 x 642533 with sparse part having weight 52550874.
Pruned matrix : 312266 x 314634 with weight 26599352.
Total sieving time: 30.88 hours.
Total relation processing time: 0.45 hours.
Matrix solve time: 3.16 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 34.78 hours.
 --------- CPU info (if available) ----------

(23·10¹⁴⁸-41)/9 = 2(5)₁₄₇1_<149> = 3³ · 17 · 151 · 1283 · 75011929299489064304755445730298699_<35> · C106

C106 = P48 · P59

P48 = 242428544050253915914646918889394792594740748663_<48>

P59 = 15803560686756702280080903994808482373671375272389819798509_<59>

Number: 25551_148
N=3831234208100258225905784789352281618753028879135330243405513044277690944977878017308340945272902471143467
  ( 106 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=242428544050253915914646918889394792594740748663 (pp48)
 r2=15803560686756702280080903994808482373671375272389819798509 (pp59)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 42.02 hours.
Scaled time: 32.06 units (timescale=0.763).
Factorization parameters were as follows:
name: 25551_148
n: 3831234208100258225905784789352281618753028879135330243405513044277690944977878017308340945272902471143467
m: 100000000000000000000000000000
c5: 23000
c0: -41
skew: 0.28
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 5650001)
Primes: RFBsize:114155, AFBsize:113913, largePrimes:3272514 encountered
Relations: rels:3445255, finalFF:267676
Max relations in full relation-set: 28
Initial matrix: 228135 x 267676 with sparse part having weight 36440840.
Pruned matrix : 218281 x 219485 with weight 28929745.
Total sieving time: 41.16 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.59 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 42.02 hours.
 --------- CPU info (if available) ----------

Jul 29, 2008 (3rd)

By Sinkiti Sibata / GMP-ECM, GGNFS

8·10²¹²-1 = 7(9)₂₁₂_<213> = 4049 · 194729 · 119979793 · 486354823 · C188

C188 = P32 · P157

P32 = 10363055718258968541866287435591_<32>

P157 = 1677885836761735105027686433776347699057186426741928740520860590753000052575004869637655827915676182908115006877848710311065778076524792688071381438849355831_<157>

(23·10¹⁵²-41)/9 = 2(5)₁₅₁1_<153> = 251 · 15727 · 30313 · 103850550449_<12> · 534229782631_<12> · C119

C119 = P35 · P85

P35 = 19790119266604017679102945476566143_<35>

P85 = 1945142794525748056047069045389871786110518491818897667080431528816127400819396477203_<85>

Number: 25551_152
N=38494607894239986573312408816526294980131769999525671688250208724577379801467092036352155350111476847297481563421138029
  ( 119 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=19790119266604017679102945476566143 (pp35)
 r2=1945142794525748056047069045389871786110518491818897667080431528816127400819396477203 (pp85)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 43.36 hours.
Scaled time: 33.39 units (timescale=0.770).
Factorization parameters were as follows:
name: 25551_152
n: 38494607894239986573312408816526294980131769999525671688250208724577379801467092036352155350111476847297481563421138029
m: 1000000000000000000000000000000
c5: 2300
c0: -41
skew: 0.45
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2700001)
Primes: RFBsize:176302, AFBsize:176434, largePrimes:5926245 encountered
Relations: rels:5993828, finalFF:528516
Max relations in full relation-set: 28
Initial matrix: 352803 x 528516 with sparse part having weight 59010423.
Pruned matrix : 295070 x 296898 with weight 34887846.
Total sieving time: 41.80 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 1.27 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 43.36 hours.
 --------- CPU info (if available) ----------

Jul 29, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(22·10¹⁸⁶-31)/9 = 2(4)₁₈₅1_<187> = 2609147 · 11184881843_<11> · 20693708759_<11> · 107449652673263951068137572239_<30> · C131

C131 = P60 · P72

P60 = 171456587163938150377867556321935189380057680476175447590519_<60>

P72 = 219711454591472501320115502574137369201432836002086108434234387703221959_<72>

Number: 24441_186
N=37670976165078443863256836601861142328673369625675002713509577133696652081698435733705187027373757745600233596423796059159601006721
  ( 131 digits)
Divisors found:
 r1=171456587163938150377867556321935189380057680476175447590519 (pp60)
 r2=219711454591472501320115502574137369201432836002086108434234387703221959 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 397.44 hours.
Scaled time: 398.64 units (timescale=1.003).
Factorization parameters were as follows:
name: 24441_186
n: 37670976165078443863256836601861142328673369625675002713509577133696652081698435733705187027373757745600233596423796059159601006721
skew: 126850.64
# norm 1.14e+18
c5: 401700
c4: -88329015826
c3: -33312095062761562
c2: 1203702866763267563315
c1: 138153793740909087892531458
c0: -1041535282133753560962272111400
# alpha -5.91
Y1: 97569885487877
Y0: -9872364854022489260068993
# Murphy_E 6.68e-11
# M 633122711962913050141178229451031715178519068215028293487278893698121013088255029031311623901634808174113378784182677589098774524
type: gnfs
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.5
alambda: 2.5
qintsize: 60000
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [2700000, 17640001)
Primes: RFBsize:374362, AFBsize:373919, largePrimes:10334820 encountered
Relations: rels:12618895, finalFF:844096
Max relations in full relation-set: 28
Initial matrix: 748367 x 844096 with sparse part having weight 133631545.
Pruned matrix : 684149 x 687954 with weight 117917272.
Total sieving time: 387.86 hours.
Total relation processing time: 1.06 hours.
Matrix solve time: 7.94 hours.
Time per square root: 0.58 hours.
Prototype def-par.txt line would be:
gnfs,130,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5400000,5400000,27,27,51,51,2.5,2.5,60000
total time: 397.44 hours.
 --------- CPU info (if available) ----------

Jul 29, 2008

By Serge Batalov / pol51, Msieve, GMP-ECM

(23·10¹⁹⁵-41)/9 = 2(5)₁₉₄1_<196> = 158597 · 7029942179561563_<16> · 313306481963429959_<18> · 138881901627091563659_<21> · 337159954666957756609533851017_<30> · C108

C108 = P51 · P57

P51 = 425452593547811250316631268573489297907292332462667_<51>

P57 = 367228525511343637108246350268855498271898118507609664399_<57>

Number: 25551_195
N=156238328603539719034056512317514350799152188699229320945880126217790717414234564344734256456866329066492133
  ( 108 digits)
Divisors found:
 r1=425452593547811250316631268573489297907292332462667
 r2=367228525511343637108246350268855498271898118507609664399
Version: 
Scaled time: 0.00 units (timescale=2.314).
Factorization parameters were as follows:
name: 25551_195
n: 156238328603539719034056512317514350799152188699229320945880126217790717414234564344734256456866329066492133
skew: 18161.46
# norm 6.06e+14
c5: 19440
c4: -1287147529
c3: -42621652708216
c2: 324919101556326086
c1: 4304459856666512446668
c0: 5045724495165348220842000
# alpha -5.28
Y1: 144033260789
Y0: -381083757256829511337
# Murphy_E 1.27e-09
# M 128206860376250402135095926671172746209589861555750814743352707800749867899952792114219665913762911409522204
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1600000, 2900001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 372333 x 372574
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,26,26,49,49,2.6,2.6,100000

total time: 11.25 hours.

(23·10¹⁶⁷-41)/9 = 2(5)₁₆₆1_<168> = 43 · 1913 · 202061459 · 8243229814663_<13> · 9719287489760292844376840465897_<31> · C111

C111 = P44 · P67

P44 = 25684063928938037339841953821170973102004701_<44>

P67 = 7471758700860606702764453521083040039688701616397278375982183054061_<67>

Number: 25551_167
N=191905128134502839826363774871925281664941680452003820832204690551782529098643580568564988256211135109759140761
  ( 111 digits)
Divisors found:
 r1=25684063928938037339841953821170973102004701
 r2=7471758700860606702764453521083040039688701616397278375982183054061
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.314).
Factorization parameters were as follows:
name: 25551_167
n: 191905128134502839826363774871925281664941680452003820832204690551782529098643580568564988256211135109759140761
skew: 34967.52
# norm 4.00e+15
c5: 50760
c4: 4857904818
c3: -154098803765337
c2: -4794514057547441483
c1: 129763218046029315253297
c0: -162403929682185181213925415
# alpha -6.94
Y1: 464271068387
Y0: -1304698116443718001226
# Murphy_E 9.82e-10
# M 49869502946388985127326104835168775949738092057117596251976267998101212859840610032696852809604089189634082330
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 3100001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 404231 x 404479
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000

total time: 14.00 hours.

(23·10¹⁴⁶-41)/9 = 2(5)₁₄₅1_<147> = 43 · 6841 · 346043 · 41510532436848216902506677855337901_<35> · C101

C101 = P35 · P67

P35 = 34758835800516322384363626653111027_<35>

P67 = 1739977716010306568378337706839472575468221244846012298568319529657_<67>

Number: 25551_146
N=60479599727359666560994131358298323344894266838551584001575199716934366999703013872164853960440227739
  ( 101 digits)
Divisors found:
 r1=34758835800516322384363626653111027
 r2=1739977716010306568378337706839472575468221244846012298568319529657
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.306).
Factorization parameters were as follows:
name: 25551_146
n: 60479599727359666560994131358298323344894266838551584001575199716934366999703013872164853960440227739
skew: 9581.22
# norm 8.20e+13
c5: 23940
c4: -717855282
c3: -6785777479427
c2: 59164854376037827
c1: 270725537666604462153
c0: -1234452836689798433057766
# alpha -6.03
Y1: 129595215343
Y0: -19077200685863818687
# Murphy_E 3.21e-09
# M 16954413833068882237305959215587452485169461365335948587591155236573028568610291703407904271619835883
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1500001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 180427 x 180657
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000

total time: 5.00 hours.

(23·10¹³⁶-41)/9 = 2(5)₁₃₅1_<137> = 3 · 587 · 5081 · C130

C130 = P64 · P66

P64 = 7220707395104081979889441231486340266276055853078025872679218893_<64>

P66 = 395546029374132684362629681712347760388410687843986837692961179827_<66>

Number: 25551_136
N=2856122139405856309563107813059951282752130483951642176474844660794454712203535608497877323817032394969305938353534250598068871511
  ( 130 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=7220707395104081979889441231486340266276055853078025872679218893
 r2=395546029374132684362629681712347760388410687843986837692961179827
Version: Msieve 1.36
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.294).
Factorization parameters were as follows:
n: 2856122139405856309563107813059951282752130483951642176474844660794454712203535608497877323817032394969305938353534250598068871511
Y1: 1
Y0: -1000000000000000000000000000
c5: 230
c0: -41
skew: 0.71
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [500000, 2225001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 167043 x 167264
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000

total time: 6.60 hours.

(23·10¹²⁸-41)/9 = 2(5)₁₂₇1_<129> = 2455552249163861923_<19> · C111

C111 = P36 · P75

P36 = 183984724928350103604095598822455287_<36>

P75 = 565658580426499955089656149121889215128319053548001037907750693173909533651_<75>

Number: 25551_128
N=104072538323130598266669657959877765401398196056849442449371065528617787768961145538112189660598674708969362837
  ( 111 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=183984724928350103604095598822455287
 r2=565658580426499955089656149121889215128319053548001037907750693173909533651
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.314).
Factorization parameters were as follows:
n: 104072538323130598266669657959877765401398196056849442449371065528617787768961145538112189660598674708969362837
Y1: 1
Y0: -10000000000000000000000000
c5: 23000
c0: -41
skew: 0.28
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [400000, 1050001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 120882 x 121130
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000

total time: 2.60 hours.

(23·10¹⁵¹-41)/9 = 2(5)₁₅₀1_<152> = 3 · 7 · 19 · C149

C149 = P42 · P107

P42 = 828705755470883248206443600902260497750813_<42>

P107 = 77288001192943139407705039988537472974515304633897945114412907051296370165896505908384922416246634351671973_<107>

Number: 25551_151
N=64049011417432470064049011417432470064049011417432470064049011417432470064049011417432470064049011417432470064049011417432470064049011417432470064049
  ( 149 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=828705755470883248206443600902260497750813
 r2=77288001192943139407705039988537472974515304633897945114412907051296370165896505908384922416246634351671973
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.312).
Factorization parameters were as follows:
n: 64049011417432470064049011417432470064049011417432470064049011417432470064049011417432470064049011417432470064049011417432470064049011417432470064049
Y1: 1
Y0: -1000000000000000000000000000000
c5: 230
c0: -41
skew: 0.71
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1200000, 3100001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 580869 x 581117
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,52,52,2.5,2.5,100000

total time: 14.25 hours.

(23·10¹⁷⁶-41)/9 = 2(5)₁₇₅1_<177> = 1693 · 40766729 · 6784935167_<10> · 582406709601371_<15> · 64712766329852691432002761083917_<32> · C110

C110 = P39 · P71

P39 = 771073511127576234777110033082908100809_<39>

P71 = 18778663554365193587028132136971846756713170062564978859065837339119323_<71>

Jul 28, 2008 (9th)

By Sinkiti Sibata / GGNFS

(23·10¹²⁷-41)/9 = 2(5)₁₂₆1_<128> = 3 · 7 · 13789 · 636704041316348681226905897_<27> · C96

C96 = P40 · P56

P40 = 7221520930973206646401819070774877612779_<40>

P56 = 19194065806847188314532804326356425958335559911996902133_<56>

Number: 25551_127
N=138610347974624100139747647275393532986136399287735632429301347986696578956797567157662333157607
  ( 96 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=7221520930973206646401819070774877612779 (pp40)
 r2=19194065806847188314532804326356425958335559911996902133 (pp56)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.25 hours.
Scaled time: 4.06 units (timescale=0.774).
Factorization parameters were as follows:
name: 25551_127
n: 138610347974624100139747647275393532986136399287735632429301347986696578956797567157662333157607
m: 10000000000000000000000000
c5: 2300
c0: -41
skew: 0.45
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1050001)
Primes: RFBsize:63951, AFBsize:63839, largePrimes:1565208 encountered
Relations: rels:1597866, finalFF:199561
Max relations in full relation-set: 28
Initial matrix: 127857 x 199561 with sparse part having weight 16075767.
Pruned matrix : 109221 x 109924 with weight 7153577.
Total sieving time: 5.11 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.25 hours.
 --------- CPU info (if available) ----------

Jul 28, 2008 (8th)

By Jo Yeong Uk / GGNFS

8·10²³⁷-1 = 7(9)₂₃₇_<238> = 19 · 31 · 569 · 33529 · 441702386307151_<15> · 35149384885764499121265377855887521968365553602811950790861159929701230228471_<77> · C137

C137 = P52 · P86

P52 = 1236107286628145196448639851671015323071433818391231_<52>

P86 = 37096948202534582401901585244832896057767553242001774619573918018896075253502000311741_<86>

Number: 79999_237
N=45855807984819870790284032074741112260037755149041837570580988639808010607112972363240352571450865017457653731943683977750690941100743171
  ( 137 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=1236107286628145196448639851671015323071433818391231 (pp52)
 r2=37096948202534582401901585244832896057767553242001774619573918018896075253502000311741 (pp86)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 30.73 hours.
Scaled time: 73.26 units (timescale=2.384).
Factorization parameters were as follows:
n: 45855807984819870790284032074741112260037755149041837570580988639808010607112972363240352571450865017457653731943683977750690941100743171
m: 200000000000000000000000000
c6: 25
c3: 10
c0: 4
skew: 0.74
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3900001)
Primes: RFBsize:283146, AFBsize:282762, largePrimes:5755281 encountered
Relations: rels:5770382, finalFF:637340
Max relations in full relation-set: 28
Initial matrix: 565974 x 637340 with sparse part having weight 42624067.
Pruned matrix : 511711 x 514604 with weight 30656236.
Total sieving time: 29.14 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 1.44 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,159,6,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 30.73 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047052k/8912896k available (2459k kernel code, 339236k reserved, 1247k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673804)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348)
Calibrating delay using timer specific routine.. 5344.23 BogoMIPS (lpj=2672116)
Calibrating delay using timer specific routine.. 5589.60 BogoMIPS (lpj=2794804)

Jul 28, 2008 (7th)

By suberi / GMP-ECM

(4·10²⁰⁵-1)/3 = 1(3)₂₀₅_<206> = 13 · 2722799 · 769133399 · C189

C189 = P35 · P155

P35 = 16552386941879045763447940586089963_<35>

P155 = 29588128831725251679987662009307565255386626445186833657115513568355695849046387928726745167267846248912352318255956907081595132326285283802772607783082707_<155>

Jul 28, 2008 (6th)

By Robert Backstrom / GGNFS, Msieve

(22·10¹⁶⁵-13)/9 = 2(4)₁₆₄3_<166> = 7 · 17 · 3191 · C160

C160 = P52 · P109

P52 = 5754480652293022944296874651263801107670250103676807_<52>

P109 = 1118665569732113050387533457391188058592674819391297562139857816414188357774603895007548142093328554147528381_<109>

Number: n
N=6437339377409796050458206890820675914782501321849119884034257179315892240109247501361350975154503460216218525433781576978435790904683193657699160307599483959467
  ( 160 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Jul 28 17:54:55 2008  prp52 factor: 5754480652293022944296874651263801107670250103676807
Mon Jul 28 17:54:55 2008  prp109 factor: 1118665569732113050387533457391188058592674819391297562139857816414188357774603895007548142093328554147528381
Mon Jul 28 17:54:55 2008  elapsed time 02:54:38 (Msieve 1.36)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 40.31 hours.
Scaled time: 52.76 units (timescale=1.309).
Factorization parameters were as follows:
name: KA_2_4_164_3
n: 6437339377409796050458206890820675914782501321849119884034257179315892240109247501361350975154503460216218525433781576978435790904683193657699160307599483959467
type: snfs
skew: 0.90
deg: 5
c5: 22
c0: -13
m: 1000000000000000000000000000000000
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 2300000)
Primes: RFBsize:348513, AFBsize:348457, largePrimes:9839460 encountered
Relations: rels:9290956, finalFF:745978
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 39.81 hours.
Total relation processing time: 0.49 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,50,50,2.5,2.5,100000
total time: 40.31 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(23·10¹²⁵-41)/9 = 2(5)₁₂₄1_<126> = 43 · C124

C124 = P42 · P83

P42 = 249348569303014160413787592148654698519463_<42>

P83 = 23834716483005383332708850249577163177780742690701649474076750209456743894544822939_<83>

Number: n
N=5943152454780361757105943152454780361757105943152454780361757105943152454780361757105943152454780361757105943152454780361757
  ( 124 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=249348569303014160413787592148654698519463 (pp42)
 r2=23834716483005383332708850249577163177780742690701649474076750209456743894544822939 (pp83)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.59 hours.
Scaled time: 2.90 units (timescale=1.818).
Factorization parameters were as follows:
name: KA_2_5_124_1
n: 5943152454780361757105943152454780361757105943152454780361757105943152454780361757105943152454780361757105943152454780361757
skew: 1.12
deg: 5
c5: 23
c0: -41
m: 10000000000000000000000000
type: snfs
rlim: 700000
alim: 700000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [100000, 320001)
Primes: RFBsize:56543, AFBsize:56629, largePrimes:5090222 encountered
Relations: rels:4337119, finalFF:156374
Max relations in full relation-set: 48
Initial matrix: 113237 x 156374 with sparse part having weight 17243698.
Pruned matrix : 101383 x 102013 with weight 7505512.
Total sieving time: 1.44 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.05 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,700000,700000,28,28,50,50,2.5,2.5,50000
total time: 1.59 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(28·10¹⁶⁹-1)/9 = 3(1)₁₆₉_<170> = 569 · 66874311668453_<14> · C153

C153 = P65 · P89

P65 = 44747666732132274776543864200416504217245710983578615464026424207_<65>

P89 = 18271471956786769290650039107080148906269339162611613818652179674703425122513940651184189_<89>

Number: n
N=817605737827795112675191444680284193664087344513277738051760753443865670302478953404332802895920027643909527487197553597209356778647497395851301805263123
  ( 153 digits)
SNFS difficulty: 171 digits.
Divisors found:

Mon Jul 28 21:12:01 2008  prp65 factor: 44747666732132274776543864200416504217245710983578615464026424207
Mon Jul 28 21:12:01 2008  prp89 factor: 18271471956786769290650039107080148906269339162611613818652179674703425122513940651184189
Mon Jul 28 21:12:01 2008  elapsed time 02:26:33 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 48.38 hours.
Scaled time: 88.49 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_3_1_169
n: 817605737827795112675191444680284193664087344513277738051760753443865670302478953404332802895920027643909527487197553597209356778647497395851301805263123
skew: 0.81
deg: 5
c5: 14
c0: -5
m: 10000000000000000000000000000000000
type: snfs
rlim: 6000000
alim: 6000000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 3100001)
Primes: RFBsize:412849, AFBsize:414176, largePrimes:9904175 encountered
Relations: rels:9455000, finalFF:839308
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 48.10 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,50,50,2.5,2.5,100000
total time: 48.38 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jul 28, 2008 (5th)

By Sinkiti Sibata / GGNFS

(23·10¹²⁹-41)/9 = 2(5)₁₂₈1_<130> = 347 · 1399 · 59004638297548789745241165391_<29> · C95

C95 = P36 · P60

P36 = 145724632415306209970889384614530979_<36>

P60 = 612236216310466332533975530312917979837581554624783714920903_<60>

Number: 25551_129
N=89217897573180606659720594531071090386214846727194734208262478987142825655424436387351428154037
  ( 95 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=145724632415306209970889384614530979 (pp36)
 r2=612236216310466332533975530312917979837581554624783714920903 (pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.18 hours.
Scaled time: 4.01 units (timescale=0.774).
Factorization parameters were as follows:
name: 25551_129
n: 89217897573180606659720594531071090386214846727194734208262478987142825655424436387351428154037
m: 100000000000000000000000000
c5: 23
c0: -410
skew: 1.78
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1050001)
Primes: RFBsize:63951, AFBsize:64059, largePrimes:1499300 encountered
Relations: rels:1490747, finalFF:160397
Max relations in full relation-set: 28
Initial matrix: 128075 x 160397 with sparse part having weight 12552187.
Pruned matrix : 119298 x 120002 with weight 7667375.
Total sieving time: 5.02 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.18 hours.
 --------- CPU info (if available) ----------

(23·10¹¹⁶-41)/9 = 2(5)₁₁₅1_<117> = 17 · 192406883 · C107

C107 = P38 · P70

P38 = 20871150723274008192701347204335976081_<38>

P70 = 3743427330215324631982859564971087424753593345379490493751515455230261_<70>

Number: 25551_116
N=78129636030547262195749898698837870196137347232609306808107078432860782708361889269454031878999438043387141
  ( 107 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=20871150723274008192701347204335976081 (pp38)
 r2=3743427330215324631982859564971087424753593345379490493751515455230261 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.23 hours.
Scaled time: 1.73 units (timescale=0.774).
Factorization parameters were as follows:
name: 25551_116
n: 78129636030547262195749898698837870196137347232609306808107078432860782708361889269454031878999438043387141
m: 100000000000000000000000
c5: 230
c0: -41
skew: 0.71
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63644, largePrimes:2232224 encountered
Relations: rels:2412467, finalFF:298474
Max relations in full relation-set: 28
Initial matrix: 112809 x 298474 with sparse part having weight 28115143.
Pruned matrix : 79906 x 80534 with weight 5836660.
Total sieving time: 2.12 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.23 hours.
 --------- CPU info (if available) ----------

(23·10¹²³-41)/9 = 2(5)₁₂₂1_<124> = 1453 · 1801 · 9391 · 6693819476983_<13> · C101

C101 = P45 · P56

P45 = 637191652502528066422659078234237565527319133_<45>

P56 = 24380919769593584418550698024252096421356470057475816983_<56>

Number: 25551_123
N=15535318557518891893677625380007670301471136199536056513238867420641462692932163565132174374942235739
  ( 101 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=637191652502528066422659078234237565527319133 (pp45)
 r2=24380919769593584418550698024252096421356470057475816983 (pp56)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.15 hours.
Scaled time: 3.19 units (timescale=0.768).
Factorization parameters were as follows:
name: 25551_123
n: 15535318557518891893677625380007670301471136199536056513238867420641462692932163565132174374942235739
m: 1000000000000000000000000
c5: 23000
c0: -41
skew: 0.28
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:49098, AFBsize:63559, largePrimes:2391319 encountered
Relations: rels:2706287, finalFF:384069
Max relations in full relation-set: 28
Initial matrix: 112724 x 384069 with sparse part having weight 40247857.
Pruned matrix : 85697 x 86324 with weight 9432873.
Total sieving time: 4.00 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 4.15 hours.
 --------- CPU info (if available) ----------

(23·10¹³³-41)/9 = 2(5)₁₃₂1_<134> = 3 · 7 · 19 · 1406343509201398365268977301_<28> · C104

C104 = P39 · P66

P39 = 131983281958163855510539651678444328449_<39>

P66 = 345065940183956376607582992204291886943136677148509477565980637101_<66>

Number: 25551_133
N=45542935277458017797569348660685401934522573265115886086415534445131430705420105041865756177125119186349
  ( 104 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=131983281958163855510539651678444328449 (pp39)
 r2=345065940183956376607582992204291886943136677148509477565980637101 (pp66)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 10.59 hours.
Scaled time: 5.01 units (timescale=0.473).
Factorization parameters were as follows:
name: 25551_133
n: 45542935277458017797569348660685401934522573265115886086415534445131430705420105041865756177125119186349
m: 100000000000000000000000000
c5: 23000
c0: -41
skew: 0.28
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1450001)
Primes: RFBsize:78498, AFBsize:63559, largePrimes:1565148 encountered
Relations: rels:1564919, finalFF:169848
Max relations in full relation-set: 28
Initial matrix: 142124 x 169848 with sparse part having weight 15160791.
Pruned matrix : 133632 x 134406 with weight 10401980.
Total sieving time: 10.13 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.31 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 10.59 hours.
 --------- CPU info (if available) ----------

Jul 28, 2008 (4th)

By Serge Batalov / GMP-ECM, Msieve, pol51

8·10²⁴⁴-1 = 7(9)₂₄₄_<245> = 89 · 1278578053639_<13> · 108861017508663575689495374381113_<33> · C199

C199 = P36 · C164

P36 = 142573390866785288763609707121204263_<36>

C164 = [45296210130250230198807436160507101560969066892484152346441941909506494187913106289607271581488076574862891981551400056470584444467889627923713436760753843396214751_<164>]

8·10²⁴⁰-1 = 7(9)₂₄₀_<241> = 7 · 23 · 167 · 1063 · 1327 · 53831 · 2010123697_<10> · 14590058377_<11> · 967282300096325356931642416182002212551860417333658191869546350550040969_<72> · C135

C135 = P56 · P80

P56 = 12638631559884545162091883790692457456172929864285579791_<56>

P80 = 10928936369148320848662567406798716031938309146132546684068294609008875247151417_<80>

Number: 79999_240
N=138126800111087979621904572738473262040684851838378352665408113514452160684022609766361862880248315626676076038065194239443863012213847
  ( 135 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=12638631559884545162091883790692457456172929864285579791
 r2=10928936369148320848662567406798716031938309146132546684068294609008875247151417
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
n: 138126800111087979621904572738473262040684851838378352665408113514452160684022609766361862880248315626676076038065194239443863012213847
Y1: 1
Y0: -1000000000000000000000000000
c6: 1
c3: 5
c0: 25
skew: 1.7
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [2500000, 6000001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 808067 x 808315
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.25 hours. * 4 dep
Prototype def-par.txt line would be:
snfs,162,6,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.5,2.5,100000

total time: 25.90 hours.

(23·10¹³⁴-41)/9 = 2(5)₁₃₃1_<135> = 83 · C133

C133 = P62 · P71

P62 = 61675709953442697785653352579529799727020527376375559085086927_<62>

P71 = 49922126545103830085717272367270909155555235254621911382926371134183211_<71>

Number: 25551_134
N=3078982597054886211512717536813922356091030789825970548862115127175368139223560910307898259705488621151271753681392235609103078982597
  ( 133 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=61675709953442697785653352579529799727020527376375559085086927
 r2=49922126545103830085717272367270909155555235254621911382926371134183211
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.303).
Factorization parameters were as follows:
n: 3078982597054886211512717536813922356091030789825970548862115127175368139223560910307898259705488621151271753681392235609103078982597
Y1: 1
Y0: -1000000000000000000000000000
c5: 23
c0: -410
skew: 1.78
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [500000, 1625001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 145782 x 146030
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000

total time: 4.5 hours.

(23·10¹⁷⁰-41)/9 = 2(5)₁₆₉1_<171> = 47 · 167 · 1233615293_<10> · 645304315442331619894177_<24> · 8914696587075694200020688570908983_<34> · C100

C100 = P39 · P62

P39 = 285490091589476305221345080451232055137_<39>

P62 = 16070488449447674612650589351851462929548050466307798710623429_<62>

Number: 25551_170
N=4587965219320437679186724585504871860492353253197962059126245596532976638080543930484448622172004773
  ( 100 digits)
Divisors found:
 r1=285490091589476305221345080451232055137
 r2=16070488449447674612650589351851462929548050466307798710623429
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.315).
Factorization parameters were as follows:
name: 25551_170
n: 4587965219320437679186724585504871860492353253197962059126245596532976638080543930484448622172004773
skew: 4343.54
# norm 1.85e+14
c5: 102600
c4: -2099554410
c3: 313677236699
c2: -32073952736029022
c1: -22993856991668603067
c0: 77448256609396649268195
# alpha -6.35
Y1: 13929288857
Y0: -8513290624657879186
# Murphy_E 3.34e-09
# M 881146291402212354249118032869459916813881084351627622763479243021417493888375943481775157365108946
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1400001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: 4089960 relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 188015 x 188257
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000

total time: 2.80 hours.

(23·10¹⁴⁴-41)/9 = 2(5)₁₄₃1_<145> = C145

C145 = P53 · P93

P53 = 11328951549049208258659188667017358765383634275585517_<53>

P93 = 225577410627202540610471998982892547446702289733649826841945206400113122054353971517703547003_<93>

Number: 25551_144
N=2555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555551
  ( 145 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=11328951549049208258659188667017358765383634275585517
 r2=225577410627202540610471998982892547446702289733649826841945206400113122054353971517703547003
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
n: 2555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555551
Y1: 1
Y0: -100000000000000000000000000000
c5: 23
c0: -410
skew: 1.78
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved rational special-q in [750000, 2750001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: 3186702 relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 255651 x 255899
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000

total time: 7.02 hours.

Jul 28, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(23·10¹²¹-41)/9 = 2(5)₁₂₀1_<122> = 3³ · 7² · 107 · 242689 · 2785847 · 774795187 · C96

C96 = P48 · P48

P48 = 552729096969604125117866209022368136492287800707_<48>

P48 = 623498064629031326448330932831149966744250542153_<48>

Number: 25551_121
N=344625522224700355890781569301728917200166256280370455883285888961664239432175325341492766702171
  ( 96 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=552729096969604125117866209022368136492287800707 (pp48)
 r2=623498064629031326448330932831149966744250542153 (pp48)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 2.99 hours.
Scaled time: 1.42 units (timescale=0.473).
Factorization parameters were as follows:
name: 25551_121
n: 344625522224700355890781569301728917200166256280370455883285888961664239432175325341492766702171
m: 1000000000000000000000000
c5: 230
c0: -41
skew: 0.71
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:63644, largePrimes:2079639 encountered
Relations: rels:2058172, finalFF:128435
Max relations in full relation-set: 28
Initial matrix: 112809 x 128435 with sparse part having weight 11139017.
Pruned matrix : 108190 x 108818 with weight 8118576.
Total sieving time: 2.71 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.99 hours.
 --------- CPU info (if available) ----------

Jul 28, 2008 (2nd)

By Serge Batalov / GMP-ECM, Msieve, pol51

8·10²⁴⁴-1 = 7(9)₂₄₄_<245> = 89 · 1278578053639_<13> · C231

C231 = P33 · C199

P33 = 108861017508663575689495374381113_<33>

C199 = [6458034271684205445370439176812586281872425037340884899946467880064597890608060770039709215095343983538806570804236640838846920029060722859175686181158626178828082778050969836074995833443582884683513_<199>]

8·10²⁴¹-1 = 7(9)₂₄₁_<242> = 149 · 24421 · 31350871 · 1697371865690194829_<19> · C210

C210 = P31 · C180

P31 = 4084686957513171056405214141139_<31>

C180 = [101147437776188067596893019641822094170077201992981329794320726118257488337588143534303319427488460340571418858976260720363458708418693527978581840212562659143024599069105778741431_<180>]

(23·10¹¹⁴-41)/9 = 2(5)₁₁₃1_<115> = 12671 · 3204884250067103630129_<22> · C89

C89 = P27 · P62

P27 = 725788414881940170954537007_<27>

P62 = 86706579727612278786969624143583485674657111291579725893503327_<62>

(23·10¹⁵³-41)/9 = 2(5)₁₅₂1_<154> = 157 · 1511 · 71889401 · 6594980699_<10> · 10359967718793949674331_<23> · 126119780815898289136469561_<27> · C83

C83 = P41 · P42

P41 = 50235185876494027386262953460826258885293_<41>

P42 = 346173000949072010309520257023196154046249_<42>

Sun Jul 27 11:25:56 2008  Msieve v. 1.36
Sun Jul 27 11:25:56 2008  random seeds: 42d2437e c33efa51
Sun Jul 27 11:25:56 2008  factoring 17390065048100375790461411356970700872395622645753315257013857083257878410307915957 (83 digits)
Sun Jul 27 11:25:57 2008  no P-1/P+1/ECM available, skipping
Sun Jul 27 11:25:57 2008  commencing quadratic sieve (83-digit input)
Sun Jul 27 11:25:57 2008  using multiplier of 13
Sun Jul 27 11:25:57 2008  using 64kb Opteron sieve core
Sun Jul 27 11:25:57 2008  sieve interval: 6 blocks of size 65536
Sun Jul 27 11:25:57 2008  processing polynomials in batches of 17
Sun Jul 27 11:25:57 2008  using a sieve bound of 1356389 (52353 primes)
Sun Jul 27 11:25:57 2008  using large prime bound of 123431399 (26 bits)
Sun Jul 27 11:25:57 2008  using trial factoring cutoff of 27 bits
Sun Jul 27 11:25:57 2008  polynomial 'A' values have 11 factors
Sun Jul 27 11:42:17 2008  52737 relations (28001 full + 24736 combined from 268831 partial), need 52449
Sun Jul 27 11:42:17 2008  begin with 296832 relations
Sun Jul 27 11:42:17 2008  reduce to 74247 relations in 2 passes
Sun Jul 27 11:42:17 2008  attempting to read 74247 relations
Sun Jul 27 11:42:18 2008  recovered 74247 relations
Sun Jul 27 11:42:18 2008  recovered 64353 polynomials
Sun Jul 27 11:42:18 2008  attempting to build 52737 cycles
Sun Jul 27 11:42:18 2008  found 52737 cycles in 1 passes
Sun Jul 27 11:42:18 2008  distribution of cycle lengths:
Sun Jul 27 11:42:18 2008     length 1 : 28001
Sun Jul 27 11:42:18 2008     length 2 : 24736
Sun Jul 27 11:42:18 2008  largest cycle: 2 relations
Sun Jul 27 11:42:18 2008  matrix is 52353 x 52737 (8.1 MB) with weight 1696688 (32.17/col)
Sun Jul 27 11:42:18 2008  sparse part has weight 1696688 (32.17/col)
Sun Jul 27 11:42:19 2008  filtering completed in 3 passes
Sun Jul 27 11:42:19 2008  matrix is 36662 x 36726 (6.1 MB) with weight 1317403 (35.87/col)
Sun Jul 27 11:42:19 2008  sparse part has weight 1317403 (35.87/col)
Sun Jul 27 11:42:19 2008  saving the first 48 matrix rows for later
Sun Jul 27 11:42:19 2008  matrix is 36614 x 36726 (4.1 MB) with weight 989538 (26.94/col)
Sun Jul 27 11:42:19 2008  sparse part has weight 717356 (19.53/col)
Sun Jul 27 11:42:19 2008  matrix includes 64 packed rows
Sun Jul 27 11:42:19 2008  using block size 14690 for processor cache size 1024 kB
Sun Jul 27 11:42:19 2008  commencing Lanczos iteration
Sun Jul 27 11:42:19 2008  memory use: 4.1 MB
Sun Jul 27 11:42:26 2008  lanczos halted after 581 iterations (dim = 36608)
Sun Jul 27 11:42:26 2008  recovered 14 nontrivial dependencies
Sun Jul 27 11:42:26 2008  prp41 factor: 50235185876494027386262953460826258885293
Sun Jul 27 11:42:26 2008  prp42 factor: 346173000949072010309520257023196154046249
Sun Jul 27 11:42:26 2008  elapsed time 00:16:30

(23·10¹²⁴-41)/9 = 2(5)₁₂₃1_<125> = 3 · 47 · 3643631 · 17073588094550355706752106093964111_<35> · C82

C82 = P36 · P47

P36 = 155830978679555689187019330766573207_<36>

P47 = 18696194936136122483576503549609207686186338653_<47>

Sun Jul 27 11:25:25 2008  Msieve v. 1.36
Sun Jul 27 11:25:25 2008  random seeds: 795a1938 d119b872
Sun Jul 27 11:25:25 2008  factoring 2913446354481845142744359062908868931976606350837226718898980159766073710818270171 (82 digits)
Sun Jul 27 11:25:26 2008  no P-1/P+1/ECM available, skipping
Sun Jul 27 11:25:26 2008  commencing quadratic sieve (82-digit input)
Sun Jul 27 11:25:26 2008  using multiplier of 1
Sun Jul 27 11:25:26 2008  using 64kb Opteron sieve core
Sun Jul 27 11:25:26 2008  sieve interval: 6 blocks of size 65536
Sun Jul 27 11:25:26 2008  processing polynomials in batches of 17
Sun Jul 27 11:25:26 2008  using a sieve bound of 1337729 (51471 primes)
Sun Jul 27 11:25:26 2008  using large prime bound of 125746526 (26 bits)
Sun Jul 27 11:25:26 2008  using trial factoring cutoff of 27 bits
Sun Jul 27 11:25:26 2008  polynomial 'A' values have 10 factors
Sun Jul 27 11:46:04 2008  51676 relations (25977 full + 25699 combined from 278377 partial), need 51567
Sun Jul 27 11:46:05 2008  begin with 304354 relations
Sun Jul 27 11:46:05 2008  reduce to 74155 relations in 2 passes
Sun Jul 27 11:46:05 2008  attempting to read 74155 relations
Sun Jul 27 11:46:06 2008  recovered 74155 relations
Sun Jul 27 11:46:06 2008  recovered 65726 polynomials
Sun Jul 27 11:46:06 2008  attempting to build 51676 cycles
Sun Jul 27 11:46:07 2008  found 51676 cycles in 1 passes
Sun Jul 27 11:46:07 2008  distribution of cycle lengths:
Sun Jul 27 11:46:07 2008     length 1 : 25977
Sun Jul 27 11:46:07 2008     length 2 : 25699
Sun Jul 27 11:46:07 2008  largest cycle: 2 relations
Sun Jul 27 11:46:07 2008  matrix is 51471 x 51676 (7.7 MB) with weight 1608107 (31.12/col)
Sun Jul 27 11:46:07 2008  sparse part has weight 1608107 (31.12/col)
Sun Jul 27 11:46:08 2008  filtering completed in 3 passes
Sun Jul 27 11:46:08 2008  matrix is 37409 x 37473 (6.1 MB) with weight 1301480 (34.73/col)
Sun Jul 27 11:46:08 2008  sparse part has weight 1301480 (34.73/col)
Sun Jul 27 11:46:08 2008  saving the first 48 matrix rows for later
Sun Jul 27 11:46:08 2008  matrix is 37361 x 37473 (4.6 MB) with weight 1010936 (26.98/col)
Sun Jul 27 11:46:08 2008  sparse part has weight 827779 (22.09/col)
Sun Jul 27 11:46:08 2008  matrix includes 64 packed rows
Sun Jul 27 11:46:08 2008  using block size 14989 for processor cache size 1024 kB
Sun Jul 27 11:46:09 2008  commencing Lanczos iteration
Sun Jul 27 11:46:09 2008  memory use: 4.4 MB
Sun Jul 27 11:46:22 2008  lanczos halted after 593 iterations (dim = 37361)
Sun Jul 27 11:46:22 2008  recovered 18 nontrivial dependencies
Sun Jul 27 11:46:23 2008  prp36 factor: 155830978679555689187019330766573207
Sun Jul 27 11:46:23 2008  prp47 factor: 18696194936136122483576503549609207686186338653
Sun Jul 27 11:46:23 2008  elapsed time 00:20:58

(23·10¹⁷⁰-41)/9 = 2(5)₁₆₉1_<171> = 47 · 167 · 1233615293_<10> · 645304315442331619894177_<24> · C134

C134 = P34 · C100

P34 = 8914696587075694200020688570908983_<34>

C100 = [4587965219320437679186724585504871860492353253197962059126245596532976638080543930484448622172004773_<100>]

(23·10¹⁴⁶-41)/9 = 2(5)₁₄₅1_<147> = 43 · 6841 · 346043 · C136

C136 = P35 · C101

P35 = 41510532436848216902506677855337901_<35>

C101 = [60479599727359666560994131358298323344894266838551584001575199716934366999703013872164853960440227739_<101>]

(23·10¹⁹⁵-41)/9 = 2(5)₁₉₄1_<196> = 158597 · 7029942179561563_<16> · 313306481963429959_<18> · 138881901627091563659_<21> · C137

C137 = P30 · C108

P30 = 337159954666957756609533851017_<30>

C108 = [156238328603539719034056512317514350799152188699229320945880126217790717414234564344734256456866329066492133_<108>]

(23·10¹⁴⁸-41)/9 = 2(5)₁₄₇1_<149> = 3³ · 17 · 151 · 1283 · C141

C141 = P35 · C106

P35 = 75011929299489064304755445730298699_<35>

C106 = [3831234208100258225905784789352281618753028879135330243405513044277690944977878017308340945272902471143467_<106>]

(23·10¹⁵⁷-41)/9 = 2(5)₁₅₆1_<158> = 3² · 7 · 14776651 · 63748651 · C141

C141 = P30 · P111

P30 = 973336363550106887302722574739_<30>

P111 = 442420062949587264507358090096128210983570197191636875054556465288607675852564435098117942495764116067637731443_<111>

(23·10¹⁰⁶-41)/9 = 2(5)₁₀₅1_<107> = 3 · 89 · 304585559 · 183954605179_<12> · C85

C85 = P32 · P54

P32 = 12361526776253110052746469951419_<32>

P54 = 138191705900215663268288927238977959384385858170547267_<54>

Sun Jul 27 11:50:55 2008  Msieve v. 1.36
Sun Jul 27 11:50:55 2008  random seeds: 2bb3be20 caa580c6
Sun Jul 27 11:50:55 2008  factoring 1708260472741610815635081495099835617949910688096929711288607302314546926614133221873 (85 digits)
Sun Jul 27 11:50:55 2008  no P-1/P+1/ECM available, skipping
Sun Jul 27 11:50:55 2008  commencing quadratic sieve (85-digit input)
Sun Jul 27 11:50:55 2008  using multiplier of 1
Sun Jul 27 11:50:56 2008  using 64kb Opteron sieve core
Sun Jul 27 11:50:56 2008  sieve interval: 6 blocks of size 65536
Sun Jul 27 11:50:56 2008  processing polynomials in batches of 17
Sun Jul 27 11:50:56 2008  using a sieve bound of 1409879 (54118 primes)
Sun Jul 27 11:50:56 2008  using large prime bound of 118429836 (26 bits)
Sun Jul 27 11:50:56 2008  using trial factoring cutoff of 27 bits
Sun Jul 27 11:50:56 2008  polynomial 'A' values have 11 factors
Sun Jul 27 12:27:36 2008  54264 relations (27466 full + 26798 combined from 283153 partial), need 54214
Sun Jul 27 12:27:36 2008  begin with 310619 relations
Sun Jul 27 12:27:36 2008  reduce to 77728 relations in 2 passes
Sun Jul 27 12:27:36 2008  attempting to read 77728 relations
Sun Jul 27 12:27:37 2008  recovered 77728 relations
Sun Jul 27 12:27:37 2008  recovered 72460 polynomials
Sun Jul 27 12:27:37 2008  attempting to build 54264 cycles
Sun Jul 27 12:27:37 2008  found 54264 cycles in 1 passes
Sun Jul 27 12:27:37 2008  distribution of cycle lengths:
Sun Jul 27 12:27:37 2008     length 1 : 27466
Sun Jul 27 12:27:37 2008     length 2 : 26798
Sun Jul 27 12:27:37 2008  largest cycle: 2 relations
Sun Jul 27 12:27:37 2008  matrix is 54118 x 54264 (8.2 MB) with weight 1722644 (31.75/col)
Sun Jul 27 12:27:37 2008  sparse part has weight 1722644 (31.75/col)
Sun Jul 27 12:27:38 2008  filtering completed in 3 passes
Sun Jul 27 12:27:38 2008  matrix is 39821 x 39884 (6.6 MB) with weight 1398732 (35.07/col)
Sun Jul 27 12:27:38 2008  sparse part has weight 1398732 (35.07/col)
Sun Jul 27 12:27:38 2008  saving the first 48 matrix rows for later
Sun Jul 27 12:27:38 2008  matrix is 39773 x 39884 (4.2 MB) with weight 1024154 (25.68/col)
Sun Jul 27 12:27:38 2008  sparse part has weight 701631 (17.59/col)
Sun Jul 27 12:27:38 2008  matrix includes 64 packed rows
Sun Jul 27 12:27:38 2008  using block size 15953 for processor cache size 1024 kB
Sun Jul 27 12:27:38 2008  commencing Lanczos iteration
Sun Jul 27 12:27:38 2008  memory use: 4.3 MB
Sun Jul 27 12:27:46 2008  lanczos halted after 631 iterations (dim = 39770)
Sun Jul 27 12:27:46 2008  recovered 14 nontrivial dependencies
Sun Jul 27 12:27:46 2008  prp32 factor: 12361526776253110052746469951419
Sun Jul 27 12:27:46 2008  prp54 factor: 138191705900215663268288927238977959384385858170547267
Sun Jul 27 12:27:46 2008  elapsed time 00:36:51

(23·10¹¹⁰-41)/9 = 2(5)₁₀₉1_<111> = 52498139 · 68759837 · C95

C95 = P43 · P53

P43 = 1171236310664623846065075156444685421318659_<43>

P53 = 60445232405964426967246594540875308055954431145200123_<53>

Number: 25551_110
N=70795651000427540270331785995431991726223223369658715988001782164765787215865399899805108995057
  ( 95 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=1171236310664623846065075156444685421318659
 r2=60445232405964426967246594540875308055954431145200123
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.176).
Factorization parameters were as follows:
n: 70795651000427540270331785995431991726223223369658715988001782164765787215865399899805108995057
Y1: 1
Y0: -10000000000000000000000
c5: 23
c0: -41
skew: 1.12
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 400001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: 2.8M relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 66260 x 66481
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000

total time: 1.05 hours.

(23·10¹⁸⁰-41)/9 = 2(5)₁₇₉1_<181> = 17 · 160625847619_<12> · 23288197500401_<14> · 10538502885230213_<17> · 14005677645847267_<17> · 452648203174615703323010093477_<30> · C93

C93 = P36 · P57

P36 = 818721351585225269696284670558586233_<36>

P57 = 734691701926879427540330661208791006085582518574130629367_<57>

Number: 25551_180
N=601507783200024177533706526882724961664302389935805095370359219106224905189670063398031704511
  ( 93 digits)
Divisors found:
 r1=818721351585225269696284670558586233
 r2=734691701926879427540330661208791006085582518574130629367
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
name: 25551_180
n: 601507783200024177533706526882724961664302389935805095370359219106224905189670063398031704511
skew: 9274.72
# norm 5.56e+12
c5: 960
c4: 51491975
c3: -375693115044
c2: -3597295424721214
c1: 12421001845831235314
c0: 64030193958855804894760
# alpha -4.84
Y1: 14132136997
Y0: -910587610201992171
# Murphy_E 7.07e-09
# M 172801455112640510589520181640160855778357793905387688415191739720540490264493458130883360178
type: gnfs
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 900001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 109001 x 109222
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,92,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000

total time: 1.60 hours.

(23·10¹⁴³-41)/9 = 2(5)₁₄₂1_<144> = 557 · 171012781 · 136207903799352110227_<21> · C113

C113 = P33 · P80

P33 = 538844847458477932858080232424621_<33>

P80 = 36554051399146403713935390141869213541499333355306590438897345084105764804979409_<80>

(23·10¹³⁸-41)/9 = 2(5)₁₃₇1_<139> = C139

C139 = P35 · P105

P35 = 17609003514447728631938833758128093_<35>

P105 = 145127778153873886153305871603820300439044982225316042826202236046692596812484867625963184012287196067307_<105>

(23·10¹⁷⁶-41)/9 = 2(5)₁₇₅1_<177> = 1693 · 40766729 · 6784935167_<10> · 582406709601371_<15> · C141

C141 = P32 · C110

P32 = 64712766329852691432002761083917_<32>

C110 = [14479730041147820385756519417126351350432451092133329416395602786113828306192530413105615533147360150563832307_<110>]

Jul 28, 2008

Factorizations of 255...551 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors are probably greater than 10³⁰.

Jul 27, 2008 (4th)

By Serge Batalov / GMP-ECM

8·10²⁴⁹-1 = 7(9)₂₄₉_<250> = 139 · 6513641919379205078817101_<25> · 30704788883921543079717165000137354872639579175495937407099_<59> · C165

C165 = P30 · P135

P30 = 444308886544865560271771281999_<30>

P135 = 647679560070206617765843309810908725678476935981017638468004383156312447877119496409280870778743697648282559776979950903559036235285741_<135>

8·10²⁴⁶-1 = 7(9)₂₄₆_<247> = 7² · 4519 · 234721 · 227403769 · 423619321 · 91904895863405227344778390349737714039_<38> · 982772344963126877180586765965485256911_<39> · C143

C143 = P36 · P107

P36 = 727185362958603102583458640927672321_<36>

P107 = 24327052797346741204514652628175478116899457476934725356694836765790319302103867872875822020632685040373489_<107>

Jul 27, 2008 (3rd)

By Jo Yeong Uk / GGNFS

8·10²³¹-1 = 7(9)₂₃₁_<232> = 331 · 1549 · 2719 · 3296551 · 180273339366603915157042541456190941_<36> · 336541551884960929475454162660123389_<36> · C146

C146 = P68 · P78

P68 = 86993443529090471243193900012390628379624840454127261893376643990701_<68>

P78 = 329825971258905280264523732622444591114643795678979992003823731515025390553941_<78>

Number: 79999_231
N=28692697005138993302709192211409576219617822299744756725421307261784974933066555140257538805109891878235215013147269934963361194111890447242902641
  ( 146 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=86993443529090471243193900012390628379624840454127261893376643990701 (pp68)
 r2=329825971258905280264523732622444591114643795678979992003823731515025390553941 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.78 hours.
Scaled time: 59.18 units (timescale=2.388).
Factorization parameters were as follows:
n: 28692697005138993302709192211409576219617822299744756725421307261784974933066555140257538805109891878235215013147269934963361194111890447242902641
m: 100000000000000000000000000
c6: 1
c3: 5
c0: 25
skew: 1.71
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3100001)
Primes: RFBsize:216816, AFBsize:216710, largePrimes:5807273 encountered
Relations: rels:5811297, finalFF:564255
Max relations in full relation-set: 28
Initial matrix: 433591 x 564255 with sparse part having weight 50527041.
Pruned matrix : 358974 x 361205 with weight 33138080.
Total sieving time: 23.66 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.98 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,156,6,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 24.78 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047052k/8912896k available (2459k kernel code, 339236k reserved, 1247k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673804)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348)
Calibrating delay using timer specific routine.. 5344.23 BogoMIPS (lpj=2672116)
Calibrating delay using timer specific routine.. 5589.60 BogoMIPS (lpj=2794804)

Jul 27, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(22·10¹⁶²+23)/9 = 2(4)₁₆₁7_<163> = 1978727 · 1171413239_<10> · 1087986601832676187_<19> · C129

C129 = P55 · P75

P55 = 1030690545220291183793531315683239605395413174248632823_<55>

P75 = 940442666446536063195756357805894289825335687502835965056411741932351986299_<75>

Number: 24447_162
N=969305364628204696618841104157701934175888050442734215063287899040826831867856381020984867573714343451139369729680252409177692077
  ( 129 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=1030690545220291183793531315683239605395413174248632823 (pp55)
 r2=940442666446536063195756357805894289825335687502835965056411741932351986299 (pp75)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 95.03 hours.
Scaled time: 72.98 units (timescale=0.768).
Factorization parameters were as follows:
name: 24447_162
n: 969305364628204696618841104157701934175888050442734215063287899040826831867856381020984867573714343451139369729680252409177692077
m: 100000000000000000000000000000000
c5: 2200
c0: 23
skew: 0.4
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 5350001)
Primes: RFBsize:315948, AFBsize:315882, largePrimes:6095209 encountered
Relations: rels:6363736, finalFF:864607
Max relations in full relation-set: 28
Initial matrix: 631897 x 864607 with sparse part having weight 68497139.
Pruned matrix : 463354 x 466577 with weight 52859718.
Total sieving time: 90.96 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 3.65 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 95.03 hours.
 --------- CPU info (if available) ----------

Jul 27, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(85·10¹⁸²+41)/9 = 9(4)₁₈₁9_<183> = 13 · 103 · C180

C180 = P36 · C145

P36 = 104574808336266590413440953679885241_<36>

C145 = [6744795118571178385715723334774127654765899499968956986278497873607085936148420292629447731798091830209139268833767631800242442027606210314918251_<145>]

(71·10¹⁶⁹-17)/9 = 7(8)₁₆₈7_<170> = 7 · 11 · 2517919 · 22273117 · C155

C155 = P53 · P103

P53 = 11409640629076421191434060010145846556226043653471327_<53>

P103 = 1601144010506807619000508842408173481687372550772951863625802499128877259926572721944100979348066363311_<103>

Number: n
N=18268477755280836423775397397311493833809308462958858798539984335848791528224787061958360337859405752134076680695538897022388485946815868458429689903283697
  ( 155 digits)
SNFS difficulty: 171 digits.
Divisors found:

Sun Jul 27 06:14:21 2008  prp53 factor: 11409640629076421191434060010145846556226043653471327
Sun Jul 27 06:14:21 2008  prp103 factor: 1601144010506807619000508842408173481687372550772951863625802499128877259926572721944100979348066363311
Sun Jul 27 06:14:21 2008  elapsed time 04:24:45 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 81.67 hours.
Scaled time: 117.77 units (timescale=1.442).
Factorization parameters were as follows:
name: KA_7_8_168_7
n: 18268477755280836423775397397311493833809308462958858798539984335848791528224787061958360337859405752134076680695538897022388485946815868458429689903283697
skew: 1.19
deg: 5
c5: 71
c0: -170
m: 10000000000000000000000000000000000
type: snfs
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 3900001)
Primes: RFBsize:425648, AFBsize:425813, largePrimes:10128244 encountered
Relations: rels:9731875, finalFF:881380
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 81.20 hours.
Total relation processing time: 0.47 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,50,50,2.5,2.5,100000
total time: 81.67 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(68·10¹⁶⁹+13)/9 = 7(5)₁₆₈7_<170> = 7 · 11 · 474977 · C163

C163 = P32 · P46 · P86

P32 = 12564720581656893961516793698787_<32>

P46 = 7968617766944774753846532883783787495699428027_<46>

P86 = 20633232290617592691462578937718847171342995492350851612982494029893918840047147814217_<86>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 2065870518448222210720184306273737972536019599351086981014324864658670295574819372813802017742419067114789223438694886786057516429723926086907873394376951391291033 (163 digits)
Using B1=290000, B2=172085560, polynomial Dickson(3), sigma=929903015
Step 1 took 3703ms
Step 2 took 1859ms
********** Factor found in step 2: 12564720581656893961516793698787
Found probable prime factor of 32 digits: 12564720581656893961516793698787
Composite cofactor 164418341420513981191767033032572250364100248544748569751915035921047786398535014962302739673567607106739107738403172999090158859859 has 132 digits

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 164418341420513981191767033032572250364100248544748569751915035921047786398535014962302739673567607106739107738403172999090158859859 (132 digits)
Using B1=3744000, B2=8561285470, polynomial Dickson(6), sigma=1706818246
Step 1 took 36187ms
Step 2 took 15657ms
********** Factor found in step 2: 7968617766944774753846532883783787495699428027
Found probable prime factor of 46 digits: 7968617766944774753846532883783787495699428027
Probable prime cofactor 20633232290617592691462578937718847171342995492350851612982494029893918840047147814217 has 86 digits

Jul 26, 2008 (5th)

By Robert Backstrom / GGNFS, Msieve

(35·10¹⁶⁹-53)/9 = 3(8)₁₆₈3_<170> = 3³ · 11² · 661 · 2207 · 7726057 · C154

C154 = P65 · P89

P65 = 59462556413862442092449340501731601838252568471681890551614913937_<65>

P89 = 17761151691851101595704380123061264611926150229274494050475365714951019876727414514520043_<89>

Number: n
N=1056123484451864485860196229763977615884332123194476548802930056924154205342208938356587023654483801371879875439683279449403528714039431756768156306539291
  ( 154 digits)
SNFS difficulty: 170 digits.
Divisors found:

Sat Jul 26 20:46:42 2008  prp65 factor: 59462556413862442092449340501731601838252568471681890551614913937
Sat Jul 26 20:46:42 2008  prp89 factor: 17761151691851101595704380123061264611926150229274494050475365714951019876727414514520043
Sat Jul 26 20:46:42 2008  elapsed time 03:16:11 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 75.91 hours.
Scaled time: 132.69 units (timescale=1.748).
Factorization parameters were as follows:
name: KA_3_8_168_3
n: 1056123484451864485860196229763977615884332123194476548802930056924154205342208938356587023654483801371879875439683279449403528714039431756768156306539291
type: snfs
skew: 1.72
deg: 5
c5: 7
c0: -106
m: 10000000000000000000000000000000000
rlim: 6000000
alim: 6000000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
qintsize: 100000
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 2500001)
Primes: RFBsize:412849, AFBsize:412531, largePrimes:10050797 encountered
Relations: rels:9692589, finalFF:916683
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 75.46 hours.
Total relation processing time: 0.45 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,50,50,2.6,2.6,100000
total time: 75.91 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jul 26, 2008 (4th)

By Wataru Sakai / GGNFS

(31·10¹⁸⁹-13)/9 = 3(4)₁₈₈3_<190> = 11 · C189

C189 = P47 · P51 · P93

P47 = 18960275308406929724116517425722392691269164543_<47>

P51 = 148127824952087837453635732252173826200808100223731_<51>

P93 = 111492387161833705684170668928437133194092717290960694048484857650925015218158645936453543861_<93>

Number: 34443_189
N=313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313
  ( 189 digits)
SNFS difficulty: 191 digits.
Divisors found:
 r1=18960275308406929724116517425722392691269164543 (pp47)
 r2=148127824952087837453635732252173826200808100223731 (pp51)
 r3=111492387161833705684170668928437133194092717290960694048484857650925015218158645936453543861 (pp93)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 1502.39 hours.
Scaled time: 2836.51 units (timescale=1.888).
Factorization parameters were as follows:
n: 313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313
m: 100000000000000000000000000000000000000
c5: 31
c0: -130
skew: 1.33
type: snfsFactor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 25500001)
Primes: RFBsize:501962, AFBsize:503087, largePrimes:7478270 encountered
Relations: rels:8154107, finalFF:1168778
Max relations in full relation-set: 32
Initial matrix: 1005114 x 1168778 with sparse part having weight 159477313.
Pruned matrix : 892881 x 897970 with weight 142693512.
Total sieving time: 1489.05 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 12.84 hours.
Time per square root: 0.32 hours.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 1502.39 hours.
 --------- CPU info (if available) ----------

Jul 26, 2008 (3rd)

By Jo Yeong Uk / GGNFS

8·10²²⁸-1 = 7(9)₂₂₈_<229> = 7 · 71 · 3449 · 4847041 · 15820639 · 17076769 · 18395633 · 130854596492286412438405476816657478703173293235697757911_<57> · C139

C139 = P43 · P96

P43 = 1528903929139327175345777358726109783347673_<43>

P96 = 968389496066443829563630012210817722372169284170780283664563868997439143831062269183972619538007_<96>

Number: 79999_228
N=1480574505473238989199098674408682671411071598963681517151759583539213670859023764835487170244141115567827261158255099210189135575118507711
  ( 139 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=1528903929139327175345777358726109783347673 (pp43)
 r2=968389496066443829563630012210817722372169284170780283664563868997439143831062269183972619538007 (pp96)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 20.80 hours.
Scaled time: 49.37 units (timescale=2.374).
Factorization parameters were as follows:
n: 1480574505473238989199098674408682671411071598963681517151759583539213670859023764835487170244141115567827261158255099210189135575118507711
m: 20000000000000000000000000
c6: 25
c3: 10
c0: 4
skew: 0.74
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2600001)
Primes: RFBsize:176302, AFBsize:175893, largePrimes:5789972 encountered
Relations: rels:5766761, finalFF:478712
Max relations in full relation-set: 28
Initial matrix: 352261 x 478712 with sparse part having weight 49162015.
Pruned matrix : 300961 x 302786 with weight 30294030.
Total sieving time: 20.06 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.60 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,153,6,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 20.80 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047052k/8912896k available (2459k kernel code, 339236k reserved, 1247k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673804)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348)
Calibrating delay using timer specific routine.. 5344.23 BogoMIPS (lpj=2672116)
Calibrating delay using timer specific routine.. 5589.60 BogoMIPS (lpj=2794804)

Jul 26, 2008 (2nd)

By matsui / GGNFS

(14·10¹⁷⁹+31)/9 = 1(5)₁₇₈9_<180> = 3² · 937 · C176

C176 = P45 · P49 · P83

P45 = 175295153066532340613622437887691574772872821_<45>

P49 = 8441086165595067651650397848876928006494892885709_<49>

P83 = 12466231410440518465524895241428903373602741675890690732557533120565315438138006407_<83>

N=18446051886108805354625347510441782942672305888243277072875080701477001726023426485895358182800374191338261064337193828478068961882551352490875792192049751637087104892156475223
  ( 176 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=175295153066532340613622437887691574772872821 (pp45)
 r2=8441086165595067651650397848876928006494892885709 (pp49)
 r3=12466231410440518465524895241428903373602741675890690732557533120565315438138006407 (pp83)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 315.32 hours.
Scaled time: 610.14 units (timescale=1.935).
Factorization parameters were as follows:
n: 18446051886108805354625347510441782942672305888243277072875080701477001726023426485895358182800374191338261064337193828478068961882551352490875792192049751637087104892156475223
m: 1000000000000000000000000000000000000
c5: 7
c0: 155
skew: 1.86
type: snfs

Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 10200001)
Primes: RFBsize:501962, AFBsize:499942, largePrimes:6632716 encountered
Relations: rels:7100185, finalFF:1147043
Max relations in full relation-set: 28
Initial matrix: 1001969 x 1147043 with sparse part having weight 77618795.
Pruned matrix : 881350 x 886423 with weight 59827143.
Total sieving time: 308.53 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 6.25 hours.
Time per square root: 0.40 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 315.32 hours.

Jul 26, 2008

By Robert Backstrom / GGNFS, GMP-ECM, Msieve

8·10²³⁴-1 = 7(9)₂₃₄_<235> = 7 · 127 · 359 · 967 · 46271 · 18821440207_<11> · 6017479539201391_<16> · 3860717760049320127_<19> · 948031877361413200744641307998671084939526110708897790110817166822633_<69> · C109

C109 = P45 · P64

P45 = 282121745180560667036164213290041989056941689_<45>

P64 = 4790307443776610893726570695190991776424749473108915987693203239_<64>

Number: n
N=1351449895989687962880757239485494608558029508437965645529620904507286128520390416692603853519156577248930671
  ( 109 digits)
Divisors found:
 r1=282121745180560667036164213290041989056941689 (pp45)
 r2=4790307443776610893726570695190991776424749473108915987693203239 (pp64)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 11.28 hours.
Scaled time: 20.56 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_7_9_234
n: 1351449895989687962880757239485494608558029508437965645529620904507286128520390416692603853519156577248930671
skew: 23681.14
# norm 8.45e+14
c5: 35400
c4: 909978134
c3: -10843425355649
c2: -859297610146079263
c1: 1071555635925958284545
c0: 159770744406752924182690785
# alpha -5.97
Y1: 174057782899
Y0: -520425527026525197052
# Murphy_E 1.21e-09
# M 430725653313612678331739255995629435060729388392356940731188563969563801629981448267959244966784299042202987
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:230209, AFBsize:230422, largePrimes:6728311 encountered
Relations: rels:6387483, finalFF:548322
Max relations in full relation-set: 48
Initial matrix: 460713 x 548322 with sparse part having weight 36052224.
Pruned matrix : 375310 x 377677 with weight 17297185.
Polynomial selection time: 1.36 hours.
Total sieving time: 8.95 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.69 hours.
Total square root time: 0.10 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 11.28 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

2·10¹⁸³-7 = 1(9)₁₈₂3_<184> = 811 · 2624277319_<10> · 2755493291_<10> · 101591439292081_<15> · 16322026806562391_<17> · C132

C132 = P40 · P46 · P47

P40 = 6162314909610575169723533703783208734587_<40>

P46 = 2296936960460684436839110679001518570233133723_<46>

P47 = 14530343872204972792659597373865720056086160057_<47>

Sat Jul 26 07:08:12 2008  
Sat Jul 26 07:08:12 2008  
Sat Jul 26 07:08:12 2008  Msieve v. 1.36
Sat Jul 26 07:08:12 2008  random seeds: 6c176500 b95488c8
Sat Jul 26 07:08:12 2008  factoring 33375283888271021987099616586864311324910632800353159555401618973887857681828893792862302211 (92 digits)
Sat Jul 26 07:08:12 2008  searching for 15-digit factors
Sat Jul 26 07:08:13 2008  commencing quadratic sieve (92-digit input)
Sat Jul 26 07:08:13 2008  using multiplier of 3
Sat Jul 26 07:08:13 2008  using 64kb Opteron sieve core
Sat Jul 26 07:08:13 2008  sieve interval: 18 blocks of size 65536
Sat Jul 26 07:08:13 2008  processing polynomials in batches of 6
Sat Jul 26 07:08:13 2008  using a sieve bound of 1816147 (68235 primes)
Sat Jul 26 07:08:13 2008  using large prime bound of 197960023 (27 bits)
Sat Jul 26 07:08:13 2008  using double large prime bound of 858695942807652 (42-50 bits)
Sat Jul 26 07:08:13 2008  using trial factoring cutoff of 50 bits
Sat Jul 26 07:08:13 2008  polynomial 'A' values have 12 factors
Sat Jul 26 07:29:14 2008  
Sat Jul 26 07:29:14 2008  
Sat Jul 26 07:29:14 2008  Msieve v. 1.36
Sat Jul 26 07:29:14 2008  random seeds: ae82c9e0 243e55c6
Sat Jul 26 07:29:14 2008  factoring 33375283888271021987099616586864311324910632800353159555401618973887857681828893792862302211 (92 digits)
Sat Jul 26 07:29:14 2008  searching for 15-digit factors
Sat Jul 26 07:29:15 2008  commencing quadratic sieve (92-digit input)
Sat Jul 26 07:29:15 2008  using multiplier of 3
Sat Jul 26 07:29:15 2008  using 64kb Opteron sieve core
Sat Jul 26 07:29:15 2008  sieve interval: 18 blocks of size 65536
Sat Jul 26 07:29:15 2008  processing polynomials in batches of 6
Sat Jul 26 07:29:15 2008  using a sieve bound of 1816147 (68235 primes)
Sat Jul 26 07:29:15 2008  using large prime bound of 197960023 (27 bits)
Sat Jul 26 07:29:15 2008  using double large prime bound of 858695942807652 (42-50 bits)
Sat Jul 26 07:29:15 2008  using trial factoring cutoff of 50 bits
Sat Jul 26 07:29:15 2008  polynomial 'A' values have 12 factors
Sat Jul 26 07:29:15 2008  restarting with 3580 full and 178004 partial relations
Sat Jul 26 08:43:06 2008  68500 relations (16968 full + 51532 combined from 874683 partial), need 68331
Sat Jul 26 08:43:08 2008  begin with 891651 relations
Sat Jul 26 08:43:08 2008  reduce to 174938 relations in 12 passes
Sat Jul 26 08:43:08 2008  attempting to read 174938 relations
Sat Jul 26 08:43:10 2008  recovered 174938 relations
Sat Jul 26 08:43:10 2008  recovered 157541 polynomials
Sat Jul 26 08:43:10 2008  attempting to build 68500 cycles
Sat Jul 26 08:43:10 2008  found 68500 cycles in 6 passes
Sat Jul 26 08:43:11 2008  distribution of cycle lengths:
Sat Jul 26 08:43:11 2008     length 1 : 16968
Sat Jul 26 08:43:11 2008     length 2 : 12406
Sat Jul 26 08:43:11 2008     length 3 : 11767
Sat Jul 26 08:43:11 2008     length 4 : 9209
Sat Jul 26 08:43:11 2008     length 5 : 7086
Sat Jul 26 08:43:11 2008     length 6 : 4525
Sat Jul 26 08:43:11 2008     length 7 : 2793
Sat Jul 26 08:43:11 2008     length 9+: 3746
Sat Jul 26 08:43:11 2008  largest cycle: 20 relations
Sat Jul 26 08:43:11 2008  matrix is 68235 x 68500 (17.0 MB) with weight 4195226 (61.24/col)
Sat Jul 26 08:43:11 2008  sparse part has weight 4195226 (61.24/col)
Sat Jul 26 08:43:11 2008  filtering completed in 3 passes
Sat Jul 26 08:43:11 2008  matrix is 64825 x 64889 (16.2 MB) with weight 3993054 (61.54/col)
Sat Jul 26 08:43:11 2008  sparse part has weight 3993054 (61.54/col)
Sat Jul 26 08:43:12 2008  saving the first 48 matrix rows for later
Sat Jul 26 08:43:12 2008  matrix is 64777 x 64889 (9.5 MB) with weight 3068327 (47.29/col)
Sat Jul 26 08:43:12 2008  sparse part has weight 2106581 (32.46/col)
Sat Jul 26 08:43:12 2008  matrix includes 64 packed rows
Sat Jul 26 08:43:12 2008  using block size 25955 for processor cache size 1024 kB
Sat Jul 26 08:43:12 2008  commencing Lanczos iteration
Sat Jul 26 08:43:12 2008  memory use: 9.7 MB
Sat Jul 26 08:43:37 2008  lanczos halted after 1025 iterations (dim = 64774)
Sat Jul 26 08:43:38 2008  recovered 16 nontrivial dependencies
Sat Jul 26 08:43:38 2008  prp46 factor: 2296936960460684436839110679001518570233133723
Sat Jul 26 08:43:38 2008  prp47 factor: 14530343872204972792659597373865720056086160057
Sat Jul 26 08:43:38 2008  elapsed time 01:14:24

Jul 25, 2008 (7th)

By Robert Backstrom / GGNFS, Msieve

(2·10¹⁶⁹+1)/3 = (6)₁₆₈7_<169> = 7 · 766169 · 5025529 · C156

C156 = P46 · P111

P46 = 1261440917199733159119900387950410686385690243_<46>

P111 = 196081864308815835019995393044774169560246557899424260150099777307102229210524305885773367324515406034150789967_<111>

Number: n
N=247345686759946268316263131816608663902423313937075401253427394805496653944142877381675229300044388850675738926738552046324162639205415759533671843014191981
  ( 156 digits)
SNFS difficulty: 170 digits.
Divisors found:

Sat Jul 26 00:24:03 2008  prp46 factor: 1261440917199733159119900387950410686385690243
Sat Jul 26 00:24:03 2008  prp111 factor: 196081864308815835019995393044774169560246557899424260150099777307102229210524305885773367324515406034150789967
Sat Jul 26 00:24:03 2008  elapsed time 02:24:18 (Msieve 1.36)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 53.75 hours.
Scaled time: 70.47 units (timescale=1.311).
Factorization parameters were as follows:
name: KA_6_168_7
n: 247345686759946268316263131816608663902423313937075401253427394805496653944142877381675229300044388850675738926738552046324162639205415759533671843014191981
skew: 1.38
deg: 5
c5: 1
c0: 5
m: 10000000000000000000000000000000000
type: snfs
rlim: 6000000
alim: 6000000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 2100001)
Primes: RFBsize:412849, AFBsize:412271, largePrimes:9846876 encountered
Relations: rels:9579900, finalFF:971104
Max relations in full relation-set: 28
Initial matrix: 825184 x 971103 with sparse part having weight 57456378.
Pruned matrix : 
Total sieving time: 53.39 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,50,50,2.5,2.5,100000
total time: 53.75 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jul 25, 2008 (6th)

By Kenji Ibusuki / GGNFS

5·10¹⁹⁰-7 = 4(9)₁₈₉3_<191> = 19 · 43 · C188

C188 = P37 · P67 · P86

P37 = 1765787545312409783860474993038088441_<37>

P67 = 1221634377469420523013631539626062841035324877347830895794628620683_<67>

P86 = 28370582518084984958701082392541132842482155696727816580550567234311865111305350903443_<86>

Number: 49993_190
N=61199510403916768665850673194614443084455324357405140758873929008567931456548347613219094247246022031823745410036719706242350061199510403916768665850673194614443084455324357405140758873929
  ( 188 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=1765787545312409783860474993038088441 (pp37)
 r2=1221634377469420523013631539626062841035324877347830895794628620683 (pp67)
 r3=28370582518084984958701082392541132842482155696727816580550567234311865111305350903443 (pp86)
Version: GGNFS-0.77.1
Total time: 476.75 hours.
Scaled time: 1380.66 units (timescale=2.896).
Factorization parameters were as follows:
n: 61199510403916768665850673194614443084455324357405140758873929008567931456548347613219094247246022031823745410036719706242350061199510403916768665850673194614443084455324357405140758873929
m: 100000000000000000000000000000000000000
type: snfs
skew: 1.070
c0: -7
c5: 5
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 29/29
Sieved special-q in [3700000, 11800001)
Relations: rels:18218529, finalFF:1213632
Initial matrix: 1003163 x 1213632 with sparse part having weight 169464967.
Pruned matrix : 952997 x 958076 with weight 121817026.
Total sieving time: 462.13 hours.
Total relation processing time: 0.88 hours.
Matrix solve time: 13.50 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,7400000,7400000,29,29,51,51,2.6,2.6,100000
total time: 476.75 hours.
 --------- CPU info (if available) ----------

Jul 25, 2008 (5th)

By suberi / GMP-ECM

(4·10²⁴³-1)/3 = 1(3)₂₄₃_<244> = 31 · 83 · 157 · 131231 · 299197 · 1442216753248456277_<19> · 4038335633468132831_<19> · C191

C191 = P35 · P156

P35 = 35657045111837177984079582344894317_<35>

P156 = 404787718601259261978273194650372481814255336058492445066139143092845027355459172172060392549607938205765428041891254949939762856614330735166038645561890001_<156>

(4·10²⁴⁵-1)/3 = 1(3)₂₄₅_<246> = 293 · 4428013 · 436570924477_<12> · 197820650760877883_<18> · 1940832977077439598289_<22> · 245134337177055685486188936209_<30> · C157

C157 = P31 · C127

P31 = 1675203063576126721567576664071_<31>

C127 = [1493055747910029065087937422859586920491486247404972020337179301095994338939893155969148811179362195548241166474252224587374317_<127>]

Jul 25, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(2·10¹⁶⁹-17)/3 = (6)₁₆₈1_<169> = 238729 · 571138289 · C155

C155 = P41 · P44 · P72

P41 = 11817386542506337749843599398989802401983_<41>

P44 = 13085479642349468381361523918766801187989977_<44>

P72 = 316192233564917210640549980219740383800204370022180000336001159014458091_<72>

Number: n
N=48894756307188046205660588215055908169171174475099021113090591883003280000280409811352237979810160283919583949322319878169034135110728714578780893777197581
  ( 155 digits)
SNFS difficulty: 170 digits.
Divisors found:

Fri Jul 25 11:48:36 2008  prp41 factor: 11817386542506337749843599398989802401983
Fri Jul 25 11:48:36 2008  prp44 factor: 13085479642349468381361523918766801187989977
Fri Jul 25 11:48:36 2008  prp72 factor: 316192233564917210640549980219740383800204370022180000336001159014458091
Fri Jul 25 11:48:36 2008  elapsed time 02:12:34 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 45.36 hours.
Scaled time: 76.02 units (timescale=1.676).
Factorization parameters were as follows:
name: KA_6_168_1
n: 48894756307188046205660588215055908169171174475099021113090591883003280000280409811352237979810160283919583949322319878169034135110728714578780893777197581
skew: 2.43
deg: 5
c5: 1
c0: -85
m: 10000000000000000000000000000000000
type: snfs
rlim: 6000000
alim: 6000000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 2600001)
Primes: RFBsize:412849, AFBsize:413336, largePrimes:9838235 encountered
Relations: rels:9447054, finalFF:885558
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 45.07 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,50,50,2.5,2.5,100000
total time: 45.36 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

8·10²¹⁹-1 = 7(9)₂₁₉_<220> = 19 · 29 · 61 · 91734541 · 1119024901_<10> · 589635422899_<12> · 100236345329109106048850820884161_<33> · 5936402484004975288098822472966741469_<37> · C118

C118 = P32 · P86

P32 = 78804181274997851192664174029191_<32>

P86 = 83859934851872620017547819860052379897723933994052604566651127218360972849629908176429_<86>

Jul 25, 2008 (3rd)

By Jo Yeong Uk / GGNFS, GMP-ECM

8·10²¹³-1 = 7(9)₂₁₃_<214> = 311 · 14341 · 49801 · 118018309 · 812126836567325311_<18> · 48223863818791257229_<20> · 15900386507052020800133836615165276113430575119_<47> · C111

C111 = P42 · P70

P42 = 173118702419871755400126634132558566548011_<42>

P70 = 2830904217224319706645261082037462977679894136530963560822965061287591_<70>

Number: 79999_213
N=490082464760816993503044892873304511247077521030235243425978837079485571213821882640228393121233082755780031501
  ( 111 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=173118702419871755400126634132558566548011 (pp42)
 r2=2830904217224319706645261082037462977679894136530963560822965061287591 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.44 hours.
Scaled time: 24.97 units (timescale=2.392).
Factorization parameters were as follows:
n: 490082464760816993503044892873304511247077521030235243425978837079485571213821882640228393121233082755780031501
m: 1000000000000000000000000
c6: 1
c3: 5
c0: 25
skew: 1.71
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1550001)
Primes: RFBsize:114155, AFBsize:113645, largePrimes:3474537 encountered
Relations: rels:3489348, finalFF:285283
Max relations in full relation-set: 28
Initial matrix: 227865 x 285283 with sparse part having weight 27887141.
Pruned matrix : 209026 x 210229 with weight 17824594.
Total sieving time: 10.16 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,144,6,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 10.44 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047052k/8912896k available (2459k kernel code, 339236k reserved, 1247k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673804)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348)
Calibrating delay using timer specific routine.. 5344.23 BogoMIPS (lpj=2672116)
Calibrating delay using timer specific routine.. 5589.60 BogoMIPS (lpj=2794804)

8·10²¹⁶-1 = 7(9)₂₁₆_<217> = 7 · 10337 · 113209 · 14053183457400553_<17> · 1539265796448195743859457_<25> · 125696116580006172197631576931601768549558111_<45> · C123

C123 = P36 · P88

P36 = 147283812222899232001715996680222327_<36>

P88 = 2438660054892819457675742999944584962791806880889823383873998562744490822150544305736417_<88>

Jul 25, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(22·10¹⁶⁸+41)/9 = 2(4)₁₆₇9_<169> = 7 · 31 · 82189 · C162

C162 = P43 · P119

P43 = 2899543658506815033242105025684834449702477_<43>

P119 = 47269073375747822390380499935334445424904739368471132437674465794253492151242396483956332265049621005799300244584991649_<119>

Number: n
N=137058741950142926413591313022560984084757574577851131616469494271994331848507452416459940031691843703418912251112149144183098966311067137682739252527847579614573
  ( 162 digits)
SNFS difficulty: 169 digits.
Divisors found:

Fri Jul 25 01:46:01 2008  prp43 factor: 2899543658506815033242105025684834449702477
Fri Jul 25 01:46:01 2008  prp119 factor: 47269073375747822390380499935334445424904739368471132437674465794253492151242396483956332265049621005799300244584991649
Fri Jul 25 01:46:01 2008  elapsed time 02:23:22 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 54.93 hours.
Scaled time: 100.46 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_4_167_9
n: 137058741950142926413591313022560984084757574577851131616469494271994331848507452416459940031691843703418912251112149144183098966311067137682739252527847579614573
skew: 0.57
deg: 5
c5: 1375
c0: 82
m: 2000000000000000000000000000000000
type: snfs
rlim: 5800000
alim: 5800000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 3200001)
Primes: RFBsize:399993, AFBsize:399636, largePrimes:10053706 encountered
Relations: rels:9578110, finalFF:811962
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 54.61 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,50,50,2.5,2.5,100000
total time: 54.93 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jul 25, 2008

By Jo Yeong Uk / GGNFS

8·10²⁰⁷-1 = 7(9)₂₀₇_<208> = 31 · 439 · 212039 · 995881 · 4155919 · 35458744861_<11> · 339679388641_<12> · 2626410054718091_<16> · 7442213814490672036679386751621599_<34> · C115

C115 = P42 · P73

P42 = 541832960047230906014967345407576299650631_<42>

P73 = 5251106845463258052650105055200096921760782933920709388847288619870698129_<73>

Number: 79999_207
N=2845222765601634215803869063836629035398868860105421171772198973101369113582035289814048310534414748999136765369399
  ( 115 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=541832960047230906014967345407576299650631 (pp42)
 r2=5251106845463258052650105055200096921760782933920709388847288619870698129 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.37 hours.
Scaled time: 12.78 units (timescale=2.379).
Factorization parameters were as follows:
n: 2845222765601634215803869063836629035398868860105421171772198973101369113582035289814048310534414748999136765369399
m: 100000000000000000000000
c6: 4
c3: 2
c0: 1
skew: 0.79
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [650000, 1800001)
Primes: RFBsize:100021, AFBsize:99911, largePrimes:2422278 encountered
Relations: rels:2600965, finalFF:242584
Max relations in full relation-set: 28
Initial matrix: 199997 x 242584 with sparse part having weight 25213545.
Pruned matrix : 185672 x 186735 with weight 17433607.
Total sieving time: 5.15 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,138,6,0,0,0,0,0,0,0,0,1300000,1300000,25,25,47,47,2.3,2.3,50000
total time: 5.37 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047052k/8912896k available (2459k kernel code, 339236k reserved, 1247k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673804)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348)
Calibrating delay using timer specific routine.. 5344.23 BogoMIPS (lpj=2672116)
Calibrating delay using timer specific routine.. 5589.60 BogoMIPS (lpj=2794804)

Jul 24, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(22·10¹⁶⁰+41)/9 = 2(4)₁₅₉9_<161> = 2609 · 6053 · 133979 · 3698763923775038153208904926649_<31> · C118

C118 = P46 · P73

P46 = 2175120316596344341395729390310266840279264737_<46>

P73 = 1436014378583454632133875028269996384218596726067989942997243612917575231_<73>

Number: 24449_160
N=3123504049781346520649845866412023805576131973733178763648331210776077464897935701049859097482628566670996489562929247
  ( 118 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=2175120316596344341395729390310266840279264737 (pp46)
 r2=1436014378583454632133875028269996384218596726067989942997243612917575231 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 70.37 hours.
Scaled time: 54.82 units (timescale=0.779).
Factorization parameters were as follows:
name: 24449_160
n: 3123504049781346520649845866412023805576131973733178763648331210776077464897935701049859097482628566670996489562929247
m: 100000000000000000000000000000000
c5: 22
c0: 41
skew: 1.13
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4300001)
Primes: RFBsize:283146, AFBsize:282794, largePrimes:5837251 encountered
Relations: rels:5919740, finalFF:686098
Max relations in full relation-set: 28
Initial matrix: 566006 x 686098 with sparse part having weight 53196518.
Pruned matrix : 483417 x 486311 with weight 38131690.
Total sieving time: 67.10 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 2.94 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 70.37 hours.
 --------- CPU info (if available) ----------

Jul 24, 2008 (2nd)

Factorizations of 799...99 were extended to n=250. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors are probably greater than 10³⁰.

Note the algebraic factorization 8·10^3k-1 = (2·10^k-1)(4·10^2k+2·10^k+1).

"Efforts by ECM" section was added in "Contribution and Reservation" pages.

Jul 24, 2008

By Jo Yeong Uk / GGNFS

(4·10²³⁵-1)/3 = 1(3)₂₃₅_<236> = 13 · 67 · 677 · 7079 · 48775637 · 7554172820434544567959_<22> · 17218527001291015325523195827_<29> · 6303239909341182749584186343717_<31> · 103002075143888028035790451977073523_<36> · C102

C102 = P46 · P57

P46 = 1989378140372439563653744711213759800430408243_<46>

P57 = 389804622956411924070438346247626600778953706285860014157_<57>

Number: 13333_235
N=775468795925606718265168401955990662675462021136190876422142039835490928358779949182032553037269496151
  ( 102 digits)
Divisors found:
 r1=1989378140372439563653744711213759800430408243 (pp46)
 r2=389804622956411924070438346247626600778953706285860014157 (pp57)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.05 hours.
Scaled time: 9.64 units (timescale=2.380).
Factorization parameters were as follows:
name: 13333_235
n: 775468795925606718265168401955990662675462021136190876422142039835490928358779949182032553037269496151
skew: 7498.52
# norm 1.34e+14
c5: 31320
c4: 1422114954
c3: -74642879737
c2: -36382164166013463
c1: 102204763625923220477
c0: -178970016479028225265815
# alpha -5.96
Y1: 4898667461
Y0: -30112573504914213526
# Murphy_E 2.76e-09
# M 715234690321575102484757119045421095899911177627116595345331779978125106824482793025729130387051609948
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [750000, 1350001)
Primes: RFBsize:114155, AFBsize:114862, largePrimes:4398781 encountered
Relations: rels:4343529, finalFF:318275
Max relations in full relation-set: 28
Initial matrix: 229097 x 318275 with sparse part having weight 27359727.
Pruned matrix : 184410 x 185619 with weight 13182842.
Polynomial selection time: 0.31 hours.
Total sieving time: 3.52 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,49,49,2.6,2.6,50000
total time: 4.05 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047052k/8912896k available (2459k kernel code, 339236k reserved, 1247k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673804)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348)
Calibrating delay using timer specific routine.. 5344.23 BogoMIPS (lpj=2672116)
Calibrating delay using timer specific routine.. 5589.60 BogoMIPS (lpj=2794804)

Jul 23, 2008

By Sinkiti Sibata / GGNFS

(22·10¹⁴⁸+41)/9 = 2(4)₁₄₇9_<149> = 5063780237_<10> · 28583166325918913_<17> · C123

C123 = P41 · P82

P41 = 17402239799437999024534166513064894599063_<41>

P82 = 9704872554934624715117145597971219813583628402942201073104426199442049345595512483_<82>

Number: 24449_148
N=168886519423956864772830398013728626154547408630592155514741531403323179695674542221418226218787968070077564086556296603429
  ( 123 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=17402239799437999024534166513064894599063 (pp41)
 r2=9704872554934624715117145597971219813583628402942201073104426199442049345595512483 (pp82)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 38.93 hours.
Scaled time: 30.29 units (timescale=0.778).
Factorization parameters were as follows:
name: 24449_148
n: 168886519423956864772830398013728626154547408630592155514741531403323179695674542221418226218787968070077564086556296603429
m: 200000000000000000000000000000
c5: 1375
c0: 82
skew: 0.57
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 5250001)
Primes: RFBsize:114155, AFBsize:114334, largePrimes:3203085 encountered
Relations: rels:3335826, finalFF:257222
Max relations in full relation-set: 28
Initial matrix: 228555 x 257222 with sparse part having weight 34263507.
Pruned matrix : 221405 x 222611 with weight 28567526.
Total sieving time: 38.06 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.62 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 38.93 hours.
 --------- CPU info (if available) ----------

Jul 22, 2008 (4th)

By Robert Backstrom / GMP-ECM

(8·10¹⁶⁹-71)/9 = (8)₁₆₈1_<169> = 89 · 463 · 673 · 419791 · C156

C156 = P41 · P116

P41 = 47781549603347332166946262947607610229479_<41>

P116 = 15979679407133185494514008168674390360680444782139128263236808135037861497132308268172748142259881307507065765651839_<116>

Jul 22, 2008 (3rd)

By suberi / GMP-ECM

(4·10²³⁵-1)/3 = 1(3)₂₃₅_<236> = 13 · 67 · 677 · 7079 · 48775637 · 7554172820434544567959_<22> · 17218527001291015325523195827_<29> · 6303239909341182749584186343717_<31> · C137

C137 = P36 · C102

P36 = 103002075143888028035790451977073523_<36>

C102 = [775468795925606718265168401955990662675462021136190876422142039835490928358779949182032553037269496151_<102>]

Jul 22, 2008 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(22·10¹⁵⁵+41)/9 = 2(4)₁₅₄9_<156> = 3 · 31129227631_<11> · 1579287976025387_<16> · C130

C130 = P47 · P83

P47 = 45999919755091463993377327103075511881496406927_<47>

P83 = 36030655935244507282549301863752200400900959948706991027890149836194085839645629857_<83>

GMP-ECM 6.0.1 [powered by GMP 4.1.4] [ECM]
Input number is 1657407281744557318977622952657209008164750830211547757484769227847986576290000102482091734717402424938133879682164532903292819439 (130 digits)
Using B1=3870000, B2=5773430343, polynomial Dickson(6), sigma=219387156
Step 1 took 51500ms
Step 2 took 25750ms
********** Factor found in step 2: 45999919755091463993377327103075511881496406927
Found probable prime factor of 47 digits: 45999919755091463993377327103075511881496406927
Probable prime cofactor 36030655935244507282549301863752200400900959948706991027890149836194085839645629857 has 83 digits

7·10¹⁶⁹-9 = 6(9)₁₆₈1_<170> = 208699 · 241417849 · C157

C157 = P42 · P115

P42 = 260261239348850539688922265966919165310599_<42>

P115 = 5338248691337501107137922770641624082752782783076792345043666099791736776212975427477023032244417290856029907636859_<115>

Number: n
N=1389339220359877542274357801042835125646101146451738583460851033141648832587493612920864982552675488236762722326237405531715310872085039395485860784835768541
  ( 157 digits)
SNFS difficulty: 170 digits.
Divisors found:

Tue Jul 22 11:26:18 2008  prp42 factor: 260261239348850539688922265966919165310599
Tue Jul 22 11:26:18 2008  prp115 factor: 5338248691337501107137922770641624082752782783076792345043666099791736776212975427477023032244417290856029907636859
Tue Jul 22 11:26:18 2008  elapsed time 04:16:58 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 76.95 hours.
Scaled time: 111.43 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_6_9_168_1
n: 1389339220359877542274357801042835125646101146451738583460851033141648832587493612920864982552675488236762722326237405531715310872085039395485860784835768541
skew: 1.67
deg: 5
c5: 7
c0: -90
m: 10000000000000000000000000000000000
type: snfs
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 3500001)
Primes: RFBsize:425648, AFBsize:426372, largePrimes:10109777 encountered
Relations: rels:9700992, finalFF:871192
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 76.51 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,50,50,2.5,2.5,100000
total time: 76.95 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(22·10¹⁵⁸+41)/9 = 2(4)₁₅₇9_<159> = 3² · 23 · 6473 · 8629 · C149

C149 = P61 · P89

P61 = 1105326103418514975838635653554146491496662790047875884527581_<61>

P89 = 19127284756894328245610160409392789398531145245398183946272241072229624360054573707039191_<89>

Number: n
N=21141887129314365340413439278686685605805369645401750927238009940322413589021656829320590485472112245817998315002378156081032695372500342703287426971
  ( 149 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=1105326103418514975838635653554146491496662790047875884527581 (pp61)
 r2=19127284756894328245610160409392789398531145245398183946272241072229624360054573707039191 (pp89)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 25.64 hours.
Scaled time: 46.74 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_2_4_157_9
n: 21141887129314365340413439278686685605805369645401750927238009940322413589021656829320590485472112245817998315002378156081032695372500342703287426971
skew: 0.57
deg: 5
c5: 1375
c0: 82
m: 20000000000000000000000000000000
type: snfs
rlim: 3800000
alim: 3800000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:269987, AFBsize:269724, largePrimes:9478739 encountered
Relations: rels:8787558, finalFF:611556
Max relations in full relation-set: 48
Initial matrix: 539777 x 611556 with sparse part having weight 54924569.
Pruned matrix : 481221 x 483983 with weight 35223051.
Total sieving time: 23.38 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.00 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3800000,3800000,28,28,50,50,2.5,2.5,100000
total time: 25.64 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(22·10¹⁵⁰+41)/9 = 2(4)₁₄₉9_<151> = 7 · 23476275923_<11> · C140

C140 = P50 · P90

P50 = 16097965590711520018626138438225266068918017570413_<50>

P90 = 924021191327169870580703157780617527631433867785181172624034019357349260873271768572067393_<90>

Number: n
N=14874861343073046583956967287786005221131697004818390945830695295766361927386448243115974657528153010128905799588150001926913642418358843309
  ( 140 digits)
SNFS difficulty: 151 digits.
Divisors found:

Tue Jul 22 16:05:34 2008  prp50 factor: 16097965590711520018626138438225266068918017570413
Tue Jul 22 16:05:34 2008  prp90 factor: 924021191327169870580703157780617527631433867785181172624034019357349260873271768572067393
Tue Jul 22 16:05:34 2008  elapsed time 00:49:27 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 25.87 hours.
Scaled time: 44.79 units (timescale=1.731).
Factorization parameters were as follows:
name: KA_2_4_149_9
n: 14874861343073046583956967287786005221131697004818390945830695295766361927386448243115974657528153010128905799588150001926913642418358843309
type: snfs
skew: 1.13
deg: 5
c5: 22
c0: 41
m: 1000000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
qintsize: 100000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1200001)
Primes: RFBsize:148933, AFBsize:148322, largePrimes:6170485 encountered
Relations: rels:5474077, finalFF:325172
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 25.66 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,50,50,2.3,2.3,100000
total time: 25.87 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jul 22, 2008

By Sinkiti Sibata / GGNFS

(22·10¹⁴³+41)/9 = 2(4)₁₄₂9_<144> = 3 · 97 · 2457442313_<10> · C132

C132 = P61 · P71

P61 = 6803073944175257199768043132997513943459774741129425881805173_<61>

P71 = 50245672019300841540350636053956247113188991898199365782683211009817511_<71>

Number: 24449_143
N=341825022122081335958998419546470762029091886554630659976017195508658914361214371124388440953080000138856974651484571068809985784403
  ( 132 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=6803073944175257199768043132997513943459774741129425881805173 (pp61)
 r2=50245672019300841540350636053956247113188991898199365782683211009817511 (pp71)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 20.21 hours.
Scaled time: 15.56 units (timescale=0.770).
Factorization parameters were as follows:
name: 24449_143
n: 341825022122081335958998419546470762029091886554630659976017195508658914361214371124388440953080000138856974651484571068809985784403
m: 20000000000000000000000000000
c5: 1375
c0: 82
skew: 0.57
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2950001)
Primes: RFBsize:100021, AFBsize:100230, largePrimes:2954435 encountered
Relations: rels:3008883, finalFF:265588
Max relations in full relation-set: 28
Initial matrix: 200317 x 265588 with sparse part having weight 31931584.
Pruned matrix : 184165 x 185230 with weight 21048063.
Total sieving time: 19.70 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.33 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 20.21 hours.
 --------- CPU info (if available) ----------

(22·10¹⁷³+41)/9 = 2(4)₁₇₂9_<174> = 3 · C173

C173 = P70 · P104

P70 = 7247333544342156249361332950765992322106652729740454583309021232849433_<70>

P104 = 11242960046332128968771133199614355501934832225686603228803080298550488784257145880620332675742271558851_<104>

Number: 24449_173
N=81481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481483
  ( 173 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=7247333544342156249361332950765992322106652729740454583309021232849433 (pp70)
 r2=11242960046332128968771133199614355501934832225686603228803080298550488784257145880620332675742271558851 (pp104)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 271.39 hours.
Scaled time: 273.83 units (timescale=1.009).
Factorization parameters were as follows:
name: 24449_173
n: 81481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481483
m: 20000000000000000000000000000000000
c5: 1375
c0: 82
skew: 0.57
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 13400001)
Primes: RFBsize:501962, AFBsize:501393, largePrimes:6712203 encountered
Relations: rels:7232983, finalFF:1179697
Max relations in full relation-set: 28
Initial matrix: 1003421 x 1179697 with sparse part having weight 85859116.
Pruned matrix : 855294 x 860375 with weight 65427418.
Total sieving time: 264.22 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 6.86 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,174,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 271.39 hours.
 --------- CPU info (if available) ----------

Jul 21, 2008 (3rd)

By Wataru Sakai / GGNFS

6·10¹⁹⁶+1 = 6(0)₁₉₅1_<197> = C197

C197 = P67 · P131

P67 = 4526985911422555852980453461875447673693370404671619628486604463189_<67>

P131 = 13253851718117155717822280766012995701858464863771693748201984239161431357726436028994453405662098135543550990120795749232748691709_<131>

Number: 60001_196
N=60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
  ( 197 digits)
SNFS difficulty: 196 digits.
Divisors found:
 r1=4526985911422555852980453461875447673693370404671619628486604463189 (pp67)
 r2=13253851718117155717822280766012995701858464863771693748201984239161431357726436028994453405662098135543550990120795749232748691709 (pp131)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 2601.57 hours.
Scaled time: 5190.14 units (timescale=1.995).
Factorization parameters were as follows:
n: 60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
m: 1000000000000000000000000000000000000000
c5: 60
c0: 1
skew: 0.44
type: snfsFactor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 43700001)
Primes: RFBsize:501962, AFBsize:501211, largePrimes:8270429 encountered
Relations: rels:9230838, finalFF:1133951
Max relations in full relation-set: 32
Initial matrix: 1003240 x 1133951 with sparse part having weight 191292090.
Pruned matrix : 927307 x 932387 with weight 174534450.
Total sieving time: 2581.77 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 19.00 hours.
Time per square root: 0.36 hours.
Prototype def-par.txt line would be:
snfs,196,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 2601.57 hours.
 --------- CPU info (if available) ----------

Jul 21, 2008 (2nd)

By Jo Yeong Uk / GMP-ECM, Msieve

(22·10¹⁶⁶+41)/9 = 2(4)₁₆₅9_<167> = 53 · 83 · 8819 · 530427087249316307_<18> · 50263678452053034167_<20> · C122

C122 = P35 · P36 · P52

P35 = 57372938262772414492411144007923057_<35>

P36 = 225361366817860241485519425537206353_<36>

P52 = 1827849120928944890321391127384847605488278593446721_<52>

Mon Jul 21 12:58:41 2008  
Mon Jul 21 12:58:41 2008  
Mon Jul 21 12:58:41 2008  Msieve v. 1.34
Mon Jul 21 12:58:41 2008  random seeds: 002e7883 9734cdf0
Mon Jul 21 12:58:41 2008  factoring 104869074768719184432156021238416395118856035807718212846525806858901934786582196946097 (87 digits)
Mon Jul 21 12:58:41 2008  no P-1/P+1/ECM available, skipping
Mon Jul 21 12:58:41 2008  commencing quadratic sieve (87-digit input)
Mon Jul 21 12:58:41 2008  using multiplier of 1
Mon Jul 21 12:58:41 2008  using 32kb Intel Core sieve core
Mon Jul 21 12:58:41 2008  sieve interval: 17 blocks of size 32768
Mon Jul 21 12:58:41 2008  processing polynomials in batches of 12
Mon Jul 21 12:58:41 2008  using a sieve bound of 1470841 (55895 primes)
Mon Jul 21 12:58:41 2008  using large prime bound of 117667280 (26 bits)
Mon Jul 21 12:58:41 2008  using double large prime bound of 336651265440320 (41-49 bits)
Mon Jul 21 12:58:41 2008  using trial factoring cutoff of 49 bits
Mon Jul 21 12:58:41 2008  polynomial 'A' values have 11 factors
Mon Jul 21 13:34:54 2008  56176 relations (15553 full + 40623 combined from 590767 partial), need 55991
Mon Jul 21 13:34:54 2008  begin with 606320 relations
Mon Jul 21 13:34:54 2008  reduce to 134589 relations in 9 passes
Mon Jul 21 13:34:54 2008  attempting to read 134589 relations
Mon Jul 21 13:34:55 2008  recovered 134589 relations
Mon Jul 21 13:34:55 2008  recovered 114672 polynomials
Mon Jul 21 13:34:55 2008  attempting to build 56176 cycles
Mon Jul 21 13:34:55 2008  found 56176 cycles in 5 passes
Mon Jul 21 13:34:55 2008  distribution of cycle lengths:
Mon Jul 21 13:34:55 2008     length 1 : 15553
Mon Jul 21 13:34:55 2008     length 2 : 11023
Mon Jul 21 13:34:55 2008     length 3 : 10008
Mon Jul 21 13:34:55 2008     length 4 : 7469
Mon Jul 21 13:34:55 2008     length 5 : 5111
Mon Jul 21 13:34:55 2008     length 6 : 3141
Mon Jul 21 13:34:55 2008     length 7 : 1794
Mon Jul 21 13:34:55 2008     length 9+: 2077
Mon Jul 21 13:34:55 2008  largest cycle: 18 relations
Mon Jul 21 13:34:55 2008  matrix is 55895 x 56176 (13.3 MB) with weight 3027730 (53.90/col)
Mon Jul 21 13:34:55 2008  sparse part has weight 3027730 (53.90/col)
Mon Jul 21 13:34:55 2008  filtering completed in 3 passes
Mon Jul 21 13:34:55 2008  matrix is 51376 x 51440 (12.2 MB) with weight 2791920 (54.28/col)
Mon Jul 21 13:34:55 2008  sparse part has weight 2791920 (54.28/col)
Mon Jul 21 13:34:56 2008  saving the first 48 matrix rows for later
Mon Jul 21 13:34:56 2008  matrix is 51328 x 51440 (7.6 MB) with weight 2134271 (41.49/col)
Mon Jul 21 13:34:56 2008  sparse part has weight 1470468 (28.59/col)
Mon Jul 21 13:34:56 2008  matrix includes 64 packed rows
Mon Jul 21 13:34:56 2008  using block size 20576 for processor cache size 4096 kB
Mon Jul 21 13:34:56 2008  commencing Lanczos iteration
Mon Jul 21 13:34:56 2008  memory use: 7.1 MB
Mon Jul 21 13:35:05 2008  lanczos halted after 813 iterations (dim = 51328)
Mon Jul 21 13:35:05 2008  recovered 17 nontrivial dependencies
Mon Jul 21 13:35:05 2008  prp35 factor: 57372938262772414492411144007923057
Mon Jul 21 13:35:05 2008  prp52 factor: 1827849120928944890321391127384847605488278593446721
Mon Jul 21 13:35:05 2008  elapsed time 00:36:24

Jul 21, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(22·10¹⁵⁶+41)/9 = 2(4)₁₅₅9_<157> = 7² · 992111 · C149

C149 = P35 · P115

P35 = 34403366202778334391060150858471779_<35>

P115 = 1461580998276864345860844458718294113767553420340741001484818970216017514257778694796433577617315925915621203003029_<115>

8·10¹⁶⁸-9 = 7(9)₁₆₇1_<169> = 17 · 168837552669242694718423_<24> · C145

C145 = P44 · P102

P44 = 11681215841603794478271720614912632360063687_<44>

P102 = 238607433000818367820061770438598453100921190268658947143978441159074725390668672932146359772318330023_<102>

Number: n
N=2787224926293575534663953848834295056925125529822509299870571408485875014665190039863959156312828009389084493476356617788753739536968981764174801
  ( 145 digits)
SNFS difficulty: 168 digits.
Divisors found:

Mon Jul 21 11:20:53 2008  prp44 factor: 11681215841603794478271720614912632360063687
Mon Jul 21 11:20:53 2008  prp102 factor: 238607433000818367820061770438598453100921190268658947143978441159074725390668672932146359772318330023
Mon Jul 21 11:20:53 2008  elapsed time 02:05:02 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 43.83 hours.
Scaled time: 79.91 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_7_9_167_1
n: 2787224926293575534663953848834295056925125529822509299870571408485875014665190039863959156312828009389084493476356617788753739536968981764174801
skew: 0.51
deg: 5
c5: 250
c0: -9
m: 2000000000000000000000000000000000
type: snfs
rlim: 5800000
alim: 5800000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 2500001)
Primes: RFBsize:399993, AFBsize:399254, largePrimes:9743482 encountered
Relations: rels:9275445, finalFF:825351
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 43.56 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,50,50,2.5,2.5,100000
total time: 43.83 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jul 20, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(22·10¹⁵¹+41)/9 = 2(4)₁₅₀9_<152> = 50777 · C147

C147 = P59 · P89

P59 = 30747866532082367838345848099460820768463553615562170458503_<59>

P89 = 15656624858700526687871150149500413269209603785459994790145094019676577696231079026640879_<89>

Number: n
N=481407811498206755902169179834264419805117365036225937815240058381638230782528397590335081718976001820596814393218276866385261918672714899352944137
  ( 147 digits)
SNFS difficulty: 152 digits.
Divisors found:

Sun Jul 20 13:39:18 2008  prp59 factor: 30747866532082367838345848099460820768463553615562170458503
Sun Jul 20 13:39:18 2008  prp89 factor: 15656624858700526687871150149500413269209603785459994790145094019676577696231079026640879
Sun Jul 20 13:39:18 2008  elapsed time 01:23:08 (Msieve 1.36)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 20.54 hours.
Scaled time: 26.78 units (timescale=1.304).
Factorization parameters were as follows:
name: KA_2_4_150_9
n: 481407811498206755902169179834264419805117365036225937815240058381638230782528397590335081718976001820596814393218276866385261918672714899352944137
skew: 0.71
deg: 5
c5: 220
c0: 41
m: 1000000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1100001)
Primes: RFBsize:148933, AFBsize:149787, largePrimes:8214123 encountered
Relations: rels:7234772, finalFF:302813
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 20.33 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,50,50,2.5,2.5,100000
total time: 20.54 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(19·10¹⁶⁶+71)/9 = 2(1)₁₆₅9_<167> = 7 · 7253 · 54378083 · 50343939967158130056229_<23> · C132

C132 = P63 · P69

P63 = 301435271504692523257664371180080720857128869883045784752185487_<63>

P69 = 503883585883986267026777603663420832974904119028443835373022979452021_<69>

Number: n
N=151888285517697453349404132924871468767777805685695965312726172612353451929406967016381249252832945080495001996679890790773409019227
  ( 132 digits)
SNFS difficulty: 167 digits.
Divisors found:

Sun Jul 20 14:20:37 2008  prp63 factor: 301435271504692523257664371180080720857128869883045784752185487
Sun Jul 20 14:20:37 2008  prp69 factor: 503883585883986267026777603663420832974904119028443835373022979452021
Sun Jul 20 14:20:37 2008  elapsed time 02:27:03 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 58.26 hours.
Scaled time: 106.55 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_1_165_9
n: 151888285517697453349404132924871468767777805685695965312726172612353451929406967016381249252832945080495001996679890790773409019227
skew: 0.82
deg: 5
c5: 190
c0: 71
m: 1000000000000000000000000000000000
type: snfs
rlim: 5200000
alim: 5200000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5200000/5200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 3600000)
Primes: RFBsize:361407, AFBsize:361798, largePrimes:10438565 encountered
Relations: rels:10034059, finalFF:839198
Max relations in full relation-set: 28
Initial matrix: 723272 x 839198 with sparse part having weight 83825767.
Pruned matrix : 631948 x 635628 with weight 56173117.
Total sieving time: 57.88 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5200000,5200000,28,28,50,50,2.5,2.5,100000
total time: 58.26 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(28·10¹⁶⁹+17)/9 = 3(1)₁₆₈3_<170> = 3 · 11 · 19 · 310055033 · C159

C159 = P46 · P113

P46 = 2415206321322037173599420711140338010790023979_<46>

P113 = 66260538169077111369916032292205300925953034481165074616471999679785377784367854169703990146660279900274172153217_<113>

Number: n
N=160032870640155162550188298305797990544533418321959766573500508174037736228648792769050260989051569394837206366583950880158878277647558739735213553585491990443
  ( 159 digits)
SNFS difficulty: 171 digits.
Divisors found:

Sun Jul 20 15:32:22 2008  prp46 factor: 2415206321322037173599420711140338010790023979
Sun Jul 20 15:32:22 2008  prp113 factor: 66260538169077111369916032292205300925953034481165074616471999679785377784367854169703990146660279900274172153217
Sun Jul 20 15:32:22 2008  elapsed time 03:30:08 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 63.65 hours.
Scaled time: 111.13 units (timescale=1.746).
Factorization parameters were as follows:
name: KA_3_1_168_3
n: 160032870640155162550188298305797990544533418321959766573500508174037736228648792769050260989051569394837206366583950880158878277647558739735213553585491990443
type: snfs
skew: 1.43
deg: 5
c5: 14
c0: 85
m: 10000000000000000000000000000000000
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
qintsize: 100000
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 2300001)
Primes: RFBsize:425648, AFBsize:425672, largePrimes:10044587 encountered
Relations: rels:9775401, finalFF:976677
Max relations in full relation-set: 28
Initial matrix: 851386 x 976677 with sparse part having weight 58701082.
Pruned matrix : 
Total sieving time: 63.27 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,50,50,2.6,2.6,100000
total time: 63.65 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jul 20, 2008

By Sinkiti Sibata / GGNFS

(22·10¹⁴¹+41)/9 = 2(4)₁₄₀9_<142> = 29 · 149 · 5449 · 452946459853_<12> · 67357504684949_<14> · C109

C109 = P54 · P56

P54 = 330751162736293369432428637738428342414840410247225443_<54>

P56 = 10288329338218503898012571540672054405004510290431734211_<56>

Number: 24449_141
N=3402876891229689848436598461222854587652833006566211367190450112565004405320662633342669332652310661572730473
  ( 109 digits)
Divisors found:
 r1=330751162736293369432428637738428342414840410247225443 (pp54)
 r2=10288329338218503898012571540672054405004510290431734211 (pp56)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 22.97 hours.
Scaled time: 17.71 units (timescale=0.771).
Factorization parameters were as follows:
name: 24449_141
n: 3402876891229689848436598461222854587652833006566211367190450112565004405320662633342669332652310661572730473
skew: 30807.09
# norm 3.85e+15
c5: 69120
c4: 2895205464
c3: -280193627009614
c2: -2131733424676079691
c1: 98239689575495530872726
c0: -135859311080054690787186605
# alpha -6.94
Y1: 341702854723
Y0: -547578302901837438032
# Murphy_E 1.13e-09
# M 2624517538539014615930987387730867606025583956109033825991318871842305983421265016580000378459286719069186525
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2900001)
Primes: RFBsize:230209, AFBsize:230058, largePrimes:7228712 encountered
Relations: rels:6973746, finalFF:525266
Max relations in full relation-set: 28
Initial matrix: 460344 x 525266 with sparse part having weight 39329504.
Pruned matrix : 407937 x 410302 with weight 26054930.
Total sieving time: 20.82 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 1.61 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 22.97 hours.
 --------- CPU info (if available) ----------

(22·10¹⁵⁴+41)/9 = 2(4)₁₅₃9_<155> = 17 · 3610089887_<10> · 616771282165439_<15> · 104974090577393839_<18> · 925466719406338609_<18> · C94

C94 = P45 · P50

P45 = 459905896132990216649786240439121054688244443_<45>

P50 = 14453638434218503727640096477729668894378052287453_<50>

Number: 24449_154
N=6647313536471490523384054516889594848412193076035299505863961930987106914439120763464965873679
  ( 94 digits)
Divisors found:
 r1=459905896132990216649786240439121054688244443 (pp45)
 r2=14453638434218503727640096477729668894378052287453 (pp50)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 8.02 hours.
Scaled time: 6.14 units (timescale=0.765).
Factorization parameters were as follows:
name: 24449_154
n:  6647313536471490523384054516889594848412193076035299505863961930987106914439120763464965873679
m:  3925432779428596964968
deg: 4
c4: 27996000
c3: -86903748365
c2: 550027718475813193
c1: 229055727357494269
c0: -454436951428866878844665
skew: 1635.250
type: gnfs
# adj. I(F,S) = 55.859
# E(F1,F2) = 3.999849e-05
# GGNFS version 0.77.1-20050930-nocona polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1216504368.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1380001)
Primes: RFBsize:92938, AFBsize:93133, largePrimes:1934443 encountered
Relations: rels:2058820, finalFF:267616
Max relations in full relation-set: 28
Initial matrix: 186148 x 267616 with sparse part having weight 23334623.
Pruned matrix : 154321 x 155315 with weight 11475763.
Total sieving time: 7.74 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,93,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 8.02 hours.
 --------- CPU info (if available) ----------

(22·10¹³⁹+41)/9 = 2(4)₁₃₈9_<140> = 1181 · 1423 · 5985013 · 27989977 · 1178781981409_<13> · C107

C107 = P36 · P72

P36 = 316278564394734722828161457146528573_<36>

P72 = 232891954950910687233387848924968216474272090842685731013040356996107539_<72>

Number: 24449_139
N=73658733170957263936885436254788076953910255688365008131780721746620663191907956191768368728974527244211847
  ( 107 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=316278564394734722828161457146528573 (pp36)
 r2=232891954950910687233387848924968216474272090842685731013040356996107539 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.91 hours.
Scaled time: 9.29 units (timescale=0.780).
Factorization parameters were as follows:
name: 24449_139
n: 73658733170957263936885436254788076953910255688365008131780721746620663191907956191768368728974527244211847
m: 10000000000000000000000000000
c5: 11
c0: 205
skew: 1.8
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1950001)
Primes: RFBsize:100021, AFBsize:100200, largePrimes:2746564 encountered
Relations: rels:2719321, finalFF:249721
Max relations in full relation-set: 28
Initial matrix: 200286 x 249721 with sparse part having weight 24385516.
Pruned matrix : 185707 x 186772 with weight 16198328.
Total sieving time: 11.48 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 11.91 hours.
 --------- CPU info (if available) ----------

Jul 19, 2008 (5th)

By Sinkiti Sibata / GGNFS

(22·10¹³⁷+41)/9 = 2(4)₁₃₆9_<138> = 3 · 197 · 4721 · 21532792806979_<14> · 2558904966847610279_<19> · C100

C100 = P45 · P55

P45 = 866628596690676908124381538472636863619623849_<45>

P55 = 1834725747446334136962416765898795700139838509999294251_<55>

Number: 24449_137
N=1590025799821669844965039915392518155073858809059005816989579180428522176731895180810762304088192099
  ( 100 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=866628596690676908124381538472636863619623849 (pp45)
 r2=1834725747446334136962416765898795700139838509999294251 (pp55)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 15.16 hours.
Scaled time: 7.16 units (timescale=0.472).
Factorization parameters were as follows:
name: 24449_137
n: 1590025799821669844965039915392518155073858809059005816989579180428522176731895180810762304088192099
m: 1000000000000000000000000000
c5: 2200
c0: 41
skew: 0.45
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 2050001)
Primes: RFBsize:78498, AFBsize:63670, largePrimes:1652714 encountered
Relations: rels:1677088, finalFF:173641
Max relations in full relation-set: 28
Initial matrix: 142235 x 173641 with sparse part having weight 18526781.
Pruned matrix : 134432 x 135207 with weight 12954715.
Total sieving time: 14.63 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.37 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 15.16 hours.
 --------- CPU info (if available) ----------

Jul 19, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve

(22·10¹³⁵+41)/9 = 2(4)₁₃₄9_<136> = 19 · 59 · 197217048137_<12> · 3473512671526180949462569_<25> · C97

C97 = P34 · P64

P34 = 2065104407058693668461888789327799_<34>

P64 = 1541413660666489857341708687188271597185167763339609496930078327_<64>

Number: n
N=3183180143742841983978949218813441515939722303188901929973696523261819759463827185617358748512273
  ( 97 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=2065104407058693668461888789327799 (pp34)
 r2=1541413660666489857341708687188271597185167763339609496930078327 (pp64)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 5.54 hours.
Scaled time: 7.25 units (timescale=1.309).
Factorization parameters were as follows:
name: KA_2_4_134_9
n: 3183180143742841983978949218813441515939722303188901929973696523261819759463827185617358748512273
skew: 1.13
deg: 5
c5: 22
c0: 41
m: 1000000000000000000000000000
type: snfs
rlim: 950000
alim: 950000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 950000/950000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [100000, 700001)
Primes: RFBsize:74907, AFBsize:74185, largePrimes:7821834 encountered
Relations: rels:7065344, finalFF:237913
Max relations in full relation-set: 28
Initial matrix: 149158 x 237913 with sparse part having weight 25256409.
Pruned matrix : 129264 x 130073 with weight 11067695.
Total sieving time: 4.87 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.42 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,950000,950000,28,28,50,50,2.5,2.5,75000
total time: 5.54 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(65·10¹⁶⁷+43)/9 = 7(2)₁₆₆7_<168> = 11 · 5879 · 31159 · 286831 · 517095792649_<12> · C142

C142 = P49 · P93

P49 = 6350896847958870927475301612070577433786600427541_<49>

P93 = 380503836982596483446568644330742044611360532394516326298199791512990729260726018085652941203_<93>

Number: n
N=2416540618929028067669513756315393816139046863325989248996067013124199091486295011457802290992087222445824703172180542641244773807423934871823
  ( 142 digits)
SNFS difficulty: 168 digits.
Divisors found:

Sat Jul 19 16:15:17 2008  prp49 factor: 6350896847958870927475301612070577433786600427541
Sat Jul 19 16:15:17 2008  prp93 factor: 380503836982596483446568644330742044611360532394516326298199791512990729260726018085652941203
Sat Jul 19 16:15:17 2008  elapsed time 02:23:29 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 44.76 hours.
Scaled time: 82.09 units (timescale=1.834).
Factorization parameters were as follows:
name: KA_7_2_166_7
n: 2416540618929028067669513756315393816139046863325989248996067013124199091486295011457802290992087222445824703172180542641244773807423934871823
skew: 0.37
deg: 5
c5: 6500
c0: 43
m: 1000000000000000000000000000000000
type: snfs
rlim: 5800000
alim: 5800000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 2700209)
Primes: RFBsize:399993, AFBsize:399914, largePrimes:9845687 encountered
Relations: rels:9387478, finalFF:832705
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 44.42 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,50,50,2.5,2.5,100000
total time: 44.76 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jul 19, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(22·10¹⁴⁵+41)/9 = 2(4)₁₄₄9_<146> = 107 · 649488379249_<12> · C132

C132 = P36 · P97

P36 = 330656667519370766780036608680693031_<36>

P97 = 1063769965393139226970800550235148159416860116316758164927268244022746113357233560752845829368053_<97>

Number: 24449_145
N=351742631764091784060929143940635209161080432608066070671172188248276741820313159008906507475054840176158667869578115152472811138643
  ( 132 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=330656667519370766780036608680693031 (pp36)
 r2=1063769965393139226970800550235148159416860116316758164927268244022746113357233560752845829368053 (pp97)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 22.76 hours.
Scaled time: 17.66 units (timescale=0.776).
Factorization parameters were as follows:
name: 24449_145
n: 351742631764091784060929143940635209161080432608066070671172188248276741820313159008906507475054840176158667869578115152472811138643
m: 100000000000000000000000000000
c5: 22
c0: 41
skew: 1.13
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 3250001)
Primes: RFBsize:114155, AFBsize:113514, largePrimes:2953981 encountered
Relations: rels:2977548, finalFF:281309
Max relations in full relation-set: 28
Initial matrix: 227735 x 281309 with sparse part having weight 31945458.
Pruned matrix : 212164 x 213366 with weight 22643648.
Total sieving time: 22.10 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.47 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 22.76 hours.
 --------- CPU info (if available) ----------

Jul 19, 2008 (2nd)

By Serge Batalov / Msieve

(4·10²⁰⁷-1)/3 = 1(3)₂₀₇_<208> = 227 · C205

C205 = P100 · P106

P100 = 3999406295062729501331514001724671368377647689512510156551098073080765712556308639257272683646862107_<100>

P106 = 1468646766913267291096484238457962531138809604380942950365724174756132537097046980347507927618050634373797_<106>

Number: 13333_207
N=5873715124816446402349486049926578560939794419970631424375917767988252569750367107195301027900146842878120411160058737151248164464023494860499265785609397944199706314243759177679882525697503671071953010279
  ( 205 digits)
SNFS difficulty: 207 digits.
Divisors found:
 r1=3999406295062729501331514001724671368377647689512510156551098073080765712556308639257272683646862107 (p100)
 r2=1468646766913267291096484238457962531138809604380942950365724174756132537097046980347507927618050634373797 (p106)

Version: Msieve 1.36
Total time: 25 CPU-days. (timescale=2.952).
Factorization parameters were as follows:
n: 5873715124816446402349486049926578560939794419970631424375917767988252569750367107195301027900146842878120411160058737151248164464023494860499265785609397944199706314243759177679882525697503671071953010279
Y0: -200000000000000000000000000000000000000000
Y1: 1
c0: -2
c5: 25
skew: 0.65
type: snfs
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
rlim: 20000000
alim: 20000000
Factor base limits: 20000000/20000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved rational special-q in [10000000, 22300001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: 42704260 relations (38902786 unique relations and about 34331443 large ideals)
Max relations in full relation-set: 
Initial matrix: 3899964 x 3900911 (1179.1 MB) with weight 369366720 (94.69/col)
sparse part has weight 266186760 (68.24/col)
(memory use: 1591.7 MB)
Pruned matrix : 3845390 x 3845638 (1123.7 MB) with weight 283186391 (73.64/col)
sparse part has weight 256108183 (66.60/col)
Total sieving time: 20 CPU-days..
Total relation processing time: 1.00 hours.
Matrix solve time: 84:14:53
recovered 48 nontrivial dependencies
Time per square root: 01:02:59 (on 1st dependency)
Prototype def-par.txt line would be:
snfs,207,5,0,0,0,0,0,0,0,0,20000000,20000000,29,29,58,58,2.6,2.6,100000

total time: 25 CPU-days. (8 calendar days; the matrix step was on a single CPU)

 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS

All stages were under 2.0Gb of memory (the C200+'s _can_ be now done on home computers)

P.S. Many thanks to JasonP, the greatest.

C205 is the largest snfs-factored composite number in our tables so far and P100 is also the largest snfs-discovered prime factor in our tables so far. In addition, this effort shows that you can factor numbers which have 200 digits or more by your home computers with 2GB memory. Congratulations on the exciting records!!! See also www.mersenneforum.org.

(22·10¹²¹+41)/9 = 2(4)₁₂₀9_<122> = 131041 · 2319738263_<10> · C107

C107 = P35 · P73

P35 = 25062368393601465451556297653785029_<35>

P73 = 3208572650535973954961225795597759882808586084195449958716499723851512507_<73>

Number: 24449_121
N=80414429785366873756397237324162557271658995122046202935508783138144456898631522252449895246859675082857703
  ( 107 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=25062368393601465451556297653785029
 r2=3208572650535973954961225795597759882808586084195449958716499723851512507
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.314).
Factorization parameters were as follows:
n: 80414429785366873756397237324162557271658995122046202935508783138144456898631522252449895246859675082857703
Y1: 1
Y0: -1000000000000000000000000
c5: 220
c0: 41
skew: 0.71
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 500001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 102792 x 103019
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000

total time: 1.10 hours.

Jul 19, 2008

By Robert Backstrom / GGNFS, GMP-ECM

(22·10¹¹⁴+41)/9 = 2(4)₁₁₃9_<115> = 7² · 23 · 53 · C110

C110 = P38 · P73

P38 = 36786423298913986934702187003334911349_<38>

P73 = 1112481561942967290761054206790315374836962739575611381377759806988761071_<73>

Number: n
N=40924217649870995704817338474903223526216611884020767180265598172547662762124264526702121920685145811127294779
  ( 110 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=36786423298913986934702187003334911349 (pp38)
 r2=1112481561942967290761054206790315374836962739575611381377759806988761071 (pp73)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 1.32 hours.
Scaled time: 1.73 units (timescale=1.308).
Factorization parameters were as follows:
name: KA_2_4_113_9
n: 40924217649870995704817338474903223526216611884020767180265598172547662762124264526702121920685145811127294779
skew: 1.80
deg: 5
c5: 11
c0: 205
m: 100000000000000000000000
type: snfs
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [100000, 200001)
Primes: RFBsize:41538, AFBsize:41594, largePrimes:3882954 encountered
Relations: rels:3287386, finalFF:111057
Max relations in full relation-set: 28
Initial matrix: 83197 x 111057 with sparse part having weight 8625133.
Pruned matrix : 74572 x 75051 with weight 4207667.
Total sieving time: 1.16 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.06 hours.
Total square root time: 0.03 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,500000,500000,28,28,50,50,2.5,2.5,50000
total time: 1.32 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(22·10¹³¹+41)/9 = 2(4)₁₃₀9_<132> = 3² · 4787 · 6966823 · 1281492591809_<13> · 19736198501419_<14> · C95

C95 = P32 · P63

P32 = 38341155108220418699692555245493_<32>

P63 = 839836335247171403374568311996768228503199306945428622409955187_<63>

Jul 18, 2008 (8th)

By Jo Yeong Uk / GMP-ECM

8·10¹⁶⁷+3 = 8(0)₁₆₆3_<168> = 251467910385709_<15> · 126974570731714215575127079_<27> · C128

C128 = P45 · P83

P45 = 837436146854618446845679601742976105039316057_<45>

P83 = 29918440904777602878053870979485087624956432150490430623595618437356372457311766689_<83>

GMP-ECM 6.2 [powered by GMP 4.2.2] [ECM]
Input number is 25054783871194560239401225829811852453817515096204346029171349857158592954195626273041212563779604664854740343106865830915425273 (128 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=127447873
Step 1 took 6030ms
Step 2 took 2946ms
********** Factor found in step 2: 837436146854618446845679601742976105039316057
Found probable prime factor of 45 digits: 837436146854618446845679601742976105039316057
Probable prime cofactor 29918440904777602878053870979485087624956432150490430623595618437356372457311766689 has 83 digits

Jul 18, 2008 (7th)

By Robert Backstrom / GGNFS, Msieve

5·10¹⁶⁸-1 = 4(9)₁₆₈_<169> = 71 · 461 · 1609 · 14951 · 80777981 · C149

C149 = P41 · P45 · P64

P41 = 22639721157902129095414403005942496800349_<41>

P45 = 457434303099638694586122437203847366912844131_<45>

P64 = 7590871641081854629092704253048698545019692817001067700599918729_<64>

Number: n
N=78612471559442958193948932412621943215928354030608716743603360935146350691540877706643356686115717423275593902051381288373526750237641857883878895151
  ( 149 digits)
SNFS difficulty: 169 digits.
Divisors found:

Fri Jul 18 13:57:52 2008  prp41 factor: 22639721157902129095414403005942496800349
Fri Jul 18 13:57:52 2008  prp45 factor: 457434303099638694586122437203847366912844131
Fri Jul 18 13:57:52 2008  prp64 factor: 7590871641081854629092704253048698545019692817001067700599918729
Fri Jul 18 13:57:52 2008  elapsed time 03:10:45 (Msieve 1.36)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 55.74 hours.
Scaled time: 36.51 units (timescale=0.655).
Factorization parameters were as follows:
name: KA_4_9_168
n: 78612471559442958193948932412621943215928354030608716743603360935146350691540877706643356686115717423275593902051381288373526750237641857883878895151
skew: 0.91
deg: 5
c5: 8
c0: -5
m: 5000000000000000000000000000000000
type: snfs
rlim: 5800000
alim: 5800000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 2402509)
Primes: RFBsize:399993, AFBsize:399814, largePrimes:9619479 encountered
Relations: rels:9166302, finalFF:834416
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 55.38 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,50,50,2.5,2.5,100000
total time: 55.74 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jul 18, 2008 (6th)

By Sinkiti Sibata / Msieve, GGNFS

(22·10¹³⁶+41)/9 = 2(4)₁₃₅9_<137> = 23 · 61 · 178844202666818707982925019_<27> · 8717675454678942130350489919_<28> · C80

C80 = P36 · P44

P36 = 531452776093609479259543855857961849_<36>

P44 = 21027239274346636115400378553683570984303247_<44>

Fri Jul 18 13:45:18 2008  Msieve v. 1.36
Fri Jul 18 13:45:18 2008  random seeds: 46217630 d69eac1b
Fri Jul 18 13:45:18 2008  factoring 11174984685936094268528804965283109768871202961445260752328824538012748772823703 (80 digits)
Fri Jul 18 13:45:19 2008  no P-1/P+1/ECM available, skipping
Fri Jul 18 13:45:19 2008  commencing quadratic sieve (80-digit input)
Fri Jul 18 13:45:19 2008  using multiplier of 1
Fri Jul 18 13:45:19 2008  using 64kb Pentium 4 sieve core
Fri Jul 18 13:45:19 2008  sieve interval: 6 blocks of size 65536
Fri Jul 18 13:45:19 2008  processing polynomials in batches of 17
Fri Jul 18 13:45:19 2008  using a sieve bound of 1186657 (45938 primes)
Fri Jul 18 13:45:19 2008  using large prime bound of 118665700 (26 bits)
Fri Jul 18 13:45:19 2008  using trial factoring cutoff of 27 bits
Fri Jul 18 13:45:19 2008  polynomial 'A' values have 10 factors
Fri Jul 18 14:00:45 2008  46148 relations (23831 full + 22317 combined from 251282 partial), need 46034
Fri Jul 18 14:00:46 2008  begin with 275113 relations
Fri Jul 18 14:00:46 2008  reduce to 65721 relations in 2 passes
Fri Jul 18 14:00:46 2008  attempting to read 65721 relations
Fri Jul 18 14:00:48 2008  recovered 65721 relations
Fri Jul 18 14:00:48 2008  recovered 53985 polynomials
Fri Jul 18 14:00:48 2008  attempting to build 46148 cycles
Fri Jul 18 14:00:48 2008  found 46148 cycles in 1 passes
Fri Jul 18 14:00:48 2008  distribution of cycle lengths:
Fri Jul 18 14:00:48 2008     length 1 : 23831
Fri Jul 18 14:00:48 2008     length 2 : 22317
Fri Jul 18 14:00:48 2008  largest cycle: 2 relations
Fri Jul 18 14:00:48 2008  matrix is 45938 x 46148 (6.0 MB) with weight 1395149 (30.23/col)
Fri Jul 18 14:00:48 2008  sparse part has weight 1395149 (30.23/col)
Fri Jul 18 14:00:48 2008  filtering completed in 3 passes
Fri Jul 18 14:00:48 2008  matrix is 32312 x 32375 (4.7 MB) with weight 1091791 (33.72/col)
Fri Jul 18 14:00:48 2008  sparse part has weight 1091791 (33.72/col)
Fri Jul 18 14:00:48 2008  saving the first 48 matrix rows for later
Fri Jul 18 14:00:48 2008  matrix is 32264 x 32375 (2.8 MB) with weight 793320 (24.50/col)
Fri Jul 18 14:00:48 2008  sparse part has weight 546231 (16.87/col)
Fri Jul 18 14:00:48 2008  matrix includes 64 packed rows
Fri Jul 18 14:00:48 2008  using block size 12950 for processor cache size 512 kB
Fri Jul 18 14:00:49 2008  commencing Lanczos iteration
Fri Jul 18 14:00:49 2008  memory use: 3.4 MB
Fri Jul 18 14:00:57 2008  lanczos halted after 512 iterations (dim = 32262)
Fri Jul 18 14:00:57 2008  recovered 16 nontrivial dependencies
Fri Jul 18 14:00:57 2008  prp36 factor: 531452776093609479259543855857961849
Fri Jul 18 14:00:57 2008  prp44 factor: 21027239274346636115400378553683570984303247
Fri Jul 18 14:00:57 2008  elapsed time 00:15:39

(22·10¹¹⁹+41)/9 = 2(4)₁₁₈9_<120> = 3 · 607 · 19426872662255651093434709_<26> · C91

C91 = P41 · P51

P41 = 47566566335345876577853460008460440738421_<41>

P51 = 145266519005140854768685462486158749326268729347421_<51>

Fri Jul 18 14:36:07 2008  Msieve v. 1.36
Fri Jul 18 14:36:07 2008  random seeds: 02092aa2 9098e17e
Fri Jul 18 14:36:07 2008  factoring 6909829512562814960843460860887417512953556989063562541544742552648533771432775918691962241 (91 digits)
Fri Jul 18 14:36:08 2008  no P-1/P+1/ECM available, skipping
Fri Jul 18 14:36:08 2008  commencing quadratic sieve (91-digit input)
Fri Jul 18 14:36:08 2008  using multiplier of 1
Fri Jul 18 14:36:08 2008  using 64kb Pentium 4 sieve core
Fri Jul 18 14:36:08 2008  sieve interval: 18 blocks of size 65536
Fri Jul 18 14:36:08 2008  processing polynomials in batches of 6
Fri Jul 18 14:36:08 2008  using a sieve bound of 1719241 (64706 primes)
Fri Jul 18 14:36:08 2008  using large prime bound of 165047136 (27 bits)
Fri Jul 18 14:36:08 2008  using double large prime bound of 619005322436736 (42-50 bits)
Fri Jul 18 14:36:08 2008  using trial factoring cutoff of 50 bits
Fri Jul 18 14:36:08 2008  polynomial 'A' values have 12 factors
Fri Jul 18 17:27:51 2008  65119 relations (16691 full + 48428 combined from 768023 partial), need 64802
Fri Jul 18 17:27:53 2008  begin with 784714 relations
Fri Jul 18 17:27:54 2008  reduce to 163266 relations in 10 passes
Fri Jul 18 17:27:54 2008  attempting to read 163266 relations
Fri Jul 18 17:27:59 2008  recovered 163266 relations
Fri Jul 18 17:27:59 2008  recovered 143283 polynomials
Fri Jul 18 17:27:59 2008  attempting to build 65119 cycles
Fri Jul 18 17:27:59 2008  found 65119 cycles in 5 passes
Fri Jul 18 17:27:59 2008  distribution of cycle lengths:
Fri Jul 18 17:27:59 2008     length 1 : 16691
Fri Jul 18 17:27:59 2008     length 2 : 12043
Fri Jul 18 17:27:59 2008     length 3 : 11400
Fri Jul 18 17:27:59 2008     length 4 : 8911
Fri Jul 18 17:27:59 2008     length 5 : 6291
Fri Jul 18 17:27:59 2008     length 6 : 3993
Fri Jul 18 17:27:59 2008     length 7 : 2570
Fri Jul 18 17:27:59 2008     length 9+: 3220
Fri Jul 18 17:27:59 2008  largest cycle: 19 relations
Fri Jul 18 17:27:59 2008  matrix is 64706 x 65119 (16.1 MB) with weight 3956681 (60.76/col)
Fri Jul 18 17:27:59 2008  sparse part has weight 3956681 (60.76/col)
Fri Jul 18 17:28:01 2008  filtering completed in 3 passes
Fri Jul 18 17:28:01 2008  matrix is 60964 x 61028 (15.1 MB) with weight 3719537 (60.95/col)
Fri Jul 18 17:28:01 2008  sparse part has weight 3719537 (60.95/col)
Fri Jul 18 17:28:01 2008  saving the first 48 matrix rows for later
Fri Jul 18 17:28:01 2008  matrix is 60916 x 61028 (9.7 MB) with weight 2948615 (48.32/col)
Fri Jul 18 17:28:01 2008  sparse part has weight 2173245 (35.61/col)
Fri Jul 18 17:28:01 2008  matrix includes 64 packed rows
Fri Jul 18 17:28:01 2008  using block size 21845 for processor cache size 512 kB
Fri Jul 18 17:28:02 2008  commencing Lanczos iteration
Fri Jul 18 17:28:02 2008  memory use: 9.4 MB
Fri Jul 18 17:28:40 2008  lanczos halted after 965 iterations (dim = 60913)
Fri Jul 18 17:28:40 2008  recovered 15 nontrivial dependencies
Fri Jul 18 17:28:42 2008  prp41 factor: 47566566335345876577853460008460440738421
Fri Jul 18 17:28:42 2008  prp51 factor: 145266519005140854768685462486158749326268729347421
Fri Jul 18 17:28:42 2008  elapsed time 02:52:35

(22·10¹²²+41)/9 = 2(4)₁₂₁9_<123> = 3³ · 17 · 397 · 509 · 226522559 · 20019177865109_<14> · C93

C93 = P37 · P57

P37 = 2479394702744903130958322262280605137_<37>

P57 = 234399040945537669940119153419177139386619105466093573281_<57>

Fri Jul 18 17:41:27 2008  Msieve v. 1.36
Fri Jul 18 17:41:27 2008  random seeds: f13eb197 24f0b957
Fri Jul 18 17:41:27 2008  factoring 581167740448851748884915075302866508210009792004549285245839702179434977036441317607334544497 (93 digits)
Fri Jul 18 17:41:28 2008  no P-1/P+1/ECM available, skipping
Fri Jul 18 17:41:28 2008  commencing quadratic sieve (93-digit input)
Fri Jul 18 17:41:29 2008  using multiplier of 17
Fri Jul 18 17:41:29 2008  using 64kb Pentium 4 sieve core
Fri Jul 18 17:41:29 2008  sieve interval: 18 blocks of size 65536
Fri Jul 18 17:41:29 2008  processing polynomials in batches of 6
Fri Jul 18 17:41:29 2008  using a sieve bound of 1956901 (72801 primes)
Fri Jul 18 17:41:29 2008  using large prime bound of 244612625 (27 bits)
Fri Jul 18 17:41:29 2008  using double large prime bound of 1256787622996125 (42-51 bits)
Fri Jul 18 17:41:29 2008  using trial factoring cutoff of 51 bits
Fri Jul 18 17:41:29 2008  polynomial 'A' values have 12 factors
Fri Jul 18 21:47:43 2008  73312 relations (18883 full + 54429 combined from 988028 partial), need 72897
Fri Jul 18 21:47:46 2008  begin with 1006911 relations
Fri Jul 18 21:47:47 2008  reduce to 185758 relations in 11 passes
Fri Jul 18 21:47:47 2008  attempting to read 185758 relations
Fri Jul 18 21:47:53 2008  recovered 185758 relations
Fri Jul 18 21:47:53 2008  recovered 166149 polynomials
Fri Jul 18 21:47:54 2008  attempting to build 73312 cycles
Fri Jul 18 21:47:54 2008  found 73312 cycles in 5 passes
Fri Jul 18 21:47:54 2008  distribution of cycle lengths:
Fri Jul 18 21:47:54 2008     length 1 : 18883
Fri Jul 18 21:47:54 2008     length 2 : 13309
Fri Jul 18 21:47:54 2008     length 3 : 12540
Fri Jul 18 21:47:54 2008     length 4 : 9829
Fri Jul 18 21:47:54 2008     length 5 : 7230
Fri Jul 18 21:47:54 2008     length 6 : 4642
Fri Jul 18 21:47:54 2008     length 7 : 3012
Fri Jul 18 21:47:54 2008     length 9+: 3867
Fri Jul 18 21:47:54 2008  largest cycle: 18 relations
Fri Jul 18 21:47:54 2008  matrix is 72801 x 73312 (18.6 MB) with weight 4575927 (62.42/col)
Fri Jul 18 21:47:54 2008  sparse part has weight 4575927 (62.42/col)
Fri Jul 18 21:47:56 2008  filtering completed in 3 passes
Fri Jul 18 21:47:56 2008  matrix is 68635 x 68698 (17.4 MB) with weight 4293577 (62.50/col)
Fri Jul 18 21:47:56 2008  sparse part has weight 4293577 (62.50/col)
Fri Jul 18 21:47:56 2008  saving the first 48 matrix rows for later
Fri Jul 18 21:47:56 2008  matrix is 68587 x 68698 (10.7 MB) with weight 3329385 (48.46/col)
Fri Jul 18 21:47:56 2008  sparse part has weight 2391376 (34.81/col)
Fri Jul 18 21:47:56 2008  matrix includes 64 packed rows
Fri Jul 18 21:47:56 2008  using block size 21845 for processor cache size 512 kB
Fri Jul 18 21:47:57 2008  commencing Lanczos iteration
Fri Jul 18 21:47:57 2008  memory use: 10.6 MB
Fri Jul 18 21:48:46 2008  lanczos halted after 1086 iterations (dim = 68583)
Fri Jul 18 21:48:46 2008  recovered 14 nontrivial dependencies
Fri Jul 18 21:48:50 2008  prp37 factor: 2479394702744903130958322262280605137
Fri Jul 18 21:48:50 2008  prp57 factor: 234399040945537669940119153419177139386619105466093573281
Fri Jul 18 21:48:50 2008  elapsed time 04:07:23

(22·10¹³⁸+41)/9 = 2(4)₁₃₇9_<139> = 7 · 17 · 31 · 193 · 373 · 673 · 937 · 41161 · C120

C120 = P36 · P84

P36 = 610651208920497670366733893531787309_<36>

P84 = 580726416089174434252413269353020068317056403185036791065062056709332599816085902681_<84>

Number: 24449_138
N=354621288036922317129460378447709402989326839295547924604905462758134623744329528219757499403532898824792484232564875429
  ( 120 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=610651208920497670366733893531787309 (pp36)
 r2=580726416089174434252413269353020068317056403185036791065062056709332599816085902681 (pp84)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 13.03 hours.
Scaled time: 10.18 units (timescale=0.781).
Factorization parameters were as follows:
name: 24449_138
n: 354621288036922317129460378447709402989326839295547924604905462758134623744329528219757499403532898824792484232564875429
m: 2000000000000000000000000000
c5: 1375
c0: 82
skew: 0.57
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 2125001)
Primes: RFBsize:78498, AFBsize:64075, largePrimes:1684247 encountered
Relations: rels:1730964, finalFF:191244
Max relations in full relation-set: 28
Initial matrix: 142639 x 191244 with sparse part having weight 20674544.
Pruned matrix : 131077 x 131854 with weight 12803762.
Total sieving time: 12.77 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 13.03 hours.
 --------- CPU info (if available) ----------

Jul 18, 2008 (5th)

By Serge Batalov / GMP-ECM, Msieve

(22·10¹³⁰+41)/9 = 2(4)₁₂₉9_<131> = 623007889151_<12> · 391864797803729335146086239_<27> · C93

C93 = P34 · P59

P34 = 2404106623587392833380957646953757_<34>

P59 = 41648239554086215738636228680214783731775995314642888620213_<59>

(22·10¹⁴⁰+41)/9 = 2(4)₁₃₉9_<141> = 3² · 53 · 385157668968708457_<18> · C121

C121 = P33 · P88

P33 = 636996487870315120894764412495687_<33>

P88 = 2088748759088354916772576445771665562338190776869101189675739705777594695442923658592843_<88>

(22·10¹¹²+41)/9 = 2(4)₁₁₁9_<113> = 6389 · 882751 · C103

C103 = P49 · P55

P49 = 3337089450937904685056902869759131185338950859791_<49>

P55 = 1298796820924815062861063233533242770022606282492927501_<55>

Number: 24449_112
N=4334201170019887212757136278967289763497618984157758520106755541166969075712698056910874692340579012291
  ( 103 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=3337089450937904685056902869759131185338950859791
 r2=1298796820924815062861063233533242770022606282492927501
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.300).
Factorization parameters were as follows:
n: 4334201170019887212757136278967289763497618984157758520106755541166969075712698056910874692340579012291
Y1: 1
Y0: -10000000000000000000000
c5: 2200
c0: 41
skew: 0.45
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 400001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 85491 x 85712
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000

total time: 0.90 hours.

(22·10¹⁹⁶+41)/9 = 2(4)₁₉₅9_<197> = 61 · 29927 · 14045039 · 175281864497_<12> · 78685402711417120250969_<23> · 121595069518936332737259113161_<30> · 164769187376264668609706570911_<30> · C91

C91 = P34 · P57

P34 = 5803154930334451126145780382617113_<34>

P57 = 594534302111706146898488870469731843809863616765324450427_<57>

Thu Jul 17 23:11:07 2008  Msieve v. 1.36
Thu Jul 17 23:11:07 2008  random seeds: 1f8931f2 b1016748
Thu Jul 17 23:11:07 2008  factoring 3450174666552499603958825634868719551155941132530381444028934776059628299672087790690357251 (91 digits)
Thu Jul 17 23:11:08 2008  no P-1/P+1/ECM available, skipping
Thu Jul 17 23:11:08 2008  commencing quadratic sieve (91-digit input)
Thu Jul 17 23:11:08 2008  using multiplier of 11
Thu Jul 17 23:11:08 2008  using 64kb Opteron sieve core
Thu Jul 17 23:11:08 2008  sieve interval: 18 blocks of size 65536
Thu Jul 17 23:11:08 2008  processing polynomials in batches of 6
Thu Jul 17 23:11:08 2008  using a sieve bound of 1684919 (63529 primes)
Thu Jul 17 23:11:08 2008  using large prime bound of 155012548 (27 bits)
Thu Jul 17 23:11:08 2008  using double large prime bound of 552917357712160 (42-49 bits)
Thu Jul 17 23:11:08 2008  using trial factoring cutoff of 49 bits
Thu Jul 17 23:11:08 2008  polynomial 'A' values have 12 factors
Fri Jul 18 00:45:24 2008  64103 relations (17260 full + 46843 combined from 724321 partial), need 63625
Fri Jul 18 00:45:24 2008  begin with 741581 relations
Fri Jul 18 00:45:25 2008  reduce to 156628 relations in 10 passes
Fri Jul 18 00:45:25 2008  attempting to read 156628 relations
Fri Jul 18 00:45:26 2008  recovered 156628 relations
Fri Jul 18 00:45:26 2008  recovered 134292 polynomials
Fri Jul 18 00:45:26 2008  attempting to build 64103 cycles
Fri Jul 18 00:45:26 2008  found 64103 cycles in 5 passes
Fri Jul 18 00:45:26 2008  distribution of cycle lengths:
Fri Jul 18 00:45:26 2008     length 1 : 17260
Fri Jul 18 00:45:26 2008     length 2 : 12150
Fri Jul 18 00:45:26 2008     length 3 : 11287
Fri Jul 18 00:45:26 2008     length 4 : 8555
Fri Jul 18 00:45:26 2008     length 5 : 6019
Fri Jul 18 00:45:26 2008     length 6 : 3774
Fri Jul 18 00:45:26 2008     length 7 : 2313
Fri Jul 18 00:45:26 2008     length 9+: 2745
Fri Jul 18 00:45:26 2008  largest cycle: 17 relations
Fri Jul 18 00:45:27 2008  matrix is 63529 x 64103 (16.6 MB) with weight 3834011 (59.81/col)
Fri Jul 18 00:45:27 2008  sparse part has weight 3834011 (59.81/col)
Fri Jul 18 00:45:28 2008  filtering completed in 3 passes
Fri Jul 18 00:45:28 2008  matrix is 59293 x 59357 (15.4 MB) with weight 3550633 (59.82/col)
Fri Jul 18 00:45:28 2008  sparse part has weight 3550633 (59.82/col)
Fri Jul 18 00:45:28 2008  saving the first 48 matrix rows for later
Fri Jul 18 00:45:28 2008  matrix is 59245 x 59357 (9.8 MB) with weight 2743225 (46.22/col)
Fri Jul 18 00:45:28 2008  sparse part has weight 1973750 (33.25/col)
Fri Jul 18 00:45:28 2008  matrix includes 64 packed rows
Fri Jul 18 00:45:28 2008  using block size 23742 for processor cache size 1024 kB
Fri Jul 18 00:45:28 2008  commencing Lanczos iteration
Fri Jul 18 00:45:28 2008  memory use: 8.8 MB
Fri Jul 18 00:45:55 2008  lanczos halted after 939 iterations (dim = 59240)
Fri Jul 18 00:45:56 2008  recovered 14 nontrivial dependencies
Fri Jul 18 00:45:56 2008  prp34 factor: 5803154930334451126145780382617113
Fri Jul 18 00:45:56 2008  prp57 factor: 594534302111706146898488870469731843809863616765324450427

Fri Jul 18 00:45:56 2008  elapsed time 01:34:49

Jul 18, 2008 (4th)

Factorizations of 244...449 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors are probably greater than 10³⁰.

Jul 18, 2008 (3rd)

By Serge Batalov / GMP-ECM

(73·10¹⁹¹-1)/9 = 8(1)₁₉₁_<192> = 7² · 2957 · 28391329 · 81902647 · 1197538717_<10> · 4210320749_<10> · C153

C153 = P27 · C127

P27 = 281150019363827276479091879_<27>

C127 = [1698268766936150674397664693080209666761726866084951569803456920236110045824863664598013300791554963893047144133640896867139147_<127>]

Jul 18, 2008 (2nd)

By suberi / GMP-ECM

(10¹⁷⁸+53)/9 = (1)₁₇₇7_<178> = 17 · 19 · 31 · 29774267 · 17227909875533589273161569_<26> · C141

C141 = P52 · P89

P52 = 4616319830731803277321116745402333657467824322700921_<52>

P89 = 46862312350682118639301501622052895505443364470908072445277360687050905418909375922185723_<89>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1762451977
Step 1 took 88941ms
Step 2 took 29294ms
********** Factor found in step 2: 4616319830731803277321116745402333657467824322700921
Found probable prime factor of 52 digits: 4616319830731803277321116745402333657467824322700921
Probable prime cofactor 46862312350682118639301501622052895505443364470908072445277360687050905418909375922185723 has 89 digits

Jul 18, 2008

By Serge Batalov / GMP-ECM, Msieve

(43·10¹⁹⁴-7)/9 = 4(7)₁₉₄_<195> = 3 · 89 · 107 · 38917751 · 109329978532264895118221121359_<30> · 27984220393915439255871446690087_<32> · C123

C123 = P39 · P42 · P43

P39 = 150253016357827367252162610270549921517_<39>

P42 = 750043144488989115802079916490146682858549_<42>

P43 = 1246296144452316719852297075309650379237447_<43>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1189677086
Step 1 took 21161ms
Step 2 took 17730ms
********** Factor found in step 2: 150253016357827367252162610270549921517
Found probable prime factor of 39 digits: 150253016357827367252162610270549921517

Thu Jul 17 12:15:31 2008 Msieve v. 1.36
Thu Jul 17 12:15:31 2008 random seeds: c40b47a0 78880a05
Thu Jul 17 12:15:31 2008 factoring 934775879149519040345063733991838603284029386859630642611343691487753360644784884403 (84 digits)
Thu Jul 17 12:15:32 2008 no P-1/P+1/ECM available, skipping
Thu Jul 17 12:15:32 2008 commencing quadratic sieve (84-digit input)
Thu Jul 17 12:15:32 2008 using multiplier of 2
Thu Jul 17 12:15:32 2008 using 64kb Opteron sieve core
Thu Jul 17 12:15:32 2008 sieve interval: 6 blocks of size 65536
Thu Jul 17 12:15:32 2008 processing polynomials in batches of 17
Thu Jul 17 12:15:32 2008 using a sieve bound of 1409171 (53729 primes)
Thu Jul 17 12:15:32 2008 using large prime bound of 119779535 (26 bits)
Thu Jul 17 12:15:32 2008 using trial factoring cutoff of 27 bits
Thu Jul 17 12:15:32 2008 polynomial 'A' values have 11 factors
Thu Jul 17 12:52:32 2008 53862 relations (26979 full + 26883 combined from 284871 partial), need 53825
Thu Jul 17 12:52:32 2008 begin with 311850 relations
Thu Jul 17 12:52:32 2008 reduce to 77390 relations in 2 passes
Thu Jul 17 12:52:32 2008 attempting to read 77390 relations
Thu Jul 17 12:52:32 2008 recovered 77390 relations
Thu Jul 17 12:52:32 2008 recovered 72319 polynomials
Thu Jul 17 12:52:33 2008 attempting to build 53862 cycles
Thu Jul 17 12:52:33 2008 found 53862 cycles in 1 passes
Thu Jul 17 12:52:33 2008 distribution of cycle lengths:
Thu Jul 17 12:52:33 2008 length 1 : 26979
Thu Jul 17 12:52:33 2008 length 2 : 26883
Thu Jul 17 12:52:33 2008 largest cycle: 2 relations
Thu Jul 17 12:52:33 2008 matrix is 53729 x 53862 (8.4 MB) with weight 1758571 (32.65/col)
Thu Jul 17 12:52:33 2008 sparse part has weight 1758571 (32.65/col)
Thu Jul 17 12:52:33 2008 filtering completed in 3 passes
Thu Jul 17 12:52:33 2008 matrix is 39922 x 39986 (6.7 MB) with weight 1436413 (35.92/col)
Thu Jul 17 12:52:33 2008 sparse part has weight 1436413 (35.92/col)
Thu Jul 17 12:52:33 2008 saving the first 48 matrix rows for later
Thu Jul 17 12:52:33 2008 matrix is 39874 x 39986 (4.4 MB) with weight 1075978 (26.91/col)
Thu Jul 17 12:52:33 2008 sparse part has weight 761119 (19.03/col)
Thu Jul 17 12:52:33 2008 matrix includes 64 packed rows
Thu Jul 17 12:52:33 2008 using block size 15994 for processor cache size 1024 kB
Thu Jul 17 12:52:34 2008 commencing Lanczos iteration
Thu Jul 17 12:52:34 2008 memory use: 4.4 MB
Thu Jul 17 12:52:40 2008 lanczos halted after 632 iterations (dim = 39872)
Thu Jul 17 12:52:41 2008 recovered 17 nontrivial dependencies
Thu Jul 17 12:52:41 2008 prp42 factor: 750043144488989115802079916490146682858549
Thu Jul 17 12:52:41 2008 prp43 factor: 1246296144452316719852297075309650379237447
Thu Jul 17 12:52:41 2008 elapsed time 00:37:10

Jul 17, 2008 (5th)

By Wataru Sakai / GGNFS

6·10¹⁸³-1 = 5(9)₁₈₃_<184> = 7 · 2837 · C180

C180 = P63 · P118

P63 = 112649776609562047883105198303449664536396037482590034913768341_<63>

P118 = 2682029434148964127373780620479656968569866368989364416202844775610580864046145940166851280210227212021563042712498321_<118>

Number: 59999_183
N=302130016617150913943300266881514678483307316581902412004632660254796314013797270758849891736744045520922503650737700790573543481544891484969031673296742031320811722644644745455461
  ( 180 digits)
SNFS difficulty: 184 digits.
Divisors found:
 r1=112649776609562047883105198303449664536396037482590034913768341 (pp63)
 r2=2682029434148964127373780620479656968569866368989364416202844775610580864046145940166851280210227212021563042712498321 (pp118)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 571.11 hours.
Scaled time: 1149.08 units (timescale=2.012).
Factorization parameters were as follows:
n: 302130016617150913943300266881514678483307316581902412004632660254796314013797270758849891736744045520922503650737700790573543481544891484969031673296742031320811722644644745455461
m: 2000000000000000000000000000000000000
c5: 375
c0: -2
skew: 0.35
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 10800001)
Primes: RFBsize:501962, AFBsize:501426, largePrimes:6705920 encountered
Relations: rels:7228998, finalFF:1191175
Max relations in full relation-set: 32
Initial matrix: 1003454 x 1191175 with sparse part having weight 89284613.
Pruned matrix : 846750 x 851831 with weight 68965118.
Total sieving time: 563.95 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 6.82 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,184,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 571.11 hours.
 --------- CPU info (if available) ----------

(2·10¹⁷⁸+1)/3 = (6)₁₇₇7_<178> = 59 · C177

C177 = P81 · P96

P81 = 185421820977433014232739114726348871301256180810891425507564250791297781333322283_<81>

P96 = 609390791692408139110213498907677209688513214774525388871591629305745057845486938328656711665011_<96>

Number: 66667_178
N=112994350282485875706214689265536723163841807909604519774011299435028248587570621468926553672316384180790960451977401129943502824858757062146892655367231638418079096045197740113
  ( 177 digits)
SNFS difficulty: 178 digits.
Divisors found:
 r1=185421820977433014232739114726348871301256180810891425507564250791297781333322283 (pp81)
 r2=609390791692408139110213498907677209688513214774525388871591629305745057845486938328656711665011 (pp96)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 257.83 hours.
Scaled time: 519.01 units (timescale=2.013).
Factorization parameters were as follows:
n: 112994350282485875706214689265536723163841807909604519774011299435028248587570621468926553672316384180790960451977401129943502824858757062146892655367231638418079096045197740113
m: 200000000000000000000000000000000000
c5: 125
c0: 2
skew: 0.44
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 
)
Primes: RFBsize:501962, AFBsize:501581, largePrimes:6581325 encountered
Relations: rels:7061543, finalFF:1142735
Max relations in full relation-set: 32
Initial matrix: 1003608 x 1142735 with sparse part having weight 81062804.
Pruned matrix : 887061 x 892143 with weight 62469237.
Total sieving time: 255.54 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 1.98 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,178,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 257.83 hours.
 --------- CPU info (if available) ----------

(79·10¹⁷⁸-7)/9 = 8(7)₁₇₈_<179> = 3 · C179

C179 = P44 · P136

P44 = 19971896401363047141199475475638205189325457_<44>

P136 = 1465021581889557857924256214667419479705503658147178481828370509373285421613856871941147734400057046089676390097180025635682843605088587_<136>

Number: 87777_178
N=29259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259
  ( 179 digits)
SNFS difficulty: 179 digits.
Divisors found:
 r1=19971896401363047141199475475638205189325457 (pp44)
 r2=1465021581889557857924256214667419479705503658147178481828370509373285421613856871941147734400057046089676390097180025635682843605088587 (pp136)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 563.40 hours.
Scaled time: 1127.37 units (timescale=2.001).
Factorization parameters were as follows:
n: 29259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259
m: 100000000000000000000000000000000000
c5: 79000
c0: -7
skew: 0.15
type: snfsFactor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 25400001)
Primes: RFBsize:501962, AFBsize:502131, largePrimes:7373002 encountered
Relations: rels:8019550, finalFF:1174666
Max relations in full relation-set: 32
Initial matrix: 1004160 x 1174666 with sparse part having weight 144974941.
Pruned matrix : 879802 x 884886 with weight 124736252.
Total sieving time: 550.51 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 11.93 hours.
Time per square root: 0.78 hours.
Prototype def-par.txt line would be:
snfs,179,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 563.40 hours.
 --------- CPU info (if available) ----------

Jul 17, 2008 (4th)

By matsui / GGNFS

10¹⁷⁴+7 = 1(0)₁₇₃7_<175> = 29 · 71 · 487 · 11125843 · C161

C161 = P62 · P100

P62 = 11284673357060483641065406171245055689125329700802610659045727_<62>

P100 = 7943150153899727308211547689503218266715542847275764169224019083630803802075842027404310615659484239_<100>

N=89635854912843133047377276427170795358631018925432063304303551079726674670973827431931933014153835794202245565283120853861244899792595963890869576186164736796753
  ( 161 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=11284673357060483641065406171245055689125329700802610659045727 (pp62)
 r2=7943150153899727308211547689503218266715542847275764169224019083630803802075842027404310615659484239 (pp100)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 154.34 hours.
Scaled time: 221.02 units (timescale=1.432).
Factorization parameters were as follows:
n: 89635854912843133047377276427170795358631018925432063304303551079726674670973827431931933014153835794202245565283120853861244899792595963890869576186164736796753
m: 100000000000000000000000000000000000
c5: 1
c0: 70
skew: 2.34
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 11200001)
Primes: RFBsize:501962, AFBsize:503466, largePrimes:6481592 encountered
Relations: rels:6948668, finalFF:1144792
Max relations in full relation-set: 28
Initial matrix: 1005492 x 1144792 with sparse part having weight 69603650.
Pruned matrix : 885359 x 890450 with weight 52443459.
Total sieving time: 148.66 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 5.17 hours.
Time per square root: 0.39 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 154.34 hours.

Jul 17, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(5·10¹⁶⁸+13)/9 = (5)₁₆₇7_<168> = 2193410005059955014607_<22> · C147

C147 = P66 · P82

P66 = 211201992164536130541235848631497798541612474874808458918779453283_<66>

P82 = 1199249826735630800334398062812385809281436836301713944282871073656817271907107897_<82>

Number: n
N=253283952509540008450507359677177401846286089874624769147262785793068091845083311740268079983995444677484848230048759659916753262836974367351875851
  ( 147 digits)
SNFS difficulty: 169 digits.
Divisors found:

Thu Jul 17 22:16:48 2008  prp66 factor: 211201992164536130541235848631497798541612474874808458918779453283
Thu Jul 17 22:16:48 2008  prp82 factor: 1199249826735630800334398062812385809281436836301713944282871073656817271907107897
Thu Jul 17 22:16:48 2008  elapsed time 02:04:27 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 42.01 hours.
Scaled time: 76.83 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_5_167_7
n: 253283952509540008450507359677177401846286089874624769147262785793068091845083311740268079983995444677484848230048759659916753262836974367351875851
skew: 1.52
deg: 5
c5: 8
c0: 65
m: 5000000000000000000000000000000000
type: snfs
rlim: 5800000
alim: 5800000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 2700001)
Primes: RFBsize:399993, AFBsize:399999, largePrimes:9791480 encountered
Relations: rels:9307871, finalFF:813987
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 41.76 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,50,50,2.5,2.5,100000
total time: 42.01 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jul 17, 2008 (2nd)

By Robert Backstrom / GMP-ECM

(4·10¹⁶⁹+11)/3 = 1(3)₁₆₈7_<170> = 3398633569951_<13> · C157

C157 = P30 · P128

P30 = 243693271397142150776644064113_<30>

P128 = 16098701792205555493787516689184765943671906327794613923990682608079019066384014799429979843106295062079900053829846688958148599_<128>

Jul 17, 2008

By Serge Batalov / GMP-ECM, Msieve

9·10¹⁹⁹-7 = 8(9)₁₉₈3_<200> = 31 · 743 · 6841 · 12697 · 316339 · 413089877 · 107105780766623_<15> · 13919023264892149_<17> · 19620579832179617602901623499857_<32> · C113

C113 = P37 · P76

P37 = 6427503805579223317744356595461437807_<37>

P76 = 1831041340434809452833718361805463604259680227651236173580827772015915361667_<76>

Number: 89993_199
N=11769025183817619952672417054651487669578574210254607906854183871505045045861473013946425938221361597450232344269
  ( 113 digits)
Divisors found:
 r1=6427503805579223317744356595461437807
 r2=1831041340434809452833718361805463604259680227651236173580827772015915361667
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
name: 89993_199
n: 11769025183817619952672417054651487669578574210254607906854183871505045045861473013946425938221361597450232344269
skew: 53840.95
# norm 3.64e+15
c5: 8880
c4: -1129742670
c3: -155660144868577
c2: 2381642608767554524
c1: 137513208798163850234032
c0: -2172126232263059673608813344
# alpha -6.03
Y1: 231688360871
Y0: -4211784220495418937693
# Murphy_E 7.67e-10
# M 7420350881970755408277194183514819226857195980988978384894736154280999709633602187020363784915146259202193086546
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 3650001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: 7928000 relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 463893 x 464136
Total sieving time: 11.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.75 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000

total time: 12.00 hours.

(22·10¹⁸³-13)/9 = 2(4)₁₈₂3_<184> = 7 · 74821 · 3777824523836434735369063990067_<31> · C148

C148 = P30 · P54 · P64

P30 = 233948542471655416966539695957_<30>

P54 = 728025222965584731793931788563408594665953022055106061_<54>

P64 = 7253541024316580869418663127314988483163280924756047872134021891_<64>

#-- first, by ECM --
Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=369411570
Step 1 took 18298ms
Step 2 took 14326ms
********** Factor found in step 2: 233948542471655416966539695957
Found probable prime factor of 30 digits: 233948542471655416966539695957
Composite cofactor 5280760821518094650260482230697796599116648705786845313167148884685871265840183994032230085997595905486342212500781351 has 118 digits

#--then by Msieve (gnfs,118)

Number: 24443_183
N=5280760821518094650260482230697796599116648705786845313167148884685871265840183994032230085997595905486342212500781351
  ( 118 digits)
Divisors found:
 r1=728025222965584731793931788563408594665953022055106061
 r2=7253541024316580869418663127314988483163280924756047872134021891
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
name: 24443_183
n: 5280760821518094650260482230697796599116648705786845313167148884685871265840183994032230085997595905486342212500781351
skew: 37599.46
# norm 2.85e+16
c5: 114720
c4: -19508028470
c3: -143899311857623
c2: 42457844710427220106
c1: 763166056347895704407064
c0: -45130489940034694521668160
# alpha -6.40
Y1: 7577882143777
Y0: -34089038769616882470619
# Murphy_E 3.93e-10
# M 2727036486374593181091379991914029708867927407917977652616807660464128792055469928307341336543407724973003349846889828
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 3950001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: 8162000 relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 569973 x 570212
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.5,2.5,100000

total time: 27.00 hours.

(4·10¹⁹⁸-13)/9 = (4)₁₉₇3_<198> = 523 · 82737301 · 22861189383523_<14> · C174

C174 = P30 · C145

P30 = 109004345405742704229513258503_<30>

C145 = [4121656653229606688891632821619209502441186611362878540444545066393408185585679257868260089902556418333145433375944552756831904252394732003086489_<145>]

(43·10¹⁹⁴-7)/9 = 4(7)₁₉₄_<195> = 3 · 89 · 107 · 38917751 · 109329978532264895118221121359_<30> · C154

C154 = P32 · C123

P32 = 27984220393915439255871446690087_<32>

C123 = [140452895460755142568169629971827239108134551763753952081688857640992802509386073644380889037709828929708318820579567399351_<123>]

(34·10¹⁹³-43)/9 = 3(7)₁₉₂3_<194> = 3³ · 11 · 19² · 79 · 661 · 33889871 · 206690543 · 93566161264769_<14> · C155

C155 = P30 · C125

P30 = 219952497998232711504934775239_<30>

C125 = [46806479030908156153665353632537735280964258077511172703126540334606775972905563382609259392230247331755789931137661196139137_<125>]

10¹⁹¹-3 = (9)₁₉₀7_<191> = 113 · 2454455881_<10> · 13778267355178489115141197_<26> · C155

C155 = P40 · P115

P40 = 4177672914958740985247164938293269252349_<40>

P115 = 6263791373890807735811613899906525630519387461611911965595048014000039506928204827175275652877326155130619692271533_<115>

Jul 16, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(22·10¹⁶⁸+23)/9 = 2(4)₁₆₇7_<169> = 4543813 · 1878087349_<10> · C153

C153 = P36 · P47 · P72

P36 = 157077838092449523332749097610339671_<36>

P47 = 12314963809991883286233006440538730997310281149_<47>

P72 = 148079820454272076138749463653539263120184911826609262340495505792576389_<72>

Number: n
N=1823597629884456456024969058909706258632372020265790999907676961582423394895913928332215564831650488011286590649190961
  ( 118 digits)
Divisors found:

Wed Jul 16 03:18:19 2008  prp47 factor: 12314963809991883286233006440538730997310281149
Wed Jul 16 03:18:19 2008  prp72 factor: 148079820454272076138749463653539263120184911826609262340495505792576389
Wed Jul 16 03:18:19 2008  elapsed time 04:29:31 (Msieve 1.36, Dep=6)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 51.39 hours.
Scaled time: 90.04 units (timescale=1.752).
Factorization parameters were as follows:
name: KA_2_4_167_7
n: 1823597629884456456024969058909706258632372020265790999907676961582423394895913928332215564831650488011286590649190961
skew: 48983.94
# norm 6.46e+15
c5: 50040
c4: 3600602710
c3: -376262433842969
c2: -8229887425109787560
c1: 404072477709485347899232
c0: 2578150019307161193042749712
# alpha -5.44
Y1: 2056468829983
Y0: -32532837847316073020785
# Murphy_E 3.87e-10
# M 74352331651996214033401096617626779374954279297543952462796538594023349857190087022767517996283017661881645908058429
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 2300000)
Primes: RFBsize:315948, AFBsize:315738, largePrimes:9457688 encountered
Relations: rels:8737174, finalFF:664621
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 51.02 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,28,28,50,50,2.5,2.5,60000
total time: 51.39 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(83·10¹⁶⁸+61)/9 = 9(2)₁₆₇9_<169> = 5381 · 36173552095222639_<17> · C149

C149 = P39 · P111

P39 = 106355916117472562674540821070957317439_<39>

P111 = 445471353245345900119817406448596918723980474959155182424548921066868827075147451237495128565791226177408521729_<111>

2·10¹⁶⁸-7 = 1(9)₁₆₇3_<169> = 8002843 · 679331923056720559092781_<24> · C138

C138 = P55 · P84

P55 = 1743135735135318112931632042583008770405177795897939247_<55>

P84 = 211043737325077621766641712794419286115201489247799793695341755432378145694998105193_<84>

Number: n
N=367877880207854154431115542622985059730951001687730951844231434351077499649003285665322749166951767834677806526397408965900679678429209671
  ( 138 digits)
SNFS difficulty: 168 digits.
Divisors found:

Wed Jul 16 17:57:06 2008  prp55 factor: 1743135735135318112931632042583008770405177795897939247
Wed Jul 16 17:57:06 2008  prp84 factor: 211043737325077621766641712794419286115201489247799793695341755432378145694998105193
Wed Jul 16 17:57:06 2008  elapsed time 02:13:52 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 53.77 hours.
Scaled time: 98.35 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_9_167_3
n: 367877880207854154431115542622985059730951001687730951844231434351077499649003285665322749166951767834677806526397408965900679678429209671
skew: 0.65
deg: 5
c5: 125
c0: -14
m: 2000000000000000000000000000000000
type: snfs
rlim: 5500000
alim: 5500000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 3400000)
Primes: RFBsize:380800, AFBsize:381052, largePrimes:10127809 encountered
Relations: rels:9638577, finalFF:794819
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 53.49 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,50,50,2.5,2.5,100000
total time: 53.77 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jul 15, 2008 (4th)

By suberi / GMP-ECM

(4·10²¹³-1)/3 = 1(3)₂₁₃_<214> = 31 · 43 · 42929 · 1647001 · 55070453 · 109103879 · 315971342878788876787_<21> · C163

C163 = P34 · C130

P34 = 2472176201488989163470538770710003_<34>

C130 = [3014241151258482250646629430943474307709267290595380818070266010335607748326473373305206926053831950374530423789611599608439806667_<130>]

Jul 15, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(22·10¹⁵⁶+23)/9 = 2(4)₁₅₅7_<157> = 4547 · 10601 · 817603 · 2219635954465259223327708947_<28> · C116

C116 = P54 · P63

P54 = 140350244666350609226894618859195516341027638500563633_<54>

P63 = 199099872181567014671579008715002480094143366187033872354713317_<63>

Number: n
N=27943715773722063936691722152698523908458765196954280032157968841627837312957044871581762548438985303588808631000661
  ( 116 digits)
Divisors found:

Tue Jul 15 16:08:22 2008  prp54 factor: 140350244666350609226894618859195516341027638500563633
Tue Jul 15 16:08:22 2008  prp63 factor: 199099872181567014671579008715002480094143366187033872354713317
Tue Jul 15 16:08:22 2008  elapsed time 01:31:56 (Msieve 1.36)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 42.90 hours.
Scaled time: 56.33 units (timescale=1.313).
Factorization parameters were as follows:
name: n
n: 27943715773722063936691722152698523908458765196954280032157968841627837312957044871581762548438985303588808631000661
skew: 47568.43
# norm 1.44e+16
c5: 44160
c4: 4908212444
c3: -559428385396405
c2: -8122621523859034918
c1: 191177662074665609611144
c0: -1057339503448102257405097600
# alpha -6.06
Y1: 3013035451613
Y0: -14462687652541172636637
# Murphy_E 4.75e-10
# M 13749798645903224652008884833430320114302017669267970026189959974505191987149920357678449950213629431261078728068770
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1799990)
Primes: RFBsize:315948, AFBsize:315778, largePrimes:9341040 encountered
Relations: rels:8769691, finalFF:762080
Max relations in full relation-set: 28
Initial matrix: 631808 x 762080 with sparse part having weight 45124286.
Pruned matrix : 
Total sieving time: 42.50 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,28,28,50,50,2.5,2.5,60000
total time: 42.90 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(22·10¹⁶¹+23)/9 = 2(4)₁₆₀7_<162> = 7² · 73795848330403_<14> · 107546926227583_<15> · C132

C132 = P52 · P81

P52 = 1502437621398893305826089711439184886680078009309919_<52>

P81 = 418367277957308925333921233455513317862150641697102827631297773846327424699635013_<81>

Number: n
N=628570737965308867894616758650083694072525682923772825126976449775573725741245698307743195957424393590240832150518669803215300593947
  ( 132 digits)
SNFS difficulty: 162 digits.
Divisors found:

Tue Jul 15 18:20:17 2008  prp52 factor: 1502437621398893305826089711439184886680078009309919
Tue Jul 15 18:20:17 2008  prp81 factor: 418367277957308925333921233455513317862150641697102827631297773846327424699635013
Tue Jul 15 18:20:17 2008  elapsed time 01:38:49 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 47.99 hours.
Scaled time: 69.73 units (timescale=1.453).
Factorization parameters were as follows:
name: KA_2_4_160_7
n: 628570737965308867894616758650083694072525682923772825126976449775573725741245698307743195957424393590240832150518669803215300593947
skew: 0.64
deg: 5
c5: 220
c0: 23
m: 100000000000000000000000000000000
type: snfs
rlim: 4400000
alim: 4400000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2300001)
Primes: RFBsize:309335, AFBsize:309159, largePrimes:7452388 encountered
Relations: rels:6986017, finalFF:643203
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 47.75 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4400000,4400000,28,28,48,48,2.5,2.5,100000
total time: 47.99 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jul 15, 2008 (2nd)

By Jo Yeong Uk / GGNFS

(13·10¹⁹¹+41)/9 = 1(4)₁₉₀9_<192> = C192

C192 = P51 · P141

P51 = 497657554076973302518779613306102473057258401585609_<51>

P141 = 290248672528143811855534364536737651221044179346938023837658334270944573019672423163353331467770581052482338681134129509473272799800519044761_<141>

Number: 14449_191
N=144444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449
  ( 192 digits)
SNFS difficulty: 192 digits.
Divisors found:
 r1=497657554076973302518779613306102473057258401585609 (pp51)
 r2=290248672528143811855534364536737651221044179346938023837658334270944573019672423163353331467770581052482338681134129509473272799800519044761 (pp141)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 592.51 hours.
Scaled time: 1409.59 units (timescale=2.379).
Factorization parameters were as follows:
n: 144444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449
m: 100000000000000000000000000000000000000
c5: 130
c0: 41
skew: 0.79
type: snfs
Factor base limits: 16000000/16000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved algebraic special-q in [8000000, 18100001)
Primes: RFBsize:1031130, AFBsize:1029654, largePrimes:14861895 encountered
Relations: rels:16051847, finalFF:2329705
Max relations in full relation-set: 28
Initial matrix: 2060851 x 2329705 with sparse part having weight 193127240.
Pruned matrix : 1827746 x 1838114 with weight 151862872.
Total sieving time: 552.20 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 39.65 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,192,5,0,0,0,0,0,0,0,0,16000000,16000000,28,28,52,52,2.6,2.6,100000
total time: 592.51 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047052k/8912896k available (2459k kernel code, 339236k reserved, 1247k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673804)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348)
Calibrating delay using timer specific routine.. 5344.23 BogoMIPS (lpj=2672116)
Calibrating delay using timer specific routine.. 5589.60 BogoMIPS (lpj=2794804)

Jul 15, 2008

By Serge Batalov / Msieve

(22·10¹⁷⁶+23)/9 = 2(4)₁₇₅7_<177> = 13 · 1109 · 2083 · 12637 · 2201791629722900115084517_<25> · 98202646709372914952284004731_<29> · C112

C112 = P33 · P80

P33 = 263918040926244833932442223532777_<33>

P80 = 11287649866483430593118539466784682520308464734220950406084876622638519492533399_<80>

Number: 24447_176
N=2979014439423696070680381230689894498227059660077707317426808607490416509659199184543278457103523964979443719023
  ( 112 digits)
Divisors found:
 r1=263918040926244833932442223532777
 r2=11287649866483430593118539466784682520308464734220950406084876622638519492533399
Version: Msieve 1.36

Factorization parameters were as follows:
name: 24447_176
n: 2979014439423696070680381230689894498227059660077707317426808607490416509659199184543278457103523964979443719023
skew: 43254.19
# norm 3.04e+15
c5: 3840
c4: 2706565576
c3: 2492910207212
c2: -5833440226913678650
c1: -98011231431123673328307
c0: -232632515522583734331555306
# alpha -6.06
Y1: 643298896207
Y0: -3783884480249237801755
# Murphy_E 8.01e-10
# M 1300968512421426024764568100635526414813480594650460600267126043707504036536817791911229599377015845824674248517
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 3250001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 430899 x 431147
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000

total time: 15.00 hours.

Jul 14, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve

(7·10¹⁶⁷-61)/9 = (7)₁₆₆1_<167> = 114807751 · 3626102422772747707_<19> · C141

C141 = P57 · P84

P57 = 823035057767144134239967477480765928602729472785254183529_<57>

P84 = 227000032497982054005520830210122515119411890431796815636671279518904326397745213007_<84>

Number: n
N=186828984860120255606519839560874657226518689870717896574431922306201449144447043355099889582452640081134312356077616468363781250379975961703
  ( 141 digits)
SNFS difficulty: 167 digits.
Divisors found:

Mon Jul 14 15:50:30 2008  prp57 factor: 823035057767144134239967477480765928602729472785254183529
Mon Jul 14 15:50:30 2008  prp84 factor: 227000032497982054005520830210122515119411890431796815636671279518904326397745213007
Mon Jul 14 15:50:30 2008  elapsed time 01:51:25 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 69.67 hours.
Scaled time: 126.80 units (timescale=1.820).
Factorization parameters were as follows:
name: KA_7_166_1
n: 186828984860120255606519839560874657226518689870717896574431922306201449144447043355099889582452640081134312356077616468363781250379975961703
skew: 0.61
deg: 5
c5: 700
c0: -61
m: 1000000000000000000000000000000000
type: snfs
rlim: 5500000
alim: 5500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4300001)
Primes: RFBsize:380800, AFBsize:380053, largePrimes:8163761 encountered
Relations: rels:7710086, finalFF:765959
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 69.35 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.5,2.5,100000
total time: 69.67 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jul 14, 2008 (3rd)

By matsui / GGNFS

4·10¹⁷⁴+1 = 4(0)₁₇₃1_<175> = 21669802129_<11> · C165

C165 = P47 · P118

P47 = 90895849637269554525310385291775885388075787009_<47>

P118 = 2030771183197325350577624750920707697746469994254856700264575730266390155389375430973873995208761043763694185654787441_<118>

N=184588672115604069528972854978670396146283150031988000899756623707562973659121407660916256260292684834971895741761989764036760485363820924070607603839279154684153969
  ( 165 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=90895849637269554525310385291775885388075787009 (pp47)
 r2=2030771183197325350577624750920707697746469994254856700264575730266390155389375430973873995208761043763694185654787441 (pp118)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 105.95 hours.
Scaled time: 151.40 units (timescale=1.429).
Factorization parameters were as follows:
n: 184588672115604069528972854978670396146283150031988000899756623707562973659121407660916256260292684834971895741761989764036760485363820924070607603839279154684153969
m: 100000000000000000000000000000000000
c5: 2
c0: 5
skew: 1.2
type: snfs

Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 10400001)
Primes: RFBsize:501962, AFBsize:501861, largePrimes:6413242 encountered
Relations: rels:6884769, finalFF:1153553
Max relations in full relation-set: 28
Initial matrix: 1003888 x 1153553 with sparse part having weight 68214227.
Pruned matrix : 873507 x 878590 with weight 50441029.
Total sieving time: 101.00 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 4.44 hours.
Time per square root: 0.39 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 105.95 hours.

Jul 14, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(22·10¹⁵¹+23)/9 = 2(4)₁₅₀7_<152> = 3 · 97 · 8834843 · 18558168955073395708146667411_<29> · C114

C114 = P53 · P61

P53 = 70985983835086576997852624750687510213827313422930409_<53>

P61 = 7217397353726318978026298518599642790594988964775374257181581_<61>

Number: 24447_151
N=512334051883013116583423649922513914567713078285125905872387242449953931012240050043094620958754046039730239596629
  ( 114 digits)
Divisors found:
 r1=70985983835086576997852624750687510213827313422930409 (pp53)
 r2=7217397353726318978026298518599642790594988964775374257181581 (pp61)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 59.21 hours.
Scaled time: 28.00 units (timescale=0.473).
Factorization parameters were as follows:
name: 24447_151
n: 512334051883013116583423649922513914567713078285125905872387242449953931012240050043094620958754046039730239596629
skew: 58934.48
# norm 1.67e+16
c5: 39240
c4: 2548362158
c3: -848790397397041
c2: -7561237389283676814
c1: 1098028132791631657707704
c0: -101853278834969772710102272
# alpha -6.65
Y1: 698620596401
Y0: -6655248136878522324179
# Murphy_E 5.69e-10
# M 411099533570434247334050740846394508864406295354105061320770663934783270735188517730048665882061695384371932235740
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2950001)
Primes: RFBsize:250150, AFBsize:249615, largePrimes:7495265 encountered
Relations: rels:7340500, finalFF:563249
Max relations in full relation-set: 28
Initial matrix: 499845 x 563249 with sparse part having weight 48058090.
Pruned matrix : 449089 x 451652 with weight 33803649.
Total sieving time: 50.37 hours.
Total relation processing time: 0.55 hours.
Matrix solve time: 7.94 hours.
Time per square root: 0.35 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 59.21 hours.
 --------- CPU info (if available) ----------

Jul 14, 2008

By Serge Batalov / GMP-ECM, Msieve

(2·10¹⁹²+1)/3 = (6)₁₉₁7_<192> = 22441 · 437977 · 48109987 · 1526524747081880791478251001_<28> · C147

C147 = P38 · P45 · P66

P38 = 11948477248990278755249447965289499937_<38>

P45 = 166390757028721578564820877464821642636142609_<45>

P66 = 464552052602373136402651573347040115738820665732325211913648101361_<66>

# first, by ECM

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3529291452
Step 1 took 5972ms
Step 2 took 5538ms
********** Factor found in step 2: 11948477248990278755249447965289499937
Found probable prime factor of 38 digits: 11948477248990278755249447965289499937
Composite cofactor 77297167711755354438769313097704800502672814513221504344872692101599293570057314899883042225028440669682990849 has 110 digits

# then by Msieve/gnfs,110

Number: 66667_192
N=77297167711755354438769313097704800502672814513221504344872692101599293570057314899883042225028440669682990849
  ( 110 digits)
Divisors found:
 r1=166390757028721578564820877464821642636142609
 r2=464552052602373136402651573347040115738820665732325211913648101361

Factorization parameters were as follows:
name: 66667_192
n: 77297167711755354438769313097704800502672814513221504344872692101599293570057314899883042225028440669682990849
skew: 10017.40
# norm 6.40e+14
c5: 74880
c4: 2885407200
c3: 17695074766288
c2: -253585168675014076
c1: 568043165283630402721
c0: -813150504652600490326365
# alpha -5.61
Y1: 345585391877
Y0: -1006371663273310375634
# Murphy_E 1.14e-09
# M 31155127991704449356442579169587931086327302371789743816853144263449870130460753713703574862673252103015339066
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2900001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 369426 x 369674
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000

total time: 11.00 hours.

5·10¹⁹⁹-3 = 4(9)₁₉₈7_<200> = 219619 · 3639959 · 4744042763965047965693_<22> · C167

C167 = P31 · P136

P31 = 8093176768651631185069802113901_<31>

P136 = 1629055878393401770330660883294105510464026569183051106513390639156296434054875594593755637398223572917720059576936252313923440973374849_<136>

(8·10¹⁷⁴-71)/9 = (8)₁₇₃1_<174> = 7 · 53 · 12101 · C168

C168 = P28 · C141

P28 = 1939607078801257064760060301_<28>

C141 = [102079502915150872449364582616265150010758333661353575581993053425424847966829582828720569749338022010525015105109233120216741718055475742411_<141>]

(2·10¹⁸⁸+7)/9 = (2)₁₈₇3_<188> = 113 · 587 · 2659 · 1864630093819_<13> · C167

C167 = P33 · P135

P33 = 112654204167499843146979520977037_<33>

P135 = 599808355233464006448212960910397629581245269600833415238862953159561681692737075144423658619895686481443976435337829801517842607704129_<135>

(19·10¹⁹⁵+17)/9 = 2(1)₁₉₄3_<196> = 59 · 1267577 · 158612774241033861923_<21> · C168

C168 = P39 · P129

P39 = 282503324001414019100503379652927974071_<39>

P129 = 629974551490611084435937066618096229596276276489387128835727689298806791822488193421449041113663483875019510871892831411163366727_<129>

(32·10¹⁹⁵-23)/9 = 3(5)₁₉₄3_<196> = 11 · 17 · 1019 · 11597 · 67829 · 244979073043_<12> · C170

C170 = P33 · C138

P33 = 103006187361337566011944121049239_<33>

C138 = [940022626361736428027252898323336782308056104327236273583195401942375080676203948933037333853780425271367083459258236281339248935045206101_<138>]

Jul 13, 2008 (4th)

By Sinkiti Sibata / GGNFS

(22·10¹⁵⁴+23)/9 = 2(4)₁₅₃7_<155> = 3² · 1613 · 6144493 · 85808033 · 26756289861065329_<17> · C120

C120 = P58 · P62

P58 = 1798409594124660216759258210120687655281031358400703839301_<58>

P62 = 66370454423809885762078346386195882275783383739027815254557491_<62>

Number: 24447_154
N=119361262002193195821448307853344484885855650684642416843797966406457642714370053703754405333884430590534099281529753791
  ( 120 digits)
Divisors found:
 r1=1798409594124660216759258210120687655281031358400703839301 (pp58)
 r2=66370454423809885762078346386195882275783383739027815254557491 (pp62)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 70.89 hours.
Scaled time: 55.58 units (timescale=0.784).
Factorization parameters were as follows:
name: 24447_154
n: 119361262002193195821448307853344484885855650684642416843797966406457642714370053703754405333884430590534099281529753791
skew: 60960.40
# norm 1.84e+16
c5: 47940
c4: 5307530782
c3: -625612329042056
c2: -16268669865623770227
c1: 204342567025062309743036
c0: 8794015424991234094426300580
# alpha -5.74
Y1: 5404961881777
Y0: -75723797960330337216429
# Murphy_E 3.09e-10
# M 75322734279060307587904586726507012317372125376889169597155511412590324434436033530464569542901548305306847769101384234
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4350001)
Primes: RFBsize:315948, AFBsize:316629, largePrimes:7720056 encountered
Relations: rels:7821817, finalFF:759929
Max relations in full relation-set: 28
Initial matrix: 632662 x 759929 with sparse part having weight 66754450.
Pruned matrix : 529324 x 532551 with weight 43939785.
Total sieving time: 66.31 hours.
Total relation processing time: 0.50 hours.
Matrix solve time: 3.68 hours.
Time per square root: 0.39 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 70.89 hours.
 --------- CPU info (if available) ----------

Jul 13, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

4·10¹⁶⁸+7 = 4(0)₁₆₇7_<169> = 11² · 2618693672249983639196789_<25> · C143

C143 = P63 · P80

P63 = 434600913422969283935715734532476163912699428553621729133663787_<63>

P80 = 29046866416543146278620690212890391220410722501413452500320961183706650069675369_<80>

Number: n
N=12623794676704621965362748212067023827563490650371887005640338255443815536512266154311383935241401663051630078521097059654813799889624681162403
  ( 143 digits)
SNFS difficulty: 168 digits.
Divisors found:

Sun Jul 13 16:29:05 2008  prp63 factor: 434600913422969283935715734532476163912699428553621729133663787
Sun Jul 13 16:29:05 2008  prp80 factor: 29046866416543146278620690212890391220410722501413452500320961183706650069675369
Sun Jul 13 16:29:05 2008  elapsed time 01:05:28 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 47.09 hours.
Scaled time: 86.36 units (timescale=1.834).
Factorization parameters were as follows:
name: KA_4_0_167_7
n: 12623794676704621965362748212067023827563490650371887005640338255443815536512266154311383935241401663051630078521097059654813799889624681162403
skew: 0.56
deg: 5
c5: 125
c0: 7
m: 2000000000000000000000000000000000
type: snfs
rlim: 5500000
alim: 5500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2900000)
Primes: RFBsize:380800, AFBsize:380502, largePrimes:7959970 encountered
Relations: rels:7657643, finalFF:861422
Max relations in full relation-set: 28
Initial matrix: 761367 x 861422 with sparse part having weight 40728051.
Pruned matrix : 
Total sieving time: 46.84 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.5,2.5,100000
total time: 47.09 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jul 13, 2008 (2nd)

By Serge Batalov / GMP-ECM

7·10¹⁸³+9 = 7(0)₁₈₂9_<184> = 79 · 69172788077_<11> · C172

C172 = P30 · C142

P30 = 133818982259225767835521221337_<30>

C142 = [9572336242243985044301236538042107107618534026530064456879616370843986823511954236728268510314492217680175701229960850902545463856024173108379_<142>]

9·10¹⁹⁹-7 = 8(9)₁₉₈3_<200> = 31 · 743 · 6841 · 12697 · 316339 · 413089877 · 107105780766623_<15> · 13919023264892149_<17> · C144

C144 = P32 · C113

P32 = 19620579832179617602901623499857_<32>

C113 = [11769025183817619952672417054651487669578574210254607906854183871505045045861473013946425938221361597450232344269_<113>]

6·10¹⁹⁴+1 = 6(0)₁₉₃1_<195> = 153817 · 33881245227068299278185531_<26> · C165

C165 = P33 · C132

P33 = 901361069267656452128353133474957_<33>

C132 = [127728776954149061732629779151943546510736581677373866290113899810994265965188567884730521444012921154476658141238516044262272295959_<132>]

Jul 13, 2008

By Robert Backstrom / GGNFS, Msieve

(19·10¹⁶³+71)/9 = 2(1)₁₆₂9_<164> = 53 · 62755516806818389237490084489_<29> · C133

C133 = P67 · P67

P67 = 1702357182418622530789291597341299637631432288875092672261013494321_<67>

P67 = 3728486921641779431391217242278242452352917616981245286538949510667_<67>

Number: n
N=6347216490610783077441171781434338047436822507152466738398464557918916343716774041846421465798549105708434295220219648071786733422107
  ( 133 digits)
SNFS difficulty: 164 digits.
Divisors found:

Sun Jul 13 04:05:21 2008  prp67 factor: 1702357182418622530789291597341299637631432288875092672261013494321
Sun Jul 13 04:05:21 2008  prp67 factor: 3728486921641779431391217242278242452352917616981245286538949510667
Sun Jul 13 04:05:21 2008  elapsed time 02:59:59 (Msieve 1.36)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 86.99 hours.
Scaled time: 113.78 units (timescale=1.308).
Factorization parameters were as follows:
name: KA_2_1_162_9
n: 6347216490610783077441171781434338047436822507152466738398464557918916343716774041846421465798549105708434295220219648071786733422107
skew: 0.33
deg: 5
c5: 19000
c0: 71
m: 100000000000000000000000000000000
type: snfs
rlim: 4600000
alim: 4600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5700001)
Primes: RFBsize:322441, AFBsize:322667, largePrimes:8115761 encountered
Relations: rels:7560077, finalFF:650072
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 86.72 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,4600000,4600000,28,28,48,48,2.5,2.5,100000
total time: 86.99 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jul 12, 2008 (2nd)

By Serge Batalov / GMP-ECM, pol51, Msieve

(17·10¹⁹⁸-53)/9 = 1(8)₁₉₇3_<199> = 7603 · 30803 · 43261 · 102559 · 1042469 · 2250737867569_<13> · 1941823279749679397_<19> · C144

C144 = P36 · P38 · P71

P36 = 532909957499658687338853693037114127_<36>

P38 = 12127492055545606309658842712355349019_<38>

P71 = 61735571024736893980769353536098228900774070762653834895799357457201053_<71>

# by ECM --
Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=323913398
Step 1 took 6878ms
Step 2 took 5269ms
********** Factor found in step 2: 12127492055545606309658842712355349019
Found probable prime factor of 38 digits: 12127492055545606309658842712355349019
Composite cofactor 32899500531009698487939962220216476251136087124144340859751512031161508952739461583756806371723685945575731 has 107 digits
#
# then by GNFS/Msieve
#
Number: 18883_198
N=32899500531009698487939962220216476251136087124144340859751512031161508952739461583756806371723685945575731
  ( 107 digits)
Divisors found:
 r1=532909957499658687338853693037114127
 r2=61735571024736893980769353536098228900774070762653834895799357457201053
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
name: 18883_198
n: 32899500531009698487939962220216476251136087124144340859751512031161508952739461583756806371723685945575731
skew: 44376.14
# norm 8.55e+14
c5: 8100
c4: -489452472
c3: -48951202463129
c2: 862613667364327251
c1: 36219942136802215898001
c0: -363404921018249872201819607
# alpha -5.93
Y1: 88261732339
Y0: -332462181768746779864
# Murphy_E 1.37e-09
# M 18483838965041290916740587464894868353558034896369087202581405858735878552821000366540532693858814885993829
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2300001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 310515 x 310763
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000

total time: 6.00 hours.

(22·10¹⁷⁸+23)/9 = 2(4)₁₇₇7_<179> = 3 · 9511 · 7058628672138574632984994873_<28> · C147

C147 = P30 · P50 · P67

P30 = 407818136912747014681334981443_<30>

P50 = 75160945043175857866901963484673054341461063508311_<50>

P67 = 3959621107875479961537988501024588458702472685250586541345053347871_<67>

# by ECM --
#
Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=430382
Step 1 took 20824ms
Step 2 took 15058ms
********** Factor found in step 2: 407818136912747014681334981443
Found probable prime factor of 30 digits: 407818136912747014681334981443
Composite cofactor 297608864480828054398175478834481222993428795506090706648602298717700679595827000206738339572148229407385859182655881 has 117 digits
#
# then by GNFS/Msieve
#
Number: 24447_178
N=297608864480828054398175478834481222993428795506090706648602298717700679595827000206738339572148229407385859182655881
  ( 117 digits)
Divisors found:
 r1=75160945043175857866901963484673054341461063508311
 r2=3959621107875479961537988501024588458702472685250586541345053347871
Factorization parameters were as follows:
name: 24447_178
n: 297608864480828054398175478834481222993428795506090706648602298717700679595827000206738339572148229407385859182655881
skew: 56866.92
# norm 3.03e+16
c5: 11760
c4: 58587242
c3: -948018741867885
c2: 5359060334242097837
c1: 500754803694110056951611
c0: -3720239981301914611368153205
# alpha -6.05
Y1: 3414751932097
Y0: -30244587069795188032038
# Murphy_E 4.18e-10
# M 109539901323225467029707024396066592108219284886924732442320854580487753105415174514190809144234342576834319914949849
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 3850001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 570807 x 571055
Total sieving time: 15.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 01:14:42
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.5,2.5,100000

total time: 17.00 hours.

Jul 12, 2008

By Serge Batalov / GMP-ECM

(2·10¹⁸⁰+7)/9 = (2)₁₇₉3_<180> = 71 · 3581374329011_<13> · C165

C165 = P42 · P124

P42 = 282287262952400056073198405956934109921109_<42>

P124 = 3095908655365249055568580267803159689569266960813853471093469310442231639214617495399521734305189014030222056875561596808087_<124>

6·10¹⁸⁹+7 = 6(0)₁₈₈7_<190> = 6209183697097282695749827_<25> · C165

C165 = P29 · C137

P29 = 84650755361806968467920668269_<29>

C137 = [11415262534024941376215177642404391202003957780146884337777704466878931859742980790987063731573828128798768767273676353885360988327570689_<137>]

(4·10¹⁷⁴+41)/9 = (4)₁₇₃9_<174> = 401 · 1531 · 2333 · C165

C165 = P32 · C134

P32 = 11103172231868232665208082632227_<32>

C134 = [27947058444735539012965143631675640717984624676970856746909322865014587987121750699821648616857592608427104241739512228516510591633269_<134>]

(8·10¹⁹⁸-17)/9 = (8)₁₉₇7_<198> = 29 · 2551 · 26987713 · 24810652678294736989_<20> · C167

C167 = P30 · C138

P30 = 122763886401873301220354203087_<30>

C138 = [146171976769747747349388334776423064471607044898176691920488992333574187962280014690489994846698316344610133907207472343085837277045010167_<138>]

(4·10¹⁹¹-7)/3 = 1(3)₁₉₀1_<192> = 11 · 8111 · 22485379500775341739_<20> · C167

C167 = P32 · P136

P32 = 17187029396452962451764372549233_<32>

P136 = 3866968269055691419473815558756213198307575801275502239579209994484850503385131935406232395834688131221430324342382120842650685242448053_<136>

(14·10¹⁹⁶-41)/9 = 1(5)₁₉₅1_<197> = 43 · 12991941439670998826484083573_<29> · C167

C167 = P32 · C135

P32 = 31549870079323557671928299889097_<32>

C135 = [882562440577446030345916906651940795515837407245481246517202735480841275954656517617252892526279545364367486770393761420751543094322497_<135>]

(4·10¹⁹⁹-13)/9 = (4)₁₉₈3_<199> = 3 · 97 · 107 · 175859 · 682417 · 130656152593_<12> · C172

C172 = P32 · P141

P32 = 21660553494232995120193600442447_<32>

P141 = 420268522590178138077849423985006098086889585395357247913022086632798078770561566068346842586303068386567989060067693212646894386791399439703_<141>

(7·10¹⁹²-61)/9 = (7)₁₉₁1_<192> = 3 · 313 · 761 · 9139826512344133_<16> · 358804313245062117504457_<24> · C147

C147 = P31 · P117

P31 = 2736444955335091738175869222951_<31>

P117 = 121289430700501471603498088503911465819708333729664041167291526413944869019180851149006200154305108790796966792303979_<117>

(17·10¹⁹⁷-53)/9 = 1(8)₁₉₆3_<198> = 3 · 19 · 619 · 8581 · 20073649757649413_<17> · 5797970114799596368404037_<25> · C148

C148 = P31 · P118

P31 = 2604864000866961077367688444027_<31>

P118 = 2057859104406529255404097678068784747468733410880713070871039782861735411913581127133206348898129767928452882855107983_<118>

(5·10¹⁹⁷+31)/9 = (5)₁₉₆9_<197> = 7² · 43891 · 162829 · 81609246936439853_<17> · 42761497358777840501_<20> · C149

C149 = P27 · P122

P27 = 950049141625022318627404183_<27>

P122 = 47850429337345006784444707647769333495962030245726338067483271465533087330815675138269874797856518257348618342044284285431_<122>

Jul 11, 2008 (6th)

By Sinkiti Sibata / GGNFS

5·10¹⁸⁰-7 = 4(9)₁₇₉3_<181> = 109 · 1488967 · 8420351363_<10> · 25030322608453531_<17> · 10767890436875898837091171_<26> · C122

C122 = P51 · P71

P51 = 139863195581166062045796944539175077355000899883699_<51>

P71 = 97057186527914640161646341782139678769623110723336236535802668798096963_<71>

Number: 49993_180
N=13574728261911441147955700905150374565535532034665629960565878514238403995814790116946394699688601479367104968379225106137
  ( 122 digits)
Divisors found:
 r1=139863195581166062045796944539175077355000899883699 (pp51)
 r2=97057186527914640161646341782139678769623110723336236535802668798096963 (pp71)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 85.86 hours.
Scaled time: 67.31 units (timescale=0.784).
Factorization parameters were as follows:
name: 49993_180
n: 13574728261911441147955700905150374565535532034665629960565878514238403995814790116946394699688601479367104968379225106137
skew: 77051.65
# norm 4.21e+16
c5: 34020
c4: -13370552037
c3: -806276712066080
c2: 43437997914285937766
c1: 379528431266404362894308
c0: 12554215439813951821136969239
# alpha -6.11
Y1: 2279412482303
Y0: -209025725432362513645620
# Murphy_E 2.48e-10
# M 12408996827428119508990999514464920706883057660258542158125313393200473585265399403708299436417097179742052149520854139575
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 4960001)
Primes: RFBsize:348513, AFBsize:348568, largePrimes:7707588 encountered
Relations: rels:7855683, finalFF:809185
Max relations in full relation-set: 28
Initial matrix: 697159 x 809185 with sparse part having weight 68458102.
Pruned matrix : 604522 x 608071 with weight 46617823.
Total sieving time: 80.23 hours.
Total relation processing time: 0.62 hours.
Matrix solve time: 4.58 hours.
Time per square root: 0.43 hours.
Prototype def-par.txt line would be:
gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 85.86 hours.
 --------- CPU info (if available) ----------

Jul 11, 2008 (5th)

By Robert Backstrom / GGNFS, Msieve

(61·10¹⁶⁶-7)/9 = 6(7)₁₆₆_<167> = 67 · 367 · 18457172593_<11> · 59403451729_<11> · C142

C142 = P51 · P91

P51 = 571362150201701442101639602427041315624408776223453_<51>

P91 = 4400055322869183148068430795279616992237472574915031133555720308758263448099841707032943673_<91>

Number: n
N=2514025070280978156173856658318084509079462260303472446853628761692169926867747112435428341002721935384211845341853088789294874496506610562869
  ( 142 digits)
SNFS difficulty: 167 digits.
Divisors found:

Fri Jul 11 20:01:05 2008  prp51 factor: 571362150201701442101639602427041315624408776223453
Fri Jul 11 20:01:05 2008  prp91 factor: 4400055322869183148068430795279616992237472574915031133555720308758263448099841707032943673
Fri Jul 11 20:01:05 2008  elapsed time 03:52:37 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 95.20 hours.
Scaled time: 166.51 units (timescale=1.749).
Factorization parameters were as follows:
name: KA_6_7_166
n: 2514025070280978156173856658318084509079462260303472446853628761692169926867747112435428341002721935384211845341853088789294874496506610562869
type: snfs
skew: 0.41
deg: 5
c5: 610
c0: -7
m: 1000000000000000000000000000000000
rlim: 5500000
alim: 5500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4000001)
Primes: RFBsize:380800, AFBsize:381368, largePrimes:8083118 encountered
Relations: rels:7642312, finalFF:764250
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 94.85 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.6,2.6,100000
total time: 95.20 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jul 11, 2008 (4th)

By Serge Batalov / GMP-ECM

(22·10¹⁷²-13)/9 = 2(4)₁₇₁3_<173> = 832582043 · 21430900157_<11> · C154

C154 = P32 · P123

P32 = 10657958831905102704921058981771_<32>

P123 = 128540113827202101407963240722095256356240982179406016084691632863292226740107335226351658112576118368825069138632503298783_<123>

(4·10²⁴⁵-1)/3 = 1(3)₂₄₅_<246> = 293 · 4428013 · 436570924477_<12> · 197820650760877883_<18> · 1940832977077439598289_<22> · C186

C186 = P30 · C157

P30 = 245134337177055685486188936209_<30>

C157 = [2501171562988825851415370384081321419214621935721077851805784023208701598634345508830113823065528926160766234175487084012080520263262356598377156307842064507_<157>]

(22·10²⁰⁴+23)/9 = 2(4)₂₀₃7_<205> = 720023 · 50715854861597509_<17> · 1888715261066607592247_<22> · C161

C161 = P33 · P129

P33 = 192419819014657626660048413404243_<33>

P129 = 184193270944572775718293604852340692637144385757769845962737152831321614464484501568395567703368265474703829715890241313565646801_<129>

(22·10¹⁸²+23)/9 = 2(4)₁₈₁7_<183> = 13² · 17 · 19 · 3673990757_<10> · C169

C169 = P35 · C134

P35 = 44982980583091433538219963671317681_<35>

C134 = [27095967114785546061369574234256681325758554891730009334878063346192359766250427904748769055763410666798187604335850455402484330235193_<134>]

(4·10²³¹-1)/3 = 1(3)₂₃₁_<232> = 2917 · 51824844853_<11> · C217

C217 = P32 · C186

P32 = 23692560197239551081270833387477_<32>

C186 = [372265083945976876768738111732476398995298007157226123029218145214349213362722613653536404844918572502440528633936829558008893550996679328683843376684364405105826229589913544277836064729_<186>]

(22·10¹⁸⁸+23)/9 = 2(4)₁₈₇7_<189> = 13 · C188

C188 = P34 · P154

P34 = 6189273399288534095811470799393323_<34>

P154 = 3038065632321280803476378108253243566314611187787592040202073700106715272161599074003370726703208829303229285374974719559646659679887499093314088198875153_<154>

(34·10¹⁸¹-43)/9 = 3(7)₁₈₀3_<182> = 3 · 11 · 29 · 163 · 5200627 · C170

C170 = P39 · C132

P39 = 213915155316488930742987770646789353867_<39>

C132 = [217690564118948162947524692462895493375283510041319060406784879841316278978454648395634663748148125534702826272476735696747049821067_<132>]

(22·10¹⁹³-13)/9 = 2(4)₁₉₂3_<194> = 5657 · C190

C190 = P38 · C152

P38 = 56324686381350084101805638381550307243_<38>

C152 = [76717635739151528363645309382391042558552748328658787346390836596385290572482473167190784819468980117146226312447151202964037959418539144514394956959993_<152>]

(11·10¹⁹⁰+7)/9 = 1(2)₁₈₉3_<191> = 31 · 4241 · 6376025173745417_<16> · C170

C170 = P31 · C139

P31 = 1863228909427870138828633619159_<31>

C139 = [7825353626582025776538354806681030279556975533141499321701053340837219702251845795735815749187118825483332759959817834394476302231364380271_<139>]

(22·10¹⁹⁰-31)/9 = 2(4)₁₈₉1_<191> = 3 · 107 · 30301683840760864991_<20> · C169

C169 = P31 · C139

P31 = 2490251637797916931309772842307_<31>

C139 = [1009171883154106743508535605718677600660412608929316157145576041105042869396199255493030596518470433121808888282588221824147334028807874733_<139>]

(67·10¹⁸⁵+23)/9 = 7(4)₁₈₄7_<186> = 3 · 11 · 25733 · 632743 · 1531297 · C168

C168 = P32 · P137

P32 = 34750107879239961728047681359629_<32>

P137 = 26036643415171346432359099267987911251355957717634424727606538886386969243082299006926238395178631918394732555045442482566554127640653897_<137>

Jul 11, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(22·10¹⁴⁷+23)/9 = 2(4)₁₄₆7_<148> = 65203 · 128552809986493_<15> · C129

C129 = P61 · P69

P61 = 1719658046526775063872329620833713151617719446440944978655437_<61>

P69 = 169585580715031070644678516951803468114192521983834826364569163297389_<69>

Number: 24447_147
N=291629208451519068887102421369332315645823720830469690559715370792266303503783111885851927973996158741963183104053718746592753993
  ( 129 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=1719658046526775063872329620833713151617719446440944978655437 (pp61)
 r2=169585580715031070644678516951803468114192521983834826364569163297389 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 26.74 hours.
Scaled time: 27.04 units (timescale=1.011).
Factorization parameters were as follows:
name: 24447_147
n: 291629208451519068887102421369332315645823720830469690559715370792266303503783111885851927973996158741963183104053718746592753993
m: 100000000000000000000000000000
c5: 2200
c0: 23
skew: 0.4
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 4450001)
Primes: RFBsize:114155, AFBsize:113693, largePrimes:3180001 encountered
Relations: rels:3315913, finalFF:304892
Max relations in full relation-set: 28
Initial matrix: 227915 x 304892 with sparse part having weight 39345363.
Pruned matrix : 209004 x 210207 with weight 26695627.
Total sieving time: 26.30 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.33 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 26.74 hours.
 --------- CPU info (if available) ----------

Jul 11, 2008 (2nd)

By Serge Batalov / GMP-ECM, pol51, Msieve

(22·10¹⁶⁵+23)/9 = 2(4)₁₆₄7_<166> = 3630210973012969_<16> · 184423336707533618359111_<24> · C127

C127 = P33 · P41 · P54

P33 = 519065104826878486825033434428939_<33>

P41 = 13564038936664591900573721755613575846723_<41>

P54 = 518586933045876452658110256298142053169804574677366689_<54>

Number: 24447_165
N=7034133351879741953545824637111591729772173449090960338984032566235543003595723345747130010147
  ( 94 digits)
Divisors found:
 r1=13564038936664591900573721755613575846723
 r2=518586933045876452658110256298142053169804574677366689
Version: Msieve 1.36
Factorization parameters were as follows:
name: 24447_165
n: 7034133351879741953545824637111591729772173449090960338984032566235543003595723345747130010147
skew: 3323.02
# norm 2.17e+13
c5: 12480
c4: 132852514
c3: 2026591728383
c2: -2797070364676835
c1: -152907382291947879
c0: 2428472541599586000585
# alpha -6.27
Y1: 21826676509
Y0: -891613348784733154
# Murphy_E 7.04e-09
# M 985921677842606424635089187194602414969543492765505871351915733770294116031045157405970754230
type: gnfs
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 900001)
Relations: 1827435 relations 
Pruned matrix : 113960 x 114182
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,93,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000

total time: 1.70 hours.

(22·10¹⁶⁰+23)/9 = 2(4)₁₅₉7_<161> = 3 · 59 · 1185889 · 111246536441_<12> · C142

C142 = P38 · P104

P38 = 18275254618976078978614739674353667489_<38>

P104 = 57281308395505724725642726213432671439294032138257996320630107178666862119375122137370004294231648428551_<104>

(22·10¹⁵⁸+23)/9 = 2(4)₁₅₇7_<159> = 13 · 103 · 100591 · 14065771 · 77006431 · C136

C136 = P38 · P98

P38 = 41970499708599475548745693906469796007_<38>

P98 = 39921402516784417137477507774986630829373202203626798195388657530740030186361497142025588004796529_<98>

(22·10¹⁶⁴+23)/9 = 2(4)₁₆₃7_<165> = 13 · 19 · 157 · 877 · 370824437303_<12> · 3897947297568115721_<19> · C127

C127 = P40 · P88

P40 = 1995019063063025398231422514593900200743_<40>

P88 = 2492485343226881663435258057593521762659123549921057652169671101365172576804392184453401_<88>

(4·10²⁰³-1)/3 = 1(3)₂₀₃_<204> = 1296951005067479_<16> · 3007224097573595988541199_<25> · C164

C164 = P35 · C130

P35 = 22202898588664747899239883251976133_<35>

C130 = [1539712722915429936027828705221199253961258103511550016874758536693107690174955859182188496690238915491251386488264294882125167481_<130>]

Jul 11, 2008

By Sinkiti Sibata / GGNFS

(22·10¹⁴⁶+23)/9 = 2(4)₁₄₅7_<147> = 13 · 19 · 691 · 827 · 225508344619_<12> · C127

C127 = P45 · P82

P45 = 877528400546131797964133967369485080367167411_<45>

P82 = 8751366321326903185967256414898843569806199348466925509478330018011501491730031177_<82>

Number: 24447_146
N=7679572490547282653445779566837844449760348140477557883118528874893256621861959423600369133825523183623545437777492618208372747
  ( 127 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=877528400546131797964133967369485080367167411 (pp45)
 r2=8751366321326903185967256414898843569806199348466925509478330018011501491730031177 (pp82)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 22.11 hours.
Scaled time: 22.36 units (timescale=1.011).
Factorization parameters were as follows:
name: 24447_146
n: 7679572490547282653445779566837844449760348140477557883118528874893256621861959423600369133825523183623545437777492618208372747
m: 100000000000000000000000000000
c5: 220
c0: 23
skew: 0.64
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 3650001)
Primes: RFBsize:114155, AFBsize:113843, largePrimes:3064283 encountered
Relations: rels:3144276, finalFF:305371
Max relations in full relation-set: 28
Initial matrix: 228065 x 305371 with sparse part having weight 37448122.
Pruned matrix : 207710 x 208914 with weight 24673037.
Total sieving time: 21.70 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 22.11 hours.
 --------- CPU info (if available) ----------

(22·10¹⁶³+23)/9 = 2(4)₁₆₂7_<164> = 3³ · 443567 · 2488363 · 18057001737479_<14> · 73151581097461_<14> · 9341132069122380143_<19> · C104

C104 = P45 · P60

P45 = 249102491687358608662848197534804232352965847_<45>

P60 = 266868000887712185768043059435968943896537652150789168406059_<60>

Number: 24447_163
N=66477483972753334552687859983056965286835579716750839563958970783526092476680414187738718186558254866973
  ( 104 digits)
Divisors found:
 r1=249102491687358608662848197534804232352965847 (pp45)
 r2=266868000887712185768043059435968943896537652150789168406059 (pp60)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 13.82 hours.
Scaled time: 6.54 units (timescale=0.473).
Factorization parameters were as follows:
name: 24447_163
n: 66477483972753334552687859983056965286835579716750839563958970783526092476680414187738718186558254866973
skew: 17881.90
# norm 4.12e+14
c5: 26280
c4: -214869564
c3: -22555996750888
c2: -53134620097994881
c1: -558143968031074428782
c0: 7374303972577595376526720
# alpha -6.71
Y1: 12172641437
Y0: -75964372797368143719
# Murphy_E 2.22e-09
# M 29165913441586357822458021902992880104855066735453999372086240476381350149477004246431504334222637972910
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1850001)
Primes: RFBsize:169511, AFBsize:169933, largePrimes:4303283 encountered
Relations: rels:4293785, finalFF:413693
Max relations in full relation-set: 28
Initial matrix: 339528 x 413693 with sparse part having weight 29409280.
Pruned matrix : 277889 x 279650 with weight 15942175.
Polynomial selection time: 0.78 hours.
Total sieving time: 10.85 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 1.68 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 13.82 hours.
 --------- CPU info (if available) ----------

Jul 10, 2008 (8th)

By Tyler Cadigan / GGNFS, Msieve

6·10¹⁹⁹+1 = 6(0)₁₉₈1_<200> = 100827365033_<12> · 21583541164043_<14> · 10056670285225909_<17> · 2683916005958404450397_<22> · C139

C139 = P60 · P79

P60 = 479403087032713635428088886452712241517044136079900092034489_<60>

P79 = 2130718979593492245520692728000484684740606068588764504461505725233767054216707_<79>

Number: 60001_199
N=1021473256416313751511313085195015415741101216728868678354738007603336860446052672596356366452772363939729027082207007676223269169924007723
  ( 139 digits)
Divisors found:
 r1=479403087032713635428088886452712241517044136079900092034489
 r2=2130718979593492245520692728000484684740606068588764504461505725233767054216707
Version: 
Total time: 729.05 hours.
Scaled time: 1862.01 units (timescale=2.554).
Factorization parameters were as follows:
name: 60001_199
n: 1021473256416313751511313085195015415741101216728868678354738007603336860446052672596356366452772363939729027082207007676223269169924007723
skew: 280338.19
# norm 1.04e+019
c5: 252300
c4: 245677573930
c3: -164464139065339148
c2: -14892083660147997638066
c1: 2698421714535061042480987013
c0: 224570424633670708149720645350596
# alpha -5.52
Y1: 7549711331871863
Y0: -332246204352086047653102315
# Murphy_E 2.43e-011
# M 763279243787741847951479506369752047463195655372871890327270343578515699232362167261281075751089072705232087075956662908098373259288311939
type: gnfs
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.5
alambda: 2.5
qintsize: 1000000
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [2700000, 1
)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1293519 x 1293747
Total sieving time: 729.05 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,138,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5400000,5400000,27,27,51,51,2.5,2.5,
total time: 729.05 hours.
 --------- CPU info (if available) ----------

Jul 10, 2008 (7th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(22·10¹⁶³-13)/9 = 2(4)₁₆₂3_<164> = 2713 · 56432111231_<11> · 141768691238978391619_<21> · C130

C130 = P65 · P65

P65 = 27792384200043657245658680170611919922816011461860744469047783927_<65>

P65 = 40522659874175581080586722921710792443780673884463536926755858537_<65>

Number: n
N=1126221332030780515366787389894956177448864285682143722873412986001818217724292991301588775644224073995875067988739088144154334799
  ( 130 digits)
SNFS difficulty: 164 digits.
Divisors found:

Thu Jul 10 11:46:24 2008  prp65 factor: 27792384200043657245658680170611919922816011461860744469047783927
Thu Jul 10 11:46:24 2008  prp65 factor: 40522659874175581080586722921710792443780673884463536926755858537
Thu Jul 10 11:46:24 2008  elapsed time 01:44:02 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 53.83 hours.
Scaled time: 78.10 units (timescale=1.451).
Factorization parameters were as follows:
name: KA_2_4_162_3
n: 1126221332030780515366787389894956177448864285682143722873412986001818217724292991301588775644224073995875067988739088144154334799
skew: 0.45
deg: 5
c5: 1375
c0: -26
m: 200000000000000000000000000000000
type: snfs
rlim: 4600000
alim: 4600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2600001)
Primes: RFBsize:322441, AFBsize:322367, largePrimes:7552829 encountered
Relations: rels:7113306, finalFF:680302
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 53.58 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,4600000,4600000,28,28,48,48,2.5,2.5,100000
total time: 53.83 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(22·10¹⁶⁹-1)/3 = 7(3)₁₆₉_<170> = 17 · 73 · 3727 · C164

C164 = P44 · P46 · P75

P44 = 55182912468944908194699383336535592987483933_<44>

P46 = 1869960505794526294457703325188424521177501593_<46>

P75 = 153650224634059109499407293340558535698949481554589881535242993884968124551_<75>

Number: n
N=15855146230932655194315267042822804110893487217617143045345502013927881137716286716104453991644770349377516148646608321169913764580338422330791537185975315987659219
  ( 164 digits)
SNFS difficulty: 171 digits.
Divisors found:

Thu Jul 10 15:53:51 2008  prp44 factor: 55182912468944908194699383336535592987483933
Thu Jul 10 15:53:51 2008  prp46 factor: 1869960505794526294457703325188424521177501593
Thu Jul 10 15:53:51 2008  prp75 factor: 153650224634059109499407293340558535698949481554589881535242993884968124551
Thu Jul 10 15:53:51 2008  elapsed time 01:29:24 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 58.25 hours.
Scaled time: 106.53 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_7_3_169
n: 15855146230932655194315267042822804110893487217617143045345502013927881137716286716104453991644770349377516148646608321169913764580338422330791537185975315987659219
skew: 0.85
deg: 5
c5: 11
c0: -5
m: 10000000000000000000000000000000000
type: snfs
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3600001)
Primes: RFBsize:425648, AFBsize:425618, largePrimes:8091283 encountered
Relations: rels:7744929, finalFF:876648
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 57.97 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,48,48,2.5,2.5,100000
total time: 58.25 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(65·10¹⁸⁷+43)/9 = 7(2)₁₈₆7_<188> = 7 · 11 · 17 · 73 · 367 · 227627 · 12114132883_<11> · 31708861836795119_<17> · 1408778549650698007_<19> · C131

C131 = P40 · P91

P40 = 3377652857328732875380257962975302947377_<40>

P91 = 4949801375445568906672988898650230437891483199484561725621942929232193814285739846837010593_<91>

Jul 10, 2008 (6th)

By Sinkiti Sibata / GGNFS

(22·10¹⁴³+23)/9 = 2(4)₁₄₂7_<144> = 7 · 47 · 22277 · 7533054917_<10> · C127

C127 = P35 · P93

P35 = 24899585554378077503177286185969857_<35>

P93 = 177813330540874967071390044687145423961622216372486528405096995740758978152899220369615973311_<93>

Number: 24447_143
N=4427478236511424556653540737563208231598857083891635006455103628275009139523403268427254684269587423295577407426383647562486527
  ( 127 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=24899585554378077503177286185969857 (pp35)
 r2=177813330540874967071390044687145423961622216372486528405096995740758978152899220369615973311 (pp93)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 17.00 hours.
Scaled time: 16.98 units (timescale=0.999).
Factorization parameters were as follows:
name: 24447_143
n: 4427478236511424556653540737563208231598857083891635006455103628275009139523403268427254684269587423295577407426383647562486527
m: 20000000000000000000000000000
c5: 1375
c0: 46
skew: 0.51
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 3150001)
Primes: RFBsize:100021, AFBsize:99749, largePrimes:3058574 encountered
Relations: rels:3168065, finalFF:285821
Max relations in full relation-set: 28
Initial matrix: 199836 x 285821 with sparse part having weight 36330475.
Pruned matrix : 180305 x 181368 with weight 22450673.
Total sieving time: 16.66 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 17.00 hours.
 --------- CPU info (if available) ----------

(22·10¹¹⁷+23)/9 = 2(4)₁₁₆7_<118> = 911 · 954962039576383_<15> · C100

C100 = P45 · P56

P45 = 153350347540615171531355729586920964045930299_<45>

P56 = 18322761197418823300515221966963200845626965065189219581_<56>

Number: 24447_117
N=2809801797527874745136340628744054936820227528609256621780222174244995101695208495794891430931984719
  ( 100 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=153350347540615171531355729586920964045930299 (pp45)
 r2=18322761197418823300515221966963200845626965065189219581 (pp56)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 2.93 hours.
Scaled time: 1.39 units (timescale=0.473).
Factorization parameters were as follows:
name: 24447_117
n: 2809801797527874745136340628744054936820227528609256621780222174244995101695208495794891430931984719
m: 100000000000000000000000
c5: 2200
c0: 23
skew: 0.4
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:63764, largePrimes:2268593 encountered
Relations: rels:2519915, finalFF:366680
Max relations in full relation-set: 28
Initial matrix: 112929 x 366680 with sparse part having weight 33794001.
Pruned matrix : 73925 x 74553 with weight 6172791.
Total sieving time: 2.74 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,118,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.93 hours.
 --------- CPU info (if available) ----------

(22·10¹⁴⁴+23)/9 = 2(4)₁₄₃7_<145> = 29 · 281 · 6690491558713094261_<19> · C122

C122 = P35 · P88

P35 = 24491557737939074393638448434527023_<35>

P88 = 1830633552595663753669826211681350715915526535694694172275334022433701837826737468955001_<88>

Number: 24447_144
N=44835067350405226132220665937906722622652243693041125936761642925899229679585266289557561143910490252449797666019505492023
  ( 122 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=24491557737939074393638448434527023 (pp35)
 r2=1830633552595663753669826211681350715915526535694694172275334022433701837826737468955001 (pp88)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 13.14 hours.
Scaled time: 13.21 units (timescale=1.005).
Factorization parameters were as follows:
name: 24447_144
n: 44835067350405226132220665937906722622652243693041125936761642925899229679585266289557561143910490252449797666019505492023
m: 100000000000000000000000000000
c5: 11
c0: 115
skew: 1.6
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2450001)
Primes: RFBsize:114155, AFBsize:113898, largePrimes:2942200 encountered
Relations: rels:3014645, finalFF:358154
Max relations in full relation-set: 28
Initial matrix: 228118 x 358154 with sparse part having weight 35742933.
Pruned matrix : 190894 x 192098 with weight 18442775.
Total sieving time: 12.84 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 13.14 hours.
 --------- CPU info (if available) ----------

(22·10¹⁴⁵+23)/9 = 2(4)₁₄₄7_<146> = 3² · 43 · 10671352823_<11> · C133

C133 = P47 · P87

P47 = 26172017367152437248707175326456702997166050893_<47>

P87 = 226158298190510848206744669030862864131241436076272580498188671436573372939791504234879_<87>

Number: 24447_145
N=5919018907967689542617280706178958723228668739763380195197924256951909716923374279609506382494224904358851019371435845744377939696947
  ( 133 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=26172017367152437248707175326456702997166050893 (pp47)
 r2=226158298190510848206744669030862864131241436076272580498188671436573372939791504234879 (pp87)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 15.40 hours.
Scaled time: 15.57 units (timescale=1.011).
Factorization parameters were as follows:
name: 24447_145
n: 5919018907967689542617280706178958723228668739763380195197924256951909716923374279609506382494224904358851019371435845744377939696947
m: 100000000000000000000000000000
c5: 22
c0: 23
skew: 1.01
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2850001)
Primes: RFBsize:114155, AFBsize:114118, largePrimes:3011437 encountered
Relations: rels:3111828, finalFF:366744
Max relations in full relation-set: 28
Initial matrix: 228339 x 366744 with sparse part having weight 39789463.
Pruned matrix : 191140 x 192345 with weight 21006123.
Total sieving time: 15.07 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 15.40 hours.
 --------- CPU info (if available) ----------

Jul 10, 2008 (5th)

By Serge Batalov / Msieve

(22·10¹³¹+23)/9 = 2(4)₁₃₀7_<132> = 7 · 233 · 674318596793_<12> · 127599449770529340523_<21> · C97

C97 = P40 · P58

P40 = 1485468538436582264497629280992342831383_<40>

P58 = 1172597093940178493433708438105100250038657021267386646301_<58>

Number: 24447_131
N=1741856091310300700715755929448806029623162241556917825463352044460114273431692604987339103664283
  ( 97 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=1485468538436582264497629280992342831383
 r2=1172597093940178493433708438105100250038657021267386646301
Version: Msieve 1.36
Factorization parameters were as follows:
n: 1741856091310300700715755929448806029623162241556917825463352044460114273431692604987339103664283
Y1: 1
Y0: -100000000000000000000000000
c5: 220
c0: 23
skew: 0.64
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [400000, 1100001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 120923 x 121140
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 2.00 hours
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

total time: 2.00 hours

(22·10¹³⁸+23)/9 = 2(4)₁₃₇7_<139> = 2799078671_<10> · C129

C129 = P60 · P70

P60 = 155810637693047503621475661225318370708471397541118401055253_<60>

P70 = 5604901198936834141789322417044567348370536055675412409260801606914669_<70>

Number: 24447_138
N=873303230012874634363731481002180250775968434523662748614629575891775442150280471500346924134182166559206525583376303911125206257
  ( 129 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=155810637693047503621475661225318370708471397541118401055253
 r2=5604901198936834141789322417044567348370536055675412409260801606914669
Version: 
Factorization parameters were as follows:
n: 873303230012874634363731481002180250775968434523662748614629575891775442150280471500346924134182166559206525583376303911125206257
Y1: 1
Y0: -2000000000000000000000000000
c5: 1375
c0: 46
skew: 0.51
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [500000, 2600001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 174196 x 174436
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

total time: 5.80 hours

(22·10¹³²+23)/9 = 2(4)₁₃₁7_<133> = 2687 · 778785229 · 31870902618307355072948857_<26> · C95

C95 = P46 · P50

P46 = 1066310319098017272671211681952031856865065671_<46>

P50 = 34372951380569981263498111038130737929995501699787_<50>

Number: 24447_132
N=36652232754956210070888323715313598937737298897994870862991340173992678559983082119579881712077
  ( 95 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=1066310319098017272671211681952031856865065671
 r2=34372951380569981263498111038130737929995501699787
Version: Msieve 1.36
Factorization parameters were as follows:
n: 36652232754956210070888323715313598937737298897994870862991340173992678559983082119579881712077
Y1: 1
Y0: -100000000000000000000000000
c5: 2200
c0: 23
skew: 0.4
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [400000, 1250001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: 1458934 unique relations 
Pruned matrix : 130812 x 131059
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000

total time: 2.50 hours.

(22·10¹³⁷+23)/9 = 2(4)₁₃₆7_<138> = 7 · 1741 · 6477307 · 56495077137950327_<17> · C110

C110 = P37 · P73

P37 = 5838733377978851433090143474291042027_<37>

P73 = 9387709216450097303503200248806037900230421287622289557752517186938865827_<73>

Number: 24447_137
N=54812331144846873200817559961946909008650132404608284127492823677164804029605122171898283048704688433371111329
  ( 110 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=5838733377978851433090143474291042027
 r2=9387709216450097303503200248806037900230421287622289557752517186938865827
Version: 
Factorization parameters were as follows:
n: 54812331144846873200817559961946909008650132404608284127492823677164804029605122171898283048704688433371111329
Y1: 1
Y0: -1000000000000000000000000000
c5: 2200
c0: 23
skew: 0.4
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [500000, 1925001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 157294 x 157519
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000

total time: 4.00 hours.

Jul 10, 2008 (4th)

By Robert Backstrom / GMP-ECM, GGNFS

(22·10¹³⁹+23)/9 = 2(4)₁₃₈7_<140> = 3 · 4349 · C136

C136 = P36 · P41 · P60

P36 = 384822306832803106175504740480258261_<36>

P41 = 29820580306445179468434784370467918075513_<41>

P60 = 163265032757307485732791583648752186409635917475529565664157_<60>

Number: n
N=4868658020573690727126546481856282776892240686260398313613025995290300464136292012462195107123487541
  ( 100 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=29820580306445179468434784370467918075513 (pp41)
 r2=163265032757307485732791583648752186409635917475529565664157 (pp60)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.87 hours.
Scaled time: 7.06 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_2_4_138_7
n: 4868658020573690727126546481856282776892240686260398313613025995290300464136292012462195107123487541
skew: 1.60
deg: 5
c5: 11
c0: 115
m: 10000000000000000000000000000
type: snfs
rlim: 1200000
alim: 1200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 760001)
Primes: RFBsize:92938, AFBsize:92505, largePrimes:6164160 encountered
Relations: rels:5408624, finalFF:225942
Max relations in full relation-set: 48
Initial matrix: 185508 x 225942 with sparse part having weight 26325682.
Pruned matrix : 171948 x 172939 with weight 15531984.
Total sieving time: 3.49 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.23 hours.
Total square root time: 0.03 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,48,48,2.5,2.5,100000
total time: 3.87 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jul 10, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(22·10¹⁷⁴-13)/9 = 2(4)₁₇₃3_<175> = 811 · 3379049371_<10> · C162

C162 = P47 · P57 · P60

P47 = 11072656343693520216315180207406030758141993043_<47>

P57 = 287966682004537921225496398852946852204100412458502336373_<57>

P60 = 279750400108181033972244071591541983136545321330179478911277_<60>

Number: 24443_174
N=891999847055895139743115124913569524755749316127777265347092103819927701303676855809664819338719798539911436166731483759915450801415537254910271854080136443820803
  ( 162 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=11072656343693520216315180207406030758141993043 (pp47)
 r2=287966682004537921225496398852946852204100412458502336373 (pp57)
 r3=279750400108181033972244071591541983136545321330179478911277 (pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 252.40 hours.
Scaled time: 255.17 units (timescale=1.011).
Factorization parameters were as follows:
name: 24443_174
n: 891999847055895139743115124913569524755749316127777265347092103819927701303676855809664819338719798539911436166731483759915450801415537254910271854080136443820803
m: 100000000000000000000000000000000000
c5: 11
c0: -65
skew: 1.43
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 12600001)
Primes: RFBsize:501962, AFBsize:502347, largePrimes:6616943 encountered
Relations: rels:7110143, finalFF:1158815
Max relations in full relation-set: 28
Initial matrix: 1004374 x 1158815 with sparse part having weight 81668155.
Pruned matrix : 874715 x 879800 with weight 62188821.
Total sieving time: 245.38 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 6.72 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 252.40 hours.
 --------- CPU info (if available) ----------

Jul 10, 2008 (2nd)

By Serge Batalov / Msieve

(22·10¹²⁸+23)/9 = 2(4)₁₂₇7_<129> = 13 · 19 · 8194776089_<10> · 3934292331971_<13> · C104

C104 = P33 · P34 · P38

P33 = 668426865130797987405649315345219_<33>

P34 = 1388343975982515290269796897309261_<34>

P38 = 33077183561244911430284006767620500381_<38>

Number: 24447_128
N=30695838422148846501555786734418298265899042615875233041634129014791334814237998087446452640996474073579
  ( 104 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=668426865130797987405649315345219
 r2=1388343975982515290269796897309261
 r3=33077183561244911430284006767620500381
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
n: 30695838422148846501555786734418298265899042615875233041634129014791334814237998087446452640996474073579
Y1: 1
Y0: -20000000000000000000000000
c5: 1375
c0: 46
skew: 0.51
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [400000, 1000001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 118754 x 118983
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 2.00 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

total time: 2.00 hours.

(22·10¹⁸⁴+23)/9 = 2(4)₁₈₃7_<185> = 3 · 8741 · 883727969 · 428463058069_<12> · 103877743860680497_<18> · 218460649344400193524021_<24> · 144099946999744771890872989_<27> · C93

C93 = P38 · P56

P38 = 14478093885479986710222592427921863391_<38>

P56 = 51998985992916577835802224283132907761310866802294639523_<56>

Wed Jul  9 04:10:59 2008  Msieve v. 1.36
Wed Jul  9 04:10:59 2008  random seeds: c8d737d3 84691ec3
Wed Jul  9 04:10:59 2008  factoring 752846201155204981101305409504528957770644176142445561475056010325809486586027355292795402493 (93 digits)
Wed Jul  9 04:11:00 2008  no P-1/P+1/ECM available, skipping
Wed Jul  9 04:11:00 2008  commencing quadratic sieve (93-digit input)
Wed Jul  9 04:11:00 2008  using multiplier of 13
Wed Jul  9 04:11:00 2008  using 64kb Opteron sieve core
Wed Jul  9 04:11:00 2008  sieve interval: 18 blocks of size 65536
Wed Jul  9 04:11:00 2008  processing polynomials in batches of 6
Wed Jul  9 04:11:00 2008  using a sieve bound of 1946657 (72941 primes)
Wed Jul  9 04:11:00 2008  using large prime bound of 243332125 (27 bits)
Wed Jul  9 04:11:00 2008  using double large prime bound of 1244970127754625 (42-51 bits)
Wed Jul  9 04:11:00 2008  using trial factoring cutoff of 51 bits
Wed Jul  9 04:11:00 2008  polynomial 'A' values have 12 factors
Wed Jul  9 04:11:00 2008  restarting with 1770 full and 95871 partial relations
Wed Jul  9 06:13:59 2008  73176 relations (18297 full + 54879 combined from 994629 partial), need 73037
Wed Jul  9 06:13:59 2008  begin with 1012926 relations
Wed Jul  9 06:14:00 2008  reduce to 187728 relations in 10 passes
Wed Jul  9 06:14:00 2008  attempting to read 187728 relations
Wed Jul  9 06:14:02 2008  recovered 187728 relations
Wed Jul  9 06:14:02 2008  recovered 170584 polynomials
Wed Jul  9 06:14:02 2008  attempting to build 73176 cycles
Wed Jul  9 06:14:02 2008  found 73176 cycles in 5 passes
Wed Jul  9 06:14:02 2008  distribution of cycle lengths:
Wed Jul  9 06:14:02 2008     length 1 : 18297
Wed Jul  9 06:14:02 2008     length 2 : 13020
Wed Jul  9 06:14:02 2008     length 3 : 12504
Wed Jul  9 06:14:02 2008     length 4 : 10068
Wed Jul  9 06:14:02 2008     length 5 : 7265
Wed Jul  9 06:14:02 2008     length 6 : 4859
Wed Jul  9 06:14:02 2008     length 7 : 2997
Wed Jul  9 06:14:02 2008     length 9+: 4166
Wed Jul  9 06:14:02 2008  largest cycle: 21 relations
Wed Jul  9 06:14:02 2008  matrix is 72941 x 73176 (20.1 MB) with weight 4680697 (63.96/col)
Wed Jul  9 06:14:03 2008  sparse part has weight 4680697 (63.96/col)
Wed Jul  9 06:14:03 2008  filtering completed in 3 passes
Wed Jul  9 06:14:03 2008  matrix is 69245 x 69309 (19.1 MB) with weight 4458851 (64.33/col)
Wed Jul  9 06:14:03 2008  sparse part has weight 4458851 (64.33/col)
Wed Jul  9 06:14:04 2008  saving the first 48 matrix rows for later
Wed Jul  9 06:14:04 2008  matrix is 69197 x 69309 (12.5 MB) with weight 3534404 (50.99/col)
Wed Jul  9 06:14:04 2008  sparse part has weight 2592435 (37.40/col)
Wed Jul  9 06:14:04 2008  matrix includes 64 packed rows
Wed Jul  9 06:14:04 2008  using block size 27723 for processor cache size 1024 kB
Wed Jul  9 06:14:04 2008  commencing Lanczos iteration
Wed Jul  9 06:14:04 2008  memory use: 11.0 MB
Wed Jul  9 06:14:34 2008  lanczos halted after 1095 iterations (dim = 69196)
Wed Jul  9 06:14:34 2008  recovered 17 nontrivial dependencies
Wed Jul  9 06:14:34 2008  prp38 factor: 14478093885479986710222592427921863391
Wed Jul  9 06:14:34 2008  prp56 factor: 51998985992916577835802224283132907761310866802294639523
Wed Jul  9 06:14:34 2008  elapsed time 02:03:35

total time: 2.5 hours

(19·10¹⁶⁴+71)/9 = 2(1)₁₆₃9_<165> = 3 · 1547632204735021741335968620259_<31> · C134

C134 = P58 · P76

P58 = 6742027040094211846211453572461118212957579443337461963393_<58>

P76 = 6744217820260450083366667566814032486869788470472656779231418088265090202679_<76>

Number: 21119_164
N=45469698908481199516727249124846049133783177271867124530465321077300054016404482853634631520144827560167514096151705840653303648529847
  ( 134 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=6742027040094211846211453572461118212957579443337461963393
 r2=6744217820260450083366667566814032486869788470472656779231418088265090202679
Version: 
Total time: 28.00 hours.
Scaled time: 82.656 units (timescale=2.952).
Factorization parameters were as follows:
n: 45469698908481199516727249124846049133783177271867124530465321077300054016404482853634631520144827560167514096151705840653303648529847
Y0: -1000000000000000000000000000000000
Y1: 1
c5: 19
c0: 710
skew: 2.06
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 4600001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: 10573189 relations 
Max relations in full relation-set: 9708274 relations and about 9462589 large ideals
Initial matrix: 866332 x 866551 (261.2 MB) with weight 83061728 (95.85/col)
Pruned matrix : 860767 x 861015 (249.7 MB) with weight 63635070 (73.91/col)
Total sieving time: 25.00 hours.
Matrix solve time: 02:44:00.
Time per square root: 00:09:52.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.5,2.5,100000
total time: 28.00 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

Total time: 28.00 hours.

(22·10¹⁰⁹+23)/9 = 2(4)₁₀₈7_<110> = 3³ · C108

C108 = P48 · P61

P48 = 113608441459662824962269148437092967080552227087_<48>

P61 = 7969036302290367567268621003851406845020368538649090611909603_<61>

Number: 24447_109
N=905349794238683127572016460905349794238683127572016460905349794238683127572016460905349794238683127572016461
  ( 108 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=113608441459662824962269148437092967080552227087
 r2=7969036302290367567268621003851406845020368538649090611909603
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
n: 905349794238683127572016460905349794238683127572016460905349794238683127572016460905349794238683127572016461
Y1: 1
Y0: -10000000000000000000000
c5: 11
c0: 115
skew: 1.6
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 350001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 72091 x 72333
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.00 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

total time: 1.00 hours.

(22·10¹³⁶+23)/9 = 2(4)₁₃₅7_<137> = 3⁴ · 17597 · 474430838713204111_<18> · C113

C113 = P57 · P57

P57 = 160942727758616147304759991172660468836593226620551349083_<57>

P57 = 224601291731175620982413630782755053499706451971227086767_<57>

# NICE SPLIT :-)  P57 . P57

Number: 24447_136
N=36147944549324121969604965835519947229596904347641869546100384519388695605927646880868433968210753734213746884661
  ( 113 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=160942727758616147304759991172660468836593226620551349083
 r2=224601291731175620982413630782755053499706451971227086767

Factorization parameters were as follows:
n: 36147944549324121969604965835519947229596904347641869546100384519388695605927646880868433968210753734213746884661
Y1: 1
Y0: -1000000000000000000000000000
c5: 220
c0: 23
skew: 0.64
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [500000, 1925001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 156383 x 156621
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 4 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

total time: 4 hours.

Jul 10, 2008

Factorizations of 133...33 were extended to n=250. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors are probably greater than 10³⁰.

Factorizations of 244...447 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors are probably greater than 10³⁰.

Jul 9, 2008 (5th)

By matsui / GGNFS

(10¹⁷⁵-7)/3 = (3)₁₇₄1_<175> = 23 · 3323 · C170

C170 = P45 · P53 · P74

P45 = 235780448596050115929700871470352538873891461_<45>

P53 = 10421228205712331802636719386399164355520595269666467_<53>

P74 = 17749816682347588484905538626867074536389885930396621086863262194900258897_<74>

N=43613462603636490511891210578881489138067138564332038013494005329565130164379140553105932739317972671804332561375045248967451272858906087130975589544980744656260494489439
  ( 170 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=235780448596050115929700871470352538873891461 (pp45)
 r2=10421228205712331802636719386399164355520595269666467 (pp53)
 r3=17749816682347588484905538626867074536389885930396621086863262194900258897 (pp74)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 110.75 hours.
Scaled time: 314.20 units (timescale=2.837).
Factorization parameters were as follows:
n: 43613462603636490511891210578881489138067138564332038013494005329565130164379140553105932739317972671804332561375045248967451272858906087130975589544980744656260494489439
m: 100000000000000000000000000000000000
c5: 1
c0: -7
skew: 1.48
type: snfs

Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 9800001)
Primes: RFBsize:501962, AFBsize:501141, largePrimes:6403058 encountered
Relations: rels:6902001, finalFF:1178713
Max relations in full relation-set: 28
Initial matrix: 1003169 x 1178713 with sparse part having weight 65422220.
Pruned matrix : 846847 x 851926 with weight 46933518.
Total sieving time: 106.18 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 4.29 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 110.75 hours.

Jul 9, 2008 (4th)

By Sinkiti Sibata / Msieve

(22·10¹²⁶+23)/9 = 2(4)₁₂₅7_<127> = 499 · 1103 · 87797 · 448607 · 6732252439515400559819_<22> · C89

C89 = P31 · P58

P31 = 5244805083985130173131426609173_<31>

P58 = 3193512685867020820044526963651820924786832284035313015287_<58>

Wed Jul  9 16:54:55 2008  Msieve v. 1.36
Wed Jul  9 16:54:55 2008  random seeds: dd38a79e ee65a53f
Wed Jul  9 16:54:55 2008  factoring 16749351570606358764161948724391155809899067723886709775698749787610441965641844723427651 (89 digits)
Wed Jul  9 16:54:57 2008  no P-1/P+1/ECM available, skipping
Wed Jul  9 16:54:57 2008  commencing quadratic sieve (89-digit input)
Wed Jul  9 16:54:57 2008  using multiplier of 3
Wed Jul  9 16:54:57 2008  using 64kb Pentium 4 sieve core
Wed Jul  9 16:54:57 2008  sieve interval: 15 blocks of size 65536
Wed Jul  9 16:54:57 2008  processing polynomials in batches of 7
Wed Jul  9 16:54:57 2008  using a sieve bound of 1546823 (58602 primes)
Wed Jul  9 16:54:57 2008  using large prime bound of 123745840 (26 bits)
Wed Jul  9 16:54:57 2008  using double large prime bound of 368599753674560 (42-49 bits)
Wed Jul  9 16:54:57 2008  using trial factoring cutoff of 49 bits
Wed Jul  9 16:54:57 2008  polynomial 'A' values have 11 factors
Wed Jul  9 18:34:09 2008  58806 relations (15836 full + 42970 combined from 622685 partial), need 58698
Wed Jul  9 18:34:11 2008  begin with 638521 relations
Wed Jul  9 18:34:12 2008  reduce to 142912 relations in 11 passes
Wed Jul  9 18:34:12 2008  attempting to read 142912 relations
Wed Jul  9 18:34:16 2008  recovered 142912 relations
Wed Jul  9 18:34:16 2008  recovered 120166 polynomials
Wed Jul  9 18:34:16 2008  attempting to build 58806 cycles
Wed Jul  9 18:34:16 2008  found 58806 cycles in 5 passes
Wed Jul  9 18:34:16 2008  distribution of cycle lengths:
Wed Jul  9 18:34:16 2008     length 1 : 15836
Wed Jul  9 18:34:16 2008     length 2 : 11406
Wed Jul  9 18:34:16 2008     length 3 : 10376
Wed Jul  9 18:34:16 2008     length 4 : 7683
Wed Jul  9 18:34:16 2008     length 5 : 5523
Wed Jul  9 18:34:16 2008     length 6 : 3494
Wed Jul  9 18:34:16 2008     length 7 : 2010
Wed Jul  9 18:34:16 2008     length 9+: 2478
Wed Jul  9 18:34:16 2008  largest cycle: 17 relations
Wed Jul  9 18:34:16 2008  matrix is 58602 x 58806 (14.4 MB) with weight 3527793 (59.99/col)
Wed Jul  9 18:34:16 2008  sparse part has weight 3527793 (59.99/col)
Wed Jul  9 18:34:17 2008  filtering completed in 3 passes
Wed Jul  9 18:34:17 2008  matrix is 54483 x 54547 (13.4 MB) with weight 3301942 (60.53/col)
Wed Jul  9 18:34:17 2008  sparse part has weight 3301942 (60.53/col)
Wed Jul  9 18:34:18 2008  saving the first 48 matrix rows for later
Wed Jul  9 18:34:18 2008  matrix is 54435 x 54547 (9.6 MB) with weight 2709907 (49.68/col)
Wed Jul  9 18:34:18 2008  sparse part has weight 2194112 (40.22/col)
Wed Jul  9 18:34:18 2008  matrix includes 64 packed rows
Wed Jul  9 18:34:18 2008  using block size 21818 for processor cache size 512 kB
Wed Jul  9 18:34:18 2008  commencing Lanczos iteration
Wed Jul  9 18:34:18 2008  memory use: 8.8 MB
Wed Jul  9 18:34:52 2008  lanczos halted after 863 iterations (dim = 54432)
Wed Jul  9 18:34:52 2008  recovered 16 nontrivial dependencies
Wed Jul  9 18:34:53 2008  prp31 factor: 5244805083985130173131426609173
Wed Jul  9 18:34:53 2008  prp58 factor: 3193512685867020820044526963651820924786832284035313015287
Wed Jul  9 18:34:53 2008  elapsed time 01:39:58

(22·10¹¹⁴+23)/9 = 2(4)₁₁₃7_<115> = 83 · 163 · 78191 · 3416683 · 33319373 · C92

C92 = P31 · P61

P31 = 4616751856764010560641603977181_<31>

P61 = 4396627454638834962965514259782807864624263415930800244963587_<61>

Wed Jul  9 18:46:02 2008  Msieve v. 1.36
Wed Jul  9 18:46:02 2008  random seeds: 3e553e05 eee29778
Wed Jul  9 18:46:02 2008  factoring 20298137964703466931499613781729059356375064174379028443684191792924037555723406483723908247 (92 digits)
Wed Jul  9 18:46:04 2008  no P-1/P+1/ECM available, skipping
Wed Jul  9 18:46:04 2008  commencing quadratic sieve (92-digit input)
Wed Jul  9 18:46:04 2008  using multiplier of 7
Wed Jul  9 18:46:04 2008  using 64kb Pentium 4 sieve core
Wed Jul  9 18:46:04 2008  sieve interval: 18 blocks of size 65536
Wed Jul  9 18:46:04 2008  processing polynomials in batches of 6
Wed Jul  9 18:46:04 2008  using a sieve bound of 1785001 (67059 primes)
Wed Jul  9 18:46:04 2008  using large prime bound of 187425105 (27 bits)
Wed Jul  9 18:46:04 2008  using double large prime bound of 778197657514830 (42-50 bits)
Wed Jul  9 18:46:04 2008  using trial factoring cutoff of 50 bits
Wed Jul  9 18:46:04 2008  polynomial 'A' values have 12 factors
Wed Jul  9 22:25:10 2008  67378 relations (16844 full + 50534 combined from 837582 partial), need 67155
Wed Jul  9 22:25:13 2008  begin with 854426 relations
Wed Jul  9 22:25:14 2008  reduce to 171242 relations in 11 passes
Wed Jul  9 22:25:14 2008  attempting to read 171242 relations
Wed Jul  9 22:25:19 2008  recovered 171242 relations
Wed Jul  9 22:25:19 2008  recovered 153667 polynomials
Wed Jul  9 22:25:20 2008  attempting to build 67378 cycles
Wed Jul  9 22:25:20 2008  found 67378 cycles in 5 passes
Wed Jul  9 22:25:20 2008  distribution of cycle lengths:
Wed Jul  9 22:25:20 2008     length 1 : 16844
Wed Jul  9 22:25:20 2008     length 2 : 12110
Wed Jul  9 22:25:20 2008     length 3 : 11636
Wed Jul  9 22:25:20 2008     length 4 : 9235
Wed Jul  9 22:25:20 2008     length 5 : 6751
Wed Jul  9 22:25:20 2008     length 6 : 4363
Wed Jul  9 22:25:20 2008     length 7 : 2761
Wed Jul  9 22:25:20 2008     length 9+: 3678
Wed Jul  9 22:25:20 2008  largest cycle: 19 relations
Wed Jul  9 22:25:20 2008  matrix is 67059 x 67378 (16.6 MB) with weight 4070504 (60.41/col)
Wed Jul  9 22:25:20 2008  sparse part has weight 4070504 (60.41/col)
Wed Jul  9 22:25:21 2008  filtering completed in 3 passes
Wed Jul  9 22:25:21 2008  matrix is 63591 x 63654 (15.7 MB) with weight 3858318 (60.61/col)
Wed Jul  9 22:25:21 2008  sparse part has weight 3858318 (60.61/col)
Wed Jul  9 22:25:22 2008  saving the first 48 matrix rows for later
Wed Jul  9 22:25:22 2008  matrix is 63543 x 63654 (9.1 MB) with weight 2921246 (45.89/col)
Wed Jul  9 22:25:22 2008  sparse part has weight 1996484 (31.36/col)
Wed Jul  9 22:25:22 2008  matrix includes 64 packed rows
Wed Jul  9 22:25:22 2008  using block size 21845 for processor cache size 512 kB
Wed Jul  9 22:25:23 2008  commencing Lanczos iteration
Wed Jul  9 22:25:23 2008  memory use: 9.4 MB
Wed Jul  9 22:26:02 2008  lanczos halted after 1007 iterations (dim = 63543)
Wed Jul  9 22:26:02 2008  recovered 18 nontrivial dependencies
Wed Jul  9 22:26:03 2008  prp31 factor: 4616751856764010560641603977181
Wed Jul  9 22:26:03 2008  prp61 factor: 4396627454638834962965514259782807864624263415930800244963587
Wed Jul  9 22:26:03 2008  elapsed time 03:40:01

Jul 9, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(34·10¹⁶⁷-7)/9 = 3(7)₁₆₇_<168> = 19² · 61 · 3391 · 319591 · 713117 · C149

C149 = P53 · P97

P53 = 17765799744251399391751532208792506707077198483134659_<53>

P97 = 1249486269597586121075036778169187427046511143878302586983277601012099857469072501275389410982659_<97>

Number: n
N=22198122848862430580991565540343634709543895530381938659399213758074630177988467525888585175990283070868339958702115301444012179905280476799810878281
  ( 149 digits)
SNFS difficulty: 168 digits.
Divisors found:

Wed Jul 09 19:19:54 2008  prp53 factor: 17765799744251399391751532208792506707077198483134659
Wed Jul 09 19:19:54 2008  prp97 factor: 1249486269597586121075036778169187427046511143878302586983277601012099857469072501275389410982659
Wed Jul 09 19:19:54 2008  elapsed time 02:04:09

Version: GGNFS-0.77.1-20051202-athlon
Total time: 64.20 hours.
Scaled time: 117.41 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_3_7_167
n: 22198122848862430580991565540343634709543895530381938659399213758074630177988467525888585175990283070868339958702115301444012179905280476799810878281
skew: 0.29
deg: 5
c5: 3400
c0: -7
m: 1000000000000000000000000000000000
type: snfs
rlim: 5500000
alim: 5500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4000153)
Primes: RFBsize:380800, AFBsize:380992, largePrimes:8099098 encountered
Relations: rels:7674418, finalFF:781427
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 63.88 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.5,2.5,100000
total time: 64.20 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(22·10¹²⁹+23)/9 = 2(4)₁₂₈7_<130> = 767747 · 9294347693_<10> · C114

C114 = P36 · P79

P36 = 145463583266265491036564533866890587_<36>

P79 = 2354988803953860722933036576440462288212379685460602193096133727602333545086411_<79>

Jul 9, 2008 (2nd)

By Serge Batalov / Msieve

(22·10¹⁰⁸+23)/9 = 2(4)₁₀₇7_<109> = 443 · 7529 · C102

C102 = P39 · P63

P39 = 769844223455726196788224292250471499171_<39>

P63 = 951998562560586340256760402450547611450431456341933895606371031_<63>

Number: 24447_108
N=732890594125422165802971758094268585680723608201618735455244819937609023722102811025193014233434915301
  ( 102 digits)
SNFS difficulty: 109 digits.
Divisors found:
 r1=769844223455726196788224292250471499171
 r2=951998562560586340256760402450547611450431456341933895606371031
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.915).
Factorization parameters were as follows:
n: 732890594125422165802971758094268585680723608201618735455244819937609023722102811025193014233434915301
Y1: 1
Y0: -2000000000000000000000
c5: 1375
c0: 46
skew: 0.51
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 400001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 73387 x 73623
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,109,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 0.00 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

Total: 42 minutes

(22·10¹⁰²+23)/9 = 2(4)₁₀₁7_<103> = 17 · 59 · 277 · C97

C97 = P47 · P51

P47 = 10618264544595981314549183771879838048526138753_<47>

P51 = 828601906275618561461709775254426181373901654948329_<51>

Number: 24447_102
N=8798314242991042916177260436900289904454306554864088040731395864552351769400982771700942099493737
  ( 97 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=10618264544595981314549183771879838048526138753
 r2=828601906275618561461709775254426181373901654948329
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.943).
Factorization parameters were as follows:
#res: 4678
n: 8798314242991042916177260436900289904454306554864088040731395864552351769400982771700942099493737
Y1: 1
Y0: -100000000000000000000
c5: 2200
c0: 23
skew: 0.4
type: snfs
Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [225000, 285001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 47340 x 47577
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,103,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000
total time: 0.00 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

total time: 22 min

(22·10¹⁰⁷+23)/9 = 2(4)₁₀₆7_<108> = 7 · 1087 · C104

C104 = P42 · P62

P42 = 381591330607017206412657428815125306888619_<42>

P62 = 84188755147859735744695342070485785175230396419321883226185157_<62>

Number: 24447_107
N=32125699099020166177479884931586863509586600662957608679779792935266716315474365152378031862852470028183
  ( 104 digits)
SNFS difficulty: 108 digits.
Divisors found:
 r1=381591330607017206412657428815125306888619
 r2=84188755147859735744695342070485785175230396419321883226185157
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.947).
Factorization parameters were as follows:
n: 32125699099020166177479884931586863509586600662957608679779792935266716315474365152378031862852470028183
Y1: 1
Y0: -1000000000000000000000
c5: 2200
c0: 23
skew: 0.4
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 400001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 61013 x 61240
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,108,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 0.00 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

total time: 41 min

(22·10¹²⁴+23)/9 = 2(4)₁₂₃7_<125> = 3 · 43 · 103 · C121

C121 = P47 · P74

P47 = 31127363639203918155230106265371550433065849027_<47>

P74 = 59103186631439869309748970750979721507029739430928737715066147860616020803_<74>

Number: 24447_124
N=1839726382512564494953296037062124214980390189240945619360611458150405994163049931846499920557269846048351354289489308681
  ( 121 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=31127363639203918155230106265371550433065849027
 r2=59103186631439869309748970750979721507029739430928737715066147860616020803
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.945).
Factorization parameters were as follows:
n: 1839726382512564494953296037062124214980390189240945619360611458150405994163049931846499920557269846048351354289489308681
Y1: 1
Y0: -10000000000000000000000000
c5: 11
c0: 115
skew: 1.6
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 500001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 111567 x 111791
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 49min.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

total time: 49min.

(22·10¹²⁷+23)/9 = 2(4)₁₂₆7_<128> = 3² · C127

C127 = P40 · P88

P40 = 1055851411540761761126901338111649728911_<40>

P88 = 2572378417103811115329524052621719508567986338053396769025584246379410302932317285466153_<88>

N=2716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049383
  ( 127 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=1055851411540761761126901338111649728911
 r2=2572378417103811115329524052621719508567986338053396769025584246379410302932317285466153
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.821).
Factorization parameters were as follows:
n: 2716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049383
Y1: 1
Y0: -10000000000000000000000000
c5: 2200
c0: 23
skew: 0.4
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [400000, 900001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 110989 x 111235
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 1.50 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

total time: 1.50 hours.

(22·10¹²³+23)/9 = 2(4)₁₂₂7_<124> = 22142383 · 4261412657_<10> · C107

C107 = P38 · P69

P38 = 26763002716631911281029424155030335139_<38>

P69 = 967982226653429397489275031441447420090456022581392764391905774301483_<69>

Number: 24447_123
N=25906110961577137444577994220052608180999890138710163516987992524436446672531714607299587564660203114711137
  ( 107 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=26763002716631911281029424155030335139
 r2=967982226653429397489275031441447420090456022581392764391905774301483
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=1.624).
Factorization parameters were as follows:
n: 25906110961577137444577994220052608180999890138710163516987992524436446672531714607299587564660203114711137
Y1: 1
Y0: -2000000000000000000000000
c5: 1375
c0: 46
skew: 0.51
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 600001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 109891 x 110122
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.20 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

total time: 1.20 hours.

(22·10¹⁵²+23)/9 = 2(4)₁₅₁7_<153> = 13 · 150329 · 769837 · 87625711531_<11> · 769556122625057200022794067_<27> · C103

C103 = P35 · P69

P35 = 10813062888571622922756770354132923_<35>

P69 = 222830526301659720606359045665497825172567913566370741154408463204093_<69>

Number: 24447_152
N=2409480494393359654417053972732335004481060547935443629191110013513357239972483882405770870013399653839
  ( 103 digits)
Divisors found:
 r1=10813062888571622922756770354132923
 r2=222830526301659720606359045665497825172567913566370741154408463204093
Version:
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
name: 24447_152
n: 2409480494393359654417053972732335004481060547935443629191110013513357239972483882405770870013399653839
skew: 19561.08
# norm 8.91e+13
c5: 420
c4: -82996087
c3: -4257878742953
c2: 33361211199951301
c1: 145479990723098945878
c0: -843488700671868424525899
# alpha -4.74
Y1: 24707240459
Y0: -89482799835749821772
# Murphy_E 2.44e-09
# M 2165897549338724270610609111043907709624331788247989596227418375996497476424002657125822225638182266954
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1850001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 250649 x 250883
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 4.20 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

total time: 4.20 hours.

Jul 9, 2008

Factorizations of 244...447 were extended to n=200. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors are probably greater than 10³⁰.

Jul 8, 2008

By Robert Backstrom / GMP-ECM

(37·10¹⁸¹-1)/9 = 4(1)₁₈₁_<182> = 17 · 41 · 4127 · 24499 · 167471 · 245443424673836171_<18> · 246875141547236483_<18> · C131

C131 = P43 · P88

P43 = 9694281830014265153818506928082037151687589_<43>

P88 = 5930066875553988652313184804417901312203848627507573517688576121033537218672808937502993_<88>

Jul 7, 2008 (4th)

By Robert Backstrom / GGNFS

(22·10¹⁷³-31)/9 = 2(4)₁₇₂1_<174> = 29 · C172

C172 = P62 · P111

P62 = 53929390053448635802755667268850142007562273054280940188884371_<62>

P111 = 156299167589182500831339219188302177128441788079387540549837743824293003742698300050396169986960092098989076799_<111>

Number: n
N=8429118773946360153256704980842911877394636015325670498084291187739463601532567049808429118773946360153256704980842911877394636015325670498084291187739463601532567049808429
  ( 172 digits)
SNFS difficulty: 174 digits.
Divisors found:

Mon Jul 07 22:10:46 2008  prp62 factor: 53929390053448635802755667268850142007562273054280940188884371
Mon Jul 07 22:10:46 2008  prp111 factor: 156299167589182500831339219188302177128441788079387540549837743824293003742698300050396169986960092098989076799
Mon Jul 07 22:10:46 2008  elapsed time 03:58:11 (Msieve 1.36)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 195.03 hours.
Scaled time: 255.49 units (timescale=1.310).
Factorization parameters were as follows:
name: KA_2_4_172_1
n: 8429118773946360153256704980842911877394636015325670498084291187739463601532567049808429118773946360153256704980842911877394636015325670498084291187739463601532567049808429
skew: 0.54
deg: 5
c5: 1375
c0: -62
m: 20000000000000000000000000000000000
type: snfs
rlim: 7000000
alim: 7000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 7000000/7000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 7100173)
Primes: RFBsize:476648, AFBsize:475941, largePrimes:9026408 encountered
Relations: rels:8609903, finalFF:954855
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 194.26 hours.
Total relation processing time: 0.77 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,174,5,0,0,0,0,0,0,0,0,7000000,7000000,28,28,48,48,2.5,2.5,100000
total time: 195.03 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jul 7, 2008 (3rd)

By Serge Batalov / GMP-ECM

(64·10²¹⁵+53)/9 = 7(1)₂₁₄7_<216> = 3 · 11 · 3079 · C211

C211 = P45 · P47 · P120

P45 = 125676554603285221667793460094390282916482437_<45>

P47 = 81213719868582797366318791991053471705206424789_<47>

P120 = 685693711441738179761734159616977676586319021004974435893926620849586278615885854977785958434104586204829762960643199667_<120>

# I have now already sieved 38 MILLION relations (30-bit LPs!), with 320 CPU-hours on Opteron (on 8 CPUs)
#
# ...in parallel I ran a lot of ECMs, full 1M, 3M, then 11M...
# ...and when I cracked off the P47 I was disappointed, but GNFS was still unfeasible
# ...and another day later, I checked the B1=43000000 ECM processes (far from complete)
# and the number was cracked completely.
#
# What a pity!
#
# P.S. Maybe you could leave this story in a text box
#      (you usually don't for ECMs, but this may be a lesson how to avoid
#      trivial painful factorizations by two months of GGNFS)
#      Nobody likes an ECM miss!
#      The P45 and P47 are not really a miss (for home computing), but nobody wants a 30-39-digit factor, that's for sure.
#
#        --Serge

C211 = P45 . P47 . P120

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 6998642919396410789720305796954059376923943341611415661431900470549382533793056690101185067083085920370753108655024861585433199593641295492545898521864744664354927427353539727687178158110278928726476631640645931 (211 digits)
Run 3861 out of 4600:
Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=1048397889
Step 1 took 122874ms
Step 2 took 55826ms
********** Factor found in step 2: 81213719868582797366318791991053471705206424789
Found probable prime factor of 47 digits: 81213719868582797366318791991053471705206424789
Composite cofactor 86175623167136908906028312775085985010301678182392368154328956428185102943358698524469334462125149952396328912164009032468557009157053703824006666253050812289748479 has 164 digits

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Run 33 out of 1000:
Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1801021090
Step 1 took 361683ms
Step 2 took 92881ms
********** Factor found in step 2: 125676554603285221667793460094390282916482437
Found probable prime factor of 45 digits: 125676554603285221667793460094390282916482437
Probable prime cofactor 685693711441738179761734159616977676586319021004974435893926620849586278615885854977785958434104586204829762960643199667 has 120 digits

all three factors prime by APRT-CLE.

Jul 7, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(22·10¹⁶⁹-13)/9 = 2(4)₁₆₈3_<170> = 6603123233761858889_<19> · C151

C151 = P35 · P117

P35 = 34538325050649741960582584869569799_<35>

P117 = 107183885461665753591363007370745581050786551598708387085447555024370036792587759492946489199946634658942041297437413_<117>

Number: 24443_169
N=3701951876266622979874422342651354796993731339689201245901440527900042776675366699392640951666692911201609719346004277223504578989840161477542437489987
  ( 151 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=34538325050649741960582584869569799 (pp35)
 r2=107183885461665753591363007370745581050786551598708387085447555024370036792587759492946489199946634658942041297437413 (pp117)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 141.04 hours.
Scaled time: 142.17 units (timescale=1.008).
Factorization parameters were as follows:
name: 24443_169
n: 3701951876266622979874422342651354796993731339689201245901440527900042776675366699392640951666692911201609719346004277223504578989840161477542437489987
m: 10000000000000000000000000000000000
c5: 11
c0: -65
skew: 1.43
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 8300001)
Primes: RFBsize:412849, AFBsize:413107, largePrimes:6158208 encountered
Relations: rels:6424609, finalFF:926523
Max relations in full relation-set: 28
Initial matrix: 826021 x 926523 with sparse part having weight 64258799.
Pruned matrix : 747047 x 751241 with weight 49325952.
Total sieving time: 136.65 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 4.17 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 141.04 hours.
 --------- CPU info (if available) ----------

Jul 7, 2008

By Robert Backstrom / GGNFS, Msieve

3·10¹⁶⁸+7 = 3(0)₁₆₇7_<169> = 31² · 220442934797851_<15> · C152

C152 = P59 · P93

P59 = 68134668790873592384459578322644469894232860523283147276193_<59>

P93 = 207842105702935771469899396383940505601339931626765063877009064283675813950588095504388659109_<93>

Number: n
N=14161253032867268200456854209951828454345061458914538796845639216326800017761514121711220530384697406593320683898998558239446506333949451311352948292037
  ( 152 digits)
SNFS difficulty: 168 digits.
Divisors found:

Mon Jul 07 06:38:48 2008  prp59 factor: 68134668790873592384459578322644469894232860523283147276193
Mon Jul 07 06:38:48 2008  prp93 factor: 207842105702935771469899396383940505601339931626765063877009064283675813950588095504388659109
Mon Jul 07 06:38:48 2008  elapsed time 01:31:51 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 52.57 hours.
Scaled time: 96.15 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_3_0_167_7
n: 14161253032867268200456854209951828454345061458914538796845639216326800017761514121711220530384697406593320683898998558239446506333949451311352948292037
skew: 0.30
deg: 5
c5: 3000
c0: 7
m: 1000000000000000000000000000000000
type: snfs
rlim: 5500000
alim: 5500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3200129)
Primes: RFBsize:380800, AFBsize:380817, largePrimes:7815275 encountered
Relations: rels:7399067, finalFF:765549
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 52.37 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.5,2.5,100000
total time: 52.57 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(19·10¹⁶⁹+17)/9 = 2(1)₁₆₈3_<170> = 202343 · C165

C165 = P41 · P45 · P79

P41 = 11854813632301944696197779784107475828959_<41>

P45 = 989586227294571474744567542974907856207448937_<45>

P79 = 8893537356585734852905220128099726473408062960442837007302516244982560116409577_<79>

Number: n
N=104333291050894328497210731832142011886307463619255971845386848623926259426375565802182981922335396386883218649081565021330666794063106265653425673787139219597965391
  ( 165 digits)
SNFS difficulty: 171 digits.
Divisors found:

Mon Jul 07 08:20:12 2008  prp41 factor: 11854813632301944696197779784107475828959
Mon Jul 07 08:20:12 2008  prp45 factor: 989586227294571474744567542974907856207448937
Mon Jul 07 08:20:12 2008  prp79 factor: 8893537356585734852905220128099726473408062960442837007302516244982560116409577
Mon Jul 07 08:20:12 2008  elapsed time 03:35:37 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 131.75 hours.
Scaled time: 190.77 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_2_1_168_3
n: 104333291050894328497210731832142011886307463619255971845386848623926259426375565802182981922335396386883218649081565021330666794063106265653425673787139219597965391
skew: 1.55
deg: 5
c5: 19
c0: 170
m: 10000000000000000000000000000000000
type: snfs
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5900189)
Primes: RFBsize:425648, AFBsize:427217, largePrimes:8696525 encountered
Relations: rels:8265355, finalFF:868827
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 131.37 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,48,48,2.5,2.5,100000
total time: 131.75 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jul 6, 2008 (3rd)

By matsui / GGNFS

7·10¹⁷⁵-9 = 6(9)₁₇₄1_<176> = 1301 · 700849 · C167

C167 = P58 · P110

P58 = 2998263129687771495713319147093796698599357538666071288999_<58>

P110 = 25605103830539641054955333281714615256570243024259263526043334000070733816061239428491153704128112278858660541_<110>

N=76770838746934130507392324931250151067188852114401986823165103555542800872777834759409606762117612554266824567026809163243163420541346739870235062843495421078448688459
  ( 167 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=2998263129687771495713319147093796698599357538666071288999 (pp58)
 r2=25605103830539641054955333281714615256570243024259263526043334000070733816061239428491153704128112278858660541 (pp110)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 120.77 hours.
Scaled time: 343.95 units (timescale=2.848).
Factorization parameters were as follows:
n: 76770838746934130507392324931250151067188852114401986823165103555542800872777834759409606762117612554266824567026809163243163420541346739870235062843495421078448688459
m: 100000000000000000000000000000000000
c5: 7
c0: -9
skew: 1.05
type: snfs

Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 12000001)
Primes: RFBsize:501962, AFBsize:502356, largePrimes:6549781 encountered
Relations: rels:7030593, finalFF:1152542
Max relations in full relation-set: 28
Initial matrix: 1004384 x 1152542 with sparse part having weight 76779199.
Pruned matrix : 878852 x 883937 with weight 58230885.
Total sieving time: 112.93 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 7.52 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 120.77 hours.

Jul 6, 2008 (2nd)

By Wataru Sakai / GGNFS

(8·10¹⁷⁵-71)/9 = (8)₁₇₄1_<175> = 31 · C174

C174 = P76 · P98

P76 = 5771423368902638327030970168234828127947353990816013247148660980653867079991_<76>

P98 = 49682432378721834064763150900527183566952281275682356497289727057025185041987238713931398215237961_<98>

Number: 88881_175
N=286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351
  ( 174 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=5771423368902638327030970168234828127947353990816013247148660980653867079991 (pp76)
 r2=49682432378721834064763150900527183566952281275682356497289727057025185041987238713931398215237961 (pp98)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 201.98 hours.
Scaled time: 406.99 units (timescale=2.015).
Factorization parameters were as follows:
n: 286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351
m: 100000000000000000000000000000000000
c5: 8
c0: -71
skew: 1.55
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 10200001)
Primes: RFBsize:501962, AFBsize:501892, largePrimes:6609281 encountered
Relations: rels:7255516, finalFF:1306535
Max relations in full relation-set: 32
Initial matrix: 1003919 x 1306535 with sparse part having weight 79027919.
Pruned matrix : 736827 x 741910 with weight 57352113.
Total sieving time: 197.68 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 4.02 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 201.98 hours.
 --------- CPU info (if available) ----------

Jul 6, 2008

By Robert Backstrom / GGNFS, Msieve

(14·10¹⁶⁸-41)/9 = 1(5)₁₆₇1_<169> = 3³ · 37656643141339_<14> · C154

C154 = P38 · P116

P38 = 16981226766391967119183913630606464339_<38>

P116 = 90097159217599722569381430542429490640646635539748578844942039627166323665820109863974364446625831381931678300595853_<116>

Number: n
N=1529960291681783151114531193400230721051917068342751517577310648254554333940389934727118286669463974028994922153019732058807777461380973311907897295786167
  ( 154 digits)
SNFS difficulty: 169 digits.
Divisors found:

Sun Jul 06 09:20:10 2008  prp38 factor: 16981226766391967119183913630606464339
Sun Jul 06 09:20:10 2008  prp116 factor: 90097159217599722569381430542429490640646635539748578844942039627166323665820109863974364446625831381931678300595853
Sun Jul 06 09:20:10 2008  elapsed time 02:40:33 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 81.62 hours.
Scaled time: 142.92 units (timescale=1.751).
Factorization parameters were as follows:
name: KA_1_5_167_1
n: 1529960291681783151114531193400230721051917068342751517577310648254554333940389934727118286669463974028994922153019732058807777461380973311907897295786167
type: snfs
skew: 0.62
deg: 5
c5: 875
c0: -82
m: 2000000000000000000000000000000000
rlim: 5800000
alim: 5800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3800113)
Primes: RFBsize:399993, AFBsize:400415, largePrimes:8020626 encountered
Relations: rels:7627568, finalFF:810616
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 81.31 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,48,48,2.6,2.6,100000
total time: 81.62 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jul 5, 2008 (4th)

By suberi / GMP-ECM

2·10¹⁷⁵+3 = 2(0)₁₇₄3_<176> = 1607 · 9041761 · 65731411 · 1081691158291_<13> · C146

C146 = P41 · P105

P41 = 76852616085817677774513791387885482895603_<41>

P105 = 251898861882089203262483987189502786622824705946228241740108420753071099837412827838656218659332309040463_<105>

2·10¹⁷⁶+3 = 2(0)₁₇₅3_<177> = 7 · 1307 · 17785019238356023897_<20> · C154

C154 = P37 · P117

P37 = 3214888775730183633684484492940316319_<37>

P117 = 382327974808924344375250235945475131233497457127498460037175594820337444676213458154174274593752449576287105681456329_<117>

Jul 5, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(67·10¹⁶⁷+23)/9 = 7(4)₁₆₆7_<168> = 3 · 11 · 590725541875506926873_<21> · C146

C146 = P45 · P101

P45 = 757066989154644615491448690405189133528186327_<45>

P101 = 50442696473007939117602260588880692523791409579601037039522012224179074179617065626216315357828500929_<101>

Number: n
N=38188500343661731641278628082568518596787475525445421725857796402998819571882558221901996369633874551499717256707212411143098580436331158604597783
  ( 146 digits)
SNFS difficulty: 168 digits.
Divisors found:

Sat Jul  5 16:35:21 2008  prp45 factor: 757066989154644615491448690405189133528186327
Sat Jul  5 16:35:21 2008  prp101 factor: 50442696473007939117602260588880692523791409579601037039522012224179074179617065626216315357828500929
Sat Jul  5 16:35:21 2008  elapsed time 01:28:07 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 72.21 hours.
Scaled time: 60.44 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_7_4_166_7
n: 38188500343661731641278628082568518596787475525445421725857796402998819571882558221901996369633874551499717256707212411143098580436331158604597783
type: snfs
deg: 5
c5: 6700
c0: 23
skew: 0.32
m: 1000000000000000000000000000000000
rlim: 5800000
alim: 5800000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3700187)
Primes: RFBsize:399993, AFBsize:399534, largePrimes:5669956 encountered
Relations: rels:5827169, finalFF:820255
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 72.01 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5800000,5800000,27,27,48,48,2.5,2.5,100000
total time: 72.21 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

Jul 5, 2008 (2nd)

By Sinkiti Sibata / GGNFS, Msieve

(22·10¹⁶⁴-13)/9 = 2(4)₁₆₃3_<165> = 3⁴ · 29 · 3416647763_<10> · 21835992391633997_<17> · C136

C136 = P54 · P82

P54 = 188977149108201979911706385119937160520580933260307287_<54>

P82 = 7380991743316560115806233653476384595263723304504052365842469875363867165673435351_<82>

Number: 24443_164
N=1394838777243141255510981001163768886819125792240408935920463319142421907920649440350855154985034708459237944672082108063593967188702737
  ( 136 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=188977149108201979911706385119937160520580933260307287 (pp54)
 r2=7380991743316560115806233653476384595263723304504052365842469875363867165673435351 (pp82)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 83.57 hours.
Scaled time: 84.33 units (timescale=1.009).
Factorization parameters were as follows:
name: 24443_164
n: 1394838777243141255510981001163768886819125792240408935920463319142421907920649440350855154985034708459237944672082108063593967188702737
m: 1000000000000000000000000000000000
c5: 11
c0: -65
skew: 1.43
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 5400001)
Primes: RFBsize:348513, AFBsize:348832, largePrimes:5983032 encountered
Relations: rels:6212091, finalFF:859947
Max relations in full relation-set: 28
Initial matrix: 697410 x 859947 with sparse part having weight 56628198.
Pruned matrix : 568712 x 572263 with weight 39516683.
Total sieving time: 80.89 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 2.48 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 83.57 hours.
 --------- CPU info (if available) ----------

(22·10¹⁶¹-13)/9 = 2(4)₁₆₀3_<162> = 3 · 1777 · 33815254328427941_<17> · 4435250828334077701_<19> · C123

C123 = P51 · P72

P51 = 918751243450106267060747603778791899353350478837103_<51>

P72 = 332768880114005275926756609421497514018998126560607437380875803735204911_<72>

Number: 24443_161
N=305731822386241687388365973109241630242229346029252053757510744441829217228259242418405758238321559754128107663948694612833
  ( 123 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=918751243450106267060747603778791899353350478837103 (pp51)
 r2=332768880114005275926756609421497514018998126560607437380875803735204911 (pp72)
Version: GGNFS-0.77.1-20060513-k8
Total time: 73.49 hours.
Scaled time: 146.68 units (timescale=1.996).
Factorization parameters were as follows:
name: 24443_161
n: 305731822386241687388365973109241630242229346029252053757510744441829217228259242418405758238321559754128107663948694612833
m: 100000000000000000000000000000000
c5: 220
c0: -13
skew: 0.57
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4550001)
Primes: RFBsize:315948, AFBsize:316452, largePrimes:5901718 encountered
Relations: rels:6110503, finalFF:826721
Max relations in full relation-set: 28
Initial matrix: 632467 x 826721 with sparse part having weight 51666016.
Pruned matrix : 479579 x 482805 with weight 35391694.
Total sieving time: 70.08 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 2.99 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 73.49 hours.
 --------- CPU info (if available) ----------

(22·10¹⁵⁵-13)/9 = 2(4)₁₅₄3_<156> = 3² · 23 · 143981 · 218747941 · 249745250462299_<15> · 292725366458429872841_<21> · C105

C105 = P45 · P61

P45 = 482708719167218258004205150027333793774609359_<45>

P61 = 1062473059782581072690917238909162188127886673467946816631449_<61>

Wed Jul  2 12:30:04 2008  Msieve v. 1.36
Wed Jul  2 12:30:04 2008  random seeds: df1e72e0 8972023e
Wed Jul  2 12:30:04 2008  factoring 512865009837325022345519467664391330612010588131901538421543902669711759984610894342811574933034249131191 (105 digits)
Wed Jul  2 12:30:05 2008  no P-1/P+1/ECM available, skipping
Wed Jul  2 12:30:05 2008  commencing quadratic sieve (105-digit input)
Wed Jul  2 12:30:06 2008  using multiplier of 7
Wed Jul  2 12:30:06 2008  using 64kb Pentium 4 sieve core
Wed Jul  2 12:30:06 2008  sieve interval: 18 blocks of size 65536
Wed Jul  2 12:30:06 2008  processing polynomials in batches of 6
Wed Jul  2 12:30:06 2008  using a sieve bound of 3948821 (140000 primes)
Wed Jul  2 12:30:06 2008  using large prime bound of 592323150 (29 bits)
Wed Jul  2 12:30:06 2008  using double large prime bound of 6174554804868150 (44-53 bits)
Wed Jul  2 12:30:06 2008  using trial factoring cutoff of 53 bits
Wed Jul  2 12:30:06 2008  polynomial 'A' values have 14 factors
Sat Jul  5 13:38:29 2008  140161 relations (33632 full + 106529 combined from 2089225 partial), need 140096
Sat Jul  5 13:38:38 2008  begin with 2122857 relations
Sat Jul  5 13:38:40 2008  reduce to 368943 relations in 10 passes
Sat Jul  5 13:38:40 2008  attempting to read 368943 relations
Sat Jul  5 13:38:55 2008  recovered 368943 relations
Sat Jul  5 13:38:55 2008  recovered 361714 polynomials
Sat Jul  5 13:38:55 2008  attempting to build 140161 cycles
Sat Jul  5 13:38:56 2008  found 140160 cycles in 5 passes
Sat Jul  5 13:38:56 2008  distribution of cycle lengths:
Sat Jul  5 13:38:56 2008     length 1 : 33632
Sat Jul  5 13:38:56 2008     length 2 : 23929
Sat Jul  5 13:38:56 2008     length 3 : 23141
Sat Jul  5 13:38:56 2008     length 4 : 19244
Sat Jul  5 13:38:56 2008     length 5 : 14585
Sat Jul  5 13:38:56 2008     length 6 : 10068
Sat Jul  5 13:38:56 2008     length 7 : 6438
Sat Jul  5 13:38:56 2008     length 9+: 9123
Sat Jul  5 13:38:56 2008  largest cycle: 19 relations
Sat Jul  5 13:38:56 2008  matrix is 140000 x 140160 (39.1 MB) with weight 9682174 (69.08/col)
Sat Jul  5 13:38:56 2008  sparse part has weight 9682174 (69.08/col)
Sat Jul  5 13:39:00 2008  filtering completed in 3 passes
Sat Jul  5 13:39:00 2008  matrix is 134452 x 134516 (37.7 MB) with weight 9352275 (69.53/col)
Sat Jul  5 13:39:00 2008  sparse part has weight 9352275 (69.53/col)
Sat Jul  5 13:39:01 2008  saving the first 48 matrix rows for later
Sat Jul  5 13:39:01 2008  matrix is 134404 x 134516 (22.0 MB) with weight 7251326 (53.91/col)
Sat Jul  5 13:39:01 2008  sparse part has weight 4967697 (36.93/col)
Sat Jul  5 13:39:01 2008  matrix includes 64 packed rows
Sat Jul  5 13:39:01 2008  using block size 21845 for processor cache size 512 kB
Sat Jul  5 13:39:03 2008  commencing Lanczos iteration
Sat Jul  5 13:39:03 2008  memory use: 22.2 MB
Sat Jul  5 13:42:22 2008  lanczos halted after 2127 iterations (dim = 134403)
Sat Jul  5 13:42:23 2008  recovered 17 nontrivial dependencies
Sat Jul  5 13:42:25 2008  prp45 factor: 482708719167218258004205150027333793774609359
Sat Jul  5 13:42:25 2008  prp61 factor: 1062473059782581072690917238909162188127886673467946816631449
Sat Jul  5 13:42:25 2008  elapsed time 73:12:21

Jul 5, 2008

By Robert Backstrom / GGNFS, Msieve

(4·10¹⁶⁸+41)/9 = (4)₁₆₇9_<168> = 4597 · 130447182347_<12> · C153

C153 = P72 · P82

P72 = 663251634063362739752196199073426751298383313952477786487187756107043583_<72>

P82 = 1117454752021047188523688656180078402295445713630605513644151002858054731527619817_<82>

Number: n
N=741153690269829344816607101538581813580363824537014619808453740497332331010205538207186533049730298407091798388514224200756023662978131538180140673484311
  ( 153 digits)
SNFS difficulty: 168 digits.
Divisors found:

Sat Jul 05 01:16:13 2008  prp72 factor: 663251634063362739752196199073426751298383313952477786487187756107043583
Sat Jul 05 01:16:13 2008  prp82 factor: 1117454752021047188523688656180078402295445713630605513644151002858054731527619817
Sat Jul 05 01:16:13 2008  elapsed time 01:38:25 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 59.64 hours.
Scaled time: 109.07 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_4_167_9
n: 741153690269829344816607101538581813580363824537014619808453740497332331010205538207186533049730298407091798388514224200756023662978131538180140673484311
skew: 0.80
deg: 5
c5: 125
c0: 41
m: 2000000000000000000000000000000000
type: snfs
rlim: 5500000
alim: 5500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3600221)
Primes: RFBsize:380800, AFBsize:381398, largePrimes:8025714 encountered
Relations: rels:7629445, finalFF:796763
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 59.44 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.5,2.5,100000
total time: 59.64 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jul 4, 2008 (8th)

By Wataru Sakai / GGNFS

(10¹⁷⁴+17)/9 = (1)₁₇₃3_<174> = 377876511031_<12> · C162

C162 = P64 · P98

P64 = 7316041903847007779820595674552294686019937425938604329901433463_<64>

P98 = 40191240367144016302815181110516174673310246906156873550846174801629866981184855893817082957652921_<98>

Number: 11113_174
N=294040798693613020978721557691027645861505411458095217132747791724995390273507246425889611518903150754520207364042759151086227684121488178193073709170363929095423
  ( 162 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=7316041903847007779820595674552294686019937425938604329901433463 (pp64)
 r2=40191240367144016302815181110516174673310246906156873550846174801629866981184855893817082957652921 (pp98)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 194.34 hours.
Scaled time: 352.33 units (timescale=1.813).
Factorization parameters were as follows:
n: 294040798693613020978721557691027645861505411458095217132747791724995390273507246425889611518903150754520207364042759151086227684121488178193073709170363929095423
m: 100000000000000000000000000000000000
c5: 1
c0: 170
skew: 2.79
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 10100001)
Primes: RFBsize:501962, AFBsize:502431, largePrimes:6427815 encountered
Relations: rels:6885252, finalFF:1141474
Max relations in full relation-set: 32
Initial matrix: 1004457 x 1141474 with sparse part having weight 68636874.
Pruned matrix : 885866 x 890952 with weight 51307737.
Total sieving time: 187.27 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 6.75 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 194.34 hours.
 --------- CPU info (if available) ----------

(10¹⁶⁹+71)/9 = (1)₁₆₈9_<169> = 3 · 59 · 97 · 2029033 · 6513786343_<10> · C148

C148 = P41 · P107

P41 = 58256274272138916126619839433275911718637_<41>

P107 = 84051828163356372247625226617883687184833701501969291495680461061656160491744043801648027577705796315595717_<107>

Number: 11119_169
N=4896546354559178996140354102442220159529990569466487676403385572974008116436611422680942354556609657246123689866555093038830658609501137723946277729
  ( 148 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=58256274272138916126619839433275911718637 (pp41)
 r2=84051828163356372247625226617883687184833701501969291495680461061656160491744043801648027577705796315595717 (pp107)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 168.68 hours.
Scaled time: 339.73 units (timescale=2.014).
Factorization parameters were as follows:
n: 4896546354559178996140354102442220159529990569466487676403385572974008116436611422680942354556609657246123689866555093038830658609501137723946277729
m: 10000000000000000000000000000000000
c5: 1
c0: 710
skew: 3.72
type: snfsFactor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 8700001)
Primes: RFBsize:412849, AFBsize:413722, largePrimes:6522753 encountered
Relations: rels:7031474, finalFF:1142419
Max relations in full relation-set: 32
Initial matrix: 826635 x 1142419 with sparse part having weight 87304407.
Pruned matrix : 574125 x 578322 with weight 74347583.
Total sieving time: 165.14 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 3.27 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 168.68 hours.
 --------- CPU info (if available) ----------

Jul 4, 2008 (7th)

By Serge Batalov / GMP-ECM

(64·10²⁴⁹+53)/9 = 7(1)₂₄₈7_<250> = 11 · 8171 · 944916181322280177394519_<24> · C221

C221 = P40 · C182

P40 = 1115409808826481487721767396696401745727_<40>

C182 = [75065749185647424301639973766450991088912379509114416801234054773803073644854905012027429069765331464723207178998756891472876524389458263589608376114581569780896727097603078911963789_<182>]

Jul 4, 2008 (6th)

By suberi / GMP-ECM

5·10¹⁸⁸+3 = 5(0)₁₈₇3_<189> = 17 · 353 · 694042304507_<12> · C174

C174 = P45 · P129

P45 = 534714061843976765275098162965857648543309727_<45>

P129 = 224511622860875644540507133498734394246496745568262356156954776102962010083439706705021118582845752441312785525001232938868447927_<129>

Jul 4, 2008 (5th)

By Serge Batalov / Msieve

6·10²⁰⁰+1 = 6(0)₁₉₉1_<201> = 29 · C200

C200 = P84 · P116

P84 = 367530286683762818311653969900003494345257271270268514080948164981978980653079960969_<84>

P116 = 56293742099725151227484967667076511849333661046901547637197489587498221199711228253147257513850471263698402737741901_<116>

Number: 60001_200
N=20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862069
  ( 200 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=367530286683762818311653969900003494345257271270268514080948164981978980653079960969 (p84)
 r2=56293742099725151227484967667076511849333661046901547637197489587498221199711228253147257513850471263698402737741901 (p116)

Version: Msieve v. 1.36
Total time: 13 CPU-days. (1 CPU)
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
n: 20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862069
Y1: 10000000000000000000000000000000000000000
Y0: -1
c0: 6
c5: 1
skew: 1
type: snfs
lpbr: 29
lpba: 29
mfbr: 57
mfba: 57
rlambda: 2.5
alambda: 2.5
rlim: 15000000
alim: 15000000
Factor base limits: 15000000/15000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 57/57
Sieved rational special-q in [7500000, 13600001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3079496 x 3079744
Total sieving time: 12.5 days.
Matrix solve time: 53:07:51 hours.
Time per square root: 00:40:47 hours. (1st dependency!)
Prototype def-par.txt line would be:
snfs,200,5,0,0,0,0,0,0,0,0,15000000,15000000,29,29,57,57,2.5,2.5,100000

total time: 13 CPU-days.

 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

 
Fri Jun 20 21:33:29 2008  Msieve v. 1.36
Fri Jun 20 21:33:29 2008  random seeds: 009edf2b 6d52626c
Fri Jun 20 21:33:29 2008  factoring 20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862069 (200 digits)
Fri Jun 20 21:33:31 2008  no P-1/P+1/ECM available, skipping
Fri Jun 20 21:33:31 2008  commencing number field sieve (200-digit input)
Fri Jun 20 21:33:31 2008  R0: -1
Fri Jun 20 21:33:31 2008  R1:  10000000000000000000000000000000000000000
Fri Jun 20 21:33:31 2008  A0:  6
Fri Jun 20 21:33:31 2008  A1:  0
Fri Jun 20 21:33:31 2008  A2:  0
Fri Jun 20 21:33:31 2008  A3:  0
Fri Jun 20 21:33:31 2008  A4:  0
Fri Jun 20 21:33:31 2008  A5:  1
Fri Jun 20 21:33:31 2008  size score = 1.681569e-13, Murphy alpha = 0.815479, combined = 1.281333e-13
Fri Jun 20 21:33:31 2008  generating factor base
Fri Jun 20 21:33:38 2008  factor base complete:
Fri Jun 20 21:33:38 2008  970704 rational roots (max prime = 14999981)
Fri Jun 20 21:33:38 2008  969545 algebraic roots (max prime = 14999977)
...
...sieving...
...
Tue Jul  1 15:27:06 2008  filtering wants 125832 more relations
Tue Jul  1 15:27:06 2008  elapsed time 00:33:10
-> makeJobFile(): Adjusted to q0=13599901, q1=13600000.
->               client 1 q0: 13599901

Tue Jul  1 16:23:17 2008  
Tue Jul  1 16:23:17 2008  
Tue Jul  1 16:23:17 2008  Msieve v. 1.36
Tue Jul  1 16:23:17 2008  random seeds: 73293338 5ae60b30
Tue Jul  1 16:23:17 2008  factoring 20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862069 (200 digits)
Tue Jul  1 16:23:19 2008  no P-1/P+1/ECM available, skipping
Tue Jul  1 16:23:19 2008  commencing number field sieve (200-digit input)
Tue Jul  1 16:23:19 2008  R0: -1
Tue Jul  1 16:23:19 2008  R1:  10000000000000000000000000000000000000000
Tue Jul  1 16:23:19 2008  A0:  6
Tue Jul  1 16:23:19 2008  A1:  0
Tue Jul  1 16:23:19 2008  A2:  0
Tue Jul  1 16:23:19 2008  A3:  0
Tue Jul  1 16:23:19 2008  A4:  0
Tue Jul  1 16:23:19 2008  A5:  1
Tue Jul  1 16:23:19 2008  size score = 1.681569e-13, Murphy alpha = 0.815479, combined = 1.281333e-13
Tue Jul  1 16:23:27 2008  restarting with 38716423 relations
Tue Jul  1 16:23:27 2008  
Tue Jul  1 16:23:27 2008  commencing relation filtering
Tue Jul  1 16:23:27 2008  commencing duplicate removal, pass 1
Tue Jul  1 16:23:28 2008  error -9 reading relation 1
Tue Jul  1 16:24:34 2008  error -9 reading relation 8560327
Tue Jul  1 16:28:26 2008  found 4666296 hash collisions in 38716421 relations
Tue Jul  1 16:28:26 2008  commencing duplicate removal, pass 2
Tue Jul  1 16:28:52 2008  found 2885930 duplicates and 35830491 unique relations
Tue Jul  1 16:28:52 2008  memory use: 153.2 MB
Tue Jul  1 16:28:58 2008  ignoring smallest 955332 rational and 954318 algebraic ideals
Tue Jul  1 16:28:58 2008  filtering rational ideals above 14745600
Tue Jul  1 16:28:58 2008  filtering algebraic ideals above 14745600
Tue Jul  1 16:28:58 2008  need 2864475 more relations than ideals
Tue Jul  1 16:28:58 2008  commencing singleton removal, pass 1
Tue Jul  1 16:33:56 2008  relations with 0 large ideals: 349980
Tue Jul  1 16:33:56 2008  relations with 1 large ideals: 2681713
Tue Jul  1 16:33:56 2008  relations with 2 large ideals: 9046027
Tue Jul  1 16:33:56 2008  relations with 3 large ideals: 14378910
Tue Jul  1 16:33:56 2008  relations with 4 large ideals: 9313993
Tue Jul  1 16:33:56 2008  relations with 5 large ideals: 59754
Tue Jul  1 16:33:56 2008  relations with 6 large ideals: 114
Tue Jul  1 16:33:56 2008  relations with 7+ large ideals: 0
Tue Jul  1 16:33:56 2008  35830491 relations and about 33000174 large ideals
Tue Jul  1 16:33:56 2008  commencing singleton removal, pass 2
Tue Jul  1 16:38:54 2008  found 12137340 singletons
Tue Jul  1 16:38:54 2008  current dataset: 23693151 relations and about 18987468 large ideals
Tue Jul  1 16:38:54 2008  commencing singleton removal, pass 3
Tue Jul  1 16:42:10 2008  found 2831933 singletons
Tue Jul  1 16:42:10 2008  current dataset: 20861218 relations and about 16012294 large ideals
Tue Jul  1 16:42:10 2008  commencing singleton removal, pass 4
Tue Jul  1 16:45:07 2008  found 760992 singletons
Tue Jul  1 16:45:07 2008  current dataset: 20100226 relations and about 15239442 large ideals
Tue Jul  1 16:45:07 2008  commencing singleton removal, pass 5
Tue Jul  1 16:47:59 2008  found 209746 singletons
Tue Jul  1 16:47:59 2008  current dataset: 19890480 relations and about 15028746 large ideals
Tue Jul  1 16:47:59 2008  commencing singleton removal, final pass
Tue Jul  1 16:51:43 2008  memory use: 352.2 MB
Tue Jul  1 16:51:44 2008  commencing in-memory singleton removal
Tue Jul  1 16:51:47 2008  begin with 19890480 relations and 18306064 unique ideals
Tue Jul  1 16:52:34 2008  reduce to 12514527 relations and 10463483 ideals in 21 passes
Tue Jul  1 16:52:34 2008  max relations containing the same ideal: 21
Tue Jul  1 16:52:37 2008  filtering rational ideals above 720000
Tue Jul  1 16:52:37 2008  filtering algebraic ideals above 720000
Tue Jul  1 16:52:37 2008  need 116191 more relations than ideals
Tue Jul  1 16:52:37 2008  commencing singleton removal, final pass
Tue Jul  1 16:55:59 2008  keeping 11195651 ideals with weight <= 20, new excess is 1177388
Tue Jul  1 16:56:11 2008  memory use: 355.6 MB
Tue Jul  1 16:56:11 2008  commencing in-memory singleton removal
Tue Jul  1 16:56:13 2008  begin with 12514528 relations and 11195651 unique ideals
Tue Jul  1 16:56:34 2008  reduce to 12511886 relations and 11193004 ideals in 9 passes
Tue Jul  1 16:56:34 2008  max relations containing the same ideal: 20
Tue Jul  1 16:56:47 2008  removing 287933 relations and 276056 ideals in 11878 cliques
Tue Jul  1 16:56:48 2008  commencing in-memory singleton removal
Tue Jul  1 16:56:50 2008  begin with 12223953 relations and 11193004 unique ideals
Tue Jul  1 16:57:13 2008  reduce to 12217820 relations and 10910803 ideals in 9 passes
Tue Jul  1 16:57:13 2008  max relations containing the same ideal: 20
Tue Jul  1 16:57:25 2008  removing 208850 relations and 196972 ideals in 11878 cliques
Tue Jul  1 16:57:25 2008  commencing in-memory singleton removal
Tue Jul  1 16:57:29 2008  begin with 12008970 relations and 10910803 unique ideals
Tue Jul  1 16:57:59 2008  reduce to 12005805 relations and 10710657 ideals in 11 passes
Tue Jul  1 16:57:59 2008  max relations containing the same ideal: 20
Tue Jul  1 16:58:02 2008  relations with 0 large ideals: 113697
Tue Jul  1 16:58:02 2008  relations with 1 large ideals: 770261
Tue Jul  1 16:58:02 2008  relations with 2 large ideals: 2472911
Tue Jul  1 16:58:02 2008  relations with 3 large ideals: 4030039
Tue Jul  1 16:58:02 2008  relations with 4 large ideals: 3306042
Tue Jul  1 16:58:02 2008  relations with 5 large ideals: 1129408
Tue Jul  1 16:58:02 2008  relations with 6 large ideals: 171106
Tue Jul  1 16:58:02 2008  relations with 7+ large ideals: 12341
Tue Jul  1 16:58:02 2008  commencing 2-way merge
Tue Jul  1 16:58:15 2008  reduce to 6550256 relation sets and 5255140 unique ideals
Tue Jul  1 16:58:15 2008  ignored 33 oversize relation sets
Tue Jul  1 16:58:15 2008  commencing full merge
Tue Jul  1 16:59:48 2008  memory use: 454.1 MB
Tue Jul  1 16:59:49 2008  found 3213687 cycles, need 3125340
Tue Jul  1 16:59:50 2008  weight of 3125340 cycles is about 219015996 (70.08/cycle)
Tue Jul  1 16:59:50 2008  distribution of cycle lengths:
Tue Jul  1 16:59:50 2008  1 relations: 425540
Tue Jul  1 16:59:50 2008  2 relations: 415093
Tue Jul  1 16:59:50 2008  3 relations: 401689
Tue Jul  1 16:59:50 2008  4 relations: 351498
Tue Jul  1 16:59:50 2008  5 relations: 288577
Tue Jul  1 16:59:50 2008  6 relations: 247431
Tue Jul  1 16:59:50 2008  7 relations: 201519
Tue Jul  1 16:59:50 2008  8 relations: 161059
Tue Jul  1 16:59:50 2008  9 relations: 129940
Tue Jul  1 16:59:50 2008  10+ relations: 502994
Tue Jul  1 16:59:50 2008  heaviest cycle: 22 relations
Tue Jul  1 16:59:51 2008  commencing cycle optimization
Tue Jul  1 17:00:03 2008  start with 17192621 relations
Tue Jul  1 17:00:44 2008  pruned 170374 relations
Tue Jul  1 17:00:44 2008  memory use: 619.4 MB
Tue Jul  1 17:00:45 2008  distribution of cycle lengths:
Tue Jul  1 17:00:45 2008  1 relations: 425540
Tue Jul  1 17:00:45 2008  2 relations: 418823
Tue Jul  1 17:00:45 2008  3 relations: 408212
Tue Jul  1 17:00:45 2008  4 relations: 354004
Tue Jul  1 17:00:45 2008  5 relations: 291359
Tue Jul  1 17:00:45 2008  6 relations: 247776
Tue Jul  1 17:00:45 2008  7 relations: 201337
Tue Jul  1 17:00:45 2008  8 relations: 160104
Tue Jul  1 17:00:45 2008  9 relations: 128766
Tue Jul  1 17:00:45 2008  10+ relations: 489419
Tue Jul  1 17:00:45 2008  heaviest cycle: 22 relations
Tue Jul  1 17:00:55 2008  elapsed time 00:37:38
Tue Jul  1 17:00:57 2008  
Tue Jul  1 17:00:57 2008  
Tue Jul  1 17:00:57 2008  Msieve v. 1.36
Tue Jul  1 17:00:57 2008  random seeds: 325f3526 08946e45
Tue Jul  1 17:00:57 2008  factoring 20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862069 (200 digits)
Tue Jul  1 17:01:03 2008  no P-1/P+1/ECM available, skipping
Tue Jul  1 17:01:03 2008  commencing number field sieve (200-digit input)
Tue Jul  1 17:01:03 2008  R0: -1
Tue Jul  1 17:01:03 2008  R1:  10000000000000000000000000000000000000000
Tue Jul  1 17:01:03 2008  A0:  6
Tue Jul  1 17:01:03 2008  A1:  0
Tue Jul  1 17:01:03 2008  A2:  0
Tue Jul  1 17:01:03 2008  A3:  0
Tue Jul  1 17:01:03 2008  A4:  0
Tue Jul  1 17:01:03 2008  A5:  1
Tue Jul  1 17:01:03 2008  size score = 1.681569e-13, Murphy alpha = 0.815479, combined = 1.281333e-13
Tue Jul  1 17:01:03 2008  
Tue Jul  1 17:01:03 2008  commencing linear algebra
Tue Jul  1 17:01:08 2008  read 3125340 cycles
Tue Jul  1 17:01:28 2008  cycles contain 10751011 unique relations
Tue Jul  1 17:02:59 2008  read 10751011 relations
Tue Jul  1 17:03:27 2008  using 32 quadratic characters above 536868974
Tue Jul  1 17:05:31 2008  building initial matrix
Tue Jul  1 17:08:07 2008  memory use: 1308.9 MB
Tue Jul  1 17:08:10 2008  read 3125340 cycles
Tue Jul  1 17:08:13 2008  matrix is 3124507 x 3125340 (946.8 MB) with weight 299306570 (95.77/col)
Tue Jul  1 17:08:13 2008  sparse part has weight 213814726 (68.41/col)
Tue Jul  1 17:10:18 2008  filtering completed in 3 passes
Tue Jul  1 17:10:19 2008  matrix is 3079544 x 3079744 (939.5 MB) with weight 296593355 (96.30/col)
Tue Jul  1 17:10:19 2008  sparse part has weight 212416998 (68.97/col)
Tue Jul  1 17:10:58 2008  read 3079744 cycles
Tue Jul  1 17:11:01 2008  matrix is 3079544 x 3079744 (939.5 MB) with weight 296593355 (96.30/col)
Tue Jul  1 17:11:01 2008  sparse part has weight 212416998 (68.97/col)
Tue Jul  1 17:11:01 2008  saving the first 48 matrix rows for later
Tue Jul  1 17:11:03 2008  matrix is 3079496 x 3079744 (901.2 MB) with weight 229186974 (74.42/col)
Tue Jul  1 17:11:03 2008  sparse part has weight 205451830 (66.71/col)
Tue Jul  1 17:11:03 2008  matrix includes 64 packed rows
Tue Jul  1 17:11:03 2008  using block size 43690 for processor cache size 1024 kB
Tue Jul  1 17:11:22 2008  commencing Lanczos iteration
Tue Jul  1 17:11:22 2008  memory use: 866.0 MB
Thu Jul  3 22:08:36 2008  lanczos halted after 48705 iterations (dim = 3079494)
Thu Jul  3 22:08:48 2008  recovered 46 nontrivial dependencies
Thu Jul  3 22:08:48 2008  elapsed time 53:07:51
Thu Jul  3 22:08:48 2008  
Thu Jul  3 22:08:48 2008  
Thu Jul  3 22:08:48 2008  Msieve v. 1.36
Thu Jul  3 22:08:48 2008  random seeds: 93ca7f7c 9d776727
Thu Jul  3 22:08:48 2008  factoring 20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862069 (200 digits)
Thu Jul  3 22:08:50 2008  no P-1/P+1/ECM available, skipping
Thu Jul  3 22:08:50 2008  commencing number field sieve (200-digit input)
Thu Jul  3 22:08:50 2008  R0: -1
Thu Jul  3 22:08:50 2008  R1:  10000000000000000000000000000000000000000
Thu Jul  3 22:08:50 2008  A0:  6
Thu Jul  3 22:08:50 2008  A1:  0
Thu Jul  3 22:08:50 2008  A2:  0
Thu Jul  3 22:08:50 2008  A3:  0
Thu Jul  3 22:08:50 2008  A4:  0
Thu Jul  3 22:08:50 2008  A5:  1
Thu Jul  3 22:08:50 2008  size score = 1.681569e-13, Murphy alpha = 0.815479, combined = 1.281333e-13
Thu Jul  3 22:08:50 2008  
Thu Jul  3 22:08:50 2008  commencing square root phase
Thu Jul  3 22:08:50 2008  reading relations for dependency 1
Thu Jul  3 22:08:50 2008  read 1538490 cycles
Thu Jul  3 22:08:57 2008  cycles contain 6386580 unique relations
Thu Jul  3 22:09:54 2008  read 6386580 relations
Thu Jul  3 22:10:51 2008  multiplying 8458902 relations
Thu Jul  3 22:25:40 2008  multiply complete, coefficients have about 201.64 million bits
Thu Jul  3 22:25:44 2008  initial square root is modulo 17227841
Thu Jul  3 22:49:35 2008  prp84 factor: 367530286683762818311653969900003494345257271270268514080948164981978980653079960969
Thu Jul  3 22:49:35 2008  prp116 factor: 56293742099725151227484967667076511849333661046901547637197489587498221199711228253147257513850471263698402737741901
Thu Jul  3 22:49:35 2008  elapsed time 00:40:47

total time: 13 CPU-days.

C200 is the second largest snfs-factored number in our tables so far and P84 is so big as our expectations. Congratulations!

Jul 4, 2008 (4th)

By Robert Backstrom / GMP-ECM

(4·10¹⁷³+41)/9 = (4)₁₇₂9_<173> = 17 · 151 · C170

C170 = P40 · P130

P40 = 3690261951417434928982708714910132460751_<40>

P130 = 4691745193852098076874265382218613551734230024345277073373087798519293567157971656250985794207394773191162000531186646913618048697_<130>

Jul 4, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(22·10¹⁸⁶-13)/9 = 2(4)₁₈₅3_<187> = 31 · 16879 · 1543033 · 5960683 · 189223412921_<12> · 13731509942096227_<17> · 46081468145707033413173827_<26> · C115

C115 = P56 · P59

P56 = 43959204954398191758967014257475577232360237024190677731_<56>

P59 = 96500868268959376515840611142404886048601428365351772525347_<59>

Number: 24443_186
N=4242101446512566279037752919245875197556434359228304425000793653490947024758992103027621559431224282849289305947657
  ( 115 digits)
Divisors found:
 r1=43959204954398191758967014257475577232360237024190677731 (pp56)
 r2=96500868268959376515840611142404886048601428365351772525347 (pp59)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 40.02 hours.
Scaled time: 40.34 units (timescale=1.008).
Factorization parameters were as follows:
name: 24443_186
n: 4242101446512566279037752919245875197556434359228304425000793653490947024758992103027621559431224282849289305947657
skew: 41072.16
# norm 1.73e+16
c5: 28980
c4: -5531699547
c3: 372309325381604
c2: 23901648869437194434
c1: -212452296877258001651416
c0: 402545251072873544415047961
# alpha -6.80
Y1: 1980335979017
Y0: -10791941343671477762770
# Murphy_E 5.63e-10
# M 2831575661041463818221452258434492024696583287593071787784957834298756538742697938919050064827202075377543747090696
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 3050001)
Primes: RFBsize:250150, AFBsize:250878, largePrimes:7937801 encountered
Relations: rels:8210451, finalFF:866897
Max relations in full relation-set: 28
Initial matrix: 501111 x 866897 with sparse part having weight 84364678.
Pruned matrix : 288555 x 291124 with weight 56212619.
Total sieving time: 38.67 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.94 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 40.02 hours.
 --------- CPU info (if available) ----------

Jul 4, 2008 (2nd)

By Robert Backstrom / GMP-ECM

(22·10¹⁶⁸-13)/9 = 2(4)₁₆₇3_<169> = 61 · 1181 · 2753 · C161

C161 = P36 · P125

P36 = 272806960740898694897744916795109789_<36>

P125 = 45179225343192939814830264722714360700948905264435948248866595060194010598980819143752130662346477005769664390040536535097919_<125>

Jul 4, 2008

By Serge Batalov / GMP-ECM, pol51, Msieve

(22·10¹⁶⁰-13)/9 = 2(4)₁₅₉3_<161> = 83 · 343823 · 855737224949_<12> · C142

C142 = P33 · P48 · P61

P33 = 735790587500551731348419488073351_<33>

P48 = 587239052741479910497804853780708830854156297691_<48>

P61 = 2316634778346193718074128370167758320496447356746829997837303_<61>

# memo: 
# 1. started as SNFS (complexity=160) + ECM in parallel 
#    ==> ECM found P33, reduced to C109
# 2. Restarted as GNFS-109 and finished in under 8 hours

Run 618 out of 950:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2528959712
Step 1 took 5168ms
Step 2 took 2516ms
********** Factor found in step 2: 735790587500551731348419488073351
Found probable prime factor of 33 digits: 735790587500551731348419488073351
Composite cofactor ... has 109 digits
________________________________

Number: 24443_160_1
N=1360418412783987074914444113841721330588031373907259564665334948457960743026634867009277756438778267452567373
  ( 109 digits)
Divisors found:
 r1=587239052741479910497804853780708830854156297691
 r2=2316634778346193718074128370167758320496447356746829997837303
Version: 
Total time: 7.00 hours.
Scaled time: 21.00 units (timescale=2.952).
Factorization parameters were as follows:
name: 24443_160_1
n: 1360418412783987074914444113841721330588031373907259564665334948457960743026634867009277756438778267452567373
skew: 41860.23
# norm 1.64e+15
c5: 3420
c4: 1690161444
c3: -41999216776651
c2: -2882404502481927453
c1: 13452908855870193561711
c0: -31177496575363663531230471
# alpha -6.60
Y1: 24432329119
Y0: -831625922016089307142
# Murphy_E 1.22e-09
# M 698164231928883033395764254761249812600819043440596205752521820506521365412989261638914584739305378444049168
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1600000, 2800001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 383287 x 383535
Total sieving time: 6.20 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.51 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,26,26,49,49,2.6,2.6,100000

total time: 7.00 hours.

 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

Jul 3, 2008 (4th)

By Sinkiti Sibata / GGNFS

(22·10¹⁵⁹-13)/9 = 2(4)₁₅₈3_<160> = 7³ · 241 · 174319009 · C147

C147 = P53 · P94

P53 = 35979740872329018517519746209133239737925977264625179_<53>

P94 = 4714832073781596621362448799071690079103424956069158006846652811186139395908205559836553336951_<94>

Number: 24443_159
N=169638436271207498618321778981267682748389403467968388237789976659448429627083605891836793599367968896683372273498374419202359611720013660705689229
  ( 147 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=35979740872329018517519746209133239737925977264625179 (pp53)
 r2=4714832073781596621362448799071690079103424956069158006846652811186139395908205559836553336951 (pp94)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 44.04 hours.
Scaled time: 43.82 units (timescale=0.995).
Factorization parameters were as follows:
name: 24443_159
n: 169638436271207498618321778981267682748389403467968388237789976659448429627083605891836793599367968896683372273498374419202359611720013660705689229
m: 100000000000000000000000000000000
c5: 11
c0: -65
skew: 1.43
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3700001)
Primes: RFBsize:283146, AFBsize:283393, largePrimes:5721164 encountered
Relations: rels:5780761, finalFF:678838
Max relations in full relation-set: 28
Initial matrix: 566604 x 678838 with sparse part having weight 44595218.
Pruned matrix : 483941 x 486838 with weight 30357189.
Total sieving time: 42.29 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.58 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 44.04 hours.
 --------- CPU info (if available) ----------

(22·10¹⁵⁷-13)/9 = 2(4)₁₅₆3_<158> = 1901 · 45646637540051_<14> · C141

C141 = P69 · P72

P69 = 941115575237730669914918455345091326630972261040701955276054024800787_<69>

P72 = 299327281814835613590373614390897333859536305210099996132872751678060239_<72>

Number: 24443_157
N=281701567009515337244234737436856874873686680115008093807195786046964542930044212193347083470278961240801256470701268719003298688370560608093
  ( 141 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=941115575237730669914918455345091326630972261040701955276054024800787 (pp69)
 r2=299327281814835613590373614390897333859536305210099996132872751678060239 (pp72)
Version: GGNFS-0.77.1-20060513-k8
Total time: 59.57 hours.
Scaled time: 118.90 units (timescale=1.996).
Factorization parameters were as follows:
name: 24443_157
n: 281701567009515337244234737436856874873686680115008093807195786046964542930044212193347083470278961240801256470701268719003298688370560608093
m: 10000000000000000000000000000000
c5: 2200
c0: -13
skew: 0.36
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3900001)
Primes: RFBsize:283146, AFBsize:283003, largePrimes:5890953 encountered
Relations: rels:6046569, finalFF:756840
Max relations in full relation-set: 28
Initial matrix: 566216 x 756840 with sparse part having weight 51799263.
Pruned matrix : 427261 x 430156 with weight 36328521.
Total sieving time: 56.77 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 2.41 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 59.57 hours.
 --------- CPU info (if available) ----------

Jul 3, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(22·10¹⁵⁶-13)/9 = 2(4)₁₅₅3_<157> = 31 · 69610967 · C148

C148 = P68 · P80

P68 = 58736020814238558891405825208486913134774314421667326208192258974379_<68>

P80 = 19285739207270759069175268490680623206978396054095595843811679209703382453696521_<80>

Number: 24443_156
N=1132767579496231949385886206437540984692756560598462115818360616266781568801922447745841285021267505089852851103858318504307705517077245584780435459
  ( 148 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=58736020814238558891405825208486913134774314421667326208192258974379 (pp68)
 r2=19285739207270759069175268490680623206978396054095595843811679209703382453696521 (pp80)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 32.99 hours.
Scaled time: 33.28 units (timescale=1.009).
Factorization parameters were as follows:
name: 24443_156
n: 1132767579496231949385886206437540984692756560598462115818360616266781568801922447745841285021267505089852851103858318504307705517077245584780435459
m: 10000000000000000000000000000000
c5: 220
c0: -13
skew: 0.57
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2800001)
Primes: RFBsize:216816, AFBsize:216882, largePrimes:5615042 encountered
Relations: rels:5551495, finalFF:527766
Max relations in full relation-set: 28
Initial matrix: 433765 x 527766 with sparse part having weight 43035221.
Pruned matrix : 385213 x 387445 with weight 28597768.
Total sieving time: 31.80 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.02 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 32.99 hours.
 --------- CPU info (if available) ----------

Jul 3, 2008 (2nd)

By matsui / GGNFS

3·10¹⁹¹+1 = 3(0)₁₉₀1_<192> = 13 · 43 · 41981 · 90059 · 222941 · 1235130679_<10> · 8247897299_<10> · 94927819198801891456854631_<26> · C129

C129 = P61 · P69

P61 = 3509579947593832172401267969183483650808143002961993244596581_<61>

P69 = 187600851274178017217228137473536104234402691756912413319983272561371_<69>

N=658400185783387989190276926287923699496691827000194736855165613840550040610396624987732594211308692726270672023640418105459272551
  ( 129 digits)
Divisors found:
 r1=3509579947593832172401267969183483650808143002961993244596581 (pp61)
 r2=187600851274178017217228137473536104234402691756912413319983272561371 (pp69)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 321.19 hours.
Scaled time: 462.20 units (timescale=1.439).
Factorization parameters were as follows:
name: 8000
n: 658400185783387989190276926287923699496691827000194736855165613840550040610396624987732594211308692726270672023640418105459272551
skew: 72736.40
# norm 1.83e+18
c5: 786240
c4: -747480222072
c3: 20219639540097418
c2: 3368292628923275673139
c1: -8265186657456836050216142
c0: -2406243418535148656504477194428
# alpha -7.19
Y1: 82320578815277
Y0: -3842277531817596663468793
# Murphy_E 9.16e-11
# M 557761899041843066496540040677737346243348996541460686464442362588014926906968250733206482629057103019058836980746328716567488758
type: gnfs
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.5
alambda: 2.5
qintsize: 60000
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [2700000, 10680001)
Primes: RFBsize:374362, AFBsize:375087, largePrimes:9623028 encountered
Relations: rels:10716441, finalFF:852775
Max relations in full relation-set: 28
Initial matrix: 749534 x 852775 with sparse part having weight 120954160.
Pruned matrix : 674473 x 678284 with weight 101198922.
Total sieving time: 308.26 hours.
Total relation processing time: 0.80 hours.
Matrix solve time: 11.52 hours.
Time per square root: 0.62 hours.
Prototype def-par.txt line would be:
gnfs,128,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5400000,5400000,27,27,51,51,2.5,2.5,60000
total time: 321.19 hours.

Jul 3, 2008

By Serge Batalov / pol51, Msieve

(22·10¹⁷¹-13)/9 = 2(4)₁₇₀3_<172> = 7 · 31 · 827 · 5246447 · 479536609 · 4338158526930879037_<19> · 242847323361115062389_<21> · C112

C112 = P38 · P75

P38 = 17489659331233420841041848831787915121_<38>

P75 = 293837879123436495340659649946267814150481624381132301381989520081108118583_<75>

Number: 24443_171
N=5139124404481049086395651731906800311483837611273017081671461373903727665577251446454615728185746159540406793543
  ( 112 digits)
Divisors found:
 r1=17489659331233420841041848831787915121
 r2=293837879123436495340659649946267814150481624381132301381989520081108118583
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.925).
Factorization parameters were as follows:
name: 24443_171
n: 5139124404481049086395651731906800311483837611273017081671461373903727665577251446454615728185746159540406793543
skew: 23580.22
# norm 7.24e+15
c5: 148800
c4: -4636284728
c3: -470193859049548
c2: 438239297947085878
c1: 79112332684214555643067
c0: -394126047946406209907151014
# alpha -6.39
Y1: 86199672119
Y0: -2030754175241905544721
# Murphy_E 7.70e-10
# M 2640026109499838171364872472237626803511669852765746996736091001649567901109710655658807811642173908560437128601
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 3550001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 445649 x 445892
Total sieving time: 11.00 hours.
Total relation processing time: 0.80 hours.
Matrix solve time: 1.00 hours.
Time per square root: 0.79 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 0.00 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

Tue Jul  1 20:09:33 2008  Msieve v. 1.36
Tue Jul  1 20:09:33 2008  random seeds: 702b4d8c a9e2f611
Tue Jul  1 20:09:33 2008  factoring 5139124404481049086395651731906800311483837611273017081671461373903727665577251446454615728185746159540406793543 (112 digits)
Tue Jul  1 20:09:33 2008  no P-1/P+1/ECM available, skipping
Tue Jul  1 20:09:33 2008  commencing number field sieve (112-digit input)
Tue Jul  1 20:09:33 2008  R0: -2030754175241905544721
Tue Jul  1 20:09:33 2008  R1:  86199672119
Tue Jul  1 20:09:33 2008  A0: -394126047946406209907151014
Tue Jul  1 20:09:33 2008  A1:  79112332684214555643067
Tue Jul  1 20:09:33 2008  A2:  438239297947085878
Tue Jul  1 20:09:33 2008  A3: -470193859049548
Tue Jul  1 20:09:33 2008  A4: -4636284728
Tue Jul  1 20:09:33 2008  A5:  148800
Tue Jul  1 20:09:33 2008  size score = 1.249103e-11, Murphy alpha = -6.388435, combined = 1.050556e-10
Tue Jul  1 20:09:33 2008  generating factor base
Tue Jul  1 20:09:35 2008  factor base complete:
Tue Jul  1 20:09:35 2008  250150 rational roots (max prime = 3499999)
Tue Jul  1 20:09:35 2008  250613 algebraic roots (max prime = 3499999)
Tue Jul  1 20:09:36 2008  a range: [-4000000, 4000000]
Tue Jul  1 20:09:36 2008  b range: [1, 300]
Tue Jul  1 20:09:36 2008  number of hash buckets: 54
Tue Jul  1 20:09:36 2008  sieve block size: 65536
Tue Jul  1 20:09:36 2008  
Tue Jul  1 20:09:36 2008  maximum RFB prime: 3499999
Tue Jul  1 20:09:36 2008  RFB entries: 250150
Tue Jul  1 20:09:36 2008  medium RFB entries: 6542
Tue Jul  1 20:09:36 2008  resieved RFB entries: 6374
Tue Jul  1 20:09:36 2008  small RFB prime powers: 26

......

Wed Jul  2 07:37:03 2008  read 222881 cycles
Wed Jul  2 07:37:04 2008  cycles contain 942396 unique relations
Wed Jul  2 07:37:13 2008  read 942396 relations
Wed Jul  2 07:37:19 2008  multiplying 1389020 relations
Wed Jul  2 07:40:48 2008  multiply complete, coefficients have about 62.98 million bits
Wed Jul  2 07:40:51 2008  initial square root is modulo 1099946581
Wed Jul  2 07:48:08 2008  reading relations for dependency 2
Wed Jul  2 07:48:08 2008  read 223005 cycles
Wed Jul  2 07:48:09 2008  cycles contain 943124 unique relations
Wed Jul  2 07:48:18 2008  read 943124 relations
Wed Jul  2 07:48:24 2008  multiplying 1390606 relations
Wed Jul  2 07:51:51 2008  multiply complete, coefficients have about 63.05 million bits
Wed Jul  2 07:51:54 2008  initial square root is modulo 1127141789
Wed Jul  2 08:00:03 2008  reading relations for dependency 3
Wed Jul  2 08:00:03 2008  read 222905 cycles
Wed Jul  2 08:00:04 2008  cycles contain 944334 unique relations
Wed Jul  2 08:00:13 2008  read 944334 relations
Wed Jul  2 08:00:19 2008  multiplying 1393096 relations
Wed Jul  2 08:04:08 2008  multiply complete, coefficients have about 63.16 million bits
Wed Jul  2 08:04:11 2008  initial square root is modulo 1169218081
Wed Jul  2 08:12:57 2008  reading relations for dependency 4
Wed Jul  2 08:12:57 2008  read 222408 cycles
Wed Jul  2 08:12:58 2008  cycles contain 941642 unique relations
Wed Jul  2 08:13:07 2008  read 941642 relations
Wed Jul  2 08:13:14 2008  multiplying 1387418 relations
Wed Jul  2 08:16:55 2008  multiply complete, coefficients have about 62.90 million bits
Wed Jul  2 08:16:58 2008  initial square root is modulo 1073482523
Wed Jul  2 08:24:19 2008  prp38 factor: 17489659331233420841041848831787915121
Wed Jul  2 08:24:19 2008  prp75 factor: 293837879123436495340659649946267814150481624381132301381989520081108118583
Wed Jul  2 08:24:19 2008  elapsed time 00:47:17

Total time: 13hrs.

Jul 2, 2008 (6th)

By suberi / GMP-ECM

10¹⁸⁶+7 = 1(0)₁₈₅7_<187> = 23 · 1674321589150079_<16> · 5169259926503910472517_<22> · C148

C148 = P44 · P105

P44 = 10519579813202962164191587968549958338845129_<44>

P105 = 477536446524351969730209842702002079292017485236107832937025486800606023755171179378285725378006234337547_<105>

Jul 2, 2008 (5th)

By Jo Yeong Uk / GMP-ECM

(22·10¹⁶⁶-13)/9 = 2(4)₁₆₅3_<167> = 204748963 · 1560730573355017_<16> · 52343527673168281003_<20> · C124

C124 = P35 · P89

P35 = 92451731827226267738142652673971531_<35>

P89 = 15807110284823092936676892186474766682999520995799709781771826467335821057469454232049481_<89>

Jul 2, 2008 (4th)

By Sinkiti Sibata / GGNFS

(22·10¹⁵⁴-13)/9 = 2(4)₁₅₃3_<155> = 3463 · 15581 · C147

C147 = P49 · P99

P49 = 2146985142350986093864164662530779984526223381689_<49>

P99 = 211010133979284123150461874857456724663907315722703385915179202631648184177974032185559336543961529_<99>

Number: 24443_154
N=453035622539013970891682854298717155295753628948673158226457545176192318250968172647477185573936425721132888801189429376654675287366209803099042481
  ( 147 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=2146985142350986093864164662530779984526223381689 (pp49)
 r2=211010133979284123150461874857456724663907315722703385915179202631648184177974032185559336543961529 (pp99)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 33.25 hours.
Scaled time: 33.45 units (timescale=1.006).
Factorization parameters were as follows:
name: 24443_154
n: 453035622539013970891682854298717155295753628948673158226457545176192318250968172647477185573936425721132888801189429376654675287366209803099042481
m: 10000000000000000000000000000000
c5: 11
c0: -65
skew: 1.43
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2800001)
Primes: RFBsize:216816, AFBsize:217057, largePrimes:5707407 encountered
Relations: rels:5715253, finalFF:588373
Max relations in full relation-set: 28
Initial matrix: 433938 x 588373 with sparse part having weight 48008079.
Pruned matrix : 348032 x 350265 with weight 29877041.
Total sieving time: 32.22 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.88 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 33.25 hours.
 --------- CPU info (if available) ----------

Jul 2, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(22·10¹⁴⁷-13)/9 = 2(4)₁₄₆3_<148> = 7 · C147

C147 = P40 · P108

P40 = 2021712041728844821895966127264309751829_<40>

P108 = 172728035446496740787707614044367729343826209385361445373501288263149880818963169788976312580236715350305881_<108>

Number: n
N=349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349
  ( 147 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=2021712041728844821895966127264309751829 (pp40)
 r2=172728035446496740787707614044367729343826209385361445373501288263149880818963169788976312580236715350305881 (pp108)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 10.68 hours.
Scaled time: 19.54 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_4_146_3
n: 349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349
skew: 0.36
deg: 5
c5: 2200
c0: -13
m: 100000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2050001)
Primes: RFBsize:114155, AFBsize:114288, largePrimes:7233951 encountered
Relations: rels:6609013, finalFF:269764
Max relations in full relation-set: 48
Initial matrix: 228510 x 269764 with sparse part having weight 44600679.
Pruned matrix : 220578 x 221784 with weight 32514856.
Total sieving time: 9.77 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.67 hours.
Total square root time: 0.04 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000
total time: 10.68 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(22·10¹⁴⁹-13)/9 = 2(4)₁₄₈3_<150> = 3 · 17 · C148

C148 = P59 · P89

P59 = 69002924247755090799484487397373660603707328555480983703141_<59>

P89 = 69461234791017154769799796429709791557515126520850419394325840918738250512555886792605573_<89>

Number: n
N=4793028322440087145969498910675381263616557734204793028322440087145969498910675381263616557734204793028322440087145969498910675381263616557734204793
  ( 148 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=69002924247755090799484487397373660603707328555480983703141 (pp59)
 r2=69461234791017154769799796429709791557515126520850419394325840918738250512555886792605573 (pp89)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 11.78 hours.
Scaled time: 21.54 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_4_148_3
n: 4793028322440087145969498910675381263616557734204793028322440087145969498910675381263616557734204793028322440087145969498910675381263616557734204793
skew: 1.43
deg: 5
c5: 11
c0: -65
m: 1000000000000000000000000000000
type: snfs
rlim: 1800000
alim: 1800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 800001)
Primes: RFBsize:135072, AFBsize:135314, largePrimes:6328487 encountered
Relations: rels:5664046, finalFF:311042
Max relations in full relation-set: 48
Initial matrix: 270451 x 311042 with sparse part having weight 32188544.
Pruned matrix : 249681 x 251097 with weight 20817556.
Total sieving time: 10.90 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.49 hours.
Total square root time: 0.26 hours, sqrts: 7.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.5,2.5,100000
total time: 11.78 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

4·10¹⁶⁸-3 = 3(9)₁₆₇7_<169> = 349 · 241074611 · C158

C158 = P77 · P82

P77 = 21544306803353103509843977179159206218824143080472857184693633917823174539019_<77>

P82 = 2206736938256127773273970339311752643567289428173222443185875220281755576364296817_<82>

Number: n
N=47542617632082091100384231437845636303263529996343334801020808732923113197004353274453935504867471617106807111737038599279044427284432373996054873344064002523
  ( 158 digits)
SNFS difficulty: 168 digits.
Divisors found:

Wed Jul  2 15:47:50 2008  prp77 factor: 21544306803353103509843977179159206218824143080472857184693633917823174539019
Wed Jul  2 15:47:50 2008  prp82 factor: 2206736938256127773273970339311752643567289428173222443185875220281755576364296817
Wed Jul  2 15:47:50 2008  elapsed time 01:07:16

Version: GGNFS-0.77.1-20050930-k8
Total time: 57.18 hours.
Scaled time: 47.92 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_3_9_167_7
n: 47542617632082091100384231437845636303263529996343334801020808732923113197004353274453935504867471617106807111737038599279044427284432373996054873344064002523
type: snfs
deg: 5
c5: 125
c0: -3
skew: 0.47
m: 2000000000000000000000000000000000
rlim: 5500000
alim: 5500000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3200111)
Primes: RFBsize:380800, AFBsize:379892, largePrimes:5594103 encountered
Relations: rels:5729847, finalFF:793042
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 57.00 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.5,2.5,100000
total time: 57.18 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

Jul 2, 2008 (2nd)

By Sinkiti Sibata / GGNFS, Msieve

(22·10¹³⁷-13)/9 = 2(4)₁₃₆3_<138> = 3³ · C136

C136 = P62 · P75

P62 = 58473762489790941516005057792881835042331950647437243978542293_<62>

P75 = 154830090572117720754725648814565048360015424986244247352985425052957023613_<75>

Number: 24443_137
N=9053497942386831275720164609053497942386831275720164609053497942386831275720164609053497942386831275720164609053497942386831275720164609
  ( 136 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=58473762489790941516005057792881835042331950647437243978542293 (pp62)
 r2=154830090572117720754725648814565048360015424986244247352985425052957023613 (pp75)
Version: GGNFS-0.77.1-20060513-k8
Total time: 12.92 hours.
Scaled time: 25.85 units (timescale=2.000).
Factorization parameters were as follows:
name: 24443_137
n: 9053497942386831275720164609053497942386831275720164609053497942386831275720164609053497942386831275720164609053497942386831275720164609
m: 1000000000000000000000000000
c5: 2200
c0: -13
skew: 0.36
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 2125001)
Primes: RFBsize:78498, AFBsize:64029, largePrimes:1671959 encountered
Relations: rels:1698646, finalFF:166229
Max relations in full relation-set: 28
Initial matrix: 142594 x 166229 with sparse part having weight 18916119.
Pruned matrix : 136939 x 137715 with weight 14393055.
Total sieving time: 12.59 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 12.92 hours.
 --------- CPU info (if available) ----------

(22·10¹³²-13)/9 = 2(4)₁₃₁3_<133> = 42227 · C128

C128 = P53 · P76

P53 = 42883627663814341521903001082675283462854504182949003_<53>

P76 = 1349890144337203998734326849512015502391489910957629428484329332974286483403_<76>

Number: 24443_132
N=57888186336809255794739016374462889725636309575495404467389216483397931286722818207413371644787563512549895669700533886954897209
  ( 128 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=42883627663814341521903001082675283462854504182949003 (pp53)
 r2=1349890144337203998734326849512015502391489910957629428484329332974286483403 (pp76)
Version: GGNFS-0.77.1-20060513-k8
Total time: 7.09 hours.
Scaled time: 14.15 units (timescale=1.997).
Factorization parameters were as follows:
name: 24443_132
n: 57888186336809255794739016374462889725636309575495404467389216483397931286722818207413371644787563512549895669700533886954897209
m: 100000000000000000000000000
c5: 2200
c0: -13
skew: 0.36
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1350001)
Primes: RFBsize:63951, AFBsize:64029, largePrimes:1557327 encountered
Relations: rels:1558691, finalFF:156948
Max relations in full relation-set: 28
Initial matrix: 128047 x 156948 with sparse part having weight 15590982.
Pruned matrix : 121238 x 121942 with weight 10526521.
Total sieving time: 6.87 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 7.09 hours.
 --------- CPU info (if available) ----------

(22·10¹⁴⁰-13)/9 = 2(4)₁₃₉3_<141> = 3 · 79392461 · C133

C133 = P41 · P92

P41 = 30903737715270715377221878457373280830821_<41>

P92 = 33209982218207158692180677111290215531825231303595299136370285580176392535478664638944361001_<92>

Number: 24443_140
N=1026312580000278382622267893691839096428582576392001269257561892198825798856159421503277011169630847965293347960097640523846231211821
  ( 133 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=30903737715270715377221878457373280830821 (pp41)
 r2=33209982218207158692180677111290215531825231303595299136370285580176392535478664638944361001 (pp92)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.16 hours.
Scaled time: 10.22 units (timescale=1.006).
Factorization parameters were as follows:
name: 24443_140
n: 1026312580000278382622267893691839096428582576392001269257561892198825798856159421503277011169630847965293347960097640523846231211821
m: 10000000000000000000000000000
c5: 22
c0: -13
skew: 0.9
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1950001)
Primes: RFBsize:100021, AFBsize:100234, largePrimes:2776498 encountered
Relations: rels:2775252, finalFF:272961
Max relations in full relation-set: 28
Initial matrix: 200321 x 272961 with sparse part having weight 27976184.
Pruned matrix : 179707 x 180772 with weight 16440918.
Total sieving time: 9.91 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 10.16 hours.
 --------- CPU info (if available) ----------

(22·10¹¹²-13)/9 = 2(4)₁₁₁3_<113> = 3259 · 13950581137_<11> · C99

C99 = P32 · P68

P32 = 13701829988800447487541383114549_<32>

P68 = 39239633019081925818391162394055049075239789099796401438595560894829_<68>

Tue Jul  1 20:15:56 2008  Msieve v. 1.36
Tue Jul  1 20:15:56 2008  random seeds: 85f03703 ba89e7ee
Tue Jul  1 20:15:56 2008  factoring 537654780450380973069393496111123321611416061591593186743289377877472784652282513278331113448767121 (99 digits)
Tue Jul  1 20:15:58 2008  no P-1/P+1/ECM available, skipping
Tue Jul  1 20:15:58 2008  commencing quadratic sieve (99-digit input)
Tue Jul  1 20:15:58 2008  using multiplier of 1
Tue Jul  1 20:15:58 2008  using 64kb Pentium 4 sieve core
Tue Jul  1 20:15:58 2008  sieve interval: 18 blocks of size 65536
Tue Jul  1 20:15:58 2008  processing polynomials in batches of 6
Tue Jul  1 20:15:58 2008  using a sieve bound of 2608889 (95294 primes)
Tue Jul  1 20:15:58 2008  using large prime bound of 391333350 (28 bits)
Tue Jul  1 20:15:58 2008  using double large prime bound of 2928089178039000 (43-52 bits)
Tue Jul  1 20:15:58 2008  using trial factoring cutoff of 52 bits
Tue Jul  1 20:15:58 2008  polynomial 'A' values have 13 factors
Wed Jul  2 11:21:29 2008  95448 relations (22485 full + 72963 combined from 1440354 partial), need 95390
Wed Jul  2 11:21:34 2008  begin with 1462839 relations
Wed Jul  2 11:21:36 2008  reduce to 252560 relations in 11 passes
Wed Jul  2 11:21:36 2008  attempting to read 252560 relations
Wed Jul  2 11:21:45 2008  recovered 252560 relations
Wed Jul  2 11:21:45 2008  recovered 242733 polynomials
Wed Jul  2 11:21:45 2008  attempting to build 95448 cycles
Wed Jul  2 11:21:45 2008  found 95448 cycles in 5 passes
Wed Jul  2 11:21:45 2008  distribution of cycle lengths:
Wed Jul  2 11:21:45 2008     length 1 : 22485
Wed Jul  2 11:21:45 2008     length 2 : 16133
Wed Jul  2 11:21:45 2008     length 3 : 16027
Wed Jul  2 11:21:45 2008     length 4 : 13262
Wed Jul  2 11:21:45 2008     length 5 : 10160
Wed Jul  2 11:21:45 2008     length 6 : 6709
Wed Jul  2 11:21:45 2008     length 7 : 4445
Wed Jul  2 11:21:45 2008     length 9+: 6227
Wed Jul  2 11:21:45 2008  largest cycle: 20 relations
Wed Jul  2 11:21:46 2008  matrix is 95294 x 95448 (25.3 MB) with weight 6255327 (65.54/col)
Wed Jul  2 11:21:46 2008  sparse part has weight 6255327 (65.54/col)
Wed Jul  2 11:21:48 2008  filtering completed in 3 passes
Wed Jul  2 11:21:48 2008  matrix is 91505 x 91569 (24.4 MB) with weight 6039314 (65.95/col)
Wed Jul  2 11:21:48 2008  sparse part has weight 6039314 (65.95/col)
Wed Jul  2 11:21:48 2008  saving the first 48 matrix rows for later
Wed Jul  2 11:21:49 2008  matrix is 91457 x 91569 (14.3 MB) with weight 4638240 (50.65/col)
Wed Jul  2 11:21:49 2008  sparse part has weight 3191337 (34.85/col)
Wed Jul  2 11:21:49 2008  matrix includes 64 packed rows
Wed Jul  2 11:21:49 2008  using block size 21845 for processor cache size 512 kB
Wed Jul  2 11:21:49 2008  commencing Lanczos iteration
Wed Jul  2 11:21:49 2008  memory use: 14.5 MB
Wed Jul  2 11:23:17 2008  lanczos halted after 1447 iterations (dim = 91455)
Wed Jul  2 11:23:17 2008  recovered 15 nontrivial dependencies
Wed Jul  2 11:23:19 2008  prp32 factor: 13701829988800447487541383114549
Wed Jul  2 11:23:19 2008  prp68 factor: 39239633019081925818391162394055049075239789099796401438595560894829
Wed Jul  2 11:23:19 2008  elapsed time 15:07:23

(22·10¹³⁹-13)/9 = 2(4)₁₃₈3_<140> = 149 · 168851 · C132

C132 = P36 · P97

P36 = 153134131586673253525316680340706127_<36>

P97 = 6344804807107506932431402272201079387020389960080550065808574943830533716609237345358028267464891_<97>

Number: 24443_139
N=971606174223357976843188915513989536799608138864038956885201254815241556023578249678947093000919656158644315431926796046363121087157
  ( 132 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=153134131586673253525316680340706127 (pp36)
 r2=6344804807107506932431402272201079387020389960080550065808574943830533716609237345358028267464891 (pp97)
Version: GGNFS-0.77.1-20060513-k8
Total time: 10.28 hours.
Scaled time: 20.44 units (timescale=1.989).
Factorization parameters were as follows:
name: 24443_139
n: 971606174223357976843188915513989536799608138864038956885201254815241556023578249678947093000919656158644315431926796046363121087157
m: 10000000000000000000000000000
c5: 11
c0: -65
skew: 1.43
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1750001)
Primes: RFBsize:100021, AFBsize:100099, largePrimes:2766896 encountered
Relations: rels:2782205, finalFF:298407
Max relations in full relation-set: 28
Initial matrix: 200185 x 298407 with sparse part having weight 27881999.
Pruned matrix : 171496 x 172560 with weight 14209059.
Total sieving time: 9.82 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 10.28 hours.
 --------- CPU info (if available) ----------

Jul 2, 2008

By Serge Batalov / GMP-ECM, pol51, Msieve

(22·10¹⁹⁰-13)/9 = 2(4)₁₈₉3_<191> = 37579 · 197712115002913632677_<21> · 4324556297448073545291529_<25> · 5173627017798433092541301317_<28> · C114

C114 = P44 · P70

P44 = 23032466315154297903558471524435237785670147_<44>

P70 = 6384465648362112581210497692982220217680658290277639789815364462792251_<70>

(68·10¹⁷⁹+13)/9 = 7(5)₁₇₈7_<180> = 11 · 9857 · 33493 · 30812581 · 6965459779_<10> · 2442025749808860916183882823027_<31> · C123

C123 = P44 · P79

P44 = 57629319515256167066500951939735023830699563_<44>

P79 = 6888161396207106342594867165412911745264595604363393849592578966611969346616013_<79>

(22·10¹⁹⁵-13)/9 = 2(4)₁₉₄3_<196> = 7 · 26837687 · 95955997 · 466934099 · 34189412940043_<14> · 387163017726257_<15> · 28293299911166088280426132237163_<32> · C111

C111 = P31 · P40 · P41

P31 = 4432786487726332261901992580177_<31>

P40 = 2282361128060960866345069318662723827857_<40>

P41 = 76644156088849870258058669364338740667237_<41>

Number: 24443_195
N=775425755799446841939053048525302354064197837605938152294567158088550638083405933820635565662056629872055556293
  ( 111 digits)
Divisors found:
 r1=4432786487726332261901992580177
 r2=2282361128060960866345069318662723827857
 r3=76644156088849870258058669364338740667237
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.844).
Factorization parameters were as follows:
name: 24443_195
n: 775425755799446841939053048525302354064197837605938152294567158088550638083405933820635565662056629872055556293
skew: 38578.42
# norm 4.25e+14
c5: 5940
c4: -241464251
c3: -28961153603108
c2: 292489093069413502
c1: 20420682911241094723856
c0: 133575367865294507252877085
# alpha -4.46
Y1: 309827997097
Y0: -2649422183486934259056
# Murphy_E 8.30e-10
# M 627846271663089527779179125876741566414536726272675783926772171413507244872142141742899588517629762116642887585
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2500001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 432467 x 432707
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 0.00 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)
Calibrating delay using timer specific routine.. 5600.62 BogoMIPS (lpj=11201256)
Calibrating delay using timer specific routine.. 5600.69 BogoMIPS (lpj=11201386)
Calibrating delay using timer specific routine.. 5600.70 BogoMIPS (lpj=11201415)
Calibrating delay using timer specific routine.. 5600.65 BogoMIPS (lpj=11201310)
Calibrating delay using timer specific routine.. 5600.66 BogoMIPS (lpj=11201320)
Calibrating delay using timer specific routine.. 5600.75 BogoMIPS (lpj=11201501)
Calibrating delay using timer specific routine.. 5600.56 BogoMIPS (lpj=11201124)
saving the first 48 matrix rows for later
matrix is 432467 x 432707 (127.7 MB) with weight 34239845 (79.13/col)
sparse part has weight 29137637 (67.34/col)
matrix includes 64 packed rows
using block size 43690 for processor cache size 1024 kB
commencing Lanczos iteration
memory use: 117.7 MB
linear algebra completed 431051 out of 432707 dimensions (99.6%)
lanczos halted after 6840 iterations (dim = 432466)
recovered 44 nontrivial dependencies
elapsed time 00:40:04
=>nice -n 19  "/depts/BioInf/Batalov/MERSE/ggbin/msieve" -s 24443_195.dat -l ggnfs.log -i 24443_195.ini -v -nf 24443_195.fb -t 1 -nc3

Msieve v. 1.36
Tue Jul  1 17:52:34 2008
random seeds: 6a729032 ef40d2b8
factoring 775425755799446841939053048525302354064197837605938152294567158088550638083405933820635565662056629872055556293 (111 digits)
no P-1/P+1/ECM available, skipping
commencing number field sieve (111-digit input)
R0: -2649422183486934259056
R1:  309827997097
A0:  133575367865294507252877085
A1:  20420682911241094723856
A2:  292489093069413502
A3: -28961153603108
A4: -241464251
A5:  5940
size score = 2.646882e-11, Murphy alpha = -4.459988, combined = 1.170534e-10

commencing square root phase
reading relations for dependency 1
read 216070 cycles
cycles contain 940344 unique relations
read 940344 relations
multiplying 1324484 relations
multiply complete, coefficients have about 54.75 million bits
initial square root is modulo 72519241
reading relations for dependency 2
read 216114 cycles
cycles contain 940777 unique relations
read 940777 relations
multiplying 1325292 relations
multiply complete, coefficients have about 54.78 million bits
initial square root is modulo 73261117
prp31 factor: 4432786487726332261901992580177
prp40 factor: 2282361128060960866345069318662723827857
prp41 factor: 76644156088849870258058669364338740667237
elapsed time 00:20:08
-> Computing time scale for this machine...
sumName = g111-24443_195.txt
-> Factorization summary written to g111-24443_195.txt.

Tue Jul  1 03:08:15 2008  Msieve v. 1.36
Tue Jul  1 03:08:15 2008  random seeds: 2448e225 c3c7c117
Tue Jul  1 03:08:15 2008  factoring 775425755799446841939053048525302354064197837605938152294567158088550638083405933820635565662056629872055556293 (111 digits)
Tue Jul  1 03:08:16 2008  no P-1/P+1/ECM available, skipping
Tue Jul  1 03:08:16 2008  commencing number field sieve (111-digit input)
Tue Jul  1 03:08:16 2008  R0: -2649422183486934259056
Tue Jul  1 03:08:16 2008  R1:  309827997097
Tue Jul  1 03:08:16 2008  A0:  133575367865294507252877085
....
Tue Jul  1 18:02:16 2008  read 216114 cycles
Tue Jul  1 18:02:17 2008  cycles contain 940777 unique relations
Tue Jul  1 18:02:27 2008  read 940777 relations
Tue Jul  1 18:02:33 2008  multiplying 1325292 relations
Tue Jul  1 18:05:57 2008  multiply complete, coefficients have about 54.78 million bits
Tue Jul  1 18:05:59 2008  initial square root is modulo 73261117
Tue Jul  1 18:12:42 2008  prp31 factor: 4432786487726332261901992580177
Tue Jul  1 18:12:42 2008  prp40 factor: 2282361128060960866345069318662723827857
Tue Jul  1 18:12:42 2008  prp41 factor: 76644156088849870258058669364338740667237
Tue Jul  1 18:12:42 2008  elapsed time 00:20:08

Total time: 15hr 04mn

Jul 1, 2008 (7th)

By Robert Backstrom / GGNFS, Msieve

(22·10¹¹⁴-13)/9 = 2(4)₁₁₃3_<115> = C115

C115 = P44 · P71

P44 = 33598656294760900291371699381269381784370549_<44>

P71 = 72754232282366932679878294542235391018639436852035736262753056974819407_<71>

Number: n
N=2444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443
  ( 115 digits)
SNFS difficulty: 116 digits.
Divisors found:

Tue Jul 01 23:04:53 2008  prp44 factor: 33598656294760900291371699381269381784370549
Tue Jul 01 23:04:53 2008  prp71 factor: 72754232282366932679878294542235391018639436852035736262753056974819407
Tue Jul 01 23:04:53 2008  elapsed time 00:04:17 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.76 hours.
Scaled time: 1.38 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_4_113_3
n: 2444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443
skew: 1.43
deg: 5
c5: 11
c0: -65
m: 100000000000000000000000
type: snfs
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 180347)
Primes: RFBsize:41538, AFBsize:41593, largePrimes:3591138 encountered
Relations: rels:2958004, finalFF:89757
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 0.71 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.5,2.5,50000
total time: 0.76 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(22·10¹¹⁶-13)/9 = 2(4)₁₁₅3_<117> = 3 · 19 · 105879019 · 137400189118849_<15> · C93

C93 = P41 · P52

P41 = 52216810517743850150033554179233611101121_<41>

P52 = 5645439212850785908811753527171750497376343817221849_<52>

Number: n
N=294786829666870480000441341655921667461151477270136085258399731059313122304735247508029592729
  ( 93 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=52216810517743850150033554179233611101121 (pp41)
 r2=5645439212850785908811753527171750497376343817221849 (pp52)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.87 hours.
Scaled time: 1.58 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_4_115_3
n: 294786829666870480000441341655921667461151477270136085258399731059313122304735247508029592729
skew: 0.57
deg: 5
c5: 220
c0: -13
m: 100000000000000000000000
type: snfs
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 200001)
Primes: RFBsize:41538, AFBsize:41738, largePrimes:3695260 encountered
Relations: rels:3062905, finalFF:93831
Max relations in full relation-set: 48
Initial matrix: 83343 x 93831 with sparse part having weight 8682819.
Pruned matrix : 80055 x 80535 with weight 5877569.
Total sieving time: 0.77 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.03 hours.
Total square root time: 0.02 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.5,2.5,50000
total time: 0.87 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jul 1, 2008 (6th)

By Sinkiti Sibata / GGNFS

(22·10¹²⁹-13)/9 = 2(4)₁₂₈3_<130> = 7 · 241 · 39293 · 13299361 · 2695989282557_<13> · C103

C103 = P39 · P64

P39 = 250682305473299306497685825723691855583_<39>

P64 = 4102771067678316053775037080369167598169783113856398411976486603_<64>

Number: 24443_129
N=1028492110074749967929747272840552481537648574781359688266748220360933344058801859376100555290010254549
  ( 103 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=250682305473299306497685825723691855583 (pp39)
 r2=4102771067678316053775037080369167598169783113856398411976486603 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.48 hours.
Scaled time: 8.96 units (timescale=2.000).
Factorization parameters were as follows:
name: 24443_129
n: 1028492110074749967929747272840552481537648574781359688266748220360933344058801859376100555290010254549
m: 100000000000000000000000000
c5: 11
c0: -65
skew: 1.43
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:63789, largePrimes:1469819 encountered
Relations: rels:1461589, finalFF:164980
Max relations in full relation-set: 28
Initial matrix: 127805 x 164980 with sparse part having weight 11368937.
Pruned matrix : 116430 x 117133 with weight 6330418.
Total sieving time: 4.32 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.48 hours.
 --------- CPU info (if available) ----------

(22·10¹¹⁷-13)/9 = 2(4)₁₁₆3_<118> = 7² · 17 · 233 · 1621 · C109

C109 = P52 · P58

P52 = 4229313234714843164288246278132448514515779114889059_<52>

P58 = 1837072866508690204598997309979916246707045110648608172733_<58>

Number: 24443_117
N=7769556587460737839239858142009053023060286573645996521722787955598485746053241569530231076455526632003828247
  ( 109 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=4229313234714843164288246278132448514515779114889059 (pp52)
 r2=1837072866508690204598997309979916246707045110648608172733 (pp58)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.31 hours.
Scaled time: 1.56 units (timescale=0.677).
Factorization parameters were as follows:
name: 24443_117
n: 7769556587460737839239858142009053023060286573645996521722787955598485746053241569530231076455526632003828247
m: 100000000000000000000000
c5: 2200
c0: -13
skew: 0.36
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64029, largePrimes:1982637 encountered
Relations: rels:1949806, finalFF:139200
Max relations in full relation-set: 28
Initial matrix: 113194 x 139200 with sparse part having weight 11012584.
Pruned matrix : 103684 x 104313 with weight 6438928.
Total sieving time: 2.02 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,118,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.31 hours.
 --------- CPU info (if available) ----------

Jul 1, 2008 (5th)

By Robert Backstrom / GMP-ECM

(22·10¹²¹-13)/9 = 2(4)₁₂₀3_<122> = 10139 · 21610123627320666846739365871_<29> · C90

C90 = P33 · P58

P33 = 106291118910715568757506518867309_<33>

P58 = 1049616908171780243294136059455718184430708493672261067883_<58>

Jul 1, 2008 (4th)

By Serge Batalov / PRIMO 3.0.6

4·10²²⁴⁵+3 = 4(0)₂₂₄₄3_<2246> is prime.

Jul 1, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(22·10¹⁶⁴-31)/9 = 2(4)₁₆₃1_<165> = 2083 · 73135006949_<11> · C151

C151 = P71 · P80

P71 = 51845043108470586834361561919780616245850625521525516787582746406578547_<71>

P80 = 30949836173738031868495545589299632987292537377947824460601813620688132316642509_<80>

Number: n
N=1604595590627550625150237684729477444026023270824767911255148304083581825227614724819356366988897922998432503475970715695690680776482715993969227654423
  ( 151 digits)
SNFS difficulty: 166 digits.
Divisors found:

Tue Jul 01 12:05:17 2008  prp71 factor: 51845043108470586834361561919780616245850625521525516787582746406578547
Tue Jul 01 12:05:17 2008  prp80 factor: 30949836173738031868495545589299632987292537377947824460601813620688132316642509
Tue Jul 01 12:05:17 2008  elapsed time 02:20:11 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 58.82 hours.
Scaled time: 103.57 units (timescale=1.761).
Factorization parameters were as follows:
name: KA_2_4_163_1
n: 1604595590627550625150237684729477444026023270824767911255148304083581825227614724819356366988897922998432503475970715695690680776482715993969227654423
type: snfs
skew: 1.70
deg: 5
c5: 11
c0: -155
m: 1000000000000000000000000000000000
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2600267)
Primes: RFBsize:348513, AFBsize:348353, largePrimes:7679016 encountered
Relations: rels:7285979, finalFF:745129
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 58.55 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000
total time: 58.82 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

6·10¹⁶⁸+7 = 6(0)₁₆₇7_<169> = 13 · 162683 · 1905773 · C157

C157 = P32 · P34 · P91

P32 = 92496541056236438247583376263031_<32>

P34 = 1737404675144043985388097795414143_<34>

P91 = 9263350086582064127298447027451667014374897979566099083674205980098110320670551785060577237_<91>

(17·10¹⁶⁹-53)/9 = 1(8)₁₆₈3_<170> = 13³ · 1153 · C163

C163 = P34 · P130

P34 = 1899184819671361163387290225408063_<34>

P130 = 3926266888112567544073047887536313671079408556962007900627998803362902182734040273650475604473730549935716930277198186398648831001_<130>

7·10¹⁷³+9 = 7(0)₁₇₂9_<174> = 727 · C171

C171 = P50 · P57 · P65

P50 = 46703390984381129306990060832824441396119105760387_<50>

P57 = 803575513133626214041688443279256687479553115056384050651_<57>

P65 = 25655974804389045502754045805223424190216260512796697773191686191_<65>

Number: n
N=962861072902338376891334250343878954607977991746905089408528198074277854195323246217331499312242090784044016506189821182943603851444291609353507565337001375515818431911967
  ( 171 digits)
SNFS difficulty: 173 digits.
Divisors found:

Tue Jul 01 15:01:54 2008  prp50 factor: 46703390984381129306990060832824441396119105760387
Tue Jul 01 15:01:54 2008  prp57 factor: 803575513133626214041688443279256687479553115056384050651
Tue Jul 01 15:01:54 2008  prp65 factor: 25655974804389045502754045805223424190216260512796697773191686191
Tue Jul 01 15:01:54 2008  elapsed time 03:00:18 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 143.54 hours.
Scaled time: 262.54 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_7_0_172_9
n: 962861072902338376891334250343878954607977991746905089408528198074277854195323246217331499312242090784044016506189821182943603851444291609353507565337001375515818431911967
skew: 0.26
deg: 5
c5: 7000
c0: 9
m: 10000000000000000000000000000000000
type: snfs
rlim: 7200000
alim: 7200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 7200000/7200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 8200537)
Primes: RFBsize:489319, AFBsize:488763, largePrimes:9369787 encountered
Relations: rels:8949267, finalFF:985202
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 142.94 hours.
Total relation processing time: 0.61 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,7200000,7200000,28,28,48,48,2.5,2.5,100000
total time: 143.54 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jul 1, 2008 (2nd)

Factorizations of 11...11 (Repunit) was extended to n=100000 and Factorizations of 100...001 was extended to n=50000.

Jul 1, 2008

The factor table of 244...443 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

June 2008

Jun 30, 2008 (4th)

By suberi / GMP-ECM

(64·10²⁴⁶+53)/9 = 7(1)₂₄₅7_<247> = 13 · 17 · 1160548621_<10> · C236

C236 = P40 · P196

P40 = 3653540712889564696115226712823703119009_<40>

P196 = 7588709004594473714701606971400814241433489374368336268700131770235266770437697694816355315610746815222410425117554914203426930343872298340279245942146302647290762688407537944247691411211636284693_<196>

Jun 30, 2008 (3rd)

By Serge Batalov / PRIMO 3.0.6

(11·10²¹³⁶+1)/3 = 3(6)₂₁₃₅7_<2137> is prime.

(22·10²²⁰⁴-1)/3 = 7(3)₂₂₀₄_<2205> is prime.

Jun 30, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(22·10¹⁶⁷-31)/9 = 2(4)₁₆₆1_<168> = 23 · 2539 · 37321 · C159

C159 = P44 · P115

P44 = 17383069455340930576859078822201728294481827_<44>

P115 = 6452230846702379390519960216544745384363065802954977313588048296249399827777355779886850218076924772405182266503159_<115>

Number: n
N=112159576950120681443763221790573388303510799505846499774493764431806325745620236083497493365726993165082508258285562019154441967021394020693105366603163591493
  ( 159 digits)
SNFS difficulty: 168 digits.
Divisors found:

Mon Jun 30 13:30:40 2008  prp44 factor: 17383069455340930576859078822201728294481827
Mon Jun 30 13:30:40 2008  prp115 factor: 6452230846702379390519960216544745384363065802954977313588048296249399827777355779886850218076924772405182266503159
Mon Jun 30 13:30:40 2008  elapsed time 01:27:40 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 64.33 hours.
Scaled time: 117.66 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_4_166_1
n: 112159576950120681443763221790573388303510799505846499774493764431806325745620236083497493365726993165082508258285562019154441967021394020693105366603163591493
skew: 0.43
deg: 5
c5: 2200
c0: -31
m: 1000000000000000000000000000000000
type: snfs
rlim: 5500000
alim: 5500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3900000)
Primes: RFBsize:380800, AFBsize:380504, largePrimes:8273794 encountered
Relations: rels:7946017, finalFF:867342
Max relations in full relation-set: 28
Initial matrix: 761371 x 867342 with sparse part having weight 46178197.
Pruned matrix : 664153 x 668023 with weight 29900504.
Total sieving time: 63.98 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.5,2.5,100000
total time: 64.33 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(22·10¹⁶⁶-31)/9 = 2(4)₁₆₅1_<167> = 3 · 71 · 64951 · C160

C160 = P49 · P112

P49 = 1054167195644633213538682942324589961665224175651_<49>

P112 = 1676120464464856575059394614578455426232363135439230363648406284394705342167031244505148822086872348576246745457_<112>

Number: n
N=1766911209587497953093599302301376953102490078251437681439192871104381428198667673452673889623000339399549117991254544465513254335857550718764621943204454267507
  ( 160 digits)
SNFS difficulty: 167 digits.
Divisors found:

Mon Jun 30 13:57:25 2008  prp49 factor: 1054167195644633213538682942324589961665224175651
Mon Jun 30 13:57:25 2008  prp112 factor: 1676120464464856575059394614578455426232363135439230363648406284394705342167031244505148822086872348576246745457
Mon Jun 30 13:57:25 2008  elapsed time 01:54:07 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 64.73 hours.
Scaled time: 93.66 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_2_4_165_1
n: 1766911209587497953093599302301376953102490078251437681439192871104381428198667673452673889623000339399549117991254544465513254335857550718764621943204454267507
skew: 0.68
deg: 5
c5: 220
c0: -31
m: 1000000000000000000000000000000000
type: snfs
rlim: 5200000
alim: 5200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5200000/5200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3000000)
Primes: RFBsize:361407, AFBsize:361244, largePrimes:7999134 encountered
Relations: rels:7698324, finalFF:845404
Max relations in full relation-set: 28
Initial matrix: 722718 x 845404 with sparse part having weight 44159497.
Pruned matrix : 607145 x 610822 with weight 26410081.
Total sieving time: 64.45 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5200000,5200000,28,28,48,48,2.5,2.5,100000
total time: 64.73 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jun 30, 2008

By Serge Batalov / GMP-ECM

(13·10¹⁶⁹-31)/9 = 1(4)₁₆₈1_<170> = 11 · 233435160481_<12> · C157

C157 = P32 · P34 · P92

P32 = 23177318032476375616378164979441_<32>

P34 = 3889428202100559149737103058094361_<34>

P92 = 62401200909819595851686241736549279149882130176261860111226874344359239380766173789767518451_<92>

Jun 29, 2008 (4th)

By suberi / GMP-ECM

2·10¹⁷¹-3 = 1(9)₁₇₀7_<172> = 4691 · 2769503838393179_<16> · C153

C153 = P32 · P37 · P85

P32 = 56976208855415157152685472638791_<32>

P37 = 1494197448543319671819667216019537347_<37>

P85 = 1808260737095189373997972911343245292873628525108905125242459880129553110340203951049_<85>

Jun 29, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(22·10¹⁶²-31)/9 = 2(4)₁₆₁1_<163> = 63737 · 175819093 · C150

C150 = P47 · P104

P47 = 14301556867419987422995670262853271843431921849_<47>

P104 = 15252435624754255559351197971224772317866956646695045907287784752020816148507378065192759386215178367749_<104>

Number: n
N=218133575454085489914759947173598865752402947025291892634882341632830313219197266117538854778381938634304794779037061562662852396167085943869950047901
  ( 150 digits)
SNFS difficulty: 163 digits.
Divisors found:

Sun Jun 29 16:01:24 2008  prp47 factor: 14301556867419987422995670262853271843431921849
Sun Jun 29 16:01:24 2008  prp104 factor: 15252435624754255559351197971224772317866956646695045907287784752020816148507378065192759386215178367749
Sun Jun 29 16:01:24 2008  elapsed time 00:52:21 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 44.63 hours.
Scaled time: 37.44 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_2_4_161_1
n: 218133575454085489914759947173598865752402947025291892634882341632830313219197266117538854778381938634304794779037061562662852396167085943869950047901
type: snfs
deg: 5
c5: 2200
c0: -31
skew: 0.43
m: 100000000000000000000000000000000
rlim: 4500000
alim: 4500000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2500000
)
Primes: RFBsize:315948, AFBsize:315573, largePrimes:5606089 encountered
Relations: rels:5690538, finalFF:717744
Max relations in full relation-set: 28
Initial matrix: 631588 x 717744 with sparse part having weight 42037180.
Pruned matrix : 552185 x 555406 with weight 26967299.
Total sieving time: 44.45 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.5,2.5,100000
total time: 44.63 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

Jun 29, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(22·10¹⁵²-31)/9 = 2(4)₁₅₁1_<153> = 241 · 33589 · 43063 · C141

C141 = P36 · P41 · P65

P36 = 267966650482880119367198545606586717_<36>

P41 = 31215354255566197538002781232347164771547_<41>

P65 = 83832565493279521861357860130355126983160895444458139420999716557_<65>

Number: 24441_152
N=701232074521790742830270859869370784937896181312621274744822033496199307723301462181157327064017251111525772069827393633543232268035105331843
  ( 141 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=267966650482880119367198545606586717 (pp36)
 r2=31215354255566197538002781232347164771547 (pp41)
 r3=83832565493279521861357860130355126983160895444458139420999716557 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 44.29 hours.
Scaled time: 29.94 units (timescale=0.676).
Factorization parameters were as follows:
name: 24441_152
n: 701232074521790742830270859869370784937896181312621274744822033496199307723301462181157327064017251111525772069827393633543232268035105331843
m: 1000000000000000000000000000000
c5: 2200
c0: -31
skew: 0.43
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2400001)
Primes: RFBsize:176302, AFBsize:176210, largePrimes:5703677 encountered
Relations: rels:5676502, finalFF:516785
Max relations in full relation-set: 28
Initial matrix: 352579 x 516785 with sparse part having weight 48496265.
Pruned matrix : 293926 x 295752 with weight 26826377.
Total sieving time: 40.17 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 3.70 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 44.29 hours.
 --------- CPU info (if available) ----------

Jun 29, 2008

By Serge Batalov / pol51, Msieve 1.36, GMP-ECM

(7·10¹⁸⁰+17)/3 = 2(3)₁₇₉9_<181> = 4739322601106537_<16> · 54789725825058929_<17> · 5635025408798334073151006813_<28> · C121

C121 = P47 · P74

P47 = 41874999678888405957858413767086436069870427179_<47>

P74 = 38081205768930982523881149611719815860882075982791143081161151118407749709_<74>

Number: 23339_180
N=1594650479345668205679297248996417788309645764071629470283797649136969454552884601269365941059206432039370206471942940911
  (121 digits)
Divisors found:
 r1=41874999678888405957858413767086436069870427179 (prp47)
 r2=38081205768930982523881149611719815860882075982791143081161151118407749709 (prp74)
Version: 
Total time: 34 hours.
Scaled time: 97.648 units (timescale=2.872).
Factorization parameters were as follows:

# poly selected by pol51 - 1.5 hours

name: 23339_180
n: 1594650479345668205679297248996417788309645764071629470283797649136969454552884601269365941059206432039370206471942940911
skew: 35462.53
# norm 6.04e+16
c5: 38340
c4: -7645887822
c3: 2237821005459970
c2: 7602474157459019760
c1: -538696810513896633321935
c0: -1823549329867625284056766348
# alpha -5.80
Y1: 139319909443
Y0: -132985012360110909014155
# Murphy_E 2.48e-10
# M 788889806718177053534508787704877298154248623318878955959190838689725553459502855482663675053605970537986455887147354079
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 4840001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 667726 x 667974
Total sieving time: 30:45:50 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 01:51:54 hours.
Time per square root: 00:38:04 hours.
Prototype def-par.txt line would be:
gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 0.00 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

Thu Jun 26 23:58:49 2008  Msieve v. 1.36
Thu Jun 26 23:58:49 2008  random seeds: 90f676d8 a0df0a85
Thu Jun 26 23:58:49 2008  factoring 1594650479345668205679297248996417788309645764071629470283797649136969454552884601269365941059206432039370206471942940911 (121 digits)
Thu Jun 26 23:58:51 2008  no P-1/P+1/ECM available, skipping
Thu Jun 26 23:58:51 2008  commencing number field sieve (121-digit input)
Thu Jun 26 23:58:51 2008  R0: -132985012360110909014155
Thu Jun 26 23:58:51 2008  R1:  139319909443
Thu Jun 26 23:58:51 2008  A0: -1823549329867625284056766348
Thu Jun 26 23:58:51 2008  A1: -538696810513896633321935
Thu Jun 26 23:58:51 2008  A2:  7602474157459019760
Thu Jun 26 23:58:51 2008  A3:  2237821005459970
Thu Jun 26 23:58:51 2008  A4: -7645887822
Thu Jun 26 23:58:51 2008  A5:  38340
Thu Jun 26 23:58:51 2008  size score = 1.875082e-12, Murphy alpha = -5.801511, combined = 1.296806e-11
Thu Jun 26 23:58:51 2008  generating factor base
Thu Jun 26 23:58:54 2008  factor base complete:
Thu Jun 26 23:58:54 2008  348513 rational roots (max prime = 4999999)
Thu Jun 26 23:58:54 2008  348157 algebraic roots (max prime = 4999999)
Thu Jun 26 23:58:54 2008  a range: [-4000000, 4000000]
Thu Jun 26 23:58:54 2008  b range: [1, 300]
Thu Jun 26 23:58:54 2008  number of hash buckets: 77
Thu Jun 26 23:58:54 2008  sieve block size: 65536
Thu Jun 26 23:58:54 2008  
Thu Jun 26 23:58:54 2008  maximum RFB prime: 4999999
Thu Jun 26 23:58:54 2008  RFB entries: 348513
Thu Jun 26 23:58:54 2008  medium RFB entries: 6542
Thu Jun 26 23:58:54 2008  resieved RFB entries: 6374
Thu Jun 26 23:58:54 2008  small RFB prime powers: 25
Thu Jun 26 23:58:54 2008  projective RFB roots: 5
Thu Jun 26 23:58:54 2008  RFB trial factoring cutoff: 58 or 87 bits
Thu Jun 26 23:58:54 2008  single large prime RFB range: 22 - 27 bits
Thu Jun 26 23:58:54 2008  double large prime RFB range: 45 - 52 bits
Thu Jun 26 23:58:54 2008  triple large prime RFB range: 70 - 79 bits
Thu Jun 26 23:58:54 2008  ...

Sat Jun 28 14:45:50 2008  
Sat Jun 28 14:45:50 2008  Msieve v. 1.36
Sat Jun 28 14:45:50 2008  random seeds: 6a3598f8 87614cc3
Sat Jun 28 14:45:50 2008  factoring 1594650479345668205679297248996417788309645764071629470283797649136969454552884601269365941059206432039370206471942940911 (121 digits)
Sat Jun 28 14:45:51 2008  no P-1/P+1/ECM available, skipping
Sat Jun 28 14:45:51 2008  commencing number field sieve (121-digit input)
Sat Jun 28 14:45:51 2008  R0: -132985012360110909014155
Sat Jun 28 14:45:51 2008  R1:  139319909443
Sat Jun 28 14:45:51 2008  A0: -1823549329867625284056766348
Sat Jun 28 14:45:51 2008  A1: -538696810513896633321935
Sat Jun 28 14:45:51 2008  A2:  7602474157459019760
Sat Jun 28 14:45:51 2008  A3:  2237821005459970
Sat Jun 28 14:45:51 2008  A4: -7645887822
Sat Jun 28 14:45:51 2008  A5:  38340
Sat Jun 28 14:45:51 2008  size score = 1.875082e-12, Murphy alpha = -5.801511, combined = 1.296806e-11
Sat Jun 28 14:45:53 2008  restarting with 9447173 relations
Sat Jun 28 14:45:53 2008  
Sat Jun 28 14:45:53 2008  commencing relation filtering
Sat Jun 28 14:45:53 2008  commencing duplicate removal, pass 1
Sat Jun 28 14:47:13 2008  found 1803884 hash collisions in 9447173 relations
Sat Jun 28 14:47:13 2008  commencing duplicate removal, pass 2
Sat Jun 28 14:47:20 2008  found 1954127 duplicates and 7493046 unique relations
Sat Jun 28 14:47:20 2008  memory use: 65.3 MB
Sat Jun 28 14:47:22 2008  ignoring smallest 334421 rational and 334153 algebraic ideals
Sat Jun 28 14:47:22 2008  filtering rational ideals above 4784128
Sat Jun 28 14:47:22 2008  filtering algebraic ideals above 4784128
Sat Jun 28 14:47:22 2008  need 1002861 more relations than ideals
Sat Jun 28 14:47:22 2008  commencing singleton removal, pass 1
Sat Jun 28 14:48:31 2008  relations with 0 large ideals: 149207
Sat Jun 28 14:48:31 2008  relations with 1 large ideals: 1077069
Sat Jun 28 14:48:31 2008  relations with 2 large ideals: 2678793
Sat Jun 28 14:48:31 2008  relations with 3 large ideals: 2659073
Sat Jun 28 14:48:31 2008  relations with 4 large ideals: 899179
Sat Jun 28 14:48:31 2008  relations with 5 large ideals: 29496
Sat Jun 28 14:48:31 2008  relations with 6 large ideals: 229
Sat Jun 28 14:48:31 2008  relations with 7+ large ideals: 0
Sat Jun 28 14:48:31 2008  7493046 relations and about 7336098 large ideals
Sat Jun 28 14:48:31 2008  commencing singleton removal, pass 2
Sat Jun 28 14:49:38 2008  found 3525823 singletons
Sat Jun 28 14:49:38 2008  current dataset: 3967223 relations and about 3186249 large ideals
Sat Jun 28 14:49:38 2008  commencing singleton removal, pass 3
Sat Jun 28 14:50:14 2008  found 677892 singletons
Sat Jun 28 14:50:14 2008  current dataset: 3289331 relations and about 2463551 large ideals
Sat Jun 28 14:50:14 2008  commencing singleton removal, pass 4
Sat Jun 28 14:50:44 2008  found 196603 singletons
Sat Jun 28 14:50:44 2008  current dataset: 3092728 relations and about 2262445 large ideals
Sat Jun 28 14:50:44 2008  commencing singleton removal, final pass
Sat Jun 28 14:51:13 2008  memory use: 48.8 MB
Sat Jun 28 14:51:14 2008  commencing in-memory singleton removal
Sat Jun 28 14:51:14 2008  begin with 3092728 relations and 2380225 unique ideals
Sat Jun 28 14:51:18 2008  reduce to 2697937 relations and 1977905 ideals in 14 passes
Sat Jun 28 14:51:18 2008  max relations containing the same ideal: 39
Sat Jun 28 14:51:19 2008  filtering rational ideals above 720000
Sat Jun 28 14:51:19 2008  filtering algebraic ideals above 720000
Sat Jun 28 14:51:19 2008  need 116384 more relations than ideals
Sat Jun 28 14:51:19 2008  commencing singleton removal, final pass
Sat Jun 28 14:51:49 2008  keeping 2366367 ideals with weight <= 20, new excess is 279161
Sat Jun 28 14:51:50 2008  memory use: 67.1 MB
Sat Jun 28 14:51:51 2008  commencing in-memory singleton removal
Sat Jun 28 14:51:52 2008  begin with 2697937 relations and 2366367 unique ideals
Sat Jun 28 14:51:57 2008  reduce to 2684931 relations and 2353350 ideals in 12 passes
Sat Jun 28 14:51:57 2008  max relations containing the same ideal: 20
Sat Jun 28 14:52:00 2008  removing 147313 relations and 135061 ideals in 12252 cliques
Sat Jun 28 14:52:00 2008  commencing in-memory singleton removal
Sat Jun 28 14:52:00 2008  begin with 2537618 relations and 2353350 unique ideals
Sat Jun 28 14:52:03 2008  reduce to 2532155 relations and 2212784 ideals in 7 passes
Sat Jun 28 14:52:03 2008  max relations containing the same ideal: 20
Sat Jun 28 14:52:05 2008  removing 108716 relations and 96464 ideals in 12252 cliques
Sat Jun 28 14:52:05 2008  commencing in-memory singleton removal
Sat Jun 28 14:52:05 2008  begin with 2423439 relations and 2212784 unique ideals
Sat Jun 28 14:52:08 2008  reduce to 2420149 relations and 2113014 ideals in 7 passes
Sat Jun 28 14:52:08 2008  max relations containing the same ideal: 20
Sat Jun 28 14:52:09 2008  relations with 0 large ideals: 14446
Sat Jun 28 14:52:09 2008  relations with 1 large ideals: 117305
Sat Jun 28 14:52:09 2008  relations with 2 large ideals: 394599
Sat Jun 28 14:52:09 2008  relations with 3 large ideals: 691417
Sat Jun 28 14:52:09 2008  relations with 4 large ideals: 675705
Sat Jun 28 14:52:09 2008  relations with 5 large ideals: 376977
Sat Jun 28 14:52:09 2008  relations with 6 large ideals: 123053
Sat Jun 28 14:52:09 2008  relations with 7+ large ideals: 26647
Sat Jun 28 14:52:09 2008  commencing 2-way merge
Sat Jun 28 14:52:11 2008  reduce to 1418089 relation sets and 1110954 unique ideals
Sat Jun 28 14:52:11 2008  commencing full merge
Sat Jun 28 14:52:32 2008  memory use: 108.3 MB
Sat Jun 28 14:52:32 2008  found 697143 cycles, need 671154
Sat Jun 28 14:52:32 2008  weight of 671154 cycles is about 47207664 (70.34/cycle)
Sat Jun 28 14:52:32 2008  distribution of cycle lengths:
Sat Jun 28 14:52:32 2008  1 relations: 82867
Sat Jun 28 14:52:32 2008  2 relations: 77630
Sat Jun 28 14:52:32 2008  3 relations: 77110
Sat Jun 28 14:52:32 2008  4 relations: 70420
Sat Jun 28 14:52:32 2008  5 relations: 62652
Sat Jun 28 14:52:32 2008  6 relations: 53841
Sat Jun 28 14:52:32 2008  7 relations: 45748
Sat Jun 28 14:52:32 2008  8 relations: 39137
Sat Jun 28 14:52:32 2008  9 relations: 32448
Sat Jun 28 14:52:32 2008  10+ relations: 129301
Sat Jun 28 14:52:32 2008  heaviest cycle: 20 relations
Sat Jun 28 14:52:32 2008  commencing cycle optimization
Sat Jun 28 14:52:34 2008  start with 3953499 relations
Sat Jun 28 14:52:43 2008  pruned 44706 relations
Sat Jun 28 14:52:43 2008  memory use: 133.5 MB
Sat Jun 28 14:52:43 2008  distribution of cycle lengths:
Sat Jun 28 14:52:43 2008  1 relations: 82867
Sat Jun 28 14:52:43 2008  2 relations: 78135
Sat Jun 28 14:52:43 2008  3 relations: 78214
Sat Jun 28 14:52:43 2008  4 relations: 71049
Sat Jun 28 14:52:43 2008  5 relations: 63458
Sat Jun 28 14:52:43 2008  6 relations: 54339
Sat Jun 28 14:52:43 2008  7 relations: 46219
Sat Jun 28 14:52:43 2008  8 relations: 39107
Sat Jun 28 14:52:43 2008  9 relations: 32511
Sat Jun 28 14:52:43 2008  10+ relations: 125255
Sat Jun 28 14:52:43 2008  heaviest cycle: 20 relations
Sat Jun 28 14:52:44 2008  elapsed time 00:06:54
Sat Jun 28 14:52:45 2008  
Sat Jun 28 14:52:45 2008  
Sat Jun 28 14:52:45 2008  Msieve v. 1.36
Sat Jun 28 14:52:45 2008  random seeds: 4fe81a4b 0280ad61
Sat Jun 28 14:52:45 2008  factoring 1594650479345668205679297248996417788309645764071629470283797649136969454552884601269365941059206432039370206471942940911 (121 digits)
Sat Jun 28 14:52:46 2008  no P-1/P+1/ECM available, skipping
Sat Jun 28 14:52:46 2008  commencing number field sieve (121-digit input)
Sat Jun 28 14:52:46 2008  R0: -132985012360110909014155
Sat Jun 28 14:52:46 2008  R1:  139319909443
Sat Jun 28 14:52:46 2008  A0: -1823549329867625284056766348
Sat Jun 28 14:52:46 2008  A1: -538696810513896633321935
Sat Jun 28 14:52:46 2008  A2:  7602474157459019760
Sat Jun 28 14:52:46 2008  A3:  2237821005459970
Sat Jun 28 14:52:46 2008  A4: -7645887822
Sat Jun 28 14:52:46 2008  A5:  38340
Sat Jun 28 14:52:46 2008  size score = 1.875082e-12, Murphy alpha = -5.801511, combined = 1.296806e-11
Sat Jun 28 14:52:46 2008  
Sat Jun 28 14:52:46 2008  commencing linear algebra
Sat Jun 28 14:52:46 2008  read 671154 cycles
Sat Jun 28 14:52:48 2008  cycles contain 2240490 unique relations
Sat Jun 28 14:53:09 2008  read 2240490 relations
Sat Jun 28 14:53:13 2008  using 32 quadratic characters above 134214782
Sat Jun 28 14:53:39 2008  building initial matrix
Sat Jun 28 14:54:06 2008  memory use: 294.3 MB
Sat Jun 28 14:54:09 2008  read 671154 cycles
Sat Jun 28 14:54:10 2008  matrix is 670952 x 671154 (204.8 MB) with weight 68700036 (102.36/col)
Sat Jun 28 14:54:10 2008  sparse part has weight 45644834 (68.01/col)
Sat Jun 28 14:54:24 2008  filtering completed in 2 passes
Sat Jun 28 14:54:24 2008  matrix is 667774 x 667974 (204.4 MB) with weight 68497158 (102.54/col)
Sat Jun 28 14:54:24 2008  sparse part has weight 45560828 (68.21/col)
Sat Jun 28 14:54:32 2008  read 667974 cycles
Sat Jun 28 14:54:33 2008  matrix is 667774 x 667974 (204.4 MB) with weight 68497158 (102.54/col)
Sat Jun 28 14:54:33 2008  sparse part has weight 45560828 (68.21/col)
Sat Jun 28 14:54:33 2008  saving the first 48 matrix rows for later
Sat Jun 28 14:54:34 2008  matrix is 667726 x 667974 (199.0 MB) with weight 53617419 (80.27/col)
Sat Jun 28 14:54:34 2008  sparse part has weight 45486108 (68.10/col)
Sat Jun 28 14:54:34 2008  matrix includes 64 packed rows
Sat Jun 28 14:54:34 2008  using block size 43690 for processor cache size 1024 kB
Sat Jun 28 14:54:38 2008  commencing Lanczos iteration
Sat Jun 28 14:54:38 2008  memory use: 183.9 MB
Sat Jun 28 16:44:37 2008  lanczos halted after 10561 iterations (dim = 667725)
Sat Jun 28 16:44:39 2008  recovered 43 nontrivial dependencies
Sat Jun 28 16:44:39 2008  elapsed time 01:51:54
Sat Jun 28 16:44:40 2008  
Sat Jun 28 16:44:40 2008  
Sat Jun 28 16:44:40 2008  Msieve v. 1.36
Sat Jun 28 16:44:40 2008  random seeds: 5793e7f0 d0222ab8
Sat Jun 28 16:44:40 2008  factoring 1594650479345668205679297248996417788309645764071629470283797649136969454552884601269365941059206432039370206471942940911 (121 digits)
Sat Jun 28 16:44:40 2008  no P-1/P+1/ECM available, skipping
Sat Jun 28 16:44:40 2008  commencing number field sieve (121-digit input)
Sat Jun 28 16:44:40 2008  R0: -132985012360110909014155
Sat Jun 28 16:44:40 2008  R1:  139319909443
Sat Jun 28 16:44:40 2008  A0: -1823549329867625284056766348
Sat Jun 28 16:44:40 2008  A1: -538696810513896633321935
Sat Jun 28 16:44:40 2008  A2:  7602474157459019760
Sat Jun 28 16:44:40 2008  A3:  2237821005459970
Sat Jun 28 16:44:40 2008  A4: -7645887822
Sat Jun 28 16:44:40 2008  A5:  38340
Sat Jun 28 16:44:40 2008  size score = 1.875082e-12, Murphy alpha = -5.801511, combined = 1.296806e-11
Sat Jun 28 16:44:40 2008  
Sat Jun 28 16:44:40 2008  commencing square root phase
Sat Jun 28 16:44:40 2008  reading relations for dependency 1
Sat Jun 28 16:44:41 2008  read 333636 cycles
Sat Jun 28 16:44:41 2008  cycles contain 1366577 unique relations
Sat Jun 28 16:44:54 2008  read 1366577 relations
Sat Jun 28 16:45:04 2008  multiplying 1949326 relations
Sat Jun 28 16:52:18 2008  multiply complete, coefficients have about 89.97 million bits
Sat Jun 28 16:52:21 2008  initial square root is modulo 2871293
Sat Jun 28 17:03:37 2008  reading relations for dependency 2
Sat Jun 28 17:03:37 2008  read 333906 cycles
Sat Jun 28 17:03:38 2008  cycles contain 1370087 unique relations
Sat Jun 28 17:03:51 2008  read 1370087 relations
Sat Jun 28 17:04:00 2008  multiplying 1955116 relations
Sat Jun 28 17:11:15 2008  multiply complete, coefficients have about 90.24 million bits
Sat Jun 28 17:11:19 2008  initial square root is modulo 2999401
Sat Jun 28 17:22:44 2008  prp47 factor: 41874999678888405957858413767086436069870427179
Sat Jun 28 17:22:44 2008  prp74 factor: 38081205768930982523881149611719815860882075982791143081161151118407749709
Sat Jun 28 17:22:44 2008  elapsed time 00:38:04

Total time: 34 hours.

(8·10¹⁶⁸-17)/9 = (8)₁₆₇7_<168> = 3947 · 71699 · 373247252387_<12> · 1024799923094265919_<19> · C130

C130 = P41 · P90

P41 = 13086962130596681403157479104708270412239_<41>

P90 = 627469619736798457013692142254079987778839619064291230581747063260251518592308215913277437_<90>

Jun 28, 2008

By Sinkiti Sibata / GGNFS

(22·10¹⁵⁷-31)/9 = 2(4)₁₅₆1_<158> = 3 · 7³ · 18541 · 1732231 · 3794897 · C138

C138 = P44 · P94

P44 = 44098693698355178723007115893291109054904999_<44>

P94 = 4419774566759251381250748538579444137486855579222989929121298784868474730416401309522649387033_<94>

Number: 24441_157
N=194906284835296689056161059734252486653472926503376515699092856713705334417156440133625881676221606796262345126825254838818544669397477967
  ( 138 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=44098693698355178723007115893291109054904999 (pp44)
 r2=4419774566759251381250748538579444137486855579222989929121298784868474730416401309522649387033 (pp94)
Version: GGNFS-0.77.1-20060513-k8
Total time: 54.43 hours.
Scaled time: 108.85 units (timescale=2.000).
Factorization parameters were as follows:
name: 24441_157
n: 194906284835296689056161059734252486653472926503376515699092856713705334417156440133625881676221606796262345126825254838818544669397477967
m: 10000000000000000000000000000000
c5: 2200
c0: -31
skew: 0.43
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3700001)
Primes: RFBsize:283146, AFBsize:282969, largePrimes:5939096 encountered
Relations: rels:6178732, finalFF:832302
Max relations in full relation-set: 28
Initial matrix: 566182 x 832302 with sparse part having weight 55094693.
Pruned matrix : 372755 x 375649 with weight 39705875.
Total sieving time: 52.04 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.03 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 54.43 hours.
 --------- CPU info (if available) ----------

Jun 27, 2008 (4th)

By suberi / GMP-ECM

(16·10²⁴⁰-61)/9 = 1(7)₂₃₉1_<241> = 214259 · 45971639314341857839_<20> · C216

C216 = P43 · P173

P43 = 3635546933168771123588232262171985799019073_<43>

P173 = 49645358754231505271704520463941124503054131985354822418891186123680825347035422254985426027429954370789824305822464117472409850554663118163426845863590649176484170127543527_<173>

Jun 27, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(13·10¹⁷²+41)/9 = 1(4)₁₇₁9_<173> = 3547 · C169

C169 = P78 · P91

P78 = 695174701333859421685033528060504335793719122110800973735698497489652426318743_<78>

P91 = 5857950471415925447371678650915658511220611799017059207971764941934442613310213419314598469_<91>

Number: n
N=4072298969395106976161388340694796854932180559471227641512389186479967421608244839144190708893274441625160542555524230178867900886508160260627134041286846474328853804467
  ( 169 digits)
SNFS difficulty: 173 digits.
Divisors found:

Thu Jun 26 22:17:23 2008  prp78 factor: 695174701333859421685033528060504335793719122110800973735698497489652426318743
Thu Jun 26 22:17:23 2008  prp91 factor: 5857950471415925447371678650915658511220611799017059207971764941934442613310213419314598469
Thu Jun 26 22:17:23 2008  elapsed time 01:59:04 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 136.56 hours.
Scaled time: 114.43 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_1_4_171_9
n: 4072298969395106976161388340694796854932180559471227641512389186479967421608244839144190708893274441625160542555524230178867900886508160260627134041286846474328853804467
type: snfs
deg: 5
c5: 1300
c0: 41
skew: 0.50
m: 10000000000000000000000000000000000
rlim: 6500000
alim: 6500000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6500000/6500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 6800177)
Primes: RFBsize:444757, AFBsize:445323, largePrimes:6021958 encountered
Relations: rels:6219222, finalFF:891387
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 136.26 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,6500000,6500000,27,27,48,48,2.5,2.5,100000
total time: 136.56 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(19·10¹⁶⁰+71)/9 = 2(1)₁₅₉9_<161> = 7 · 379 · 593389409 · 559762404127_<12> · C137

C137 = P67 · P70

P67 = 3099176592679107542715695147437752731506212235694176436016316355489_<67>

P70 = 7730080230344753874735172128135993331930898349569035397737365097724549_<70>

Number: n
N=23956883709415985088805146185238519992526664677894688593124161720632613338572606501599381490541484980237314702722541489720018966486199461
  ( 137 digits)
SNFS difficulty: 161 digits.
Divisors found:

Fri Jun 27 00:53:52 2008  prp67 factor: 3099176592679107542715695147437752731506212235694176436016316355489
Fri Jun 27 00:53:52 2008  prp70 factor: 7730080230344753874735172128135993331930898349569035397737365097724549
Fri Jun 27 00:53:52 2008  elapsed time 01:43:21 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 48.04 hours.
Scaled time: 84.50 units (timescale=1.759).
Factorization parameters were as follows:
name: KA_2_1_159_9
n: 23956883709415985088805146185238519992526664677894688593124161720632613338572606501599381490541484980237314702722541489720018966486199461
type: snfs
skew: 1.30
deg: 5
c5: 19
c0: 71
m: 100000000000000000000000000000000
rlim: 4200000
alim: 4200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2300131)
Primes: RFBsize:296314, AFBsize:296822, largePrimes:7204240 encountered
Relations: rels:6697074, finalFF:620996
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 47.72 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4200000,4200000,28,28,48,48,2.3,2.3,100000
total time: 48.04 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jun 27, 2008 (2nd)

By Serge Batalov / GMP-ECM

8·10¹⁷⁴-3 = 7(9)₁₇₃7_<175> = 73 · 383 · C171

C171 = P33 · C138

P33 = 804673696565514864785886378683159_<33>

C138 = [355589188251300183599349551020909011128214064008671840079518563313901833340223003003363699479461924771115130765652610192085570225362572237_<138>]

Jun 27, 2008

By Sinkiti Sibata / GGNFS

(22·10¹⁴³-31)/9 = 2(4)₁₄₂1_<144> = 1429 · 2131 · 8539 · 30697 · 101377089370163640052001_<24> · C106

C106 = P53 · P53

P53 = 51705751863367893367331438399782672546461708678915431_<53>

P53 = 58422867534690837233698901081105668200911196544155883_<53>

Number: 24441_143
N=3020798291895136359891852704095799554819730181878610339127208508607228112945999193267116836929465838130573
  ( 106 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=51705751863367893367331438399782672546461708678915431 (pp53)
 r2=58422867534690837233698901081105668200911196544155883 (pp53)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 21.09 hours.
Scaled time: 14.26 units (timescale=0.676).
Factorization parameters were as follows:
name: 24441_143
n: 3020798291895136359891852704095799554819730181878610339127208508607228112945999193267116836929465838130573
m: 20000000000000000000000000000
c5: 1375
c0: -62
skew: 0.54
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2650001)
Primes: RFBsize:100021, AFBsize:99985, largePrimes:2812854 encountered
Relations: rels:2793602, finalFF:225695
Max relations in full relation-set: 28
Initial matrix: 200072 x 225695 with sparse part having weight 25021839.
Pruned matrix : 193287 x 194351 with weight 20050117.
Total sieving time: 19.53 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.29 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 21.09 hours.
 --------- CPU info (if available) ----------

(22·10¹⁵⁴-31)/9 = 2(4)₁₅₃1_<155> = 3 · 179 · 1549 · 60258383 · 38677036373_<11> · C131

C131 = P35 · P96

P35 = 25070638326752702413568294387068201_<35>

P96 = 502942589916015173876187946749795727665325828159843838684451355988388130195810478642949230888423_<96>

Number: 24441_154
N=12609091770904717240693985056152712545732991754181146303169573493897991028211382495502130245846221909822164021358484594677522337023
  ( 131 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=25070638326752702413568294387068201 (pp35)
 r2=502942589916015173876187946749795727665325828159843838684451355988388130195810478642949230888423 (pp96)
Version: GGNFS-0.77.1-20060513-k8
Total time: 37.39 hours.
Scaled time: 73.43 units (timescale=1.964).
Factorization parameters were as follows:
name: 24441_154
n: 12609091770904717240693985056152712545732991754181146303169573493897991028211382495502130245846221909822164021358484594677522337023
m: 10000000000000000000000000000000
c5: 11
c0: -155
skew: 1.7
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2800001)
Primes: RFBsize:216816, AFBsize:216508, largePrimes:6026421 encountered
Relations: rels:6304162, finalFF:822234
Max relations in full relation-set: 28
Initial matrix: 433389 x 822234 with sparse part having weight 69650706.
Pruned matrix : 285741 x 287971 with weight 37845723.
Total sieving time: 35.53 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.54 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 37.39 hours.
 --------- CPU info (if available) ----------

Jun 26, 2008 (4th)

By suberi / GMP-ECM

2·10¹⁹²+3 = 2(0)₁₉₁3_<193> = 79 · 173 · 276519843869_<12> · 35108586452041_<14> · C164

C164 = P35 · C130

P35 = 10356144553255211560838847446569517_<35>

C130 = [1455522925575811754655315825187997365065439919940867408609722558444730235468189624497400802537194515833119641347147862725255416513_<130>]

Jun 26, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(7·10¹⁶⁴+17)/3 = 2(3)₁₆₃9_<165> = 96972986953_<11> · C154

C154 = P71 · P84

P71 = 20447108973637357731169193895657060177008590426856381850872885970740323_<71>

P84 = 117677680826937163671024204749611691538446639389633232890693130285209291102895498081_<84>

Number: n
N=2406168363633299719066077856603911691342633210075679056961401519069627139871496470530434083135582234263916180531155483725562058518778534518235727395820163
  ( 154 digits)
SNFS difficulty: 165 digits.
Divisors found:

Thu Jun 26 13:04:03 2008  prp71 factor: 20447108973637357731169193895657060177008590426856381850872885970740323
Thu Jun 26 13:04:03 2008  prp84 factor: 117677680826937163671024204749611691538446639389633232890693130285209291102895498081
Thu Jun 26 13:04:03 2008  elapsed time 02:18:29 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 79.25 hours.
Scaled time: 115.15 units (timescale=1.453).
Factorization parameters were as follows:
name: KA_2_3_163_9
n: 2406168363633299719066077856603911691342633210075679056961401519069627139871496470530434083135582234263916180531155483725562058518778534518235727395820163
skew: 1.89
deg: 5
c5: 7
c0: 170
m: 1000000000000000000000000000000000
type: snfs
rlim: 4800000
alim: 4800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3800081)
Primes: RFBsize:335439, AFBsize:336417, largePrimes:8020664 encountered
Relations: rels:7582836, finalFF:722525
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 78.95 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,4800000,4800000,28,28,48,48,2.5,2.5,100000
total time: 79.25 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(19·10¹⁵⁹+71)/9 = 2(1)₁₅₈9_<160> = 13 · 21427248679_<11> · 352051289081_<12> · C137

C137 = P66 · P71

P66 = 250401041858585819131096746756630366154245800973610054933853193899_<66>

P71 = 85972441214000396829052981243585775513440893313292234278082838842690863_<71>

Number: n
N=21527588851111722002830557879225910998694697479830930289731614802312922945498898793081333700260607997346333469572376218484361244054644837
  ( 137 digits)
SNFS difficulty: 161 digits.
Divisors found:

Thu Jun 26 14:22:48 2008  prp66 factor: 250401041858585819131096746756630366154245800973610054933853193899
Thu Jun 26 14:22:48 2008  prp71 factor: 85972441214000396829052981243585775513440893313292234278082838842690863
Thu Jun 26 14:22:48 2008  elapsed time 01:04:02 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 32.37 hours.
Scaled time: 59.20 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_1_158_9
n: 21527588851111722002830557879225910998694697479830930289731614802312922945498898793081333700260607997346333469572376218484361244054644837
skew: 2.06
deg: 5
c5: 19
c0: 710
m: 100000000000000000000000000000000
type: snfs
rlim: 4200000
alim: 4200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100097)
Primes: RFBsize:296314, AFBsize:296187, largePrimes:7325398 encountered
Relations: rels:6841474, finalFF:613001
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 32.20 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4200000,4200000,28,28,48,48,2.5,2.5,100000
total time: 32.37 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(7·10¹⁷⁰+17)/3 = 2(3)₁₆₉9_<171> = 239 · C168

C168 = P31 · P48 · P90

P31 = 2734097213579852352604376181511_<31>

P48 = 587102801544801723967976976231640540307396605327_<48>

P90 = 608206110816364789917478064076131806984451756354900504967234326972616286107690838688949133_<90>

Number: n
N=357079511576955902498941916492360411034102781813871575217201017566042447728954311622582640108988805296696748643381230960452338753179831491
  ( 138 digits)
SNFS difficulty: 170 digits.
Divisors found:

Thu Jun 26 19:55:29 2008  prp48 factor: 587102801544801723967976976231640540307396605327
Thu Jun 26 19:55:29 2008  prp90 factor: 608206110816364789917478064076131806984451756354900504967234326972616286107690838688949133
Thu Jun 26 19:55:29 2008  elapsed time 02:50:04 (Msieve 1.36)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 109.62 hours.
Scaled time: 143.49 units (timescale=1.309).
Factorization parameters were as follows:
name: KA_2_3_169_9
n: 357079511576955902498941916492360411034102781813871575217201017566042447728954311622582640108988805296696748643381230960452338753179831491
skew: 1.19
deg: 5
c5: 7
c0: 17
m: 10000000000000000000000000000000000
type: snfs
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4200113)
Primes: RFBsize:425648, AFBsize:426207, largePrimes:8293957 encountered
Relations: rels:7938547, finalFF:885064
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 109.19 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,48,48,2.5,2.5,100000
total time: 109.62 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jun 26, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(22·10¹⁴⁰-31)/9 = 2(4)₁₃₉1_<141> = 17 · 1447 · 8237 · 86711 · 93229 · 881417 · C117

C117 = P35 · P82

P35 = 63355190713391485500322124879334139_<35>

P82 = 2672420577333034720731187670756586117081501976010031863655603623277223815204027931_<82>

Number: 24441_140
N=169311715343326193553763454607944049710794497657459785323473749818757455099325376029901018323588244645974454037836409
  ( 117 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=63355190713391485500322124879334139 (pp35)
 r2=2672420577333034720731187670756586117081501976010031863655603623277223815204027931 (pp82)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 13.15 hours.
Scaled time: 8.89 units (timescale=0.676).
Factorization parameters were as follows:
name: 24441_140
n: 169311715343326193553763454607944049710794497657459785323473749818757455099325376029901018323588244645974454037836409
m: 10000000000000000000000000000
c5: 22
c0: -31
skew: 1.07
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1850001)
Primes: RFBsize:100021, AFBsize:99815, largePrimes:2696036 encountered
Relations: rels:2660778, finalFF:252054
Max relations in full relation-set: 28
Initial matrix: 199902 x 252054 with sparse part having weight 23135386.
Pruned matrix : 183699 x 184762 with weight 14732105.
Total sieving time: 12.01 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.92 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 13.15 hours.
 --------- CPU info (if available) ----------

(22·10¹⁵³-31)/9 = 2(4)₁₅₂1_<154> = 4450992226721_<13> · 3130978137030994435259_<22> · C120

C120 = P55 · P65

P55 = 4672251179457423783044554303760906137448973750934054087_<55>

P65 = 37541975175578769737137485685757194683231428146965223756007180237_<65>

Number: 24441_153
N=175405537793259231219488124213779154690238530622835181016940877487171118032255677027504477326241747103099776251715478619
  ( 120 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=4672251179457423783044554303760906137448973750934054087 (pp55)
 r2=37541975175578769737137485685757194683231428146965223756007180237 (pp65)
Version: GGNFS-0.77.1-20060513-k8
Total time: 37.78 hours.
Scaled time: 74.38 units (timescale=1.969).
Factorization parameters were as follows:
name: 24441_153
n: 175405537793259231219488124213779154690238530622835181016940877487171118032255677027504477326241747103099776251715478619
m: 2000000000000000000000000000000
c5: 1375
c0: -62
skew: 0.54
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2800001)
Primes: RFBsize:216816, AFBsize:216848, largePrimes:5787943 encountered
Relations: rels:5857389, finalFF:638086
Max relations in full relation-set: 28
Initial matrix: 433730 x 638086 with sparse part having weight 53254032.
Pruned matrix : 322563 x 324795 with weight 33104563.
Total sieving time: 35.94 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.51 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 37.78 hours.
 --------- CPU info (if available) ----------

Jun 26, 2008

By Serge Batalov / pol51, Msieve, GMP-ECM

(22·10¹⁵⁰-31)/9 = 2(4)₁₄₉1_<151> = 78839 · 47567413 · 613925800595764424450450712559_<30> · C109

C109 = P41 · P68

P41 = 45972127484749710794015017878432605888239_<41>

P68 = 23095057306620505652516576474633038696841517536460420603268895763763_<68>

Number: 24441_150
N=1061728918767558176817203458627519930862711303791793816419560970916391073286967729158741586433757396924083357
  ( 109 digits)
Divisors found:
 r1=45972127484749710794015017878432605888239 (p41)
 r2=23095057306620505652516576474633038696841517536460420603268895763763 (p68)

Version: Msieve v. 1.36; pol51 - gnfs,109
Total time: 9.60 hours.
Scaled time: 28.33 units (timescale=2.951).
Factorization parameters were as follows:
name: 24441_150
n: 1061728918767558176817203458627519930862711303791793816419560970916391073286967729158741586433757396924083357
skew: 11015.45
# norm 1.37e+14
c5: 3600
c4: 1023682614
c3: -5433223933674
c2: -100960073103402731
c1: 129616438775426891628
c0: 1513442468498894463493856
# alpha -4.31
Y1: 108792954869
Y0: -783319249020200496039
# Murphy_E 1.21e-09
# M 527144102954660051708727624048815718732776484104453757771420413640585603452113943932347220759815262186792022
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2700001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 429719 x 429967
Total sieving time: 5.50 hours. 
Total relation processing time: 0.00 hours. (see below)
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 5.60 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

Tue Jun 24 20:43:05 2008  Msieve v. 1.36
Tue Jun 24 20:43:05 2008  random seeds: 419df898 1074d5e8
Tue Jun 24 20:43:05 2008  factoring 1061728918767558176817203458627519930862711303791793816419560970916391073286967729158741586433757396924083357 (109 digits)
Tue Jun 24 20:43:05 2008  no P-1/P+1/ECM available, skipping
Tue Jun 24 20:43:05 2008  commencing number field sieve (109-digit input)
Tue Jun 24 20:43:05 2008  R0: -783319249020200496039
Tue Jun 24 20:43:05 2008  R1:  108792954869
Tue Jun 24 20:43:05 2008  A0:  1513442468498894463493856
Tue Jun 24 20:43:05 2008  A1:  129616438775426891628
Tue Jun 24 20:43:05 2008  A2: -100960073103402731
Tue Jun 24 20:43:05 2008  A3: -5433223933674
Tue Jun 24 20:43:05 2008  A4:  1023682614
Tue Jun 24 20:43:05 2008  A5:  3600
Tue Jun 24 20:43:05 2008  size score = 5.545366e-11, Murphy alpha = -4.305145, combined = 2.328970e-10
Tue Jun 24 20:43:05 2008  generating factor base
Tue Jun 24 20:43:07 2008  factor base complete:
Tue Jun 24 20:43:07 2008  230209 rational roots (max prime = 3199997)
Tue Jun 24 20:43:07 2008  229805 algebraic roots (max prime = 3199997)
Tue Jun 24 20:43:07 2008  a range: [-4000000, 4000000]
Tue Jun 24 20:43:07 2008  b range: [1, 300]
...
Wed Jun 25 02:46:14 2008  sparse part has weight 29438035 (67.80/col)
Wed Jun 25 02:46:28 2008  filtering completed in 3 passes
Wed Jun 25 02:46:28 2008  matrix is 429767 x 429967 (131.2 MB) with weight 43306866 (100.72/col)
Wed Jun 25 02:46:28 2008  sparse part has weight 29228734 (67.98/col)
Wed Jun 25 02:46:33 2008  read 429967 cycles
Wed Jun 25 02:46:34 2008  matrix is 429767 x 429967 (131.2 MB) with weight 43306866 (100.72/col)
Wed Jun 25 02:46:34 2008  sparse part has weight 29228734 (67.98/col)
Wed Jun 25 02:46:34 2008  saving the first 48 matrix rows for later
Wed Jun 25 02:46:34 2008  matrix is 429719 x 429967 (126.5 MB) with weight 33748060 (78.49/col)
Wed Jun 25 02:46:34 2008  sparse part has weight 28857124 (67.11/col)
Wed Jun 25 02:46:34 2008  matrix includes 64 packed rows
Wed Jun 25 02:46:34 2008  using block size 43690 for processor cache size 1024 kB
Wed Jun 25 02:46:37 2008  commencing Lanczos iteration
Wed Jun 25 02:46:37 2008  memory use: 116.5 MB
Wed Jun 25 03:22:14 2008  lanczos halted after 6796 iterations (dim = 429715)
Wed Jun 25 03:22:15 2008  recovered 41 nontrivial dependencies
Wed Jun 25 03:22:15 2008  elapsed time 00:36:53
Wed Jun 25 03:22:15 2008  
Wed Jun 25 03:22:15 2008  
Wed Jun 25 03:22:15 2008  Msieve v. 1.36
Wed Jun 25 03:22:15 2008  random seeds: 17402b89 00ef29ea
Wed Jun 25 03:22:15 2008  factoring 1061728918767558176817203458627519930862711303791793816419560970916391073286967729158741586433757396924083357 (109 digits)
Wed Jun 25 03:22:16 2008  no P-1/P+1/ECM available, skipping
Wed Jun 25 03:22:16 2008  commencing number field sieve (109-digit input)
Wed Jun 25 03:22:16 2008  R0: -783319249020200496039
Wed Jun 25 03:22:16 2008  R1:  108792954869
Wed Jun 25 03:22:16 2008  A0:  1513442468498894463493856
Wed Jun 25 03:22:16 2008  A1:  129616438775426891628
Wed Jun 25 03:22:16 2008  A2: -100960073103402731
Wed Jun 25 03:22:16 2008  A3: -5433223933674
Wed Jun 25 03:22:16 2008  A4:  1023682614
Wed Jun 25 03:22:16 2008  A5:  3600
Wed Jun 25 03:22:16 2008  size score = 5.545366e-11, Murphy alpha = -4.305145, combined = 2.328970e-10
Wed Jun 25 03:22:16 2008  
Wed Jun 25 03:22:16 2008  commencing square root phase
Wed Jun 25 03:22:16 2008  reading relations for dependency 1
Wed Jun 25 03:22:16 2008  read 215006 cycles
Wed Jun 25 03:22:17 2008  cycles contain 966311 unique relations
Wed Jun 25 03:22:26 2008  read 966311 relations
Wed Jun 25 03:22:31 2008  multiplying 1374744 relations
Wed Jun 25 03:25:41 2008  multiply complete, coefficients have about 57.91 million bits
Wed Jun 25 03:25:44 2008  initial square root is modulo 205847419
Wed Jun 25 03:32:07 2008  prp41 factor: 45972127484749710794015017878432605888239
Wed Jun 25 03:32:07 2008  prp68 factor: 23095057306620505652516576474633038696841517536460420603268895763763
Wed Jun 25 03:32:07 2008  elapsed time 00:09:52

(16·10¹⁸⁴-43)/9 = 1(7)₁₈₃3_<185> = 7 · 3598093 · 13132245417019_<14> · 107537092713773_<15> · 104005733668072867117900455439_<30> · C121

C121 = P43 · P78

P43 = 9530320599055730642353200206233150010763811_<43>

P78 = 504248918081124804358394041346970391553990768685952091678182150911229308328301_<78>

(22·10¹⁸⁴-31)/9 = 2(4)₁₈₃1_<185> = 3 · 7019 · 6705079 · 202293075931_<12> · 425042380540337999804473_<24> · 2233556149517112120304444591_<28> · C111

C111 = P45 · P67

P45 = 114423653990361075653055464062935164466831611_<45>

P67 = 7878686770508480786149343903599253200453322043489051808630270100369_<67>

Number: 24441_184
N=901508128927097743805796506111739621599509328568185510262339660197159877020209849161252647032352169836391964459
  ( 111 digits)
Divisors found:
 r1=114423653990361075653055464062935164466831611 (prp45)
 r2=7878686770508480786149343903599253200453322043489051808630270100369 (prp67)
Version: 
Total time: 10.00 hours.
Scaled time: 29.45 units (timescale=2.945).
Factorization parameters were as follows:
name: 24441_184
n: 901508128927097743805796506111739621599509328568185510262339660197159877020209849161252647032352169836391964459
skew: 46520.21
# norm 8.13e+15
c5: 18900
c4: -3935161950
c3: -315632321754924
c2: 6956788420149104008
c1: 165764613453978096609019
c0: -2648291551878358192286209268
# alpha -6.76
Y1: 308911050547
Y0: -2166227912833797164915
# Murphy_E 8.47e-10
# M 495691579157807496339000308739825919751575707403851431472491711303878872482938118133184764017988135434894218932
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 3100001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 429325 x 429573
Total sieving time: 8.90 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 00:38:19 hours.
Time per square root: 00:31:06 hours. (2nd dep.)
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 10.00 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

Jun 25, 2008 (4th)

By Robert Backstrom / Msieve, GGNFS

(22·10¹⁰⁸-31)/9 = 2(4)₁₀₇1_<109> = 17 · 181 · 104959 · 482753 · 21544099 · C87

C87 = P42 · P46

P42 = 138995389975794491309068904263146176694797_<42>

P46 = 5235754528978806667489969821427816016907360493_<46>

Wed Jun 25 05:45:44 2008  
Wed Jun 25 05:45:44 2008  
Wed Jun 25 05:45:44 2008  Msieve v. 1.36
Wed Jun 25 05:45:44 2008  random seeds: 2c2f2650 d595796d
Wed Jun 25 05:45:44 2008  factoring 727745742572941432727590326080685974558243874913479827895808647003715217085608116454921 (87 digits)
Wed Jun 25 05:45:44 2008  searching for 15-digit factors
Wed Jun 25 05:45:45 2008  commencing quadratic sieve (87-digit input)
Wed Jun 25 05:45:45 2008  using multiplier of 1
Wed Jun 25 05:45:45 2008  using 64kb Opteron sieve core
Wed Jun 25 05:45:45 2008  sieve interval: 11 blocks of size 65536
Wed Jun 25 05:45:45 2008  processing polynomials in batches of 10
Wed Jun 25 05:45:45 2008  using a sieve bound of 1499123 (56987 primes)
Wed Jun 25 05:45:45 2008  using large prime bound of 119929840 (26 bits)
Wed Jun 25 05:45:45 2008  using double large prime bound of 348392707234640 (42-49 bits)
Wed Jun 25 05:45:45 2008  using trial factoring cutoff of 49 bits
Wed Jun 25 05:45:45 2008  polynomial 'A' values have 11 factors
Wed Jun 25 06:18:28 2008  57110 relations (15937 full + 41173 combined from 597887 partial), need 57083
Wed Jun 25 06:18:29 2008  begin with 613823 relations
Wed Jun 25 06:18:29 2008  reduce to 136931 relations in 10 passes
Wed Jun 25 06:18:29 2008  attempting to read 136931 relations
Wed Jun 25 06:18:31 2008  recovered 136931 relations
Wed Jun 25 06:18:31 2008  recovered 114809 polynomials
Wed Jun 25 06:18:31 2008  attempting to build 57110 cycles
Wed Jun 25 06:18:31 2008  found 57110 cycles in 5 passes
Wed Jun 25 06:18:31 2008  distribution of cycle lengths:
Wed Jun 25 06:18:31 2008     length 1 : 15937
Wed Jun 25 06:18:31 2008     length 2 : 11207
Wed Jun 25 06:18:31 2008     length 3 : 9996
Wed Jun 25 06:18:31 2008     length 4 : 7557
Wed Jun 25 06:18:31 2008     length 5 : 5191
Wed Jun 25 06:18:31 2008     length 6 : 3117
Wed Jun 25 06:18:31 2008     length 7 : 1859
Wed Jun 25 06:18:31 2008     length 9+: 2246
Wed Jun 25 06:18:31 2008  largest cycle: 18 relations
Wed Jun 25 06:18:31 2008  matrix is 56987 x 57110 (13.0 MB) with weight 3192278 (55.90/col)
Wed Jun 25 06:18:31 2008  sparse part has weight 3192278 (55.90/col)
Wed Jun 25 06:18:32 2008  filtering completed in 3 passes
Wed Jun 25 06:18:32 2008  matrix is 52584 x 52648 (12.2 MB) with weight 2979847 (56.60/col)
Wed Jun 25 06:18:32 2008  sparse part has weight 2979847 (56.60/col)
Wed Jun 25 06:18:32 2008  saving the first 48 matrix rows for later
Wed Jun 25 06:18:32 2008  matrix is 52536 x 52648 (7.8 MB) with weight 2338595 (44.42/col)
Wed Jun 25 06:18:32 2008  sparse part has weight 1724452 (32.75/col)
Wed Jun 25 06:18:32 2008  matrix includes 64 packed rows
Wed Jun 25 06:18:32 2008  using block size 21059 for processor cache size 1024 kB
Wed Jun 25 06:18:32 2008  commencing Lanczos iteration
Wed Jun 25 06:18:32 2008  memory use: 7.7 MB
Wed Jun 25 06:18:48 2008  lanczos halted after 832 iterations (dim = 52534)
Wed Jun 25 06:18:48 2008  recovered 15 nontrivial dependencies
Wed Jun 25 06:18:48 2008  prp42 factor: 138995389975794491309068904263146176694797
Wed Jun 25 06:18:48 2008  prp46 factor: 5235754528978806667489969821427816016907360493
Wed Jun 25 06:18:48 2008  elapsed time 00:33:04

(11·10¹⁶⁸+61)/9 = 1(2)₁₆₇9_<169> = 284576113 · C160

C160 = P45 · P116

P45 = 411666912515401882965759279521788799204135831_<45>

P116 = 10432917434026609382438829606769439297165342068877860732100883252228761348457631305397697008539566408107238406463843_<116>

Number: n
N=4294886908593843300622432151296627704737193533254220188966535719820666122536511777508965491500062137057238610263195991513954729651614231663295725113169362258533
  ( 160 digits)
SNFS difficulty: 169 digits.
Divisors found:

Wed Jun 25 12:13:26 2008  prp45 factor: 411666912515401882965759279521788799204135831
Wed Jun 25 12:13:26 2008  prp116 factor: 10432917434026609382438829606769439297165342068877860732100883252228761348457631305397697008539566408107238406463843
Wed Jun 25 12:13:26 2008  elapsed time 02:24:39 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 101.65 hours.
Scaled time: 63.02 units (timescale=0.620).
Factorization parameters were as follows:
name: KA_1_2_167_9
n: 4294886908593843300622432151296627704737193533254220188966535719820666122536511777508965491500062137057238610263195991513954729651614231663295725113169362258533
type: snfs
deg: 5
c5: 11000
c0: 61
skew: 0.35
m: 1000000000000000000000000000000000
rlim: 5800000
alim: 5800000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5300093)
Primes: RFBsize:399993, AFBsize:401226, largePrimes:5866471 encountered
Relations: rels:6006996, finalFF:811405
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 101.36 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,5800000,5800000,27,27,48,48,2.5,2.5,100000
total time: 101.65 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

Jun 25, 2008 (3rd)

By suberi / GMP-ECM

2·10¹⁹⁰+3 = 2(0)₁₈₉3_<191> = 76949 · 1032007 · C180

C180 = P33 · C148

P33 = 209094547936744449194474908906729_<33>

C148 = [1204485741923092584911687923487690778909963227537014315607526677383436191113446013891831878203679688385334440434720800302150846416269081049293062249_<148>]

2·10¹⁹¹+3 = 2(0)₁₉₀3_<192> = 2221 · 283112539 · 5806007837521_<13> · C167

C167 = P40 · C128

P40 = 2980061483271130133454822323000539259581_<40>

C128 = [18383131354982444551956076518958438866176346336034655261991448351404481492241607264551622466419738184569706208252244605090183537_<128>]

Jun 25, 2008 (2nd)

By Serge Batalov / Msieve, Pol51

(22·10¹⁰⁶-31)/9 = 2(4)₁₀₅1_<107> = 3² · 19 · 229 · 2557 · C99

C99 = P46 · P53

P46 = 9631591007156665672864019700139260889641266659_<46>

P53 = 25346606237218165683573730083344826363369886203189673_<53>

Number: vs
N=244128144696331536415917888750242967148917292732461485370154311413947192044016455404328933748012507
  ( 99 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=9631591007156665672864019700139260889641266659
 r2=25346606237218165683573730083344826363369886203189673
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
#res:5730
n: 244128144696331536415917888750242967148917292732461485370154311413947192044016455404328933748012507
name: 24441_106
Y0: -1000000000000000000000
Y1: 1
c5: 220
c0: -31
skew: 0.68
type: snfsFactor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 350001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 67178 x 67407
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,107,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 0.00 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

Msieve v. 1.36
Tue Jun 24 17:07:38 2008
random seeds: 6635feda 25f502d1
factoring 244128144696331536415917888750242967148917292732461485370154311413947192044016455404328933748012507 (99 digits)
no P-1/P+1/ECM available, skipping
commencing number field sieve (99-digit input)
R0: -1000000000000000000000
R1:  1
A0: -31
A1:  0
A2:  0
A3:  0
A4:  0
A5:  220
size score = 1.115181e-07, Murphy alpha = -0.098283, combined = 1.152321e-07

commencing square root phase
reading relations for dependency 1
read 33759 cycles
cycles contain 150066 unique relations
read 150066 relations
multiplying 248786 relations
multiply complete, coefficients have about 6.50 million bits
initial square root is modulo 29586071
reading relations for dependency 2
read 33549 cycles
cycles contain 149442 unique relations
read 149442 relations
multiplying 247648 relations
multiply complete, coefficients have about 6.47 million bits
initial square root is modulo 27412771
reading relations for dependency 3
read 33871 cycles
cycles contain 150712 unique relations
read 150712 relations
multiplying 250366 relations
multiply complete, coefficients have about 6.54 million bits
initial square root is modulo 33020791
prp46 factor: 9631591007156665672864019700139260889641266659
prp53 factor: 25346606237218165683573730083344826363369886203189673
elapsed time 00:02:09

# 25 minutes. total! :-)

(22·10¹¹⁶-31)/9 = 2(4)₁₁₅1_<117> = 106816327 · 2341301839_<10> · C99

C99 = P44 · P56

P44 = 74779328381478672337559932601827975176268631_<44>

P56 = 13070841991426997088803843630742662043950302826857829687_<56>

Number: s99
N=977428785499340052582306526584012835139359060523885018765669359761522729518706248747753495558648497
  ( 99 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=74779328381478672337559932601827975176268631
 r2=13070841991426997088803843630742662043950302826857829687
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.943).
Factorization parameters were as follows:
#res: 4974
name: 24441_116
n: 977428785499340052582306526584012835139359060523885018765669359761522729518706248747753495558648497
Y1: 1
Y0: -100000000000000000000000
c5: 220
c0: -31
skew: 0.68
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [300000, 400001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 99420 x 99635
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 0.00 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)
Calibrating delay using timer specific routine.. 5600.56 BogoMIPS (lpj=11201124)

___________screen log_________

Msieve v. 1.36
Tue Jun 24 17:41:00 2008
random seeds: a8b54151 bdb568c5
factoring 977428785499340052582306526584012835139359060523885018765669359761522729518706248747753495558648497 (99 digits)
no P-1/P+1/ECM available, skipping
commencing number field sieve (99-digit input)
R0: -100000000000000000000000
R1:  1
A0: -31
A1:  0
A2:  0
A3:  0
A4:  0
A5:  220
size score = 2.402585e-08, Murphy alpha = -0.098283, combined = 2.482600e-08

commencing linear algebra
read 99882 cycles
cycles contain 356766 unique relations
read 356766 relations
using 32 quadratic characters above 33550338
building initial matrix
memory use: 48.3 MB
read 99882 cycles
matrix is 99716 x 99882 (30.2 MB) with weight 9788440 (98.00/col)
sparse part has weight 6817281 (68.25/col)
filtering completed in 2 passes
matrix is 99468 x 99635 (30.2 MB) with weight 9773494 (98.09/col)
sparse part has weight 6809835 (68.35/col)
read 99635 cycles
matrix is 99468 x 99635 (30.2 MB) with weight 9773494 (98.09/col)
sparse part has weight 6809835 (68.35/col)
saving the first 48 matrix rows for later
matrix is 99420 x 99635 (28.8 MB) with weight 7580439 (76.08/col)
sparse part has weight 6566360 (65.90/col)
matrix includes 64 packed rows
using block size 39854 for processor cache size 1024 kB
commencing Lanczos iteration
memory use: 25.9 MB
linear algebra completed 96425 out of 99635 dimensions (96.8%)
lanczos halted after 1573 iterations (dim = 99418)
recovered 50 nontrivial dependencies
elapsed time 00:03:35
=>nice -n 19  "/depts/BioInf/Batalov/MERSE/ggbin/msieve" -s s99.dat -l ggnfs.log -i s99.ini -v -nf s99.fb -t 1 -nc3

Msieve v. 1.36
Tue Jun 24 17:44:35 2008
random seeds: ac726169 0a8b790a
factoring 977428785499340052582306526584012835139359060523885018765669359761522729518706248747753495558648497 (99 digits)
no P-1/P+1/ECM available, skipping
commencing number field sieve (99-digit input)
R0: -100000000000000000000000
R1:  1
A0: -31
A1:  0
A2:  0
A3:  0
A4:  0
A5:  220
size score = 2.402585e-08, Murphy alpha = -0.098283, combined = 2.482600e-08

commencing square root phase
reading relations for dependency 1
read 49629 cycles
cycles contain 223442 unique relations
read 223442 relations
multiplying 346538 relations
multiply complete, coefficients have about 9.09 million bits
initial square root is modulo 168731

prp44 factor: 74779328381478672337559932601827975176268631
prp56 factor: 13070841991426997088803843630742662043950302826857829687

elapsed time 00:01:08
-> Computing time scale for this machine...
sumName = s117-s99.txt
-> Factorization summary written to s117-s99.txt.

Start: 2008-06-24 17:10 
Finish: 2008-06-24 17:47

(22·10¹³⁷-31)/9 = 2(4)₁₃₆1_<138> = 107 · 6260299 · C129

C129 = P40 · P89

P40 = 4230643473881898745530247026033528758893_<40>

P89 = 86257107301040353258760835519646764214155993239698998324248576055986190717546106427894309_<89>

Tue Jun 24 17:18:34 2008  Msieve v. 1.36
Tue Jun 24 17:18:34 2008  random seeds: 61323b09 a250f5eb
Tue Jun 24 17:18:34 2008  factoring 364923068079077051345646208213109615163068484659184173606608115958004538540567489875997792910118943908918763856606819776147839937 (129 digits)
Tue Jun 24 17:18:35 2008  no P-1/P+1/ECM available, skipping
Tue Jun 24 17:18:35 2008  commencing number field sieve (129-digit input)
Tue Jun 24 17:18:35 2008  R0: -1000000000000000000000000000
Tue Jun 24 17:18:35 2008  R1:  1
Tue Jun 24 17:18:35 2008  A0: -31
Tue Jun 24 17:18:35 2008  A1:  0
Tue Jun 24 17:18:35 2008  A2:  0
Tue Jun 24 17:18:35 2008  A3:  0
Tue Jun 24 17:18:35 2008  A4:  0
Tue Jun 24 17:18:35 2008  A5:  2200
Tue Jun 24 17:18:35 2008  size score = 7.036318e-10, Murphy alpha = -0.077176, combined = 7.219677e-10
Tue Jun 24 17:18:35 2008  generating factor base
Tue Jun 24 17:18:36 2008  factor base complete:
Tue Jun 24 17:18:36 2008  78498 rational roots (max prime = 999983)
Tue Jun 24 17:18:36 2008  64300 algebraic roots (max prime = 799999)
Tue Jun 24 17:18:36 2008  a range: [-2000000, 2000000]
Tue Jun 24 17:18:36 2008  b range: [1, 200]
Tue Jun 24 17:18:36 2008  number of hash buckets: 16
Tue Jun 24 17:18:36 2008  sieve block size: 65536
Tue Jun 24 17:18:36 2008  
Tue Jun 24 17:18:36 2008  maximum RFB prime: 999983
Tue Jun 24 17:18:36 2008  RFB entries: 78498
Tue Jun 24 17:18:36 2008  medium RFB entries: 6542
Tue Jun 24 17:18:36 2008  resieved RFB entries: 6374
Tue Jun 24 17:18:36 2008  small RFB prime powers: 28
Tue Jun 24 17:18:36 2008  projective RFB roots: 0
Tue Jun 24 17:18:36 2008  RFB trial factoring cutoff: 52 or 78 bits
Tue Jun 24 17:18:36 2008  single large prime RFB range: 20 - 25 bits
Tue Jun 24 17:18:36 2008  double large prime RFB range: 40 - 48 bits
Tue Jun 24 17:18:36 2008  triple large prime RFB range: 63 - 73 bits
...
Tue Jun 24 19:41:53 2008  restarting with 1854989 relations
Tue Jun 24 19:41:53 2008  
Tue Jun 24 19:41:53 2008  commencing relation filtering
Tue Jun 24 19:41:53 2008  commencing duplicate removal, pass 1
Tue Jun 24 19:42:07 2008  found 320701 hash collisions in 1854989 relations
Tue Jun 24 19:42:07 2008  commencing duplicate removal, pass 2
Tue Jun 24 19:42:08 2008  found 368524 duplicates and 1486465 unique relations
Tue Jun 24 19:42:08 2008  memory use: 39.7 MB
Tue Jun 24 19:42:08 2008  ignoring smallest 86756 rational and 87067 algebraic ideals
Tue Jun 24 19:42:08 2008  filtering rational ideals above 1114112
Tue Jun 24 19:42:08 2008  filtering algebraic ideals above 1114112
Tue Jun 24 19:42:08 2008  need 260734 more relations than ideals
Tue Jun 24 19:42:08 2008  commencing singleton removal, pass 1
Tue Jun 24 19:42:20 2008  relations with 0 large ideals: 43587
Tue Jun 24 19:42:20 2008  relations with 1 large ideals: 319974
Tue Jun 24 19:42:20 2008  relations with 2 large ideals: 715856
Tue Jun 24 19:42:20 2008  relations with 3 large ideals: 331819
Tue Jun 24 19:42:20 2008  relations with 4 large ideals: 56954
Tue Jun 24 19:42:20 2008  relations with 5 large ideals: 3204
Tue Jun 24 19:42:20 2008  relations with 6 large ideals: 15071
Tue Jun 24 19:42:20 2008  relations with 7+ large ideals: 0
Tue Jun 24 19:42:20 2008  1486465 relations and about 1477266 large ideals
Tue Jun 24 19:42:20 2008  commencing singleton removal, pass 2
Tue Jun 24 19:42:33 2008  found 825689 singletons
Tue Jun 24 19:42:33 2008  current dataset: 660776 relations and about 478158 large ideals
Tue Jun 24 19:42:33 2008  commencing singleton removal, pass 3
Tue Jun 24 19:42:38 2008  found 117444 singletons
Tue Jun 24 19:42:38 2008  current dataset: 543332 relations and about 353249 large ideals
Tue Jun 24 19:42:38 2008  commencing singleton removal, final pass
Tue Jun 24 19:42:43 2008  memory use: 15.3 MB
Tue Jun 24 19:42:43 2008  commencing in-memory singleton removal
Tue Jun 24 19:42:43 2008  begin with 543332 relations and 357367 unique ideals
Tue Jun 24 19:42:44 2008  reduce to 500693 relations and 314037 ideals in 9 passes
Tue Jun 24 19:42:44 2008  max relations containing the same ideal: 21
Tue Jun 24 19:42:44 2008  filtering rational ideals above 445644
Tue Jun 24 19:42:44 2008  filtering algebraic ideals above 445644
Tue Jun 24 19:42:44 2008  need 74845 more relations than ideals
Tue Jun 24 19:42:44 2008  commencing singleton removal, final pass
Tue Jun 24 19:42:49 2008  keeping 412739 ideals with weight <= 20, new excess is 75080
Tue Jun 24 19:42:49 2008  memory use: 16.5 MB
Tue Jun 24 19:42:49 2008  commencing in-memory singleton removal
Tue Jun 24 19:42:49 2008  begin with 500711 relations and 412739 unique ideals
Tue Jun 24 19:42:49 2008  reduce to 500015 relations and 412037 ideals in 6 passes
Tue Jun 24 19:42:49 2008  max relations containing the same ideal: 20
Tue Jun 24 19:42:50 2008  relations with 0 large ideals: 1946
Tue Jun 24 19:42:50 2008  relations with 1 large ideals: 11438
Tue Jun 24 19:42:50 2008  relations with 2 large ideals: 68326
Tue Jun 24 19:42:50 2008  relations with 3 large ideals: 149117
Tue Jun 24 19:42:50 2008  relations with 4 large ideals: 153528
Tue Jun 24 19:42:50 2008  relations with 5 large ideals: 82207
Tue Jun 24 19:42:50 2008  relations with 6 large ideals: 29396
Tue Jun 24 19:42:50 2008  relations with 7+ large ideals: 4057
Tue Jun 24 19:42:50 2008  commencing 2-way merge
Tue Jun 24 19:42:50 2008  reduce to 317885 relation sets and 229906 unique ideals
Tue Jun 24 19:42:50 2008  commencing full merge
Tue Jun 24 19:42:55 2008  memory use: 25.6 MB
Tue Jun 24 19:42:55 2008  found 159297 cycles, need 148106
Tue Jun 24 19:42:55 2008  weight of 148106 cycles is about 10444887 (70.52/cycle)
Tue Jun 24 19:42:55 2008  distribution of cycle lengths:
Tue Jun 24 19:42:55 2008  1 relations: 9928
Tue Jun 24 19:42:55 2008  2 relations: 14156
Tue Jun 24 19:42:55 2008  3 relations: 16705
Tue Jun 24 19:42:55 2008  4 relations: 16718
Tue Jun 24 19:42:55 2008  5 relations: 16065
Tue Jun 24 19:42:55 2008  6 relations: 14160
Tue Jun 24 19:42:55 2008  7 relations: 12125
Tue Jun 24 19:42:55 2008  8 relations: 10328
Tue Jun 24 19:42:55 2008  9 relations: 8802
Tue Jun 24 19:42:55 2008  10+ relations: 29119
Tue Jun 24 19:42:55 2008  heaviest cycle: 18 relations
Tue Jun 24 19:42:55 2008  commencing cycle optimization
Tue Jun 24 19:42:56 2008  start with 917995 relations
Tue Jun 24 19:42:58 2008  pruned 13768 relations
Tue Jun 24 19:42:58 2008  memory use: 28.1 MB
Tue Jun 24 19:42:58 2008  distribution of cycle lengths:
Tue Jun 24 19:42:58 2008  1 relations: 9928
Tue Jun 24 19:42:58 2008  2 relations: 14233
Tue Jun 24 19:42:58 2008  3 relations: 16970
Tue Jun 24 19:42:58 2008  4 relations: 16921
Tue Jun 24 19:42:58 2008  5 relations: 16400
Tue Jun 24 19:42:58 2008  6 relations: 14355
Tue Jun 24 19:42:58 2008  7 relations: 12496
Tue Jun 24 19:42:58 2008  8 relations: 10360
Tue Jun 24 19:42:58 2008  9 relations: 8865
Tue Jun 24 19:42:58 2008  10+ relations: 27578
Tue Jun 24 19:42:58 2008  heaviest cycle: 18 relations
Tue Jun 24 19:42:58 2008  elapsed time 00:01:07
Tue Jun 24 19:42:58 2008  
Tue Jun 24 19:42:58 2008  
Tue Jun 24 19:42:58 2008  Msieve v. 1.36
Tue Jun 24 19:42:58 2008  random seeds: 2b1162a1 26955b9f
Tue Jun 24 19:42:58 2008  factoring 364923068079077051345646208213109615163068484659184173606608115958004538540567489875997792910118943908918763856606819776147839937 (129 digits)
Tue Jun 24 19:42:59 2008  no P-1/P+1/ECM available, skipping
Tue Jun 24 19:42:59 2008  commencing number field sieve (129-digit input)
Tue Jun 24 19:42:59 2008  R0: -1000000000000000000000000000
Tue Jun 24 19:42:59 2008  R1:  1
Tue Jun 24 19:42:59 2008  A0: -31
Tue Jun 24 19:42:59 2008  A1:  0
Tue Jun 24 19:42:59 2008  A2:  0
Tue Jun 24 19:42:59 2008  A3:  0
Tue Jun 24 19:42:59 2008  A4:  0
Tue Jun 24 19:42:59 2008  A5:  2200
Tue Jun 24 19:42:59 2008  size score = 7.036318e-10, Murphy alpha = -0.077176, combined = 7.219677e-10
Tue Jun 24 19:42:59 2008  
Tue Jun 24 19:42:59 2008  commencing linear algebra
Tue Jun 24 19:42:59 2008  read 148106 cycles
Tue Jun 24 19:43:00 2008  cycles contain 434300 unique relations
Tue Jun 24 19:43:03 2008  read 434300 relations
Tue Jun 24 19:43:04 2008  using 32 quadratic characters above 33549864
Tue Jun 24 19:43:08 2008  building initial matrix
Tue Jun 24 19:43:13 2008  memory use: 59.8 MB
Tue Jun 24 19:43:14 2008  read 148106 cycles
Tue Jun 24 19:43:14 2008  matrix is 147922 x 148106 (44.4 MB) with weight 14140130 (95.47/col)
Tue Jun 24 19:43:14 2008  sparse part has weight 10001765 (67.53/col)
Tue Jun 24 19:43:16 2008  filtering completed in 2 passes
Tue Jun 24 19:43:16 2008  matrix is 147661 x 147845 (44.3 MB) with weight 14122072 (95.52/col)
Tue Jun 24 19:43:16 2008  sparse part has weight 9991367 (67.58/col)
Tue Jun 24 19:43:17 2008  read 147845 cycles
Tue Jun 24 19:43:17 2008  matrix is 147661 x 147845 (44.3 MB) with weight 14122072 (95.52/col)
Tue Jun 24 19:43:17 2008  sparse part has weight 9991367 (67.58/col)
Tue Jun 24 19:43:17 2008  saving the first 48 matrix rows for later
Tue Jun 24 19:43:17 2008  matrix is 147613 x 147845 (41.9 MB) with weight 10871070 (73.53/col)
Tue Jun 24 19:43:17 2008  sparse part has weight 9508778 (64.32/col)
Tue Jun 24 19:43:17 2008  matrix includes 64 packed rows
Tue Jun 24 19:43:17 2008  using block size 43690 for processor cache size 1024 kB
Tue Jun 24 19:43:19 2008  commencing Lanczos iteration
Tue Jun 24 19:43:19 2008  memory use: 38.1 MB
...
linear algebra completed 145627 out of 147845 dimensions (98.5%)
lanczos halted after 2337 iterations (dim = 147613)
recovered 51 nontrivial dependencies
elapsed time 00:04:39
=>nice -n 19  "/depts/BioInf/Batalov/MERSE/ggbin/msieve" -s vs3.dat -l ggnfs.log -i vs3.ini -v -nf vs3.fb -t 1 -nc3

Msieve v. 1.36
Tue Jun 24 19:47:37 2008
random seeds: df5fa5c3 612405f0
factoring 364923068079077051345646208213109615163068484659184173606608115958004538540567489875997792910118943908918763856606819776147839937 (129 digits)
no P-1/P+1/ECM available, skipping
commencing number field sieve (129-digit input)
R0: -1000000000000000000000000000
R1:  1
A0: -31
A1:  0
A2:  0
A3:  0
A4:  0
A5:  2200
size score = 7.036318e-10, Murphy alpha = -0.077176, combined = 7.219677e-10

commencing square root phase
reading relations for dependency 1
read 74221 cycles
cycles contain 270946 unique relations
read 270946 relations
multiplying 452950 relations
multiply complete, coefficients have about 13.57 million bits
initial square root is modulo 62672501
prp40 factor: 4230643473881898745530247026033528758893
prp89 factor: 86257107301040353258760835519646764214155993239698998324248576055986190717546106427894309
elapsed time 00:01:57
-> Computing time scale for this machine...
sumName = s138-vs3.txt
-> Factorization summary written to s138-vs3.txt.

N=364923068079077051345646208213109615163068484659184173606608115958004538540567489875997792910118943908918763856606819776147839937
  ( 129 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=4230643473881898745530247026033528758893
 r2=86257107301040353258760835519646764214155993239698998324248576055986190717546106427894309
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.944).
Factorization parameters were as follows:
#res:2795
name: 24441_137
n: 364923068079077051345646208213109615163068484659184173606608115958004538540567489875997792910118943908918763856606819776147839937
Y1: 1
Y0: -1000000000000000000000000000
c5: 2200
c0: -31
skew: 0.43
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [500000, 1325001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 147613 x 147845
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 0.00 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

(22·10¹⁹⁴-31)/9 = 2(4)₁₉₃1_<195> = 278595861831598911140273_<24> · 11894864327951802442292729804333_<32> · 35018293618452818567197231650421_<32> · C109

C109 = P49 · P60

P49 = 5372482836426580900512209972203814089751370013919_<49>

P60 = 392081183737090877140072638124636771184362766568147368455751_<60>

Number: 24441_194
N=2106449430113337418439686498093665737072417104177983028241236957255256900579714385299982462974479850405598169
  ( 109 digits)
Divisors found:
 r1=5372482836426580900512209972203814089751370013919
 r2=392081183737090877140072638124636771184362766568147368455751
Version: 
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.944).
Factorization parameters were as follows:
name: 24441_194
n: 2106449430113337418439686498093665737072417104177983028241236957255256900579714385299982462974479850405598169
skew: 40436.56
# norm 9.50e+14
c5: 6300
c4: -6074415
c3: 15044965730376
c2: -513817562282863186
c1: -38591011017509739247904
c0: -189964629514345907912503176
# alpha -5.99
Y1: 85707496171
Y0: -803234042785158511595
# Murphy_E 1.13e-09
# M 1924700740393856439702834402358433334952951283649528228384901939772757800330389208057432806240169632309889192
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2800001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: 7534340 relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 384322 x 384563
Total sieving time: 7.98 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.33 hours.
Time per square root: 0.10 hours. x 4 times
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 0.00 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

Jun 25, 2008

By Sinkiti Sibata / Msieve, GGNFS

(22·10¹¹⁷-31)/9 = 2(4)₁₁₆1_<118> = 29 · 461 · 349093 · 406887201344489491693_<21> · C88

C88 = P34 · P54

P34 = 4410818249195386441095460907024479_<34>

P54 = 291841410464168265137439674268152491306019075364735359_<54>

Wed Jun 25 06:06:08 2008  Msieve v. 1.36
Wed Jun 25 06:06:08 2008  random seeds: 170cc727 b201353d
Wed Jun 25 06:06:08 2008  factoring 1287259419146274799029762849499144221452245222008169345367185110030166353130963969852961 (88 digits)
Wed Jun 25 06:06:09 2008  no P-1/P+1/ECM available, skipping
Wed Jun 25 06:06:09 2008  commencing quadratic sieve (88-digit input)
Wed Jun 25 06:06:09 2008  using multiplier of 1
Wed Jun 25 06:06:09 2008  using 64kb Pentium 4 sieve core
Wed Jun 25 06:06:09 2008  sieve interval: 12 blocks of size 65536
Wed Jun 25 06:06:09 2008  processing polynomials in batches of 9
Wed Jun 25 06:06:09 2008  using a sieve bound of 1508383 (57210 primes)
Wed Jun 25 06:06:09 2008  using large prime bound of 120670640 (26 bits)
Wed Jun 25 06:06:09 2008  using double large prime bound of 352275850752880 (42-49 bits)
Wed Jun 25 06:06:09 2008  using trial factoring cutoff of 49 bits
Wed Jun 25 06:06:09 2008  polynomial 'A' values have 11 factors
Wed Jun 25 07:24:25 2008  57416 relations (15610 full + 41806 combined from 604346 partial), need 57306
Wed Jun 25 07:24:27 2008  begin with 619956 relations
Wed Jun 25 07:24:28 2008  reduce to 138236 relations in 10 passes
Wed Jun 25 07:24:28 2008  attempting to read 138236 relations
Wed Jun 25 07:24:31 2008  recovered 138236 relations
Wed Jun 25 07:24:31 2008  recovered 115495 polynomials
Wed Jun 25 07:24:32 2008  attempting to build 57416 cycles
Wed Jun 25 07:24:32 2008  found 57416 cycles in 5 passes
Wed Jun 25 07:24:32 2008  distribution of cycle lengths:
Wed Jun 25 07:24:32 2008     length 1 : 15610
Wed Jun 25 07:24:32 2008     length 2 : 11329
Wed Jun 25 07:24:32 2008     length 3 : 10241
Wed Jun 25 07:24:32 2008     length 4 : 7591
Wed Jun 25 07:24:32 2008     length 5 : 5209
Wed Jun 25 07:24:32 2008     length 6 : 3257
Wed Jun 25 07:24:32 2008     length 7 : 1922
Wed Jun 25 07:24:32 2008     length 9+: 2257
Wed Jun 25 07:24:32 2008  largest cycle: 19 relations
Wed Jun 25 07:24:32 2008  matrix is 57210 x 57416 (13.2 MB) with weight 3220877 (56.10/col)
Wed Jun 25 07:24:32 2008  sparse part has weight 3220877 (56.10/col)
Wed Jun 25 07:24:33 2008  filtering completed in 3 passes
Wed Jun 25 07:24:33 2008  matrix is 52838 x 52902 (12.2 MB) with weight 2996218 (56.64/col)
Wed Jun 25 07:24:33 2008  sparse part has weight 2996218 (56.64/col)
Wed Jun 25 07:24:33 2008  saving the first 48 matrix rows for later
Wed Jun 25 07:24:33 2008  matrix is 52790 x 52902 (7.7 MB) with weight 2328421 (44.01/col)
Wed Jun 25 07:24:33 2008  sparse part has weight 1694223 (32.03/col)
Wed Jun 25 07:24:33 2008  matrix includes 64 packed rows
Wed Jun 25 07:24:33 2008  using block size 21160 for processor cache size 512 kB
Wed Jun 25 07:24:34 2008  commencing Lanczos iteration
Wed Jun 25 07:24:34 2008  memory use: 7.7 MB
Wed Jun 25 07:25:04 2008  lanczos halted after 837 iterations (dim = 52788)
Wed Jun 25 07:25:04 2008  recovered 16 nontrivial dependencies
Wed Jun 25 07:25:05 2008  prp34 factor: 4410818249195386441095460907024479
Wed Jun 25 07:25:05 2008  prp54 factor: 291841410464168265137439674268152491306019075364735359
Wed Jun 25 07:25:05 2008  elapsed time 01:18:57

(22·10¹¹⁸-31)/9 = 2(4)₁₁₇1_<119> = 3 · 14983 · 622449689 · C105

C105 = P46 · P60

P46 = 4537615633666849151611716577755232938567642751_<46>

P60 = 192543196468245533005352464734298731237544060158976608782531_<60>

Number: 24441_118
N=873687018450498585860962414011205494434864693142153285668563056838354780242500796832845469760044657582781
  ( 105 digits)
SNFS difficulty: 119 digits.
Divisors found:
 r1=4537615633666849151611716577755232938567642751 (pp46)
 r2=192543196468245533005352464734298731237544060158976608782531 (pp60)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.79 hours.
Scaled time: 7.58 units (timescale=2.001).
Factorization parameters were as follows:
name: 24441_118
n: 873687018450498585860962414011205494434864693142153285668563056838354780242500796832845469760044657582781
m: 200000000000000000000000
c5: 1375
c0: -62
skew: 0.54
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:63870, largePrimes:2479128 encountered
Relations: rels:3033113, finalFF:650178
Max relations in full relation-set: 28
Initial matrix: 113034 x 650178 with sparse part having weight 58691005.
Pruned matrix : 72863 x 73492 with weight 7919281.
Total sieving time: 3.65 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,119,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.79 hours.
 --------- CPU info (if available) ----------

(22·10¹³³-31)/9 = 2(4)₁₃₂1_<134> = 3² · 7 · 139 · 1889 · 72848313288111029_<17> · 12107233034358661681_<20> · C91

C91 = P34 · P57

P34 = 5639657496580140043807608755154479_<34>

P57 = 297081584751261613839479981912844720413453322599248782527_<57>

Wed Jun 25 07:41:23 2008  Msieve v. 1.36
Wed Jun 25 07:41:23 2008  random seeds: c50e3e98 41efd23e
Wed Jun 25 07:41:23 2008  factoring 1675438386538360779538911366534090700731296549280307459985836895534653957674705576560988433 (91 digits)
Wed Jun 25 07:41:25 2008  no P-1/P+1/ECM available, skipping
Wed Jun 25 07:41:25 2008  commencing quadratic sieve (91-digit input)
Wed Jun 25 07:41:25 2008  using multiplier of 3
Wed Jun 25 07:41:25 2008  using 64kb Pentium 4 sieve core
Wed Jun 25 07:41:25 2008  sieve interval: 18 blocks of size 65536
Wed Jun 25 07:41:25 2008  processing polynomials in batches of 6
Wed Jun 25 07:41:25 2008  using a sieve bound of 1648001 (62353 primes)
Wed Jun 25 07:41:25 2008  using large prime bound of 145024088 (27 bits)
Wed Jun 25 07:41:25 2008  using double large prime bound of 490447101569216 (42-49 bits)
Wed Jun 25 07:41:25 2008  using trial factoring cutoff of 49 bits
Wed Jun 25 07:41:25 2008  polynomial 'A' values have 12 factors
Wed Jun 25 10:35:54 2008  62959 relations (16185 full + 46774 combined from 698397 partial), need 62449
Wed Jun 25 10:35:57 2008  begin with 714582 relations
Wed Jun 25 10:35:58 2008  reduce to 156061 relations in 11 passes
Wed Jun 25 10:35:58 2008  attempting to read 156061 relations
Wed Jun 25 10:36:02 2008  recovered 156061 relations
Wed Jun 25 10:36:02 2008  recovered 138295 polynomials
Wed Jun 25 10:36:02 2008  attempting to build 62959 cycles
Wed Jun 25 10:36:02 2008  found 62959 cycles in 5 passes
Wed Jun 25 10:36:02 2008  distribution of cycle lengths:
Wed Jun 25 10:36:02 2008     length 1 : 16185
Wed Jun 25 10:36:02 2008     length 2 : 11807
Wed Jun 25 10:36:02 2008     length 3 : 11185
Wed Jun 25 10:36:02 2008     length 4 : 8494
Wed Jun 25 10:36:02 2008     length 5 : 6109
Wed Jun 25 10:36:02 2008     length 6 : 3932
Wed Jun 25 10:36:02 2008     length 7 : 2309
Wed Jun 25 10:36:02 2008     length 9+: 2938
Wed Jun 25 10:36:02 2008  largest cycle: 21 relations
Wed Jun 25 10:36:03 2008  matrix is 62353 x 62959 (15.9 MB) with weight 3905559 (62.03/col)
Wed Jun 25 10:36:03 2008  sparse part has weight 3905559 (62.03/col)
Wed Jun 25 10:36:04 2008  filtering completed in 3 passes
Wed Jun 25 10:36:04 2008  matrix is 58686 x 58749 (14.8 MB) with weight 3639529 (61.95/col)
Wed Jun 25 10:36:04 2008  sparse part has weight 3639529 (61.95/col)
Wed Jun 25 10:36:04 2008  saving the first 48 matrix rows for later
Wed Jun 25 10:36:04 2008  matrix is 58638 x 58749 (9.6 MB) with weight 2901339 (49.39/col)
Wed Jun 25 10:36:04 2008  sparse part has weight 2164287 (36.84/col)
Wed Jun 25 10:36:04 2008  matrix includes 64 packed rows
Wed Jun 25 10:36:04 2008  using block size 21845 for processor cache size 512 kB
Wed Jun 25 10:36:05 2008  commencing Lanczos iteration
Wed Jun 25 10:36:05 2008  memory use: 9.2 MB
Wed Jun 25 10:36:43 2008  lanczos halted after 929 iterations (dim = 58636)
Wed Jun 25 10:36:43 2008  recovered 18 nontrivial dependencies
Wed Jun 25 10:36:44 2008  prp34 factor: 5639657496580140043807608755154479
Wed Jun 25 10:36:44 2008  prp57 factor: 297081584751261613839479981912844720413453322599248782527
Wed Jun 25 10:36:44 2008  elapsed time 02:55:21

(22·10¹²³-31)/9 = 2(4)₁₂₂1_<124> = 23 · 433 · 1117 · 68729 · 501031 · C106

C106 = P30 · P37 · P41

P30 = 112756411670894054808299206741_<30>

P37 = 1273632833538519302423429506126087703_<37>

P41 = 44434587248671470710438581903003136233111_<41>

Number: 24441_123
N=6381262987518437582596006673142664010499591113432826140506374373786489676493680985755553880923201431516453
  ( 106 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=112756411670894054808299206741 (pp30)
 r2=1273632833538519302423429506126087703 (pp37)
 r3=44434587248671470710438581903003136233111 (pp41)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.80 hours.
Scaled time: 5.54 units (timescale=1.980).
Factorization parameters were as follows:
name: 24441_123
n: 6381262987518437582596006673142664010499591113432826140506374373786489676493680985755553880923201431516453
m: 2000000000000000000000000
c5: 1375
c0: -62
skew: 0.54
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:63870, largePrimes:2087371 encountered
Relations: rels:2089010, finalFF:148808
Max relations in full relation-set: 28
Initial matrix: 113034 x 148808 with sparse part having weight 13134472.
Pruned matrix : 103383 x 104012 with weight 7096421.
Total sieving time: 2.64 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.80 hours.
 --------- CPU info (if available) ----------

(22·10¹²⁶-31)/9 = 2(4)₁₂₅1_<127> = 251 · 947197 · 7866056173_<10> · 147800376943_<12> · C97

C97 = P48 · P50

P48 = 125539892302209994144376261639415159617845478621_<48>

P50 = 70445263698076214469967576860456601215668550017537_<50>

Number: 24441_126
N=8843690817857271302023221252006081640529860641541495178285378366218188996613539373465225708576477
  ( 97 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=125539892302209994144376261639415159617845478621 (pp48)
 r2=70445263698076214469967576860456601215668550017537 (pp50)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.06 hours.
Scaled time: 8.12 units (timescale=1.999).
Factorization parameters were as follows:
name: 24441_126
n: 8843690817857271302023221252006081640529860641541495178285378366218188996613539373465225708576477
m: 10000000000000000000000000
c5: 220
c0: -31
skew: 0.68
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:49098, AFBsize:64395, largePrimes:2456079 encountered
Relations: rels:2883954, finalFF:504666
Max relations in full relation-set: 28
Initial matrix: 113560 x 504666 with sparse part having weight 50686424.
Pruned matrix : 82776 x 83407 with weight 10580662.
Total sieving time: 3.89 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 4.06 hours.
 --------- CPU info (if available) ----------

(22·10¹³⁶-31)/9 = 2(4)₁₃₅1_<137> = 3 · 102913 · 15234311306269949_<17> · 1562581549839689958881_<22> · C94

C94 = P41 · P53

P41 = 70140031482922619884047309665806073419879_<41>

P53 = 47419525476324695463991738004843827169691997828599769_<53>

Wed Jun 25 10:55:40 2008  Msieve v. 1.36
Wed Jun 25 10:55:40 2008  random seeds: df7de77d 5750ec7f
Wed Jun 25 10:55:40 2008  factoring 3326007009814665382594988238225932795513919969611140665785160095361635024439266642871779407951 (94 digits)
Wed Jun 25 10:55:41 2008  no P-1/P+1/ECM available, skipping
Wed Jun 25 10:55:42 2008  commencing quadratic sieve (94-digit input)
Wed Jun 25 10:55:42 2008  using multiplier of 31
Wed Jun 25 10:55:42 2008  using 64kb Pentium 4 sieve core
Wed Jun 25 10:55:42 2008  sieve interval: 18 blocks of size 65536
Wed Jun 25 10:55:42 2008  processing polynomials in batches of 6
Wed Jun 25 10:55:42 2008  using a sieve bound of 2021197 (75294 primes)
Wed Jun 25 10:55:42 2008  using large prime bound of 270840398 (28 bits)
Wed Jun 25 10:55:42 2008  using double large prime bound of 1509677378791104 (42-51 bits)
Wed Jun 25 10:55:42 2008  using trial factoring cutoff of 51 bits
Wed Jun 25 10:55:42 2008  polynomial 'A' values have 12 factors
Wed Jun 25 15:40:24 2008  75402 relations (19171 full + 56231 combined from 1058328 partial), need 75390
Wed Jun 25 15:40:28 2008  begin with 1077499 relations
Wed Jun 25 15:40:29 2008  reduce to 192564 relations in 10 passes
Wed Jun 25 15:40:29 2008  attempting to read 192564 relations
Wed Jun 25 15:40:35 2008  recovered 192564 relations
Wed Jun 25 15:40:35 2008  recovered 174670 polynomials
Wed Jun 25 15:40:35 2008  attempting to build 75402 cycles
Wed Jun 25 15:40:35 2008  found 75402 cycles in 5 passes
Wed Jun 25 15:40:35 2008  distribution of cycle lengths:
Wed Jun 25 15:40:35 2008     length 1 : 19171
Wed Jun 25 15:40:35 2008     length 2 : 13461
Wed Jun 25 15:40:35 2008     length 3 : 13067
Wed Jun 25 15:40:35 2008     length 4 : 10176
Wed Jun 25 15:40:35 2008     length 5 : 7411
Wed Jun 25 15:40:35 2008     length 6 : 4990
Wed Jun 25 15:40:35 2008     length 7 : 3086
Wed Jun 25 15:40:35 2008     length 9+: 4040
Wed Jun 25 15:40:35 2008  largest cycle: 22 relations
Wed Jun 25 15:40:36 2008  matrix is 75294 x 75402 (20.0 MB) with weight 4929129 (65.37/col)
Wed Jun 25 15:40:36 2008  sparse part has weight 4929129 (65.37/col)
Wed Jun 25 15:40:38 2008  filtering completed in 4 passes
Wed Jun 25 15:40:38 2008  matrix is 71405 x 71469 (19.1 MB) with weight 4713847 (65.96/col)
Wed Jun 25 15:40:38 2008  sparse part has weight 4713847 (65.96/col)
Wed Jun 25 15:40:38 2008  saving the first 48 matrix rows for later
Wed Jun 25 15:40:38 2008  matrix is 71357 x 71469 (12.9 MB) with weight 3798547 (53.15/col)
Wed Jun 25 15:40:38 2008  sparse part has weight 2962125 (41.45/col)
Wed Jun 25 15:40:38 2008  matrix includes 64 packed rows
Wed Jun 25 15:40:38 2008  using block size 21845 for processor cache size 512 kB
Wed Jun 25 15:40:39 2008  commencing Lanczos iteration
Wed Jun 25 15:40:39 2008  memory use: 11.9 MB
Wed Jun 25 15:41:38 2008  lanczos halted after 1130 iterations (dim = 71357)
Wed Jun 25 15:41:38 2008  recovered 18 nontrivial dependencies
Wed Jun 25 15:41:40 2008  prp41 factor: 70140031482922619884047309665806073419879
Wed Jun 25 15:41:40 2008  prp53 factor: 47419525476324695463991738004843827169691997828599769
Wed Jun 25 15:41:40 2008  elapsed time 04:46:00

(22·10¹³⁰-31)/9 = 2(4)₁₂₉1_<131> = 3 · 5791 · 117231343 · C119

C119 = P50 · P69

P50 = 85995374291128139645665669095946376417031817673599_<50>

P69 = 139568213783908770745527523180712684153776037520035004684966931153181_<69>

Number: 24441_130
N=12002220783491424354719810893455669531170424853954026778227280515249519161486614070059907571911548826570017617728568419
  ( 119 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=85995374291128139645665669095946376417031817673599 (pp50)
 r2=139568213783908770745527523180712684153776037520035004684966931153181 (pp69)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.42 hours.
Scaled time: 8.76 units (timescale=1.982).
Factorization parameters were as follows:
name: 24441_130
n: 12002220783491424354719810893455669531170424853954026778227280515249519161486614070059907571911548826570017617728568419
m: 100000000000000000000000000
c5: 22
c0: -31
skew: 1.07
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:63540, largePrimes:1452971 encountered
Relations: rels:1426412, finalFF:147328
Max relations in full relation-set: 28
Initial matrix: 127557 x 147328 with sparse part having weight 11031003.
Pruned matrix : 122110 x 122811 with weight 7660398.
Total sieving time: 4.23 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.42 hours.
 --------- CPU info (if available) ----------

(22·10¹³⁸-31)/9 = 2(4)₁₃₇1_<139> = 137977193 · 18449653031753849_<17> · C114

C114 = P46 · P69

P46 = 3825837938755335201721050723402917950510257463_<46>

P69 = 250990967874013770505290290531406928058853824186456271102008457235151_<69>

Number: 24441_138
N=960250767177323400882844976192636287552667446686675098746530710972955996716839535226165913888973758453802143681913
  ( 114 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=3825837938755335201721050723402917950510257463 (pp46)
 r2=250990967874013770505290290531406928058853824186456271102008457235151 (pp69)
Version: GGNFS-0.77.1-20060513-k8
Total time: 13.38 hours.
Scaled time: 26.78 units (timescale=2.002).
Factorization parameters were as follows:
name: 24441_138
n: 960250767177323400882844976192636287552667446686675098746530710972955996716839535226165913888973758453802143681913
m: 2000000000000000000000000000
c5: 1375
c0: -62
skew: 0.54
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 2125001)
Primes: RFBsize:78498, AFBsize:63870, largePrimes:1660537 encountered
Relations: rels:1687384, finalFF:168711
Max relations in full relation-set: 28
Initial matrix: 142434 x 168711 with sparse part having weight 18605604.
Pruned matrix : 135990 x 136766 with weight 13766077.
Total sieving time: 13.07 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 13.38 hours.
 --------- CPU info (if available) ----------

Jun 24, 2008 (5th)

By matsui / GGNFS

6·10¹⁷⁶+7 = 6(0)₁₇₅7_<177> = 149 · C175

C175 = P45 · P131

P45 = 230266112072425854835615673997286041414191311_<45>

P131 = 17487790979496472353574388242068301111731661211926813193993672549877478287762758543465832179237070194085811306528123110099573405413_<131>

N=4026845637583892617449664429530201342281879194630872483221476510067114093959731543624161073825503355704697986577181208053691275167785234899328859060402684563758389261744966443
  ( 175 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=230266112072425854835615673997286041414191311 (pp45)
 r2=17487790979496472353574388242068301111731661211926813193993672549877478287762758543465832179237070194085811306528123110099573405413 (pp131)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 252.84 hours.
Scaled time: 347.40 units (timescale=1.374).
Factorization parameters were as follows:
n: 4026845637583892617449664429530201342281879194630872483221476510067114093959731543624161073825503355704697986577181208053691275167785234899328859060402684563758389261744966443
m: 100000000000000000000000000000000000
c5: 60
c0: 7
skew: 0.65
type: snfs

Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 14200001)
Primes: RFBsize:501962, AFBsize:502341, largePrimes:6688647 encountered
Relations: rels:7170745, finalFF:1136864
Max relations in full relation-set: 28
Initial matrix: 1004370 x 1136864 with sparse part having weight 89462948.
Pruned matrix : 897008 x 902093 with weight 70418949.
Total sieving time: 237.69 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 14.56 hours.
Time per square root: 0.34 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 252.84 hours.

Jun 24, 2008 (4th)

By suberi / GMP-ECM, Msieve

(64·10²⁰⁵+53)/9 = 7(1)₂₀₄7_<206> = 7 · 11 · 239 · 39217 · 303337 · 818638853244139_<15> · 32171339726493257_<17> · C161

C161 = P43 · P118

P43 = 6792360722740653194989864506125393681527657_<43>

P118 = 1815795106708801594507912771850228677646491129523164275329155811015085729329124219820438570716764628453647583068010181_<118>

2·10¹⁸⁷+3 = 2(0)₁₈₆3_<188> = 2650288267127376709_<19> · 21691476478039441219_<20> · C150

C150 = P31 · P33 · P87

P31 = 4899431565604784118723228083483_<31>

P33 = 389595763391679786994327160166767_<33>

P87 = 182258522814260407226204545556975019230375927589496525253684233311399812906067616297913_<87>

2·10¹⁸⁴+3 = 2(0)₁₈₃3_<185> = 241 · 4253 · 41715550696982867_<17> · 45046753479013599736939609_<26> · C137

C137 = P35 · P44 · P59

P35 = 16450357456538149478222257267964459_<35>

P44 = 56831071349735800699564104034197250430260949_<44>

P59 = 11106952378085416134328784349105056515147150726616078638907_<59>

Tue Jun 24 18:53:10 2008  
Tue Jun 24 18:53:10 2008  
Tue Jun 24 18:53:10 2008  Msieve v. 1.36
Tue Jun 24 18:53:10 2008  random seeds: 93ee3b85 0329cb0a
Tue Jun 24 18:53:10 2008  factoring 182713336872251556937124341395782902015287266671894633925232526091403812179727966275170606313 (93 digits)
Tue Jun 24 18:53:11 2008  no P-1/P+1/ECM available, skipping
Tue Jun 24 18:53:11 2008  commencing quadratic sieve (93-digit input)
Tue Jun 24 18:53:11 2008  using multiplier of 10
Tue Jun 24 18:53:11 2008  using 64kb Opteron sieve core
Tue Jun 24 18:53:11 2008  sieve interval: 18 blocks of size 65536
Tue Jun 24 18:53:11 2008  processing polynomials in batches of 6
Tue Jun 24 18:53:11 2008  using a sieve bound of 1884611 (70588 primes)
Tue Jun 24 18:53:11 2008  using large prime bound of 220499487 (27 bits)
Tue Jun 24 18:53:11 2008  using double large prime bound of 1042638218764623 (42-50 bits)
Tue Jun 24 18:53:11 2008  using trial factoring cutoff of 50 bits
Tue Jun 24 18:53:11 2008  polynomial 'A' values have 12 factors
Tue Jun 24 21:54:01 2008  70947 relations (18129 full + 52818 combined from 924198 partial), need 70684
Tue Jun 24 21:54:01 2008  begin with 942327 relations
Tue Jun 24 21:54:02 2008  reduce to 180003 relations in 11 passes
Tue Jun 24 21:54:02 2008  attempting to read 180003 relations
Tue Jun 24 21:54:04 2008  recovered 180003 relations
Tue Jun 24 21:54:04 2008  recovered 162383 polynomials
Tue Jun 24 21:54:04 2008  attempting to build 70947 cycles
Tue Jun 24 21:54:04 2008  found 70947 cycles in 6 passes
Tue Jun 24 21:54:05 2008  distribution of cycle lengths:
Tue Jun 24 21:54:05 2008     length 1 : 18129
Tue Jun 24 21:54:05 2008     length 2 : 12833
Tue Jun 24 21:54:05 2008     length 3 : 12206
Tue Jun 24 21:54:05 2008     length 4 : 9619
Tue Jun 24 21:54:05 2008     length 5 : 6914
Tue Jun 24 21:54:05 2008     length 6 : 4575
Tue Jun 24 21:54:05 2008     length 7 : 2879
Tue Jun 24 21:54:05 2008     length 9+: 3792
Tue Jun 24 21:54:05 2008  largest cycle: 20 relations
Tue Jun 24 21:54:05 2008  matrix is 70588 x 70947 (18.9 MB) with weight 4387637 (61.84/col)
Tue Jun 24 21:54:05 2008  sparse part has weight 4387637 (61.84/col)
Tue Jun 24 21:54:06 2008  filtering completed in 4 passes
Tue Jun 24 21:54:06 2008  matrix is 66689 x 66753 (17.8 MB) with weight 4139213 (62.01/col)
Tue Jun 24 21:54:06 2008  sparse part has weight 4139213 (62.01/col)
Tue Jun 24 21:54:07 2008  saving the first 48 matrix rows for later
Tue Jun 24 21:54:07 2008  matrix is 66641 x 66753 (10.8 MB) with weight 3149445 (47.18/col)
Tue Jun 24 21:54:07 2008  sparse part has weight 2163279 (32.41/col)
Tue Jun 24 21:54:07 2008  matrix includes 64 packed rows
Tue Jun 24 21:54:07 2008  using block size 21845 for processor cache size 512 kB
Tue Jun 24 21:54:07 2008  commencing Lanczos iteration
Tue Jun 24 21:54:07 2008  memory use: 10.0 MB
Tue Jun 24 21:54:45 2008  lanczos halted after 1055 iterations (dim = 66638)
Tue Jun 24 21:54:45 2008  recovered 16 nontrivial dependencies
Tue Jun 24 21:54:46 2008  prp35 factor: 16450357456538149478222257267964459
Tue Jun 24 21:54:46 2008  prp59 factor: 11106952378085416134328784349105056515147150726616078638907
Tue Jun 24 21:54:46 2008  elapsed time 03:01:36

Jun 24, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(7·10¹⁷⁹+17)/3 = 2(3)₁₇₈9_<180> = 22109 · 90469 · 1256323 · 35493226964893_<14> · 193576298168347_<15> · 952212640912740996809_<21> · C116

C116 = P49 · P68

P49 = 1083418340932707176216084357421154856286028373779_<49>

P68 = 13100226135502534549666209653747467840650514145509640203419928010693_<68>

Number: 23339_179
N=14193025265569445974228728704378542441338653383710387152481587867346291078132553015148374680826377638347769312818847
  ( 116 digits)
Divisors found:
 r1=1083418340932707176216084357421154856286028373779 (pp49)
 r2=13100226135502534549666209653747467840650514145509640203419928010693 (pp68)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 68.57 hours.
Scaled time: 46.28 units (timescale=0.675).
Factorization parameters were as follows:
name: 23339_179
n: 14193025265569445974228728704378542441338653383710387152481587867346291078132553015148374680826377638347769312818847
skew: 53352.58
# norm 4.55e+15
c5: 22800
c4: -1212675256
c3: -208058952557963
c2: 6664111048874094952
c1: 245754196746015982431972
c0: 1432227789190934188360900848
# alpha -5.51
Y1: 2378383133929
Y0: -14415469381987635808679
# Murphy_E 5.17e-10
# M 814671274571655966892064727200267112760459559660949635982948791244348566256512818571951807542954013572351015531657
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 3570001)
Primes: RFBsize:315948, AFBsize:315628, largePrimes:7558239 encountered
Relations: rels:7641850, finalFF:796002
Max relations in full relation-set: 28
Initial matrix: 631652 x 796002 with sparse part having weight 57923912.
Pruned matrix : 485483 x 488705 with weight 31317677.
Polynomial selection time: 3.01 hours.
Total sieving time: 54.29 hours.
Total relation processing time: 0.54 hours.
Matrix solve time: 10.31 hours.
Time per square root: 0.42 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 68.57 hours.
 --------- CPU info (if available) ----------

7·10¹⁸²+3 = 7(0)₁₈₁3_<183> = 19 · 37 · C180

C180 = P76 · P105

P76 = 5796213552807101290302139288236547086048674920761890437988566399723613188147_<76>

P105 = 171790180884158531835765998721853676674416631560705620499042258287282118632167531441001689658431400392783_<105>

Number: 70003_182
N=995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943101
  ( 180 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=5796213552807101290302139288236547086048674920761890437988566399723613188147 (pp76)
 r2=171790180884158531835765998721853676674416631560705620499042258287282118632167531441001689658431400392783 (pp105)
Version: GGNFS-0.77.1-20060513-k8
Total time: 549.90 hours.
Scaled time: 1098.71 units (timescale=1.998).
Factorization parameters were as follows:
name: 70003_182
n: 995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943101
m: 1000000000000000000000000000000000000
c5: 700
c0: 3
skew: 0.34
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 9800001)
Primes: RFBsize:501962, AFBsize:501711, largePrimes:6541906 encountered
Relations: rels:7006429, finalFF:1144045
Max relations in full relation-set: 28
Initial matrix: 1003740 x 1144045 with sparse part having weight 73023928.
Pruned matrix : 886255 x 891337 with weight 55995755.
Total sieving time: 538.86 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 10.28 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 549.90 hours.
 --------- CPU info (if available) ----------

Jun 24, 2008 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(19·10¹⁶²+71)/9 = 2(1)₁₆₁9_<163> = 73 · C161

C161 = P32 · P59 · P70

P32 = 43940526090123600470562056510603_<32>

P59 = 73998714678262655889943985399989215015429575850397477288273_<59>

P70 = 8894034356803247423111327983734140548254674728357494938725391032087637_<70>

Number: n
N=658147110707748824755832441227848690652084205220911259328710039673874479237845455658772436193296458069020869661212196684848380901
  ( 129 digits)
SNFS difficulty: 163 digits.
Divisors found:

Tue Jun 24 03:33:39 2008  prp59 factor: 73998714678262655889943985399989215015429575850397477288273
Tue Jun 24 03:33:39 2008  prp70 factor: 8894034356803247423111327983734140548254674728357494938725391032087637
Tue Jun 24 03:33:39 2008  elapsed time 01:05:25 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 43.80 hours.
Scaled time: 80.10 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_1_161_9
n: 658147110707748824755832441227848690652084205220911259328710039673874479237845455658772436193296458069020869661212196684848380901
skew: 0.52
deg: 5
c5: 1900
c0: 71
m: 100000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3000299)
Primes: RFBsize:315948, AFBsize:316312, largePrimes:7290029 encountered
Relations: rels:6865799, finalFF:650394
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 43.52 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000
total time: 43.80 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jun 24, 2008

The factor table of 244...441 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Jun 23, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(7·10¹⁵⁹+17)/3 = 2(3)₁₅₈9_<160> = 103 · 36353 · 678599 · 9047282575964125799445511_<25> · C123

C123 = P45 · P78

P45 = 913307551148821962130752701805568948809731623_<45>

P78 = 111135008099498608276431343957760234609000836576351644580968422062061256514043_<78>

Number: 23339_159
N=101500442094257568219640318443861829710581176391361977483716297025113928351635619590108271896052359109780634699299360681789
  ( 123 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=913307551148821962130752701805568948809731623 (pp45)
 r2=111135008099498608276431343957760234609000836576351644580968422062061256514043 (pp78)
Version: GGNFS-0.77.1-20060513-k8
Total time: 75.68 hours.
Scaled time: 149.77 units (timescale=1.979).
Factorization parameters were as follows:
name: 23339_159
n: 101500442094257568219640318443861829710581176391361977483716297025113928351635619590108271896052359109780634699299360681789
m: 100000000000000000000000000000000
c5: 7
c0: 170
skew: 1.89
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4500001)
Primes: RFBsize:283146, AFBsize:283272, largePrimes:5891949 encountered
Relations: rels:5985703, finalFF:688056
Max relations in full relation-set: 28
Initial matrix: 566483 x 688056 with sparse part having weight 56480525.
Pruned matrix : 485332 x 488228 with weight 41065012.
Total sieving time: 71.84 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 3.41 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 75.68 hours.
 --------- CPU info (if available) ----------

Jun 23, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(4·10¹⁶⁹+23)/9 = (4)₁₆₈7_<169> = 7 · 17 · 57349 · C162

C162 = P48 · P115

P48 = 503852761342782171346683824703620971518120723133_<48>

P115 = 1292531178579433361975754521183369234349970232633887731714815503149502104258374903219488361379931169871046875018089_<115>

Number: n
N=651245403448888201173742846862948449416442601615326305125501583104310676359217130736814653555598830812614734176523550767729598480019278166432893988531145135752837
  ( 162 digits)
SNFS difficulty: 170 digits.
Divisors found:

Mon Jun 23 18:23:51 2008  prp48 factor: 503852761342782171346683824703620971518120723133
Mon Jun 23 18:23:51 2008  prp115 factor: 1292531178579433361975754521183369234349970232633887731714815503149502104258374903219488361379931169871046875018089
Mon Jun 23 18:23:51 2008  elapsed time 01:31:12 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 68.29 hours.
Scaled time: 124.91 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_4_168_7
n: 651245403448888201173742846862948449416442601615326305125501583104310676359217130736814653555598830812614734176523550767729598480019278166432893988531145135752837
skew: 2.25
deg: 5
c5: 2
c0: 115
m: 10000000000000000000000000000000000
type: snfs
rlim: 5750000
alim: 5750000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5750000/5750000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4116257)
Primes: RFBsize:396826, AFBsize:396180, largePrimes:8129248 encountered
Relations: rels:7699340, finalFF:795201
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 68.06 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,5750000,5750000,28,28,48,48,2.5,2.5,100000
total time: 68.29 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(7·10¹⁶³+17)/3 = 2(3)₁₆₂9_<164> = 239 · C161

C161 = P52 · P110

P52 = 1538551780009680675999212973840188207025515314791083_<52>

P110 = 63455134257676194489120480630580987480409038207260499417697608713351090232023365272936682525567211829286754047_<110>

Number: n
N=97629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762901
  ( 161 digits)
SNFS difficulty: 163 digits.
Divisors found:

Mon Jun 23 20:47:10 2008  prp52 factor: 1538551780009680675999212973840188207025515314791083
Mon Jun 23 20:47:10 2008  prp110 factor: 63455134257676194489120480630580987480409038207260499417697608713351090232023365272936682525567211829286754047
Mon Jun 23 20:47:10 2008  elapsed time 02:10:56 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 61.47 hours.
Scaled time: 108.18 units (timescale=1.760).
Factorization parameters were as follows:
name: KA_2_3_162_9
n: 97629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762901
type: snfs
skew: 0.30
deg: 5
c5: 7000
c0: 17
m: 100000000000000000000000000000000
rlim: 4600000
alim: 4600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3000001)
Primes: RFBsize:322441, AFBsize:322486, largePrimes:7447109 encountered
Relations: rels:6929923, finalFF:646339
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 61.20 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4600000,4600000,28,28,48,48,2.3,2.3,100000
total time: 61.47 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jun 23, 2008

By suberi / GMP-ECM

(64·10¹⁸⁴+53)/9 = 7(1)₁₈₃7_<185> = 19 · 239 · 379 · 3653118301152191_<16> · C164

C164 = P40 · P124

P40 = 6408857844198902795079491084505047743261_<40>

P124 = 1764827968268619245848314702240512687857444858790408730674667676478953242420913659802142902523798197322058590130173904669953_<124>

Jun 22, 2008 (5th)

By Wataru Sakai / GGNFS

(7·10¹⁷³-61)/9 = (7)₁₇₂1_<173> = 5647 · 4150793 · 4174507 · C156

C156 = P76 · P81

P76 = 4697092831087200551529024233831603689378002454075748867575435175236949613467_<76>

P81 = 169228042188601079552332909893272905914334638988209627060854725312063782925308629_<81>

Number: 77771_173
N=794879823783000459297146595802866396258287289283368570900870245484647858993845972343965939158115233217484416191400328069663743260194300173826749173229706743
  ( 156 digits)
SNFS difficulty: 173 digits.
Divisors found:
 r1=4697092831087200551529024233831603689378002454075748867575435175236949613467 (pp76)
 r2=169228042188601079552332909893272905914334638988209627060854725312063782925308629 (pp81)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 278.56 hours.
Scaled time: 497.22 units (timescale=1.785).
Factorization parameters were as follows:
n: 794879823783000459297146595802866396258287289283368570900870245484647858993845972343965939158115233217484416191400328069663743260194300173826749173229706743
m: 10000000000000000000000000000000000
c5: 7000
c0: -61
skew: 0.39
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 13600001)
Primes: RFBsize:501962, AFBsize:502027, largePrimes:6884572 encountered
Relations: rels:7500187, finalFF:1264391
Max relations in full relation-set: 32
Initial matrix: 1004056 x 1264391 with sparse part having weight 98282831.
Pruned matrix : 783753 x 788837 with weight 77243787.
Total sieving time: 270.20 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 7.94 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 278.56 hours.
 --------- CPU info (if available) ----------

Jun 22, 2008 (4th)

By matsui / GGNFS

10¹⁷¹+3 = 1(0)₁₇₀3_<172> = 11766503516695099357653883_<26> · C146

C146 = P49 · P98

P49 = 3324774752229019712326210320791873479173334110257_<49>

P98 = 25561735879742056874997330779164365467172026436929398740217995340496906772469307561544143733079913_<98>

N=84987014076113040368276240003085477274619465136310452297603910182168194570059311533447910927491502082842012464686661684313334515329656218133967641
  ( 146 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=3324774752229019712326210320791873479173334110257 (pp49)
 r2=25561735879742056874997330779164365467172026436929398740217995340496906772469307561544143733079913 (pp98)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 141.52 hours.
Scaled time: 192.33 units (timescale=1.359).
Factorization parameters were as follows:
n: 84987014076113040368276240003085477274619465136310452297603910182168194570059311533447910927491502082842012464686661684313334515329656218133967641
m: 10000000000000000000000000000000000
c5: 10
c0: 3
skew: 0.79
type: snfs

Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 8500001)
Primes: RFBsize:412849, AFBsize:412801, largePrimes:6211987 encountered
Relations: rels:6507104, finalFF:950866
Max relations in full relation-set: 28
Initial matrix: 825716 x 950866 with sparse part having weight 68018418.
Pruned matrix : 726189 x 730381 with weight 51238543.
Total sieving time: 129.70 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 11.39 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 141.52 hours.

Jun 22, 2008 (3rd)

By Serge Batalov / pol51, Msieve 1.36

(7·10¹⁶⁷+17)/3 = 2(3)₁₆₆9_<168> = 19 · 172264217003920050943279_<24> · 157079089306604304108830836083629_<33> · C111

C111 = P38 · P74

P38 = 44403506544729569591382802255945107907_<38>

P74 = 10220978328444765863502623751657798456955829517191510572947586215944141713_<74>

Sat Jun 21 09:55:24 2008  Msieve v. 1.36
Sat Jun 21 09:55:24 2008  random seeds: 4fcf0dfc 252e6970
Sat Jun 21 09:55:24 2008  factoring 453847278100636257345202489577127970120979761678674473533642473400515264972284842096436647814028980618284824691 (111 digits)
Sat Jun 21 09:55:25 2008  no P-1/P+1/ECM available, skipping
Sat Jun 21 09:55:25 2008  commencing number field sieve (111-digit input)
Sat Jun 21 09:55:25 2008  R0: -2648889719843403962270
Sat Jun 21 09:55:25 2008  R1:  284568061549
Sat Jun 21 09:55:25 2008  A0:  1173007414994245235539459029
Sat Jun 21 09:55:25 2008  A1:  99595796075874533170621
Sat Jun 21 09:55:25 2008  A2: -978964025831487987
Sat Jun 21 09:55:25 2008  A3: -74405497406433
Sat Jun 21 09:55:25 2008  A4:  828092306
Sat Jun 21 09:55:25 2008  A5:  3480
Sat Jun 21 09:55:25 2008  size score = 1.835450e-11, Murphy alpha = -5.910601, combined = 1.316405e-10
Sat Jun 21 09:55:25 2008
Sat Jun 21 09:55:25 2008  commencing linear algebra
Sat Jun 21 09:55:25 2008  read 468867 cycles
Sat Jun 21 09:55:26 2008  cycles contain 1696762 unique relations
Sat Jun 21 09:55:41 2008  read 1696762 relations
Sat Jun 21 09:55:43 2008  using 32 quadratic characters above 134217410
Sat Jun 21 09:56:02 2008  building initial matrix
Sat Jun 21 09:56:19 2008  memory use: 214.2 MB
Sat Jun 21 09:56:22 2008  read 468867 cycles
Sat Jun 21 09:56:22 2008  matrix is 468576 x 468867 (142.8 MB) with weight 47963556 (102.30/col)
Sat Jun 21 09:56:22 2008  sparse part has weight 31802368 (67.83/col)
Sat Jun 21 09:56:34 2008  filtering completed in 3 passes
Sat Jun 21 09:56:34 2008  matrix is 465332 x 465532 (142.1 MB) with weight 47694935 (102.45/col)
Sat Jun 21 09:56:34 2008  sparse part has weight 31664613 (68.02/col)
Sat Jun 21 09:56:40 2008  read 465532 cycles
Sat Jun 21 09:56:41 2008  matrix is 465332 x 465532 (142.1 MB) with weight 47694935 (102.45/col)
Sat Jun 21 09:56:41 2008  sparse part has weight 31664613 (68.02/col)
Sat Jun 21 09:56:41 2008  saving the first 48 matrix rows for later
Sat Jun 21 09:56:41 2008  matrix is 465284 x 465532 (138.4 MB) with weight 37310151 (80.15/col)
Sat Jun 21 09:56:41 2008  sparse part has weight 31614095 (67.91/col)
Sat Jun 21 09:56:41 2008  matrix includes 64 packed rows
Sat Jun 21 09:56:41 2008  using block size 43690 for processor cache size 1024 kB
Sat Jun 21 09:56:44 2008  commencing Lanczos iteration
Sat Jun 21 09:56:44 2008  memory use: 126.8 MB
Sat Jun 21 10:39:05 2008  lanczos halted after 7359 iterations (dim = 465284)
Sat Jun 21 10:39:06 2008  recovered 44 nontrivial dependencies
Sat Jun 21 10:39:06 2008  elapsed time 00:43:42
Sat Jun 21 10:39:06 2008
Sat Jun 21 10:39:06 2008
Sat Jun 21 10:39:06 2008  Msieve v. 1.36
Sat Jun 21 10:39:06 2008  random seeds: b323b31d 6a581883
Sat Jun 21 10:39:06 2008  factoring 453847278100636257345202489577127970120979761678674473533642473400515264972284842096436647814028980618284824691 (111 digits)
Sat Jun 21 10:39:07 2008  no P-1/P+1/ECM available, skipping
Sat Jun 21 10:39:07 2008  commencing number field sieve (111-digit input)
Sat Jun 21 10:39:07 2008  R0: -2648889719843403962270
Sat Jun 21 10:39:07 2008  R1:  284568061549
Sat Jun 21 10:39:07 2008  A0:  1173007414994245235539459029
Sat Jun 21 10:39:07 2008  A1:  99595796075874533170621
Sat Jun 21 10:39:07 2008  A2: -978964025831487987
Sat Jun 21 10:39:07 2008  A3: -74405497406433
Sat Jun 21 10:39:07 2008  A4:  828092306
Sat Jun 21 10:39:07 2008  A5:  3480
Sat Jun 21 10:39:07 2008  size score = 1.835450e-11, Murphy alpha = -5.910601, combined = 1.316405e-10
Sat Jun 21 10:39:07 2008
Sat Jun 21 10:39:07 2008  commencing square root phase
Sat Jun 21 10:39:07 2008  reading relations for dependency 1
Sat Jun 21 10:39:07 2008  read 233173 cycles
Sat Jun 21 10:39:08 2008  cycles contain 1034223 unique relations
Sat Jun 21 10:39:17 2008  read 1034223 relations
Sat Jun 21 10:39:23 2008  multiplying 1470374 relations
Sat Jun 21 10:42:36 2008  multiply complete, coefficients have about 60.48 million bits
Sat Jun 21 10:42:38 2008  initial square root is modulo 481325497

prp38 factor: 44403506544729569591382802255945107907
prp74 factor: 10220978328444765863502623751657798456955829517191510572947586215944141713

Sat Jun 21 10:49:18 2008  elapsed time 00:10:12

Jun 22, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(7·10¹⁵⁴+17)/3 = 2(3)₁₅₃9_<155> = 30269 · 129967723442083_<15> · 1419277675450441_<16> · C121

C121 = P41 · P80

P41 = 53214050296629292416897411287835743443231_<41>

P80 = 78532516246414065130742159934751039833478176834632670589017775608994139603053867_<80>

Number: 23339_154
N=4179033269457535108462874239499699892492658734372965840608209926925321293346293445858237021220932202079153367369349524277
  ( 121 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=53214050296629292416897411287835743443231 (pp41)
 r2=78532516246414065130742159934751039833478176834632670589017775608994139603053867 (pp80)
Version: GGNFS-0.77.1-20060513-k8
Total time: 49.94 hours.
Scaled time: 99.43 units (timescale=1.991).
Factorization parameters were as follows:
name: 23339_154
n: 4179033269457535108462874239499699892492658734372965840608209926925321293346293445858237021220932202079153367369349524277
m: 10000000000000000000000000000000
c5: 7
c0: 170
skew: 1.89
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3200001)
Primes: RFBsize:216816, AFBsize:216831, largePrimes:5819124 encountered
Relations: rels:5836380, finalFF:567100
Max relations in full relation-set: 28
Initial matrix: 433712 x 567100 with sparse part having weight 52312857.
Pruned matrix : 372931 x 375163 with weight 34242270.
Total sieving time: 47.37 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 2.21 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 49.94 hours.
 --------- CPU info (if available) ----------

Jun 22, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(4·10¹⁸⁶-31)/9 = (4)₁₈₅1_<186> = 3 · 499 · C183

C183 = P42 · P141

P42 = 598138986459096730395341182841727820103903_<42>

P141 = 496356337189696433117694214004247077816195442584545699193391463991218138922878239760308283346772475928822571944307529233372143772747733213151_<141>

(7·10¹⁶²+17)/3 = 2(3)₁₆₁9_<163> = 43 · 1290083 · 245861039 · C147

C147 = P41 · P106

P41 = 43557628308424616166797635232339288714119_<41>

P106 = 3927685813921292174635198623350959368323057014448428705707920626668776971593108079668441340990588761661091_<106>

Number: n
N=171080678795055855404521716225376616271445673441345458338745464113339205428455017351146799445290278089868761209155962498970919891782836131864643829
  ( 147 digits)
SNFS difficulty: 162 digits.
Divisors found:

Sun Jun 22 17:30:45 2008  prp41 factor: 43557628308424616166797635232339288714119
Sun Jun 22 17:30:45 2008  prp106 factor: 3927685813921292174635198623350959368323057014448428705707920626668776971593108079668441340990588761661091
Sun Jun 22 17:30:45 2008  elapsed time 01:24:32 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 43.24 hours.
Scaled time: 79.08 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_3_161_9
n: 171080678795055855404521716225376616271445673441345458338745464113339205428455017351146799445290278089868761209155962498970919891782836131864643829
skew: 0.48
deg: 5
c5: 700
c0: 17
m: 100000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2673527)
Primes: RFBsize:315948, AFBsize:319141, largePrimes:7588284 encountered
Relations: rels:7132335, finalFF:663363
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 43.01 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000
total time: 43.24 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jun 21, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve

(7·10¹⁶¹+17)/3 = 2(3)₁₆₀9_<162> = 23 · 199 · C158

C158 = P75 · P84

P75 = 417946621514914850377965094249262197174211343113481758802230384518928472269_<75>

P84 = 121976187229760653869170760767223283184214542228118013644651384235208199727139732903_<84>

Number: n
N=50979535357949166120457359260068458233194960308790328453863520501056004660986089869638045298958560920544752749253513946544315781807588667977569004442502366907
  ( 158 digits)
SNFS difficulty: 161 digits.
Divisors found:

Sat Jun 21 20:08:55 2008  prp75 factor: 417946621514914850377965094249262197174211343113481758802230384518928472269
Sat Jun 21 20:08:55 2008  prp84 factor: 121976187229760653869170760767223283184214542228118013644651384235208199727139732903
Sat Jun 21 20:08:55 2008  elapsed time 01:17:34 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 39.59 hours.
Scaled time: 42.24 units (timescale=1.067).
Factorization parameters were as follows:
name: KA_2_3_160_9
n: 50979535357949166120457359260068458233194960308790328453863520501056004660986089869638045298958560920544752749253513946544315781807588667977569004442502366907
m: 100000000000000000000000000000000
deg: 5
c5: 70
c0: 17
skew: 0.75
type: snfs
# These parameters should be manually set:
rlim: 4000000
alim: 4000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1900001)
Primes: RFBsize:283146, AFBsize:283347, largePrimes:7532339 encountered
Relations: rels:7183166, finalFF:710737
Max relations in full relation-set: 28
Initial matrix: 566560 x 710737 with sparse part having weight 43297736.
Pruned matrix : 437204 x 440100 with weight 23469831.
Total sieving time: 39.36 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000
total time: 39.59 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jun 21, 2008 (3rd)

By Serge Batalov / pol51, Msieve 1.36

(7·10¹⁸²+17)/3 = 2(3)₁₈₁9_<183> = 67 · 263 · 1900937 · 13440434009_<11> · 48375581147_<11> · 951589712077612133_<18> · 488665648860358418437252373_<27> · C107

C107 = P52 · P56

P52 = 1477088288774321744891374447367639204725377033864653_<52>

P56 = 15598075496263923715557038856491111313580736481605334217_<56>

Number: 23339_182
N=23039734642949158512389218312077989194926064666066772598653542994568986691659234818295104220330335207731701
  ( 107 digits)
Divisors found:
 r1=1477088288774321744891374447367639204725377033864653
 r2=15598075496263923715557038856491111313580736481605334217
Version: Msieve v. 1.36
Total time: 4.03 hours.
Factorization parameters were as follows:
name: 23339_182
n: 23039734642949158512389218312077989194926064666066772598653542994568986691659234818295104220330335207731701
skew: 14986.36
# norm 3.69e+14
c5: 14580
c4: -403641738
c3: 23116709876478
c2: 73595465736422882
c1: -2826481295785857219317
c0: -1754227893603197984715460
# alpha -5.74
Y1: 36932884747
Y0: -275260764929799055773
# Murphy_E 1.48e-09
# M 10668570985258081896153286729973393070486963170843217333059578589374620638201361193672818543994648530861085
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2550001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 280216 x 280442
Total sieving time: 4.03 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 00:16:07
Time per square root: 00:05:19
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 0.03 hours.
 --------- CPU info (if available) ----------
Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init)
Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

_________________log____________

Msieve v. 1.36
...
Fri Jun 20 21:20:34 2008  restarting with 813821 relations
Fri Jun 20 22:00:18 2008  restarting with 1447052 relations
Fri Jun 20 22:41:11 2008  restarting with 2082702 relations
Fri Jun 20 23:23:05 2008  restarting with 2928687 relations
Sat Jun 21 00:06:00 2008  restarting with 4146072 relations
Sat Jun 21 00:50:01 2008  restarting with 5343099 relations
...
Msieve v. 1.36
Sat Jun 21 00:53:44 2008
random seeds: 30e59766 2c15b3e7
factoring 23039734642949158512389218312077989194926064666066772598653542994568986691659234818295104220330335207731701 (107 digits)

commencing number field sieve (107-digit input)
R0: -275260764929799055773
R1:  36932884747
A0: -1754227893603197984715460
A1: -2826481295785857219317
A2:  73595465736422882
A3:  23116709876478
A4: -403641738
A5:  14580
size score = 5.079226e-11, Murphy alpha = -5.726172, combined = 3.425672e-10

commencing linear algebra
read 280900 cycles
cycles contain 903261 unique relations
read 903261 relations
using 32 quadratic characters above 67108650
building initial matrix
memory use: 118.1 MB
read 280900 cycles
matrix is 280722 x 280900 (84.8 MB) with weight 28464436 (101.33/col)
sparse part has weight 18846930 (67.09/col)
filtering completed in 2 passes
matrix is 280264 x 280442 (84.7 MB) with weight 28429949 (101.38/col)
sparse part has weight 18829626 (67.14/col)
read 280442 cycles
matrix is 280264 x 280442 (84.7 MB) with weight 28429949 (101.38/col)
sparse part has weight 18829626 (67.14/col)
saving the first 48 matrix rows for later
matrix is 280216 x 280442 (81.6 MB) with weight 22142180 (78.95/col)
sparse part has weight 18586804 (66.28/col)
matrix includes 64 packed rows
using block size 43690 for processor cache size 1024 kB
commencing Lanczos iteration
memory use: 74.7 MB
linear algebra completed 279198 out of 280442 dimensions (99.6%)
lanczos halted after 4434 iterations (dim = 280213)
recovered 40 nontrivial dependencies
elapsed time 00:16:07

Msieve v. 1.36
Sat Jun 21 01:09:51 2008
commencing square root phase
reading relations for dependency 1
read 139967 cycles
cycles contain 565071 unique relations
read 565071 relations
multiplying 874324 relations
multiply complete, coefficients have about 36.33 million bits
initial square root is modulo 164987
prp52 factor: 1477088288774321744891374447367639204725377033864653
prp56 factor: 15598075496263923715557038856491111313580736481605334217
elapsed time 00:05:19
-> Computing time scale for this machine...
sumName = g107-23339_182.txt
-> Factorization summary written to g107-23339_182.txt.

Jun 21, 2008 (2nd)

By suberi / GMP-ECM

(64·10¹⁹⁸+53)/9 = 7(1)₁₉₇7_<199> = 13 · 17 · 239 · 659 · 17164139387516599_<17> · C176

C176 = P37 · P140

P37 = 1053947316666084614295602974773924601_<37>

P140 = 11293301951476245566388760055470099805134724921150625162401162556882527928893529688436385162911773878376001344332111171233605201210655091323_<140>

Jun 21, 2008

By Sinkiti Sibata / GGNFS

(7·10¹⁵⁰+17)/3 = 2(3)₁₄₉9_<151> = 9927675833_<10> · 27850032279480012968457853_<26> · C115

C115 = P46 · P70

P46 = 2162964817432196944368364287263298935912589503_<46>

P70 = 3901701488783183216290172472354578578481164704106467605063761861590737_<70>

Number: 23339_150
N=8439243048360848899390133873267331807205480475339932256875802759406740186112702376997344956850716178544540468233711
  ( 115 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=2162964817432196944368364287263298935912589503 (pp46)
 r2=3901701488783183216290172472354578578481164704106467605063761861590737 (pp70)
Version: GGNFS-0.77.1-20060513-k8
Total time: 26.01 hours.
Scaled time: 52.10 units (timescale=2.003).
Factorization parameters were as follows:
name: 23339_150
n: 8439243048360848899390133873267331807205480475339932256875802759406740186112702376997344956850716178544540468233711
m: 1000000000000000000000000000000
c5: 7
c0: 17
skew: 1.19
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176653, largePrimes:6113908 encountered
Relations: rels:6522242, finalFF:919725
Max relations in full relation-set: 28
Initial matrix: 353020 x 919725 with sparse part having weight 85181103.
Pruned matrix : 219865 x 221694 with weight 38860597.
Total sieving time: 24.89 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.84 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 26.01 hours.
 --------- CPU info (if available) ----------

Jun 20, 2008 (4th)

By Wataru Sakai / GGNFS

(19·10¹⁷⁹+17)/9 = 2(1)₁₇₈3_<180> = 3 · 7 · C179

C179 = P52 · P58 · P70

P52 = 1849590095332545517981729396507306427776395737285843_<52>

P58 = 1590976674832112443983760714051680873712445958345760173293_<58>

P70 = 3416272406688343554143889986701948138927926610009907327005065997766947_<70>

Number: 21113_179
N=10052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910053
  ( 179 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=1849590095332545517981729396507306427776395737285843 (pp52)
 r2=1590976674832112443983760714051680873712445958345760173293 (pp58)
 r3=3416272406688343554143889986701948138927926610009907327005065997766947 (pp70)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 552.22 hours.
Scaled time: 1112.17 units (timescale=2.014).
Factorization parameters were as follows:
n: 10052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910053
m: 1000000000000000000000000000000000000
c5: 19
c0: 170
skew: 1.55
type: snfsFactor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 10800001)
Primes: RFBsize:501962, AFBsize:503851, largePrimes:6702609 encountered
Relations: rels:7184475, finalFF:1158871
Max relations in full relation-set: 32
Initial matrix: 1005878 x 1158871 with sparse part having weight 84778609.
Pruned matrix : 880411 x 885504 with weight 65680688.
Total sieving time: 545.72 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 6.15 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 552.22 hours.
 --------- CPU info (if available) ----------

(7·10¹⁷⁴+11)/9 = (7)₁₇₃9_<174> = 251261 · 504617 · C163

C163 = P75 · P89

P75 = 151293655346678656951755233333841852499976949563535402282411057817628895559_<75>

P89 = 40545984826172869298143920767413765609952888879712288603313656316625649848981920183195313_<89>

Number: 77779_174
N=6134350253982660622277335689861201645599590140587053606604573046120563089433155514660435665006240828163050381504272365473039274996529904470390521720915719775314967
  ( 163 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=151293655346678656951755233333841852499976949563535402282411057817628895559 (pp75)
 r2=40545984826172869298143920767413765609952888879712288603313656316625649848981920183195313 (pp89)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 291.50 hours.
Scaled time: 585.04 units (timescale=2.007).
Factorization parameters were as follows:
n: 6134350253982660622277335689861201645599590140587053606604573046120563089433155514660435665006240828163050381504272365473039274996529904470390521720915719775314967
m: 100000000000000000000000000000000000
c5: 7
c0: 110
skew: 1.73
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 14300001)
Primes: RFBsize:501962, AFBsize:502982, largePrimes:6844410 encountered
Relations: rels:7419841, finalFF:1221660
Max relations in full relation-set: 32
Initial matrix: 1005009 x 1221660 with sparse part having weight 100226513.
Pruned matrix : 824853 x 829942 with weight 78137577.
Total sieving time: 283.78 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 7.36 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 291.50 hours.

Jun 20, 2008 (3rd)

By suberi / GMP-ECM

4·10¹⁷¹-3 = 3(9)₁₇₀7_<172> = 7 · 992551249 · 11060804449_<11> · 19009303771_<11> · C142

C142 = P37 · P106

P37 = 1249207319055289192086424463607428111_<37>

P106 = 2191904185664257747583477319317672323649397459016399392947765286350833997120102120957046738111957790744991_<106>

4·10¹⁸²-3 = 3(9)₁₈₁7_<183> = 3313 · 11483 · 176053 · C170

C170 = P35 · P136

P35 = 39387975579353615896504296945339241_<35>

P136 = 1516268457802174096132783680473005131671559431263031934817627015235299434290293219117245850021882172515022423742506186276722478373533891_<136>

Jun 20, 2008 (2nd)

By Sinkiti Sibata / Msieve, GGNFS

(17·10¹⁸¹+1)/9 = 1(8)₁₈₀9_<182> = 19 · 44839 · 48731 · 1008779 · 12003314779_<11> · 5830558817883227437007237_<25> · 758822763085731218605641418771_<30> · C100

C100 = P45 · P56

P45 = 242103400334044748484073044835249209568097447_<45>

P56 = 35078653987811118622758840608304843178836958530915817471_<56>

Thu Jun 19 06:38:30 2008  Msieve v. 1.36
Thu Jun 19 06:38:30 2008  random seeds: 57997b87 8224c00e
Thu Jun 19 06:38:30 2008  factoring 8492661409590470524891423727868139850632579649757129010224121294326903739481230882899276916193096537 (100 digits)
Thu Jun 19 06:38:31 2008  no P-1/P+1/ECM available, skipping
Thu Jun 19 06:38:31 2008  commencing quadratic sieve (100-digit input)
Thu Jun 19 06:38:32 2008  using multiplier of 17
Thu Jun 19 06:38:32 2008  using 64kb Pentium 4 sieve core
Thu Jun 19 06:38:32 2008  sieve interval: 18 blocks of size 65536
Thu Jun 19 06:38:32 2008  processing polynomials in batches of 6
Thu Jun 19 06:38:32 2008  using a sieve bound of 2751379 (100000 primes)
Thu Jun 19 06:38:32 2008  using large prime bound of 412706850 (28 bits)
Thu Jun 19 06:38:32 2008  using double large prime bound of 3222218636339400 (43-52 bits)
Thu Jun 19 06:38:32 2008  using trial factoring cutoff of 52 bits
Thu Jun 19 06:38:32 2008  polynomial 'A' values have 13 factors
Fri Jun 20 04:01:17 2008  100109 relations (23520 full + 76589 combined from 1507622 partial), need 100096
Fri Jun 20 04:01:23 2008  begin with 1531142 relations
Fri Jun 20 04:01:25 2008  reduce to 264987 relations in 10 passes
Fri Jun 20 04:01:25 2008  attempting to read 264987 relations
Fri Jun 20 04:01:34 2008  recovered 264987 relations
Fri Jun 20 04:01:34 2008  recovered 256717 polynomials
Fri Jun 20 04:01:35 2008  attempting to build 100109 cycles
Fri Jun 20 04:01:35 2008  found 100109 cycles in 6 passes
Fri Jun 20 04:01:35 2008  distribution of cycle lengths:
Fri Jun 20 04:01:35 2008     length 1 : 23520
Fri Jun 20 04:01:35 2008     length 2 : 17176
Fri Jun 20 04:01:35 2008     length 3 : 16902
Fri Jun 20 04:01:35 2008     length 4 : 13567
Fri Jun 20 04:01:35 2008     length 5 : 10292
Fri Jun 20 04:01:35 2008     length 6 : 7180
Fri Jun 20 04:01:35 2008     length 7 : 4698
Fri Jun 20 04:01:35 2008     length 9+: 6774
Fri Jun 20 04:01:35 2008  largest cycle: 20 relations
Fri Jun 20 04:01:36 2008  matrix is 100000 x 100109 (28.3 MB) with weight 7027440 (70.20/col)
Fri Jun 20 04:01:36 2008  sparse part has weight 7027440 (70.20/col)
Fri Jun 20 04:01:38 2008  filtering completed in 3 passes
Fri Jun 20 04:01:38 2008  matrix is 96171 x 96234 (27.4 MB) with weight 6799375 (70.65/col)
Fri Jun 20 04:01:38 2008  sparse part has weight 6799375 (70.65/col)
Fri Jun 20 04:01:39 2008  saving the first 48 matrix rows for later
Fri Jun 20 04:01:39 2008  matrix is 96123 x 96234 (17.6 MB) with weight 5431041 (56.44/col)
Fri Jun 20 04:01:39 2008  sparse part has weight 4041126 (41.99/col)
Fri Jun 20 04:01:39 2008  matrix includes 64 packed rows
Fri Jun 20 04:01:39 2008  using block size 21845 for processor cache size 512 kB
Fri Jun 20 04:01:40 2008  commencing Lanczos iteration
Fri Jun 20 04:01:40 2008  memory use: 16.6 MB
Fri Jun 20 04:03:29 2008  lanczos halted after 1521 iterations (dim = 96123)
Fri Jun 20 04:03:29 2008  recovered 18 nontrivial dependencies
Fri Jun 20 04:03:33 2008  prp45 factor: 242103400334044748484073044835249209568097447
Fri Jun 20 04:03:33 2008  prp56 factor: 35078653987811118622758840608304843178836958530915817471
Fri Jun 20 04:03:33 2008  elapsed time 21:25:03

(7·10¹⁴⁶+17)/3 = 2(3)₁₄₅9_<147> = 41873810519116707626863_<23> · C124

C124 = P59 · P66

P59 = 21804397652798991947920303404221539210667198756143728491239_<59>

P66 = 255558427991811864344755703271114165099174644030525182217947392227_<66>

Number: 23339_146
N=5572297587457662816333162127727176214809046786511556224921466488809034721917819970726236103796689823938279599964261266199253
  ( 124 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=21804397652798991947920303404221539210667198756143728491239 (pp59)
 r2=255558427991811864344755703271114165099174644030525182217947392227 (pp66)
Version: GGNFS-0.77.1-20060513-k8
Total time: 19.48 hours.
Scaled time: 39.02 units (timescale=2.003).
Factorization parameters were as follows:
name: 23339_146
n: 5572297587457662816333162127727176214809046786511556224921466488809034721917819970726236103796689823938279599964261266199253
m: 100000000000000000000000000000
c5: 70
c0: 17
skew: 0.75
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2850001)
Primes: RFBsize:114155, AFBsize:114392, largePrimes:2827827 encountered
Relations: rels:2801739, finalFF:256860
Max relations in full relation-set: 28
Initial matrix: 228614 x 256860 with sparse part having weight 27064766.
Pruned matrix : 220197 x 221404 with weight 21616388.
Total sieving time: 18.70 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.57 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 19.48 hours.
 --------- CPU info (if available) ----------

(19·10¹⁵³+71)/9 = 2(1)₁₅₂9_<154> = 13 · 17 · 1931 · 17681 · 79167967819_<11> · C133

C133 = P55 · P79

P55 = 2330871598302278901853376041628293375034044869755858891_<55>

P79 = 1516218784411238460729939570299747737958774664936753931542252342962491493263081_<79>

Number: 21119_153
N=3534111301396561829241944371109709550951878020320586502879799576712460981422857149193925613075150874769889794783911449876155375903171
  ( 133 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=2330871598302278901853376041628293375034044869755858891 (pp55)
 r2=1516218784411238460729939570299747737958774664936753931542252342962491493263081 (pp79)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 55.24 hours.
Scaled time: 37.23 units (timescale=0.674).
Factorization parameters were as follows:
name: 21119_153
n: 3534111301396561829241944371109709550951878020320586502879799576712460981422857149193925613075150874769889794783911449876155375903171
m: 1000000000000000000000000000000
c5: 19000
c0: 71
skew: 0.33
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2700001)
Primes: RFBsize:176302, AFBsize:176259, largePrimes:5780933 encountered
Relations: rels:5751272, finalFF:468492
Max relations in full relation-set: 28
Initial matrix: 352628 x 468492 with sparse part having weight 49607110.
Pruned matrix : 312585 x 314412 with weight 31405699.
Total sieving time: 50.22 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 4.53 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 55.24 hours.
 --------- CPU info (if available) ----------

Jun 20, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(19·10¹⁷³+17)/9 = 2(1)₁₇₂3_<174> = 3 · 7 · C173

C173 = P38 · P57 · P79

P38 = 11908775400215661195548462282129043797_<38>

P57 = 826889165198643841886538166294656560201100292366830050189_<57>

P79 = 1020886335567388225849072357898453571339187176611699612014911899812973186198741_<79>

Number: n
N=844159849780020235129746469497252431004627125959824403139627884770709057725585735018317388737365147113252112148503478738967403158612049
  ( 135 digits)
SNFS difficulty: 174 digits.
Divisors found:

Fri Jun 20 02:44:06 2008  prp57 factor: 826889165198643841886538166294656560201100292366830050189
Fri Jun 20 02:44:06 2008  prp79 factor: 1020886335567388225849072357898453571339187176611699612014911899812973186198741
Fri Jun 20 02:44:06 2008  elapsed time 02:59:28 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 96.48 hours.
Scaled time: 80.94 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_2_1_172_3
n: 844159849780020235129746469497252431004627125959824403139627884770709057725585735018317388737365147113252112148503478738967403158612049
type: snfs
deg: 5
c5: 19000
c0: 17
skew: 0.25
m: 10000000000000000000000000000000000
rlim: 4500000
alim: 4500000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 11300747)
Primes: RFBsize:315948, AFBsize:315306, largePrimes:6194474 encountered
Relations: rels:6248801, finalFF:651129
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 96.15 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,174,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.5,2.5,100000
total time: 96.48 hours.
 --------- CPU info (if available) ----------

8·10¹⁶⁹+9 = 8(0)₁₆₈9_<170> = 2083 · 21187 · C163

C163 = P33 · P130

P33 = 347913094655913140947256232930961_<33>

P130 = 5210272953749998271101503426402444733270293388626467088714412188109283843702487962421130258535164821785639637952029491481694049489_<130>

(11·10¹⁶⁷+61)/9 = 1(2)₁₆₆9_<168> = 3⁴ · 449 · 33087070891123_<14> · C150

C150 = P72 · P78

P72 = 748005811625541632642916647689589194648693239663159298286037563308548193_<72>

P78 = 135786164695082180429353840411133841148804527719360141316474387898066866066119_<78>

Number: n
N=101568840330264413237388822930979889101910651497072026084643242058579491153939325114881169376679390422211703898084569112611049921791675345871035972967
  ( 150 digits)
SNFS difficulty: 168 digits.
Divisors found:

Fri Jun 20 20:10:57 2008  prp72 factor: 748005811625541632642916647689589194648693239663159298286037563308548193
Fri Jun 20 20:10:57 2008  prp78 factor: 135786164695082180429353840411133841148804527719360141316474387898066866066119
Fri Jun 20 20:10:57 2008  elapsed time 02:27:34 (Msieve 1.36)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 113.07 hours.
Scaled time: 148.57 units (timescale=1.314).
Factorization parameters were as follows:
name: KA_1_2_166_9
n: 101568840330264413237388822930979889101910651497072026084643242058579491153939325114881169376679390422211703898084569112611049921791675345871035972967
skew: 0.56
deg: 5
c5: 1100
c0: 61
m: 1000000000000000000000000000000000
type: snfs
rlim: 3800000
alim: 3800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5000001)
Primes: RFBsize:269987, AFBsize:269319, largePrimes:7804913 encountered
Relations: rels:7226972, finalFF:542557
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 112.54 hours.
Total relation processing time: 0.53 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,3800000,3800000,28,28,48,48,2.5,2.5,100000
total time: 113.07 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jun 19, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(19·10¹⁵⁴+71)/9 = 2(1)₁₅₃9_<155> = 7 · 73 · 4483 · 33487 · 83735683584829_<14> · C130

C130 = P46 · P85

P46 = 1791677943138389668968679508662606052300273107_<46>

P85 = 1834318275709524259788133515195304765934811811430526130176162937982551937357179892483_<85>

Number: n
N=3286507595284397990244440725109649136011496454300802589054816534378305641090379440018700033067620390985386802795054882189796354681
  ( 130 digits)
SNFS difficulty: 156 digits.
Divisors found:

Fri Jun 20 00:19:02 2008  prp46 factor: 1791677943138389668968679508662606052300273107
Fri Jun 20 00:19:02 2008  prp85 factor: 1834318275709524259788133515195304765934811811430526130176162937982551937357179892483
Fri Jun 20 00:19:02 2008  elapsed time 00:29:43 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 23.65 hours.
Scaled time: 43.12 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_2_1_153_9
n: 3286507595284397990244440725109649136011496454300802589054816534378305641090379440018700033067620390985386802795054882189796354681
skew: 2.06
deg: 5
c5: 19
c0: 710
m: 10000000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1800311)
Primes: RFBsize:114155, AFBsize:114373, largePrimes:7133643 encountered
Relations: rels:6460420, finalFF:245971
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 23.49 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000
total time: 23.65 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jun 19, 2008 (2nd)

By Sinkiti Sibata / GGNFS, Msieve

(7·10¹⁵⁸+17)/3 = 2(3)₁₅₇9_<159> = 242357443 · 28030229173069_<14> · 1454061345137057_<16> · 16465999087301435553750282083_<29> · C94

C94 = P44 · P50

P44 = 19146295587768898703757081073237370039739239_<44>

P50 = 74926974982117317392890572430494126577076446433113_<50>

Wed Jun 18 20:51:43 2008  Msieve v. 1.36
Wed Jun 18 20:51:43 2008  random seeds: 1a54057b b92e04e7
Wed Jun 18 20:51:43 2008  factoring 1434574010504983451855968360270997415967569984416379180128533164708864833002769858886175021007 (94 digits)
Wed Jun 18 20:51:45 2008  no P-1/P+1/ECM available, skipping
Wed Jun 18 20:51:45 2008  commencing quadratic sieve (94-digit input)
Wed Jun 18 20:51:45 2008  using multiplier of 3
Wed Jun 18 20:51:45 2008  using 64kb Pentium 4 sieve core
Wed Jun 18 20:51:45 2008  sieve interval: 18 blocks of size 65536
Wed Jun 18 20:51:45 2008  processing polynomials in batches of 6
Wed Jun 18 20:51:45 2008  using a sieve bound of 1987303 (74118 primes)
Wed Jun 18 20:51:45 2008  using large prime bound of 256362087 (27 bits)
Wed Jun 18 20:51:45 2008  using double large prime bound of 1367529713306016 (42-51 bits)
Wed Jun 18 20:51:45 2008  using trial factoring cutoff of 51 bits
Wed Jun 18 20:51:45 2008  polynomial 'A' values have 12 factors
Thu Jun 19 01:10:48 2008  74480 relations (18948 full + 55532 combined from 1022585 partial), need 74214
Thu Jun 19 01:10:52 2008  begin with 1041533 relations
Thu Jun 19 01:10:53 2008  reduce to 189783 relations in 11 passes
Thu Jun 19 01:10:53 2008  attempting to read 189783 relations
Thu Jun 19 01:10:59 2008  recovered 189783 relations
Thu Jun 19 01:10:59 2008  recovered 170542 polynomials
Thu Jun 19 01:10:59 2008  attempting to build 74480 cycles
Thu Jun 19 01:10:59 2008  found 74480 cycles in 5 passes
Thu Jun 19 01:10:59 2008  distribution of cycle lengths:
Thu Jun 19 01:10:59 2008     length 1 : 18948
Thu Jun 19 01:10:59 2008     length 2 : 13347
Thu Jun 19 01:10:59 2008     length 3 : 12736
Thu Jun 19 01:10:59 2008     length 4 : 10257
Thu Jun 19 01:10:59 2008     length 5 : 7348
Thu Jun 19 01:10:59 2008     length 6 : 4791
Thu Jun 19 01:10:59 2008     length 7 : 3039
Thu Jun 19 01:10:59 2008     length 9+: 4014
Thu Jun 19 01:10:59 2008  largest cycle: 21 relations
Thu Jun 19 01:10:59 2008  matrix is 74118 x 74480 (18.5 MB) with weight 4549876 (61.09/col)
Thu Jun 19 01:10:59 2008  sparse part has weight 4549876 (61.09/col)
Thu Jun 19 01:11:01 2008  filtering completed in 3 passes
Thu Jun 19 01:11:01 2008  matrix is 70109 x 70173 (17.5 MB) with weight 4299746 (61.27/col)
Thu Jun 19 01:11:01 2008  sparse part has weight 4299746 (61.27/col)
Thu Jun 19 01:11:01 2008  saving the first 48 matrix rows for later
Thu Jun 19 01:11:01 2008  matrix is 70061 x 70173 (10.1 MB) with weight 3250963 (46.33/col)
Thu Jun 19 01:11:01 2008  sparse part has weight 2225728 (31.72/col)
Thu Jun 19 01:11:01 2008  matrix includes 64 packed rows
Thu Jun 19 01:11:01 2008  using block size 21845 for processor cache size 512 kB
Thu Jun 19 01:11:02 2008  commencing Lanczos iteration
Thu Jun 19 01:11:02 2008  memory use: 10.4 MB
Thu Jun 19 01:11:52 2008  lanczos halted after 1110 iterations (dim = 70060)
Thu Jun 19 01:11:52 2008  recovered 17 nontrivial dependencies
Thu Jun 19 01:11:53 2008  prp44 factor: 19146295587768898703757081073237370039739239
Thu Jun 19 01:11:53 2008  prp50 factor: 74926974982117317392890572430494126577076446433113
Thu Jun 19 01:11:53 2008  elapsed time 04:20:10

(7·10¹⁴³+17)/3 = 2(3)₁₄₂9_<144> = 1867 · 4339 · C137

C137 = P39 · P98

P39 = 535765703863921912750851250492181849899_<39>

P98 = 53761070475339461599109698874173573872281314889937566690752801724933075409845431841588828412544097_<98>

Number: 23339_143
N=28803337763698157643877095499400293933947116002027590388062843451513839654040641262698825840165587919945978105595422803989295198372496203
  ( 137 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=535765703863921912750851250492181849899 (pp39)
 r2=53761070475339461599109698874173573872281314889937566690752801724933075409845431841588828412544097 (pp98)
Version: GGNFS-0.77.1-20060513-k8
Total time: 18.67 hours.
Scaled time: 37.52 units (timescale=2.010).
Factorization parameters were as follows:
name: 23339_143
n: 28803337763698157643877095499400293933947116002027590388062843451513839654040641262698825840165587919945978105595422803989295198372496203
m: 10000000000000000000000000000
c5: 7000
c0: 17
skew: 0.3
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2750001)
Primes: RFBsize:100021, AFBsize:100228, largePrimes:2937213 encountered
Relations: rels:2987873, finalFF:275507
Max relations in full relation-set: 28
Initial matrix: 200316 x 275507 with sparse part having weight 32504675.
Pruned matrix : 181772 x 182837 with weight 20348065.
Total sieving time: 18.00 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.46 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 18.67 hours.
 --------- CPU info (if available) ----------

(7·10¹⁴⁴+17)/3 = 2(3)₁₄₃9_<145> = 6112388617_<10> · C135

C135 = P45 · P90

P45 = 626946312457987940199614144659177704270837173_<45>

P90 = 608885279634814638970724327573961019652307778580222127000169140138289548248184830103481879_<90>

Number: 23339_144
N=381738380776997859744121916215088281147051506809213294713740439081334892377529819179907247270716742343762095474325325171538145565088067
  ( 135 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=626946312457987940199614144659177704270837173 (pp45)
 r2=608885279634814638970724327573961019652307778580222127000169140138289548248184830103481879 (pp90)
Version: GGNFS-0.77.1-20060513-k8
Total time: 29.13 hours.
Scaled time: 58.34 units (timescale=2.003).
Factorization parameters were as follows:
name: 23339_144
n: 381738380776997859744121916215088281147051506809213294713740439081334892377529819179907247270716742343762095474325325171538145565088067
m: 100000000000000000000000000000
c5: 7
c0: 170
skew: 1.89
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 4150001)
Primes: RFBsize:100021, AFBsize:100013, largePrimes:3149571 encountered
Relations: rels:3284509, finalFF:230295
Max relations in full relation-set: 28
Initial matrix: 200099 x 230295 with sparse part having weight 31044379.
Pruned matrix : 193206 x 194270 with weight 25166348.
Total sieving time: 28.35 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.53 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 29.13 hours.
 --------- CPU info (if available) ----------

Jun 19, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(7·10¹⁶⁰+17)/3 = 2(3)₁₅₉9_<161> = 3701 · 35593 · 69389 · 459841 · 93435119 · 17324364797_<11> · 3387727253081_<13> · 102689731400639_<15> · C97

C97 = P44 · P54

P44 = 38407669121855954038639728065299289990791621_<44>

P54 = 256669293719185842934861313379909281435703545898255851_<54>

Number: n
N=9858069306906950463503372591344284125766706149980496147484008217952622305609424926370754685024471
  ( 97 digits)
Divisors found:

Thu Jun 19 03:19:13 2008  prp44 factor: 38407669121855954038639728065299289990791621
Thu Jun 19 03:19:13 2008  prp54 factor: 256669293719185842934861313379909281435703545898255851
Thu Jun 19 03:19:13 2008  elapsed time 00:16:07 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.39 hours.
Scaled time: 9.30 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_2_3_159_9
n:  9858069306906950463503372591344284125766706149980496147484008217952622305609424926370754685024471
m:  15110236062892358326859
deg: 4
c4: 189106680
c3: -174424676846
c2: -1805591920498891697
c1: 846965004993150148
c0: 1950101995051999511698950
skew: 1635.250
type: gnfs
# adj. I(F,S) = 54.947
# E(F1,F2) = 2.502940e-05
# GGNFS version 0.77.1-20051202-athlon polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1213786088.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved  special-q in [100000, 1060357)
Primes: RFBsize:92938, AFBsize:93239, largePrimes:1777853 encountered
Relations: rels:1790024, finalFF:200325
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 6.30 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,96,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 6.39 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(7·10¹⁵⁶+17)/3 = 2(3)₁₅₅9_<157> = 31 · 239 · 128262209 · 54153681173_<11> · C134

C134 = P39 · P95

P39 = 527845703954308242079195374698855965483_<39>

P95 = 85898088634340166008079398675596416314617721039017551057834275703819076412196974341860416371741_<95>

(19·10¹⁵⁸+71)/9 = 2(1)₁₅₇9_<159> = 3 · 5111043929_<10> · 8586699613_<10> · C139

C139 = P61 · P79

P61 = 1552232375168401888226285240732768948412176616299065734638659_<61>

P79 = 1032992611981958171657311747096309357508297728486040740667074691813325998649211_<79>

Number: n
N=1603444575628166296323850859232332205498429149271953164507338103129857597627597826527727616013810322286400015061749747416092265207180448049
  ( 139 digits)
SNFS difficulty: 159 digits.
Divisors found:

Thu Jun 19 18:40:36 2008  prp61 factor: 1552232375168401888226285240732768948412176616299065734638659
Thu Jun 19 18:40:36 2008  prp79 factor: 1032992611981958171657311747096309357508297728486040740667074691813325998649211
Thu Jun 19 18:40:36 2008  elapsed time 01:19:33 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 48.30 hours.
Scaled time: 84.96 units (timescale=1.759).
Factorization parameters were as follows:
name: KA_2_1_157_9
n: 1603444575628166296323850859232332205498429149271953164507338103129857597627597826527727616013810322286400015061749747416092265207180448049
type: snfs
skew: 0.33
deg: 5
c5: 19000
c0: 71
m: 10000000000000000000000000000000
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2500213)
Primes: RFBsize:203362, AFBsize:203478, largePrimes:7041615 encountered
Relations: rels:6395775, finalFF:429719
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 48.07 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.3,2.3,100000
total time: 48.30 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(7·10¹⁵²+17)/3 = 2(3)₁₅₁9_<153> = 23029 · 840704633 · 1326812001547_<13> · C127

C127 = P45 · P83

P45 = 610101261968507830368749150447308985874102137_<45>

P83 = 14888363041956731209585176317112178230936915291439811404040951408011091747600139293_<83>

Number: n
N=9083409080543093805913755278938747676141202257994375217606729563473712226337971583897960187761658473791899659290793982508969141
  ( 127 digits)
SNFS difficulty: 152 digits.
Divisors found:

Thu Jun 19 19:24:26 2008  prp45 factor: 610101261968507830368749150447308985874102137
Thu Jun 19 19:24:26 2008  prp83 factor: 14888363041956731209585176317112178230936915291439811404040951408011091747600139293
Thu Jun 19 19:24:26 2008  elapsed time 00:51:02 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 18.07 hours.
Scaled time: 33.05 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_3_151_9
n: 9083409080543093805913755278938747676141202257994375217606729563473712226337971583897960187761658473791899659290793982508969141
skew: 0.48
deg: 5
c5: 700
c0: 17
m: 1000000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1500157)
Primes: RFBsize:114155, AFBsize:114427, largePrimes:6826015 encountered
Relations: rels:6086022, finalFF:228605
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 17.92 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000
total time: 18.07 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jun 18, 2008 (4th)

By suberi / GMP-ECM

(16·10²⁴⁴-61)/9 = 1(7)₂₄₃1_<245> = 13 · 11093 · 1330706156723_<13> · 3353370740535258743_<19> · C209

C209 = P35 · C175

P35 = 23927338568455349437657020835689181_<35>

C175 = [1154587832011312664684319787690887343855960034230279419823600016435051159772210847611408481790922675000344963443900485817612482088891032224245876772595417312934546709619016891_<175>]

(16·10²⁵⁰-61)/9 = 1(7)₂₄₉1_<251> = 13 · 1117 · 3001 · 68960274559011859_<17> · 105187359738922024391561_<24> · C203

C203 = P35 · P169

P35 = 47127519770374767542490387021015569_<35>

P169 = 1193377463091214465280930122329596329399002506548645441537440214904924329099256353065394411257513274567225314616795075715769044965685150587906045369454735928523088581121_<169>

Jun 18, 2008 (3rd)

By Sinkiti Sibata / GGNFS, Msieve

(7·10¹¹⁷+17)/3 = 2(3)₁₁₆9_<118> = 23 · 2333 · 594170435227_<12> · C101

C101 = P40 · P62

P40 = 7055000601307972440354361852306418014519_<40>

P62 = 10373519245946236498753585760743609141393461815640085096926917_<62>

Number: 23339_117
N=73185184517830523349631685351219188493971228777679019193467213732990802157068577513278831575587907923
  ( 101 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=7055000601307972440354361852306418014519 (pp40)
 r2=10373519245946236498753585760743609141393461815640085096926917 (pp62)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.27 hours.
Scaled time: 4.53 units (timescale=1.996).
Factorization parameters were as follows:
name: 23339_117
n: 73185184517830523349631685351219188493971228777679019193467213732990802157068577513278831575587907923
m: 100000000000000000000000
c5: 700
c0: 17
skew: 0.48
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64083, largePrimes:2285266 encountered
Relations: rels:2533749, finalFF:360298
Max relations in full relation-set: 28
Initial matrix: 113248 x 360298 with sparse part having weight 33638715.
Pruned matrix : 75040 x 75670 with weight 6289789.
Total sieving time: 2.15 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.27 hours.
 --------- CPU info (if available) ----------

(7·10¹²³+17)/3 = 2(3)₁₂₂9_<124> = 541 · 8875041087261656332723028987_<28> · C93

C93 = P41 · P53

P41 = 39640352959941520079217079058662355588447_<41>

P53 = 12259468301921439444803232407524450529599277231054411_<53>

Wed Jun 18 10:30:39 2008  Msieve v. 1.36
Wed Jun 18 10:30:39 2008  random seeds: 071b2352 82b713c7
Wed Jun 18 10:30:39 2008  factoring 485969650589380773048129474294923494937486054697957352921123969457889678948105771180179989717 (93 digits)
Wed Jun 18 10:30:40 2008  no P-1/P+1/ECM available, skipping
Wed Jun 18 10:30:40 2008  commencing quadratic sieve (93-digit input)
Wed Jun 18 10:30:40 2008  using multiplier of 13
Wed Jun 18 10:30:40 2008  using 64kb Pentium 4 sieve core
Wed Jun 18 10:30:40 2008  sieve interval: 18 blocks of size 65536
Wed Jun 18 10:30:40 2008  processing polynomials in batches of 6
Wed Jun 18 10:30:40 2008  using a sieve bound of 1922351 (71765 primes)
Wed Jun 18 10:30:40 2008  using large prime bound of 232604471 (27 bits)
Wed Jun 18 10:30:40 2008  using double large prime bound of 1147922137951622 (42-51 bits)
Wed Jun 18 10:30:40 2008  using trial factoring cutoff of 51 bits
Wed Jun 18 10:30:40 2008  polynomial 'A' values have 12 factors
Wed Jun 18 10:30:45 2008  restarting with 18575 full and 956051 partial relations
Wed Jun 18 10:30:45 2008  72209 relations (18575 full + 53634 combined from 956051 partial), need 71861
Wed Jun 18 10:30:48 2008  begin with 974626 relations
Wed Jun 18 10:30:49 2008  reduce to 182680 relations in 11 passes
Wed Jun 18 10:30:49 2008  attempting to read 182680 relations
Wed Jun 18 10:30:55 2008  recovered 182680 relations
Wed Jun 18 10:30:55 2008  recovered 161924 polynomials
Wed Jun 18 10:30:55 2008  attempting to build 72209 cycles
Wed Jun 18 10:30:55 2008  found 72209 cycles in 6 passes
Wed Jun 18 10:30:55 2008  distribution of cycle lengths:
Wed Jun 18 10:30:55 2008     length 1 : 18575
Wed Jun 18 10:30:55 2008     length 2 : 13202
Wed Jun 18 10:30:55 2008     length 3 : 12365
Wed Jun 18 10:30:55 2008     length 4 : 9549
Wed Jun 18 10:30:55 2008     length 5 : 7117
Wed Jun 18 10:30:55 2008     length 6 : 4605
Wed Jun 18 10:30:55 2008     length 7 : 2941
Wed Jun 18 10:30:55 2008     length 9+: 3855
Wed Jun 18 10:30:55 2008  largest cycle: 19 relations
Wed Jun 18 10:30:56 2008  matrix is 71765 x 72209 (18.3 MB) with weight 4519177 (62.58/col)
Wed Jun 18 10:30:56 2008  sparse part has weight 4519177 (62.58/col)
Wed Jun 18 10:30:57 2008  filtering completed in 3 passes
Wed Jun 18 10:30:57 2008  matrix is 67627 x 67691 (17.2 MB) with weight 4244832 (62.71/col)
Wed Jun 18 10:30:57 2008  sparse part has weight 4244832 (62.71/col)
Wed Jun 18 10:30:58 2008  saving the first 48 matrix rows for later
Wed Jun 18 10:30:58 2008  matrix is 67579 x 67691 (10.6 MB) with weight 3302713 (48.79/col)
Wed Jun 18 10:30:58 2008  sparse part has weight 2369433 (35.00/col)
Wed Jun 18 10:30:58 2008  matrix includes 64 packed rows
Wed Jun 18 10:30:58 2008  using block size 21845 for processor cache size 512 kB
Wed Jun 18 10:30:58 2008  commencing Lanczos iteration
Wed Jun 18 10:30:58 2008  memory use: 10.4 MB
Wed Jun 18 10:31:46 2008  lanczos halted after 1070 iterations (dim = 67575)
Wed Jun 18 10:31:47 2008  recovered 15 nontrivial dependencies
Wed Jun 18 10:31:48 2008  prp41 factor: 39640352959941520079217079058662355588447
Wed Jun 18 10:31:48 2008  prp53 factor: 12259468301921439444803232407524450529599277231054411
Wed Jun 18 10:31:48 2008  elapsed time 00:01:09

(7·10¹¹⁸+17)/3 = 2(3)₁₁₇9_<119> = 19227743 · C112

C112 = P49 · P63

P49 = 3093087719815041604894591181802808992385054200749_<49>

P63 = 392334265399879349992246101266524172412020862047021909878065977_<63>

Number: 23339_118
N=1213524298371022190869377302023088894694157984810455045781157639424103667982941800986903836468655386819624816773
  ( 112 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=3093087719815041604894591181802808992385054200749 (pp49)
 r2=392334265399879349992246101266524172412020862047021909878065977 (pp63)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.32 hours.
Scaled time: 4.58 units (timescale=1.973).
Factorization parameters were as follows:
name: 23339_118
n: 1213524298371022190869377302023088894694157984810455045781157639424103667982941800986903836468655386819624816773
m: 100000000000000000000000
c5: 7000
c0: 17
skew: 0.3
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64188, largePrimes:2227594 encountered
Relations: rels:2431241, finalFF:324093
Max relations in full relation-set: 28
Initial matrix: 113353 x 324093 with sparse part having weight 30217094.
Pruned matrix : 77229 x 77859 with weight 5970872.
Total sieving time: 2.20 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,118,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.32 hours.
 --------- CPU info (if available) ----------

(7·10¹²⁶+17)/3 = 2(3)₁₂₅9_<127> = 31 · 3613 · 86753 · 731135486302163043392089_<24> · C93

C93 = P41 · P52

P41 = 68030424514091868787676449965273815693041_<41>

P52 = 4827936880554905413919785453314420134437806840877729_<52>

Wed Jun 18 10:40:16 2008  Msieve v. 1.36
Wed Jun 18 10:40:16 2008  random seeds: b05deab3 ec6c7f99
Wed Jun 18 10:40:16 2008  factoring 328446595511390663902274889915254013499180885468671028135877513010323355822376511174877183889 (93 digits)
Wed Jun 18 10:40:17 2008  no P-1/P+1/ECM available, skipping
Wed Jun 18 10:40:17 2008  commencing quadratic sieve (93-digit input)
Wed Jun 18 10:40:17 2008  using multiplier of 19
Wed Jun 18 10:40:17 2008  using 64kb Pentium 4 sieve core
Wed Jun 18 10:40:17 2008  sieve interval: 18 blocks of size 65536
Wed Jun 18 10:40:17 2008  processing polynomials in batches of 6
Wed Jun 18 10:40:17 2008  using a sieve bound of 1919377 (71765 primes)
Wed Jun 18 10:40:17 2008  using large prime bound of 232244617 (27 bits)
Wed Jun 18 10:40:17 2008  using double large prime bound of 1144727446588341 (42-51 bits)
Wed Jun 18 10:40:17 2008  using trial factoring cutoff of 51 bits
Wed Jun 18 10:40:17 2008  polynomial 'A' values have 12 factors
Wed Jun 18 14:37:22 2008  72231 relations (18362 full + 53869 combined from 958546 partial), need 71861
Wed Jun 18 14:37:26 2008  begin with 976908 relations
Wed Jun 18 14:37:27 2008  reduce to 183295 relations in 10 passes
Wed Jun 18 14:37:27 2008  attempting to read 183295 relations
Wed Jun 18 14:37:32 2008  recovered 183295 relations
Wed Jun 18 14:37:32 2008  recovered 163365 polynomials
Wed Jun 18 14:37:33 2008  attempting to build 72231 cycles
Wed Jun 18 14:37:33 2008  found 72231 cycles in 5 passes
Wed Jun 18 14:37:33 2008  distribution of cycle lengths:
Wed Jun 18 14:37:33 2008     length 1 : 18362
Wed Jun 18 14:37:33 2008     length 2 : 13186
Wed Jun 18 14:37:33 2008     length 3 : 12410
Wed Jun 18 14:37:33 2008     length 4 : 9670
Wed Jun 18 14:37:33 2008     length 5 : 7135
Wed Jun 18 14:37:33 2008     length 6 : 4786
Wed Jun 18 14:37:33 2008     length 7 : 2899
Wed Jun 18 14:37:33 2008     length 9+: 3783
Wed Jun 18 14:37:33 2008  largest cycle: 19 relations
Wed Jun 18 14:37:33 2008  matrix is 71765 x 72231 (18.7 MB) with weight 4625287 (64.03/col)
Wed Jun 18 14:37:33 2008  sparse part has weight 4625287 (64.03/col)
Wed Jun 18 14:37:35 2008  filtering completed in 3 passes
Wed Jun 18 14:37:35 2008  matrix is 67539 x 67603 (17.6 MB) with weight 4340466 (64.21/col)
Wed Jun 18 14:37:35 2008  sparse part has weight 4340466 (64.21/col)
Wed Jun 18 14:37:35 2008  saving the first 48 matrix rows for later
Wed Jun 18 14:37:35 2008  matrix is 67491 x 67603 (11.0 MB) with weight 3412442 (50.48/col)
Wed Jun 18 14:37:35 2008  sparse part has weight 2475447 (36.62/col)
Wed Jun 18 14:37:35 2008  matrix includes 64 packed rows
Wed Jun 18 14:37:35 2008  using block size 21845 for processor cache size 512 kB
Wed Jun 18 14:37:36 2008  commencing Lanczos iteration
Wed Jun 18 14:37:36 2008  memory use: 10.6 MB
Wed Jun 18 14:38:25 2008  lanczos halted after 1069 iterations (dim = 67490)
Wed Jun 18 14:38:25 2008  recovered 18 nontrivial dependencies
Wed Jun 18 14:38:26 2008  prp41 factor: 68030424514091868787676449965273815693041
Wed Jun 18 14:38:26 2008  prp52 factor: 4827936880554905413919785453314420134437806840877729
Wed Jun 18 14:38:26 2008  elapsed time 03:58:10

(7·10¹¹⁹+17)/3 = 2(3)₁₁₈9_<120> = 47 · 1667 · 1598728711_<10> · 526853357803_<12> · C94

C94 = P43 · P52

P43 = 2487899235307330769877021031219003735293763_<43>

P52 = 1421169944438458969216053661423570617164050231393409_<52>

Wed Jun 18 14:47:16 2008  Msieve v. 1.36
Wed Jun 18 14:47:16 2008  random seeds: 31d20917 2261db0f
Wed Jun 18 14:47:16 2008  factoring 3535727618010203827241863252367638975873802814867733018263403913509911611397412713507437008067 (94 digits)
Wed Jun 18 14:47:17 2008  no P-1/P+1/ECM available, skipping
Wed Jun 18 14:47:17 2008  commencing quadratic sieve (94-digit input)
Wed Jun 18 14:47:18 2008  using multiplier of 3
Wed Jun 18 14:47:18 2008  using 64kb Pentium 4 sieve core
Wed Jun 18 14:47:18 2008  sieve interval: 18 blocks of size 65536
Wed Jun 18 14:47:18 2008  processing polynomials in batches of 6
Wed Jun 18 14:47:18 2008  using a sieve bound of 2023201 (75294 primes)
Wed Jun 18 14:47:18 2008  using large prime bound of 271108934 (28 bits)
Wed Jun 18 14:47:18 2008  using double large prime bound of 1512372783942046 (42-51 bits)
Wed Jun 18 14:47:18 2008  using trial factoring cutoff of 51 bits
Wed Jun 18 14:47:18 2008  polynomial 'A' values have 12 factors
Wed Jun 18 20:40:18 2008  75496 relations (18487 full + 57009 combined from 1076904 partial), need 75390
Wed Jun 18 20:40:22 2008  begin with 1095391 relations
Wed Jun 18 20:40:23 2008  reduce to 196684 relations in 12 passes
Wed Jun 18 20:40:23 2008  attempting to read 196684 relations
Wed Jun 18 20:40:29 2008  recovered 196684 relations
Wed Jun 18 20:40:29 2008  recovered 181534 polynomials
Wed Jun 18 20:40:29 2008  attempting to build 75496 cycles
Wed Jun 18 20:40:30 2008  found 75496 cycles in 6 passes
Wed Jun 18 20:40:30 2008  distribution of cycle lengths:
Wed Jun 18 20:40:30 2008     length 1 : 18487
Wed Jun 18 20:40:30 2008     length 2 : 13231
Wed Jun 18 20:40:30 2008     length 3 : 12825
Wed Jun 18 20:40:30 2008     length 4 : 10112
Wed Jun 18 20:40:30 2008     length 5 : 7521
Wed Jun 18 20:40:30 2008     length 6 : 5337
Wed Jun 18 20:40:30 2008     length 7 : 3381
Wed Jun 18 20:40:30 2008     length 9+: 4602
Wed Jun 18 20:40:30 2008  largest cycle: 21 relations
Wed Jun 18 20:40:30 2008  matrix is 75294 x 75496 (19.6 MB) with weight 4844871 (64.17/col)
Wed Jun 18 20:40:30 2008  sparse part has weight 4844871 (64.17/col)
Wed Jun 18 20:40:31 2008  filtering completed in 3 passes
Wed Jun 18 20:40:31 2008  matrix is 71867 x 71931 (18.8 MB) with weight 4647852 (64.62/col)
Wed Jun 18 20:40:31 2008  sparse part has weight 4647852 (64.62/col)
Wed Jun 18 20:40:32 2008  saving the first 48 matrix rows for later
Wed Jun 18 20:40:32 2008  matrix is 71819 x 71931 (11.7 MB) with weight 3646166 (50.69/col)
Wed Jun 18 20:40:32 2008  sparse part has weight 2648356 (36.82/col)
Wed Jun 18 20:40:32 2008  matrix includes 64 packed rows
Wed Jun 18 20:40:32 2008  using block size 21845 for processor cache size 512 kB
Wed Jun 18 20:40:33 2008  commencing Lanczos iteration
Wed Jun 18 20:40:33 2008  memory use: 11.5 MB
Wed Jun 18 20:41:29 2008  lanczos halted after 1137 iterations (dim = 71817)
Wed Jun 18 20:41:29 2008  recovered 17 nontrivial dependencies
Wed Jun 18 20:41:31 2008  prp43 factor: 2487899235307330769877021031219003735293763
Wed Jun 18 20:41:31 2008  prp52 factor: 1421169944438458969216053661423570617164050231393409
Wed Jun 18 20:41:31 2008  elapsed time 05:54:15

(7·10¹⁴²+17)/3 = 2(3)₁₄₁9_<143> = 239 · 359 · 3864886943178480283_<19> · C119

C119 = P46 · P73

P46 = 8736112065016231832182289058545466897704748911_<46>

P73 = 8054330474086409141498305541361295838218114061746685318944976380558270903_<73>

Number: 23339_142
N=70363533630294185294165706482946113409918647922182584068184418398232967632488922819202335829444250304263960981932236633
  ( 119 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=8736112065016231832182289058545466897704748911 (pp46)
 r2=8054330474086409141498305541361295838218114061746685318944976380558270903 (pp73)
Version: GGNFS-0.77.1-20060513-k8
Total time: 18.48 hours.
Scaled time: 37.14 units (timescale=2.010).
Factorization parameters were as follows:
name: 23339_142
n: 70363533630294185294165706482946113409918647922182584068184418398232967632488922819202335829444250304263960981932236633
m: 10000000000000000000000000000
c5: 700
c0: 17
skew: 0.48
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2750001)
Primes: RFBsize:100021, AFBsize:100193, largePrimes:2963927 encountered
Relations: rels:3028488, finalFF:283712
Max relations in full relation-set: 28
Initial matrix: 200281 x 283712 with sparse part having weight 33966330.
Pruned matrix : 180243 x 181308 with weight 20552126.
Total sieving time: 17.84 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.44 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 18.48 hours.
 --------- CPU info (if available) ----------

Jun 18, 2008 (2nd)

By Jo Yeong Uk / GGNFS

(19·10¹⁷⁵+71)/9 = 2(1)₁₇₄9_<176> = C176

C176 = P80 · P96

P80 = 60850084350740294278005008684441134760052865768236487179773355418574426998451693_<80>

P96 = 346936431335518371490342055169677665804525006321550138544617865907161312009720281338190068074283_<96>

Number: 21119_175
N=21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111119
  ( 176 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=60850084350740294278005008684441134760052865768236487179773355418574426998451693 (pp80)
 r2=346936431335518371490342055169677665804525006321550138544617865907161312009720281338190068074283 (pp96)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 155.75 hours.
Scaled time: 367.09 units (timescale=2.357).
Factorization parameters were as follows:
n: 21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111119
m: 100000000000000000000000000000000000
c5: 19
c0: 71
skew: 1.3
type: snfs
Factor base limits: 8400000/8400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [4200000, 7100001)
Primes: RFBsize:564877, AFBsize:565827, largePrimes:10879977 encountered
Relations: rels:10992982, finalFF:1297142
Max relations in full relation-set: 28
Initial matrix: 1130769 x 1297142 with sparse part having weight 89502042.
Pruned matrix : 985530 x 991247 with weight 62042272.
Total sieving time: 147.48 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 7.98 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,8400000,8400000,28,28,50,50,2.6,2.6,100000
total time: 155.75 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047200k/8912896k available (2440k kernel code, 339088k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.81 BogoMIPS (lpj=2672409)
Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672208)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672385)

Jun 18, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(7·10¹⁰²+17)/3 = 2(3)₁₀₁9_<103> = C103

C103 = P34 · P69

P34 = 6419956900481202228469077758003149_<34>

P69 = 363449999665642674884178819352787543464290520450591658241900375546311_<69>

(7·10¹⁵³+17)/3 = 2(3)₁₅₂9_<154> = 560459 · 230304748630662063984749951147_<30> · 262935549327310361422795083043_<30> · C89

C89 = P40 · P50

P40 = 1895549872520483456073059398581094704841_<40>

P50 = 36269830185861666534847203262383843474869227650761_<50>

Wed Jun 18 08:10:17 2008  
Wed Jun 18 08:10:17 2008  
Wed Jun 18 08:10:17 2008  Msieve v. 1.36
Wed Jun 18 08:10:17 2008  random seeds: 6aa74100 9e706eaf
Wed Jun 18 08:10:17 2008  factoring 68751271985149664776156554199563981434395577319158661478300292012981830544670599124034001 (89 digits)
Wed Jun 18 08:10:18 2008  searching for 15-digit factors
Wed Jun 18 08:10:19 2008  commencing quadratic sieve (89-digit input)
Wed Jun 18 08:10:19 2008  using multiplier of 5
Wed Jun 18 08:10:19 2008  using 64kb Opteron sieve core
Wed Jun 18 08:10:19 2008  sieve interval: 17 blocks of size 65536
Wed Jun 18 08:10:19 2008  processing polynomials in batches of 6
Wed Jun 18 08:10:19 2008  using a sieve bound of 1564307 (59333 primes)
Wed Jun 18 08:10:19 2008  using large prime bound of 125144560 (26 bits)
Wed Jun 18 08:10:19 2008  using double large prime bound of 376132987801280 (42-49 bits)
Wed Jun 18 08:10:19 2008  using trial factoring cutoff of 49 bits
Wed Jun 18 08:10:19 2008  polynomial 'A' values have 11 factors
Wed Jun 18 08:50:40 2008  59748 relations (16594 full + 43154 combined from 626616 partial), need 59429
Wed Jun 18 08:50:41 2008  begin with 643209 relations
Wed Jun 18 08:50:41 2008  reduce to 143702 relations in 11 passes
Wed Jun 18 08:50:41 2008  attempting to read 143702 relations
Wed Jun 18 08:50:42 2008  recovered 143702 relations
Wed Jun 18 08:50:42 2008  recovered 117032 polynomials
Wed Jun 18 08:50:43 2008  attempting to build 59748 cycles
Wed Jun 18 08:50:43 2008  found 59748 cycles in 5 passes
Wed Jun 18 08:50:43 2008  distribution of cycle lengths:
Wed Jun 18 08:50:43 2008     length 1 : 16594
Wed Jun 18 08:50:43 2008     length 2 : 11669
Wed Jun 18 08:50:43 2008     length 3 : 10367
Wed Jun 18 08:50:43 2008     length 4 : 7898
Wed Jun 18 08:50:43 2008     length 5 : 5487
Wed Jun 18 08:50:43 2008     length 6 : 3538
Wed Jun 18 08:50:43 2008     length 7 : 1911
Wed Jun 18 08:50:43 2008     length 9+: 2284
Wed Jun 18 08:50:43 2008  largest cycle: 18 relations
Wed Jun 18 08:50:43 2008  matrix is 59333 x 59748 (14.6 MB) with weight 3578395 (59.89/col)
Wed Jun 18 08:50:43 2008  sparse part has weight 3578395 (59.89/col)
Wed Jun 18 08:50:44 2008  filtering completed in 3 passes
Wed Jun 18 08:50:44 2008  matrix is 54872 x 54936 (13.5 MB) with weight 3307764 (60.21/col)
Wed Jun 18 08:50:44 2008  sparse part has weight 3307764 (60.21/col)
Wed Jun 18 08:50:44 2008  saving the first 48 matrix rows for later
Wed Jun 18 08:50:44 2008  matrix is 54824 x 54936 (10.0 MB) with weight 2755556 (50.16/col)
Wed Jun 18 08:50:44 2008  sparse part has weight 2295339 (41.78/col)
Wed Jun 18 08:50:44 2008  matrix includes 64 packed rows
Wed Jun 18 08:50:44 2008  using block size 21974 for processor cache size 1024 kB
Wed Jun 18 08:50:44 2008  commencing Lanczos iteration
Wed Jun 18 08:50:44 2008  memory use: 9.0 MB
Wed Jun 18 08:51:06 2008  lanczos halted after 868 iterations (dim = 54822)
Wed Jun 18 08:51:06 2008  recovered 16 nontrivial dependencies
Wed Jun 18 08:51:07 2008  prp40 factor: 1895549872520483456073059398581094704841
Wed Jun 18 08:51:07 2008  prp50 factor: 36269830185861666534847203262383843474869227650761
Wed Jun 18 08:51:07 2008  elapsed time 00:40:50

(7·10¹⁰⁴+17)/3 = 2(3)₁₀₃9_<105> = 1549 · 431213149 · C93

C93 = P38 · P55

P38 = 84021039913865811864528095862181648183_<38>

P55 = 4157625043236494780959904525049407778407073398238277733_<55>

Number: n
N=349327979704661599779941625272810754908557163679461621704641746110472048389941659397248809139
  ( 93 digits)
SNFS difficulty: 105 digits.
Divisors found:
 r1=84021039913865811864528095862181648183 (pp38)
 r2=4157625043236494780959904525049407778407073398238277733 (pp55)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.70 hours.
Scaled time: 1.27 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_3_103_9
n: 349327979704661599779941625272810754908557163679461621704641746110472048389941659397248809139
skew: 1.89
deg: 5
c5: 7
c0: 170
m: 1000000000000000000000
type: snfs
rlim: 600000
alim: 600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 160001)
Primes: RFBsize:49098, AFBsize:49011, largePrimes:4196488 encountered
Relations: rels:3702660, finalFF:250006
Max relations in full relation-set: 48
Initial matrix: 98174 x 250005 with sparse part having weight 17311302.
Pruned matrix : 56789 x 57343 with weight 2371582.
Total sieving time: 0.63 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.01 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,105,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.5,2.5,50000
total time: 0.70 hours.
 --------- CPU info (if available) ----------

(19·10¹⁵⁷+71)/9 = 2(1)₁₅₆9_<158> = 149 · 331 · 447977019071_<12> · C141

C141 = P68 · P74

P68 = 77929169194250521052812225269081813650033303291080915556048887978241_<68>

P74 = 12261427866582958791184193364468933936256879057608293595733557701239457191_<74>

Number: n
N=955522886778041600093440240348014365106179622949600182179310014977255835521154610734965233983597443817269068745577149968079675757884258981031
  ( 141 digits)
SNFS difficulty: 158 digits.
Divisors found:

Wed Jun 18 10:38:00 2008  prp68 factor: 77929169194250521052812225269081813650033303291080915556048887978241
Wed Jun 18 10:38:00 2008  prp74 factor: 12261427866582958791184193364468933936256879057608293595733557701239457191
Wed Jun 18 10:38:00 2008  elapsed time 01:11:42 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 35.86 hours.
Scaled time: 51.68 units (timescale=1.441).
Factorization parameters were as follows:
name: KA_2_1_156_9
n: 955522886778041600093440240348014365106179622949600182179310014977255835521154610734965233983597443817269068745577149968079675757884258981031
skew: 0.52
deg: 5
c5: 1900
c0: 71
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1800167)
Primes: RFBsize:216816, AFBsize:217002, largePrimes:7060869 encountered
Relations: rels:6477932, finalFF:461756
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 35.65 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 35.86 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(7·10¹¹¹+17)/3 = 2(3)₁₁₀9_<112> = 31 · 283 · C108

C108 = P42 · P67

P42 = 141365583583934397402332467178657836374287_<42>

P67 = 1881416574075439492986128061851660298139048768985554696504455656689_<67>

Number: n
N=265967551958661043352710969261750066491887989665260838177742315437516622971997416315209544435578859379155743
  ( 108 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=141365583583934397402332467178657836374287 (pp42)
 r2=1881416574075439492986128061851660298139048768985554696504455656689 (pp67)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.71 hours.
Scaled time: 1.30 units (timescale=1.818).
Factorization parameters were as follows:
name: KA_2_3_110_9
n: 265967551958661043352710969261750066491887989665260838177742315437516622971997416315209544435578859379155743
skew: 0.75
deg: 5
c5: 70
c0: 17
m: 10000000000000000000000
type: snfs
rlim: 600000
alim: 600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 160001)
Primes: RFBsize:49098, AFBsize:49186, largePrimes:3947445 encountered
Relations: rels:3357682, finalFF:166084
Max relations in full relation-set: 48
Initial matrix: 98351 x 166084 with sparse part having weight 12282582.
Pruned matrix : 73535 x 74090 with weight 3129235.
Total sieving time: 0.63 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.02 hours.
Total square root time: 0.02 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.5,2.5,50000
total time: 0.71 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(7·10¹¹³+17)/3 = 2(3)₁₁₂9_<114> = 19 · 29 · 10193 · 73999 · C102

C102 = P40 · P62

P40 = 8339601674524220895513383477312681123489_<40>

P62 = 67321224002953796493692732850668437799328402691094933774632243_<62>

Number: n
N=561432192426053654517340771240223116430397943672531177239167575604615218442742295215856972269044055827
  ( 102 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=8339601674524220895513383477312681123489 (pp40)
 r2=67321224002953796493692732850668437799328402691094933774632243 (pp62)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.10 hours.
Scaled time: 1.58 units (timescale=1.443).
Factorization parameters were as follows:
name: KA_2_3_112_9
n: 561432192426053654517340771240223116430397943672531177239167575604615218442742295215856972269044055827
skew: 0.30
deg: 5
c5: 7000
c0: 17
m: 10000000000000000000000
type: snfs
rlim: 600000
alim: 600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 180001)
Primes: RFBsize:49098, AFBsize:49326, largePrimes:3980336 encountered
Relations: rels:3357490, finalFF:133469
Max relations in full relation-set: 28
Initial matrix: 98491 x 133469 with sparse part having weight 9073890.
Pruned matrix : 84080 x 84636 with weight 3936525.
Total sieving time: 0.94 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.05 hours.
Total square root time: 0.03 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.5,2.5,50000
total time: 1.10 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(19·10¹⁶¹+71)/9 = 2(1)₁₆₀9_<162> = 3⁵ · C159

C159 = P30 · P57 · P74

P30 = 286786067147872235350150512053_<30>

P57 = 112622410320040502526431761387219772249611150037774127671_<57>

P74 = 26898121553328486879024622069541410307556323510188262663095503894721747591_<74>

Number: n
N=3029331282417286052913425605800649802144685572686579710389061333460545261055441205830769603801466446700995622384536686522670690561
  ( 130 digits)
SNFS difficulty: 162 digits.
Divisors found:

Wed Jun 18 21:16:51 2008  prp57 factor: 112622410320040502526431761387219772249611150037774127671
Wed Jun 18 21:16:51 2008  prp74 factor: 26898121553328486879024622069541410307556323510188262663095503894721747591
Wed Jun 18 21:16:51 2008  elapsed time 01:28:47 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 47.58 hours.
Scaled time: 87.02 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_1_160_9
n: 3029331282417286052913425605800649802144685572686579710389061333460545261055441205830769603801466446700995622384536686522670690561
skew: 0.82
deg: 5
c5: 190
c0: 71
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3300203)
Primes: RFBsize:216816, AFBsize:216642, largePrimes:7501597 encountered
Relations: rels:6884203, finalFF:446447
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 47.36 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 47.58 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jun 17, 2008 (4th)

By matsui / GGNFS

2·10¹⁷⁴-7 = 1(9)₁₇₃3_<175> = 45162104857_<11> · C164

C164 = P50 · P115

P50 = 15567016412456914292718994439665667659340737216997_<50>

P115 = 2844791473480904522073711775181098198268760967308959673803332033658988249807406032658488263343289877533029503274317_<115>

N=44284915557694729347765040994665790317727838758514044960205208090042409601502511298241282501081457510774761806182217110651884955832318902850555861105887073645966049
  ( 164 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=15567016412456914292718994439665667659340737216997 (pp50)
 
 r2=2844791473480904522073711775181098198268760967308959673803332033658988249807406032658488263343289877533029503274317 (pp115)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 243.25 hours.
Scaled time: 308.92 units (timescale=1.270).
Factorization parameters were as follows:
n: 44284915557694729347765040994665790317727838758514044960205208090042409601502511298241282501081457510774761806182217110651884955832318902850555861105887073645966049
m: 100000000000000000000000000000000000
c5: 1
c0: -35
skew: 2.04
type: snfs

Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 11600001)
Primes: RFBsize:501962, AFBsize:501746, largePrimes:6521482 encountered
Relations: rels:6972572, finalFF:1128905
Max relations in full relation-set: 28
Initial matrix: 1003772 x 1128905 with sparse part having weight 73472770.
Pruned matrix : 897602 x 902684 with weight 56663657.
Total sieving time: 203.55 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 39.17 hours.
Time per square root: 0.39 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 243.25 hours.

Jun 17, 2008 (3rd)

By suberi / GMP-ECM

(16·10²⁴⁷-61)/9 = 1(7)₂₄₆1_<248> = 11 · 1519462863204010887343118174303851_<34> · C214

C214 = P40 · P174

P40 = 2446972297993506364536910147344312252817_<40>

P174 = 434675983297164654943064917508776598208565289076376758993205934839973130416427780890879508995035601216645271796689898925197909151263983145235974828216649664885501680694980083_<174>

Jun 17, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(19·10¹⁵²+71)/9 = 2(1)₁₅₁9_<153> = 3² · 5495167 · C145

C145 = P49 · P96

P49 = 4901819949628641796466086337480125061060531270983_<49>

P96 = 870823883755497713499331899758122000845092549202887776729665908427056553088983618255881653274831_<96>

Number: 21119_152
N=4268621886005792021144542126464362252040163679003165895314335328381610626839328108400852990174236765408001271564047120580100681827647844634528873
  ( 145 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=4901819949628641796466086337480125061060531270983 (pp49)
 r2=870823883755497713499331899758122000845092549202887776729665908427056553088983618255881653274831 (pp96)
Version: GGNFS-0.77.1-20060513-k8
Total time: 35.70 hours.
Scaled time: 71.08 units (timescale=1.991).
Factorization parameters were as follows:
name: 21119_152
n: 4268621886005792021144542126464362252040163679003165895314335328381610626839328108400852990174236765408001271564047120580100681827647844634528873
m: 1000000000000000000000000000000
c5: 1900
c0: 71
skew: 0.52
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2500001)
Primes: RFBsize:176302, AFBsize:176824, largePrimes:5811367 encountered
Relations: rels:5835518, finalFF:527410
Max relations in full relation-set: 28
Initial matrix: 353193 x 527410 with sparse part having weight 54511221.
Pruned matrix : 293898 x 295727 with weight 31266050.
Total sieving time: 33.99 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.40 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 35.70 hours.
 --------- CPU info (if available) ----------

Jun 17, 2008

The factor table of 233...339 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Jun 16, 2008 (3rd)

By Robert Backstrom / GMP-ECM

(19·10¹⁶⁷+71)/9 = 2(1)₁₆₆9_<168> = 3 · 2243 · 235493 · C159

C159 = P44 · P116

P44 = 10766075811599655430741404354340972913661347_<44>

P116 = 12374427833338457331814433209166661760078812457314883748540314012065840097373485608599199199387260515247162077378041_<116>

Jun 16, 2008 (2nd)

By suberi / GMP-ECM

(17·10¹⁸¹+1)/9 = 1(8)₁₈₀9_<182> = 19 · 44839 · 48731 · 1008779 · 12003314779_<11> · 5830558817883227437007237_<25> · C130

C130 = P30 · C100

P30 = 758822763085731218605641418771_<30>

C100 = [8492661409590470524891423727868139850632579649757129010224121294326903739481230882899276916193096537_<100>]

(17·10¹⁹⁰+1)/9 = 1(8)₁₈₉9_<191> = 13 · 649123 · 707912267722698978623_<21> · C163

C163 = P32 · C132

P32 = 24592951456281913764228758669239_<32>

C132 = [128571873140924523664948060149189103090155858942672937006248438418113765818485839629694932311203935787591124351688800743261858830663_<132>]

Jun 16, 2008

By Sinkiti Sibata / GGNFS

(19·10¹⁷⁸+71)/9 = 2(1)₁₇₇9_<179> = 7 · 73 · 107 · 173 · 35321990716170607082142191_<26> · 3823874316784361716576388467133_<31> · C116

C116 = P29 · P87

P29 = 27406547521000446067339104767_<29>

P87 = 602916541684842867507687365160027289170544020368979297591614953242064948580130894740539_<87>

Number: 21119_178
N=16523860850882892395144792212261432649907044400229056482377148949941650807074754921165115690888775495900605003049413
  ( 116 digits)
Divisors found:
 r1=27406547521000446067339104767 (pp29)
 r2=602916541684842867507687365160027289170544020368979297591614953242064948580130894740539 (pp87)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 73.94 hours.
Scaled time: 49.98 units (timescale=0.676).
Factorization parameters were as follows:
name: 21119_178
n: 16523860850882892395144792212261432649907044400229056482377148949941650807074754921165115690888775495900605003049413
skew: 40127.03
# norm 7.16e+15
c5: 40080
c4: -7945983226
c3: -232895586882496
c2: 10778743211792435213
c1: 140457272524332146727036
c0: -2681001619694258614734421287
# alpha -5.71
Y1: 2400596004961
Y0: -13275163457864381099522
# Murphy_E 4.83e-10
# M 4699310249935613700118238101142154720824295796173609648981454158679885067087264384430956907404713390557562756410728
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 3630001)
Primes: RFBsize:315948, AFBsize:315637, largePrimes:7499982 encountered
Relations: rels:7511772, finalFF:737157
Max relations in full relation-set: 28
Initial matrix: 631664 x 737157 with sparse part having weight 56387280.
Pruned matrix : 538707 x 541929 with weight 34822728.
Polynomial selection time: 3.11 hours.
Total sieving time: 56.46 hours.
Total relation processing time: 0.53 hours.
Matrix solve time: 13.40 hours.
Time per square root: 0.44 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 73.94 hours.
 --------- CPU info (if available) ----------

(19·10¹⁵¹+71)/9 = 2(1)₁₅₀9_<152> = 389 · 46451 · 38559392769341_<14> · C131

C131 = P42 · P90

P42 = 123898729947282037215260261192283618233521_<42>

P90 = 244550965417535587962509097180011853513331875232412883300691306397524357045415864687563861_<90>

Number: 21119_151
N=30299554022614350384504348767263079177531164143037702442023852003276625984676290612901044365561203878923175331353497936833698384581
  ( 131 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=123898729947282037215260261192283618233521 (pp42)
 r2=244550965417535587962509097180011853513331875232412883300691306397524357045415864687563861 (pp90)
Version: GGNFS-0.77.1-20060513-k8
Total time: 35.56 hours.
Scaled time: 70.79 units (timescale=1.991).
Factorization parameters were as follows:
name: 21119_151
n: 30299554022614350384504348767263079177531164143037702442023852003276625984676290612901044365561203878923175331353497936833698384581
m: 1000000000000000000000000000000
c5: 190
c0: 71
skew: 0.82
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2500001)
Primes: RFBsize:176302, AFBsize:176344, largePrimes:5725559 encountered
Relations: rels:5654649, finalFF:438134
Max relations in full relation-set: 28
Initial matrix: 352713 x 438134 with sparse part having weight 46113828.
Pruned matrix : 323557 x 325384 with weight 31379717.
Total sieving time: 33.71 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.52 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 35.56 hours.
 --------- CPU info (if available) ----------

Jun 15, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(82·10¹⁸⁵-1)/9 = 9(1)₁₈₅_<186> = 773 · C184

C184 = P88 · P96

P88 = 4548789624633850866889146735134298403699896616070473264408962177272708854038293242583257_<88>

P96 = 259117053935733073539510463672622076339997265026506332376996259338801062100873517406377001946451_<96>

Number: n
N=1178668966508552537013080350725887595227828086819031191605577116573235590053183843610751760816443869483972976857841023429639212304154089406353313209716831967802213597815150208423170907
  ( 184 digits)
SNFS difficulty: 186 digits.
Divisors found:

Mon Jun 16 00:16:49 2008  prp88 factor: 4548789624633850866889146735134298403699896616070473264408962177272708854038293242583257
Mon Jun 16 00:16:49 2008  prp96 factor: 259117053935733073539510463672622076339997265026506332376996259338801062100873517406377001946451
Mon Jun 16 00:16:49 2008  elapsed time 02:53:05 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 96.97 hours.
Scaled time: 81.16 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_9_1_185
n: 1178668966508552537013080350725887595227828086819031191605577116573235590053183843610751760816443869483972976857841023429639212304154089406353313209716831967802213597815150208423170907
type: snfs
skew: 0.41
deg: 5
c5: 82
c0: -1
m: 10000000000000000000000000000000000000
rlim: 7000000
alim: 7000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 7000000/7000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 13400077)
Primes: RFBsize:476648, AFBsize:476605, largePrimes:9021915 encountered
Relations: rels:8836726, finalFF:1037910
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 96.58 hours.
Total relation processing time: 0.39 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,7000000,7000000,28,28,48,48,2.6,2.6,100000
total time: 96.97 hours.
 --------- CPU info (if available) ----------

Jun 15, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(19·10¹⁴⁸+71)/9 = 2(1)₁₄₇9_<149> = 7 · 47 · 417006279637_<12> · C135

C135 = P37 · P48 · P51

P37 = 1665401849509587677728439136819520339_<37>

P48 = 396630940851504929651395216684056457143555288557_<48>

P51 = 232952280196970654163617482290594633816545512331261_<51>

Number: 21119_148
N=153876605963533264497237871153137488274836088714222638533355576644654978814571391424895423745228899363662939247215583153132173003687803
  ( 135 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=1665401849509587677728439136819520339 (pp37)
 r2=396630940851504929651395216684056457143555288557 (pp48)
 r3=232952280196970654163617482290594633816545512331261 (pp51)
Version: GGNFS-0.77.1-20060513-k8
Total time: 41.46 hours.
Scaled time: 83.04 units (timescale=2.003).
Factorization parameters were as follows:
name: 21119_148
n: 153876605963533264497237871153137488274836088714222638533355576644654978814571391424895423745228899363662939247215583153132173003687803
m: 100000000000000000000000000000
c5: 19000
c0: 71
skew: 0.33
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 5650001)
Primes: RFBsize:114155, AFBsize:114198, largePrimes:3268956 encountered
Relations: rels:3440669, finalFF:266667
Max relations in full relation-set: 28
Initial matrix: 228420 x 266667 with sparse part having weight 36402146.
Pruned matrix : 218879 x 220085 with weight 29047573.
Total sieving time: 40.45 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.70 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 41.46 hours.
 --------- CPU info (if available) ----------

Jun 15, 2008

By Kenji Ibusuki / GGNFS

(5·10¹⁷⁵+1)/3 = 1(6)₁₇₄7_<176> = 827 · C173

C173 = P80 · P93

P80 = 74865668108657376632912517989779780300464176273350461362789666667834688689397123_<80>

P93 = 269190999771828025899329511919947740033568840333403347746509215638814772035381976837532003227_<93>

Number: 16667_175
N=20153164046755340588472390165255945183393792825473599355098750503829101168883514711809754131398629584844820636839983877468762595727529222087867795243853284965739621120515921
  ( 173 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=74865668108657376632912517989779780300464176273350461362789666667834688689397123 (pp80)
 r2=269190999771828025899329511919947740033568840333403347746509215638814772035381976837532003227 (pp93)
Version: GGNFS-0.77.1
Total time: 127.09 hours.
Scaled time: 369.83 units (timescale=2.910).
Factorization parameters were as follows:
n: 20153164046755340588472390165255945183393792825473599355098750503829101168883514711809754131398629584844820636839983877468762595727529222087867795243853284965739621120515921
m: 100000000000000000000000000000000000
c5: 5
c0: 1
skew: 0.725
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [3700000, 9800001)
Relations: rels:6928497, finalFF:1184727
Initial matrix: 1003098 x 1184727 with sparse part having weight 67068111.
Pruned matrix : 926698 x 931777 with weight 43275106.
Total sieving time: 122.35 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 4.46 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 127.09 hours.
 --------- CPU info (if available) ----------

Jun 14, 2008 (4th)

By Wataru Sakai / GGNFS

10¹⁸⁹-9 = (9)₁₈₈1_<189> = 680546965633716247679_<21> · 210016417538123401200815971279_<30> · C139

C139 = P49 · P90

P49 = 8147900155250040965434833800626154533552907527597_<49>

P90 = 858702947397860145236409007951942850049599814990863975327405594646045661188912043740978083_<90>

Number: 99991_189
N=6996625878416692438029157723410875624263386189411081125190307294339622079250688809160942796831099033973415942935043602179220749546094656551
  ( 139 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=8147900155250040965434833800626154533552907527597 (pp49)
 r2=858702947397860145236409007951942850049599814990863975327405594646045661188912043740978083 (pp90)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 1147.35 hours.
Scaled time: 2311.91 units (timescale=2.015).
Factorization parameters were as follows:
n: 6996625878416692438029157723410875624263386189411081125190307294339622079250688809160942796831099033973415942935043602179220749546094656551
m: 100000000000000000000000000000000000000
c5: 1
c0: -90
skew: 2.46
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 19900001)
Primes: RFBsize:501962, AFBsize:502106, largePrimes:7170030 encountered
Relations: rels:7740301, finalFF:1148030
Max relations in full relation-set: 32
Initial matrix: 1004132 x 1148030 with sparse part having weight 138656677.
Pruned matrix : 902449 x 907533 with weight 118637521.
Total sieving time: 1134.16 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 12.76 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 1147.35 hours.

(7·10¹⁶⁹-61)/9 = (7)₁₆₈1_<169> = 83 · 10855381 · C160

C160 = P34 · P37 · P90

P34 = 2283299320810328736384747634415821_<34>

P37 = 7182607341442258629005707341782603917_<37>

P90 = 526365474032812165742184427823758439905684973552785490890082763434216262625675882189775261_<90>

Number: 77771_169
N=8632416125912358472599711150945987261239466130360599340201719910084255418766178636140990039845884947093500679833045032154108060156156409675885963645590464968677
  ( 160 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=2283299320810328736384747634415821 (pp34)
 r2=7182607341442258629005707341782603917 (pp37)
 r3=526365474032812165742184427823758439905684973552785490890082763434216262625675882189775261 (pp90)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 169.71 hours.
Scaled time: 340.62 units (timescale=2.007).
Factorization parameters were as follows:
n: 8632416125912358472599711150945987261239466130360599340201719910084255418766178636140990039845884947093500679833045032154108060156156409675885963645590464968677
m: 10000000000000000000000000000000000
c5: 7
c0: -610
skew: 2.44
type: snfsFactor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 9400001)
Primes: RFBsize:412849, AFBsize:413557, largePrimes:6523136 encountered
Relations: rels:6974496, finalFF:1087069
Max relations in full relation-set: 32
Initial matrix: 826471 x 1087069 with sparse part having weight 90460735.
Pruned matrix : 620311 x 624507 with weight 73420826.
Total sieving time: 165.44 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 3.97 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 169.71 hours.

Jun 14, 2008 (3rd)

By Wataru Sakai / GGNFS

(8·10¹⁶⁸-53)/9 = (8)₁₆₇3_<168> = 115509593 · C160

C160 = P25 · P36 · P100

P25 = 4168773560957646476042689_<25>

P36 = 496029423131682367523442139895210347_<36>

P100 = 3721462779361461935113578380790887976223197458450833632455359550260813918839667749389547619007630657_<100>

Number: 88883_168
N=7695368547345577513106542492006606662434425588261651037839678725981563184010949539826435791258383958541771408448204720874472208458815095027552290733886395815531
  ( 160 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=4168773560957646476042689 (pp25)
 r2=496029423131682367523442139895210347 (pp36)
 r3=3721462779361461935113578380790887976223197458450833632455359550260813918839667749389547619007630657 (pp100)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 143.40 hours.
Scaled time: 283.22 units (timescale=1.975).
Factorization parameters were as follows:
n: 7695368547345577513106542492006606662434425588261651037839678725981563184010949539826435791258383958541771408448204720874472208458815095027552290733886395815531
m: 2000000000000000000000000000000000
c5: 250
c0: -53
skew: 0.73
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 7750001)
Primes: RFBsize:380800, AFBsize:380967, largePrimes:6441404 encountered
Relations: rels:6900311, finalFF:1078860
Max relations in full relation-set: 32
Initial matrix: 761833 x 1078860 with sparse part having weight 88535141.
Pruned matrix : 523358 x 527231 with weight 78341106.
Total sieving time: 140.02 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 3.11 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 143.40 hours.

Jun 14, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(19·10¹⁴⁷+71)/9 = 2(1)₁₄₆9_<148> = 13 · 59 · 887 · C142

C142 = P46 · P96

P46 = 3726369897506049222488673132552815264516392147_<46>

P96 = 832733708305847517955059751402619654460601103742913699994890502633673002797961698240750355056813_<96>

Number: 21119_147
N=3103073823269493305608185320794955251225673330272722625540159409801891601138730101334958690738026912142670841770836038315449012332431972047511
  ( 142 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=3726369897506049222488673132552815264516392147 (pp46)
 r2=832733708305847517955059751402619654460601103742913699994890502633673002797961698240750355056813 (pp96)
Version: GGNFS-0.77.1-20060513-k8
Total time: 32.77 hours.
Scaled time: 65.86 units (timescale=2.010).
Factorization parameters were as follows:
name: 21119_147
n: 3103073823269493305608185320794955251225673330272722625540159409801891601138730101334958690738026912142670841770836038315449012332431972047511
m: 100000000000000000000000000000
c5: 1900
c0: 71
skew: 0.52
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 4450001)
Primes: RFBsize:114155, AFBsize:114603, largePrimes:3082436 encountered
Relations: rels:3151468, finalFF:259813
Max relations in full relation-set: 28
Initial matrix: 228825 x 259813 with sparse part having weight 32779060.
Pruned matrix : 220551 x 221759 with weight 26667026.
Total sieving time: 31.77 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.74 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 32.77 hours.
 --------- CPU info (if available) ----------

Jun 14, 2008

By Robert Backstrom / GGNFS, Msieve

8·10¹⁶⁹-7 = 7(9)₁₆₈3_<170> = 73 · 8753 · C165

C165 = P39 · P47 · P79

P39 = 473048713356314168354682550298167494871_<39>

P47 = 36110938960348331268870320405592134697102786337_<47>

P79 = 7329351527850956899400617896031539095927171138622765905330195821735845789339911_<79>

Number: n
N=125201692100868743241064902992163939095636877532399850383977939461851826927440924364092780713931348782178791146362343087066821708095384909127046852038205296344580097
  ( 165 digits)
SNFS difficulty: 170 digits.
Divisors found:

Sat Jun 14 02:35:32 2008  prp39 factor: 473048713356314168354682550298167494871
Sat Jun 14 02:35:32 2008  prp47 factor: 36110938960348331268870320405592134697102786337
Sat Jun 14 02:35:32 2008  prp79 factor: 7329351527850956899400617896031539095927171138622765905330195821735845789339911
Sat Jun 14 02:35:32 2008  elapsed time 02:21:24 (Msieve 1.36)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 105.41 hours.
Scaled time: 88.65 units (timescale=0.841).
Factorization parameters were as follows:
name: KA_7_9_168_3
n: 125201692100868743241064902992163939095636877532399850383977939461851826927440924364092780713931348782178791146362343087066821708095384909127046852038205296344580097
skew: 1.54
deg: 5
c5: 4
c0: -35
m: 10000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4500163)
Primes: RFBsize:230209, AFBsize:230217, largePrimes:7834629 encountered
Relations: rels:7288384, finalFF:441299
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 105.03 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 105.41 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jun 13, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(4·10¹⁶⁸+23)/9 = (4)₁₆₇7_<168> = 3⁴ · 1265197 · C160

C160 = P79 · P82

P79 = 1058672780199082273664589389440212686058586452944274704237975222290582762325807_<79>

P82 = 4096496258940085111741497387505341221216333433858971073571460415594977424825412453_<82>

Number: n
N=4336849083527239547972258343025079717439059867917162838793986325132038379037038505060451811007624025646486151026521390158802326996657968801408094232028341074571
  ( 160 digits)
SNFS difficulty: 168 digits.
Divisors found:

Fri Jun 13 23:45:43 2008  prp79 factor: 1058672780199082273664589389440212686058586452944274704237975222290582762325807
Fri Jun 13 23:45:43 2008  prp82 factor: 4096496258940085111741497387505341221216333433858971073571460415594977424825412453
Fri Jun 13 23:45:43 2008  elapsed time 02:28:18 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 70.39 hours.
Scaled time: 101.99 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_4_167_7
n: 4336849083527239547972258343025079717439059867917162838793986325132038379037038505060451811007624025646486151026521390158802326996657968801408094232028341074571
skew: 0.71
deg: 5
c5: 125
c0: 23
m: 2000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3500269)
Primes: RFBsize:250150, AFBsize:250086, largePrimes:7571750 encountered
Relations: rels:7011455, finalFF:533831
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 70.12 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 70.39 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jun 13, 2008

By Sinkiti Sibata / GGNFS

(19·10¹⁴³+71)/9 = 2(1)₁₄₂9_<144> = 3² · 211 · C141

C141 = P63 · P78

P63 = 773537122612256721050443498792233896398463284176095668716900509_<63>

P78 = 143715948709430888732671112113368641464136741032198092002947921700020431129809_<78>

Number: 21119_143
N=111169621438183839447662512433444502954771517172780995845766777836288104850506114329179100111169621438183839447662512433444502954771517172781
  ( 141 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=773537122612256721050443498792233896398463284176095668716900509 (pp63)
 r2=143715948709430888732671112113368641464136741032198092002947921700020431129809 (pp78)
Version: GGNFS-0.77.1-20060513-k8
Total time: 22.98 hours.
Scaled time: 46.18 units (timescale=2.010).
Factorization parameters were as follows:
name: 21119_143
n: 111169621438183839447662512433444502954771517172780995845766777836288104850506114329179100111169621438183839447662512433444502954771517172781
m: 10000000000000000000000000000
c5: 19000
c0: 71
skew: 0.33
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 3350001)
Primes: RFBsize:100021, AFBsize:99934, largePrimes:3035935 encountered
Relations: rels:3122816, finalFF:265596
Max relations in full relation-set: 28
Initial matrix: 200022 x 265596 with sparse part having weight 33581023.
Pruned matrix : 184436 x 185500 with weight 22513251.
Total sieving time: 22.36 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.38 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 22.98 hours.
 --------- CPU info (if available) ----------

(19·10¹⁴⁴+71)/9 = 2(1)₁₄₃9_<145> = 1999 · 4507 · C138

C138 = P60 · P78

P60 = 279576733790481204623483289144205990927420007608424299189687_<60>

P78 = 838126770218144510957697953206157504729388016127259238924760043036739444411909_<78>

Number: 21119_144
N=234320744919953998644664146041415550365721035702132307679367874653003350034359437441275675680208765477825568110337741658838195568952782483
  ( 138 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=279576733790481204623483289144205990927420007608424299189687 (pp60)
 r2=838126770218144510957697953206157504729388016127259238924760043036739444411909 (pp78)
Version: GGNFS-0.77.1-20060513-k8
Total time: 24.32 hours.
Scaled time: 48.56 units (timescale=1.997).
Factorization parameters were as follows:
name: 21119_144
n: 234320744919953998644664146041415550365721035702132307679367874653003350034359437441275675680208765477825568110337741658838195568952782483
m: 100000000000000000000000000000
c5: 19
c0: 710
skew: 2.06
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 3450001)
Primes: RFBsize:114155, AFBsize:114373, largePrimes:2976517 encountered
Relations: rels:3009909, finalFF:285451
Max relations in full relation-set: 28
Initial matrix: 228593 x 285451 with sparse part having weight 32777468.
Pruned matrix : 212266 x 213472 with weight 22989071.
Total sieving time: 23.51 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.56 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 24.32 hours.
 --------- CPU info (if available) ----------

Jun 12, 2008

By Sinkiti Sibata / GGNFS, Msieve

(19·10¹⁴¹+71)/9 = 2(1)₁₄₀9_<142> = 13 · 29 · 347 · 941 · 8111 · 16967418035004781_<17> · C114

C114 = P48 · P66

P48 = 650231791063999630808600501041274974102363870523_<48>

P66 = 191642700766968311023323590286528352074786023369003402963652968777_<66>

Number: 21119_141
N=124612176564047940613189812872850872746123053929396105024813316924095670437315190625530573100811253768993389660371
  ( 114 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=650231791063999630808600501041274974102363870523 (pp48)
 r2=191642700766968311023323590286528352074786023369003402963652968777 (pp66)
Version: GGNFS-0.77.1-20060513-k8
Total time: 18.56 hours.
Scaled time: 37.06 units (timescale=1.997).
Factorization parameters were as follows:
name: 21119_141
n: 124612176564047940613189812872850872746123053929396105024813316924095670437315190625530573100811253768993389660371
m: 10000000000000000000000000000
c5: 190
c0: 71
skew: 0.82
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2750001)
Primes: RFBsize:100021, AFBsize:100044, largePrimes:2926502 encountered
Relations: rels:2964235, finalFF:258827
Max relations in full relation-set: 28
Initial matrix: 200132 x 258827 with sparse part having weight 31021926.
Pruned matrix : 185082 x 186146 with weight 20907215.
Total sieving time: 17.93 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.41 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 18.56 hours.
 --------- CPU info (if available) ----------

(19·10¹³²+71)/9 = 2(1)₁₃₁9_<133> = 5750351 · 3070993112983_<13> · 345044156871461_<15> · C99

C99 = P32 · P68

P32 = 24188464339752121280456516669389_<32>

P68 = 14323690221972322118217528148496229598451511026018742414164385860167_<68>

Msieve v. 1.36
Wed Jun 11 20:43:23 2008
random seeds: 525b3299 f77d553e
factoring 3464680701478336600321379322542504153075346018260327430665746703964294
14515780339704184084723327963 (99 digits)
no P-1/P+1/ECM available, skipping
commencing quadratic sieve (99-digit input)
using multiplier of 1
using 64kb Pentium 4 sieve core
sieve interval: 18 blocks of size 65536
processing polynomials in batches of 6
using a sieve bound of 2608121 (95294 primes)
using large prime bound of 391218150 (28 bits)
using double large prime bound of 2926537886090700 (43-52 bits)
using trial factoring cutoff of 52 bits
polynomial 'A' values have 13 factors

sieving in progress (press Ctrl-C to pause)
95438 relations (21959 full + 73479 combined from 1457579 partial), need 95390
95438 relations (21959 full + 73479 combined from 1457579 partial), need 95390
sieving complete, commencing postprocessing
begin with 1479538 relations
reduce to 254860 relations in 12 passes
attempting to read 254860 relations
recovered 254860 relations
recovered 246051 polynomials
attempting to build 95438 cycles
found 95438 cycles in 6 passes
distribution of cycle lengths:
   length 1 : 21959
   length 2 : 16209
   length 3 : 15947
   length 4 : 12888
   length 5 : 10074
   length 6 : 6948
   length 7 : 4671
   length 9+: 6742
largest cycle: 22 relations
matrix is 95294 x 95438 (26.0 MB) with weight 6442385 (67.50/col)
sparse part has weight 6442385 (67.50/col)
filtering completed in 3 passes
matrix is 91866 x 91930 (25.2 MB) with weight 6238098 (67.86/col)
sparse part has weight 6238098 (67.86/col)
saving the first 48 matrix rows for later
matrix is 91818 x 91930 (14.9 MB) with weight 4870259 (52.98/col)
sparse part has weight 3352459 (36.47/col)
matrix includes 64 packed rows
using block size 21845 for processor cache size 512 kB
commencing Lanczos iteration
memory use: 14.9 MB
linear algebra completed 88334 out of 91930 dimensions (96.1%)
lanczos halted after 1453 iterations (dim = 91814)
recovered 14 nontrivial dependencies
prp32 factor: 24188464339752121280456516669389
prp68 factor: 143236902219723221182175281484962295984515110260187424141643858601
67
elapsed time 17:08:08

(19·10¹⁴²+71)/9 = 2(1)₁₄₁9_<143> = 7 · 97 · 2348733871051_<13> · C128

C128 = P32 · P47 · P50

P32 = 16065327225299271269093343103523_<32>

P47 = 35702000102923126067043311456968363449168793523_<47>

P50 = 23079446206702040089175443834158184126317648059459_<50>

Number: 21119_142
N=13237546736842859505402038877708992687784678505751658372756797808700605511230085366853429133351356265970701486042520921806832811
  ( 128 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=16065327225299271269093343103523 (pp32)
 r2=35702000102923126067043311456968363449168793523 (pp47)
 r3=23079446206702040089175443834158184126317648059459 (pp50)
Version: GGNFS-0.77.1-20060513-k8
Total time: 17.07 hours.
Scaled time: 34.10 units (timescale=1.997).
Factorization parameters were as follows:
name: 21119_142
n: 13237546736842859505402038877708992687784678505751658372756797808700605511230085366853429133351356265970701486042520921806832811
m: 10000000000000000000000000000
c5: 1900
c0: 71
skew: 0.52
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2550001)
Primes: RFBsize:100021, AFBsize:100279, largePrimes:2828872 encountered
Relations: rels:2812879, finalFF:226712
Max relations in full relation-set: 28
Initial matrix: 200367 x 226712 with sparse part having weight 25694109.
Pruned matrix : 193388 x 194453 with weight 20533623.
Total sieving time: 16.39 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.49 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 17.07 hours.
 --------- CPU info (if available) ----------

Jun 11, 2008 (3rd)

By Sinkiti Sibata / Msieve, GGNFS

(19·10¹³⁷+71)/9 = 2(1)₁₃₆9_<138> = 3 · 17 · 53 · 760317572544031769_<18> · 6801356722860337047229446691_<28> · C89

C89 = P37 · P52

P37 = 4250715591941833113363929326424495917_<37>

P52 = 3553140787460875292162304042118460409815632172652911_<52>

Msieve v. 1.36
Wed Jun 11 06:15:26 2008
random seeds: 842cce61 e20be948
factoring 1510339094562442555697562556990930700341045654578517230076181491079231
5112232985777664387 (89 digits)
no P-1/P+1/ECM available, skipping
commencing quadratic sieve (89-digit input)
using multiplier of 3
using 64kb Pentium 4 sieve core
sieve interval: 14 blocks of size 65536
processing polynomials in batches of 8
using a sieve bound of 1533041 (58333 primes)
using large prime bound of 122643280 (26 bits)
using double large prime bound of 362709283500240 (42-49 bits)
using trial factoring cutoff of 49 bits
polynomial 'A' values have 11 factors

sieving in progress (press Ctrl-C to pause)
58569 relations (15723 full + 42846 combined from 617873 partial), need 58429
58569 relations (15723 full + 42846 combined from 617873 partial), need 58429
sieving complete, commencing postprocessing
begin with 633596 relations
reduce to 142553 relations in 9 passes
attempting to read 142553 relations
recovered 142553 relations
recovered 122273 polynomials
attempting to build 58569 cycles
found 58569 cycles in 5 passes
distribution of cycle lengths:
   length 1 : 15723
   length 2 : 10979
   length 3 : 10473
   length 4 : 7863
   length 5 : 5457
   length 6 : 3524
   length 7 : 2049
   length 9+: 2501
largest cycle: 19 relations
matrix is 58333 x 58569 (14.2 MB) with weight 3487711 (59.55/col)
sparse part has weight 3487711 (59.55/col)
filtering completed in 3 passes
matrix is 54502 x 54566 (13.3 MB) with weight 3275180 (60.02/col)
sparse part has weight 3275180 (60.02/col)
saving the first 48 matrix rows for later
matrix is 54454 x 54566 (9.3 MB) with weight 2650970 (48.58/col)
sparse part has weight 2107434 (38.62/col)
matrix includes 64 packed rows
using block size 21826 for processor cache size 512 kB
commencing Lanczos iteration
memory use: 8.6 MB
lanczos halted after 863 iterations (dim = 54450)
recovered 15 nontrivial dependencies
prp37 factor: 4250715591941833113363929326424495917
prp52 factor: 3553140787460875292162304042118460409815632172652911
elapsed time 01:41:49

(19·10¹³⁶+71)/9 = 2(1)₁₃₅9_<137> = 7 · 151 · 5652617 · 847338798749_<12> · 16543089495237673789393867_<26> · C90

C90 = P42 · P49

P42 = 133603222497974916207566236359895495592119_<42>

P49 = 1886669803486077342881805363901015169384078657663_<49>

Msieve v. 1.36
Wed Jun 11 08:06:37 2008
random seeds: 96543fac dba2f462
factoring 2520651655353610024525327841485970561287114260186228248857235222627385
01167092198881757897 (90 digits)
no P-1/P+1/ECM available, skipping
commencing quadratic sieve (90-digit input)
using multiplier of 17
using 64kb Pentium 4 sieve core
sieve interval: 18 blocks of size 65536
processing polynomials in batches of 6
using a sieve bound of 1575269 (59429 primes)
using large prime bound of 126021520 (26 bits)
using double large prime bound of 380890718607520 (42-49 bits)
using trial factoring cutoff of 49 bits
polynomial 'A' values have 12 factors

sieving in progress (press Ctrl-C to pause)
59947 relations (16155 full + 43792 combined from 629724 partial), need 59525
59947 relations (16155 full + 43792 combined from 629724 partial), need 59525
sieving complete, commencing postprocessing
begin with 645879 relations
reduce to 144865 relations in 10 passes
attempting to read 144865 relations
recovered 144865 relations
recovered 123874 polynomials
attempting to build 59947 cycles
found 59947 cycles in 5 passes
distribution of cycle lengths:
   length 1 : 16155
   length 2 : 11799
   length 3 : 10594
   length 4 : 7866
   length 5 : 5532
   length 6 : 3513
   length 7 : 2054
   length 9+: 2434
largest cycle: 17 relations
matrix is 59429 x 59947 (14.3 MB) with weight 3521971 (58.75/col)
sparse part has weight 3521971 (58.75/col)
filtering completed in 3 passes
matrix is 55467 x 55530 (13.3 MB) with weight 3266995 (58.83/col)
sparse part has weight 3266995 (58.83/col)
saving the first 48 matrix rows for later
matrix is 55419 x 55530 (8.1 MB) with weight 2513840 (45.27/col)
sparse part has weight 1789178 (32.22/col)
matrix includes 64 packed rows
using block size 21845 for processor cache size 512 kB
commencing Lanczos iteration
memory use: 8.1 MB
lanczos halted after 878 iterations (dim = 55419)
recovered 18 nontrivial dependencies
prp42 factor: 133603222497974916207566236359895495592119
prp49 factor: 1886669803486077342881805363901015169384078657663
elapsed time 02:05:15

(19·10¹¹²+71)/9 = 2(1)₁₁₁9_<113> = 7 · 565391 · C106

C106 = P45 · P62

P45 = 192943753209624529109523104943977732198649113_<45>

P62 = 27646072217246202886997945868549461853782928111418179513056399_<62>

Number: 21119_112
N=5334136935099808580284923205132405491095318135366526656801882265322610145927107109722326448450493580324087
  ( 106 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=192943753209624529109523104943977732198649113 (pp45)
 r2=27646072217246202886997945868549461853782928111418179513056399 (pp62)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.53 hours.
Scaled time: 1.72 units (timescale=0.677).
Factorization parameters were as follows:
name: 21119_112
n: 5334136935099808580284923205132405491095318135366526656801882265322610145927107109722326448450493580324087
m: 10000000000000000000000
c5: 1900
c0: 71
skew: 0.52
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64189, largePrimes:2361199 encountered
Relations: rels:2768899, finalFF:523002
Max relations in full relation-set: 28
Initial matrix: 113354 x 523002 with sparse part having weight 43837723.
Pruned matrix : 64947 x 65577 with weight 6285656.
Total sieving time: 2.33 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.53 hours.
 --------- CPU info (if available) ----------

(19·10¹³⁴+71)/9 = 2(1)₁₃₃9_<135> = 3³ · 457257134670580393_<18> · C116

C116 = P38 · P79

P38 = 10698206939899017923623609042878690937_<38>

P79 = 1598364563201131516546710489349534778051921624547529288544666400228846159595517_<79>

Number: 21119_134
N=17099634862527007633774249557468016889650724451448309765314701595321185322430397101421106833371432310268550373729429
  ( 116 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=10698206939899017923623609042878690937 (pp38)
 r2=1598364563201131516546710489349534778051921624547529288544666400228846159595517 (pp79)
Version: GGNFS-0.77.1-20060513-k8
Total time: 9.94 hours.
Scaled time: 19.86 units (timescale=1.997).
Factorization parameters were as follows:
name: 21119_134
n: 17099634862527007633774249557468016889650724451448309765314701595321185322430397101421106833371432310268550373729429
m: 1000000000000000000000000000
c5: 19
c0: 710
skew: 2.06
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1675001)
Primes: RFBsize:78498, AFBsize:64144, largePrimes:1647026 encountered
Relations: rels:1684261, finalFF:198191
Max relations in full relation-set: 28
Initial matrix: 142707 x 198191 with sparse part having weight 19597404.
Pruned matrix : 128343 x 129120 with weight 11138560.
Total sieving time: 9.69 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 9.94 hours.
 --------- CPU info (if available) ----------

(19·10¹¹⁴+71)/9 = 2(1)₁₁₃9_<115> = 73 · 691 · C110

C110 = P46 · P64

P46 = 8668069487682906600652956127049454670277290771_<46>

P64 = 4828228328398470071417068118715193261966974633062620905686001823_<64>

Number: 21119_114
N=41851418652957022998455902922330375098846442739549810897668875981030293818986006207226198106994253139407075533
  ( 110 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=8668069487682906600652956127049454670277290771 (pp46)
 r2=4828228328398470071417068118715193261966974633062620905686001823 (pp64)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.38 hours.
Scaled time: 1.62 units (timescale=0.678).
Factorization parameters were as follows:
name: 21119_114
n: 41851418652957022998455902922330375098846442739549810897668875981030293818986006207226198106994253139407075533
m: 100000000000000000000000
c5: 19
c0: 710
skew: 2.06
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64144, largePrimes:2134265 encountered
Relations: rels:2237799, finalFF:245661
Max relations in full relation-set: 28
Initial matrix: 113307 x 245661 with sparse part having weight 20999251.
Pruned matrix : 83577 x 84207 with weight 4754404.
Total sieving time: 2.17 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.38 hours.
 --------- CPU info (if available) ----------

(19·10¹²⁴+71)/9 = 2(1)₁₂₃9_<125> = 7 · 23 · 53 · 545437 · 2033243 · 384102041 · C100

C100 = P40 · P61

P40 = 1253918638360010980630156828555485474091_<40>

P61 = 4631903386600872960769452069902828289819525693679554924387983_<61>

Number: 21119_124
N=5808029987541690152973383463236766090906255370289806657893139849685671618439794418005456394778248453
  ( 100 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=1253918638360010980630156828555485474091 (pp40)
 r2=4631903386600872960769452069902828289819525693679554924387983 (pp61)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 4.21 hours.
Scaled time: 2.85 units (timescale=0.678).
Factorization parameters were as follows:
name: 21119_124
n: 5808029987541690152973383463236766090906255370289806657893139849685671618439794418005456394778248453
m: 10000000000000000000000000
c5: 19
c0: 710
skew: 2.06
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:49098, AFBsize:64144, largePrimes:2250891 encountered
Relations: rels:2388831, finalFF:237058
Max relations in full relation-set: 28
Initial matrix: 113307 x 237058 with sparse part having weight 23832349.
Pruned matrix : 93307 x 93937 with weight 7260611.
Total sieving time: 3.90 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 4.21 hours.
 --------- CPU info (if available) ----------

(19·10¹³⁸+71)/9 = 2(1)₁₃₇9_<139> = 73 · 997 · 195919 · 66563467303261_<14> · C115

C115 = P34 · P82

P34 = 1603870692511431841860591622009493_<34>

P82 = 1386791687162605489137851193896744499618556517677168287616017596826355620762034277_<82>

Number: 21119_138
N=2224234543658585009229052576859222565158549335853153762487314124689686259971732751014408988258302505370921285391561
  ( 115 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=1603870692511431841860591622009493 (pp34)
 r2=1386791687162605489137851193896744499618556517677168287616017596826355620762034277 (pp82)
Version: GGNFS-0.77.1-20060513-k8
Total time: 17.15 hours.
Scaled time: 34.34 units (timescale=2.003).
Factorization parameters were as follows:
name: 21119_138
n: 2224234543658585009229052576859222565158549335853153762487314124689686259971732751014408988258302505370921285391561
m: 1000000000000000000000000000
c5: 19000
c0: 71
skew: 0.33
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 2725001)
Primes: RFBsize:78498, AFBsize:63999, largePrimes:1750118 encountered
Relations: rels:1816378, finalFF:175667
Max relations in full relation-set: 28
Initial matrix: 142564 x 175667 with sparse part having weight 21332623.
Pruned matrix : 135273 x 136049 with weight 15303043.
Total sieving time: 16.81 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 17.15 hours.
 --------- CPU info (if available) ----------

Jun 11, 2008 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS

(19·10¹⁰²+71)/9 = 2(1)₁₀₁9_<103> = 23 · 47 · 101611 · 763513 · 100996333 · C81

C81 = P30 · P51

P30 = 980156943101230219900359753653_<30>

P51 = 254288669710884780374892372181242723179308431072557_<51>

(19·10¹⁰⁸+71)/9 = 2(1)₁₀₇9_<109> = 8243 · 19120670782441660997_<20> · C86

C86 = P36 · P50

P36 = 450603619990888308306431347840461433_<36>

P50 = 29725419435685684489852635686211058845046578616633_<50>

Number: n
N=13394381603467477755945469483667385640135036286832826097295226247555419210533528815089
  ( 86 digits)
SNFS difficulty: 109 digits.
Divisors found:
 r1=450603619990888308306431347840461433 (pp36)
 r2=29725419435685684489852635686211058845046578616633 (pp50)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.73 hours.
Scaled time: 1.33 units (timescale=1.818).
Factorization parameters were as follows:
name: KA_2_1_107_9
n: 13394381603467477755945469483667385640135036286832826097295226247555419210533528815089
skew: 0.33
deg: 5
c5: 19000
c0: 71
m: 1000000000000000000000
type: snfs
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 180001)
Primes: RFBsize:41538, AFBsize:41668, largePrimes:3476528 encountered
Relations: rels:2873720, finalFF:99266
Max relations in full relation-set: 48
Initial matrix: 83273 x 99266 with sparse part having weight 7851229.
Pruned matrix : 77272 x 77752 with weight 4272405.
Total sieving time: 0.63 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.02 hours.
Total square root time: 0.03 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,109,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.5,2.5,50000
total time: 0.73 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(19·10¹²⁵+71)/9 = 2(1)₁₂₄9_<126> = 3² · 107 · C123

C123 = P34 · P90

P34 = 1413942013724739012664646934719861_<34>

P90 = 155043371987302231298493040834790288681640158330016874349793071994628235823840962820138833_<90>

(86·10¹⁹³+31)/9 = 9(5)₁₉₂9_<194> = 3 · 11 · 2699 · 46103930161_<11> · 8491960607515969_<16> · 193493468565567926104105693906747_<33> · C131

C131 = P41 · P90

P41 = 14340220886360533482512595413716049258071_<41>

P90 = 987577181992017289168545019941442943274336687209294613113211426445489576560981167267446169_<90>

(19·10¹²⁶+71)/9 = 2(1)₁₂₅9_<127> = 422096513 · 5145216763_<10> · 3313220862453003712927_<22> · C87

C87 = P37 · P50

P37 = 5784939440621316381615971654557277699_<37>

P50 = 50716169772551226915531892187055375653717528087137_<50>

Number: n
N=293389970794478209096552836142598741462779930913674529100775827845706558862965578857763
  ( 87 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=5784939440621316381615971654557277699 (pp37)
 r2=50716169772551226915531892187055375653717528087137 (pp50)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.33 hours.
Scaled time: 4.27 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_1_125_9
n: 293389970794478209096552836142598741462779930913674529100775827845706558862965578857763
skew: 0.82
deg: 5
c5: 190
c0: 71
m: 10000000000000000000000000
type: snfs
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 400001)
Primes: RFBsize:78498, AFBsize:78712, largePrimes:5072487 encountered
Relations: rels:4367200, finalFF:184214
Max relations in full relation-set: 48
Initial matrix: 157277 x 184214 with sparse part having weight 17282688.
Pruned matrix : 146383 x 147233 with weight 10383105.
Total sieving time: 2.11 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.12 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000
total time: 2.33 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jun 11, 2008

The factor table of 211...119 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Jun 10, 2008 (2nd)

By matsui

8·10¹⁷¹-3 = 7(9)₁₇₀7_<172> = 11 · 26691667 · C164

C164 = P57 · P108

P57 = 161588169710480273544767312890977071902081766318608100651_<57>

P108 = 168621148114846076028702461887800700665968272691501216143530445055605532067216607241423609435786388774673031_<108>

055605532067216607241423609435786388774673031
results=N=27247182698357778580381387467209420555384297551469051098504740347342384899649494625896811642647599614993221394799834992423937880210806139336567953109587620463243181
  ( 164 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=161588169710480273544767312890977071902081766318608100651 (pp57)
 r2=168621148114846076028702461887800700665968272691501216143530445055605532067216607241423609435786388774673031 (pp108)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 109.34 hours.
Scaled time: 185.99 units (timescale=1.701).
Factorization parameters were as follows:
n: 27247182698357778580381387467209420555384297551469051098504740347342384899649494625896811642647599614993221394799834992423937880210806139336567953109587620463243181
m: 20000000000000000000000000000000000
c5: 5
c0: -6
skew: 1.04
type: snfs

Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 7100001)
Primes: RFBsize:412849, AFBsize:411941, largePrimes:6008728 encountered
Relations: rels:6280371, finalFF:935359
Max relations in full relation-set: 28
Initial matrix: 824855 x 935359 with sparse part having weight 54634880.
Pruned matrix : 732551 x 736739 with weight 40305644.
Total sieving time: 100.86 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 8.11 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 109.34 hours.

Jun 10, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(19·10¹⁶⁷+53)/9 = 2(1)₁₆₆7_<168> = 31 · 320083 · 17760384342751_<14> · C148

C148 = P52 · P96

P52 = 2570425101530933072476288537139463003096717765694241_<52>

P96 = 466046740920626307089573465132231484958654650900514236799839493101275990757147969483111772494719_<96>

Number: n
N=1197938241349061336458522844018218127092204612969583280105998588522712770492267602126630070931892286913675016319536632794797252743959696031541213279
  ( 148 digits)
SNFS difficulty: 168 digits.
Divisors found:

Tue Jun 10 16:41:52 2008  prp52 factor: 2570425101530933072476288537139463003096717765694241
Tue Jun 10 16:41:52 2008  prp96 factor: 466046740920626307089573465132231484958654650900514236799839493101275990757147969483111772494719
Tue Jun 10 16:41:52 2008  elapsed time 03:13:45 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 114.73 hours.
Scaled time: 199.06 units (timescale=1.735).
Factorization parameters were as follows:
name: KA_2_1_166_7
n: 1197938241349061336458522844018218127092204612969583280105998588522712770492267602126630070931892286913675016319536632794797252743959696031541213279
type: snfs
skew: 0.49
deg: 5
c5: 1900
c0: 53
m: 1000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5300001)
Primes: RFBsize:230209, AFBsize:229847, largePrimes:7977913 encountered
Relations: rels:7375544, finalFF:472087
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 114.37 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.6,2.6,100000
total time: 114.73 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(17·10¹⁶⁸-53)/9 = 1(8)₁₆₇3_<169> = 3371 · 48487 · 520151 · C155

C155 = P39 · P117

P39 = 149492575450278766064355105465537861991_<39>

P117 = 148618640254097296463041504915115243088101259415265146325211387004955010597261896312036315375075730295290862505541119_<117>

Jun 9, 2008

By Robert Backstrom / GGNFS, Msieve

(19·10¹⁶⁷+17)/9 = 2(1)₁₆₆3_<168> = 3³ · 7 · 12719167273_<11> · C155

C155 = P72 · P84

P72 = 331020430061825622240821487692762096553201092980731173026412142307290539_<72>

P84 = 265299120281487299747115556364341636867465798157268399080428918610074877812977268511_<84>

Number: n
N=87819428890601930193174578949148272157511969157371746212193242682491669105644340286172556451630474536351991658958191443143132235435038495193586597492917429
  ( 155 digits)
SNFS difficulty: 168 digits.
Divisors found:

Mon Jun 09 13:43:34 2008  prp72 factor: 331020430061825622240821487692762096553201092980731173026412142307290539
Mon Jun 09 13:43:34 2008  prp84 factor: 265299120281487299747115556364341636867465798157268399080428918610074877812977268511
Mon Jun 09 13:43:34 2008  elapsed time 02:21:05 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 86.64 hours.
Scaled time: 125.88 units (timescale=1.453).
Factorization parameters were as follows:
name: KA_2_1_166_3
n: 87819428890601930193174578949148272157511969157371746212193242682491669105644340286172556451630474536351991658958191443143132235435038495193586597492917429
skew: 0.39
deg: 5
c5: 1900
c0: 17
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4400001)
Primes: RFBsize:250150, AFBsize:249376, largePrimes:7844574 encountered
Relations: rels:7268414, finalFF:533461
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 86.33 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 86.64 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jun 8, 2008

By matsui / GGNFS

8·10¹⁷⁰-3 = 7(9)₁₆₉7_<171> = 19 · 283 · 313 · 12939739 · C158

C158 = P79 · P80

P79 = 1329287407066634342417708533382270111835295739849982262342044058728813534610871_<79>

P80 = 27635110530649598980061095653778265322075333231930656337853079914922096864534713_<80>

N=36735004421287046871645786893404694611759911810832769307831335234685028075163714623640129986468296706960744230461691070339391812014777047625593680940926665023
  ( 158 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=1329287407066634342417708533382270111835295739849982262342044058728813534610871 (pp79)
 r2=27635110530649598980061095653778265322075333231930656337853079914922096864534713 (pp80)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 108.76 hours.
Scaled time: 123.12 units (timescale=1.132).
Factorization parameters were as follows:
n: 36735004421287046871645786893404694611759911810832769307831335234685028075163714623640129986468296706960744230461691070339391812014777047625593680940926665023
m: 10000000000000000000000000000000000
c5: 8
c0: -3
skew: 0.82
type: snfs

Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 6800001)
Primes: RFBsize:412849, AFBsize:412856, largePrimes:5993930 encountered
Relations: rels:6267516, finalFF:937691
Max relations in full relation-set: 28
Initial matrix: 825770 x 937691 with sparse part having weight 51657631.
Pruned matrix : 732164 x 736356 with weight 37657512.
Total sieving time: 100.31 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 7.99 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 108.76 hours.

Jun 7, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(19·10¹⁷¹+53)/9 = 2(1)₁₇₀7_<172> = 29 · 73 · C168

C168 = P78 · P91

P78 = 168661868577202193078498353096651456486993533110668327480176859986366715725113_<78>

P91 = 5912529573202205892596710183074556787793902601590008372374823072400078491492372186687664177_<91>

Number: n
N=997218285834251823859759617907941006665616963207893770009972182858342518238597596179079410066656169632078937700099721828583425182385975961790794100666561696320789377001
  ( 168 digits)
SNFS difficulty: 172 digits.
Divisors found:

Sat Jun 07 11:15:53 2008  prp78 factor: 168661868577202193078498353096651456486993533110668327480176859986366715725113
Sat Jun 07 11:15:53 2008  prp91 factor: 5912529573202205892596710183074556787793902601590008372374823072400078491492372186687664177
Sat Jun 07 11:15:53 2008  elapsed time 01:54:10 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 62.34 hours.
Scaled time: 114.01 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_1_170_7
n: 997218285834251823859759617907941006665616963207893770009972182858342518238597596179079410066656169632078937700099721828583425182385975961790794100666561696320789377001
skew: 0.77
deg: 5
c5: 190
c0: 53
m: 10000000000000000000000000000000000
type: snfs
rlim: 3800000
alim: 3800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 8399990)
Primes: RFBsize:269987, AFBsize:270102, largePrimes:8759196 encountered
Relations: rels:8275802, finalFF:614142
Max relations in full relation-set: 28
Initial matrix: 540156 x 614142 with sparse part having weight 104508632.
Pruned matrix : 
Total sieving time: 62.04 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,3800000,3800000,28,28,48,48,2.5,2.5,100000
total time: 62.34 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(52·10¹⁶⁶-7)/9 = 5(7)₁₆₆_<167> = 3 · 8537 · 255757 · 525541 · 542555873 · C143

C143 = P39 · P105

P39 = 194347402850767085232324193773663394853_<39>

P105 = 159175768603678496522767736976312094223274142566031220136596573878529488740968790595578468802481799156919_<105>

Number: n
N=30935397224899588137032400403776143825219089737083473114490349480239274430387787920586369380476002430395991417734593542513905288852266803937907
  ( 143 digits)
SNFS difficulty: 168 digits.
Divisors found:

Sat Jun 07 21:27:14 2008  prp39 factor: 194347402850767085232324193773663394853
Sat Jun 07 21:27:14 2008  prp105 factor: 159175768603678496522767736976312094223274142566031220136596573878529488740968790595578468802481799156919
Sat Jun 07 21:27:14 2008  elapsed time 02:26:22 (Msieve 1.36)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 117.71 hours.
Scaled time: 154.31 units (timescale=1.311).
Factorization parameters were as follows:
name: KA_5_7_166
n: 30935397224899588137032400403776143825219089737083473114490349480239274430387787920586369380476002430395991417734593542513905288852266803937907
skew: 0.84
deg: 5
c5: 65
c0: -28
m: 2000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4300573)
Primes: RFBsize:216816, AFBsize:217161, largePrimes:7714153 encountered
Relations: rels:7106257, finalFF:456914
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 117.23 hours.
Total relation processing time: 0.48 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 117.71 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(82·10¹⁹⁶-1)/9 = 9(1)₁₉₆_<197> = 6529 · 2016943147_<10> · 4747717717776043_<16> · 52903728369300534371_<20> · 7068156580783016438441_<22> · C127

C127 = P44 · P83

P44 = 81658001383391490714853549764552732910419977_<44>

P83 = 47725989393250425685698093318853962668514004436283556924989693866905105524709738757_<83>

Jun 5, 2008 (2nd)

By matsui / GGNFS

6·10¹⁷¹+7 = 6(0)₁₇₀7_<172> = 71 · 59218811 · C163

C163 = P33 · P130

P33 = 474552042132264250970127542339833_<33>

P130 = 3007110393444661684023615721112945500024818563987365700417287479523557838981587406237779335223878760263992906197715985864050125259_<130>

N=1427030378126320819926009326355609214191592305614026387757663739937321748163843163823614696626347803048833326070026186799440477847153697330073801556443529595141747
  ( 163 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=474552042132264250970127542339833 (pp33)
 r2=3007110393444661684023615721112945500024818563987365700417287479523557838981587406237779335223878760263992906197715985864050125259 (pp130)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 263.39 hours.
Scaled time: 447.23 units (timescale=1.698).
Factorization parameters were as follows:
n: 1427030378126320819926009326355609214191592305614026387757663739937321748163843163823614696626347803048833326070026186799440477847153697330073801556443529595141747
m: 10000000000000000000000000000000000
c5: 60
c0: 7
skew: 0.65
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 9100001)
Primes: RFBsize:412849, AFBsize:413211, largePrimes:6243772 encountered
Relations: rels:6522967, finalFF:932713
Max relations in full relation-set: 28
Initial matrix: 826127 x 932713 with sparse part having weight 72156280.
Pruned matrix : 744394 x 748588 with weight 56055920.
Total sieving time: 252.14 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 10.74 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 263.39 hours.

Jun 5, 2008

By Robert Backstrom / GGNFS, Msieve

(19·10¹⁵³+53)/9 = 2(1)₁₅₂7_<154> = 1879 · 18211 · 657339007961513351528016261555491_<33> · C113

C113 = P41 · P73

P41 = 49440282722308466810657310201766051159457_<41>

P73 = 1898366959062654878216846059729855418347441491497031988617483026838153539_<73>

Number: n
N=93855799166746640492272622125497718479246182956099212617130611814947101236895121008505256986359336706235937868323
  ( 113 digits)
Divisors found:

Thu Jun  5 01:27:19 2008  prp41 factor: 49440282722308466810657310201766051159457
Thu Jun  5 01:27:19 2008  prp73 factor: 1898366959062654878216846059729855418347441491497031988617483026838153539
Thu Jun  5 01:27:19 2008  elapsed time 00:54:53 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 25.54 hours.
Scaled time: 21.33 units (timescale=0.835).
Factorization parameters were as follows:
name: KA_2_1_152_7
n: 93855799166746640492272622125497718479246182956099212617130611814947101236895121008505256986359336706235937868323
skew: 11116.69
# norm 1.92e+15
c5: 103440
c4: 11953367872
c3: 15928492693912
c2: -722423903459076173
c1: 1332711082941591543402
c0: -5152737654335827118703105
# alpha -5.25
Y1: 725795780941
Y0: -3904385166972887532266
# Murphy_E 6.57e-10
# M 41592232628683845462355480330603808426187404799596563145996588259114680645002794406922771259457385042957096841561
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1600097)
Primes: RFBsize:250150, AFBsize:250146, largePrimes:6949358 encountered
Relations: rels:6614567, finalFF:545217
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 25.35 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 25.54 hours.
 --------- CPU info (if available) ----------

Jun 4, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve

(4·10¹⁶⁶-7)/3 = 1(3)₁₆₅1_<167> = 29 · 53 · 277 · 617 · 5838767041_<10> · 7353513077_<10> · C139

C139 = P54 · P85

P54 = 192731134450942355826572331465468888732090323885616437_<54>

P85 = 6133834322965081225387775111756706302035506281288803413842786108108282065805336181223_<85>

Number: n
N=1182180847599188046818857534724658900852626590739814972842019783607392083840022685023727597960406156943676045299525683368653969430899562451
  ( 139 digits)
SNFS difficulty: 166 digits.
Divisors found:

Wed Jun 04 17:41:20 2008  prp54 factor: 192731134450942355826572331465468888732090323885616437
Wed Jun 04 17:41:20 2008  prp85 factor: 6133834322965081225387775111756706302035506281288803413842786108108282065805336181223
Wed Jun 04 17:41:20 2008  elapsed time 00:53:13 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 36.64 hours.
Scaled time: 66.69 units (timescale=1.820).
Factorization parameters were as follows:
name: KA_1_3_165_1
n: 1182180847599188046818857534724658900852626590739814972842019783607392083840022685023727597960406156943676045299525683368653969430899562451
skew: 0.32
deg: 5
c5: 40
c0: -7
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2500529)
Primes: RFBsize:230209, AFBsize:229712, largePrimes:7212995 encountered
Relations: rels:6635279, finalFF:484405
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 36.46 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 36.64 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jun 4, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(19·10¹⁴³+53)/9 = 2(1)₁₄₂7_<144> = 29 · 642821741 · 4284759633206018989819201_<25> · C109

C109 = P45 · P65

P45 = 113218888779812679914545263801430398846511411_<45>

P65 = 23344102690036781800016467479390952616696847561433570010070708823_<65>

Number: 21117_143
N=2642993366127800393414430806581459942303114996968280892797448071154662899280821918339828161151241489527879253
  ( 109 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=113218888779812679914545263801430398846511411 (pp45)
 r2=23344102690036781800016467479390952616696847561433570010070708823 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 29.34 hours.
Scaled time: 19.86 units (timescale=0.677).
Factorization parameters were as follows:
name: 21117_143
n: 2642993366127800393414430806581459942303114996968280892797448071154662899280821918339828161151241489527879253
m: 10000000000000000000000000000
c5: 19000
c0: 53
skew: 0.31
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 3550001)
Primes: RFBsize:100021, AFBsize:100113, largePrimes:3009325 encountered
Relations: rels:3070164, finalFF:227045
Max relations in full relation-set: 28
Initial matrix: 200201 x 227045 with sparse part having weight 29056454.
Pruned matrix : 193665 x 194730 with weight 23731295.
Total sieving time: 27.51 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 1.46 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 29.34 hours.
 --------- CPU info (if available) ----------

Jun 4, 2008 (2nd)

By matsui / GGNFS

2·10¹⁶⁹-1 = 1(9)₁₆₉_<170> = 9479 · 22528741 · C158

C158 = P47 · P112

P47 = 58898760265545578947543164298726379592443127301_<47>

P112 = 1590099849864182210494369250009957128474833068460631622744916529265419584880420247201933949436069843089442684241_<112>

N=93654909855430485828763065681998364104412095025723340870348581107002829762155361242962287920426721940792480679499437178241372396724687925920080647933909563541
  ( 158 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=58898760265545578947543164298726379592443127301 (pp47)
 r2=1590099849864182210494369250009957128474833068460631622744916529265419584880420247201933949436069843089442684241 (pp112)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 177.49 hours.
Scaled time: 151.40 units (timescale=0.853).
Factorization parameters were as follows:
n: 93654909855430485828763065681998364104412095025723340870348581107002829762155361242962287920426721940792480679499437178241372396724687925920080647933909563541
m: 10000000000000000000000000000000000
c5: 1
c0: -5
skew: 1.38
type: snfs

Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 6500001)
Primes: RFBsize:412849, AFBsize:412271, largePrimes:5956885 encountered
Relations: rels:6224596, finalFF:933623
Max relations in full relation-set: 28
Initial matrix: 825184 x 933623 with sparse part having weight 47674635.
Pruned matrix : 733184 x 737373 with weight 34636533.
Total sieving time: 165.67 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 11.27 hours.
Time per square root: 0.32 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 177.49 hours.

Jun 4, 2008

GMP-ECM 6.2.1 has been released.

HOW TO for Japanese

Jun 3, 2008 (4th)

By Wataru Sakai / GGNFS

(10¹⁷⁵+11)/3 = (3)₁₇₄7_<175> = 7 · 66593 · C169

C169 = P38 · P132

P38 = 31384625954292517272083270912284988437_<38>

P132 = 227842725978933038527191595324104875211606210309617485656031157323032196340886078968896526888348315502943618148510280830511973874051_<132>

Number: 33337_175
N=7150758731255179830855952970889976280933288426568501050803995557948676144282289072282014483146734284241229415647147240557959402282379171842028298412603069248662629348287
  ( 169 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=31384625954292517272083270912284988437 (pp38)
 r2=227842725978933038527191595324104875211606210309617485656031157323032196340886078968896526888348315502943618148510280830511973874051 (pp132)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 176.55 hours.
Scaled time: 353.46 units (timescale=2.002).
Factorization parameters were as follows:
n: 7150758731255179830855952970889976280933288426568501050803995557948676144282289072282014483146734284241229415647147240557959402282379171842028298412603069248662629348287
m: 100000000000000000000000000000000000
c5: 1
c0: 11
skew: 1.62
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 9400001)
Primes: RFBsize:501962, AFBsize:502027, largePrimes:6547456 encountered
Relations: rels:7183440, finalFF:1298613
Max relations in full relation-set: 32
Initial matrix: 1004053 x 1298613 with sparse part having weight 71578861.
Pruned matrix : 741890 x 746974 with weight 50609168.
Total sieving time: 172.03 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 4.25 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 176.55 hours.

Jun 3, 2008 (3rd)

By Jo Yeong Uk / GGNFS

(19·10¹⁶³+53)/9 = 2(1)₁₆₂7_<164> = 3³ · 73 · 2689 · 10424563 · 923076685159_<12> · 2946551431987_<13> · 34825517084278748077301_<23> · C103

C103 = P52 · P52

P52 = 1651232239649515659508639079209693572743461625197213_<52>

P52 = 2442970742799471533588610599827101256283903212427009_<52>

Number: 21117_163
N=4033912051031012261593993832795928814631065204377255803288434374957097404460879570195369709261992725917
  ( 103 digits)
Divisors found:
 r1=1651232239649515659508639079209693572743461625197213 (pp52)
 r2=2442970742799471533588610599827101256283903212427009 (pp52)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.38 hours.
Scaled time: 12.75 units (timescale=2.370).
Factorization parameters were as follows:
name: 21117_163
n: 4033912051031012261593993832795928814631065204377255803288434374957097404460879570195369709261992725917
skew: 7340.12
# norm 1.81e+14
c5: 146160
c4: -398831628
c3: -29546363044896
c2: 15604863772449401
c1: 569711961235965527372
c0: 29241800285831870731743
# alpha -5.87
Y1: 45608002259
Y0: -30773715148705995392
# Murphy_E 2.35e-09
# M 3172093150204558832540147395143702792889572096330200074127881341980114758822844799745116817020563794105
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1680001)
Primes: RFBsize:135072, AFBsize:135442, largePrimes:4395510 encountered
Relations: rels:4347033, finalFF:334703
Max relations in full relation-set: 28
Initial matrix: 270597 x 334703 with sparse part having weight 27697377.
Pruned matrix : 229725 x 231141 with weight 16357860.
Polynomial selection time: 0.35 hours.
Total sieving time: 4.66 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 5.38 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047200k/8912896k available (2440k kernel code, 339088k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 5347.62 BogoMIPS (lpj=2673811)
Calibrating delay using timer specific routine.. 5214.21 BogoMIPS (lpj=2607107)
Calibrating delay using timer specific routine.. 5344.19 BogoMIPS (lpj=2672095)
Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672350)

Jun 3, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(19·10¹³⁴+53)/9 = 2(1)₁₃₃7_<135> = 7 · 47 · 4597 · 8609 · C125

C125 = P43 · P82

P43 = 5403622215874456846832096554592058096621793_<43>

P82 = 3000564753507592297355998545136918553987659979517034764910691658674627703147614257_<82>

Number: 21117_134
N=16213918362223489302223535692633389562153429015595671952321814050862732998694287615956975520679013858527672865365139183702801
  ( 125 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=5403622215874456846832096554592058096621793 (pp43)
 r2=3000564753507592297355998545136918553987659979517034764910691658674627703147614257 (pp82)
Version: GGNFS-0.77.1-20060513-k8
Total time: 10.54 hours.
Scaled time: 20.86 units (timescale=1.979).
Factorization parameters were as follows:
name: 21117_134
n: 16213918362223489302223535692633389562153429015595671952321814050862732998694287615956975520679013858527672865365139183702801
m: 1000000000000000000000000000
c5: 19
c0: 530
skew: 1.95
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1675001)
Primes: RFBsize:78498, AFBsize:64098, largePrimes:1614720 encountered
Relations: rels:1625307, finalFF:171469
Max relations in full relation-set: 28
Initial matrix: 142661 x 171469 with sparse part having weight 16936085.
Pruned matrix : 134817 x 135594 with weight 11860232.
Total sieving time: 10.24 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 10.54 hours.
 --------- CPU info (if available) ----------

(19·10¹⁵¹+53)/9 = 2(1)₁₅₀7_<152> = 3 · 59 · 113 · 19777 · 496132729 · 255184099217_<12> · C123

C123 = P35 · P39 · P50

P35 = 10802596959816835717153878679789093_<35>

P39 = 510747305679292439904818708357078624189_<39>

P50 = 76403494685203056879146028205246866036211171137461_<50>

Number: 21117_151
N=421548434642298635067245499858189780855963517184294121673147892868581238049980895146232704403663085255385064268683122684997
  ( 123 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=10802596959816835717153878679789093 (pp35)
 r2=510747305679292439904818708357078624189 (pp39)
 r3=76403494685203056879146028205246866036211171137461 (pp50)
Version: GGNFS-0.77.1-20060513-k8
Total time: 30.64 hours.
Scaled time: 61.38 units (timescale=2.003).
Factorization parameters were as follows:
name: 21117_151
n: 421548434642298635067245499858189780855963517184294121673147892868581238049980895146232704403663085255385064268683122684997
m: 1000000000000000000000000000000
c5: 190
c0: 53
skew: 0.77
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2300001)
Primes: RFBsize:176302, AFBsize:176488, largePrimes:5745499 encountered
Relations: rels:5739824, finalFF:530707
Max relations in full relation-set: 28
Initial matrix: 352857 x 530707 with sparse part having weight 50577699.
Pruned matrix : 289862 x 291690 with weight 27680081.
Total sieving time: 29.18 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.16 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 30.64 hours.
 --------- CPU info (if available) ----------

Jun 3, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(17·10¹⁸⁵-53)/9 = 1(8)₁₈₄3_<186> = 3³ · 31 · C183

C183 = P82 · P102

P82 = 1597997386322290245461276699108764584415883034598743632467843957463923933713820829_<82>

P102 = 141222823208483395121283940637151729989074192145153563988529735450619888690572081943928291407031714371_<102>

Number: n
N=225673702376211336784813487322447895924598433559007035709544670118146820655781229257931766892340369042878003451480153989114562591265100225673702376211336784813487322447895924598433559
  ( 183 digits)
SNFS difficulty: 186 digits.
Divisors found:

Tue Jun  3 00:59:42 2008  prp82 factor: 1597997386322290245461276699108764584415883034598743632467843957463923933713820829
Tue Jun  3 00:59:42 2008  prp102 factor: 141222823208483395121283940637151729989074192145153563988529735450619888690572081943928291407031714371
Tue Jun  3 00:59:42 2008  elapsed time 03:01:31 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 96.19 hours.
Scaled time: 80.61 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_1_8_184_3
n: 225673702376211336784813487322447895924598433559007035709544670118146820655781229257931766892340369042878003451480153989114562591265100225673702376211336784813487322447895924598433559
type: snfs
deg: 5
c5: 17
c0: -53
skew: 1.26
m: 10000000000000000000000000000000000000
rlim: 7000000
alim: 7000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 7000000/7000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 13400077)
Primes: RFBsize:476648, AFBsize:476034, largePrimes:6576115 encountered
Relations: rels:6884940, finalFF:988009
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 95.96 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,7000000,7000000,27,27,48,48,2.5,2.5,100000
total time: 96.19 hours.
 --------- CPU info (if available) ----------

(19·10¹⁵⁷+53)/9 = 2(1)₁₅₆7_<158> = 3 · 137 · 1669 · 2416956391_<10> · C143

C143 = P43 · P100

P43 = 9327754593722757997158137149780069754362391_<43>

P100 = 1365107984440039824790803736415625965715893749320105011201077904595167216578438035906087890833714123_<100>

(19·10¹⁴¹+53)/9 = 2(1)₁₄₀7_<142> = 137 · 40690807 · C132

C132 = P41 · P92

P41 = 27198025104878136528579769327922885245327_<41>

P92 = 13923770326764645462911775434681406383095756757842407468021553475546864212753687318351193869_<92>

Number: n
N=378699054901902081739421275414128653081310010809454075711845569972130486756125779321498871746559742832580196694097046465935403300163
  ( 132 digits)
SNFS difficulty: 142 digits.
Divisors found:

Tue Jun 03 04:22:47 2008  prp41 factor: 27198025104878136528579769327922885245327
Tue Jun 03 04:22:47 2008  prp92 factor: 13923770326764645462911775434681406383095756757842407468021553475546864212753687318351193869
Tue Jun 03 04:22:47 2008  elapsed time 00:24:28 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 5.78 hours.
Scaled time: 10.50 units (timescale=1.817).
Factorization parameters were as follows:
name: KA_2_1_140_7
n: 378699054901902081739421275414128653081310010809454075711845569972130486756125779321498871746559742832580196694097046465935403300163
skew: 0.77
deg: 5
c5: 190
c0: 53
m: 10000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 960581)
Primes: RFBsize:148933, AFBsize:149140, largePrimes:6361799 encountered
Relations: rels:5656427, finalFF:321577
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 5.59 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 5.78 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(19·10¹⁴⁶+53)/9 = 2(1)₁₄₅7_<147> = 7 · 1190149 · C140

C140 = P68 · P72

P68 = 58331886632896092336330712812119256134195174608064860440080724285391_<68>

P72 = 434415879950414804346950736783159062697316149855191019881795289997876609_<72>

Number: n
N=25340297860797394889344720836408011711272059346124022059556181754326692481494947404678035044484959579624197247704892546000676159168919319119
  ( 140 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=58331886632896092336330712812119256134195174608064860440080724285391 (pp68)
 r2=434415879950414804346950736783159062697316149855191019881795289997876609 (pp72)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 9.19 hours.
Scaled time: 16.71 units (timescale=1.819).
Factorization parameters were as follows:
name: KA_2_1_145_7
n: 25340297860797394889344720836408011711272059346124022059556181754326692481494947404678035044484959579624197247704892546000676159168919319119
skew: 0.77
deg: 5
c5: 190
c0: 53
m: 100000000000000000000000000000
type: snfs
rlim: 2400000
alim: 2400000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:176302, AFBsize:176488, largePrimes:6869920 encountered
Relations: rels:6255073, finalFF:414560
Max relations in full relation-set: 48
Initial matrix: 352857 x 414560 with sparse part having weight 36005432.
Pruned matrix : 309414 x 311242 with weight 21939980.
Total sieving time: 8.14 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.76 hours.
Total square root time: 0.10 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,2400000,2400000,28,28,48,48,2.5,2.5,100000
total time: 9.19 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(19·10¹⁶⁰+53)/9 = 2(1)₁₅₉7_<161> = 3 · 173 · 4217 · 22205549 · 356050365606344610424786395461843_<33> · C115

C115 = P40 · P75

P40 = 1942156014418176018702442345855437715753_<40>

P75 = 628178499120351639880606186016433190873849204059410375565924824840997233549_<75>

Jun 2, 2008 (4th)

By Jo Yeong Uk / GMP-ECM, Msieve, GGNFS

(19·10¹³⁹+53)/9 = 2(1)₁₃₈7_<140> = 3 · 73 · 269 · 1314345485719339431777602851_<28> · C108

C108 = P33 · P36 · P39

P33 = 510099375329014604799283301482189_<33>

P36 = 838519257079062659185170193098878123_<36>

P39 = 637437084815224855533017008762999621951_<39>

Mon Jun  2 11:12:44 2008  
Mon Jun  2 11:12:44 2008  
Mon Jun  2 11:12:44 2008  Msieve v. 1.34
Mon Jun  2 11:12:44 2008  random seeds: eb11b0bc f0692308
Mon Jun  2 11:12:44 2008  factoring 534503270793905799138212310001265257409229574257419045318153661011224477973 (75 digits)
Mon Jun  2 11:12:44 2008  no P-1/P+1/ECM available, skipping
Mon Jun  2 11:12:44 2008  commencing quadratic sieve (75-digit input)
Mon Jun  2 11:12:44 2008  using multiplier of 29
Mon Jun  2 11:12:44 2008  using 32kb Intel Core sieve core
Mon Jun  2 11:12:44 2008  sieve interval: 12 blocks of size 32768
Mon Jun  2 11:12:44 2008  processing polynomials in batches of 17
Mon Jun  2 11:12:44 2008  using a sieve bound of 667091 (26908 primes)
Mon Jun  2 11:12:44 2008  using large prime bound of 66709100 (25 bits)
Mon Jun  2 11:12:44 2008  using trial factoring cutoff of 26 bits
Mon Jun  2 11:12:44 2008  polynomial 'A' values have 10 factors
Mon Jun  2 11:15:58 2008  27434 relations (14226 full + 13208 combined from 147476 partial), need 27004
Mon Jun  2 11:15:58 2008  begin with 161702 relations
Mon Jun  2 11:15:58 2008  reduce to 38984 relations in 2 passes
Mon Jun  2 11:15:58 2008  attempting to read 38984 relations
Mon Jun  2 11:15:58 2008  recovered 38984 relations
Mon Jun  2 11:15:58 2008  recovered 30274 polynomials
Mon Jun  2 11:15:58 2008  attempting to build 27434 cycles
Mon Jun  2 11:15:58 2008  found 27434 cycles in 1 passes
Mon Jun  2 11:15:58 2008  distribution of cycle lengths:
Mon Jun  2 11:15:58 2008     length 1 : 14226
Mon Jun  2 11:15:58 2008     length 2 : 13208
Mon Jun  2 11:15:58 2008  largest cycle: 2 relations
Mon Jun  2 11:15:58 2008  matrix is 26908 x 27434 (4.0 MB) with weight 827908 (30.18/col)
Mon Jun  2 11:15:58 2008  sparse part has weight 827908 (30.18/col)
Mon Jun  2 11:15:58 2008  filtering completed in 5 passes
Mon Jun  2 11:15:58 2008  matrix is 23022 x 23086 (3.3 MB) with weight 677687 (29.35/col)
Mon Jun  2 11:15:58 2008  sparse part has weight 677687 (29.35/col)
Mon Jun  2 11:15:59 2008  saving the first 48 matrix rows for later
Mon Jun  2 11:15:59 2008  matrix is 22974 x 23086 (2.3 MB) with weight 496279 (21.50/col)
Mon Jun  2 11:15:59 2008  sparse part has weight 359701 (15.58/col)
Mon Jun  2 11:15:59 2008  matrix includes 64 packed rows
Mon Jun  2 11:15:59 2008  commencing Lanczos iteration
Mon Jun  2 11:15:59 2008  memory use: 3.1 MB
Mon Jun  2 11:16:04 2008  lanczos halted after 364 iterations (dim = 22967)
Mon Jun  2 11:16:05 2008  recovered 14 nontrivial dependencies
Mon Jun  2 11:16:05 2008  prp36 factor: 838519257079062659185170193098878123
Mon Jun  2 11:16:05 2008  prp39 factor: 637437084815224855533017008762999621951
Mon Jun  2 11:16:05 2008  elapsed time 00:03:21

(19·10¹⁵⁸+53)/9 = 2(1)₁₅₇7_<159> = 7² · 551826959 · C148

C148 = P39 · P110

P39 = 460989874520911044064786431843221905337_<39>

P110 = 16936384759591687512192175264040477850108231701305445403165968977141397799585486877387463283782557291612041451_<110>

(19·10¹⁵⁰+53)/9 = 2(1)₁₄₉7_<151> = C151

C151 = P31 · P120

P31 = 9985015037288028821227614289837_<31>

P120 = 211427935083460583094406150513915501270969623409084899062206666680722548922350472589902425296793812587271223307267489441_<120>

Number: 21117_150
N=2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117
  ( 151 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=9985015037288028821227614289837 (pp31)
 r2=211427935083460583094406150513915501270969623409084899062206666680722548922350472589902425296793812587271223307267489441 (pp120)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 14.11 hours.
Scaled time: 33.61 units (timescale=2.382).
Factorization parameters were as follows:
n: 2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117
m: 1000000000000000000000000000000
c5: 19
c0: 53
skew: 1.23
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2200001)
Primes: RFBsize:176302, AFBsize:177173, largePrimes:5510831 encountered
Relations: rels:5384542, finalFF:442565
Max relations in full relation-set: 28
Initial matrix: 353540 x 442565 with sparse part having weight 39552834.
Pruned matrix : 316742 x 318573 with weight 24798877.
Total sieving time: 13.43 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.57 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 14.11 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047200k/8912896k available (2440k kernel code, 339088k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 5347.62 BogoMIPS (lpj=2673811)
Calibrating delay using timer specific routine.. 5214.21 BogoMIPS (lpj=2607107)
Calibrating delay using timer specific routine.. 5344.19 BogoMIPS (lpj=2672095)
Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672350)

Jun 2, 2008 (3rd)

By Sinkiti Sibata / GGNFS, Msieve

(19·10¹²⁴+53)/9 = 2(1)₁₂₃7_<125> = 3 · 306525654222521_<15> · C110

C110 = P52 · P58

P52 = 2320545677943061507893706868698246585867969028650453_<52>

P58 = 9893111122056882575541062637026092122141686702534903437003_<58>

Number: 21117_124
N=22957416255699530501295404822326167390114094473872188918375242049826145386407603389399279197768288688392912359
  ( 110 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=2320545677943061507893706868698246585867969028650453 (pp52)
 r2=9893111122056882575541062637026092122141686702534903437003 (pp58)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.45 hours.
Scaled time: 6.93 units (timescale=2.010).
Factorization parameters were as follows:
name: 21117_124
n: 22957416255699530501295404822326167390114094473872188918375242049826145386407603389399279197768288688392912359
m: 10000000000000000000000000
c5: 19
c0: 530
skew: 1.95
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:49098, AFBsize:64098, largePrimes:2259309 encountered
Relations: rels:2381189, finalFF:206711
Max relations in full relation-set: 28
Initial matrix: 113261 x 206711 with sparse part having weight 21468806.
Pruned matrix : 99556 x 100186 with weight 8063758.
Total sieving time: 3.27 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.45 hours.
 --------- CPU info (if available) ----------

(19·10¹⁰⁸+53)/9 = 2(1)₁₀₇7_<109> = 262411 · 460121017 · C95

C95 = P32 · P63

P32 = 40715325956793234293671007002897_<32>

P63 = 429436612371250961547371918499935905158308605193850743956973903_<63>

Sun Jun  1 23:08:03 2008  Msieve v. 1.35
Sun Jun  1 23:08:03 2008  random seeds: a3301bb0 3d53df02
Sun Jun  1 23:08:03 2008  factoring 17484651650476548830770449081096030553402318344900536526344925522349690719762578371973674396991 (95 digits)
Sun Jun  1 23:08:04 2008  searching for 15-digit factors
Sun Jun  1 23:08:06 2008  commencing quadratic sieve (95-digit input)
Sun Jun  1 23:08:06 2008  using multiplier of 11
Sun Jun  1 23:08:07 2008  using 64kb Pentium 4 sieve core
Sun Jun  1 23:08:07 2008  sieve interval: 18 blocks of size 65536
Sun Jun  1 23:08:07 2008  processing polynomials in batches of 6
Sun Jun  1 23:08:07 2008  using a sieve bound of 2128183 (78667 primes)
Sun Jun  1 23:08:07 2008  using large prime bound of 310714718 (28 bits)
Sun Jun  1 23:08:07 2008  using double large prime bound of 1933086450144842 (43-51 bits)
Sun Jun  1 23:08:07 2008  using trial factoring cutoff of 51 bits
Sun Jun  1 23:08:07 2008  polynomial 'A' values have 12 factors
Mon Jun  2 06:07:09 2008  78793 relations (19031 full + 59762 combined from 1177846 partial), need 78763
Mon Jun  2 06:07:13 2008  begin with 1196877 relations
Mon Jun  2 06:07:15 2008  reduce to 206885 relations in 12 passes
Mon Jun  2 06:07:15 2008  attempting to read 206885 relations
Mon Jun  2 06:07:21 2008  recovered 206885 relations
Mon Jun  2 06:07:21 2008  recovered 192966 polynomials
Mon Jun  2 06:07:22 2008  attempting to build 78793 cycles
Mon Jun  2 06:07:22 2008  found 78793 cycles in 6 passes
Mon Jun  2 06:07:22 2008  distribution of cycle lengths:
Mon Jun  2 06:07:22 2008     length 1 : 19031
Mon Jun  2 06:07:22 2008     length 2 : 13437
Mon Jun  2 06:07:22 2008     length 3 : 13297
Mon Jun  2 06:07:22 2008     length 4 : 10751
Mon Jun  2 06:07:22 2008     length 5 : 8138
Mon Jun  2 06:07:22 2008     length 6 : 5588
Mon Jun  2 06:07:22 2008     length 7 : 3479
Mon Jun  2 06:07:22 2008     length 9+: 5072
Mon Jun  2 06:07:22 2008  largest cycle: 21 relations
Mon Jun  2 06:07:22 2008  matrix is 78667 x 78793 (21.6 MB) with weight 5352964 (67.94/col)
Mon Jun  2 06:07:22 2008  sparse part has weight 5352964 (67.94/col)
Mon Jun  2 06:07:24 2008  filtering completed in 3 passes
Mon Jun  2 06:07:24 2008  matrix is 75293 x 75357 (20.8 MB) with weight 5158753 (68.46/col)
Mon Jun  2 06:07:24 2008  sparse part has weight 5158753 (68.46/col)
Mon Jun  2 06:07:25 2008  saving the first 48 matrix rows for later
Mon Jun  2 06:07:25 2008  matrix is 75245 x 75357 (14.5 MB) with weight 4257881 (56.50/col)
Mon Jun  2 06:07:25 2008  sparse part has weight 3344104 (44.38/col)
Mon Jun  2 06:07:25 2008  matrix includes 64 packed rows
Mon Jun  2 06:07:25 2008  using block size 21845 for processor cache size 512 kB
Mon Jun  2 06:07:26 2008  commencing Lanczos iteration
Mon Jun  2 06:07:26 2008  memory use: 13.1 MB
Mon Jun  2 06:08:33 2008  lanczos halted after 1192 iterations (dim = 75245)
Mon Jun  2 06:08:34 2008  recovered 18 nontrivial dependencies
Mon Jun  2 06:08:35 2008  prp32 factor: 40715325956793234293671007002897
Mon Jun  2 06:08:35 2008  prp63 factor: 429436612371250961547371918499935905158308605193850743956973903
Mon Jun  2 06:08:35 2008  elapsed time 07:00:32

(19·10¹²⁶+53)/9 = 2(1)₁₂₅7_<127> = 6903268719584384055121_<22> · C105

C105 = P48 · P58

P48 = 103864082049619335708579914537850517920687452179_<48>

P58 = 2944360108581633473932191940997116495964585541314631028463_<58>

Number: 21117_126
N=305813259901348875505100926497148986989091453916083398966422966908277463737129647551735449182057900370877
  ( 105 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=103864082049619335708579914537850517920687452179 (pp48)
 r2=2944360108581633473932191940997116495964585541314631028463 (pp58)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.39 hours.
Scaled time: 6.76 units (timescale=1.997).
Factorization parameters were as follows:
name: 21117_126
n: 305813259901348875505100926497148986989091453916083398966422966908277463737129647551735449182057900370877
m: 10000000000000000000000000
c5: 190
c0: 53
skew: 0.77
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:49098, AFBsize:63698, largePrimes:2194925 encountered
Relations: rels:2237426, finalFF:145939
Max relations in full relation-set: 28
Initial matrix: 112863 x 145939 with sparse part having weight 14497090.
Pruned matrix : 107817 x 108445 with weight 8805731.
Total sieving time: 3.20 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.39 hours.
 --------- CPU info (if available) ----------

(19·10¹²⁷+53)/9 = 2(1)₁₂₆7_<128> = 3² · 6983 · 9613105129_<10> · 61692263912471_<14> · C99

C99 = P42 · P58

P42 = 291916727489587673555967133607481146004727_<42>

P58 = 1940319099666381182533341297772978664273656217246287082027_<58>

Number: 21117_127
N=566411601860153100701394847632673604425475046837779231967780131659685243669308032364681161978741629
  ( 99 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=291916727489587673555967133607481146004727 (pp42)
 r2=1940319099666381182533341297772978664273656217246287082027 (pp58)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.45 hours.
Scaled time: 8.94 units (timescale=2.010).
Factorization parameters were as follows:
name: 21117_127
n: 566411601860153100701394847632673604425475046837779231967780131659685243669308032364681161978741629
m: 10000000000000000000000000
c5: 1900
c0: 53
skew: 0.49
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:63753, largePrimes:1434124 encountered
Relations: rels:1402381, finalFF:144834
Max relations in full relation-set: 28
Initial matrix: 127771 x 144834 with sparse part having weight 9933985.
Pruned matrix : 122878 x 123580 with weight 7074809.
Total sieving time: 4.27 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.45 hours.
 --------- CPU info (if available) ----------

(19·10¹²⁹+53)/9 = 2(1)₁₂₈7_<130> = 699157 · 830191 · C118

C118 = P38 · P81

P38 = 32446483245581804133518445040362730189_<38>

P81 = 112096158128274832108557939489689899902140999040333373890236189338415740274281619_<81>

Number: 21117_129
N=3637126116603157908916080743469907732373168181016890173585191244364727938683418468784020814756624198363984843499095991
  ( 118 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=32446483245581804133518445040362730189 (pp38)
 r2=112096158128274832108557939489689899902140999040333373890236189338415740274281619 (pp81)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.11 hours.
Scaled time: 12.20 units (timescale=1.997).
Factorization parameters were as follows:
name: 21117_129
n: 3637126116603157908916080743469907732373168181016890173585191244364727938683418468784020814756624198363984843499095991
m: 100000000000000000000000000
c5: 19
c0: 530
skew: 1.95
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1150001)
Primes: RFBsize:63951, AFBsize:64098, largePrimes:1511991 encountered
Relations: rels:1492598, finalFF:146143
Max relations in full relation-set: 28
Initial matrix: 128114 x 146143 with sparse part having weight 13064371.
Pruned matrix : 123752 x 124456 with weight 9702245.
Total sieving time: 5.90 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 6.11 hours.
 --------- CPU info (if available) ----------

(19·10¹³⁸+53)/9 = 2(1)₁₃₇7_<139> = 49169 · 59530109 · 361883017 · 1553270333_<10> · 1742932671511_<13> · C96

C96 = P30 · P67

P30 = 153982827554613533780693879837_<30>

P67 = 4780957545125991811271590664511031750645306007121798055625197067351_<67>

Mon Jun  2 06:17:46 2008  Msieve v. 1.35
Mon Jun  2 06:17:46 2008  random seeds: fbc554e4 1547fed8
Mon Jun  2 06:17:46 2008  factoring 736185361217064049236247539127012918759713514368891194303392952937676728083414902290966389901787 (96 digits)
Mon Jun  2 06:17:48 2008  searching for 15-digit factors
Mon Jun  2 06:17:50 2008  commencing quadratic sieve (96-digit input)
Mon Jun  2 06:17:50 2008  using multiplier of 3
Mon Jun  2 06:17:50 2008  using 64kb Pentium 4 sieve core
Mon Jun  2 06:17:50 2008  sieve interval: 18 blocks of size 65536
Mon Jun  2 06:17:50 2008  processing polynomials in batches of 6
Mon Jun  2 06:17:50 2008  using a sieve bound of 2299951 (84630 primes)
Mon Jun  2 06:17:50 2008  using large prime bound of 344992650 (28 bits)
Mon Jun  2 06:17:50 2008  using double large prime bound of 2333767984535850 (43-52 bits)
Mon Jun  2 06:17:50 2008  using trial factoring cutoff of 52 bits
Mon Jun  2 06:17:50 2008  polynomial 'A' values have 12 factors
Mon Jun  2 15:43:57 2008  84765 relations (20102 full + 64663 combined from 1294956 partial), need 84726
Mon Jun  2 15:44:02 2008  begin with 1315058 relations
Mon Jun  2 15:44:04 2008  reduce to 225164 relations in 11 passes
Mon Jun  2 15:44:04 2008  attempting to read 225164 relations
Mon Jun  2 15:44:11 2008  recovered 225164 relations
Mon Jun  2 15:44:11 2008  recovered 212776 polynomials
Mon Jun  2 15:44:12 2008  attempting to build 84765 cycles
Mon Jun  2 15:44:12 2008  found 84765 cycles in 6 passes
Mon Jun  2 15:44:12 2008  distribution of cycle lengths:
Mon Jun  2 15:44:12 2008     length 1 : 20102
Mon Jun  2 15:44:12 2008     length 2 : 14231
Mon Jun  2 15:44:12 2008     length 3 : 13930
Mon Jun  2 15:44:12 2008     length 4 : 11635
Mon Jun  2 15:44:12 2008     length 5 : 9103
Mon Jun  2 15:44:12 2008     length 6 : 6090
Mon Jun  2 15:44:12 2008     length 7 : 3877
Mon Jun  2 15:44:12 2008     length 9+: 5797
Mon Jun  2 15:44:12 2008  largest cycle: 19 relations
Mon Jun  2 15:44:12 2008  matrix is 84630 x 84765 (23.9 MB) with weight 5923925 (69.89/col)
Mon Jun  2 15:44:12 2008  sparse part has weight 5923925 (69.89/col)
Mon Jun  2 15:44:14 2008  filtering completed in 3 passes
Mon Jun  2 15:44:14 2008  matrix is 81223 x 81287 (23.1 MB) with weight 5721340 (70.38/col)
Mon Jun  2 15:44:14 2008  sparse part has weight 5721340 (70.38/col)
Mon Jun  2 15:44:15 2008  saving the first 48 matrix rows for later
Mon Jun  2 15:44:15 2008  matrix is 81175 x 81287 (17.2 MB) with weight 4837727 (59.51/col)
Mon Jun  2 15:44:15 2008  sparse part has weight 4015307 (49.40/col)
Mon Jun  2 15:44:15 2008  matrix includes 64 packed rows
Mon Jun  2 15:44:15 2008  using block size 21845 for processor cache size 512 kB
Mon Jun  2 15:44:16 2008  commencing Lanczos iteration
Mon Jun  2 15:44:16 2008  memory use: 15.0 MB
Mon Jun  2 15:45:40 2008  lanczos halted after 1285 iterations (dim = 81173)
Mon Jun  2 15:45:40 2008  recovered 16 nontrivial dependencies
Mon Jun  2 15:45:42 2008  prp30 factor: 153982827554613533780693879837
Mon Jun  2 15:45:42 2008  prp67 factor: 4780957545125991811271590664511031750645306007121798055625197067351
Mon Jun  2 15:45:42 2008  elapsed time 09:27:56

(19·10¹⁴⁸+53)/9 = 2(1)₁₄₇7_<149> = 3 · 109 · 163 · 24029 · 182617 · 368507 · 1351981 · 253573542341957_<15> · 63117301189870715519_<20> · C89

C89 = P39 · P50

P39 = 362057969379015044200712589221264255659_<39>

P50 = 31264539269177925749669527557963065564867851547731_<50>

Mon Jun  2 15:54:31 2008  Msieve v. 1.35
Mon Jun  2 15:54:31 2008  random seeds: 05a7b83d b339eb60
Mon Jun  2 15:54:31 2008  factoring 11319575601369034829580537568191960657052642282608078063135992672601045638966210825359729 (89 digits)
Mon Jun  2 15:54:33 2008  searching for 15-digit factors
Mon Jun  2 15:54:34 2008  commencing quadratic sieve (89-digit input)
Mon Jun  2 15:54:34 2008  using multiplier of 1
Mon Jun  2 15:54:34 2008  using 64kb Pentium 4 sieve core
Mon Jun  2 15:54:34 2008  sieve interval: 14 blocks of size 65536
Mon Jun  2 15:54:34 2008  processing polynomials in batches of 8
Mon Jun  2 15:54:34 2008  using a sieve bound of 1536389 (58333 primes)
Mon Jun  2 15:54:34 2008  using large prime bound of 122911120 (26 bits)
Mon Jun  2 15:54:34 2008  using double large prime bound of 364136361200880 (42-49 bits)
Mon Jun  2 15:54:34 2008  using trial factoring cutoff of 49 bits
Mon Jun  2 15:54:34 2008  polynomial 'A' values have 11 factors
Mon Jun  2 17:24:07 2008  58499 relations (15792 full + 42707 combined from 617918 partial), need 58429
Mon Jun  2 17:24:09 2008  begin with 633710 relations
Mon Jun  2 17:24:10 2008  reduce to 142214 relations in 11 passes
Mon Jun  2 17:24:10 2008  attempting to read 142214 relations
Mon Jun  2 17:24:13 2008  recovered 142214 relations
Mon Jun  2 17:24:13 2008  recovered 118727 polynomials
Mon Jun  2 17:24:14 2008  attempting to build 58499 cycles
Mon Jun  2 17:24:14 2008  found 58499 cycles in 5 passes
Mon Jun  2 17:24:14 2008  distribution of cycle lengths:
Mon Jun  2 17:24:14 2008     length 1 : 15792
Mon Jun  2 17:24:14 2008     length 2 : 11349
Mon Jun  2 17:24:14 2008     length 3 : 10193
Mon Jun  2 17:24:14 2008     length 4 : 7776
Mon Jun  2 17:24:14 2008     length 5 : 5432
Mon Jun  2 17:24:14 2008     length 6 : 3467
Mon Jun  2 17:24:14 2008     length 7 : 2040
Mon Jun  2 17:24:14 2008     length 9+: 2450
Mon Jun  2 17:24:14 2008  largest cycle: 18 relations
Mon Jun  2 17:24:14 2008  matrix is 58333 x 58499 (13.8 MB) with weight 3374198 (57.68/col)
Mon Jun  2 17:24:14 2008  sparse part has weight 3374198 (57.68/col)
Mon Jun  2 17:24:15 2008  filtering completed in 3 passes
Mon Jun  2 17:24:15 2008  matrix is 54272 x 54335 (12.9 MB) with weight 3169633 (58.34/col)
Mon Jun  2 17:24:15 2008  sparse part has weight 3169633 (58.34/col)
Mon Jun  2 17:24:15 2008  saving the first 48 matrix rows for later
Mon Jun  2 17:24:15 2008  matrix is 54224 x 54335 (8.5 MB) with weight 2506354 (46.13/col)
Mon Jun  2 17:24:15 2008  sparse part has weight 1906309 (35.08/col)
Mon Jun  2 17:24:15 2008  matrix includes 64 packed rows
Mon Jun  2 17:24:15 2008  using block size 21734 for processor cache size 512 kB
Mon Jun  2 17:24:16 2008  commencing Lanczos iteration
Mon Jun  2 17:24:16 2008  memory use: 8.2 MB
Mon Jun  2 17:24:47 2008  lanczos halted after 858 iterations (dim = 54222)
Mon Jun  2 17:24:47 2008  recovered 15 nontrivial dependencies
Mon Jun  2 17:24:48 2008  prp39 factor: 362057969379015044200712589221264255659
Mon Jun  2 17:24:48 2008  prp50 factor: 31264539269177925749669527557963065564867851547731
Mon Jun  2 17:24:48 2008  elapsed time 01:30:17

(19·10¹³²+53)/9 = 2(1)₁₃₁7_<133> = 229637 · 624509 · 1096168133_<10> · 2996578231_<10> · C103

C103 = P30 · P74

P30 = 274774136419884955287483432737_<30>

P74 = 16309921890964946701578150469724656682279803131647250107014492259289394799_<74>

Number: 21117_132
N=4481544702665670260142350017053071939841557981489925134501982700492970878648611368462978938115754134863
  ( 103 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=274774136419884955287483432737 (pp30)
 r2=16309921890964946701578150469724656682279803131647250107014492259289394799 (pp74)
Version: GGNFS-0.77.1-20060513-k8
Total time: 7.69 hours.
Scaled time: 15.49 units (timescale=2.016).
Factorization parameters were as follows:
name: 21117_132
n: 4481544702665670260142350017053071939841557981489925134501982700492970878648611368462978938115754134863
m: 100000000000000000000000000
c5: 1900
c0: 53
skew: 0.49
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1450001)
Primes: RFBsize:63951, AFBsize:63753, largePrimes:1604706 encountered
Relations: rels:1630922, finalFF:175301
Max relations in full relation-set: 28
Initial matrix: 127771 x 175301 with sparse part having weight 17797755.
Pruned matrix : 117290 x 117992 with weight 10304530.
Total sieving time: 7.45 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 7.69 hours.
 --------- CPU info (if available) ----------

(19·10¹⁴⁴+53)/9 = 2(1)₁₄₃7_<145> = 43 · 9819072943_<10> · 10619340031061_<14> · 1221482300914250354995629197_<28> · C93

C93 = P32 · P61

P32 = 59460061664238851775266882472133_<32>

P61 = 6482792018674955359906067036006848637517667147841276577049253_<61>

Mon Jun  2 17:39:49 2008  Msieve v. 1.35
Mon Jun  2 17:39:49 2008  random seeds: ecb5fe42 7f1f0941
Mon Jun  2 17:39:49 2008  factoring 385467213186848311654808549004712309847359247130531463837047964694710049428655567891140966649 (93 digits)
Mon Jun  2 17:39:51 2008  searching for 15-digit factors
Mon Jun  2 17:39:53 2008  commencing quadratic sieve (93-digit input)
Mon Jun  2 17:39:53 2008  using multiplier of 1
Mon Jun  2 17:39:53 2008  using 64kb Pentium 4 sieve core
Mon Jun  2 17:39:53 2008  sieve interval: 18 blocks of size 65536
Mon Jun  2 17:39:53 2008  processing polynomials in batches of 6
Mon Jun  2 17:39:53 2008  using a sieve bound of 1914511 (71765 primes)
Mon Jun  2 17:39:53 2008  using large prime bound of 231655831 (27 bits)
Mon Jun  2 17:39:53 2008  using double large prime bound of 1139509009637394 (42-51 bits)
Mon Jun  2 17:39:53 2008  using trial factoring cutoff of 51 bits
Mon Jun  2 17:39:53 2008  polynomial 'A' values have 12 factors
Mon Jun  2 21:14:02 2008  72278 relations (18172 full + 54106 combined from 957428 partial), need 71861
Mon Jun  2 21:14:06 2008  begin with 975600 relations
Mon Jun  2 21:14:07 2008  reduce to 184070 relations in 13 passes
Mon Jun  2 21:14:07 2008  attempting to read 184070 relations
Mon Jun  2 21:14:12 2008  recovered 184070 relations
Mon Jun  2 21:14:12 2008  recovered 162815 polynomials
Mon Jun  2 21:14:13 2008  attempting to build 72278 cycles
Mon Jun  2 21:14:13 2008  found 72278 cycles in 6 passes
Mon Jun  2 21:14:13 2008  distribution of cycle lengths:
Mon Jun  2 21:14:13 2008     length 1 : 18172
Mon Jun  2 21:14:13 2008     length 2 : 13053
Mon Jun  2 21:14:13 2008     length 3 : 12368
Mon Jun  2 21:14:13 2008     length 4 : 9884
Mon Jun  2 21:14:13 2008     length 5 : 7240
Mon Jun  2 21:14:13 2008     length 6 : 4805
Mon Jun  2 21:14:13 2008     length 7 : 2998
Mon Jun  2 21:14:13 2008     length 9+: 3758
Mon Jun  2 21:14:13 2008  largest cycle: 22 relations
Mon Jun  2 21:14:13 2008  matrix is 71765 x 72278 (17.3 MB) with weight 4257237 (58.90/col)
Mon Jun  2 21:14:13 2008  sparse part has weight 4257237 (58.90/col)
Mon Jun  2 21:14:15 2008  filtering completed in 3 passes
Mon Jun  2 21:14:15 2008  matrix is 67846 x 67910 (16.3 MB) with weight 4001883 (58.93/col)
Mon Jun  2 21:14:15 2008  sparse part has weight 4001883 (58.93/col)
Mon Jun  2 21:14:15 2008  saving the first 48 matrix rows for later
Mon Jun  2 21:14:15 2008  matrix is 67798 x 67910 (8.9 MB) with weight 2957170 (43.55/col)
Mon Jun  2 21:14:15 2008  sparse part has weight 1922201 (28.31/col)
Mon Jun  2 21:14:15 2008  matrix includes 64 packed rows
Mon Jun  2 21:14:15 2008  using block size 21845 for processor cache size 512 kB
Mon Jun  2 21:14:16 2008  commencing Lanczos iteration
Mon Jun  2 21:14:16 2008  memory use: 9.6 MB
Mon Jun  2 21:14:59 2008  lanczos halted after 1073 iterations (dim = 67795)
Mon Jun  2 21:14:59 2008  recovered 15 nontrivial dependencies
Mon Jun  2 21:15:02 2008  prp32 factor: 59460061664238851775266882472133
Mon Jun  2 21:15:02 2008  prp61 factor: 6482792018674955359906067036006848637517667147841276577049253
Mon Jun  2 21:15:02 2008  elapsed time 03:35:13

Jun 2, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(19·10¹²⁸+53)/9 = 2(1)₁₂₇7_<129> = 7 · C128

C128 = P51 · P78

P51 = 271141390923736296890969959857913248646126105732399_<51>

P78 = 111228794895475322398277643129562837424306229357728734610117553484069301696869_<78>

Number: n
N=30158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158731
  ( 128 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=271141390923736296890969959857913248646126105732399 (pp51)
 r2=111228794895475322398277643129562837424306229357728734610117553484069301696869 (pp78)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.76 hours.
Scaled time: 5.03 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_2_1_127_7
n: 30158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158731
skew: 0.49
deg: 5
c5: 19000
c0: 53
m: 10000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 420001)
Primes: RFBsize:114155, AFBsize:114222, largePrimes:5215005 encountered
Relations: rels:4612501, finalFF:288380
Max relations in full relation-set: 48
Initial matrix: 228444 x 288380 with sparse part having weight 17831781.
Pruned matrix : 180854 x 182060 with weight 8358571.
Total sieving time: 2.48 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.14 hours.
Total square root time: 0.04 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,50000
total time: 2.76 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(11·10¹⁷²+61)/9 = 1(2)₁₇₁9_<173> = 7 · 17 · C171

C171 = P41 · P51 · P80

P41 = 12028479575122500852357107894999807304683_<41>

P51 = 731295526744164282624207366517572340820823022344947_<51>

P80 = 11676147223871752732879615382398657779764886931536666306447311056887715314521891_<80>

Number: n
N=102707749766573295985060690943043884220354808590102707749766573295985060690943043884220354808590102707749766573295985060690943043884220354808590102707749766573295985060691
  ( 171 digits)
SNFS difficulty: 173 digits.
Divisors found:

Mon Jun 02 12:00:46 2008  prp41 factor: 12028479575122500852357107894999807304683
Mon Jun 02 12:00:46 2008  prp51 factor: 731295526744164282624207366517572340820823022344947
Mon Jun 02 12:00:46 2008  prp80 factor: 11676147223871752732879615382398657779764886931536666306447311056887715314521891
Mon Jun 02 12:00:46 2008  elapsed time 02:16:33 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 132.61 hours.
Scaled time: 241.74 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_1_2_171_9
n: 102707749766573295985060690943043884220354808590102707749766573295985060690943043884220354808590102707749766573295985060690943043884220354808590102707749766573295985060691
skew: 0.56
deg: 5
c5: 1100
c0: 61
m: 10000000000000000000000000000000000
type: snfs
rlim: 3800000
alim: 3800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 8900279)
Primes: RFBsize:269987, AFBsize:269319, largePrimes:8671566 encountered
Relations: rels:8126828, finalFF:570564
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 132.21 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,3800000,3800000,28,28,48,48,2.5,2.5,100000
total time: 132.61 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(19·10¹³³+53)/9 = 2(1)₁₃₂7_<134> = 3 · 71 · 137 · C129

C129 = P37 · P93

P37 = 4513613610675304606872458634030936047_<37>

P93 = 160282660468278098339555574832288507693386513616326522786634467104125332769066378678664671231_<93>

Number: n
N=723453997844868616946338751623011929375659199859878383575309657349340704948806110520924954974507765707518971629180326620441763857
  ( 129 digits)
SNFS difficulty: 134 digits.
Divisors found:

Mon Jun 02 13:50:41 2008  prp37 factor: 4513613610675304606872458634030936047
Mon Jun 02 13:50:41 2008  prp93 factor: 160282660468278098339555574832288507693386513616326522786634467104125332769066378678664671231
Mon Jun 02 13:50:41 2008  elapsed time 00:18:55 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.56 hours.
Scaled time: 6.52 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_1_132_7
n: 723453997844868616946338751623011929375659199859878383575309657349340704948806110520924954974507765707518971629180326620441763857
skew: 0.31
deg: 5
c5: 19000
c0: 53
m: 100000000000000000000000000
type: snfs
rlim: 1600000
alim: 1600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 560001)
Primes: RFBsize:121127, AFBsize:121110, largePrimes:5674008 encountered
Relations: rels:5002947, finalFF:281155
Max relations in full relation-set: 28
Initial matrix: 242304 x 281155 with sparse part having weight 20748030.
Pruned matrix : 
Total sieving time: 3.46 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1600000,1600000,28,28,48,48,2.5,2.5,75000
total time: 3.56 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(19·10¹⁶⁶+53)/9 = 2(1)₁₆₅7_<167> = 3 · 94597 · 2198191 · 12154976546378825893_<20> · 22397921288742578946556385747021_<32> · C105

C105 = P33 · P72

P33 = 334551636295269131863698068034581_<33>

P72 = 371554093246116187712128253073382931231925606666989345072655834471049849_<72>

Jun 2, 2008

By Tyler Cadigan / GGNFS, Msieve

8·10¹⁹⁷+9 = 8(0)₁₉₆9_<198> = 7 · 12219247 · 15213705288655807_<17> · 4865154059575323971503_<22> · 37114608851460783280897610347_<29> · C124

C124 = P62 · P63

P62 = 16621692800680584305294747562998773325126469691178650296201467_<62>

P63 = 204831038833285778102275560455244890057538477743970633200511049_<63>

Number: 80009_197
N=3404638603531151408492144608513648227826645811936364923836164689727994762576449290071236221548482768741339116814127863508883
  ( 124 digits)
Divisors found:
 r1=16621692800680584305294747562998773325126469691178650296201467
 r2=204831038833285778102275560455244890057538477743970633200511049
Version: 
Total time: 81.57 hours.
Scaled time: 206.94 units (timescale=2.537).
Factorization parameters were as follows:
name: 80009_197
n: 3404638603531151408492144608513648227826645811936364923836164689727994762576449290071236221548482768741339116814127863508883
skew: 70717.79
# norm 3.61e+017
c5: 478800
c4: 81917542588
c3: -13839480355966165
c2: -262680385946951499111
c1: 21383762814069117708461157
c0: 68693812172939743478896238955
# alpha -6.89
Y1: 27372789176161
Y0: -371862411727914405008552
# Murphy_E 1.72e-010
# M 1446656491575742184387572950846474116950583333787238843359449638130640620324693639485660327461752000793094567024696147419232
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 6100001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 737464 x 737712
Polynomial selection time: 9.10 hours.
Total sieving time: 72.47 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 81.57 hours.
 --------- CPU info (if available) ----------

Jun 1, 2008 (4th)

By Sinkiti Sibata / GGNFS

(19·10¹¹⁷+53)/9 = 2(1)₁₁₆7_<118> = 137 · 173 · C113

C113 = P48 · P66

P48 = 340739379185554837829678627965128592230514605529_<48>

P66 = 261409937598548866812402751089866267362790132318322972151795257473_<66>

Number: 21117_117
N=89072659850264170756976967685376613269951103797776933931526564748791659048610232104599430872583904101561584368217
  ( 113 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=340739379185554837829678627965128592230514605529 (pp48)
 r2=261409937598548866812402751089866267362790132318322972151795257473 (pp66)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.90 hours.
Scaled time: 7.82 units (timescale=2.003).
Factorization parameters were as follows:
name: 21117_117
n: 89072659850264170756976967685376613269951103797776933931526564748791659048610232104599430872583904101561584368217
m: 100000000000000000000000
c5: 1900
c0: 53
skew: 0.49
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:63753, largePrimes:2477594 encountered
Relations: rels:2999016, finalFF:614924
Max relations in full relation-set: 28
Initial matrix: 112918 x 614924 with sparse part having weight 56713889.
Pruned matrix : 73573 x 74201 with weight 7485835.
Total sieving time: 3.76 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,118,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.90 hours.
 --------- CPU info (if available) ----------

(19·10¹¹⁸+53)/9 = 2(1)₁₁₇7_<119> = 3² · 647 · 16240958219_<11> · C105

C105 = P36 · P69

P36 = 355681218568581823872236281324646653_<36>

P69 = 627612694100122250224375210065246217931458194520185206310045788028397_<69>

Number: 21117_118
N=223230047826642066205521963974483683939638118880420228496218591190724410961696681286005167031723555005241
  ( 105 digits)
SNFS difficulty: 119 digits.
Divisors found:
 r1=355681218568581823872236281324646653 (pp36)
 r2=627612694100122250224375210065246217931458194520185206310045788028397 (pp69)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.31 hours.
Scaled time: 6.60 units (timescale=1.991).
Factorization parameters were as follows:
name: 21117_118
n: 223230047826642066205521963974483683939638118880420228496218591190724410961696681286005167031723555005241
m: 100000000000000000000000
c5: 19000
c0: 53
skew: 0.31
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:63858, largePrimes:2468293 encountered
Relations: rels:2965236, finalFF:582489
Max relations in full relation-set: 28
Initial matrix: 113023 x 582489 with sparse part having weight 56724991.
Pruned matrix : 76137 x 76766 with weight 9107278.
Total sieving time: 3.16 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,119,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.31 hours.
 --------- CPU info (if available) ----------

(16·10¹⁶⁴-7)/9 = 1(7)₁₆₄_<165> = 3 · 2579 · 51439 · 4963080423026380935320657_<25> · C131

C131 = P62 · P70

P62 = 27077574071931379632102132928358669855145747323367902682258041_<62>

P70 = 3323925597838468353082294553807010837436662578376074591306828959271647_<70>

Number: 17777_164
N=90003841585059920924224866844440249713658946274123664702277080206963969563210631887340234268972054822694480502697694149336669063527
  ( 131 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=27077574071931379632102132928358669855145747323367902682258041 (pp62)
 r2=3323925597838468353082294553807010837436662578376074591306828959271647 (pp70)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 131.28 hours.
Scaled time: 88.88 units (timescale=0.677).
Factorization parameters were as follows:
name: 17777_164
n: 90003841585059920924224866844440249713658946274123664702277080206963969563210631887340234268972054822694480502697694149336669063527
m: 1000000000000000000000000000000000
c5: 8
c0: -35
skew: 1.34
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 5500001)
Primes: RFBsize:348513, AFBsize:349436, largePrimes:5872683 encountered
Relations: rels:6032223, finalFF:800929
Max relations in full relation-set: 28
Initial matrix: 698014 x 800929 with sparse part having weight 49993017.
Pruned matrix : 618137 x 621691 with weight 36216756.
Total sieving time: 112.92 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 17.71 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 131.28 hours.
 --------- CPU info (if available) ----------

Jun 1, 2008 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(19·10¹⁰⁵+53)/9 = 2(1)₁₀₄7_<106> = 753148849 · C97

C97 = P33 · P64

P33 = 911966845446144824010461085219467_<33>

P64 = 3073627441612605884921881130730293562533139400059580806969126199_<64>

(19·10¹¹³+53)/9 = 2(1)₁₁₂7_<114> = 55057 · C109

C109 = P38 · P71

P38 = 58757645619987456838275424826062650763_<38>

P71 = 65258060544098108161363500386786898008268259644863574985134074625486487_<71>

(19·10¹²²+53)/9 = 2(1)₁₂₁7_<123> = 7 · 31 · 229 · 7699981 · 260740884419_<12> · C100

C100 = P48 · P52

P48 = 589368244104645491805519232085371347662733937127_<48>

P52 = 3590296830419907767433446957296372459019708981878273_<52>

Number: n
N=2116006938759055201081299150385079711667157232288061779372701201257089798938424952493683560749341671
  ( 100 digits)
SNFS difficulty: 123 digits.
Divisors found:

Mon Jun 02 00:23:15 2008  prp48 factor: 589368244104645491805519232085371347662733937127
Mon Jun 02 00:23:15 2008  prp52 factor: 3590296830419907767433446957296372459019708981878273
Mon Jun 02 00:23:15 2008  elapsed time 00:13:21 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.61 hours.
Scaled time: 2.94 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_2_1_121_7
n: 2116006938759055201081299150385079711667157232288061779372701201257089798938424952493683560749341671
skew: 0.49
deg: 5
c5: 1900
c0: 53
m: 1000000000000000000000000
type: snfs
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 280337)
Primes: RFBsize:78498, AFBsize:78301, largePrimes:4407787 encountered
Relations: rels:3743887, finalFF:172633
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 1.55 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000
total time: 1.61 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jun 1, 2008 (2nd)

By Wataru Sakai / GGNFS

(61·10¹⁶⁷-7)/9 = 6(7)₁₆₇_<168> = 114611656331_<12> · C157

C157 = P74 · P83

P74 = 93444174992472819257688502885450481471938296013132895952362893249876854697_<74>

P83 = 63285804116327054211214121309466806760944769236184213402549280405475070400939982011_<83>

Number: 67777_167
N=5913689754385421924941064638506622593709715696454659744653592670342697115329570254212974844663993897741044747015015353375643536731026442195443240180440855667
  ( 157 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=93444174992472819257688502885450481471938296013132895952362893249876854697 (pp74)
 r2=63285804116327054211214121309466806760944769236184213402549280405475070400939982011 (pp83)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 150.31 hours.
Scaled time: 302.28 units (timescale=2.011).
Factorization parameters were as follows:
n: 5913689754385421924941064638506622593709715696454659744653592670342697115329570254212974844663993897741044747015015353375643536731026442195443240180440855667
m: 1000000000000000000000000000000000
c5: 6100
c0: -7
skew: 0.26
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 8450001)
Primes: RFBsize:380800, AFBsize:380633, largePrimes:6496633 encountered
Relations: rels:6945548, finalFF:1064739
Max relations in full relation-set: 32
Initial matrix: 761500 x 1064739 with sparse part having weight 95376348.
Pruned matrix : 538647 x 542518 with weight 86032135.
Total sieving time: 146.14 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 3.87 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 150.31 hours.

Jun 1, 2008

The factor table of 211...117 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

May 2008

May 31, 2008 (2nd)

By Wataru Sakai / GGNFS

(88·10¹⁸⁶-7)/9 = 9(7)₁₈₆_<187> = 3 · 1409 · C184

C184 = P45 · P139

P45 = 558420727813527386131594937710331258974213667_<45>

P139 = 4142346123281926087234853809987716740634386737763126789276317393359104216309692071188150104114601670997665342345732871848423998398042842953_<139>

Number: 97777_186
N=2313171937018636805719843335173356465052703519701390531766685066897983860368530347238651000184002313171937018636805719843335173356465052703519701390531766685066897983860368530347238651
  ( 184 digits)
SNFS difficulty: 188 digits.
Divisors found:
 r1=558420727813527386131594937710331258974213667 (pp45)
 r2=4142346123281926087234853809987716740634386737763126789276317393359104216309692071188150104114601670997665342345732871848423998398042842953 (pp139)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 1038.03 hours.
Scaled time: 2089.55 units (timescale=2.013).
Factorization parameters were as follows:
n: 2313171937018636805719843335173356465052703519701390531766685066897983860368530347238651000184002313171937018636805719843335173356465052703519701390531766685066897983860368530347238651
m: 20000000000000000000000000000000000000
c5: 55
c0: -14
skew: 0.76
type: snfsFactor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 18500001)
Primes: RFBsize:501962, AFBsize:502197, largePrimes:7109241 encountered
Relations: rels:7656762, finalFF:1148858
Max relations in full relation-set: 32
Initial matrix: 1004225 x 1148858 with sparse part having weight 131543991.
Pruned matrix : 898696 x 903781 with weight 111532419.
Total sieving time: 1027.27 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 10.30 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,188,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 1038.03 hours.
 --------- CPU info (if available) ----------

May 31, 2008

By Robert Backstrom / GGNFS, Msieve

(31·10¹⁶⁸-13)/9 = 3(4)₁₆₇3_<169> = 36649913 · C161

C161 = P65 · P97

P65 = 19121035045106931156034589094324433473093786433375865827509070283_<65>

P97 = 4915128075224843895655346118121567445584594295484859874268072710814547659240553180841233721217017_<97>

Number: n
N=93982336177563216710622053712499793504133132442754896701786016366381127410710209447003174180643878866627717354866420677299955512703248284503279569707148948605811
  ( 161 digits)
SNFS difficulty: 169 digits.
Divisors found:

Sat May 31 11:47:02 2008  prp65 factor: 19121035045106931156034589094324433473093786433375865827509070283
Sat May 31 11:47:02 2008  prp97 factor: 4915128075224843895655346118121567445584594295484859874268072710814547659240553180841233721217017
Sat May 31 11:47:02 2008  elapsed time 01:26:56 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 85.06 hours.
Scaled time: 71.28 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_3_4_167_3
n: 93982336177563216710622053712499793504133132442754896701786016366381127410710209447003174180643878866627717354866420677299955512703248284503279569707148948605811
type: snfs
deg: 5
c5: 31000
c0: -13
skew: 0.21
m: 1000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5000399)
Primes: RFBsize:250150, AFBsize:249832, largePrimes:5816711 encountered
Relations: rels:5725824, finalFF:539421
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 84.83 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,48,48,2.5,2.5,100000
total time: 85.06 hours.
 --------- CPU info (if available) ----------

May 30, 2008 (4th)

By matsui / GGNFS

5·10¹⁷⁶-1 = 4(9)₁₇₆_<177> = 48409 · 48550259 · C165

C165 = P49 · P117

P49 = 1685407140856189648612097538079896782968048556689_<49>

P117 = 126225619910469676004414039354831078351797442441561563713439568704176968850333129983096588258532811794520832130928061_<117>

N=212741561156104821848315308047573885814443504412799746904803957756367500051206620397368345024193419561880193183093279952257728632311539958871940330087867729139350029
  ( 165 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=1685407140856189648612097538079896782968048556689 (pp49)
 r2=126225619910469676004414039354831078351797442441561563713439568704176968850333129983096588258532811794520832130928061 (pp117)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 224.48 hours.
Scaled time: 191.48 units (timescale=0.853).
Factorization parameters were as follows:
n: 212741561156104821848315308047573885814443504412799746904803957756367500051206620397368345024193419561880193183093279952257728632311539958871940330087867729139350029
m: 100000000000000000000000000000000000
c5: 50
c0: -1
skew: 0.46
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 11500001)
Primes: RFBsize:501962, AFBsize:501581, largePrimes:6465156 encountered
Relations: rels:6924137, finalFF:1134653
Max relations in full relation-set: 28
Initial matrix: 1003608 x 1134653 with sparse part having weight 71856558.
Pruned matrix : 891266 x 896348 with weight 54923948.
Total sieving time: 201.76 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 21.99 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 224.48 hours.

6·10¹⁶⁹+1 = 6(0)₁₆₈1_<170> = 1163 · 50207 · C163

C163 = P45 · P118

P45 = 409692145250436913282056636020822590790365187_<45>

P118 = 2508127593417771961783639597835041387496768657625863183136324428934170806705227815812321776714203987196208985026667903_<118>

N=1027560174309142608757097293901442353677272223690396393496701814419515587240107125888332192941343217411815342435883798768712320331745747155358072952011347141492861
  ( 163 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=409692145250436913282056636020822590790365187 (pp45)
 r2=2508127593417771961783639597835041387496768657625863183136324428934170806705227815812321776714203987196208985026667903 (pp118)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 153.02 hours.
Scaled time: 177.66 units (timescale=1.161).
Factorization parameters were as follows:
n: 1027560174309142608757097293901442353677272223690396393496701814419515587240107125888332192941343217411815342435883798768712320331745747155358072952011347141492861
m: 10000000000000000000000000000000000
c5: 3
c0: 5
skew: 1.11
type: snfs

Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 7100001)
Primes: RFBsize:412849, AFBsize:412211, largePrimes:6020639 encountered
Relations: rels:6285070, finalFF:929842
Max relations in full relation-set: 28
Initial matrix: 825125 x 929842 with sparse part having weight 54766796.
Pruned matrix : 737962 x 742151 with weight 40674202.
Total sieving time: 140.47 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 12.05 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 153.02 hours.

May 30, 2008 (3rd)

By Tyler Cadigan / GGNFS, Msieve

(5·10¹⁹⁰+13)/9 = (5)₁₈₉7_<190> = 811 · 907 · 10837804441_<11> · 2785656325929626661973_<22> · 141420727163771568086127494461_<30> · C124

C124 = P59 · P65

P59 = 33459437467275085321414055603258376333697163788226609596037_<59>

P65 = 52868721344425856941945570027921282052374118429357469698868995441_<65>

Number: 55557_190
N=1768957675798608538570697178394242001598658689261756493802670073290117602123758045787374992447868719160331461600669004667317
  ( 124 digits)
Divisors found:
 r1=33459437467275085321414055603258376333697163788226609596037
 r2=52868721344425856941945570027921282052374118429357469698868995441
Version: 
Total time: 60.52 hours.
Scaled time: 155.16 units (timescale=2.564).
Factorization parameters were as follows:
name: 55557_190
n: 1768957675798608538570697178394242001598658689261756493802670073290117602123758045787374992447868719160331461600669004667317
skew: 59353.52
# norm 1.07e+017
c5: 491040
c4: 50867111448
c3: -4995511819788260
c2: -163948178132283273278
c1: 9083007404135601852054231
c0: -19006103892754768805129373210
# alpha -6.34
Y1: 76272196706117
Y0: -324577192860632699954327
# Murphy_E 1.84e-010
# M 995658799633167449149780343758990313985724368125209995426425707408614893747362482071898928066623208284832232387742176621524
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 5440001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 717956 x 718204
Total sieving time: 60.52 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 60.52 hours.
 --------- CPU info (if available) ----------

May 30, 2008 (2nd)

By Jo Yeong Uk / GGNFS

(19·10¹⁶⁸+17)/9 = 2(1)₁₆₇3_<169> = C169

C169 = P72 · P97

P72 = 227487177154295025504685455361271692724662216695338616060397175372579537_<72>

P97 = 9280132346445324494177855519611117213830193530355304266419412531346231676756164736608771764227449_<97>

Number: 21113_168
N=2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113
  ( 169 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=227487177154295025504685455361271692724662216695338616060397175372579537 (pp72)
 r2=9280132346445324494177855519611117213830193530355304266419412531346231676756164736608771764227449 (pp97)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 99.00 hours.
Scaled time: 233.44 units (timescale=2.358).
Factorization parameters were as follows:
n: 2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113
m: 10000000000000000000000000000000000
c5: 19
c0: 1700
skew: 2.46
type: snfs
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 49/49
Sieved algebraic special-q in [4000000, 9200001)
Primes: RFBsize:539777, AFBsize:539370, largePrimes:9999580 encountered
Relations: rels:9956522, finalFF:1241056
Max relations in full relation-set: 28
Initial matrix: 1079214 x 1241056 with sparse part having weight 74507988.
Pruned matrix : 936892 x 942352 with weight 53685074.
Total sieving time: 92.81 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 5.91 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,49,49,2.6,2.6,100000
total time: 99.00 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047200k/8912896k available (2439k kernel code, 339088k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673806)
Calibrating delay using timer specific routine.. 5344.78 BogoMIPS (lpj=2672394)
Calibrating delay using timer specific routine.. 5344.44 BogoMIPS (lpj=2672223)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672388)

May 30, 2008

By Sinkiti Sibata / GGNFS

(19·10¹⁶¹+17)/9 = 2(1)₁₆₀3_<162> = 3 · 7 · 36833 · 1060859273_<10> · 14564381097589_<14> · 4408021099498508159119_<22> · C112

C112 = P33 · P79

P33 = 706991398277505775759368626955089_<33>

P79 = 5668225218241225832747085084677390231483282542289051212302192258793615146195383_<79>

Number: 21113_161
N=4007386472796184589094423777355566076795903284996272377907741299098845716620028610166554514234937212618360154087
  ( 112 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=706991398277505775759368626955089 (pp33)
 r2=5668225218241225832747085084677390231483282542289051212302192258793615146195383 (pp79)
Version: GGNFS-0.77.1-20060513-k8
Total time: 83.43 hours.
Scaled time: 167.11 units (timescale=2.003).
Factorization parameters were as follows:
name: 21113_161
n: 4007386472796184589094423777355566076795903284996272377907741299098845716620028610166554514234937212618360154087
m: 100000000000000000000000000000000
c5: 190
c0: 17
skew: 0.62
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4950001)
Primes: RFBsize:315948, AFBsize:315511, largePrimes:5815229 encountered
Relations: rels:5896613, finalFF:711219
Max relations in full relation-set: 28
Initial matrix: 631526 x 711219 with sparse part having weight 50842856.
Pruned matrix : 575041 x 578262 with weight 38160172.
Total sieving time: 78.98 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 3.97 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 83.43 hours.
 --------- CPU info (if available) ----------

May 29, 2008

By Robert Backstrom / GGNFS, Msieve

8·10¹⁷¹-7 = 7(9)₁₇₀3_<172> = 17 · 1151 · C168

C168 = P77 · P92

P77 = 24647086395999836771837331424225869225743402319273339674995455701866527506633_<77>

P92 = 16588234057078252813498282677454365397090590853140579319578237953322061447834122710199965663_<92>

Number: n
N=408851637961874584760055194971124853068942607451321101855164307252005928348750447181479020800327081310369499667808044155976899882455154085961056881484131445801604742679
  ( 168 digits)
SNFS difficulty: 172 digits.
Divisors found:

Thu May 29 01:44:12 2008  prp77 factor: 24647086395999836771837331424225869225743402319273339674995455701866527506633
Thu May 29 01:44:12 2008  prp92 factor: 16588234057078252813498282677454365397090590853140579319578237953322061447834122710199965663
Thu May 29 01:44:12 2008  elapsed time 02:24:36 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 112.41 hours.
Scaled time: 162.21 units (timescale=1.443).
Factorization parameters were as follows:
name: KA_7_9_170_3
n: 408851637961874584760055194971124853068942607451321101855164307252005928348750447181479020800327081310369499667808044155976899882455154085961056881484131445801604742679
skew: 1.23
deg: 5
c5: 5
c0: -14
m: 20000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5600521)
Primes: RFBsize:250150, AFBsize:251001, largePrimes:7971414 encountered
Relations: rels:7366966, finalFF:511955
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 112.09 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 112.41 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(19·10¹⁵⁹+17)/9 = 2(1)₁₅₈3_<160> = 12497 · C156

C156 = P60 · P96

P60 = 582369490753755763634044705532923835566861195555346804624251_<60>

P96 = 290072599328501239090268348704294814519427609152777687487796440289248834506309310228248097076379_<96>

Number: n
N=168929431952557502689534377139402345451797320245747868377299440754670009691214780436193575346972162207818765392583108835009291118757390662647924390742667129
  ( 156 digits)
SNFS difficulty: 161 digits.
Divisors found:

Thu May 29 15:37:16 2008  prp60 factor: 582369490753755763634044705532923835566861195555346804624251
Thu May 29 15:37:16 2008  prp96 factor: 290072599328501239090268348704294814519427609152777687487796440289248834506309310228248097076379
Thu May 29 15:37:16 2008  elapsed time 01:22:49 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 53.77 hours.
Scaled time: 94.26 units (timescale=1.753).
Factorization parameters were as follows:
name: KA_2_1_158_3
n: 168929431952557502689534377139402345451797320245747868377299440754670009691214780436193575346972162207818765392583108835009291118757390662647924390742667129
type: snfs
skew: 1.55
deg: 5
c5: 19
c0: 170
m: 100000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2700281)
Primes: RFBsize:216816, AFBsize:217381, largePrimes:7215613 encountered
Relations: rels:6592180, finalFF:463705
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 53.51 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 53.77 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

May 28, 2008 (4th)

By Jo Yeong Uk / GGNFS

8·10¹⁹⁰-1 = 7(9)₁₉₀_<191> = 1501424845230313_<16> · 10411475502106841_<17> · 103604998163265343797785903_<27> · C134

C134 = P47 · P88

P47 = 32138196181722492086192711480655875703076973473_<47>

P88 = 1536993045250756022561115557188611458176946430424547082249899017269102518555851907736337_<88>

Number: 79999_190
N=49396184018211872703363301156464019861680357260098919357763832482898095600406839309173237178282301476725054664245512034332052427188401
  ( 134 digits)
Divisors found:
 r1=32138196181722492086192711480655875703076973473 (pp47)
 r2=1536993045250756022561115557188611458176946430424547082249899017269102518555851907736337 (pp88)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 290.79 hours.
Scaled time: 686.84 units (timescale=2.362).
Factorization parameters were as follows:
name: 79999_190
n: 49396184018211872703363301156464019861680357260098919357763832482898095600406839309173237178282301476725054664245512034332052427188401
skew: 242940.86
# norm 1.21e+18
c5: 85620
c4: -57151682624
c3: -22590728647291809
c2: 2381445185413331717122
c1: 409182909531414672114959920
c0: -32297630581163036627596487351520
# alpha -5.20
Y1: 459331903161439
Y0: -56522857115853633824740049
# Murphy_E 4.45e-11
# M 32787906899257365478808558482535562409527935353125941152465342791486689256008806739515137488792928799075273456259046471198536266016954
type: gnfs
rlim: 11000000
alim: 11000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 11000000/11000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved algebraic special-q in [5500000, 10200001)
Primes: RFBsize:726517, AFBsize:726481, largePrimes:14857336 encountered
Relations: rels:15289846, finalFF:1685493
Max relations in full relation-set: 28
Initial matrix: 1453075 x 1685493 with sparse part having weight 147115281.
Pruned matrix : 1241084 x 1248413 with weight 99292092.
Polynomial selection time: 19.85 hours.
Total sieving time: 255.28 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 14.72 hours.
Time per square root: 0.59 hours.
Prototype def-par.txt line would be:
gnfs,133,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,11000000,11000000,28,28,52,52,2.6,2.6,100000
total time: 290.79 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047200k/8912896k available (2439k kernel code, 339088k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673806)
Calibrating delay using timer specific routine.. 5344.78 BogoMIPS (lpj=2672394)
Calibrating delay using timer specific routine.. 5344.44 BogoMIPS (lpj=2672223)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672388)

May 28, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(14·10¹⁶⁵-41)/9 = 1(5)₁₆₄1_<166> = 3 · 11 · 59 · 58451 · 5169785550529046037137_<22> · C136

C136 = P63 · P74

P63 = 145830821819731044721528535735047502903441900884043243247216827_<63>

P74 = 18130332859509736343289311799201732135771943135308657063773868356166511517_<74>

Number: n
N=2643961340767579204510392201562942474383505436157630831674023493387373870717733728070420140402288953838976680468196570012720491891696559
  ( 136 digits)
SNFS difficulty: 166 digits.
Divisors found:

Wed May 28 10:17:40 2008  prp63 factor: 145830821819731044721528535735047502903441900884043243247216827
Wed May 28 10:17:40 2008  prp74 factor: 18130332859509736343289311799201732135771943135308657063773868356166511517
Wed May 28 10:17:40 2008  elapsed time 00:53:14 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 35.95 hours.
Scaled time: 65.76 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_5_164_1
n: 2643961340767579204510392201562942474383505436157630831674023493387373870717733728070420140402288953838976680468196570012720491891696559
skew: 1.24
deg: 5
c5: 14
c0: -41
m: 1000000000000000000000000000000000
type: snfs
rlim: 3300000
alim: 3300000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3300000/3300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2500339)
Primes: RFBsize:236900, AFBsize:237378, largePrimes:7332565 encountered
Relations: rels:6804891, finalFF:530984
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 35.79 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3300000,3300000,28,28,48,48,2.5,2.5,100000
total time: 35.95 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

May 28, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(19·10¹⁴³+17)/9 = 2(1)₁₄₂3_<144> = 3 · 7² · 51721 · 69073 · 445257779 · 44907917730197_<14> · C110

C110 = P34 · P76

P34 = 7235857084230512962952890011521047_<34>

P76 = 2778395777322023419518611783612670148440288856654912472918162716876208274883_<76>

Number: 21113_143
N=20104074768131705952223948574828629453469311264939980616550632557451952625753174430604740451277750586715962501
  ( 110 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=7235857084230512962952890011521047 (pp34)
 r2=2778395777322023419518611783612670148440288856654912472918162716876208274883 (pp76)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 25.03 hours.
Scaled time: 16.95 units (timescale=0.677).
Factorization parameters were as follows:
name: 21113_143
n: 20104074768131705952223948574828629453469311264939980616550632557451952625753174430604740451277750586715962501
m: 10000000000000000000000000000
c5: 19000
c0: 17
skew: 0.25
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 3150001)
Primes: RFBsize:100021, AFBsize:99493, largePrimes:2950613 encountered
Relations: rels:2989844, finalFF:241915
Max relations in full relation-set: 28
Initial matrix: 199581 x 241915 with sparse part having weight 29623414.
Pruned matrix : 188729 x 189790 with weight 21916761.
Total sieving time: 23.39 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 1.32 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 25.03 hours.
 --------- CPU info (if available) ----------

(19·10¹⁵³+17)/9 = 2(1)₁₅₂3_<154> = 631 · 28080280900663_<14> · 15270966995993801_<17> · 297851429000810929_<18> · C104

C104 = P34 · P71

P34 = 1071730829955083205875392845598093_<34>

P71 = 24441526913452149544679014625447927498593580679196528341183377269394693_<71>

Number: 21113_153
N=26194737924323575364340387280235007936643629413751244947257148265834095820142465320158206394355665120449
  ( 104 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=1071730829955083205875392845598093 (pp34)
 r2=24441526913452149544679014625447927498593580679196528341183377269394693 (pp71)
Version: GGNFS-0.77.1-20060513-k8
Total time: 39.96 hours.
Scaled time: 80.56 units (timescale=2.016).
Factorization parameters were as follows:
name: 21113_153
n: 26194737924323575364340387280235007936643629413751244947257148265834095820142465320158206394355665120449
m: 1000000000000000000000000000000
c5: 19000
c0: 17
skew: 0.25
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2700001)
Primes: RFBsize:176302, AFBsize:175753, largePrimes:5892888 encountered
Relations: rels:5941175, finalFF:513449
Max relations in full relation-set: 28
Initial matrix: 352122 x 513449 with sparse part having weight 57240124.
Pruned matrix : 298760 x 300584 with weight 34325060.
Total sieving time: 38.09 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.54 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 39.96 hours.
 --------- CPU info (if available) ----------

May 28, 2008

By Tyler Cadigan / GGNFS, Msieve

6·10¹⁹²+7 = 6(0)₁₉₁7_<193> = 13 · 29 · 31 · 3208007417_<10> · 15475455343_<11> · 310826606681_<12> · 40049826089950582237612221318425371_<35> · C123

C123 = P53 · P71

P53 = 10102569630990212054844298716593986140238949067257353_<53>

P71 = 82227811572357690683721133099265358362960911903422547606796172190078277_<71>

Number: 6007_192
N=830712192013686323660709168931323872031297610912396291073166633804134415081608887012251142715040805151323146247750773820781
  ( 123 digits)
Divisors found:
 r1=10102569630990212054844298716593986140238949067257353
 r2=82227811572357690683721133099265358362960911903422547606796172190078277
Version: 
Total time: 74.14 hours.
Scaled time: 188.47 units (timescale=2.542).
Factorization parameters were as follows:
name: 6007_192
n: 830712192013686323660709168931323872031297610912396291073166633804134415081608887012251142715040805151323146247750773820781
skew: 77203.59
# norm 1.08e+017
c5: 172080
c4: 14838727404
c3: 1262193336427372
c2: -114796568745882147319
c1: -8195967742681946605855362
c0: -73190742726070200388319319520
# alpha -6.58
Y1: 23760673514311
Y0: -344146629317608937143053
# Murphy_E 1.96e-010
# M 283682133566270285574732015551287576199838655615985021782250332088258772742605296116457305471500075826863743323124395905458
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 5800001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 746953 x 747201
Polynomial selection time: 7.91 hours.
Total sieving time: 66.23 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,122,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 74.14 hours.
 --------- CPU info (if available) ----------

May 27, 2008 (4th)

By Sinkiti Sibata / GGNFS

(23·10¹⁷⁸+1)/3 = 7(6)₁₇₇7_<179> = 41 · C178

C178 = P45 · P133

P45 = 790936180336816702545701154890239344559082933_<45>

P133 = 2364184046291440600473811766553734828935527300679265758252039337569876107665435775119234232224612425238722596889930956255213593885639_<133>

Number: 76667_178
N=1869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699187
  ( 178 digits)
SNFS difficulty: 179 digits.
Divisors found:
 r1=790936180336816702545701154890239344559082933 (pp45)
 r2=2364184046291440600473811766553734828935527300679265758252039337569876107665435775119234232224612425238722596889930956255213593885639 (pp133)
Version: GGNFS-0.77.1-20060513-k8
Total time: 423.45 hours.
Scaled time: 845.63 units (timescale=1.997).
Factorization parameters were as follows:
name: 76667_178
n: 1869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699187
m: 100000000000000000000000000000000000
c5: 23000
c0: 1
skew: 0.13
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 16000001)
Primes: RFBsize:501962, AFBsize:502881, largePrimes:6769862 encountered
Relations: rels:7271637, finalFF:1134889
Max relations in full relation-set: 28
Initial matrix: 1004910 x 1134889 with sparse part having weight 96349025.
Pruned matrix : 901341 x 906429 with weight 77225160.
Total sieving time: 408.94 hours.
Total relation processing time: 0.88 hours.
Matrix solve time: 13.25 hours.
Time per square root: 0.38 hours.
Prototype def-par.txt line would be:
snfs,179,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 423.45 hours.
 --------- CPU info (if available) ----------

May 27, 2008 (3rd)

By matsui / GGNFS

3·10¹⁷⁵-1 = 2(9)₁₇₅_<176> = 19 · 1358197 · C169

C169 = P69 · P100

P69 = 127908438358629022538945818383105074917390387700273693347951544125819_<69>

P100 = 9088782074048181389749646028623925455114377328452874707792183747630337777668429784177679834126974147_<100>

N=1162531921673404249588938400262298202380764622820586874789848135742497319298266281269250802040460528495536826821843494295048974176019655779723141472810916546754728201393
  ( 169 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=127908438358629022538945818383105074917390387700273693347951544125819 (pp69)
 r2=9088782074048181389749646028623925455114377328452874707792183747630337777668429784177679834126974147 (pp100)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 170.28 hours.
Scaled time: 289.65 units (timescale=1.701).
Factorization parameters were as follows:
n: 1162531921673404249588938400262298202380764622820586874789848135742497319298266281269250802040460528495536826821843494295048974176019655779723141472810916546754728201393
m: 100000000000000000000000000000000000
c5: 3
c0: -1
skew: 0.8
type: snfs

Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 10100001)
Primes: RFBsize:501962, AFBsize:501561, largePrimes:6368718 encountered
Relations: rels:6829866, finalFF:1143743
Max relations in full relation-set: 28
Initial matrix: 1003588 x 1143743 with sparse part having weight 64710672.
Pruned matrix : 882352 x 887433 with weight 47911814.
Total sieving time: 156.22 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 13.47 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 170.28 hours.

May 27, 2008 (2nd)

By Jo Yeong Uk / GMP-ECM

(19·10¹⁶⁰+17)/9 = 2(1)₁₅₉3_<161> = 1091 · 13723 · 321889 · 24546888341483136439651_<23> · C126

C126 = P35 · P91

P35 = 56346892794173538280415510697608311_<35>

P91 = 3167121486201706714211853387395270653867058889451744908587689927499196954815248430586933829_<91>

May 27, 2008

By Robert Backstrom / GGNFS, Msieve

(19·10¹⁵²+17)/9 = 2(1)₁₅₁3_<153> = 3 · C152

C152 = P54 · P99

P54 = 356046920829177338700138389053899011999976498823798123_<54>

P99 = 197643530258564893467617294435465707705350739812651298588563852360274701722217491033354235201386377_<99>

Number: n
N=70370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370371
  ( 152 digits)
SNFS difficulty: 153 digits.
Divisors found:

Tue May 27 02:50:46 2008  prp54 factor: 356046920829177338700138389053899011999976498823798123
Tue May 27 02:50:46 2008  prp99 factor: 197643530258564893467617294435465707705350739812651298588563852360274701722217491033354235201386377
Tue May 27 02:50:46 2008  elapsed time 00:31:20 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 16.60 hours.
Scaled time: 30.36 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_1_151_3
n: 70370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370371
skew: 0.39
deg: 5
c5: 1900
c0: 17
m: 1000000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1300000)
Primes: RFBsize:114155, AFBsize:113552, largePrimes:6914825 encountered
Relations: rels:6240853, finalFF:256978
Max relations in full relation-set: 28
Initial matrix: 227774 x 256978 with sparse part having weight 40034553.
Pruned matrix : 
Total sieving time: 16.46 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000
total time: 16.60 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(16·10¹⁶⁸-61)/9 = 1(7)₁₆₇1_<169> = 97 · 238529 · C161

C161 = P63 · P99

P63 = 276893190703697940414783252826468932935031019517441970031773419_<63>

P99 = 277493155611403703683054353264914582179810037056175052898430042343277972816202057969029288816183393_<99>

Number: n
N=76835965255679333973559409330624423751270416654595016187825171305664481341363095091369416050073652795282571393565786043425949148796049816924626372032818926630667
  ( 161 digits)
SNFS difficulty: 169 digits.
Divisors found:

Tue May 27 10:02:13 2008  prp63 factor: 276893190703697940414783252826468932935031019517441970031773419
Tue May 27 10:02:13 2008  prp99 factor: 277493155611403703683054353264914582179810037056175052898430042343277972816202057969029288816183393
Tue May 27 10:02:13 2008  elapsed time 01:01:22 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 72.06 hours.
Scaled time: 60.46 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_1_7_167_1
n: 76835965255679333973559409330624423751270416654595016187825171305664481341363095091369416050073652795282571393565786043425949148796049816924626372032818926630667
type: snfs
deg: 5
c5: 500
c0: -61
skew: 0.66
m: 2000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4300447)
Primes: RFBsize:250150, AFBsize:250362, largePrimes:5832541 encountered
Relations: rels:5819193, finalFF:557034
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 71.86 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,48,48,2.5,2.5,100000
total time: 72.06 hours.
 --------- CPU info (if available) ----------

May 26, 2008 (4th)

By Jo Yeong Uk / GMP-ECM, GGNFS

(19·10¹⁴⁸+17)/9 = 2(1)₁₄₇3_<149> = 36373501 · 102958766380241_<15> · C127

C127 = P32 · P96

P32 = 26224511757071848012274148820403_<32>

P96 = 214958808080422153827853526584090210525279684543816668859493746840385486703480148495405135657631_<96>

(19·10¹⁴²+17)/9 = 2(1)₁₄₁3_<143> = 71 · 7109 · 115015969 · 189613733299_<12> · 322231073053166813_<18> · C100

C100 = P32 · P69

P32 = 11861150895327891743346144866743_<32>

P69 = 501790053285023603948131322212264157408448417965160016833219189411523_<69>

Number: 21113_142
N=5951807539788288225430884682457532216240948269068902899898204239271953616323682713929151105423679589
  ( 100 digits)
Divisors found:
 r1=11861150895327891743346144866743 (pp32)
 r2=501790053285023603948131322212264157408448417965160016833219189411523 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.25 hours.
Scaled time: 7.74 units (timescale=2.380).
Factorization parameters were as follows:
name: 21113_142
n: 5951807539788288225430884682457532216240948269068902899898204239271953616323682713929151105423679589
skew: 7751.50
# norm 1.17e+14
c5: 89760
c4: 286433780
c3: -13296024916531
c2: -35606200466171418
c1: 108194047644569709036
c0: 685898863072462815714288
# alpha -6.78
Y1: 9344433943
Y0: -9211130300927092855
# Murphy_E 3.58e-09
# M 2709477439678778205764349730250602373095667669738940728520330933270108509389153091541589441957421898
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [750000, 1250001)
Primes: RFBsize:114155, AFBsize:113795, largePrimes:3865589 encountered
Relations: rels:3805363, finalFF:322396
Max relations in full relation-set: 28
Initial matrix: 228035 x 322396 with sparse part having weight 25128749.
Pruned matrix : 170035 x 171239 with weight 11283215.
Polynomial selection time: 0.25 hours.
Total sieving time: 2.79 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,48,48,2.5,2.5,50000
total time: 3.25 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047200k/8912896k available (2439k kernel code, 339088k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673806)
Calibrating delay using timer specific routine.. 5344.78 BogoMIPS (lpj=2672394)
Calibrating delay using timer specific routine.. 5344.44 BogoMIPS (lpj=2672223)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672388)

May 26, 2008 (3rd)

By Sinkiti Sibata / Msieve, GGNFS

(19·10¹⁰⁵+17)/9 = 2(1)₁₀₄3_<106> = 237581 · 3150047 · C94

C94 = P42 · P52

P42 = 783359782782066587583950077100340582667033_<42>

P52 = 3600983077686881125873890262969601465402154039814123_<52>

Mon May 26 05:54:40 2008  Msieve v. 1.35
Mon May 26 05:54:40 2008  random seeds: a13198c8 f211c8f4
Mon May 26 05:54:40 2008  factoring 2820865321538692810538614558530976382470612956300835716173321479649426366217666289278919907059 (94 digits)
Mon May 26 05:54:41 2008  searching for 15-digit factors
Mon May 26 05:54:43 2008  commencing quadratic sieve (94-digit input)
Mon May 26 05:54:43 2008  using multiplier of 1
Mon May 26 05:54:43 2008  using 64kb Pentium 4 sieve core
Mon May 26 05:54:43 2008  sieve interval: 18 blocks of size 65536
Mon May 26 05:54:43 2008  processing polynomials in batches of 6
Mon May 26 05:54:43 2008  using a sieve bound of 2022583 (75294 primes)
Mon May 26 05:54:43 2008  using large prime bound of 271026122 (28 bits)
Mon May 26 05:54:43 2008  using double large prime bound of 1511541411162932 (42-51 bits)
Mon May 26 05:54:43 2008  using trial factoring cutoff of 51 bits
Mon May 26 05:54:43 2008  polynomial 'A' values have 12 factors
Mon May 26 11:23:20 2008  75572 relations (18222 full + 57350 combined from 1082030 partial), need 75390
Mon May 26 11:23:23 2008  begin with 1100252 relations
Mon May 26 11:23:25 2008  reduce to 198215 relations in 11 passes
Mon May 26 11:23:25 2008  attempting to read 198215 relations
Mon May 26 11:23:31 2008  recovered 198215 relations
Mon May 26 11:23:31 2008  recovered 182210 polynomials
Mon May 26 11:23:31 2008  attempting to build 75572 cycles
Mon May 26 11:23:31 2008  found 75572 cycles in 6 passes
Mon May 26 11:23:31 2008  distribution of cycle lengths:
Mon May 26 11:23:31 2008     length 1 : 18222
Mon May 26 11:23:31 2008     length 2 : 13030
Mon May 26 11:23:31 2008     length 3 : 12664
Mon May 26 11:23:31 2008     length 4 : 10226
Mon May 26 11:23:31 2008     length 5 : 7717
Mon May 26 11:23:31 2008     length 6 : 5365
Mon May 26 11:23:31 2008     length 7 : 3504
Mon May 26 11:23:31 2008     length 9+: 4844
Mon May 26 11:23:31 2008  largest cycle: 22 relations
Mon May 26 11:23:32 2008  matrix is 75294 x 75572 (19.5 MB) with weight 4796606 (63.47/col)
Mon May 26 11:23:32 2008  sparse part has weight 4796606 (63.47/col)
Mon May 26 11:23:33 2008  filtering completed in 3 passes
Mon May 26 11:23:33 2008  matrix is 71948 x 72012 (18.6 MB) with weight 4589082 (63.73/col)
Mon May 26 11:23:33 2008  sparse part has weight 4589082 (63.73/col)
Mon May 26 11:23:34 2008  saving the first 48 matrix rows for later
Mon May 26 11:23:34 2008  matrix is 71900 x 72012 (11.0 MB) with weight 3534900 (49.09/col)
Mon May 26 11:23:34 2008  sparse part has weight 2463053 (34.20/col)
Mon May 26 11:23:34 2008  matrix includes 64 packed rows
Mon May 26 11:23:34 2008  using block size 21845 for processor cache size 512 kB
Mon May 26 11:23:34 2008  commencing Lanczos iteration
Mon May 26 11:23:34 2008  memory use: 11.1 MB
Mon May 26 11:24:28 2008  lanczos halted after 1138 iterations (dim = 71898)
Mon May 26 11:24:28 2008  recovered 16 nontrivial dependencies
Mon May 26 11:24:29 2008  prp42 factor: 783359782782066587583950077100340582667033
Mon May 26 11:24:29 2008  prp52 factor: 3600983077686881125873890262969601465402154039814123
Mon May 26 11:24:29 2008  elapsed time 05:29:49

(19·10¹³⁷+17)/9 = 2(1)₁₃₆3_<138> = 3 · 7 · 59 · 107 · 3137 · 10378477 · 52018972561_<11> · C111

C111 = P54 · P58

P54 = 257906784564331830598010239861334619288706259471606201_<54>

P58 = 3645720115445636970073274698358696904155253499404580769129_<58>

Number: 21113_137
N=940255952396088864380528059344305845250199889392668041299317576046841164705609190752329635215726376937585768929
  ( 111 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=257906784564331830598010239861334619288706259471606201 (pp54)
 r2=3645720115445636970073274698358696904155253499404580769129 (pp58)
Version: GGNFS-0.77.1-20060513-k8
Total time: 11.28 hours.
Scaled time: 22.67 units (timescale=2.010).
Factorization parameters were as follows:
name: 21113_137
n: 940255952396088864380528059344305845250199889392668041299317576046841164705609190752329635215726376937585768929
m: 1000000000000000000000000000
c5: 1900
c0: 17
skew: 0.39
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1825001)
Primes: RFBsize:78498, AFBsize:63278, largePrimes:1661033 encountered
Relations: rels:1702175, finalFF:196033
Max relations in full relation-set: 28
Initial matrix: 141843 x 196033 with sparse part having weight 20035278.
Pruned matrix : 128428 x 129201 with weight 11672377.
Total sieving time: 11.00 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 11.28 hours.
 --------- CPU info (if available) ----------

(19·10¹²¹+17)/9 = 2(1)₁₂₀3_<122> = 1609 · 14898491627884431173138326429_<29> · C90

C90 = P38 · P53

P38 = 36218395286981478538085535848918712611_<38>

P53 = 24315518894413952771658466169562042509604178782165703_<53>

Mon May 26 11:50:07 2008  Msieve v. 1.35
Mon May 26 11:50:07 2008  random seeds: d5e0c8e8 ebb720e0
Mon May 26 11:50:07 2008  factoring 880669074925951398734942256801317450090466445248385516105451227031149812348095397237780533 (90 digits)
Mon May 26 11:50:08 2008  searching for 15-digit factors
Mon May 26 11:50:10 2008  commencing quadratic sieve (90-digit input)
Mon May 26 11:50:10 2008  using multiplier of 2
Mon May 26 11:50:10 2008  using 64kb Pentium 4 sieve core
Mon May 26 11:50:10 2008  sieve interval: 18 blocks of size 65536
Mon May 26 11:50:10 2008  processing polynomials in batches of 6
Mon May 26 11:50:10 2008  using a sieve bound of 1615001 (61176 primes)
Mon May 26 11:50:10 2008  using large prime bound of 135660084 (27 bits)
Mon May 26 11:50:10 2008  using double large prime bound of 434924330062824 (42-49 bits)
Mon May 26 11:50:10 2008  using trial factoring cutoff of 49 bits
Mon May 26 11:50:10 2008  polynomial 'A' values have 12 factors
Mon May 26 14:06:03 2008  61929 relations (16287 full + 45642 combined from 670328 partial), need 61272
Mon May 26 14:06:06 2008  begin with 686615 relations
Mon May 26 14:06:07 2008  reduce to 151202 relations in 10 passes
Mon May 26 14:06:07 2008  attempting to read 151202 relations
Mon May 26 14:06:10 2008  recovered 151202 relations
Mon May 26 14:06:10 2008  recovered 129702 polynomials
Mon May 26 14:06:11 2008  attempting to build 61929 cycles
Mon May 26 14:06:11 2008  found 61929 cycles in 5 passes
Mon May 26 14:06:11 2008  distribution of cycle lengths:
Mon May 26 14:06:11 2008     length 1 : 16287
Mon May 26 14:06:11 2008     length 2 : 11799
Mon May 26 14:06:11 2008     length 3 : 11002
Mon May 26 14:06:11 2008     length 4 : 8442
Mon May 26 14:06:11 2008     length 5 : 5835
Mon May 26 14:06:11 2008     length 6 : 3725
Mon May 26 14:06:11 2008     length 7 : 2334
Mon May 26 14:06:11 2008     length 9+: 2505
Mon May 26 14:06:11 2008  largest cycle: 17 relations
Mon May 26 14:06:11 2008  matrix is 61176 x 61929 (15.2 MB) with weight 3728877 (60.21/col)
Mon May 26 14:06:11 2008  sparse part has weight 3728877 (60.21/col)
Mon May 26 14:06:12 2008  filtering completed in 4 passes
Mon May 26 14:06:12 2008  matrix is 57269 x 57333 (14.0 MB) with weight 3437413 (59.96/col)
Mon May 26 14:06:12 2008  sparse part has weight 3437413 (59.96/col)
Mon May 26 14:06:13 2008  saving the first 48 matrix rows for later
Mon May 26 14:06:13 2008  matrix is 57221 x 57333 (8.8 MB) with weight 2690503 (46.93/col)
Mon May 26 14:06:13 2008  sparse part has weight 1954397 (34.09/col)
Mon May 26 14:06:13 2008  matrix includes 64 packed rows
Mon May 26 14:06:13 2008  using block size 21845 for processor cache size 512 kB
Mon May 26 14:06:14 2008  commencing Lanczos iteration
Mon May 26 14:06:14 2008  memory use: 8.6 MB
Mon May 26 14:06:46 2008  lanczos halted after 907 iterations (dim = 57216)
Mon May 26 14:06:47 2008  recovered 14 nontrivial dependencies
Mon May 26 14:06:47 2008  prp38 factor: 36218395286981478538085535848918712611
Mon May 26 14:06:47 2008  prp53 factor: 24315518894413952771658466169562042509604178782165703
Mon May 26 14:06:47 2008  elapsed time 02:16:40

(19·10¹²⁵+17)/9 = 2(1)₁₂₄3_<126> = 3 · 7 · 1987 · 3727 · 3160957 · 5400152789_<10> · 21795220773379_<14> · C88

C88 = P32 · P57

P32 = 21769371741788386995971686002193_<32>

P57 = 167611083343969985171953195615674438687622824552784462787_<57>

Mon May 26 14:25:38 2008  Msieve v. 1.35
Mon May 26 14:25:38 2008  random seeds: 8498d380 d66b9c6e
Mon May 26 14:25:38 2008  factoring 3648787981358758376443619313888158885179582879218339340017561379606686032816905208891891 (88 digits)
Mon May 26 14:25:40 2008  searching for 15-digit factors
Mon May 26 14:25:42 2008  commencing quadratic sieve (88-digit input)
Mon May 26 14:25:42 2008  using multiplier of 11
Mon May 26 14:25:42 2008  using 64kb Pentium 4 sieve core
Mon May 26 14:25:42 2008  sieve interval: 13 blocks of size 65536
Mon May 26 14:25:42 2008  processing polynomials in batches of 8
Mon May 26 14:25:42 2008  using a sieve bound of 1517707 (57529 primes)
Mon May 26 14:25:42 2008  using large prime bound of 121416560 (26 bits)
Mon May 26 14:25:42 2008  using double large prime bound of 356205104400640 (42-49 bits)
Mon May 26 14:25:42 2008  using trial factoring cutoff of 49 bits
Mon May 26 14:25:42 2008  polynomial 'A' values have 11 factors
Mon May 26 15:46:08 2008  57807 relations (16257 full + 41550 combined from 604944 partial), need 57625
Mon May 26 15:46:10 2008  begin with 621201 relations
Mon May 26 15:46:11 2008  reduce to 137587 relations in 9 passes
Mon May 26 15:46:11 2008  attempting to read 137587 relations
Mon May 26 15:46:15 2008  recovered 137587 relations
Mon May 26 15:46:15 2008  recovered 113718 polynomials
Mon May 26 15:46:15 2008  attempting to build 57807 cycles
Mon May 26 15:46:15 2008  found 57807 cycles in 5 passes
Mon May 26 15:46:15 2008  distribution of cycle lengths:
Mon May 26 15:46:15 2008     length 1 : 16257
Mon May 26 15:46:15 2008     length 2 : 11581
Mon May 26 15:46:15 2008     length 3 : 10022
Mon May 26 15:46:15 2008     length 4 : 7636
Mon May 26 15:46:15 2008     length 5 : 5168
Mon May 26 15:46:15 2008     length 6 : 3243
Mon May 26 15:46:15 2008     length 7 : 1807
Mon May 26 15:46:15 2008     length 9+: 2093
Mon May 26 15:46:15 2008  largest cycle: 16 relations
Mon May 26 15:46:15 2008  matrix is 57529 x 57807 (13.6 MB) with weight 3346142 (57.88/col)
Mon May 26 15:46:15 2008  sparse part has weight 3346142 (57.88/col)
Mon May 26 15:46:16 2008  filtering completed in 3 passes
Mon May 26 15:46:16 2008  matrix is 52880 x 52944 (12.6 MB) with weight 3088437 (58.33/col)
Mon May 26 15:46:16 2008  sparse part has weight 3088437 (58.33/col)
Mon May 26 15:46:17 2008  saving the first 48 matrix rows for later
Mon May 26 15:46:17 2008  matrix is 52832 x 52944 (8.7 MB) with weight 2490713 (47.04/col)
Mon May 26 15:46:17 2008  sparse part has weight 1970280 (37.21/col)
Mon May 26 15:46:17 2008  matrix includes 64 packed rows
Mon May 26 15:46:17 2008  using block size 21177 for processor cache size 512 kB
Mon May 26 15:46:18 2008  commencing Lanczos iteration
Mon May 26 15:46:18 2008  memory use: 8.2 MB
Mon May 26 15:46:48 2008  lanczos halted after 837 iterations (dim = 52831)
Mon May 26 15:46:48 2008  recovered 17 nontrivial dependencies
Mon May 26 15:46:49 2008  prp32 factor: 21769371741788386995971686002193
Mon May 26 15:46:49 2008  prp57 factor: 167611083343969985171953195615674438687622824552784462787
Mon May 26 15:46:49 2008  elapsed time 01:21:11

(19·10¹³²+17)/9 = 2(1)₁₃₁3_<133> = 31 · 911 · 333483323 · 46928703599228182185833657_<26> · C94

C94 = P46 · P48

P46 = 4998028003187250350588924237218853249700597287_<46>

P48 = 955695757724238214604079143204207742822053446549_<48>

Number: 21113_132
N=4776594159633000514124122320061907346291707194004929543799695356781805365347420856122228912563
  ( 94 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=4998028003187250350588924237218853249700597287 (pp46)
 r2=955695757724238214604079143204207742822053446549 (pp48)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.35 hours.
Scaled time: 12.80 units (timescale=2.016).
Factorization parameters were as follows:
name: 21113_132
n: 4776594159633000514124122320061907346291707194004929543799695356781805365347420856122228912563
m: 100000000000000000000000000
c5: 1900
c0: 17
skew: 0.39
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1250001)
Primes: RFBsize:63951, AFBsize:63278, largePrimes:1568200 encountered
Relations: rels:1587419, finalFF:178535
Max relations in full relation-set: 28
Initial matrix: 127296 x 178535 with sparse part having weight 16438184.
Pruned matrix : 115008 x 115708 with weight 8856615.
Total sieving time: 6.16 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 6.35 hours.
 --------- CPU info (if available) ----------

(19·10¹⁷¹+17)/9 = 2(1)₁₇₀3_<172> = 31633729472340713_<17> · 291104186737583782427_<21> · 6438741037805110785691_<22> · 8577629963433708883037_<22> · C91

C91 = P39 · P52

P39 = 730838499256988735456103400088494610213_<39>

P52 = 5679662912466728551265886075488345660885194579796953_<52>

Mon May 26 16:05:50 2008  Msieve v. 1.35
Mon May 26 16:05:50 2008  random seeds: f9076ce4 4dd5fde8
Mon May 26 16:05:50 2008  factoring 4150916319232761671539358595025702780677783501173809882863812208715661747821991680420080989 (91 digits)
Mon May 26 16:05:51 2008  searching for 15-digit factors
Mon May 26 16:05:53 2008  commencing quadratic sieve (91-digit input)
Mon May 26 16:05:53 2008  using multiplier of 5
Mon May 26 16:05:53 2008  using 64kb Pentium 4 sieve core
Mon May 26 16:05:53 2008  sieve interval: 18 blocks of size 65536
Mon May 26 16:05:53 2008  processing polynomials in batches of 6
Mon May 26 16:05:53 2008  using a sieve bound of 1715599 (64706 primes)
Mon May 26 16:05:53 2008  using large prime bound of 164697504 (27 bits)
Mon May 26 16:05:53 2008  using double large prime bound of 616646889281472 (42-50 bits)
Mon May 26 16:05:53 2008  using trial factoring cutoff of 50 bits
Mon May 26 16:05:53 2008  polynomial 'A' values have 12 factors
Mon May 26 19:12:04 2008  65311 relations (16822 full + 48489 combined from 768000 partial), need 64802
Mon May 26 19:12:07 2008  begin with 784822 relations
Mon May 26 19:12:08 2008  reduce to 163602 relations in 10 passes
Mon May 26 19:12:08 2008  attempting to read 163602 relations
Mon May 26 19:12:13 2008  recovered 163602 relations
Mon May 26 19:12:13 2008  recovered 144384 polynomials
Mon May 26 19:12:13 2008  attempting to build 65311 cycles
Mon May 26 19:12:13 2008  found 65311 cycles in 5 passes
Mon May 26 19:12:13 2008  distribution of cycle lengths:
Mon May 26 19:12:13 2008     length 1 : 16822
Mon May 26 19:12:13 2008     length 2 : 11982
Mon May 26 19:12:13 2008     length 3 : 11293
Mon May 26 19:12:13 2008     length 4 : 8641
Mon May 26 19:12:13 2008     length 5 : 6470
Mon May 26 19:12:13 2008     length 6 : 4167
Mon May 26 19:12:13 2008     length 7 : 2635
Mon May 26 19:12:13 2008     length 9+: 3301
Mon May 26 19:12:13 2008  largest cycle: 19 relations
Mon May 26 19:12:13 2008  matrix is 64706 x 65311 (16.2 MB) with weight 3988777 (61.07/col)
Mon May 26 19:12:13 2008  sparse part has weight 3988777 (61.07/col)
Mon May 26 19:12:15 2008  filtering completed in 3 passes
Mon May 26 19:12:15 2008  matrix is 60989 x 61053 (15.1 MB) with weight 3724320 (61.00/col)
Mon May 26 19:12:15 2008  sparse part has weight 3724320 (61.00/col)
Mon May 26 19:12:15 2008  saving the first 48 matrix rows for later
Mon May 26 19:12:15 2008  matrix is 60941 x 61053 (9.4 MB) with weight 2900914 (47.51/col)
Mon May 26 19:12:15 2008  sparse part has weight 2093272 (34.29/col)
Mon May 26 19:12:15 2008  matrix includes 64 packed rows
Mon May 26 19:12:15 2008  using block size 21845 for processor cache size 512 kB
Mon May 26 19:12:16 2008  commencing Lanczos iteration
Mon May 26 19:12:16 2008  memory use: 9.3 MB
Mon May 26 19:12:54 2008  lanczos halted after 965 iterations (dim = 60941)
Mon May 26 19:12:54 2008  recovered 18 nontrivial dependencies
Mon May 26 19:12:55 2008  prp39 factor: 730838499256988735456103400088494610213
Mon May 26 19:12:55 2008  prp52 factor: 5679662912466728551265886075488345660885194579796953
Mon May 26 19:12:55 2008  elapsed time 03:07:05

(19·10¹¹⁷+17)/9 = 2(1)₁₁₆3_<118> = 31 · 61 · 61231 · 704964570643_<12> · C98

C98 = P47 · P51

P47 = 63460649118500649720004637763831639443635857911_<47>

P51 = 407545788120013284598901938387320489819499387145561_<51>

Number: 21113_117
N=25863120259606973612140943358534400942067297352716633976505979254681934314828742357338679670383071
  ( 98 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=63460649118500649720004637763831639443635857911 (pp47)
 r2=407545788120013284598901938387320489819499387145561 (pp51)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.34 hours.
Scaled time: 1.58 units (timescale=0.677).
Factorization parameters were as follows:
name: 21113_117
n: 25863120259606973612140943358534400942067297352716633976505979254681934314828742357338679670383071
m: 100000000000000000000000
c5: 1900
c0: 17
skew: 0.39
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63278, largePrimes:2061617 encountered
Relations: rels:2076260, finalFF:171414
Max relations in full relation-set: 28
Initial matrix: 112443 x 171414 with sparse part having weight 13981284.
Pruned matrix : 94931 x 95557 with weight 5424242.
Total sieving time: 2.10 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,118,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.34 hours.
 --------- CPU info (if available) ----------

May 26, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(8·10¹⁶⁹-17)/9 = (8)₁₆₈7_<169> = 7 · 23 · 347651 · 570290792567_<12> · C150

C150 = P34 · P42 · P75

P34 = 7647057099881162934899256947975591_<34>

P42 = 288971669211010444364343532804847944865909_<42>

P75 = 126017877051932162637963203064793127409653634778576315963511553718382954729_<75>

Number: n
N=36415596282124724946851084768003952823187763054201007070477049673615397913960005932770460940694364915011993122433661
  ( 116 digits)
Divisors found:

Mon May 26 03:32:21 2008  prp42 factor: 288971669211010444364343532804847944865909
Mon May 26 03:32:21 2008  prp75 factor: 126017877051932162637963203064793127409653634778576315963511553718382954729
Mon May 26 03:32:21 2008  elapsed time 00:58:59 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 33.79 hours.
Scaled time: 60.41 units (timescale=1.788).
Factorization parameters were as follows:
name: KA_8_168_7
n: 36415596282124724946851084768003952823187763054201007070477049673615397913960005932770460940694364915011993122433661
skew: 32602.77
# norm 9.87e+15
c5: 51240
c4: -17444291338
c3: -204845419034853
c2: 16621713388589075462
c1: 140528977229607893092002
c0: -7240200765027653070058015
# alpha -6.04
Y1: 1095222391577
Y0: -14802594722064352791642
# Murphy_E 4.67e-10
# M 7330779924285220432966678097907383861727993586497700469151769799760136608191069016539989636153384426399706445238266
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 2139990)
Primes: RFBsize:315948, AFBsize:315812, largePrimes:6713940 encountered
Relations: rels:6667215, finalFF:756278
Max relations in full relation-set: 28
Initial matrix: 631844 x 756278 with sparse part having weight 46156257.
Pruned matrix : 
Total sieving time: 33.56 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 33.79 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(19·10¹¹⁰+17)/9 = 2(1)₁₀₉3_<111> = 3 · 6607 · C107

C107 = P43 · P64

P43 = 2270199252456242699778729641333819680492093_<43>

P64 = 4691606222865481103080585512540588248203889051546135228221187921_<64>

Number: n
N=10650880939968271586252515569906216190460174113874734428692352106912421730039408259477882604869134307608653
  ( 107 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=2270199252456242699778729641333819680492093 (pp43)
 r2=4691606222865481103080585512540588248203889051546135228221187921 (pp64)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.77 hours.
Scaled time: 1.34 units (timescale=1.754).
Factorization parameters were as follows:
name: KA_2_1_109_3
n: 10650880939968271586252515569906216190460174113874734428692352106912421730039408259477882604869134307608653
type: snfs
skew: 0.98
deg: 5
c5: 19
c0: 17
m: 10000000000000000000000
rlim: 600000
alim: 600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 160001)
Primes: RFBsize:49098, AFBsize:49036, largePrimes:3053133 encountered
Relations: rels:2566808, finalFF:139977
Max relations in full relation-set: 28
Initial matrix: 98201 x 139977 with sparse part having weight 6770974.
Pruned matrix : 74778 x 75333 with weight 2487548.
Total sieving time: 0.67 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.03 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.4,2.4,50000
total time: 0.77 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(16·10¹⁶⁸-43)/9 = 1(7)₁₆₇3_<169> = 3 · 19 · 191 · 1162727 · 32142403 · C151

C151 = P40 · P43 · P69

P40 = 1135576527475659333289157303954971991389_<40>

P43 = 7332359625542663552102105388324769736487451_<43>

P69 = 524750651552389632583331633911460165026537808342751045471152014055281_<69>

Number: n
N=3847660490919948366761919261633749695877165825894476197911616472552930306305900066786080295040588420179076778731
  ( 112 digits)
Divisors found:

Mon May 26 10:32:20 2008  prp43 factor: 7332359625542663552102105388324769736487451
Mon May 26 10:32:20 2008  prp69 factor: 524750651552389632583331633911460165026537808342751045471152014055281
Mon May 26 10:32:20 2008  elapsed time 00:41:20 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 18.45 hours.
Scaled time: 33.75 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_7_167_3
n: 3847660490919948366761919261633749695877165825894476197911616472552930306305900066786080295040588420179076778731
skew: 36788.59
# norm 6.05e+15
c5: 78000
c4: -5631153824
c3: -347034960848259
c2: 5737219763925262545
c1: 298212253611090490023001
c0: 1359075478596552538555591221
# alpha -6.64
Y1: 390452078753
Y0: -2180828685196191746234
# Murphy_E 7.85e-10
# M 3106697242966918702106236308821846260072575737044410193218342945966571983336045922057382424617833389701926414309
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1300000)
Primes: RFBsize:250150, AFBsize:249801, largePrimes:6529947 encountered
Relations: rels:6131649, finalFF:518517
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 18.27 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 18.45 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(19·10¹¹⁶+17)/9 = 2(1)₁₁₅3_<117> = 3 · 83 · 71527 · 5602253 · C103

C103 = P49 · P54

P49 = 2966325687678056937474314854464720978353817202219_<49>

P54 = 713280224924002374089503089945616997448142074923965033_<54>

Number: n
N=2115821453704850469983635766404803392743827058719309562419615688657939260968947379262777059130246008227
  ( 103 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=2966325687678056937474314854464720978353817202219 (pp49)
 r2=713280224924002374089503089945616997448142074923965033 (pp54)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.45 hours.
Scaled time: 2.53 units (timescale=1.751).
Factorization parameters were as follows:
name: KA_2_1_115_3
n: 2115821453704850469983635766404803392743827058719309562419615688657939260968947379262777059130246008227
type: snfs
skew: 0.62
deg: 5
c5: 190
c0: 17
m: 100000000000000000000000
rlim: 700000
alim: 700000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 240001)
Primes: RFBsize:56543, AFBsize:56433, largePrimes:3684144 encountered
Relations: rels:3161105, finalFF:179094
Max relations in full relation-set: 28
Initial matrix: 113043 x 179094 with sparse part having weight 10761539.
Pruned matrix : 84754 x 85383 with weight 3472881.
Total sieving time: 1.29 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.05 hours.
Total square root time: 0.03 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,700000,700000,28,28,48,48,2.4,2.4,50000
total time: 1.45 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(19·10¹²⁴+17)/9 = 2(1)₁₂₃3_<125> = 223718153 · 834759311 · C108

C108 = P46 · P62

P46 = 2098106958390013566678652050706071014416820177_<46>

P62 = 53879179111506794848560367490910458372207156743626422470530943_<62>

Number: n
N=113044280606194274951039755402217484921209733464583986651108663909704532766448392160888427078429686945236911
  ( 108 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=2098106958390013566678652050706071014416820177 (pp46)
 r2=53879179111506794848560367490910458372207156743626422470530943 (pp62)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.99 hours.
Scaled time: 3.63 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_2_1_123_3
n: 113044280606194274951039755402217484921209733464583986651108663909704532766448392160888427078429686945236911
skew: 1.55
deg: 5
c5: 19
c0: 170
m: 10000000000000000000000000
type: snfs
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 400001)
Primes: RFBsize:78498, AFBsize:78541, largePrimes:4987460 encountered
Relations: rels:4343076, finalFF:223428
Max relations in full relation-set: 48
Initial matrix: 157104 x 223428 with sparse part having weight 18618193.
Pruned matrix : 128827 x 129676 with weight 6954852.
Total sieving time: 1.80 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.07 hours.
Total square root time: 0.05 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000
total time: 1.99 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(19·10¹⁴⁵+17)/9 = 2(1)₁₄₄3_<146> = 28447 · 41017 · C137

C137 = P35 · P102

P35 = 78028900325725980152501066021599909_<35>

P102 = 231875700865027574418442587619581173200268280817376948139532338530122326771487269224347720783283635043_<102>

(19·10¹⁴⁰+17)/9 = 2(1)₁₃₉3_<141> = 3⁴ · 103142892767_<12> · C128

C128 = P37 · P92

P37 = 1338967039267258903607662253178789037_<37>

P92 = 18871954411427858011578814863318916834385230348366099626180972019620251580610578675135514787_<92>

May 26, 2008

The factor table of 211...113 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

May 25, 2008

By Sinkiti Sibata / GGNFS

6·10¹⁶⁴+1 = 6(0)₁₆₃1_<165> = 127301 · 9028519 · 731813929840206967957739_<24> · C129

C129 = P48 · P82

P48 = 369270152835869755547632504844697137215152321611_<48>

P82 = 1931781669601575696400721360944887567321529473091599594216511185010148045718575651_<82>

Number: 60001_164
N=713349312379305508790666689367172868406630219599967618257841050319008187812555276771966182501762848278868158748777307060785693761
  ( 129 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=369270152835869755547632504844697137215152321611 (pp48)
 r2=1931781669601575696400721360944887567321529473091599594216511185010148045718575651 (pp82)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 109.83 hours.
Scaled time: 74.35 units (timescale=0.677).
Factorization parameters were as follows:
name: 60001_164
n: 713349312379305508790666689367172868406630219599967618257841050319008187812555276771966182501762848278868158748777307060785693761
m: 1000000000000000000000000000000000
c5: 3
c0: 5
skew: 1.11
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 5000001)
Primes: RFBsize:348513, AFBsize:347746, largePrimes:5774254 encountered
Relations: rels:5921824, finalFF:793765
Max relations in full relation-set: 28
Initial matrix: 696324 x 793765 with sparse part having weight 43434956.
Pruned matrix : 618590 x 622135 with weight 30984281.
Total sieving time: 93.90 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 15.32 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 109.83 hours.
 --------- CPU info (if available) ----------

May 22, 2008

By Wataru Sakai / GGNFS

(10¹⁷⁵+53)/9 = (1)₁₇₄7_<175> = 7 · 193 · 3954197657_<10> · C162

C162 = P37 · P125

P37 = 2610737759979808348888414895912745601_<37>

P125 = 79667376637152748251187653628669585032369930493112417006130329078837954943743446933778194805256207158514266300958092844163331_<125>

Number: 11117_175
N=207990628425147882873116937733374674024084023398128816882295841907268463261365926197669521747703201029768219977406412612707085785431852504776846402074903895756931
  ( 162 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=2610737759979808348888414895912745601 (pp37)
 r2=79667376637152748251187653628669585032369930493112417006130329078837954943743446933778194805256207158514266300958092844163331 (pp125)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 229.61 hours.
Scaled time: 462.67 units (timescale=2.015).
Factorization parameters were as follows:
n: 207990628425147882873116937733374674024084023398128816882295841907268463261365926197669521747703201029768219977406412612707085785431852504776846402074903895756931
m: 100000000000000000000000000000000000
c5: 1
c0: 53
skew: 2.21
type: snfsFactor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 11500001)
Primes: RFBsize:501962, AFBsize:502556, largePrimes:6722972 encountered
Relations: rels:7341404, finalFF:1276844
Max relations in full relation-set: 32
Initial matrix: 1004582 x 1276844 with sparse part having weight 84011642.
Pruned matrix : 767989 x 773075 with weight 63465184.
Total sieving time: 223.38 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 5.93 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 229.61 hours.

May 21, 2008

By Robert Backstrom / GGNFS, Msieve

(5·10¹⁶⁵-41)/9 = (5)₁₆₄1_<165> = 19 · 23 · 6579711991137624748790221_<25> · C138

C138 = P68 · P70

P68 = 21083373136695693791397262348539885288424420557620875447965111556739_<68>

P70 = 9164295383350239108257431989856648493254559513704497509580294208734917_<70>

Number: n
N=193214259102070796294938693019973703949380505820952443293645400138485561727618230806612603709067289274548366084025358207192680957655955663
  ( 138 digits)
SNFS difficulty: 165 digits.
Divisors found:

Wed May 21 17:27:32 2008  prp68 factor: 21083373136695693791397262348539885288424420557620875447965111556739
Wed May 21 17:27:32 2008  prp70 factor: 9164295383350239108257431989856648493254559513704497509580294208734917
Wed May 21 17:27:32 2008  elapsed time 00:46:27 (Msieve 1.36)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 30.38 hours.
Scaled time: 55.56 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_5_164_1
n: 193214259102070796294938693019973703949380505820952443293645400138485561727618230806612603709067289274548366084025358207192680957655955663
skew: 1.52
deg: 5
c5: 5
c0: -41
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3200000)
Primes: RFBsize:230209, AFBsize:230198, largePrimes:8031343 encountered
Relations: rels:7742603, finalFF:745531
Max relations in full relation-set: 28
Initial matrix: 460472 x 745531 with sparse part having weight 73265518.
Pruned matrix : 
Total sieving time: 30.20 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 30.38 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

May 20, 2008 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(5·10¹⁶⁸-23)/9 = (5)₁₆₇3_<168> = 127709 · 3157451059191428479609_<22> · C142

C142 = P37 · P49 · P56

P37 = 4534229354659272615202786707505221491_<37>

P49 = 5307729004237646738094282755789801851124238131627_<49>

P56 = 57247580658584769147297015573859650130443012417569320109_<56>

Number: n
N=303854644284004501603054739515143078103688249906898718160532334889375027156095800934456094438098839987343
  ( 105 digits)
Divisors found:

Wed May 21 00:10:06 2008  prp49 factor: 5307729004237646738094282755789801851124238131627
Wed May 21 00:10:06 2008  prp56 factor: 57247580658584769147297015573859650130443012417569320109
Wed May 21 00:10:06 2008  elapsed time 00:25:35 (Msieve 1.35)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 9.19 hours.
Scaled time: 13.30 units (timescale=1.447).
Factorization parameters were as follows:
name: n
n: 303854644284004501603054739515143078103688249906898718160532334889375027156095800934456094438098839987343
skew: 4247.77
# norm 1.75e+13
c5: 55080
c4: 365730018
c3: -2888912593427
c2: -4861785643557040
c1: 22243646095735652084
c0: 22141020713593788522960
# alpha -3.84
Y1: 103926725093
Y0: -88783796969622700957
# Murphy_E 2.08e-09
# M 123198688195128300348499142709450541348104311857436014602214916670286578204588240644864396042236949963164
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved  special-q in [100000, 1300000)
Primes: RFBsize:183072, AFBsize:182479, largePrimes:4258432 encountered
Relations: rels:4351739, finalFF:511925
Max relations in full relation-set: 28
Initial matrix: 365631 x 511925 with sparse part having weight 32012362.
Pruned matrix : 
Total sieving time: 9.03 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 9.19 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 20, 2008

By Robert Backstrom / GGNFS, Msieve

(52·10¹⁶⁸-7)/9 = 5(7)₁₆₈_<169> = 2273 · 4327 · C162

C162 = P68 · P95

P68 = 20752002809996857119171828649866996717199970697800523504969822088337_<68>

P95 = 28308345385696301109711060065796518182592934915052319190743442789270172132944796227018696827351_<95>

Number: n
N=587454862990331204679340078964552962269954511449433145032585048015227824203092906924250259883817922025511831629019452313797736511559038665815896458549823159705287
  ( 162 digits)
SNFS difficulty: 171 digits.
Divisors found:

Tue May 20 09:17:49 2008  prp68 factor: 20752002809996857119171828649866996717199970697800523504969822088337
Tue May 20 09:17:49 2008  prp95 factor: 28308345385696301109711060065796518182592934915052319190743442789270172132944796227018696827351
Tue May 20 09:17:49 2008  elapsed time 01:32:25 (Msieve 1.35)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 84.28 hours.
Scaled time: 154.14 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_5_7_168
n: 587454862990331204679340078964552962269954511449433145032585048015227824203092906924250259883817922025511831629019452313797736511559038665815896458549823159705287
skew: 1.68
deg: 5
c5: 13
c0: -175
m: 10000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5601451)
Primes: RFBsize:250150, AFBsize:250051, largePrimes:8242669 encountered
Relations: rels:7702797, finalFF:542216
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 83.96 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 84.28 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

May 19, 2008 (4th)

By Wataru Sakai / GGNFS

(10¹⁷⁴+53)/9 = (1)₁₇₃7_<174> = 3² · 24256521885311_<14> · C159

C159 = P43 · P52 · P65

P43 = 2027653539543295031938083824511414251255561_<43>

P52 = 8392517209536205849446943360188330150487682685953111_<52>

P65 = 29908901503673913152403882822870481251319731298983207281605651573_<65>

Number: 11117
N=508963282976766783534262853063054603099914669847218516424297079463077466707163153543756764845578381588268013787077522720355911520232708905656308189050983576283
  ( 159 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=2027653539543295031938083824511414251255561 (pp43)
 r2=8392517209536205849446943360188330150487682685953111 (pp52)
 r3=29908901503673913152403882822870481251319731298983207281605651573 (pp65)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 269.79 hours.
Scaled time: 543.10 units (timescale=2.013).
Factorization parameters were as follows:
n: 508963282976766783534262853063054603099914669847218516424297079463077466707163153543756764845578381588268013787077522720355911520232708905656308189050983576283
m: 100000000000000000000000000000000000
c5: 1
c0: 530
skew: 3.51
type: snfsFactor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 12900001)
Primes: RFBsize:501962, AFBsize:502251, largePrimes:6702326 encountered
Relations: rels:7292639, finalFF:1245904
Max relations in full relation-set: 32
Initial matrix: 1004277 x 1245904 with sparse part having weight 85068839.
Pruned matrix : 795304 x 800389 with weight 63132763.
Total sieving time: 263.47 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 6.01 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 269.79 hours.
 --------- CPU info (if available) ----------

May 19, 2008 (3rd)

By Jo Yeong Uk / GGNFS

8·10¹⁸²-1 = 7(9)₁₈₂_<183> = 6689 · 45833 · 64965178089572382042423526852742694223_<38> · C137

C137 = P46 · P92

P46 = 2829679223950790825954049626119361318023850447_<46>

P92 = 14194910762760110159567326572030778175180115767221826639366766883637151712659720504442682567_<92>

Number: 79999_182
N=40167044071217756780187592392246187076622588646967716036404892251010744662016892972703963262216033825927684995558723281578766771102057449
  ( 137 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=2829679223950790825954049626119361318023850447 (pp46)
 r2=14194910762760110159567326572030778175180115767221826639366766883637151712659720504442682567 (pp92)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 198.43 hours.
Scaled time: 470.07 units (timescale=2.369).
Factorization parameters were as follows:
n: 40167044071217756780187592392246187076622588646967716036404892251010744662016892972703963262216033825927684995558723281578766771102057449
m: 2000000000000000000000000000000000000
c5: 25
c0: -1
skew: 0.53
type: snfs
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [5000000, 8700001)
Primes: RFBsize:664579, AFBsize:664195, largePrimes:11026461 encountered
Relations: rels:11383611, finalFF:1565933
Max relations in full relation-set: 28
Initial matrix: 1328838 x 1565933 with sparse part having weight 91203312.
Pruned matrix : 1110337 x 1117045 with weight 59728587.
Total sieving time: 189.97 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 8.13 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000
total time: 198.43 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047200k/8912896k available (2439k kernel code, 339088k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673806)
Calibrating delay using timer specific routine.. 5344.78 BogoMIPS (lpj=2672394)
Calibrating delay using timer specific routine.. 5344.44 BogoMIPS (lpj=2672223)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672388)

May 19, 2008 (2nd)

By Robert Backstrom / GGNFS

(17·10¹⁶³-53)/9 = 1(8)₁₆₂3_<164> = 13 · 1733 · 23472466891217_<14> · C146

C146 = P47 · P99

P47 = 37464998032005354061197314116355187433310192513_<47>

P99 = 953410757092344732158061608063141390017470114019584701189414810489033337617424683715457001145387587_<99>

Number: n
N=35719532138157430052106995256408556683128572464714853419483400421642599338267848370829079226006677548827900672142510416094914152945325824970536131
  ( 146 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=37464998032005354061197314116355187433310192513 (pp47)
 r2=953410757092344732158061608063141390017470114019584701189414810489033337617424683715457001145387587 (pp99)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 62.14 hours.
Scaled time: 113.65 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_8_162_3
n: 35719532138157430052106995256408556683128572464714853419483400421642599338267848370829079226006677548827900672142510416094914152945325824970536131
skew: 0.32
deg: 5
c5: 17000
c0: -53
m: 100000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 4000001)
Primes: RFBsize:230209, AFBsize:230502, largePrimes:7910428 encountered
Relations: rels:7389998, finalFF:540625
Max relations in full relation-set: 48
Initial matrix: 460778 x 540625 with sparse part having weight 70572678.
Pruned matrix : 433405 x 435772 with weight 49582594.
Total sieving time: 58.94 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 2.75 hours.
Total square root time: 0.16 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 62.14 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

May 19, 2008

Msieve 1.36 has been released. The option "ECM=1" seems not to work with the latest GMP-ECM 6.2 on Cygwin.

HOW TO for Japanese

May 18, 2008 (2nd)

By Wataru Sakai / GGNFS

(10¹⁹²+53)/9 = (1)₁₉₁7_<192> = 3² · C191

C191 = P83 · P108

P83 = 14123720387393002847291410763872967484180831506670434762025325964606545058458745507_<83>

P108 = 874109559926262470155627544776491563984637426442504930902793822720147512252658789539043366361166147669006359_<108>

Number: 11117_192
N=12345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679013
  ( 191 digits)
SNFS difficulty: 192 digits.
Divisors found:
 r1=14123720387393002847291410763872967484180831506670434762025325964606545058458745507 (pp83)
 r2=874109559926262470155627544776491563984637426442504930902793822720147512252658789539043366361166147669006359 (pp108)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 1917.76 hours.
Scaled time: 3607.30 units (timescale=1.881).
Factorization parameters were as follows:
n: 12345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679013
m: 100000000000000000000000000000000000000
c5: 100
c0: 53
skew: 0.88
type: snfsFactor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 33200001)
Primes: RFBsize:501962, AFBsize:501086, largePrimes:7793203 encountered
Relations: rels:8555123, finalFF:1127939
Max relations in full relation-set: 32
Initial matrix: 1003112 x 1127939 with sparse part having weight 174268786.
Pruned matrix : 926899 x 931978 with weight 156610693.
Total sieving time: 1901.26 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 15.94 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,192,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 1917.76 hours.
 --------- CPU info (if available) ----------

10¹⁷⁹-9 = (9)₁₇₈1_<179> = 569 · 8951 · 944482695820147111_<18> · C155

C155 = P51 · P104

P51 = 546906270091264303592773419636796433846880957980999_<51>

P104 = 38010997664106318499368894010475771853596823493322466917536870017901952887416421331572081502939677862201_<104>

Number: 99991_179
N=20788452954924146764603039522194137117407445350777136241530147122589364351329595415517377430574666346326413082578657526895364119580095412547818049498318799
  ( 155 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=546906270091264303592773419636796433846880957980999 (pp51)
 r2=38010997664106318499368894010475771853596823493322466917536870017901952887416421331572081502939677862201 (pp104)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 378.09 hours.
Scaled time: 732.36 units (timescale=1.937).
Factorization parameters were as follows:
n: 20788452954924146764603039522194137117407445350777136241530147122589364351329595415517377430574666346326413082578657526895364119580095412547818049498318799
m: 1000000000000000000000000000000000000
c5: 1
c0: -90
skew: 2.46
type: snfsFactor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 
)
Primes: RFBsize:501962, AFBsize:502106, largePrimes:6681820 encountered
Relations: rels:7298544, finalFF:1280046
Max relations in full relation-set: 32
Initial matrix: 1004132 x 1280046 with sparse part having weight 79504127.
Pruned matrix : 763803 x 768887 with weight 58674310.
Total sieving time: 372.79 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 5.00 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 378.09 hours.
 --------- CPU info (if available) ----------

May 18, 2008

GMP-ECM 6.2 has been released.

HOW TO for Japanese

May 17, 2008 (3rd)

By Wataru Sakai / GGNFS

10¹⁸⁵-9 = (9)₁₈₄1_<185> = 43 · 68239 · C179

C179 = P46 · P62 · P72

P46 = 2538313576960440629507448895847540063266132079_<46>

P62 = 29377049543046125556029128856057470051512089568061282636870001_<62>

P72 = 457030771896922620319211488891391699946102749496004569879285614325665077_<72>

Number: 99991_185
N=34079945417559419236834150286424901261878138975972616082258082655454819023561851863338055677770026483525583985424688943818187580790770605501798228319957522756031553939863209915083
  ( 179 digits)
SNFS difficulty: 185 digits.
Divisors found:
 r1=2538313576960440629507448895847540063266132079 (pp46)
 r2=29377049543046125556029128856057470051512089568061282636870001 (pp62)
 r3=457030771896922620319211488891391699946102749496004569879285614325665077 (pp72)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 551.24 hours.
Scaled time: 1091.46 units (timescale=1.980).
Factorization parameters were as follows:
n: 34079945417559419236834150286424901261878138975972616082258082655454819023561851863338055677770026483525583985424688943818187580790770605501798228319957522756031553939863209915083
m: 10000000000000000000000000000000000000
c5: 1
c0: -9
skew: 1.55
type: snfsFactor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 10800001)
Primes: RFBsize:501962, AFBsize:501561, largePrimes:6796158 encountered
Relations: rels:7433227, finalFF:1293690
Max relations in full relation-set: 32
Initial matrix: 1003587 x 1293690 with sparse part having weight 91676647.
Pruned matrix : 758115 x 763196 with weight 74168224.
Total sieving time: 544.72 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 6.19 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,185,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 551.24 hours.
 --------- CPU info (if available) ----------

May 17, 2008 (2nd)

By matsui / GMP-ECM, GGNFS

4·10¹⁹⁵+3 = 4(0)₁₉₄3_<196> = 334619 · C191

C191 = P34 · C157

P34 = 1899148878726749048488989889567829_<34>

C157 = [6294342673917283095296597333781389878764955396535221356317197348749861635004950569207387365842036953134093517964225806435213623451826519913911915772485876053_<157>]

(31·10¹⁷⁹-13)/9 = 3(4)₁₇₈3_<180> = 11 · C179

C179 = P68 · P112

P68 = 30083976209855206209867424244392759793889864427042762736211518417297_<68>

P112 = 1040857468264898047169776135475785954744385602127018579283000666366877231179930173843719367433591547037710900129_<112>

N=31313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313
  ( 179 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=30083976209855206209867424244392759793889864427042762736211518417297 (pp68)
 r2=1040857468264898047169776135475785954744385602127018579283000666366877231179930173843719367433591547037710900129 (pp112)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 488.40 hours.
Scaled time: 829.79 units (timescale=1.699).
Factorization parameters were as follows:
n: 31313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313
m: 1000000000000000000000000000000000000
c5: 31
c0: -130
skew: 1.33
type: snfs

Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 10000001)
Primes: RFBsize:501962, AFBsize:503087, largePrimes:6595694 encountered
Relations: rels:7075180, finalFF:1156780
Max relations in full relation-set: 28
Initial matrix: 1005114 x 1156780 with sparse part having weight 74860798.
Pruned matrix : 877750 x 882839 with weight 57165750.
Total sieving time: 473.22 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 14.75 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 488.40 hours.

May 17, 2008

(17·10¹⁵¹+1)/9 = 1(8)₁₅₀9_<152> = 1999 · 23053 · 136739 · 3036797 · 10115327 · 241307805079199_<15> · C111

C111 = P44 · P68

P44 = 16052814829035632996593744878571920614918011_<44>

P68 = 25191586207757365324351562684284330771481754244914451059244679310463_<68>

Number: 18889_151
N=404395868642816960618253208929134675199315393867524038135573530299426396894733529649892305557335362882759449093
  ( 111 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=16052814829035632996593744878571920614918011 (pp44)
 r2=25191586207757365324351562684284330771481754244914451059244679310463 (pp68)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 34.49 hours.
Scaled time: 23.32 units (timescale=0.676).
Factorization parameters were as follows:
name: 18889_151
n: 404395868642816960618253208929134675199315393867524038135573530299426396894733529649892305557335362882759449093
m: 1000000000000000000000000000000
c5: 170
c0: 1
skew: 0.36
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176638, largePrimes:5642853 encountered
Relations: rels:5669604, finalFF:579959
Max relations in full relation-set: 28
Initial matrix: 353007 x 579959 with sparse part having weight 52116995.
Pruned matrix : 262184 x 264013 with weight 25401214.
Total sieving time: 31.27 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 2.85 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 34.49 hours.
 --------- CPU info (if available) ----------

(5·10¹⁹⁵+7)/3 = 1(6)₁₉₄9_<196> = C196

C196 = P56 · P140

P56 = 70933856352032678645751387076184010145835868792093142469_<56>

P140 = 23496067355978549054213838968500546792259877842124452223684145406670771881352881209782499995258163300154998364416791685762865175855683321801_<140>

Number: 16669_195
N=1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
  ( 196 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=70933856352032678645751387076184010145835868792093142469 (pp56)
 r2=23496067355978549054213838968500546792259877842124452223684145406670771881352881209782499995258163300154998364416791685762865175855683321801 (pp140)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2741.50 hours.
Scaled time: 5510.41 units (timescale=2.010).
Factorization parameters were as follows:
name: 16669_195
n: 1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
m: 1000000000000000000000000000000000000000
c5: 5
c0: 7
skew: 1.07
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 37900000
)
Primes: RFBsize:501962, AFBsize:501136, largePrimes:8055645 encountered
Relations: rels:8992598, finalFF:1135865
Max relations in full relation-set: 28
Initial matrix: 1003163 x 1135865 with sparse part having weight 171400953.
Pruned matrix : 919129 x 924208 with weight 156929395.
Total sieving time: 2711.16 hours.
Total relation processing time: 3.34 hours.
Matrix solve time: 26.46 hours.
Time per square root: 0.54 hours.
Prototype def-par.txt line would be:
snfs,195,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 2741.50 hours.
 --------- CPU info (if available) ----------

May 16, 2008 (3rd)

By Makoto Kamada / GMP-ECM

2·10¹⁹³-7 = 1(9)₁₉₂3_<194> = 13 · 19 · 59 · 107 · C188

C188 = P34 · C154

P34 = 5988949810510825396976938071071359_<34>

C154 = [2141640541578786521330418665807384878608009014861807243660439094425838336861612412560917549794060720323430428012100399379490077809110556314251517234498057_<154>]

May 16, 2008 (2nd)

By Jo Yeong Uk / GGNFS

(17·10¹⁶⁷+1)/9 = 1(8)₁₆₆9_<168> = 3 · 439 · 1869749428162746085682491_<25> · 163609302509880042320150939_<27> · C114

C114 = P47 · P67

P47 = 67491671682398385317058511254298691184136924241_<47>

P67 = 6946708088484961654717938698979654691930307591413856517996301354013_<67>

Number: 18889_167
N=468844941581488303298926571089388851951033336400850491856810847637557401770554274615923511541962492525097502329133
  ( 114 digits)
Divisors found:
 r1=67491671682398385317058511254298691184136924241 (pp47)
 r2=6946708088484961654717938698979654691930307591413856517996301354013 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 17.62 hours.
Scaled time: 41.71 units (timescale=2.367).
Factorization parameters were as follows:
name: 18889_167
n: 468844941581488303298926571089388851951033336400850491856810847637557401770554274615923511541962492525097502329133
skew: 46684.93
# norm 8.48e+15
c5: 25920
c4: -676451736
c3: 130428591787688
c2: 3765533627980100596
c1: 36339129263182235163297
c0: -2557412519550371046968785290
# alpha -7.07
Y1: 636525890843
Y0: -7103609029808023059391
# Murphy_E 6.52e-10
# M 180139406609668129580026728876662211747894112506436949390916334295806210579842840786329647593722407771469041647991
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 70000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2730001)
Primes: RFBsize:250150, AFBsize:251199, largePrimes:7420613 encountered
Relations: rels:7298007, finalFF:609288
Max relations in full relation-set: 28
Initial matrix: 501430 x 609288 with sparse part having weight 49346372.
Pruned matrix : 410627 x 413198 with weight 29226622.
Polynomial selection time: 1.18 hours.
Total sieving time: 15.33 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.87 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.4,2.4,70000
total time: 17.62 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047200k/8912896k available (2439k kernel code, 339088k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673806)
Calibrating delay using timer specific routine.. 5344.78 BogoMIPS (lpj=2672394)
Calibrating delay using timer specific routine.. 5344.44 BogoMIPS (lpj=2672223)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672388)

May 16, 2008

By Robert Backstrom / GGNFS, Msieve

(16·10¹⁶⁴+11)/9 = 1(7)₁₆₃9_<165> = 8837 · 591781793 · C152

C152 = P60 · P92

P60 = 819054711215580220780088216797582579278329688084587866978373_<60>

P92 = 41504779040362072486741147317329424235777767852517739678824079973857105583247144975259600203_<92>

Number: n
N=33994684810970224044938855284325010320587366934543670749637725820422739011723947723559014858582979941037256593746246806758495085353818012064597627409719
  ( 152 digits)
SNFS difficulty: 166 digits.
Divisors found:

Fri May 16 01:29:50 2008  prp60 factor: 819054711215580220780088216797582579278329688084587866978373
Fri May 16 01:29:50 2008  prp92 factor: 41504779040362072486741147317329424235777767852517739678824079973857105583247144975259600203
Fri May 16 01:29:50 2008  elapsed time 01:08:56 (Msieve 1.35)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 51.96 hours.
Scaled time: 73.43 units (timescale=1.413).
Factorization parameters were as follows:
name: KA_1_7_163_9
n: 33994684810970224044938855284325010320587366934543670749637725820422739011723947723559014858582979941037256593746246806758495085353818012064597627409719
skew: 1.47
deg: 5
c5: 1
c0: 220
m: 2000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3400223)
Primes: RFBsize:230209, AFBsize:230048, largePrimes:7594820 encountered
Relations: rels:7045114, finalFF:515446
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 51.77 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 51.96 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

May 15, 2008 (4th)

By Philippe Strohl / GMP-ECM, Msieve

(10¹⁹⁸+71)/9 = (1)₁₉₇9_<198> = 4001 · 5031332503_<10> · 58763767963_<11> · 13275389735735891_<17> · 1080515019909211499629_<22> · C136

C136 = P41 · P42 · P55

P41 = 10069084871636180530120147336924416212569_<41>

P42 = 372936171880615158098090212029283260211837_<42>

P55 = 1743788007353172537521605567071655468363222761077697113_<55>

May 15, 2008 (3rd)

By Jo Yeong Uk / GGNFS

(17·10¹⁶⁰+1)/9 = 1(8)₁₅₉9_<161> = 13 · 2776731921313909477_<19> · 23804872312724088177544609_<26> · C116

C116 = P49 · P67

P49 = 3019027540589841111615402443598033601002863914943_<49>

P67 = 7281086248778730252929784206334560094320704875958402009234594411847_<67>

Number: 18889_160
N=21981799910472962006573451120284964892454411201578582142123383849630370984496422039098541921072986649975632919529721
  ( 116 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=3019027540589841111615402443598033601002863914943 (pp49)
 r2=7281086248778730252929784206334560094320704875958402009234594411847 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.37 hours.
Scaled time: 58.03 units (timescale=2.381).
Factorization parameters were as follows:
n: 21981799910472962006573451120284964892454411201578582142123383849630370984496422039098541921072986649975632919529721
m: 100000000000000000000000000000000
c5: 17
c0: 1
skew: 0.57
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:282982, largePrimes:5612739 encountered
Relations: rels:5636302, finalFF:651682
Max relations in full relation-set: 28
Initial matrix: 566193 x 651682 with sparse part having weight 40463301.
Pruned matrix : 498218 x 501112 with weight 27564761.
Total sieving time: 23.12 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 1.14 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 24.37 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047200k/8912896k available (2439k kernel code, 339088k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673806)
Calibrating delay using timer specific routine.. 5344.78 BogoMIPS (lpj=2672394)
Calibrating delay using timer specific routine.. 5344.44 BogoMIPS (lpj=2672223)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672388)

May 15, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(17·10¹⁵⁰+1)/9 = 1(8)₁₄₉9_<151> = 12599100967_<11> · 232362627870787_<15> · C126

C126 = P50 · P77

P50 = 12255622955186676467421637879285692660200973908309_<50>

P77 = 52645976406605495742233878007732625356159233240897545278160906703716316402849_<77>

Number: 18889_150
N=645209236947010492147224285543187145714532531053986933972672816337481145452624873946152946638065994199823548790633407632372341
  ( 126 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=12255622955186676467421637879285692660200973908309 (pp50)
 r2=52645976406605495742233878007732625356159233240897545278160906703716316402849 (pp77)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 27.02 hours.
Scaled time: 18.02 units (timescale=0.667).
Factorization parameters were as follows:
name: 18889_150
n: 645209236947010492147224285543187145714532531053986933972672816337481145452624873946152946638065994199823548790633407632372341
m: 1000000000000000000000000000000
c5: 17
c0: 1
skew: 0.57
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:176118, largePrimes:5313564 encountered
Relations: rels:5181418, finalFF:453835
Max relations in full relation-set: 28
Initial matrix: 352485 x 453835 with sparse part having weight 36996961.
Pruned matrix : 294072 x 295898 with weight 21718071.
Total sieving time: 23.62 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.06 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 27.02 hours.
 --------- CPU info (if available) ----------

May 15, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(17·10¹⁵⁶+1)/9 = 1(8)₁₅₅9_<157> = 1570653419_<10> · 413097321610859_<15> · 67407421335827431871_<20> · C113

C113 = P43 · P71

P43 = 1683915841330240179281702206131814655635817_<43>

P71 = 25647531544462176640389814319070297296091174784612085044944710867824487_<71>

Number: n
N=43188284658736900485468870637293355701575449624772259430741937853997084709199848904019254042856968584304546850879
  ( 113 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=1683915841330240179281702206131814655635817 (pp43)
 r2=25647531544462176640389814319070297296091174784612085044944710867824487 (pp71)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 18.48 hours.
Scaled time: 33.68 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_1_8_155_9
n: 43188284658736900485468870637293355701575449624772259430741937853997084709199848904019254042856968584304546850879
skew: 0.36
deg: 5
c5: 170
c0: 1
m: 10000000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:148933, AFBsize:149105, largePrimes:6785053 encountered
Relations: rels:6136287, finalFF:337877
Max relations in full relation-set: 48
Initial matrix: 298105 x 337877 with sparse part having weight 40377415.
Pruned matrix : 280312 x 281866 with weight 28247297.
Total sieving time: 17.45 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.83 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 18.48 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(13·10¹⁶⁸+23)/9 = 1(4)₁₆₇7_<169> = 6197231736504198581_<19> · 6827481749527884299_<19> · C131

C131 = P57 · P75

P57 = 125991706661408379069740433560492000863719150637957632449_<57>

P75 = 270957140149426777544289571433775011527741409316792143226462515238075645737_<75>

Number: n
N=34138352519520697488492384808044363669564458449619491153150511809519512581286624284223734680550286431913886638391088083143379719913
  ( 131 digits)
SNFS difficulty: 169 digits.
Divisors found:

Thu May 15 13:35:04 2008  prp57 factor: 125991706661408379069740433560492000863719150637957632449
Thu May 15 13:35:04 2008  prp75 factor: 270957140149426777544289571433775011527741409316792143226462515238075645737
Thu May 15 13:35:04 2008  elapsed time 01:35:31 (Msieve 1.35)

Version: GGNFS-0.77.1-20050930-k8
Total time: 71.47 hours.
Scaled time: 60.11 units (timescale=0.841).
Factorization parameters were as follows:
name: KA_1_4_167_7
n: 34138352519520697488492384808044363669564458449619491153150511809519512581286624284223734680550286431913886638391088083143379719913
type: snfs
deg: 5
c5: 13000
c0: 23
skew: 0.28
m: 1000000000000000000000000000000000
rlim: 3400000
alim: 3400000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 9101657)
Primes: RFBsize:243539, AFBsize:243864, largePrimes:6295660 encountered
Relations: rels:6358983, finalFF:386411
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 71.23 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,48,48,2.5,2.5,100000
total time: 71.47 hours.
 --------- CPU info (if available) ----------

(17·10¹⁶⁶+1)/9 = 1(8)₁₆₅9_<167> = 13 · 745033 · 7085413956200779_<16> · 671347539145262415473123_<24> · C120

C120 = P33 · P87

P33 = 878173932625410668935107562634861_<33>

P87 = 466868291565041584191404564367635894529401621360028875543317445660814498485125130692393_<87>

May 14, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(17·10¹³⁶+1)/9 = 1(8)₁₃₅9_<137> = 13 · 131 · 683 · 456409592321987984917_<21> · C110

C110 = P45 · P66

P45 = 135271113016603325460958519014799560369771317_<45>

P66 = 263033602744615290623211932004282702100555610794776909675214160549_<66>

Number: 18889_136
N=35580848204031197632957661319571263404262342057907723715152309747795286599815779076172254024688540843253173033
  ( 110 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=135271113016603325460958519014799560369771317 (pp45)
 r2=263033602744615290623211932004282702100555610794776909675214160549 (pp66)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 8.98 hours.
Scaled time: 6.08 units (timescale=0.677).
Factorization parameters were as follows:
name: 18889_136
n: 35580848204031197632957661319571263404262342057907723715152309747795286599815779076172254024688540843253173033
m: 1000000000000000000000000000
c5: 170
c0: 1
skew: 0.36
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1300001)
Primes: RFBsize:78498, AFBsize:63758, largePrimes:1536783 encountered
Relations: rels:1537478, finalFF:174059
Max relations in full relation-set: 28
Initial matrix: 142323 x 174059 with sparse part having weight 14424184.
Pruned matrix : 132346 x 133121 with weight 9309259.
Total sieving time: 8.46 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.37 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 8.98 hours.
 --------- CPU info (if available) ----------

May 14, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(17·10¹⁴⁶+1)/9 = 1(8)₁₄₅9_<147> = 3² · 7 · 171598487 · C137

C137 = P40 · P97

P40 = 3210829111399465992677672913074119450171_<40>

P97 = 5441707777847825911517573089597079709549116073352279752874414335353976222031085839213018547986339_<97>

Number: n
N=17472393748842697564100529228848415796336457975702693130378453345976558074187660708043800543522486486548479317292793680457479225899213969
  ( 137 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=3210829111399465992677672913074119450171 (pp40)
 r2=5441707777847825911517573089597079709549116073352279752874414335353976222031085839213018547986339 (pp97)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.41 hours.
Scaled time: 11.66 units (timescale=1.818).
Factorization parameters were as follows:
name: KA_1_8_145_9
n: 17472393748842697564100529228848415796336457975702693130378453345976558074187660708043800543522486486548479317292793680457479225899213969
skew: 0.36
deg: 5
c5: 170
c0: 1
m: 100000000000000000000000000000
type: snfs
rlim: 1600000
alim: 1600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:121127, AFBsize:121025, largePrimes:6566213 encountered
Relations: rels:5867774, finalFF:300967
Max relations in full relation-set: 48
Initial matrix: 242219 x 300967 with sparse part having weight 33169592.
Pruned matrix : 220316 x 221591 with weight 18533404.
Total sieving time: 5.78 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.40 hours.
Total square root time: 0.11 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1600000,1600000,28,28,48,48,2.5,2.5,100000
total time: 6.41 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

May 14, 2008

By Jo Yeong Uk / GGNFS

(17·10¹⁵⁵+1)/9 = 1(8)₁₅₄9_<156> = 3² · 233707265677436331129169_<24> · C131

C131 = P43 · P89

P43 = 7432798877836175924862195765978994856188367_<43>

P89 = 12082013223071163764032145160054775612064289873932471918156403070758301397897940923198927_<89>

Number: 18889_155
N=89803174326445185097380030661135204861505848627374060515671755601306327312337475431786542613761787651305075448165637035599724282209
  ( 131 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=7432798877836175924862195765978994856188367 (pp43)
 r2=12082013223071163764032145160054775612064289873932471918156403070758301397897940923198927 (pp89)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 15.92 hours.
Scaled time: 37.90 units (timescale=2.380).
Factorization parameters were as follows:
n: 89803174326445185097380030661135204861505848627374060515671755601306327312337475431786542613761787651305075448165637035599724282209
m: 10000000000000000000000000000000
c5: 17
c0: 1
skew: 0.57
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:216621, largePrimes:5652876 encountered
Relations: rels:5672516, finalFF:606082
Max relations in full relation-set: 28
Initial matrix: 433502 x 606082 with sparse part having weight 47143850.
Pruned matrix : 323248 x 325479 with weight 29229758.
Total sieving time: 15.24 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.58 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 15.92 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047200k/8912896k available (2439k kernel code, 339088k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348)
Calibrating delay using timer specific routine.. 5344.38 BogoMIPS (lpj=2672192)
Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672358)

May 13, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(17·10¹³⁸+1)/9 = 1(8)₁₃₇9_<139> = 4510061376844003663_<19> · C120

C120 = P50 · P71

P50 = 31840264865105550282268277463062426428832090106619_<50>

P71 = 13153680477112431114501007873566580075045768560448657392843078514243637_<71>

Number: 18889_138
N=418816670342227751757005180681984987355373125957642242039607767360886430241132243704166233930906908148091812021472333303
  ( 120 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=31840264865105550282268277463062426428832090106619 (pp50)
 r2=13153680477112431114501007873566580075045768560448657392843078514243637 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 13.84 hours.
Scaled time: 9.37 units (timescale=0.677).
Factorization parameters were as follows:
name: 18889_138
n: 418816670342227751757005180681984987355373125957642242039607767360886430241132243704166233930906908148091812021472333303
m: 1000000000000000000000000000
c5: 17000
c0: 1
skew: 0.14
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1900001)
Primes: RFBsize:78498, AFBsize:63878, largePrimes:1627941 encountered
Relations: rels:1648597, finalFF:175753
Max relations in full relation-set: 28
Initial matrix: 142443 x 175753 with sparse part having weight 18062658.
Pruned matrix : 133976 x 134752 with weight 12318345.
Total sieving time: 13.17 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.49 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 13.84 hours.
 --------- CPU info (if available) ----------

(17·10¹³³+1)/9 = 1(8)₁₃₂9_<134> = 107 · 227 · 4813 · 685170157317962653049_<21> · C105

C105 = P37 · P69

P37 = 1234014527104641903445029379611028313_<37>

P69 = 191100667533990229020460551789426582958270387694681889491226478787821_<69>

Number: 18889_133
N=235820999876338346487677767402600117955663203582401779655854919539426132493778302474140196027811550575973
  ( 105 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=1234014527104641903445029379611028313 (pp37)
 r2=191100667533990229020460551789426582958270387694681889491226478787821 (pp69)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 7.65 hours.
Scaled time: 5.18 units (timescale=0.677).
Factorization parameters were as follows:
name: 18889_133
n: 235820999876338346487677767402600117955663203582401779655854919539426132493778302474140196027811550575973
m: 100000000000000000000000000
c5: 17000
c0: 1
skew: 0.14
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1150001)
Primes: RFBsize:78498, AFBsize:63878, largePrimes:1524268 encountered
Relations: rels:1529587, finalFF:179780
Max relations in full relation-set: 28
Initial matrix: 142443 x 179780 with sparse part having weight 13890647.
Pruned matrix : 129461 x 130237 with weight 8271331.
Total sieving time: 7.21 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 7.65 hours.
 --------- CPU info (if available) ----------

May 13, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(17·10¹⁴⁸+1)/9 = 1(8)₁₄₇9_<149> = 13 · 23 · 79 · 2579 · C141

C141 = P39 · P50 · P54

P39 = 125681550014263882017357848163817899931_<39>

P50 = 20778615782132915248991027933944063474034054154181_<50>

P54 = 118732236759698250781220009050291048271486353167257761_<54>

Number: n
N=310067887339372044057852532081215001964982278863308124029803280292445671423201078818835634127341864552129161310084319113472281721057927336871
  ( 141 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=125681550014263882017357848163817899931 (pp39)
 r2=20778615782132915248991027933944063474034054154181 (pp50)
 r3=118732236759698250781220009050291048271486353167257761 (pp54)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 10.43 hours.
Scaled time: 19.02 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_1_8_147_9
n: 310067887339372044057852532081215001964982278863308124029803280292445671423201078818835634127341864552129161310084319113472281721057927336871
skew: 1.43
deg: 5
c5: 17
c0: 100
m: 1000000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 750001)
Primes: RFBsize:114155, AFBsize:114282, largePrimes:6189604 encountered
Relations: rels:5491469, finalFF:264671
Max relations in full relation-set: 48
Initial matrix: 228504 x 264671 with sparse part having weight 29914799.
Pruned matrix : 213309 x 214515 with weight 19462184.
Total sieving time: 9.85 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.39 hours.
Total square root time: 0.07 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000
total time: 10.43 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(13·10¹⁷⁰+23)/9 = 1(4)₁₆₉7_<171> = 3² · 7² · C168

C168 = P42 · P126

P42 = 446315784615474862410026239878656530619417_<42>

P126 = 733871474114925252241865494143887940469879995924979497675057972980625973036265099361056138544027803999139735087936933070351151_<126>

Number: n
N=327538422776518014613252708490803728898966994205089443184681279919375157470395565633660871756109851347946586041824137062232300327538422776518014613252708490803728898967
  ( 168 digits)
SNFS difficulty: 171 digits.
Divisors found:

Tue May 13 13:00:56 2008  prp42 factor: 446315784615474862410026239878656530619417
Tue May 13 13:00:56 2008  prp126 factor: 733871474114925252241865494143887940469879995924979497675057972980625973036265099361056138544027803999139735087936933070351151
Tue May 13 13:00:56 2008  elapsed time 01:20:02 (Msieve 1.35)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 62.30 hours.
Scaled time: 113.95 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_4_169_7
n: 327538422776518014613252708490803728898966994205089443184681279919375157470395565633660871756109851347946586041824137062232300327538422776518014613252708490803728898967
skew: 1.12
deg: 5
c5: 13
c0: 23
m: 10000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4100573)
Primes: RFBsize:250150, AFBsize:249461, largePrimes:7723547 encountered
Relations: rels:7159466, finalFF:540371
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 62.05 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 62.30 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(17·10¹⁵⁷+1)/9 = 1(8)₁₅₆9_<158> = 31 · 89 · 4993 · C151

C151 = P68 · P84

P68 = 10389319827483729125541276705287706636888901647006845589895676437721_<68>

P84 = 131979363484273526432917168541620540675529931962287016158799908174443540210525526807_<84>

Number: n
N=1371175817865845012948456863812954583599996783382846088829463742090604184668894472478134040711645734175645025100300906146378680706732730562830651486847
  ( 151 digits)
SNFS difficulty: 158 digits.
Divisors found:

Tue May 13 23:42:18 2008  prp68 factor: 10389319827483729125541276705287706636888901647006845589895676437721
Tue May 13 23:42:18 2008  prp84 factor: 131979363484273526432917168541620540675529931962287016158799908174443540210525526807
Tue May 13 23:42:18 2008  elapsed time 00:51:03 (Msieve 1.35)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 27.44 hours.
Scaled time: 39.71 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_1_8_156_9
n: 1371175817865845012948456863812954583599996783382846088829463742090604184668894472478134040711645734175645025100300906146378680706732730562830651486847
skew: 0.23
deg: 5
c5: 1700
c0: 1
m: 10000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1300001)
Primes: RFBsize:203362, AFBsize:203472, largePrimes:7091762 encountered
Relations: rels:6614208, finalFF:513664
Max relations in full relation-set: 28
Initial matrix: 406901 x 513664 with sparse part having weight 38635564.
Pruned matrix : 
Total sieving time: 27.25 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 27.44 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 13, 2008

By Jo Yeong Uk / GGNFS

(17·10¹⁵⁸+1)/9 = 1(8)₁₅₇9_<159> = 3 · 7² · 5088556838519157777959041_<25> · 773952255048761259605344760131_<30> · C102

C102 = P50 · P53

P50 = 16713340926956566201930088601647275580275612424791_<50>

P53 = 19521671710027297651795646344507570669558565769398567_<53>

Number: 18889_158
N=326272354753809409783926743501951526769302667744497378253582147117816704691884198427382049596590674497
  ( 102 digits)
Divisors found:
 r1=16713340926956566201930088601647275580275612424791 (pp50)
 r2=19521671710027297651795646344507570669558565769398567 (pp53)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.34 hours.
Scaled time: 10.10 units (timescale=2.324).
Factorization parameters were as follows:
name: 18889_158
n: 326272354753809409783926743501951526769302667744497378253582147117816704691884198427382049596590674497
skew: 9707.57
# norm 1.66e+14
c5: 58140
c4: -1204082396
c3: -16047945750919
c2: 95250222814570675
c1: 627468897543127179213
c0: -2238096650248582827457545
# alpha -5.97
Y1: 22959935999
Y0: -22378083790384944344
# Murphy_E 2.69e-09
# M 198217674374385453969471597599128458274937908501156646603931004074576906134386477000765936111891797998
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1500001)
Primes: RFBsize:135072, AFBsize:135135, largePrimes:4297434 encountered
Relations: rels:4209433, finalFF:333131
Max relations in full relation-set: 28
Initial matrix: 270296 x 333131 with sparse part having weight 25414943.
Pruned matrix : 224093 x 225508 with weight 14231777.
Polynomial selection time: 0.31 hours.
Total sieving time: 3.72 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 4.34 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047200k/8912896k available (2439k kernel code, 339088k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348)
Calibrating delay using timer specific routine.. 5344.38 BogoMIPS (lpj=2672192)
Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672358)

(17·10¹⁴³+1)/9 = 1(8)₁₄₂9_<144> = 3 · 899753171 · 82020986669_<11> · C123

C123 = P42 · P82

P42 = 651294001984968690031508343706506092549381_<42>

P82 = 1309965033693254983247199110421891812341830657407559148798183964348719311977188577_<82>

Number: 18889_143
N=853172369254454387976182331880392282540220002760894331827020690232607449767249084940972241338131506687593970016650921620837
  ( 123 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=651294001984968690031508343706506092549381 (pp42)
 r2=1309965033693254983247199110421891812341830657407559148798183964348719311977188577 (pp82)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 7.26 hours.
Scaled time: 17.35 units (timescale=2.389).
Factorization parameters were as follows:
n: 853172369254454387976182331880392282540220002760894331827020690232607449767249084940972241338131506687593970016650921620837
m: 100000000000000000000000000000
c5: 17
c0: 100
skew: 1.43
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1425001)
Primes: RFBsize:135072, AFBsize:135058, largePrimes:3620149 encountered
Relations: rels:3640316, finalFF:341971
Max relations in full relation-set: 28
Initial matrix: 270197 x 341971 with sparse part having weight 29294147.
Pruned matrix : 237673 x 239087 with weight 16973507.
Total sieving time: 6.98 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 7.26 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047200k/8912896k available (2439k kernel code, 339088k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348)
Calibrating delay using timer specific routine.. 5344.38 BogoMIPS (lpj=2672192)
Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672358)

May 12, 2008 (3rd)

By Wataru Sakai / GGNFS

10¹⁸¹-9 = (9)₁₈₀1_<181> = 613 · 4721990197_<10> · C169

C169 = P78 · P92

P78 = 118046288030005689138006772776064145473173086074955176614021148886231992477409_<78>

P92 = 29265915150079883819125682044728327718073357005292178916251770323960139756081440411297901759_<92>

Number: 99991
N=3454732649268037140651629992081894263362774944623633726957884046515864376096038447979084779442532000245131642678651564893028283221292314837219802797322498616193908862431
  ( 169 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=118046288030005689138006772776064145473173086074955176614021148886231992477409 (pp78)
 r2=29265915150079883819125682044728327718073357005292178916251770323960139756081440411297901759 (pp92)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 438.14 hours.
Scaled time: 880.23 units (timescale=2.009).
Factorization parameters were as follows:
n: 3454732649268037140651629992081894263362774944623633726957884046515864376096038447979084779442532000245131642678651564893028283221292314837219802797322498616193908862431
m: 1000000000000000000000000000000000000
c5: 10
c0: -9
skew: 0.98
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 9400001)
Primes: RFBsize:501962, AFBsize:501581, largePrimes:6755535 encountered
Relations: rels:7413387, finalFF:1315241
Max relations in full relation-set: 32
Initial matrix: 1003610 x 1315241 with sparse part having weight 83791927.
Pruned matrix : 736585 x 741667 with weight 65509568.
Total sieving time: 433.29 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 4.53 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 438.14 hours.
 --------- CPU info (if available) ----------

May 12, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(43·10¹⁶³-7)/9 = 4(7)₁₆₃_<164> = 17 · 665881683559_<12> · 3731199745103581640718101353_<28> · C124

C124 = P61 · P63

P61 = 4940707832454493415501651784634079823643014735022300729459783_<61>

P63 = 228950862555947401946978886763873337701268538465930614150009641_<63>

Number: 47777_163
N=1131179319877381526484592406638873153964107702611935425473131250001541648222905288588232080460486389335504040917062171767903
  ( 124 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=4940707832454493415501651784634079823643014735022300729459783 (pp61)
 r2=228950862555947401946978886763873337701268538465930614150009641 (pp63)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 181.33 hours.
Scaled time: 122.58 units (timescale=0.676).
Factorization parameters were as follows:
name: 47777_163
n: 1131179319877381526484592406638873153964107702611935425473131250001541648222905288588232080460486389335504040917062171767903
m: 100000000000000000000000000000000
c5: 43000
c0: -7
skew: 0.17
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 6700001)
Primes: RFBsize:348513, AFBsize:348291, largePrimes:6066233 encountered
Relations: rels:6239037, finalFF:799065
Max relations in full relation-set: 28
Initial matrix: 696871 x 799065 with sparse part having weight 64573761.
Pruned matrix : 622367 x 625915 with weight 49390580.
Total sieving time: 156.93 hours.
Total relation processing time: 0.57 hours.
Matrix solve time: 23.53 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 181.33 hours.
 --------- CPU info (if available) ----------

(17·10¹¹⁹+1)/9 = 1(8)₁₁₈9_<120> = 3² · 29 · 47 · 71 · 2417 · 44567363 · C103

C103 = P41 · P62

P41 = 86639197230970329577098695493425102913119_<41>

P62 = 23238157441907373887888004008759141749503788540363070255980273_<62>

Number: 18889_119
N=2013335305893753905147239573058748417504252779225347674038251424889645608319577440321753664083296901487
  ( 103 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=86639197230970329577098695493425102913119 (pp41)
 r2=23238157441907373887888004008759141749503788540363070255980273 (pp62)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.07 hours.
Scaled time: 1.40 units (timescale=0.676).
Factorization parameters were as follows:
name: 18889_119
n: 2013335305893753905147239573058748417504252779225347674038251424889645608319577440321753664083296901487
m: 1000000000000000000000000
c5: 17
c0: 10
skew: 0.9
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63823, largePrimes:2084723 encountered
Relations: rels:2152414, finalFF:219464
Max relations in full relation-set: 28
Initial matrix: 112986 x 219464 with sparse part having weight 18433757.
Pruned matrix : 86159 x 86787 with weight 4759705.
Total sieving time: 1.86 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.07 hours.
 --------- CPU info (if available) ----------

May 12, 2008

By Robert Backstrom / GGNFS, Msieve

(17·10¹⁵⁹-53)/9 = 1(8)₁₅₈3_<160> = 7 · 733 · C156

C156 = P47 · P109

P47 = 64373087450280690223885039799015227383176824847_<47>

P109 = 5718736130150877068395855148563309851888644433107510229967183373492458900540607629747479591403697254369712119_<109>

Number: n
N=368132701011282184542757530479222157257627926113601420559128608241841529699647025704324476493644297191364039931570627341432252755581541393273999003876220793
  ( 156 digits)
SNFS difficulty: 161 digits.
Divisors found:

Mon May 12 02:28:47 2008  prp47 factor: 64373087450280690223885039799015227383176824847
Mon May 12 02:28:47 2008  prp109 factor: 5718736130150877068395855148563309851888644433107510229967183373492458900540607629747479591403697254369712119
Mon May 12 02:28:47 2008  elapsed time 01:46:51 (Msieve 1.35)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 35.79 hours.
Scaled time: 65.47 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_8_158_3
n: 368132701011282184542757530479222157257627926113601420559128608241841529699647025704324476493644297191364039931570627341432252755581541393273999003876220793
skew: 1.99
deg: 5
c5: 17
c0: -530
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2400169)
Primes: RFBsize:216816, AFBsize:217351, largePrimes:7254373 encountered
Relations: rels:6651059, finalFF:451072
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 35.61 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 35.79 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(16·10¹⁷⁰+11)/9 = 1(7)₁₆₉9_<171> = 97 · C169

C169 = P48 · P121

P48 = 544927506016603202875320936707390870032381644203_<48>

P121 = 3363310854033769132027671298925141168506829437495958093452712839551811960294973871579104443447473715330880252358213138169_<121>

Number: n
N=1832760595647193585337915234822451317296678121420389461626575028636884306987399770904925544100801832760595647193585337915234822451317296678121420389461626575028636884307
  ( 169 digits)
SNFS difficulty: 171 digits.
Divisors found:

Mon May 12 13:11:07 2008  prp48 factor: 544927506016603202875320936707390870032381644203
Mon May 12 13:11:07 2008  prp121 factor: 3363310854033769132027671298925141168506829437495958093452712839551811960294973871579104443447473715330880252358213138169
Mon May 12 13:11:07 2008  elapsed time 01:00:41 (Msieve 1.35)

Version: GGNFS-0.77.1-20050930-k8
Total time: 45.52 hours.
Scaled time: 38.20 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_1_7_169_9
n: 1832760595647193585337915234822451317296678121420389461626575028636884306987399770904925544100801832760595647193585337915234822451317296678121420389461626575028636884307
type: snfs
deg: 5
c5: 1
c0: 22
skew: 1.86
m: 20000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5399990)
Primes: RFBsize:250150, AFBsize:250502, largePrimes:6093794 encountered
Relations: rels:6215521, finalFF:628867
Max relations in full relation-set: 28
Initial matrix: 500716 x 628867 with sparse part having weight 69517955.
Pruned matrix : 
Total sieving time: 45.32 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,48,48,2.5,2.5,100000
total time: 45.52 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(17·10¹⁵⁴+1)/9 = 1(8)₁₅₃9_<155> = 13 · 71 · C152

C152 = P75 · P78

P75 = 140600607147819071282411043598609766109102241498072762816470647254054550719_<75>

P78 = 145551777955531635886729066649473155038928609925267339235336817734887886875397_<78>

Number: n
N=20464668351992295654267485253400746358492837366076802696521006380161309738774527506921873119056217647766943541591428915372577344408330323823281569760443
  ( 152 digits)
SNFS difficulty: 156 digits.
Divisors found:

Mon May 12 18:53:45 2008  prp75 factor: 140600607147819071282411043598609766109102241498072762816470647254054550719
Mon May 12 18:53:45 2008  prp78 factor: 145551777955531635886729066649473155038928609925267339235336817734887886875397
Mon May 12 18:53:45 2008  elapsed time 00:43:24 (Msieve 1.35)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.12 hours.
Scaled time: 27.69 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_1_8_153_9
n: 20464668351992295654267485253400746358492837366076802696521006380161309738774527506921873119056217647766943541591428915372577344408330323823281569760443
skew: 0.90
deg: 5
c5: 17
c0: 10
m: 10000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 900000)
Primes: RFBsize:203362, AFBsize:203567, largePrimes:6640756 encountered
Relations: rels:6105592, finalFF:466574
Max relations in full relation-set: 28
Initial matrix: 406994 x 466574 with sparse part having weight 28924041.
Pruned matrix : 355349 x 357447 with weight 18031557.
Total sieving time: 18.96 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 19.12 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 11, 2008 (3rd)

By Sinkiti Sibata / GGNFS, Msieve

(17·10¹³²+1)/9 = 1(8)₁₃₁9_<133> = 8803 · 29339 · 78461252861251661_<17> · C107

C107 = P33 · P75

P33 = 764434950764564155154419754456677_<33>

P75 = 121936753814368589908864502423562855042102683681063541354324629952254041961_<75>

Number: 18889_132
N=93212716398477633470908531852402735461671942666641846206285286787028561038608429955683517892828816714623597
  ( 107 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=764434950764564155154419754456677 (pp33)
 r2=121936753814368589908864502423562855042102683681063541354324629952254041961 (pp75)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 6.63 hours.
Scaled time: 4.49 units (timescale=0.677).
Factorization parameters were as follows:
name: 18889_132
n: 93212716398477633470908531852402735461671942666641846206285286787028561038608429955683517892828816714623597
m: 100000000000000000000000000
c5: 1700
c0: 1
skew: 0.23
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1100001)
Primes: RFBsize:63951, AFBsize:63983, largePrimes:1499560 encountered
Relations: rels:1488645, finalFF:158343
Max relations in full relation-set: 28
Initial matrix: 128001 x 158343 with sparse part having weight 12844094.
Pruned matrix : 119794 x 120498 with weight 8038832.
Total sieving time: 6.24 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 6.63 hours.
 --------- CPU info (if available) ----------

(17·10¹¹³+1)/9 = 1(8)₁₁₂9_<114> = 3 · 53 · 89 · 2220046208670695120267_<22> · C88

C88 = P35 · P54

P35 = 18762080918146736784154405984746413_<35>

P54 = 320461795922942801708809319235463489099097846767274609_<54>

Sun May 11 03:36:19 2008  Msieve v. 1.35
Sun May 11 03:36:19 2008  random seeds: 9a6638be 9dc82e78
Sun May 11 03:36:19 2008  factoring 6012530146280878871724387278640046283639523062843790961849685220400824632099961998727517 (88 digits)
Sun May 11 03:36:21 2008  searching for 15-digit factors
Sun May 11 03:36:23 2008  commencing quadratic sieve (88-digit input)
Sun May 11 03:36:23 2008  using multiplier of 13
Sun May 11 03:36:23 2008  using 64kb Pentium 4 sieve core
Sun May 11 03:36:23 2008  sieve interval: 14 blocks of size 65536
Sun May 11 03:36:23 2008  processing polynomials in batches of 8
Sun May 11 03:36:23 2008  using a sieve bound of 1524241 (58000 primes)
Sun May 11 03:36:23 2008  using large prime bound of 121939280 (26 bits)
Sun May 11 03:36:23 2008  using double large prime bound of 358970217792320 (42-49 bits)
Sun May 11 03:36:23 2008  using trial factoring cutoff of 49 bits
Sun May 11 03:36:23 2008  polynomial 'A' values have 11 factors
Sun May 11 04:48:35 2008  58535 relations (17055 full + 41480 combined from 603615 partial), need 58096
Sun May 11 04:48:38 2008  begin with 620670 relations
Sun May 11 04:48:38 2008  reduce to 137330 relations in 11 passes
Sun May 11 04:48:38 2008  attempting to read 137330 relations
Sun May 11 04:48:42 2008  recovered 137330 relations
Sun May 11 04:48:42 2008  recovered 107941 polynomials
Sun May 11 04:48:42 2008  attempting to build 58535 cycles
Sun May 11 04:48:42 2008  found 58534 cycles in 4 passes
Sun May 11 04:48:42 2008  distribution of cycle lengths:
Sun May 11 04:48:42 2008     length 1 : 17055
Sun May 11 04:48:42 2008     length 2 : 11927
Sun May 11 04:48:42 2008     length 3 : 10231
Sun May 11 04:48:42 2008     length 4 : 7473
Sun May 11 04:48:42 2008     length 5 : 4986
Sun May 11 04:48:42 2008     length 6 : 3101
Sun May 11 04:48:42 2008     length 7 : 1787
Sun May 11 04:48:42 2008     length 9+: 1974
Sun May 11 04:48:42 2008  largest cycle: 16 relations
Sun May 11 04:48:43 2008  matrix is 58000 x 58534 (13.8 MB) with weight 3393855 (57.98/col)
Sun May 11 04:48:43 2008  sparse part has weight 3393855 (57.98/col)
Sun May 11 04:48:44 2008  filtering completed in 4 passes
Sun May 11 04:48:44 2008  matrix is 52822 x 52886 (12.6 MB) with weight 3079016 (58.22/col)
Sun May 11 04:48:44 2008  sparse part has weight 3079016 (58.22/col)
Sun May 11 04:48:44 2008  saving the first 48 matrix rows for later
Sun May 11 04:48:44 2008  matrix is 52774 x 52886 (9.2 MB) with weight 2535293 (47.94/col)
Sun May 11 04:48:44 2008  sparse part has weight 2089021 (39.50/col)
Sun May 11 04:48:44 2008  matrix includes 64 packed rows
Sun May 11 04:48:44 2008  using block size 21154 for processor cache size 512 kB
Sun May 11 04:48:45 2008  commencing Lanczos iteration
Sun May 11 04:48:45 2008  memory use: 8.3 MB
Sun May 11 04:49:16 2008  lanczos halted after 836 iterations (dim = 52774)
Sun May 11 04:49:17 2008  recovered 18 nontrivial dependencies
Sun May 11 04:49:17 2008  prp35 factor: 18762080918146736784154405984746413
Sun May 11 04:49:17 2008  prp54 factor: 320461795922942801708809319235463489099097846767274609
Sun May 11 04:49:17 2008  elapsed time 01:12:58

(17·10¹²⁹+1)/9 = 1(8)₁₂₈9_<130> = 852239 · 273146271888899_<15> · 30492449909076721_<17> · C93

C93 = P31 · P62

P31 = 6729959298046035632672774532523_<31>

P62 = 39540756448263316717593054313840418944154669628044642036622503_<62>

Sun May 11 05:52:11 2008  Msieve v. 1.35
Sun May 11 05:52:11 2008  random seeds: 8b66ad6c bf0aea57
Sun May 11 05:52:11 2008  factoring 266107681510763448035340107082246050075465189572361909539503641703667818407790475101647165069 (93 digits)
Sun May 11 05:52:13 2008  searching for 15-digit factors
Sun May 11 05:52:14 2008  commencing quadratic sieve (93-digit input)
Sun May 11 05:52:15 2008  using multiplier of 5
Sun May 11 05:52:15 2008  using 64kb Pentium 4 sieve core
Sun May 11 05:52:15 2008  sieve interval: 18 blocks of size 65536
Sun May 11 05:52:15 2008  processing polynomials in batches of 6
Sun May 11 05:52:15 2008  using a sieve bound of 1909319 (71765 primes)
Sun May 11 05:52:15 2008  using large prime bound of 231027599 (27 bits)
Sun May 11 05:52:15 2008  using double large prime bound of 1133952533144101 (42-51 bits)
Sun May 11 05:52:15 2008  using trial factoring cutoff of 51 bits
Sun May 11 05:52:15 2008  polynomial 'A' values have 12 factors
Sun May 11 10:31:39 2008  72146 relations (17646 full + 54500 combined from 969220 partial), need 71861
Sun May 11 10:31:44 2008  begin with 986866 relations
Sun May 11 10:31:45 2008  reduce to 186840 relations in 11 passes
Sun May 11 10:31:45 2008  attempting to read 186840 relations
Sun May 11 10:31:51 2008  recovered 186840 relations
Sun May 11 10:31:51 2008  recovered 170297 polynomials
Sun May 11 10:31:51 2008  attempting to build 72146 cycles
Sun May 11 10:31:51 2008  found 72146 cycles in 5 passes
Sun May 11 10:31:51 2008  distribution of cycle lengths:
Sun May 11 10:31:51 2008     length 1 : 17646
Sun May 11 10:31:51 2008     length 2 : 12583
Sun May 11 10:31:51 2008     length 3 : 12249
Sun May 11 10:31:51 2008     length 4 : 9903
Sun May 11 10:31:51 2008     length 5 : 7433
Sun May 11 10:31:51 2008     length 6 : 4817
Sun May 11 10:31:51 2008     length 7 : 3200
Sun May 11 10:31:51 2008     length 9+: 4315
Sun May 11 10:31:51 2008  largest cycle: 22 relations
Sun May 11 10:31:51 2008  matrix is 71765 x 72146 (18.0 MB) with weight 4433526 (61.45/col)
Sun May 11 10:31:51 2008  sparse part has weight 4433526 (61.45/col)
Sun May 11 10:31:53 2008  filtering completed in 3 passes
Sun May 11 10:31:53 2008  matrix is 68458 x 68522 (17.1 MB) with weight 4218924 (61.57/col)
Sun May 11 10:31:53 2008  sparse part has weight 4218924 (61.57/col)
Sun May 11 10:31:53 2008  saving the first 48 matrix rows for later
Sun May 11 10:31:54 2008  matrix is 68410 x 68522 (10.0 MB) with weight 3180791 (46.42/col)
Sun May 11 10:31:54 2008  sparse part has weight 2218415 (32.38/col)
Sun May 11 10:31:54 2008  matrix includes 64 packed rows
Sun May 11 10:31:54 2008  using block size 21845 for processor cache size 512 kB
Sun May 11 10:31:54 2008  commencing Lanczos iteration
Sun May 11 10:31:54 2008  memory use: 10.3 MB
Sun May 11 10:32:41 2008  lanczos halted after 1084 iterations (dim = 68410)
Sun May 11 10:32:41 2008  recovered 18 nontrivial dependencies
Sun May 11 10:32:42 2008  prp31 factor: 6729959298046035632672774532523
Sun May 11 10:32:42 2008  prp62 factor: 39540756448263316717593054313840418944154669628044642036622503
Sun May 11 10:32:42 2008  elapsed time 04:40:31

(17·10¹⁴⁰+1)/9 = 1(8)₁₃₉9_<141> = 3 · 7 · 3023 · 7121 · 142888091809_<12> · 959922253880171_<15> · 43808521896921204679_<20> · C86

C86 = P30 · P56

P30 = 887678841787165579554448685089_<30>

P56 = 78336004908801861872486359113613068126829797389465976247_<56>

un May 11 10:42:17 2008  Msieve v. 1.35
Sun May 11 10:42:17 2008  random seeds: 9850883f 57e30385
Sun May 11 10:42:17 2008  factoring 69537214107678954149627935760226226356182538302600223483249920864963697363052857080983 (86 digits)
Sun May 11 10:42:18 2008  searching for 15-digit factors
Sun May 11 10:42:20 2008  commencing quadratic sieve (86-digit input)
Sun May 11 10:42:20 2008  using multiplier of 7
Sun May 11 10:42:20 2008  using 64kb Pentium 4 sieve core
Sun May 11 10:42:20 2008  sieve interval: 9 blocks of size 65536
Sun May 11 10:42:20 2008  processing polynomials in batches of 12
Sun May 11 10:42:20 2008  using a sieve bound of 1466053 (56000 primes)
Sun May 11 10:42:20 2008  using large prime bound of 117284240 (26 bits)
Sun May 11 10:42:20 2008  using double large prime bound of 334681134421600 (41-49 bits)
Sun May 11 10:42:20 2008  using trial factoring cutoff of 49 bits
Sun May 11 10:42:20 2008  polynomial 'A' values have 11 factors
Sun May 11 11:33:39 2008  56345 relations (16828 full + 39517 combined from 574612 partial), need 56096
Sun May 11 11:33:42 2008  begin with 591440 relations
Sun May 11 11:33:42 2008  reduce to 130331 relations in 10 passes
Sun May 11 11:33:42 2008  attempting to read 130331 relations
Sun May 11 11:33:46 2008  recovered 130331 relations
Sun May 11 11:33:46 2008  recovered 102621 polynomials
Sun May 11 11:33:46 2008  attempting to build 56345 cycles
Sun May 11 11:33:46 2008  found 56344 cycles in 4 passes
Sun May 11 11:33:46 2008  distribution of cycle lengths:
Sun May 11 11:33:46 2008     length 1 : 16828
Sun May 11 11:33:46 2008     length 2 : 11654
Sun May 11 11:33:46 2008     length 3 : 10013
Sun May 11 11:33:46 2008     length 4 : 7125
Sun May 11 11:33:46 2008     length 5 : 4675
Sun May 11 11:33:46 2008     length 6 : 2828
Sun May 11 11:33:46 2008     length 7 : 1601
Sun May 11 11:33:46 2008     length 9+: 1620
Sun May 11 11:33:46 2008  largest cycle: 18 relations
Sun May 11 11:33:46 2008  matrix is 56000 x 56344 (12.4 MB) with weight 3029132 (53.76/col)
Sun May 11 11:33:46 2008  sparse part has weight 3029132 (53.76/col)
Sun May 11 11:33:47 2008  filtering completed in 3 passes
Sun May 11 11:33:47 2008  matrix is 50377 x 50441 (11.2 MB) with weight 2735941 (54.24/col)
Sun May 11 11:33:47 2008  sparse part has weight 2735941 (54.24/col)
Sun May 11 11:33:47 2008  saving the first 48 matrix rows for later
Sun May 11 11:33:47 2008  matrix is 50329 x 50441 (6.9 MB) with weight 2087392 (41.38/col)
Sun May 11 11:33:48 2008  sparse part has weight 1507293 (29.88/col)
Sun May 11 11:33:48 2008  matrix includes 64 packed rows
Sun May 11 11:33:48 2008  using block size 20176 for processor cache size 512 kB
Sun May 11 11:33:48 2008  commencing Lanczos iteration
Sun May 11 11:33:48 2008  memory use: 7.0 MB
Sun May 11 11:34:14 2008  lanczos halted after 798 iterations (dim = 50327)
Sun May 11 11:34:14 2008  recovered 16 nontrivial dependencies
Sun May 11 11:34:16 2008  prp30 factor: 887678841787165579554448685089
Sun May 11 11:34:16 2008  prp56 factor: 78336004908801861872486359113613068126829797389465976247
Sun May 11 11:34:16 2008  elapsed time 00:51:59

May 11, 2008 (2nd)

By Robert Backstrom / GGNFS

(17·10¹¹⁵+1)/9 = 1(8)₁₁₄9_<116> = 4519 · C112

C112 = P38 · P74

P38 = 85206749882772292395357406238644765829_<38>

P74 = 49055767028910420725937601905379783432564947652856091509002810221880045139_<74>

Number: n
N=4179882471539917877603206215731110619360232106414890216616262201568685304024980944653438568021440338324604755231
  ( 112 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=85206749882772292395357406238644765829 (pp38)
 r2=49055767028910420725937601905379783432564947652856091509002810221880045139 (pp74)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.05 hours.
Scaled time: 1.53 units (timescale=1.453).
Factorization parameters were as follows:
name: KA_1_8_114_9
n: 4179882471539917877603206215731110619360232106414890216616262201568685304024980944653438568021440338324604755231
skew: 0.90
deg: 5
c5: 17
c0: 1
m: 100000000000000000000000
type: snfs
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 160001)
Primes: RFBsize:78498, AFBsize:78436, largePrimes:3886230 encountered
Relations: rels:3300843, finalFF:184286
Max relations in full relation-set: 28
Initial matrix: 156999 x 184286 with sparse part having weight 7862251.
Pruned matrix : 129226 x 130074 with weight 4084209.
Total sieving time: 0.86 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.12 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000
total time: 1.05 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(17·10¹³⁴+1)/9 = 1(8)₁₃₃9_<135> = 3 · 7 · 409 · 1301 · C128

C128 = P38 · P91

P38 = 12714871233905837021626832695666376227_<38>

P91 = 1329457769065054174158179915996114710331432479966297431062804648433587475807882771460823363_<91>

Number: n
N=16903884344577886690498956031018070938463188923151073763072432517978449357170634202219835990360450574429289316652620035949391401
  ( 128 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=12714871233905837021626832695666376227 (pp38)
 r2=1329457769065054174158179915996114710331432479966297431062804648433587475807882771460823363 (pp91)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.82 hours.
Scaled time: 5.52 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_1_8_133_9
n: 16903884344577886690498956031018070938463188923151073763072432517978449357170634202219835990360450574429289316652620035949391401
skew: 0.90
deg: 5
c5: 17
c0: 10
m: 1000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 420001)
Primes: RFBsize:148933, AFBsize:148425, largePrimes:5309234 encountered
Relations: rels:4787842, finalFF:368807
Max relations in full relation-set: 28
Initial matrix: 297423 x 368807 with sparse part having weight 17430308.
Pruned matrix : 230148 x 231699 with weight 8092085.
Total sieving time: 3.08 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.59 hours.
Total square root time: 0.03 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,75000
total time: 3.82 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 11, 2008

By Robert Backstrom / GGNFS

(17·10¹⁰⁴+1)/9 = 1(8)₁₀₃9_<105> = 3 · 7 · 23 · C102

C102 = P48 · P55

P48 = 265864911884614770878329372513092064450057351103_<48>

P55 = 1470951173457249660790510390603202909803884594187358861_<55>

Number: n
N=391074304117782378651943869335173682999769956291695422130204738900391074304117782378651943869335173683
  ( 102 digits)
SNFS difficulty: 106 digits.
Divisors found:
 r1=265864911884614770878329372513092064450057351103 (pp48)
 r2=1470951173457249660790510390603202909803884594187358861 (pp55)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.65 hours.
Scaled time: 0.78 units (timescale=1.187).
Factorization parameters were as follows:
name: KA_1_8_103_9
n: 391074304117782378651943869335173682999769956291695422130204738900391074304117782378651943869335173683
skew: 0.90
deg: 5
c5: 17
c0: 10
m: 1000000000000000000000
type: snfs
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 140001)
Primes: RFBsize:63951, AFBsize:63823, largePrimes:3718009 encountered
Relations: rels:3165750, finalFF:190127
Max relations in full relation-set: 28
Initial matrix: 127839 x 190127 with sparse part having weight 7841354.
Pruned matrix : 76058 x 76761 with weight 2308544.
Total sieving time: 0.56 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.03 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,106,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000
total time: 0.65 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 10, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(17·10¹⁶⁵-53)/9 = 1(8)₁₆₄3_<166> = 7 · 29 · C163

C163 = P77 · P87

P77 = 43402480428621987030205003566889274936988593086053286493942371994002021584433_<77>

P87 = 214385705193492725009349612317191476170118142711660225267764600968001857107379610049417_<87>

Number: n
N=9304871373836891078270388615216201423097974822112753147235905856595511767925561029009304871373836891078270388615216201423097974822112753147235905856595511767925561
  ( 163 digits)
SNFS difficulty: 166 digits.
Divisors found:

Sat May 10 22:25:30 2008  prp77 factor: 43402480428621987030205003566889274936988593086053286493942371994002021584433
Sat May 10 22:25:30 2008  prp87 factor: 214385705193492725009349612317191476170118142711660225267764600968001857107379610049417
Sat May 10 22:25:30 2008  elapsed time 01:40:15 (Msieve 1.35)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 63.69 hours.
Scaled time: 92.60 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_1_8_164_3
n: 9304871373836891078270388615216201423097974822112753147235905856595511767925561029009304871373836891078270388615216201423097974822112753147235905856595511767925561
skew: 1.26
deg: 5
c5: 17
c0: -53
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3400001)
Primes: RFBsize:216816, AFBsize:215951, largePrimes:7486111 encountered
Relations: rels:6868633, finalFF:449713
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 63.43 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 63.69 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 10, 2008

The factor table of 188...889 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

May 9, 2008 (4th)

By Wataru Sakai / GGNFS

(7·10¹⁹⁶-43)/9 = (7)₁₉₅3_<196> = 3² · 773 · 1283808358934056767222095093_<28> · 2620302803462725418522123017_<28> · C138

C138 = P64 · P74

P64 = 3543854126479629404194342535389768714682873298488000234516262161_<64>

P74 = 93779089025421898269355240230012909396341206292481875062343831519528856229_<74>

Number: template
N=332339411620241921667758139292075249481033920519211972712773710323231368221675760778894882184866260658051286208269366836796238604641850869
  ( 138 digits)
Divisors found:
 r1=3543854126479629404194342535389768714682873298488000234516262161 (pp64)
 r2=93779089025421898269355240230012909396341206292481875062343831519528856229 (pp74)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 2441.17 hours.
Scaled time: 4906.75 units (timescale=2.010).
Factorization parameters were as follows:
name: template
n: 332339411620241921667758139292075249481033920519211972712773710323231368221675760778894882184866260658051286208269366836796238604641850869
skew: 633970.78
# norm 2.37e+19
c5: 139560
c4: 459904593894
c3: -126980206595135003
c2: -161343727948017254210674
c1: 28008909286869388566227571068
c0: 7362373410681343420678015225067305
# alpha -5.99
Y1: 524199648991469
Y0: -298788360335374199376115932
# Murphy_E 2.20e-11
# M 1149381156828760038636208504312778076181482399815369717819531744821170386726634917697242824590468521180129638888519451984000293384578269
type: gnfs
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.5
alambda: 2.5
qintsize: 60000
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [2700000, 38880001)
Primes: RFBsize:374362, AFBsize:374845, largePrimes:11794582 encountered
Relations: rels:17293160, finalFF:861795
Max relations in full relation-set: 32
Initial matrix: 749287 x 861795 with sparse part having weight 177161076.
Pruned matrix : 694434 x 698244 with weight 162974487.
Total sieving time: 2429.94 hours.
Total relation processing time: 1.60 hours.
Matrix solve time: 9.05 hours.
Time per square root: 0.58 hours.
Prototype def-par.txt line would be:
gnfs,137,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5400000,5400000,27,27,51,51,2.5,2.5,60000
total time: 2441.17 hours.
 --------- CPU info (if available) ----------

May 9, 2008 (3rd)

By Jo Yeong Uk / GGNFS

(14·10¹⁷⁷+31)/9 = 1(5)₁₇₆9_<178> = C178

C178 = P70 · P109

P70 = 1096328539362005176413092222756577932801642557082525242167262230187171_<70>

P109 = 1418877188457386922625323450174283086499815757388954272526173072437542925270309130364696618460095061630075629_<109>

Number: 15559_177
N=1555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555559
  ( 178 digits)
SNFS difficulty: 178 digits.
Divisors found:
 r1=1096328539362005176413092222756577932801642557082525242167262230187171 (pp70)
 r2=1418877188457386922625323450174283086499815757388954272526173072437542925270309130364696618460095061630075629 (pp109)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 219.39 hours.
Scaled time: 522.80 units (timescale=2.383).
Factorization parameters were as follows:
n: 1555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555559
m: 200000000000000000000000000000000000
c5: 175
c0: 124
skew: 0.93
type: snfs
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [4500000, 8700001)
Primes: RFBsize:602489, AFBsize:602061, largePrimes:11158562 encountered
Relations: rels:11397768, finalFF:1426718
Max relations in full relation-set: 28
Initial matrix: 1204617 x 1426718 with sparse part having weight 98668142.
Pruned matrix : 1013971 x 1020058 with weight 71526964.
Total sieving time: 210.79 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 8.25 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,178,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,50,50,2.6,2.6,100000
total time: 219.39 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.48 BogoMIPS (lpj=2672242)
Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672351)

May 9, 2008 (2nd)

By Robert Backstrom / GMP-ECM, Msieve

(4·10¹⁶⁹+17)/3 = 1(3)₁₆₈9_<170> = 787 · 540101 · 1340039 · 33282371 · 1228724437_<10> · 16622933878153_<14> · C125

C125 = P35 · P43 · P48

P35 = 54993925552292230908242328636465353_<35>

P43 = 2748027937502551074896604229460386066456913_<43>

P48 = 227855381034873924333702464731031467728937974797_<48>

Fri May  9 04:21:35 2008  
Fri May  9 04:21:35 2008  
Fri May  9 04:21:35 2008  Msieve v. 1.34
Fri May  9 04:21:35 2008  random seeds: 691b551c 6b560d30
Fri May  9 04:21:35 2008  factoring 12530661861321035695461437620308285858371167816021440960712419669439223860277708341 (83 digits)
Fri May  9 04:21:35 2008  no P-1/P+1/ECM available, skipping
Fri May  9 04:21:35 2008  commencing quadratic sieve (83-digit input)
Fri May  9 04:21:35 2008  using multiplier of 61
Fri May  9 04:21:35 2008  using 64kb Opteron sieve core
Fri May  9 04:21:35 2008  sieve interval: 6 blocks of size 65536
Fri May  9 04:21:35 2008  processing polynomials in batches of 17
Fri May  9 04:21:35 2008  using a sieve bound of 1359329 (52059 primes)
Fri May  9 04:21:35 2008  using large prime bound of 125058268 (26 bits)
Fri May  9 04:21:35 2008  using trial factoring cutoff of 27 bits
Fri May  9 04:21:35 2008  polynomial 'A' values have 11 factors
Fri May  9 04:35:11 2008  52262 relations (27275 full + 24987 combined from 270355 partial), need 52155
Fri May  9 04:35:11 2008  begin with 297630 relations
Fri May  9 04:35:11 2008  reduce to 74125 relations in 2 passes
Fri May  9 04:35:11 2008  attempting to read 74125 relations
Fri May  9 04:35:12 2008  recovered 74125 relations
Fri May  9 04:35:12 2008  recovered 66164 polynomials
Fri May  9 04:35:12 2008  attempting to build 52262 cycles
Fri May  9 04:35:12 2008  found 52262 cycles in 1 passes
Fri May  9 04:35:12 2008  distribution of cycle lengths:
Fri May  9 04:35:12 2008     length 1 : 27275
Fri May  9 04:35:12 2008     length 2 : 24987
Fri May  9 04:35:12 2008  largest cycle: 2 relations
Fri May  9 04:35:12 2008  matrix is 52059 x 52262 (7.2 MB) with weight 1681414 (32.17/col)
Fri May  9 04:35:12 2008  sparse part has weight 1681414 (32.17/col)
Fri May  9 04:35:12 2008  filtering completed in 4 passes
Fri May  9 04:35:12 2008  matrix is 44666 x 44730 (6.1 MB) with weight 1410257 (31.53/col)
Fri May  9 04:35:12 2008  sparse part has weight 1410257 (31.53/col)
Fri May  9 04:35:12 2008  saving the first 48 matrix rows for later
Fri May  9 04:35:12 2008  matrix is 44618 x 44730 (3.7 MB) with weight 1022140 (22.85/col)
Fri May  9 04:35:12 2008  sparse part has weight 706896 (15.80/col)
Fri May  9 04:35:12 2008  matrix includes 64 packed rows
Fri May  9 04:35:12 2008  commencing Lanczos iteration
Fri May  9 04:35:12 2008  memory use: 5.4 MB
Fri May  9 04:35:43 2008  lanczos halted after 707 iterations (dim = 44606)
Fri May  9 04:35:44 2008  recovered 12 nontrivial dependencies
Fri May  9 04:35:44 2008  prp35 factor: 54993925552292230908242328636465353
Fri May  9 04:35:44 2008  prp48 factor: 227855381034873924333702464731031467728937974797
Fri May  9 04:35:44 2008  elapsed time 00:14:09

May 9, 2008

By Justin Card / GGNFS

(17·10¹⁶¹-53)/9 = 1(8)₁₆₀3_<162> = 3 · 19 · 43 · 254355202674105893_<18> · 3287574485420198704133928558179_<31> · C110

C110 = P37 · P74

P37 = 6592109827352816863838466122643365447_<37>

P74 = 13980491502316873967791731851571399701122210654779288236879044841952532537_<74>

Number: worktodo
N=92160935423645611317768122235971519726726074113585668724342529983025445149705393998167342865053046962449049039
  ( 110 digits)
Divisors found:
 r1=6592109827352816863838466122643365447
 r2=13980491502316873967791731851571399701122210654779288236879044841952532537
Version:
Total time: 24.24 hours.
Scaled time: 48.91 units (timescale=2.018).
Factorization parameters were as follows:
name: worktodo
n: 92160935423645611317768122235971519726726074113585668724342529983025445149705393998167342865053046962449049039
skew: 33082.85
# norm 4.09e+15
c5: 12600
c4: 2267365945
c3: -155321015926195
c2: -2349240279840559620
c1: 12982214017744131860983
c0: -31622288422337636799496945
# alpha -6.00
Y1: 379217522827
Y0: -1488782601061726047438
# Murphy_E 9.05e-10
# M 6562666969988531225364949784099942114382953390221344757651863751224118313342204937610904748802425250931949588
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2400001)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 407644 x 407892
Total sieving time: 24.24 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 24.24 hours.
 --------- CPU info (if available) ----------

May 8, 2008 (4th)

By Jo Yeong Uk / GGNFS

8·10¹⁸¹-1 = 7(9)₁₈₁_<182> = 7821454222070056969_<19> · C164

C164 = P51 · P113

P51 = 788439573104899094381095893696862654025503474927799_<51>

P113 = 12972810228209453983816901634265018328778556886502519239281435619824317355319728543086413776308502828632117225329_<113>

Number: 79999_181
N=10228276958300330498080736507519279486105205969987660391195978740025086788072414219094013040085242030630292224665357961760845294364879206193081236289180022489020871
  ( 164 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=788439573104899094381095893696862654025503474927799 (pp51)
 r2=12972810228209453983816901634265018328778556886502519239281435619824317355319728543086413776308502828632117225329 (pp113)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 191.88 hours.
Scaled time: 453.03 units (timescale=2.361).
Factorization parameters were as follows:
n: 10228276958300330498080736507519279486105205969987660391195978740025086788072414219094013040085242030630292224665357961760845294364879206193081236289180022489020871
m: 2000000000000000000000000000000000000
c5: 5
c0: -2
skew: 0.83
type: snfs
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [5000000, 8600001)
Primes: RFBsize:664579, AFBsize:664045, largePrimes:11037168 encountered
Relations: rels:11404548, finalFF:1577413
Max relations in full relation-set: 28
Initial matrix: 1328689 x 1577413 with sparse part having weight 92971068.
Pruned matrix : 1097910 x 1104617 with weight 60006284.
Total sieving time: 183.42 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 8.15 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000
total time: 191.88 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.48 BogoMIPS (lpj=2672242)
Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672351)

May 8, 2008 (3rd)

By Justin Card / GGNFS

(17·10¹⁵⁰-53)/9 = 1(8)₁₄₉3_<151> = 139 · 1109 · 19867 · 53699 · C137

C137 = P56 · P81

P56 = 58524777302241362713821490265536758164758485666839114161_<56>

P81 = 196255486079589701227585169591220827496285377009347149826952814709503321846950741_<81>

Number: 18883_150
N=11485808617151117068599663545151818379779946947029462334170568301636248776109389736647593871953122496252803763639449645494895547442543301
  ( 137 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=58524777302241362713821490265536758164758485666839114161
 r2=196255486079589701227585169591220827496285377009347149826952814709503321846950741
Version:
Total time: 21.46 hours.
Scaled time: 43.31 units (timescale=2.018).
Factorization parameters were as follows:
n: 11485808617151117068599663545151818379779946947029462334170568301636248776109389736647593871953122496252803763639449645494895547442543301
m: 1000000000000000000000000000000
c5: 17
c0: -53
Y1: 1
Y0: -1000000000000000000000000000000
skew: 1.26
type: snfs

Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1200000)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 336747 x 336995
Total sieving time: 21.46 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 21.46 hours.
 --------- CPU info (if available) ----------

May 8, 2008 (2nd)

By Robert Backstrom / GMP-ECM, Msieve

(14·10¹⁹⁵+31)/9 = 1(5)₁₉₄9_<196> = 3517 · 72959 · 119831 · 174723560293_<12> · 29908448484246570631_<20> · 296464817923705928738027_<24> · C128

C128 = P38 · P90

P38 = 67438308398974187180622772855468793089_<38>

P90 = 484216870346117642180865357051076528493767653821960944086179418529064377186836629909208187_<90>

(4·10¹⁸⁸+11)/3 = 1(3)₁₈₇7_<189> = 647 · 3129923 · 26842061 · 6040965932401_<13> · 14857068261935316657329056727_<29> · C131

C131 = P34 · P98

P34 = 1736857011312162555994210469872451_<34>

P98 = 15735529880735063854034395949750241973639121882661501326917621354847802201149038459287456328343941_<98>

(11·10¹⁸²+61)/9 = 1(2)₁₈₁9_<183> = 3 · 5287159 · 6837552090639889_<16> · 215270056119179928842411146396979_<33> · C127

C127 = P39 · P41 · P48

P39 = 386743518904360880703905991006429255227_<39>

P41 = 15816269637526716768726379630499787809243_<41>

P48 = 855845109201103507837814977690861986896119008947_<48>

Thu May  8 22:23:43 2008  
Thu May  8 22:23:43 2008  
Thu May  8 22:23:43 2008  Msieve v. 1.34
Thu May  8 22:23:43 2008  random seeds: 447cc43b 31aa6ae9
Thu May  8 22:23:43 2008  factoring 13536277015083150708358105307944157502727791650822840210249683528781966042510629446297121 (89 digits)
Thu May  8 22:23:43 2008  no P-1/P+1/ECM available, skipping
Thu May  8 22:23:43 2008  commencing quadratic sieve (89-digit input)
Thu May  8 22:23:44 2008  using multiplier of 1
Thu May  8 22:23:44 2008  using 64kb Opteron sieve core
Thu May  8 22:23:44 2008  sieve interval: 14 blocks of size 65536
Thu May  8 22:23:44 2008  processing polynomials in batches of 8
Thu May  8 22:23:44 2008  using a sieve bound of 1520879 (58333 primes)
Thu May  8 22:23:44 2008  using large prime bound of 121670320 (26 bits)
Thu May  8 22:23:44 2008  using double large prime bound of 357546364197680 (42-49 bits)
Thu May  8 22:23:44 2008  using trial factoring cutoff of 49 bits
Thu May  8 22:23:44 2008  polynomial 'A' values have 11 factors
Thu May  8 23:01:20 2008  58833 relations (15979 full + 42854 combined from 614451 partial), need 58429
Thu May  8 23:01:20 2008  begin with 630430 relations
Thu May  8 23:01:20 2008  reduce to 142082 relations in 9 passes
Thu May  8 23:01:20 2008  attempting to read 142082 relations
Thu May  8 23:01:21 2008  recovered 142082 relations
Thu May  8 23:01:21 2008  recovered 118230 polynomials
Thu May  8 23:01:21 2008  attempting to build 58833 cycles
Thu May  8 23:01:21 2008  found 58833 cycles in 5 passes
Thu May  8 23:01:21 2008  distribution of cycle lengths:
Thu May  8 23:01:21 2008     length 1 : 15979
Thu May  8 23:01:21 2008     length 2 : 11357
Thu May  8 23:01:21 2008     length 3 : 10582
Thu May  8 23:01:21 2008     length 4 : 7805
Thu May  8 23:01:21 2008     length 5 : 5245
Thu May  8 23:01:21 2008     length 6 : 3550
Thu May  8 23:01:21 2008     length 7 : 2031
Thu May  8 23:01:21 2008     length 9+: 2284
Thu May  8 23:01:21 2008  largest cycle: 18 relations
Thu May  8 23:01:22 2008  matrix is 58333 x 58833 (14.0 MB) with weight 3422665 (58.18/col)
Thu May  8 23:01:22 2008  sparse part has weight 3422665 (58.18/col)
Thu May  8 23:01:22 2008  filtering completed in 3 passes
Thu May  8 23:01:22 2008  matrix is 54281 x 54344 (12.9 MB) with weight 3170823 (58.35/col)
Thu May  8 23:01:22 2008  sparse part has weight 3170823 (58.35/col)
Thu May  8 23:01:22 2008  saving the first 48 matrix rows for later
Thu May  8 23:01:22 2008  matrix is 54233 x 54344 (8.9 MB) with weight 2545096 (46.83/col)
Thu May  8 23:01:22 2008  sparse part has weight 2008783 (36.96/col)
Thu May  8 23:01:22 2008  matrix includes 64 packed rows
Thu May  8 23:01:22 2008  using block size 21737 for processor cache size 1024 kB
Thu May  8 23:01:23 2008  commencing Lanczos iteration
Thu May  8 23:01:23 2008  memory use: 8.4 MB
Thu May  8 23:01:41 2008  lanczos halted after 859 iterations (dim = 54229)
Thu May  8 23:01:41 2008  recovered 14 nontrivial dependencies
Thu May  8 23:01:42 2008  prp41 factor: 15816269637526716768726379630499787809243
Thu May  8 23:01:42 2008  prp48 factor: 855845109201103507837814977690861986896119008947
Thu May  8 23:01:42 2008  elapsed time 00:37:59

May 8, 2008

By Robert Backstrom / GGNFS, Msieve

(25·10¹⁸⁵-1)/3 = 8(3)₁₈₅_<186> = 877 · 1380443 · 216888485620043_<15> · 323366540549594477093_<21> · C142

C142 = P60 · P83

P60 = 880905126532956667848805335238198593911413113053283385249717_<60>

P83 = 11141405152029028996571436570066231843415229390926814860984551946924997119693480441_<83>

Number: n
N=9814520915203067108861318616106861980723536434273639929210502060032509597936265847719548119380237456211747556776071673719211139066269640285197
  ( 142 digits)
SNFS difficulty: 186 digits.
Divisors found:

Thu May  8 01:31:10 2008  prp60 factor: 880905126532956667848805335238198593911413113053283385249717
Thu May  8 01:31:10 2008  prp83 factor: 11141405152029028996571436570066231843415229390926814860984551946924997119693480441
Thu May  8 01:31:10 2008  elapsed time 02:13:43 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 80.43 hours.
Scaled time: 67.16 units (timescale=0.835).
Factorization parameters were as follows:
name: KA_8_3_185
n: 9814520915203067108861318616106861980723536434273639929210502060032509597936265847719548119380237456211747556776071673719211139066269640285197
type: snfs
deg: 5
c5: 25
c0: -1
skew: 0.53
m: 10000000000000000000000000000000000000
rlim: 7000000
alim: 7000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 7000000/7000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 9999990)
Primes: RFBsize:476648, AFBsize:475734, largePrimes:6401443 encountered
Relations: rels:6804178, finalFF:1070473
Max relations in full relation-set: 28
Initial matrix: 952446 x 1070473 with sparse part having weight 65768427.
Pruned matrix : 
Total sieving time: 80.22 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,7000000,7000000,27,27,48,48,2.5,2.5,100000
total time: 80.43 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

May 7, 2008

By Jo Yeong Uk / GMP-ECM, GGNFS

(17·10¹⁶¹-53)/9 = 1(8)₁₆₀3_<162> = 3 · 19 · 43 · 254355202674105893_<18> · C141

C141 = P31 · C110

P31 = 3287574485420198704133928558179_<31>

C110 = [92160935423645611317768122235971519726726074113585668724342529983025445149705393998167342865053046962449049039_<110>]

(17·10¹⁶⁴-53)/9 = 1(8)₁₆₃3_<165> = 3 · 3162156699067_<13> · 262881178953307_<15> · 105290032030122334034954183_<27> · C111

C111 = P55 · P57

P55 = 1216259663201331434035013956830378303572945186485863881_<55>

P57 = 591464542648869639542420113968295913254867921520280460903_<57>

Number: 18883_164
N=719374465437643719673155958990646694072313754932899142898045569823974710056813761548010949545481947900800344543
  ( 111 digits)
Divisors found:
 r1=1216259663201331434035013956830378303572945186485863881 (pp55)
 r2=591464542648869639542420113968295913254867921520280460903 (pp57)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 15.70 hours.
Scaled time: 37.30 units (timescale=2.376).
Factorization parameters were as follows:
name: 18883_164
n: 719374465437643719673155958990646694072313754932899142898045569823974710056813761548010949545481947900800344543
skew: 18557.77
# norm 3.73e+15
c5: 64800
c4: 11133954640
c3: -106032251608850
c2: -5726041892371431773
c1: 10229939804823287742570
c0: -4521566322811507267369192
# alpha -6.05
Y1: 2901225613
Y0: -1618363130240665777689
# Murphy_E 8.01e-10
# M 111225469245920816024952471555682815374427338915935731619376144303250142866072342485964589906349848316772010006
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:175934, largePrimes:7511808 encountered
Relations: rels:7245607, finalFF:405867
Max relations in full relation-set: 28
Initial matrix: 352312 x 405867 with sparse part having weight 38930358.
Pruned matrix : 317084 x 318909 with weight 27771207.
Polynomial selection time: 0.84 hours.
Total sieving time: 14.07 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.57 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000
total time: 15.70 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.48 BogoMIPS (lpj=2672242)
Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672351)

May 6, 2008 (4th)

By Jo Yeong Uk / GGNFS, GMP-ECM

(17·10¹⁴⁹-53)/9 = 1(8)₁₄₈3_<150> = 3² · 131 · 255137 · 3375511 · C135

C135 = P40 · P95

P40 = 5388930257121078729270880943678492107897_<40>

P95 = 34520499532221180433112166674230849735039209965903167809354543240545253834351079688548856476663_<95>

Number: 18883_149
N=186028564420120763869411900228851597728893983321120725406369201290270575424216972614176528429421435137778820470318466817128999458507711
  ( 135 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=5388930257121078729270880943678492107897 (pp40)
 r2=34520499532221180433112166674230849735039209965903167809354543240545253834351079688548856476663 (pp95)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 15.38 hours.
Scaled time: 36.40 units (timescale=2.367).
Factorization parameters were as follows:
n: 186028564420120763869411900228851597728893983321120725406369201290270575424216972614176528429421435137778820470318466817128999458507711
m: 1000000000000000000000000000000
c5: 17
c0: -530
skew: 1.99
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2300001)
Primes: RFBsize:176302, AFBsize:176478, largePrimes:5642114 encountered
Relations: rels:5569954, finalFF:478847
Max relations in full relation-set: 28
Initial matrix: 352845 x 478847 with sparse part having weight 44707797.
Pruned matrix : 304861 x 306689 with weight 25872555.
Total sieving time: 14.76 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.51 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 15.38 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

(17·10¹⁵⁷-53)/9 = 1(8)₁₅₆3_<158> = 13 · 103 · 1606069667_<10> · 96829103143_<11> · C134

C134 = P40 · P95

P40 = 7966230062417543067682362213686161549493_<40>

P95 = 11386826441643864898561421221923570419394152237250887959212635282363431012333153776133535984209_<95>

May 6, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(64·10¹⁶⁶+53)/9 = 7(1)₁₆₅7_<167> = 17 · 19 · 5483057904307_<13> · 125102202163039_<15> · C138

C138 = P57 · P82

P57 = 189017252553419561480806004528870537398168187166973127563_<57>

P82 = 1698031369177711247850014025611530461767387472590376241897452371528925800729051521_<82>

Number: n
N=320957224151492255429082127231488936975920891075446305694396741711567954921815157690547768799927437761891217541762696415656265015932173323
  ( 138 digits)
SNFS difficulty: 167 digits.
Divisors found:

Tue May 06 11:05:04 2008  prp57 factor: 189017252553419561480806004528870537398168187166973127563
Tue May 06 11:05:04 2008  prp82 factor: 1698031369177711247850014025611530461767387472590376241897452371528925800729051521
Tue May 06 11:05:04 2008  elapsed time 02:14:27 (Msieve 1.34)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 95.69 hours.
Scaled time: 123.35 units (timescale=1.289).
Factorization parameters were as follows:
name: KA_7_1_165_7
n: 320957224151492255429082127231488936975920891075446305694396741711567954921815157690547768799927437761891217541762696415656265015932173323
skew: 0.61
deg: 5
c5: 640
c0: 53
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4100293)
Primes: RFBsize:216816, AFBsize:215751, largePrimes:7744522 encountered
Relations: rels:7160434, finalFF:475852
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 95.27 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 95.69 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

May 6, 2008 (2nd)

By matsui / GGNFS

10¹⁷⁷-9 = (9)₁₇₆1_<177> = 1321 · 2376752857145462309881481_<25> · C150

C150 = P60 · P91

P60 = 166539912927088863044604457888822597127041055210868917788027_<60>

P91 = 1912470850607748174543437500075957519331332156283120157980757697449058309385972258440240133_<91>

N=318502728935809954002509561087485010327351554728615657106064751195435717694394036448608577571954357904487482813391637647426139449497421967533072287591
  ( 150 digits)
SNFS difficulty: 177 digits.
Divisors found:
 r1=166539912927088863044604457888822597127041055210868917788027 (pp60)
 r2=1912470850607748174543437500075957519331332156283120157980757697449058309385972258440240133 (pp91)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 284.83 hours.
Scaled time: 483.93 units (timescale=1.699).
Factorization parameters were as follows:
n: 318502728935809954002509561087485010327351554728615657106064751195435717694394036448608577571954357904487482813391637647426139449497421967533072287591
m: 100000000000000000000000000000000000
c5: 100
c0: -9
skew: 0.62
type: snfs

Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 14800001)
Primes: RFBsize:501962, AFBsize:501986, largePrimes:6735594 encountered
Relations: rels:7221193, finalFF:1133995
Max relations in full relation-set: 28
Initial matrix: 1004012 x 1133995 with sparse part having weight 89857824.
Pruned matrix : 899749 x 904833 with weight 71278579.
Total sieving time: 266.47 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 17.92 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,177,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 284.83 hours.

May 6, 2008

By Justin Card / GGNFS

(10¹⁶⁴+71)/9 = (1)₁₆₃9_<164> = 19² · 7831997 · 2098626111640319124673_<22> · C133

C133 = P47 · P86

P47 = 28129977390358023629213634794275869491272177939_<47>

P86 = 66569197414739914752363340066606515578290318079885508716380491999752942375601583635281_<86>

Number: 11119_164
N=1872590018170913600366772304304121841458097175167099440399150522128818251133408166221876789031838225191954311628349902030957910265859
  ( 133 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=28129977390358023629213634794275869491272177939 (pp47)
 r2=66569197414739914752363340066606515578290318079885508716380491999752942375601583635281 (pp86)
Version: GGNFS-0.77.1-20060722-k8
Total time: 107.01 hours.
Scaled time: 215.94 units (timescale=2.018).
Factorization parameters were as follows:
n: 1872590018170913600366772304304121841458097175167099440399150522128818251133408166221876789031838225191954311628349902030957910265859
m: 1000000000000000000000000000000000
c5: 1
c0: 710
skew: 3.72
type: snfs

Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 6000001)
Primes: RFBsize:348513, AFBsize:349267, largePrimes:5903324 encountered
Relations: rels:6042140, finalFF:784177
Max relations in full relation-set: 32
Initial matrix: 697844 x 784177 with sparse part having weight 53680249.
Pruned matrix : 633863 x 637416 with weight 40023983.
Total sieving time: 99.60 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 7.19 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 107.01 hours.
 --------- CPU info (if available) ----------

May 5, 2008 (4th)

By Robert Backstrom / GGNFS, GMP-ECM, Msieve

(17·10¹⁵⁶-53)/9 = 1(8)₁₅₅3_<157> = C157

C157 = P77 · P80

P77 = 94115205417543442260889014109032287575728859357342112763830605058897534630713_<77>

P80 = 20069965108281988776637007571562300370718669072099530779317161803679127900838091_<80>

Number: n
N=1888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883
  ( 157 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=94115205417543442260889014109032287575728859357342112763830605058897534630713 (pp77)
 r2=20069965108281988776637007571562300370718669072099530779317161803679127900838091 (pp80)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 31.24 hours.
Scaled time: 56.95 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_1_8_155_3
n: 1888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883
skew: 0.79
deg: 5
c5: 170
c0: -53
m: 10000000000000000000000000000000
type: snfs
rlim: 1800000
alim: 1800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2200001)
Primes: RFBsize:135072, AFBsize:135633, largePrimes:7506713 encountered
Relations: rels:6975775, finalFF:328656
Max relations in full relation-set: 48
Initial matrix: 270772 x 328656 with sparse part having weight 59693763.
Pruned matrix : 260051 x 261468 with weight 42450536.
Total sieving time: 29.78 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.14 hours.
Total square root time: 0.16 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.5,2.5,100000
total time: 31.24 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(4·10¹⁶⁸-7)/3 = 1(3)₁₆₇1_<169> = 59 · 2383 · C163

C163 = P35 · P47 · P82

P35 = 40023304173544835675150634644920757_<35>

P47 = 87704264899678723077483412253836681182971817527_<47>

P82 = 2701649657888416586918373900392021989279527982766201328562651932265680628922403757_<82>

Number: n
N=236946197261572085292838556629037751292137492986711183144801139487713250729956995533124609056643740923364539938459175868023248939
  ( 129 digits)
SNFS difficulty: 168 digits.
Divisors found:

Mon May 05 12:27:06 2008  prp47 factor: 87704264899678723077483412253836681182971817527
Mon May 05 12:27:06 2008  prp82 factor: 2701649657888416586918373900392021989279527982766201328562651932265680628922403757
Mon May 05 12:27:06 2008  elapsed time 01:48:02 (Msieve 1.34)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 70.29 hours.
Scaled time: 123.78 units (timescale=1.761).
Factorization parameters were as follows:
name: KA_1_3_167_1
n: 236946197261572085292838556629037751292137492986711183144801139487713250729956995533124609056643740923364539938459175868023248939
type: snfs
skew: 0.56
deg: 5
c5: 125
c0: -7
m: 2000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3299990)
Primes: RFBsize:230209, AFBsize:229892, largePrimes:7666340 encountered
Relations: rels:7167828, finalFF:516796
Max relations in full relation-set: 28
Initial matrix: 460166 x 516796 with sparse part having weight 46524840.
Pruned matrix : 
Total sieving time: 70.00 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.6,2.6,100000
total time: 70.29 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

May 5, 2008 (3rd)

By Jo Yeong Uk / GGNFS

(17·10¹⁴⁵-53)/9 = 1(8)₁₄₄3_<146> = 13 · 1693 · 21139 · 152839 · C132

C132 = P33 · P99

P33 = 906712254747545828169857551757513_<33>

P99 = 292966518254180953679091271458567512967760755284807647661567847660425624429080931183692604031429719_<99>

Number: 18883_145
N=265636332331786455948599830433367466549294462972153747320203357415347232538865457535237362193153091325035833595006246655618589728847
  ( 132 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=906712254747545828169857551757513 (pp33)
 r2=292966518254180953679091271458567512967760755284807647661567847660425624429080931183692604031429719 (pp99)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 9.04 hours.
Scaled time: 21.60 units (timescale=2.388).
Factorization parameters were as follows:
n: 265636332331786455948599830433367466549294462972153747320203357415347232538865457535237362193153091325035833595006246655618589728847
m: 100000000000000000000000000000
c5: 17
c0: -53
skew: 1.26
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1575001)
Primes: RFBsize:135072, AFBsize:134618, largePrimes:3865067 encountered
Relations: rels:4038075, finalFF:449877
Max relations in full relation-set: 28
Initial matrix: 269755 x 449877 with sparse part having weight 41845575.
Pruned matrix : 210461 x 211873 with weight 18696046.
Total sieving time: 8.75 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.22 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 9.04 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

(17·10¹⁵⁴-53)/9 = 1(8)₁₅₃3_<155> = 971 · 102437 · 371631714756730591_<18> · 101739334408004478253_<21> · C109

C109 = P37 · P73

P37 = 1274109118835390829488419042276855939_<37>

P73 = 3942049247854730324039591295348901289336792997888410316410784299138286157_<73>

Number: 18883_154
N=5022600893589905636339499417613746611203498473826015438112127303240501238047489385556412100188188698846936423
  ( 109 digits)
Divisors found:
 r1=1274109118835390829488419042276855939 (pp37)
 r2=3942049247854730324039591295348901289336792997888410316410784299138286157 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.95 hours.
Scaled time: 28.49 units (timescale=2.385).
Factorization parameters were as follows:
name: 18883_154
n: 5022600893589905636339499417613746611203498473826015438112127303240501238047489385556412100188188698846936423
skew: 13374.50
# norm 5.43e+14
c5: 30720
c4: 173704624
c3: -7232247169672
c2: -374569345942660446
c1: -1059675685050481945127
c0: 22995021347564797885400
# alpha -5.17
Y1: 208977619037
Y0: -696147622413157774917
# Murphy_E 1.15e-09
# M 4860478897446311097949180415020740955658616983891812118048734381297380893306393968043407480884279029213211245
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1200000, 1860001)
Primes: RFBsize:176302, AFBsize:176443, largePrimes:7604035 encountered
Relations: rels:7511229, finalFF:560575
Max relations in full relation-set: 28
Initial matrix: 352821 x 560575 with sparse part having weight 54604718.
Pruned matrix : 235491 x 237319 with weight 27052759.
Polynomial selection time: 0.71 hours.
Total sieving time: 10.66 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.36 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000
total time: 11.95 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

May 5, 2008 (2nd)

By Sinkiti Sibata / Msieve

(17·10¹⁴⁰-53)/9 = 1(8)₁₃₉3_<141> = 3² · 31 · 43 · 89 · 10416211045177969_<17> · 2199553991945068036403_<22> · C97

C97 = P29 · P69

P29 = 38770123268705413047738066497_<29>

P69 = 199160022643799127833796061370630292550733822605403852646915352573069_<69>

Sun May  4 20:45:00 2008  Msieve v. 1.35
Sun May  4 20:45:00 2008  random seeds: dc0174df bdb499f0
Sun May  4 20:45:00 2008  factoring 7721458628098253520507907794388559567326852814475284956638057016810555515872552885560367973369293 (97 digits)
Sun May  4 20:45:02 2008  searching for 15-digit factors
Sun May  4 20:45:04 2008  commencing quadratic sieve (97-digit input)
Sun May  4 20:45:04 2008  using multiplier of 53
Sun May  4 20:45:04 2008  using 64kb Pentium 4 sieve core
Sun May  4 20:45:04 2008  sieve interval: 18 blocks of size 65536
Sun May  4 20:45:04 2008  processing polynomials in batches of 6
Sun May  4 20:45:04 2008  using a sieve bound of 2401409 (88235 primes)
Sun May  4 20:45:04 2008  using large prime bound of 360211350 (28 bits)
Sun May  4 20:45:04 2008  using double large prime bound of 2522337833647050 (43-52 bits)
Sun May  4 20:45:04 2008  using trial factoring cutoff of 52 bits
Sun May  4 20:45:04 2008  polynomial 'A' values have 13 factors
Mon May  5 05:41:31 2008  88780 relations (22380 full + 66400 combined from 1309522 partial), need 88331
Mon May  5 05:41:37 2008  begin with 1331902 relations
Mon May  5 05:41:38 2008  reduce to 228356 relations in 11 passes
Mon May  5 05:41:39 2008  attempting to read 228356 relations
Mon May  5 05:41:46 2008  recovered 228356 relations
Mon May  5 05:41:46 2008  recovered 214407 polynomials
Mon May  5 05:41:47 2008  attempting to build 88780 cycles
Mon May  5 05:41:47 2008  found 88780 cycles in 6 passes
Mon May  5 05:41:47 2008  distribution of cycle lengths:
Mon May  5 05:41:47 2008     length 1 : 22380
Mon May  5 05:41:47 2008     length 2 : 15920
Mon May  5 05:41:47 2008     length 3 : 15021
Mon May  5 05:41:47 2008     length 4 : 11905
Mon May  5 05:41:47 2008     length 5 : 8961
Mon May  5 05:41:47 2008     length 6 : 5950
Mon May  5 05:41:47 2008     length 7 : 3672
Mon May  5 05:41:47 2008     length 9+: 4971
Mon May  5 05:41:47 2008  largest cycle: 19 relations
Mon May  5 05:41:47 2008  matrix is 88235 x 88780 (23.4 MB) with weight 5776404 (65.06/col)
Mon May  5 05:41:48 2008  sparse part has weight 5776404 (65.06/col)
Mon May  5 05:41:49 2008  filtering completed in 3 passes
Mon May  5 05:41:49 2008  matrix is 83760 x 83824 (22.1 MB) with weight 5457471 (65.11/col)
Mon May  5 05:41:49 2008  sparse part has weight 5457471 (65.11/col)
Mon May  5 05:41:50 2008  saving the first 48 matrix rows for later
Mon May  5 05:41:50 2008  matrix is 83712 x 83824 (12.8 MB) with weight 4196289 (50.06/col)
Mon May  5 05:41:50 2008  sparse part has weight 2865457 (34.18/col)
Mon May  5 05:41:50 2008  matrix includes 64 packed rows
Mon May  5 05:41:50 2008  using block size 21845 for processor cache size 512 kB
Mon May  5 05:41:51 2008  commencing Lanczos iteration
Mon May  5 05:41:51 2008  memory use: 12.9 MB
Mon May  5 05:43:03 2008  lanczos halted after 1326 iterations (dim = 83712)
Mon May  5 05:43:04 2008  recovered 18 nontrivial dependencies
Mon May  5 05:43:05 2008  prp29 factor: 38770123268705413047738066497
Mon May  5 05:43:05 2008  prp69 factor: 199160022643799127833796061370630292550733822605403852646915352573069
Mon May  5 05:43:05 2008  elapsed time 08:58:05

May 5, 2008

By Jo Yeong Uk / GGNFS

(17·10¹⁴³-53)/9 = 1(8)₁₄₂3_<144> = 3 · 19 · 82003 · 33747234085323696229891580573_<29> · C109

C109 = P54 · P55

P54 = 284184304370485849583806799703613180155918074201814599_<54>

P55 = 4213699332694306433921848962284585352045581816321987099_<55>

Number: 18883_143
N=1197467213688111895850772536711179223052372690430306061875255929817187752960564141361063736311640807267858301
  ( 109 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=284184304370485849583806799703613180155918074201814599 (pp54)
 r2=4213699332694306433921848962284585352045581816321987099 (pp55)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.08 hours.
Scaled time: 23.75 units (timescale=2.356).
Factorization parameters were as follows:
n: 1197467213688111895850772536711179223052372690430306061875255929817187752960564141361063736311640807267858301
m: 100000000000000000000000000000
c5: 17
c0: -5300
skew: 3.15
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1650001)
Primes: RFBsize:135072, AFBsize:135378, largePrimes:3801778 encountered
Relations: rels:3847640, finalFF:337434
Max relations in full relation-set: 28
Initial matrix: 270517 x 337434 with sparse part having weight 31669794.
Pruned matrix : 247287 x 248703 with weight 19935634.
Total sieving time: 9.72 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 10.08 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

May 4, 2008 (3rd)

By Jo Yeong Uk / GGNFS

(17·10¹³⁹-53)/9 = 1(8)₁₃₈3_<140> = 13 · 109363 · 10038594233_<11> · 1303876585637_<13> · C112

C112 = P46 · P66

P46 = 1093771935863111803994728995558734837426133433_<46>

P66 = 928018175045653313023689862079602922263543547526513521806182993649_<66>

Number: 18883_139
N=1015040235835836378728631986726903634233303583621327606120724533258279780022125161642706618871835169922865567017
  ( 112 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=1093771935863111803994728995558734837426133433 (pp46)
 r2=928018175045653313023689862079602922263543547526513521806182993649 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.77 hours.
Scaled time: 16.07 units (timescale=2.374).
Factorization parameters were as follows:
n: 1015040235835836378728631986726903634233303583621327606120724533258279780022125161642706618871835169922865567017
m: 10000000000000000000000000000
c5: 17
c0: -530
skew: 1.99
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1250001)
Primes: RFBsize:114155, AFBsize:114172, largePrimes:3312330 encountered
Relations: rels:3279076, finalFF:271361
Max relations in full relation-set: 28
Initial matrix: 228392 x 271361 with sparse part having weight 24091352.
Pruned matrix : 211946 x 213151 with weight 15991644.
Total sieving time: 6.51 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.77 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

(17·10¹⁷⁸-53)/9 = 1(8)₁₇₇3_<179> = 149 · 71023 · 2981057 · 738493163 · 18978130740089_<14> · 43743537687611_<14> · 93010512334718522114163289_<26> · C104

C104 = P38 · P66

P38 = 40841462947354589786207930836285747643_<38>

P66 = 257100965516938781704461385818273110825314784282900274223801951843_<66>

Number: 18883_178
N=10500379556889145330246585114238768457291202943488725603741369894166236710397268265106651792985936756049
  ( 104 digits)
Divisors found:
 r1=40841462947354589786207930836285747643 (pp38)
 r2=257100965516938781704461385818273110825314784282900274223801951843 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.95 hours.
Scaled time: 11.76 units (timescale=2.378).
Factorization parameters were as follows:
name: 18883_178
n: 10500379556889145330246585114238768457291202943488725603741369894166236710397268265106651792985936756049
skew: 14873.58
# norm 2.30e+14
c5: 16860
c4: 394657478
c3: 691223280664
c2: -129661333066021771
c1: 933196451921052844674
c0: 2280582783604846240475616
# alpha -6.26
Y1: 55451588929
Y0: -57394135822956993649
# Murphy_E 2.25e-09
# M 6839246963409309748766842326136220909111860140739734615850387672023936970225800943518710329636436932672
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1620001)
Primes: RFBsize:135072, AFBsize:135010, largePrimes:4383712 encountered
Relations: rels:4338342, finalFF:345714
Max relations in full relation-set: 28
Initial matrix: 270166 x 345714 with sparse part having weight 28239737.
Pruned matrix : 220167 x 221581 with weight 15602253.
Polynomial selection time: 0.39 hours.
Total sieving time: 4.23 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 4.95 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

May 4, 2008 (2nd)

By Sinkiti Sibata / Msieve

(17·10¹⁸⁹-53)/9 = 1(8)₁₈₈3_<190> = 7 · 1487 · 37763269 · 107409211127_<12> · 1892069578404541_<16> · 3090777110713708539900218209_<28> · 18308463842770442763352292651_<29> · C96

C96 = P34 · P63

P34 = 3425376722500250431425989302857061_<34>

P63 = 121989164029539344478888387906348661308781361217618006478634011_<63>

Sat May  3 19:48:17 2008  Msieve v. 1.35
Sat May  3 19:48:17 2008  random seeds: 695a6d9a 2c707a77
Sat May  3 19:48:17 2008  factoring 417858842864048922896196337118593534562428072576844463940803492716857825203006427509934866101671 (96 digits)
Sat May  3 19:48:19 2008  searching for 15-digit factors
Sat May  3 19:48:21 2008  commencing quadratic sieve (96-digit input)
Sat May  3 19:48:21 2008  using multiplier of 1
Sat May  3 19:48:21 2008  using 64kb Pentium 4 sieve core
Sat May  3 19:48:21 2008  sieve interval: 18 blocks of size 65536
Sat May  3 19:48:21 2008  processing polynomials in batches of 6
Sat May  3 19:48:21 2008  using a sieve bound of 2257987 (83529 primes)
Sat May  3 19:48:21 2008  using large prime bound of 338698050 (28 bits)
Sat May  3 19:48:21 2008  using double large prime bound of 2257682284654350 (43-52 bits)
Sat May  3 19:48:21 2008  using trial factoring cutoff of 52 bits
Sat May  3 19:48:21 2008  polynomial 'A' values have 12 factors
Sun May  4 04:33:19 2008  83830 relations (19972 full + 63858 combined from 1268871 partial), need 83625
Sun May  4 04:33:24 2008  begin with 1288843 relations
Sun May  4 04:33:26 2008  reduce to 222077 relations in 11 passes
Sun May  4 04:33:26 2008  attempting to read 222077 relations
Sun May  4 04:33:33 2008  recovered 222077 relations
Sun May  4 04:33:33 2008  recovered 209059 polynomials
Sun May  4 04:33:33 2008  attempting to build 83830 cycles
Sun May  4 04:33:34 2008  found 83830 cycles in 6 passes
Sun May  4 04:33:34 2008  distribution of cycle lengths:
Sun May  4 04:33:34 2008     length 1 : 19972
Sun May  4 04:33:34 2008     length 2 : 14020
Sun May  4 04:33:34 2008     length 3 : 14057
Sun May  4 04:33:34 2008     length 4 : 11320
Sun May  4 04:33:34 2008     length 5 : 8801
Sun May  4 04:33:34 2008     length 6 : 6050
Sun May  4 04:33:34 2008     length 7 : 3976
Sun May  4 04:33:34 2008     length 9+: 5634
Sun May  4 04:33:34 2008  largest cycle: 19 relations
Sun May  4 04:33:34 2008  matrix is 83529 x 83830 (23.4 MB) with weight 5800295 (69.19/col)
Sun May  4 04:33:34 2008  sparse part has weight 5800295 (69.19/col)
Sun May  4 04:33:36 2008  filtering completed in 3 passes
Sun May  4 04:33:36 2008  matrix is 80180 x 80244 (22.5 MB) with weight 5574830 (69.47/col)
Sun May  4 04:33:36 2008  sparse part has weight 5574830 (69.47/col)
Sun May  4 04:33:37 2008  saving the first 48 matrix rows for later
Sun May  4 04:33:37 2008  matrix is 80132 x 80244 (16.0 MB) with weight 4623887 (57.62/col)
Sun May  4 04:33:37 2008  sparse part has weight 3724238 (46.41/col)
Sun May  4 04:33:37 2008  matrix includes 64 packed rows
Sun May  4 04:33:37 2008  using block size 21845 for processor cache size 512 kB
Sun May  4 04:33:38 2008  commencing Lanczos iteration
Sun May  4 04:33:38 2008  memory use: 14.4 MB
Sun May  4 04:34:57 2008  lanczos halted after 1270 iterations (dim = 80131)
Sun May  4 04:34:57 2008  recovered 17 nontrivial dependencies
Sun May  4 04:34:59 2008  prp34 factor: 3425376722500250431425989302857061
Sun May  4 04:34:59 2008  prp63 factor: 121989164029539344478888387906348661308781361217618006478634011
Sun May  4 04:34:59 2008  elapsed time 08:46:42

(17·10¹³⁰-53)/9 = 1(8)₁₂₉3_<131> = 59 · 433 · 479 · 12851536795962440562749361929843_<32> · C93

C93 = P44 · P50

P44 = 11614451771081002807800660499716452065000621_<44>

P50 = 10341349396259693395744386085621912743878339580497_<50>

Sun May  4 06:17:09 2008  Msieve v. 1.35
Sun May  4 06:17:09 2008  random seeds: fc847c7a fd7eb40d
Sun May  4 06:17:09 2008  factoring 120109103810755855073665089276825555209639255049591698558354393477251802397035257825184488637 (93 digits)
Sun May  4 06:17:11 2008  searching for 15-digit factors
Sun May  4 06:17:13 2008  commencing quadratic sieve (93-digit input)
Sun May  4 06:17:13 2008  using multiplier of 13
Sun May  4 06:17:13 2008  using 64kb Pentium 4 sieve core
Sun May  4 06:17:13 2008  sieve interval: 18 blocks of size 65536
Sun May  4 06:17:13 2008  processing polynomials in batches of 6
Sun May  4 06:17:13 2008  using a sieve bound of 1852271 (69412 primes)
Sun May  4 06:17:13 2008  using large prime bound of 209306623 (27 bits)
Sun May  4 06:17:13 2008  using double large prime bound of 949312700295976 (42-50 bits)
Sun May  4 06:17:13 2008  using trial factoring cutoff of 50 bits
Sun May  4 06:17:13 2008  polynomial 'A' values have 12 factors
Sun May  4 09:46:15 2008  69873 relations (18535 full + 51338 combined from 881173 partial), need 69508
Sun May  4 09:46:19 2008  begin with 899708 relations
Sun May  4 09:46:20 2008  reduce to 174000 relations in 11 passes
Sun May  4 09:46:20 2008  attempting to read 174000 relations
Sun May  4 09:46:25 2008  recovered 174000 relations
Sun May  4 09:46:25 2008  recovered 154249 polynomials
Sun May  4 09:46:25 2008  attempting to build 69873 cycles
Sun May  4 09:46:25 2008  found 69873 cycles in 6 passes
Sun May  4 09:46:25 2008  distribution of cycle lengths:
Sun May  4 09:46:25 2008     length 1 : 18535
Sun May  4 09:46:25 2008     length 2 : 12855
Sun May  4 09:46:25 2008     length 3 : 12103
Sun May  4 09:46:25 2008     length 4 : 9383
Sun May  4 09:46:25 2008     length 5 : 6738
Sun May  4 09:46:25 2008     length 6 : 4286
Sun May  4 09:46:25 2008     length 7 : 2636
Sun May  4 09:46:25 2008     length 9+: 3337
Sun May  4 09:46:25 2008  largest cycle: 18 relations
Sun May  4 09:46:26 2008  matrix is 69412 x 69873 (17.2 MB) with weight 4220263 (60.40/col)
Sun May  4 09:46:26 2008  sparse part has weight 4220263 (60.40/col)
Sun May  4 09:46:27 2008  filtering completed in 3 passes
Sun May  4 09:46:27 2008  matrix is 65252 x 65314 (16.1 MB) with weight 3954945 (60.55/col)
Sun May  4 09:46:27 2008  sparse part has weight 3954945 (60.55/col)
Sun May  4 09:46:28 2008  saving the first 48 matrix rows for later
Sun May  4 09:46:28 2008  matrix is 65204 x 65314 (9.4 MB) with weight 3024807 (46.31/col)
Sun May  4 09:46:28 2008  sparse part has weight 2081515 (31.87/col)
Sun May  4 09:46:28 2008  matrix includes 64 packed rows
Sun May  4 09:46:28 2008  using block size 21845 for processor cache size 512 kB
Sun May  4 09:46:28 2008  commencing Lanczos iteration
Sun May  4 09:46:28 2008  memory use: 9.6 MB
Sun May  4 09:47:10 2008  lanczos halted after 1032 iterations (dim = 65202)
Sun May  4 09:47:11 2008  recovered 16 nontrivial dependencies
Sun May  4 09:47:11 2008  prp44 factor: 11614451771081002807800660499716452065000621
Sun May  4 09:47:11 2008  prp50 factor: 10341349396259693395744386085621912743878339580497
Sun May  4 09:47:11 2008  elapsed time 03:30:02

May 4, 2008

By Robert Backstrom / GGNFS, GMP-ECM

(17·10¹³⁸-53)/9 = 1(8)₁₃₇3_<139> = 1187 · 1979 · 100520408961365189_<18> · C115

C115 = P41 · P75

P41 = 52269084438711395174858006507068213911373_<41>

P75 = 153042044567989424299284094191024360306276834800651709136147324967796139843_<75>

Number: n
N=7999367550197271822646360963644905153246648798556416044418272601732208581583503314076806099132800234363381916134439
  ( 115 digits)
SNFS difficulty: 139 digits.
Divisors found:

Sun May  4 03:10:23 2008  prp41 factor: 52269084438711395174858006507068213911373
Sun May  4 03:10:23 2008  prp75 factor: 153042044567989424299284094191024360306276834800651709136147324967796139843
Sun May  4 03:10:23 2008  elapsed time 00:13:11 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 5.83 hours.
Scaled time: 4.89 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_1_8_137_3
n: 7999367550197271822646360963644905153246648798556416044418272601732208581583503314076806099132800234363381916134439
type: snfs
deg: 5
c5: 17000
c0: -53
skew: 0.32
m: 1000000000000000000000000000
rlim: 1100000
alim: 1100000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved  special-q in [100000, 2349990)
Primes: RFBsize:85714, AFBsize:85954, largePrimes:1723644 encountered
Relations: rels:1751737, finalFF:207968
Max relations in full relation-set: 28
Initial matrix: 171735 x 207968 with sparse part having weight 17947252.
Pruned matrix : 
Total sieving time: 5.74 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1100000,1100000,25,25,43,43,2.5,2.5,75000
total time: 5.83 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

6·10¹⁶⁵-7 = 5(9)₁₆₄3_<166> = 13 · 79 · 113 · 7235159683_<10> · 782556346460516558455522307_<27> · C124

C124 = P56 · P69

P56 = 89114521059015530309415870009443429755507579670159234491_<56>

P69 = 102468445422444548672703238249307270954451352766414703365751873047633_<69>

Number: n
N=9131426437483018250616136976167125291747020858040915201947647855343618380368524095147817529154557716728675938758146459509803
  ( 124 digits)
SNFS difficulty: 165 digits.
Divisors found:

Sun May 04 04:55:30 2008  prp56 factor: 89114521059015530309415870009443429755507579670159234491
Sun May 04 04:55:30 2008  prp69 factor: 102468445422444548672703238249307270954451352766414703365751873047633
Sun May 04 04:55:30 2008  elapsed time 01:53:48 (Msieve 1.34)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 63.25 hours.
Scaled time: 91.53 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_5_9_164_3
n: 9131426437483018250616136976167125291747020858040915201947647855343618380368524095147817529154557716728675938758146459509803
skew: 1.03
deg: 5
c5: 6
c0: -7
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3300149)
Primes: RFBsize:216816, AFBsize:217096, largePrimes:7508847 encountered
Relations: rels:6918012, finalFF:470957
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 62.98 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 63.25 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(17·10¹⁴⁸-53)/9 = 1(8)₁₄₇3_<149> = 599 · 1523 · 5449 · C139

C139 = P66 · P74

P66 = 196920964872399960571095869962957319355465848009092572272618008697_<66>

P74 = 19296161407988911730535538884844824784794847267080297111232954814015304743_<74>

Number: n
N=3799818722794744250790994913866933739151845029327254261031147177170091191856457432267665149073674412679857372535547483357901361918279349871
  ( 139 digits)
SNFS difficulty: 149 digits.
Divisors found:

Sun May 04 15:08:17 2008  prp66 factor: 196920964872399960571095869962957319355465848009092572272618008697
Sun May 04 15:08:17 2008  prp74 factor: 19296161407988911730535538884844824784794847267080297111232954814015304743
Sun May 04 15:08:17 2008  elapsed time 00:32:29 (Msieve 1.34)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 12.67 hours.
Scaled time: 23.17 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_8_147_3
n: 3799818722794744250790994913866933739151845029327254261031147177170091191856457432267665149073674412679857372535547483357901361918279349871
skew: 0.32
deg: 5
c5: 17000
c0: -53
m: 100000000000000000000000000000
type: snfs
rlim: 1600000
alim: 1600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2700001)
Primes: RFBsize:121127, AFBsize:121430, largePrimes:7338873 encountered
Relations: rels:6686800, finalFF:246342
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 12.49 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,1600000,1600000,28,28,48,48,2.5,2.5,100000
total time: 12.67 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

May 3, 2008 (4th)

By Justin Card / GGNFS

4·10¹⁶⁴+3 = 4(0)₁₆₃3_<165> = 13 · 11467 · 9523399993242554891943426601_<28> · C132

C132 = P56 · P76

P56 = 31445722457122043977687400352333915199796312519950578127_<56>

P76 = 8960107578000945594964516537852622453791282510444775001014858922521752127659_<76>

May 3, 2008 (3rd)

By Sinkiti Sibata / Msieve

(17·10¹⁰⁹-53)/9 = 1(8)₁₀₈3_<110> = 13 · 29 · 127² · 1489 · 6379 · C96

C96 = P33 · P64

P33 = 133163092855224104302363788449929_<33>

P64 = 2455989164158808006628046290075502317087684176170758096093506249_<64>

Sat May  3 07:03:12 2008  Msieve v. 1.35
Sat May  3 07:03:12 2008  random seeds: 6f29155d 3913c6e4
Sat May  3 07:03:12 2008  factoring 327047113118303586290974817149111522786499532420335382905249154650071096486259467066566385106321 (96 digits)
Sat May  3 07:03:13 2008  searching for 15-digit factors
Sat May  3 07:03:15 2008  commencing quadratic sieve (96-digit input)
Sat May  3 07:03:16 2008  using multiplier of 1
Sat May  3 07:03:16 2008  using 64kb Pentium 4 sieve core
Sat May  3 07:03:16 2008  sieve interval: 18 blocks of size 65536
Sat May  3 07:03:16 2008  processing polynomials in batches of 6
Sat May  3 07:03:16 2008  using a sieve bound of 2253037 (83529 primes)
Sat May  3 07:03:16 2008  using large prime bound of 337955550 (28 bits)
Sat May  3 07:03:16 2008  using double large prime bound of 2248781238410700 (43-51 bits)
Sat May  3 07:03:16 2008  using trial factoring cutoff of 51 bits
Sat May  3 07:03:16 2008  polynomial 'A' values have 12 factors
Sat May  3 14:08:38 2008  83700 relations (20716 full + 62984 combined from 1232784 partial), need 83625
Sat May  3 14:08:43 2008  begin with 1253500 relations
Sat May  3 14:08:44 2008  reduce to 217266 relations in 13 passes
Sat May  3 14:08:44 2008  attempting to read 217266 relations
Sat May  3 14:08:51 2008  recovered 217266 relations
Sat May  3 14:08:51 2008  recovered 202315 polynomials
Sat May  3 14:08:52 2008  attempting to build 83700 cycles
Sat May  3 14:08:52 2008  found 83700 cycles in 5 passes
Sat May  3 14:08:52 2008  distribution of cycle lengths:
Sat May  3 14:08:52 2008     length 1 : 20716
Sat May  3 14:08:52 2008     length 2 : 14681
Sat May  3 14:08:52 2008     length 3 : 14201
Sat May  3 14:08:52 2008     length 4 : 11285
Sat May  3 14:08:52 2008     length 5 : 8445
Sat May  3 14:08:52 2008     length 6 : 5713
Sat May  3 14:08:52 2008     length 7 : 3597
Sat May  3 14:08:52 2008     length 9+: 5062
Sat May  3 14:08:52 2008  largest cycle: 20 relations
Sat May  3 14:08:52 2008  matrix is 83529 x 83700 (22.5 MB) with weight 5575853 (66.62/col)
Sat May  3 14:08:52 2008  sparse part has weight 5575853 (66.62/col)
Sat May  3 14:08:54 2008  filtering completed in 3 passes
Sat May  3 14:08:54 2008  matrix is 79665 x 79729 (21.6 MB) with weight 5347576 (67.07/col)
Sat May  3 14:08:54 2008  sparse part has weight 5347576 (67.07/col)
Sat May  3 14:08:55 2008  saving the first 48 matrix rows for later
Sat May  3 14:08:55 2008  matrix is 79617 x 79729 (14.8 MB) with weight 4376564 (54.89/col)
Sat May  3 14:08:55 2008  sparse part has weight 3401479 (42.66/col)
Sat May  3 14:08:55 2008  matrix includes 64 packed rows
Sat May  3 14:08:55 2008  using block size 21845 for processor cache size 512 kB
Sat May  3 14:08:56 2008  commencing Lanczos iteration
Sat May  3 14:08:56 2008  memory use: 13.6 MB
Sat May  3 14:10:09 2008  lanczos halted after 1261 iterations (dim = 79617)
Sat May  3 14:10:10 2008  recovered 17 nontrivial dependencies
Sat May  3 14:10:12 2008  prp33 factor: 133163092855224104302363788449929
Sat May  3 14:10:12 2008  prp64 factor: 2455989164158808006628046290075502317087684176170758096093506249
Sat May  3 14:10:12 2008  elapsed time 07:07:00

(17·10¹¹⁴-53)/9 = 1(8)₁₁₃3_<115> = 23 · 135963488010063195216983_<24> · C90

C90 = P44 · P47

P44 = 45407051110420976718615060333667020841308287_<44>

P47 = 13302491197732416716475505613313966954879008701_<47>

Sat May  3 14:29:59 2008  Msieve v. 1.35
Sat May  3 14:29:59 2008  random seeds: 06c7da98 e99f005e
Sat May  3 14:29:59 2008  factoring 604026897711361001042648778953029296818263452928596668891224289618648285800606122496405187 (90 digits)
Sat May  3 14:30:01 2008  searching for 15-digit factors
Sat May  3 14:30:03 2008  commencing quadratic sieve (90-digit input)
Sat May  3 14:30:03 2008  using multiplier of 3
Sat May  3 14:30:03 2008  using 64kb Pentium 4 sieve core
Sat May  3 14:30:03 2008  sieve interval: 18 blocks of size 65536
Sat May  3 14:30:03 2008  processing polynomials in batches of 6
Sat May  3 14:30:03 2008  using a sieve bound of 1617893 (61176 primes)
Sat May  3 14:30:03 2008  using large prime bound of 135903012 (27 bits)
Sat May  3 14:30:03 2008  using double large prime bound of 436327220460936 (42-49 bits)
Sat May  3 14:30:03 2008  using trial factoring cutoff of 49 bits
Sat May  3 14:30:03 2008  polynomial 'A' values have 12 factors
Sat May  3 16:46:42 2008  61740 relations (16397 full + 45343 combined from 662542 partial), need 61272
Sat May  3 16:46:45 2008  begin with 678939 relations
Sat May  3 16:46:45 2008  reduce to 150588 relations in 11 passes
Sat May  3 16:46:45 2008  attempting to read 150588 relations
Sat May  3 16:46:49 2008  recovered 150588 relations
Sat May  3 16:46:49 2008  recovered 129378 polynomials
Sat May  3 16:46:50 2008  attempting to build 61740 cycles
Sat May  3 16:46:50 2008  found 61740 cycles in 5 passes
Sat May  3 16:46:50 2008  distribution of cycle lengths:
Sat May  3 16:46:50 2008     length 1 : 16397
Sat May  3 16:46:50 2008     length 2 : 11886
Sat May  3 16:46:50 2008     length 3 : 10898
Sat May  3 16:46:50 2008     length 4 : 8182
Sat May  3 16:46:50 2008     length 5 : 5849
Sat May  3 16:46:50 2008     length 6 : 3702
Sat May  3 16:46:50 2008     length 7 : 2260
Sat May  3 16:46:50 2008     length 9+: 2566
Sat May  3 16:46:50 2008  largest cycle: 18 relations
Sat May  3 16:46:50 2008  matrix is 61176 x 61740 (14.9 MB) with weight 3662101 (59.31/col)
Sat May  3 16:46:50 2008  sparse part has weight 3662101 (59.31/col)
Sat May  3 16:46:51 2008  filtering completed in 4 passes
Sat May  3 16:46:51 2008  matrix is 57220 x 57284 (13.8 MB) with weight 3399691 (59.35/col)
Sat May  3 16:46:51 2008  sparse part has weight 3399691 (59.35/col)
Sat May  3 16:46:52 2008  saving the first 48 matrix rows for later
Sat May  3 16:46:52 2008  matrix is 57172 x 57284 (8.5 MB) with weight 2623647 (45.80/col)
Sat May  3 16:46:52 2008  sparse part has weight 1877380 (32.77/col)
Sat May  3 16:46:52 2008  matrix includes 64 packed rows
Sat May  3 16:46:52 2008  using block size 21845 for processor cache size 512 kB
Sat May  3 16:46:52 2008  commencing Lanczos iteration
Sat May  3 16:46:52 2008  memory use: 8.4 MB
Sat May  3 16:47:25 2008  lanczos halted after 906 iterations (dim = 57172)
Sat May  3 16:47:25 2008  recovered 18 nontrivial dependencies
Sat May  3 16:47:27 2008  prp44 factor: 45407051110420976718615060333667020841308287
Sat May  3 16:47:27 2008  prp47 factor: 13302491197732416716475505613313966954879008701
Sat May  3 16:47:27 2008  elapsed time 02:17:28

(17·10¹¹⁶-53)/9 = 1(8)₁₁₅3_<117> = 3 · 3238037953_<10> · 200976479996422199_<18> · C89

C89 = P35 · P55

P35 = 40639575279507524445937749287780453_<35>

P55 = 2380722773741498849314583916531534950249488824911854571_<55>

Sat May  3 17:04:10 2008  Msieve v. 1.35
Sat May  3 17:04:10 2008  random seeds: f1ace691 41f2247d
Sat May  3 17:04:10 2008  factoring 96751562383105601979686446490891285119918160039771268179072666138270111858671872512500663 (89 digits)
Sat May  3 17:04:12 2008  searching for 15-digit factors
Sat May  3 17:04:14 2008  commencing quadratic sieve (89-digit input)
Sat May  3 17:04:14 2008  using multiplier of 3
Sat May  3 17:04:14 2008  using 64kb Pentium 4 sieve core
Sat May  3 17:04:14 2008  sieve interval: 17 blocks of size 65536
Sat May  3 17:04:14 2008  processing polynomials in batches of 6
Sat May  3 17:04:14 2008  using a sieve bound of 1550147 (59333 primes)
Sat May  3 17:04:14 2008  using large prime bound of 124011760 (26 bits)
Sat May  3 17:04:14 2008  using double large prime bound of 370026785535040 (42-49 bits)
Sat May  3 17:04:14 2008  using trial factoring cutoff of 49 bits
Sat May  3 17:04:14 2008  polynomial 'A' values have 11 factors
Sat May  3 19:36:18 2008  59471 relations (15268 full + 44203 combined from 634222 partial), need 59429
Sat May  3 19:36:20 2008  begin with 649490 relations
Sat May  3 19:36:21 2008  reduce to 147167 relations in 10 passes
Sat May  3 19:36:21 2008  attempting to read 147167 relations
Sat May  3 19:36:25 2008  recovered 147167 relations
Sat May  3 19:36:25 2008  recovered 129612 polynomials
Sat May  3 19:36:25 2008  attempting to build 59471 cycles
Sat May  3 19:36:25 2008  found 59471 cycles in 5 passes
Sat May  3 19:36:25 2008  distribution of cycle lengths:
Sat May  3 19:36:25 2008     length 1 : 15268
Sat May  3 19:36:25 2008     length 2 : 10961
Sat May  3 19:36:25 2008     length 3 : 10382
Sat May  3 19:36:25 2008     length 4 : 8027
Sat May  3 19:36:25 2008     length 5 : 5917
Sat May  3 19:36:25 2008     length 6 : 3876
Sat May  3 19:36:25 2008     length 7 : 2292
Sat May  3 19:36:25 2008     length 9+: 2748
Sat May  3 19:36:25 2008  largest cycle: 18 relations
Sat May  3 19:36:25 2008  matrix is 59333 x 59471 (14.9 MB) with weight 3656207 (61.48/col)
Sat May  3 19:36:25 2008  sparse part has weight 3656207 (61.48/col)
Sat May  3 19:36:26 2008  filtering completed in 3 passes
Sat May  3 19:36:26 2008  matrix is 55994 x 56058 (14.1 MB) with weight 3478766 (62.06/col)
Sat May  3 19:36:26 2008  sparse part has weight 3478766 (62.06/col)
Sat May  3 19:36:27 2008  saving the first 48 matrix rows for later
Sat May  3 19:36:27 2008  matrix is 55946 x 56058 (10.5 MB) with weight 2924982 (52.18/col)
Sat May  3 19:36:27 2008  sparse part has weight 2418502 (43.14/col)
Sat May  3 19:36:27 2008  matrix includes 64 packed rows
Sat May  3 19:36:27 2008  using block size 21845 for processor cache size 512 kB
Sat May  3 19:36:28 2008  commencing Lanczos iteration
Sat May  3 19:36:28 2008  memory use: 9.4 MB
Sat May  3 19:37:04 2008  lanczos halted after 886 iterations (dim = 55944)
Sat May  3 19:37:04 2008  recovered 16 nontrivial dependencies
Sat May  3 19:37:05 2008  prp35 factor: 40639575279507524445937749287780453
Sat May  3 19:37:05 2008  prp55 factor: 2380722773741498849314583916531534950249488824911854571
Sat May  3 19:37:05 2008  elapsed time 02:32:55

May 3, 2008 (2nd)

By Jo Yeong Uk / GGNFS, GMP-ECM

(17·10¹¹¹-53)/9 = 1(8)₁₁₀3_<112> = 7 · 741937667 · C102

C102 = P47 · P56

P47 = 21406727974433936850882602900693924335418266933_<47>

P56 = 16989893695587092805835674132504936884778981121981724779_<56>

Number: 18883_111
N=363698032655983000887109927310470195159725284363099792950451819884850031842151060166176791870362432807
  ( 102 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=21406727974433936850882602900693924335418266933 (pp47)
 r2=16989893695587092805835674132504936884778981121981724779 (pp56)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.78 hours.
Scaled time: 1.86 units (timescale=2.379).
Factorization parameters were as follows:
n: 363698032655983000887109927310470195159725284363099792950451819884850031842151060166176791870362432807
m: 10000000000000000000000
c5: 170
c0: -53
skew: 0.79
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 360001)
Primes: RFBsize:30757, AFBsize:30774, largePrimes:1077150 encountered
Relations: rels:997972, finalFF:91744
Max relations in full relation-set: 28
Initial matrix: 61598 x 91744 with sparse part having weight 4823069.
Pruned matrix : 54393 x 54764 with weight 2049154.
Total sieving time: 0.76 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,112,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.78 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

(17·10¹²⁶-53)/9 = 1(8)₁₂₅3_<127> = 2539 · 333367 · 641721697 · C109

C109 = P36 · P73

P36 = 727894902607689657739464596480166721_<36>

P73 = 4777555082205456186505940897215974516974069492382172337337363813495100943_<73>

Number: 18883_126
N=3477557991264813287478908886327964502328581041382834256329695746849099622706974067359408570904712197364317903
  ( 109 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=727894902607689657739464596480166721 (pp36)
 r2=4777555082205456186505940897215974516974069492382172337337363813495100943 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.08 hours.
Scaled time: 4.96 units (timescale=2.382).
Factorization parameters were as follows:
n: 3477557991264813287478908886327964502328581041382834256329695746849099622706974067359408570904712197364317903
m: 10000000000000000000000000
c5: 170
c0: -53
skew: 0.79
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [400000, 920001)
Primes: RFBsize:63951, AFBsize:63898, largePrimes:1458294 encountered
Relations: rels:1439137, finalFF:156132
Max relations in full relation-set: 28
Initial matrix: 127916 x 156132 with sparse part having weight 10680678.
Pruned matrix : 119166 x 119869 with weight 6532998.
Total sieving time: 2.01 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,800000,800000,25,25,45,45,2.2,2.2,40000
total time: 2.08 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

(17·10¹²⁸-53)/9 = 1(8)₁₂₇3_<129> = 3 · 313 · 2045697173576072885436493_<25> · C101

C101 = P46 · P56

P46 = 4004240923599095557112102414494870267401405247_<46>

P56 = 24557224171047782792269547057638686525422784224174595907_<56>

Number: 18883_128
N=98333041995706407541101587203287053374224097813765416091275589460900030276042794110046704210174524029
  ( 101 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=4004240923599095557112102414494870267401405247 (pp46)
 r2=24557224171047782792269547057638686525422784224174595907 (pp56)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.88 hours.
Scaled time: 6.86 units (timescale=2.385).
Factorization parameters were as follows:
n: 98333041995706407541101587203287053374224097813765416091275589460900030276042794110046704210174524029
m: 100000000000000000000000000
c5: 17
c0: -5300
skew: 3.15
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 1200001)
Primes: RFBsize:78498, AFBsize:78786, largePrimes:1601165 encountered
Relations: rels:1619904, finalFF:194549
Max relations in full relation-set: 28
Initial matrix: 157351 x 194549 with sparse part having weight 13099468.
Pruned matrix : 144276 x 145126 with weight 7867622.
Total sieving time: 2.78 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 2.88 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

(17·10¹³³-53)/9 = 1(8)₁₃₂3_<134> = 13 · 9293 · 8751737149_<10> · 27537178718993_<14> · C105

C105 = P34 · P72

P34 = 3764382625358250645569863551537179_<34>

P72 = 172345383011769458501536322137290527842023267217164289309509635505102629_<72>

Number: 18883_133
N=648773965370217964813793670013617787398115175546853715736855115418235213719596637355092244272371104143591
  ( 105 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=3764382625358250645569863551537179 (pp34)
 r2=172345383011769458501536322137290527842023267217164289309509635505102629 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.61 hours.
Scaled time: 8.59 units (timescale=2.377).
Factorization parameters were as follows:
n: 648773965370217964813793670013617787398115175546853715736855115418235213719596637355092244272371104143591
m: 1000000000000000000000000000
c5: 17
c0: -5300
skew: 3.15
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1450001)
Primes: RFBsize:107126, AFBsize:107538, largePrimes:2291876 encountered
Relations: rels:2382392, finalFF:248342
Max relations in full relation-set: 28
Initial matrix: 214731 x 248342 with sparse part having weight 19852549.
Pruned matrix : 203707 x 204844 with weight 13784270.
Total sieving time: 3.40 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 3.61 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

(17·10¹⁴²-53)/9 = 1(8)₁₄₁3_<143> = 1067029 · 1527173 · 244863342785827_<15> · 180280219243349327_<18> · C99

C99 = P31 · P68

P31 = 5812880350102104118685752874347_<31>

P68 = 45172977411817853583314487385516736976079129109325013547106832353973_<68>

(17·10¹³⁵-53)/9 = 1(8)₁₃₄3_<136> = 7 · 12526489 · 6994006470802381_<16> · C112

C112 = P40 · P73

P40 = 1347794481418895554693419393197617111453_<40>

P73 = 2285226791368354411931518719607928339055696989105013365535936167657426597_<73>

Number: 18883_135
N=3080016058196877858823811294679731916589946298223632245279662342289283579816083683606578447554446986742515515441
  ( 112 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=1347794481418895554693419393197617111453 (pp40)
 r2=2285226791368354411931518719607928339055696989105013365535936167657426597 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.16 hours.
Scaled time: 7.54 units (timescale=2.386).
Factorization parameters were as follows:
n: 3080016058196877858823811294679731916589946298223632245279662342289283579816083683606578447554446986742515515441
m: 1000000000000000000000000000
c5: 17
c0: -53
skew: 1.26
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1350001)
Primes: RFBsize:107126, AFBsize:106848, largePrimes:2339441 encountered
Relations: rels:2497590, finalFF:307796
Max relations in full relation-set: 28
Initial matrix: 214039 x 307796 with sparse part having weight 24583959.
Pruned matrix : 182104 x 183238 with weight 11697085.
Total sieving time: 3.00 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 3.16 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

May 3, 2008

By Robert Backstrom / Msieve, GGNFS

(17·10¹⁰⁷-53)/9 = 1(8)₁₀₆3_<108> = 3 · 19 · 9789899963_<10> · 1060679948543_<13> · C84

C84 = P41 · P43

P41 = 93231858661753747555233330990664897834019_<41>

P43 = 3422981886629292384067736826750714955820389_<43>

Sat May 03 01:00:14 2008  
Sat May 03 01:00:14 2008  
Sat May 03 01:00:14 2008  Msieve v. 1.34
Sat May 03 01:00:14 2008  random seeds: 58766b18 0f915d74
Sat May 03 01:00:14 2008  factoring 319130963455965377482501772162273692026572248526301173912434143259339755923298013391 (84 digits)
Sat May 03 01:00:14 2008  searching for 15-digit factors
Sat May 03 01:00:15 2008  commencing quadratic sieve (84-digit input)
Sat May 03 01:00:15 2008  using multiplier of 3
Sat May 03 01:00:15 2008  using 64kb Opteron sieve core
Sat May 03 01:00:15 2008  sieve interval: 6 blocks of size 65536
Sat May 03 01:00:15 2008  processing polynomials in batches of 17
Sat May 03 01:00:15 2008  using a sieve bound of 1398737 (53529 primes)
Sat May 03 01:00:15 2008  using large prime bound of 120291382 (26 bits)
Sat May 03 01:00:15 2008  using trial factoring cutoff of 27 bits
Sat May 03 01:00:15 2008  polynomial 'A' values have 11 factors
Sat May 03 01:20:55 2008  53671 relations (27000 full + 26671 combined from 282540 partial), need 53625
Sat May 03 01:20:55 2008  begin with 309539 relations
Sat May 03 01:20:55 2008  reduce to 76978 relations in 2 passes
Sat May 03 01:20:55 2008  attempting to read 76978 relations
Sat May 03 01:20:56 2008  recovered 76978 relations
Sat May 03 01:20:56 2008  recovered 71187 polynomials
Sat May 03 01:20:56 2008  attempting to build 53671 cycles
Sat May 03 01:20:56 2008  found 53671 cycles in 1 passes
Sat May 03 01:20:56 2008  distribution of cycle lengths:
Sat May 03 01:20:56 2008     length 1 : 27000
Sat May 03 01:20:56 2008     length 2 : 26671
Sat May 03 01:20:56 2008  largest cycle: 2 relations
Sat May 03 01:20:56 2008  matrix is 53529 x 53671 (7.4 MB) with weight 1729380 (32.22/col)
Sat May 03 01:20:56 2008  sparse part has weight 1729380 (32.22/col)
Sat May 03 01:20:56 2008  filtering completed in 4 passes
Sat May 03 01:20:56 2008  matrix is 46544 x 46608 (6.3 MB) with weight 1475595 (31.66/col)
Sat May 03 01:20:56 2008  sparse part has weight 1475595 (31.66/col)
Sat May 03 01:20:57 2008  saving the first 48 matrix rows for later
Sat May 03 01:20:57 2008  matrix is 46496 x 46608 (4.1 MB) with weight 1106357 (23.74/col)
Sat May 03 01:20:57 2008  sparse part has weight 783710 (16.81/col)
Sat May 03 01:20:57 2008  matrix includes 64 packed rows
Sat May 03 01:20:57 2008  commencing Lanczos iteration
Sat May 03 01:20:57 2008  memory use: 5.8 MB
Sat May 03 01:21:31 2008  lanczos halted after 736 iterations (dim = 46489)
Sat May 03 01:21:31 2008  recovered 14 nontrivial dependencies
Sat May 03 01:21:31 2008  prp41 factor: 93231858661753747555233330990664897834019
Sat May 03 01:21:31 2008  prp43 factor: 3422981886629292384067736826750714955820389
Sat May 03 01:21:31 2008  elapsed time 00:21:17

(17·10¹⁰⁶-53)/9 = 1(8)₁₀₅3_<107> = C107

C107 = P49 · P58

P49 = 8630106820148450673420782464300565409835605393871_<49>

P58 = 2188720172592715591130753702142474055753413658268136225373_<58>

Number: n
N=18888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883
  ( 107 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=8630106820148450673420782464300565409835605393871 (pp49)
 r2=2188720172592715591130753702142474055753413658268136225373 (pp58)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.68 hours.
Scaled time: 1.24 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_1_8_105_3
n: 18888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883
skew: 0.79
deg: 5
c5: 170
c0: -53
m: 1000000000000000000000
type: snfs
rlim: 600000
alim: 600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 160001)
Primes: RFBsize:49098, AFBsize:49096, largePrimes:3980929 encountered
Relations: rels:3421632, finalFF:187238
Max relations in full relation-set: 48
Initial matrix: 98261 x 187238 with sparse part having weight 13120897.
Pruned matrix : 67652 x 68207 with weight 2699659.
Total sieving time: 0.61 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.01 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,107,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.5,2.5,50000
total time: 0.68 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(17·10¹⁰⁴-53)/9 = 1(8)₁₀₃3_<105> = 3³ · 139 · 1215463 · C95

C95 = P32 · P64

P32 = 15853792454098265153552008138381_<32>

P64 = 2611878293362696035834569502178477397915530892823191844676083137_<64>

Number: n
N=41408176378336565319566253850826344214275710089439512380007961638247320706460090919410156581197
  ( 95 digits)
SNFS difficulty: 106 digits.
Divisors found:
 r1=15853792454098265153552008138381 (pp32)
 r2=2611878293362696035834569502178477397915530892823191844676083137 (pp64)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.60 hours.
Scaled time: 1.09 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_1_8_103_3
n: 41408176378336565319566253850826344214275710089439512380007961638247320706460090919410156581197
skew: 1.99
deg: 5
c5: 17
c0: -530
m: 1000000000000000000000
type: snfs
rlim: 600000
alim: 600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 160001)
Primes: RFBsize:49098, AFBsize:49241, largePrimes:3709422 encountered
Relations: rels:3117179, finalFF:145044
Max relations in full relation-set: 48
Initial matrix: 98404 x 145044 with sparse part having weight 9101580.
Pruned matrix : 76838 x 77394 with weight 2816172.
Total sieving time: 0.53 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.02 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,106,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.5,2.5,50000
total time: 0.60 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(23·10¹⁶⁴+1)/3 = 7(6)₁₆₃7_<165> = 13 · 86369 · 41704840921_<11> · 118056872720744949209_<21> · C129

C129 = P51 · P79

P51 = 111436804245982124976494018826930500402933157080689_<51>

P79 = 1244511588556699658378674981796798862545904148539310114593089804716974603547991_<79>

Number: n
N=138684394275849187828660560710673371912849390957781872773628671686689559292146610064299317211442794052605863374723378423270845799
  ( 129 digits)
SNFS difficulty: 166 digits.
Divisors found:

Sat May 03 10:40:40 2008  prp51 factor: 111436804245982124976494018826930500402933157080689
Sat May 03 10:40:40 2008  prp79 factor: 1244511588556699658378674981796798862545904148539310114593089804716974603547991
Sat May 03 10:40:40 2008  elapsed time 01:03:58 (Msieve 1.34)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 21.14 hours.
Scaled time: 38.67 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_7_6_163_7
n: 138684394275849187828660560710673371912849390957781872773628671686689559292146610064299317211442794052605863374723378423270845799
skew: 0.85
deg: 5
c5: 23
c0: 10
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3300000)
Primes: RFBsize:216816, AFBsize:217411, largePrimes:7366557 encountered
Relations: rels:6789767, finalFF:477036
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 20.99 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 21.14 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

4·10¹⁶⁷-3 = 3(9)₁₆₆7_<168> = 13 · 17 · 139 · 4421 · 7873915303_<10> · C150

C150 = P54 · P96

P54 = 618273762409165239603405636857538455481103354894431607_<54>

P96 = 605007623043639365025444446465689291883809981765758204992885675613074765084447457982884602953543_<96>

Number: n
N=374060339385416889430110381945106309862426286979244992667492320805419072529582709129344665255156355799651740239660308846387388622669297398516411833601
  ( 150 digits)
SNFS difficulty: 167 digits.
Divisors found:

Sat May  3 12:45:02 2008  prp54 factor: 618273762409165239603405636857538455481103354894431607
Sat May  3 12:45:02 2008  prp96 factor: 605007623043639365025444446465689291883809981765758204992885675613074765084447457982884602953543
Sat May  3 12:45:02 2008  elapsed time 00:55:23 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 25.57 hours.
Scaled time: 21.45 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_3_9_166_7
n: 374060339385416889430110381945106309862426286979244992667492320805419072529582709129344665255156355799651740239660308846387388622669297398516411833601
type: snfs
deg: 5
c5: 25
c0: -6
skew: 0.75
m: 2000000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3300203)
Primes: RFBsize:216816, AFBsize:215956, largePrimes:5607000 encountered
Relations: rels:5453742, finalFF:481499
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 25.40 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 25.57 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(17·10¹¹²-53)/9 = 1(8)₁₁₁3_<113> = 223 · 4001 · C107

C107 = P49 · P58

P49 = 8549198048140881562228719565616138334096186877231_<49>

P58 = 2476324871342590569760961715536698238992882278782339631491_<58>

Number: n
N=21170591756644794954724198870561383072268803750731475078415249202148889783035058375416111094299170598481421
  ( 107 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=8549198048140881562228719565616138334096186877231 (pp49)
 r2=2476324871342590569760961715536698238992882278782339631491 (pp58)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.93 hours.
Scaled time: 1.70 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_8_111_3
n: 21170591756644794954724198870561383072268803750731475078415249202148889783035058375416111094299170598481421
skew: 0.50
deg: 5
c5: 1700
c0: -53
m: 10000000000000000000000
type: snfs
rlim: 600000
alim: 600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 200001)
Primes: RFBsize:49098, AFBsize:49416, largePrimes:4169529 encountered
Relations: rels:3562039, finalFF:164380
Max relations in full relation-set: 48
Initial matrix: 98581 x 164380 with sparse part having weight 14493062.
Pruned matrix : 78682 x 79238 with weight 3965425.
Total sieving time: 0.84 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.02 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.5,2.5,50000
total time: 0.93 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(17·10¹²⁷-53)/9 = 1(8)₁₂₆3_<128> = 13 · 4003 · 540251 · C117

C117 = P51 · P67

P51 = 328798120789209691542180686790545783365122362891647_<51>

P67 = 2043396115186747802808184830871608870858489870879968003790681182801_<67>

Number: n
N=671864802701374144242485442869363565197753682139350317263751143697120621763729277444117459175771975912204400562963247
  ( 117 digits)
SNFS difficulty: 128 digits.
Divisors found:

Sat May  3 20:42:58 2008  prp51 factor: 328798120789209691542180686790545783365122362891647
Sat May  3 20:42:58 2008  prp67 factor: 2043396115186747802808184830871608870858489870879968003790681182801
Sat May  3 20:42:58 2008  elapsed time 00:05:26 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 2.68 hours.
Scaled time: 2.25 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_1_8_126_3
n: 671864802701374144242485442869363565197753682139350317263751143697120621763729277444117459175771975912204400562963247
type: snfs
deg: 5
c5: 1700
c0: -53
skew: 0.50
m: 10000000000000000000000000
rlim: 800000
alim: 800000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved  special-q in [100000, 521243)
Primes: RFBsize:63951, AFBsize:64318, largePrimes:1526929 encountered
Relations: rels:1490361, finalFF:138680
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 2.62 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.5,2.5,50000
total time: 2.68 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

May 2, 2008 (3rd)

By Robert Backstrom / GMP-ECM

(16·10¹⁸⁵+11)/9 = 1(7)₁₈₄9_<186> = 7 · C185

C185 = P29 · C156

P29 = 26956598084950821289292271647_<29>

C156 = [942137628672209731441123765840597029595643313299719206072714213145836957181250058636962835363668375659087382552918820565633591241200675392898887129525086251_<156>]

May 2, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(13·10¹⁶²+23)/9 = 1(4)₁₆₁7_<163> = 48440917801958347097_<20> · 170569706737281090797_<21> · C123

C123 = P37 · P86

P37 = 4896627844567999141056381026425997699_<37>

P86 = 35701747916582274558191451115278830078250818431335984974373036683747660077947671049617_<86>

Number: 14447_162
N=174818172948084317069323230611457205447676147430883678288697651601550278437647590631488396130094047936924771876587756831283
  ( 123 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=4896627844567999141056381026425997699 (pp37)
 r2=35701747916582274558191451115278830078250818431335984974373036683747660077947671049617 (pp86)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 134.15 hours.
Scaled time: 90.82 units (timescale=0.677).
Factorization parameters were as follows:
name: 14447_162
n: 174818172948084317069323230611457205447676147430883678288697651601550278437647590631488396130094047936924771876587756831283
m: 100000000000000000000000000000000
c5: 1300
c0: 23
skew: 0.45
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 5550001)
Primes: RFBsize:315948, AFBsize:315066, largePrimes:5940702 encountered
Relations: rels:6062603, finalFF:735486
Max relations in full relation-set: 28
Initial matrix: 631081 x 735486 with sparse part having weight 58557622.
Pruned matrix : 557419 x 560638 with weight 43543481.
Total sieving time: 115.98 hours.
Total relation processing time: 0.49 hours.
Matrix solve time: 17.44 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 134.15 hours.
 --------- CPU info (if available) ----------

May 2, 2008

The factor table of 188...883 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

May 1, 2008

By Robert Backstrom / GMP-ECM, Msieve

(17·10¹⁷⁹-71)/9 = 1(8)₁₇₈1_<180> = 7 · 11 · 103 · 239 · 9930637 · 14023579 · 1231364489_<10> · 684907717263391040869653253_<27> · C123

C123 = P40 · P42 · P43

P40 = 1187282062146192125179089986736275870419_<40>

P42 = 375284494633543979200133045260994522261009_<42>

P43 = 1904194805934835770754653293450160027271669_<43>

Thu May 01 01:02:37 2008  
Thu May 01 01:02:37 2008  
Thu May 01 01:02:37 2008  Msieve v. 1.34
Thu May 01 01:02:37 2008  random seeds: 9e84d5d0 7d88e2a1
Thu May 01 01:02:37 2008  factoring 714614785429074193724941033575218868394451441841244639514764707813514033355369054021 (84 digits)
Thu May 01 01:02:37 2008  searching for 15-digit factors
Thu May 01 01:02:38 2008  commencing quadratic sieve (84-digit input)
Thu May 01 01:02:38 2008  using multiplier of 29
Thu May 01 01:02:38 2008  using 64kb Opteron sieve core
Thu May 01 01:02:38 2008  sieve interval: 6 blocks of size 65536
Thu May 01 01:02:38 2008  processing polynomials in batches of 17
Thu May 01 01:02:38 2008  using a sieve bound of 1405787 (53824 primes)
Thu May 01 01:02:38 2008  using large prime bound of 119491895 (26 bits)
Thu May 01 01:02:38 2008  using double large prime bound of 346106003521495 (41-49 bits)
Thu May 01 01:02:38 2008  using trial factoring cutoff of 49 bits
Thu May 01 01:02:38 2008  polynomial 'A' values have 11 factors
Thu May 01 01:25:48 2008  54118 relations (15886 full + 38232 combined from 576589 partial), need 53920
Thu May 01 01:25:48 2008  begin with 592474 relations
Thu May 01 01:25:49 2008  reduce to 127260 relations in 11 passes
Thu May 01 01:25:49 2008  attempting to read 127260 relations
Thu May 01 01:25:50 2008  recovered 127260 relations
Thu May 01 01:25:50 2008  recovered 105898 polynomials
Thu May 01 01:25:50 2008  attempting to build 54118 cycles
Thu May 01 01:25:50 2008  found 54117 cycles in 5 passes
Thu May 01 01:25:50 2008  distribution of cycle lengths:
Thu May 01 01:25:50 2008     length 1 : 15886
Thu May 01 01:25:50 2008     length 2 : 10845
Thu May 01 01:25:50 2008     length 3 : 9537
Thu May 01 01:25:50 2008     length 4 : 6918
Thu May 01 01:25:50 2008     length 5 : 4661
Thu May 01 01:25:50 2008     length 6 : 2830
Thu May 01 01:25:50 2008     length 7 : 1579
Thu May 01 01:25:50 2008     length 9+: 1861
Thu May 01 01:25:50 2008  largest cycle: 18 relations
Thu May 01 01:25:50 2008  matrix is 53824 x 54117 (11.4 MB) with weight 2766188 (51.11/col)
Thu May 01 01:25:50 2008  sparse part has weight 2766188 (51.11/col)
Thu May 01 01:25:51 2008  filtering completed in 3 passes
Thu May 01 01:25:51 2008  matrix is 49265 x 49329 (10.4 MB) with weight 2532773 (51.34/col)
Thu May 01 01:25:51 2008  sparse part has weight 2532773 (51.34/col)
Thu May 01 01:25:51 2008  saving the first 48 matrix rows for later
Thu May 01 01:25:51 2008  matrix is 49217 x 49329 (5.6 MB) with weight 1835858 (37.22/col)
Thu May 01 01:25:51 2008  sparse part has weight 1172093 (23.76/col)
Thu May 01 01:25:51 2008  matrix includes 64 packed rows
Thu May 01 01:25:51 2008  commencing Lanczos iteration
Thu May 01 01:25:51 2008  memory use: 7.5 MB
Thu May 01 01:26:37 2008  lanczos halted after 779 iterations (dim = 49213)
Thu May 01 01:26:37 2008  recovered 16 nontrivial dependencies
Thu May 01 01:26:38 2008  prp42 factor: 375284494633543979200133045260994522261009
Thu May 01 01:26:38 2008  prp43 factor: 1904194805934835770754653293450160027271669
Thu May 01 01:26:38 2008  elapsed time 00:24:01

(2·10¹⁷³+61)/9 = (2)₁₇₂9_<173> = 24029 · 783927755987291861663_<21> · 79938271189022562029053_<23> · C125

C125 = P39 · P87

P39 = 121842971281799818523533840048423370159_<39>

P87 = 121121297489504812466235866743869623924667673289246788407622284113444086914024115748701_<87>

(71·10¹⁹⁰-17)/9 = 7(8)₁₈₉7_<191> = 15073 · 19403 · 89882231 · 27578264513_<11> · 1005770645897839_<16> · 11369559029669171813_<20> · C130

C130 = P38 · P93

P38 = 54199323118774369622038618504219850957_<38>

P93 = 175577976731131661812043593232506970976847183659624924342240801835328186189054850754452122509_<93>

April 2008

Apr 30, 2008 (2nd)

By Jo Yeong Uk / GGNFS

(16·10¹⁵⁸+11)/9 = 1(7)₁₅₇9_<159> = 23 · 71483 · 882289667416631_<15> · 1223089082743541046463_<22> · C117

C117 = P34 · P41 · P43

P34 = 2134129586476034361751373376668327_<34>

P41 = 28096861999607415883106912277348090679271_<41>

P43 = 1671086683923658132629175023545298008290231_<43>

Number: 17779_158
N=100202275398200758288755959759199695048283608989076012457803031165111105417145614149076922956946071387503593890491527
  ( 117 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=2134129586476034361751373376668327 (pp34)
 r2=28096861999607415883106912277348090679271 (pp41)
 r3=1671086683923658132629175023545298008290231 (pp43)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 22.59 hours.
Scaled time: 53.61 units (timescale=2.373).
Factorization parameters were as follows:
n: 100202275398200758288755959759199695048283608989076012457803031165111105417145614149076922956946071387503593890491527
m: 100000000000000000000000000000000
c5: 4
c0: 275
skew: 2.33
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3500001)
Primes: RFBsize:283146, AFBsize:282328, largePrimes:5697960 encountered
Relations: rels:5807108, finalFF:723224
Max relations in full relation-set: 28
Initial matrix: 565538 x 723224 with sparse part having weight 44336124.
Pruned matrix : 436240 x 439131 with weight 27143298.
Total sieving time: 21.63 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.85 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 22.59 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

Apr 30, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(28·10¹⁸⁴+17)/9 = 3(1)₁₈₃3_<185> = 3³ · C184

C184 = P42 · P60 · P82

P42 = 397173737675450362503394621695281766949091_<42>

P60 = 382277231274590218916165085392883779524628449879451093458519_<60>

P82 = 7589144149261590771957712617331762006980147309781393383050491171157371995675701711_<82>

Number: n
N=1152263374485596707818930041152263374485596707818930041152263374485596707818930041152263374485596707818930041152263374485596707818930041152263374485596707818930041152263374485596707819
  ( 184 digits)
SNFS difficulty: 186 digits.
Divisors found:

Wed Apr 30 04:16:48 2008  prp42 factor: 397173737675450362503394621695281766949091
Wed Apr 30 04:16:48 2008  prp60 factor: 382277231274590218916165085392883779524628449879451093458519
Wed Apr 30 04:16:48 2008  prp82 factor: 7589144149261590771957712617331762006980147309781393383050491171157371995675701711
Wed Apr 30 04:16:48 2008  elapsed time 04:15:04 (Msieve 1.34)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 83.28 hours.
Scaled time: 108.02 units (timescale=1.297).
Factorization parameters were as follows:
name: KA_3_1_183_3
n: 1152263374485596707818930041152263374485596707818930041152263374485596707818930041152263374485596707818930041152263374485596707818930041152263374485596707818930041152263374485596707819
skew: 1.43
deg: 5
c5: 14
c0: 85
m: 10000000000000000000000000000000000000
type: snfs
rlim: 7000000
alim: 7000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 7000000/7000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 6100319)
Primes: RFBsize:476648, AFBsize:477009, largePrimes:9217175 encountered
Relations: rels:8915077, finalFF:1033124
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 82.91 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,7000000,7000000,28,28,48,48,2.5,2.5,100000
total time: 83.28 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

6·10¹⁹⁷-1 = 5(9)₁₉₇_<198> = 1887671 · 21510659 · 29874643 · 51335819857675817_<17> · 193601769040977856894563633949553_<33> · C128

C128 = P40 · P89

P40 = 1977341005678468116703941828020617788403_<40>

P89 = 25168487085362731602320955256733472748105735580583285164870970125177601063461429215617779_<89>

(55·10¹⁸¹-1)/9 = 6(1)₁₈₁_<182> = 61 · 67 · 577 · 877 · 111781 · 143711 · 1586030472739_<13> · 20195363842211281211_<20> · C131

C131 = P38 · P94

P38 = 40766640584137816710957234478076320681_<38>

P94 = 1408685357301870566274220078616240034649709444750645317100034544822179685039407926776633883623_<94>

(16·10¹⁶²+11)/9 = 1(7)₁₆₁9_<163> = 3 · 53 · 7253 · 70321 · C152

C152 = P40 · P56 · P57

P40 = 8738921168068223070819335162356745813567_<40>

P56 = 13556939193433310268348957012659665344973696429079407199_<56>

P57 = 185036823188116760892677166163881313320229342307235722089_<57>

Number: n
N=2508532960507369683116226125792753818248735064626633650889410151638428241599905078493703429185525506304829918711
  ( 112 digits)
Divisors found:

Wed Apr 30 16:29:28 2008  prp56 factor: 13556939193433310268348957012659665344973696429079407199
Wed Apr 30 16:29:28 2008  prp57 factor: 185036823188116760892677166163881313320229342307235722089
Wed Apr 30 16:29:28 2008  elapsed time 00:49:00 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 20.01 hours.
Scaled time: 16.71 units (timescale=0.835).
Factorization parameters were as follows:
name: KA_1_7_161_9
n: 2508532960507369683116226125792753818248735064626633650889410151638428241599905078493703429185525506304829918711
skew: 43366.64
# norm 5.45e+15
c5: 43920
c4: -4846848468
c3: -236249798478376
c2: 8406881964709630013
c1: 187479335648406438045156
c0: -3098499176790197889764617485
# alpha -6.91
Y1: 499363817177
Y0: -2245709765640471211154
# Murphy_E 8.54e-10
# M 1428327081851271319039963154859251667243927909391619659471900613331547899535708849353768931258657004078679706063
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1199990)
Primes: RFBsize:250150, AFBsize:249777, largePrimes:6866749 encountered
Relations: rels:6624270, finalFF:602658
Max relations in full relation-set: 28
Initial matrix: 500007 x 602658 with sparse part having weight 37395817.
Pruned matrix : 
Total sieving time: 19.82 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 20.01 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

Apr 29, 2008 (4th)

By Wataru Sakai / GGNFS

(10¹⁷³+17)/9 = (1)₁₇₂3_<173> = 31 · 53 · 10668971 · C162

C162 = P48 · P115

P48 = 614269433286889380330990067993202633882411638463_<48>

P115 = 1031902079348278117543760295595941783929099708583219958186262256627756188911338017448835857763642355585371803328367_<115>

Number: 11113_173
N=633865905488829556896400642079141824365163309702470659600118424221394547036781255642529888084966541508328054517246866001820594204902217663114060440336321276179921
  ( 162 digits)
SNFS difficulty: 173 digits.
Divisors found:
 r1=614269433286889380330990067993202633882411638463 (pp48)
 r2=1031902079348278117543760295595941783929099708583219958186262256627756188911338017448835857763642355585371803328367 (pp115)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 188.18 hours.
Scaled time: 379.19 units (timescale=2.015).
Factorization parameters were as follows:
n: 633865905488829556896400642079141824365163309702470659600118424221394547036781255642529888084966541508328054517246866001820594204902217663114060440336321276179921
m: 10000000000000000000000000000000000
c5: 1000
c0: 17
skew: 0.44
type: snfsFactor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 10100001)
Primes: RFBsize:501962, AFBsize:502426, largePrimes:6671675 encountered
Relations: rels:7329088, finalFF:1319979
Max relations in full relation-set: 32
Initial matrix: 1004454 x 1319979 with sparse part having weight 79827464.
Pruned matrix : 724483 x 729569 with weight 58377937.
Total sieving time: 184.22 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 3.67 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 188.18 hours.
 --------- CPU info (if available) ----------

Apr 29, 2008 (3rd)

By Justin Card / GGNFS

(16·10¹⁰⁸+11)/9 = 1(7)₁₀₇9_<109> = 3 · 65998337 · 365057178973_<12> · C89

C89 = P39 · P50

P39 = 263637240968512413080732461825073633921_<39>

P50 = 93294399702451015285120102344332879893080173318533_<50>

Number: 17779_108
N=24595878135367791087706078241140290995475829227525763189262553146307598541431528166757893
  ( 89 digits)
SNFS difficulty: 109 digits.
Divisors found:
 r1=263637240968512413080732461825073633921 (pp39)
 r2=93294399702451015285120102344332879893080173318533 (pp50)
Version: GGNFS-0.77.1-20060722-k8
Total time: 1.32 hours.
Scaled time: 2.66 units (timescale=2.016).
Factorization parameters were as follows:
n: 24595878135367791087706078241140290995475829227525763189262553146307598541431528166757893
m: 2000000000000000000000
c5: 500
c0: 11
skew: 0.47
type: snfs

Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:63914, largePrimes:2364436 encountered
Relations: rels:2857998, finalFF:623070
Max relations in full relation-set: 32
Initial matrix: 113078 x 623070 with sparse part having weight 46023530.
Pruned matrix : 55805 x 56434 with weight 4401643.
Total sieving time: 1.22 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,109,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.32 hours.
 --------- CPU info (if available) ----------
Memory: 2783488k/2936036k available (1999k kernel code, 143628k reserved, 892k data, 148k init)
Calibrating delay using timer specific routine.. 4975.48 BogoMIPS (lpj=9950968)

Apr 29, 2008 (2nd)

By matsui / GGNFS

2·10¹⁸⁶-3 = 1(9)₁₈₅7_<187> = 19 · C186

C186 = P48 · P138

P48 = 536702269647034089326974744111747439562722018687_<48>

P138 = 196129518818625224605331844109132005572907239230106882174824783188659356706656419547350123734666037979415918599396117880712943463613520849_<138>

N=105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263
  ( 186 digits)
SNFS difficulty: 186 digits.
Divisors found:
 r1=536702269647034089326974744111747439562722018687 (pp48)
 r2=196129518818625224605331844109132005572907239230106882174824783188659356706656419547350123734666037979415918599396117880712943463613520849 (pp138)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 867.04 hours.
Scaled time: 1474.84 units (timescale=1.701).
Factorization parameters were as follows:
n: 105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263
m: 10000000000000000000000000000000000000
c5: 20
c0: -3
skew: 0.68
type: snfs

Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 15800001)
Primes: RFBsize:501962, AFBsize:502546, largePrimes:6966429 encountered
Relations: rels:7485469, finalFF:1145980
Max relations in full relation-set: 28
Initial matrix: 1004574 x 1145980 with sparse part having weight 110867418.
Pruned matrix : 897006 x 902092 with weight 92492864.
Total sieving time: 843.59 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 22.90 hours.
Time per square root: 0.32 hours.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 867.04 hours.

Apr 29, 2008

By Jo Yeong Uk / GGNFS

(16·10¹⁵⁴+11)/9 = 1(7)₁₅₃9_<155> = 67 · 44257 · 434857 · 118980623 · 5586083449_<10> · 5904045757_<10> · C115

C115 = P39 · P76

P39 = 424574177680638046809321367987093479461_<39>

P76 = 8275367395159157100758043906017743682611898325580244458730518452024285252847_<76>

Number: 17779_154
N=3513507306804862810538722776440328397675041984180199354540267312541637491202827793705688552751190010953335386275467
  ( 115 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=424574177680638046809321367987093479461 (pp39)
 r2=8275367395159157100758043906017743682611898325580244458730518452024285252847 (pp76)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 18.84 hours.
Scaled time: 40.37 units (timescale=2.143).
Factorization parameters were as follows:
n: 3513507306804862810538722776440328397675041984180199354540267312541637491202827793705688552751190010953335386275467
m: 20000000000000000000000000000000
c5: 1
c0: 220
skew: 2.94
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2700001)
Primes: RFBsize:216816, AFBsize:216842, largePrimes:5504362 encountered
Relations: rels:5391098, finalFF:491424
Max relations in full relation-set: 28
Initial matrix: 433721 x 491424 with sparse part having weight 37285454.
Pruned matrix : 399502 x 401734 with weight 26928509.
Total sieving time: 17.98 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.74 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 18.84 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167428k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407673)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4957.34 BogoMIPS (lpj=2478671)
Total of 4 processors activated (19393.17 BogoMIPS).

(16·10¹⁵⁷+11)/9 = 1(7)₁₅₆9_<158> = 17 · 78300281 · 419383201693_<12> · 6455324213993_<13> · C124

C124 = P46 · P79

P46 = 4914350290219746139126636107283086748016976763_<46>

P79 = 1003852793048281716132218328272508392055966130363433679564450662607859607459021_<79>

Number: 17779_157
N=4933284264854726011199914777590554288912649583309790986348928487950729049522496039958276785689365379111664392646812831729023
  ( 124 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=4914350290219746139126636107283086748016976763 (pp46)
 r2=1003852793048281716132218328272508392055966130363433679564450662607859607459021 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 26.38 hours.
Scaled time: 56.41 units (timescale=2.138).
Factorization parameters were as follows:
n: 4933284264854726011199914777590554288912649583309790986348928487950729049522496039958276785689365379111664392646812831729023
m: 20000000000000000000000000000000
c5: 50
c0: 11
skew: 0.74
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:283028, largePrimes:5726623 encountered
Relations: rels:5800542, finalFF:692066
Max relations in full relation-set: 28
Initial matrix: 566239 x 692066 with sparse part having weight 44440711.
Pruned matrix : 466921 x 469816 with weight 28684118.
Total sieving time: 25.29 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.96 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 26.38 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167428k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407673)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4957.34 BogoMIPS (lpj=2478671)
Total of 4 processors activated (19393.17 BogoMIPS).

Apr 28, 2008 (4th)

By Justin Card / GGNFS

(16·10¹⁶⁵+11)/9 = 1(7)₁₆₄9_<166> = 3 · 139 · 155609 · 92488378321_<11> · 1521710760532564759_<19> · 281473921296763649761469_<24> · C105

C105 = P41 · P65

P41 = 29020234627925602195812824299370283577151_<41>

P65 = 23831333665399274683827843453947996114011483468521275295280977823_<65>

Number: 17779_165
N=691590894466269197730146910797393517066082048486545304291390199393830336725204059012699605334945540522273
  ( 105 digits)
Divisors found:
 r1=29020234627925602195812824299370283577151 (pp41)
 r2=23831333665399274683827843453947996114011483468521275295280977823 (pp65)
Version: GGNFS-0.77.1-20060722-k8
Total time: 16.44 hours.
Scaled time: 33.17 units (timescale=2.018).
Factorization parameters were as follows:
name: 17779_165
n: 691590894466269197730146910797393517066082048486545304291390199393830336725204059012699605334945540522273
skew: 15009.73
# norm 3.47e+14
c5: 16800
c4: 1595716796
c3: -4454616847204
c2: -293960595689521449
c1: -1548469487062960190204
c0: 36690328126755034441600
# alpha -5.82
Y1: 97184239787
Y0: -132709482478364848917
# Murphy_E 1.77e-09
# M 278220095968292048864566809319835243296760349851295271958673057244600229804999456623869010072640694735745
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2300001)
Primes: RFBsize:183072, AFBsize:183403, largePrimes:4536354 encountered
Relations: rels:4756460, finalFF:577861
Max relations in full relation-set: 32
Initial matrix: 366556 x 577861 with sparse part having weight 45965216.
Pruned matrix : 226843 x 228739 with weight 22348975.
Total sieving time: 15.10 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 1.14 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 16.44 hours.
 --------- CPU info (if available) ----------

Apr 28, 2008 (3rd)

By Jo Yeong Uk / GGNFS, GMP-ECM

(16·10¹⁴⁴+11)/9 = 1(7)₁₄₃9_<145> = 3 · 89 · 313 · 119918389149593_<15> · 9474242254151046271_<19> · C107

C107 = P39 · P69

P39 = 119839803340528054651439296435684615981_<39>

P69 = 156239383006847491926868354100145305520439669088317032907096506743443_<69>

Number: 17779_144
N=18723696933586044238822912804459035527501235116307888482182981914368803208101426662639442126351540344762583
  ( 107 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=119839803340528054651439296435684615981 (pp39)
 r2=156239383006847491926868354100145305520439669088317032907096506743443 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 8.90 hours.
Scaled time: 19.00 units (timescale=2.135).
Factorization parameters were as follows:
n: 18723696933586044238822912804459035527501235116307888482182981914368803208101426662639442126351540344762583
m: 200000000000000000000000000000
c5: 1
c0: 220
skew: 2.94
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1500001)
Primes: RFBsize:135072, AFBsize:135239, largePrimes:3797650 encountered
Relations: rels:3966868, finalFF:457655
Max relations in full relation-set: 28
Initial matrix: 270375 x 457655 with sparse part having weight 41124222.
Pruned matrix : 204905 x 206320 with weight 17448813.
Total sieving time: 8.66 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 8.90 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167428k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407673)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4957.34 BogoMIPS (lpj=2478671)
Total of 4 processors activated (19393.17 BogoMIPS).

(16·10¹⁴⁵+11)/9 = 1(7)₁₄₄9_<146> = 19² · 30519143 · C136

C136 = P33 · P48 · P56

P33 = 219688159837927926313717321649179_<33>

P48 = 181683550514854037041455877867851313467232812473_<48>

P56 = 40427387536757891148686148058262026542402816481494289519_<56>

Number: 17779_145
N=1613607623978796108975503488209942683714546869329096238203971838817228567752709581275427586264502413452233709831637068300797031823380173
  ( 136 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=219688159837927926313717321649179 (pp33)
 r2=181683550514854037041455877867851313467232812473 (pp48)
 r3=40427387536757891148686148058262026542402816481494289519 (pp56)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 7.81 hours.
Scaled time: 16.64 units (timescale=2.130).
Factorization parameters were as follows:
n: 1613607623978796108975503488209942683714546869329096238203971838817228567752709581275427586264502413452233709831637068300797031823380173
m: 200000000000000000000000000000
c5: 1
c0: 22
skew: 1.86
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1425001)
Primes: RFBsize:135072, AFBsize:134864, largePrimes:3695013 encountered
Relations: rels:3765759, finalFF:378118
Max relations in full relation-set: 28
Initial matrix: 270000 x 378118 with sparse part having weight 32616641.
Pruned matrix : 226218 x 227632 with weight 16299176.
Total sieving time: 7.54 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 7.81 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167428k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407673)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4957.34 BogoMIPS (lpj=2478671)
Total of 4 processors activated (19393.17 BogoMIPS).

(16·10¹⁶³+11)/9 = 1(7)₁₆₂9_<164> = 19 · 31 · 659 · 128339 · 42696731346006600727_<20> · 33367508415177134907584971_<26> · C108

C108 = P32 · P76

P32 = 59088108152824243798798734618151_<32>

P76 = 4239353385152396199790986646873480940040953204280123465501575552424783987733_<76>

Apr 28, 2008 (2nd)

By Sinkiti Sibata / Msieve

(16·10¹⁰³+11)/9 = 1(7)₁₀₂9_<104> = 31 · 457 · 24203 · C95

C95 = P30 · P66

P30 = 331329502808201944657710910493_<30>

P66 = 156484119198691203682352050843360865193448277522438180479674417403_<66>

Sun Apr 27 17:53:55 2008  Msieve v. 1.33
Sun Apr 27 17:53:55 2008  random seeds: cc72b41b e55fc60c
Sun Apr 27 17:53:55 2008  factoring 51847805411481765012285536782252654602695323913086773291749786111357201858764951982326454509679 (95 digits)
Sun Apr 27 17:53:56 2008  searching for 15-digit factors
Sun Apr 27 17:53:58 2008  commencing quadratic sieve (95-digit input)
Sun Apr 27 17:53:59 2008  using multiplier of 1
Sun Apr 27 17:53:59 2008  using 64kb Pentium 4 sieve core
Sun Apr 27 17:53:59 2008  sieve interval: 18 blocks of size 65536
Sun Apr 27 17:53:59 2008  processing polynomials in batches of 6
Sun Apr 27 17:53:59 2008  using a sieve bound of 2160127 (80000 primes)
Sun Apr 27 17:53:59 2008  using large prime bound of 324019050 (28 bits)
Sun Apr 27 17:53:59 2008  using double large prime bound of 2084620300746750 (43-51 bits)
Sun Apr 27 17:53:59 2008  using trial factoring cutoff of 51 bits
Sun Apr 27 17:53:59 2008  polynomial 'A' values have 12 factors
Sun Apr 27 23:42:43 2008  80276 relations (20458 full + 59818 combined from 1185745 partial), need 80096
Sun Apr 27 23:42:47 2008  begin with 1206203 relations
Sun Apr 27 23:42:49 2008  reduce to 206482 relations in 12 passes
Sun Apr 27 23:42:49 2008  attempting to read 206482 relations
Sun Apr 27 23:42:55 2008  recovered 206482 relations
Sun Apr 27 23:42:55 2008  recovered 188456 polynomials
Sun Apr 27 23:42:56 2008  attempting to build 80276 cycles
Sun Apr 27 23:42:56 2008  found 80276 cycles in 7 passes
Sun Apr 27 23:42:56 2008  distribution of cycle lengths:
Sun Apr 27 23:42:56 2008     length 1 : 20458
Sun Apr 27 23:42:56 2008     length 2 : 14410
Sun Apr 27 23:42:56 2008     length 3 : 13520
Sun Apr 27 23:42:56 2008     length 4 : 10770
Sun Apr 27 23:42:56 2008     length 5 : 7925
Sun Apr 27 23:42:56 2008     length 6 : 5271
Sun Apr 27 23:42:56 2008     length 7 : 3408
Sun Apr 27 23:42:56 2008     length 9+: 4514
Sun Apr 27 23:42:56 2008  largest cycle: 24 relations
Sun Apr 27 23:42:56 2008  matrix is 80000 x 80276 (21.4 MB) with weight 5291532 (65.92/col)
Sun Apr 27 23:42:56 2008  sparse part has weight 5291532 (65.92/col)
Sun Apr 27 23:42:58 2008  filtering completed in 3 passes
Sun Apr 27 23:42:58 2008  matrix is 75601 x 75665 (20.3 MB) with weight 5013453 (66.26/col)
Sun Apr 27 23:42:58 2008  sparse part has weight 5013453 (66.26/col)
Sun Apr 27 23:42:58 2008  saving the first 48 matrix rows for later
Sun Apr 27 23:42:59 2008  matrix is 75553 x 75665 (13.5 MB) with weight 4044903 (53.46/col)
Sun Apr 27 23:42:59 2008  sparse part has weight 3073075 (40.61/col)
Sun Apr 27 23:42:59 2008  matrix includes 64 packed rows
Sun Apr 27 23:42:59 2008  using block size 21845 for processor cache size 512 kB
Sun Apr 27 23:43:00 2008  commencing Lanczos iteration
Sun Apr 27 23:43:00 2008  memory use: 12.5 MB
Sun Apr 27 23:43:59 2008  lanczos halted after 1196 iterations (dim = 75553)
Sun Apr 27 23:43:59 2008  recovered 18 nontrivial dependencies
Sun Apr 27 23:44:00 2008  prp30 factor: 331329502808201944657710910493
Sun Apr 27 23:44:00 2008  prp66 factor: 156484119198691203682352050843360865193448277522438180479674417403
Sun Apr 27 23:44:00 2008  elapsed time 05:50:05

(16·10¹¹¹+11)/9 = 1(7)₁₁₀9_<112> = 3 · 3067 · 16644371 · C101

C101 = P30 · P71

P30 = 311891772685877294689988053111_<30>

P71 = 37219551555730460553756515602487763210155431764457159024923543299294359_<71>

Mon Apr 28 01:26:31 2008  Msieve v. 1.33
Mon Apr 28 01:26:31 2008  random seeds: 780f0fe4 d2f66e36
Mon Apr 28 01:26:31 2008  factoring 11608471913290175427106165301392768225200713865227417729953035601937285096499113827092370346514700849 (101 digits)
Mon Apr 28 01:26:33 2008  searching for 15-digit factors
Mon Apr 28 01:26:35 2008  commencing quadratic sieve (101-digit input)
Mon Apr 28 01:26:35 2008  using multiplier of 1
Mon Apr 28 01:26:35 2008  using 64kb Pentium 4 sieve core
Mon Apr 28 01:26:35 2008  sieve interval: 18 blocks of size 65536
Mon Apr 28 01:26:35 2008  processing polynomials in batches of 6
Mon Apr 28 01:26:35 2008  using a sieve bound of 2825047 (102495 primes)
Mon Apr 28 01:26:35 2008  using large prime bound of 423757050 (28 bits)
Mon Apr 28 01:26:35 2008  using double large prime bound of 3379173047684850 (43-52 bits)
Mon Apr 28 01:26:35 2008  using trial factoring cutoff of 52 bits
Mon Apr 28 01:26:35 2008  polynomial 'A' values have 13 factors
Mon Apr 28 19:30:31 2008  102795 relations (24275 full + 78520 combined from 1544216 partial), need 102591
Mon Apr 28 19:30:38 2008  begin with 1568491 relations
Mon Apr 28 19:30:40 2008  reduce to 271830 relations in 12 passes
Mon Apr 28 19:30:40 2008  attempting to read 271830 relations
Mon Apr 28 19:30:50 2008  recovered 271830 relations
Mon Apr 28 19:30:50 2008  recovered 261688 polynomials
Mon Apr 28 19:30:50 2008  attempting to build 102795 cycles
Mon Apr 28 19:30:51 2008  found 102795 cycles in 6 passes
Mon Apr 28 19:30:51 2008  distribution of cycle lengths:
Mon Apr 28 19:30:51 2008     length 1 : 24275
Mon Apr 28 19:30:51 2008     length 2 : 17638
Mon Apr 28 19:30:51 2008     length 3 : 16976
Mon Apr 28 19:30:51 2008     length 4 : 14225
Mon Apr 28 19:30:51 2008     length 5 : 10704
Mon Apr 28 19:30:51 2008     length 6 : 7374
Mon Apr 28 19:30:51 2008     length 7 : 4841
Mon Apr 28 19:30:51 2008     length 9+: 6762
Mon Apr 28 19:30:51 2008  largest cycle: 19 relations
Mon Apr 28 19:30:51 2008  matrix is 102495 x 102795 (27.4 MB) with weight 6780827 (65.96/col)
Mon Apr 28 19:30:51 2008  sparse part has weight 6780827 (65.96/col)
Mon Apr 28 19:30:53 2008  filtering completed in 3 passes
Mon Apr 28 19:30:53 2008  matrix is 98309 x 98373 (26.4 MB) with weight 6514221 (66.22/col)
Mon Apr 28 19:30:53 2008  sparse part has weight 6514221 (66.22/col)
Mon Apr 28 19:30:54 2008  saving the first 48 matrix rows for later
Mon Apr 28 19:30:54 2008  matrix is 98261 x 98373 (15.4 MB) with weight 4981754 (50.64/col)
Mon Apr 28 19:30:54 2008  sparse part has weight 3455551 (35.13/col)
Mon Apr 28 19:30:54 2008  matrix includes 64 packed rows
Mon Apr 28 19:30:54 2008  using block size 21845 for processor cache size 512 kB
Mon Apr 28 19:30:55 2008  commencing Lanczos iteration
Mon Apr 28 19:30:55 2008  memory use: 15.7 MB
Mon Apr 28 19:32:32 2008  lanczos halted after 1556 iterations (dim = 98261)
Mon Apr 28 19:32:33 2008  recovered 17 nontrivial dependencies
Mon Apr 28 19:32:34 2008  prp30 factor: 311891772685877294689988053111
Mon Apr 28 19:32:34 2008  prp71 factor: 37219551555730460553756515602487763210155431764457159024923543299294359
Mon Apr 28 19:32:34 2008  elapsed time 18:06:03

Apr 28, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(16·10¹³⁰+11)/9 = 1(7)₁₂₉9_<131> = C131

C131 = P51 · P80

P51 = 740649800611949626773509486419719295510999559861201_<51>

P80 = 24002946821951728642362452236161911211145684438969667380651086125420098239262979_<80>

Number: n
N=17777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
  ( 131 digits)
SNFS difficulty: 131 digits.
Divisors found:

Mon Apr 28 01:29:04 2008  prp51 factor: 740649800611949626773509486419719295510999559861201
Mon Apr 28 01:29:04 2008  prp80 factor: 24002946821951728642362452236161911211145684438969667380651086125420098239262979
Mon Apr 28 01:29:04 2008  elapsed time 00:03:59 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 2.04 hours.
Scaled time: 1.70 units (timescale=0.835).
Factorization parameters were as follows:
name: KA_1_7_129_9
n: 17777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
type: snfs
deg: 5
c5: 1
c0: 22
skew: 1.86
m: 200000000000000000000000000
rlim: 1000000
alim: 1000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved  special-q in [100000, 439990)
Primes: RFBsize:78498, AFBsize:78572, largePrimes:1538766 encountered
Relations: rels:1564015, finalFF:194448
Max relations in full relation-set: 28
Initial matrix: 157134 x 194448 with sparse part having weight 10069071.
Pruned matrix : 
Total sieving time: 1.99 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.5,2.5,50000
total time: 2.04 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(16·10¹³⁵+11)/9 = 1(7)₁₃₄9_<136> = 3 · 31543 · C131

C131 = P42 · P90

P42 = 116913662942380963981152305353982462461229_<42>

P90 = 160689668656667462774664759034224831860341321263111183165054495696018746338066716792796019_<90>

Number: n
N=18786817759648498639716976590450895367992663747664857261281190520641428925358798864806536873239469695101689522004647389043293047351
  ( 131 digits)
SNFS difficulty: 136 digits.
Divisors found:

Mon Apr 28 03:16:59 2008  prp42 factor: 116913662942380963981152305353982462461229
Mon Apr 28 03:16:59 2008  prp90 factor: 160689668656667462774664759034224831860341321263111183165054495696018746338066716792796019
Mon Apr 28 03:16:59 2008  elapsed time 00:05:27 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 3.72 hours.
Scaled time: 3.10 units (timescale=0.833).
Factorization parameters were as follows:
name: KA_1_7_134_9
n: 18786817759648498639716976590450895367992663747664857261281190520641428925358798864806536873239469695101689522004647389043293047351
type: snfs
deg: 5
c5: 1
c0: 22
skew: 1.86
m: 2000000000000000000000000000
rlim: 1200000
alim: 1200000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved  special-q in [100000, 760000)
Primes: RFBsize:92938, AFBsize:93010, largePrimes:1459042 encountered
Relations: rels:1486909, finalFF:209935
Max relations in full relation-set: 28
Initial matrix: 186012 x 209935 with sparse part having weight 8026945.
Pruned matrix : 165211 x 166205 with weight 5314324.
Total sieving time: 3.68 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1200000,1200000,25,25,43,43,2.5,2.5,75000
total time: 3.72 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(16·10¹³⁷+11)/9 = 1(7)₁₃₆9_<138> = 7 · 28319 · 94698649 · C124

C124 = P44 · P81

P44 = 25057095028301441065470887673091378935372641_<44>

P81 = 377943618185876629077139501895581334015847645792582347898293700223261113504154307_<81>

Number: n
N=9470169156223587389224065451365074531135004558489529786850901405282576799155265960697494003782555977979977594246624610114787
  ( 124 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=25057095028301441065470887673091378935372641 (pp44)
 r2=377943618185876629077139501895581334015847645792582347898293700223261113504154307 (pp81)
Version: GGNFS-0.77.1-20051202-k8
Total time: 6.04 hours.
Scaled time: 5.06 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_1_7_136_9
n: 9470169156223587389224065451365074531135004558489529786850901405282576799155265960697494003782555977979977594246624610114787
type: snfs
deg: 5
c5: 50
c0: 11
skew: 0.74
m: 2000000000000000000000000000
rlim: 1000000
alim: 1000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [100000, 1240001)
Primes: RFBsize:78498, AFBsize:78657, largePrimes:1532234 encountered
Relations: rels:1527221, finalFF:178475
Max relations in full relation-set: 28
Initial matrix: 157220 x 178475 with sparse part having weight 11121586.
Pruned matrix : 150304 x 151154 with weight 7874976.
Total sieving time: 5.86 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,43,43,2.5,2.5,75000
total time: 6.04 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(16·10¹⁴²+11)/9 = 1(7)₁₄₁9_<143> = 326017631 · C134

C134 = P38 · P46 · P51

P38 = 27671075944796408029522595003337759929_<38>

P46 = 6590894924445613177053144476952932493083835323_<46>

P51 = 298996394724726338639789823356192339064617460410927_<51>

Number: n
N=54530111525710024491828105387888600962742956002210131321940002004915426729721184244105429309673677672290606202760174580183296214976109
  ( 134 digits)
SNFS difficulty: 143 digits.
Divisors found:

Mon Apr 28 17:53:49 2008  prp38 factor: 27671075944796408029522595003337759929
Mon Apr 28 17:53:49 2008  prp46 factor: 6590894924445613177053144476952932493083835323
Mon Apr 28 17:53:49 2008  prp51 factor: 298996394724726338639789823356192339064617460410927
Mon Apr 28 17:53:49 2008  elapsed time 00:12:27

Version: GGNFS-0.77.1-20050930-k8
Total time: 7.73 hours.
Scaled time: 6.48 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_1_7_141_9
n: 54530111525710024491828105387888600962742956002210131321940002004915426729721184244105429309673677672290606202760174580183296214976109
type: snfs
deg: 5
c5: 50
c0: 11
skew: 0.74
m: 20000000000000000000000000000
rlim: 1000000
alim: 1000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved  special-q in [100000, 1600897)
Primes: RFBsize:78498, AFBsize:78657, largePrimes:2604383 encountered
Relations: rels:2484203, finalFF:121506
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 7.63 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,45,45,2.5,2.5,100000
total time: 7.73 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(16·10¹⁶⁸+11)/9 = 1(7)₁₆₇9_<169> = 3² · 71 · C166

C166 = P34 · P133

P34 = 1920233553146556380827007015720641_<34>

P133 = 1448847117213251607625355567575003378529401722538088872843295916219662258839658830543803065160753377230243618938669969296230845983821_<133>

Apr 27, 2008 (3rd)

By Jo Yeong Uk / GGNFS, GMP-ECM

(16·10¹³⁶+11)/9 = 1(7)₁₃₅9_<137> = 23 · 53 · 441405097643_<12> · 808610497337_<12> · 2616087389059_<13> · C98

C98 = P30 · P68

P30 = 878422995771064242156524199679_<30>

P68 = 17780382705310184963084137750438109941582309771712168927829813727591_<68>

Number: 17779_136
N=15618697041954592395199300036107685358583358819631114262492224881317156816884962005048828995643289
  ( 98 digits)
Divisors found:
 r1=878422995771064242156524199679 (pp30)
 r2=17780382705310184963084137750438109941582309771712168927829813727591 (pp68)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.55 hours.
Scaled time: 5.43 units (timescale=2.131).
Factorization parameters were as follows:
name: 17779_136
n: 15618697041954592395199300036107685358583358819631114262492224881317156816884962005048828995643289
skew: 2515.38
# norm 1.60e+13
c5: 227880
c4: -100766386
c3: -2631617626383
c2: 3483269386581489
c1: 8847300392404231453
c0: -10566367372676025532153
# alpha -5.45
Y1: 27021702347
Y0: -2329100152203075420
# Murphy_E 4.63e-09
# M 5611294509854701452427197899181609930823487150004322445320319899280321733814839177639706302297392
type: gnfs
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [650000, 1000001)
Primes: RFBsize:100021, AFBsize:100521, largePrimes:3729833 encountered
Relations: rels:3572357, finalFF:257700
Max relations in full relation-set: 28
Initial matrix: 200626 x 257700 with sparse part having weight 19363794.
Pruned matrix : 163294 x 164361 with weight 9665215.
Polynomial selection time: 0.20 hours.
Total sieving time: 2.17 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,97,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1300000,1300000,26,26,48,48,2.5,2.5,50000
total time: 2.55 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167428k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407673)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4957.34 BogoMIPS (lpj=2478671)
Total of 4 processors activated (19393.17 BogoMIPS).

(16·10¹⁶⁹+11)/9 = 1(7)₁₆₈9_<170> = C170

C170 = P43 · P127

P43 = 2775860259573482934248483330570378457853049_<43>

P127 = 6404421013797493046865420439571729954912032159024481277804152948807882071405358296499945494751597025942489791947474746224573771_<127>

(16·10¹⁴¹+11)/9 = 1(7)₁₄₀9_<142> = 3² · 17 · 4799 · 4244407045105529_<16> · C120

C120 = P37 · P83

P37 = 6522369570081283852203348349906721407_<37>

P83 = 87460682613272569632304161894821897127960481192555515075521999576953130373280138819_<83>

Number: 17779_141
N=570450894855346227484587960803916244029526110944038813634612710061479771528045222860658881615959667876449462506118998333
  ( 120 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=6522369570081283852203348349906721407 (pp37)
 r2=87460682613272569632304161894821897127960481192555515075521999576953130373280138819 (pp83)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.91 hours.
Scaled time: 12.68 units (timescale=2.144).
Factorization parameters were as follows:
n: 570450894855346227484587960803916244029526110944038813634612710061479771528045222860658881615959667876449462506118998333
m: 20000000000000000000000000000
c5: 5
c0: 11
skew: 1.17
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:114558, largePrimes:3326212 encountered
Relations: rels:3407379, finalFF:377949
Max relations in full relation-set: 28
Initial matrix: 228778 x 377949 with sparse part having weight 32131042.
Pruned matrix : 176386 x 177593 with weight 12842783.
Total sieving time: 5.74 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 5.91 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167428k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407673)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4957.34 BogoMIPS (lpj=2478671)
Total of 4 processors activated (19393.17 BogoMIPS).

Apr 27, 2008 (2nd)

By Sinkiti Sibata / Msieve, GGNFS

(16·10¹²²+11)/9 = 1(7)₁₂₁9_<123> = 2957 · 484877128152342319_<18> · 8773066214071332211_<19> · C83

C83 = P29 · P54

P29 = 64143200499177888756970894601_<29>

P54 = 220339529129826668084568653822613720420620993023058483_<54>

Sun Apr 27 06:13:50 2008  Msieve v. 1.33
Sun Apr 27 06:13:50 2008  random seeds: 34d55870 5576daea
Sun Apr 27 06:13:50 2008  factoring 14133282594868918897014068537774654409902449086370890143333043941049463297651950283 (83 digits)
Sun Apr 27 06:13:52 2008  searching for 15-digit factors
Sun Apr 27 06:13:53 2008  commencing quadratic sieve (83-digit input)
Sun Apr 27 06:13:53 2008  using multiplier of 1
Sun Apr 27 06:13:53 2008  using 64kb Pentium 4 sieve core
Sun Apr 27 06:13:53 2008  sieve interval: 6 blocks of size 65536
Sun Apr 27 06:13:53 2008  processing polynomials in batches of 17
Sun Apr 27 06:13:53 2008  using a sieve bound of 1359077 (52059 primes)
Sun Apr 27 06:13:53 2008  using large prime bound of 125035084 (26 bits)
Sun Apr 27 06:13:53 2008  using trial factoring cutoff of 27 bits
Sun Apr 27 06:13:53 2008  polynomial 'A' values have 10 factors
Sun Apr 27 06:51:31 2008  52222 relations (26417 full + 25805 combined from 282787 partial), need 52155
Sun Apr 27 06:51:32 2008  begin with 309204 relations
Sun Apr 27 06:51:32 2008  reduce to 74824 relations in 2 passes
Sun Apr 27 06:51:32 2008  attempting to read 74824 relations
Sun Apr 27 06:51:34 2008  recovered 74824 relations
Sun Apr 27 06:51:34 2008  recovered 67842 polynomials
Sun Apr 27 06:51:34 2008  attempting to build 52222 cycles
Sun Apr 27 06:51:34 2008  found 52222 cycles in 1 passes
Sun Apr 27 06:51:34 2008  distribution of cycle lengths:
Sun Apr 27 06:51:34 2008     length 1 : 26417
Sun Apr 27 06:51:34 2008     length 2 : 25805
Sun Apr 27 06:51:34 2008  largest cycle: 2 relations
Sun Apr 27 06:51:34 2008  matrix is 52059 x 52222 (7.0 MB) with weight 1615986 (30.94/col)
Sun Apr 27 06:51:34 2008  sparse part has weight 1615986 (30.94/col)
Sun Apr 27 06:51:35 2008  filtering completed in 4 passes
Sun Apr 27 06:51:35 2008  matrix is 45234 x 45298 (5.9 MB) with weight 1376746 (30.39/col)
Sun Apr 27 06:51:35 2008  sparse part has weight 1376746 (30.39/col)
Sun Apr 27 06:51:35 2008  saving the first 48 matrix rows for later
Sun Apr 27 06:51:35 2008  matrix is 45186 x 45298 (4.6 MB) with weight 1113733 (24.59/col)
Sun Apr 27 06:51:35 2008  sparse part has weight 928738 (20.50/col)
Sun Apr 27 06:51:35 2008  matrix includes 64 packed rows
Sun Apr 27 06:51:35 2008  commencing Lanczos iteration
Sun Apr 27 06:51:35 2008  memory use: 6.3 MB
Sun Apr 27 06:52:36 2008  lanczos halted after 716 iterations (dim = 45172)
Sun Apr 27 06:52:36 2008  recovered 10 nontrivial dependencies
Sun Apr 27 06:52:37 2008  prp29 factor: 64143200499177888756970894601
Sun Apr 27 06:52:37 2008  prp54 factor: 220339529129826668084568653822613720420620993023058483
Sun Apr 27 06:52:37 2008  elapsed time 00:38:47

(16·10¹²³+11)/9 = 1(7)₁₂₂9_<124> = 3⁵ · 53 · C120

C120 = P46 · P74

P46 = 3127936728760055563783574813204076500296280377_<46>

P74 = 44130349846097590297953030403378448580759948085469636863079649654491796613_<74>

Number: 17779_123
N=138036942136639318097505845001768598321125691263124293639085160165989422919308780012250778614626739481153643743906963101
  ( 120 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=3127936728760055563783574813204076500296280377 (pp46)
 r2=44130349846097590297953030403378448580759948085469636863079649654491796613 (pp74)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.64 hours.
Scaled time: 1.78 units (timescale=0.677).
Factorization parameters were as follows:
name: 17779_123
n: 138036942136639318097505845001768598321125691263124293639085160165989422919308780012250778614626739481153643743906963101
m: 2000000000000000000000000
c5: 500
c0: 11
skew: 0.47
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:63914, largePrimes:2151100 encountered
Relations: rels:2241438, finalFF:227478
Max relations in full relation-set: 28
Initial matrix: 113078 x 227478 with sparse part having weight 20178265.
Pruned matrix : 88548 x 89177 with weight 5335089.
Total sieving time: 2.40 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.64 hours.
 --------- CPU info (if available) ----------

(16·10¹²⁴+11)/9 = 1(7)₁₂₃9_<125> = 12300377951_<11> · 595919247296270033_<18> · C97

C97 = P32 · P65

P32 = 51816470851532967590612913006763_<32>

P65 = 46806242024873304391156980530608793867173799266257699394339756951_<65>

Number: 17779_124
N=2425334275551645003990077583460898220356269581536513355431225872560438064950944002546028039259613
  ( 97 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=51816470851532967590612913006763 (pp32)
 r2=46806242024873304391156980530608793867173799266257699394339756951 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 3.05 hours.
Scaled time: 2.07 units (timescale=0.677).
Factorization parameters were as follows:
name: 17779_124
n: 2425334275551645003990077583460898220356269581536513355431225872560438064950944002546028039259613
m: 10000000000000000000000000
c5: 8
c0: 55
skew: 1.47
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:64019, largePrimes:2066221 encountered
Relations: rels:2056554, finalFF:139191
Max relations in full relation-set: 28
Initial matrix: 113182 x 139191 with sparse part having weight 12160681.
Pruned matrix : 105923 x 106552 with weight 7525402.
Total sieving time: 2.72 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.05 hours.
 --------- CPU info (if available) ----------

Apr 27, 2008

By Robert Backstrom / GMP-ECM, GGNFS

(16·10¹²⁸+11)/9 = 1(7)₁₂₇9_<129> = C129

C129 = P29 · P100

P29 = 32710453956769251258301493239_<29>

P100 = 5434891793697886900299526331565538939027676011247994752035924882091324105223592214028104168618741861_<100>

(16·10¹⁴⁰+11)/9 = 1(7)₁₃₉9_<141> = C141

C141 = P33 · P108

P33 = 325913857692204415401309983425939_<33>

P108 = 545474743039838751488576360288698540556507517839459352048194572123867434191137681771453058583347982000134561_<108>

(16·10¹¹⁵+11)/9 = 1(7)₁₁₄9_<116> = 4106117 · 31044253863947_<14> · C96

C96 = P33 · P63

P33 = 376009549465429802217359002735787_<33>

P63 = 370907873250938245237270331446578676378971815606577371756099183_<63>

(16·10¹³²+11)/9 = 1(7)₁₃₁9_<133> = 3² · 10258433 · 1163149133_<10> · 4572945031709856547_<19> · C97

C97 = P39 · P58

P39 = 393755777432321520680320952896244231087_<39>

P58 = 9193811940508378094496295181426517692653384859674800617411_<58>

(16·10¹¹⁷+11)/9 = 1(7)₁₁₆9_<118> = 3 · 54319 · C113

C113 = P45 · P68

P45 = 385663420156498117850474192254799661294286001_<45>

P68 = 28287593603832924128934670018553127378252757220332340058030657206447_<68>

Number: n
N=10909490097251285785684430725760647150952568946272806800430652121588994506389892902899401546283852659154119048447
  ( 113 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=385663420156498117850474192254799661294286001 (pp45)
 r2=28287593603832924128934670018553127378252757220332340058030657206447 (pp68)
Version: GGNFS-0.77.1-20051202-k8
Total time: 1.04 hours.
Scaled time: 0.87 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_1_7_116_9
n: 10909490097251285785684430725760647150952568946272806800430652121588994506389892902899401546283852659154119048447
type: snfs
deg: 5
c5: 50
c0: 11
skew: 0.74
m: 200000000000000000000000
rlim: 600000
alim: 600000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [100000, 220001)
Primes: RFBsize:49098, AFBsize:49122, largePrimes:1775672 encountered
Relations: rels:1748487, finalFF:152025
Max relations in full relation-set: 28
Initial matrix: 98285 x 152025 with sparse part having weight 11114209.
Pruned matrix : 80390 x 80945 with weight 3947440.
Total sieving time: 0.96 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,118,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.5,2.5,50000
total time: 1.04 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

Apr 26, 2008 (2nd)

The factor table of 177...779 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Apr 26, 2008

By Robert Backstrom / GGNFS

(85·10¹⁶⁷+41)/9 = 9(4)₁₆₆9_<168> = 11 · 2179 · 466717 · C158

C158 = P75 · P84

P75 = 478777639625485469663091713680607336457292333499171590319017223759486984099_<75>

P84 = 176335202682166386931839569414134269241546576483219882902726853160083292707756562887_<84>

Number: n
N=84425352123049197208177915165707899447036189177692463379021379908918745208076669939396868139201725618297748923996932993146192178295917212487074132321862533813
  ( 158 digits)
SNFS difficulty: 168 digits.
Divisors found:

Sat Apr 26 04:46:51 2008  prp75 factor: 478777639625485469663091713680607336457292333499171590319017223759486984099
Sat Apr 26 04:46:51 2008  prp84 factor: 176335202682166386931839569414134269241546576483219882902726853160083292707756562887
Sat Apr 26 04:46:51 2008  elapsed time 01:20:35 (Msieve 1.34)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 70.44 hours.
Scaled time: 128.83 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_9_4_166_9
n: 84425352123049197208177915165707899447036189177692463379021379908918745208076669939396868139201725618297748923996932993146192178295917212487074132321862533813
skew: 0.34
deg: 5
c5: 8500
c0: 41
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5000001)
Primes: RFBsize:230209, AFBsize:229823, largePrimes:7938150 encountered
Relations: rels:7368085, finalFF:505504
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 70.15 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 70.44 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(16·10¹⁶⁴-43)/9 = 1(7)₁₆₃3_<165> = 11063693333597774647989287_<26> · C140

C140 = P53 · P87

P53 = 37825696522622096171083659643078327824572061489197777_<53>

P87 = 424805772907959277493320907232824775148202682469380305573348520991402189391592516027227_<87>

Number: n
N=16068574247074387113577017620238159213093751526506479937667554421487231709771454916780284266738393304073675357872389785275140835203319874379
  ( 140 digits)
SNFS difficulty: 165 digits.
Divisors found:

Sat Apr 26 11:25:38 2008  prp53 factor: 37825696522622096171083659643078327824572061489197777
Sat Apr 26 11:25:38 2008  prp87 factor: 424805772907959277493320907232824775148202682469380305573348520991402189391592516027227
Sat Apr 26 11:25:38 2008  elapsed time 01:38:39 (Msieve 1.34)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 76.73 hours.
Scaled time: 100.59 units (timescale=1.311).
Factorization parameters were as follows:
name: KA_1_7_163_3
n: 16068574247074387113577017620238159213093751526506479937667554421487231709771454916780284266738393304073675357872389785275140835203319874379
skew: 1.93
deg: 5
c5: 8
c0: -215
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3500001)
Primes: RFBsize:216816, AFBsize:216381, largePrimes:7668818 encountered
Relations: rels:7112633, finalFF:424994
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 76.41 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 76.73 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Apr 25, 2008

By Robert Backstrom / GGNFS

(5·10¹⁶⁶-11)/3 = 1(6)₁₆₅3_<167> = 17 · 19 · 73 · 756571 · 10397899 · C149

C149 = P70 · P80

P70 = 2332212323169386388539679035029940177328309787579459539882098944585367_<70>

P80 = 38526539008572372320474777732088353752020424841256198151210841483240600452254379_<80>

Number: n
N=89852069044858560668750522416608538221723838872348015749209852062494094029896856524204751899820732855080213308886948940351550969450891700210565072093
  ( 149 digits)
SNFS difficulty: 166 digits.
Divisors found:

Fri Apr 25 04:39:41 2008  prp70 factor: 2332212323169386388539679035029940177328309787579459539882098944585367
Fri Apr 25 04:39:41 2008  prp80 factor: 38526539008572372320474777732088353752020424841256198151210841483240600452254379
Fri Apr 25 04:39:41 2008  elapsed time 01:01:06 (Msieve 1.34)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 49.93 hours.
Scaled time: 91.03 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_1_6_165_3
n: 89852069044858560668750522416608538221723838872348015749209852062494094029896856524204751899820732855080213308886948940351550969450891700210565072093
skew: 0.74
deg: 5
c5: 50
c0: -11
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3400247)
Primes: RFBsize:230209, AFBsize:229978, largePrimes:7618075 encountered
Relations: rels:7060809, finalFF:508891
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 49.69 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 49.93 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(16·10¹⁶²-43)/9 = 1(7)₁₆₁3_<163> = 3 · 6173 · 25301 · 172688383333_<12> · C143

C143 = P66 · P77

P66 = 326773001141993809558562853170105920525309244037613952095021260743_<66>

P77 = 67237717844254366899445055496166348279678953568775065861539166002421097389093_<77>

Number: n
N=21971470849905589781816163859762807759659618505769802309846316269757328765929790453755702044661205491733330322156227744695485489829202477276099
  ( 143 digits)
SNFS difficulty: 163 digits.
Divisors found:

Fri Apr 25 07:05:56 2008  prp66 factor: 326773001141993809558562853170105920525309244037613952095021260743
Fri Apr 25 07:05:56 2008  prp77 factor: 67237717844254366899445055496166348279678953568775065861539166002421097389093
Fri Apr 25 07:05:56 2008  elapsed time 01:24:53 (Msieve 1.34)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 49.89 hours.
Scaled time: 72.29 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_1_7_161_3
n: 21971470849905589781816163859762807759659618505769802309846316269757328765929790453755702044661205491733330322156227744695485489829202477276099
skew: 0.97
deg: 5
c5: 50
c0: -43
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2500001)
Primes: RFBsize:216816, AFBsize:217591, largePrimes:7367926 encountered
Relations: rels:6812297, finalFF:451630
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 49.66 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 49.89 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Apr 24, 2008 (3rd)

By Jo Yeong Uk / GGNFS

8·10¹⁸⁷-1 = 7(9)₁₈₇_<188> = 50221 · 718693111 · 5015358357341_<13> · 153590809952823656448053791352618581_<36> · C127

C127 = P39 · P89

P39 = 102746196181289754298239251281338562669_<39>

P89 = 28004524047110445703490411149385111933719827225584358402128727994530576296739317131430321_<89>

Number: 79999_187
N=2877358321708056371637969064791902153383448514723182208423678494914578167998439620341180341926287474457161806866745674265286749
  ( 127 digits)
Divisors found:
 r1=102746196181289754298239251281338562669 (pp39)
 r2=28004524047110445703490411149385111933719827225584358402128727994530576296739317131430321 (pp89)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 105.29 hours.
Scaled time: 225.52 units (timescale=2.142).
Factorization parameters were as follows:
name: 79999_187
n: 2877358321708056371637969064791902153383448514723182208423678494914578167998439620341180341926287474457161806866745674265286749
skew: 118531.10
# norm 1.27e+18
c5: 211680
c4: 27888457668
c3: -30707314002614800
c2: -457033680365705694301
c1: 74995606544574695438010410
c0: 1800229401639660547285944025875
# alpha -6.47
Y1: 79155702651047
Y0: -1685242049280354239419882
# Murphy_E 1.10e-10
# M 1590663983762522431907323915639751824626006268440442543393364548175785465778167857020397429970250589216784389782494022134624971
type: gnfs
rlim: 10000000
alim: 10000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved algebraic special-q in [5000000, 9400001)
Primes: RFBsize:664579, AFBsize:664026, largePrimes:14317582 encountered
Relations: rels:14420782, finalFF:1501288
Max relations in full relation-set: 28
Initial matrix: 1328687 x 1501288 with sparse part having weight 116492666.
Pruned matrix : 1169118 x 1175825 with weight 77386664.
Total sieving time: 94.61 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 9.80 hours.
Time per square root: 0.50 hours.
Prototype def-par.txt line would be:
gnfs,126,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,10000000,10000000,28,28,52,52,2.5,2.5,100000
total time: 105.29 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407673)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.06 BogoMIPS).

Apr 24, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(16·10¹⁵⁷-43)/9 = 1(7)₁₅₆3_<158> = · 457 · 467333 · 4456892921623_<13> · C136

C136 = P58 · P78

P58 = 2901114003506502307610374028265030500707093188178486117273_<58>

P78 = 495215781372945896967601620398746944009945389531259589750405256931914950509179_<78>

Number: 17773_157
N=1436677438098467843084575873801589371763127357660342525685576450844456202363206072561849265365343365545478507747923070405695314056948867
  ( 136 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=2901114003506502307610374028265030500707093188178486117273 (pp58)
 r2=495215781372945896967601620398746944009945389531259589750405256931914950509179 (pp78)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 66.41 hours.
Scaled time: 44.96 units (timescale=0.677).
Factorization parameters were as follows:
name: 17773_157
n: 1436677438098467843084575873801589371763127357660342525685576450844456202363206072561849265365343365545478507747923070405695314056948867
m: 20000000000000000000000000000000
c5: 50
c0: -43
skew: 0.97
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:283917, largePrimes:5731714 encountered
Relations: rels:5820203, finalFF:703323
Max relations in full relation-set: 28
Initial matrix: 567128 x 703323 with sparse part having weight 45486140.
Pruned matrix : 458529 x 461428 with weight 29111704.
Total sieving time: 57.29 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 8.63 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 66.41 hours.
 --------- CPU info (if available) ----------

Apr 24, 2008

By Robert Backstrom / GMP-ECM

8·10¹⁷²+3 = 8(0)₁₇₁3_<173> = 7 · 11² · 53 · 261587 · 13420331 · 14742878852145643127878371424312249_<35> · C122

C122 = P41 · P82

P41 = 14102707670245966200868549502313038790457_<41>

P82 = 2441555056445183184204788723617272663411410204503080174188931011979879367292787673_<82>

Apr 23, 2008

By Robert Backstrom / GGNFS, Msieve

10¹⁸⁴+3 = 1(0)₁₈₃3_<185> = 7 · C184

C184 = P67 · P117

P67 = 9818100172727968626557779746645595165748218531909597522519996742899_<67>

P117 = 145503855474974097626225854491524811807124225128548763972026441569570512183910306970186124416727300719805279405934471_<117>

Number: n
N=1428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429
  ( 184 digits)
SNFS difficulty: 185 digits.
Divisors found:

Wed Apr 23 01:45:47 2008  prp67 factor: 9818100172727968626557779746645595165748218531909597522519996742899
Wed Apr 23 01:45:47 2008  prp117 factor: 145503855474974097626225854491524811807124225128548763972026441569570512183910306970186124416727300719805279405934471
Wed Apr 23 01:45:47 2008  elapsed time 03:35:36 (Msieve 1.34)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 75.46 hours.
Scaled time: 97.80 units (timescale=1.296).
Factorization parameters were as follows:
name: KA_1_0_183_3
n: 1428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429
skew: 1.97
deg: 5
c5: 1
c0: 30
m: 10000000000000000000000000000000000000
type: snfs
rlim: 7000000
alim: 7000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 7000000/7000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4699990)
Primes: RFBsize:476648, AFBsize:475219, largePrimes:9263849 encountered
Relations: rels:9010978, finalFF:1072839
Max relations in full relation-set: 28
Initial matrix: 951931 x 1072839 with sparse part having weight 55004411.
Pruned matrix : 
Total sieving time: 75.09 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,185,5,0,0,0,0,0,0,0,0,7000000,7000000,28,28,48,48,2.5,2.5,100000
total time: 75.46 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Apr 22, 2008 (2nd)

By Wataru Sakai / GGNFS

(16·10¹⁸²-7)/9 = 1(7)₁₈₂_<183> = 3 · 227 · 30853 · 1396054142825212027_<19> · 30844830282414589468929329921501_<32> · C126

C126 = P50 · P76

P50 = 77353780133776529862472058000124963556450822141289_<50>

P76 = 2540193343944179996047245110605127443108044311279781450571038782918768697763_<76>

Number: template
N=196493557424740682427240818584015055922748541801083874106162700859906957590919852245108331779080425865538457466900821724236507
  ( 126 digits)
Divisors found:
 r1=77353780133776529862472058000124963556450822141289 (pp50)
 r2=2540193343944179996047245110605127443108044311279781450571038782918768697763 (pp76)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 175.25 hours.
Scaled time: 353.13 units (timescale=2.015).
Factorization parameters were as follows:
name: template
n: 196493557424740682427240818584015055922748541801083874106162700859906957590919852245108331779080425865538457466900821724236507
skew: 532555.37
# norm 4.26e+17
c5: 360
c4: -1530324443
c3: 3607202194095335
c2: 98272719477410458842
c1: -109507700429145984560920665
c0: 91593504604744425816368538465
# alpha -5.05
Y1: 33768739669423
Y0: -3527058784468384430641268
# Murphy_E 1.08e-10
# M 167783583878167419122603057044635014571958614459810334116778788696171969889816762212443121528709944125342409454564030436877113
type: gnfs
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.5
alambda: 2.5
qintsize: 60000
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [2700000, 9480001)
Primes: RFBsize:374362, AFBsize:374330, largePrimes:9514076 encountered
Relations: rels:10472238, finalFF:937321
Max relations in full relation-set: 32
Initial matrix: 748767 x 937321 with sparse part having weight 138147417.
Pruned matrix : 617364 x 621171 with weight 115795060.
Total sieving time: 169.06 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 5.52 hours.
Time per square root: 0.42 hours.
Prototype def-par.txt line would be:
gnfs,125,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5400000,5400000,27,27,51,51,2.5,2.5,60000
total time: 175.25 hours.
 --------- CPU info (if available) ----------

Apr 22, 2008

By Jo Yeong Uk / GGNFS

(5·10¹⁶¹-11)/3 = 1(6)₁₆₀3_<162> = 7 · 1259 · 29803 · 148639 · 6067219597_<10> · 88884873097_<11> · 405666641269_<12> · C116

C116 = P33 · P84

P33 = 121384631786385382186720547431793_<33>

P84 = 160761351830866943488566918884895797008739383646571499046004747235276493743031507551_<84>

Number: 16663_161
N=19513957497471335445827696533813670496727362690069642235708411907732675763782069629125383015431683072942154136968943
  ( 116 digits)
Divisors found:
 r1=121384631786385382186720547431793 (pp33)
 r2=160761351830866943488566918884895797008739383646571499046004747235276493743031507551 (pp84)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 25.38 hours.
Scaled time: 54.26 units (timescale=2.138).
Factorization parameters were as follows:
name: 16663_161
n: 19513957497471335445827696533813670496727362690069642235708411907732675763782069629125383015431683072942154136968943
skew: 24827.25
# norm 1.19e+16
c5: 39600
c4: 13149981748
c3: -456242557359933
c2: -6241594165039819254
c1: 13965529947566801370158
c0: -32658529279555611788809464
# alpha -6.00
Y1: 4007171096653
Y0: -13756933333544773509065
# Murphy_E 4.99e-10
# M 9725444623948773597185089542966777252611422691702276753671161477699391779206570499114792041792732623559418709227838
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 70000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 3080001)
Primes: RFBsize:250150, AFBsize:251683, largePrimes:7620277 encountered
Relations: rels:7585076, finalFF:636556
Max relations in full relation-set: 28
Initial matrix: 501916 x 636556 with sparse part having weight 57705817.
Pruned matrix : 397719 x 400292 with weight 35269443.
Polynomial selection time: 1.51 hours.
Total sieving time: 22.62 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.96 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.4,2.4,70000
total time: 25.38 hours.
 --------- CPU info (if available) ----------

Apr 21, 2008

By Sinkiti Sibata / GGNFS

(16·10¹⁵¹-43)/9 = 1(7)₁₅₀3_<152> = 13 · 71 · 660625704667_<12> · C137

C137 = P40 · P98

P40 = 2059807738909432649830264775862735198581_<40>

P98 = 14154470212110609361234331264093140155481663019204352112608445144751444243122493047528117504605313_<98>

Number: 17773_151
N=29155487283068471826109014159539684461899607166052702691944454477590659352794774953445901173552777684030303570065790988266341893082660853
  ( 137 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=2059807738909432649830264775862735198581 (pp40)
 r2=14154470212110609361234331264093140155481663019204352112608445144751444243122493047528117504605313 (pp98)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 34.51 hours.
Scaled time: 23.33 units (timescale=0.676).
Factorization parameters were as follows:
name: 17773_151
n: 29155487283068471826109014159539684461899607166052702691944454477590659352794774953445901173552777684030303570065790988266341893082660853
m: 2000000000000000000000000000000
c5: 5
c0: -43
skew: 1.54
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:175898, largePrimes:5380793 encountered
Relations: rels:5213423, finalFF:415029
Max relations in full relation-set: 28
Initial matrix: 352265 x 415029 with sparse part having weight 35736426.
Pruned matrix : 322290 x 324115 with weight 24241194.
Total sieving time: 30.40 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 3.76 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 34.51 hours.
 --------- CPU info (if available) ----------

Apr 20, 2008 (3rd)

By Wataru Sakai / GMP-ECM

(16·10¹⁹¹-43)/9 = 1(7)₁₉₀3_<192> = 678961553437_<12> · 1221328889923_<13> · C168

C168 = P38 · P130

P38 = 64024419926416439664546147244965522487_<38>

P130 = 3348528562739821307034868195960668802228141828168170031835393402661109187594911879893998700809150934886296138950389462224621424829_<130>

Apr 20, 2008 (2nd)

By Jo Yeong Uk / GGNFS

10¹⁷⁵+3 = 1(0)₁₇₄3_<176> = 13 · 1550513 · C168

C168 = P41 · P127

P41 = 84605989629414611161564159889389410528733_<41>

P127 = 5863813190635906011331311978267233281067998931182925784006119151460092105536944514992383719950101352924989857277216412589708939_<127>

Number: 10003_175
N=496113717995766066307880533236915285953249517566617777967182970559272467092653056911337880281707260262099853899471187426851132992261767060817439627549571806730566444287
  ( 168 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=84605989629414611161564159889389410528733 (pp41)
 r2=5863813190635906011331311978267233281067998931182925784006119151460092105536944514992383719950101352924989857277216412589708939 (pp127)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 105.85 hours.
Scaled time: 226.62 units (timescale=2.141).
Factorization parameters were as follows:
n: 496113717995766066307880533236915285953249517566617777967182970559272467092653056911337880281707260262099853899471187426851132992261767060817439627549571806730566444287
m: 100000000000000000000000000000000000
c5: 1
c0: 3
skew: 1.25
type: snfs
Factor base limits: 8400000/8400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [4200000, 6000001)
Primes: RFBsize:564877, AFBsize:564406, largePrimes:10850911 encountered
Relations: rels:11119170, finalFF:1442537
Max relations in full relation-set: 28
Initial matrix: 1129347 x 1442537 with sparse part having weight 89062627.
Pruned matrix : 837022 x 842732 with weight 50559156.
Total sieving time: 100.83 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 4.76 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,8400000,8400000,28,28,50,50,2.6,2.6,100000
total time: 105.85 hours.
 --------- CPU info (if available) ----------

(16·10¹⁵⁹-43)/9 = 1(7)₁₅₈3_<160> = 3 · 225493 · 10664310082475575481_<20> · C135

C135 = P50 · P85

P50 = 50742578999008560483591754078912162960258196529877_<50>

P85 = 4856438048175192886765210965298149844959246658051867441833610068768177210758899421951_<85>

Number: 17773_159
N=246428191313320666306972352915263184365357951694412511444685487421882568203843254315116845466116984910218199201031653835403409401130027
  ( 135 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=50742578999008560483591754078912162960258196529877 (pp50)
 r2=4856438048175192886765210965298149844959246658051867441833610068768177210758899421951 (pp85)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 36.12 hours.
Scaled time: 77.31 units (timescale=2.140).
Factorization parameters were as follows:
n: 246428191313320666306972352915263184365357951694412511444685487421882568203843254315116845466116984910218199201031653835403409401130027
m: 200000000000000000000000000000000
c5: 1
c0: -860
skew: 3.86
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4200001)
Primes: RFBsize:283146, AFBsize:282747, largePrimes:5782527 encountered
Relations: rels:5844803, finalFF:676274
Max relations in full relation-set: 28
Initial matrix: 565957 x 676274 with sparse part having weight 47468304.
Pruned matrix : 489177 x 492070 with weight 33466786.
Total sieving time: 34.67 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.32 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 36.12 hours.
 --------- CPU info (if available) ----------

Apr 20, 2008

By Sinkiti Sibata / GGNFS

(16·10¹⁴⁹-43)/9 = 1(7)₁₄₈3_<150> = 74257 · 1756286687473_<13> · 40000271800450469_<17> · C116

C116 = P34 · P82

P34 = 8451328395281915175077609691314123_<34>

P82 = 4032336289143467545190727664762401688975731101155506963337129845941832951058267739_<82>

Number: 17773_149
N=34078598179763894284357022031702951463430782892473350643743951375598986101203012608356279387739075999304334885977897
  ( 116 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=8451328395281915175077609691314123 (pp34)
 r2=4032336289143467545190727664762401688975731101155506963337129845941832951058267739 (pp82)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 33.88 hours.
Scaled time: 22.94 units (timescale=0.677).
Factorization parameters were as follows:
name: 17773_149
n: 34078598179763894284357022031702951463430782892473350643743951375598986101203012608356279387739075999304334885977897
m: 1000000000000000000000000000000
c5: 8
c0: -215
skew: 1.93
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:175813, largePrimes:5492730 encountered
Relations: rels:5379374, finalFF:457983
Max relations in full relation-set: 28
Initial matrix: 352180 x 457983 with sparse part having weight 40625337.
Pruned matrix : 304476 x 306300 with weight 23877941.
Total sieving time: 30.09 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 3.43 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 33.88 hours.
 --------- CPU info (if available) ----------

Apr 19, 2008 (3rd)

By Wataru Sakai / Msieve

(16·10¹⁶³-43)/9 = 1(7)₁₆₂3_<164> = 13 · 1193 · 6396333453947_<13> · 6011603269643265989_<19> · 37780493521163729849057_<23> · C105

C105 = P38 · P68

P38 = 13909049981855630404289973234462069073_<38>

P68 = 56729267307243269741500070065132179405855567563697922136760577391119_<68>

Thu Apr 17 23:17:26 2008  Msieve v. 1.35
Thu Apr 17 23:17:26 2008  random seeds: 610e60e2 1e46c7c2
Thu Apr 17 23:17:26 2008  factoring
789050214410495208081559944595870731751665549451986335130440150439214112960298838225645198526905114762687
(105 digits)
Thu Apr 17 23:17:27 2008  searching for 15-digit factors
Thu Apr 17 23:17:28 2008  commencing quadratic sieve (105-digit input)
Thu Apr 17 23:17:28 2008  using multiplier of 7
Thu Apr 17 23:17:28 2008  using 32kb Intel Core sieve core
Thu Apr 17 23:17:28 2008  sieve interval: 38 blocks of size 32768
Thu Apr 17 23:17:28 2008  processing polynomials in batches of 6
Thu Apr 17 23:17:28 2008  using a sieve bound of 4083571 (144667 primes)
Thu Apr 17 23:17:28 2008  using large prime bound of 612535650 (29 bits)
Thu Apr 17 23:17:28 2008  using double large prime bound of
6558982124812350 (44-53 bits)
Thu Apr 17 23:17:28 2008  using trial factoring cutoff of 53 bits
Thu Apr 17 23:17:28 2008  polynomial 'A' values have 14 factors
Sat Apr 19 06:43:23 2008  144798 relations (34124 full + 110674
combined from 2149152 partial), need 144763
Sat Apr 19 06:43:26 2008  begin with 2183276 relations
Sat Apr 19 06:43:27 2008  reduce to 381872 relations in 15 passes
Sat Apr 19 06:43:27 2008  attempting to read 381872 relations
Sat Apr 19 06:43:32 2008  recovered 381872 relations
Sat Apr 19 06:43:32 2008  recovered 374155 polynomials
Sat Apr 19 06:43:32 2008  attempting to build 144798 cycles
Sat Apr 19 06:43:32 2008  found 144798 cycles in 6 passes
Sat Apr 19 06:43:32 2008  distribution of cycle lengths:
Sat Apr 19 06:43:32 2008     length 1 : 34124
Sat Apr 19 06:43:32 2008     length 2 : 24668
Sat Apr 19 06:43:32 2008     length 3 : 24516
Sat Apr 19 06:43:32 2008     length 4 : 19930
Sat Apr 19 06:43:32 2008     length 5 : 15205
Sat Apr 19 06:43:32 2008     length 6 : 10259
Sat Apr 19 06:43:32 2008     length 7 : 6779
Sat Apr 19 06:43:32 2008     length 9+: 9317
Sat Apr 19 06:43:32 2008  largest cycle: 21 relations
Sat Apr 19 06:43:33 2008  matrix is 144667 x 144798 (40.5 MB) with
weight 10044000 (69.37/col)
Sat Apr 19 06:43:33 2008  sparse part has weight 10044000 (69.37/col)
Sat Apr 19 06:43:33 2008  filtering completed in 3 passes
Sat Apr 19 06:43:33 2008  matrix is 139120 x 139183 (39.2 MB) with
weight 9715429 (69.80/col)
Sat Apr 19 06:43:33 2008  sparse part has weight 9715429 (69.80/col)
Sat Apr 19 06:43:34 2008  saving the first 48 matrix rows for later
Sat Apr 19 06:43:34 2008  matrix is 139072 x 139183 (22.9 MB) with
weight 7554305 (54.28/col)
Sat Apr 19 06:43:34 2008  sparse part has weight 5178932 (37.21/col)
Sat Apr 19 06:43:34 2008  matrix includes 64 packed rows
Sat Apr 19 06:43:34 2008  using block size 55673 for processor cache
size 6144 kB
Sat Apr 19 06:43:35 2008  commencing Lanczos iteration
Sat Apr 19 06:43:35 2008  memory use: 23.1 MB
Sat Apr 19 06:45:04 2008  lanczos halted after 2201 iterations (dim = 139068)
Sat Apr 19 06:45:04 2008  recovered 15 nontrivial dependencies
Sat Apr 19 06:45:05 2008  prp38 factor: 13909049981855630404289973234462069073
Sat Apr 19 06:45:05 2008  prp68 factor:
56729267307243269741500070065132179405855567563697922136760577391119
Sat Apr 19 06:45:05 2008  elapsed time 31:27:39

Apr 19, 2008 (2nd)

By Robert Backstrom / GGNFS

(16·10¹⁴⁵-43)/9 = 1(7)₁₄₄3_<146> = 13 · 59 · 113 · 6113 · 97900993 · C129

C129 = P65 · P65

P65 = 16622796863443524019743377225276094967799622716440295866198684081_<65>

P65 = 20618547874697345788229642446357994038980128189862291645786008147_<65>

Number: n
N=342737932940279177877666996901874480937332396368251728885802533313270128140969346250666588135979889005893165891963390853345207907
  ( 129 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=16622796863443524019743377225276094967799622716440295866198684081 (pp65)
 r2=20618547874697345788229642446357994038980128189862291645786008147 (pp65)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 5.98 hours.
Scaled time: 10.86 units (timescale=1.818).
Factorization parameters were as follows:
name: KA_1_7_144_3
n: 342737932940279177877666996901874480937332396368251728885802533313270128140969346250666588135979889005893165891963390853345207907
skew: 1.22
deg: 5
c5: 16
c0: -43
m: 100000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:114155, AFBsize:114182, largePrimes:6568235 encountered
Relations: rels:5836571, finalFF:264019
Max relations in full relation-set: 48
Initial matrix: 228401 x 264019 with sparse part having weight 31268000.
Pruned matrix : 216769 x 217975 with weight 21023686.
Total sieving time: 5.41 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.41 hours.
Total square root time: 0.03 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000
total time: 5.98 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Apr 19, 2008

By Jo Yeong Uk / GGNFS, GMP-ECM

(16·10¹⁵⁵-43)/9 = 1(7)₁₅₄3_<156> = 29 · 3673 · 234391757431997529389_<21> · C130

C130 = P35 · P95

P35 = 88308179609882380758786014994362513_<35>

P95 = 80633456936717508249547250917177803523254243013044383853109355147287095866161662111291070396717_<95>

Number: 17773_155
N=7120593797733366076311318086086978160341727352661331057070689454547745192982183077839045352871475585630105847818565550177423069821
  ( 130 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=88308179609882380758786014994362513 (pp35)
 r2=80633456936717508249547250917177803523254243013044383853109355147287095866161662111291070396717 (pp95)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 20.46 hours.
Scaled time: 43.68 units (timescale=2.135).
Factorization parameters were as follows:
n: 7120593797733366076311318086086978160341727352661331057070689454547745192982183077839045352871475585630105847818565550177423069821
m: 20000000000000000000000000000000
c5: 1
c0: -86
skew: 2.44
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2800001)
Primes: RFBsize:216816, AFBsize:217561, largePrimes:5624338 encountered
Relations: rels:5571441, finalFF:535073
Max relations in full relation-set: 28
Initial matrix: 434441 x 535073 with sparse part having weight 42701966.
Pruned matrix : 379229 x 381465 with weight 27894484.
Total sieving time: 19.62 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.72 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 20.46 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407670)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Total of 4 processors activated (19246.09 BogoMIPS).

Apr 18, 2008 (4th)

By Wataru Sakai / GMP-ECM

(16·10¹⁷⁷-43)/9 = 1(7)₁₇₆3_<178> = 3 · 39341 · 55469 · C168

C168 = P28 · P140

P28 = 3540849013711996267182661087_<28>

P140 = 76692532456878501730549593664595518204648519628890706699390350654932773905434667749384344629111220283370888580298809813332301394964563882217_<140>

Apr 18, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(16·10¹⁵⁸-43)/9 = 1(7)₁₅₇3_<159> = 17 · 112897531 · C149

C149 = P39 · P111

P39 = 515585271951048556898212277218261286633_<39>

P111 = 179656777145804708129547858060856269933397255736927677551557880399873254058579628363977016884753579212620803503_<111>

Number: n
N=92628388302568645595550127548210992985873169297302502712303507160362538255924552544689072063877202571563233471253199962663372400097705975507053475399
  ( 149 digits)
SNFS difficulty: 160 digits.
Divisors found:

Fri Apr 18 17:59:12 2008  prp39 factor: 515585271951048556898212277218261286633
Fri Apr 18 17:59:12 2008  prp111 factor: 179656777145804708129547858060856269933397255736927677551557880399873254058579628363977016884753579212620803503
Fri Apr 18 17:59:12 2008  elapsed time 00:35:03 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 29.43 hours.
Scaled time: 24.66 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_1_7_157_3
n: 92628388302568645595550127548210992985873169297302502712303507160362538255924552544689072063877202571563233471253199962663372400097705975507053475399
type: snfs
deg: 5
c5: 4
c0: -1075
skew: 2.44
m: 100000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1899990)
Primes: RFBsize:216816, AFBsize:216841, largePrimes:5530400 encountered
Relations: rels:5435017, finalFF:515675
Max relations in full relation-set: 28
Initial matrix: 433721 x 515675 with sparse part having weight 39258233.
Pruned matrix : 
Total sieving time: 29.27 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 29.43 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

Apr 18, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(16·10¹¹⁸-43)/9 = 1(7)₁₁₇3_<119> = 7 · 1319 · 649573 · 3859171 · C102

C102 = P47 · P56

P47 = 47350955974127276757526684432655467293045031819_<47>

P56 = 16221234355104901470997952766497166240721117007085516953_<56>

Number: 17773_118
N=768090953794573057816630109157861769746161838397065624797169366829056643479552845083229414945948927507
  ( 102 digits)
SNFS difficulty: 119 digits.
Divisors found:
 r1=47350955974127276757526684432655467293045031819 (pp47)
 r2=16221234355104901470997952766497166240721117007085516953 (pp56)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.26 hours.
Scaled time: 1.53 units (timescale=0.677).
Factorization parameters were as follows:
name: 17773_118
n: 768090953794573057816630109157861769746161838397065624797169366829056643479552845083229414945948927507
m: 200000000000000000000000
c5: 500
c0: -43
skew: 0.61
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64058, largePrimes:2018699 encountered
Relations: rels:2002457, finalFF:151962
Max relations in full relation-set: 28
Initial matrix: 113222 x 151962 with sparse part having weight 11986315.
Pruned matrix : 100073 x 100703 with weight 5851889.
Total sieving time: 1.99 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,119,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.26 hours.
 --------- CPU info (if available) ----------

Apr 18, 2008

By Jo Yeong Uk / GGNFS, GMP-ECM

(16·10¹³⁸-43)/9 = 1(7)₁₃₇3_<139> = 3² · 14639 · 51266269 · C126

C126 = P59 · P68

P59 = 11632544748654663205292509039845800240928717050619027960643_<59>

P68 = 22626485891727523197151601650522464210578871505272726012964428807469_<68>

Number: 17773_138
N=263203609640323824392458107325806099995043923027122226226760883014902997330558765169460769491743099274902294390038895556442567
  ( 126 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=11632544748654663205292509039845800240928717050619027960643 (pp59)
 r2=22626485891727523197151601650522464210578871505272726012964428807469 (pp68)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.90 hours.
Scaled time: 12.67 units (timescale=2.145).
Factorization parameters were as follows:
n: 263203609640323824392458107325806099995043923027122226226760883014902997330558765169460769491743099274902294390038895556442567
m: 10000000000000000000000000000
c5: 4
c0: -1075
skew: 3.06
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:114037, largePrimes:3315183 encountered
Relations: rels:3373564, finalFF:357868
Max relations in full relation-set: 28
Initial matrix: 228256 x 357868 with sparse part having weight 30397126.
Pruned matrix : 180827 x 182032 with weight 12710286.
Total sieving time: 5.73 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 5.90 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407670)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Total of 4 processors activated (19246.09 BogoMIPS).

8·10¹⁸⁷-1 = 7(9)₁₈₇_<188> = 50221 · 718693111 · 5015358357341_<13> · C162

C162 = P36 · C127

P36 = 153590809952823656448053791352618581_<36>

C127 = [2877358321708056371637969064791902153383448514723182208423678494914578167998439620341180341926287474457161806866745674265286749_<127>]

(16·10¹⁴⁶-43)/9 = 1(7)₁₄₅3_<147> = 1759223 · 66378044054429_<14> · C127

C127 = P55 · P73

P55 = 1056295968541772519047500174110259791732144028688415153_<55>

P73 = 1441273845342654536010084697268847716723542480648916997795263989062923623_<73>

Number: 17773_146
N=1522411752400144126632930397778883985122615881675977475582863474157301360548134270400340874386530077118346961505716336554859319
  ( 127 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=1056295968541772519047500174110259791732144028688415153 (pp55)
 r2=1441273845342654536010084697268847716723542480648916997795263989062923623 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 9.88 hours.
Scaled time: 21.20 units (timescale=2.146).
Factorization parameters were as follows:
n: 1522411752400144126632930397778883985122615881675977475582863474157301360548134270400340874386530077118346961505716336554859319
m: 200000000000000000000000000000
c5: 5
c0: -43
skew: 1.54
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1575001)
Primes: RFBsize:135072, AFBsize:134733, largePrimes:3762790 encountered
Relations: rels:3832797, finalFF:363069
Max relations in full relation-set: 28
Initial matrix: 269870 x 363069 with sparse part having weight 33914108.
Pruned matrix : 236804 x 238217 with weight 18742821.
Total sieving time: 9.56 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.24 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 9.88 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407670)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Total of 4 processors activated (19246.09 BogoMIPS).

8·10¹⁸⁴-1 = 7(9)₁₈₄_<185> = 1999080062901581503437318550484654902159553_<43> · C143

C143 = P35 · P109

P35 = 15637703450006173973828739274219217_<35>

P109 = 2559097461890393718243754256765145837067277294067140964364353690368762236330319581826659779608172818332729999_<109>

Apr 17, 2008 (3th)

By Sinkiti Sibata / Msieve, GGNFS

(16·10¹²⁶-43)/9 = 1(7)₁₂₅3_<127> = 3 · 17 · 109 · 2289551683_<10> · C114

C114 = P34 · P80

P34 = 3874799090028982983788638177832431_<34>

P80 = 36047998691929861569706472795198049716524625691428470311891766732822101755440039_<80>

Number: 17773_126
N=139678752528855796515825665771919737666695102874942258747881123820068740828534251491647142474744904176151610104809
  ( 114 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=3874799090028982983788638177832431 (pp34)
 r2=36047998691929861569706472795198049716524625691428470311891766732822101755440039 (pp80)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.68 hours.
Scaled time: 5.34 units (timescale=1.992).
Factorization parameters were as follows:
name: 17773_126
n: 139678752528855796515825665771919737666695102874942258747881123820068740828534251491647142474744904176151610104809
m: 20000000000000000000000000
c5: 5
c0: -43
skew: 1.54
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:63728, largePrimes:2127400 encountered
Relations: rels:2149094, finalFF:154047
Max relations in full relation-set: 28
Initial matrix: 112891 x 154047 with sparse part having weight 14322637.
Pruned matrix : 103876 x 104504 with weight 7465249.
Total sieving time: 2.51 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.68 hours.
 --------- CPU info (if available) ----------

(16·10¹²⁵-43)/9 = 1(7)₁₂₄3_<126> = 139 · 467649979411443427_<18> · C106

C106 = P31 · P32 · P44

P31 = 1103899759447808710603942658389_<31>

P32 = 85253848617475439469702760423117_<32>

P44 = 29060168036435085334340301632974120249835357_<44>

Number: 17773_125
N=2734901902818018639322144720567010346065153400121065763221178022074487392487751189852112831885124154884141
  ( 106 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=1103899759447808710603942658389 (pp31)
 r2=85253848617475439469702760423117 (pp32)
 r3=29060168036435085334340301632974120249835357 (pp44)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.14 hours.
Scaled time: 6.28 units (timescale=2.000).
Factorization parameters were as follows:
name: 17773_125
n: 2734901902818018639322144720567010346065153400121065763221178022074487392487751189852112831885124154884141
m: 20000000000000000000000000
c5: 1
c0: -86
skew: 2.44
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:63853, largePrimes:2190075 encountered
Relations: rels:2273813, finalFF:198568
Max relations in full relation-set: 28
Initial matrix: 113015 x 198568 with sparse part having weight 19369229.
Pruned matrix : 97297 x 97926 with weight 6884251.
Total sieving time: 2.99 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.14 hours.
 --------- CPU info (if available) ----------

(16·10¹¹⁹-43)/9 = 1(7)₁₁₈3_<120> = 96881956739185113311_<20> · C100

C100 = P34 · P67

P34 = 1468279725698321121821741190940259_<34>

P67 = 1249757551140585021286231031388970942154095925690579253003177838577_<67>

Wed Apr 16 18:47:15 2008  Msieve v. 1.33
Wed Apr 16 18:47:15 2008  random seeds: b6b676bf 3e282a6a
Wed Apr 16 18:47:15 2008  factoring 1834993674378103706510951864175520316649357398636129200483879762498449964268488473520406877952571443 (100 digits)
Wed Apr 16 18:47:16 2008  searching for 15-digit factors
Wed Apr 16 18:47:18 2008  commencing quadratic sieve (100-digit input)
Wed Apr 16 18:47:18 2008  using multiplier of 7
Wed Apr 16 18:47:18 2008  using 64kb Pentium 4 sieve core
Wed Apr 16 18:47:18 2008  sieve interval: 18 blocks of size 65536
Wed Apr 16 18:47:18 2008  processing polynomials in batches of 6
Wed Apr 16 18:47:18 2008  using a sieve bound of 2676997 (97647 primes)
Wed Apr 16 18:47:18 2008  using large prime bound of 401549550 (28 bits)
Wed Apr 16 18:47:18 2008  using double large prime bound of 3067117780557750 (43-52 bits)
Wed Apr 16 18:47:18 2008  using trial factoring cutoff of 52 bits
Wed Apr 16 18:47:18 2008  polynomial 'A' values have 13 factors
Thu Apr 17 12:45:34 2008  97796 relations (22955 full + 74841 combined from 1478103 partial), need 97743
Thu Apr 17 12:45:40 2008  begin with 1501058 relations
Thu Apr 17 12:45:42 2008  reduce to 259398 relations in 12 passes
Thu Apr 17 12:45:42 2008  attempting to read 259398 relations
Thu Apr 17 12:45:51 2008  recovered 259398 relations
Thu Apr 17 12:45:51 2008  recovered 250343 polynomials
Thu Apr 17 12:45:51 2008  attempting to build 97796 cycles
Thu Apr 17 12:45:51 2008  found 97796 cycles in 6 passes
Thu Apr 17 12:45:51 2008  distribution of cycle lengths:
Thu Apr 17 12:45:51 2008     length 1 : 22955
Thu Apr 17 12:45:51 2008     length 2 : 16414
Thu Apr 17 12:45:51 2008     length 3 : 16469
Thu Apr 17 12:45:51 2008     length 4 : 13428
Thu Apr 17 12:45:51 2008     length 5 : 10245
Thu Apr 17 12:45:51 2008     length 6 : 7142
Thu Apr 17 12:45:51 2008     length 7 : 4639
Thu Apr 17 12:45:51 2008     length 9+: 6504
Thu Apr 17 12:45:51 2008  largest cycle: 22 relations
Thu Apr 17 12:45:52 2008  matrix is 97647 x 97796 (26.6 MB) with weight 6573420 (67.22/col)
Thu Apr 17 12:45:52 2008  sparse part has weight 6573420 (67.22/col)
Thu Apr 17 12:45:54 2008  filtering completed in 3 passes
Thu Apr 17 12:45:54 2008  matrix is 93857 x 93921 (25.6 MB) with weight 6345777 (67.57/col)
Thu Apr 17 12:45:54 2008  sparse part has weight 6345777 (67.57/col)
Thu Apr 17 12:45:55 2008  saving the first 48 matrix rows for later
Thu Apr 17 12:45:55 2008  matrix is 93809 x 93921 (15.0 MB) with weight 4909957 (52.28/col)
Thu Apr 17 12:45:55 2008  sparse part has weight 3371549 (35.90/col)
Thu Apr 17 12:45:55 2008  matrix includes 64 packed rows
Thu Apr 17 12:45:55 2008  using block size 21845 for processor cache size 512 kB
Thu Apr 17 12:45:56 2008  commencing Lanczos iteration
Thu Apr 17 12:45:56 2008  memory use: 15.1 MB
Thu Apr 17 12:47:24 2008  lanczos halted after 1485 iterations (dim = 93807)
Thu Apr 17 12:47:25 2008  recovered 17 nontrivial dependencies
Thu Apr 17 12:47:26 2008  prp34 factor: 1468279725698321121821741190940259
Thu Apr 17 12:47:26 2008  prp67 factor: 1249757551140585021286231031388970942154095925690579253003177838577
Thu Apr 17 12:47:26 2008  elapsed time 18:00:11

(16·10¹²⁰-43)/9 = 1(7)₁₁₉3_<121> = 3⁴ · C119

C119 = P50 · P69

P50 = 85510357558761421141383126907634041186486316417099_<50>

P69 = 256669185187810792308602187020497433738883870719060728193378032088567_<69>

Number: 17773_120
N=21947873799725651577503429355281207133058984910836762688614540466392318244170096021947873799725651577503429355281207133
  ( 119 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=85510357558761421141383126907634041186486316417099 (pp50)
 r2=256669185187810792308602187020497433738883870719060728193378032088567 (pp69)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.59 hours.
Scaled time: 1.75 units (timescale=0.677).
Factorization parameters were as follows:
name: 17773_120
n: 21947873799725651577503429355281207133058984910836762688614540466392318244170096021947873799725651577503429355281207133
m: 2000000000000000000000000
c5: 1
c0: -86
skew: 2.44
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:63853, largePrimes:2194643 encountered
Relations: rels:2335783, finalFF:263665
Max relations in full relation-set: 28
Initial matrix: 113015 x 263665 with sparse part having weight 24306850.
Pruned matrix : 84489 x 85118 with weight 5577315.
Total sieving time: 2.36 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.59 hours.
 --------- CPU info (if available) ----------

Apr 17, 2008 (2nd)

By Robert Backstrom / GGNFS, GMP-ECM, Msieve

(16·10¹⁴⁴-43)/9 = 1(7)₁₄₃3_<145> = 3 · 227 · C142

C142 = P39 · P52 · P52

P39 = 122929344325063661695898389182280845929_<39>

P52 = 3221391447437790783926804430055858823974940817522169_<52>

P52 = 6592213962798872415463349088189519733800364363571333_<52>

Number: n
N=2610540055473976178821993799967368249306575297764725077500407896883667808777940936531244901288954152390275738293359438733888073095121553271333
  ( 142 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=122929344325063661695898389182280845929 (pp39)
 r2=3221391447437790783926804430055858823974940817522169 (pp52)
 r3=6592213962798872415463349088189519733800364363571333 (pp52)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.63 hours.
Scaled time: 12.12 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_7_143_3
n: 2610540055473976178821993799967368249306575297764725077500407896883667808777940936531244901288954152390275738293359438733888073095121553271333
skew: 1.93
deg: 5
c5: 8
c0: -215
m: 100000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:114155, AFBsize:114062, largePrimes:6704802 encountered
Relations: rels:5987168, finalFF:270894
Max relations in full relation-set: 48
Initial matrix: 228282 x 270894 with sparse part having weight 34317305.
Pruned matrix : 216547 x 217752 with weight 22303479.
Total sieving time: 5.95 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.43 hours.
Total square root time: 0.11 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000
total time: 6.63 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(16·10¹⁶¹-43)/9 = 1(7)₁₆₀3_<162> = 103 · 1021849 · 334680190961971_<15> · 24695725106873857_<17> · 218931718291791250301_<21> · C102

C102 = P35 · P68

P35 = 36407080834751143443498565731037777_<35>

P68 = 25639360582377136928119325942391403410234951772381760032053460807861_<68>

Number: n
N=933454273273936577612474901491001066341309617815789327012871967840898500121908855872904953600329564997
  ( 102 digits)
Divisors found:
 r1=36407080834751143443498565731037777 (pp35)
 r2=25639360582377136928119325942391403410234951772381760032053460807861 (pp68)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 5.34 hours.
Scaled time: 9.74 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_1_7_160_3
n: 933454273273936577612474901491001066341309617815789327012871967840898500121908855872904953600329564997
skew: 11093.37
# norm 3.99e+13
c5: 1800
c4: 372271082
c3: -473746083165
c2: -47756910272386885
c1: 76919695839272232985
c0: 206237387055222311017528
# alpha -5.02
Y1: 13814165629
Y0: -55329866672127928995
# Murphy_E 2.56e-09
# M 833706548574107714639820363179423211715410901127672776498804591771767671390163419824815462115955586024
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:169511, AFBsize:169583, largePrimes:4051501 encountered
Relations: rels:4057067, finalFF:469111
Max relations in full relation-set: 48
Initial matrix: 339174 x 469111 with sparse part having weight 27040198.
Pruned matrix : 217394 x 219153 with weight 8801689.
Total sieving time: 4.95 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.19 hours.
Total square root time: 0.10 hours, sqrts: 2.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 5.34 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(14·10¹⁶⁶-23)/9 = 1(5)₁₆₅3_<167> = 107 · 127 · 507742003 · C154

C154 = P40 · P42 · P73

P40 = 3383246862790582749480921165155169175417_<40>

P42 = 432508300655604026409962871945358873577669_<42>

P73 = 1540730929988680743737736570091962036281428096254323888738391539667343483_<73>

Number: n
N=666378916296932729031689796754642939121851670277389480145678840927507410551912991473639321490092225320869301481127
  ( 114 digits)
Divisors found:

Thu Apr 17 22:20:15 2008  prp42 factor: 432508300655604026409962871945358873577669
Thu Apr 17 22:20:15 2008  prp73 factor: 1540730929988680743737736570091962036281428096254323888738391539667343483
Thu Apr 17 22:20:15 2008  elapsed time 00:44:24 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 26.74 hours.
Scaled time: 22.39 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_1_5_165_3
n: 666378916296932729031689796754642939121851670277389480145678840927507410551912991473639321490092225320869301481127
skew: 21772.53
# norm 1.15e+16
c5: 127920
c4: -23604014380
c3: -521830973354640
c2: 13654652291457606849
c1: 43808656190295530955502
c0: -112301076362569465313946696
# alpha -6.55
Y1: 1193146480793
Y0: -5538090041817291334015
# Murphy_E 5.94e-10
# M 424840657608522257635537657543679823340115623023876770799204026916388698189137461913456436848462018965001840737620
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1500151)
Primes: RFBsize:250150, AFBsize:250624, largePrimes:6967090 encountered
Relations: rels:6656946, finalFF:539540
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 26.53 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 26.74 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

Apr 17, 2008

By Jo Yeong Uk / GMP-ECM, GGNFS

(5·10¹⁷²-11)/3 = 1(6)₁₇₁3_<173> = 449 · 613 · 14983621 · 640773929 · 765796020212228084429127317516663_<33> · C118

C118 = P48 · P71

P48 = 320495677550936751308035792497362918849303147407_<48>

P71 = 25697154737133609560344670840251726771651958436082806086312019002604671_<71>

Number: 16663_172
N=8235827018608900184232630962747782531914857076776112095668712602895011246947560520007279169172594208954918011259738097
  ( 118 digits)
Divisors found:
 r1=320495677550936751308035792497362918849303147407 (pp48)
 r2=25697154737133609560344670840251726771651958436082806086312019002604671 (pp71)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 36.65 hours.
Scaled time: 78.44 units (timescale=2.140).
Factorization parameters were as follows:
name: 16663_172
n: 8235827018608900184232630962747782531914857076776112095668712602895011246947560520007279169172594208954918011259738097
skew: 23994.76
# norm 3.56e+15
c5: 81780
c4: -8722177613
c3: -172048388133462
c2: 5431487071876079458
c1: 32188035299275822248228
c0: -42858347921993434993922144
# alpha -4.89
Y1: 2047839378167
Y0: -39866902854599812345335
# Murphy_E 3.69e-10
# M 4397100284139661905595764503103251667391894199048783655171359813332510445129267787214586724263171904117759984428094451
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4125001)
Primes: RFBsize:315948, AFBsize:315538, largePrimes:7637241 encountered
Relations: rels:7680602, finalFF:728503
Max relations in full relation-set: 28
Initial matrix: 631569 x 728503 with sparse part having weight 61666293.
Pruned matrix : 551228 x 554449 with weight 41570758.
Polynomial selection time: 1.98 hours.
Total sieving time: 32.52 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.82 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000
total time: 36.65 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407670)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Total of 4 processors activated (19246.09 BogoMIPS).

(16·10¹³³-43)/9 = 1(7)₁₃₂3_<134> = 13 · 233 · 25933 · 97813 · 71667448168957_<14> · C107

C107 = P49 · P58

P49 = 3342143748489434590572597197368580584310674477981_<49>

P58 = 9660103826638798656998936740469404831436423757669777126209_<58>

Number: 17773_133
N=32285455613959725746999532746011021932043083571604268600338314952656034453773659817804519379721595428504029
  ( 107 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=3342143748489434590572597197368580584310674477981 (pp49)
 r2=9660103826638798656998936740469404831436423757669777126209 (pp58)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.97 hours.
Scaled time: 6.35 units (timescale=2.135).
Factorization parameters were as follows:
n: 32285455613959725746999532746011021932043083571604268600338314952656034453773659817804519379721595428504029
m: 1000000000000000000000000000
c5: 4
c0: -1075
skew: 3.06
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1250001)
Primes: RFBsize:107126, AFBsize:107108, largePrimes:2273625 encountered
Relations: rels:2404790, finalFF:294421
Max relations in full relation-set: 28
Initial matrix: 214298 x 294421 with sparse part having weight 21471334.
Pruned matrix : 181853 x 182988 with weight 10321115.
Total sieving time: 2.83 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 2.97 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407670)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Total of 4 processors activated (19246.09 BogoMIPS).

8·10¹⁹⁴-1 = 7(9)₁₉₄_<195> = 17 · 50287 · 3097537 · 119605714808559453334057_<24> · C160

C160 = P28 · P132

P28 = 5565233219278259235319671553_<28>

P132 = 453872150920361109687290122732532032688530998219435391743981449214557842553014055993102429286314732251554440782531327487375989287353_<132>

(16·10¹³⁴-43)/9 = 1(7)₁₃₃3_<135> = 263 · 197047159 · C124

C124 = P58 · P67

P58 = 2863834785747777662736218202774989738378574194792058607181_<58>

P67 = 1197853171614762586665272443737488891329168220783862099262703556449_<67>

Number: 17773_134
N=3430453581088659560179837616813547764407849068970136086958872262619484904091371908295926398270918423889605423047490150260269
  ( 124 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=2863834785747777662736218202774989738378574194792058607181 (pp58)
 r2=1197853171614762586665272443737488891329168220783862099262703556449 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.41 hours.
Scaled time: 7.33 units (timescale=2.147).
Factorization parameters were as follows:
n: 3430453581088659560179837616813547764407849068970136086958872262619484904091371908295926398270918423889605423047490150260269
m: 2000000000000000000000000000
c5: 1
c0: -860
skew: 3.86
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1350001)
Primes: RFBsize:107126, AFBsize:106968, largePrimes:2335679 encountered
Relations: rels:2477311, finalFF:295035
Max relations in full relation-set: 28
Initial matrix: 214158 x 295035 with sparse part having weight 23189974.
Pruned matrix : 186064 x 187198 with weight 11633275.
Total sieving time: 3.25 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 3.41 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407670)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Total of 4 processors activated (19246.09 BogoMIPS).

8·10¹⁷⁸-1 = 7(9)₁₇₈_<179> = 17 · 54799 · C173

C173 = P40 · P134

P40 = 5885133257828395389165904720779636286561_<40>

P134 = 14591909625581121136482174824446665198803833208568420920881318532185496567756234695562377208236552712810015744424723901294952789939873_<134>

8·10¹⁸⁵-1 = 7(9)₁₈₅_<186> = 1949 · 88692237787921626581_<20> · C163

C163 = P34 · P129

P34 = 9213214841645127155231659857590189_<34>

P129 = 502321002341718432286600942522787211853191175238165401879857931010912161900095448258817976719920746592180033543258552863249190139_<129>

8·10¹⁸²-1 = 7(9)₁₈₂_<183> = 6689 · 45833 · C175

C175 = P38 · C137

P38 = 64965178089572382042423526852742694223_<38>

C137 = [40167044071217756780187592392246187076622588646967716036404892251010744662016892972703963262216033825927684995558723281578766771102057449_<137>]

Apr 16, 2008 (4th)

By Sinkiti Sibata / Msieve, GGNFS

(16·10¹¹²-43)/9 = 1(7)₁₁₁3_<113> = 7² · 193 · 20145617 · 175080692421274249_<18> · C84

C84 = P37 · P48

P37 = 2746131666830462403852624787266510433_<37>

P48 = 194081392436622661770145240283408879646755217701_<48>

Wed Apr 16 12:58:21 2008  Msieve v. 1.33
Wed Apr 16 12:58:21 2008  random seeds: b6b6c24f 7a2fe73c
Wed Apr 16 12:58:21 2008  factoring 532973057712759689286185744598002512654979895804101219214304241467155374801502774533 (84 digits)
Wed Apr 16 12:58:22 2008  searching for 15-digit factors
Wed Apr 16 12:58:24 2008  commencing quadratic sieve (84-digit input)
Wed Apr 16 12:58:24 2008  using multiplier of 17
Wed Apr 16 12:58:24 2008  using 64kb Pentium 4 sieve core
Wed Apr 16 12:58:24 2008  sieve interval: 6 blocks of size 65536
Wed Apr 16 12:58:24 2008  processing polynomials in batches of 17
Wed Apr 16 12:58:24 2008  using a sieve bound of 1409171 (53610 primes)
Wed Apr 16 12:58:24 2008  using large prime bound of 119779535 (26 bits)
Wed Apr 16 12:58:24 2008  using double large prime bound of 347607157783030 (41-49 bits)
Wed Apr 16 12:58:24 2008  using trial factoring cutoff of 49 bits
Wed Apr 16 12:58:24 2008  polynomial 'A' values have 11 factors
Wed Apr 16 13:43:34 2008  54072 relations (15871 full + 38201 combined from 574707 partial), need 53706
Wed Apr 16 13:43:36 2008  begin with 590578 relations
Wed Apr 16 13:43:37 2008  reduce to 126745 relations in 10 passes
Wed Apr 16 13:43:37 2008  attempting to read 126745 relations
Wed Apr 16 13:43:40 2008  recovered 126745 relations
Wed Apr 16 13:43:40 2008  recovered 103500 polynomials
Wed Apr 16 13:43:40 2008  attempting to build 54072 cycles
Wed Apr 16 13:43:40 2008  found 54072 cycles in 6 passes
Wed Apr 16 13:43:40 2008  distribution of cycle lengths:
Wed Apr 16 13:43:40 2008     length 1 : 15871
Wed Apr 16 13:43:40 2008     length 2 : 11043
Wed Apr 16 13:43:40 2008     length 3 : 9527
Wed Apr 16 13:43:40 2008     length 4 : 6881
Wed Apr 16 13:43:40 2008     length 5 : 4611
Wed Apr 16 13:43:40 2008     length 6 : 2779
Wed Apr 16 13:43:40 2008     length 7 : 1614
Wed Apr 16 13:43:40 2008     length 9+: 1746
Wed Apr 16 13:43:40 2008  largest cycle: 23 relations
Wed Apr 16 13:43:41 2008  matrix is 53610 x 54072 (11.5 MB) with weight 2792115 (51.64/col)
Wed Apr 16 13:43:41 2008  sparse part has weight 2792115 (51.64/col)
Wed Apr 16 13:43:41 2008  filtering completed in 3 passes
Wed Apr 16 13:43:41 2008  matrix is 48794 x 48858 (10.4 MB) with weight 2519161 (51.56/col)
Wed Apr 16 13:43:41 2008  sparse part has weight 2519161 (51.56/col)
Wed Apr 16 13:43:41 2008  saving the first 48 matrix rows for later
Wed Apr 16 13:43:41 2008  matrix is 48746 x 48858 (5.8 MB) with weight 1866562 (38.20/col)
Wed Apr 16 13:43:41 2008  sparse part has weight 1221018 (24.99/col)
Wed Apr 16 13:43:41 2008  matrix includes 64 packed rows
Wed Apr 16 13:43:41 2008  commencing Lanczos iteration
Wed Apr 16 13:43:41 2008  memory use: 7.6 MB
Wed Apr 16 13:45:18 2008  lanczos halted after 773 iterations (dim = 48746)
Wed Apr 16 13:45:18 2008  recovered 18 nontrivial dependencies
Wed Apr 16 13:45:19 2008  prp37 factor: 2746131666830462403852624787266510433
Wed Apr 16 13:45:19 2008  prp48 factor: 194081392436622661770145240283408879646755217701
Wed Apr 16 13:45:19 2008  elapsed time 00:46:58

(16·10¹⁴⁷-43)/9 = 1(7)₁₄₆3_<148> = 3³ · 47 · 2309 · 4518779 · 603559456090055808011_<21> · 6987589127253189423927781_<25> · C89

C89 = P36 · P54

P36 = 215360073973402846985925692625318647_<36>

P54 = 147828512122673638011891093090638637018899493413484911_<54>

Wed Apr 16 13:56:32 2008  Msieve v. 1.33
Wed Apr 16 13:56:32 2008  random seeds: 051d1ddb 36376896
Wed Apr 16 13:56:32 2008  factoring 31836359306117074203320389250315624977093890041136677461587471134178603659539208101435417 (89 digits)
Wed Apr 16 13:56:33 2008  searching for 15-digit factors
Wed Apr 16 13:56:35 2008  commencing quadratic sieve (89-digit input)
Wed Apr 16 13:56:35 2008  using multiplier of 1
Wed Apr 16 13:56:35 2008  using 64kb Pentium 4 sieve core
Wed Apr 16 13:56:35 2008  sieve interval: 16 blocks of size 65536
Wed Apr 16 13:56:35 2008  processing polynomials in batches of 7
Wed Apr 16 13:56:35 2008  using a sieve bound of 1553807 (59000 primes)
Wed Apr 16 13:56:35 2008  using large prime bound of 124304560 (26 bits)
Wed Apr 16 13:56:35 2008  using double large prime bound of 371600775237280 (42-49 bits)
Wed Apr 16 13:56:35 2008  using trial factoring cutoff of 49 bits
Wed Apr 16 13:56:35 2008  polynomial 'A' values have 11 factors
Wed Apr 16 15:44:03 2008  59162 relations (15809 full + 43353 combined from 628278 partial), need 59096
Wed Apr 16 15:44:05 2008  begin with 644087 relations
Wed Apr 16 15:44:06 2008  reduce to 144799 relations in 10 passes
Wed Apr 16 15:44:06 2008  attempting to read 144799 relations
Wed Apr 16 15:44:09 2008  recovered 144799 relations
Wed Apr 16 15:44:09 2008  recovered 122538 polynomials
Wed Apr 16 15:44:10 2008  attempting to build 59162 cycles
Wed Apr 16 15:44:10 2008  found 59162 cycles in 6 passes
Wed Apr 16 15:44:10 2008  distribution of cycle lengths:
Wed Apr 16 15:44:10 2008     length 1 : 15809
Wed Apr 16 15:44:10 2008     length 2 : 11122
Wed Apr 16 15:44:10 2008     length 3 : 10318
Wed Apr 16 15:44:10 2008     length 4 : 7943
Wed Apr 16 15:44:10 2008     length 5 : 5657
Wed Apr 16 15:44:10 2008     length 6 : 3567
Wed Apr 16 15:44:10 2008     length 7 : 2188
Wed Apr 16 15:44:10 2008     length 9+: 2558
Wed Apr 16 15:44:10 2008  largest cycle: 20 relations
Wed Apr 16 15:44:10 2008  matrix is 59000 x 59162 (14.3 MB) with weight 3504517 (59.24/col)
Wed Apr 16 15:44:10 2008  sparse part has weight 3504517 (59.24/col)
Wed Apr 16 15:44:11 2008  filtering completed in 3 passes
Wed Apr 16 15:44:11 2008  matrix is 55126 x 55190 (13.4 MB) with weight 3298366 (59.76/col)
Wed Apr 16 15:44:11 2008  sparse part has weight 3298366 (59.76/col)
Wed Apr 16 15:44:11 2008  saving the first 48 matrix rows for later
Wed Apr 16 15:44:11 2008  matrix is 55078 x 55190 (9.4 MB) with weight 2687805 (48.70/col)
Wed Apr 16 15:44:11 2008  sparse part has weight 2138294 (38.74/col)
Wed Apr 16 15:44:11 2008  matrix includes 64 packed rows
Wed Apr 16 15:44:11 2008  using block size 21845 for processor cache size 512 kB
Wed Apr 16 15:44:12 2008  commencing Lanczos iteration
Wed Apr 16 15:44:12 2008  memory use: 8.8 MB
Wed Apr 16 15:44:43 2008  lanczos halted after 872 iterations (dim = 55078)
Wed Apr 16 15:44:43 2008  recovered 17 nontrivial dependencies
Wed Apr 16 15:44:44 2008  prp36 factor: 215360073973402846985925692625318647
Wed Apr 16 15:44:44 2008  prp54 factor: 147828512122673638011891093090638637018899493413484911
Wed Apr 16 15:44:44 2008  elapsed time 01:48:12

(16·10¹¹⁰-43)/9 = 1(7)₁₀₉3_<111> = 17 · 223 · 18191 · 2170920051541_<13> · C91

C91 = P30 · P61

P30 = 644318852795425173737822057861_<30>

P61 = 1842987738890828356532876930775288642859248655760493846825733_<61>

Wed Apr 16 15:55:31 2008  Msieve v. 1.33
Wed Apr 16 15:55:31 2008  random seeds: c0087b2b 2066460a
Wed Apr 16 15:55:31 2008  factoring 1187471745638173122414222944023909080821371944500674767638801121464815734387399444709737113 (91 digits)
Wed Apr 16 15:55:32 2008  searching for 15-digit factors
Wed Apr 16 15:55:34 2008  commencing quadratic sieve (91-digit input)
Wed Apr 16 15:55:34 2008  using multiplier of 23
Wed Apr 16 15:55:34 2008  using 64kb Pentium 4 sieve core
Wed Apr 16 15:55:34 2008  sieve interval: 18 blocks of size 65536
Wed Apr 16 15:55:34 2008  processing polynomials in batches of 6
Wed Apr 16 15:55:34 2008  using a sieve bound of 1652509 (62297 primes)
Wed Apr 16 15:55:34 2008  using large prime bound of 145420792 (27 bits)
Wed Apr 16 15:55:34 2008  using double large prime bound of 492864656290952 (42-49 bits)
Wed Apr 16 15:55:34 2008  using trial factoring cutoff of 49 bits
Wed Apr 16 15:55:34 2008  polynomial 'A' values have 12 factors
Wed Apr 16 18:22:20 2008  62911 relations (16720 full + 46191 combined from 692900 partial), need 62393
Wed Apr 16 18:22:23 2008  begin with 709620 relations
Wed Apr 16 18:22:23 2008  reduce to 152950 relations in 9 passes
Wed Apr 16 18:22:23 2008  attempting to read 152950 relations
Wed Apr 16 18:22:27 2008  recovered 152950 relations
Wed Apr 16 18:22:27 2008  recovered 131618 polynomials
Wed Apr 16 18:22:28 2008  attempting to build 62911 cycles
Wed Apr 16 18:22:28 2008  found 62911 cycles in 5 passes
Wed Apr 16 18:22:28 2008  distribution of cycle lengths:
Wed Apr 16 18:22:28 2008     length 1 : 16720
Wed Apr 16 18:22:28 2008     length 2 : 12357
Wed Apr 16 18:22:28 2008     length 3 : 11143
Wed Apr 16 18:22:28 2008     length 4 : 8369
Wed Apr 16 18:22:28 2008     length 5 : 5829
Wed Apr 16 18:22:28 2008     length 6 : 3720
Wed Apr 16 18:22:28 2008     length 7 : 2165
Wed Apr 16 18:22:28 2008     length 9+: 2608
Wed Apr 16 18:22:28 2008  largest cycle: 20 relations
Wed Apr 16 18:22:28 2008  matrix is 62297 x 62911 (15.4 MB) with weight 3773523 (59.98/col)
Wed Apr 16 18:22:28 2008  sparse part has weight 3773523 (59.98/col)
Wed Apr 16 18:22:29 2008  filtering completed in 3 passes
Wed Apr 16 18:22:29 2008  matrix is 57938 x 58002 (14.2 MB) with weight 3482288 (60.04/col)
Wed Apr 16 18:22:29 2008  sparse part has weight 3482288 (60.04/col)
Wed Apr 16 18:22:30 2008  saving the first 48 matrix rows for later
Wed Apr 16 18:22:30 2008  matrix is 57890 x 58002 (8.5 MB) with weight 2661136 (45.88/col)
Wed Apr 16 18:22:30 2008  sparse part has weight 1882903 (32.46/col)
Wed Apr 16 18:22:30 2008  matrix includes 64 packed rows
Wed Apr 16 18:22:30 2008  using block size 21845 for processor cache size 512 kB
Wed Apr 16 18:22:30 2008  commencing Lanczos iteration
Wed Apr 16 18:22:30 2008  memory use: 8.5 MB
Wed Apr 16 18:23:03 2008  lanczos halted after 917 iterations (dim = 57890)
Wed Apr 16 18:23:03 2008  recovered 19 nontrivial dependencies
Wed Apr 16 18:23:05 2008  prp30 factor: 644318852795425173737822057861
Wed Apr 16 18:23:05 2008  prp61 factor: 1842987738890828356532876930775288642859248655760493846825733
Wed Apr 16 18:23:05 2008  elapsed time 02:27:34

Apr 16, 2008 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS

8·10¹⁶⁷+9 = 8(0)₁₆₆9_<168> = 7² · 967 · 59723 · 85525507 · 104791781467_<12> · C140

C140 = P38 · P102

P38 = 32070636141063417698309974804038142769_<38>

P102 = 983547553579979304561951273616176372155814093748174239324385537878449421978287184323475247763731622141_<102>

(16·10¹¹¹-43)/9 = 1(7)₁₁₀3_<112> = 3² · 10274066749_<11> · C101

C101 = P37 · P64

P37 = 2225084121385833837269896643903724031_<37>

P64 = 8640644676536263769574342271241601366043048979121263003270936663_<64>

Number: n
N=19226161268297874886381163435979431186147422624412897339015610496841133983714092394936499375232048553
  ( 101 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=2225084121385833837269896643903724031 (pp37)
 r2=8640644676536263769574342271241601366043048979121263003270936663 (pp64)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.67 hours.
Scaled time: 1.22 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_7_110_3
n: 19226161268297874886381163435979431186147422624412897339015610496841133983714092394936499375232048553
skew: 1.54
deg: 5
c5: 5
c0: -43
m: 20000000000000000000000
type: snfs
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 10000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 170001)
Primes: RFBsize:41538, AFBsize:41437, largePrimes:3529069 encountered
Relations: rels:2913505, finalFF:95356
Max relations in full relation-set: 48
Initial matrix: 83040 x 95356 with sparse part having weight 7738673.
Pruned matrix : 78525 x 79004 with weight 4764399.
Total sieving time: 0.58 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.02 hours.
Total square root time: 0.02 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,112,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.5,2.5,50000
total time: 0.67 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Apr 16, 2008 (2nd)

By Jo Yeong Uk / GMP-ECM

8·10¹⁷⁰-1 = 7(9)₁₇₀_<171> = 79 · 5711 · 27751 · 271927760593_<12> · C150

C150 = P32 · P119

P32 = 14008580624750494404998711251129_<32>

P119 = 16773527998674156443599016288925581723244594369965881175195561165229044921073548889200126000428046790680088466419299393_<119>

(16·10¹⁴²-43)/9 = 1(7)₁₄₁3_<143> = 7 · 17 · 2709756296960221278752815673_<28> · C113

C113 = P34 · P80

P34 = 5500591316638770792347012316501127_<34>

P80 = 10022842335671191323150316599085734859085649805584448266612992605807362427757077_<80>

8·10¹⁷³-1 = 7(9)₁₇₃_<174> = 30169 · 829284774211_<12> · 528320520638157539_<18> · C140

C140 = P34 · P107

P34 = 2380128402987626355750914791239491_<34>

P107 = 25428896472579987859772918652405527101836770281382986409039510776347763971977279943001852490967033956157589_<107>

Apr 16, 2008

The factor table of 177...773 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Apr 15, 2008 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

4·10¹⁹⁴+3 = 4(0)₁₉₃3_<195> = 13 · 487 · 10747520347_<11> · 1061459829998311_<16> · 56889821479343939004524558081383_<32> · C134

C134 = P37 · P98

P37 = 1097437743804222790112801602356295333_<37>

P98 = 88707711400317344925950831681572035023026603223066152620648506409066689217254920192657566027207151_<98>

(31·10¹⁶⁵-13)/9 = 3(4)₁₆₄3_<166> = 11 · 167881116341_<12> · 1805455694335159_<16> · C139

C139 = P49 · P90

P49 = 7347822245464475165282519977448389173180184038157_<49>

P90 = 140598010033950929058795866865500565051420080556908773879274375567266916603580233027144711_<90>

Number: n
N=1033089185795502125725549943468951191075287560678144964465240476031654211528331590947854279300951567277909959275083588067187997223584737627
  ( 139 digits)
SNFS difficulty: 166 digits.
Divisors found:

Tue Apr 15 11:10:58 2008  prp49 factor: 7347822245464475165282519977448389173180184038157
Tue Apr 15 11:10:58 2008  prp90 factor: 140598010033950929058795866865500565051420080556908773879274375567266916603580233027144711
Tue Apr 15 11:10:58 2008  elapsed time 01:00:36 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 46.01 hours.
Scaled time: 38.47 units (timescale=0.836).
Factorization parameters were as follows:
name: KA_3_4_164_3
n: 1033089185795502125725549943468951191075287560678144964465240476031654211528331590947854279300951567277909959275083588067187997223584737627
type: snfs
deg: 5
c5: 31
c0: -13
skew: 0.84
m: 1000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2900189)
Primes: RFBsize:230209, AFBsize:231088, largePrimes:5568743 encountered
Relations: rels:5432587, finalFF:503551
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 45.83 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,48,48,2.5,2.5,100000
total time: 46.01 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

Apr 15, 2008

By Jo Yeong Uk / GGNFS

(5·10¹⁶⁸-11)/3 = 1(6)₁₆₇3_<169> = 4120200831685709_<16> · 23283723302621145827_<20> · 7002077822382344086391_<22> · C112

C112 = P36 · P76

P36 = 717427856562862178965744919216242153_<36>

P76 = 3458380435415848667465634528539779826524512908443732339648083491542419594767_<76>

Number: 16663_168
N=2481138462959330325490993384397680976466694579370363415914673815102702133510771942578531055673159342874803613351
  ( 112 digits)
Divisors found:
 r1=717427856562862178965744919216242153 (pp36)
 r2=3458380435415848667465634528539779826524512908443732339648083491542419594767 (pp76)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 17.75 hours.
Scaled time: 37.84 units (timescale=2.132).
Factorization parameters were as follows:
name: 16663_168
n: 2481138462959330325490993384397680976466694579370363415914673815102702133510771942578531055673159342874803613351
skew: 39431.34
# norm 3.83e+15
c5: 49140
c4: 25817859
c3: -129120732929669
c2: -13844558931293250
c1: -38168703002247717958437
c0: -14214612319618440379396535
# alpha -6.15
Y1: 948140859907
Y0: -2191003897547610215284
# Murphy_E 7.79e-10
# M 626313471121193201721002423945625760926830506962689097707011606329236140510462918777889081342378696446678369389
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1400000, 2310001)
Primes: RFBsize:203362, AFBsize:203549, largePrimes:7651451 encountered
Relations: rels:7592999, finalFF:593633
Max relations in full relation-set: 28
Initial matrix: 406998 x 593633 with sparse part having weight 57772171.
Pruned matrix : 279566 x 281664 with weight 33387440.
Polynomial selection time: 0.93 hours.
Total sieving time: 16.05 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.51 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000
total time: 17.75 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407670)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Total of 4 processors activated (19246.09 BogoMIPS).

(5·10¹⁶²-11)/3 = 1(6)₁₆₁3_<163> = 79² · 1703047673933057999_<19> · 233440442843090372721489089_<27> · C114

C114 = P52 · P63

P52 = 1306190477930074137492388256168123171756279944035161_<52>

P63 = 514262846899694625766088991599592595724106922026482072425101233_<63>

Number: 16663_162
N=671725233773592668158357861381849172992458792903099915618738967360228871501589617429534879024002483836109936453513
  ( 114 digits)
Divisors found:
 r1=1306190477930074137492388256168123171756279944035161 (pp52)
 r2=514262846899694625766088991599592595724106922026482072425101233 (pp63)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 20.21 hours.
Scaled time: 43.07 units (timescale=2.131).
Factorization parameters were as follows:
name: 16663_162
n: 671725233773592668158357861381849172992458792903099915618738967360228871501589617429534879024002483836109936453513
skew: 78136.67
# norm 7.46e+15
c5: 10200
c4: 383189044
c3: -309484053417710
c2: -2304352732987123077
c1: 541567228155987031479672
c0: 5146408181504792994975174915
# alpha -6.63
Y1: 790123132007
Y0: -9198521293021626091202
# Murphy_E 6.63e-10
# M 149167548420111073124963642693625400845864591092677417612563808371518751186252456902329787959070180331393959520234
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 70000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2800001)
Primes: RFBsize:250150, AFBsize:249746, largePrimes:7531910 encountered
Relations: rels:7489527, finalFF:657062
Max relations in full relation-set: 28
Initial matrix: 499975 x 657062 with sparse part having weight 55624613.
Pruned matrix : 371906 x 374469 with weight 31096495.
Polynomial selection time: 1.18 hours.
Total sieving time: 17.97 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.78 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.4,2.4,70000
total time: 20.21 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407670)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Total of 4 processors activated (19246.09 BogoMIPS).

Apr 14, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(5·10¹⁶⁵-11)/3 = 1(6)₁₆₄3_<166> = C166

C166 = P79 · P87

P79 = 2245517242112414977206809019850729467395498042626696714518847161837856305294667_<79>

P87 = 742219491977176312144123372249810594188783117241757062443391872162301374408886058723989_<87>

Number: n
N=1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
  ( 166 digits)
SNFS difficulty: 165 digits.
Divisors found:

Mon Apr 14 12:44:39 2008  prp79 factor: 2245517242112414977206809019850729467395498042626696714518847161837856305294667
Mon Apr 14 12:44:39 2008  prp87 factor: 742219491977176312144123372249810594188783117241757062443391872162301374408886058723989
Mon Apr 14 12:44:39 2008  elapsed time 01:37:42 (Msieve 1.34)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 60.64 hours.
Scaled time: 79.13 units (timescale=1.305).
Factorization parameters were as follows:
name: KA_1_6_164_3
n: 1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
skew: 1.17
deg: 5
c5: 5
c0: -11
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2700199)
Primes: RFBsize:216816, AFBsize:217082, largePrimes:7364083 encountered
Relations: rels:6800164, finalFF:446721
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 60.37 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 60.64 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

9·10¹⁶⁵-1 = 8(9)₁₆₅_<166> = 1139239 · 3500008777892854273507_<22> · C139

C139 = P66 · P74

P66 = 107006813752674037531328510242074918993021462449577391740200262799_<66>

P74 = 21093424816570316132097077241926854067827836439105917046567434042812717837_<74>

Number: n
N=2257140180752772341749697563476673520949004624616088331617541248692208685477716800333936267810500726303368685688650280142696027086834845763
  ( 139 digits)
SNFS difficulty: 165 digits.
Divisors found:

Mon Apr 14 14:15:03 2008  prp66 factor: 107006813752674037531328510242074918993021462449577391740200262799
Mon Apr 14 14:15:03 2008  prp74 factor: 21093424816570316132097077241926854067827836439105917046567434042812717837
Mon Apr 14 14:15:03 2008  elapsed time 00:46:12 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 38.69 hours.
Scaled time: 32.38 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_8_9_165
n: 2257140180752772341749697563476673520949004624616088331617541248692208685477716800333936267810500726303368685688650280142696027086834845763
type: snfs
deg: 5
c5: 9
c0: -1
skew: 0.72
m: 1000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2500363)
Primes: RFBsize:230209, AFBsize:230192, largePrimes:5532216 encountered
Relations: rels:5417337, finalFF:495898
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 38.51 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,48,48,2.5,2.5,100000
total time: 38.69 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(28·10¹⁷⁰+17)/9 = 3(1)₁₆₉3_<171> = 1364116464566141004805456799576331094877_<40> · C132

C132 = P35 · P97

P35 = 23585939755509836363182840530964787_<35>

P97 = 9669652926621334818015115351221646782123712466665679277267133617240759474730728542857515285098287_<97>

Apr 14, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(5·10¹⁴⁸-11)/3 = 1(6)₁₄₇3_<149> = 19 · 47 · 21136991855671866611141813801269_<32> · C114

C114 = P44 · P71

P44 = 77581006255394308296816310422507819092440721_<44>

P71 = 11381479025872568962993334130062892789418939418216468034738922176619159_<71>

Number: 16663_148
N=882986595501858891160847091201028575717445778711899220284603910447793803044973296304248132142102675473785400373639
  ( 114 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=77581006255394308296816310422507819092440721 (pp44)
 r2=11381479025872568962993334130062892789418939418216468034738922176619159 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 30.17 hours.
Scaled time: 20.43 units (timescale=0.677).
Factorization parameters were as follows:
name: 16663_148
n: 882986595501858891160847091201028575717445778711899220284603910447793803044973296304248132142102675473785400373639
m: 500000000000000000000000000000
c5: 8
c0: -55
skew: 1.47
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 3650001)
Primes: RFBsize:114155, AFBsize:114253, largePrimes:2934910 encountered
Relations: rels:2944993, finalFF:258683
Max relations in full relation-set: 28
Initial matrix: 228473 x 258683 with sparse part having weight 30088083.
Pruned matrix : 220063 x 221269 with weight 24230101.
Total sieving time: 27.97 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 1.87 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 30.17 hours.
 --------- CPU info (if available) ----------

Apr 14, 2008 (2nd)

By Jo Yeong Uk / GGNFS

(5·10¹⁷⁰-11)/3 = 1(6)₁₆₉3_<171> = C171

C171 = P67 · P104

P67 = 2804670536816483766033030070325032866365359271873179603347962930801_<67>

P104 = 59424686243485168857371524605765216738985593764108704179128271614469158986252195899906766898342583066263_<104>

Number: 16663_170
N=166666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
  ( 171 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=2804670536816483766033030070325032866365359271873179603347962930801 (pp67)
 r2=59424686243485168857371524605765216738985593764108704179128271614469158986252195899906766898342583066263 (pp104)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 77.89 hours.
Scaled time: 167.32 units (timescale=2.148).
Factorization parameters were as follows:
n: 166666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
m: 10000000000000000000000000000000000
c5: 5
c0: -11
skew: 1.17
type: snfs
Factor base limits: 7000000/7000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [3500000, 7400001)
Primes: RFBsize:476648, AFBsize:476585, largePrimes:6660039 encountered
Relations: rels:7150884, finalFF:1119821
Max relations in full relation-set: 28
Initial matrix: 953298 x 1119821 with sparse part having weight 64956325.
Pruned matrix : 810449 x 815279 with weight 45109511.
Total sieving time: 73.83 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 3.86 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,7000000,7000000,27,27,49,49,2.6,2.6,100000
total time: 77.89 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407670)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Total of 4 processors activated (19246.09 BogoMIPS).

Apr 14, 2008

Jason Papadopoulos's Msieve Version 1.35 was released.

HOW TO for Japanese

Apr 13, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(5·10¹⁵⁹-11)/3 = 1(6)₁₅₈3_<160> = 66617 · 21944655402216352685141777_<26> · C130

C130 = P57 · P73

P57 = 249338152176387828895115662897439191770188346492207387691_<57>

P73 = 4572420640210901723153537570503316526388708355459392492824185811297632077_<73>

Number: n
N=1140078913403362475426734419368691054460014958124652265589751664211254989625522656680600371254324341321370031223969601514216564207
  ( 130 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=249338152176387828895115662897439191770188346492207387691 (pp57)
 r2=4572420640210901723153537570503316526388708355459392492824185811297632077 (pp73)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 22.36 hours.
Scaled time: 40.90 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_6_158_3
n: 1140078913403362475426734419368691054460014958124652265589751664211254989625522656680600371254324341321370031223969601514216564207
skew: 1.86
deg: 5
c5: 1
c0: -22
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:216816, AFBsize:216967, largePrimes:7093950 encountered
Relations: rels:6596572, finalFF:526491
Max relations in full relation-set: 48
Initial matrix: 433847 x 526491 with sparse part having weight 41986594.
Pruned matrix : 359802 x 362035 with weight 24165523.
Total sieving time: 21.11 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.06 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 22.36 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

5·10¹⁶⁴-3 = 4(9)₁₆₃7_<165> = 7 · 17 · 265628159462057789779216016761_<30> · C134

C134 = P65 · P70

P65 = 14415395583187368964117409453669561022245725587364267441064003881_<65>

P70 = 1097292384810779781467311229833121140205885608438153270649880660837643_<70>

Number: n
N=15817903797466449690025501204524752190149137263149117955395138235556021194425072941823375150554994336662924330944593886562016862892483
  ( 134 digits)
SNFS difficulty: 165 digits.
Divisors found:

Sun Apr 13 15:27:18 2008  prp65 factor: 14415395583187368964117409453669561022245725587364267441064003881
Sun Apr 13 15:27:18 2008  prp70 factor: 1097292384810779781467311229833121140205885608438153270649880660837643
Sun Apr 13 15:27:18 2008  elapsed time 00:48:41 (Msieve 1.34)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 28.01 hours.
Scaled time: 51.37 units (timescale=1.834).
Factorization parameters were as follows:
name: KA_4_9_163_7
n: 15817903797466449690025501204524752190149137263149117955395138235556021194425072941823375150554994336662924330944593886562016862892483
skew: 1.43
deg: 5
c5: 1
c0: -6
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2000261)
Primes: RFBsize:230209, AFBsize:230282, largePrimes:7108660 encountered
Relations: rels:6564318, finalFF:502203
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 27.86 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 28.01 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(2·10¹⁷⁷+43)/9 = (2)₁₇₆7_<177> = 5555233 · 4431534533_<10> · 9207448973929_<13> · 2993559071886717761227_<22> · C126

C126 = P38 · P88

P38 = 96018067606635797646393749559985680613_<38>

P88 = 3410758378305553129463494314744010333879148182725934296703293055767983843116651912665817_<88>

Apr 12, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(5·10¹⁴⁵-11)/3 = 1(6)₁₄₄3_<146> = 13 · 29 · 136045673 · 524365382060364953_<18> · C117

C117 = P48 · P69

P48 = 782208664539194981412341792228712859716363821171_<48>

P69 = 792256901871551573562908486122649158368373345051205572768889156804581_<69>

Number: 16663_145
N=619710213184906401442171112855315553108109013330960148072201601903639776804276018815261015424998164044556841277584351
  ( 117 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=782208664539194981412341792228712859716363821171 (pp48)
 r2=792256901871551573562908486122649158368373345051205572768889156804581 (pp69)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 16.78 hours.
Scaled time: 11.36 units (timescale=0.677).
Factorization parameters were as follows:
name: 16663_145
n: 619710213184906401442171112855315553108109013330960148072201601903639776804276018815261015424998164044556841277584351
m: 100000000000000000000000000000
c5: 5
c0: -11
skew: 1.17
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2250001)
Primes: RFBsize:100021, AFBsize:100464, largePrimes:2713581 encountered
Relations: rels:2665288, finalFF:225945
Max relations in full relation-set: 28
Initial matrix: 200550 x 225945 with sparse part having weight 23304396.
Pruned matrix : 193546 x 194612 with weight 18417270.
Total sieving time: 15.37 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.17 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 16.78 hours.
 --------- CPU info (if available) ----------

(5·10¹³⁴-11)/3 = 1(6)₁₃₃3_<135> = 17 · 73 · 50664461 · 775886330194411_<15> · C109

C109 = P55 · P55

P55 = 1514562294684404165773916125751733937523450013323054647_<55>

P55 = 2255736153622223157008861495416148949542640027113330839_<55>

Number: 16663_134
N=3416452925032645934485143394771495867369932302980206841897365478739597445039157195025694908555018430187358833
  ( 109 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=1514562294684404165773916125751733937523450013323054647 (pp55)
 r2=2255736153622223157008861495416148949542640027113330839 (pp55)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 6.96 hours.
Scaled time: 4.71 units (timescale=0.677).
Factorization parameters were as follows:
name: 16663_134
n: 3416452925032645934485143394771495867369932302980206841897365478739597445039157195025694908555018430187358833
m: 1000000000000000000000000000
c5: 1
c0: -22
skew: 1.86
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:64044, largePrimes:1509703 encountered
Relations: rels:1514301, finalFF:179475
Max relations in full relation-set: 28
Initial matrix: 142606 x 179475 with sparse part having weight 12642214.
Pruned matrix : 129762 x 130539 with weight 7432855.
Total sieving time: 6.54 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 6.96 hours.
 --------- CPU info (if available) ----------

Apr 12, 2008

By Robert Backstrom / GGNFS, Msieve

(5·10¹⁵³-11)/3 = 1(6)₁₅₂3_<154> = 3819031 · C147

C147 = P41 · P50 · P57

P41 = 24146838789382262583920577322514279965903_<41>

P50 = 28350609396736902451470157465466104446889245761819_<50>

P57 = 637489278118176076476491206382010478850794755031832879789_<57>

Number: n
N=436410876650822333378981911031009349404774841227176911281072781725696038253333546301841138934632022276505916465895842863455852195666038496850815473
  ( 147 digits)
SNFS difficulty: 154 digits.
Divisors found:

Sat Apr 12 10:45:05 2008  prp41 factor: 24146838789382262583920577322514279965903
Sat Apr 12 10:45:05 2008  prp50 factor: 28350609396736902451470157465466104446889245761819
Sat Apr 12 10:45:05 2008  prp57 factor: 637489278118176076476491206382010478850794755031832879789
Sat Apr 12 10:45:05 2008  elapsed time 00:27:23 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 16.36 hours.
Scaled time: 13.73 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_1_6_152_3
n: 436410876650822333378981911031009349404774841227176911281072781725696038253333546301841138934632022276505916465895842863455852195666038496850815473
type: snfs
deg: 5
c5: 8
c0: -55
skew: 1.47
m: 5000000000000000000000000000000
rlim: 2400000
alim: 2400000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1099990)
Primes: RFBsize:176302, AFBsize:176364, largePrimes:5290147 encountered
Relations: rels:5091653, finalFF:422983
Max relations in full relation-set: 28
Initial matrix: 352731 x 422983 with sparse part having weight 32754194.
Pruned matrix : 
Total sieving time: 16.23 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.5,2.5,100000
total time: 16.36 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(4·10¹⁶⁷+11)/3 = 1(3)₁₆₆7_<168> = 9293 · C164

C164 = P45 · P53 · P67

P45 = 224864619045978638314145645571117372544626209_<45>

P53 = 23565455558677248911299805619150071026683171590171297_<53>

P67 = 2707608271774091657130405693450396883166513443249779410037377585533_<67>

Number: n
N=14347716919545177373650417877255281753291007568420675060081064600595430252161124861006492341906094192761576814089458014993364180924710355464686681731769432189102909
  ( 164 digits)
SNFS difficulty: 167 digits.
Divisors found:

Sat Apr 12 21:37:02 2008  prp45 factor: 224864619045978638314145645571117372544626209
Sat Apr 12 21:37:02 2008  prp53 factor: 23565455558677248911299805619150071026683171590171297
Sat Apr 12 21:37:02 2008  prp67 factor: 2707608271774091657130405693450396883166513443249779410037377585533
Sat Apr 12 21:37:02 2008  elapsed time 01:43:43 (Msieve 1.34)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 63.71 hours.
Scaled time: 92.25 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_1_3_166_7
n: 14347716919545177373650417877255281753291007568420675060081064600595430252161124861006492341906094192761576814089458014993364180924710355464686681731769432189102909
skew: 0.97
deg: 5
c5: 25
c0: 22
m: 2000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3300127)
Primes: RFBsize:230209, AFBsize:229923, largePrimes:7513121 encountered
Relations: rels:6955203, finalFF:510760
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 63.46 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 63.71 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Apr 11, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(5·10¹⁴³-11)/3 = 1(6)₁₄₂3_<144> = 7² · 67 · 331 · C138

C138 = P38 · P100

P38 = 28798534375392779303628140531657338781_<38>

P100 = 5325734193132791638248472962622411091501534140325790522239722750062612132583107197711871318984210851_<100>

Number: n
N=153373339235139427101498488198995159230667060529401822504715463314784361686235571019678106170546858775976459032907476919613045200043312631
  ( 138 digits)
SNFS difficulty: 144 digits.
Divisors found:

Fri Apr 11 06:57:45 2008  prp38 factor: 28798534375392779303628140531657338781
Fri Apr 11 06:57:45 2008  prp100 factor: 5325734193132791638248472962622411091501534140325790522239722750062612132583107197711871318984210851
Fri Apr 11 06:57:45 2008  elapsed time 00:23:37 (Msieve 1.34)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.52 hours.
Scaled time: 13.08 units (timescale=1.739).
Factorization parameters were as follows:
name: KA_1_6_142_3
n: 153373339235139427101498488198995159230667060529401822504715463314784361686235571019678106170546858775976459032907476919613045200043312631
type: snfs
skew: 1.47
deg: 5
c5: 8
c0: -55
m: 50000000000000000000000000000
rlim: 1300000
alim: 1300000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1299990)
Primes: RFBsize:100021, AFBsize:100094, largePrimes:5326819 encountered
Relations: rels:4686212, finalFF:250627
Max relations in full relation-set: 28
Initial matrix: 200180 x 250627 with sparse part having weight 20240544.
Pruned matrix : 
Total sieving time: 7.38 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,28,28,48,48,2.3,2.3,100000
total time: 7.52 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(4·10¹⁶⁶+17)/3 = 1(3)₁₆₅9_<167> = 23 · 14934599 · C158

C158 = P40 · P49 · P70

P40 = 4174243305008880150142804690262251278349_<40>

P49 = 7364569572438135830466677565409660399752515893267_<49>

P70 = 1262676814439812792538853247661616472122117327064522172690220773124829_<70>

Number: n
N=38816585897454376370203041341417520056828335718762951002257396990744760548637933715654773052226878857184125827938004994260332153467299638252418262869453947707
  ( 158 digits)
SNFS difficulty: 166 digits.
Divisors found:

Fri Apr 11 07:07:03 2008  prp40 factor: 4174243305008880150142804690262251278349
Fri Apr 11 07:07:03 2008  prp49 factor: 7364569572438135830466677565409660399752515893267
Fri Apr 11 07:07:03 2008  prp70 factor: 1262676814439812792538853247661616472122117327064522172690220773124829
Fri Apr 11 07:07:03 2008  elapsed time 00:55:29 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 54.76 hours.
Scaled time: 45.78 units (timescale=0.836).
Factorization parameters were as follows:
name: KA_1_3_165_9
n: 38816585897454376370203041341417520056828335718762951002257396990744760548637933715654773052226878857184125827938004994260332153467299638252418262869453947707
type: snfs
deg: 5
c5: 40
c0: 17
skew: 0.84
m: 1000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3300001)
Primes: RFBsize:230209, AFBsize:230272, largePrimes:5779326 encountered
Relations: rels:5745407, finalFF:535328
Max relations in full relation-set: 28
Initial matrix: 460547 x 535328 with sparse part having weight 49032993.
Pruned matrix : 
Total sieving time: 54.57 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,48,48,2.5,2.5,100000
total time: 54.76 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(4·10¹⁹⁷+41)/9 = (4)₁₉₆9_<197> = 23 · 71² · 149 · 233 · 677664049 · 2468169467_<10> · 22402204398569599_<17> · 4434981126357605717_<19> · C134

C134 = P40 · P95

P40 = 2078833007212834249538418304107943881613_<40>

P95 = 31962386728259488329238937951744272406806378777600988877444685328307968295581798047594803451847_<95>

(5·10¹⁵⁰-11)/3 = 1(6)₁₄₉3_<151> = 17 · 73 · C148

C148 = P60 · P88

P60 = 421508304886553720011487693851764078006034468054366993384417_<60>

P88 = 3186183852220802244203025392870376136376593039760043939060786645463566852296231191997279_<88>

Number: n
N=1343002954606500134300295460650013430029546065001343002954606500134300295460650013430029546065001343002954606500134300295460650013430029546065001343
  ( 148 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=421508304886553720011487693851764078006034468054366993384417 (pp60)
 r2=3186183852220802244203025392870376136376593039760043939060786645463566852296231191997279 (pp88)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 10.06 hours.
Scaled time: 18.40 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_6_149_3
n: 1343002954606500134300295460650013430029546065001343002954606500134300295460650013430029546065001343002954606500134300295460650013430029546065001343
skew: 1.17
deg: 5
c5: 5
c0: -11
m: 1000000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 700001)
Primes: RFBsize:148933, AFBsize:149461, largePrimes:6183051 encountered
Relations: rels:5595336, finalFF:372683
Max relations in full relation-set: 48
Initial matrix: 298459 x 372683 with sparse part having weight 30927493.
Pruned matrix : 243552 x 245108 with weight 16516457.
Total sieving time: 9.53 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.40 hours.
Total square root time: 0.03 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 10.06 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(5·10¹⁵¹-11)/3 = 1(6)₁₅₀3_<152> = 13 · 61 · 19826901180373766972341_<23> · C127

C127 = P44 · P83

P44 = 46530459068806937674122576450802907831043811_<44>

P83 = 22781555975659239394922705505015311151556624542606348511511085464549559681088943041_<83>

Number: n
N=1060036257849146338773355785054145385311743017990749268402929154561767396758361119623350696044828967927053540184320041754569251
  ( 127 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=46530459068806937674122576450802907831043811 (pp44)
 r2=22781555975659239394922705505015311151556624542606348511511085464549559681088943041 (pp83)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 12.84 hours.
Scaled time: 23.49 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_6_150_3
n: 1060036257849146338773355785054145385311743017990749268402929154561767396758361119623350696044828967927053540184320041754569251
skew: 0.74
deg: 5
c5: 50
c0: -11
m: 1000000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:148933, AFBsize:149221, largePrimes:6479496 encountered
Relations: rels:5837996, finalFF:344927
Max relations in full relation-set: 48
Initial matrix: 298219 x 344927 with sparse part having weight 33847276.
Pruned matrix : 270062 x 271617 with weight 21493159.
Total sieving time: 12.13 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.56 hours.
Total square root time: 0.04 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 12.84 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Apr 11, 2008

By Sinkiti Sibata / Msieve, GGNFS

(5·10¹⁵⁴-11)/3 = 1(6)₁₅₃3_<155> = 20747 · 1103982904122717018242570941_<28> · 514096729678132664523698534537_<30> · C94

C94 = P45 · P49

P45 = 585300977028591004285181609982549579278364431_<45>

P49 = 2418282339557813003254540703695423879556104787327_<49>

Thu Apr 10 21:13:18 2008  Msieve v. 1.33
Thu Apr 10 21:13:18 2008  random seeds: 5f0a8418 665aa333
Thu Apr 10 21:13:18 2008  factoring 1415423016074174819521263294353965449508917291651641663096371423565430400347476027033656365937 (94 digits)
Thu Apr 10 21:13:20 2008  searching for 15-digit factors
Thu Apr 10 21:13:21 2008  commencing quadratic sieve (94-digit input)
Thu Apr 10 21:13:22 2008  using multiplier of 1
Thu Apr 10 21:13:22 2008  using 64kb Pentium 4 sieve core
Thu Apr 10 21:13:22 2008  sieve interval: 18 blocks of size 65536
Thu Apr 10 21:13:22 2008  processing polynomials in batches of 6
Thu Apr 10 21:13:22 2008  using a sieve bound of 1983061 (74118 primes)
Thu Apr 10 21:13:22 2008  using large prime bound of 255814869 (27 bits)
Thu Apr 10 21:13:22 2008  using double large prime bound of 1362279921846333 (42-51 bits)
Thu Apr 10 21:13:22 2008  using trial factoring cutoff of 51 bits
Thu Apr 10 21:13:22 2008  polynomial 'A' values have 12 factors
Fri Apr 11 03:21:49 2008  74217 relations (17169 full + 57048 combined from 1052711 partial), need 74214
Fri Apr 11 03:21:52 2008  begin with 1069880 relations
Fri Apr 11 03:21:54 2008  reduce to 197432 relations in 11 passes
Fri Apr 11 03:21:54 2008  attempting to read 197432 relations
Fri Apr 11 03:22:00 2008  recovered 197432 relations
Fri Apr 11 03:22:00 2008  recovered 184174 polynomials
Fri Apr 11 03:22:00 2008  attempting to build 74217 cycles
Fri Apr 11 03:22:00 2008  found 74217 cycles in 5 passes
Fri Apr 11 03:22:00 2008  distribution of cycle lengths:
Fri Apr 11 03:22:00 2008     length 1 : 17169
Fri Apr 11 03:22:00 2008     length 2 : 12312
Fri Apr 11 03:22:00 2008     length 3 : 12345
Fri Apr 11 03:22:00 2008     length 4 : 10360
Fri Apr 11 03:22:00 2008     length 5 : 7835
Fri Apr 11 03:22:00 2008     length 6 : 5380
Fri Apr 11 03:22:00 2008     length 7 : 3675
Fri Apr 11 03:22:00 2008     length 9+: 5141
Fri Apr 11 03:22:00 2008  largest cycle: 19 relations
Fri Apr 11 03:22:01 2008  matrix is 74118 x 74217 (19.0 MB) with weight 4695268 (63.26/col)
Fri Apr 11 03:22:01 2008  sparse part has weight 4695268 (63.26/col)
Fri Apr 11 03:22:02 2008  filtering completed in 3 passes
Fri Apr 11 03:22:02 2008  matrix is 71310 x 71374 (18.4 MB) with weight 4545762 (63.69/col)
Fri Apr 11 03:22:02 2008  sparse part has weight 4545762 (63.69/col)
Fri Apr 11 03:22:03 2008  saving the first 48 matrix rows for later
Fri Apr 11 03:22:03 2008  matrix is 71262 x 71374 (10.9 MB) with weight 3510302 (49.18/col)
Fri Apr 11 03:22:03 2008  sparse part has weight 2421855 (33.93/col)
Fri Apr 11 03:22:03 2008  matrix includes 64 packed rows
Fri Apr 11 03:22:03 2008  using block size 21845 for processor cache size 512 kB
Fri Apr 11 03:22:04 2008  commencing Lanczos iteration
Fri Apr 11 03:22:04 2008  memory use: 11.1 MB
Fri Apr 11 03:22:53 2008  lanczos halted after 1128 iterations (dim = 71260)
Fri Apr 11 03:22:53 2008  recovered 15 nontrivial dependencies
Fri Apr 11 03:22:54 2008  prp45 factor: 585300977028591004285181609982549579278364431
Fri Apr 11 03:22:54 2008  prp49 factor: 2418282339557813003254540703695423879556104787327
Fri Apr 11 03:22:54 2008  elapsed time 06:09:36

(5·10¹²⁹-11)/3 = 1(6)₁₂₈3_<130> = 258787 · C124

C124 = P37 · P88

P37 = 5066833232812900348371444210929217377_<37>

P88 = 1271070628221685741151778990506755714714922860599778130191770040148883980132610080516237_<88>

Number: 16663_129
N=6440302900326008132814502531683070118153797009380945204614863446257604387649559934102820723864284785042010095818826551050349
  ( 124 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=5066833232812900348371444210929217377 (pp37)
 r2=1271070628221685741151778990506755714714922860599778130191770040148883980132610080516237 (pp88)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 4.48 hours.
Scaled time: 3.03 units (timescale=0.677).
Factorization parameters were as follows:
name: 16663_129
n: 6440302900326008132814502531683070118153797009380945204614863446257604387649559934102820723864284785042010095818826551050349
m: 100000000000000000000000000
c5: 1
c0: -22
skew: 1.86
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:63951, AFBsize:64044, largePrimes:1431982 encountered
Relations: rels:1420951, finalFF:163891
Max relations in full relation-set: 28
Initial matrix: 128059 x 163891 with sparse part having weight 9321009.
Pruned matrix : 116287 x 116991 with weight 5139628.
Total sieving time: 4.18 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.48 hours.
 --------- CPU info (if available) ----------

(5·10¹³³-11)/3 = 1(6)₁₃₂3_<134> = 13 · 5693 · 929178817187244089_<18> · C111

C111 = P47 · P64

P47 = 26383737838315756222354254062173633796804502149_<47>

P64 = 9186045454305410246170305021305223071642869327656871729015051787_<64>

Number: 16663_133
N=242362215037246103331022315073602170502581559779716014453310837872533146895368113827105214017523348267987790263
  ( 111 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=26383737838315756222354254062173633796804502149 (pp47)
 r2=9186045454305410246170305021305223071642869327656871729015051787 (pp64)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 7.41 hours.
Scaled time: 5.02 units (timescale=0.677).
Factorization parameters were as follows:
name: 16663_133
n: 242362215037246103331022315073602170502581559779716014453310837872533146895368113827105214017523348267987790263
m: 500000000000000000000000000
c5: 8
c0: -55
skew: 1.47
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1150001)
Primes: RFBsize:78498, AFBsize:64019, largePrimes:1542285 encountered
Relations: rels:1556716, finalFF:188341
Max relations in full relation-set: 28
Initial matrix: 142582 x 188341 with sparse part having weight 14359518.
Pruned matrix : 127065 x 127841 with weight 7978424.
Total sieving time: 6.99 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 7.41 hours.
 --------- CPU info (if available) ----------

Apr 10, 2008 (6th)

By suberi / GGNFS

(61·10¹⁶⁴-7)/9 = 6(7)₁₆₄_<165> = 317 · 3495769463_<10> · 4497534330479_<13> · 110614628030592113_<18> · C124

C124 = P46 · P78

P46 = 5132819123667913656014282950111020599968382579_<46>

P78 = 239520267690880254444053983762177434375240421775507117542386875504206305181039_<78>

Number: 67777_164
N=1229414210509808080396481586136781304990112987408467724961865348285630111489772284606331844141937676322340980381636608719581
  ( 124 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=5132819123667913656014282950111020599968382579 (pp46)
 r2=239520267690880254444053983762177434375240421775507117542386875504206305181039 (pp78)
Version: GGNFS-0.77.1-20060722-k8
Total time: 148.21 hours.
Scaled time: 280.42 units (timescale=1.892).
Factorization parameters were as follows:
n: 1229414210509808080396481586136781304990112987408467724961865348285630111489772284606331844141937676322340980381636608719581
m: 1000000000000000000000000000000000
c5: 61
c0: -70
skew: 1.03
type: snfs

Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 
)
Primes: RFBsize:348513, AFBsize:347762, largePrimes:6076829 encountered
Relations: rels:6274668, finalFF:827831
Max relations in full relation-set: 32
Initial matrix: 696340 x 827831 with sparse part having weight 69285818.
Pruned matrix : 599091 x 602636 with weight 51254532.
Total sieving time: 144.01 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 3.82 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 148.21 hours.
 --------- CPU info (if available) ----------
Memory: 896148k/915904k available (2823k kernel code, 19044k reserved, 1312k data, 204k init)
Calibrating delay using timer specific routine.. 3594.37 BogoMIPS (lpj=7188757)
Calibrating delay using timer specific routine.. 3591.04 BogoMIPS (lpj=7182090)

Apr 10, 2008 (5th)

By Jo Yeong Uk / GMP-ECM, Msieve

(5·10¹⁴¹-11)/3 = 1(6)₁₄₀3_<142> = 149 · 173273 · 92704098020668750136839_<23> · C111

C111 = P32 · P34 · P46

P32 = 15188722265464115071522657576259_<32>

P34 = 7712334843403732256679766516486637_<34>

P46 = 5944639679663139196197290964556363337121607987_<46>

Thu Apr 10 09:23:24 2008  
Thu Apr 10 09:23:24 2008  
Thu Apr 10 09:23:24 2008  Msieve v. 1.34
Thu Apr 10 09:23:24 2008  random seeds: f379aa7d 8ca47774
Thu Apr 10 09:23:24 2008  factoring 45847051732946429718609863722692727709273793212213606054363232586927611237969719 (80 digits)
Thu Apr 10 09:23:24 2008  no P-1/P+1/ECM available, skipping
Thu Apr 10 09:23:24 2008  commencing quadratic sieve (80-digit input)
Thu Apr 10 09:23:24 2008  using multiplier of 5
Thu Apr 10 09:23:24 2008  using 32kb Intel Core sieve core
Thu Apr 10 09:23:24 2008  sieve interval: 12 blocks of size 32768
Thu Apr 10 09:23:24 2008  processing polynomials in batches of 17
Thu Apr 10 09:23:24 2008  using a sieve bound of 1262311 (48647 primes)
Thu Apr 10 09:23:24 2008  using large prime bound of 126231100 (26 bits)
Thu Apr 10 09:23:24 2008  using trial factoring cutoff of 27 bits
Thu Apr 10 09:23:24 2008  polynomial 'A' values have 10 factors
Thu Apr 10 09:38:17 2008  48752 relations (24624 full + 24128 combined from 267948 partial), need 48743
Thu Apr 10 09:38:17 2008  begin with 292572 relations
Thu Apr 10 09:38:17 2008  reduce to 69970 relations in 2 passes
Thu Apr 10 09:38:17 2008  attempting to read 69970 relations
Thu Apr 10 09:38:18 2008  recovered 69970 relations
Thu Apr 10 09:38:18 2008  recovered 60666 polynomials
Thu Apr 10 09:38:18 2008  attempting to build 48752 cycles
Thu Apr 10 09:38:18 2008  found 48752 cycles in 1 passes
Thu Apr 10 09:38:18 2008  distribution of cycle lengths:
Thu Apr 10 09:38:18 2008     length 1 : 24624
Thu Apr 10 09:38:18 2008     length 2 : 24128
Thu Apr 10 09:38:18 2008  largest cycle: 2 relations
Thu Apr 10 09:38:18 2008  matrix is 48647 x 48752 (7.2 MB) with weight 1506429 (30.90/col)
Thu Apr 10 09:38:18 2008  sparse part has weight 1506429 (30.90/col)
Thu Apr 10 09:38:18 2008  filtering completed in 4 passes
Thu Apr 10 09:38:18 2008  matrix is 41826 x 41890 (6.1 MB) with weight 1269861 (30.31/col)
Thu Apr 10 09:38:18 2008  sparse part has weight 1269861 (30.31/col)
Thu Apr 10 09:38:18 2008  saving the first 48 matrix rows for later
Thu Apr 10 09:38:18 2008  matrix is 41778 x 41890 (4.4 MB) with weight 957728 (22.86/col)
Thu Apr 10 09:38:18 2008  sparse part has weight 728581 (17.39/col)
Thu Apr 10 09:38:18 2008  matrix includes 64 packed rows
Thu Apr 10 09:38:18 2008  commencing Lanczos iteration
Thu Apr 10 09:38:18 2008  memory use: 6.0 MB
Thu Apr 10 09:38:40 2008  lanczos halted after 662 iterations (dim = 41759)
Thu Apr 10 09:38:40 2008  recovered 8 nontrivial dependencies
Thu Apr 10 09:38:41 2008  prp34 factor: 7712334843403732256679766516486637
Thu Apr 10 09:38:41 2008  prp46 factor: 5944639679663139196197290964556363337121607987
Thu Apr 10 09:38:41 2008  elapsed time 00:15:17

Apr 10, 2008 (4th)

By matsui / GGNFS

8·10¹⁷⁷-7 = 7(9)₁₇₆3_<178> = 19 · 73 · C175

C175 = P69 · P106

P69 = 845024513588440108342229237258611536863418925832842805605254098132291_<69>

P106 = 6825653191658678389031719639341109854130190201976846345079951503520340161289026704590084570366199203022329_<106>

N=5767844268204758471521268925739005046863734679163662581110310021629416005767844268204758471521268925739005046863734679163662581110310021629416005767844268204758471521268925739
  ( 175 digits)
SNFS difficulty: 177 digits.
Divisors found:
 r1=845024513588440108342229237258611536863418925832842805605254098132291 (pp69)
  r2=6825653191658678389031719639341109854130190201976846345079951503520340161289026704590084570366199203022329 (pp106)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 228.94 hours.
Scaled time: 386.00 units (timescale=1.686).
Factorization parameters were as follows:
n: 5767844268204758471521268925739005046863734679163662581110310021629416005767844268204758471521268925739005046863734679163662581110310021629416005767844268204758471521268925739
m: 200000000000000000000000000000000000
c5: 25
c0: -7
skew: 0.78
type: snfs

Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 12000001)
Primes: RFBsize:501962, AFBsize:501206, largePrimes:6478564 encountered
Relations: rels:6931375, finalFF:1126384
Max relations in full relation-set: 28
Initial matrix: 1003232 x 1126384 with sparse part having weight 71657504.
Pruned matrix : 899663 x 904743 with weight 55336059.
Total sieving time: 212.90 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 15.65 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,177,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 228.94 hours.

Apr 10, 2008 (3rd)

By Sinkiti Sibata / Msieve, GGNFS

(5·10¹⁴⁴-11)/3 = 1(6)₁₄₃3_<145> = 372005757821_<12> · 1993489673710399_<16> · 164034934577678887904605096215469_<33> · C86

C86 = P31 · P56

P31 = 1009810979515396265762537150309_<31>

P56 = 13567775824120341503281816335779422365608641008294822157_<56>

Thu Apr 10 06:45:04 2008  Msieve v. 1.33
Thu Apr 10 06:45:04 2008  random seeds: 4d5118a6 bb53e94c
Thu Apr 10 06:45:04 2008  factoring 13700888994800274861698196701203613805538875258560664517465359702368373723918732596513 (86 digits)
Thu Apr 10 06:45:05 2008  searching for 15-digit factors
Thu Apr 10 06:45:07 2008  commencing quadratic sieve (86-digit input)
Thu Apr 10 06:45:07 2008  using multiplier of 17
Thu Apr 10 06:45:07 2008  using 64kb Pentium 4 sieve core
Thu Apr 10 06:45:07 2008  sieve interval: 6 blocks of size 65536
Thu Apr 10 06:45:07 2008  processing polynomials in batches of 17
Thu Apr 10 06:45:07 2008  using a sieve bound of 1442429 (54984 primes)
Thu Apr 10 06:45:07 2008  using large prime bound of 115394320 (26 bits)
Thu Apr 10 06:45:07 2008  using double large prime bound of 325036373888400 (41-49 bits)
Thu Apr 10 06:45:07 2008  using trial factoring cutoff of 49 bits
Thu Apr 10 06:45:07 2008  polynomial 'A' values have 11 factors
Thu Apr 10 07:35:14 2008  55128 relations (16556 full + 38572 combined from 563178 partial), need 55080
Thu Apr 10 07:35:17 2008  begin with 579734 relations
Thu Apr 10 07:35:17 2008  reduce to 127826 relations in 12 passes
Thu Apr 10 07:35:17 2008  attempting to read 127826 relations
Thu Apr 10 07:35:21 2008  recovered 127826 relations
Thu Apr 10 07:35:21 2008  recovered 106966 polynomials
Thu Apr 10 07:35:21 2008  attempting to build 55128 cycles
Thu Apr 10 07:35:21 2008  found 55128 cycles in 5 passes
Thu Apr 10 07:35:21 2008  distribution of cycle lengths:
Thu Apr 10 07:35:21 2008     length 1 : 16556
Thu Apr 10 07:35:21 2008     length 2 : 11240
Thu Apr 10 07:35:21 2008     length 3 : 9653
Thu Apr 10 07:35:21 2008     length 4 : 7016
Thu Apr 10 07:35:21 2008     length 5 : 4631
Thu Apr 10 07:35:21 2008     length 6 : 2772
Thu Apr 10 07:35:21 2008     length 7 : 1589
Thu Apr 10 07:35:21 2008     length 9+: 1671
Thu Apr 10 07:35:21 2008  largest cycle: 20 relations
Thu Apr 10 07:35:21 2008  matrix is 54984 x 55128 (12.1 MB) with weight 2963153 (53.75/col)
Thu Apr 10 07:35:21 2008  sparse part has weight 2963153 (53.75/col)
Thu Apr 10 07:35:22 2008  filtering completed in 3 passes
Thu Apr 10 07:35:22 2008  matrix is 49629 x 49691 (11.1 MB) with weight 2706362 (54.46/col)
Thu Apr 10 07:35:22 2008  sparse part has weight 2706362 (54.46/col)
Thu Apr 10 07:35:22 2008  saving the first 48 matrix rows for later
Thu Apr 10 07:35:22 2008  matrix is 49581 x 49691 (6.8 MB) with weight 2076867 (41.80/col)
Thu Apr 10 07:35:22 2008  sparse part has weight 1488655 (29.96/col)
Thu Apr 10 07:35:22 2008  matrix includes 64 packed rows
Thu Apr 10 07:35:22 2008  commencing Lanczos iteration
Thu Apr 10 07:35:22 2008  memory use: 8.7 MB
Thu Apr 10 07:37:04 2008  lanczos halted after 786 iterations (dim = 49581)
Thu Apr 10 07:37:05 2008  recovered 18 nontrivial dependencies
Thu Apr 10 07:37:05 2008  prp31 factor: 1009810979515396265762537150309
Thu Apr 10 07:37:05 2008  prp56 factor: 13567775824120341503281816335779422365608641008294822157
Thu Apr 10 07:37:05 2008  elapsed time 00:52:01

(5·10¹³⁸-11)/3 = 1(6)₁₃₇3_<139> = 337 · 17600112488381_<14> · 64322575613083129_<17> · 1246141681788805723_<19> · C88

C88 = P36 · P52

P36 = 566733070758170868253771341604578479_<36>

P52 = 6185773308782255639310478822145178597967633181529103_<52>

Thu Apr 10 07:48:01 2008  Msieve v. 1.33
Thu Apr 10 07:48:01 2008  random seeds: 6c3c1403 9c5365fb
Thu Apr 10 07:48:01 2008  factoring 3505682302300098820331687118529707211660926175889383687226721329786765058955918985974337 (88 digits)
Thu Apr 10 07:48:02 2008  searching for 15-digit factors
Thu Apr 10 07:48:04 2008  commencing quadratic sieve (88-digit input)
Thu Apr 10 07:48:04 2008  using multiplier of 17
Thu Apr 10 07:48:04 2008  using 64kb Pentium 4 sieve core
Thu Apr 10 07:48:04 2008  sieve interval: 13 blocks of size 65536
Thu Apr 10 07:48:04 2008  processing polynomials in batches of 8
Thu Apr 10 07:48:04 2008  using a sieve bound of 1510507 (57667 primes)
Thu Apr 10 07:48:04 2008  using large prime bound of 120840560 (26 bits)
Thu Apr 10 07:48:04 2008  using double large prime bound of 353169224858800 (42-49 bits)
Thu Apr 10 07:48:04 2008  using trial factoring cutoff of 49 bits
Thu Apr 10 07:48:04 2008  polynomial 'A' values have 11 factors
Thu Apr 10 09:21:58 2008  58012 relations (16032 full + 41980 combined from 609335 partial), need 57763
Thu Apr 10 09:22:01 2008  begin with 625367 relations
Thu Apr 10 09:22:01 2008  reduce to 139986 relations in 9 passes
Thu Apr 10 09:22:01 2008  attempting to read 139986 relations
Thu Apr 10 09:22:05 2008  recovered 139986 relations
Thu Apr 10 09:22:05 2008  recovered 119002 polynomials
Thu Apr 10 09:22:05 2008  attempting to build 58012 cycles
Thu Apr 10 09:22:05 2008  found 58011 cycles in 4 passes
Thu Apr 10 09:22:05 2008  distribution of cycle lengths:
Thu Apr 10 09:22:05 2008     length 1 : 16032
Thu Apr 10 09:22:05 2008     length 2 : 11280
Thu Apr 10 09:22:05 2008     length 3 : 10151
Thu Apr 10 09:22:05 2008     length 4 : 7452
Thu Apr 10 09:22:05 2008     length 5 : 5389
Thu Apr 10 09:22:05 2008     length 6 : 3403
Thu Apr 10 09:22:05 2008     length 7 : 1988
Thu Apr 10 09:22:05 2008     length 9+: 2316
Thu Apr 10 09:22:05 2008  largest cycle: 18 relations
Thu Apr 10 09:22:06 2008  matrix is 57667 x 58011 (14.0 MB) with weight 3443627 (59.36/col)
Thu Apr 10 09:22:06 2008  sparse part has weight 3443627 (59.36/col)
Thu Apr 10 09:22:07 2008  filtering completed in 3 passes
Thu Apr 10 09:22:07 2008  matrix is 53492 x 53555 (13.0 MB) with weight 3196363 (59.68/col)
Thu Apr 10 09:22:07 2008  sparse part has weight 3196363 (59.68/col)
Thu Apr 10 09:22:07 2008  saving the first 48 matrix rows for later
Thu Apr 10 09:22:07 2008  matrix is 53444 x 53555 (9.6 MB) with weight 2662668 (49.72/col)
Thu Apr 10 09:22:07 2008  sparse part has weight 2200954 (41.10/col)
Thu Apr 10 09:22:07 2008  matrix includes 64 packed rows
Thu Apr 10 09:22:07 2008  using block size 21422 for processor cache size 512 kB
Thu Apr 10 09:22:08 2008  commencing Lanczos iteration
Thu Apr 10 09:22:08 2008  memory use: 8.7 MB
Thu Apr 10 09:22:37 2008  lanczos halted after 846 iterations (dim = 53440)
Thu Apr 10 09:22:38 2008  recovered 15 nontrivial dependencies
Thu Apr 10 09:22:38 2008  prp36 factor: 566733070758170868253771341604578479
Thu Apr 10 09:22:38 2008  prp52 factor: 6185773308782255639310478822145178597967633181529103
Thu Apr 10 09:22:38 2008  elapsed time 01:34:37

(5·10¹³⁶-11)/3 = 1(6)₁₃₅3_<137> = 79 · 367 · 134401 · 4789658941_<10> · 396271367827_<12> · 198762889748084687_<18> · C89

C89 = P34 · P55

P34 = 8068301980104416383890347409737059_<34>

P55 = 1405200720180081873965164341710238376930548187931746661_<55>

Thu Apr 10 09:33:05 2008  Msieve v. 1.33
Thu Apr 10 09:33:05 2008  random seeds: 0142229e 3af44813
Thu Apr 10 09:33:05 2008  factoring 11337583753073106518116561988542402958930646986405793606004811557150675788314536611209999 (89 digits)
Thu Apr 10 09:33:06 2008  searching for 15-digit factors
Thu Apr 10 09:33:08 2008  commencing quadratic sieve (89-digit input)
Thu Apr 10 09:33:08 2008  using multiplier of 3
Thu Apr 10 09:33:08 2008  using 64kb Pentium 4 sieve core
Thu Apr 10 09:33:08 2008  sieve interval: 14 blocks of size 65536
Thu Apr 10 09:33:08 2008  processing polynomials in batches of 8
Thu Apr 10 09:33:08 2008  using a sieve bound of 1533307 (58333 primes)
Thu Apr 10 09:33:08 2008  using large prime bound of 122664560 (26 bits)
Thu Apr 10 09:33:08 2008  using double large prime bound of 362822632808640 (42-49 bits)
Thu Apr 10 09:33:08 2008  using trial factoring cutoff of 49 bits
Thu Apr 10 09:33:08 2008  polynomial 'A' values have 11 factors
Thu Apr 10 11:40:42 2008  58719 relations (15129 full + 43590 combined from 628696 partial), need 58429
Thu Apr 10 11:40:45 2008  begin with 643825 relations
Thu Apr 10 11:40:45 2008  reduce to 144836 relations in 11 passes
Thu Apr 10 11:40:45 2008  attempting to read 144836 relations
Thu Apr 10 11:40:49 2008  recovered 144836 relations
Thu Apr 10 11:40:49 2008  recovered 127614 polynomials
Thu Apr 10 11:40:49 2008  attempting to build 58719 cycles
Thu Apr 10 11:40:49 2008  found 58719 cycles in 5 passes
Thu Apr 10 11:40:49 2008  distribution of cycle lengths:
Thu Apr 10 11:40:49 2008     length 1 : 15129
Thu Apr 10 11:40:49 2008     length 2 : 11176
Thu Apr 10 11:40:49 2008     length 3 : 10479
Thu Apr 10 11:40:49 2008     length 4 : 7871
Thu Apr 10 11:40:49 2008     length 5 : 5641
Thu Apr 10 11:40:49 2008     length 6 : 3557
Thu Apr 10 11:40:49 2008     length 7 : 2180
Thu Apr 10 11:40:49 2008     length 9+: 2686
Thu Apr 10 11:40:49 2008  largest cycle: 17 relations
Thu Apr 10 11:40:50 2008  matrix is 58333 x 58719 (14.4 MB) with weight 3540941 (60.30/col)
Thu Apr 10 11:40:50 2008  sparse part has weight 3540941 (60.30/col)
Thu Apr 10 11:40:51 2008  filtering completed in 3 passes
Thu Apr 10 11:40:51 2008  matrix is 54761 x 54825 (13.5 MB) with weight 3321850 (60.59/col)
Thu Apr 10 11:40:51 2008  sparse part has weight 3321850 (60.59/col)
Thu Apr 10 11:40:51 2008  saving the first 48 matrix rows for later
Thu Apr 10 11:40:51 2008  matrix is 54713 x 54825 (9.5 MB) with weight 2731547 (49.82/col)
Thu Apr 10 11:40:51 2008  sparse part has weight 2167317 (39.53/col)
Thu Apr 10 11:40:51 2008  matrix includes 64 packed rows
Thu Apr 10 11:40:51 2008  using block size 21845 for processor cache size 512 kB
Thu Apr 10 11:40:52 2008  commencing Lanczos iteration
Thu Apr 10 11:40:52 2008  memory use: 8.8 MB
Thu Apr 10 11:41:28 2008  lanczos halted after 866 iterations (dim = 54712)
Thu Apr 10 11:41:28 2008  recovered 17 nontrivial dependencies
Thu Apr 10 11:41:29 2008  prp34 factor: 8068301980104416383890347409737059
Thu Apr 10 11:41:29 2008  prp55 factor: 1405200720180081873965164341710238376930548187931746661
Thu Apr 10 11:41:29 2008  elapsed time 02:08:24

(5·10¹¹⁹-11)/3 = 1(6)₁₁₈3_<120> = 7 · 733 · 34313 · C111

C111 = P39 · P73

P39 = 101104783942079007388364625845026040897_<39>

P73 = 9363028368878613663743614793519812822060379795258031152047919513400120493_<73>

Number: 16663_119
N=946646960279028659715896214466534268244143257606707337535752891397296333493000489535755981252974684242545802221
  ( 111 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=101104783942079007388364625845026040897 (pp39)
 r2=9363028368878613663743614793519812822060379795258031152047919513400120493 (pp73)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.13 hours.
Scaled time: 1.43 units (timescale=0.675).
Factorization parameters were as follows:
name: 16663_119
n: 946646960279028659715896214466534268244143257606707337535752891397296333493000489535755981252974684242545802221
m: 1000000000000000000000000
c5: 1
c0: -22
skew: 1.86
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64044, largePrimes:2132126 encountered
Relations: rels:2254968, finalFF:263067
Max relations in full relation-set: 28
Initial matrix: 113206 x 263067 with sparse part having weight 22310391.
Pruned matrix : 81108 x 81738 with weight 4690802.
Total sieving time: 1.92 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.13 hours.
 --------- CPU info (if available) ----------

(5·10¹²⁴-11)/3 = 1(6)₁₂₃3_<125> = 155782489099_<12> · C114

C114 = P35 · P79

P35 = 79040799952020878573456251998858247_<35>

P79 = 1353563964903948324773516845167090881007930444243617150102530821798840472293571_<79>

Number: 16663_124
N=106986778572237188918038053454011120432923406069133029873611126531552369406827118389351077489337777850129398430037
  ( 114 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=79040799952020878573456251998858247 (pp35)
 r2=1353563964903948324773516845167090881007930444243617150102530821798840472293571 (pp79)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 3.07 hours.
Scaled time: 2.07 units (timescale=0.675).
Factorization parameters were as follows:
name: 16663_124
n: 106986778572237188918038053454011120432923406069133029873611126531552369406827118389351077489337777850129398430037
m: 10000000000000000000000000
c5: 1
c0: -22
skew: 1.86
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:64044, largePrimes:2230601 encountered
Relations: rels:2398863, finalFF:282622
Max relations in full relation-set: 28
Initial matrix: 113206 x 282622 with sparse part having weight 27237143.
Pruned matrix : 84072 x 84702 with weight 6352895.
Total sieving time: 2.83 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.07 hours.
 --------- CPU info (if available) ----------

Apr 10, 2008 (2nd)

By Robert Backstrom / GMP-ECM, Msieve, GGNFS

(5·10¹³⁰-11)/3 = 1(6)₁₂₉3_<131> = 19 · 197 · 14107 · 191413 · 649724783 · 14480781147778646998269769_<26> · C84

C84 = P38 · P46

P38 = 53531600126183563743099708638553112189_<38>

P46 = 3274094258896914280404842697764802626556431917_<46>

8·10¹⁶³+9 = 8(0)₁₆₂9_<164> = 503 · 1087 · 399924341 · 29222738487023707_<17> · C134

C134 = P56 · P78

P56 = 36035228405537339175432279337085862878520760605668457943_<56>

P78 = 347429290363042316932943294898674175631435388823749992448700892981477531332209_<78>

Number: n
N=12519693833005982629763709812980179231976207191212881316914731579887782131176373995769271932131678712789550263792631222521491477786087
  ( 134 digits)
SNFS difficulty: 163 digits.
Divisors found:

Thu Apr 10 07:25:28 2008  prp56 factor: 36035228405537339175432279337085862878520760605668457943
Thu Apr 10 07:25:28 2008  prp78 factor: 347429290363042316932943294898674175631435388823749992448700892981477531332209
Thu Apr 10 07:25:28 2008  elapsed time 01:12:32 (Msieve 1.34)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 51.50 hours.
Scaled time: 90.43 units (timescale=1.756).
Factorization parameters were as follows:
name: KA_8_0_162_9
n: 12519693833005982629763709812980179231976207191212881316914731579887782131176373995769271932131678712789550263792631222521491477786087
type: snfs
skew: 0.51
deg: 5
c5: 250
c0: 9
m: 200000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2599990)
Primes: RFBsize:230209, AFBsize:229672, largePrimes:7298720 encountered
Relations: rels:6770473, finalFF:539596
Max relations in full relation-set: 28
Initial matrix: 459948 x 539596 with sparse part having weight 38448691.
Pruned matrix : 
Total sieving time: 51.26 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 51.50 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(5·10¹⁰⁹-11)/3 = 1(6)₁₀₈3_<110> = 13 · 313 · 2312775383_<10> · C97

C97 = P38 · P59

P38 = 58445511121979509375071556501778835511_<38>

P59 = 30302359249263881160048008087323480234166016216705306154379_<59>

(5·10¹²⁵-11)/3 = 1(6)₁₂₄3_<126> = 7 · 89 · 556121386394051411573_<21> · C102

C102 = P31 · P72

P31 = 2082317813011810225828417141867_<31>

P72 = 231017080921821034361454488681781206591379258747165236540837184499456591_<72>

(5·10¹¹⁵-11)/3 = 1(6)₁₁₄3_<116> = 13 · 243311 · 6251989363_<10> · 415576023843179_<15> · C85

C85 = P39 · P47

P39 = 101724403988483751381031110691554232729_<39>

P47 = 19936539876112083560045113778507889458461515877_<47>

Thu Apr 10 08:23:12 2008  
Thu Apr 10 08:23:12 2008  
Thu Apr 10 08:23:12 2008  Msieve v. 1.34
Thu Apr 10 08:23:12 2008  random seeds: 37c399e0 09f2c22c
Thu Apr 10 08:23:12 2008  factoring 2028032636490141387528493438386065303545798771129933058079434458815434399092986538333 (85 digits)
Thu Apr 10 08:23:12 2008  searching for 15-digit factors
Thu Apr 10 08:23:13 2008  commencing quadratic sieve (85-digit input)
Thu Apr 10 08:23:13 2008  using multiplier of 37
Thu Apr 10 08:23:13 2008  using 64kb Opteron sieve core
Thu Apr 10 08:23:13 2008  sieve interval: 6 blocks of size 65536
Thu Apr 10 08:23:13 2008  processing polynomials in batches of 17
Thu Apr 10 08:23:13 2008  using a sieve bound of 1426129 (54372 primes)
Thu Apr 10 08:23:13 2008  using large prime bound of 116942578 (26 bits)
Thu Apr 10 08:23:13 2008  using double large prime bound of 332928269126164 (41-49 bits)
Thu Apr 10 08:23:13 2008  using trial factoring cutoff of 49 bits
Thu Apr 10 08:23:13 2008  polynomial 'A' values have 11 factors
Thu Apr 10 08:47:08 2008  54480 relations (16137 full + 38343 combined from 569033 partial), need 54468
Thu Apr 10 08:47:08 2008  begin with 585169 relations
Thu Apr 10 08:47:09 2008  reduce to 127178 relations in 10 passes
Thu Apr 10 08:47:09 2008  attempting to read 127178 relations
Thu Apr 10 08:47:10 2008  recovered 127178 relations
Thu Apr 10 08:47:10 2008  recovered 106669 polynomials
Thu Apr 10 08:47:10 2008  attempting to build 54480 cycles
Thu Apr 10 08:47:10 2008  found 54480 cycles in 5 passes
Thu Apr 10 08:47:10 2008  distribution of cycle lengths:
Thu Apr 10 08:47:10 2008     length 1 : 16137
Thu Apr 10 08:47:10 2008     length 2 : 11237
Thu Apr 10 08:47:10 2008     length 3 : 9540
Thu Apr 10 08:47:10 2008     length 4 : 6859
Thu Apr 10 08:47:10 2008     length 5 : 4566
Thu Apr 10 08:47:10 2008     length 6 : 2788
Thu Apr 10 08:47:10 2008     length 7 : 1597
Thu Apr 10 08:47:10 2008     length 9+: 1756
Thu Apr 10 08:47:10 2008  largest cycle: 19 relations
Thu Apr 10 08:47:11 2008  matrix is 54372 x 54480 (11.8 MB) with weight 2874410 (52.76/col)
Thu Apr 10 08:47:11 2008  sparse part has weight 2874410 (52.76/col)
Thu Apr 10 08:47:11 2008  filtering completed in 3 passes
Thu Apr 10 08:47:11 2008  matrix is 49520 x 49584 (10.8 MB) with weight 2639553 (53.23/col)
Thu Apr 10 08:47:11 2008  sparse part has weight 2639553 (53.23/col)
Thu Apr 10 08:47:11 2008  saving the first 48 matrix rows for later
Thu Apr 10 08:47:11 2008  matrix is 49472 x 49584 (6.4 MB) with weight 1990780 (40.15/col)
Thu Apr 10 08:47:11 2008  sparse part has weight 1368376 (27.60/col)
Thu Apr 10 08:47:11 2008  matrix includes 64 packed rows
Thu Apr 10 08:47:11 2008  commencing Lanczos iteration
Thu Apr 10 08:47:11 2008  memory use: 8.2 MB
Thu Apr 10 08:47:59 2008  lanczos halted after 783 iterations (dim = 49462)
Thu Apr 10 08:47:59 2008  recovered 11 nontrivial dependencies
Thu Apr 10 08:47:59 2008  prp39 factor: 101724403988483751381031110691554232729
Thu Apr 10 08:47:59 2008  prp47 factor: 19936539876112083560045113778507889458461515877
Thu Apr 10 08:47:59 2008  elapsed time 00:24:47

(5·10¹⁰²-11)/3 = 1(6)₁₀₁3_<103> = 17 · 47 · 73 · C98

C98 = P41 · P57

P41 = 42247654314238814538592060301512367110661_<41>

P57 = 676357809987191111919877049341177444192239827754611671229_<57>

Number: n
N=28574530949074470942559477886170498511266937553220063892651202130517027562992553477234671192872369
  ( 98 digits)
SNFS difficulty: 102 digits.
Divisors found:
 r1=42247654314238814538592060301512367110661 (pp41)
 r2=676357809987191111919877049341177444192239827754611671229 (pp57)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.41 hours.
Scaled time: 0.73 units (timescale=1.753).
Factorization parameters were as follows:
name: KA_1_6_101_3
n: 28574530949074470942559477886170498511266937553220063892651202130517027562992553477234671192872369
type: snfs
skew: 0.47
deg: 5
c5: 500
c0: -11
m: 100000000000000000000
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 300001)
Primes: RFBsize:41538, AFBsize:41853, largePrimes:2461385 encountered
Relations: rels:1937861, finalFF:105591
Max relations in full relation-set: 28
Initial matrix: 83457 x 105591 with sparse part having weight 2650651.
Pruned matrix : 56554 x 57035 with weight 1104019.
Total sieving time: 0.35 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.01 hours.
Total square root time: 0.01 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,102,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.2,2.2,20000
total time: 0.41 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(5·10¹²⁶-11)/3 = 1(6)₁₂₅3_<127> = 73 · 103 · 151 · 8036239 · C114

C114 = P42 · P73

P42 = 136601909891494683571867166667984462907181_<42>

P73 = 1337217654640463702420039415634113857360702296152706815677177592790424453_<73>

Number: n
N=182666485564512480286199842770473113380890893561775030331297841982007142001745032870406824625614600794059331696993
  ( 114 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=136601909891494683571867166667984462907181 (pp42)
 r2=1337217654640463702420039415634113857360702296152706815677177592790424453 (pp73)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.66 hours.
Scaled time: 3.03 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_6_125_3
n: 182666485564512480286199842770473113380890893561775030331297841982007142001745032870406824625614600794059331696993
skew: 0.74
deg: 5
c5: 50
c0: -11
m: 10000000000000000000000000
type: snfs
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 25000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 300001)
Primes: RFBsize:78498, AFBsize:78657, largePrimes:4602854 encountered
Relations: rels:3926609, finalFF:176847
Max relations in full relation-set: 48
Initial matrix: 157220 x 176847 with sparse part having weight 12529569.
Pruned matrix : 145751 x 146601 with weight 7887455.
Total sieving time: 1.48 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.09 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000
total time: 1.66 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(14·10¹⁷⁰+31)/9 = 1(5)₁₆₉9_<171> = 3⁴ · 173 · 241 · 1063 · 947388505673668601_<18> · 329773997817300200297648891_<27> · C117

C117 = P43 · P74

P43 = 4570257576393376741108870562574935143559999_<43>

P74 = 30347219042826632639068219128539563087330388614267880782603290658707817769_<74>

Number: n
N=138694607752947776402054601038374261634077577246418128378721610395375037159280518817908354940816419747823675209822231
  ( 117 digits)
Divisors found:

Thu Apr 10 19:09:13 2008  prp43 factor: 4570257576393376741108870562574935143559999
Thu Apr 10 19:09:13 2008  prp74 factor: 30347219042826632639068219128539563087330388614267880782603290658707817769
Thu Apr 10 19:09:13 2008  elapsed time 01:18:33 (Msieve 1.34)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 49.69 hours.
Scaled time: 64.80 units (timescale=1.304).
Factorization parameters were as follows:
name: KA_1_5_169_9
n: 138694607752947776402054601038374261634077577246418128378721610395375037159280518817908354940816419747823675209822231
skew: 94836.36
# norm 1.77e+16
c5: 1920
c4: 4251138112
c3: -309124278511618
c2: -29561456463897609891
c1: 487127672626518629193186
c0: 32056092180814696347161000619
# alpha -6.09
Y1: 31913420429
Y0: -37303665233241543560500
# Murphy_E 4.26e-10
# M 30440368514637758849034089320960643934931022425993500010937446988681486641564356323500538790935064017609701630427635
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 2020001)
Primes: RFBsize:315948, AFBsize:316044, largePrimes:6564918 encountered
Relations: rels:6479500, finalFF:721077
Max relations in full relation-set: 28
Initial matrix: 632068 x 721077 with sparse part having weight 38916166.
Pruned matrix : 
Total sieving time: 49.37 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 49.69 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(5·10¹³⁵-11)/3 = 1(6)₁₃₄3_<136> = 2309 · C132

C132 = P51 · P81

P51 = 769471589341802815698410458609829329351462222537643_<51>

P81 = 938063477252786787981200026222114693270614493438014472876357993296728209029600049_<81>

Number: n
N=721813194745199942254944420384004619604446369279630431644290457629565468456763389634762523458928829218998123285693662480150137144507
  ( 132 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=769471589341802815698410458609829329351462222537643 (pp51)
 r2=938063477252786787981200026222114693270614493438014472876357993296728209029600049 (pp81)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.40 hours.
Scaled time: 4.40 units (timescale=1.834).
Factorization parameters were as follows:
name: KA_1_6_134_3
n: 721813194745199942254944420384004619604446369279630431644290457629565468456763389634762523458928829218998123285693662480150137144507
skew: 1.17
deg: 5
c5: 5
c0: -11
m: 1000000000000000000000000000
type: snfs
rlim: 1200000
alim: 1200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 25000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 475001)
Primes: RFBsize:92938, AFBsize:93450, largePrimes:5497865 encountered
Relations: rels:4850841, finalFF:262120
Max relations in full relation-set: 48
Initial matrix: 186453 x 262120 with sparse part having weight 23107069.
Pruned matrix : 153848 x 154844 with weight 9218030.
Total sieving time: 2.18 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.12 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,48,48,2.5,2.5,75000
total time: 2.40 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Apr 10, 2008

The factor table of 166...663 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Apr 9, 2008

By Robert Backstrom / GGNFS, Msieve

4·10¹⁶⁴+9 = 4(0)₁₆₃9_<165> = 433 · 325501909 · 155697059191893120469_<21> · C134

C134 = P58 · P76

P58 = 2480292169582768150613622571493155466576298122188305452881_<58>

P76 = 7349119396569529045017568501654084454037447639806748910113839336437017179473_<76>

Number: n
N=18227963292640241073752649952343065729223968280713818502150062554437260230889566308369202243770405504513631798743471894619440521911713
  ( 134 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=2480292169582768150613622571493155466576298122188305452881 (pp58)
 r2=7349119396569529045017568501654084454037447639806748910113839336437017179473 (pp76)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 46.42 hours.
Scaled time: 84.63 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_4_0_163_9
n: 18227963292640241073752649952343065729223968280713818502150062554437260230889566308369202243770405504513631798743471894619440521911713
skew: 1.86
deg: 5
c5: 2
c0: 45
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3100001)
Primes: RFBsize:230209, AFBsize:230302, largePrimes:7625564 encountered
Relations: rels:7110539, finalFF:542315
Max relations in full relation-set: 48
Initial matrix: 460576 x 542315 with sparse part having weight 55660953.
Pruned matrix : 428423 x 430789 with weight 36977980.
Total sieving time: 44.05 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 2.04 hours.
Total square root time: 0.13 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 46.42 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(16·10¹⁶³-1)/3 = 5(3)₁₆₃_<164> = 9203 · 649751 · 754067 · 210126893 · 1470754547_<10> · C131

C131 = P40 · P46 · P46

P40 = 5241938648266082638689856097053647927227_<40>

P46 = 1203492293151321834268051001544618500679611569_<46>

P46 = 6066739234889810264566998524928554913682222871_<46>

Number: n
N=38272829910055922554986494307292612701700316471903274256011625905419437445035817954191202482574294773808756113465281446661881046973
  ( 131 digits)
SNFS difficulty: 164 digits.
Divisors found:

Wed Apr 09 22:10:04 2008  prp40 factor: 5241938648266082638689856097053647927227
Wed Apr 09 22:10:04 2008  prp46 factor: 1203492293151321834268051001544618500679611569
Wed Apr 09 22:10:04 2008  prp46 factor: 6066739234889810264566998524928554913682222871
Wed Apr 09 22:10:04 2008  elapsed time 01:02:53 (Msieve 1.34)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 32.31 hours.
Scaled time: 59.09 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_5_3_163
n: 38272829910055922554986494307292612701700316471903274256011625905419437445035817954191202482574294773808756113465281446661881046973
skew: 0.29
deg: 5
c5: 500
c0: -1
m: 200000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2299990)
Primes: RFBsize:230209, AFBsize:229657, largePrimes:7314015 encountered
Relations: rels:6796872, finalFF:529923
Max relations in full relation-set: 28
Initial matrix: 459932 x 529922 with sparse part having weight 46577315.
Pruned matrix : 
Total sieving time: 32.13 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 32.31 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Apr 8, 2008

By Sinkiti Sibata / GGNFS

(14·10¹⁵²+31)/9 = 1(5)₁₅₁9_<153> = 3² · 17 · 67 · 123377 · 127319953639_<12> · 56178496930208414688605633_<26> · C107

C107 = P39 · P69

P39 = 111313093274540417476741014421320134743_<39>

P69 = 154479995522690870591367172547336505227910968599671963282858372345637_<69>

Number: 15559_152
N=17195646150667874950992453422444333642975476026069684108426569369939091078615552957010779914767445808166291
  ( 107 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=111313093274540417476741014421320134743 (pp39)
 r2=154479995522690870591367172547336505227910968599671963282858372345637 (pp69)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 51.75 hours.
Scaled time: 34.93 units (timescale=0.675).
Factorization parameters were as follows:
name: 15559_152
n: 17195646150667874950992453422444333642975476026069684108426569369939091078615552957010779914767445808166291
m: 1000000000000000000000000000000
c5: 1400
c0: 31
skew: 0.47
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2600001)
Primes: RFBsize:176302, AFBsize:175914, largePrimes:5759456 encountered
Relations: rels:5717101, finalFF:466652
Max relations in full relation-set: 28
Initial matrix: 352283 x 466652 with sparse part having weight 48829191.
Pruned matrix : 312843 x 314668 with weight 30625407.
Total sieving time: 46.57 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 4.73 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 51.75 hours.
 --------- CPU info (if available) ----------

Apr 7, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(14·10¹⁵³+31)/9 = 1(5)₁₅₂9_<154> = 61 · 541 · 23624025645827704817_<20> · C130

C130 = P62 · P69

P62 = 12618987396929809067039217391491187497627561020701168808432897_<62>

P69 = 158117527310291680588589078011395917240084089263123655628504089737791_<69>

Number: n
N=1995283084362275608981993720845150085222935999336634693921193036336245407655677090547930521602073409192525797082004482958348510527
  ( 130 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=12618987396929809067039217391491187497627561020701168808432897 (pp62)
 r2=158117527310291680588589078011395917240084089263123655628504089737791 (pp69)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 21.43 hours.
Scaled time: 39.19 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_5_152_9
n: 1995283084362275608981993720845150085222935999336634693921193036336245407655677090547930521602073409192525797082004482958348510527
skew: 0.59
deg: 5
c5: 875
c0: 62
m: 2000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:183072, AFBsize:183212, largePrimes:7007383 encountered
Relations: rels:6444936, finalFF:443762
Max relations in full relation-set: 48
Initial matrix: 366350 x 443762 with sparse part having weight 44001931.
Pruned matrix : 316482 x 318377 with weight 26418976.
Total sieving time: 19.91 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.94 hours.
Total square root time: 0.41 hours, sqrts: 8.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 21.43 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(14·10¹⁶⁴+31)/9 = 1(5)₁₆₃9_<165> = 3 · 3167 · 3557 · 2115203 · C151

C151 = P51 · P100

P51 = 292044997922927091627528286394099949348817998187813_<51>

P100 = 7451273714795980303658961535674894947248661146078209917201810829662662013768700449007211187583249433_<100>

Number: n
N=2176107216560753301911443296557873067276016343298831494475440440002350484312812223305933949454487812090080679805129498136087304244961797327267959760029
  ( 151 digits)
SNFS difficulty: 165 digits.
Divisors found:

Mon Apr  7 19:21:33 2008  prp51 factor: 292044997922927091627528286394099949348817998187813
Mon Apr  7 19:21:33 2008  prp100 factor: 7451273714795980303658961535674894947248661146078209917201810829662662013768700449007211187583249433
Mon Apr  7 19:21:33 2008  elapsed time 00:56:16 (Msieve 1.34)

Version: GGNFS-0.77.1-20050930-k8
Total time: 58.46 hours.
Scaled time: 49.16 units (timescale=0.841).
Factorization parameters were as follows:
name: KA_1_5_163_9
n: 2176107216560753301911443296557873067276016343298831494475440440002350484312812223305933949454487812090080679805129498136087304244961797327267959760029
type: snfs
deg: 5
c5: 7
c0: 155
skew: 1.86
m: 1000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3700369)
Primes: RFBsize:230209, AFBsize:229318, largePrimes:5754763 encountered
Relations: rels:5663009, finalFF:469183
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 58.27 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,48,48,2.5,2.5,100000
total time: 58.46 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(14·10¹⁶⁵+31)/9 = 1(5)₁₆₄9_<166> = 76012247 · 1729666074743_<13> · C146

C146 = P68 · P78

P68 = 67547527870814968644720759872728356155144540584072588165080323596693_<68>

P78 = 175158101286561444194143776900975745196879694692553333454908567390260925183803_<78>

Number: n
N=11831496728453040368588747027393946948515280652340570548132594078197001463889134283214599455363721462782675641132374892459492277581995839067963479
  ( 146 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Apr 07 20:40:51 2008  prp68 factor: 67547527870814968644720759872728356155144540584072588165080323596693
Mon Apr 07 20:40:51 2008  prp78 factor: 175158101286561444194143776900975745196879694692553333454908567390260925183803
Mon Apr 07 20:40:51 2008  elapsed time 01:01:41 (Msieve 1.34)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 50.67 hours.
Scaled time: 92.93 units (timescale=1.834).
Factorization parameters were as follows:
name: KA_1_5_164_9
n: 11831496728453040368588747027393946948515280652340570548132594078197001463889134283214599455363721462782675641132374892459492277581995839067963479
skew: 1.17
deg: 5
c5: 14
c0: 31
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3400001)
Primes: RFBsize:230209, AFBsize:230543, largePrimes:7686963 encountered
Relations: rels:7146455, finalFF:522792
Max relations in full relation-set: 28
Initial matrix: 460818 x 522792 with sparse part having weight 59672004.
Pruned matrix : 
Total sieving time: 50.44 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 50.67 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Apr 7, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(14·10¹⁵⁷+31)/9 = 1(5)₁₅₆9_<158> = 93463993209661_<14> · C144

C144 = P47 · P98

P47 = 16264286654890748144075190501147967098201002951_<47>

P98 = 10233075398052231822492848466935430038785598384068263986570291327906585563875283488105494739268469_<98>

Number: n
N=166433671635031744544481049109629997491990532133453025037392323621256408259802421916610388923754892468719810052105215109107568842740899850252019
  ( 144 digits)
SNFS difficulty: 158 digits.
Divisors found:

Mon Apr 07 01:06:15 2008  prp47 factor: 16264286654890748144075190501147967098201002951
Mon Apr 07 01:06:15 2008  prp98 factor: 10233075398052231822492848466935430038785598384068263986570291327906585563875283488105494739268469
Mon Apr 07 01:06:15 2008  elapsed time 02:22:14 (Msieve 1.34, Dep=8)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 47.92 hours.
Scaled time: 84.11 units (timescale=1.755).
Factorization parameters were as follows:
name: KA_1_5_156_9
n: 166433671635031744544481049109629997491990532133453025037392323621256408259802421916610388923754892468719810052105215109107568842740899850252019
type: snfs
skew: 0.47
deg: 5
c5: 1400
c0: 31
m: 10000000000000000000000000000000
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2400001)
Primes: RFBsize:183072, AFBsize:182717, largePrimes:7075797 encountered
Relations: rels:6427225, finalFF:371726
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 47.69 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.3,2.3,100000
total time: 47.92 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(46·10¹⁹⁴-1)/9 = 5(1)₁₉₄_<195> = 7 · 73 · 59809 · 41535100907534041_<17> · 735190796811265416174712160511408781_<36> · C135

C135 = P34 · P102

P34 = 2131759063791372047774111469573847_<34>

P102 = 256906108706152053755199843207572059233131041311072028161736752737669098210183763610380354496349308547_<102>

Apr 6, 2008

By Jo Yeong Uk / GGNFS

(14·10¹⁵⁶+31)/9 = 1(5)₁₅₅9_<157> = 846400273673407_<15> · 5647119458626703_<16> · C126

C126 = P39 · P88

P39 = 181595105240033914022977640506121267719_<39>

P88 = 1792167585191447108689726343859434077154164335650452972726213569904570307167543559971441_<88>

Number: 15559_156
N=325448861240618282863068539156450995311385946677891062779075151268243362097776381667860754237370696771018560283140022355213079
  ( 126 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=181595105240033914022977640506121267719 (pp39)
 r2=1792167585191447108689726343859434077154164335650452972726213569904570307167543559971441 (pp88)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.96 hours.
Scaled time: 53.59 units (timescale=2.147).
Factorization parameters were as follows:
n: 325448861240618282863068539156450995311385946677891062779075151268243362097776381667860754237370696771018560283140022355213079
m: 10000000000000000000000000000000
c5: 140
c0: 31
skew: 0.74
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3100001)
Primes: RFBsize:216816, AFBsize:216762, largePrimes:5719874 encountered
Relations: rels:5700036, finalFF:548025
Max relations in full relation-set: 28
Initial matrix: 433645 x 548025 with sparse part having weight 48656988.
Pruned matrix : 380612 x 382844 with weight 32093823.
Total sieving time: 24.02 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.80 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 24.96 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4042900k/4718592k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405130)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19246.09 BogoMIPS).

(14·10¹⁶⁶+31)/9 = 1(5)₁₆₅9_<167> = 14762153720019369394560342817_<29> · 25959036563720881399909794087532397_<35> · C104

C104 = P49 · P55

P49 = 9597033958947512940770715759079012159641836757583_<49>

P55 = 4229706193320175468626508490317354141097461889488396877_<55>

Number: 15559_166
N=40592633973664338092756074639611100697720162425602675161336639117666924326656515110040772765234343268291
  ( 104 digits)
Divisors found:
 r1=9597033958947512940770715759079012159641836757583 (pp49)
 r2=4229706193320175468626508490317354141097461889488396877 (pp55)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.75 hours.
Scaled time: 12.23 units (timescale=2.128).
Factorization parameters were as follows:
name: 15559_166
n: 40592633973664338092756074639611100697720162425602675161336639117666924326656515110040772765234343268291
skew: 26811.40
# norm 3.74e+14
c5: 15120
c4: 6077326
c3: -23724512303077
c2: 86864477756364696
c1: 8298547771000702870996
c0: 33119074129593578932976192
# alpha -6.43
Y1: 72405459907
Y0: -76873924976831669127
# Murphy_E 2.13e-09
# M 1233879129425926695567871031059691043818742592710023171099250854072614931552306628519699357283862227743
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1680001)
Primes: RFBsize:135072, AFBsize:134910, largePrimes:4428331 encountered
Relations: rels:4423357, finalFF:366133
Max relations in full relation-set: 28
Initial matrix: 270065 x 366133 with sparse part having weight 30992146.
Pruned matrix : 212490 x 213904 with weight 16099938.
Polynomial selection time: 0.39 hours.
Total sieving time: 5.03 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 5.75 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4042900k/4718592k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405130)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19246.09 BogoMIPS).

Apr 5, 2008 (4th)

By matsui / GGNFS

7·10¹⁷⁵+3 = 7(0)₁₇₄3_<176> = 113 · 487 · 8389 · C168

C168 = P50 · P118

P50 = 15382421157285425929466447017738051797673565880227_<50>

P118 = 9857249360937578381060501178705637693417639727420036892990380567114305681621039301876173072701917734426786021572283771_<118>

N=151628361122324449605999010616279199054547780878970071028724500558327034384345390656706742598481954467220514093835588185333846845161508345996485657487401215720241896017
  ( 168 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=15382421157285425929466447017738051797673565880227 (pp50)
 r2=9857249360937578381060501178705637693417639727420036892990380567114305681621039301876173072701917734426786021572283771 (pp118)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 186.17 hours.
Scaled time: 315.56 units (timescale=1.695).
Factorization parameters were as follows:
n: 151628361122324449605999010616279199054547780878970071028724500558327034384345390656706742598481954467220514093835588185333846845161508345996485657487401215720241896017
m: 100000000000000000000000000000000000
c5: 7
c0: 3
skew: 0.84
type: snfs

Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 10600001)
Primes: RFBsize:501962, AFBsize:500771, largePrimes:6392766 encountered
Relations: rels:6833029, finalFF:1124040
Max relations in full relation-set: 28
Initial matrix: 1002798 x 1124040 with sparse part having weight 66158404.
Pruned matrix : 898702 x 903779 with weight 50386598.
Total sieving time: 171.47 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 14.30 hours.
Time per square root: 0.26 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 186.17 hours.

Apr 5, 2008 (3rd)

By Robert Backstrom / GMP-ECM

(52·10¹⁶³-7)/9 = 5(7)₁₆₃_<164> = 3 · 19 · 89 · 4463 · 2537021 · 55830371 · 1248226627_<10> · C134

C134 = P37 · P97

P37 = 6420478316845888866764229697079609081_<37>

P97 = 2248089943587469434480299083386367776545352478097162371514379969035559192349878360635205285279419_<97>

(14·10¹⁶²+31)/9 = 1(5)₁₆₁9_<163> = 29 · 3806347 · 26170223 · C147

C147 = P38 · P40 · P70

P38 = 50365446354722171931533546718702257843_<38>

P40 = 3543988444207413403410274704260989655419_<40>

P70 = 3016801554260539634880325171364479046731365413823735186731506096436023_<70>

Apr 5, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(14·10¹³⁰+31)/9 = 1(5)₁₂₉9_<131> = 523 · 517830371 · 22205400930628594589_<20> · C100

C100 = P39 · P62

P39 = 223052339348662090783561338193275827047_<39>

P62 = 11596606412490730336161701177308159280832170437567286305560181_<62>

Number: 15559_130
N=2586650188811753255072196313522140231922638767244339815312972931926665126576983403300759137406015507
  ( 100 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=223052339348662090783561338193275827047 (pp39)
 r2=11596606412490730336161701177308159280832170437567286305560181 (pp62)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 6.44 hours.
Scaled time: 4.35 units (timescale=0.675).
Factorization parameters were as follows:
name: 15559_130
n: 2586650188811753255072196313522140231922638767244339815312972931926665126576983403300759137406015507
m: 100000000000000000000000000
c5: 14
c0: 31
skew: 1.17
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1050001)
Primes: RFBsize:63951, AFBsize:63629, largePrimes:1507105 encountered
Relations: rels:1507107, finalFF:169181
Max relations in full relation-set: 28
Initial matrix: 127646 x 169181 with sparse part having weight 13212589.
Pruned matrix : 116035 x 116737 with weight 7300210.
Total sieving time: 6.08 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 6.44 hours.
 --------- CPU info (if available) ----------

(14·10¹³⁴+31)/9 = 1(5)₁₃₃9_<135> = 3² · 29 · 5014409 · 329843551356450621367_<21> · C105

C105 = P40 · P66

P40 = 1306557661964407021017588295478647094717_<40>

P66 = 275796458917595587577783322712081943077119699195249979743129914969_<66>

Number: 15559_134
N=360343976541436324001467268397547805706577207259650798154874784983464628358958156247401923595203099118773
  ( 105 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=1306557661964407021017588295478647094717 (pp40)
 r2=275796458917595587577783322712081943077119699195249979743129914969 (pp66)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 10.14 hours.
Scaled time: 6.84 units (timescale=0.674).
Factorization parameters were as follows:
name: 15559_134
n: 360343976541436324001467268397547805706577207259650798154874784983464628358958156247401923595203099118773
m: 1000000000000000000000000000
c5: 7
c0: 155
skew: 1.86
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1450001)
Primes: RFBsize:78498, AFBsize:63449, largePrimes:1554550 encountered
Relations: rels:1547172, finalFF:162708
Max relations in full relation-set: 28
Initial matrix: 142012 x 162708 with sparse part having weight 14524899.
Pruned matrix : 135927 x 136701 with weight 10750022.
Total sieving time: 9.55 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.43 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 10.14 hours.
 --------- CPU info (if available) ----------

Apr 5, 2008

By Tyler Cadigan / GGNFS, Msieve

(25·10¹⁸¹-1)/3 = 8(3)₁₈₁_<182> = 69591715019881213_<17> · 747152275895293013_<18> · C148

C148 = P46 · P102

P46 = 1780413985668047124967711027196123828460629329_<46>

P102 = 900183594319564916679896379547677509715284513197543620154816703452344181111024772817941782678605403333_<102>

Number: 83333_181
N=1602699460995484998900532952740942402090779344283258132988336035926159888755217576890505832750581638436871049644705615184704800910461748317054153557
  ( 148 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=1780413985668047124967711027196123828460629329
 r2=900183594319564916679896379547677509715284513197543620154816703452344181111024772817941782678605403333
Version: 
Total time: 331.70 hours.
Scaled time: 850.47 units (timescale=2.564).
Factorization parameters were as follows:
n: 1602699460995484998900532952740942402090779344283258132988336035926159888755217576890505832750581638436871049644705615184704800910461748317054153557
m: 1000000000000000000000000000000000000
c5: 250
c0: -1
skew: 0.33
type: snfs
Y0: -1000000000000000000000000000000000000
Y1: 1Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 9300001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 873628 x 873876
Total sieving time: 331.70 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 331.70 hours.
 --------- CPU info (if available) ----------

Apr 4, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(14·10¹³⁸+31)/9 = 1(5)₁₃₇9_<139> = 23 · 587 · 22085650154593_<14> · 214708517662039_<15> · C107

C107 = P38 · P70

P38 = 18889071044965985559683161450105284079_<38>

P70 = 1286321494635454249284329017256606479419057950477955932294681889062123_<70>

Number: 15559_138
N=24297418098835928184871286994621343003982194045684419344835498431243228852905498778636408028046235793839717
  ( 107 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=18889071044965985559683161450105284079 (pp38)
 r2=1286321494635454249284329017256606479419057950477955932294681889062123 (pp70)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 21.58 hours.
Scaled time: 14.57 units (timescale=0.675).
Factorization parameters were as follows:
name: 15559_138
n: 24297418098835928184871286994621343003982194045684419344835498431243228852905498778636408028046235793839717
m: 2000000000000000000000000000
c5: 875
c0: 62
skew: 0.59
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 2800001)
Primes: RFBsize:78498, AFBsize:63759, largePrimes:1746679 encountered
Relations: rels:1808224, finalFF:167624
Max relations in full relation-set: 28
Initial matrix: 142323 x 167624 with sparse part having weight 20269469.
Pruned matrix : 136875 x 137650 with weight 15512291.
Total sieving time: 20.76 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.59 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 21.58 hours.
 --------- CPU info (if available) ----------

Apr 4, 2008 (2nd)

By JMB / GMP-ECM

(14·10¹⁶⁶+31)/9 = 1(5)₁₆₅9_<167> = 14762153720019369394560342817_<29> · C139

C139 = P35 · C104

P35 = 25959036563720881399909794087532397_<35>

C104 = [40592633973664338092756074639611100697720162425602675161336639117666924326656515110040772765234343268291_<104>]

Apr 4, 2008

By Robert Backstrom / GGNFS, Msieve

(67·10¹⁶³+23)/9 = 7(4)₁₆₂7_<164> = 7 · 11 · 15981307 · 550172091423481695139_<21> · C135

C135 = P60 · P75

P60 = 173899319743099863715074733204526874599504106558134328664339_<60>

P75 = 632314053644234448964586908637373660241500036550939211425372049855075000713_<75>

Number: n
N=109958983792734326039438991504943363864512677413094518012785059431448235356759293336664332882078371346096185002361452719220446762673707
  ( 135 digits)
SNFS difficulty: 164 digits.
Divisors found:

Fri Apr  4 07:32:32 2008  prp60 factor: 173899319743099863715074733204526874599504106558134328664339
Fri Apr  4 07:32:32 2008  prp75 factor: 632314053644234448964586908637373660241500036550939211425372049855075000713
Fri Apr  4 07:32:32 2008  elapsed time 00:45:38 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 43.82 hours.
Scaled time: 36.68 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_7_4_162_7
n: 109958983792734326039438991504943363864512677413094518012785059431448235356759293336664332882078371346096185002361452719220446762673707
type: snfs
deg: 5
c5: 67000
c0: 23
skew: 0.20
m: 100000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2699990)
Primes: RFBsize:216816, AFBsize:217321, largePrimes:5672603 encountered
Relations: rels:5598931, finalFF:511786
Max relations in full relation-set: 28
Initial matrix: 434204 x 511786 with sparse part having weight 45127507.
Pruned matrix : 
Total sieving time: 43.62 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 43.82 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

7·10¹⁶³+1 = 7(0)₁₆₂1_<164> = 2621 · 637097 · 6177922939_<10> · 156791141329_<12> · C134

C134 = P51 · P84

P51 = 402780568113496127134113047287312945816114000773181_<51>

P84 = 107446665123360825440701365404164787206317314310967090805791720700790075639081056243_<84>

Number: n
N=43277428820287843704931976867461084748542006794075993513996138833643569977396426813266834171274514636681677977157534242400032147018983
  ( 134 digits)
SNFS difficulty: 163 digits.
Divisors found:

Fri Apr  4 12:59:40 2008  prp51 factor: 402780568113496127134113047287312945816114000773181
Fri Apr  4 12:59:40 2008  prp84 factor: 107446665123360825440701365404164787206317314310967090805791720700790075639081056243
Fri Apr  4 12:59:40 2008  elapsed time 00:46:52 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 46.82 hours.
Scaled time: 39.19 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_7_0_162_1
n: 43277428820287843704931976867461084748542006794075993513996138833643569977396426813266834171274514636681677977157534242400032147018983
type: snfs
deg: 5
c5: 7000
c0: 1
skew: 0.17
m: 100000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2800000)
Primes: RFBsize:216816, AFBsize:216861, largePrimes:5723566 encountered
Relations: rels:5651846, finalFF:500770
Max relations in full relation-set: 28
Initial matrix: 433744 x 500770 with sparse part having weight 45553627.
Pruned matrix : 406474 x 408706 with weight 33499165.
Total sieving time: 46.61 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 46.82 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(13·10¹⁶³+23)/9 = 1(4)₁₆₂7_<164> = 3517 · 18983905542455313683_<20> · C141

C141 = P57 · P84

P57 = 290489182949177909802781675636329039795637507570364531197_<57>

P84 = 744754172766735844931657694994085417458424028852613801213846101237458452241664067741_<84>

Number: n
N=216343031144999981427906166521244760111099649120079328867161315613682148972954519919802708175175124782467477196706782976510301435255515815977
  ( 141 digits)
SNFS difficulty: 164 digits.
Divisors found:

Fri Apr 04 22:01:13 2008  prp57 factor: 290489182949177909802781675636329039795637507570364531197
Fri Apr 04 22:01:13 2008  prp84 factor: 744754172766735844931657694994085417458424028852613801213846101237458452241664067741
Fri Apr 04 22:01:13 2008  elapsed time 01:07:56 (Msieve 1.34)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 59.80 hours.
Scaled time: 109.37 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_4_162_7
n: 216343031144999981427906166521244760111099649120079328867161315613682148972954519919802708175175124782467477196706782976510301435255515815977
skew: 0.28
deg: 5
c5: 13000
c0: 23
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4100293)
Primes: RFBsize:216816, AFBsize:217281, largePrimes:7819749 encountered
Relations: rels:7249599, finalFF:485822
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 59.59 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 59.80 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(22·10¹⁶⁵-1)/3 = 7(3)₁₆₅_<166> = 23 · 17497 · 274487009 · 25658674533179_<14> · C139

C139 = P65 · P75

P65 = 22933717666057774298302333628801575787136259295500785394358195651_<65>

P75 = 112818292849299160345823913937988573038591955291961894176315107848186283963_<75>

Number: n
N=2587342875772451627047024007058209064159419996689996703791353347801727846113147460534304001711336122904729486466052945321623131575397644913
  ( 139 digits)
SNFS difficulty: 166 digits.
Divisors found:

Sat Apr 05 00:36:54 2008  prp65 factor: 22933717666057774298302333628801575787136259295500785394358195651
Sat Apr 05 00:36:54 2008  prp75 factor: 112818292849299160345823913937988573038591955291961894176315107848186283963
Sat Apr 05 00:36:54 2008  elapsed time 01:27:54 (Msieve 1.34)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 61.02 hours.
Scaled time: 79.45 units (timescale=1.302).
Factorization parameters were as follows:
name: KA_7_3_165
n: 2587342875772451627047024007058209064159419996689996703791353347801727846113147460534304001711336122904729486466052945321623131575397644913
skew: 0.54
deg: 5
c5: 22
c0: -1
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2800247)
Primes: RFBsize:216816, AFBsize:216967, largePrimes:7383104 encountered
Relations: rels:6815983, finalFF:485019
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 60.76 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 61.02 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Apr 3, 2008 (5th)

By JMB / GMP-ECM

(14·10¹⁴⁸+31)/9 = 1(5)₁₄₇9_<149> = 9949 · 54403 · 826856108189_<12> · 64934003080483_<14> · C114

C114 = P34 · P81

P34 = 2499113539947715325949124365216803_<34>

P81 = 214188003419738864023748273782105619197066640540736946746378416198577330759441277_<81>

Apr 3, 2008 (4th)

By Sinkiti Sibata / GGNFS

(13·10¹⁶⁰+41)/9 = 1(4)₁₅₉9_<161> = 13177488726749_<14> · 107919830762963_<15> · 6948432863413003_<16> · C118

C118 = P44 · P74

P44 = 58318421562202336729024884964580815360748989_<44>

P74 = 25065380822971939726203162891930045767767595089719334854800459231611917481_<74>

Number: 14449_160
N=1461773445451219721817054132646300865765733841567085507878396932965774862914627039808990861227821796075443086622176709
  ( 118 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=58318421562202336729024884964580815360748989 (pp44)
 r2=25065380822971939726203162891930045767767595089719334854800459231611917481 (pp74)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 78.30 hours.
Scaled time: 52.85 units (timescale=0.675).
Factorization parameters were as follows:
name: 14449_160
n: 1461773445451219721817054132646300865765733841567085507878396932965774862914627039808990861227821796075443086622176709
m: 100000000000000000000000000000000
c5: 13
c0: 41
skew: 1.26
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3900001)
Primes: RFBsize:283146, AFBsize:282373, largePrimes:5738534 encountered
Relations: rels:5817356, finalFF:694775
Max relations in full relation-set: 28
Initial matrix: 565586 x 694775 with sparse part having weight 46693987.
Pruned matrix : 469450 x 472341 with weight 31381838.
Total sieving time: 68.01 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 9.75 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 78.30 hours.
 --------- CPU info (if available) ----------

(14·10¹²⁰+31)/9 = 1(5)₁₁₉9_<121> = 17 · 107 · 50466277 · C110

C110 = P49 · P62

P49 = 1421577012344853500890676274711460113354683750921_<49>

P62 = 11920134834947284852618265683350810943104485024229298831379833_<62>

Number: 15559_120
N=16945389665412174607218409292531530192930180494329638763325905364366947215583860888478225208800730066514576193
  ( 110 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=1421577012344853500890676274711460113354683750921 (pp49)
 r2=11920134834947284852618265683350810943104485024229298831379833 (pp62)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.59 hours.
Scaled time: 1.75 units (timescale=0.675).
Factorization parameters were as follows:
name: 15559_120
n: 16945389665412174607218409292531530192930180494329638763325905364366947215583860888478225208800730066514576193
m: 1000000000000000000000000
c5: 14
c0: 31
skew: 1.17
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:63629, largePrimes:2164814 encountered
Relations: rels:2280226, finalFF:244401
Max relations in full relation-set: 28
Initial matrix: 112793 x 244401 with sparse part having weight 22393749.
Pruned matrix : 86473 x 87100 with weight 5524265.
Total sieving time: 2.35 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.59 hours.
 --------- CPU info (if available) ----------

(14·10¹²⁹+31)/9 = 1(5)₁₂₈9_<130> = 331 · 647 · 1181 · 320796426397_<12> · C110

C110 = P43 · P67

P43 = 4707523717355474776435082396044989377741827_<43>

P67 = 4072689638852448957226819815433219768108727767837548269928546344633_<67>

Number: 15559_129
N=19172283068325806568537723586178607998494065432808843189221587559772708200225606297331105435664949712841064491
  ( 110 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=4707523717355474776435082396044989377741827 (pp43)
 r2=4072689638852448957226819815433219768108727767837548269928546344633 (pp67)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 6.23 hours.
Scaled time: 4.21 units (timescale=0.675).
Factorization parameters were as follows:
name: 15559_129
n: 19172283068325806568537723586178607998494065432808843189221587559772708200225606297331105435664949712841064491
m: 100000000000000000000000000
c5: 7
c0: 155
skew: 1.86
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1050001)
Primes: RFBsize:63951, AFBsize:63449, largePrimes:1489289 encountered
Relations: rels:1474945, finalFF:157286
Max relations in full relation-set: 28
Initial matrix: 127465 x 157286 with sparse part having weight 12062069.
Pruned matrix : 118994 x 119695 with weight 7467431.
Total sieving time: 5.86 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.24 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 6.23 hours.
 --------- CPU info (if available) ----------

Apr 3, 2008 (3rd)

By Robert Backstrom / Msieve, GMP-ECM, GGNFS

(14·10¹⁵⁸+31)/9 = 1(5)₁₅₇9_<159> = 3 · 53 · 127 · 7280174849_<10> · 109124535209_<12> · 21948898589324162190187_<23> · 33736169926864163126149367_<26> · C86

C86 = P41 · P45

P41 = 18462693075720592159694382676395345089159_<41>

P45 = 709278681425545386232340021289077175661076813_<45>

Thu Apr 03 02:41:55 2008  
Thu Apr 03 02:41:55 2008  
Thu Apr 03 02:41:55 2008  Msieve v. 1.33
Thu Apr 03 02:41:55 2008  random seeds: 42b0e064 b812c0af
Thu Apr 03 02:41:55 2008  factoring 13095194600311648587363642228835280059379349527210239503556304027577051905401432570267 (86 digits)
Thu Apr 03 02:41:56 2008  searching for 15-digit factors
Thu Apr 03 02:41:57 2008  commencing quadratic sieve (86-digit input)
Thu Apr 03 02:41:57 2008  using multiplier of 3
Thu Apr 03 02:41:57 2008  using 64kb Opteron sieve core
Thu Apr 03 02:41:57 2008  sieve interval: 6 blocks of size 65536
Thu Apr 03 02:41:57 2008  processing polynomials in batches of 17
Thu Apr 03 02:41:57 2008  using a sieve bound of 1442509 (54992 primes)
Thu Apr 03 02:41:57 2008  using large prime bound of 115400720 (26 bits)
Thu Apr 03 02:41:57 2008  using double large prime bound of 325068826146400 (41-49 bits)
Thu Apr 03 02:41:57 2008  using trial factoring cutoff of 49 bits
Thu Apr 03 02:41:57 2008  polynomial 'A' values have 11 factors
Thu Apr 03 03:20:45 2008  55145 relations (16138 full + 39007 combined from 573077 partial), need 55088
Thu Apr 03 03:20:45 2008  begin with 589214 relations
Thu Apr 03 03:20:46 2008  reduce to 130017 relations in 10 passes
Thu Apr 03 03:20:46 2008  attempting to read 130017 relations
Thu Apr 03 03:20:47 2008  recovered 130017 relations
Thu Apr 03 03:20:47 2008  recovered 111360 polynomials
Thu Apr 03 03:20:47 2008  attempting to build 55144 cycles
Thu Apr 03 03:20:47 2008  found 55143 cycles in 5 passes
Thu Apr 03 03:20:48 2008  distribution of cycle lengths:
Thu Apr 03 03:20:48 2008     length 1 : 16138
Thu Apr 03 03:20:48 2008     length 2 : 11055
Thu Apr 03 03:20:48 2008     length 3 : 9584
Thu Apr 03 03:20:48 2008     length 4 : 7023
Thu Apr 03 03:20:48 2008     length 5 : 4907
Thu Apr 03 03:20:48 2008     length 6 : 2885
Thu Apr 03 03:20:48 2008     length 7 : 1679
Thu Apr 03 03:20:48 2008     length 9+: 1872
Thu Apr 03 03:20:48 2008  largest cycle: 18 relations
Thu Apr 03 03:20:48 2008  matrix is 54992 x 55143 (12.0 MB) with weight 2919220 (52.94/col)
Thu Apr 03 03:20:48 2008  sparse part has weight 2919220 (52.94/col)
Thu Apr 03 03:20:49 2008  filtering completed in 4 passes
Thu Apr 03 03:20:49 2008  matrix is 50096 x 50160 (11.0 MB) with weight 2691005 (53.65/col)
Thu Apr 03 03:20:49 2008  sparse part has weight 2691005 (53.65/col)
Thu Apr 03 03:20:50 2008  saving the first 48 matrix rows for later
Thu Apr 03 03:20:50 2008  matrix is 50048 x 50160 (6.5 MB) with weight 2016906 (40.21/col)
Thu Apr 03 03:20:50 2008  sparse part has weight 1390909 (27.73/col)
Thu Apr 03 03:20:50 2008  matrix includes 64 packed rows
Thu Apr 03 03:20:50 2008  using block size 20064 for processor cache size 512 kB
Thu Apr 03 03:20:50 2008  commencing Lanczos iteration
Thu Apr 03 03:20:50 2008  memory use: 6.8 MB
Thu Apr 03 03:21:10 2008  lanczos halted after 792 iterations (dim = 50039)
Thu Apr 03 03:21:10 2008  recovered 12 nontrivial dependencies
Thu Apr 03 03:21:11 2008  prp41 factor: 18462693075720592159694382676395345089159
Thu Apr 03 03:21:11 2008  prp45 factor: 709278681425545386232340021289077175661076813
Thu Apr 03 03:21:11 2008  elapsed time 00:39:16

(14·10¹²²+31)/9 = 1(5)₁₂₁9_<123> = 3 · 157 · C120

C120 = P35 · P86

P35 = 10603836885495071034474476095145129_<35>

P86 = 31145949892586395406949575512425987474943569710446787657049654966993983919833639672201_<86>

(14·10¹⁴⁷+31)/9 = 1(5)₁₄₆9_<148> = 781077391688879_<15> · C133

C133 = P35 · P98

P35 = 48666565188027890092729966818877889_<35>

P98 = 40922368653085930485059904571405162735697559903875161667841200639610533122749207940850079133777289_<98>

(14·10¹⁵⁰+31)/9 = 1(5)₁₄₉9_<151> = 39569 · 18139119101745599_<17> · C130

C130 = P33 · P97

P33 = 335061822392136720484534754789419_<33>

P97 = 6468287466652218202909758335139916011634361647250202124939424960816497412784711946727546397178331_<97>

(14·10¹⁴⁰+31)/9 = 1(5)₁₃₉9_<141> = 3 · 233 · 241 · 5903 · C132

C132 = P40 · P42 · P51

P40 = 3145814278159836132977122915782215478379_<40>

P42 = 136993138600366227200200711944926574507283_<42>

P51 = 362983287496566443500422296301603020385805008326731_<51>

Number: n
N=156429452288643464911081002531058371361509167836384377115150014761470851983993732172191342450556465613504105350691617341742398323867
  ( 132 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=3145814278159836132977122915782215478379 (pp40)
 r2=136993138600366227200200711944926574507283 (pp42)
 r3=362983287496566443500422296301603020385805008326731 (pp51)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.22 hours.
Scaled time: 12.66 units (timescale=1.752).
Factorization parameters were as follows:
name: KA_1_5_139_9
n: 156429452288643464911081002531058371361509167836384377115150014761470851983993732172191342450556465613504105350691617341742398323867
type: snfs
skew: 1.17
deg: 5
c5: 14
c0: 31
m: 10000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 950001)
Primes: RFBsize:148933, AFBsize:148581, largePrimes:5725582 encountered
Relations: rels:5089339, finalFF:358359
Max relations in full relation-set: 28
Initial matrix: 297580 x 358359 with sparse part having weight 19209340.
Pruned matrix : 245434 x 246985 with weight 10431835.
Total sieving time: 6.09 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.87 hours.
Total square root time: 0.12 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 7.22 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Apr 3, 2008 (2nd)

By Jo Yeong Uk / GMP-ECM, GGNFS

(14·10¹⁵⁵+31)/9 = 1(5)₁₅₄9_<156> = 3 · 54905849 · 154308125187053473_<18> · C130

C130 = P31 · P99

P31 = 7674360746381837411521751272723_<31>

P99 = 797470552787996185165803170580988931064736161642896696883978483018377247210575889135871920756199543_<99>

(14·10¹⁴⁶+31)/9 = 1(5)₁₄₅9_<147> = 3 · 83 · 2017 · 157915345952665151_<18> · 585854257405781501_<18> · C106

C106 = P39 · P67

P39 = 788446662848643115165841844345577532321_<39>

P67 = 4246137320921946481553619461943257958828954529607621070878133125813_<67>

Number: 15559_146
N=3347852800677986669372738417402636472582245561438340610458401501686074563594432546426620601309782766901973
  ( 106 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=788446662848643115165841844345577532321 (pp39)
 r2=4246137320921946481553619461943257958828954529607621070878133125813 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 9.94 hours.
Scaled time: 21.33 units (timescale=2.145).
Factorization parameters were as follows:
n: 3347852800677986669372738417402636472582245561438340610458401501686074563594432546426620601309782766901973
m: 100000000000000000000000000000
c5: 140
c0: 31
skew: 0.74
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1575001)
Primes: RFBsize:135072, AFBsize:134614, largePrimes:3693349 encountered
Relations: rels:3686817, finalFF:304236
Max relations in full relation-set: 28
Initial matrix: 269753 x 304236 with sparse part having weight 27282670.
Pruned matrix : 256253 x 257665 with weight 20349781.
Total sieving time: 9.58 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.27 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 9.94 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.33 BogoMIPS (lpj=2407668)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Apr 3, 2008

By Jo Yeong Uk / GGNFS, GMP-ECM

(14·10¹⁰⁴+31)/9 = 1(5)₁₀₃9_<105> = 3 · 17 · 415039 · 960259 · C91

C91 = P31 · P61

P31 = 6123112702612974422656257278677_<31>

P61 = 1249872758938303891586631981770280688173300314576830254317117_<61>

Number: 15559_104
N=7653111766905052625714127478056069869442270615205235958642237021066340455316087033400214209
  ( 91 digits)
SNFS difficulty: 105 digits.
Divisors found:
 r1=6123112702612974422656257278677 (pp31)
 r2=1249872758938303891586631981770280688173300314576830254317117 (pp61)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.41 hours.
Scaled time: 0.87 units (timescale=2.135).
Factorization parameters were as follows:
n: 7653111766905052625714127478056069869442270615205235958642237021066340455316087033400214209
m: 1000000000000000000000
c5: 7
c0: 155
skew: 1.86
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 260001)
Primes: RFBsize:30757, AFBsize:30265, largePrimes:962732 encountered
Relations: rels:875648, finalFF:78657
Max relations in full relation-set: 28
Initial matrix: 61087 x 78657 with sparse part having weight 3216591.
Pruned matrix : 52909 x 53278 with weight 1608056.
Total sieving time: 0.39 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,105,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.41 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.33 BogoMIPS (lpj=2407668)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

(14·10¹⁰⁹+31)/9 = 1(5)₁₀₈9_<110> = 19 · 55335037 · C101

C101 = P46 · P55

P46 = 9501681575912170966662527503987525172261786003_<46>

P55 = 1557152862759509908452930886474382752596857671286405051_<55>

Number: 15559_109
N=14795570666960928585241814337133228280279517122079409846942244753399146743476713502376399618540301153
  ( 101 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=9501681575912170966662527503987525172261786003 (pp46)
 r2=1557152862759509908452930886474382752596857671286405051 (pp55)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.67 hours.
Scaled time: 1.44 units (timescale=2.146).
Factorization parameters were as follows:
n: 14795570666960928585241814337133228280279517122079409846942244753399146743476713502376399618540301153
m: 10000000000000000000000
c5: 7
c0: 155
skew: 1.86
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 320001)
Primes: RFBsize:30757, AFBsize:30265, largePrimes:1063994 encountered
Relations: rels:991255, finalFF:96554
Max relations in full relation-set: 28
Initial matrix: 61087 x 96554 with sparse part having weight 4661689.
Pruned matrix : 51141 x 51510 with weight 1737634.
Total sieving time: 0.65 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.67 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.33 BogoMIPS (lpj=2407668)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

(14·10¹⁸⁰+31)/9 = 1(5)₁₇₉9_<181> = C181

C181 = P33 · P148

P33 = 224540162641475926200940032590041_<33>

P148 = 6927738615916639493795372224802362230619590881114688329834073792904549303518808372499279890767099431963254595662524485909980595129219530776688881599_<148>

(14·10¹¹⁰+31)/9 = 1(5)₁₀₉9_<111> = 3 · 241 · 4723 · C104

C104 = P46 · P59

P46 = 1303282840472408036468985773035703330564633891_<46>

P59 = 34953494903639795656060613382861445837052916896715844002181_<59>

Number: 15559_110
N=45554290122453511114807516366761624584426921010585482934533181273112904583513232105843701083030470516271
  ( 104 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=1303282840472408036468985773035703330564633891 (pp46)
 r2=34953494903639795656060613382861445837052916896715844002181 (pp59)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.60 hours.
Scaled time: 1.27 units (timescale=2.130).
Factorization parameters were as follows:
n: 45554290122453511114807516366761624584426921010585482934533181273112904583513232105843701083030470516271
m: 10000000000000000000000
c5: 14
c0: 31
skew: 1.17
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 300001)
Primes: RFBsize:30757, AFBsize:30605, largePrimes:979923 encountered
Relations: rels:884896, finalFF:73064
Max relations in full relation-set: 28
Initial matrix: 61428 x 73064 with sparse part having weight 3324838.
Pruned matrix : 56970 x 57341 with weight 2019227.
Total sieving time: 0.57 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.60 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.33 BogoMIPS (lpj=2407668)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

(14·10¹¹²+31)/9 = 1(5)₁₁₁9_<113> = 277 · 1367 · 332573 · C102

C102 = P37 · P65

P37 = 6092182038573200834431033938985160341_<37>

P65 = 20275771240622793997064761967146282229636836482089466349375858957_<65>

Number: 15559_112
N=123523689370341250516149913321329516008019385631608532341465796759702347383365229527627429013246024337
  ( 102 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=6092182038573200834431033938985160341 (pp37)
 r2=20275771240622793997064761967146282229636836482089466349375858957 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.81 hours.
Scaled time: 1.72 units (timescale=2.135).
Factorization parameters were as follows:
n: 123523689370341250516149913321329516008019385631608532341465796759702347383365229527627429013246024337
m: 20000000000000000000000
c5: 175
c0: 124
skew: 0.93
type: snfs
Factor base limits: 450000/450000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [225000, 375001)
Primes: RFBsize:37706, AFBsize:37740, largePrimes:1287788 encountered
Relations: rels:1247576, finalFF:110750
Max relations in full relation-set: 28
Initial matrix: 75513 x 110750 with sparse part having weight 8140654.
Pruned matrix : 67086 x 67527 with weight 3384017.
Total sieving time: 0.77 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,450000,450000,25,25,44,44,2.3,2.3,25000
total time: 0.81 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.33 BogoMIPS (lpj=2407668)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

(14·10¹¹⁵+31)/9 = 1(5)₁₁₄9_<116> = 3279678159671671397_<19> · C97

C97 = P39 · P59

P39 = 467835898086147901719587583613501434971_<39>

P59 = 10138197686463485465002382573752151496026773591252758195457_<59>

Number: 15559_115
N=4743012819621551624636543784883103395485170841183928305043751488713980500978238376905549993126747
  ( 97 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=467835898086147901719587583613501434971 (pp39)
 r2=10138197686463485465002382573752151496026773591252758195457 (pp59)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.75 hours.
Scaled time: 1.60 units (timescale=2.122).
Factorization parameters were as follows:
n: 4743012819621551624636543784883103395485170841183928305043751488713980500978238376905549993126747
m: 100000000000000000000000
c5: 14
c0: 31
skew: 1.17
type: snfs
Factor base limits: 450000/450000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [225000, 375001)
Primes: RFBsize:37706, AFBsize:37565, largePrimes:1292652 encountered
Relations: rels:1256566, finalFF:114016
Max relations in full relation-set: 28
Initial matrix: 75337 x 114016 with sparse part having weight 8559587.
Pruned matrix : 66510 x 66950 with weight 3395592.
Total sieving time: 0.71 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,450000,450000,25,25,44,44,2.3,2.3,25000
total time: 0.75 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init)
Calibrating delay using timer specific routine.. 4815.33 BogoMIPS (lpj=2407668)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Apr 2, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(14·10¹⁶³+13)/9 = 1(5)₁₆₂7_<164> = 88001 · C159

C159 = P59 · P100

P59 = 49844159806140022457656033933584078006954093974713327381627_<59>

P100 = 3546366690789890875339022615239880757403094877861401298222832779627443194683536889140462772150874591_<100>

Number: n
N=176765668066903280139493364343081959927223049233026392376854303423319684498534738872916848167129413933427524182174697509750520511761861291980267900996074539557
  ( 159 digits)
SNFS difficulty: 164 digits.
Divisors found:

Thu Apr 03 01:28:54 2008  prp59 factor: 49844159806140022457656033933584078006954093974713327381627
Thu Apr 03 01:28:54 2008  prp100 factor: 3546366690789890875339022615239880757403094877861401298222832779627443194683536889140462772150874591
Thu Apr 03 01:28:54 2008  elapsed time 02:02:23 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 70.94 hours.
Scaled time: 124.29 units (timescale=1.752).
Factorization parameters were as follows:
name: KA_1_5_162_7
n: 176765668066903280139493364343081959927223049233026392376854303423319684498534738872916848167129413933427524182174697509750520511761861291980267900996074539557
type: snfs
skew: 0.49
deg: 5
c5: 875
c0: 26
m: 200000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3500383)
Primes: RFBsize:216816, AFBsize:217331, largePrimes:7559625 encountered
Relations: rels:6970216, finalFF:449362
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 70.68 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 70.94 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Apr 2, 2008 (2nd)

The factor table of 155...559 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Apr 2, 2008

By Robert Backstrom / GMP-ECM

(13·10¹⁷⁷+41)/9 = 1(4)₁₇₆9_<178> = 3 · 7 · 31 · 23894417 · 387048321879097_<15> · 102901558413798602757536612189167_<33> · C121

C121 = P45 · P76

P45 = 332959311000289726554119341499581353472911353_<45>

P76 = 7002370898982811465985212519192627896899356817719697064270507631837030185901_<76>

Apr 1, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(13·10¹⁶⁵+41)/9 = 1(4)₁₆₄9_<166> = 3² · 7³ · 17 · 311 · C158

C158 = P35 · P124

P35 = 16314950226194202535821847388584579_<35>

P124 = 5424617863803991143762455161408372822546229535063185548695922017790727738160207197999393097074876903892876721001455128856499_<124>

(14·10¹⁵²+13)/9 = 1(5)₁₅₁7_<153> = 63788093921_<11> · C142

C142 = P54 · P89

P54 = 173460172689027899665086107807131828832709509246937443_<54>

P89 = 14058731181313703042304048180548635368310516923726637061756330334276648276290706574486519_<89>

Number: n
N=2438629938499296133491619142929611093991847945494523527378368041823708212062716661647080595097808104570147460693796634688057769776161039830917
  ( 142 digits)
SNFS difficulty: 153 digits.
Divisors found:

Tue Apr 01 07:40:21 2008  prp54 factor: 173460172689027899665086107807131828832709509246937443
Tue Apr 01 07:40:21 2008  prp89 factor: 14058731181313703042304048180548635368310516923726637061756330334276648276290706574486519
Tue Apr 01 07:40:21 2008  elapsed time 00:53:45 (Msieve 1.33)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 29.91 hours.
Scaled time: 39.03 units (timescale=1.305).
Factorization parameters were as follows:
name: KA_1_5_151_7
n: 2438629938499296133491619142929611093991847945494523527378368041823708212062716661647080595097808104570147460693796634688057769776161039830917
skew: 0.39
deg: 5
c5: 1400
c0: 13
m: 1000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1200000
)
Primes: RFBsize:203362, AFBsize:203057, largePrimes:7157192 encountered
Relations: rels:6740859, finalFF:571144
Max relations in full relation-set: 28
Initial matrix: 406486 x 571144 with sparse part having weight 41884449.
Pruned matrix : 277790 x 279886 with weight 22751566.
Total sieving time: 27.09 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 2.62 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 29.91 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(14·10¹⁶²-23)/9 = 1(5)₁₆₁3_<163> = 17² · 30817 · 372124977656909_<15> · C141

C141 = P48 · P93

P48 = 472035414783518016243135774561543103921057694177_<48>

P93 = 994337733365949129428898253056275129686355332723981707011105870757951405338818661021405862917_<93>

Number: n
N=469362624404298939135494109270052332408386538926431489548931993834927472197048244992417935599677767202896447674317093792319483188200971134309
  ( 141 digits)
SNFS difficulty: 163 digits.
Divisors found:

Tue Apr  1 16:01:03 2008  prp48 factor: 472035414783518016243135774561543103921057694177
Tue Apr  1 16:01:03 2008  prp93 factor: 994337733365949129428898253056275129686355332723981707011105870757951405338818661021405862917
Tue Apr  1 16:01:03 2008  elapsed time 00:46:15 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 37.68 hours.
Scaled time: 31.61 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_1_5_161_3
n: 469362624404298939135494109270052332408386538926431489548931993834927472197048244992417935599677767202896447674317093792319483188200971134309
type: snfs
deg: 5
c5: 1400
c0: -23
skew: 0.44
m: 100000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2400001)
Primes: RFBsize:216816, AFBsize:216901, largePrimes:5556168 encountered
Relations: rels:5418684, finalFF:465647
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 37.50 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 37.68 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(11·10¹⁶⁵+61)/9 = 1(2)₁₆₄9_<166> = 409 · 80599 · C158

C158 = P50 · P54 · P55

P50 = 84487268400846963130771961910946989225423105211073_<50>

P54 = 404346314135854308052527269390940411387810076224120869_<54>

P55 = 1085306631461643435651060404463146659487393443172166287_<55>

Number: n
N=37076370572108520285117694169011671267321814898181595809391309168633542846173451775619238671177620592167679409414133382357732851260970228149682256009783901419
  ( 158 digits)
SNFS difficulty: 166 digits.
Divisors found:

Wed Apr  2 00:28:00 2008  prp50 factor: 84487268400846963130771961910946989225423105211073
Wed Apr  2 00:28:00 2008  prp54 factor: 404346314135854308052527269390940411387810076224120869
Wed Apr  2 00:28:00 2008  prp55 factor: 1085306631461643435651060404463146659487393443172166287
Wed Apr  2 00:28:00 2008  elapsed time 00:53:00 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 45.93 hours.
Scaled time: 38.49 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_1_2_164_9
n: 37076370572108520285117694169011671267321814898181595809391309168633542846173451775619238671177620592167679409414133382357732851260970228149682256009783901419
type: snfs
deg: 5
c5: 11
c0: 61
skew: 1.41
m: 1000000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2900001)
Primes: RFBsize:216816, AFBsize:216278, largePrimes:5612922 encountered
Relations: rels:5482602, finalFF:460483
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 45.74 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 45.93 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

March 2008

Mar 31, 2008 (3rd)

By Jo Yeong Uk / GMP-ECM, Msieve

(14·10¹⁷⁴+13)/9 = 1(5)₁₇₃7_<175> = 3² · 73 · 1693 · 93923 · 1821722621_<10> · 1002239634413_<13> · 403374339915168794569779581_<27> · C116

C116 = P32 · P42 · P43

P32 = 31629929246645939988995179923731_<32>

P42 = 169880476199414315120627039721035669406193_<42>

P43 = 3762594880955972138233267550313660219155021_<43>

Mon Mar 31 01:13:54 2008  
Mon Mar 31 01:13:54 2008  
Mon Mar 31 01:13:54 2008  Msieve v. 1.32
Mon Mar 31 01:13:54 2008  random seeds: 94f519b9 93265061
Mon Mar 31 01:13:54 2008  factoring 639191410122279163148017701746752433185828061621198481956163067234502766843284445053 (84 digits)
Mon Mar 31 01:13:55 2008  no P-1/P+1/ECM available, skipping
Mon Mar 31 01:13:55 2008  commencing quadratic sieve (84-digit input)
Mon Mar 31 01:13:55 2008  using multiplier of 53
Mon Mar 31 01:13:55 2008  using 32kb Intel Core sieve core
Mon Mar 31 01:13:55 2008  sieve interval: 12 blocks of size 32768
Mon Mar 31 01:13:55 2008  processing polynomials in batches of 17
Mon Mar 31 01:13:55 2008  using a sieve bound of 1406651 (53824 primes)
Mon Mar 31 01:13:55 2008  using large prime bound of 119565335 (26 bits)
Mon Mar 31 01:13:55 2008  using double large prime bound of 346488982123175 (41-49 bits)
Mon Mar 31 01:13:55 2008  using trial factoring cutoff of 49 bits
Mon Mar 31 01:13:55 2008  polynomial 'A' values have 11 factors
Mon Mar 31 01:38:27 2008  54052 relations (16129 full + 37923 combined from 570254 partial), need 53920
Mon Mar 31 01:38:27 2008  begin with 586383 relations
Mon Mar 31 01:38:28 2008  reduce to 126153 relations in 10 passes
Mon Mar 31 01:38:28 2008  attempting to read 126153 relations
Mon Mar 31 01:38:28 2008  recovered 126153 relations
Mon Mar 31 01:38:28 2008  recovered 103827 polynomials
Mon Mar 31 01:38:29 2008  attempting to build 54052 cycles
Mon Mar 31 01:38:29 2008  found 54052 cycles in 5 passes
Mon Mar 31 01:38:29 2008  distribution of cycle lengths:
Mon Mar 31 01:38:29 2008     length 1 : 16129
Mon Mar 31 01:38:29 2008     length 2 : 11039
Mon Mar 31 01:38:29 2008     length 3 : 9492
Mon Mar 31 01:38:29 2008     length 4 : 6896
Mon Mar 31 01:38:29 2008     length 5 : 4448
Mon Mar 31 01:38:29 2008     length 6 : 2780
Mon Mar 31 01:38:29 2008     length 7 : 1585
Mon Mar 31 01:38:29 2008     length 9+: 1683
Mon Mar 31 01:38:29 2008  largest cycle: 17 relations
Mon Mar 31 01:38:29 2008  matrix is 53824 x 54052 with weight 2770048 (avg 51.25/col)
Mon Mar 31 01:38:29 2008  filtering completed in 3 passes
Mon Mar 31 01:38:29 2008  matrix is 48951 x 49015 with weight 2526076 (avg 51.54/col)
Mon Mar 31 01:38:30 2008  saving the first 48 matrix rows for later
Mon Mar 31 01:38:30 2008  matrix is 48903 x 49015 with weight 1850677 (avg 37.76/col)
Mon Mar 31 01:38:30 2008  matrix includes 64 packed rows
Mon Mar 31 01:38:30 2008  commencing Lanczos iteration
Mon Mar 31 01:39:09 2008  lanczos halted after 774 iterations (dim = 48897)
Mon Mar 31 01:39:09 2008  recovered 13 nontrivial dependencies
Mon Mar 31 01:39:09 2008  prp42 factor: 169880476199414315120627039721035669406193
Mon Mar 31 01:39:09 2008  prp43 factor: 3762594880955972138233267550313660219155021
Mon Mar 31 01:39:09 2008  elapsed time 00:25:15

Mar 31, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(14·10¹⁵⁰+13)/9 = 1(5)₁₄₉7_<151> = 3 · 73 · 197 · 557 · 176419 · 311807 · C133

C133 = P47 · P86

P47 = 14358513758759727537788034211482912833199697379_<47>

P86 = 81955722749024612832935938121912440352553752416715091318119876776484248323691661939801_<86>

Number: n
N=1176762372700967503894089274669101300884685882156992693160611125133501836249059891526266152790525198162083125242864944859765315481579
  ( 133 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=14358513758759727537788034211482912833199697379 (pp47)
 r2=81955722749024612832935938121912440352553752416715091318119876776484248323691661939801 (pp86)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.00 hours.
Scaled time: 27.51 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_1_5_149_7
n: 1176762372700967503894089274669101300884685882156992693160611125133501836249059891526266152790525198162083125242864944859765315481579
skew: 0.99
deg: 5
c5: 14
c0: 13
m: 1000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:183072, AFBsize:182921, largePrimes:6875726 encountered
Relations: rels:6448717, finalFF:540389
Max relations in full relation-set: 28
Initial matrix: 366059 x 540389 with sparse part having weight 38593507.
Pruned matrix : 232412 x 234306 with weight 19896749.
Total sieving time: 17.18 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.60 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 19.00 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(14·10¹⁵⁹+13)/9 = 1(5)₁₅₈7_<160> = 3 · 28901 · 517487 · C149

C149 = P63 · P86

P63 = 554744215891826596967898958649652091064445903153743400082444519_<63>

P86 = 62497000567154822830083056990318365077569268883257990021576401794532332846554110732723_<86>

Number: n
N=34669849575217344310845040652106352293609204790812820723875869971786291483583767823534769101797762193083626549678947507787187663376379745032085295237
  ( 149 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=554744215891826596967898958649652091064445903153743400082444519 (pp63)
 r2=62497000567154822830083056990318365077569268883257990021576401794532332846554110732723 (pp86)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 29.54 hours.
Scaled time: 53.85 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_1_5_158_7
n: 34669849575217344310845040652106352293609204790812820723875869971786291483583767823534769101797762193083626549678947507787187663376379745032085295237
skew: 1.56
deg: 5
c5: 7
c0: 65
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1900001)
Primes: RFBsize:203362, AFBsize:203982, largePrimes:7130306 encountered
Relations: rels:6561429, finalFF:456380
Max relations in full relation-set: 48
Initial matrix: 407409 x 456380 with sparse part having weight 44465696.
Pruned matrix : 375407 x 377508 with weight 31102632.
Total sieving time: 27.88 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.43 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 29.54 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(14·10¹⁶⁰+13)/9 = 1(5)₁₅₉7_<161> = 61 · 10139 · 17681143 · C148

C148 = P45 · P103

P45 = 176720868675475223470096867570916437052715191_<45>

P103 = 8049379325259462249231277994447239129423049602136274705815379461742465805843495476803214658460885605691_<103>

Number: n
N=1422493306658262792422596582282164491360765077603258821754623045986835929330369940044454657354844441330750682548671902495714714097457993700151751981
  ( 148 digits)
SNFS difficulty: 161 digits.
Divisors found:

Mon Mar 31 18:59:06 2008  prp45 factor: 176720868675475223470096867570916437052715191
Mon Mar 31 18:59:06 2008  prp103 factor: 8049379325259462249231277994447239129423049602136274705815379461742465805843495476803214658460885605691
Mon Mar 31 18:59:06 2008  elapsed time 00:50:23 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 30.71 hours.
Scaled time: 56.16 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_5_159_7
n: 1422493306658262792422596582282164491360765077603258821754623045986835929330369940044454657354844441330750682548671902495714714097457993700151751981
skew: 0.99
deg: 5
c5: 14
c0: 13
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100277)
Primes: RFBsize:203362, AFBsize:202952, largePrimes:7188501 encountered
Relations: rels:6611896, finalFF:448791
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 30.53 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 30.71 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(14·10¹⁶⁵-23)/9 = 1(5)₁₆₄3_<166> = 1081741 · 348427632923_<12> · C148

C148 = P39 · P109

P39 = 535728913589613419728258074511925624737_<39>

P109 = 7703792187315390144299929098071704967894750175677556891822468858120439691344477047932722475841300620157500383_<109>

Mar 31, 2008

By matsui / GGNFS

3·10¹⁷⁰-7 = 2(9)₁₆₉3_<171> = 571 · 19364771 · C161

C161 = P46 · P115

P46 = 6500447580664317282363738571189216214014916119_<46>

P115 = 4173779680365580296879466841090799172626675464658891545229584269857535434533778203229820960806843647214822728845567_<115>

N=27131436025458323930591267505429410259473495251355363977569652855593983278520297559202448651242915986462611185758700258775413350613530637554314092810703209994473
  ( 161 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=6500447580664317282363738571189216214014916119 (pp46)
 r2=4173779680365580296879466841090799172626675464658891545229584269857535434533778203229820960806843647214822728845567 (pp115)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 116.18 hours.
Scaled time: 98.99 units (timescale=0.852).
Factorization parameters were as follows:
n: 27131436025458323930591267505429410259473495251355363977569652855593983278520297559202448651242915986462611185758700258775413350613530637554314092810703209994473
m: 10000000000000000000000000000000000
c5: 3
c0: -7
skew: 1.18
type: snfs

Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 7100001)
Primes: RFBsize:412849, AFBsize:411971, largePrimes:6063193 encountered
Relations: rels:6355607, finalFF:953328
Max relations in full relation-set: 28
Initial matrix: 824885 x 953328 with sparse part having weight 55798413.
Pruned matrix : 718666 x 722854 with weight 40153351.
Total sieving time: 107.72 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 8.05 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 116.18 hours.

Mar 30, 2008

By Jo Yeong Uk / GGNFS

(14·10¹⁵⁹-23)/9 = 1(5)₁₅₈3_<160> = 2360483 · 226593244838333_<15> · 118365524892972602913743693_<27> · C113

C113 = P52 · P62

P52 = 2430749538295306145725728141599656700945070902478673_<52>

P62 = 10108163321139107412078827980136296192052017344921530333358643_<62>

Number: 15553_159
N=24570413325872433726374752132935798567129323835655643445013749975132033066760666479547157867771337118765767720739
  ( 113 digits)
Divisors found:
 r1=2430749538295306145725728141599656700945070902478673 (pp52)
 r2=10108163321139107412078827980136296192052017344921530333358643 (pp62)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 19.76 hours.
Scaled time: 36.72 units (timescale=1.858).
Factorization parameters were as follows:
name: 15553_159
n: 24570413325872433726374752132935798567129323835655643445013749975132033066760666479547157867771337118765767720739
skew: 21469.36
# norm 6.53e+14
c5: 43920
c4: -1018208888
c3: -52825621881145
c2: 440927432653850745
c1: 9501511920375097228487
c0: -45005353793894983316532848
# alpha -4.95
Y1: 684329137657
Y0: -3544462736890836314475
# Murphy_E 7.69e-10
# M 19596200183058475987666150282800979262971493155179127731599566306585118493722288584774250903399448011868899771762
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1400000, 2380001)
Primes: RFBsize:203362, AFBsize:203762, largePrimes:7714693 encountered
Relations: rels:7680934, finalFF:595056
Max relations in full relation-set: 28
Initial matrix: 407203 x 595056 with sparse part having weight 57185218.
Pruned matrix : 284718 x 286818 with weight 34334574.
Polynomial selection time: 1.06 hours.
Total sieving time: 17.98 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.48 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000
total time: 19.76 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178324k/8912896k available (2439k kernel code, 208016k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 4812.94 BogoMIPS (lpj=2406472)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405149)
Calibrating delay using timer specific routine.. 4809.88 BogoMIPS (lpj=2404940)
Calibrating delay using timer specific routine.. 4918.32 BogoMIPS (lpj=2459163)

Mar 30, 2008

By Sinkiti Sibata / GGNFS

(13·10¹⁵¹+41)/9 = 1(4)₁₅₀9_<152> = 293 · 313 · 1888625094100861_<16> · C131

C131 = P48 · P84

P48 = 229099467826487034018759913891943497136975872769_<48>

P84 = 364014806146565362202173145442854541103475488915524144605594396975532850513975154329_<84>

Number: 14449_151
N=83395598369139965832168475774983316304583398622039903708156716045086640578730352860276260120758099296926726038305105508796243567001
  ( 131 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=229099467826487034018759913891943497136975872769 (pp48)
 r2=364014806146565362202173145442854541103475488915524144605594396975532850513975154329 (pp84)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 44.48 hours.
Scaled time: 30.03 units (timescale=0.675).
Factorization parameters were as follows:
name: 14449_151
n: 83395598369139965832168475774983316304583398622039903708156716045086640578730352860276260120758099296926726038305105508796243567001
m: 1000000000000000000000000000000
c5: 130
c0: 41
skew: 0.79
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2400001)
Primes: RFBsize:176302, AFBsize:175999, largePrimes:5654496 encountered
Relations: rels:5576359, finalFF:468391
Max relations in full relation-set: 28
Initial matrix: 352368 x 468391 with sparse part having weight 45018980.
Pruned matrix : 311238 x 313063 with weight 27264252.
Total sieving time: 39.99 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 4.07 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 44.48 hours.
 --------- CPU info (if available) ----------

Mar 29, 2008 (4th)

By Jo Yeong Uk / GGNFS

(14·10¹⁴⁵+13)/9 = 1(5)₁₄₄7_<146> = 17 · 351580221955260353971_<21> · C124

C124 = P62 · P62

P62 = 34459589968363234442648214731087099673642284116938602851917257_<62>

P62 = 75526970244148897784211551730428691782297907191091326903221343_<62>

Number: 15557_145
N=2602628426166141865724615540157791063643988462510517691652800254234982874875625259606153468156270329530203198865116992416151
  ( 124 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=34459589968363234442648214731087099673642284116938602851917257 (pp62)
 r2=75526970244148897784211551730428691782297907191091326903221343 (pp62)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.28 hours.
Scaled time: 19.10 units (timescale=1.859).
Factorization parameters were as follows:
n: 2602628426166141865724615540157791063643988462510517691652800254234982874875625259606153468156270329530203198865116992416151
m: 100000000000000000000000000000
c5: 14
c0: 13
skew: 0.99
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1575001)
Primes: RFBsize:135072, AFBsize:134738, largePrimes:3901017 encountered
Relations: rels:4097730, finalFF:468243
Max relations in full relation-set: 28
Initial matrix: 269876 x 468243 with sparse part having weight 45370850.
Pruned matrix : 206519 x 207932 with weight 19996486.
Total sieving time: 10.01 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 10.28 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178324k/8912896k available (2439k kernel code, 208016k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 4812.94 BogoMIPS (lpj=2406472)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405149)
Calibrating delay using timer specific routine.. 4809.88 BogoMIPS (lpj=2404940)
Calibrating delay using timer specific routine.. 4918.32 BogoMIPS (lpj=2459163)

(14·10¹⁵⁸+13)/9 = 1(5)₁₅₇7_<159> = 73 · 157 · 995019451 · 208167547279001467_<18> · 4497526422252317257_<19> · C110

C110 = P46 · P65

P46 = 1210558913543004506210542223385032067495000517_<46>

P65 = 12035351112751119719236488570794160664363849366208366689915448269_<65>

Number: 15557_158
N=14569501567160585814901710440786511367556393436049973012285870292289222161159866566292118930478367602441755073
  ( 110 digits)
Divisors found:
 r1=1210558913543004506210542223385032067495000517 (pp46)
 r2=12035351112751119719236488570794160664363849366208366689915448269 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 14.56 hours.
Scaled time: 27.06 units (timescale=1.859).
Factorization parameters were as follows:
name: 15557_158
n: 14569501567160585814901710440786511367556393436049973012285870292289222161159866566292118930478367602441755073
skew: 23466.91
# norm 4.30e+14
c5: 720
c4: -141763316
c3: -19615208060397
c2: 21839928663373314
c1: 1559345164302976886012
c0: -57832564243336272936728
# alpha -4.47
Y1: 336403296409
Y0: -1824843363352675883485
# Murphy_E 1.08e-09
# M 8863611329542007331398799307946931115871032908372565814999860843772890406313742186603022619801783138163488601
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1200000, 1920001)
Primes: RFBsize:176302, AFBsize:176832, largePrimes:7632173 encountered
Relations: rels:7526024, finalFF:533618
Max relations in full relation-set: 28
Initial matrix: 353208 x 533618 with sparse part having weight 52117188.
Pruned matrix : 249410 x 251240 with weight 27367049.
Polynomial selection time: 0.78 hours.
Total sieving time: 13.25 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.32 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000
total time: 14.56 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178324k/8912896k available (2439k kernel code, 208016k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 4812.94 BogoMIPS (lpj=2406472)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405149)
Calibrating delay using timer specific routine.. 4809.88 BogoMIPS (lpj=2404940)
Calibrating delay using timer specific routine.. 4918.32 BogoMIPS (lpj=2459163)

Mar 29, 2008 (3rd)

By Sinkiti Sibata / GGNFS, Msieve

(14·10¹³⁷+13)/9 = 1(5)₁₃₆7_<138> = 19 · C136

C136 = P41 · P96

P41 = 11764073559559998843123355711907785474687_<41>

P96 = 695943837946402020118337584433250306357753583192431662177817987316706993990755327964810915425369_<96>

Number: 15557_137
N=8187134502923976608187134502923976608187134502923976608187134502923976608187134502923976608187134502923976608187134502923976608187134503
  ( 136 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=11764073559559998843123355711907785474687 (pp41)
 r2=695943837946402020118337584433250306357753583192431662177817987316706993990755327964810915425369 (pp96)
Version: GGNFS-0.77.1-20060513-k8
Total time: 12.38 hours.
Scaled time: 24.38 units (timescale=1.969).
Factorization parameters were as follows:
name: 15557_137
n: 8187134502923976608187134502923976608187134502923976608187134502923976608187134502923976608187134502923976608187134502923976608187134503
m: 1000000000000000000000000000
c5: 1400
c0: 13
skew: 0.39
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1975001)
Primes: RFBsize:78498, AFBsize:63883, largePrimes:1650833 encountered
Relations: rels:1672542, finalFF:169267
Max relations in full relation-set: 28
Initial matrix: 142448 x 169267 with sparse part having weight 18473523.
Pruned matrix : 135850 x 136626 with weight 13522889.
Total sieving time: 12.04 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 12.38 hours.
 --------- CPU info (if available) ----------

(14·10¹³⁹+13)/9 = 1(5)₁₃₈7_<140> = 1228783 · 7130213 · 28968643363421_<14> · C113

C113 = P32 · P82

P32 = 57299449684752614248272600835231_<32>

P82 = 1069619274128639137021858419038897362426876526582588171608739640247634879294468933_<82>

Number: 15557_139
N=61288595779775571881113368796770804969316105944305619154906190416003544310391843891264168410337157483134381378523
  ( 113 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=57299449684752614248272600835231 (pp32)
 r2=1069619274128639137021858419038897362426876526582588171608739640247634879294468933 (pp82)
Version: GGNFS-0.77.1-20060513-k8
Total time: 10.24 hours.
Scaled time: 20.48 units (timescale=1.999).
Factorization parameters were as follows:
name: 15557_139
n: 61288595779775571881113368796770804969316105944305619154906190416003544310391843891264168410337157483134381378523
m: 10000000000000000000000000000
c5: 7
c0: 65
skew: 1.56
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1750001)
Primes: RFBsize:100021, AFBsize:100618, largePrimes:2719554 encountered
Relations: rels:2699900, finalFF:266940
Max relations in full relation-set: 28
Initial matrix: 200704 x 266940 with sparse part having weight 24490485.
Pruned matrix : 180448 x 181515 with weight 14444246.
Total sieving time: 9.83 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 10.24 hours.
 --------- CPU info (if available) ----------

(14·10¹²⁵+13)/9 = 1(5)₁₂₄7_<126> = 29 · 857 · 532964659 · 6612379979563_<13> · C100

C100 = P31 · P70

P31 = 1189183889824656181212523560943_<31>

P70 = 1493487098247526373754498223558905495812451565384158118329898981129999_<70>

Fri Mar 28 23:21:28 2008  Msieve v. 1.33
Fri Mar 28 23:21:28 2008  random seeds: 5386582e d8e5e839
Fri Mar 28 23:21:28 2008  factoring 1776030796896931864902419817154526194496709500799185020793318268673546294348199531369033949482029057 (100 digits)
Fri Mar 28 23:21:30 2008  searching for 15-digit factors
Fri Mar 28 23:21:32 2008  commencing quadratic sieve (100-digit input)
Fri Mar 28 23:21:32 2008  using multiplier of 1
Fri Mar 28 23:21:32 2008  using 64kb Pentium 4 sieve core
Fri Mar 28 23:21:32 2008  sieve interval: 18 blocks of size 65536
Fri Mar 28 23:21:32 2008  processing polynomials in batches of 6
Fri Mar 28 23:21:32 2008  using a sieve bound of 2674031 (97647 primes)
Fri Mar 28 23:21:32 2008  using large prime bound of 401104650 (28 bits)
Fri Mar 28 23:21:32 2008  using double large prime bound of 3061003663568100 (43-52 bits)
Fri Mar 28 23:21:32 2008  using trial factoring cutoff of 52 bits
Fri Mar 28 23:21:32 2008  polynomial 'A' values have 13 factors
Sat Mar 29 20:55:01 2008  97755 relations (22380 full + 75375 combined from 1494977 partial), need 97743
Sat Mar 29 20:55:06 2008  begin with 1517357 relations
Sat Mar 29 20:55:08 2008  reduce to 261925 relations in 11 passes
Sat Mar 29 20:55:08 2008  attempting to read 261925 relations
Sat Mar 29 20:55:18 2008  recovered 261925 relations
Sat Mar 29 20:55:18 2008  recovered 254042 polynomials
Sat Mar 29 20:55:18 2008  attempting to build 97755 cycles
Sat Mar 29 20:55:18 2008  found 97755 cycles in 6 passes
Sat Mar 29 20:55:18 2008  distribution of cycle lengths:
Sat Mar 29 20:55:18 2008     length 1 : 22380
Sat Mar 29 20:55:18 2008     length 2 : 16289
Sat Mar 29 20:55:18 2008     length 3 : 16175
Sat Mar 29 20:55:18 2008     length 4 : 13411
Sat Mar 29 20:55:18 2008     length 5 : 10254
Sat Mar 29 20:55:18 2008     length 6 : 7237
Sat Mar 29 20:55:18 2008     length 7 : 4951
Sat Mar 29 20:55:18 2008     length 9+: 7058
Sat Mar 29 20:55:18 2008  largest cycle: 20 relations
Sat Mar 29 20:55:19 2008  matrix is 97647 x 97755 (25.5 MB) with weight 6299176 (64.44/col)
Sat Mar 29 20:55:19 2008  sparse part has weight 6299176 (64.44/col)
Sat Mar 29 20:55:21 2008  filtering completed in 3 passes
Sat Mar 29 20:55:21 2008  matrix is 94278 x 94342 (24.7 MB) with weight 6109336 (64.76/col)
Sat Mar 29 20:55:21 2008  sparse part has weight 6109336 (64.76/col)
Sat Mar 29 20:55:22 2008  saving the first 48 matrix rows for later
Sat Mar 29 20:55:22 2008  matrix is 94230 x 94342 (13.9 MB) with weight 4602553 (48.79/col)
Sat Mar 29 20:55:22 2008  sparse part has weight 3082742 (32.68/col)
Sat Mar 29 20:55:22 2008  matrix includes 64 packed rows
Sat Mar 29 20:55:22 2008  using block size 21845 for processor cache size 512 kB
Sat Mar 29 20:55:23 2008  commencing Lanczos iteration
Sat Mar 29 20:55:23 2008  memory use: 14.7 MB
Sat Mar 29 20:56:49 2008  lanczos halted after 1491 iterations (dim = 94229)
Sat Mar 29 20:56:49 2008  recovered 16 nontrivial dependencies
Sat Mar 29 20:56:51 2008  prp31 factor: 1189183889824656181212523560943
Sat Mar 29 20:56:51 2008  prp70 factor: 1493487098247526373754498223558905495812451565384158118329898981129999
Sat Mar 29 20:56:51 2008  elapsed time 21:35:23

Mar 29, 2008 (2nd)

By matsui / GGNFS

4·10¹⁷⁰-3 = 3(9)₁₆₉7_<171> = 229 · 73679 · C164

C164 = P43 · P49 · P73

P43 = 1360033104762423088299063931973963977671913_<43>

P49 = 3590519653945782877764230523114444807700131409621_<49>

P73 = 4854829677573519382682020652046055052653649124445093405710647102555118179_<73>

N=23707228529563299218829039529492118265169025723587584073981725638496414074246653917314283943017068434056358364630332296517449616657078080527647043936784438053634167
  ( 164 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=1360033104762423088299063931973963977671913 (pp43)
 r2=3590519653945782877764230523114444807700131409621 (pp49)
 r3=4854829677573519382682020652046055052653649124445093405710647102555118179 (pp73)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 130.67 hours.
Scaled time: 146.09 units (timescale=1.118).
Factorization parameters were as follows:
n: 23707228529563299218829039529492118265169025723587584073981725638496414074246653917314283943017068434056358364630332296517449616657078080527647043936784438053634167
m: 10000000000000000000000000000000000
c5: 4
c0: -3
skew: 0.94
type: snfs

Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 7100001)
Primes: RFBsize:412849, AFBsize:412766, largePrimes:6063551 encountered
Relations: rels:6355124, finalFF:952227
Max relations in full relation-set: 28
Initial matrix: 825682 x 952227 with sparse part having weight 57621045.
Pruned matrix : 720478 x 724670 with weight 41769639.
Total sieving time: 120.70 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 9.54 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 130.67 hours.

Mar 29, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(14·10¹⁵³+13)/9 = 1(5)₁₅₂7_<154> = 3 · 29 · 1427 · 1587981827_<10> · C139

C139 = P39 · P101

P39 = 460973496523002946310180089475028301423_<39>

P101 = 17116730623418638738910176920615522214699754984748042446821276475378442415835456701206067027207625333_<101>

(7·10¹⁶⁸-61)/9 = (7)₁₆₇1_<168> = 3² · 17 · 23 · 47 · C163

C163 = P49 · P114

P49 = 9004468253267221996176999390369665257953454115627_<49>

P114 = 522252267863776517383648685895265872874245070718524906770519125645126330038946823665531693031823946346738290819761_<114>

Number: n
N=4702603966176185072994490563553341300888053168984042721141631010851594552234845354868572296153874576177817548371320296371537959755115257464208145313149757110505147
  ( 163 digits)
SNFS difficulty: 168 digits.
Divisors found:

Sat Mar 29 12:07:22 2008  prp49 factor: 9004468253267221996176999390369665257953454115627
Sat Mar 29 12:07:22 2008  prp114 factor: 522252267863776517383648685895265872874245070718524906770519125645126330038946823665531693031823946346738290819761
Sat Mar 29 12:07:22 2008  elapsed time 01:18:21 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 53.48 hours.
Scaled time: 44.81 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_7_167_1
n: 4702603966176185072994490563553341300888053168984042721141631010851594552234845354868572296153874576177817548371320296371537959755115257464208145313149757110505147
type: snfs
deg: 5
c5: 7000
c0: -61
skew: 0.39
m: 1000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5900423)
Primes: RFBsize:250150, AFBsize:250007, largePrimes:5947814 encountered
Relations: rels:5883970, finalFF:552579
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 53.23 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,48,48,2.5,2.5,100000
total time: 53.48 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

Mar 28, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve

(13·10¹⁵⁵+41)/9 = 1(4)₁₅₄9_<156> = 89 · 13367 · C150

C150 = P42 · P108

P42 = 454914555226406458961012387411117835014677_<42>

P108 = 266899067010205212556633241991383306589388963910132941966984708011973578478898221181824191297352863936423299_<108>

Number: n
N=121416270359290357390659745192079138751431661272515363127578519668548525460104621598254669132724514794899433238189675937172497122667885312432549759423
  ( 150 digits)
SNFS difficulty: 156 digits.
Divisors found:

Fri Mar 28 14:54:39 2008  prp42 factor: 454914555226406458961012387411117835014677
Fri Mar 28 14:54:39 2008  prp108 factor: 266899067010205212556633241991383306589388963910132941966984708011973578478898221181824191297352863936423299
Fri Mar 28 14:54:39 2008  elapsed time 00:26:12 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-k8
Total time: 19.04 hours.
Scaled time: 15.96 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_1_4_154_9
n: 121416270359290357390659745192079138751431661272515363127578519668548525460104621598254669132724514794899433238189675937172497122667885312432549759423
type: snfs
deg: 5
c5: 13
c0: 41
skew: 1.26
m: 10000000000000000000000000000000
rlim: 2400000
alim: 2400000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:176302, AFBsize:175494, largePrimes:5415952 encountered
Relations: rels:5271524, finalFF:461511
Max relations in full relation-set: 28
Initial matrix: 351863 x 461511 with sparse part having weight 38322948.
Pruned matrix : 274203 x 276026 with weight 22148987.
Total sieving time: 18.13 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.77 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.5,2.5,100000
total time: 19.04 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(13·10¹⁵⁷+41)/9 = 1(4)₁₅₆9_<158> = 23 · 199 · C154

C154 = P51 · P103

P51 = 554967349862577519760631952619203509296695751946839_<51>

P103 = 5686597597373431858875045737803935242817252645892081260193915454685731257129233895079087021649744633383_<103>

Number: n
N=3155875998349234093171169858956618843007307066734639380477265554827276479013424610977593280411720437938484694001408006214648119826184060398611414560726337
  ( 154 digits)
SNFS difficulty: 158 digits.
Divisors found:

Fri Mar 28 15:13:48 2008  prp51 factor: 554967349862577519760631952619203509296695751946839
Fri Mar 28 15:13:48 2008  prp103 factor: 5686597597373431858875045737803935242817252645892081260193915454685731257129233895079087021649744633383
Fri Mar 28 15:13:48 2008  elapsed time 00:45:02 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-k8
Total time: 28.18 hours.
Scaled time: 23.73 units (timescale=0.842).
Factorization parameters were as follows:
name: KA_1_4_156_9
n: 3155875998349234093171169858956618843007307066734639380477265554827276479013424610977593280411720437938484694001408006214648119826184060398611414560726337
type: snfs
deg: 5
c5: 1300
c0: 41
skew: 0.50
m: 10000000000000000000000000000000
rlim: 2800000
alim: 2800000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1700001)
Primes: RFBsize:203362, AFBsize:203738, largePrimes:5556469 encountered
Relations: rels:5457604, finalFF:504339
Max relations in full relation-set: 28
Initial matrix: 407167 x 504339 with sparse part having weight 41011748.
Pruned matrix : 336332 x 338431 with weight 25630672.
Total sieving time: 26.88 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.14 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,48,48,2.5,2.5,100000
total time: 28.18 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(13·10¹⁸⁴+23)/9 = 1(4)₁₈₃7_<185> = C185

C185 = P45 · P66 · P75

P45 = 130313823514075667946558550056804849533881379_<45>

P66 = 134178502432547024473255568544090457894328704524614680930133832431_<66>

P75 = 826090095056379329198269351883150800396104341540990784443107295090242772603_<75>

Number: n
N=14444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447
  ( 185 digits)
SNFS difficulty: 186 digits.
Divisors found:
 r1=130313823514075667946558550056804849533881379 (pp45)
 r2=134178502432547024473255568544090457894328704524614680930133832431 (pp66)
 r3=826090095056379329198269351883150800396104341540990784443107295090242772603 (pp75)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 360.94 hours.
Scaled time: 474.28 units (timescale=1.314).
Factorization parameters were as follows:
name: KA_1_4_183_7
n: 14444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447
type: snfs
deg: 5
c5: 13
c0: 230
skew: 1.78
m: 10000000000000000000000000000000000000
rlim: 8000000
alim: 8000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 22200001)
Primes: RFBsize:539777, AFBsize:538330, largePrimes:6770291 encountered
Relations: rels:7309531, finalFF:1208038
Max relations in full relation-set: 28
Initial matrix: 1078172 x 1208038 with sparse part having weight 76505435.
Pruned matrix : 964515 x 969969 with weight 57010962.
Total sieving time: 339.65 hours.
Total relation processing time: 0.54 hours.
Matrix solve time: 20.19 hours.
Total square root time: 0.57 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,8000000,8000000,27,27,48,48,2.5,2.5,100000
total time: 360.94 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Mar 28, 2008 (3rd)

By Tyler Cadigan / GGNFS, Msieve

(25·10¹⁷⁹-1)/3 = 8(3)₁₇₉_<180> = 664507 · C175

C175 = P76 · P99

P76 = 2926458049828320152153838355641986293834526340146035098618125303277291517849_<76>

P99 = 428525717516297107753879753190106264709390407138076594167027664710084445341842935008628078191572231_<99>

Number: 83333_179
N=1254062535584024447196693689206183431225454861022281681507242712768011974792339784732641391788699492004348085623376929563320376359215679192744897094136455046121911933709251119
  ( 175 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=2926458049828320152153838355641986293834526340146035098618125303277291517849
 r2=428525717516297107753879753190106264709390407138076594167027664710084445341842935008628078191572231
Version: 
Total time: 248.38 hours.
Scaled time: 641.31 units (timescale=2.582).
Factorization parameters were as follows:
n: 1254062535584024447196693689206183431225454861022281681507242712768011974792339784732641391788699492004348085623376929563320376359215679192744897094136455046121911933709251119
m: 1000000000000000000000000000000000000
c5: 5
c0: -2
skew: 0.83
type: snfs
Y0: -1000000000000000000000000000000000000
Y1: 1Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 7900001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 826206 x 826454
Total sieving time: 248.38 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 248.38 hours.
 --------- CPU info (if available) ----------

Mar 28, 2008 (2nd)

By Sinkiti Sibata / Msieve, GGNFS

(14·10¹⁴²+13)/9 = 1(5)₁₄₁7_<143> = 47 · 67 · 73 · 1553 · 40771 · 223602356241339263_<18> · 2483578528016102363689_<22> · C91

C91 = P34 · P57

P34 = 7467290566568150971516456465404349_<34>

P57 = 257721032809974451455373522337667266256407960889221270449_<57>

Fri Mar 28 07:33:40 2008  Msieve v. 1.33
Fri Mar 28 07:33:40 2008  random seeds: c299d4da fc74c7f6
Fri Mar 28 07:33:40 2008  factoring 1924477837108123147224947210103213537481957824666511682922405032895670732495495234269782701 (91 digits)
Fri Mar 28 07:33:42 2008  searching for 15-digit factors
Fri Mar 28 07:33:43 2008  commencing quadratic sieve (91-digit input)
Fri Mar 28 07:33:44 2008  using multiplier of 1
Fri Mar 28 07:33:44 2008  using 64kb Pentium 4 sieve core
Fri Mar 28 07:33:44 2008  sieve interval: 18 blocks of size 65536
Fri Mar 28 07:33:44 2008  processing polynomials in batches of 6
Fri Mar 28 07:33:44 2008  using a sieve bound of 1648187 (62353 primes)
Fri Mar 28 07:33:44 2008  using large prime bound of 145040456 (27 bits)
Fri Mar 28 07:33:44 2008  using double large prime bound of 490546837774928 (42-49 bits)
Fri Mar 28 07:33:44 2008  using trial factoring cutoff of 49 bits
Fri Mar 28 07:33:44 2008  polynomial 'A' values have 12 factors
Fri Mar 28 10:12:04 2008  62951 relations (16059 full + 46892 combined from 705930 partial), need 62449
Fri Mar 28 10:12:06 2008  begin with 721989 relations
Fri Mar 28 10:12:07 2008  reduce to 156795 relations in 10 passes
Fri Mar 28 10:12:07 2008  attempting to read 156795 relations
Fri Mar 28 10:12:11 2008  recovered 156795 relations
Fri Mar 28 10:12:11 2008  recovered 137251 polynomials
Fri Mar 28 10:12:12 2008  attempting to build 62951 cycles
Fri Mar 28 10:12:12 2008  found 62951 cycles in 5 passes
Fri Mar 28 10:12:12 2008  distribution of cycle lengths:
Fri Mar 28 10:12:12 2008     length 1 : 16059
Fri Mar 28 10:12:12 2008     length 2 : 11660
Fri Mar 28 10:12:12 2008     length 3 : 10892
Fri Mar 28 10:12:12 2008     length 4 : 8647
Fri Mar 28 10:12:12 2008     length 5 : 6192
Fri Mar 28 10:12:12 2008     length 6 : 3994
Fri Mar 28 10:12:12 2008     length 7 : 2473
Fri Mar 28 10:12:12 2008     length 9+: 3034
Fri Mar 28 10:12:12 2008  largest cycle: 19 relations
Fri Mar 28 10:12:12 2008  matrix is 62353 x 62951 (15.5 MB) with weight 3812304 (60.56/col)
Fri Mar 28 10:12:12 2008  sparse part has weight 3812304 (60.56/col)
Fri Mar 28 10:12:13 2008  filtering completed in 4 passes
Fri Mar 28 10:12:13 2008  matrix is 58760 x 58824 (14.5 MB) with weight 3554457 (60.43/col)
Fri Mar 28 10:12:13 2008  sparse part has weight 3554457 (60.43/col)
Fri Mar 28 10:12:14 2008  saving the first 48 matrix rows for later
Fri Mar 28 10:12:14 2008  matrix is 58712 x 58824 (9.1 MB) with weight 2809478 (47.76/col)
Fri Mar 28 10:12:14 2008  sparse part has weight 2043760 (34.74/col)
Fri Mar 28 10:12:14 2008  matrix includes 64 packed rows
Fri Mar 28 10:12:14 2008  using block size 21845 for processor cache size 512 kB
Fri Mar 28 10:12:15 2008  commencing Lanczos iteration
Fri Mar 28 10:12:15 2008  memory use: 9.0 MB
Fri Mar 28 10:12:47 2008  lanczos halted after 929 iterations (dim = 58708)
Fri Mar 28 10:12:47 2008  recovered 15 nontrivial dependencies
Fri Mar 28 10:12:49 2008  prp34 factor: 7467290566568150971516456465404349
Fri Mar 28 10:12:49 2008  prp57 factor: 257721032809974451455373522337667266256407960889221270449
Fri Mar 28 10:12:49 2008  elapsed time 02:39:09

(14·10¹³⁵+13)/9 = 1(5)₁₃₄7_<136> = 3 · 1381 · 222396359378344723344489169_<27> · C106

C106 = P45 · P61

P45 = 850464992838381187711643030456490530458087993_<45>

P61 = 1985118687022080519125853658451963101859713733308921760886547_<61>

Number: 15557_135
N=1688273949941570375095874217711031864364334175058727202308319719669742426148965973319064328338454215930171
  ( 106 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=850464992838381187711643030456490530458087993 (pp45)
 r2=1985118687022080519125853658451963101859713733308921760886547 (pp61)
Version: GGNFS-0.77.1-20060513-k8
Total time: 8.33 hours.
Scaled time: 16.63 units (timescale=1.996).
Factorization parameters were as follows:
name: 15557_135
n: 1688273949941570375095874217711031864364334175058727202308319719669742426148965973319064328338454215930171
m: 1000000000000000000000000000
c5: 14
c0: 13
skew: 0.99
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1375001)
Primes: RFBsize:78498, AFBsize:63758, largePrimes:1552807 encountered
Relations: rels:1544617, finalFF:162642
Max relations in full relation-set: 28
Initial matrix: 142322 x 162642 with sparse part having weight 14896086.
Pruned matrix : 136528 x 137303 with weight 11093629.
Total sieving time: 8.09 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 8.33 hours.
 --------- CPU info (if available) ----------

(14·10¹⁴¹+13)/9 = 1(5)₁₄₀7_<142> = 3 · 58771 · 2195681 · 8652793169_<10> · 3248156225927037467732225359_<28> · C93

C93 = P45 · P48

P45 = 183423493947434274718688357884837548361877507_<45>

P48 = 779441909528350662423303508331947392118799809777_<48>

Fri Mar 28 10:32:18 2008  Msieve v. 1.33
Fri Mar 28 10:32:18 2008  random seeds: 272e5fe1 63dbf71a
Fri Mar 28 10:32:18 2008  factoring 142967958374750041269888592393394485067234229144975090352486633805456865490049829790174985939 (93 digits)
Fri Mar 28 10:32:20 2008  searching for 15-digit factors
Fri Mar 28 10:32:21 2008  commencing quadratic sieve (93-digit input)
Fri Mar 28 10:32:22 2008  using multiplier of 1
Fri Mar 28 10:32:22 2008  using 64kb Pentium 4 sieve core
Fri Mar 28 10:32:22 2008  sieve interval: 18 blocks of size 65536
Fri Mar 28 10:32:22 2008  processing polynomials in batches of 6
Fri Mar 28 10:32:22 2008  using a sieve bound of 1882073 (70588 primes)
Fri Mar 28 10:32:22 2008  using large prime bound of 220202541 (27 bits)
Fri Mar 28 10:32:22 2008  using double large prime bound of 1040112169045794 (42-50 bits)
Fri Mar 28 10:32:22 2008  using trial factoring cutoff of 50 bits
Fri Mar 28 10:32:22 2008  polynomial 'A' values have 12 factors
Fri Mar 28 14:10:29 2008  70703 relations (18168 full + 52535 combined from 917138 partial), need 70684
Fri Mar 28 14:10:32 2008  begin with 935306 relations
Fri Mar 28 14:10:33 2008  reduce to 178180 relations in 11 passes
Fri Mar 28 14:10:33 2008  attempting to read 178180 relations
Fri Mar 28 14:10:38 2008  recovered 178180 relations
Fri Mar 28 14:10:38 2008  recovered 158900 polynomials
Fri Mar 28 14:10:38 2008  attempting to build 70703 cycles
Fri Mar 28 14:10:38 2008  found 70703 cycles in 5 passes
Fri Mar 28 14:10:38 2008  distribution of cycle lengths:
Fri Mar 28 14:10:38 2008     length 1 : 18168
Fri Mar 28 14:10:38 2008     length 2 : 12994
Fri Mar 28 14:10:38 2008     length 3 : 12118
Fri Mar 28 14:10:38 2008     length 4 : 9543
Fri Mar 28 14:10:38 2008     length 5 : 6839
Fri Mar 28 14:10:38 2008     length 6 : 4582
Fri Mar 28 14:10:38 2008     length 7 : 2854
Fri Mar 28 14:10:38 2008     length 9+: 3605
Fri Mar 28 14:10:38 2008  largest cycle: 18 relations
Fri Mar 28 14:10:39 2008  matrix is 70588 x 70703 (17.5 MB) with weight 4300534 (60.83/col)
Fri Mar 28 14:10:39 2008  sparse part has weight 4300534 (60.83/col)
Fri Mar 28 14:10:40 2008  filtering completed in 3 passes
Fri Mar 28 14:10:40 2008  matrix is 66643 x 66705 (16.6 MB) with weight 4094844 (61.39/col)
Fri Mar 28 14:10:40 2008  sparse part has weight 4094844 (61.39/col)
Fri Mar 28 14:10:41 2008  saving the first 48 matrix rows for later
Fri Mar 28 14:10:41 2008  matrix is 66595 x 66705 (9.7 MB) with weight 3134744 (46.99/col)
Fri Mar 28 14:10:41 2008  sparse part has weight 2143080 (32.13/col)
Fri Mar 28 14:10:41 2008  matrix includes 64 packed rows
Fri Mar 28 14:10:41 2008  using block size 21845 for processor cache size 512 kB
Fri Mar 28 14:10:41 2008  commencing Lanczos iteration
Fri Mar 28 14:10:41 2008  memory use: 9.9 MB
Fri Mar 28 14:11:23 2008  lanczos halted after 1055 iterations (dim = 66592)
Fri Mar 28 14:11:23 2008  recovered 16 nontrivial dependencies
Fri Mar 28 14:11:24 2008  prp45 factor: 183423493947434274718688357884837548361877507
Fri Mar 28 14:11:24 2008  prp48 factor: 779441909528350662423303508331947392118799809777
Fri Mar 28 14:11:24 2008  elapsed time 03:39:06

(14·10¹³¹+13)/9 = 1(5)₁₃₀7_<132> = 31 · 4337 · 1609599583_<10> · 58700195699_<11> · C107

C107 = P35 · P72

P35 = 56357955441055287971571773968585783_<35>

P72 = 217281014777808196009137828237449697839477601469693193097765221967813121_<72>

Number: 15557_131
N=12245513749034989852895705411736070721553443053147682733202564222569324669871927096396592972496605601458743
  ( 107 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=56357955441055287971571773968585783 (pp35)
 r2=217281014777808196009137828237449697839477601469693193097765221967813121 (pp72)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.08 hours.
Scaled time: 10.10 units (timescale=1.988).
Factorization parameters were as follows:
name: 15557_131
n: 12245513749034989852895705411736070721553443053147682733202564222569324669871927096396592972496605601458743
m: 100000000000000000000000000
c5: 140
c0: 13
skew: 0.62
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1050001)
Primes: RFBsize:63951, AFBsize:63398, largePrimes:1483814 encountered
Relations: rels:1458460, finalFF:144699
Max relations in full relation-set: 28
Initial matrix: 127416 x 144699 with sparse part having weight 11561520.
Pruned matrix : 123053 x 123754 with weight 8514307.
Total sieving time: 4.88 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.08 hours.
 --------- CPU info (if available) ----------

(14·10¹²⁷+13)/9 = 1(5)₁₂₆7_<128> = 179 · 1777 · C122

C122 = P41 · P82

P41 = 13425840129506340057442209524427842613367_<41>

P82 = 3642533847136935011456148310820503413649474104862561436305997644166338839113473537_<82>

Number: 15557_127
N=48904077097976174632267538835950225430329679849459278098972769860557010451849220346750865514835925074762107863531076969079
  ( 122 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=13425840129506340057442209524427842613367 (pp41)
 r2=3642533847136935011456148310820503413649474104862561436305997644166338839113473537 (pp82)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.44 hours.
Scaled time: 8.83 units (timescale=1.988).
Factorization parameters were as follows:
name: 15557_127
n: 48904077097976174632267538835950225430329679849459278098972769860557010451849220346750865514835925074762107863531076969079
m: 10000000000000000000000000
c5: 1400
c0: 13
skew: 0.39
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:63883, largePrimes:1566066 encountered
Relations: rels:1612994, finalFF:215096
Max relations in full relation-set: 28
Initial matrix: 127901 x 215096 with sparse part having weight 15848189.
Pruned matrix : 104475 x 105178 with weight 6326007.
Total sieving time: 4.30 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.44 hours.
 --------- CPU info (if available) ----------

(14·10¹⁵⁵+13)/9 = 1(5)₁₅₄7_<156> = 19 · 1429 · 4003 · 62347 · 177383443 · 28629367194611_<14> · 2853238433322186027101981_<25> · C97

C97 = P43 · P54

P43 = 2306054698995868998921453543665437775116819_<43>

P54 = 687014726607656415295394436693947860736093596616456341_<54>

Fri Mar 28 14:24:16 2008  Msieve v. 1.33
Fri Mar 28 14:24:16 2008  random seeds: 8d254ebd b45fce0d
Fri Mar 28 14:24:16 2008  factoring 1584293538572948347292846286312605310049603816960943641183522320318649105786798116802819088299279 (97 digits)
Fri Mar 28 14:24:17 2008  searching for 15-digit factors
Fri Mar 28 14:24:19 2008  commencing quadratic sieve (97-digit input)
Fri Mar 28 14:24:20 2008  using multiplier of 31
Fri Mar 28 14:24:20 2008  using 64kb Pentium 4 sieve core
Fri Mar 28 14:24:20 2008  sieve interval: 18 blocks of size 65536
Fri Mar 28 14:24:20 2008  processing polynomials in batches of 6
Fri Mar 28 14:24:20 2008  using a sieve bound of 2334881 (85814 primes)
Fri Mar 28 14:24:20 2008  using large prime bound of 350232150 (28 bits)
Fri Mar 28 14:24:20 2008  using double large prime bound of 2397953724173250 (43-52 bits)
Fri Mar 28 14:24:20 2008  using trial factoring cutoff of 52 bits
Fri Mar 28 14:24:20 2008  polynomial 'A' values have 13 factors
Fri Mar 28 23:05:04 2008  86008 relations (21231 full + 64777 combined from 1284617 partial), need 85910
Fri Mar 28 23:05:09 2008  begin with 1305848 relations
Fri Mar 28 23:05:10 2008  reduce to 223087 relations in 11 passes
Fri Mar 28 23:05:10 2008  attempting to read 223087 relations
Fri Mar 28 23:05:18 2008  recovered 223087 relations
Fri Mar 28 23:05:18 2008  recovered 209473 polynomials
Fri Mar 28 23:05:18 2008  attempting to build 86008 cycles
Fri Mar 28 23:05:19 2008  found 86008 cycles in 5 passes
Fri Mar 28 23:05:19 2008  distribution of cycle lengths:
Fri Mar 28 23:05:19 2008     length 1 : 21231
Fri Mar 28 23:05:19 2008     length 2 : 15103
Fri Mar 28 23:05:19 2008     length 3 : 14640
Fri Mar 28 23:05:19 2008     length 4 : 11690
Fri Mar 28 23:05:19 2008     length 5 : 8817
Fri Mar 28 23:05:19 2008     length 6 : 5845
Fri Mar 28 23:05:19 2008     length 7 : 3640
Fri Mar 28 23:05:19 2008     length 9+: 5042
Fri Mar 28 23:05:19 2008  largest cycle: 20 relations
Fri Mar 28 23:05:19 2008  matrix is 85814 x 86008 (23.1 MB) with weight 5717670 (66.48/col)
Fri Mar 28 23:05:19 2008  sparse part has weight 5717670 (66.48/col)
Fri Mar 28 23:05:21 2008  filtering completed in 3 passes
Fri Mar 28 23:05:21 2008  matrix is 81869 x 81933 (22.2 MB) with weight 5481881 (66.91/col)
Fri Mar 28 23:05:21 2008  sparse part has weight 5481881 (66.91/col)
Fri Mar 28 23:05:22 2008  saving the first 48 matrix rows for later
Fri Mar 28 23:05:22 2008  matrix is 81821 x 81933 (13.9 MB) with weight 4319361 (52.72/col)
Fri Mar 28 23:05:22 2008  sparse part has weight 3151156 (38.46/col)
Fri Mar 28 23:05:22 2008  matrix includes 64 packed rows
Fri Mar 28 23:05:22 2008  using block size 21845 for processor cache size 512 kB
Fri Mar 28 23:05:23 2008  commencing Lanczos iteration
Fri Mar 28 23:05:23 2008  memory use: 13.4 MB
Fri Mar 28 23:06:30 2008  lanczos halted after 1296 iterations (dim = 81820)
Fri Mar 28 23:06:30 2008  recovered 17 nontrivial dependencies
Fri Mar 28 23:06:32 2008  prp43 factor: 2306054698995868998921453543665437775116819
Fri Mar 28 23:06:32 2008  prp54 factor: 687014726607656415295394436693947860736093596616456341
Fri Mar 28 23:06:32 2008  elapsed time 08:42:16

Mar 28, 2008

By Jo Yeong Uk / GGNFS, GMP-ECM

(14·10¹⁴⁰+13)/9 = 1(5)₁₃₉7_<141> = C141

C141 = P44 · P48 · P50

P44 = 18651903176326491578590588753852342945211347_<44>

P48 = 252881043399032213036236815115213828278264819281_<48>

P50 = 32979654314807824846613071587603169379763120964151_<50>

Number: 15557_140
N=155555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555557
  ( 141 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=18651903176326491578590588753852342945211347 (pp44)
 r2=252881043399032213036236815115213828278264819281 (pp48)
 r3=32979654314807824846613071587603169379763120964151 (pp50)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.85 hours.
Scaled time: 12.72 units (timescale=1.858).
Factorization parameters were as follows:
n: 155555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555557
m: 10000000000000000000000000000
c5: 14
c0: 13
skew: 0.99
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1200001)
Primes: RFBsize:114155, AFBsize:113567, largePrimes:3340555 encountered
Relations: rels:3374677, finalFF:329395
Max relations in full relation-set: 28
Initial matrix: 227788 x 329395 with sparse part having weight 29643874.
Pruned matrix : 192119 x 193321 with weight 14135088.
Total sieving time: 6.64 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.85 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178324k/8912896k available (2439k kernel code, 208016k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 4812.92 BogoMIPS (lpj=2406460)
Calibrating delay using timer specific routine.. 4810.27 BogoMIPS (lpj=2405136)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)

(14·10¹⁴³+13)/9 = 1(5)₁₄₂7_<144> = 463 · 757473732247_<12> · C129

C129 = P32 · P98

P32 = 31023256647461269459083296692481_<32>

P98 = 14297153258489824550197407114241491781702207804512304053903211398529910877204888068953512227503277_<98>

(13·10¹⁵⁸+41)/9 = 1(4)₁₅₇9_<159> = 8395064813_<10> · 6547652897573_<13> · C136

C136 = P35 · P38 · P64

P35 = 16799381951211795792021653942974259_<35>

P38 = 95310855936913632436908778587893374381_<38>

P64 = 1641177169129370612168524976686946831629697557566826514744860519_<64>

Number: 14449_158
N=2627792935900529823600728141082774214194696712267598876097811277856833048373726072482011878352451161589375769614853730389213107897394401
  ( 136 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=16799381951211795792021653942974259 (pp35)
 r2=95310855936913632436908778587893374381 (pp38)
 r3=1641177169129370612168524976686946831629697557566826514744860519 (pp64)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 45.46 hours.
Scaled time: 84.51 units (timescale=1.859).
Factorization parameters were as follows:
n: 2627792935900529823600728141082774214194696712267598876097811277856833048373726072482011878352451161589375769614853730389213107897394401
m: 100000000000000000000000000000000
c5: 13
c0: 4100
skew: 3.16
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4700001)
Primes: RFBsize:283146, AFBsize:283233, largePrimes:5900455 encountered
Relations: rels:5998416, finalFF:691121
Max relations in full relation-set: 28
Initial matrix: 566446 x 691121 with sparse part having weight 57637285.
Pruned matrix : 482715 x 485611 with weight 41998325.
Total sieving time: 43.81 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.49 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 45.46 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178324k/8912896k available (2439k kernel code, 208016k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 4812.92 BogoMIPS (lpj=2406460)
Calibrating delay using timer specific routine.. 4810.27 BogoMIPS (lpj=2405136)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)

(14·10¹⁴⁸+13)/9 = 1(5)₁₄₇7_<149> = 23 · 127 · 9617431 · 28592942638103_<14> · C125

C125 = P31 · P94

P31 = 2955942702886671963377337782719_<31>

P94 = 6551489141217456900333363868481004414477273935372377844460384722109044250808853571620019992051_<94>

(14·10¹⁴⁴+13)/9 = 1(5)₁₄₃7_<145> = 3 · 177917731 · 7896795631_<10> · C126

C126 = P35 · P91

P35 = 40279116793142065245222699843631961_<35>

P91 = 9162504531036749318413204160760887020649789519572774169774160166578798106315855757126370539_<91>

(14·10¹⁵⁴+13)/9 = 1(5)₁₅₃7_<155> = 181 · 194674953680161_<15> · 1859392175839927_<16> · 49084445312330203738301_<23> · C100

C100 = P41 · P59

P41 = 91289570793444294608922077211552637967747_<41>

P59 = 52985961482047564535054459735932602456339456869443192968833_<59>

Number: 15557_154
N=4837065681774093718251116801511046020210139612900427557252330234045588282189199187430521628630229251
  ( 100 digits)
Divisors found:
 r1=91289570793444294608922077211552637967747 (pp41)
 r2=52985961482047564535054459735932602456339456869443192968833 (pp59)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.89 hours.
Scaled time: 7.22 units (timescale=1.858).
Factorization parameters were as follows:
name: 15557_154
n: 4837065681774093718251116801511046020210139612900427557252330234045588282189199187430521628630229251
skew: 1367.70
# norm 2.96e+13
c5: 1198800
c4: 4597956255
c3: -6493910268984
c2: -5946587059349494
c1: 7130478681524009176
c0: 62082080180362892391
# alpha -5.23
Y1: 44023727389
Y0: -5262162593316141434
# Murphy_E 3.39e-09
# M 1269640190083716933541114628036959286252817572829869594382248791084356352137432559737845299331323783
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [750000, 1300001)
Primes: RFBsize:114155, AFBsize:114143, largePrimes:3920628 encountered
Relations: rels:3890336, finalFF:335002
Max relations in full relation-set: 28
Initial matrix: 228377 x 335002 with sparse part having weight 26931258.
Pruned matrix : 170218 x 171423 with weight 11732275.
Polynomial selection time: 0.25 hours.
Total sieving time: 3.42 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,48,48,2.5,2.5,50000
total time: 3.89 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178324k/8912896k available (2439k kernel code, 208016k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 4812.92 BogoMIPS (lpj=2406460)
Calibrating delay using timer specific routine.. 4810.27 BogoMIPS (lpj=2405136)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)

(14·10¹⁵⁸-23)/9 = 1(5)₁₅₇3_<159> = 3 · 727 · C155

C155 = P53 · P103

P53 = 14588197216044197579705519152242955035773942876598287_<53>

P103 = 4889092283367864506268890541041439684319959055354301808203619167574234059984462242015485343648252218499_<103>

Number: 15553_158
N=71323042437210250140098833358805848489479851240511488104335422079576137347801721942024555504610525243262519741199246013551378063069947526618778338173111213
  ( 155 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=14588197216044197579705519152242955035773942876598287 (pp53)
 r2=4889092283367864506268890541041439684319959055354301808203619167574234059984462242015485343648252218499 (pp103)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 41.96 hours.
Scaled time: 77.92 units (timescale=1.857).
Factorization parameters were as follows:
n: 71323042437210250140098833358805848489479851240511488104335422079576137347801721942024555504610525243262519741199246013551378063069947526618778338173111213
m: 100000000000000000000000000000000
c5: 7
c0: -1150
skew: 2.77
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4500001)
Primes: RFBsize:283146, AFBsize:282822, largePrimes:5807321 encountered
Relations: rels:5848810, finalFF:648376
Max relations in full relation-set: 28
Initial matrix: 566034 x 648376 with sparse part having weight 50939019.
Pruned matrix : 513937 x 516831 with weight 38008732.
Total sieving time: 40.30 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.50 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 41.96 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178324k/8912896k available (2439k kernel code, 208016k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 4812.92 BogoMIPS (lpj=2406460)
Calibrating delay using timer specific routine.. 4810.27 BogoMIPS (lpj=2405136)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)

Mar 27, 2008 (4th)

The factor table of 155...557 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Mar 27, 2008 (3rd)

By matsui / GGNFS

5·10¹⁷⁴+9 = 5(0)₁₇₃9_<175> = 7² · 282683 · C168

C168 = P55 · P113

P55 = 6932341858585301203147155694949322507634968456323255381_<55>

P113 = 52070801363035000937721717804698385278518754334939026472475690096827289091076030500703551512192216650466491354767_<113>

N=360972595899048093606258456234274680075402843612160358177224116405865169371590749196456952898923991227788363499692848418149499977150434679590255674723839720370412751227
  ( 168 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=6932341858585301203147155694949322507634968456323255381 (pp55)
 r2=52070801363035000937721717804698385278518754334939026472475690096827289091076030500703551512192216650466491354767 (pp113)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 179.84 hours.
Scaled time: 204.47 units (timescale=1.137).
Factorization parameters were as follows:
n: 360972595899048093606258456234274680075402843612160358177224116405865169371590749196456952898923991227788363499692848418149499977150434679590255674723839720370412751227
m: 100000000000000000000000000000000000
c5: 1
c0: 18
skew: 1.78
type: snfs

Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 10200001)
Primes: RFBsize:501962, AFBsize:502056, largePrimes:6407087 encountered
Relations: rels:6887568, finalFF:1161225
Max relations in full relation-set: 28
Initial matrix: 1004085 x 1161225 with sparse part having weight 66785490.
Pruned matrix : 866238 x 871322 with weight 48815069.
Total sieving time: 165.19 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 14.16 hours.
Time per square root: 0.36 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 179.84 hours.

Mar 27, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(13·10¹⁵⁰+41)/9 = 1(4)₁₄₉9_<151> = 3 · 149 · 223 · 457 · 1436593 · 468280357 · 1327754658863_<13> · C116

C116 = P37 · P79

P37 = 5273931011586111902421401925826174831_<37>

P79 = 6731010863188734060301094219283696900836548322318543641341967238597466709527349_<79>

Number: 14449_150
N=35498886930694068488696556445873016251270100374402327779600134140366575898525334967906326211481837444518708649953019
  ( 116 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=5273931011586111902421401925826174831 (pp37)
 r2=6731010863188734060301094219283696900836548322318543641341967238597466709527349 (pp79)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 30.51 hours.
Scaled time: 20.60 units (timescale=0.675).
Factorization parameters were as follows:
name: 14449_150
n: 35498886930694068488696556445873016251270100374402327779600134140366575898525334967906326211481837444518708649953019
m: 1000000000000000000000000000000
c5: 13
c0: 41
skew: 1.26
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:175494, largePrimes:5501118 encountered
Relations: rels:5456438, finalFF:525614
Max relations in full relation-set: 28
Initial matrix: 351863 x 525614 with sparse part having weight 45683886.
Pruned matrix : 270724 x 272547 with weight 23014047.
Total sieving time: 27.43 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 2.73 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 30.51 hours.
 --------- CPU info (if available) ----------

Mar 27, 2008

By Jo Yeong Uk / GGNFS

(13·10¹⁵³+41)/9 = 1(4)₁₅₂9_<154> = 3 · 7 · 65532938855809_<14> · 162935348628421_<15> · C124

C124 = P41 · P83

P41 = 64509374281942124842464642137452130975431_<41>

P83 = 99858206116329719031014868769440016414121759112914631130939441108095968385953976191_<83>

Number: 14449_153
N=6441790393481636167681455717217930089359769786440678435578407466998230206440351866658550195452745142800533270101709779963321
  ( 124 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=64509374281942124842464642137452130975431 (pp41)
 r2=99858206116329719031014868769440016414121759112914631130939441108095968385953976191 (pp83)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 25.95 hours.
Scaled time: 47.65 units (timescale=1.836).
Factorization parameters were as follows:
n: 6441790393481636167681455717217930089359769786440678435578407466998230206440351866658550195452745142800533270101709779963321
m: 10000000000000000000000000000000
c5: 13
c0: 4100
skew: 3.16
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3100001)
Primes: RFBsize:216816, AFBsize:216987, largePrimes:5681241 encountered
Relations: rels:5609321, finalFF:505447
Max relations in full relation-set: 28
Initial matrix: 433870 x 505447 with sparse part having weight 43815349.
Pruned matrix : 402967 x 405200 with weight 31494206.
Total sieving time: 24.96 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.86 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 25.95 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178324k/8912896k available (2439k kernel code, 208016k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 4812.92 BogoMIPS (lpj=2406460)
Calibrating delay using timer specific routine.. 4810.27 BogoMIPS (lpj=2405136)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)

Mar 25, 2008

By Sinkiti Sibata / GGNFS

(14·10¹⁴⁹-23)/9 = 1(5)₁₄₈3_<150> = 3 · 19 · 61 · C146

C146 = P52 · P95

P52 = 3356563431989464838102279492452770144334227580418669_<52>

P95 = 13328644255702782199398300118670013826308047575946272170431865182527315159031646426963541568881_<95>

Number: 15553_149
N=44738439906688396766049915316524462339820407119803150864410571054229380372607292365704790208672866136196593487361390726360527913590898923081839389
  ( 146 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=3356563431989464838102279492452770144334227580418669 (pp52)
 r2=13328644255702782199398300118670013826308047575946272170431865182527315159031646426963541568881 (pp95)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 34.05 hours.
Scaled time: 22.99 units (timescale=0.675).
Factorization parameters were as follows:
name: 15553_149
n: 44738439906688396766049915316524462339820407119803150864410571054229380372607292365704790208672866136196593487361390726360527913590898923081839389
m: 1000000000000000000000000000000
c5: 7
c0: -115
skew: 1.75
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176253, largePrimes:5595123 encountered
Relations: rels:5569052, finalFF:530347
Max relations in full relation-set: 28
Initial matrix: 352620 x 530347 with sparse part having weight 46594351.
Pruned matrix : 278318 x 280145 with weight 23634117.
Total sieving time: 30.74 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 2.94 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 34.05 hours.
 --------- CPU info (if available) ----------

Mar 24, 2008 (2nd)

By Jo Yeong Uk / GGNFS

(13·10¹⁷⁶+41)/9 = 1(4)₁₇₅9_<177> = C177

C177 = P65 · P112

P65 = 27808173143646712634660391407710352012010711814864118729595098669_<65>

P112 = 5194316206904279433881048138938401523659364545671879176946965575026753080885093603550898063065486182518914359621_<112>

Number: 14449_176
N=144444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449
  ( 177 digits)
SNFS difficulty: 177 digits.
Divisors found:
 r1=27808173143646712634660391407710352012010711814864118729595098669 (pp65)
 r2=5194316206904279433881048138938401523659364545671879176946965575026753080885093603550898063065486182518914359621 (pp112)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 204.63 hours.
Scaled time: 380.21 units (timescale=1.858).
Factorization parameters were as follows:
n: 144444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449
m: 100000000000000000000000000000000000
c5: 130
c0: 41
skew: 0.79
type: snfs
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [4500000, 7900001)
Primes: RFBsize:602489, AFBsize:600866, largePrimes:10966505 encountered
Relations: rels:11138115, finalFF:1368651
Max relations in full relation-set: 28
Initial matrix: 1203422 x 1368651 with sparse part having weight 91983625.
Pruned matrix : 1058351 x 1064432 with weight 64848531.
Total sieving time: 196.42 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 7.84 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,177,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,50,50,2.6,2.6,100000
total time: 204.63 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178324k/8912896k available (2439k kernel code, 208016k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 4812.91 BogoMIPS (lpj=2406459)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405110)
Calibrating delay using timer specific routine.. 4809.52 BogoMIPS (lpj=2404760)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405116)

Mar 24, 2008

By Sinkiti Sibata / GGNFS

(14·10¹⁴⁶-23)/9 = 1(5)₁₄₅3_<147> = 3² · 17 · 9007 · 2781397012235323853321_<22> · C119

C119 = P39 · P81

P39 = 105919920953310151356411194198742339101_<39>

P81 = 383153944492844763111161253251402110359504657912538041799224423031962917815854683_<81>

Number: 15553_146
N=40583635513631102698432965511202053180932113770520479983068613766399546890836472954025354188279221472737487682924859983
  ( 119 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=105919920953310151356411194198742339101 (pp39)
 r2=383153944492844763111161253251402110359504657912538041799224423031962917815854683 (pp81)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 32.78 hours.
Scaled time: 22.12 units (timescale=0.675).
Factorization parameters were as follows:
name: 15553_146
n: 40583635513631102698432965511202053180932113770520479983068613766399546890836472954025354188279221472737487682924859983
m: 100000000000000000000000000000
c5: 140
c0: -23
skew: 0.7
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 3950001)
Primes: RFBsize:114155, AFBsize:113947, largePrimes:3019088 encountered
Relations: rels:3057061, finalFF:262687
Max relations in full relation-set: 28
Initial matrix: 228169 x 262687 with sparse part having weight 32216803.
Pruned matrix : 218774 x 219978 with weight 25544316.
Total sieving time: 30.47 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 1.93 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 32.78 hours.
 --------- CPU info (if available) ----------

Mar 23, 2008

Jason Papadopoulos's Msieve Version 1.34 was released.

HOW TO for Japanese

Mar 22, 2008 (2nd)

By matsui / GGNFS

8·10¹⁷⁵-3 = 7(9)₁₇₄7_<176> = 7² · 11 · C174

C174 = P35 · P139

P35 = 23845405656471461086656552291936781_<35>

P139 = 6224385850428249598700767268572320083297682242040150160618374892128763951342044866744404597104779601236466339628501125503574499709383067683_<139>

N=148423005565862708719851576994434137291280148423005565862708719851576994434137291280148423005565862708719851576994434137291280148423005565862708719851576994434137291280148423
  ( 174 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=23845405656471461086656552291936781 (pp35)
 r2=6224385850428249598700767268572320083297682242040150160618374892128763951342044866744404597104779601236466339628501125503574499709383067683 (pp139)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 164.37 hours.
Scaled time: 191.16 units (timescale=1.163).
Factorization parameters were as follows:
n: 148423005565862708719851576994434137291280148423005565862708719851576994434137291280148423005565862708719851576994434137291280148423005565862708719851576994434137291280148423
m: 100000000000000000000000000000000000
c5: 8
c0: -3
skew: 0.82
type: snfs

Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 9999999
)
Primes: RFBsize:501962, AFBsize:502156, largePrimes:6367552 encountered
Relations: rels:6839182, finalFF:1153977
Max relations in full relation-set: 28
Initial matrix: 1004183 x 1153977 with sparse part having weight 64267694.
Pruned matrix : 872629 x 877713 with weight 47053168.
Total sieving time: 156.72 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 7.16 hours.
Time per square root: 0.34 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 164.37 hours.

Mar 22, 2008

By Sinkiti Sibata / Msieve, GGNFS

(14·10¹⁷²-23)/9 = 1(5)₁₇₁3_<173> = 146620853411992717_<18> · 48732841755745228357_<20> · 157497047898162804731_<21> · 1087171254746335852469_<22> · C95

C95 = P41 · P54

P41 = 59153305041058215728786305575326180793937_<41>

P54 = 214940696862403157894398875584911842395797860592706359_<54>

Number: 15553_154
N=29332292490325663814719515383691975304656640266784115156065107203761488181559402971368249961736184353
  ( 101 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=95870625299777853092472666927690315569741 (pp41)
 r2=305957037399167054607851451384826644981270222698168907376933 (pp60)
Version: GGNFS-0.77.1-20060513-k8
Total time: 40.32 hours.
Scaled time: 80.60 units (timescale=1.999).
Factorization parameters were as follows:
name: 15553_154
n: 29332292490325663814719515383691975304656640266784115156065107203761488181559402971368249961736184353
m: 10000000000000000000000000000000
c5: 7
c0: -115
skew: 1.75
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2800001)
Primes: RFBsize:216816, AFBsize:216496, largePrimes:5747979 encountered
Relations: rels:5768604, finalFF:592648
Max relations in full relation-set: 28
Initial matrix: 433377 x 592648 with sparse part having weight 49565434.
Pruned matrix : 350847 x 353077 with weight 30783997.
Total sieving time: 38.33 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.66 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 40.32 hours.
 --------- CPU info (if available) ----------

(14·10¹⁵⁴-23)/9 = 1(5)₁₅₃3_<155> = 151 · 10993 · 71999 · 525466275970973936861_<21> · 8444521211546589929213_<22> · C101

C101 = P41 · P60

P41 = 95870625299777853092472666927690315569741_<41>

P60 = 305957037399167054607851451384826644981270222698168907376933_<60>

Fri Mar 21 21:27:39 2008  Msieve v. 1.33
Fri Mar 21 21:27:39 2008  random seeds: 59a25932 53de64be
Fri Mar 21 21:27:39 2008  factoring 12714452607239358532562745136775421026098425976970363512265686475547346928780346430570128545383 (95 digits)
Fri Mar 21 21:27:41 2008  searching for 15-digit factors
Fri Mar 21 21:27:43 2008  commencing quadratic sieve (95-digit input)
Fri Mar 21 21:27:43 2008  using multiplier of 7
Fri Mar 21 21:27:43 2008  using 64kb Pentium 4 sieve core
Fri Mar 21 21:27:43 2008  sieve interval: 18 blocks of size 65536
Fri Mar 21 21:27:43 2008  processing polynomials in batches of 6
Fri Mar 21 21:27:43 2008  using a sieve bound of 2093807 (77512 primes)
Fri Mar 21 21:27:43 2008  using large prime bound of 297320594 (28 bits)
Fri Mar 21 21:27:43 2008  using double large prime bound of 1785685485840044 (42-51 bits)
Fri Mar 21 21:27:43 2008  using trial factoring cutoff of 51 bits
Fri Mar 21 21:27:43 2008  polynomial 'A' values have 12 factors
Sat Mar 22 02:44:08 2008  77717 relations (19430 full + 58287 combined from 1125756 partial), need 77608
Sat Mar 22 02:44:13 2008  begin with 1145186 relations
Sat Mar 22 02:44:14 2008  reduce to 199983 relations in 10 passes
Sat Mar 22 02:44:14 2008  attempting to read 199983 relations
Sat Mar 22 02:44:20 2008  recovered 199983 relations
Sat Mar 22 02:44:20 2008  recovered 182356 polynomials
Sat Mar 22 02:44:21 2008  attempting to build 77717 cycles
Sat Mar 22 02:44:21 2008  found 77717 cycles in 7 passes
Sat Mar 22 02:44:21 2008  distribution of cycle lengths:
Sat Mar 22 02:44:21 2008     length 1 : 19430
Sat Mar 22 02:44:21 2008     length 2 : 13873
Sat Mar 22 02:44:21 2008     length 3 : 13261
Sat Mar 22 02:44:21 2008     length 4 : 10546
Sat Mar 22 02:44:21 2008     length 5 : 7814
Sat Mar 22 02:44:21 2008     length 6 : 5092
Sat Mar 22 02:44:21 2008     length 7 : 3301
Sat Mar 22 02:44:21 2008     length 9+: 4400
Sat Mar 22 02:44:21 2008  largest cycle: 23 relations
Sat Mar 22 02:44:21 2008  matrix is 77512 x 77717 (20.8 MB) with weight 5138619 (66.12/col)
Sat Mar 22 02:44:21 2008  sparse part has weight 5138619 (66.12/col)
Sat Mar 22 02:44:23 2008  filtering completed in 3 passes
Sat Mar 22 02:44:23 2008  matrix is 73413 x 73476 (19.8 MB) with weight 4892739 (66.59/col)
Sat Mar 22 02:44:23 2008  sparse part has weight 4892739 (66.59/col)
Sat Mar 22 02:44:23 2008  saving the first 48 matrix rows for later
Sat Mar 22 02:44:24 2008  matrix is 73365 x 73476 (13.6 MB) with weight 3977170 (54.13/col)
Sat Mar 22 02:44:24 2008  sparse part has weight 3115293 (42.40/col)
Sat Mar 22 02:44:24 2008  matrix includes 64 packed rows
Sat Mar 22 02:44:24 2008  using block size 21845 for processor cache size 512 kB
Sat Mar 22 02:44:25 2008  commencing Lanczos iteration
Sat Mar 22 02:44:25 2008  memory use: 12.4 MB
Sat Mar 22 02:45:22 2008  lanczos halted after 1163 iterations (dim = 73363)
Sat Mar 22 02:45:22 2008  recovered 17 nontrivial dependencies
Sat Mar 22 02:45:23 2008  prp41 factor: 59153305041058215728786305575326180793937
Sat Mar 22 02:45:23 2008  prp54 factor: 214940696862403157894398875584911842395797860592706359
Sat Mar 22 02:45:23 2008  elapsed time 05:17:44

Mar 21, 2008

By Sinkiti Sibata / GGNFS

(14·10¹³²-23)/9 = 1(5)₁₃₁3_<133> = 59 · 71 · 97 · 7823 · 16007597 · C116

C116 = P34 · P82

P34 = 7196110320984271887768290805077603_<34>

P82 = 4248211658617179794953002753092149992005253913469193885224487376180475161049101837_<82>

Number: 15553_132
N=30570599762300799760623180349250549785396977164422221332055957515459038129517087760322197185377808927798602234856711
  ( 116 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=7196110320984271887768290805077603 (pp34)
 r2=4248211658617179794953002753092149992005253913469193885224487376180475161049101837 (pp82)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 6.85 hours.
Scaled time: 4.62 units (timescale=0.675).
Factorization parameters were as follows:
name: 15553_132
n: 30570599762300799760623180349250549785396977164422221332055957515459038129517087760322197185377808927798602234856711
m: 100000000000000000000000000
c5: 1400
c0: -23
skew: 0.44
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1100001)
Primes: RFBsize:63951, AFBsize:63708, largePrimes:1471928 encountered
Relations: rels:1451773, finalFF:152003
Max relations in full relation-set: 28
Initial matrix: 127726 x 152003 with sparse part having weight 11651770.
Pruned matrix : 121041 x 121743 with weight 7752542.
Total sieving time: 6.45 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.27 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 6.85 hours.
 --------- CPU info (if available) ----------

(14·10¹⁵³-23)/9 = 1(5)₁₅₂3_<154> = C154

C154 = P40 · P54 · P60

P40 = 3282864968103111044049116015189636325629_<40>

P54 = 750520966883775487075871543212035736560922760348863037_<54>

P60 = 631349262219539973921775256331377718345779965714457540134361_<60>

Number: 15553_153
N=1555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553
  ( 154 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=3282864968103111044049116015189636325629 (pp40)
 r2=750520966883775487075871543212035736560922760348863037 (pp54)
 r3=631349262219539973921775256331377718345779965714457540134361 (pp60)
Version: GGNFS-0.77.1-20060513-k8
Total time: 47.73 hours.
Scaled time: 94.84 units (timescale=1.987).
Factorization parameters were as follows:
name: 15553_153
n: 1555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553
m: 2000000000000000000000000000000
c5: 875
c0: -46
skew: 0.55
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2900001)
Primes: RFBsize:176302, AFBsize:176403, largePrimes:5995663 encountered
Relations: rels:6090467, finalFF:516187
Max relations in full relation-set: 28
Initial matrix: 352771 x 516187 with sparse part having weight 60940354.
Pruned matrix : 300632 x 302459 with weight 37411755.
Total sieving time: 45.67 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 1.70 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 47.73 hours.
 --------- CPU info (if available) ----------

(14·10¹³⁴-23)/9 = 1(5)₁₃₃3_<135> = 3 · 43 · 1841849 · 6133187 · 266089199 · 1845161925989_<13> · C99

C99 = P45 · P55

P45 = 215339786052217239372566579524945255357716889_<45>

P55 = 1009647045755365143845638829136615216297983945249227441_<55>

Number: 15553_134
N=217417178821213519897591666112568676084285561292677561587515695663261258375232990435242424847951049
  ( 99 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=215339786052217239372566579524945255357716889 (pp45)
 r2=1009647045755365143845638829136615216297983945249227441 (pp55)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 10.16 hours.
Scaled time: 6.86 units (timescale=0.675).
Factorization parameters were as follows:
name: 15553_134
n: 217417178821213519897591666112568676084285561292677561587515695663261258375232990435242424847951049
m: 1000000000000000000000000000
c5: 7
c0: -115
skew: 1.75
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1450001)
Primes: RFBsize:78498, AFBsize:64213, largePrimes:1584221 encountered
Relations: rels:1601133, finalFF:186184
Max relations in full relation-set: 28
Initial matrix: 142776 x 186184 with sparse part having weight 16736449.
Pruned matrix : 129917 x 130694 with weight 10014781.
Total sieving time: 9.64 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.35 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 10.16 hours.
 --------- CPU info (if available) ----------

Mar 20, 2008 (5th)

By Kenji Ibusuki / GGNFS

4·10¹⁷⁰+1 = 4(0)₁₆₉1_<171> = 89 · 809 · 12037 · 389533 · C157

C157 = P53 · P104

P53 = 50122020190096192578898087923762046470485403737718517_<53>

P104 = 23639069626409130088066491289529080774163216816334627185245521359044363228829638540915634190946573122893_<104>

Number: 40001_170
N=1184837925089968078544520908542592436150696161669648582832799154284494683403914446462403262666786104631720001979278062769291401761650003730882381331682709681
  ( 157 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=50122020190096192578898087923762046470485403737718517 (pp53)
 r2=23639069626409130088066491289529080774163216816334627185245521359044363228829638540915634190946573122893 (pp104)
Version: GGNFS-0.77.1
Total time: 78.39 hours.
Scaled time: 228.11 units (timescale=2.910).
Factorization parameters were as follows:
n: 1184837925089968078544520908542592436150696161669648582832799154284494683403914446462403262666786104631720001979278062769291401761650003730882381331682709681
m: 10000000000000000000000000000000000
c5: 4
c0: 1
skew: 0.76
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [3000000, 6700001)
Relations: rels:6317037, finalFF:948920
Initial matrix: 825604 x 948920 with sparse part having weight 54336203.
Pruned matrix : 777410 x 781602 with weight 36172201.
Total sieving time: 75.20 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 2.98 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 78.39 hours.
 --------- CPU info (if available) ----------

Mar 20, 2008 (4th)

By matsui / GGNFS

(10¹⁷⁰-7)/3 = (3)₁₆₉1_<170> = 1223 · 1338241 · 15591659 · 188781916091_<12> · 31872508364263293913_<20> · C123

C123 = P48 · P75

P48 = 580886318748190657139044362291165865116443036239_<48>

P75 = 373729902486897603627174044597757752130374463217098463335616446710076649499_<75>

N=217094587261734213548195463421530504205064288592142575659125525045291823980927102240839454448872345229344019259079758194261
  ( 123 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=580886318748190657139044362291165865116443036239 (pp48)
 r2=373729902486897603627174044597757752130374463217098463335616446710076649499 (pp75)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 121.53 hours.
Scaled time: 145.71 units (timescale=1.199).
Factorization parameters were as follows:
n: 217094587261734213548195463421530504205064288592142575659125525045291823980927102240839454448872345229344019259079758194261
m: 10000000000000000000000000000000000
c5: 1
c0: -7
skew: 1.48
type: snfs

Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 6700001)
Primes: RFBsize:412849, AFBsize:412321, largePrimes:6051704 encountered
Relations: rels:6370117, finalFF:976583
Max relations in full relation-set: 28
Initial matrix: 825236 x 976583 with sparse part having weight 54355320.
Pruned matrix : 696718 x 700908 with weight 37929732.
Total sieving time: 109.72 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 11.39 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 121.53 hours.

Mar 20, 2008 (3rd)

By Jo Yeong Uk / GMP-ECM

(14·10¹⁵⁵-23)/9 = 1(5)₁₅₄3_<156> = 3³ · 43 · 47 · 195929 · 39917387 · C138

C138 = P32 · P107

P32 = 27496531615303751255508385977877_<32>

P107 = 13256128530106065804015121820004168812872800900839223596915403773061273707418701227696707739151908971363929_<107>

(14·10¹⁵¹-23)/9 = 1(5)₁₅₀3_<152> = 13 · 2213 · 517619 · 7681936333_<10> · 1717634052520051_<16> · C116

C116 = P29 · P88

P29 = 16820895951350324317170195241_<29>

P88 = 4706521871418196358281662023008824663095196031484100339389156478064745201226851468713141_<88>

Mar 20, 2008 (2nd)

By Sinkiti Sibata / GGNFS, Msieve

(14·10¹³⁶-23)/9 = 1(5)₁₃₅3_<137> = 2609 · 40819 · 2874721 · 14085762626082570811_<20> · C103

C103 = P41 · P62

P41 = 86564637715095292547101787933942319569693_<41>

P62 = 41670863835479319614069605921391221377496695827764326594084421_<62>

Number: 15553_136
N=3607223231193333588521443657845306759593847350118466937436125963882416398551207258919445340876035052753
  ( 103 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=86564637715095292547101787933942319569693 (pp41)
 r2=41670863835479319614069605921391221377496695827764326594084421 (pp62)
Version: GGNFS-0.77.1-20060513-k8
Total time: 11.88 hours.
Scaled time: 23.46 units (timescale=1.974).
Factorization parameters were as follows:
name: 15553_136
n: 3607223231193333588521443657845306759593847350118466937436125963882416398551207258919445340876035052753
m: 1000000000000000000000000000
c5: 140
c0: -23
skew: 0.7
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1975001)
Primes: RFBsize:78498, AFBsize:63933, largePrimes:1678180 encountered
Relations: rels:1716318, finalFF:184796
Max relations in full relation-set: 28
Initial matrix: 142498 x 184796 with sparse part having weight 20279499.
Pruned matrix : 132168 x 132944 with weight 13105300.
Total sieving time: 11.59 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 11.88 hours.
 --------- CPU info (if available) ----------

(14·10¹⁰⁷-23)/9 = 1(5)₁₀₆3_<108> = 3 · 1951 · 8748821 · C97

C97 = P38 · P59

P38 = 70116552119131233253697742765797176049_<38>

P59 = 43324835157711520807946225794361876690197612007341872469969_<59>

Wed Mar 19 21:19:59 2008  Msieve v. 1.33
Wed Mar 19 21:19:59 2008  random seeds: ba38696c 9d0b82cb
Wed Mar 19 21:19:59 2008  factoring 3037788062388449092580779371481569043270450892455898354863806802156173024445878302412156758572481 (97 digits)
Wed Mar 19 21:20:01 2008  searching for 15-digit factors
Wed Mar 19 21:20:03 2008  commencing quadratic sieve (97-digit input)
Wed Mar 19 21:20:03 2008  using multiplier of 41
Wed Mar 19 21:20:03 2008  using 64kb Pentium 4 sieve core
Wed Mar 19 21:20:03 2008  sieve interval: 18 blocks of size 65536
Wed Mar 19 21:20:03 2008  processing polynomials in batches of 6
Wed Mar 19 21:20:03 2008  using a sieve bound of 2368859 (87059 primes)
Wed Mar 19 21:20:03 2008  using large prime bound of 355328850 (28 bits)
Wed Mar 19 21:20:03 2008  using double large prime bound of 2461131624868650 (43-52 bits)
Wed Mar 19 21:20:03 2008  using trial factoring cutoff of 52 bits
Wed Mar 19 21:20:03 2008  polynomial 'A' values have 13 factors
Thu Mar 20 07:23:56 2008  87413 relations (21168 full + 66245 combined from 1314170 partial), need 87155
Thu Mar 20 07:24:01 2008  begin with 1335338 relations
Thu Mar 20 07:24:02 2008  reduce to 228891 relations in 10 passes
Thu Mar 20 07:24:02 2008  attempting to read 228891 relations
Thu Mar 20 07:24:10 2008  recovered 228891 relations
Thu Mar 20 07:24:10 2008  recovered 216532 polynomials
Thu Mar 20 07:24:11 2008  attempting to build 87413 cycles
Thu Mar 20 07:24:11 2008  found 87413 cycles in 6 passes
Thu Mar 20 07:24:11 2008  distribution of cycle lengths:
Thu Mar 20 07:24:11 2008     length 1 : 21168
Thu Mar 20 07:24:11 2008     length 2 : 15264
Thu Mar 20 07:24:11 2008     length 3 : 14623
Thu Mar 20 07:24:11 2008     length 4 : 11881
Thu Mar 20 07:24:11 2008     length 5 : 8950
Thu Mar 20 07:24:11 2008     length 6 : 6114
Thu Mar 20 07:24:11 2008     length 7 : 3907
Thu Mar 20 07:24:11 2008     length 9+: 5506
Thu Mar 20 07:24:11 2008  largest cycle: 19 relations
Thu Mar 20 07:24:11 2008  matrix is 87059 x 87413 (23.6 MB) with weight 5834793 (66.75/col)
Thu Mar 20 07:24:11 2008  sparse part has weight 5834793 (66.75/col)
Thu Mar 20 07:24:13 2008  filtering completed in 3 passes
Thu Mar 20 07:24:13 2008  matrix is 83194 x 83258 (22.5 MB) with weight 5570899 (66.91/col)
Thu Mar 20 07:24:13 2008  sparse part has weight 5570899 (66.91/col)
Thu Mar 20 07:24:14 2008  saving the first 48 matrix rows for later
Thu Mar 20 07:24:14 2008  matrix is 83146 x 83258 (13.8 MB) with weight 4369149 (52.48/col)
Thu Mar 20 07:24:14 2008  sparse part has weight 3120596 (37.48/col)
Thu Mar 20 07:24:14 2008  matrix includes 64 packed rows
Thu Mar 20 07:24:14 2008  using block size 21845 for processor cache size 512 kB
Thu Mar 20 07:24:15 2008  commencing Lanczos iteration
Thu Mar 20 07:24:15 2008  memory use: 13.5 MB
Thu Mar 20 07:25:24 2008  lanczos halted after 1316 iterations (dim = 83143)
Thu Mar 20 07:25:24 2008  recovered 16 nontrivial dependencies
Thu Mar 20 07:25:28 2008  prp38 factor: 70116552119131233253697742765797176049
Thu Mar 20 07:25:28 2008  prp59 factor: 43324835157711520807946225794361876690197612007341872469969
Thu Mar 20 07:25:28 2008  elapsed time 10:05:29

(14·10¹³¹-23)/9 = 1(5)₁₃₀3_<132> = 3 · 19 · C130

C130 = P45 · P85

P45 = 468056747262877864591378985344497462087808873_<45>

P85 = 5830585394328821340439305519151218975641216570980360445799468073046721537499689235073_<85>

Number: 15553_131
N=2729044834307992202729044834307992202729044834307992202729044834307992202729044834307992202729044834307992202729044834307992202729
  ( 130 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=468056747262877864591378985344497462087808873 (pp45)
 r2=5830585394328821340439305519151218975641216570980360445799468073046721537499689235073 (pp85)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 7.84 hours.
Scaled time: 5.30 units (timescale=0.675).
Factorization parameters were as follows:
name: 15553_131
n: 2729044834307992202729044834307992202729044834307992202729044834307992202729044834307992202729044834307992202729044834307992202729
m: 100000000000000000000000000
c5: 140
c0: -23
skew: 0.7
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1250001)
Primes: RFBsize:63951, AFBsize:63933, largePrimes:1536054 encountered
Relations: rels:1530353, finalFF:157374
Max relations in full relation-set: 28
Initial matrix: 127951 x 157374 with sparse part having weight 14195039.
Pruned matrix : 120613 x 121316 with weight 9276025.
Total sieving time: 7.40 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 7.84 hours.
 --------- CPU info (if available) ----------

(14·10¹³⁸-23)/9 = 1(5)₁₃₇3_<139> = 8111 · C135

C135 = P36 · P41 · P60

P36 = 108711266578758459613216246008874649_<36>

P41 = 10324155343485704388884033718797007786067_<41>

P60 = 170876381427759404236156771629665436841780455921013486760381_<60>

Number: 15553_138
N=191783449088343675940766311867285853230866176248989712187838189564240606035699119166015972821545500623296209537116946807490513568679023
  ( 135 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=108711266578758459613216246008874649 (pp36)
 r2=10324155343485704388884033718797007786067 (pp41)
 r3=170876381427759404236156771629665436841780455921013486760381 (pp60)
Version: GGNFS-0.77.1-20060513-k8
Total time: 19.92 hours.
Scaled time: 39.85 units (timescale=2.000).
Factorization parameters were as follows:
name: 15553_138
n: 191783449088343675940766311867285853230866176248989712187838189564240606035699119166015972821545500623296209537116946807490513568679023
m: 2000000000000000000000000000
c5: 875
c0: -46
skew: 0.55
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 3175001)
Primes: RFBsize:78498, AFBsize:63723, largePrimes:1800247 encountered
Relations: rels:1887080, finalFF:161274
Max relations in full relation-set: 28
Initial matrix: 142287 x 161274 with sparse part having weight 20694509.
Pruned matrix : 138410 x 139185 with weight 16896378.
Total sieving time: 19.54 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 19.92 hours.
 --------- CPU info (if available) ----------

Mar 20, 2008

By Kenichiroh Yamaguchi / Msieve

(14·10¹⁸³-23)/9 = 1(5)₁₈₂3_<184> = 173 · 22501 · 12153853259_<11> · 989929583017_<12> · 1872165481279_<13> · 21311468009719_<14> · 634859922851017_<15> · 6013661672725536345979_<22> · C93

C93 = P34 · P59

P34 = 8747097848694413689758101801203081_<34>

P59 = 24927620489480658641554644061289498862540687696094550232089_<59>

Thu Mar 20 00:47:44 2008  
Thu Mar 20 00:47:44 2008  
Thu Mar 20 00:47:44 2008  Msieve v. 1.33
Thu Mar 20 00:47:44 2008  random seeds: ec6f1bc8 e3913f34
Thu Mar 20 00:47:44 2008  factoring 218044335556607056762155154297125159650663090901409983335965799460624173261563216247971866209 (93 digits)
Thu Mar 20 00:47:46 2008  searching for 15-digit factors
Thu Mar 20 00:47:47 2008  commencing quadratic sieve (93-digit input)
Thu Mar 20 00:47:48 2008  using multiplier of 1
Thu Mar 20 00:47:48 2008  using 32kb Pentium M sieve core
Thu Mar 20 00:47:48 2008  sieve interval: 36 blocks of size 32768
Thu Mar 20 00:47:48 2008  processing polynomials in batches of 6
Thu Mar 20 00:47:48 2008  using a sieve bound of 1888307 (70588 primes)
Thu Mar 20 00:47:48 2008  using large prime bound of 220931919 (27 bits)
Thu Mar 20 00:47:48 2008  using double large prime bound of 1046321638060374 (42-50 bits)
Thu Mar 20 00:47:48 2008  using trial factoring cutoff of 50 bits
Thu Mar 20 00:47:48 2008  polynomial 'A' values have 12 factors
Thu Mar 20 04:02:02 2008  71110 relations (18516 full + 52594 combined from 918052 partial), need 70684
Thu Mar 20 04:02:03 2008  begin with 936567 relations
Thu Mar 20 04:02:04 2008  reduce to 178995 relations in 10 passes
Thu Mar 20 04:02:04 2008  attempting to read 178995 relations
Thu Mar 20 04:02:07 2008  recovered 178995 relations
Thu Mar 20 04:02:07 2008  recovered 159948 polynomials
Thu Mar 20 04:02:07 2008  attempting to build 71110 cycles
Thu Mar 20 04:02:07 2008  found 71110 cycles in 6 passes
Thu Mar 20 04:02:07 2008  distribution of cycle lengths:
Thu Mar 20 04:02:07 2008     length 1 : 18516
Thu Mar 20 04:02:07 2008     length 2 : 12937
Thu Mar 20 04:02:07 2008     length 3 : 12446
Thu Mar 20 04:02:07 2008     length 4 : 9530
Thu Mar 20 04:02:07 2008     length 5 : 6740
Thu Mar 20 04:02:07 2008     length 6 : 4538
Thu Mar 20 04:02:07 2008     length 7 : 2826
Thu Mar 20 04:02:07 2008     length 9+: 3577
Thu Mar 20 04:02:07 2008  largest cycle: 19 relations
Thu Mar 20 04:02:08 2008  matrix is 70588 x 71110 (17.4 MB) with weight 4281603 (60.21/col)
Thu Mar 20 04:02:08 2008  sparse part has weight 4281603 (60.21/col)
Thu Mar 20 04:02:08 2008  filtering completed in 3 passes
Thu Mar 20 04:02:08 2008  matrix is 66351 x 66415 (16.3 MB) with weight 4003888 (60.29/col)
Thu Mar 20 04:02:08 2008  sparse part has weight 4003888 (60.29/col)
Thu Mar 20 04:02:09 2008  saving the first 48 matrix rows for later
Thu Mar 20 04:02:09 2008  matrix is 66303 x 66415 (9.7 MB) with weight 3093727 (46.58/col)
Thu Mar 20 04:02:09 2008  sparse part has weight 2156021 (32.46/col)
Thu Mar 20 04:02:09 2008  matrix includes 64 packed rows
Thu Mar 20 04:02:09 2008  using block size 26566 for processor cache size 2048 kB
Thu Mar 20 04:02:09 2008  commencing Lanczos iteration
Thu Mar 20 04:02:09 2008  memory use: 9.9 MB
Thu Mar 20 04:02:45 2008  lanczos halted after 1050 iterations (dim = 66301)
Thu Mar 20 04:02:45 2008  recovered 15 nontrivial dependencies
Thu Mar 20 04:02:45 2008  prp34 factor: 8747097848694413689758101801203081
Thu Mar 20 04:02:45 2008  prp59 factor: 24927620489480658641554644061289498862540687696094550232089
Thu Mar 20 04:02:45 2008  elapsed time 03:15:01

Mar 19, 2008 (3rd)

By Sinkiti Sibata / GGNFS, Msieve

(14·10¹²³-23)/9 = 1(5)₁₂₂3_<124> = 12211 · 657201752020148171_<18> · C102

C102 = P44 · P59

P44 = 10753755444545527374527909643755701962882929_<44>

P59 = 18025006361564828534200757555861583140142606308789337325697_<59>

Number: 15553_123
N=193836510298645541604861266883321392503284953654360361313167961067989394247181929303493116733154326513
  ( 102 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=10753755444545527374527909643755701962882929 (pp44)
 r2=18025006361564828534200757555861583140142606308789337325697 (pp59)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.51 hours.
Scaled time: 7.00 units (timescale=1.993).
Factorization parameters were as follows:
name: 15553_123
n: 193836510298645541604861266883321392503284953654360361313167961067989394247181929303493116733154326513
m: 2000000000000000000000000
c5: 875
c0: -46
skew: 0.55
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:49098, AFBsize:63723, largePrimes:2340173 encountered
Relations: rels:2569764, finalFF:299018
Max relations in full relation-set: 28
Initial matrix: 112887 x 299018 with sparse part having weight 32153223.
Pruned matrix : 90356 x 90984 with weight 8670527.
Total sieving time: 3.34 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.51 hours.
 --------- CPU info (if available) ----------

(14·10¹¹³-23)/9 = 1(5)₁₁₂3_<114> = 3 · 19² · 43 · 107 · 7975586407_<10> · 1923781173683_<13> · C85

C85 = P33 · P53

P33 = 113861384206662076954599416574707_<33>

P53 = 17869404599998095262189940211282723567677418286716373_<53>

Wed Mar 19 09:31:21 2008  Msieve v. 1.33
Wed Mar 19 09:31:21 2008  random seeds: 98abfa35 0fbf67a6
Wed Mar 19 09:31:21 2008  factoring 2034635142704677792494468631959407918934723927715575304293361053666704254742074577711 (85 digits)
Wed Mar 19 09:31:22 2008  searching for 15-digit factors
Wed Mar 19 09:31:24 2008  commencing quadratic sieve (85-digit input)
Wed Mar 19 09:31:24 2008  using multiplier of 39
Wed Mar 19 09:31:24 2008  using 64kb Pentium 4 sieve core
Wed Mar 19 09:31:24 2008  sieve interval: 6 blocks of size 65536
Wed Mar 19 09:31:24 2008  processing polynomials in batches of 17
Wed Mar 19 09:31:24 2008  using a sieve bound of 1426127 (54401 primes)
Wed Mar 19 09:31:24 2008  using large prime bound of 116942414 (26 bits)
Wed Mar 19 09:31:24 2008  using double large prime bound of 332927451401090 (41-49 bits)
Wed Mar 19 09:31:24 2008  using trial factoring cutoff of 49 bits
Wed Mar 19 09:31:24 2008  polynomial 'A' values have 11 factors
Wed Mar 19 10:18:33 2008  54724 relations (16675 full + 38049 combined from 565949 partial), need 54497
Wed Mar 19 10:18:35 2008  begin with 582624 relations
Wed Mar 19 10:18:35 2008  reduce to 126334 relations in 10 passes
Wed Mar 19 10:18:35 2008  attempting to read 126334 relations
Wed Mar 19 10:18:39 2008  recovered 126334 relations
Wed Mar 19 10:18:39 2008  recovered 104312 polynomials
Wed Mar 19 10:18:39 2008  attempting to build 54724 cycles
Wed Mar 19 10:18:39 2008  found 54724 cycles in 5 passes
Wed Mar 19 10:18:39 2008  distribution of cycle lengths:
Wed Mar 19 10:18:39 2008     length 1 : 16675
Wed Mar 19 10:18:39 2008     length 2 : 11194
Wed Mar 19 10:18:39 2008     length 3 : 9660
Wed Mar 19 10:18:39 2008     length 4 : 6962
Wed Mar 19 10:18:39 2008     length 5 : 4369
Wed Mar 19 10:18:39 2008     length 6 : 2716
Wed Mar 19 10:18:39 2008     length 7 : 1554
Wed Mar 19 10:18:39 2008     length 9+: 1594
Wed Mar 19 10:18:39 2008  largest cycle: 17 relations
Wed Mar 19 10:18:39 2008  matrix is 54401 x 54724 (11.9 MB) with weight 2911019 (53.19/col)
Wed Mar 19 10:18:39 2008  sparse part has weight 2911019 (53.19/col)
Wed Mar 19 10:18:39 2008  filtering completed in 3 passes
Wed Mar 19 10:18:39 2008  matrix is 49171 x 49235 (10.8 MB) with weight 2634621 (53.51/col)
Wed Mar 19 10:18:39 2008  sparse part has weight 2634621 (53.51/col)
Wed Mar 19 10:18:40 2008  saving the first 48 matrix rows for later
Wed Mar 19 10:18:40 2008  matrix is 49123 x 49235 (6.5 MB) with weight 2016709 (40.96/col)
Wed Mar 19 10:18:40 2008  sparse part has weight 1406841 (28.57/col)
Wed Mar 19 10:18:40 2008  matrix includes 64 packed rows
Wed Mar 19 10:18:40 2008  commencing Lanczos iteration
Wed Mar 19 10:18:40 2008  memory use: 8.4 MB
Wed Mar 19 10:20:19 2008  lanczos halted after 778 iterations (dim = 49121)
Wed Mar 19 10:20:20 2008  recovered 17 nontrivial dependencies
Wed Mar 19 10:20:21 2008  prp33 factor: 113861384206662076954599416574707
Wed Mar 19 10:20:21 2008  prp53 factor: 17869404599998095262189940211282723567677418286716373
Wed Mar 19 10:20:21 2008  elapsed time 00:49:00

(14·10¹²⁶-23)/9 = 1(5)₁₂₅3_<127> = 1096928051_<10> · 12498625107494737_<17> · C102

C102 = P42 · P60

P42 = 363241471005671447535513678139960218287887_<42>

P60 = 312355901867046413627024946541023325632565835499451550899237_<60>

Number: 15553_126
N=113460617271489095821001999614229916567009542616345391734366387186548576373031471892411915187394642219
  ( 102 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=363241471005671447535513678139960218287887 (pp42)
 r2=312355901867046413627024946541023325632565835499451550899237 (pp60)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.44 hours.
Scaled time: 6.89 units (timescale=2.004).
Factorization parameters were as follows:
name: 15553_126
n: 113460617271489095821001999614229916567009542616345391734366387186548576373031471892411915187394642219
m: 10000000000000000000000000
c5: 140
c0: -23
skew: 0.7
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:49098, AFBsize:63933, largePrimes:2213987 encountered
Relations: rels:2276628, finalFF:160025
Max relations in full relation-set: 28
Initial matrix: 113098 x 160025 with sparse part having weight 16087550.
Pruned matrix : 105821 x 106450 with weight 8492782.
Total sieving time: 3.25 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.44 hours.
 --------- CPU info (if available) ----------

(14·10¹¹²-23)/9 = 1(5)₁₁₁3_<113> = 19421 · 8916931 · 2328765211_<10> · C92

C92 = P37 · P55

P37 = 8602097249074871783783820192981298307_<37>

P55 = 4484029687158018042424643794202980992275372478191873239_<55>

Wed Mar 19 10:47:13 2008  Msieve v. 1.33
Wed Mar 19 10:47:13 2008  random seeds: 40f75615 29c48224
Wed Mar 19 10:47:13 2008  factoring 38572059436672044932250519700222956042161785286721937826457048311314788122676721518589306373 (92 digits)
Wed Mar 19 10:47:14 2008  searching for 15-digit factors
Wed Mar 19 10:47:16 2008  commencing quadratic sieve (92-digit input)
Wed Mar 19 10:47:16 2008  using multiplier of 5
Wed Mar 19 10:47:16 2008  using 64kb Pentium 4 sieve core
Wed Mar 19 10:47:16 2008  sieve interval: 18 blocks of size 65536
Wed Mar 19 10:47:16 2008  processing polynomials in batches of 6
Wed Mar 19 10:47:16 2008  using a sieve bound of 1821679 (68077 primes)
Wed Mar 19 10:47:16 2008  using large prime bound of 198563011 (27 bits)
Wed Mar 19 10:47:16 2008  using double large prime bound of 863409753664201 (42-50 bits)
Wed Mar 19 10:47:16 2008  using trial factoring cutoff of 50 bits
Wed Mar 19 10:47:16 2008  polynomial 'A' values have 12 factors
Wed Mar 19 14:27:08 2008  68403 relations (17106 full + 51297 combined from 870879 partial), need 68173
Wed Mar 19 14:27:11 2008  begin with 887985 relations
Wed Mar 19 14:27:12 2008  reduce to 174296 relations in 10 passes
Wed Mar 19 14:27:12 2008  attempting to read 174296 relations
Wed Mar 19 14:27:17 2008  recovered 174296 relations
Wed Mar 19 14:27:17 2008  recovered 156172 polynomials
Wed Mar 19 14:27:18 2008  attempting to build 68403 cycles
Wed Mar 19 14:27:18 2008  found 68403 cycles in 6 passes
Wed Mar 19 14:27:18 2008  distribution of cycle lengths:
Wed Mar 19 14:27:18 2008     length 1 : 17106
Wed Mar 19 14:27:18 2008     length 2 : 12193
Wed Mar 19 14:27:18 2008     length 3 : 11888
Wed Mar 19 14:27:18 2008     length 4 : 9338
Wed Mar 19 14:27:18 2008     length 5 : 6854
Wed Mar 19 14:27:18 2008     length 6 : 4505
Wed Mar 19 14:27:18 2008     length 7 : 2791
Wed Mar 19 14:27:18 2008     length 9+: 3728
Wed Mar 19 14:27:18 2008  largest cycle: 22 relations
Wed Mar 19 14:27:18 2008  matrix is 68077 x 68403 (17.0 MB) with weight 4177014 (61.06/col)
Wed Mar 19 14:27:18 2008  sparse part has weight 4177014 (61.06/col)
Wed Mar 19 14:27:19 2008  filtering completed in 3 passes
Wed Mar 19 14:27:19 2008  matrix is 64492 x 64556 (16.1 MB) with weight 3955024 (61.27/col)
Wed Mar 19 14:27:19 2008  sparse part has weight 3955024 (61.27/col)
Wed Mar 19 14:27:20 2008  saving the first 48 matrix rows for later
Wed Mar 19 14:27:20 2008  matrix is 64444 x 64556 (9.5 MB) with weight 3034679 (47.01/col)
Wed Mar 19 14:27:20 2008  sparse part has weight 2092995 (32.42/col)
Wed Mar 19 14:27:20 2008  matrix includes 64 packed rows
Wed Mar 19 14:27:20 2008  using block size 21845 for processor cache size 512 kB
Wed Mar 19 14:27:21 2008  commencing Lanczos iteration
Wed Mar 19 14:27:21 2008  memory use: 9.6 MB
Wed Mar 19 14:27:59 2008  lanczos halted after 1020 iterations (dim = 64444)
Wed Mar 19 14:28:00 2008  recovered 18 nontrivial dependencies
Wed Mar 19 14:28:00 2008  prp37 factor: 8602097249074871783783820192981298307
Wed Mar 19 14:28:00 2008  prp55 factor: 4484029687158018042424643794202980992275372478191873239
Wed Mar 19 14:28:00 2008  elapsed time 03:40:47

(14·10¹²⁸-23)/9 = 1(5)₁₂₇3_<129> = 3³ · 10490799089_<11> · 10003931977271_<14> · C104

C104 = P33 · P72

P33 = 187409363464363718474869100062621_<33>

P72 = 292921450878592546975162520988878794100375547144807005806036350434938361_<72>

Number: 15553_128
N=54896222654214913716199732368230513011479825410843239174868664298416887368955153223689788344131375104181
  ( 104 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=187409363464363718474869100062621 (pp33)
 r2=292921450878592546975162520988878794100375547144807005806036350434938361 (pp72)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.79 hours.
Scaled time: 11.55 units (timescale=1.996).
Factorization parameters were as follows:
name: 15553_128
n: 54896222654214913716199732368230513011479825410843239174868664298416887368955153223689788344131375104181
m: 20000000000000000000000000
c5: 875
c0: -46
skew: 0.55
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1150001)
Primes: RFBsize:63951, AFBsize:63723, largePrimes:1580931 encountered
Relations: rels:1611418, finalFF:193201
Max relations in full relation-set: 28
Initial matrix: 127740 x 193201 with sparse part having weight 17142434.
Pruned matrix : 111485 x 112187 with weight 8144756.
Total sieving time: 5.60 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.79 hours.
 --------- CPU info (if available) ----------

(14·10¹²⁹-23)/9 = 1(5)₁₂₈3_<130> = C130

C130 = P46 · P84

P46 = 5749413403024550933574604752036293641351380377_<46>

P84 = 270559002547500945368356658064162976416834648929786395630819569640571746923377726089_<84>

Number: 15553_129
N=1555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553
  ( 130 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=5749413403024550933574604752036293641351380377 (pp46)
 r2=270559002547500945368356658064162976416834648929786395630819569640571746923377726089 (pp84)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.45 hours.
Scaled time: 8.83 units (timescale=1.986).
Factorization parameters were as follows:
name: 15553_129
n: 1555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553
m: 100000000000000000000000000
c5: 7
c0: -115
skew: 1.75
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64213, largePrimes:1449116 encountered
Relations: rels:1418473, finalFF:143850
Max relations in full relation-set: 28
Initial matrix: 128229 x 143850 with sparse part having weight 10566283.
Pruned matrix : 124066 x 124771 with weight 7799437.
Total sieving time: 4.26 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.45 hours.
 --------- CPU info (if available) ----------

(14·10¹¹⁸-23)/9 = 1(5)₁₁₇3_<119> = 331068349 · 5144266036542673_<16> · C94

C94 = P40 · P55

P40 = 4090898917791232952071545697006570921621_<40>

P55 = 2232675951016315988867127284632626987970566041942101009_<55>

Wed Mar 19 14:37:35 2008  Msieve v. 1.33
Wed Mar 19 14:37:35 2008  random seeds: f6411e96 e5f28ecf
Wed Mar 19 14:37:35 2008  factoring 9133651631791158911928100522746171669608341045686510741665627960105811317649914017350204015589 (94 digits)
Wed Mar 19 14:37:37 2008  searching for 15-digit factors
Wed Mar 19 14:37:39 2008  commencing quadratic sieve (94-digit input)
Wed Mar 19 14:37:39 2008  using multiplier of 21
Wed Mar 19 14:37:39 2008  using 64kb Pentium 4 sieve core
Wed Mar 19 14:37:39 2008  sieve interval: 18 blocks of size 65536
Wed Mar 19 14:37:39 2008  processing polynomials in batches of 6
Wed Mar 19 14:37:39 2008  using a sieve bound of 2093807 (77340 primes)
Wed Mar 19 14:37:39 2008  using large prime bound of 297320594 (28 bits)
Wed Mar 19 14:37:39 2008  using double large prime bound of 1785685485840044 (42-51 bits)
Wed Mar 19 14:37:39 2008  using trial factoring cutoff of 51 bits
Wed Mar 19 14:37:39 2008  polynomial 'A' values have 12 factors
Wed Mar 19 21:09:10 2008  77649 relations (18843 full + 58806 combined from 1137793 partial), need 77436
Wed Mar 19 21:09:14 2008  begin with 1156636 relations
Wed Mar 19 21:09:16 2008  reduce to 203477 relations in 12 passes
Wed Mar 19 21:09:16 2008  attempting to read 203477 relations
Wed Mar 19 21:09:22 2008  recovered 203477 relations
Wed Mar 19 21:09:22 2008  recovered 189051 polynomials
Wed Mar 19 21:09:23 2008  attempting to build 77649 cycles
Wed Mar 19 21:09:23 2008  found 77648 cycles in 5 passes
Wed Mar 19 21:09:23 2008  distribution of cycle lengths:
Wed Mar 19 21:09:23 2008     length 1 : 18843
Wed Mar 19 21:09:23 2008     length 2 : 13506
Wed Mar 19 21:09:23 2008     length 3 : 13112
Wed Mar 19 21:09:23 2008     length 4 : 10424
Wed Mar 19 21:09:23 2008     length 5 : 7886
Wed Mar 19 21:09:23 2008     length 6 : 5463
Wed Mar 19 21:09:23 2008     length 7 : 3500
Wed Mar 19 21:09:23 2008     length 9+: 4914
Wed Mar 19 21:09:23 2008  largest cycle: 19 relations
Wed Mar 19 21:09:23 2008  matrix is 77340 x 77648 (21.5 MB) with weight 5315713 (68.46/col)
Wed Mar 19 21:09:23 2008  sparse part has weight 5315713 (68.46/col)
Wed Mar 19 21:09:25 2008  filtering completed in 3 passes
Wed Mar 19 21:09:25 2008  matrix is 73810 x 73874 (20.5 MB) with weight 5076979 (68.72/col)
Wed Mar 19 21:09:25 2008  sparse part has weight 5076979 (68.72/col)
Wed Mar 19 21:09:26 2008  saving the first 48 matrix rows for later
Wed Mar 19 21:09:26 2008  matrix is 73762 x 73874 (14.4 MB) with weight 4199014 (56.84/col)
Wed Mar 19 21:09:26 2008  sparse part has weight 3337062 (45.17/col)
Wed Mar 19 21:09:26 2008  matrix includes 64 packed rows
Wed Mar 19 21:09:26 2008  using block size 21845 for processor cache size 512 kB
Wed Mar 19 21:09:27 2008  commencing Lanczos iteration
Wed Mar 19 21:09:27 2008  memory use: 13.0 MB
Wed Mar 19 21:10:26 2008  lanczos halted after 1168 iterations (dim = 73758)
Wed Mar 19 21:10:27 2008  recovered 16 nontrivial dependencies
Wed Mar 19 21:10:28 2008  prp40 factor: 4090898917791232952071545697006570921621
Wed Mar 19 21:10:28 2008  prp55 factor: 2232675951016315988867127284632626987970566041942101009
Wed Mar 19 21:10:28 2008  elapsed time 06:32:53

(14·10¹³⁵-23)/9 = 1(5)₁₃₄3_<136> = C136

C136 = P36 · P100

P36 = 421082122543377471948099040072049191_<36>

P100 = 3694185699834148430250517608597883013280312326005666129435829336555704216470266353772323806409529783_<100>

Number: 15553_135
N=1555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553
  ( 136 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=421082122543377471948099040072049191 (pp36)
 r2=3694185699834148430250517608597883013280312326005666129435829336555704216470266353772323806409529783 (pp100)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.90 hours.
Scaled time: 13.68 units (timescale=1.983).
Factorization parameters were as follows:
name: 15553_135
n: 1555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553
m: 1000000000000000000000000000
c5: 14
c0: -23
skew: 1.1
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1225001)
Primes: RFBsize:78498, AFBsize:63993, largePrimes:1583247 encountered
Relations: rels:1614463, finalFF:201783
Max relations in full relation-set: 28
Initial matrix: 142559 x 201783 with sparse part having weight 16529259.
Pruned matrix : 124806 x 125582 with weight 8623929.
Total sieving time: 6.66 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 6.90 hours.
 --------- CPU info (if available) ----------

Mar 19, 2008 (2nd)

By Jo Yeong Uk / GMP-ECM, Msieve, GGNFS

(14·10¹⁴³-23)/9 = 1(5)₁₄₂3_<144> = 3 · 22139693374793_<14> · C130

C130 = P31 · P99

P31 = 4033985856450760851705573910811_<31>

P99 = 580574956790360292326396245650795930374736048470567567465451678105744062669016644038536851027792137_<99>

(14·10¹⁴⁷-23)/9 = 1(5)₁₄₆3_<148> = 179 · 415957 · 16374811 · 653133609550067634665059_<24> · C109

C109 = P29 · P35 · P45

P29 = 56584859883732260957279040013_<29>

P35 = 80733674721485964418028247214298861_<35>

P45 = 427612866165966729085518073472242602764976743_<45>

Wed Mar 19 10:25:07 2008  
Wed Mar 19 10:25:07 2008  
Wed Mar 19 10:25:07 2008  Msieve v. 1.32
Wed Mar 19 10:25:07 2008  random seeds: f8d730fa 637ad895
Wed Mar 19 10:25:07 2008  factoring 34522758043765468944146280720649561007338052832042965993511737760269487716389723 (80 digits)
Wed Mar 19 10:25:07 2008  no P-1/P+1/ECM available, skipping
Wed Mar 19 10:25:07 2008  commencing quadratic sieve (80-digit input)
Wed Mar 19 10:25:07 2008  using multiplier of 13
Wed Mar 19 10:25:07 2008  using 32kb Intel Core sieve core
Wed Mar 19 10:25:07 2008  sieve interval: 12 blocks of size 32768
Wed Mar 19 10:25:07 2008  processing polynomials in batches of 17
Wed Mar 19 10:25:07 2008  using a sieve bound of 1255967 (48647 primes)
Wed Mar 19 10:25:07 2008  using large prime bound of 125596700 (26 bits)
Wed Mar 19 10:25:07 2008  using trial factoring cutoff of 27 bits
Wed Mar 19 10:25:07 2008  polynomial 'A' values have 10 factors
Wed Mar 19 10:36:44 2008  48821 relations (25337 full + 23484 combined from 262308 partial), need 48743
Wed Mar 19 10:36:44 2008  begin with 287645 relations
Wed Mar 19 10:36:44 2008  reduce to 69412 relations in 2 passes
Wed Mar 19 10:36:44 2008  attempting to read 69412 relations
Wed Mar 19 10:36:45 2008  recovered 69412 relations
Wed Mar 19 10:36:45 2008  recovered 58119 polynomials
Wed Mar 19 10:36:45 2008  attempting to build 48821 cycles
Wed Mar 19 10:36:45 2008  found 48821 cycles in 1 passes
Wed Mar 19 10:36:45 2008  distribution of cycle lengths:
Wed Mar 19 10:36:45 2008     length 1 : 25337
Wed Mar 19 10:36:45 2008     length 2 : 23484
Wed Mar 19 10:36:45 2008  largest cycle: 2 relations
Wed Mar 19 10:36:45 2008  matrix is 48647 x 48821 with weight 1508644 (avg 30.90/col)
Wed Mar 19 10:36:45 2008  filtering completed in 4 passes
Wed Mar 19 10:36:45 2008  matrix is 41292 x 41356 with weight 1250071 (avg 30.23/col)
Wed Mar 19 10:36:45 2008  saving the first 48 matrix rows for later
Wed Mar 19 10:36:45 2008  matrix is 41244 x 41356 with weight 912138 (avg 22.06/col)
Wed Mar 19 10:36:45 2008  matrix includes 64 packed rows
Wed Mar 19 10:36:45 2008  commencing Lanczos iteration
Wed Mar 19 10:37:08 2008  lanczos halted after 654 iterations (dim = 41227)
Wed Mar 19 10:37:08 2008  recovered 10 nontrivial dependencies
Wed Mar 19 10:37:08 2008  prp35 factor: 80733674721485964418028247214298861
Wed Mar 19 10:37:08 2008  prp45 factor: 427612866165966729085518073472242602764976743
Wed Mar 19 10:37:08 2008  elapsed time 00:12:01

(14·10¹⁰⁶-23)/9 = 1(5)₁₀₅3_<107> = 103 · 139 · C103

C103 = P37 · P66

P37 = 9347544516743237437692714740238292837_<37>

P66 = 116234742855085529578876954254245021476557271363549685111789948257_<66>

Number: 15553_106
N=1086509433230114937176472414301568453974684330205738321963788192746773455022389855106206297098243735109
  ( 103 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=9347544516743237437692714740238292837 (pp37)
 r2=116234742855085529578876954254245021476557271363549685111789948257 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.51 hours.
Scaled time: 0.95 units (timescale=1.856).
Factorization parameters were as follows:
n: 1086509433230114937176472414301568453974684330205738321963788192746773455022389855106206297098243735109
m: 1000000000000000000000
c5: 140
c0: -23
skew: 0.7
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 280001)
Primes: RFBsize:30757, AFBsize:30714, largePrimes:977479 encountered
Relations: rels:888661, finalFF:78082
Max relations in full relation-set: 28
Initial matrix: 61538 x 78082 with sparse part having weight 3514921.
Pruned matrix : 54793 x 55164 with weight 1839048.
Total sieving time: 0.49 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,107,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.51 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178324k/8912896k available (2439k kernel code, 208016k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 4812.91 BogoMIPS (lpj=2406459)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405110)
Calibrating delay using timer specific routine.. 4809.52 BogoMIPS (lpj=2404760)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405116)

(14·10¹¹⁵-23)/9 = 1(5)₁₁₄3_<116> = 13 · 881 · 17189 · C107

C107 = P41 · P67

P41 = 21428391549316742681539165554993157989289_<41>

P67 = 3687449493348667986819089625807553114935732965345671067328548973481_<67>

Number: 15553_115
N=79016111561804901439724518048042668393209341149478405645387815768537964430607278443932418912722354943045009
  ( 107 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=21428391549316742681539165554993157989289 (pp41)
 r2=3687449493348667986819089625807553114935732965345671067328548973481 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.70 hours.
Scaled time: 1.29 units (timescale=1.852).
Factorization parameters were as follows:
n: 79016111561804901439724518048042668393209341149478405645387815768537964430607278443932418912722354943045009
m: 100000000000000000000000
c5: 14
c0: -23
skew: 1.1
type: snfs
Factor base limits: 450000/450000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [225000, 350001)
Primes: RFBsize:37706, AFBsize:37874, largePrimes:1330452 encountered
Relations: rels:1334974, finalFF:152187
Max relations in full relation-set: 28
Initial matrix: 75648 x 152187 with sparse part having weight 10819504.
Pruned matrix : 58958 x 59400 with weight 2741608.
Total sieving time: 0.66 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,450000,450000,25,25,44,44,2.3,2.3,25000
total time: 0.70 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178324k/8912896k available (2439k kernel code, 208016k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 4812.91 BogoMIPS (lpj=2406459)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405110)
Calibrating delay using timer specific routine.. 4809.52 BogoMIPS (lpj=2404760)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405116)

Mar 19, 2008

The factor table of 155...553 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Mar 18, 2008

By matsui / GGNFS

(5·10¹⁶⁹+7)/3 = 1(6)₁₆₈9_<170> = 269 · 72333221754181_<14> · C153

C153 = P48 · P53 · P54

P48 = 133553343132611065513453492437199063759951936543_<48>

P53 = 41410460248177205270577696479970680990973907664429989_<53>

P54 = 154879464781860811388364739624524998886174833420229623_<54>

N=856561717379015803405657536995682255393219509779765949997691370068391354702603316745078491194928969705420851888432244686858900220387445762659400177323821
  ( 153 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=133553343132611065513453492437199063759951936543 (pp48)
 r2=41410460248177205270577696479970680990973907664429989 (pp53)
 r3=154879464781860811388364739624524998886174833420229623 (pp54)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 129.13 hours.
Scaled time: 143.08 units (timescale=1.108).
Factorization parameters were as follows:
n: 856561717379015803405657536995682255393219509779765949997691370068391354702603316745078491194928969705420851888432244686858900220387445762659400177323821
m: 10000000000000000000000000000000000
c5: 1
c0: 14
skew: 1.7
type: snfs

Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 6500001)
Primes: RFBsize:412849, AFBsize:412741, largePrimes:5966140 encountered
Relations: rels:6244816, finalFF:943149
Max relations in full relation-set: 28
Initial matrix: 825654 x 943149 with sparse part having weight 48340192.
Pruned matrix : 725369 x 729561 with weight 34629757.
Total sieving time: 117.73 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 11.00 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 129.13 hours.

Mar 17, 2008

By Robert Backstrom / GMP-ECM

(13·10¹⁶⁴+41)/9 = 1(4)₁₆₃9_<165> = 1102271 · C159

C159 = P42 · P117

P42 = 310858280205973042295350064207669674079891_<42>

P117 = 421550900452233303155039018641729142102897981293204893760745450029677022449219253781047183543781801689390473334874309_<117>

Mar 16, 2008 (3rd)

By matsui / GGNFS

(32·10¹⁶⁵-23)/9 = 3(5)₁₆₄3_<166> = 11 · 19² · 29 · 47 · 7487 · 26065774177_<11> · 65884869659758319_<17> · C128

C128 = P47 · P82

P47 = 30477371599865741466703860063313965404859571013_<47>

P82 = 1676370705983994919127781209659746453528383554471372426173858599217463167063091237_<82>

N=51091372945403489730523310016243629310252962374795853267961684716887552607352787611729710825690056622399766686516174317499513081
  ( 128 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=30477371599865741466703860063313965404859571013 (pp47)
 r2=1676370705983994919127781209659746453528383554471372426173858599217463167063091237 (pp82)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 84.17 hours.
Scaled time: 143.01 units (timescale=1.699).
Factorization parameters were as follows:
n: 51091372945403489730523310016243629310252962374795853267961684716887552607352787611729710825690056622399766686516174317499513081
m: 2000000000000000000000000000000000
c5: 1
c0: -23
skew: 1.87
type: snfs

Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 4600001)
Primes: RFBsize:348513, AFBsize:348066, largePrimes:5689503 encountered
Relations: rels:5841604, finalFF:796947
Max relations in full relation-set: 28
Initial matrix: 696643 x 796947 with sparse part having weight 40407504.
Pruned matrix : 610235 x 613782 with weight 27188343.
Total sieving time: 79.40 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 4.48 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 84.17 hours.

Mar 16, 2008 (2nd)

By Tyler Cadigan / GGNFS, Msieve

(25·10¹⁸³-1)/3 = 8(3)₁₈₃_<184> = 13 · 264283155301751969_<18> · 3549264066261561396021839666828027_<34> · C132

C132 = P64 · P68

P64 = 8935144544408999776115842763978720444245031871108628792866831079_<64>

P68 = 76483195332826533787093208520476398502764772883004976691618763747133_<68>

Number: 83333_183
N=683388405517072877233927862242245555525777832139299820368098214942685744600601296640806157169483609696082817414193194488909381546507
  ( 132 digits)
SNFS difficulty: 184 digits.
Divisors found:
 r1=8935144544408999776115842763978720444245031871108628792866831079
 r2=76483195332826533787093208520476398502764772883004976691618763747133
Version: 
Total time: 358.73 hours.
Scaled time: 927.31 units (timescale=2.585).
Factorization parameters were as follows:
n: 683388405517072877233927862242245555525777832139299820368098214942685744600601296640806157169483609696082817414193194488909381546507
m: 5000000000000000000000000000000000000
c5: 8
c0: -1
skew: 0.66
type: snfs
Y0: -5000000000000000000000000000000000000
Y1: 1Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 9700001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 896227 x 896475
Total sieving time: 358.73 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,184,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 358.73 hours.
 --------- CPU info (if available) ----------

Mar 16, 2008

By Jo Yeong Uk / GGNFS

(13·10¹⁵⁶+41)/9 = 1(4)₁₅₅9_<157> = 3² · 945224161592701729_<18> · 78240352765175835206467754968382924481389_<41> · C97

C97 = P35 · P62

P35 = 56811743013055887298662901382398663_<35>

P62 = 38199229693458428198506848714264339346199481273611746416402587_<62>

Number: 14449_156
N=2170164820641453841771054721472954317615265554044202740819058596701382825101488628052277538541181
  ( 97 digits)
Divisors found:
 r1=56811743013055887298662901382398663 (pp35)
 r2=38199229693458428198506848714264339346199481273611746416402587 (pp62)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.13 hours.
Scaled time: 9.54 units (timescale=1.859).
Factorization parameters were as follows:
name: 14449_156
n:  2170164820641453841771054721472954317615265554044202740819058596701382825101488628052277538541181
m:  1296386468790859477
deg: 5
c5: 592680
c4: 2039452145
c3: -70890504460049
c2: -17771658792168670
c1: 66587067320650168689
c0: 30394714584259330224570
skew: 1379.250
type: gnfs
# adj. I(F,S) = 47.320
# E(F1,F2) = 4.478483e-03
# GGNFS version 0.77.1-20050930-nocona polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=58.00000000, seed=1205573568.
# maxskew=1500.0
# These parameters should be manually set:
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000

type: gnfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [650000, 1450001)
Primes: RFBsize:100021, AFBsize:99767, largePrimes:3951704 encountered
Relations: rels:3905347, finalFF:266868
Max relations in full relation-set: 28
Initial matrix: 199871 x 266868 with sparse part having weight 26369457.
Pruned matrix : 169463 x 170526 with weight 14580729.
Polynomial selection time: 0.28 hours.
Total sieving time: 4.61 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
gnfs,96,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1300000,1300000,26,26,48,48,2.5,2.5,50000
total time: 5.13 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178324k/8912896k available (2439k kernel code, 208016k reserved, 1234k data, 192k init)
Calibrating delay using timer specific routine.. 4812.91 BogoMIPS (lpj=2406459)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405110)
Calibrating delay using timer specific routine.. 4809.52 BogoMIPS (lpj=2404760)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405116)

Mar 15, 2008 (2nd)

By Robert Backstrom / GMP-ECM

(13·10¹⁵⁹+41)/9 = 1(4)₁₅₈9_<160> = 3 · 7 · C158

C158 = P36 · P123

P36 = 323994497004687485543951803426936081_<36>

P123 = 212297027940180242688781043672877820471173117695010579301262769776723616074689965201258808111992813367497457405314499547149_<123>

Mar 15, 2008

By Sinkiti Sibata / GGNFS, GMP-ECM

(13·10¹⁴⁴+41)/9 = 1(4)₁₄₃9_<145> = 3 · 113 · C142

C142 = P33 · P43 · P67

P33 = 383015513599750490805951630014399_<33>

P43 = 5624483396558590000322516765930782632188359_<43>

P67 = 1977890027058051288896753962852997307409954782630180176907476871251_<67>

Number: 14449_144
N=4260898066207800721075057358243198951163552933464437889216650278597181252048508685676827269747623729924614880367092756473287446738774172402491
  ( 142 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=383015513599750490805951630014399 (pp33)
 r2=5624483396558590000322516765930782632188359 (pp43)
 r3=1977890027058051288896753962852997307409954782630180176907476871251 (pp67)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 29.36 hours.
Scaled time: 19.79 units (timescale=0.674).
Factorization parameters were as follows:
name: 14449_144
n: 4260898066207800721075057358243198951163552933464437889216650278597181252048508685676827269747623729924614880367092756473287446738774172402491
m: 100000000000000000000000000000
c5: 13
c0: 410
skew: 1.99
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 3550001)
Primes: RFBsize:114155, AFBsize:114263, largePrimes:2973559 encountered
Relations: rels:2997988, finalFF:273808
Max relations in full relation-set: 28
Initial matrix: 228483 x 273808 with sparse part having weight 31696103.
Pruned matrix : 215545 x 216751 with weight 23512675.
Total sieving time: 27.25 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 1.78 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 29.36 hours.
 --------- CPU info (if available) ----------

(11·10¹⁹⁹+61)/9 = 1(2)₁₉₈9_<200> = 19 · 449 · C196

C196 = P31 · C165

P31 = 3841095258017395523843912468543_<31>

C165 = [372988254599477911916222836024223504927065229009928696460004135733498615633072233566730189925228638215606368739612714868913553887169813562866201417920242857682106313_<165>]

Mar 14, 2008 (4th)

By Jo Yeong Uk / GMP-ECM

(13·10¹⁵⁶+41)/9 = 1(4)₁₅₅9_<157> = 3² · 945224161592701729_<18> · C138

C138 = P41 · C97

P41 = 78240352765175835206467754968382924481389_<41>

C97 = [2170164820641453841771054721472954317615265554044202740819058596701382825101488628052277538541181_<97>]

Mar 14, 2008 (3rd)

By Robert Backstrom / GGNFS

(13·10¹⁶¹+23)/9 = 1(4)₁₆₀7_<162> = 3³ · 17 · 103 · 1724029 · 46124385028404659193551_<23> · C128

C128 = P62 · P67

P62 = 19676012510318678785250017004699445567484314567847182516372343_<62>

P67 = 1952714211361224583977547309784021653764745429767765757488007042063_<67>

Number: n
N=38421629251820527636078806431119924133505460598130764167098822263247643780007103800496891083800862720674047482882007176570863609
  ( 128 digits)
SNFS difficulty: 162 digits.
Divisors found:

Fri Mar 14 19:16:14 2008  prp62 factor: 19676012510318678785250017004699445567484314567847182516372343
Fri Mar 14 19:16:14 2008  prp67 factor: 1952714211361224583977547309784021653764745429767765757488007042063
Fri Mar 14 19:16:14 2008  elapsed time 01:25:31 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 60.45 hours.
Scaled time: 106.09 units (timescale=1.755).
Factorization parameters were as follows:
name: KA_1_4_160_7
n: 38421629251820527636078806431119924133505460598130764167098822263247643780007103800496891083800862720674047482882007176570863609
type: snfs
skew: 0.71
deg: 5
c5: 130
c0: 23
m: 100000000000000000000000000000000
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3000161)
Primes: RFBsize:203362, AFBsize:203442, largePrimes:7433398 encountered
Relations: rels:6842408, finalFF:440642
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 60.18 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.3,2.3,100000
total time: 60.45 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Mar 14, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(13·10¹³⁹+41)/9 = 1(4)₁₃₈9_<140> = 7237 · C136

C136 = P37 · P45 · P55

P37 = 1080444914227488251714735602663923887_<37>

P45 = 310581946039662137936555730848539967041553081_<45>

P55 = 5947896926520727366907749778159525455328262786721888891_<55>

Number: 14449_139
N=1995916048700351588288578754241321603488247125113229852762808407412525140865613437120967865751615924339428553882056714722183839221285677
  ( 136 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=1080444914227488251714735602663923887 (pp37)
 r2=310581946039662137936555730848539967041553081 (pp45)
 r3=5947896926520727366907749778159525455328262786721888891 (pp55)
Version: GGNFS-0.77.1-20060513-k8
Total time: 14.24 hours.
Scaled time: 28.50 units (timescale=2.001).
Factorization parameters were as follows:
name: 14449_139
n: 1995916048700351588288578754241321603488247125113229852762808407412525140865613437120967865751615924339428553882056714722183839221285677
m: 10000000000000000000000000000
c5: 13
c0: 410
skew: 1.99
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2150001)
Primes: RFBsize:100021, AFBsize:100074, largePrimes:2804952 encountered
Relations: rels:2798715, finalFF:256766
Max relations in full relation-set: 28
Initial matrix: 200160 x 256766 with sparse part having weight 26772641.
Pruned matrix : 184200 x 185264 with weight 17454800.
Total sieving time: 13.62 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 14.24 hours.
 --------- CPU info (if available) ----------

(13·10¹⁴⁹+41)/9 = 1(4)₁₄₈9_<150> = 17 · C148

C148 = P72 · P77

P72 = 137347660736329540541751855501034585413185542247087385476267638114996691_<72>

P77 = 61862954058280063245229953724726901319795857549507692379899427183521908512267_<77>

Number: 14449_149
N=8496732026143790849673202614379084967320261437908496732026143790849673202614379084967320261437908496732026143790849673202614379084967320261437908497
  ( 148 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=137347660736329540541751855501034585413185542247087385476267638114996691 (pp72)
 r2=61862954058280063245229953724726901319795857549507692379899427183521908512267 (pp77)
Version: GGNFS-0.77.1-20060513-k8
Total time: 25.99 hours.
Scaled time: 50.86 units (timescale=1.957).
Factorization parameters were as follows:
name: 14449_149
n: 8496732026143790849673202614379084967320261437908496732026143790849673202614379084967320261437908496732026143790849673202614379084967320261437908497
m: 1000000000000000000000000000000
c5: 13
c0: 410
skew: 1.99
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:175984, largePrimes:5486687 encountered
Relations: rels:5319822, finalFF:408667
Max relations in full relation-set: 28
Initial matrix: 352351 x 408667 with sparse part having weight 36707080.
Pruned matrix : 328589 x 330414 with weight 26026219.
Total sieving time: 24.40 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 1.30 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 25.99 hours.
 --------- CPU info (if available) ----------

Mar 14, 2008

By matsui / GGNFS

2·10¹⁶⁵-9 = 1(9)₁₆₄1_<166> = 11 · 457527644458064916785243595451_<30> · C135

C135 = P50 · P86

P50 = 10380464989853334806493414428274868458216509448469_<50>

P86 = 38282753110901991590906115105218234489358257188870210443245138602465182775068426383299_<86>

N=397392778382916963637700048853965083487465415508744847291870178477993817516199866163976430024051422843226002208841256962925794882719231
  ( 135 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=10380464989853334806493414428274868458216509448469 (pp50)
 r2=38282753110901991590906115105218234489358257188870210443245138602465182775068426383299 (pp86)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 59.33 hours.
Scaled time: 68.94 units (timescale=1.162).
Factorization parameters were as follows:
n: 397392778382916963637700048853965083487465415508744847291870178477993817516199866163976430024051422843226002208841256962925794882719231
m: 1000000000000000000000000000000000
c5: 2
c0: -9
skew: 1.35
type: snfs

Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 4800001)
Primes: RFBsize:348513, AFBsize:348526, largePrimes:5812903 encountered
Relations: rels:6016526, finalFF:840605
Max relations in full relation-set: 28
Initial matrix: 697104 x 840605 with sparse part having weight 45363679.
Pruned matrix : 575958 x 579507 with weight 29914315.
Total sieving time: 52.99 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 6.00 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 59.33 hours.

Mar 13, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(13·10¹²⁸+41)/9 = 1(4)₁₂₇9_<129> = C129

C129 = P63 · P66

P63 = 879276544604910226814961729129827481250658463712668818370122309_<63>

P66 = 164276467205602984226476216588935499461222868575837590383237340461_<66>

Number: n
N=144444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449
  ( 129 digits)
SNFS difficulty: 129 digits.
Divisors found:

Thu Mar 13 15:18:03 2008  prp63 factor: 879276544604910226814961729129827481250658463712668818370122309
Thu Mar 13 15:18:03 2008  prp66 factor: 164276467205602984226476216588935499461222868575837590383237340461
Thu Mar 13 15:18:03 2008  elapsed time 00:11:24 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 3.16 hours.
Scaled time: 2.64 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_1_4_127_9
n: 144444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449
type: snfs
deg: 5
c5: 13000
c0: 41
skew: 0.32
m: 10000000000000000000000000
rlim: 800000
alim: 800000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved  special-q in [100000, 650833)
Primes: RFBsize:63951, AFBsize:63689, largePrimes:1559983 encountered
Relations: rels:1533763, finalFF:136673
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 3.08 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.5,2.5,50000
total time: 3.16 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

Mar 13, 2008

By Sinkiti Sibata / GGNFS

(13·10¹²⁹+41)/9 = 1(4)₁₂₈9_<130> = 3² · 7 · 83 · 677 · 2287 · 506887362987697_<15> · C105

C105 = P39 · P66

P39 = 403320046055777109046610052427009389053_<39>

P66 = 872702249677073427449981915399492394603014246802684484605353730059_<66>

Number: 14449_129
N=351978311532737548449964405792590044432251798869824835323670785490076165265575416679098233153448271644127
  ( 105 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=403320046055777109046610052427009389053 (pp39)
 r2=872702249677073427449981915399492394603014246802684484605353730059 (pp66)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 6.68 hours.
Scaled time: 4.51 units (timescale=0.675).
Factorization parameters were as follows:
name: 14449_129
n: 351978311532737548449964405792590044432251798869824835323670785490076165265575416679098233153448271644127
m: 100000000000000000000000000
c5: 13
c0: 410
skew: 1.99
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1100001)
Primes: RFBsize:63951, AFBsize:63919, largePrimes:1499538 encountered
Relations: rels:1486985, finalFF:157544
Max relations in full relation-set: 28
Initial matrix: 127935 x 157544 with sparse part having weight 12577546.
Pruned matrix : 119718 x 120421 with weight 7910460.
Total sieving time: 6.28 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 6.68 hours.
 --------- CPU info (if available) ----------

(13·10¹⁴³+41)/9 = 1(4)₁₄₂9_<144> = 547 · 4261 · 83933 · 101654957 · C124

C124 = P33 · P37 · P55

P33 = 468058260349480289619458523204589_<33>

P37 = 4838491154143931941878764558030793391_<37>

P55 = 3207235198502778015162165152178878034108309665144891213_<55>

Number: 14449_143
N=7263411930756334431054815675240590460026383859273092312980615738433171499794833346952595861772049365179133319212109264595687
  ( 124 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=468058260349480289619458523204589 (pp33)
 r2=4838491154143931941878764558030793391 (pp37)
 r3=3207235198502778015162165152178878034108309665144891213 (pp55)
Version: GGNFS-0.77.1-20060513-k8
Total time: 26.76 hours.
Scaled time: 53.26 units (timescale=1.990).
Factorization parameters were as follows:
name: 14449_143
n: 7263411930756334431054815675240590460026383859273092312980615738433171499794833346952595861772049365179133319212109264595687
m: 10000000000000000000000000000
c5: 13000
c0: 41
skew: 0.32
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 3750001)
Primes: RFBsize:100021, AFBsize:99689, largePrimes:3101893 encountered
Relations: rels:3216219, finalFF:250113
Max relations in full relation-set: 28
Initial matrix: 199777 x 250113 with sparse part having weight 32911341.
Pruned matrix : 187996 x 189058 with weight 23930321.
Total sieving time: 26.00 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.49 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 26.76 hours.
 --------- CPU info (if available) ----------

(13·10¹³³+41)/9 = 1(4)₁₃₂9_<134> = 17 · 6596820397_<10> · 2010236816539094083_<19> · C104

C104 = P42 · P63

P42 = 517649884092539390536611188644180047608897_<42>

P63 = 123775280010902446150077540889220597396514583675408960720813351_<63>

Number: 14449_133
N=64072259351165258960611191479962903530231838357246417129235599200904516844792796123931176281428583983847
  ( 104 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=517649884092539390536611188644180047608897 (pp42)
 r2=123775280010902446150077540889220597396514583675408960720813351 (pp63)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 12.38 hours.
Scaled time: 8.34 units (timescale=0.674).
Factorization parameters were as follows:
name: 14449_133
n: 64072259351165258960611191479962903530231838357246417129235599200904516844792796123931176281428583983847
m: 100000000000000000000000000
c5: 13000
c0: 41
skew: 0.32
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1675001)
Primes: RFBsize:78498, AFBsize:63689, largePrimes:1620424 encountered
Relations: rels:1639559, finalFF:180627
Max relations in full relation-set: 28
Initial matrix: 142254 x 180627 with sparse part having weight 17980539.
Pruned matrix : 131501 x 132276 with weight 11572853.
Total sieving time: 11.67 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.53 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 12.38 hours.
 --------- CPU info (if available) ----------

(13·10¹³⁸+41)/9 = 1(4)₁₃₇9_<139> = 3² · 991 · 3784737996862957_<16> · C119

C119 = P38 · P82

P38 = 39275505097585155078710771613618699661_<38>

P82 = 1089499611449474155941188972488893793360282827843797035637321410126382085780847823_<82>

Number: 14449_138
N=42790647543300868000531012460873380607706485262150894592544299144950220581224389005057327334131687329290331967382688003
  ( 119 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=39275505097585155078710771613618699661 (pp38)
 r2=1089499611449474155941188972488893793360282827843797035637321410126382085780847823 (pp82)
Version: GGNFS-0.77.1-20060513-k8
Total time: 19.87 hours.
Scaled time: 39.73 units (timescale=1.999).
Factorization parameters were as follows:
name: 14449_138
n: 42790647543300868000531012460873380607706485262150894592544299144950220581224389005057327334131687329290331967382688003
m: 1000000000000000000000000000
c5: 13000
c0: 41
skew: 0.32
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 3175001)
Primes: RFBsize:78498, AFBsize:63689, largePrimes:1805783 encountered
Relations: rels:1896587, finalFF:166064
Max relations in full relation-set: 28
Initial matrix: 142254 x 166064 with sparse part having weight 21301289.
Pruned matrix : 137347 x 138122 with weight 16677403.
Total sieving time: 19.49 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 19.87 hours.
 --------- CPU info (if available) ----------

Mar 12, 2008 (5th)

By Sinkiti Sibata / GGNFS

(13·10¹¹²+41)/9 = 1(4)₁₁₁9_<113> = 307 · C110

C110 = P46 · P64

P46 = 8572768217428917273838004418010090479942244487_<46>

P64 = 5488344773042031843138651813870233083606331551067207445911659661_<64>

Number: 14449_112
N=47050307636626854867897213174086138255519363011219688744118711545421643141512848353239232718060079623597538907
  ( 110 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=8572768217428917273838004418010090479942244487 (pp46)
 r2=5488344773042031843138651813870233083606331551067207445911659661 (pp64)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.81 hours.
Scaled time: 1.20 units (timescale=0.666).
Factorization parameters were as follows:
name: 14449_112
n: 47050307636626854867897213174086138255519363011219688744118711545421643141512848353239232718060079623597538907
m: 10000000000000000000000
c5: 1300
c0: 41
skew: 0.5
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:64309, largePrimes:2003845 encountered
Relations: rels:2009047, finalFF:176679
Max relations in full relation-set: 28
Initial matrix: 113474 x 176679 with sparse part having weight 13565947.
Pruned matrix : 92176 x 92807 with weight 4749967.
Total sieving time: 1.60 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.81 hours.
 --------- CPU info (if available) ----------

(13·10¹²⁵+41)/9 = 1(4)₁₂₄9_<126> = 1554391 · 2591023 · C113

C113 = P39 · P74

P39 = 381289435910446427225910525930919899803_<39>

P74 = 94062069350457232819353561152321954296011723467198330678707421280406128331_<74>

Number: 14449_125
N=35864873363205130270954386390806827723737536465615384529439091825776660100342021248266317605381766728041679618793
  ( 113 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=381289435910446427225910525930919899803 (pp39)
 r2=94062069350457232819353561152321954296011723467198330678707421280406128331 (pp74)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.79 hours.
Scaled time: 5.59 units (timescale=2.001).
Factorization parameters were as follows:
name: 14449_125
n: 35864873363205130270954386390806827723737536465615384529439091825776660100342021248266317605381766728041679618793
m: 10000000000000000000000000
c5: 13
c0: 41
skew: 1.26
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:64124, largePrimes:2267632 encountered
Relations: rels:2464267, finalFF:301761
Max relations in full relation-set: 28
Initial matrix: 113289 x 301761 with sparse part having weight 29886474.
Pruned matrix : 84010 x 84640 with weight 7199058.
Total sieving time: 2.63 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.79 hours.
 --------- CPU info (if available) ----------

(13·10¹²⁶+41)/9 = 1(4)₁₂₅9_<127> = 3 · 15605633977681604575639_<23> · C104

C104 = P42 · P62

P42 = 904847641670711020711019082822834496093841_<42>

P62 = 34097513719109247682145677399500333906397624571462875526708317_<62>

Number: 14449_126
N=30853054875570717616725973948709528454911957351445666387478574633512858115600884689245414260005067175597
  ( 104 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=904847641670711020711019082822834496093841 (pp42)
 r2=34097513719109247682145677399500333906397624571462875526708317 (pp62)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.69 hours.
Scaled time: 9.36 units (timescale=1.995).
Factorization parameters were as follows:
name: 14449_126
n: 30853054875570717616725973948709528454911957351445666387478574633512858115600884689245414260005067175597
m: 10000000000000000000000000
c5: 130
c0: 41
skew: 0.79
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:49098, AFBsize:63954, largePrimes:2306923 encountered
Relations: rels:2474799, finalFF:204406
Max relations in full relation-set: 28
Initial matrix: 113119 x 204406 with sparse part having weight 22772454.
Pruned matrix : 98877 x 99506 with weight 9226871.
Total sieving time: 4.48 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 4.69 hours.
 --------- CPU info (if available) ----------

(13·10¹²⁴+41)/9 = 1(4)₁₂₃9_<125> = 59 · 3203 · C119

C119 = P31 · P41 · P48

P31 = 5175757663323323463917452916699_<31>

P41 = 87280545998199448610509108990088503350991_<41>

P48 = 169200056742758350400056102242352593752657930093_<48>

Number: 14449_124
N=76434933586862128430679100866478166361220912833013776514837490511778917246249249614738536670835310352288608901847549937
  ( 119 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=5175757663323323463917452916699 (pp31)
 r2=87280545998199448610509108990088503350991 (pp41)
 r3=169200056742758350400056102242352593752657930093 (pp48)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 4.26 hours.
Scaled time: 2.88 units (timescale=0.675).
Factorization parameters were as follows:
name: 14449_124
n: 76434933586862128430679100866478166361220912833013776514837490511778917246249249614738536670835310352288608901847549937
m: 10000000000000000000000000
c5: 13
c0: 410
skew: 1.99
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:49098, AFBsize:63919, largePrimes:2203916 encountered
Relations: rels:2274248, finalFF:176608
Max relations in full relation-set: 28
Initial matrix: 113082 x 176608 with sparse part having weight 17252242.
Pruned matrix : 102053 x 102682 with weight 7545808.
Total sieving time: 3.90 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 4.26 hours.
 --------- CPU info (if available) ----------

(13·10¹³¹+41)/9 = 1(4)₁₃₀9_<132> = 4651 · 22379822107417_<14> · C115

C115 = P43 · P72

P43 = 2249090272651913721819392572240308879238027_<43>

P72 = 617008271333123742480108012577387394787114276114628954373956069679259761_<72>

Number: 14449_131
N=1387707301201101239142370408651903318062058439543780296573801125314505866008428422395864867644533736113263082131547
  ( 115 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=2249090272651913721819392572240308879238027 (pp43)
 r2=617008271333123742480108012577387394787114276114628954373956069679259761 (pp72)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.47 hours.
Scaled time: 12.90 units (timescale=1.995).
Factorization parameters were as follows:
name: 14449_131
n: 1387707301201101239142370408651903318062058439543780296573801125314505866008428422395864867644533736113263082131547
m: 100000000000000000000000000
c5: 130
c0: 41
skew: 0.79
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1250001)
Primes: RFBsize:63951, AFBsize:63954, largePrimes:1541842 encountered
Relations: rels:1537508, finalFF:155468
Max relations in full relation-set: 28
Initial matrix: 127972 x 155468 with sparse part having weight 14753604.
Pruned matrix : 121290 x 121993 with weight 9959479.
Total sieving time: 6.24 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 6.47 hours.
 --------- CPU info (if available) ----------

Mar 12, 2008 (4th)

By matsui / GGNFS

10¹⁷¹+7 = 1(0)₁₇₀7_<172> = 353 · 16139676313_<11> · 2503433995697_<13> · C146

C146 = P44 · P103

P44 = 18280520184492143617094205240248705703843689_<44>

P103 = 3835356858729892849185282132443271335225604500851042024555355541432430314460970459178772287450451105111_<103>

N=70112318470742189230991216185000433908480319262349860717935684928869182527261387878088634070747265932543928645509144531113608713830541790452994479
  ( 146 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=18280520184492143617094205240248705703843689 (pp44)
 r2=3835356858729892849185282132443271335225604500851042024555355541432430314460970459178772287450451105111 (pp103)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 173.95 hours.
Scaled time: 186.30 units (timescale=1.071).
Factorization parameters were as follows:
n: 70112318470742189230991216185000433908480319262349860717935684928869182527261387878088634070747265932543928645509144531113608713830541790452994479
m: 10000000000000000000000000000000000
c5: 10
c0: 7
skew: 0.93
type: snfs

Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 9100001)
Primes: RFBsize:412849, AFBsize:412181, largePrimes:6263624 encountered
Relations: rels:6537561, finalFF:925066
Max relations in full relation-set: 28
Initial matrix: 825096 x 925066 with sparse part having weight 73008744.
Pruned matrix : 748237 x 752426 with weight 57526687.
Total sieving time: 157.26 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 16.18 hours.
Time per square root: 0.36 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 173.95 hours.

Mar 12, 2008 (3rd)

By Jo Yeong Uk / GGNFS, GMP-ECM

(13·10¹⁷¹+23)/9 = 1(4)₁₇₀7_<172> = C172

C172 = P79 · P93

P79 = 3983898590622918946099742220376300090916709488135066216815900242393474298893881_<79>

P93 = 362570585467285289874408318951946873117767996253948597783388693466115940756746792298079012887_<93>

Number: 14447_171
N=1444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447
  ( 172 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=3983898590622918946099742220376300090916709488135066216815900242393474298893881 (pp79)
 r2=362570585467285289874408318951946873117767996253948597783388693466115940756746792298079012887 (pp93)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 131.74 hours.
Scaled time: 244.78 units (timescale=1.858).
Factorization parameters were as follows:
n: 1444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447
m: 10000000000000000000000000000000000
c5: 130
c0: 23
skew: 0.71
type: snfs
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 49/49
Sieved algebraic special-q in [4000000, 10200001)
Primes: RFBsize:539777, AFBsize:539940, largePrimes:10162557 encountered
Relations: rels:10122806, finalFF:1244958
Max relations in full relation-set: 28
Initial matrix: 1079784 x 1244958 with sparse part having weight 84970128.
Pruned matrix : 939205 x 944667 with weight 62887516.
Total sieving time: 124.92 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 6.48 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,49,49,2.6,2.6,100000
total time: 131.74 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2435k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.89 BogoMIPS (lpj=2406449)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)

(13·10¹⁴⁶+41)/9 = 1(4)₁₄₅9_<147> = 439 · 636164869 · 4027095081240337127431_<22> · C114

C114 = P29 · P85

P29 = 77842537158874070251175271923_<29>

P85 = 1649900575553862884781770255109051972716668375312218449809275241329788226651058294303_<85>

Mar 12, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(2·10¹⁷⁸+61)/9 = (2)₁₇₇9_<178> = 3 · 2027 · 20297 · 2066378869_<10> · 3247837269569_<13> · 163433233996276243474084319_<27> · C122

C122 = P46 · P76

P46 = 9668963333839804970616649746421126785511167893_<46>

P76 = 1697681163681159193851768896483106359487408211693779675029441305133012994731_<76>

Number: n
N=16414816924183620628070288142730847259538958407278070871366182577042951560674699400450759287353464473072300307093265371783
  ( 122 digits)
Divisors found:

Wed Mar 12 04:59:52 2008  prp46 factor: 9668963333839804970616649746421126785511167893
Wed Mar 12 04:59:52 2008  prp76 factor: 1697681163681159193851768896483106359487408211693779675029441305133012994731
Wed Mar 12 04:59:52 2008  elapsed time 01:49:29 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 70.21 hours.
Scaled time: 58.76 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_2_177_9
n: 16414816924183620628070288142730847259538958407278070871366182577042951560674699400450759287353464473072300307093265371783
skew: 48529.68
# norm 1.17e+17
c5: 30240
c4: -49685839936
c3: 2178758267704620
c2: 9727614241047290652
c1: -1794383631406455012036071
c0: -18641026174809989700473846580
# alpha -6.51
Y1: 1447263605209
Y0: -222296067764273622309011
# Murphy_E 2.31e-10
# M 503199048986875789014469484545092288568881604151045417589810804443826108233596466928631049481635113331976691027497880165
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 3700093)
Primes: RFBsize:348513, AFBsize:349115, largePrimes:7324235 encountered
Relations: rels:7332295, finalFF:780478
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 69.95 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 70.21 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(13·10¹⁰⁴+41)/9 = 1(4)₁₀₃9_<105> = 11959 · 232891 · 17284853 · C88

C88 = P34 · P55

P34 = 1079735338858603736315862602698429_<34>

P55 = 2778883020604898417243505418183286377453379744603666533_<55>

Mar 12, 2008

The factor table of 144...449 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Mar 11, 2008

By Jo Yeong Uk / GMP-ECM, Msieve

7·10¹⁶³-9 = 6(9)₁₆₂1_<164> = 83 · 2447 · 590732534224585594774305619_<27> · C132

C132 = P42 · P45 · P47

P42 = 129176060038429313134294565540217914223913_<42>

P45 = 120256406964389982245302914445931857545867029_<45>

P47 = 37558205196955967532214995487858032886370144357_<47>

Tue Mar 11 20:26:37 2008  
Tue Mar 11 20:26:37 2008  
Tue Mar 11 20:26:37 2008  Msieve v. 1.32
Tue Mar 11 20:26:37 2008  random seeds: d1acc543 915d5279
Tue Mar 11 20:26:37 2008  factoring 4516614809017203638734673756033070566719308001891393690896873800964334745942246243456705353 (91 digits)
Tue Mar 11 20:26:37 2008  no P-1/P+1/ECM available, skipping
Tue Mar 11 20:26:37 2008  commencing quadratic sieve (91-digit input)
Tue Mar 11 20:26:38 2008  using multiplier of 1
Tue Mar 11 20:26:38 2008  using 32kb Intel Core sieve core
Tue Mar 11 20:26:38 2008  sieve interval: 36 blocks of size 32768
Tue Mar 11 20:26:38 2008  processing polynomials in batches of 6
Tue Mar 11 20:26:38 2008  using a sieve bound of 1714723 (64706 primes)
Tue Mar 11 20:26:38 2008  using large prime bound of 164613408 (27 bits)
Tue Mar 11 20:26:38 2008  using double large prime bound of 616080330033312 (42-50 bits)
Tue Mar 11 20:26:38 2008  using trial factoring cutoff of 50 bits
Tue Mar 11 20:26:38 2008  polynomial 'A' values have 12 factors
Tue Mar 11 22:05:45 2008  65009 relations (16375 full + 48634 combined from 767780 partial), need 64802
Tue Mar 11 22:05:45 2008  begin with 784155 relations
Tue Mar 11 22:05:46 2008  reduce to 163081 relations in 12 passes
Tue Mar 11 22:05:46 2008  attempting to read 163081 relations
Tue Mar 11 22:05:47 2008  recovered 163081 relations
Tue Mar 11 22:05:47 2008  recovered 143891 polynomials
Tue Mar 11 22:05:47 2008  attempting to build 65009 cycles
Tue Mar 11 22:05:47 2008  found 65009 cycles in 5 passes
Tue Mar 11 22:05:48 2008  distribution of cycle lengths:
Tue Mar 11 22:05:48 2008     length 1 : 16375
Tue Mar 11 22:05:48 2008     length 2 : 12106
Tue Mar 11 22:05:48 2008     length 3 : 11255
Tue Mar 11 22:05:48 2008     length 4 : 8787
Tue Mar 11 22:05:48 2008     length 5 : 6474
Tue Mar 11 22:05:48 2008     length 6 : 4192
Tue Mar 11 22:05:48 2008     length 7 : 2595
Tue Mar 11 22:05:48 2008     length 9+: 3225
Tue Mar 11 22:05:48 2008  largest cycle: 23 relations
Tue Mar 11 22:05:48 2008  matrix is 64706 x 65009 with weight 3948865 (avg 60.74/col)
Tue Mar 11 22:05:48 2008  filtering completed in 3 passes
Tue Mar 11 22:05:48 2008  matrix is 61147 x 61211 with weight 3734333 (avg 61.01/col)
Tue Mar 11 22:05:49 2008  saving the first 48 matrix rows for later
Tue Mar 11 22:05:49 2008  matrix is 61099 x 61211 with weight 2944184 (avg 48.10/col)
Tue Mar 11 22:05:49 2008  matrix includes 64 packed rows
Tue Mar 11 22:05:49 2008  using block size 24484 for processor cache size 4096 kB
Tue Mar 11 22:05:50 2008  commencing Lanczos iteration
Tue Mar 11 22:06:05 2008  lanczos halted after 968 iterations (dim = 61099)
Tue Mar 11 22:06:06 2008  recovered 17 nontrivial dependencies
Tue Mar 11 22:06:06 2008  prp45 factor: 120256406964389982245302914445931857545867029
Tue Mar 11 22:06:06 2008  prp47 factor: 37558205196955967532214995487858032886370144357
Tue Mar 11 22:06:06 2008  elapsed time 01:39:29

Mar 10, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(13·10¹⁵⁶+23)/9 = 1(4)₁₅₅7_<157> = 19 · C155

C155 = P42 · P53 · P61

P42 = 389980758750449231614133227379820419633329_<42>

P53 = 91675205847127951535304492278434084611246814323398249_<53>

P61 = 2126435275612637276891658087461597168753509864505325623463053_<61>

Number: n
N=76023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391813
  ( 155 digits)
SNFS difficulty: 157 digits.
Divisors found:

Mon Mar 10 12:45:32 2008  prp42 factor: 389980758750449231614133227379820419633329
Mon Mar 10 12:45:32 2008  prp53 factor: 91675205847127951535304492278434084611246814323398249
Mon Mar 10 12:45:32 2008  prp61 factor: 2126435275612637276891658087461597168753509864505325623463053
Mon Mar 10 12:45:32 2008  elapsed time 01:37:27 (Msieve 1.33)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 37.46 hours.
Scaled time: 48.66 units (timescale=1.299).
Factorization parameters were as follows:
name: KA_1_4_155_7
n: 76023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391813
skew: 0.71
deg: 5
c5: 130
c0: 23
m: 10000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700189)
Primes: RFBsize:203362, AFBsize:203442, largePrimes:7079060 encountered
Relations: rels:6512185, finalFF:431363
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 37.25 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 37.46 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(25·10¹⁷²-7)/9 = 2(7)₁₇₂_<173> = 3² · 4937 · 205072881269_<12> · 12416644610658474999659088434521057_<35> · C123

C123 = P42 · P82

P42 = 116405331338301067025460027374215198811209_<42>

P82 = 2109145336369723547308865649415737033622345460437054290338930752168934409301836277_<82>

Mar 10, 2008

By Sinkiti Sibata / GGNFS

(13·10¹⁵¹+23)/9 = 1(4)₁₅₀7_<152> = 47 · 1459 · 1489 · 6550441069_<10> · C134

C134 = P34 · P42 · P58

P34 = 2731118671267928548408841950780937_<34>

P42 = 926226113280928870632802667563416935974873_<42>

P58 = 8537384850979962295167735815770595423638734296748278114279_<58>

Number: 14447_151
N=21596454139160159728583367398724798070601192188565630667951343431788486011447546922981570292793501563082365331104250185971848293598279
  ( 134 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=2731118671267928548408841950780937 (pp34)
 r2=926226113280928870632802667563416935974873 (pp42)
 r3=8537384850979962295167735815770595423638734296748278114279 (pp58)
Version: GGNFS-0.77.1-20060513-k8
Total time: 30.82 hours.
Scaled time: 61.71 units (timescale=2.002).
Factorization parameters were as follows:
name: 14447_151
n: 21596454139160159728583367398724798070601192188565630667951343431788486011447546922981570292793501563082365331104250185971848293598279
m: 1000000000000000000000000000000
c5: 130
c0: 23
skew: 0.71
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2300001)
Primes: RFBsize:176302, AFBsize:176533, largePrimes:5744567 encountered
Relations: rels:5739630, finalFF:530151
Max relations in full relation-set: 28
Initial matrix: 352902 x 530151 with sparse part having weight 51970091.
Pruned matrix : 290719 x 292547 with weight 28566604.
Total sieving time: 29.39 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.10 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 30.82 hours.
 --------- CPU info (if available) ----------

(4·10¹⁶³+11)/3 = 1(3)₁₆₂7_<164> = 457 · 3461 · 28350228528705291234487_<23> · C135

C135 = P57 · P79

P57 = 139264282223215405733533065658698214852552428148010156791_<57>

P79 = 2135131501215430631229036018332690103622289502314800149143766658044782641913293_<79>

Number: 13337_163
N=297347555968943318517168374915449211547556632286503794637272357540890612022634850535944311114254649675656903511660872954505705157122763
  ( 135 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=139264282223215405733533065658698214852552428148010156791 (pp57)
 r2=2135131501215430631229036018332690103622289502314800149143766658044782641913293 (pp79)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 107.67 hours.
Scaled time: 72.68 units (timescale=0.675).
Factorization parameters were as follows:
name: 13337_163
n: 297347555968943318517168374915449211547556632286503794637272357540890612022634850535944311114254649675656903511660872954505705157122763
m: 200000000000000000000000000000000
c5: 125
c0: 11
skew: 0.62
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4850001)
Primes: RFBsize:315948, AFBsize:316157, largePrimes:5861775 encountered
Relations: rels:6006525, finalFF:767511
Max relations in full relation-set: 28
Initial matrix: 632170 x 767511 with sparse part having weight 52013479.
Pruned matrix : 529404 x 532628 with weight 36397514.
Total sieving time: 93.52 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 13.52 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 107.67 hours.
 --------- CPU info (if available) ----------

Mar 9, 2008 (3rd)

By matsui / GGNFS

3·10¹⁶⁵+7 = 3(0)₁₆₄7_<166> = 71 · 739 · 24680319817_<11> · 12015226484473081913_<20> · C132

C132 = P46 · P86

P46 = 7814625344423111337812529497145365416512918941_<46>

P86 = 24673318295604171900567002523536315906661600240732917021551158395138773289853506329223_<86>

N=192812738483846806238630987193800388580669468550195254565079242547722043989395273633963041899135344900887963261307880863289858512843
  ( 132 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=7814625344423111337812529497145365416512918941 (pp46)
 r2=24673318295604171900567002523536315906661600240732917021551158395138773289853506329223 (pp86)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 90.67 hours.
Scaled time: 154.22 units (timescale=1.701).
Factorization parameters were as follows:
n: 192812738483846806238630987193800388580669468550195254565079242547722043989395273633963041899135344900887963261307880863289858512843
m: 1000000000000000000000000000000000
c5: 3
c0: 7
skew: 1.18
type: snfs

Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 5000001)
Primes: RFBsize:348513, AFBsize:347701, largePrimes:5840417 encountered
Relations: rels:6040079, finalFF:838247
Max relations in full relation-set: 28
Initial matrix: 696279 x 838247 with sparse part having weight 46329810.
Pruned matrix : 579285 x 582830 with weight 31436435.
Total sieving time: 86.39 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.93 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 90.67 hours.

Mar 9, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(13·10¹⁴⁹+23)/9 = 1(4)₁₄₈7_<150> = 3 · 59 · 642789047 · 8628460657_<10> · 384131451857134907_<18> · C111

C111 = P43 · P69

P43 = 1869299252728233162593593784842467695639821_<43>

P69 = 204911855236147914759409599454283650327219283947887580206394976351047_<69>

Number: 14447_149
N=383041577868087188812664780595180230412072536147911341266120897719996165650338793121853080533129917090568242587
  ( 111 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=1869299252728233162593593784842467695639821 (pp43)
 r2=204911855236147914759409599454283650327219283947887580206394976351047 (pp69)
Version: GGNFS-0.77.1-20060513-k8
Total time: 26.05 hours.
Scaled time: 51.80 units (timescale=1.988).
Factorization parameters were as follows:
name: 14447_149
n: 383041577868087188812664780595180230412072536147911341266120897719996165650338793121853080533129917090568242587
m: 1000000000000000000000000000000
c5: 13
c0: 230
skew: 1.78
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176123, largePrimes:5908890 encountered
Relations: rels:6100436, finalFF:719350
Max relations in full relation-set: 28
Initial matrix: 352490 x 719350 with sparse part having weight 66689794.
Pruned matrix : 236910 x 238736 with weight 31888992.
Total sieving time: 24.90 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.86 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 26.05 hours.
 --------- CPU info (if available) ----------

Mar 9, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(13·10¹⁶⁴+23)/9 = 1(4)₁₆₃7_<165> = 3 · 7 · C163

C163 = P30 · P38 · P96

P30 = 839545558995717980676973391993_<30>

P38 = 20177046110532699947312283019200501521_<38>

P96 = 406050166580568139538183636120785029941680983190292244345051790690796540227700452076761314334219_<96>

(13·10¹⁹⁹+23)/9 = 1(4)₁₉₈7_<200> = 88301 · 97171 · 14709557 · 9380701384113676637_<19> · 96637000536716385619_<20> · 57251133189500039825065474428151_<32> · C112

C112 = P45 · P67

P45 = 333670648710684229453163570612770033938844831_<45>

P67 = 6608731526570938248049146439234589449529372334618254009651625581707_<67>

Number: n
N=2205139735625675455818440066649785353479042891137898839136974049458833516499762054740029875402695374463985106517
  ( 112 digits)
Divisors found:

Sun Mar  9 15:40:53 2008  prp45 factor: 333670648710684229453163570612770033938844831
Sun Mar  9 15:40:53 2008  prp67 factor: 6608731526570938248049146439234589449529372334618254009651625581707
Sun Mar  9 15:40:53 2008  elapsed time 00:47:41 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 22.43 hours.
Scaled time: 18.82 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_1_4_198_7
n: 2205139735625675455818440066649785353479042891137898839136974049458833516499762054740029875402695374463985106517
skew: 12947.06
# norm 1.05e+15
c5: 79260
c4: 4596673684
c3: -60634614034228
c2: -616319288220440177
c1: 784693312699527700878
c0: 10872847761019001446446576
# alpha -5.24
Y1: 715729016893
Y0: -1944798252444552188581
# Murphy_E 8.28e-10
# M 306958205911432083419999205075881375379766157974305319669852638518609333434617979646532294229843553801664968650
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1300253)
Primes: RFBsize:250150, AFBsize:250374, largePrimes:6817999 encountered
Relations: rels:6507370, finalFF:555111
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 22.25 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 22.43 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(13·10¹⁵⁴+23)/9 = 1(4)₁₅₃7_<155> = 19919 · 3679468548146533_<16> · 7630751612715717403_<19> · C116

C116 = P58 · P59

P58 = 2262802058462321464484841458672901509492655613223530140187_<58>

P59 = 11413907115688684242996799010354104342118227296131335025701_<59>

Number: n
N=25827412516478093045584474130625154149704594415060748731377938994171532661092038308190184824436264190771407777946087
  ( 116 digits)
SNFS difficulty: 156 digits.
Divisors found:

Sun Mar 09 18:04:06 2008  prp58 factor: 2262802058462321464484841458672901509492655613223530140187
Sun Mar 09 18:04:06 2008  prp59 factor: 11413907115688684242996799010354104342118227296131335025701
Sun Mar 09 18:04:06 2008  elapsed time 01:05:20 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 25.24 hours.
Scaled time: 36.50 units (timescale=1.446).
Factorization parameters were as follows:
name: KA_1_4_153_7
n: 25827412516478093045584474130625154149704594415060748731377938994171532661092038308190184824436264190771407777946087
skew: 1.78
deg: 5
c5: 13
c0: 230
m: 10000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1399990)
Primes: RFBsize:183072, AFBsize:182796, largePrimes:6936275 encountered
Relations: rels:6366622, finalFF:410123
Max relations in full relation-set: 28
Initial matrix: 365933 x 410123 with sparse part having weight 33136403.
Pruned matrix : 
Total sieving time: 25.06 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 25.24 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(34·10¹⁸⁷-7)/9 = 3(7)₁₈₇_<188> = 37 · 181 · 339749 · 165027393137_<12> · 2970433401408271_<16> · 178766094923463611022611_<24> · C129

C129 = P37 · P92

P37 = 7833169297986926978487842335902637991_<37>

P92 = 24187968600683302527739149792104175270573397807449410184317187911155868346087250303023744367_<92>

(13·10¹⁹⁵+23)/9 = 1(4)₁₉₄7_<196> = 103 · 331 · 577 · 911725164517_<12> · 563220168489614860626764656859_<30> · 41654141427322616652855513644521_<32> · C115

C115 = P50 · P65

P50 = 37391517136576492214407196832292095434789606457973_<50>

P65 = 91809241027487944385754632122283696654344609873546408374196174673_<65>

Number: n
N=3432886809175397032196339913330534024884982534747861246146538642357430422156175510072541804926634570136593541517829
  ( 115 digits)
Divisors found:

Sun Mar 09 22:18:21 2008  prp50 factor: 37391517136576492214407196832292095434789606457973
Sun Mar 09 22:18:21 2008  prp65 factor: 91809241027487944385754632122283696654344609873546408374196174673
Sun Mar 09 22:18:21 2008  elapsed time 01:09:35 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 27.63 hours.
Scaled time: 50.54 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_4_194_7
n: 3432886809175397032196339913330534024884982534747861246146538642357430422156175510072541804926634570136593541517829
skew: 63552.14
# norm 2.83e+16
c5: 80640
c4: -8836498296
c3: -1373598062853518
c2: 37201918264484422373
c1: 1921950600134982397290562
c0: -16625469219239268679518449376
# alpha -7.09
Y1: 2512263133757
Y0: -8429942835838585877603
# Murphy_E 5.26e-10
# M 106777821378733491274746654241528362728436178840541836325753017700893053191371109931252808924794581284601019233135
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1700341)
Primes: RFBsize:250150, AFBsize:250791, largePrimes:7112358 encountered
Relations: rels:6818052, finalFF:557631
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 27.43 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 27.63 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Mar 8, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(13·10¹⁴⁸+23)/9 = 1(4)₁₄₇7_<149> = 29 · 82893068831154629_<17> · C130

C130 = P41 · P44 · P47

P41 = 10326766722762193030677743410047854627737_<41>

P44 = 18781709518265729197727134979077408403048257_<44>

P47 = 30980265889559158971246250118179234976988163463_<47>

Number: 14447_148
N=6008756802119248777049510774562217755723689828737153396106397864957468248863689090466755395432392753749237979010664160141839808367
  ( 130 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=10326766722762193030677743410047854627737 (pp41)
 r2=18781709518265729197727134979077408403048257 (pp44)
 r3=30980265889559158971246250118179234976988163463 (pp47)
Version: GGNFS-0.77.1-20060513-k8
Total time: 50.14 hours.
Scaled time: 100.43 units (timescale=2.003).
Factorization parameters were as follows:
name: 14447_148
n: 6008756802119248777049510774562217755723689828737153396106397864957468248863689090466755395432392753749237979010664160141839808367
m: 100000000000000000000000000000
c5: 13000
c0: 23
skew: 0.28
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 6650001)
Primes: RFBsize:114155, AFBsize:114567, largePrimes:3408107 encountered
Relations: rels:3661191, finalFF:257461
Max relations in full relation-set: 28
Initial matrix: 228789 x 257461 with sparse part having weight 36674363.
Pruned matrix : 222194 x 223401 with weight 30863209.
Total sieving time: 49.04 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.72 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 50.14 hours.
 --------- CPU info (if available) ----------

Mar 8, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(4·10¹⁵⁸+11)/3 = 1(3)₁₅₇7_<159> = 8233 · 1527862686242403797544393553027_<31> · C125

C125 = P57 · P68

P57 = 287883469723032768443947642361131998993548767401991588961_<57>

P68 = 36819642567197130462621523866484529898124568522097561899681003205787_<68>

Number: n
N=10599766456206583622902219875082963980035743593315729410558814794508496584089071087989307287849025249575541272349851000517307
  ( 125 digits)
SNFS difficulty: 158 digits.
Divisors found:

Sat Mar 08 06:26:55 2008  prp57 factor: 287883469723032768443947642361131998993548767401991588961
Sat Mar 08 06:26:55 2008  prp68 factor: 36819642567197130462621523866484529898124568522097561899681003205787
Sat Mar 08 06:26:55 2008  elapsed time 01:39:35 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 36.63 hours.
Scaled time: 64.10 units (timescale=1.750).
Factorization parameters were as follows:
name: KA_1_3_157_7
n: 10599766456206583622902219875082963980035743593315729410558814794508496584089071087989307287849025249575541272349851000517307
type: snfs
skew: 0.62
deg: 5
c5: 125
c0: 11
m: 20000000000000000000000000000000
rlim: 2400000
alim: 2400000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2800000)
Primes: RFBsize:176302, AFBsize:176929, largePrimes:7011112 encountered
Relations: rels:6417268, finalFF:404337
Max relations in full relation-set: 28
Initial matrix: 353296 x 404337 with sparse part having weight 36767863.
Pruned matrix : 325440 x 327270 with weight 26935597.
Total sieving time: 36.43 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,2400000,2400000,28,28,48,48,2.3,2.3,100000
total time: 36.63 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(4·10¹⁵⁹+11)/3 = 1(3)₁₅₈7_<160> = 7² · 797 · 911291 · C149

C149 = P72 · P78

P72 = 204085081256816882314444265811755088306232143029920183782151756286272303_<72>

P78 = 183576039185885640888108236068058657286106092960627488427886381858697479384073_<78>

Number: n
N=37465130874056071128739882858608333273867038510555797284685508890275122646470838126444335066949288631674709132239035959872852775412243385761599230119
  ( 149 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=204085081256816882314444265811755088306232143029920183782151756286272303 (pp72)
 r2=183576039185885640888108236068058657286106092960627488427886381858697479384073 (pp78)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 23.35 hours.
Scaled time: 42.71 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_3_158_7
n: 37465130874056071128739882858608333273867038510555797284685508890275122646470838126444335066949288631674709132239035959872852775412243385761599230119
skew: 1.94
deg: 5
c5: 2
c0: 55
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1600001)
Primes: RFBsize:203362, AFBsize:203108, largePrimes:7174383 encountered
Relations: rels:6696120, finalFF:533294
Max relations in full relation-set: 48
Initial matrix: 406535 x 533294 with sparse part having weight 47341680.
Pruned matrix : 315527 x 317623 with weight 26303198.
Total sieving time: 22.28 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.89 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 23.35 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(13·10¹⁵⁷+23)/9 = 1(4)₁₅₆7_<158> = 16927 · 2524139 · 1130777445877727136149_<22> · C126

C126 = P38 · P43 · P46

P38 = 29470374557264323160093526813499099303_<38>

P43 = 8608324398240878863428561563214391554918361_<43>

P46 = 1178490710904896662118258002202295955986767897_<46>

Sat Mar 08 17:12:46 2008  
Sat Mar 08 17:12:46 2008  
Sat Mar 08 17:12:46 2008  Msieve v. 1.33
Sat Mar 08 17:12:46 2008  random seeds: 523c0940 fc91d192
Sat Mar 08 17:12:46 2008  factoring 10144830339782860097185251752019345282487397788395193165545200757788964500311106090656817 (89 digits)
Sat Mar 08 17:12:46 2008  searching for 15-digit factors
Sat Mar 08 17:12:47 2008  commencing quadratic sieve (89-digit input)
Sat Mar 08 17:12:47 2008  using multiplier of 5
Sat Mar 08 17:12:47 2008  using 64kb Opteron sieve core
Sat Mar 08 17:12:47 2008  sieve interval: 14 blocks of size 65536
Sat Mar 08 17:12:47 2008  processing polynomials in batches of 8
Sat Mar 08 17:12:47 2008  using a sieve bound of 1536659 (58333 primes)
Sat Mar 08 17:12:47 2008  using large prime bound of 122932720 (26 bits)
Sat Mar 08 17:12:47 2008  using double large prime bound of 364251493350800 (42-49 bits)
Sat Mar 08 17:12:47 2008  using trial factoring cutoff of 49 bits
Sat Mar 08 17:12:47 2008  polynomial 'A' values have 11 factors
Sat Mar 08 17:58:29 2008  58751 relations (15710 full + 43041 combined from 622765 partial), need 58429
Sat Mar 08 17:58:29 2008  begin with 638474 relations
Sat Mar 08 17:58:30 2008  reduce to 143363 relations in 13 passes
Sat Mar 08 17:58:30 2008  attempting to read 143363 relations
Sat Mar 08 17:58:31 2008  recovered 143363 relations
Sat Mar 08 17:58:31 2008  recovered 123286 polynomials
Sat Mar 08 17:58:31 2008  attempting to build 58751 cycles
Sat Mar 08 17:58:31 2008  found 58751 cycles in 6 passes
Sat Mar 08 17:58:31 2008  distribution of cycle lengths:
Sat Mar 08 17:58:31 2008     length 1 : 15710
Sat Mar 08 17:58:31 2008     length 2 : 11202
Sat Mar 08 17:58:31 2008     length 3 : 10379
Sat Mar 08 17:58:31 2008     length 4 : 7870
Sat Mar 08 17:58:31 2008     length 5 : 5483
Sat Mar 08 17:58:31 2008     length 6 : 3491
Sat Mar 08 17:58:31 2008     length 7 : 2100
Sat Mar 08 17:58:31 2008     length 9+: 2516
Sat Mar 08 17:58:31 2008  largest cycle: 18 relations
Sat Mar 08 17:58:32 2008  matrix is 58333 x 58751 (14.3 MB) with weight 3525812 (60.01/col)
Sat Mar 08 17:58:32 2008  sparse part has weight 3525812 (60.01/col)
Sat Mar 08 17:58:32 2008  filtering completed in 3 passes
Sat Mar 08 17:58:32 2008  matrix is 54292 x 54356 (13.3 MB) with weight 3271260 (60.18/col)
Sat Mar 08 17:58:32 2008  sparse part has weight 3271260 (60.18/col)
Sat Mar 08 17:58:32 2008  saving the first 48 matrix rows for later
Sat Mar 08 17:58:32 2008  matrix is 54244 x 54356 (9.7 MB) with weight 2718251 (50.01/col)
Sat Mar 08 17:58:32 2008  sparse part has weight 2219258 (40.83/col)
Sat Mar 08 17:58:32 2008  matrix includes 64 packed rows
Sat Mar 08 17:58:32 2008  using block size 21742 for processor cache size 1024 kB
Sat Mar 08 17:58:33 2008  commencing Lanczos iteration
Sat Mar 08 17:58:33 2008  memory use: 8.8 MB
Sat Mar 08 17:58:51 2008  lanczos halted after 859 iterations (dim = 54239)
Sat Mar 08 17:58:51 2008  recovered 15 nontrivial dependencies
Sat Mar 08 17:58:52 2008  prp43 factor: 8608324398240878863428561563214391554918361
Sat Mar 08 17:58:52 2008  prp46 factor: 1178490710904896662118258002202295955986767897
Sat Mar 08 17:58:52 2008  elapsed time 00:46:06

Mar 8, 2008

By Tyler Cadigan / GGNFS, Msieve

(25·10¹⁶⁹-1)/3 = 8(3)₁₆₉_<170> = 557 · 613961582036334773951_<21> · C147

C147 = P73 · P75

P73 = 1502550005296206405957000095663916919632979691817218255829004648364096639_<73>

P75 = 162178555506473282695383179715970565193863003032111870610103191330901171721_<75>

Number: 83333_169
N=243681389435182535496184708589226424729855760913476797889743725884416113338127752125962521749882308307893002238055583876382795647110212672777945719
  ( 147 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=1502550005296206405957000095663916919632979691817218255829004648364096639
 r2=162178555506473282695383179715970565193863003032111870610103191330901171721
Version: 
Total time: 78.18 hours.
Scaled time: 202.08 units (timescale=2.585).
Factorization parameters were as follows:
n: 243681389435182535496184708589226424729855760913476797889743725884416113338127752125962521749882308307893002238055583876382795647110212672777945719
m: 10000000000000000000000000000000000
c5: 5
c0: -2
skew: 0.83
type: snfs
Y0: -10000000000000000000000000000000000
Y1: 1Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 6900001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 704024 x 704272
Total sieving time: 78.18 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 78.18 hours.
 --------- CPU info (if available) ----------

Mar 7, 2008 (4th)

By Jo Yeong Uk / GMP-ECM

(55·10¹⁶⁵-1)/9 = 6(1)₁₆₅_<166> = 3² · 7 · 89 · 57373 · 10715141 · 5243570455225517035661_<22> · C129

C129 = P47 · P83

P47 = 22145408397734698123468423600952926184208679147_<47>

P83 = 15267691382164727203242189694802421271145941451138137866402055973027833433215497983_<83>

Mar 7, 2008 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(17·10¹⁸⁸-71)/9 = 1(8)₁₈₇1_<189> = 46281797 · C181

C181 = P28 · P35 · P46 · P73

P28 = 6703837968824142319548566209_<28>

P35 = 18284711636540291744488699704039629_<35>

P46 = 6046424374440345331609702538553541573262983367_<46>

P73 = 5506630666650624530936151410813003802749830770712958032362796387418558279_<73>

Number: n
N=33295425883877024213133089544859699420354642783993157073687282792277335584942812196574757512858061420648601761497145393
  ( 119 digits)
Divisors found:
 r1=6046424374440345331609702538553541573262983367 (pp46)
 r2=5506630666650624530936151410813003802749830770712958032362796387418558279 (pp73)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 25.37 hours.
Scaled time: 46.26 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_1_8_187_1
n: 33295425883877024213133089544859699420354642783993157073687282792277335584942812196574757512858061420648601761497145393
skew: 64252.80
# norm 8.56e+16
c5: 80640
c4: -29279627402
c3: -2582745450093933
c2: 100280207548859379378
c1: 2258234003440599349820122
c0: -63862789341497878474545813540
# alpha -6.91
Y1: 3752897193449
Y0: -52865099013389977999601
# Murphy_E 3.30e-10
# M 4584119993252203722295177747872564209385270252930595333008198134004344128971819458287365846308288885592951846116008855
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 49/49
Sieved algebraic special-q in [100000, 2800001)
Primes: RFBsize:315948, AFBsize:316483, largePrimes:8200805 encountered
Relations: rels:7746394, finalFF:721237
Max relations in full relation-set: 48
Initial matrix: 632512 x 721237 with sparse part having weight 44335568.
Pruned matrix : 545734 x 548960 with weight 25937410.
Total sieving time: 23.18 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 1.77 hours.
Total square root time: 0.18 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,28,28,49,49,2.4,2.4,60000
total time: 25.37 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(4·10¹⁵⁶+17)/3 = 1(3)₁₅₅9_<157> = 7 · 101062276260401384471623631_<27> · C130

C130 = P63 · P67

P63 = 269480152008343856451946294957810061032767470763934370924086361_<63>

P67 = 6993987264537114565683739230936559086147454821094183445847542744347_<67>

Number: n
N=1884740751191882668563906253662372628699360247371667353287240058299223854681737727018135369552948233020909693280492841805572551267
  ( 130 digits)
SNFS difficulty: 156 digits.
Divisors found:

Fri Mar 07 11:25:48 2008  prp63 factor: 269480152008343856451946294957810061032767470763934370924086361
Fri Mar 07 11:25:48 2008  prp67 factor: 6993987264537114565683739230936559086147454821094183445847542744347
Fri Mar 07 11:25:48 2008  elapsed time 00:50:09 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 24.70 hours.
Scaled time: 35.57 units (timescale=1.440).
Factorization parameters were as follows:
name: KA_1_3_155_9
n: 1884740751191882668563906253662372628699360247371667353287240058299223854681737727018135369552948233020909693280492841805572551267
skew: 0.84
deg: 5
c5: 40
c0: 17
m: 10000000000000000000000000000000
type: snfs
rlim: 2400000
alim: 2400000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1200001)
Primes: RFBsize:176302, AFBsize:176288, largePrimes:7013324 encountered
Relations: rels:6491415, finalFF:440292
Max relations in full relation-set: 28
Initial matrix: 352656 x 440292 with sparse part having weight 37857733.
Pruned matrix : 
Total sieving time: 24.46 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2400000,2400000,28,28,48,48,2.5,2.5,100000
total time: 24.70 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Mar 7, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(13·10¹⁴⁶+23)/9 = 1(4)₁₄₅7_<147> = 3 · 7 · 3479557 · C139

C139 = P56 · P84

P56 = 19622489662095236649338844058215831256042080388367537519_<56>

P84 = 100740356624526186007814934359778825461356811979856485445035129252550852026602460329_<84>

Number: 14447_146
N=1976776606420552474604757697116868126281106151819578844915690956724341146553514392293869106578310652277539441623835125651592517920616583751
  ( 139 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=19622489662095236649338844058215831256042080388367537519 (pp56)
 r2=100740356624526186007814934359778825461356811979856485445035129252550852026602460329 (pp84)
Version: GGNFS-0.77.1-20060513-k8
Total time: 29.62 hours.
Scaled time: 59.31 units (timescale=2.002).
Factorization parameters were as follows:
name: 14447_146
n: 1976776606420552474604757697116868126281106151819578844915690956724341146553514392293869106578310652277539441623835125651592517920616583751
m: 100000000000000000000000000000
c5: 130
c0: 23
skew: 0.71
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 4050001)
Primes: RFBsize:114155, AFBsize:114037, largePrimes:3084976 encountered
Relations: rels:3164913, finalFF:290275
Max relations in full relation-set: 28
Initial matrix: 228259 x 290275 with sparse part having weight 36106723.
Pruned matrix : 211753 x 212958 with weight 25442972.
Total sieving time: 28.63 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.71 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 29.62 hours.
 --------- CPU info (if available) ----------

Mar 7, 2008

By matsui / GGNFS

3·10¹⁶⁹-7 = 2(9)₁₆₈3_<170> = 19 · 43055561 · 10073117473_<11> · 310792818964334717_<18> · C134

C134 = P54 · P80

P54 = 275860320126853307413096987739888963147811740022702997_<54>

P80 = 42463353702343919630941476770580199897205148009535304984674887647746788420522251_<80>

N=11713954345988395280440301043503701161036869491532050378454230366913521079611328147373022160571672903577472106907091023297491402886247
  ( 134 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=275860320126853307413096987739888963147811740022702997 (pp54)
 r2=42463353702343919630941476770580199897205148009535304984674887647746788420522251 (pp80)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 161.74 hours.
Scaled time: 179.53 units (timescale=1.110).
Factorization parameters were as follows:
n: 11713954345988395280440301043503701161036869491532050378454230366913521079611328147373022160571672903577472106907091023297491402886247
m: 10000000000000000000000000000000000
c5: 3
c0: -70
skew: 1.88
type: snfs

Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 9100001)
Primes: RFBsize:412849, AFBsize:410791, largePrimes:6338389 encountered
Relations: rels:6667763, finalFF:975562
Max relations in full relation-set: 28
Initial matrix: 823705 x 975562 with sparse part having weight 74465554.
Pruned matrix : 701852 x 706034 with weight 56385039.
Total sieving time: 145.54 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 15.65 hours.
Time per square root: 0.38 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 161.74 hours.

Mar 6, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(13·10¹⁴⁰+23)/9 = 1(4)₁₃₉7_<141> = 3 · 7 · 97 · 116639 · 361213 · 235765177 · C118

C118 = P31 · P37 · P52

P31 = 1745882905442085615069163292717_<31>

P37 = 1274538776841461345684727695080517503_<37>

P52 = 3208151205533195406082282981411310434662624665968979_<52>

Number: 14447_140
N=7138763506562734907929089171012437671823306257454994838166422259301218421238798466853549934921216720059849128421380329
  ( 118 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=1745882905442085615069163292717 (pp31)
 r2=1274538776841461345684727695080517503 (pp37)
 r3=3208151205533195406082282981411310434662624665968979 (pp52)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 10.31 hours.
Scaled time: 6.96 units (timescale=0.675).
Factorization parameters were as follows:
name: 14447_140
n: 7138763506562734907929089171012437671823306257454994838166422259301218421238798466853549934921216720059849128421380329
m: 10000000000000000000000000000
c5: 13
c0: 23
skew: 1.12
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1550001)
Primes: RFBsize:100021, AFBsize:99688, largePrimes:2626869 encountered
Relations: rels:2591427, finalFF:265976
Max relations in full relation-set: 28
Initial matrix: 199774 x 265976 with sparse part having weight 20939938.
Pruned matrix : 176848 x 177910 with weight 11548586.
Total sieving time: 9.39 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.73 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 10.31 hours.
 --------- CPU info (if available) ----------

(13·10¹⁴⁴+23)/9 = 1(4)₁₄₃7_<145> = 127 · 5309 · 698531 · 18250784633_<11> · 489889502898266347_<18> · C105

C105 = P46 · P59

P46 = 7974072093667475428695114878478870116137528321_<46>

P59 = 43016877271613784214536967602395329942184013449106489386429_<59>

Number: 14447_144
N=343019680608294166377258712561601712210065487114888595979284146082967927864376668302191058491283900555709
  ( 105 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=7974072093667475428695114878478870116137528321 (pp46)
 r2=43016877271613784214536967602395329942184013449106489386429 (pp59)
Version: GGNFS-0.77.1-20060513-k8
Total time: 19.57 hours.
Scaled time: 39.18 units (timescale=2.002).
Factorization parameters were as follows:
name: 14447_144
n: 343019680608294166377258712561601712210065487114888595979284146082967927864376668302191058491283900555709
m: 100000000000000000000000000000
c5: 13
c0: 230
skew: 1.78
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2850001)
Primes: RFBsize:114155, AFBsize:113437, largePrimes:2875075 encountered
Relations: rels:2875950, finalFF:280563
Max relations in full relation-set: 28
Initial matrix: 227657 x 280563 with sparse part having weight 29021959.
Pruned matrix : 211417 x 212619 with weight 20180901.
Total sieving time: 18.84 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.53 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 19.57 hours.
 --------- CPU info (if available) ----------

(13·10¹⁴⁵+23)/9 = 1(4)₁₄₄7_<146> = 17 · 349 · 649123 · 1775611609_<10> · C127

C127 = P40 · P41 · P46

P40 = 9343080165895605403209672061982422960039_<40>

P41 = 89613447463680659731752405803506450728307_<41>

P46 = 2522831592649101185126932192574929950666412669_<46>

Number: 14447_145
N=2112280166645633371402320469707436810566363949074645713931457172472612598537165215521411575103320180556079680290992286560813937
  ( 127 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=9343080165895605403209672061982422960039 (pp40)
 r2=89613447463680659731752405803506450728307 (pp41)
 r3=2522831592649101185126932192574929950666412669 (pp46)
Version: GGNFS-0.77.1-20060513-k8
Total time: 14.85 hours.
Scaled time: 29.66 units (timescale=1.997).
Factorization parameters were as follows:
name: 14447_145
n: 2112280166645633371402320469707436810566363949074645713931457172472612598537165215521411575103320180556079680290992286560813937
m: 100000000000000000000000000000
c5: 13
c0: 23
skew: 1.12
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2250001)
Primes: RFBsize:114155, AFBsize:113862, largePrimes:2792569 encountered
Relations: rels:2794001, finalFF:306269
Max relations in full relation-set: 28
Initial matrix: 228082 x 306269 with sparse part having weight 26826257.
Pruned matrix : 201383 x 202587 with weight 15672670.
Total sieving time: 14.25 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.38 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 14.85 hours.
 --------- CPU info (if available) ----------

Mar 6, 2008 (2nd)

By Tyler Cadigan / GGNFS, Msieve

4·10²⁰⁰+7 = 4(0)₁₉₉7_<201> = 11 · 37 · 1283 · 3862363 · 850829939689_<12> · 7902206235541_<13> · 2427955288687425440124619_<25> · C140

C140 = P45 · P95

P45 = 744937326890658098750633812878347827267331909_<45>

P95 = 16309261376519004401367144323776493633648587766960444190910507407496460267050598624335377069811_<95>

Number: 40007_200
N=12149377573385122056574232610071460610855950465269956343856882780433448036952149168175437914747399741923901170515075147862469359004400899199
  ( 140 digits)
Divisors found:
 r1=744937326890658098750633812878347827267331909
 r2=16309261376519004401367144323776493633648587766960444190910507407496460267050598624335377069811
Version: 
Total time: 897.57 hours.
Scaled time: 2311.24 units (timescale=2.575).
Factorization parameters were as follows:
name: 40007_200
n: 12149377573385122056574232610071460610855950465269956343856882780433448036952149168175437914747399741923901170515075147862469359004400899199
skew: 223679.33
# norm 4.09e+019
c5: 2156280
c4: -61228026700
c3: -702373789849651771
c2: -6571146189541794526408
c1: 3301605854013914710688065716
c0: 152604628744953457221152044405968
# alpha -6.36
Y1: 5913557570755153
Y0: -354952153975377700897678475
# Murphy_E 2.08e-011
# M 3547188172572132846724638033940689355703420623635097032285416273587374461874203363023125145717872143374372253454257726653217575781190678802
type: gnfs
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.5
alambda: 2.5
qintsize: 60000
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [2700000, 18780001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1492185 x 1492433
Total sieving time: 897.57 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,139,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5400000,5400000,27,27,51,51,2.5,2.5,60000
total time: 897.57 hours.
 --------- CPU info (if available) ----------

C140 is the largest composite number factored by gnfs so far in our tables.

Mar 6, 2008

By Robert Backstrom / GGNFS, Msieve

(13·10¹³⁸+23)/9 = 1(4)₁₃₇7_<139> = 19 · 599 · 1429883584413769044754647369821_<31> · C104

C104 = P48 · P57

P48 = 586128798116731777961115493247664079920542415073_<48>

P57 = 151435145516772344278889031078601478025961666278540775039_<57>

Number: n
N=88760499834378156773800488192000265442408738331560349865331863425464199466716830610347313449706255762847
  ( 104 digits)
SNFS difficulty: 139 digits.
Divisors found:

Thu Mar 06 02:47:26 2008  prp48 factor: 586128798116731777961115493247664079920542415073
Thu Mar 06 02:47:26 2008  prp57 factor: 151435145516772344278889031078601478025961666278540775039
Thu Mar 06 02:47:26 2008  elapsed time 00:45:26 (Msieve 1.33)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 9.08 hours.
Scaled time: 11.82 units (timescale=1.302).
Factorization parameters were as follows:
name: KA_1_4_137_7
n: 88760499834378156773800488192000265442408738331560349865331863425464199466716830610347313449706255762847
skew: 0.28
deg: 5
c5: 13000
c0: 23
m: 1000000000000000000000000000
type: snfs
rlim: 2400000
alim: 2400000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 900000)
Primes: RFBsize:176302, AFBsize:176793, largePrimes:6399945 encountered
Relations: rels:5818426, finalFF:424389
Max relations in full relation-set: 28
Initial matrix: 353162 x 424389 with sparse part having weight 24345376.
Pruned matrix : 291445 x 293274 with weight 13197182.
Total sieving time: 8.01 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.86 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,2400000,2400000,28,28,48,48,2.5,2.5,75000
total time: 9.08 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(4·10¹⁵⁰+17)/3 = 1(3)₁₄₉9_<151> = 7 · 334069789 · 334196431 · C133

C133 = P62 · P71

P62 = 57126890860326108568751429326137900970835253270245426672695033_<62>

P71 = 29864902280999244026736715876111318231690393560147974398473655578471991_<71>

Number: n
N=1706089013160948065796653250284267745523856895624707272826723480789142535712807929895649433301290486998952660344553525854016075320703
  ( 133 digits)
SNFS difficulty: 150 digits.
Divisors found:

Thu Mar  6 21:59:20 2008  prp62 factor: 57126890860326108568751429326137900970835253270245426672695033
Thu Mar  6 21:59:20 2008  prp71 factor: 29864902280999244026736715876111318231690393560147974398473655578471991
Thu Mar  6 21:59:20 2008  elapsed time 00:17:18 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 11.81 hours.
Scaled time: 9.91 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_1_3_149_9
n: 1706089013160948065796653250284267745523856895624707272826723480789142535712807929895649433301290486998952660344553525854016075320703
type: snfs
deg: 5
c5: 4
c0: 17
skew: 1.34
m: 1000000000000000000000000000000
rlim: 2000000
alim: 2000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 700001)
Primes: RFBsize:148933, AFBsize:149130, largePrimes:5287368 encountered
Relations: rels:5151793, finalFF:463201
Max relations in full relation-set: 28
Initial matrix: 298127 x 463201 with sparse part having weight 38170491.
Pruned matrix : 
Total sieving time: 11.69 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,48,48,2.5,2.5,100000
total time: 11.81 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

Mar 5, 2008 (3rd)

By Jo Yeong Uk / GGNFS

(11·10¹⁸¹+43)/9 = 1(2)₁₈₀7_<182> = C182

C182 = P86 · P96

P86 = 17516603088503986712003230092449997330331139625362369248432951964013027291978138942617_<86>

P96 = 697750708882795525763097607759634404119636066233661493021512854651497704755817469884947029848331_<96>

Number: 12227_181
N=12222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227
  ( 182 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=17516603088503986712003230092449997330331139625362369248432951964013027291978138942617 (pp86)
 r2=697750708882795525763097607759634404119636066233661493021512854651497704755817469884947029848331 (pp96)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 281.88 hours.
Scaled time: 523.45 units (timescale=1.857).
Factorization parameters were as follows:
n: 12222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227
m: 1000000000000000000000000000000000000
c5: 110
c0: 43
skew: 0.83
type: snfs
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [5000000, 9700001)
Primes: RFBsize:664579, AFBsize:664856, largePrimes:11128366 encountered
Relations: rels:11398297, finalFF:1494512
Max relations in full relation-set: 28
Initial matrix: 1329502 x 1494512 with sparse part having weight 95004589.
Pruned matrix : 1185360 x 1192071 with weight 70601132.
Total sieving time: 270.41 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 11.09 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000
total time: 281.88 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2435k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.89 BogoMIPS (lpj=2406449)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)

Mar 5, 2008 (2nd)

By Sinkiti Sibata / GGNFS, Msieve

(13·10¹²⁵+23)/9 = 1(4)₁₂₄7_<126> = 3² · C125

C125 = P48 · P77

P48 = 464247637731423992081446576515259298176781598923_<48>

P77 = 34570736416615334709852602535504361723332346937596499346376073111611171864021_<77>

Number: 14447_125
N=16049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049383
  ( 125 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=464247637731423992081446576515259298176781598923 (pp48)
 r2=34570736416615334709852602535504361723332346937596499346376073111611171864021 (pp77)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.83 hours.
Scaled time: 5.66 units (timescale=2.002).
Factorization parameters were as follows:
name: 14447_125
n: 16049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049383
m: 10000000000000000000000000
c5: 13
c0: 23
skew: 1.12
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:63813, largePrimes:2376187 encountered
Relations: rels:2731413, finalFF:452003
Max relations in full relation-set: 28
Initial matrix: 112976 x 452003 with sparse part having weight 44179581.
Pruned matrix : 76716 x 77344 with weight 8442795.
Total sieving time: 2.68 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.83 hours.
 --------- CPU info (if available) ----------

(13·10¹¹³+23)/9 = 1(4)₁₁₂7_<114> = 3 · 17 · 1058632741_<10> · C103

C103 = P49 · P54

P49 = 3726222878100481201794626013271269800973447843967_<49>

P54 = 717986894749436893374924732971774453291142110739897151_<54>

Number: 14447_113
N=2675379193391674015768106248403252111180850469561315262597489035104281804503651150211094236768275838017
  ( 103 digits)
SNFS difficulty: 114 digits.
Divisors found:
 r1=3726222878100481201794626013271269800973447843967 (pp49)
 r2=717986894749436893374924732971774453291142110739897151 (pp54)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.39 hours.
Scaled time: 1.61 units (timescale=0.675).
Factorization parameters were as follows:
name: 14447_113
n: 2675379193391674015768106248403252111180850469561315262597489035104281804503651150211094236768275838017
m: 10000000000000000000000
c5: 13000
c0: 23
skew: 0.28
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64288, largePrimes:2136650 encountered
Relations: rels:2262567, finalFF:264304
Max relations in full relation-set: 28
Initial matrix: 113453 x 264304 with sparse part having weight 22736905.
Pruned matrix : 81275 x 81906 with weight 4814859.
Total sieving time: 2.17 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,114,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.39 hours.
 --------- CPU info (if available) ----------

(13·10¹²⁰+23)/9 = 1(4)₁₁₉7_<121> = 19 · 29 · 1741 · 22441 · C110

C110 = P29 · P81

P29 = 76702542741648809846780802317_<29>

P81 = 874779316283849878292104906255438129819684224118598047597761358345503878142800761_<81>

Number: 14447_120
N=67097797896772318011892964303753466558069514586862341013698816283812181113638336610629295943339477297058163237
  ( 110 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=76702542741648809846780802317 (pp29)
 r2=874779316283849878292104906255438129819684224118598047597761358345503878142800761 (pp81)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.18 hours.
Scaled time: 4.36 units (timescale=1.996).
Factorization parameters were as follows:
name: 14447_120
n: 67097797896772318011892964303753466558069514586862341013698816283812181113638336610629295943339477297058163237
m: 1000000000000000000000000
c5: 13
c0: 23
skew: 1.12
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63813, largePrimes:2107928 encountered
Relations: rels:2204496, finalFF:243834
Max relations in full relation-set: 28
Initial matrix: 112976 x 243834 with sparse part having weight 20361502.
Pruned matrix : 82767 x 83395 with weight 4575859.
Total sieving time: 2.06 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.18 hours.
 --------- CPU info (if available) ----------

(13·10¹²²+23)/9 = 1(4)₁₂₁7_<123> = 3 · 7 · C121

C121 = P57 · P65

P57 = 275974403633615893708374712313364033866417253364443479869_<57>

P65 = 24923713169568184598667917122586887747016051523773565479357462303_<65>

Number: 14447_122
N=6878306878306878306878306878306878306878306878306878306878306878306878306878306878306878306878306878306878306878306878307
  ( 121 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=275974403633615893708374712313364033866417253364443479869 (pp57)
 r2=24923713169568184598667917122586887747016051523773565479357462303 (pp65)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.80 hours.
Scaled time: 5.56 units (timescale=1.989).
Factorization parameters were as follows:
name: 14447_122
n: 6878306878306878306878306878306878306878306878306878306878306878306878306878306878306878306878306878306878306878306878307
m: 1000000000000000000000000
c5: 1300
c0: 23
skew: 0.45
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:63628, largePrimes:2267670 encountered
Relations: rels:2437211, finalFF:267892
Max relations in full relation-set: 28
Initial matrix: 112793 x 267892 with sparse part having weight 26595405.
Pruned matrix : 87574 x 88201 with weight 6983607.
Total sieving time: 2.65 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.80 hours.
 --------- CPU info (if available) ----------

(13·10¹⁰²+23)/9 = 1(4)₁₀₁7_<103> = 19 · 127 · 719 · C96

C96 = P32 · P65

P32 = 70434883300550025768921698856829_<32>

P65 = 11820254604073182658618421398181422566578014985987820143827603769_<65>

Number: 14447_102
N=832558253620683769846827853787144186216895642601442259875629886356438810202527480346341671788501
  ( 96 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=70434883300550025768921698856829 (pp32)
 r2=11820254604073182658618421398181422566578014985987820143827603769 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 0.99 hours.
Scaled time: 0.67 units (timescale=0.675).
Factorization parameters were as follows:
name: 14447_102
n: 832558253620683769846827853787144186216895642601442259875629886356438810202527480346341671788501
m: 100000000000000000000
c5: 1300
c0: 23
skew: 0.45
type: snfs
Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [250000, 330001)
Primes: RFBsize:37706, AFBsize:41177, largePrimes:1166798 encountered
Relations: rels:1153342, finalFF:152299
Max relations in full relation-set: 28
Initial matrix: 78950 x 152299 with sparse part having weight 5949155.
Pruned matrix : 50513 x 50971 with weight 1512615.
Total sieving time: 0.91 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,103,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000
total time: 0.99 hours.
 --------- CPU info (if available) ----------

(13·10¹²⁷+23)/9 = 1(4)₁₂₆7_<128> = 103 · 67089542389_<11> · 202509386109599571491_<21> · C95

C95 = P35 · P60

P35 = 14549579140164833600801209324805687_<35>

P60 = 709435963265061108754917795311933782934023902804157269931073_<60>

Wed Mar  5 10:06:03 2008  Msieve v. 1.33
Wed Mar  5 10:06:03 2008  random seeds: 27375a1b 327ed101
Wed Mar  5 10:06:03 2008  factoring 10321994692404078283128677812981837955842846798890256131362566317922455981262533583263608412151 (95 digits)
Wed Mar  5 10:06:04 2008  searching for 15-digit factors
Wed Mar  5 10:06:06 2008  commencing quadratic sieve (95-digit input)
Wed Mar  5 10:06:06 2008  using multiplier of 7
Wed Mar  5 10:06:06 2008  using 64kb Pentium 4 sieve core
Wed Mar  5 10:06:06 2008  sieve interval: 18 blocks of size 65536
Wed Mar  5 10:06:06 2008  processing polynomials in batches of 6
Wed Mar  5 10:06:06 2008  using a sieve bound of 2089273 (77647 primes)
Wed Mar  5 10:06:06 2008  using large prime bound of 296676766 (28 bits)
Wed Mar  5 10:06:06 2008  using double large prime bound of 1778731187411554 (42-51 bits)
Wed Mar  5 10:06:06 2008  using trial factoring cutoff of 51 bits
Wed Mar  5 10:06:06 2008  polynomial 'A' values have 12 factors
Wed Mar  5 12:08:31 2008  12072 relations (7942 full + 4130 combined from 454959 partial), need 77743
Wed Mar  5 12:08:31 2008  elapsed time 02:02:28
Wed Mar  5 12:14:47 2008  
Wed Mar  5 12:14:47 2008  
Wed Mar  5 12:14:47 2008  Msieve v. 1.33
Wed Mar  5 12:14:47 2008  random seeds: 86a08dc3 c441004f
Wed Mar  5 12:14:47 2008  factoring 10321994692404078283128677812981837955842846798890256131362566317922455981262533583263608412151 (95 digits)
Wed Mar  5 12:14:49 2008  searching for 15-digit factors
Wed Mar  5 12:14:50 2008  commencing quadratic sieve (95-digit input)
Wed Mar  5 12:14:51 2008  using multiplier of 7
Wed Mar  5 12:14:51 2008  using 64kb Pentium 4 sieve core
Wed Mar  5 12:14:51 2008  sieve interval: 18 blocks of size 65536
Wed Mar  5 12:14:51 2008  processing polynomials in batches of 6
Wed Mar  5 12:14:51 2008  using a sieve bound of 2089273 (77647 primes)
Wed Mar  5 12:14:51 2008  using large prime bound of 296676766 (28 bits)
Wed Mar  5 12:14:51 2008  using double large prime bound of 1778731187411554 (42-51 bits)
Wed Mar  5 12:14:51 2008  using trial factoring cutoff of 51 bits
Wed Mar  5 12:14:51 2008  polynomial 'A' values have 12 factors
Wed Mar  5 12:14:53 2008  restarting with 7942 full and 454959 partial relations
Wed Mar  5 15:14:40 2008  77879 relations (19845 full + 58034 combined from 1123077 partial), need 77743
Wed Mar  5 15:14:44 2008  begin with 1142922 relations
Wed Mar  5 15:14:45 2008  reduce to 199389 relations in 11 passes
Wed Mar  5 15:14:45 2008  attempting to read 199389 relations
Wed Mar  5 15:14:52 2008  recovered 199389 relations
Wed Mar  5 15:14:52 2008  recovered 180691 polynomials
Wed Mar  5 15:14:52 2008  attempting to build 77879 cycles
Wed Mar  5 15:14:52 2008  found 77879 cycles in 5 passes
Wed Mar  5 15:14:52 2008  distribution of cycle lengths:
Wed Mar  5 15:14:52 2008     length 1 : 19845
Wed Mar  5 15:14:52 2008     length 2 : 13964
Wed Mar  5 15:14:52 2008     length 3 : 13369
Wed Mar  5 15:14:52 2008     length 4 : 10242
Wed Mar  5 15:14:52 2008     length 5 : 7679
Wed Mar  5 15:14:52 2008     length 6 : 5238
Wed Mar  5 15:14:52 2008     length 7 : 3216
Wed Mar  5 15:14:52 2008     length 9+: 4326
Wed Mar  5 15:14:52 2008  largest cycle: 20 relations
Wed Mar  5 15:14:53 2008  matrix is 77647 x 77879 (20.6 MB) with weight 5088222 (65.33/col)
Wed Mar  5 15:14:53 2008  sparse part has weight 5088222 (65.33/col)
Wed Mar  5 15:14:54 2008  filtering completed in 3 passes
Wed Mar  5 15:14:54 2008  matrix is 73464 x 73528 (19.6 MB) with weight 4841271 (65.84/col)
Wed Mar  5 15:14:54 2008  sparse part has weight 4841271 (65.84/col)
Wed Mar  5 15:14:55 2008  saving the first 48 matrix rows for later
Wed Mar  5 15:14:55 2008  matrix is 73416 x 73528 (13.1 MB) with weight 3903883 (53.09/col)
Wed Mar  5 15:14:55 2008  sparse part has weight 2988911 (40.65/col)
Wed Mar  5 15:14:55 2008  matrix includes 64 packed rows
Wed Mar  5 15:14:55 2008  using block size 21845 for processor cache size 512 kB
Wed Mar  5 15:14:56 2008  commencing Lanczos iteration
Wed Mar  5 15:14:56 2008  memory use: 12.2 MB
Wed Mar  5 15:15:52 2008  lanczos halted after 1163 iterations (dim = 73416)
Wed Mar  5 15:15:52 2008  recovered 18 nontrivial dependencies
Wed Mar  5 15:15:54 2008  prp35 factor: 14549579140164833600801209324805687
Wed Mar  5 15:15:54 2008  prp60 factor: 709435963265061108754917795311933782934023902804157269931073
Wed Mar  5 15:15:54 2008  elapsed time 03:01:07

(13·10¹²⁸+23)/9 = 1(4)₁₂₇7_<129> = 3 · 7⁴ · 359 · 66612700003_<11> · C111

C111 = P40 · P72

P40 = 1331167551723961827044232908143687891357_<40>

P72 = 629945850433649252006066469143506208365518616550926335658920273196015541_<72>

Number: 14447_128
N=838563475440429911604775130570202481413951328063949760496483468128502165941145216382236679614537068220491579137
  ( 111 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=1331167551723961827044232908143687891357 (pp40)
 r2=629945850433649252006066469143506208365518616550926335658920273196015541 (pp72)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.14 hours.
Scaled time: 10.24 units (timescale=1.994).
Factorization parameters were as follows:
name: 14447_128
n: 838563475440429911604775130570202481413951328063949760496483468128502165941145216382236679614537068220491579137
m: 10000000000000000000000000
c5: 13000
c0: 23
skew: 0.28
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1050001)
Primes: RFBsize:63951, AFBsize:64288, largePrimes:1511938 encountered
Relations: rels:1504917, finalFF:163874
Max relations in full relation-set: 28
Initial matrix: 128306 x 163874 with sparse part having weight 13141347.
Pruned matrix : 118297 x 119002 with weight 7752790.
Total sieving time: 4.95 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.14 hours.
 --------- CPU info (if available) ----------

Mar 5, 2008

By Robert Backstrom / Msieve, GGNFS, GMP-ECM

(13·10¹¹¹+23)/9 = 1(4)₁₁₀7_<112> = 863 · 386881426812688222963_<21> · C88

C88 = P30 · P58

P30 = 536034555099477259492189339343_<30>

P58 = 8070851920836102438701243831587152825693030353472471416341_<58>

Tue Mar 04 23:42:15 2008  
Tue Mar 04 23:42:15 2008  
Tue Mar 04 23:42:15 2008  Msieve v. 1.33
Tue Mar 04 23:42:15 2008  random seeds: 57339918 0c0c728b
Tue Mar 04 23:42:15 2008  factoring 4326255518659141629515683748908033460381740031260391059780038497503711961665328284403963 (88 digits)
Tue Mar 04 23:42:16 2008  searching for 15-digit factors
Tue Mar 04 23:42:17 2008  commencing quadratic sieve (88-digit input)
Tue Mar 04 23:42:17 2008  using multiplier of 3
Tue Mar 04 23:42:17 2008  using 64kb Opteron sieve core
Tue Mar 04 23:42:17 2008  sieve interval: 14 blocks of size 65536
Tue Mar 04 23:42:17 2008  processing polynomials in batches of 8
Tue Mar 04 23:42:17 2008  using a sieve bound of 1527521 (57923 primes)
Tue Mar 04 23:42:17 2008  using large prime bound of 122201680 (26 bits)
Tue Mar 04 23:42:17 2008  using double large prime bound of 360361878370480 (42-49 bits)
Tue Mar 04 23:42:17 2008  using trial factoring cutoff of 49 bits
Tue Mar 04 23:42:17 2008  polynomial 'A' values have 11 factors
Wed Mar 05 00:49:17 2008  58176 relations (15416 full + 42760 combined from 618473 partial), need 58019
Wed Mar 05 00:49:17 2008  begin with 633888 relations
Wed Mar 05 00:49:18 2008  reduce to 142616 relations in 9 passes
Wed Mar 05 00:49:18 2008  attempting to read 142616 relations
Wed Mar 05 00:49:20 2008  recovered 142616 relations
Wed Mar 05 00:49:20 2008  recovered 122108 polynomials
Wed Mar 05 00:49:20 2008  attempting to build 58176 cycles
Wed Mar 05 00:49:20 2008  found 58176 cycles in 5 passes
Wed Mar 05 00:49:20 2008  distribution of cycle lengths:
Wed Mar 05 00:49:20 2008     length 1 : 15416
Wed Mar 05 00:49:20 2008     length 2 : 10978
Wed Mar 05 00:49:20 2008     length 3 : 10060
Wed Mar 05 00:49:20 2008     length 4 : 7766
Wed Mar 05 00:49:20 2008     length 5 : 5579
Wed Mar 05 00:49:20 2008     length 6 : 3567
Wed Mar 05 00:49:20 2008     length 7 : 2188
Wed Mar 05 00:49:20 2008     length 9+: 2622
Wed Mar 05 00:49:20 2008  largest cycle: 19 relations
Wed Mar 05 00:49:20 2008  matrix is 57923 x 58176 (14.2 MB) with weight 3482798 (59.87/col)
Wed Mar 05 00:49:20 2008  sparse part has weight 3482798 (59.87/col)
Wed Mar 05 00:49:21 2008  filtering completed in 3 passes
Wed Mar 05 00:49:21 2008  matrix is 54291 x 54355 (13.3 MB) with weight 3277175 (60.29/col)
Wed Mar 05 00:49:21 2008  sparse part has weight 3277175 (60.29/col)
Wed Mar 05 00:49:21 2008  saving the first 48 matrix rows for later
Wed Mar 05 00:49:21 2008  matrix is 54243 x 54355 (9.4 MB) with weight 2674396 (49.20/col)
Wed Mar 05 00:49:21 2008  sparse part has weight 2135619 (39.29/col)
Wed Mar 05 00:49:21 2008  matrix includes 64 packed rows
Wed Mar 05 00:49:21 2008  using block size 21742 for processor cache size 512 kB
Wed Mar 05 00:49:22 2008  commencing Lanczos iteration
Wed Mar 05 00:49:22 2008  memory use: 8.7 MB
Wed Mar 05 00:49:50 2008  lanczos halted after 859 iterations (dim = 54239)
Wed Mar 05 00:49:50 2008  recovered 16 nontrivial dependencies
Wed Mar 05 00:49:50 2008  prp30 factor: 536034555099477259492189339343
Wed Mar 05 00:49:50 2008  prp58 factor: 8070851920836102438701243831587152825693030353472471416341
Wed Mar 05 00:49:50 2008  elapsed time 01:07:35

(13·10¹⁰⁹+23)/9 = 1(4)₁₀₈7_<110> = 61 · 277 · 503 · 1831601 · 2156071 · C90

C90 = P41 · P49

P41 = 51656325972977006306990866008287770891019_<41>

P49 = 8331166415227273953870412449749267635633640111533_<49>

Tue Mar 04 23:46:07 2008  
Tue Mar 04 23:46:07 2008  
Tue Mar 04 23:46:07 2008  Msieve v. 1.33
Tue Mar 04 23:46:07 2008  random seeds: 8428a2f4 b1ad526f
Tue Mar 04 23:46:07 2008  factoring 430357448080098369958342847236693571262718451457671118447147565165570370519810229948022127 (90 digits)
Tue Mar 04 23:46:07 2008  searching for 15-digit factors
Tue Mar 04 23:46:08 2008  commencing quadratic sieve (90-digit input)
Tue Mar 04 23:46:09 2008  using multiplier of 2
Tue Mar 04 23:46:09 2008  using 64kb Opteron sieve core
Tue Mar 04 23:46:09 2008  sieve interval: 18 blocks of size 65536
Tue Mar 04 23:46:09 2008  processing polynomials in batches of 6
Tue Mar 04 23:46:09 2008  using a sieve bound of 1574231 (60000 primes)
Tue Mar 04 23:46:09 2008  using large prime bound of 125938480 (26 bits)
Tue Mar 04 23:46:09 2008  using double large prime bound of 380439116353840 (42-49 bits)
Tue Mar 04 23:46:09 2008  using trial factoring cutoff of 49 bits
Tue Mar 04 23:46:09 2008  polynomial 'A' values have 11 factors
Wed Mar 05 01:00:09 2008  60199 relations (16261 full + 43938 combined from 633692 partial), need 60096
Wed Mar 05 01:00:09 2008  begin with 649952 relations
Wed Mar 05 01:00:10 2008  reduce to 146246 relations in 9 passes
Wed Mar 05 01:00:10 2008  attempting to read 146246 relations
Wed Mar 05 01:00:11 2008  recovered 146246 relations
Wed Mar 05 01:00:11 2008  recovered 124895 polynomials
Wed Mar 05 01:00:11 2008  attempting to build 60199 cycles
Wed Mar 05 01:00:11 2008  found 60199 cycles in 5 passes
Wed Mar 05 01:00:12 2008  distribution of cycle lengths:
Wed Mar 05 01:00:12 2008     length 1 : 16261
Wed Mar 05 01:00:12 2008     length 2 : 11453
Wed Mar 05 01:00:12 2008     length 3 : 10730
Wed Mar 05 01:00:12 2008     length 4 : 8114
Wed Mar 05 01:00:12 2008     length 5 : 5490
Wed Mar 05 01:00:12 2008     length 6 : 3603
Wed Mar 05 01:00:12 2008     length 7 : 2053
Wed Mar 05 01:00:12 2008     length 9+: 2495
Wed Mar 05 01:00:12 2008  largest cycle: 18 relations
Wed Mar 05 01:00:12 2008  matrix is 60000 x 60199 (15.0 MB) with weight 3689568 (61.29/col)
Wed Mar 05 01:00:12 2008  sparse part has weight 3689568 (61.29/col)
Wed Mar 05 01:00:13 2008  filtering completed in 3 passes
Wed Mar 05 01:00:13 2008  matrix is 56104 x 56168 (14.1 MB) with weight 3476829 (61.90/col)
Wed Mar 05 01:00:13 2008  sparse part has weight 3476829 (61.90/col)
Wed Mar 05 01:00:14 2008  saving the first 48 matrix rows for later
Wed Mar 05 01:00:14 2008  matrix is 56056 x 56168 (10.7 MB) with weight 2936910 (52.29/col)
Wed Mar 05 01:00:14 2008  sparse part has weight 2473574 (44.04/col)
Wed Mar 05 01:00:14 2008  matrix includes 64 packed rows
Wed Mar 05 01:00:14 2008  using block size 21845 for processor cache size 512 kB
Wed Mar 05 01:00:15 2008  commencing Lanczos iteration
Wed Mar 05 01:00:15 2008  memory use: 9.5 MB
Wed Mar 05 01:00:45 2008  lanczos halted after 888 iterations (dim = 56056)
Wed Mar 05 01:00:45 2008  recovered 18 nontrivial dependencies
Wed Mar 05 01:00:46 2008  prp41 factor: 51656325972977006306990866008287770891019
Wed Mar 05 01:00:46 2008  prp49 factor: 8331166415227273953870412449749267635633640111533
Wed Mar 05 01:00:46 2008  elapsed time 01:14:39

(13·10¹⁴³+23)/9 = 1(4)₁₄₂7_<144> = 3² · 2389 · 72881353 · 6508800369946252997_<19> · 8247464312828826073_<19> · C94

C94 = P36 · P59

P36 = 123511028190274527084942581597557283_<36>

P59 = 13902683100663382375897508514348828772415433347065218804613_<59>

Wed Mar 05 03:26:30 2008  
Wed Mar 05 03:26:30 2008  
Wed Mar 05 03:26:30 2008  Msieve v. 1.33
Wed Mar 05 03:26:30 2008  random seeds: 65fa8740 8a59d135
Wed Mar 05 03:26:30 2008  factoring 1717134684366488291394731960743091276564277158246508109775225266573224151784451098838052146479 (94 digits)
Wed Mar 05 03:26:30 2008  searching for 15-digit factors
Wed Mar 05 03:26:31 2008  commencing quadratic sieve (94-digit input)
Wed Mar 05 03:26:32 2008  using multiplier of 15
Wed Mar 05 03:26:32 2008  using 64kb Opteron sieve core
Wed Mar 05 03:26:32 2008  sieve interval: 18 blocks of size 65536
Wed Mar 05 03:26:32 2008  processing polynomials in batches of 6
Wed Mar 05 03:26:32 2008  using a sieve bound of 1990243 (74118 primes)
Wed Mar 05 03:26:32 2008  using large prime bound of 256741347 (27 bits)
Wed Mar 05 03:26:32 2008  using double large prime bound of 1371173633837307 (42-51 bits)
Wed Mar 05 03:26:32 2008  using trial factoring cutoff of 51 bits
Wed Mar 05 03:26:32 2008  polynomial 'A' values have 12 factors
Wed Mar 05 06:35:53 2008  74238 relations (18185 full + 56053 combined from 1032668 partial), need 74214
Wed Mar 05 06:35:57 2008  begin with 1050852 relations
Wed Mar 05 06:35:58 2008  reduce to 191869 relations in 11 passes
Wed Mar 05 06:35:58 2008  attempting to read 191869 relations
Wed Mar 05 06:36:00 2008  recovered 191869 relations
Wed Mar 05 06:36:00 2008  recovered 176205 polynomials
Wed Mar 05 06:36:00 2008  attempting to build 74238 cycles
Wed Mar 05 06:36:01 2008  found 74238 cycles in 6 passes
Wed Mar 05 06:36:01 2008  distribution of cycle lengths:
Wed Mar 05 06:36:01 2008     length 1 : 18185
Wed Mar 05 06:36:01 2008     length 2 : 13189
Wed Mar 05 06:36:01 2008     length 3 : 12714
Wed Mar 05 06:36:01 2008     length 4 : 10226
Wed Mar 05 06:36:01 2008     length 5 : 7472
Wed Mar 05 06:36:01 2008     length 6 : 5043
Wed Mar 05 06:36:01 2008     length 7 : 3156
Wed Mar 05 06:36:01 2008     length 9+: 4253
Wed Mar 05 06:36:01 2008  largest cycle: 24 relations
Wed Mar 05 06:36:02 2008  matrix is 74118 x 74238 (19.7 MB) with weight 4865840 (65.54/col)
Wed Mar 05 06:36:02 2008  sparse part has weight 4865840 (65.54/col)
Wed Mar 05 06:36:03 2008  filtering completed in 3 passes
Wed Mar 05 06:36:03 2008  matrix is 70536 x 70600 (18.9 MB) with weight 4665097 (66.08/col)
Wed Mar 05 06:36:03 2008  sparse part has weight 4665097 (66.08/col)
Wed Mar 05 06:36:04 2008  saving the first 48 matrix rows for later
Wed Mar 05 06:36:04 2008  matrix is 70488 x 70600 (12.2 MB) with weight 3707945 (52.52/col)
Wed Mar 05 06:36:04 2008  sparse part has weight 2783659 (39.43/col)
Wed Mar 05 06:36:04 2008  matrix includes 64 packed rows
Wed Mar 05 06:36:04 2008  using block size 21845 for processor cache size 512 kB
Wed Mar 05 06:36:05 2008  commencing Lanczos iteration
Wed Mar 05 06:36:05 2008  memory use: 11.6 MB
Wed Mar 05 06:36:57 2008  lanczos halted after 1116 iterations (dim = 70488)
Wed Mar 05 06:36:57 2008  recovered 19 nontrivial dependencies
Wed Mar 05 06:36:58 2008  prp36 factor: 123511028190274527084942581597557283
Wed Mar 05 06:36:58 2008  prp59 factor: 13902683100663382375897508514348828772415433347065218804613
Wed Mar 05 06:36:58 2008  elapsed time 03:10:28

(13·10¹²⁹+23)/9 = 1(4)₁₂₈7_<130> = 17 · 71986679 · 388579423 · 131638082375417_<15> · C98

C98 = P47 · P52

P47 = 13768205563065773942619038565998211282092437391_<47>

P52 = 1675950144686658660252724258618579568960643440587009_<52>

Wed Mar 05 03:30:18 2008  
Wed Mar 05 03:30:18 2008  
Wed Mar 05 03:30:18 2008  Msieve v. 1.33
Wed Mar 05 03:30:18 2008  random seeds: d10cd0c0 9dd72070
Wed Mar 05 03:30:18 2008  factoring 23074826105495742506622674792561962201588789050204835605232101724517444864855960547764664620453519 (98 digits)
Wed Mar 05 03:30:19 2008  searching for 15-digit factors
Wed Mar 05 03:30:20 2008  commencing quadratic sieve (98-digit input)
Wed Mar 05 03:30:20 2008  using multiplier of 11
Wed Mar 05 03:30:20 2008  using 64kb Opteron sieve core
Wed Mar 05 03:30:20 2008  sieve interval: 18 blocks of size 65536
Wed Mar 05 03:30:20 2008  processing polynomials in batches of 6
Wed Mar 05 03:30:20 2008  using a sieve bound of 2473349 (90330 primes)
Wed Mar 05 03:30:20 2008  using large prime bound of 371002350 (28 bits)
Wed Mar 05 03:30:20 2008  using double large prime bound of 2659977403806750 (43-52 bits)
Wed Mar 05 03:30:20 2008  using trial factoring cutoff of 52 bits
Wed Mar 05 03:30:20 2008  polynomial 'A' values have 13 factors
Wed Mar 05 12:38:05 2008  90750 relations (21941 full + 68809 combined from 1363815 partial), need 90426
Wed Mar 05 12:38:08 2008  begin with 1385755 relations
Wed Mar 05 12:38:09 2008  reduce to 237350 relations in 11 passes
Wed Mar 05 12:38:09 2008  attempting to read 237350 relations
Wed Mar 05 12:38:14 2008  recovered 237350 relations
Wed Mar 05 12:38:14 2008  recovered 225131 polynomials
Wed Mar 05 12:38:14 2008  attempting to build 90750 cycles
Wed Mar 05 12:38:14 2008  found 90750 cycles in 6 passes
Wed Mar 05 12:38:14 2008  distribution of cycle lengths:
Wed Mar 05 12:38:14 2008     length 1 : 21941
Wed Mar 05 12:38:14 2008     length 2 : 15721
Wed Mar 05 12:38:14 2008     length 3 : 15481
Wed Mar 05 12:38:14 2008     length 4 : 12234
Wed Mar 05 12:38:14 2008     length 5 : 9403
Wed Mar 05 12:38:14 2008     length 6 : 6298
Wed Mar 05 12:38:14 2008     length 7 : 4060
Wed Mar 05 12:38:14 2008     length 9+: 5612
Wed Mar 05 12:38:14 2008  largest cycle: 20 relations
Wed Mar 05 12:38:15 2008  matrix is 90330 x 90750 (24.6 MB) with weight 6080981 (67.01/col)
Wed Mar 05 12:38:15 2008  sparse part has weight 6080981 (67.01/col)
Wed Mar 05 12:38:16 2008  filtering completed in 3 passes
Wed Mar 05 12:38:16 2008  matrix is 86232 x 86294 (23.4 MB) with weight 5793589 (67.14/col)
Wed Mar 05 12:38:16 2008  sparse part has weight 5793589 (67.14/col)
Wed Mar 05 12:38:17 2008  saving the first 48 matrix rows for later
Wed Mar 05 12:38:17 2008  matrix is 86184 x 86294 (14.4 MB) with weight 4567270 (52.93/col)
Wed Mar 05 12:38:17 2008  sparse part has weight 3257116 (37.74/col)
Wed Mar 05 12:38:17 2008  matrix includes 64 packed rows
Wed Mar 05 12:38:17 2008  using block size 21845 for processor cache size 512 kB
Wed Mar 05 12:38:18 2008  commencing Lanczos iteration
Wed Mar 05 12:38:18 2008  memory use: 14.0 MB
Wed Mar 05 12:39:35 2008  lanczos halted after 1364 iterations (dim = 86180)
Wed Mar 05 12:39:35 2008  recovered 15 nontrivial dependencies
Wed Mar 05 12:39:36 2008  prp47 factor: 13768205563065773942619038565998211282092437391
Wed Mar 05 12:39:36 2008  prp52 factor: 1675950144686658660252724258618579568960643440587009
Wed Mar 05 12:39:36 2008  elapsed time 09:09:18

(13·10¹⁸²+23)/9 = 1(4)₁₈₁7_<183> = 3 · 7 · 431 · 504877 · 302900359194380622368791_<24> · 620741362332478637843569_<24> · 1652669751954615254434527463_<28> · C99

C99 = P45 · P54

P45 = 102018902795014993632340869013035640829170549_<45>

P54 = 997106370883333600948149656195325748620925984243486157_<54>

Number: n
N=101723697927436979167016362493984010049479223127573581459834966967550634921943382131172246473590193
  ( 99 digits)
Divisors found:
 r1=102018902795014993632340869013035640829170549 (pp45)
 r2=997106370883333600948149656195325748620925984243486157 (pp54)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.25 hours.
Scaled time: 6.15 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_1_4_181_7
n: 101723697927436979167016362493984010049479223127573581459834966967550634921943382131172246473590193
skew: 6786.40
# norm 6.40e+12
c5: 6720
c4: -46547316
c3: -657241524361
c2: 745994210091040
c1: 19255522875488259842
c0: 27254605737004070974296
# alpha -4.83
Y1: 3483090343
Y0: -6855053980282929445
# Murphy_E 4.58e-09
# M 75668479141657735935132313982434429942620819883454237349454038312847628844105708453299769010362350
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 600001)
Primes: RFBsize:135072, AFBsize:135868, largePrimes:3060466 encountered
Relations: rels:2953693, finalFF:326435
Max relations in full relation-set: 28
Initial matrix: 271017 x 326435 with sparse part having weight 13200354.
Pruned matrix : 198762 x 200181 with weight 5770811.
Total sieving time: 3.70 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.31 hours.
Total square root time: 0.13 hours, sqrts: 3.
Prototype def-par.txt line would be:
gnfs,98,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 4.25 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(7·10¹⁶⁷-1)/3 = 2(3)₁₆₇_<168> = 17 · 3747630585556522367279_<22> · 206478253946877556425611_<24> · C122

C122 = P43 · P80

P43 = 1475524985797736524823505686019457306026851_<43>

P80 = 12021265864330860490642857097445746591366152448633295697093349156568276428128971_<80>

Mar 4, 2008

The factor table of 144...447 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Mar 3, 2008 (3rd)

By Sinkiti Sibata / PFGW

(4·10¹⁴²⁹⁶+17)/3 is PRP.

Mar 3, 2008 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(4·10¹⁵⁹+17)/3 = 1(3)₁₅₈9_<160> = 13 · 5336181127_<10> · 74302623841_<11> · 15962304105811289_<17> · C122

C122 = P34 · P88

P34 = 6712335232775758523886486797289601_<34>

P88 = 2414301214334435801406014836781291748305862176834703050235565295072747708123609133613961_<88>

(4·10¹⁵⁸+17)/3 = 1(3)₁₅₇9_<159> = 210713 · 247727401 · 8261945423_<10> · 694394829684084648059_<21> · C114

C114 = P37 · P78

P37 = 2314877192735084930952330849764046313_<37>

P78 = 192334239043421111920406360429117553604774190411975262010918731321162335043383_<78>

(2·10¹⁸⁴-17)/3 = (6)₁₈₃1_<184> = 4219 · C181

C181 = P41 · P140

P41 = 28609253572869545857217493537739138154543_<41>

P140 = 55232244030516686639554241888671996746003277183153779948952860532194772336143354262308238021016571932827843863807642854182781471008243425233_<140>

Number: n
N=1580153274867662163229833293829501461641779252587500987595796792288852018645808643438413526112032867188117247372995180532511653630402149008453820020541992573279608121987832819783519
  ( 181 digits)
SNFS difficulty: 185 digits.
Divisors found:

Mon Mar 03 02:24:58 2008  prp41 factor: 28609253572869545857217493537739138154543
Mon Mar 03 02:24:58 2008  prp140 factor: 55232244030516686639554241888671996746003277183153779948952860532194772336143354262308238021016571932827843863807642854182781471008243425233
Mon Mar 03 02:24:58 2008  elapsed time 03:13:48 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 265.53 hours.  [ CPU 1 of 3 ]
Scaled time: 384.49 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_6_183_1
n: 1580153274867662163229833293829501461641779252587500987595796792288852018645808643438413526112032867188117247372995180532511653630402149008453820020541992573279608121987832819783519
type: snfs
deg: 5
c5: 1
c0: -85
skew: 2.43
m: 10000000000000000000000000000000000000
rlim: 8000000
alim: 8000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 10943909)
Primes: RFBsize:539777, AFBsize:540420, largePrimes:4532205 encountered
Relations: rels:4098423, finalFF:397632
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 265.37 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,185,5,0,0,0,0,0,0,0,0,8000000,8000000,27,27,48,48,2.5,2.5,100000
total time: 265.53 hours.
 --------- CPU info (if available) ----------

10¹⁸³+3 = 1(0)₁₈₂3_<184> = 151 · C181

C181 = P85 · P97

P85 = 6020764512776596637935748594527916970455883912337190641386916348913598221840340985957_<85>

P97 = 1099946118510003646349468098078650177107070925385139448756306534652901227896353302429603211134929_<97>

Number: n
N=6622516556291390728476821192052980132450331125827814569536423841059602649006622516556291390728476821192052980132450331125827814569536423841059602649006622516556291390728476821192053
  ( 181 digits)
SNFS difficulty: 183 digits.
Divisors found:

Mon Mar 03 02:33:02 2008  prp85 factor: 6020764512776596637935748594527916970455883912337190641386916348913598221840340985957
Mon Mar 03 02:33:02 2008  prp97 factor: 1099946118510003646349468098078650177107070925385139448756306534652901227896353302429603211134929
Mon Mar 03 02:33:02 2008  elapsed time 01:55:13 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 267.26 hours.  [ CPU 1 of 4 ]
Scaled time: 225.03 units (timescale=0.842).
Factorization parameters were as follows:
name: KA_1_0_182_3
n: 6622516556291390728476821192052980132450331125827814569536423841059602649006622516556291390728476821192052980132450331125827814569536423841059602649006622516556291390728476821192053
type: snfs
deg: 5
c5: 1000
c0: 3
skew: 0.31
m: 1000000000000000000000000000000000000
rlim: 8000000
alim: 8000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 18522211)
Primes: RFBsize:539777, AFBsize:539335, largePrimes:5050824 encountered
Relations: rels:4702361, finalFF:450163
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 267.12 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,183,5,0,0,0,0,0,0,0,0,8000000,8000000,27,27,48,48,2.5,2.5,100000
total time: 267.26 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

Mar 3, 2008

By Sinkiti Sibata / PRIMO

(4·10²⁶⁶⁸+17)/3 is prime.

Mar 2, 2008 (2nd)

By matsui / GGNFS

3·10¹⁸⁰+1 = 3(0)₁₇₉1_<181> = 661 · C178

C178 = P54 · P55 · P70

P54 = 430259544631759600727768857693217721153099730144795861_<54>

P55 = 1538326517326993101925943385140082111132168130040478949_<55>

P70 = 6857104304052897516728603587977821413916030196167551914714888140645269_<70>

N=4538577912254160363086232980332829046898638426626323751891074130105900151285930408472012102874432677760968229954614220877458396369137670196671709531013615733736762481089258698941
  ( 178 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=430259544631759600727768857693217721153099730144795861 (pp54)
 r2=1538326517326993101925943385140082111132168130040478949 (pp55)
 r3=6857104304052897516728603587977821413916030196167551914714888140645269 (pp70)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 355.58 hours.
Scaled time: 400.03 units (timescale=1.125).
Factorization parameters were as follows:
n: 4538577912254160363086232980332829046898638426626323751891074130105900151285930408472012102874432677760968229954614220877458396369137670196671709531013615733736762481089258698941
m: 1000000000000000000000000000000000000
c5: 3
c0: 1
skew: 0.80
type: snfs

Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 8000001)
Primes: RFBsize:501962, AFBsize:501561, largePrimes:6416877 encountered
Relations: rels:6927553, finalFF:1185317
Max relations in full relation-set: 28
Initial matrix: 1003588 x 1185317 with sparse part having weight 59042752.
Pruned matrix : 844680 x 849761 with weight 42505130.
Total sieving time: 338.73 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 16.32 hours.
Time per square root: 0.38 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 355.58 hours.

Mar 3, 2008

By Sinkiti Sibata / PRIMO

(4·10²⁶⁶⁸+17)/3 is prime.

Mar 2, 2008 (2nd)

By matsui / GGNFS

3·10¹⁸⁰+1 = 3(0)₁₇₉1_<181> = 661 · C178

C178 = P54 · P55 · P70

P54 = 430259544631759600727768857693217721153099730144795861_<54>

P55 = 1538326517326993101925943385140082111132168130040478949_<55>

P70 = 6857104304052897516728603587977821413916030196167551914714888140645269_<70>

N=4538577912254160363086232980332829046898638426626323751891074130105900151285930408472012102874432677760968229954614220877458396369137670196671709531013615733736762481089258698941
  ( 178 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=430259544631759600727768857693217721153099730144795861 (pp54)
 r2=1538326517326993101925943385140082111132168130040478949 (pp55)
 r3=6857104304052897516728603587977821413916030196167551914714888140645269 (pp70)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 355.58 hours.
Scaled time: 400.03 units (timescale=1.125).
Factorization parameters were as follows:
n: 4538577912254160363086232980332829046898638426626323751891074130105900151285930408472012102874432677760968229954614220877458396369137670196671709531013615733736762481089258698941
m: 1000000000000000000000000000000000000
c5: 3
c0: 1
skew: 0.80
type: snfs

Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 8000001)
Primes: RFBsize:501962, AFBsize:501561, largePrimes:6416877 encountered
Relations: rels:6927553, finalFF:1185317
Max relations in full relation-set: 28
Initial matrix: 1003588 x 1185317 with sparse part having weight 59042752.
Pruned matrix : 844680 x 849761 with weight 42505130.
Total sieving time: 338.73 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 16.32 hours.
Time per square root: 0.38 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 355.58 hours.

Mar 2, 2008

By Kenji Ibusuki / GGNFS

4·10¹⁶⁵+1 = 4(0)₁₆₄1_<166> = 23743 · 80900761 · 513790423 · 61142992571_<11> · C134

C134 = P64 · P70

P64 = 7779120398579544883895822513251508700047607501669183213883240931_<64>

P70 = 8521353913589854424771282379603548481995888227244581651836279018886769_<70>

Number: 40001_165
N=66288638052722473026075484215560691185478806573826992792051302562378578914894418060101191373980449366238323280750797702826113435141939
  ( 134 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=7779120398579544883895822513251508700047607501669183213883240931 (pp64)
 r2=8521353913589854424771282379603548481995888227244581651836279018886769 (pp70)
Version: GGNFS-0.77.1
Total time: 51.86 hours.
Scaled time: 150.19 units (timescale=2.896).
Factorization parameters were as follows:
n: 66288638052722473026075484215560691185478806573826992792051302562378578914894418060101191373980449366238323280750797702826113435141939
m: 1000000000000000000000000000000000
c5: 4
c0: 1
skew: 0.76
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [2500000, 5000001)
Relations: rels:6616882, finalFF:1050519
Initial matrix: 696753 x 1050519 with sparse part having weight 62728387.
Pruned matrix : 562745 x 566292 with weight 26430629.
Total sieving time: 50.22 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 1.47 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 51.86 hours.
 --------- CPU info (if available) ----------

February 2008

Feb 29, 2008

By Sinkiti Sibata / PRIMO

(4·10²⁵¹⁰+17)/3 is prime.

Feb 28, 2008

By Hugo Platzer / GGNFS, Msieve

(4·10¹¹⁵+17)/3 = 1(3)₁₁₄9_<116> = 44273161259577833937371461_<26> · C90

C90 = P39 · P51

P39 = 319366236020566864959345447725369918009_<39>

P51 = 942994595128733071671702794426078062922265699564311_<51>

Number: pal/pal
N=301160634434001859043915236810290858557068276203651269507515584105353054975494297092576799
  ( 90 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=319366236020566864959345447725369918009 (pp39)
 r2=942994595128733071671702794426078062922265699564311 (pp51)
Version: GGNFS-0.77.0
Total time: 1.74 hours.
Scaled time: 2.06 units (timescale=1.188).
Factorization parameters were as follows:
n: 301160634434001859043915236810290858557068276203651269507515584105353054975494297092576799
m: 100000000000000000000000
c5: 4
c0: 17
skew: 1.34
type: snfs

Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Sieved special-q in [250000, 410001)
Relations: rels:1114412, finalFF:123645
Initial matrix: 79657 x 123645 with sparse part having weight 5708692.
Pruned matrix : 71040 x 71502 with weight 1969930.
Total sieving time: 1.65 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000
total time: 1.74 hours.
 --------- CPU info (if available) ----------

(4·10¹⁰²+17)/3 = 1(3)₁₀₁9_<103> = 7 · 90997 · C97

C97 = P36 · P61

P36 = 908549692702934028385232905262450753_<36>

P61 = 2303906956496829188740684010099011404683762570088688116424697_<61>

Number: pal/pal
N=2093213957341346156362036006419887207165908661562364431689794064377841865011771711992598395446841
  ( 97 digits)
SNFS difficulty: 102 digits.
Divisors found:
 r1=908549692702934028385232905262450753 (pp36)
 r2=2303906956496829188740684010099011404683762570088688116424697 (pp61)
Version: GGNFS-0.77.0
Total time: 1.06 hours.
Scaled time: 1.30 units (timescale=1.226).
Factorization parameters were as follows:
n: 2093213957341346156362036006419887207165908661562364431689794064377841865011771711992598395446841
m: 200000000000000000000
c5: 25
c0: 34
skew: 1.06
type: snfs

Factor base limits: 300000/350000
Large primes per side: 3
Large prime bits: 25/25
Sieved special-q in [175000, 255001)
Relations: rels:834056, finalFF:65949
Initial matrix: 55703 x 65949 with sparse part having weight 1722162.
Pruned matrix : 48155 x 48497 with weight 1039638.
Total sieving time: 1.01 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,102,5,0,0,0,0,0,0,0,0,300000,350000,25,25,43,43,2.1,2.1,10000
total time: 1.06 hours.
 --------- CPU info (if available) ----------

(4·10¹⁰⁵+17)/3 = 1(3)₁₀₄9_<106> = 13 · 61 · 103 · 109 · 269 · 761 · 821 · 24439 · C86

C86 = P37 · P50

P37 = 1130021764079074147902253763132106677_<37>

P50 = 32266472809078491624666219453514850051247682267147_<50>

Mon Feb 25 19:02:32 2008  
Mon Feb 25 19:02:32 2008  
Mon Feb 25 19:02:32 2008  Msieve v. 1.33
Mon Feb 25 19:02:32 2008  random seeds: 489d45ae e59eb9a7
Mon Feb 25 19:02:32 2008  factoring 36461816524324356163353669314329958450145184317692851469585242129594363032425616440519 (86 digits)
Mon Feb 25 19:02:33 2008  no P-1/P+1/ECM available, skipping
Mon Feb 25 19:02:33 2008  commencing quadratic sieve (86-digit input)
Mon Feb 25 19:02:33 2008  using multiplier of 5
Mon Feb 25 19:02:33 2008  using 64kb Pentium 4 sieve core
Mon Feb 25 19:02:33 2008  sieve interval: 8 blocks of size 65536
Mon Feb 25 19:02:33 2008  processing polynomials in batches of 13
Mon Feb 25 19:02:33 2008  using a sieve bound of 1461401 (55581 primes)
Mon Feb 25 19:02:33 2008  using large prime bound of 116912080 (26 bits)
Mon Feb 25 19:02:33 2008  using double large prime bound of 332771997435520 (41-49 bits)
Mon Feb 25 19:02:33 2008  using trial factoring cutoff of 49 bits
Mon Feb 25 19:02:33 2008  polynomial 'A' values have 11 factors
Mon Feb 25 19:55:41 2008  28010 relations (11626 full + 16384 combined from 433728 partial), need 55677
Mon Feb 25 19:55:41 2008  elapsed time 00:53:09
Tue Feb 26 14:33:17 2008  
Tue Feb 26 14:33:17 2008  
Tue Feb 26 14:33:17 2008  Msieve v. 1.33
Tue Feb 26 14:33:17 2008  random seeds: 1bd18fdc 512ff2e1
Tue Feb 26 14:33:17 2008  factoring 36461816524324356163353669314329958450145184317692851469585242129594363032425616440519 (86 digits)
Tue Feb 26 14:33:18 2008  no P-1/P+1/ECM available, skipping
Tue Feb 26 14:33:18 2008  commencing quadratic sieve (86-digit input)
Tue Feb 26 14:33:19 2008  using multiplier of 5
Tue Feb 26 14:33:19 2008  using 64kb Pentium 4 sieve core
Tue Feb 26 14:33:19 2008  sieve interval: 8 blocks of size 65536
Tue Feb 26 14:33:19 2008  processing polynomials in batches of 13
Tue Feb 26 14:33:19 2008  using a sieve bound of 1461401 (55581 primes)
Tue Feb 26 14:33:19 2008  using large prime bound of 116912080 (26 bits)
Tue Feb 26 14:33:19 2008  using double large prime bound of 332771997435520 (41-49 bits)
Tue Feb 26 14:33:19 2008  using trial factoring cutoff of 49 bits
Tue Feb 26 14:33:19 2008  polynomial 'A' values have 11 factors
Tue Feb 26 14:33:19 2008  restarting with 11626 full and 433728 partial relations
Tue Feb 26 14:52:43 2008  55935 relations (15723 full + 40212 combined from 587434 partial), need 55677
Tue Feb 26 14:52:43 2008  begin with 603157 relations
Tue Feb 26 14:52:44 2008  reduce to 133993 relations in 11 passes
Tue Feb 26 14:52:44 2008  attempting to read 133993 relations
Tue Feb 26 14:52:47 2008  recovered 133993 relations
Tue Feb 26 14:52:47 2008  recovered 114567 polynomials
Tue Feb 26 14:52:47 2008  attempting to build 55935 cycles
Tue Feb 26 14:52:47 2008  found 55935 cycles in 5 passes
Tue Feb 26 14:52:47 2008  distribution of cycle lengths:
Tue Feb 26 14:52:47 2008     length 1 : 15723
Tue Feb 26 14:52:47 2008     length 2 : 10989
Tue Feb 26 14:52:47 2008     length 3 : 9938
Tue Feb 26 14:52:47 2008     length 4 : 7222
Tue Feb 26 14:52:47 2008     length 5 : 4960
Tue Feb 26 14:52:47 2008     length 6 : 3120
Tue Feb 26 14:52:47 2008     length 7 : 1800
Tue Feb 26 14:52:47 2008     length 9+: 2183
Tue Feb 26 14:52:47 2008  largest cycle: 18 relations
Tue Feb 26 14:52:47 2008  matrix is 55581 x 55935 (12.6 MB) with weight 3078328 (55.03/col)
Tue Feb 26 14:52:47 2008  sparse part has weight 3078328 (55.03/col)
Tue Feb 26 14:52:48 2008  filtering completed in 4 passes
Tue Feb 26 14:52:48 2008  matrix is 51012 x 51076 (11.6 MB) with weight 2828283 (55.37/col)
Tue Feb 26 14:52:48 2008  sparse part has weight 2828283 (55.37/col)
Tue Feb 26 14:52:48 2008  saving the first 48 matrix rows for later
Tue Feb 26 14:52:49 2008  matrix is 50964 x 51076 (6.8 MB) with weight 2143902 (41.97/col)
Tue Feb 26 14:52:49 2008  sparse part has weight 1474804 (28.87/col)
Tue Feb 26 14:52:49 2008  matrix includes 64 packed rows
Tue Feb 26 14:52:49 2008  using block size 20430 for processor cache size 2048 kB
Tue Feb 26 14:52:49 2008  commencing Lanczos iteration
Tue Feb 26 14:52:49 2008  memory use: 7.0 MB
Tue Feb 26 14:53:11 2008  lanczos halted after 807 iterations (dim = 50964)
Tue Feb 26 14:53:11 2008  recovered 19 nontrivial dependencies
Tue Feb 26 14:53:12 2008  prp37 factor: 1130021764079074147902253763132106677
Tue Feb 26 14:53:12 2008  prp50 factor: 32266472809078491624666219453514850051247682267147
Tue Feb 26 14:53:12 2008  elapsed time 00:19:55

(4·10¹⁰³+17)/3 = 1(3)₁₀₂9_<104> = 71 · 272825425082537387_<18> · C84

C84 = P34 · P51

P34 = 5999573294919686788638217605693019_<34>

P51 = 114729521955095979857325671845756990670861614334053_<51>

Mon Feb 25 16:51:57 2008  
Mon Feb 25 16:51:57 2008  
Mon Feb 25 16:51:57 2008  Msieve v. 1.33
Mon Feb 25 16:51:57 2008  random seeds: 865e6202 3cef8fa7
Mon Feb 25 16:51:57 2008  factoring 688328176060695733567653133817593886237944056362101592634801269296206820707236076007 (84 digits)
Mon Feb 25 16:51:58 2008  no P-1/P+1/ECM available, skipping
Mon Feb 25 16:51:58 2008  commencing quadratic sieve (84-digit input)
Mon Feb 25 16:51:58 2008  using multiplier of 7
Mon Feb 25 16:51:58 2008  using 64kb Pentium 4 sieve core
Mon Feb 25 16:51:58 2008  sieve interval: 6 blocks of size 65536
Mon Feb 25 16:51:58 2008  processing polynomials in batches of 17
Mon Feb 25 16:51:58 2008  using a sieve bound of 1408987 (53824 primes)
Mon Feb 25 16:51:58 2008  using large prime bound of 119763895 (26 bits)
Mon Feb 25 16:51:58 2008  using double large prime bound of 347525361371830 (41-49 bits)
Mon Feb 25 16:51:58 2008  using trial factoring cutoff of 49 bits
Mon Feb 25 16:51:58 2008  polynomial 'A' values have 11 factors
Mon Feb 25 17:34:06 2008  54044 relations (16264 full + 37780 combined from 570002 partial), need 53920
Mon Feb 25 17:34:07 2008  begin with 586266 relations
Mon Feb 25 17:34:07 2008  reduce to 124740 relations in 10 passes
Mon Feb 25 17:34:07 2008  attempting to read 124740 relations
Mon Feb 25 17:34:09 2008  recovered 124740 relations
Mon Feb 25 17:34:09 2008  recovered 97661 polynomials
Mon Feb 25 17:34:10 2008  attempting to build 54044 cycles
Mon Feb 25 17:34:10 2008  found 54044 cycles in 5 passes
Mon Feb 25 17:34:10 2008  distribution of cycle lengths:
Mon Feb 25 17:34:10 2008     length 1 : 16264
Mon Feb 25 17:34:10 2008     length 2 : 11387
Mon Feb 25 17:34:10 2008     length 3 : 9603
Mon Feb 25 17:34:10 2008     length 4 : 6775
Mon Feb 25 17:34:10 2008     length 5 : 4392
Mon Feb 25 17:34:10 2008     length 6 : 2597
Mon Feb 25 17:34:10 2008     length 7 : 1454
Mon Feb 25 17:34:10 2008     length 9+: 1572
Mon Feb 25 17:34:10 2008  largest cycle: 16 relations
Mon Feb 25 17:34:10 2008  matrix is 53824 x 54044 (11.5 MB) with weight 2806436 (51.93/col)
Mon Feb 25 17:34:10 2008  sparse part has weight 2806436 (51.93/col)
Mon Feb 25 17:34:10 2008  filtering completed in 3 passes
Mon Feb 25 17:34:10 2008  matrix is 48513 x 48577 (10.4 MB) with weight 2532665 (52.14/col)
Mon Feb 25 17:34:10 2008  sparse part has weight 2532665 (52.14/col)
Mon Feb 25 17:34:11 2008  saving the first 48 matrix rows for later
Mon Feb 25 17:34:11 2008  matrix is 48465 x 48577 (6.2 MB) with weight 1903865 (39.19/col)
Mon Feb 25 17:34:11 2008  sparse part has weight 1328744 (27.35/col)
Mon Feb 25 17:34:11 2008  matrix includes 64 packed rows
Mon Feb 25 17:34:11 2008  commencing Lanczos iteration
Mon Feb 25 17:34:11 2008  memory use: 8.0 MB
Mon Feb 25 17:35:38 2008  lanczos halted after 768 iterations (dim = 48457)
Mon Feb 25 17:35:38 2008  recovered 13 nontrivial dependencies
Mon Feb 25 17:35:39 2008  prp34 factor: 5999573294919686788638217605693019
Mon Feb 25 17:35:39 2008  prp51 factor: 114729521955095979857325671845756990670861614334053
Mon Feb 25 17:35:39 2008  elapsed time 00:43:42

Feb 27, 2008 (2nd)

By Jo Yeong Uk / GMP-ECM, Msieve

(4·10¹⁴⁸+17)/3 = 1(3)₁₄₇9_<149> = 457 · 12401 · 545549 · C136

C136 = P33 · P103

P33 = 532912808365383321830732841180011_<33>

P103 = 8092373263092864819628133138996361186520651603049089855317300239501384692261426760504261399767313194493_<103>

(4·10¹⁵⁴+17)/3 = 1(3)₁₅₃9_<155> = 28097 · C150

C150 = P36 · P115

P36 = 415104467682959200738565774465754443_<36>

P115 = 1143197793410399407185698538514618525118222228412394584420498452315299754453223670868380083914065328519933881066609_<115>

(4·10¹⁵⁷+17)/3 = 1(3)₁₅₆9_<158> = 3989 · 13487875393271_<14> · 2257449223315382094947915963_<28> · C114

C114 = P29 · P37 · P48

P29 = 47215344192327994418258987129_<29>

P37 = 7609598281654676371263513938560727761_<37>

P48 = 305540140613631168561515299376375435879608838323_<48>

Wed Feb 27 19:01:59 2008  
Wed Feb 27 19:01:59 2008  
Wed Feb 27 19:01:59 2008  Msieve v. 1.32
Wed Feb 27 19:01:59 2008  random seeds: df8c8585 3390fcdc
Wed Feb 27 19:01:59 2008  factoring 2325037728990015935986003917297505539985894435563542929797489279175271175442666784803 (85 digits)
Wed Feb 27 19:02:00 2008  no P-1/P+1/ECM available, skipping
Wed Feb 27 19:02:00 2008  commencing quadratic sieve (85-digit input)
Wed Feb 27 19:02:00 2008  using multiplier of 3
Wed Feb 27 19:02:00 2008  using 32kb Intel Core sieve core
Wed Feb 27 19:02:00 2008  sieve interval: 12 blocks of size 32768
Wed Feb 27 19:02:00 2008  processing polynomials in batches of 17
Wed Feb 27 19:02:00 2008  using a sieve bound of 1424231 (54412 primes)
Wed Feb 27 19:02:00 2008  using large prime bound of 116786942 (26 bits)
Wed Feb 27 19:02:00 2008  using double large prime bound of 332131201862394 (41-49 bits)
Wed Feb 27 19:02:00 2008  using trial factoring cutoff of 49 bits
Wed Feb 27 19:02:00 2008  polynomial 'A' values have 11 factors
Wed Feb 27 19:33:30 2008  54805 relations (15971 full + 38834 combined from 576753 partial), need 54508
Wed Feb 27 19:33:31 2008  begin with 592724 relations
Wed Feb 27 19:33:31 2008  reduce to 130102 relations in 10 passes
Wed Feb 27 19:33:31 2008  attempting to read 130102 relations
Wed Feb 27 19:33:32 2008  recovered 130102 relations
Wed Feb 27 19:33:32 2008  recovered 110815 polynomials
Wed Feb 27 19:33:32 2008  attempting to build 54805 cycles
Wed Feb 27 19:33:32 2008  found 54805 cycles in 5 passes
Wed Feb 27 19:33:32 2008  distribution of cycle lengths:
Wed Feb 27 19:33:32 2008     length 1 : 15971
Wed Feb 27 19:33:32 2008     length 2 : 10733
Wed Feb 27 19:33:32 2008     length 3 : 9599
Wed Feb 27 19:33:32 2008     length 4 : 7051
Wed Feb 27 19:33:32 2008     length 5 : 4787
Wed Feb 27 19:33:32 2008     length 6 : 2900
Wed Feb 27 19:33:32 2008     length 7 : 1741
Wed Feb 27 19:33:32 2008     length 9+: 2023
Wed Feb 27 19:33:32 2008  largest cycle: 16 relations
Wed Feb 27 19:33:32 2008  matrix is 54412 x 54805 with weight 2920282 (avg 53.28/col)
Wed Feb 27 19:33:33 2008  filtering completed in 3 passes
Wed Feb 27 19:33:33 2008  matrix is 49677 x 49741 with weight 2662605 (avg 53.53/col)
Wed Feb 27 19:33:33 2008  saving the first 48 matrix rows for later
Wed Feb 27 19:33:33 2008  matrix is 49629 x 49741 with weight 2029250 (avg 40.80/col)
Wed Feb 27 19:33:33 2008  matrix includes 64 packed rows
Wed Feb 27 19:33:33 2008  commencing Lanczos iteration
Wed Feb 27 19:34:24 2008  lanczos halted after 786 iterations (dim = 49629)
Wed Feb 27 19:34:24 2008  recovered 18 nontrivial dependencies
Wed Feb 27 19:34:25 2008  prp37 factor: 7609598281654676371263513938560727761
Wed Feb 27 19:34:25 2008  prp48 factor: 305540140613631168561515299376375435879608838323
Wed Feb 27 19:34:25 2008  elapsed time 00:32:26

Feb 27, 2008

By Sinkiti Sibata / GGNFS

(4·10¹³⁷+17)/3 = 1(3)₁₃₆9_<138> = 6552669181_<10> · C128

C128 = P31 · P98

P31 = 1714801068361452362148879871541_<31>

P98 = 11866065698073971314555419688519586074878423197647649070453154014930648060685107891975630143616059_<98>

Number: 13339_137
N=20347942136304429029183631746254234306862886526261416848618003401892376616431131460981554065323923352408492867165444245144676919
  ( 128 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=1714801068361452362148879871541 (pp31)
 r2=11866065698073971314555419688519586074878423197647649070453154014930648060685107891975630143616059 (pp98)
Version: GGNFS-0.77.1-20060513-k8
Total time: 10.83 hours.
Scaled time: 21.50 units (timescale=1.986).
Factorization parameters were as follows:
name: 13339_137
n: 20347942136304429029183631746254234306862886526261416848618003401892376616431131460981554065323923352408492867165444245144676919
m: 2000000000000000000000000000
c5: 25
c0: 34
skew: 1.06
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1825001)
Primes: RFBsize:78498, AFBsize:63478, largePrimes:1643983 encountered
Relations: rels:1666339, finalFF:176380
Max relations in full relation-set: 28
Initial matrix: 142040 x 176380 with sparse part having weight 18465089.
Pruned matrix : 133405 x 134179 with weight 12556937.
Total sieving time: 10.51 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 10.83 hours.
 --------- CPU info (if available) ----------

(4·10¹⁴⁰+17)/3 = 1(3)₁₃₉9_<141> = 139 · 149 · 419 · 2656035623_<10> · C124

C124 = P38 · P87

P38 = 26537771762988932797230520985691326549_<38>

P87 = 217984339902061538043658310872268089617507279115184973919874854501815077478362601957973_<87>

Number: 13339_140
N=5784818660226710392893078633225827009749351932038762240593991255227477040501870714437762806715702310280279904345671117125177
  ( 124 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=26537771762988932797230520985691326549 (pp38)
 r2=217984339902061538043658310872268089617507279115184973919874854501815077478362601957973 (pp87)
Version: GGNFS-0.77.1-20060513-k8
Total time: 9.46 hours.
Scaled time: 18.92 units (timescale=2.001).
Factorization parameters were as follows:
name: 13339_140
n: 5784818660226710392893078633225827009749351932038762240593991255227477040501870714437762806715702310280279904345671117125177
m: 10000000000000000000000000000
c5: 4
c0: 17
skew: 1.34
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1550001)
Primes: RFBsize:100021, AFBsize:100163, largePrimes:2673595 encountered
Relations: rels:2647843, finalFF:269918
Max relations in full relation-set: 28
Initial matrix: 200248 x 269918 with sparse part having weight 22264975.
Pruned matrix : 177577 x 178642 with weight 12371339.
Total sieving time: 9.05 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 9.46 hours.
 --------- CPU info (if available) ----------

(4·10¹⁴²+17)/3 = 1(3)₁₄₁9_<143> = 1459 · 356837938640928229_<18> · C122

C122 = P40 · P82

P40 = 4952433461126705550942268828114546821893_<40>

P82 = 5171229039310035816298410533513362321815097567656651449551330364234046974538947393_<82>

Number: 13339_142
N=25610167729429129154219135122692807752943626214310846468823181205165725036518490526562875573240011146514873716817667674949
  ( 122 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=4952433461126705550942268828114546821893 (pp40)
 r2=5171229039310035816298410533513362321815097567656651449551330364234046974538947393 (pp82)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 17.78 hours.
Scaled time: 12.00 units (timescale=0.675).
Factorization parameters were as follows:
name: 13339_142
n: 25610167729429129154219135122692807752943626214310846468823181205165725036518490526562875573240011146514873716817667674949
m: 20000000000000000000000000000
c5: 25
c0: 34
skew: 1.06
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2350001)
Primes: RFBsize:100021, AFBsize:99703, largePrimes:2800788 encountered
Relations: rels:2789786, finalFF:244586
Max relations in full relation-set: 28
Initial matrix: 199788 x 244586 with sparse part having weight 26053579.
Pruned matrix : 187306 x 188368 with weight 18253445.
Total sieving time: 16.40 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.13 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 17.78 hours.
 --------- CPU info (if available) ----------

(4·10¹⁴³+17)/3 = 1(3)₁₄₂9_<144> = 47 · 107 · 1019 · 3559 · C133

C133 = P53 · P81

P53 = 21530592730890687406724972323507960444311519390746899_<53>

P81 = 339546253576180671194251388956900458789709973584370940213518247026860941408782729_<81>

Number: 13339_143
N=7310632099048481632442417594674736817587577048810320179589357685324612306601759726202069186552803790311886326790976822657893721507371
  ( 133 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=21530592730890687406724972323507960444311519390746899 (pp53)
 r2=339546253576180671194251388956900458789709973584370940213518247026860941408782729 (pp81)
Version: GGNFS-0.77.1-20060513-k8
Total time: 14.08 hours.
Scaled time: 28.10 units (timescale=1.995).
Factorization parameters were as follows:
name: 13339_143
n: 7310632099048481632442417594674736817587577048810320179589357685324612306601759726202069186552803790311886326790976822657893721507371
m: 20000000000000000000000000000
c5: 125
c0: 17
skew: 0.67
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2150001)
Primes: RFBsize:100021, AFBsize:100153, largePrimes:2776914 encountered
Relations: rels:2762452, finalFF:254297
Max relations in full relation-set: 28
Initial matrix: 200239 x 254297 with sparse part having weight 25949347.
Pruned matrix : 184883 x 185948 with weight 17064295.
Total sieving time: 13.53 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.35 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 14.08 hours.
 --------- CPU info (if available) ----------

Feb 26, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(4·10¹⁵⁰+11)/3 = 1(3)₁₄₉7_<151> = 67 · 97 · 181 · 51437 · 67069940098328863_<17> · C128

C123 = P45 · P78

P45 = 842567218953103748778820051250784569042311499_<45>

P78 = 389946940241801961370181471323403096587030785968251538514409936744648047951767_<78>

Number: 13337_150
N=328556508978807216467909242087984532386542899298545695789839803490270877924857370271680502884986361766553459019686141468733
  ( 123 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=842567218953103748778820051250784569042311499 (pp45)
 r2=389946940241801961370181471323403096587030785968251538514409936744648047951767 (pp78)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 23.88 hours.
Scaled time: 16.09 units (timescale=0.674).
Factorization parameters were as follows:
name: 13337_150
n: 328556508978807216467909242087984532386542899298545695789839803490270877924857370271680502884986361766553459019686141468733
m: 1000000000000000000000000000000
c5: 4
c0: 11
skew: 1.22
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1800001)
Primes: RFBsize:176302, AFBsize:175914, largePrimes:5199684 encountered
Relations: rels:5061012, finalFF:454047
Max relations in full relation-set: 28
Initial matrix: 352280 x 454047 with sparse part having weight 34543199.
Pruned matrix : 283186 x 285011 with weight 20367249.
Total sieving time: 20.94 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 2.64 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 23.88 hours.
 --------- CPU info (if available) ----------

(4·10¹²⁸+17)/3 = 1(3)₁₂₇9_<129> = 30905143 · C121

C121 = P40 · P82

P40 = 2264647650843887046315670559789081872837_<40>

P82 = 1905054208279908717959032447092198327666493476216888547860932106950160593631866329_<82>

Number: 13339_128
N=4314276537511356389237006065085456272871260726194773903273423887193575947321561765086585534754954323729656689610960005373
  ( 121 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=2264647650843887046315670559789081872837 (pp40)
 r2=1905054208279908717959032447092198327666493476216888547860932106950160593631866329 (pp82)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.50 hours.
Scaled time: 8.93 units (timescale=1.986).
Factorization parameters were as follows:
name:13339_128
n: 4314276537511356389237006065085456272871260726194773903273423887193575947321561765086585534754954323729656689610960005373
m: 20000000000000000000000000
c5: 125
c0: 17
skew: 0.67
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64073, largePrimes:1650177 encountered
Relations: rels:1772225, finalFF:282784
Max relations in full relation-set: 28
Initial matrix: 128089 x 282784 with sparse part having weight 20216596.
Pruned matrix : 93487 x 94191 with weight 6406529.
Total sieving time: 4.36 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.50 hours.
 --------- CPU info (if available) ----------

(4·10¹²¹+17)/3 = 1(3)₁₂₀9_<122> = 38737 · 198811 · C112

C112 = P49 · P64

P49 = 1066128263744179842966023845014133805371522028417_<49>

P64 = 1623913477852878066050128577369053541152591491514652526106580081_<64>

Number: 13339_121
N=1731300056614061539047787291401292101287271622335940759125354484590113946145583400138478407257787884223968161777
  ( 112 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=1066128263744179842966023845014133805371522028417 (pp49)
 r2=1623913477852878066050128577369053541152591491514652526106580081 (pp64)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.64 hours.
Scaled time: 1.78 units (timescale=0.675).
Factorization parameters were as follows:
name: 13339_121
n: 1731300056614061539047787291401292101287271622335940759125354484590113946145583400138478407257787884223968161777
m: 1000000000000000000000000
c5: 40
c0: 17
skew: 0.84
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:64053, largePrimes:2177636 encountered
Relations: rels:2321030, finalFF:268528
Max relations in full relation-set: 28
Initial matrix: 113217 x 268528 with sparse part having weight 24912659.
Pruned matrix : 83980 x 84610 with weight 5656348.
Total sieving time: 2.40 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.64 hours.
 --------- CPU info (if available) ----------

(4·10¹³⁵+17)/3 = 1(3)₁₃₄9_<136> = 13 · 179 · 4441 · 449193700977237001_<18> · C111

C111 = P55 · P56

P55 = 4380977512855558196767027709308224937234411105284163883_<55>

P56 = 65562710303983445700242735959728821688792651648307630519_<56>

Number: 13339_135
N=287228759523614873835871623098592515574414650930219728909431025522262906433847741731199852827139960161808345277
  ( 111 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=4380977512855558196767027709308224937234411105284163883 (pp55)
 r2=65562710303983445700242735959728821688792651648307630519 (pp56)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.81 hours.
Scaled time: 11.63 units (timescale=2.001).
Factorization parameters were as follows:
name: 13339_135
n: 287228759523614873835871623098592515574414650930219728909431025522262906433847741731199852827139960161808345277
m: 1000000000000000000000000000
c5: 4
c0: 17
skew: 1.34
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:64243, largePrimes:1496217 encountered
Relations: rels:1480212, finalFF:161368
Max relations in full relation-set: 28
Initial matrix: 142805 x 161368 with sparse part having weight 12113242.
Pruned matrix : 136801 x 137579 with weight 8839142.
Total sieving time: 5.58 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.81 hours.
 --------- CPU info (if available) ----------

(4·10¹²⁶+17)/3 = 1(3)₁₂₅9_<127> = 7 · 1451 · 484973620564064677_<18> · C105

C105 = P45 · P61

P45 = 236131606868916230324368736021180849580845243_<45>

P61 = 1146307265998928188707147607605206865081607528799744013788257_<61>

Number: 13339_126
N=270679376685841095843311932998986459968041182656991480680590979940930784945538563824171799516828487711451
  ( 105 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=236131606868916230324368736021180849580845243 (pp45)
 r2=1146307265998928188707147607605206865081607528799744013788257 (pp61)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 3.58 hours.
Scaled time: 2.42 units (timescale=0.675).
Factorization parameters were as follows:
name: 13339_126
n: 270679376685841095843311932998986459968041182656991480680590979940930784945538563824171799516828487711451
m: 10000000000000000000000000
c5: 40
c0: 17
skew: 0.84
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 700001)
Primes: RFBsize:49098, AFBsize:64053, largePrimes:2202658 encountered
Relations: rels:2318750, finalFF:227942
Max relations in full relation-set: 28
Initial matrix: 113217 x 227942 with sparse part having weight 22222821.
Pruned matrix : 92940 x 93570 with weight 6724861.
Total sieving time: 3.29 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.58 hours.
 --------- CPU info (if available) ----------

(4·10¹³⁶+17)/3 = 1(3)₁₃₅9_<137> = 499 · 7487 · C130

C130 = P30 · P100

P30 = 956208466723298533771784872423_<30>

P100 = 3732310555325491082117959675188859828864096907351170143183605318022765214999058108875422540141456161_<100>

Number: 13339_136
N=3568866953442970710576578115047601101316653162966331576826240522539223855305999559780261292809562850379089508878404152590832348103
  ( 130 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=956208466723298533771784872423 (pp30)
 r2=3732310555325491082117959675188859828864096907351170143183605318022765214999058108875422540141456161 (pp100)
Version: GGNFS-0.77.1-20060513-k8
Total time: 7.93 hours.
Scaled time: 15.76 units (timescale=1.988).
Factorization parameters were as follows:
name: 13339_136
n: 3568866953442970710576578115047601101316653162966331576826240522539223855305999559780261292809562850379089508878404152590832348103
m: 1000000000000000000000000000
c5: 40
c0: 17
skew: 0.84
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1375001)
Primes: RFBsize:78498, AFBsize:64053, largePrimes:1600737 encountered
Relations: rels:1625919, finalFF:194313
Max relations in full relation-set: 28
Initial matrix: 142617 x 194313 with sparse part having weight 17340077.
Pruned matrix : 127910 x 128687 with weight 9762916.
Total sieving time: 7.66 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 7.93 hours.
 --------- CPU info (if available) ----------

Feb 26, 2008

By Jo Yeong Uk / Msieve, GGNFS, GMP-ECM

(4·10¹²⁹+17)/3 = 1(3)₁₂₈9_<130> = 13 · 13254286387148048113_<20> · 660386597469019359051247846799_<30> · C80

C80 = P33 · P47

P33 = 365060056289000062010732444238977_<33>

P47 = 32097888713326155328978718452411150896824316697_<47>

Mon Feb 25 23:07:08 2008  
Mon Feb 25 23:07:08 2008  
Mon Feb 25 23:07:08 2008  Msieve v. 1.32
Mon Feb 25 23:07:08 2008  random seeds: ed514adf 848fe788
Mon Feb 25 23:07:08 2008  factoring 11717657060444906039226517298146590277694612229277754702118211578659202199298969 (80 digits)
Mon Feb 25 23:07:09 2008  no P-1/P+1/ECM available, skipping
Mon Feb 25 23:07:09 2008  commencing quadratic sieve (79-digit input)
Mon Feb 25 23:07:09 2008  using multiplier of 1
Mon Feb 25 23:07:09 2008  using 32kb Intel Core sieve core
Mon Feb 25 23:07:09 2008  sieve interval: 12 blocks of size 32768
Mon Feb 25 23:07:09 2008  processing polynomials in batches of 17
Mon Feb 25 23:07:09 2008  using a sieve bound of 1182691 (45941 primes)
Mon Feb 25 23:07:09 2008  using large prime bound of 118269100 (26 bits)
Mon Feb 25 23:07:09 2008  using trial factoring cutoff of 27 bits
Mon Feb 25 23:07:09 2008  polynomial 'A' values have 10 factors
Mon Feb 25 23:17:56 2008  46269 relations (23525 full + 22744 combined from 251467 partial), need 46037
Mon Feb 25 23:17:56 2008  begin with 274992 relations
Mon Feb 25 23:17:56 2008  reduce to 66226 relations in 2 passes
Mon Feb 25 23:17:56 2008  attempting to read 66226 relations
Mon Feb 25 23:17:57 2008  recovered 66226 relations
Mon Feb 25 23:17:57 2008  recovered 55745 polynomials
Mon Feb 25 23:17:57 2008  attempting to build 46269 cycles
Mon Feb 25 23:17:57 2008  found 46269 cycles in 1 passes
Mon Feb 25 23:17:57 2008  distribution of cycle lengths:
Mon Feb 25 23:17:57 2008     length 1 : 23525
Mon Feb 25 23:17:57 2008     length 2 : 22744
Mon Feb 25 23:17:57 2008  largest cycle: 2 relations
Mon Feb 25 23:17:57 2008  matrix is 45941 x 46269 with weight 1371427 (avg 29.64/col)
Mon Feb 25 23:17:57 2008  filtering completed in 4 passes
Mon Feb 25 23:17:57 2008  matrix is 39547 x 39611 with weight 1149437 (avg 29.02/col)
Mon Feb 25 23:17:57 2008  saving the first 48 matrix rows for later
Mon Feb 25 23:17:57 2008  matrix is 39499 x 39611 with weight 837611 (avg 21.15/col)
Mon Feb 25 23:17:57 2008  matrix includes 64 packed rows
Mon Feb 25 23:17:57 2008  commencing Lanczos iteration
Mon Feb 25 23:18:17 2008  lanczos halted after 626 iterations (dim = 39493)
Mon Feb 25 23:18:17 2008  recovered 14 nontrivial dependencies
Mon Feb 25 23:18:17 2008  prp33 factor: 365060056289000062010732444238977
Mon Feb 25 23:18:17 2008  prp47 factor: 32097888713326155328978718452411150896824316697
Mon Feb 25 23:18:17 2008  elapsed time 00:11:09

(4·10¹²⁴+17)/3 = 1(3)₁₂₃9_<125> = 92152271 · 413087444597_<12> · 23123862157206241782847_<23> · C83

C83 = P41 · P42

P41 = 33682194968730310840375233374150796019583_<41>

P42 = 449707304395848847455968925235148050890497_<42>

Tue Feb 26 00:09:56 2008  
Tue Feb 26 00:09:56 2008  
Tue Feb 26 00:09:56 2008  Msieve v. 1.32
Tue Feb 26 00:09:56 2008  random seeds: 65ed768f 19de7d2d
Tue Feb 26 00:09:56 2008  factoring 15147129105523130449266249388626985891346493244029314228392643742208865666200602751 (83 digits)
Tue Feb 26 00:09:57 2008  no P-1/P+1/ECM available, skipping
Tue Feb 26 00:09:57 2008  commencing quadratic sieve (82-digit input)
Tue Feb 26 00:09:57 2008  using multiplier of 31
Tue Feb 26 00:09:57 2008  using 32kb Intel Core sieve core
Tue Feb 26 00:09:57 2008  sieve interval: 12 blocks of size 32768
Tue Feb 26 00:09:57 2008  processing polynomials in batches of 17
Tue Feb 26 00:09:57 2008  using a sieve bound of 1350541 (52059 primes)
Tue Feb 26 00:09:57 2008  using large prime bound of 124249772 (26 bits)
Tue Feb 26 00:09:57 2008  using trial factoring cutoff of 27 bits
Tue Feb 26 00:09:57 2008  polynomial 'A' values have 11 factors
Tue Feb 26 00:26:53 2008  52429 relations (27593 full + 24836 combined from 269723 partial), need 52155
Tue Feb 26 00:26:54 2008  begin with 297316 relations
Tue Feb 26 00:26:54 2008  reduce to 74133 relations in 2 passes
Tue Feb 26 00:26:54 2008  attempting to read 74133 relations
Tue Feb 26 00:26:54 2008  recovered 74133 relations
Tue Feb 26 00:26:54 2008  recovered 65067 polynomials
Tue Feb 26 00:26:54 2008  attempting to build 52429 cycles
Tue Feb 26 00:26:54 2008  found 52429 cycles in 1 passes
Tue Feb 26 00:26:54 2008  distribution of cycle lengths:
Tue Feb 26 00:26:54 2008     length 1 : 27593
Tue Feb 26 00:26:54 2008     length 2 : 24836
Tue Feb 26 00:26:54 2008  largest cycle: 2 relations
Tue Feb 26 00:26:54 2008  matrix is 52059 x 52429 with weight 1691215 (avg 32.26/col)
Tue Feb 26 00:26:54 2008  filtering completed in 4 passes
Tue Feb 26 00:26:54 2008  matrix is 44234 x 44298 with weight 1396136 (avg 31.52/col)
Tue Feb 26 00:26:55 2008  saving the first 48 matrix rows for later
Tue Feb 26 00:26:55 2008  matrix is 44186 x 44298 with weight 1030375 (avg 23.26/col)
Tue Feb 26 00:26:55 2008  matrix includes 64 packed rows
Tue Feb 26 00:26:55 2008  commencing Lanczos iteration
Tue Feb 26 00:27:21 2008  lanczos halted after 700 iterations (dim = 44175)
Tue Feb 26 00:27:21 2008  recovered 13 nontrivial dependencies
Tue Feb 26 00:27:21 2008  prp41 factor: 33682194968730310840375233374150796019583
Tue Feb 26 00:27:21 2008  prp42 factor: 449707304395848847455968925235148050890497
Tue Feb 26 00:27:21 2008  elapsed time 00:17:25

(4·10¹¹⁷+17)/3 = 1(3)₁₁₆9_<118> = 13 · 5237 · 7919 · C109

C109 = P33 · P37 · P40

P33 = 723106245094697489786689511373211_<33>

P37 = 1124531409652827761547009490788252799_<37>

P40 = 3041366547432398229574496599264058102209_<40>

Number: 13339_117
N=2473104498593961880619564636823302910234312758577257036607839368934660595840602892623273796477189635668904101
  ( 109 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=723106245094697489786689511373211 (pp33)
 r2=1124531409652827761547009490788252799 (pp37)
 r3=3041366547432398229574496599264058102209 (pp40)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.96 hours.
Scaled time: 1.78 units (timescale=1.856).
Factorization parameters were as follows:
n: 2473104498593961880619564636823302910234312758577257036607839368934660595840602892623273796477189635668904101
m: 200000000000000000000000
c5: 25
c0: 34
skew: 1.06
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 450001)
Primes: RFBsize:49098, AFBsize:48661, largePrimes:1872252 encountered
Relations: rels:1911209, finalFF:182604
Max relations in full relation-set: 28
Initial matrix: 97823 x 182604 with sparse part having weight 15576316.
Pruned matrix : 79563 x 80116 with weight 4540075.
Total sieving time: 0.91 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.96 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2435k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.91 BogoMIPS (lpj=2406455)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405110)
Calibrating delay using timer specific routine.. 4810.31 BogoMIPS (lpj=2405155)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)

(4·10¹²⁰+17)/3 = 1(3)₁₁₉9_<121> = 7 · 1163 · 3631 · 1113317 · C107

C107 = P42 · P66

P42 = 217864194199759946513098280992116925864009_<42>

P66 = 185964493728313965614110121580783555616158402525331494591164931853_<66>

Number: 13339_120
N=40515004575885434417965215165127114851969961825105124857145999259505190381310511895041336508050733630378677
  ( 107 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=217864194199759946513098280992116925864009 (pp42)
 r2=185964493728313965614110121580783555616158402525331494591164931853 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.80 hours.
Scaled time: 1.48 units (timescale=1.858).
Factorization parameters were as follows:
n: 40515004575885434417965215165127114851969961825105124857145999259505190381310511895041336508050733630378677
m: 1000000000000000000000000
c5: 4
c0: 17
skew: 1.34
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 450001)
Primes: RFBsize:49098, AFBsize:49461, largePrimes:1837125 encountered
Relations: rels:1852045, finalFF:164665
Max relations in full relation-set: 28
Initial matrix: 98623 x 164665 with sparse part having weight 13791456.
Pruned matrix : 83260 x 83817 with weight 4715712.
Total sieving time: 0.74 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.80 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2435k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.91 BogoMIPS (lpj=2406459)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405113)
Calibrating delay using timer specific routine.. 4809.97 BogoMIPS (lpj=2404989)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)

(4·10¹⁹⁷+17)/3 = 1(3)₁₉₆9_<198> = C198

C198 = P44 · C154

P44 = 30911517865801875999507572028613382077670753_<44>

C154 = [4313386806567757392671601783903255857588579313081814644131577195810056098206845332856572255132864229461765584994838840653666401244846784162380204100450363_<154>]

Feb 25, 2008 (2nd)

By Jo Yeong Uk / GGNFS

(4·10¹⁴⁶+11)/3 = 1(3)₁₄₅7_<147> = 137 · 15868498319799913439_<20> · C125

C125 = P34 · P34 · P58

P34 = 3373815312296460190139766384592183_<34>

P34 = 6790688513659658695196059113391453_<34>

P58 = 2676992930436323638563724011958164341185215909432586996541_<58>

Number: 13337_146
N=61331323866859234793535149039669162933374982327254070525498118062757055024749503269364810023134339956117348152633622026641359
  ( 125 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=3373815312296460190139766384592183 (pp34)
 r2=6790688513659658695196059113391453 (pp34)
 r3=2676992930436323638563724011958164341185215909432586996541 (pp58)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 9.35 hours.
Scaled time: 17.36 units (timescale=1.857).
Factorization parameters were as follows:
n: 61331323866859234793535149039669162933374982327254070525498118062757055024749503269364810023134339956117348152633622026641359
m: 200000000000000000000000000000
c5: 5
c0: 44
skew: 1.54
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1500001)
Primes: RFBsize:135072, AFBsize:135714, largePrimes:3758274 encountered
Relations: rels:3890188, finalFF:425896
Max relations in full relation-set: 28
Initial matrix: 270852 x 425896 with sparse part having weight 38438323.
Pruned matrix : 214967 x 216385 with weight 17402299.
Total sieving time: 9.07 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 9.35 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2435k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.91 BogoMIPS (lpj=2406455)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405110)
Calibrating delay using timer specific routine.. 4810.31 BogoMIPS (lpj=2405155)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)

Feb 25, 2008

The factor table of 133...339 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Feb 24, 2008 (2nd)

By Hugo Platzer / Msieve

(4·10¹⁴⁵+11)/3 = 1(3)₁₄₄7_<146> = 17 · 31 · 2003011 · 4749509160841_<13> · 149747426454337_<15> · C110

C110 = P42 · P69

P42 = 102626434436458488227945394792517443917521_<42>

P69 = 173052329411585166509799947374407788780786872404668069218460927279653_<69>

Sat Feb 23 16:13:24 2008  
Sat Feb 23 16:13:24 2008  
Sat Feb 23 16:13:24 2008  Msieve v. 1.33
Sat Feb 23 16:13:24 2008  random seeds: 175687d3 05d4ec8b
Sat Feb 23 16:13:24 2008  factoring 17759743538434462005501867658007215151785228754151261903789786747070005048229801123394965288753029945833500213 (110 digits)
Sat Feb 23 16:13:26 2008  no P-1/P+1/ECM available, skipping
Sat Feb 23 16:13:26 2008  commencing number field sieve (110-digit input)
Sat Feb 23 16:13:26 2008  R0: -100000000000000000000000000000
Sat Feb 23 16:13:26 2008  R1:  1
Sat Feb 23 16:13:26 2008  A0:  11
Sat Feb 23 16:13:26 2008  A1:  0
Sat Feb 23 16:13:26 2008  A2:  0
Sat Feb 23 16:13:26 2008  A3:  0
Sat Feb 23 16:13:26 2008  A4:  0
Sat Feb 23 16:13:26 2008  A5:  4
Sat Feb 23 16:13:26 2008  size score = 6.148189e-10, Murphy alpha = 0.264305, combined = 5.629699e-10
Sat Feb 23 16:13:31 2008  restarting with 2588237 relations
Sat Feb 23 16:13:33 2008  added 11057 free relations
Sat Feb 23 16:13:33 2008  
Sat Feb 23 16:13:33 2008  commencing relation filtering
Sat Feb 23 16:13:33 2008  commencing duplicate removal, pass 1
Sat Feb 23 16:14:06 2008  found 12443 hash collisions in 2599294 relations
Sat Feb 23 16:14:06 2008  commencing duplicate removal, pass 2
Sat Feb 23 16:14:09 2008  found 0 duplicates and 2599294 unique relations
Sat Feb 23 16:14:09 2008  memory use: 36.5 MB
Sat Feb 23 16:14:10 2008  ignoring smallest 136043 rational and 135518 algebraic ideals
Sat Feb 23 16:14:10 2008  filtering rational ideals above 1813985
Sat Feb 23 16:14:10 2008  filtering algebraic ideals above 1813985
Sat Feb 23 16:14:10 2008  need 461653 more relations than ideals
Sat Feb 23 16:14:10 2008  commencing singleton removal, pass 1
Sat Feb 23 16:14:40 2008  relations with 0 large ideals: 83025
Sat Feb 23 16:14:40 2008  relations with 1 large ideals: 588085
Sat Feb 23 16:14:40 2008  relations with 2 large ideals: 1248703
Sat Feb 23 16:14:40 2008  relations with 3 large ideals: 577206
Sat Feb 23 16:14:40 2008  relations with 4 large ideals: 92848
Sat Feb 23 16:14:40 2008  relations with 5 large ideals: 5058
Sat Feb 23 16:14:40 2008  relations with 6 large ideals: 4369
Sat Feb 23 16:14:40 2008  relations with 7+ large ideals: 0
Sat Feb 23 16:14:40 2008  2599294 relations and about 2552882 large ideals
Sat Feb 23 16:14:40 2008  commencing singleton removal, pass 2
Sat Feb 23 16:15:13 2008  found 1440752 singletons
Sat Feb 23 16:15:13 2008  current dataset: 1158542 relations and about 817492 large ideals
Sat Feb 23 16:15:13 2008  commencing singleton removal, pass 3
Sat Feb 23 16:15:29 2008  found 194821 singletons
Sat Feb 23 16:15:29 2008  current dataset: 963721 relations and about 611281 large ideals
Sat Feb 23 16:15:29 2008  commencing singleton removal, final pass
Sat Feb 23 16:15:43 2008  memory use: 15.3 MB
Sat Feb 23 16:15:43 2008  commencing in-memory singleton removal
Sat Feb 23 16:15:44 2008  begin with 963721 relations and 623692 unique ideals
Sat Feb 23 16:15:44 2008  reduce to 883576 relations and 542216 ideals in 10 passes
Sat Feb 23 16:15:44 2008  max relations containing the same ideal: 28
Sat Feb 23 16:15:44 2008  dataset has 25.7% excess relations
Sat Feb 23 16:15:46 2008  ignoring smallest 123430 rational and 122825 algebraic ideals
Sat Feb 23 16:15:46 2008  filtering rational ideals above 1632586
Sat Feb 23 16:15:46 2008  filtering algebraic ideals above 1632586
Sat Feb 23 16:15:46 2008  need 307223 more relations than ideals
Sat Feb 23 16:15:46 2008  commencing singleton removal, final pass
Sat Feb 23 16:15:59 2008  memory use: 15.3 MB
Sat Feb 23 16:15:59 2008  commencing in-memory singleton removal
Sat Feb 23 16:15:59 2008  begin with 883577 relations and 567386 unique ideals
Sat Feb 23 16:15:59 2008  reduce to 882237 relations and 566044 ideals in 7 passes
Sat Feb 23 16:15:59 2008  max relations containing the same ideal: 28
Sat Feb 23 16:16:00 2008  dataset has 16.4% excess relations
Sat Feb 23 16:16:01 2008  ignoring smallest 110719 rational and 110299 algebraic ideals
Sat Feb 23 16:16:01 2008  filtering rational ideals above 1451187
Sat Feb 23 16:16:01 2008  filtering algebraic ideals above 1451187
Sat Feb 23 16:16:01 2008  need 293285 more relations than ideals
Sat Feb 23 16:16:01 2008  commencing singleton removal, final pass
Sat Feb 23 16:16:14 2008  memory use: 15.3 MB
Sat Feb 23 16:16:14 2008  commencing in-memory singleton removal
Sat Feb 23 16:16:14 2008  begin with 882238 relations and 591202 unique ideals
Sat Feb 23 16:16:14 2008  reduce to 881380 relations and 590342 ideals in 6 passes
Sat Feb 23 16:16:14 2008  max relations containing the same ideal: 28
Sat Feb 23 16:16:14 2008  dataset has 7.2% excess relations
Sat Feb 23 16:16:15 2008  relations with 0 large ideals: 44235
Sat Feb 23 16:16:15 2008  relations with 1 large ideals: 181651
Sat Feb 23 16:16:15 2008  relations with 2 large ideals: 309586
Sat Feb 23 16:16:15 2008  relations with 3 large ideals: 241636
Sat Feb 23 16:16:15 2008  relations with 4 large ideals: 88087
Sat Feb 23 16:16:15 2008  relations with 5 large ideals: 12113
Sat Feb 23 16:16:15 2008  relations with 6 large ideals: 4072
Sat Feb 23 16:16:15 2008  relations with 7+ large ideals: 0
Sat Feb 23 16:16:15 2008  commencing 2-way merge
Sat Feb 23 16:16:15 2008  reduce to 564943 relation sets and 273905 unique ideals
Sat Feb 23 16:16:15 2008  commencing full merge
Sat Feb 23 16:16:22 2008  memory use: 19.8 MB
Sat Feb 23 16:16:22 2008  found 295769 cycles, need 232105
Sat Feb 23 16:16:22 2008  weight of 232105 cycles is about 12331805 (53.13/cycle)
Sat Feb 23 16:16:22 2008  distribution of cycle lengths:
Sat Feb 23 16:16:22 2008  1 relations: 45548
Sat Feb 23 16:16:22 2008  2 relations: 28579
Sat Feb 23 16:16:22 2008  3 relations: 26155
Sat Feb 23 16:16:22 2008  4 relations: 23813
Sat Feb 23 16:16:22 2008  5 relations: 22040
Sat Feb 23 16:16:22 2008  6 relations: 19736
Sat Feb 23 16:16:22 2008  7 relations: 17520
Sat Feb 23 16:16:22 2008  8 relations: 15457
Sat Feb 23 16:16:22 2008  9 relations: 13409
Sat Feb 23 16:16:22 2008  10+ relations: 19848
Sat Feb 23 16:16:22 2008  heaviest cycle: 13 relations
Sat Feb 23 16:16:22 2008  matrix not dense enough, retrying
Sat Feb 23 16:16:22 2008  dataset has 7.2% excess relations
Sat Feb 23 16:16:24 2008  ignoring smallest 97887 rational and 97616 algebraic ideals
Sat Feb 23 16:16:24 2008  filtering rational ideals above 1269789
Sat Feb 23 16:16:24 2008  filtering algebraic ideals above 1269789
Sat Feb 23 16:16:24 2008  need 293285 more relations than ideals
Sat Feb 23 16:16:24 2008  commencing singleton removal, final pass
Sat Feb 23 16:16:37 2008  memory use: 15.3 MB
Sat Feb 23 16:16:37 2008  commencing in-memory singleton removal
Sat Feb 23 16:16:37 2008  begin with 881381 relations and 615815 unique ideals
Sat Feb 23 16:16:37 2008  reduce to 880876 relations and 615308 ideals in 7 passes
Sat Feb 23 16:16:37 2008  max relations containing the same ideal: 31
Sat Feb 23 16:16:37 2008  dataset has -2.2% excess relations
Sat Feb 23 16:16:38 2008  relations with 0 large ideals: 29853
Sat Feb 23 16:16:38 2008  relations with 1 large ideals: 135797
Sat Feb 23 16:16:38 2008  relations with 2 large ideals: 280412
Sat Feb 23 16:16:38 2008  relations with 3 large ideals: 275356
Sat Feb 23 16:16:38 2008  relations with 4 large ideals: 130074
Sat Feb 23 16:16:38 2008  relations with 5 large ideals: 24264
Sat Feb 23 16:16:38 2008  relations with 6 large ideals: 5118
Sat Feb 23 16:16:38 2008  relations with 7+ large ideals: 2
Sat Feb 23 16:16:38 2008  commencing 2-way merge
Sat Feb 23 16:16:38 2008  reduce to 563895 relation sets and 298327 unique ideals
Sat Feb 23 16:16:38 2008  commencing full merge
Sat Feb 23 16:16:47 2008  memory use: 20.7 MB
Sat Feb 23 16:16:47 2008  found 277379 cycles, need 216527
Sat Feb 23 16:16:47 2008  weight of 216527 cycles is about 13335440 (61.59/cycle)
Sat Feb 23 16:16:47 2008  distribution of cycle lengths:
Sat Feb 23 16:16:47 2008  1 relations: 32177
Sat Feb 23 16:16:47 2008  2 relations: 22556
Sat Feb 23 16:16:47 2008  3 relations: 22387
Sat Feb 23 16:16:47 2008  4 relations: 21245
Sat Feb 23 16:16:47 2008  5 relations: 20362
Sat Feb 23 16:16:47 2008  6 relations: 18654
Sat Feb 23 16:16:47 2008  7 relations: 17219
Sat Feb 23 16:16:47 2008  8 relations: 15456
Sat Feb 23 16:16:47 2008  9 relations: 13974
Sat Feb 23 16:16:47 2008  10+ relations: 32497
Sat Feb 23 16:16:47 2008  heaviest cycle: 15 relations
Sat Feb 23 16:16:47 2008  commencing cycle optimization
Sat Feb 23 16:16:48 2008  start with 1172495 relations
Sat Feb 23 16:16:51 2008  pruned 41529 relations
Sat Feb 23 16:16:51 2008  memory use: 29.2 MB
Sat Feb 23 16:16:51 2008  distribution of cycle lengths:
Sat Feb 23 16:16:51 2008  1 relations: 32177
Sat Feb 23 16:16:51 2008  2 relations: 23166
Sat Feb 23 16:16:51 2008  3 relations: 23482
Sat Feb 23 16:16:51 2008  4 relations: 22187
Sat Feb 23 16:16:51 2008  5 relations: 21489
Sat Feb 23 16:16:51 2008  6 relations: 19596
Sat Feb 23 16:16:51 2008  7 relations: 17994
Sat Feb 23 16:16:51 2008  8 relations: 16017
Sat Feb 23 16:16:51 2008  9 relations: 13859
Sat Feb 23 16:16:51 2008  10+ relations: 26560
Sat Feb 23 16:16:51 2008  heaviest cycle: 15 relations
Sat Feb 23 16:16:51 2008  
Sat Feb 23 16:16:51 2008  commencing linear algebra
Sat Feb 23 16:16:52 2008  read 216527 cycles
Sat Feb 23 16:16:52 2008  cycles contain 583896 unique relations
Sat Feb 23 16:17:00 2008  read 583896 relations
Sat Feb 23 16:17:01 2008  using 32 quadratic characters above 67093592
Sat Feb 23 16:17:16 2008  building initial matrix
Sat Feb 23 16:17:28 2008  memory use: 71.2 MB
Sat Feb 23 16:17:29 2008  read 216527 cycles
Sat Feb 23 16:17:30 2008  matrix is 216207 x 216527 (53.4 MB) with weight 18522721 (85.54/col)
Sat Feb 23 16:17:30 2008  sparse part has weight 12477653 (57.63/col)
Sat Feb 23 16:17:34 2008  filtering completed in 3 passes
Sat Feb 23 16:17:34 2008  matrix is 214854 x 215054 (53.1 MB) with weight 18423986 (85.67/col)
Sat Feb 23 16:17:34 2008  sparse part has weight 12419321 (57.75/col)
Sat Feb 23 16:17:37 2008  read 215054 cycles
Sat Feb 23 16:17:38 2008  matrix is 214854 x 215054 (53.1 MB) with weight 18423986 (85.67/col)
Sat Feb 23 16:17:38 2008  sparse part has weight 12419321 (57.75/col)
Sat Feb 23 16:17:38 2008  saving the first 48 matrix rows for later
Sat Feb 23 16:17:38 2008  matrix is 214806 x 215054 (50.4 MB) with weight 13723478 (63.81/col)
Sat Feb 23 16:17:38 2008  sparse part has weight 11933368 (55.49/col)
Sat Feb 23 16:17:38 2008  matrix includes 64 packed rows
Sat Feb 23 16:17:38 2008  using block size 65536 for processor cache size 2048 kB
Sat Feb 23 16:17:40 2008  commencing Lanczos iteration
Sat Feb 23 16:17:40 2008  memory use: 50.1 MB
Sat Feb 23 16:29:15 2008  lanczos halted after 3399 iterations (dim = 214804)
Sat Feb 23 16:29:16 2008  recovered 50 nontrivial dependencies
Sat Feb 23 16:29:16 2008  
Sat Feb 23 16:29:16 2008  commencing square root phase
Sat Feb 23 16:29:16 2008  reading relations for dependency 1
Sat Feb 23 16:29:16 2008  read 107635 cycles
Sat Feb 23 16:29:17 2008  cycles contain 354348 unique relations
Sat Feb 23 16:29:22 2008  read 354348 relations
Sat Feb 23 16:29:25 2008  multiplying 564220 relations
Sat Feb 23 16:30:31 2008  multiply complete, coefficients have about 12.42 million bits
Sat Feb 23 16:30:32 2008  initial square root is modulo 13694671
Sat Feb 23 16:32:21 2008  reading relations for dependency 2
Sat Feb 23 16:32:21 2008  read 107185 cycles
Sat Feb 23 16:32:21 2008  cycles contain 353436 unique relations
Sat Feb 23 16:32:26 2008  read 353436 relations
Sat Feb 23 16:32:29 2008  multiplying 562622 relations
Sat Feb 23 16:33:36 2008  multiply complete, coefficients have about 12.39 million bits
Sat Feb 23 16:33:36 2008  initial square root is modulo 13126801
Sat Feb 23 16:35:25 2008  prp42 factor: 102626434436458488227945394792517443917521
Sat Feb 23 16:35:25 2008  prp69 factor: 173052329411585166509799947374407788780786872404668069218460927279653
Sat Feb 23 16:35:25 2008  elapsed time 00:22:01

Feb 24, 2008

By matsui / GGNFS

8·10¹⁷⁶+9 = 8(0)₁₇₅9_<177> = 17 · 3217 · C173

C173 = P81 · P93

P81 = 103961611179868503438377681867481435196874462689578948106251372965474787726477889_<81>

P93 = 140707421063833161706485449146184930821888979205845979668829757316153913675077037413502917929_<93>

N=14628170198760262575655067746713233008466053502532501965660370458410283603649728464590685512625939402804951635612280348881859240432262429373365759110607251915376035400171881
  ( 173 digits)

SNFS difficulty: 177 digits.
Divisors found:
 r1=103961611179868503438377681867481435196874462689578948106251372965474787726477889 (pp81)
 r2=140707421063833161706485449146184930821888979205845979668829757316153913675077037413502917929 (pp93)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 228.46 hours.
Scaled time: 435.44 units (timescale=1.906).
Factorization parameters were as follows:
n: 14628170198760262575655067746713233008466053502532501965660370458410283603649728464590685512625939402804951635612280348881859240432262429373365759110607251915376035400171881
m: 200000000000000000000000000000000000
c5: 5
c0: 18
skew: 1.29
type: snfs

Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 12000001)
Primes: RFBsize:501962, AFBsize:501791, largePrimes:6541923 encountered
Relations: rels:7040504, finalFF:1165775
Max relations in full relation-set: 28
Initial matrix: 1003819 x 1165775 with sparse part having weight 75529051.
Pruned matrix : 866295 x 871378 with weight 56505835.
Total sieving time: 204.60 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 23.41 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,177,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 228.46 hours.

Feb 22, 2008

By Sinkiti Sibata / GGNFS

(7·10¹⁶²-1)/3 = 2(3)₁₆₂_<163> = 1376191 · 1156149411505234849191678643368749_<34> · C124

C124 = P59 · P65

P59 = 18483157127083474363681317601965029524109620367701902163793_<59>

P65 = 79342878811142759961839897023661739977240662042432474165513682759_<65>

Number: 23333_162
N=1466506895981493687124535379820325804475916309373929762311497311107375702506795513963671876299233601761427778500890258144887
  ( 124 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=18483157127083474363681317601965029524109620367701902163793 (pp59)
 r2=79342878811142759961839897023661739977240662042432474165513682759 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 85.52 hours.
Scaled time: 57.30 units (timescale=0.670).
Factorization parameters were as follows:
name: 23333_162
n: 1466506895981493687124535379820325804475916309373929762311497311107375702506795513963671876299233601761427778500890258144887
m: 100000000000000000000000000000000
c5: 700
c0: -1
skew: 0.27
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4250001)
Primes: RFBsize:315948, AFBsize:315791, largePrimes:5746913 encountered
Relations: rels:5875322, finalFF:758492
Max relations in full relation-set: 28
Initial matrix: 631806 x 758492 with sparse part having weight 45680761.
Pruned matrix : 528671 x 531894 with weight 30022387.
Total sieving time: 73.60 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 11.37 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 85.52 hours.
 --------- CPU info (if available) ----------

Feb 21, 2008

By Sinkiti Sibata / GGNFS

(4·10¹⁴⁴+11)/3 = 1(3)₁₄₃7_<145> = 33501037 · 19162171112298569164633600877_<29> · C109

C109 = P54 · P55

P54 = 447889331573911295153276557347209198287124299467688541_<54>

P55 = 4637298522548643845125317323631350351129872341828192293_<55>

Number: 13337_144
N=2076996535572998507838714029821161997717606507974074306074404130017920430096263222528986801630708133180614513
  ( 109 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=447889331573911295153276557347209198287124299467688541 (pp54)
 r2=4637298522548643845125317323631350351129872341828192293 (pp55)
Version: GGNFS-0.77.1-20060513-k8
Total time: 15.65 hours.
Scaled time: 31.27 units (timescale=1.998).
Factorization parameters were as follows:
name: 13337_144
n: 2076996535572998507838714029821161997717606507974074306074404130017920430096263222528986801630708133180614513
m: 100000000000000000000000000000
c5: 2
c0: 55
skew: 1.94
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2350001)
Primes: RFBsize:100021, AFBsize:99789, largePrimes:2823314 encountered
Relations: rels:2832613, finalFF:264170
Max relations in full relation-set: 28
Initial matrix: 199875 x 264170 with sparse part having weight 28900389.
Pruned matrix : 182618 x 183681 with weight 18326210.
Total sieving time: 15.05 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 15.65 hours.
 --------- CPU info (if available) ----------

Feb 20, 2008 (3rd)

By Jo Yeong Uk / GMP-ECM, GGNFS

(4·10¹⁵⁸+11)/3 = 1(3)₁₅₇7_<159> = 8233 · C155

C155 = P31 · C125

P31 = 1527862686242403797544393553027_<31>

C125 = [10599766456206583622902219875082963980035743593315729410558814794508496584089071087989307287849025249575541272349851000517307_<125>]

(4·10¹⁵⁷+11)/3 = 1(3)₁₅₆7_<158> = C158

C158 = P73 · P85

P73 = 4766737278377335686560797181373572835442956918758084311522740015959165729_<73>

P85 = 2797161361045722925353515065028853432915519784372454180355700451963746101938543639353_<85>

Number: 13337_157
N=13333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337
  ( 158 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=4766737278377335686560797181373572835442956918758084311522740015959165729 (pp73)
 r2=2797161361045722925353515065028853432915519784372454180355700451963746101938543639353 (pp85)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 21.35 hours.
Scaled time: 39.60 units (timescale=1.855).
Factorization parameters were as follows:
n: 13333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337
m: 20000000000000000000000000000000
c5: 25
c0: 22
skew: 0.97
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2800001)
Primes: RFBsize:216816, AFBsize:216262, largePrimes:5564985 encountered
Relations: rels:5470103, finalFF:504877
Max relations in full relation-set: 28
Initial matrix: 433141 x 504877 with sparse part having weight 39439439.
Pruned matrix : 394545 x 396774 with weight 27271708.
Total sieving time: 20.39 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.83 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 21.35 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2435k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.91 BogoMIPS (lpj=2406455)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405110)
Calibrating delay using timer specific routine.. 4810.31 BogoMIPS (lpj=2405155)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)

Feb 20, 2008 (2nd)

By Robert Backstrom / GGNFS, GMP-ECM

(4·10¹⁴⁹+11)/3 = 1(3)₁₄₈7_<150> = 21313 · 758361679 · 1214454453872951_<16> · C121

C121 = P37 · P85

P37 = 2717076605390979007381323216479100539_<37>

P85 = 2499969194587184389860981086852270761643057631388490569409971104066011589674512322579_<85>

Number: n
N=6792607812810966812696054335486176763506067853623183131083234129992086750249270424315302728986609775323759382373740770081
  ( 121 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=2717076605390979007381323216479100539 (pp37)
 r2=2499969194587184389860981086852270761643057631388490569409971104066011589674512322579 (pp85)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 10.10 hours.
Scaled time: 18.48 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_3_148_7
n: 6792607812810966812696054335486176763506067853623183131083234129992086750249270424315302728986609775323759382373740770081
skew: 1.94
deg: 5
c5: 2
c0: 55
m: 1000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 660001)
Primes: RFBsize:183072, AFBsize:182867, largePrimes:6264948 encountered
Relations: rels:5745258, finalFF:448309
Max relations in full relation-set: 48
Initial matrix: 366004 x 448309 with sparse part having weight 28960939.
Pruned matrix : 296128 x 298022 with weight 15039151.
Total sieving time: 9.34 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.60 hours.
Total square root time: 0.04 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 10.10 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(4·10¹³⁸+11)/3 = 1(3)₁₃₇7_<139> = 137 · 229 · C134

C134 = P64 · P70

P64 = 4867627495557587497174692021304110944538390547912798179387518159_<64>

P70 = 8731027407103137131104076747312662661769083489277298849485078143666291_<70>

Number: n
N=42499389071282100319807902761397804906554468279518481921822373803376576461713362870408737874393055599825752504807743388688787598678269
  ( 134 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=4867627495557587497174692021304110944538390547912798179387518159 (pp64)
 r2=8731027407103137131104076747312662661769083489277298849485078143666291 (pp70)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.89 hours.
Scaled time: 7.11 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_3_137_7
n: 42499389071282100319807902761397804906554468279518481921822373803376576461713362870408737874393055599825752504807743388688787598678269
skew: 3.08
deg: 5
c5: 1
c0: 275
m: 10000000000000000000000000000
type: snfs
rlim: 2200000
alim: 2200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 580001)
Primes: RFBsize:162662, AFBsize:163221, largePrimes:5751332 encountered
Relations: rels:5168007, finalFF:374032
Max relations in full relation-set: 48
Initial matrix: 325947 x 374032 with sparse part having weight 20090079.
Pruned matrix : 280278 x 281971 with weight 11315150.
Total sieving time: 3.20 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.44 hours.
Total square root time: 0.14 hours, sqrts: 5.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,2200000,2200000,28,28,48,48,2.5,2.5,75000
total time: 3.89 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(8·10¹⁸⁶-17)/9 = (8)₁₈₅7_<186> = 122041 · C181

C181 = P30 · C152

P30 = 600760122234227247339021404369_<30>

C152 = [12123851911813520689442426339677939520762900296076844725658595042305449072115945719786865839939239072337205062999312826980398145833769450425203032477503_<152>]

Feb 20, 2008

By Sinkiti Sibata / GGNFS

(4·10¹³¹+11)/3 = 1(3)₁₃₀7_<132> = 356287746791328491_<18> · C114

C114 = P52 · P63

P52 = 1893443194224894718878463833501834090719818444796249_<52>

P63 = 197644880595999725041267819674714849507845501682832456060475843_<63>

Number: 13337_131
N=374229354037887632864664831865915772225602984855244535305283336279006481767188196074768411542491621513546121512907
  ( 114 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=1893443194224894718878463833501834090719818444796249 (pp52)
 r2=197644880595999725041267819674714849507845501682832456060475843 (pp63)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.49 hours.
Scaled time: 8.92 units (timescale=1.988).
Factorization parameters were as follows:
name: 13337_131
n: 374229354037887632864664831865915772225602984855244535305283336279006481767188196074768411542491621513546121512907
m: 100000000000000000000000000
c5: 40
c0: 11
skew: 0.77
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64254, largePrimes:1531023 encountered
Relations: rels:1559054, finalFF:197232
Max relations in full relation-set: 28
Initial matrix: 128271 x 197232 with sparse part having weight 14484832.
Pruned matrix : 109223 x 109928 with weight 6425650.
Total sieving time: 4.33 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.49 hours.
 --------- CPU info (if available) ----------

(4·10¹²⁷+11)/3 = 1(3)₁₂₆7_<128> = 29 · 131 · 18199825817_<11> · C114

C114 = P36 · P39 · P39

P36 = 227060322506798993332149127795092037_<36>

P39 = 913336927466122993434262778590061373449_<39>

P39 = 929886502764280214041355493551431541603_<39>

Number: 13337_127
N=192842259547018009597079694636074182400710045315079783185799547260078047160967977004619128485484268956703784377639
  ( 114 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=227060322506798993332149127795092037 (pp36)
 r2=913336927466122993434262778590061373449 (pp39)
 r3=929886502764280214041355493551431541603 (pp39)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.12 hours.
Scaled time: 6.21 units (timescale=1.992).
Factorization parameters were as follows:
name: 13337_127
n: 192842259547018009597079694636074182400710045315079783185799547260078047160967977004619128485484268956703784377639
m: 20000000000000000000000000
c5: 25
c0: 22
skew: 0.97
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:63951, AFBsize:63939, largePrimes:1400313 encountered
Relations: rels:1394145, finalFF:169686
Max relations in full relation-set: 28
Initial matrix: 127954 x 169686 with sparse part having weight 8194603.
Pruned matrix : 110799 x 111502 with weight 4097518.
Total sieving time: 3.00 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 3.12 hours.
 --------- CPU info (if available) ----------

(4·10¹⁵¹+11)/3 = 1(3)₁₅₀7_<152> = 633619426343_<12> · 442973859605351119_<18> · 3975218224563891047_<19> · C104

C104 = P46 · P58

P46 = 2337821818609044897355108471584512338289378161_<46>

P58 = 5111634251655468130247648332197620987017296367122312286583_<58>

Number: 13337_151
N=11950090082269470772012979307480787589555936665450276418632716974465848898807642129099590952613093513863
  ( 104 digits)
Divisors found:
 r1=2337821818609044897355108471584512338289378161 (pp46)
 r2=5111634251655468130247648332197620987017296367122312286583 (pp58)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 14.67 hours.
Scaled time: 9.91 units (timescale=0.675).
Factorization parameters were as follows:
name: 13337_151
n: 11950090082269470772012979307480787589555936665450276418632716974465848898807642129099590952613093513863
skew: 6800.61
# norm 1.74e+14
c5: 29640
c4: -1232540113
c3: 2169770658470
c2: -20196984656031629
c1: -134467529912451149353
c0: 32693537318913341764250
# alpha -5.44
Y1: 26651928809
Y0: -52613891591132659327
# Murphy_E 2.20e-09
# M 1484081719694419706365100096805128173093244655510772422378879253150230070968344633840020539840777333680
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1950001)
Primes: RFBsize:169511, AFBsize:170092, largePrimes:4530487 encountered
Relations: rels:4761478, finalFF:578150
Max relations in full relation-set: 28
Initial matrix: 339686 x 578150 with sparse part having weight 44365745.
Pruned matrix : 189798 x 191560 with weight 21055717.
Polynomial selection time: 0.79 hours.
Total sieving time: 12.20 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 1.27 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 14.67 hours.
 --------- CPU info (if available) ----------

(4·10¹⁴³+11)/3 = 1(3)₁₄₂7_<144> = 19 · 394478557247107_<15> · C128

C128 = P45 · P83

P45 = 540221890483900213100183282378870340497411947_<45>

P83 = 32929835114364724990528981056819343712336652054415144940805074403713200462062903587_<83>

Number: 13337_143
N=17789417778805232112908786998844581501787575892209776794081262433217844819211255327899323908514311530976008988829918089682953889
  ( 128 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=540221890483900213100183282378870340497411947 (pp45)
 r2=32929835114364724990528981056819343712336652054415144940805074403713200462062903587 (pp83)
Version: GGNFS-0.77.1-20060513-k8
Total time: 13.31 hours.
Scaled time: 26.61 units (timescale=1.999).
Factorization parameters were as follows:
name: 13337_143
n: 17789417778805232112908786998844581501787575892209776794081262433217844819211255327899323908514311530976008988829918089682953889
m: 20000000000000000000000000000
c5: 125
c0: 11
skew: 0.62
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2150001)
Primes: RFBsize:100021, AFBsize:100439, largePrimes:2797871 encountered
Relations: rels:2800510, finalFF:269837
Max relations in full relation-set: 28
Initial matrix: 200525 x 269837 with sparse part having weight 27631150.
Pruned matrix : 181432 x 182498 with weight 16800760.
Total sieving time: 12.78 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.35 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 13.31 hours.
 --------- CPU info (if available) ----------

Feb 19, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(4·10¹²⁵+11)/3 = 1(3)₁₂₄7_<126> = 19 · 2225471936246839129_<19> · C106

C106 = P38 · P69

P38 = 15803345655438486511972481152450794613_<38>

P69 = 199532651776252834039911251067175851500401630254970536186458226795599_<69>

Number: 13337_125
N=3153283465566365633508056367141023771988625666319413811577363839922534166099217033045727316239036281308187
  ( 106 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=15803345655438486511972481152450794613 (pp38)
 r2=199532651776252834039911251067175851500401630254970536186458226795599 (pp69)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1.95 hours.
Scaled time: 3.86 units (timescale=1.981).
Factorization parameters were as follows:
name: 13337_125
n: 3153283465566365633508056367141023771988625666319413811577363839922534166099217033045727316239036281308187
m: 10000000000000000000000000
c5: 4
c0: 11
skew: 1.22
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63629, largePrimes:2080670 encountered
Relations: rels:2108833, finalFF:178021
Max relations in full relation-set: 28
Initial matrix: 112791 x 178021 with sparse part having weight 15251272.
Pruned matrix : 95760 x 96387 with weight 5778001.
Total sieving time: 1.82 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.95 hours.
 --------- CPU info (if available) ----------

(4·10¹¹³+11)/3 = 1(3)₁₁₂7_<114> = 17 · 397 · C110

C110 = P39 · P71

P39 = 304155774352865478339206504203892550259_<39>

P71 = 64953602405091887197954344906663271278940558317913767517079385452861407_<71>

Number: 13337_113
N=19756013236528868474341877809058132068948486195485750975453153553612880920630216822245270904331505902108954413
  ( 110 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=304155774352865478339206504203892550259 (pp39)
 r2=64953602405091887197954344906663271278940558317913767517079385452861407 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.86 hours.
Scaled time: 1.26 units (timescale=0.675).
Factorization parameters were as follows:
name: 13337_113
n: 19756013236528868474341877809058132068948486195485750975453153553612880920630216822245270904331505902108954413
m: 20000000000000000000000
c5: 125
c0: 11
skew: 0.62
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:64204, largePrimes:2116619 encountered
Relations: rels:2254082, finalFF:285131
Max relations in full relation-set: 28
Initial matrix: 113367 x 285131 with sparse part having weight 22834055.
Pruned matrix : 74586 x 75216 with weight 4095384.
Total sieving time: 1.68 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.86 hours.
 --------- CPU info (if available) ----------

Feb 19, 2008 (2nd)

By Jo Yeong Uk / GGNFS

(4·10¹³⁶+11)/3 = 1(3)₁₃₅7_<137> = C137 = P48 · P89

P48 = 645109945959932436794670252937099004445884900281_<48>

P89 = 20668311528654469407072421372850207222818010052176468364973643563797095494823416253615777_<89>

Number: 13337_136
N=13333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337
  ( 137 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=645109945959932436794670252937099004445884900281 (pp48)
 r2=20668311528654469407072421372850207222818010052176468364973643563797095494823416253615777 (pp89)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.28 hours.
Scaled time: 6.10 units (timescale=1.857).
Factorization parameters were as follows:
n: 13333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337
m: 2000000000000000000000000000
c5: 5
c0: 44
skew: 1.54
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1250001)
Primes: RFBsize:107126, AFBsize:107659, largePrimes:2240727 encountered
Relations: rels:2306072, finalFF:241669
Max relations in full relation-set: 28
Initial matrix: 214851 x 241669 with sparse part having weight 17262603.
Pruned matrix : 203670 x 204808 with weight 12258523.
Total sieving time: 3.06 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 3.28 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406452)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405111)
Calibrating delay using timer specific routine.. 4809.73 BogoMIPS (lpj=2404867)
Calibrating delay using timer specific routine.. 4714.04 BogoMIPS (lpj=2357021)

(4·10¹⁹²-13)/9 = (4)₁₉₁3_<192> = C192

C192 = P89 · P104

P89 = 35045847515642783523626070569435470884822385339002400825581256172358614490951464260070747_<89>

P104 = 12681800440011210614082687744739066189716084468441089520538508971989616998911936443662265342146313320769_<104>

Number: 44443_192
N=444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443
  ( 192 digits)
SNFS difficulty: 192 digits.
Divisors found:
 r1=35045847515642783523626070569435470884822385339002400825581256172358614490951464260070747 (pp89)
 r2=12681800440011210614082687744739066189716084468441089520538508971989616998911936443662265342146313320769 (pp104)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 677.17 hours.
Scaled time: 1257.51 units (timescale=1.857).
Factorization parameters were as follows:
n: 444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443
m: 200000000000000000000000000000000000000
c5: 25
c0: -26
skew: 1.01
type: snfs
Factor base limits: 16000000/16000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 51/51
Sieved algebraic special-q in [8000000, 18400001)
Primes: RFBsize:1031130, AFBsize:1032793, largePrimes:12950076 encountered
Relations: rels:14092984, finalFF:2343105
Max relations in full relation-set: 28
Initial matrix: 2063987 x 2343105 with sparse part having weight 150351956.
Pruned matrix : 1810027 x 1820410 with weight 111950679.
Total sieving time: 646.41 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 30.15 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,192,5,0,0,0,0,0,0,0,0,16000000,16000000,28,28,51,51,2.6,2.6,100000
total time: 677.17 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406452)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405111)
Calibrating delay using timer specific routine.. 4809.73 BogoMIPS (lpj=2404867)
Calibrating delay using timer specific routine.. 4714.04 BogoMIPS (lpj=2357021)

Feb 19, 2008

By Robert Backstrom / GMP-ECM, GGNFS

(4·10¹⁰²+11)/3 = 1(3)₁₀₁7_<103> = 307266829 · C94

C94 = P43 · P52

P43 = 1646560534466985058328605054610083645298993_<43>

P52 = 2635392807135816561786044834867478808294813224484621_<52>

Number: n
N=4339333789047998192259579485338241093812743885000789764173773971980988983790805916551875286653
  ( 94 digits)
SNFS difficulty: 102 digits.
Divisors found:
 r1=1646560534466985058328605054610083645298993 (pp43)
 r2=2635392807135816561786044834867478808294813224484621 (pp52)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.43 hours.
Scaled time: 0.79 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_3_101_7
n: 4339333789047998192259579485338241093812743885000789764173773971980988983790805916551875286653
skew: 1.00
deg: 5
c5: 25
c0: 22
m: 200000000000000000000
type: snfs
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 140001)
Primes: RFBsize:41538, AFBsize:41568, largePrimes:3448580 encountered
Relations: rels:2920109, finalFF:148659
Max relations in full relation-set: 48
Initial matrix: 83170 x 148659 with sparse part having weight 9271658.
Pruned matrix : 58314 x 58793 with weight 1969435.
Total sieving time: 0.38 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.01 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,102,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.5,2.5,20000
total time: 0.43 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(4·10¹¹⁵+11)/3 = 1(3)₁₁₄7_<116> = 31 · 275416674221551_<15> · C100

C100 = P46 · P54

P46 = 1805025368704280366962983811597818948051327631_<46>

P54 = 865174086391486453505012758489951524756223702524904967_<54>

Number: n
N=1561661174282181750855560882405506568818194843939868509965372037918767188901167683328566806456243177
  ( 100 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=1805025368704280366962983811597818948051327631 (pp46)
 r2=865174086391486453505012758489951524756223702524904967 (pp54)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.77 hours.
Scaled time: 1.42 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_3_114_7
n: 1561661174282181750855560882405506568818194843939868509965372037918767188901167683328566806456243177
skew: 1.00
deg: 5
c5: 4
c0: 11
m: 100000000000000000000000
type: snfs
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 160001)
Primes: RFBsize:63951, AFBsize:63629, largePrimes:4202404 encountered
Relations: rels:3652012, finalFF:223982
Max relations in full relation-set: 48
Initial matrix: 127644 x 223982 with sparse part having weight 12430380.
Pruned matrix : 80889 x 81591 with weight 2898267.
Total sieving time: 0.70 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.02 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000
total time: 0.77 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(4·10¹²²+11)/3 = 1(3)₁₂₁7_<123> = 137 · 311 · 75767110971407101_<17> · C101

C101 = P34 · P67

P34 = 5272921641050465131362660361244101_<34>

P67 = 7832956869217103170630125848353003163038606291478854203546482793191_<67>

(4·10¹³⁹+11)/3 = 1(3)₁₃₈7_<140> = 4311337 · 21247651 · 149032782893_<12> · 175317660870361_<15> · C100

C100 = P36 · P65

P36 = 337617990811478180020888640562676309_<36>

P65 = 16499955819490232143991256389127069993152179641301496930299925443_<65>

(4·10¹¹⁶+11)/3 = 1(3)₁₁₅7_<117> = 120383704907_<12> · C106

C106 = P35 · P71

P35 = 28802954401798198620925160019003859_<35>

P71 = 38453333520441584543202578333588710413505012991763189928723152862992649_<71>

(4·10¹²⁹+11)/3 = 1(3)₁₂₈7_<130> = 7 · 17 · C128

C128 = P31 · P97

P31 = 1623689600151579293848901161081_<31>

P97 = 6900630386294950804431484242986375136955298070601334173121463514139852321236962540139980145351783_<97>

(4·10¹²⁴+11)/3 = 1(3)₁₂₃7_<125> = 157 · 257 · 863 · 3114563 · 734742979 · C102

C102 = P40 · P62

P40 = 2203938796192403342392271268196078673989_<40>

P62 = 75921201152552818087132501075621030841933093815300464956718367_<62>

Number: n
N=167325680673638563081548947403636743907474465909076656035498500293151015645904444990307855678281455963
  ( 102 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=2203938796192403342392271268196078673989 (pp40)
 r2=75921201152552818087132501075621030841933093815300464956718367 (pp62)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.44 hours.
Scaled time: 2.63 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_3_123_7
n: 167325680673638563081548947403636743907474465909076656035498500293151015645904444990307855678281455963
skew: 1.94
deg: 5
c5: 2
c0: 55
m: 10000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 240001)
Primes: RFBsize:114155, AFBsize:113953, largePrimes:4515312 encountered
Relations: rels:3995223, finalFF:291897
Max relations in full relation-set: 48
Initial matrix: 228173 x 291897 with sparse part having weight 12613705.
Pruned matrix : 166879 x 168083 with weight 5210343.
Total sieving time: 1.28 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.08 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,50000
total time: 1.44 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(4·10¹³⁰+11)/3 = 1(3)₁₂₉7_<131> = 23 · 31 · 137 · C126

C126 = P33 · P93

P33 = 586747933411274964170925848158487_<33>

P93 = 232636079856833912272452423645428068658508651978665240250136011794304923321522084851723290271_<93>

(4·10¹³⁴+11)/3 = 1(3)₁₃₃7_<135> = 50604613 · C127

C127 = P40 · P87

P40 = 3820162630866551606713037132751079542817_<40>

P87 = 689710403238257935905626272855854844006021482308071303691508206972486304337202234301797_<87>

Number: n
N=2634805908570693611140417837664983888590025050351305588155240577244081153892696172448415588779096746245907133670468605961542149
  ( 127 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=3820162630866551606713037132751079542817 (pp40)
 r2=689710403238257935905626272855854844006021482308071303691508206972486304337202234301797 (pp87)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.69 hours.
Scaled time: 4.92 units (timescale=1.828).
Factorization parameters were as follows:
name: KA_1_3_133_7
n: 2634805908570693611140417837664983888590025050351305588155240577244081153892696172448415588779096746245907133670468605961542149
skew: 1.94
deg: 5
c5: 2
c0: 55
m: 1000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 420001)
Primes: RFBsize:148933, AFBsize:148701, largePrimes:5227610 encountered
Relations: rels:4670599, finalFF:342239
Max relations in full relation-set: 48
Initial matrix: 297699 x 342239 with sparse part having weight 16564263.
Pruned matrix : 253523 x 255075 with weight 9103303.
Total sieving time: 2.32 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.25 hours.
Total square root time: 0.05 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,75000
total time: 2.69 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Feb 18, 2008 (3rd)

By Robert Backstrom / GMP-ECM

(4·10¹⁵⁶+11)/3 = 1(3)₁₅₅7_<157> = 71 · 2161 · 14831 · 658453 · 394839461087_<12> · 126692824237732751_<18> · 1333267352305266238694551_<25> · C89

C89 = P31 · P58

P31 = 3843061199517217692568521094769_<31>

P58 = 3471868696924966252462632988741475891496853178404981998763_<58>

Feb 18, 2008 (2nd)

The factor table of 133...337 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Feb 18, 2008

By Robert Backstrom / GMP-ECM

(79·10¹⁸³-7)/9 = 8(7)₁₈₃_<184> = 1913 · C181

C181 = P32 · P37 · P114

P32 = 12153807173571949007375230348211_<32>

P37 = 2375716400628936749079408376044022391_<37>

P114 = 158914188404109477281052206971033581029810208002769801689981446299251940791541808338262878938295863778304036304629_<114>

Feb 17, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(11·10¹⁴⁹+61)/9 = 1(2)₁₄₈9_<150> = 3² · 43 · C147

C147 = P31 · P55 · P61

P31 = 6242261523111451604167188855731_<31>

P55 = 5345904564855449996407866180568566463290283484418398029_<55>

P61 = 9464028719153806681139681352642106781803923220341415398103633_<61>

Number: 12229_149
N=315819695664656904966982486362331323571633649153028997990238300315819695664656904966982486362331323571633649153028997990238300315819695664656904967
  ( 147 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=6242261523111451604167188855731 (pp31)
 r2=5345904564855449996407866180568566463290283484418398029 (pp55)
 r3=9464028719153806681139681352642106781803923220341415398103633 (pp61)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 37.15 hours.
Scaled time: 25.08 units (timescale=0.675).
Factorization parameters were as follows:
name: 12229_149
n: 315819695664656904966982486362331323571633649153028997990238300315819695664656904966982486362331323571633649153028997990238300315819695664656904967
m: 1000000000000000000000000000000
c5: 11
c0: 610
skew: 2.23
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2200001)
Primes: RFBsize:176302, AFBsize:175370, largePrimes:5628786 encountered
Relations: rels:5580248, finalFF:504483
Max relations in full relation-set: 28
Initial matrix: 351737 x 504483 with sparse part having weight 45930839.
Pruned matrix : 290346 x 292168 with weight 24671675.
Total sieving time: 33.54 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 3.22 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 37.15 hours.
 --------- CPU info (if available) ----------

Feb 17, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(71·10¹⁸⁴-17)/9 = 7(8)₁₈₃7_<185> = 584027 · 67972403356899191_<17> · 12252647954833593078177200604809_<32> · C132

C132 = P31 · P37 · P65

P31 = 2689572403442632769337374190077_<31>

P37 = 1925866741774738582164323933510316983_<37>

P65 = 31312003673636456198021235073960417940459037776283793591711449889_<65>

Number: n
N=60302746493384886847709617108784565070134687576182721026645805344525114269394313542409814350910164887
  ( 101 digits)
Divisors found:

Sun Feb 17 10:05:35 2008  prp37 factor: 1925866741774738582164323933510316983
Sun Feb 17 10:05:35 2008  prp65 factor: 31312003673636456198021235073960417940459037776283793591711449889
Sun Feb 17 10:05:35 2008  elapsed time 00:11:39 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-k8
Total time: 5.51 hours.
Scaled time: 4.60 units (timescale=0.835).
Factorization parameters were as follows:
name: KA_7_8_183
n: 60302746493384886847709617108784565070134687576182721026645805344525114269394313542409814350910164887
skew: 1591.76
# norm 2.54e+13
c5: 490680
c4: -2420530822
c3: 1607362527322
c2: 7712572522997431
c1: -1015553300418810242
c0: -2676058812104523333649
# alpha -5.19
Y1: 13671193657
Y0: -10420973927095743510
# Murphy_E 3.29e-09
# M 13575008737661884978698488583945020638176130417697145616183711579278417102206895065551839353226346846
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 800001)
Primes: RFBsize:135072, AFBsize:136018, largePrimes:3464132 encountered
Relations: rels:3423937, finalFF:377196
Max relations in full relation-set: 28
Initial matrix: 271178 x 377196 with sparse part having weight 20957178.
Pruned matrix : 173729 x 175148 with weight 7500817.
Polynomial selection time: 0.55 hours.
Total sieving time: 4.69 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 5.51 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(46·10¹⁶³-1)/9 = 5(1)₁₆₃_<164> = 3 · 199 · 1481 · 33637 · 65609 · 348944548907_<12> · 3094508928368237_<16> · C122

C122 = P50 · P72

P50 = 42383839285525795753607722140791837846064285912043_<50>

P72 = 572343567840351351004052047916227199387688191587467882881579520189050963_<72>

Number: n
N=24258117795449882016463515363358612414330257454310490695425839412626146864798222116552055288007645093745929170939062447409
  ( 122 digits)
SNFS difficulty: 164 digits.
Divisors found:

Sun Feb 17 11:29:09 2008  prp50 factor: 42383839285525795753607722140791837846064285912043
Sun Feb 17 11:29:09 2008  prp72 factor: 572343567840351351004052047916227199387688191587467882881579520189050963
Sun Feb 17 11:29:09 2008  elapsed time 01:33:30 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 64.27 hours.
Scaled time: 93.38 units (timescale=1.453).
Factorization parameters were as follows:
name: KA_5_1_163
n: 24258117795449882016463515363358612414330257454310490695425839412626146864798222116552055288007645093745929170939062447409
skew: 0.23
deg: 5
c5: 2875
c0: -2
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3200001)
Primes: RFBsize:216816, AFBsize:217086, largePrimes:7722673 encountered
Relations: rels:7223944, finalFF:486300
Max relations in full relation-set: 28
Initial matrix: 433968 x 486300 with sparse part having weight 47481030.
Pruned matrix : 
Total sieving time: 64.00 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 64.27 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Feb 16, 2008 (2nd)

By matsui / GGNFS

3·10¹⁷⁹-1 = 2(9)₁₇₉_<180> = 7 · 83 · 269 · 8731 · 81853 · 116981 · 341557 · 12603850771_<11> · 40741126949_<11> · 135924365039_<12> · C123

C123 = P59 · P65

P59 = 65229101266939367735801851025243606155752420471073669310383_<59>

P65 = 14765247618055126790247356701740302955486828755600519733418471207_<65>

N=963123832109553152595040489985247676605852097732313677970697180432654991239607824625799134317843703968468200269973831642281
  ( 123 digits)
Divisors found:
 r1=65229101266939367735801851025243606155752420471073669310383 (pp59)
 r2=14765247618055126790247356701740302955486828755600519733418471207 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 105.78 hours.
Scaled time: 136.98 units (timescale=1.295).
Factorization parameters were as follows:
name: 3000
n: 963123832109553152595040489985247676605852097732313677970697180432654991239607824625799134317843703968468200269973831642281
skew: 96096.19
# norm 9.91e+16
c5: 66240
c4: -32279355888
c3: -2129454685216800
c2: 294388916535552239654
c1: 12148253690490472323530277
c0: 57066639980311126901329358611
# alpha -6.31
Y1: 16016640817309
Y0: -429055962076730058362034
# Murphy_E 1.89e-10
# M 61974167399733499335733838603131508133502921043676458000972502662641628379410764569675900458759902446519498408010415736179
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 5920001)
Primes: RFBsize:348513, AFBsize:348802, largePrimes:7933036 encountered
Relations: rels:8259254, finalFF:863393
Max relations in full relation-set: 28
Initial matrix: 697393 x 863393 with sparse part having weight 88990510.
Pruned matrix : 565520 x 569070 with weight 62336262.
Total sieving time: 91.13 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 13.66 hours.
Time per square root: 0.65 hours.
Prototype def-par.txt 
line would be:
gnfs,122,5,maxs1,maxskew,goodScore,efrac,j0,j1,e
StepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 105.78 hours.

Feb 16, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(2·10¹⁷⁹-17)/3 = (6)₁₇₈1_<179> = 7 · 1303 · 2113 · 29119157 · 5793684977_<10> · 336644628636372600585073_<24> · C131

C131 = P30 · P40 · P63

P30 = 117733382538191803231594866287_<30>

P40 = 2026710201705934049640343657007900267053_<40>

P63 = 255252584468709657651315972742139518142414624901650982711938171_<63>

Number: n
N=517323016954539519104299878861340926635621421290927921190677439277366154322066511600055544722124380063
  ( 102 digits)
Divisors found:

Sat Feb 16 09:01:49 2008  prp40 factor: 2026710201705934049640343657007900267053
Sat Feb 16 09:01:49 2008  prp63 factor: 255252584468709657651315972742139518142414624901650982711938171
Sat Feb 16 09:01:49 2008  elapsed time 00:44:05 (Msieve 1.33)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 6.88 hours.
Scaled time: 8.90 units (timescale=1.293).
Factorization parameters were as follows:
name: KA_6_178_1
n: 517323016954539519104299878861340926635621421290927921190677439277366154322066511600055544722124380063
skew: 15433.97
# norm 1.78e+14
c5: 11340
c4: -210213358
c3: 822174645868
c2: 75764522101157211
c1: 818325393752775442490
c0: -2819299342594052083394120
# alpha -6.47
Y1: 26670758489
Y0: -34027575905630961057
# Murphy_E 2.65e-09
# M 40674032749483108661264023893591174142795240211848184405971828080856584641743182758663277192319315897
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved  special-q in [100000, 800000)
Primes: RFBsize:169511, AFBsize:169673, largePrimes:3882109 encountered
Relations: rels:3787702, finalFF:401409
Max relations in full relation-set: 28
Initial matrix: 339268 x 401409 with sparse part having weight 19928409.
Pruned matrix : 268583 x 270343 with weight 9451561.
Total sieving time: 6.19 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.52 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 6.88 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(2·10¹⁷⁶+43)/9 = (2)₁₇₅7_<176> = 3 · 48971055909467_<14> · 228716882727738050432210325227_<30> C132

C132 = P36 · P97

P36 = 404075342846215616011831753904136079_<36>

P97 = 1636689099026739176899658261871273953653786966383885960693665967442392548030342512207866446134919_<97>

(4·10¹⁸⁶+23)/9 = (4)₁₈₅7_<186> = 3² · 31 · 47 · 179 · 12743 · 18541 · 1519769856019001_<16> · 2375090177092212015679433_<25> · C132

C132 = P30 · P103

P30 = 118270750950320247085810333307_<30>

P103 = 1877250672708337815991348552500624443658145975176294067599617799874145110659688921540769920338722450837_<103>

Feb 15, 2008 (4th)

By Sinkiti Sibata / GGNFS

(11·10¹⁵⁸+61)/9 = 1(2)₁₅₇9_<159> = 3² · 29 · 2417 · 850637 · 20357861 · 34953302776819747_<17> · C123

C123 = P35 · P37 · P52

P35 = 11920843112330238846091327134150343_<35>

P37 = 5533180785858157565411447744926232573_<37>

P52 = 4852734739010638529320321809660405214270996767425057_<52>

Number: 12229_158
N=320087257170379743745512038306524681451620506378742376663804041998523402739301653903245691152522955108248039967344338259723
  ( 123 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=11920843112330238846091327134150343 (pp35)
 r2=5533180785858157565411447744926232573 (pp37)
 r3=4852734739010638529320321809660405214270996767425057 (pp52)
Version: GGNFS-0.77.1-20060513-k8
Total time: 65.85 hours.
Scaled time: 131.77 units (timescale=2.001).
Factorization parameters were as follows:
name: 12229_158
n: 320087257170379743745512038306524681451620506378742376663804041998523402739301653903245691152522955108248039967344338259723
m: 10000000000000000000000000000000
c5: 11000
c0: 61
skew: 0.35
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4100001)
Primes: RFBsize:283146, AFBsize:284229, largePrimes:5875710 encountered
Relations: rels:6004080, finalFF:729809
Max relations in full relation-set: 28
Initial matrix: 567442 x 729809 with sparse part having weight 53653069.
Pruned matrix : 449842 x 452743 with weight 37603921.
Total sieving time: 62.66 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 2.73 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 65.85 hours.
 --------- CPU info (if available) ----------

(11·10¹⁴⁸+61)/9 = 1(2)₁₄₇9_<149> = 7² · 1633007 · 73216302241_<11> · 2824656770917_<13> · C117

C117 = P53 · P65

P53 = 11902378768854297574550472754083771786485974613585009_<53>

P65 = 62052432086827128788540349410927173560773558990532128882788082911_<65>

Number: 12229_148
N=738571550226024392405858563209788417084723191785980144725541056915264197135700547827962950228341820185276112038681199
  ( 117 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=11902378768854297574550472754083771786485974613585009 (pp53)
 r2=62052432086827128788540349410927173560773558990532128882788082911 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 49.88 hours.
Scaled time: 33.72 units (timescale=0.676).
Factorization parameters were as follows:
name: 12229_148
n: 738571550226024392405858563209788417084723191785980144725541056915264197135700547827962950228341820185276112038681199
m: 100000000000000000000000000000
c5: 11000
c0: 61
skew: 0.35
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 5750001)
Primes: RFBsize:114155, AFBsize:114409, largePrimes:3268022 encountered
Relations: rels:3436305, finalFF:267502
Max relations in full relation-set: 28
Initial matrix: 228631 x 267502 with sparse part having weight 36416837.
Pruned matrix : 219053 x 220260 with weight 28994291.
Total sieving time: 47.18 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 2.20 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 49.88 hours.
 --------- CPU info (if available) ----------

Feb 15, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(65·10¹⁶²+43)/9 = 7(2)₁₆₁7_<163> = 3 · 677 · 10193 · 1573237 · 10037269604188014489625787_<26> · C125

C125 = P54 · P72

P54 = 137954707191964580423759095965459263169617010356229781_<54>

P72 = 160144723690182851686046435792735566441355086416901397233226149694716271_<72>

Number: n
N=22092718465017248771037776619885496253769731032787367896536812757589874812967027353750731118374142593784616914591704075466651
  ( 125 digits)
SNFS difficulty: 163 digits.
Divisors found:

Fri Feb 15 11:54:20 2008  prp54 factor: 137954707191964580423759095965459263169617010356229781
Fri Feb 15 11:54:20 2008  prp72 factor: 160144723690182851686046435792735566441355086416901397233226149694716271
Fri Feb 15 11:54:20 2008  elapsed time 00:55:13 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 35.21 hours.
Scaled time: 64.41 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_7_2_161_7
n: 22092718465017248771037776619885496253769731032787367896536812757589874812967027353750731118374142593784616914591704075466651
skew: 0.37
deg: 5
c5: 6500
c0: 43
m: 100000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2300001)
Primes: RFBsize:230209, AFBsize:230052, largePrimes:7364839 encountered
Relations: rels:6841139, finalFF:523751
Max relations in full relation-set: 28
Initial matrix: 460328 x 523751 with sparse part having weight 47945873.
Pruned matrix : 
Total sieving time: 35.04 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 35.21 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Feb 15, 2008 (2nd)

By Jo Yeong Uk / GGNFS

(11·10¹⁶⁹+43)/9 = 1(2)₁₆₈7_<170> = C170

C170 = P48 · P122

P48 = 227030126709317368877348740835730359515559877331_<48>

P122 = 53835243803881555060152528124341137855983903787606163934998794151883156545332025716371870291431461909592002513314902039617_<122>

Number: 12227_169
N=12222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227
  ( 170 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=227030126709317368877348740835730359515559877331 (pp48)
 r2=53835243803881555060152528124341137855983903787606163934998794151883156545332025716371870291431461909592002513314902039617 (pp122)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 97.15 hours.
Scaled time: 180.60 units (timescale=1.859).
Factorization parameters were as follows:
n: 12222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227
m: 10000000000000000000000000000000000
c5: 11
c0: 430
skew: 2.08
type: snfs
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 49/49
Sieved algebraic special-q in [4000000, 8500001)
Primes: RFBsize:539777, AFBsize:539881, largePrimes:9820148 encountered
Relations: rels:9752653, finalFF:1218038
Max relations in full relation-set: 28
Initial matrix: 1079723 x 1218038 with sparse part having weight 64331651.
Pruned matrix : 958872 x 964334 with weight 46529221.
Total sieving time: 91.68 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 5.20 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,49,49,2.6,2.6,100000
total time: 97.15 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406452)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405111)
Calibrating delay using timer specific routine.. 4809.73 BogoMIPS (lpj=2404867)
Calibrating delay using timer specific routine.. 4714.04 BogoMIPS (lpj=2357021)

Feb 15, 2008

By Robert Backstrom / GMP-ECM, Msieve

2·10¹⁷⁴+9 = 2(0)₁₇₃9_<175> = 11 · 449 · 773713 · 2243296177_<10> · 74158382575383580813200721_<26> · C130

C130 = P34 · P46 · P50

P34 = 6474833169609810754024951641805051_<34>

P46 = 6504635362555600808299400218239308558804216297_<46>

P50 = 74698635967538385695610601830647283165089131842313_<50>

Thu Feb 14 23:19:07 2008  
Thu Feb 14 23:19:07 2008  
Thu Feb 14 23:19:07 2008  Msieve v. 1.33
Thu Feb 14 23:19:07 2008  random seeds: a04a6710 79a96968
Thu Feb 14 23:19:07 2008  factoring 485887389049117890210490665624086802374006262683353795179735136350962989087028228699823748774961 (96 digits)
Thu Feb 14 23:19:08 2008  no P-1/P+1/ECM available, skipping
Thu Feb 14 23:19:08 2008  commencing quadratic sieve (96-digit input)
Thu Feb 14 23:19:08 2008  using multiplier of 1
Thu Feb 14 23:19:08 2008  using 64kb Opteron sieve core
Thu Feb 14 23:19:08 2008  sieve interval: 18 blocks of size 65536
Thu Feb 14 23:19:08 2008  processing polynomials in batches of 6
Thu Feb 14 23:19:08 2008  using a sieve bound of 2263381 (83529 primes)
Thu Feb 14 23:19:08 2008  using large prime bound of 339507150 (28 bits)
Thu Feb 14 23:19:08 2008  using double large prime bound of 2267399519796450 (43-52 bits)
Thu Feb 14 23:19:08 2008  using trial factoring cutoff of 52 bits
Thu Feb 14 23:19:08 2008  polynomial 'A' values have 12 factors
Fri Feb 15 02:20:26 2008  83856 relations (20273 full + 63583 combined from 1263041 partial), need 83625
Fri Feb 15 02:20:27 2008  begin with 1283314 relations
Fri Feb 15 02:20:28 2008  reduce to 220570 relations in 12 passes
Fri Feb 15 02:20:28 2008  attempting to read 220570 relations
Fri Feb 15 02:20:29 2008  recovered 220570 relations
Fri Feb 15 02:20:29 2008  recovered 205365 polynomials
Fri Feb 15 02:20:30 2008  attempting to build 83856 cycles
Fri Feb 15 02:20:30 2008  found 83856 cycles in 5 passes
Fri Feb 15 02:20:30 2008  distribution of cycle lengths:
Fri Feb 15 02:20:30 2008     length 1 : 20273
Fri Feb 15 02:20:30 2008     length 2 : 14503
Fri Feb 15 02:20:30 2008     length 3 : 13852
Fri Feb 15 02:20:30 2008     length 4 : 11290
Fri Feb 15 02:20:30 2008     length 5 : 8508
Fri Feb 15 02:20:30 2008     length 6 : 6030
Fri Feb 15 02:20:30 2008     length 7 : 3857
Fri Feb 15 02:20:30 2008     length 9+: 5543
Fri Feb 15 02:20:30 2008  largest cycle: 20 relations
Fri Feb 15 02:20:30 2008  matrix is 83529 x 83856 (22.9 MB) with weight 5672561 (67.65/col)
Fri Feb 15 02:20:30 2008  sparse part has weight 5672561 (67.65/col)
Fri Feb 15 02:20:31 2008  filtering completed in 3 passes
Fri Feb 15 02:20:31 2008  matrix is 79794 x 79858 (21.9 MB) with weight 5427260 (67.96/col)
Fri Feb 15 02:20:31 2008  sparse part has weight 5427260 (67.96/col)
Fri Feb 15 02:20:31 2008  saving the first 48 matrix rows for later
Fri Feb 15 02:20:31 2008  matrix is 79746 x 79858 (15.2 MB) with weight 4438378 (55.58/col)
Fri Feb 15 02:20:31 2008  sparse part has weight 3514587 (44.01/col)
Fri Feb 15 02:20:31 2008  matrix includes 64 packed rows
Fri Feb 15 02:20:31 2008  using block size 31943 for processor cache size 1024 kB
Fri Feb 15 02:20:32 2008  commencing Lanczos iteration
Fri Feb 15 02:20:32 2008  memory use: 13.9 MB
Fri Feb 15 02:21:17 2008  lanczos halted after 1263 iterations (dim = 79745)
Fri Feb 15 02:21:17 2008  recovered 16 nontrivial dependencies
Fri Feb 15 02:21:18 2008  prp46 factor: 6504635362555600808299400218239308558804216297
Fri Feb 15 02:21:18 2008  prp50 factor: 74698635967538385695610601830647283165089131842313
Fri Feb 15 02:21:18 2008  elapsed time 03:02:11

Feb 14, 2008 (2nd)

By Robert Backstrom / GMP-ECM, Msieve

(4·10¹⁷³+23)/9 = (4)₁₇₂7_<173> = 13 · 547 · 3457 · 7742677 · 92344480022803_<14> · 17066676439984957_<17> · C129

C129 = P32 · P98

P32 = 11547865405892626687884211439681_<32>

P98 = 12830236827967471491637490179825912863260274126012053520529623406724702467484496830797955662017043_<98>

(71·10¹⁶⁸-17)/9 = 7(8)₁₆₇7_<169> = 3³ · 61 · 692912981 · 1573653452257_<13> · 170069809907779157_<18> · C128

C128 = P32 · P42 · P55

P32 = 81536190423163571092923033457303_<32>

P42 = 115590451395574759743903097570647982150751_<42>

P55 = 2740531773173258744191221418003242079036846153092673753_<55>

Thu Feb 14 11:42:36 2008  
Thu Feb 14 11:42:36 2008  
Thu Feb 14 11:42:36 2008  Msieve v. 1.33
Thu Feb 14 11:42:36 2008  random seeds: ab969178 270d785b
Thu Feb 14 11:42:36 2008  factoring 316779304725011877124301481980306957487837556226816564915372139752044167430993971558690106938503 (96 digits)
Thu Feb 14 11:42:37 2008  searching for 15-digit factors
Thu Feb 14 11:42:38 2008  commencing quadratic sieve (96-digit input)
Thu Feb 14 11:42:38 2008  using multiplier of 5
Thu Feb 14 11:42:38 2008  using 64kb Opteron sieve core
Thu Feb 14 11:42:38 2008  sieve interval: 18 blocks of size 65536
Thu Feb 14 11:42:38 2008  processing polynomials in batches of 6
Thu Feb 14 11:42:38 2008  using a sieve bound of 2265611 (83426 primes)
Thu Feb 14 11:42:38 2008  using large prime bound of 339841650 (28 bits)
Thu Feb 14 11:42:38 2008  using double large prime bound of 2271422065653900 (43-52 bits)
Thu Feb 14 11:42:38 2008  using trial factoring cutoff of 52 bits
Thu Feb 14 11:42:38 2008  polynomial 'A' values have 12 factors
Thu Feb 14 16:54:45 2008  83627 relations (20300 full + 63327 combined from 1266567 partial), need 83522
Thu Feb 14 16:54:46 2008  begin with 1286866 relations
Thu Feb 14 16:54:47 2008  reduce to 219798 relations in 11 passes
Thu Feb 14 16:54:47 2008  attempting to read 219798 relations
Thu Feb 14 16:54:50 2008  recovered 219798 relations
Thu Feb 14 16:54:50 2008  recovered 206527 polynomials
Thu Feb 14 16:54:50 2008  attempting to build 83627 cycles
Thu Feb 14 16:54:50 2008  found 83627 cycles in 5 passes
Thu Feb 14 16:54:51 2008  distribution of cycle lengths:
Thu Feb 14 16:54:51 2008     length 1 : 20300
Thu Feb 14 16:54:51 2008     length 2 : 14221
Thu Feb 14 16:54:51 2008     length 3 : 14186
Thu Feb 14 16:54:51 2008     length 4 : 11367
Thu Feb 14 16:54:51 2008     length 5 : 8506
Thu Feb 14 16:54:51 2008     length 6 : 5896
Thu Feb 14 16:54:51 2008     length 7 : 3790
Thu Feb 14 16:54:51 2008     length 9+: 5361
Thu Feb 14 16:54:51 2008  largest cycle: 19 relations
Thu Feb 14 16:54:51 2008  matrix is 83426 x 83627 (23.6 MB) with weight 5854011 (70.00/col)
Thu Feb 14 16:54:51 2008  sparse part has weight 5854011 (70.00/col)
Thu Feb 14 16:54:53 2008  filtering completed in 3 passes
Thu Feb 14 16:54:53 2008  matrix is 79580 x 79644 (22.7 MB) with weight 5620651 (70.57/col)
Thu Feb 14 16:54:53 2008  sparse part has weight 5620651 (70.57/col)
Thu Feb 14 16:54:54 2008  saving the first 48 matrix rows for later
Thu Feb 14 16:54:54 2008  matrix is 79532 x 79644 (17.0 MB) with weight 4764049 (59.82/col)
Thu Feb 14 16:54:54 2008  sparse part has weight 3989892 (50.10/col)
Thu Feb 14 16:54:54 2008  matrix includes 64 packed rows
Thu Feb 14 16:54:54 2008  using block size 21845 for processor cache size 512 kB
Thu Feb 14 16:54:55 2008  commencing Lanczos iteration
Thu Feb 14 16:54:55 2008  memory use: 14.8 MB
Thu Feb 14 16:56:09 2008  lanczos halted after 1258 iterations (dim = 79530)
Thu Feb 14 16:56:09 2008  recovered 17 nontrivial dependencies
Thu Feb 14 16:56:10 2008  prp42 factor: 115590451395574759743903097570647982150751
Thu Feb 14 16:56:10 2008  prp55 factor: 2740531773173258744191221418003242079036846153092673753
Thu Feb 14 16:56:10 2008  elapsed time 05:13:34

Feb 14, 2008

By Sinkiti Sibata / GGNFS

(11·10¹⁵⁷+61)/9 = 1(2)₁₅₆9_<158> = 1499470118834882516029_<22> · C136

C136 = P60 · P77

P60 = 298230907234615127467511105889531439850968018155959379903529_<60>

P77 = 27331263575954269106179281929739251896488872337195589729335803802039679866769_<77>

Number: 12229_157
N=8151027532125232953778580806805926102268082591328572421015894830608242951223091720643534080488498064269911620158916872675205886792927801
  ( 136 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=298230907234615127467511105889531439850968018155959379903529 (pp60)
 r2=27331263575954269106179281929739251896488872337195589729335803802039679866769 (pp77)
Version: GGNFS-0.77.1-20060513-k8
Total time: 59.82 hours.
Scaled time: 119.89 units (timescale=2.004).
Factorization parameters were as follows:
name: 12229_157
n: 8151027532125232953778580806805926102268082591328572421015894830608242951223091720643534080488498064269911620158916872675205886792927801
m: 10000000000000000000000000000000
c5: 1100
c0: 61
skew: 0.56
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3900001)
Primes: RFBsize:283146, AFBsize:282319, largePrimes:5908492 encountered
Relations: rels:6075893, finalFF:766526
Max relations in full relation-set: 28
Initial matrix: 565532 x 766526 with sparse part having weight 52202300.
Pruned matrix : 420115 x 423006 with weight 36980807.
Total sieving time: 56.81 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 2.56 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 59.82 hours.
 --------- CPU info (if available) ----------

Feb 13, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(11·10¹³⁷+61)/9 = 1(2)₁₃₆9_<138> = 3 · C137

C137 = P37 · P46 · P55

P37 = 2608315158960413241863591725014062287_<37>

P46 = 3302992739511359700540576991511204918126169779_<46>

P55 = 4728912045866904847657086157801846080638041217325830291_<55>

Number: 12229_137
N=40740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743
  ( 137 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=2608315158960413241863591725014062287 (pp37)
 r2=3302992739511359700540576991511204918126169779 (pp46)
 r3=4728912045866904847657086157801846080638041217325830291 (pp55)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 16.64 hours.
Scaled time: 11.25 units (timescale=0.676).
Factorization parameters were as follows:
name: 12229_137
n: 40740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743
m: 1000000000000000000000000000
c5: 1100
c0: 61
skew: 0.56
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 2200001)
Primes: RFBsize:78498, AFBsize:63770, largePrimes:1670073 encountered
Relations: rels:1697648, finalFF:166498
Max relations in full relation-set: 28
Initial matrix: 142335 x 166498 with sparse part having weight 18460835.
Pruned matrix : 136551 x 137326 with weight 13956169.
Total sieving time: 15.90 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.54 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 16.64 hours.
 --------- CPU info (if available) ----------

Feb 13, 2008

By Robert Backstrom / GGNFS, GMP-ECM

(11·10¹³¹+61)/9 = 1(2)₁₃₀9_<132> = 3² · 23 · 128341229 · 587699374274461_<15> · C106

C106 = P47 · P60

P47 = 27843156313687337057580167590404968827671407657_<47>

P60 = 281151200709441301666481826274926616585678854755382437224859_<60>

Number: n
N=7828136829133856296228799392803241434599084869328918335227018985215989728730754311284916914786485163345363
  ( 106 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=27843156313687337057580167590404968827671407657 (pp47)
 r2=281151200709441301666481826274926616585678854755382437224859 (pp60)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 5.23 hours.
Scaled time: 9.15 units (timescale=1.749).
Factorization parameters were as follows:
name: KA_1_2_130_9
n: 7828136829133856296228799392803241434599084869328918335227018985215989728730754311284916914786485163345363
type: snfs
skew: 0.89
deg: 5
c5: 110
c0: 61
m: 100000000000000000000000000
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 100000)
Primes: RFBsize:114155, AFBsize:114754, largePrimes:4459635 encountered
Relations: rels:3776537, finalFF:262915
Max relations in full relation-set: 28
Initial matrix: 228976 x 262915 with sparse part having weight 9371341.
Pruned matrix : 190800 x 192008 with weight 5465175.
Total sieving time: 4.71 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.38 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.2,2.2,50000
total time: 5.23 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(11·10¹⁴⁶+61)/9 = 1(2)₁₄₅9_<147> = 3 · C146

C146 = P71 · P75

P71 = 62188614383244022472029465985668051260768030696286619714122612487056057_<71>

P75 = 655115749800623400328076022959829614473983866531716207736106837240179182399_<75>

Number: n
N=40740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743
  ( 146 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=62188614383244022472029465985668051260768030696286619714122612487056057 (pp71)
 r2=655115749800623400328076022959829614473983866531716207736106837240179182399 (pp75)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.95 hours.
Scaled time: 16.36 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_2_145_9
n: 40740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743
skew: 0.89
deg: 5
c5: 110
c0: 61
m: 100000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:183072, AFBsize:183928, largePrimes:6812996 encountered
Relations: rels:6186693, finalFF:411405
Max relations in full relation-set: 48
Initial matrix: 367067 x 411405 with sparse part having weight 33106963.
Pruned matrix : 334890 x 336789 with weight 21893831.
Total sieving time: 7.91 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.80 hours.
Total square root time: 0.09 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 8.95 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(11·10¹⁴⁴+61)/9 = 1(2)₁₄₃9_<145> = C145

C145 = P45 · P100

P45 = 611795764847397761032073514896073448555427693_<45>

P100 = 1997761822570127057468384244424067756878599815628503448366355433606752749308486975935581518284356553_<100>

Number: n
N=1222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229
  ( 145 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=611795764847397761032073514896073448555427693 (pp45)
 r2=1997761822570127057468384244424067756878599815628503448366355433606752749308486975935581518284356553 (pp100)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 12.91 hours.
Scaled time: 16.84 units (timescale=1.305).
Factorization parameters were as follows:
name: KA_1_2_143_9
n: 1222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229
skew: 2.23
deg: 5
c5: 11
c0: 610
m: 100000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1250001)
Primes: RFBsize:203362, AFBsize:202469, largePrimes:6738611 encountered
Relations: rels:6158473, finalFF:455293
Max relations in full relation-set: 28
Initial matrix: 405896 x 455293 with sparse part having weight 25724138.
Pruned matrix : 361436 x 363529 with weight 16686234.
Total sieving time: 10.51 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 1.88 hours.
Total square root time: 0.30 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 12.91 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁶⁹+3 = 7(0)₁₆₈3_<170> = 61 · 73 · 1670391467493499_<16> · 32397946134897073854757_<23> · C129

C129 = P37 · P92

P37 = 5175216009374760485968852867656086119_<37>

P92 = 56128200837449627643617345573916608964872045642509134587009683630669439311948801876882681303_<92>

Feb 12, 2008 (4th)

By Tyler Cadigan / GGNFS, Msieve

(16·10¹⁹⁰-61)/9 = 1(7)₁₈₉1_<191> = 13 · 109 · 8353 · 1219891 · 61566587 · 195452790030217399_<18> · 780043984544746420521955762987_<30> · C123

C123 = P59 · P64

P59 = 34094621548106215029203735244490780734764543703560567350309_<59>

P64 = 3847265829146448766592546059775321362358930468529413258124622339_<64>

Number: 17771_190
N=131171072439709236017541566171110987272288625359372833448549849838030010503222808824551261610337811526472955528084539952751
  ( 123 digits)
Divisors found:
 r1=34094621548106215029203735244490780734764543703560567350309
 r2=3847265829146448766592546059775321362358930468529413258124622339
Version: 
Total time: 66.45 hours.
Scaled time: 171.78 units (timescale=2.585).
Factorization parameters were as follows:
name: 17771_190
n: 131171072439709236017541566171110987272288625359372833448549849838030010503222808824551261610337811526472955528084539952751
skew: 47294.61
# norm 4.29e+016
c5: 61560
c4: -17874778431
c3: -663111392301151
c2: -9801637011659482709
c1: 576431364686994339439656
c0: 1878564961861044229586185155
# alpha -5.56
Y1: 20572302513413
Y0: -292219818845037446106556
# Murphy_E 2.11e-010
# M 45786454644921295568793144589561397825475712419937552306625156200432901874416142023443502841645551053254909538820787308731
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 5440001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 752592 x 752840
Polynomial selection time: 8.04 hours.
Total sieving time: 58.42 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,122,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 66.45 hours.
 --------- CPU info (if available) ----------

Feb 12, 2008 (3rd)

By Jo Yeong Uk / GMP-ECM

(11·10¹⁶⁰+61)/9 = 1(2)₁₅₉9_<161> = 7 · 316317381526758701_<18> · C142

C142 = P34 · P109

P34 = 1483611984731557267694074530155063_<34>

P109 = 3720563711585825353249049668598930117813079072610125563407773914202785970215359546760420442923601907083314569_<109>

Feb 12, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(11·10¹¹³+61)/9 = 1(2)₁₁₂9_<114> = 3³ · 32797 · C108

C108 = P53 · P55

P53 = 89185329511743931743340432259475771218472031894737047_<53>

P55 = 1547600532511926130818633628615142423602309348889997853_<55>

Number: 12229_113
N=138023263444626509676497310867663169533598061952620126978892855175577511292498774416158458736878849829560091
  ( 108 digits)
SNFS difficulty: 114 digits.
Divisors found:
 r1=89185329511743931743340432259475771218472031894737047 (pp53)
 r2=1547600532511926130818633628615142423602309348889997853 (pp55)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.44 hours.
Scaled time: 1.65 units (timescale=0.676).
Factorization parameters were as follows:
name:12229_113
n: 138023263444626509676497310867663169533598061952620126978892855175577511292498774416158458736878849829560091
m: 10000000000000000000000
c5: 11000
c0: 61
skew: 0.35
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63930, largePrimes:2203646 encountered
Relations: rels:2410372, finalFF:336430
Max relations in full relation-set: 28
Initial matrix: 113095 x 336430 with sparse part having weight 29283357.
Pruned matrix : 73057 x 73686 with weight 5021225.
Total sieving time: 2.24 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,114,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.44 hours.
 --------- CPU info (if available) ----------

(11·10¹¹⁵+61)/9 = 1(2)₁₁₄9_<116> = 223 · 617 · C110

C110 = P34 · P77

P34 = 7212822845172862724558959691868961_<34>

P77 = 12315580379654942378938247217218906466558770709724027914022290754605779304179_<77>

Number: 12229_115
N=88830099513937846386916456906499859890706675743487744272679333838857354203561440953421533546687081438627688019
  ( 110 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=7212822845172862724558959691868961 (pp34)
 r2=12315580379654942378938247217218906466558770709724027914022290754605779304179 (pp77)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.61 hours.
Scaled time: 1.09 units (timescale=0.675).
Factorization parameters were as follows:
name: 12229_115
n: 88830099513937846386916456906499859890706675743487744272679333838857354203561440953421533546687081438627688019
m: 100000000000000000000000
c5: 11
c0: 61
skew: 1.41
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:64130, largePrimes:1981292 encountered
Relations: rels:1990054, finalFF:180327
Max relations in full relation-set: 28
Initial matrix: 113295 x 180327 with sparse part having weight 13872256.
Pruned matrix : 90740 x 91370 with weight 4669829.
Total sieving time: 1.41 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.61 hours.
 --------- CPU info (if available) ----------

(11·10¹³⁵+61)/9 = 1(2)₁₃₄9_<136> = 449 · C133

C133 = P41 · P92

P41 = 44733788040439743106075919870152803049769_<41>

P92 = 60851061573677909538404481871209053051577251320251971454994510548611542213319025413140789709_<92>

Number: 12229_135
N=2722098490472655283345706508290027220984904726552833457065082900272209849047265528334570650829002722098490472655283345706508290027221
  ( 133 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=44733788040439743106075919870152803049769 (pp41)
 r2=60851061573677909538404481871209053051577251320251971454994510548611542213319025413140789709 (pp92)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 8.34 hours.
Scaled time: 5.63 units (timescale=0.675).
Factorization parameters were as follows:
name: 12229_135
n: 2722098490472655283345706508290027220984904726552833457065082900272209849047265528334570650829002722098490472655283345706508290027221
m: 1000000000000000000000000000
c5: 11
c0: 61
skew: 1.41
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1225001)
Primes: RFBsize:78498, AFBsize:64130, largePrimes:1529572 encountered
Relations: rels:1534791, finalFF:178563
Max relations in full relation-set: 28
Initial matrix: 142695 x 178563 with sparse part having weight 14130024.
Pruned matrix : 131056 x 131833 with weight 8673274.
Total sieving time: 7.84 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.35 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 8.34 hours.
 --------- CPU info (if available) ----------

Feb 12, 2008

By Robert Backstrom / GMP-ECM, Msieve, GGNFS

(11·10¹¹²+61)/9 = 1(2)₁₁₁9_<113> = 7 · 22171 · 289088113781_<12> · C96

C96 = P41 · P56

P41 = 23364777919548735601339497408589195152559_<41>

P56 = 11659366680299595782072792886752985694167830402696085083_<56>

(11·10¹⁰⁷+61)/9 = 1(2)₁₀₆9_<108> = 3 · 43 · 967491665150369_<15> · C90

C90 = P43 · P48

P43 = 8254078063236444636671476566658758452630059_<43>

P48 = 118643694302743846510055142733530124877331720031_<48>

Tue Feb 12 09:14:45 2008  
Tue Feb 12 09:14:45 2008  
Tue Feb 12 09:14:45 2008  Msieve v. 1.33
Tue Feb 12 09:14:45 2008  random seeds: fbd5dde8 054b1945
Tue Feb 12 09:14:45 2008  factoring 979294314485608729379659265652592455768584086435122697907223765060392284274205698203011829 (90 digits)
Tue Feb 12 09:14:46 2008  searching for 15-digit factors
Tue Feb 12 09:14:46 2008  commencing quadratic sieve (90-digit input)
Tue Feb 12 09:14:46 2008  using multiplier of 5
Tue Feb 12 09:14:46 2008  using 64kb Opteron sieve core
Tue Feb 12 09:14:46 2008  sieve interval: 18 blocks of size 65536
Tue Feb 12 09:14:46 2008  processing polynomials in batches of 6
Tue Feb 12 09:14:46 2008  using a sieve bound of 1616231 (61176 primes)
Tue Feb 12 09:14:46 2008  using large prime bound of 135763404 (27 bits)
Tue Feb 12 09:14:46 2008  using double large prime bound of 435520718464356 (42-49 bits)
Tue Feb 12 09:14:46 2008  using trial factoring cutoff of 49 bits
Tue Feb 12 09:14:46 2008  polynomial 'A' values have 12 factors
Tue Feb 12 10:14:53 2008  61405 relations (16554 full + 44851 combined from 665810 partial), need 61272
Tue Feb 12 10:14:53 2008  begin with 682363 relations
Tue Feb 12 10:14:54 2008  reduce to 149843 relations in 12 passes
Tue Feb 12 10:14:54 2008  attempting to read 149843 relations
Tue Feb 12 10:14:55 2008  recovered 149843 relations
Tue Feb 12 10:14:55 2008  recovered 130637 polynomials
Tue Feb 12 10:14:55 2008  attempting to build 61405 cycles
Tue Feb 12 10:14:55 2008  found 61405 cycles in 6 passes
Tue Feb 12 10:14:56 2008  distribution of cycle lengths:
Tue Feb 12 10:14:56 2008     length 1 : 16554
Tue Feb 12 10:14:56 2008     length 2 : 11742
Tue Feb 12 10:14:56 2008     length 3 : 10834
Tue Feb 12 10:14:56 2008     length 4 : 8104
Tue Feb 12 10:14:56 2008     length 5 : 5795
Tue Feb 12 10:14:56 2008     length 6 : 3613
Tue Feb 12 10:14:56 2008     length 7 : 2201
Tue Feb 12 10:14:56 2008     length 9+: 2562
Tue Feb 12 10:14:56 2008  largest cycle: 21 relations
Tue Feb 12 10:14:56 2008  matrix is 61176 x 61405 (15.1 MB) with weight 3715538 (60.51/col)
Tue Feb 12 10:14:56 2008  sparse part has weight 3715538 (60.51/col)
Tue Feb 12 10:14:56 2008  filtering completed in 3 passes
Tue Feb 12 10:14:56 2008  matrix is 57197 x 57261 (14.2 MB) with weight 3488523 (60.92/col)
Tue Feb 12 10:14:56 2008  sparse part has weight 3488523 (60.92/col)
Tue Feb 12 10:14:57 2008  saving the first 48 matrix rows for later
Tue Feb 12 10:14:57 2008  matrix is 57149 x 57261 (9.3 MB) with weight 2781100 (48.57/col)
Tue Feb 12 10:14:57 2008  sparse part has weight 2101395 (36.70/col)
Tue Feb 12 10:14:57 2008  matrix includes 64 packed rows
Tue Feb 12 10:14:57 2008  using block size 22904 for processor cache size 1024 kB
Tue Feb 12 10:14:57 2008  commencing Lanczos iteration
Tue Feb 12 10:14:57 2008  memory use: 8.9 MB
Tue Feb 12 10:15:16 2008  lanczos halted after 905 iterations (dim = 57147)
Tue Feb 12 10:15:16 2008  recovered 16 nontrivial dependencies
Tue Feb 12 10:15:16 2008  prp43 factor: 8254078063236444636671476566658758452630059
Tue Feb 12 10:15:16 2008  prp48 factor: 118643694302743846510055142733530124877331720031
Tue Feb 12 10:15:16 2008  elapsed time 01:00:31

(11·10¹²³+61)/9 = 1(2)₁₂₂9_<124> = 70607 · 133813186965299890511_<21> · C99

C99 = P47 · P53

P47 = 10137105138517733202360425644260487744453606741_<47>

P53 = 12761142295089496212129634669299067935927677632288097_<53>

Number: n
N=129361041132907711288024614211894650311321702762232554416003033514132326809107206608063968053261877
  ( 99 digits)
SNFS difficulty: 124 digits.
Divisors found:

Tue Feb 12 11:48:55 2008  prp47 factor: 10137105138517733202360425644260487744453606741
Tue Feb 12 11:48:55 2008  prp53 factor: 12761142295089496212129634669299067935927677632288097
Tue Feb 12 11:48:55 2008  elapsed time 00:09:53 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 2.11 hours.
Scaled time: 1.77 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_1_2_122_9
n: 129361041132907711288024614211894650311321702762232554416003033514132326809107206608063968053261877
type: snfs
deg: 5
c5: 11000
c0: 61
skew: 0.24
m: 1000000000000000000000000
rlim: 700000
alim: 700000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved  special-q in [100000, 350001)
Primes: RFBsize:56543, AFBsize:56425, largePrimes:2054212 encountered
Relations: rels:2103983, finalFF:203790
Max relations in full relation-set: 28
Initial matrix: 113035 x 203790 with sparse part having weight 17909229.
Pruned matrix : 
Total sieving time: 2.05 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.5,2.5,50000
total time: 2.11 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

(11·10¹¹⁹+61)/9 = 1(2)₁₁₈9_<120> = 3 · 761 · 457061314137360899_<18> · C99

C99 = P42 · P57

P42 = 297331187884013676219113574010340108544431_<42>

P57 = 393939323086765551889841121296691017236081365848804304827_<57>

Tue Feb 12 15:42:39 2008  
Tue Feb 12 15:42:39 2008  
Tue Feb 12 15:42:39 2008  Msieve v. 1.33
Tue Feb 12 15:42:39 2008  random seeds: ac273248 99b8daf8
Tue Feb 12 15:42:39 2008  factoring 117130446887612254743317289337618603555793615683610795182304459859203598933750583971206477797268437 (99 digits)
Tue Feb 12 15:42:40 2008  searching for 15-digit factors
Tue Feb 12 15:42:41 2008  commencing quadratic sieve (99-digit input)
Tue Feb 12 15:42:41 2008  using multiplier of 1
Tue Feb 12 15:42:41 2008  using 64kb Opteron sieve core
Tue Feb 12 15:42:41 2008  sieve interval: 18 blocks of size 65536
Tue Feb 12 15:42:41 2008  processing polynomials in batches of 6
Tue Feb 12 15:42:41 2008  using a sieve bound of 2542919 (92845 primes)
Tue Feb 12 15:42:41 2008  using large prime bound of 381437850 (28 bits)
Tue Feb 12 15:42:41 2008  using double large prime bound of 2796164870269350 (43-52 bits)
Tue Feb 12 15:42:41 2008  using trial factoring cutoff of 52 bits
Tue Feb 12 15:42:41 2008  polynomial 'A' values have 13 factors
Wed Feb 13 00:08:09 2008  93124 relations (21863 full + 71261 combined from 1412845 partial), need 92941
Wed Feb 13 00:08:11 2008  begin with 1434707 relations
Wed Feb 13 00:08:12 2008  reduce to 247553 relations in 11 passes
Wed Feb 13 00:08:12 2008  attempting to read 247553 relations
Wed Feb 13 00:08:16 2008  recovered 247553 relations
Wed Feb 13 00:08:16 2008  recovered 237150 polynomials
Wed Feb 13 00:08:16 2008  attempting to build 93124 cycles
Wed Feb 13 00:08:16 2008  found 93123 cycles in 5 passes
Wed Feb 13 00:08:17 2008  distribution of cycle lengths:
Wed Feb 13 00:08:17 2008     length 1 : 21863
Wed Feb 13 00:08:17 2008     length 2 : 15753
Wed Feb 13 00:08:17 2008     length 3 : 15456
Wed Feb 13 00:08:17 2008     length 4 : 12692
Wed Feb 13 00:08:17 2008     length 5 : 9820
Wed Feb 13 00:08:17 2008     length 6 : 6695
Wed Feb 13 00:08:17 2008     length 7 : 4456
Wed Feb 13 00:08:17 2008     length 9+: 6388
Wed Feb 13 00:08:17 2008  largest cycle: 21 relations
Wed Feb 13 00:08:18 2008  matrix is 92845 x 93123 (25.1 MB) with weight 6203991 (66.62/col)
Wed Feb 13 00:08:18 2008  sparse part has weight 6203991 (66.62/col)
Wed Feb 13 00:08:20 2008  filtering completed in 3 passes
Wed Feb 13 00:08:20 2008  matrix is 89183 x 89247 (24.1 MB) with weight 5972500 (66.92/col)
Wed Feb 13 00:08:20 2008  sparse part has weight 5972500 (66.92/col)
Wed Feb 13 00:08:21 2008  saving the first 48 matrix rows for later
Wed Feb 13 00:08:21 2008  matrix is 89135 x 89247 (14.6 MB) with weight 4655973 (52.17/col)
Wed Feb 13 00:08:21 2008  sparse part has weight 3297383 (36.95/col)
Wed Feb 13 00:08:21 2008  matrix includes 64 packed rows
Wed Feb 13 00:08:21 2008  using block size 21845 for processor cache size 512 kB
Wed Feb 13 00:08:22 2008  commencing Lanczos iteration
Wed Feb 13 00:08:22 2008  memory use: 14.5 MB
Wed Feb 13 00:09:40 2008  lanczos halted after 1411 iterations (dim = 89133)
Wed Feb 13 00:09:40 2008  recovered 15 nontrivial dependencies
Wed Feb 13 00:09:41 2008  prp42 factor: 297331187884013676219113574010340108544431
Wed Feb 13 00:09:41 2008  prp57 factor: 393939323086765551889841121296691017236081365848804304827
Wed Feb 13 00:09:41 2008  elapsed time 08:27:02

Feb 11, 2008 (4th)

By Robert Backstrom / GMP-ECM

(11·10¹³⁴+61)/9 = 1(2)₁₃₃9_<135> = 3 · 887 · 35863 · 6443166705211_<13> · 5420992073158442273512673551_<28> · C86

C86 = P29 · P57

P29 = 72262687717088370908767938209_<29>

P57 = 507418660021790002190944224034674082883979558173581771547_<57>

(11·10¹¹⁷+61)/9 = 1(2)₁₁₆9_<118> = 199 · 6247 · 1710937 · 158006612980033_<15> · C91

C91 = P33 · P59

P33 = 263003561317130722985502794515043_<33>

P59 = 13827850710715765070628800684573938236616215726252446506831_<59>

(11·10¹⁰⁹+61)/9 = 1(2)₁₀₈9_<110> = 19 · 23 · 19389658353125041_<17> · C91

C91 = P32 · P59

P32 = 25963864742768432702463389177291_<32>

P59 = 55555779286126867906535634003991867240948718030556740625907_<59>

(11·10¹⁴⁷+61)/9 = 1(2)₁₄₆9_<148> = 227 · 50647 · 32830739197093_<14> · 3144183907883242907077468873230638509_<37> · C91

C91 = P35 · P56

P35 = 48362529052411789499072324359991381_<35>

P56 = 21294771654514384272421899428463822955945910176527190253_<56>

Feb 11, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(11·10¹⁶⁶+7)/9 = 1(2)₁₆₅3_<167> = 32443 · 121369 · 67617421 · C149

C149 = P42 · P108

P42 = 101989684325869449705527286805060691736463_<42>

P108 = 450097442915430795779994542402496558803504752094572069564062884789059603979985386323743477433742726962278103_<108>

Number: 12223_166
N=45905296118825831622186591617833147208955244311512453516285503045623177834727084405817833581225020542229541491682063403005260492580868462169391569689
  ( 149 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=101989684325869449705527286805060691736463 (pp42)
 r2=450097442915430795779994542402496558803504752094572069564062884789059603979985386323743477433742726962278103 (pp108)
Version: GGNFS-0.77.1-20060513-k8
Total time: 143.84 hours.
Scaled time: 286.53 units (timescale=1.992).
Factorization parameters were as follows:
name: 12223_166
n: 45905296118825831622186591617833147208955244311512453516285503045623177834727084405817833581225020542229541491682063403005260492580868462169391569689
m: 1000000000000000000000000000000000
c5: 110
c0: 7
skew: 0.58
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 7050001)
Primes: RFBsize:380800, AFBsize:381423, largePrimes:6105750 encountered
Relations: rels:6346470, finalFF:883846
Max relations in full relation-set: 28
Initial matrix: 762290 x 883846 with sparse part having weight 64492068.
Pruned matrix : 667219 x 671094 with weight 48020573.
Total sieving time: 137.22 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 5.98 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 143.84 hours.
 --------- CPU info (if available) ----------

Feb 11, 2008 (2nd)

By Robert Backstrom / GMP-ECM, Msieve

9·10¹⁶⁸-7 = 8(9)₁₆₇3_<169> = 11369 · 646974011 · 57572701889099_<14> · 5558386317692349989_<19> · C124

C124 = P44 · P80

P44 = 49210457799346902131698308801292711620150749_<44>

P80 = 77698147296321048398209905863232249781232086869460260825621557916054516169171993_<80>

(43·10¹⁶⁹-7)/9 = 4(7)₁₆₉_<170> = 367 · 4950421240482181291_<19> · 2775699859016352530477357_<25> · C124

C124 = P34 · P91

P34 = 3156831836580797731306525780758247_<34>

P91 = 3001191966934602598099805375944976471798484695463390773319663402408270737672035770264235879_<91>

(88·10¹⁷⁴-7)/9 = 9(7)₁₇₄_<175> = 3 · 17 · 95379796597_<11> · 54666930292056143_<17> · 511970441008370800237_<21> · C125

C125 = P30 · P30 · P33 · P34

P30 = 173757058143498816926924955673_<30>

P30 = 465925434517972487069313694967_<30>

P33 = 412578114115540514069896286025893_<33>

P34 = 2150200504074416197658991311110927_<34>

4·10¹⁷³+9 = 4(0)₁₇₂9_<174> = 241 · 2609 · 49277 · 37490161253921_<14> · 817315416761140501205161_<24> · C126

C126 = P39 · P88

P39 = 192750975747012200555324918025716343881_<39>

P88 = 2185853367735352411488999932909611191071596551799121040574783002059359617054726183998413_<88>

(5·10¹⁶⁹-23)/9 = (5)₁₆₈3_<169> = 3 · 6774331 · 306184391 · 557012815014644105825820881_<27> · C127

C127 = P31 · P35 · P62

P31 = 2087471764369186746744924457169_<31>

P35 = 76293479821546473110280044511336659_<35>

P62 = 10064299668743025389207488369674286100888124822116938935677981_<62>

(13·10¹⁷⁵-1)/3 = 4(3)₁₇₅_<176> = 53 · 1006333 · 5346101863_<10> · 77007123278857_<14> · 204401323997546371_<18> · C127

C127 = P32 · P96

P32 = 28651730387084497770902398579711_<32>

P96 = 336978213701637697571422651263830961732419798315444065386385634383590453793058262972127890968327_<96>

4·10¹⁷⁶+3 = 4(0)₁₇₅3_<177> = 13² · 14479 · 1727839 · 30175961085952909008534878737421283007_<38> · C127

C127 = P34 · P93

P34 = 3661730251935283360279392267311779_<34>

P93 = 856217277330621580192849824402420828954681540263284216581477838361242201893253167019116379159_<93>

Feb 11, 2008

The factor table of 122...229 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Feb 10, 2008 (3rd)

By Tyler Cadigan / GGNFS, Msieve

(64·10¹⁸¹-1)/9 = 7(1)₁₈₁_<182> = 2027 · 4241 · 706523 · 1094470049_<10> · C161

C161 = P72 · P89

P72 = 902771192272967778558243776478070514120292619368690645567010419017401517_<72>

P89 = 11849705735852950447627236292576531232583382440257054318850407174201209353635326074829147_<89>

Number: 71111_181
N=10697572975239793063606032978084292467067822049528412583082347469153753461107302080860461265886162919093566187463970134567420022290339189108159132374275673615999
  ( 161 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=902771192272967778558243776478070514120292619368690645567010419017401517
 r2=11849705735852950447627236292576531232583382440257054318850407174201209353635326074829147
Version: 
Total time: 306.07 hours.
Scaled time: 790.28 units (timescale=2.582).
Factorization parameters were as follows:
n: 10697572975239793063606032978084292467067822049528412583082347469153753461107302080860461265886162919093566187463970134567420022290339189108159132374275673615999
m: 2000000000000000000000000000000000000
c5: 20
c4: 0
c3: 0
c2: 0
c1: 0
c0: -1
skew: 0.55
type: snfs
Y1: 1
Y0: -2000000000000000000000000000000000000
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 8900001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 860542 x 860790
Total sieving time: 306.07 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 306.07 hours.
 --------- CPU info (if available) ----------

Feb 10, 2008 (2nd)

By JMB / GMP-ECM

(2·10¹⁷⁴+61)/9 = (2)₁₇₃9_<174> = 7 · 31 · 2039 · 2287 · 1601389 · 1020612252807407600156466188953_<31> · C127

C127 = P31 · P97

P31 = 1020612252807407600156466188953_<31>

P97 = 9267549867506020078240059593658577219817808702660486443916526167862619471929169641286722869220679_<97>

(2·10¹⁷⁸+61)/9 = (2)₁₇₇9_<178> = 3 · 2027 · 20297 · 2066378869_<10> · 3247837269569_<13> · C148

C148 = P27 · C122

P27 = 163433233996276243474084319_<27>

C122 = [16414816924183620628070288142730847259538958407278070871366182577042951560674699400450759287353464473072300307093265371783_<122>]

Feb 10, 2008

By Robert Backstrom / GMP-ECM, Msieve

(43·10¹⁶⁷-7)/9 = 4(7)₁₆₇_<168> = 3 · 113 · 491 · 993431 · 3245863392116255245078685507_<28> · C129

C129 = P29 · P101

P29 = 27530433290624738915011972223_<29>

P101 = 32334322329331329096070235876248176740375231051072784305900774570153124823803731961300200455222281203_<101>

5·10¹⁶⁸-3 = 4(9)₁₆₇7_<169> = 2957 · 5297 · 38287 · 66179 · 1421954227_<10> · 1694194073272983839_<19> · C125

C125 = P34 · P91

P34 = 8731823085626565428330649512690831_<34>

P91 = 5989126214432165607435098739078535035401301616100708973660232195133893598575906722810990487_<91>

2·10¹⁶⁷-3 = 1(9)₁₆₆7_<168> = 7 · 77550151291532631003351523_<26> · C141

C141 = P37 · P105

P37 = 1416288347210403639057173330195587867_<37>

P105 = 260134302671767920102022631505867541342722247157905131978577734973578865145671722044817281277952599937931_<105>

(82·10¹⁶⁹-1)/9 = 9(1)₁₆₉_<170> = 7 · 13 · 1193432857_<10> · 478477940789_<12> · 17915037325037174830484621_<26> · C122

C122 = P32 · P91

P32 = 32484371140271987256060780720151_<32>

P91 = 3012852418652154785011905762729241593097128731869132200674495589633594003211540806300169387_<91>

9·10¹⁷³-7 = 8(9)₁₇₂3_<174> = 317 · 31815104256736732410487_<23> · 1143831950766122847147685783_<28> · C122

C122 = P35 · P88

P35 = 32933203402548031161720747926069273_<35>

P88 = 2368938010738226751172660755825073523676287922290421869222162020029734816560986221793413_<88>

(10¹⁷³+71)/9 = (1)₁₇₂9_<173> = 23² · 107 · 424722629 · 3163656490366535907132680457817794161_<37> · C123

C123 = P36 · P40 · P47

P36 = 187679214118451681266132692899356843_<36>

P40 = 9195777497317241672839400152874797906417_<40>

P47 = 84648387182546183617852698023055943681186500107_<47>

Feb 9, 2008 (2nd)

By JMB / GMP-ECM

(2·10¹⁶⁸+61)/9 = (2)₁₆₇9_<168> = 7 · 14455081350043_<14> · C154

C154 = P39 · P116

P39 = 124665318009842949761185556866477754527_<39>

P116 = 17616647193806251861229772487131487378494707726207548488604765361306707918929630500734870981346369090407284002821927_<116>

(2·10¹⁶⁹+61)/9 = (2)₁₆₈9_<169> = 3 · 397 · 2174019307913_<13> · C153

C153 = P33 · P121

P33 = 155563984348954661900854974395441_<33>

P121 = 5517003634007995443119710663047195342439310806021769462472359559639148189247375617671640931735072033807669397978259390843_<121>

Feb 9, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(28·10¹⁶⁶+17)/9 = 3(1)₁₆₅3_<167> = 3² · 3098612050986082314588917513_<28> · C139

C139 = P35 · P104

P35 = 15690324817273401715948623986515369_<35>

P104 = 71100699358036734069101432325185455650755867126782812613471077612512751318328514905837455085857243459281_<104>

7·10¹⁶⁷+1 = 7(0)₁₆₆1_<168> = 94126111912362384454419640507_<29> · C139

C139 = P35 · P105

P35 = 45944168788570289296719424358942927_<35>

P105 = 161866703314530544206931137643404221120769747950795429104385791774237543764981165611916824698958062426909_<105>

8·10¹⁶⁷-9 = 7(9)₁₆₆1_<168> = 2371 · 3152099 · 68098319 · 39805790809_<11> · C140

C140 = P33 · P108

P33 = 328122692405400099376586451015551_<33>

P108 = 120348219501465859000916415860703533989146155732677824787903392809000729377628019185401396804542816303837799_<108>

(46·10¹⁹⁹-1)/9 = 5(1)₁₉₉_<200> = 3 · 55921 · 341701 · 476351 · 614051 · 58174269328757521_<17> · 582857153092184281963_<21> · C140

C140 = P33 · P108

P33 = 152159122038178839896993789376937_<33>

P108 = 590813353794208480835899546789264311537044346698701181714273385252084401898654909485599983690398143316984447_<108>

(34·10¹⁶⁶-43)/9 = 3(7)₁₆₅3_<167> = 3³ · 334306839006823133579471153_<27> · C139

C139 = P31 · P48 · P61

P31 = 6442347110462974423706047241203_<31>

P48 = 482409865451456968711095592247299291866460859567_<48>

P61 = 1346688281084137187308096903842451133318456201425034896421683_<61>

Number: n
N=649655712482852483347779169077738335847188574070186547360431816947990739875046547488854069593255264676791261
  ( 108 digits)
Divisors found:

Sat Feb  9 22:44:45 2008  prp48 factor: 482409865451456968711095592247299291866460859567
Sat Feb  9 22:44:45 2008  prp61 factor: 1346688281084137187308096903842451133318456201425034896421683
Sat Feb  9 22:44:45 2008  elapsed time 00:20:13 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 7.97 hours.
Scaled time: 6.67 units (timescale=0.837).
Factorization parameters were as follows:
name: n
n: 649655712482852483347779169077738335847188574070186547360431816947990739875046547488854069593255264676791261
skew: 14944.95
# norm 2.97e+15
c5: 485280
c4: -211392396
c3: -172714567923928
c2: -549425193124079357
c1: -877342288911281723800
c0: 100702957185654776225441700
# alpha -8.28
Y1: 195526208023
Y0: -266279787393641041081
# Murphy_E 1.54e-09
# M 53391717093376356172982235894071299555959712989798205258165735547349383107399703860337342131677000333041742
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved  special-q in [100000, 1150651)
Primes: RFBsize:183072, AFBsize:183595, largePrimes:4066133 encountered
Relations: rels:3988898, finalFF:410603
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 7.83 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 7.97 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

Feb 8, 2008 (3rd)

By matsui / GGNFS

4·10¹⁷⁵+1 = 4(0)₁₇₄1_<176> = 16811 · C172

C172 = P47 · P51 · P75

P47 = 33374333358396914109100082498630504183786129383_<47>

P51 = 105371111708302205780401868932937382113312422601077_<51>

P75 = 676600448832315856534571187702619060715236193076202145589311912099919790801_<75>

N=2379394444113972993873059306406519540776872286003212182499553863541728630063648801380048777586104336446374397715781333650585925881863065849741240854202605436916304800428291
  ( 172 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=33374333358396914109100082498630504183786129383 (pp47)
 r2=105371111708302205780401868932937382113312422601077 (pp51)
 r3=676600448832315856534571187702619060715236193076202145589311912099919790801 (pp75)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 193.78 hours.
Scaled time: 329.61 units (timescale=1.701).
Factorization parameters were as follows:
n: 2379394444113972993873059306406519540776872286003212182499553863541728630063648801380048777586104336446374397715781333650585925881863065849741240854202605436916304800428291
m: 100000000000000000000000000000000000
c5: 4
c0: 1
skew: 0.76
type: snfs

Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 10400001)
Primes: RFBsize:501962, AFBsize:501936, large
Primes:6393125 encountered
Relations: rels:6843406, finalFF:1132531
Max relations in full relation-set: 28
Initial matrix: 1003962 x 1132531 with sparse part having weight 66657298.
Pruned matrix : 892499 x 897582 with weight 50296953.
Total sieving time: 176.54 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 16.83 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 193.78 hours.

Feb 8, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(11·10¹⁶¹+7)/9 = 1(2)₁₆₀3_<162> = 3² · 23 · 409 · 10077835316092177735308344255341_<32> · C126

C126 = P39 · P87

P39 = 260689377498163087443735013320304256953_<39>

P87 = 549497764648131597130953367858390114380546441669938042117834896217907773886247268939477_<87>

Number: 12223_161
N=143248230202753553250627324007667704007774209136426780649557690599037990179649906991462317956463890376489091431485736813433581
  ( 126 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=260689377498163087443735013320304256953 (pp39)
 r2=549497764648131597130953367858390114380546441669938042117834896217907773886247268939477 (pp87)
Version: GGNFS-0.77.1-20060513-k8
Total time: 78.87 hours.
Scaled time: 157.58 units (timescale=1.998).
Factorization parameters were as follows:
name: 12223_161
n: 143248230202753553250627324007667704007774209136426780649557690599037990179649906991462317956463890376489091431485736813433581
m: 100000000000000000000000000000000
c5: 110
c0: 7
skew: 0.58
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4750001)
Primes: RFBsize:315948, AFBsize:316567, largePrimes:5881541 encountered
Relations: rels:6019866, finalFF:761148
Max relations in full relation-set: 28
Initial matrix: 632582 x 761148 with sparse part having weight 52817466.
Pruned matrix : 536094 x 539320 with weight 37129453.
Total sieving time: 74.82 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 3.51 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 78.87 hours.
 --------- CPU info (if available) ----------

(11·10¹⁵⁹+7)/9 = 1(2)₁₅₈3_<160> = 19 · 1574569 · 140094047 · 1752430422887_<13> · 3867814284039329713_<19> · C113

C113 = P51 · P63

P51 = 411917824030997137139094198484004214186454078374563_<51>

P63 = 104447539825442495437964036453728510925486296174666075535780023_<63>

Number: 12223_159
N=43023803330287187273746316838635004481199686462719115124977818948619389370183740498431606534990591450192166754949
  ( 113 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=411917824030997137139094198484004214186454078374563 (pp51)
 r2=104447539825442495437964036453728510925486296174666075535780023 (pp63)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 82.36 hours.
Scaled time: 55.59 units (timescale=0.675).
Factorization parameters were as follows:
name: 12223_159
n: 43023803330287187273746316838635004481199686462719115124977818948619389370183740498431606534990591450192166754949
m: 100000000000000000000000000000000
c5: 11
c0: 70
skew: 1.45
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4000001)
Primes: RFBsize:283146, AFBsize:282983, largePrimes:5738850 encountered
Relations: rels:5793505, finalFF:674155
Max relations in full relation-set: 28
Initial matrix: 566194 x 674155 with sparse part having weight 43837589.
Pruned matrix : 489774 x 492668 with weight 30368801.
Total sieving time: 71.12 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 10.68 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 82.36 hours.
 --------- CPU info (if available) ----------

Feb 7, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(2·10¹⁶⁷+61)/9 = (2)₁₆₆9_<167> = 2111 · 1832969 · 283308492690325304249221_<24> · C134

C134 = P37 · P97

P37 = 5293786095595604399312089576073126581_<37>

P97 = 3829289055393909099323406022568046034410055633038604578659954318885645966267504426432067768012731_<97>

3·10¹⁶⁷+7 = 3(0)₁₆₆7_<168> = 73 · 2820908683_<10> · 47840528956935069857729_<23> · C134

C134 = P40 · P95

P40 = 1357442863346680718028321638854705863851_<40>

P95 = 22433231368448594492739585313305402233259675370737675880559365524717784659590253895181940293287_<95>

9·10¹⁹⁶-7 = 8(9)₁₉₅3_<197> = 731413 · 15089069 · 101668669 · 13688355513133121_<17> · 20476877778258297685878989_<26> · C135

C135 = P32 · P104

P32 = 23222917624869682986808856353387_<32>

P104 = 12322489474660531695741954992123566822217378113251020935855509359836204616518712285683147287205008714067_<104>

(11·10¹⁶⁷+43)/9 = 1(2)₁₆₆7_<168> = 7² · 19 · C165

C165 = P75 · P90

P75 = 541971448192550699513304798616393006342507476379452171739705124200789773013_<75>

P90 = 242227856921645093713988883275176251092372232052137498460161900833598670237188488521812109_<90>

Number: n
N=131280582408401957274137725265544814416994868122687671559852010979830528702709153836973385845566296694116242988423439551259100131280582408401957274137725265544814417
  ( 165 digits)
SNFS difficulty: 168 digits.
Divisors found:

Thu Feb 07 23:20:45 2008  prp75 factor: 541971448192550699513304798616393006342507476379452171739705124200789773013
Thu Feb 07 23:20:45 2008  prp90 factor: 242227856921645093713988883275176251092372232052137498460161900833598670237188488521812109
Thu Feb 07 23:20:45 2008  elapsed time 01:25:46 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 74.38 hours.
Scaled time: 136.04 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_2_166_7
n: 131280582408401957274137725265544814416994868122687671559852010979830528702709153836973385845566296694116242988423439551259100131280582408401957274137725265544814417
skew: 0.55
deg: 5
c5: 1100
c0: 43
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5131969)
Primes: RFBsize:250150, AFBsize:250467, largePrimes:8087111 encountered
Relations: rels:7536817, finalFF:549247
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 74.14 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 74.38 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(37·10¹⁹⁴-1)/9 = 4(1)₁₉₄_<195> = 3² · 137 · 937 · 1471 · 206291 · 756005167 · 3310998276737_<13> · 86160185894982385604741_<23> · C136

C136 = P33 · P104

P33 = 227665057537224694948644929138647_<33>

P104 = 23882339520004120338160997543040692573102301514832723172916776549468348272189791118195375411520469002007_<104>

Feb 6, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

3·10¹⁶⁵-1 = 2(9)₁₆₅_<166> = 17 · 563 · 10366352216620195513339_<23> · C140

C140 = P59 · P81

P59 = 32537822232223537739373298666992795881162109492993066147359_<59>

P81 = 929286216648341931114487283109312466413415118752186358498797622230367374713700369_<81>

Number: n
N=30236949720159319152255112676945296055617775960741404375126742070045530650217672185324750510281942081046922358241732522840944089077526675471
  ( 140 digits)
SNFS difficulty: 165 digits.
Divisors found:

Wed Feb 06 19:22:09 2008  prp59 factor: 32537822232223537739373298666992795881162109492993066147359
Wed Feb 06 19:22:09 2008  prp81 factor: 929286216648341931114487283109312466413415118752186358498797622230367374713700369
Wed Feb 06 19:22:09 2008  elapsed time 01:17:35 (Msieve 1.33)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 48.16 hours.
Scaled time: 63.14 units (timescale=1.311).
Factorization parameters were as follows:
name: KA_2_9_165
n: 30236949720159319152255112676945296055617775960741404375126742070045530650217672185324750510281942081046922358241732522840944089077526675471
skew: 0.80
deg: 5
c5: 3
c0: -1
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100001)
Primes: RFBsize:230209, AFBsize:230192, largePrimes:7367519 encountered
Relations: rels:6892734, finalFF:544123
Max relations in full relation-set: 28
Initial matrix: 460466 x 544123 with sparse part having weight 41822415.
Pruned matrix : 
Total sieving time: 47.92 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 48.16 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Feb 6, 2008 (2nd)

By Jo Yeong Uk / GGNFS

(11·10¹⁹⁵+7)/9 = 1(2)₁₉₄3_<196> = 19 · 1381 · 2084369471_<10> · 579482349518918778349_<21> · 5743319303613011520138439_<25> · 19053471272924412355461223_<26> · C111

C111 = P52 · P59

P52 = 4691572442730948975926971646226019258011380478343997_<52>

P59 = 75116005013147098086271597306014879649488629658821732388887_<59>

Number: 12223_195
N=352412179127720740013907904143564416698937087894671770725472299693443506152847629222680315553965315424565961339
  ( 111 digits)
Divisors found:
 r1=4691572442730948975926971646226019258011380478343997 (pp52)
 r2=75116005013147098086271597306014879649488629658821732388887 (pp59)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 20.99 hours.
Scaled time: 38.89 units (timescale=1.853).
Factorization parameters were as follows:
name: 12223_195
n: 352412179127720740013907904143564416698937087894671770725472299693443506152847629222680315553965315424565961339
skew: 34427.94
# norm 1.21e+15
c5: 2940
c4: -1952990832
c3: -13969156205551
c2: 2547772263330774383
c1: -2753925105065485237741
c0: -55382786679887219119766175
# alpha -5.69
Y1: 32531887111
Y0: -2604602399830499331596
# Murphy_E 8.81e-10
# M 309779091830781573053660742294457742119204166492528584961833291120202055958849242113189450704981453714341382827
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1200000, 2040001)
Primes: RFBsize:176302, AFBsize:175883, largePrimes:7508048 encountered
Relations: rels:7241972, finalFF:409200
Max relations in full relation-set: 28
Initial matrix: 352265 x 409200 with sparse part having weight 39556757.
Pruned matrix : 313974 x 315799 with weight 27717209.
Total sieving time: 20.26 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.49 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000
total time: 20.99 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)

Feb 6, 2008

By Sinkiti Sibata / GGNFS

(11·10¹⁵⁵+7)/9 = 1(2)₁₅₄3_<156> = 3 · 1979 · 2333 · 832109 · 4940333 · 484929907573939_<15> · C121

C121 = P55 · P67

P55 = 4264116202467938770951293907576359430192576324566865877_<55>

P67 = 1038063556762454948769332965821742017541903031000047864051013665693_<67>

Number: 12223_155
N=4426423631582280997263144548425906821817226170288044990471077946959857011196243187970733067231824314700177486874047257761
  ( 121 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=4264116202467938770951293907576359430192576324566865877 (pp55)
 r2=1038063556762454948769332965821742017541903031000047864051013665693 (pp67)
Version: GGNFS-0.77.1-20060513-k8
Total time: 27.06 hours.
Scaled time: 54.16 units (timescale=2.002).
Factorization parameters were as follows:
name: 12223_155
n: 4426423631582280997263144548425906821817226170288044990471077946959857011196243187970733067231824314700177486874047257761
m: 10000000000000000000000000000000
c5: 11
c0: 7
skew: 0.91
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2400001)
Primes: RFBsize:216816, AFBsize:216272, largePrimes:5579968 encountered
Relations: rels:5574910, finalFF:586449
Max relations in full relation-set: 28
Initial matrix: 433153 x 586449 with sparse part having weight 43927938.
Pruned matrix : 323992 x 326221 with weight 27346196.
Total sieving time: 25.55 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 1.23 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 27.06 hours.
 --------- CPU info (if available) ----------

Feb 5, 2008 (3rd)

By Jo Yeong Uk / GGNFS

(11·10¹⁷²+7)/9 = 1(2)₁₇₁3_<173> = 41 · 47 · 112217052089437_<15> · 98927200774175682049_<20> · 2356137621413028954776819_<25> · C111

C111 = P36 · P76

P36 = 111487462047472904549551202867568979_<36>

P76 = 2175039767542759059001773194327055783343681329625388358095052729519501204773_<76>

Number: 12223_172
N=242489663535667639241651384176198619583752763717021557825727032888978929081904591019907021815847107960181536767
  ( 111 digits)
Divisors found:
 r1=111487462047472904549551202867568979 (pp36)
 r2=2175039767542759059001773194327055783343681329625388358095052729519501204773 (pp76)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 16.82 hours.
Scaled time: 31.26 units (timescale=1.858).
Factorization parameters were as follows:
name: 12223_172
n: 242489663535667639241651384176198619583752763717021557825727032888978929081904591019907021815847107960181536767
skew: 32353.91
# norm 3.37e+15
c5: 40320
c4: -2363866290
c3: 72861550321301
c2: 4433137019570566225
c1: -78112732505301434752569
c0: -447267567058045530535974555
# alpha -6.74
Y1: 109208032219
Y0: -1431643645502336882936
# Murphy_E 9.03e-10
# M 13490647646898210578774861483495916783026841972197418764250733041946106194943433052920323966293034641219362176
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1200000, 2040001)
Primes: RFBsize:176302, AFBsize:176469, largePrimes:7677263 encountered
Relations: rels:7584793, finalFF:522842
Max relations in full relation-set: 28
Initial matrix: 352854 x 522842 with sparse part having weight 54628482.
Pruned matrix : 258861 x 260689 with weight 29452672.
Polynomial selection time: 0.86 hours.
Total sieving time: 15.33 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.39 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000
total time: 16.82 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)

Feb 5, 2008 (2nd)

By Sinkiti Sibata / GGNFS

(11·10¹⁵²+7)/9 = 1(2)₁₅₁3_<153> = 3² · 41 · 3209 · 1679541668501_<13> · 4449251166733119007_<19> · C116

C116 = P55 · P61

P55 = 8511935397927024191899434347488658797919067426392222579_<55>

P61 = 1622736735024800828915830534770168951277226403012313894450871_<61>

Number: 12223_152
N=13812630256374128058975491572338375909272705190772233288419791120726713032137426286286429659495567817867100412416309
  ( 116 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=8511935397927024191899434347488658797919067426392222579 (pp55)
 r2=1622736735024800828915830534770168951277226403012313894450871 (pp61)
Version: GGNFS-0.77.1-20060513-k8
Total time: 33.22 hours.
Scaled time: 66.25 units (timescale=1.994).
Factorization parameters were as follows:
name: 12223_152
n: 13812630256374128058975491572338375909272705190772233288419791120726713032137426286286429659495567817867100412416309
m: 1000000000000000000000000000000
c5: 1100
c0: 7
skew: 0.36
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2300001)
Primes: RFBsize:176302, AFBsize:175784, largePrimes:5725226 encountered
Relations: rels:5716673, finalFF:530496
Max relations in full relation-set: 28
Initial matrix: 352153 x 530496 with sparse part having weight 50516089.
Pruned matrix : 288883 x 290707 with weight 27675748.
Total sieving time: 31.64 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.29 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 33.22 hours.
 --------- CPU info (if available) ----------

Feb 5, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(11·10¹⁶³+43)/9 = 1(2)₁₆₂7_<164> = 113 · 3451661 · 294424687 · C147

C147 = P34 · P44 · P69

P34 = 3212438113559117047787995708543127_<34>

P44 = 85399350297534323459073364282519538599251337_<44>

P69 = 387953825000560041646082303950754107610352645432704733536989058413903_<69>

Number: n
N=33131004600491156047449733045194672547442039666553616380896628350782674308658517596250464372112320545716472138311
  ( 113 digits)
Divisors found:
 r1=85399350297534323459073364282519538599251337 (pp44)
 r2=387953825000560041646082303950754107610352645432704733536989058413903 (pp69)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 23.43 hours.
Scaled time: 42.84 units (timescale=1.828).
Factorization parameters were as follows:
name: KA_1_2_162_7
n: 33131004600491156047449733045194672547442039666553616380896628350782674308658517596250464372112320545716472138311
skew: 28302.88
# norm 4.59e+15
c5: 67860
c4: -3555859626
c3: -286213861045720
c2: 2436750071245123937
c1: 62076746826681929023734
c0: -171681952438916685211104945
# alpha -6.04
Y1: 1026639632953
Y0: -3449256605174613017842
# Murphy_E 7.06e-10
# M 14313394424989021120980462687781058952527077536141995833789940857339061995942088651721890218689067737197530374193
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:250150, AFBsize:250126, largePrimes:9402281 encountered
Relations: rels:8572818, finalFF:572608
Max relations in full relation-set: 48
Initial matrix: 500360 x 572608 with sparse part having weight 42902050.
Pruned matrix : 432356 x 434921 with weight 24320488.
Total sieving time: 21.70 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 1.33 hours.
Total square root time: 0.15 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,28,28,50,50,2.6,2.6,100000
total time: 23.43 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(61·10¹⁸⁸-7)/9 = 6(7)₁₈₈_<189> = 761 · 14923 · 34667944967_<11> · 9342443007080306141_<19> · 8519617172494291276031_<22> · C131

C131 = P39 · P42 · P51

P39 = 824978914747918693560935356005485199233_<39>

P42 = 240133410788291625341200280280267296905327_<42>

P51 = 109179840536766784953562310705149908464858846735857_<51>

Tue Feb 05 09:17:00 2008  
Tue Feb 05 09:17:00 2008  
Tue Feb 05 09:17:00 2008  Msieve v. 1.33
Tue Feb 05 09:17:00 2008  random seeds: 9b5e2ca0 656e7f58
Tue Feb 05 09:17:00 2008  factoring 90071066358372683019711240485258915593667540152249648664868090325489848213660787369997681 (89 digits)
Tue Feb 05 09:17:00 2008  searching for 15-digit factors
Tue Feb 05 09:17:01 2008  commencing quadratic sieve (89-digit input)
Tue Feb 05 09:17:01 2008  using multiplier of 1
Tue Feb 05 09:17:01 2008  using 64kb Opteron sieve core
Tue Feb 05 09:17:01 2008  sieve interval: 17 blocks of size 65536
Tue Feb 05 09:17:01 2008  processing polynomials in batches of 6
Tue Feb 05 09:17:01 2008  using a sieve bound of 1555153 (59333 primes)
Tue Feb 05 09:17:01 2008  using large prime bound of 124412240 (26 bits)
Tue Feb 05 09:17:01 2008  using double large prime bound of 372180460082400 (42-49 bits)
Tue Feb 05 09:17:01 2008  using trial factoring cutoff of 49 bits
Tue Feb 05 09:17:01 2008  polynomial 'A' values have 11 factors
Tue Feb 05 09:59:23 2008  59447 relations (16301 full + 43146 combined from 623387 partial), need 59429
Tue Feb 05 09:59:24 2008  begin with 639687 relations
Tue Feb 05 09:59:25 2008  reduce to 143634 relations in 10 passes
Tue Feb 05 09:59:25 2008  attempting to read 143634 relations
Tue Feb 05 09:59:26 2008  recovered 143634 relations
Tue Feb 05 09:59:26 2008  recovered 118660 polynomials
Tue Feb 05 09:59:26 2008  attempting to build 59447 cycles
Tue Feb 05 09:59:26 2008  found 59447 cycles in 6 passes
Tue Feb 05 09:59:26 2008  distribution of cycle lengths:
Tue Feb 05 09:59:26 2008     length 1 : 16301
Tue Feb 05 09:59:26 2008     length 2 : 11449
Tue Feb 05 09:59:26 2008     length 3 : 10574
Tue Feb 05 09:59:26 2008     length 4 : 7994
Tue Feb 05 09:59:26 2008     length 5 : 5383
Tue Feb 05 09:59:26 2008     length 6 : 3363
Tue Feb 05 09:59:26 2008     length 7 : 1997
Tue Feb 05 09:59:26 2008     length 9+: 2386
Tue Feb 05 09:59:26 2008  largest cycle: 17 relations
Tue Feb 05 09:59:26 2008  matrix is 59333 x 59447 (14.4 MB) with weight 3545673 (59.64/col)
Tue Feb 05 09:59:26 2008  sparse part has weight 3545673 (59.64/col)
Tue Feb 05 09:59:27 2008  filtering completed in 3 passes
Tue Feb 05 09:59:27 2008  matrix is 55126 x 55189 (13.6 MB) with weight 3334863 (60.43/col)
Tue Feb 05 09:59:27 2008  sparse part has weight 3334863 (60.43/col)
Tue Feb 05 09:59:27 2008  saving the first 48 matrix rows for later
Tue Feb 05 09:59:27 2008  matrix is 55078 x 55189 (10.1 MB) with weight 2797379 (50.69/col)
Tue Feb 05 09:59:27 2008  sparse part has weight 2327254 (42.17/col)
Tue Feb 05 09:59:27 2008  matrix includes 64 packed rows
Tue Feb 05 09:59:27 2008  using block size 22075 for processor cache size 1024 kB
Tue Feb 05 09:59:28 2008  commencing Lanczos iteration
Tue Feb 05 09:59:28 2008  memory use: 9.1 MB
Tue Feb 05 09:59:47 2008  lanczos halted after 872 iterations (dim = 55078)
Tue Feb 05 09:59:48 2008  recovered 17 nontrivial dependencies
Tue Feb 05 09:59:49 2008  prp39 factor: 824978914747918693560935356005485199233
Tue Feb 05 09:59:49 2008  prp51 factor: 109179840536766784953562310705149908464858846735857
Tue Feb 05 09:59:49 2008  elapsed time 00:42:49

(11·10¹⁶²+43)/9 = 1(2)₁₆₁7_<163> = 3 · 29 · 326742809 · C152

C152 = P51 · P102

P51 = 318837544764593718793341618330869638110392459849809_<51>

P102 = 134851390385127161706957990388292357099558851675798087663094956194342092914353779808237658244386936541_<102>

Number: n
N=42995686218485684425354382121193634172142999966913173892702721973494978030934860093628100416097942649000816546309174279218259378307775145242162473970669
  ( 152 digits)
SNFS difficulty: 163 digits.
Divisors found:

Tue Feb  5 10:34:00 2008  prp51 factor: 318837544764593718793341618330869638110392459849809
Tue Feb  5 10:34:00 2008  prp102 factor: 134851390385127161706957990388292357099558851675798087663094956194342092914353779808237658244386936541
Tue Feb  5 10:34:00 2008  elapsed time 01:01:47 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 50.89 hours.
Scaled time: 42.55 units (timescale=0.836).
Factorization parameters were as follows:
name: KA_1_2_161_7
n: 42995686218485684425354382121193634172142999966913173892702721973494978030934860093628100416097942649000816546309174279218259378307775145242162473970669
type: snfs
deg: 5
c5: 1100
c0: 43
skew: 0.52
m: 100000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3200191)
Primes: RFBsize:216816, AFBsize:216802, largePrimes:5671714 encountered
Relations: rels:5520680, finalFF:479300
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 50.71 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 50.89 hours.
 --------- CPU info (if available) ----------
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Total of 2 processors activated (12009.47 BogoMIPS).

(5·10¹⁸⁹-17)/3 = 1(6)₁₈₈1_<190> = 11 · 139 · 308923723 · 4624276074181_<13> · 26156789250217_<14> · 2912928289309013648987_<22> · C131

C131 = P41 · P43 · P48

P41 = 20868712662673929425351208727898548430827_<41>

P43 = 1186280973757452857825332756781618820498731_<43>

P48 = 404528197374300908699982328463045462331168395041_<48>

Tue Feb 05 13:28:32 2008  
Tue Feb 05 13:28:32 2008  
Tue Feb 05 13:28:32 2008  Msieve v. 1.33
Tue Feb 05 13:28:32 2008  random seeds: 9aae636c ffa3d539
Tue Feb 05 13:28:32 2008  factoring 479884103893532766339493695699275521182139215549108179534976372846630679623126216447192971 (90 digits)
Tue Feb 05 13:28:32 2008  searching for 15-digit factors
Tue Feb 05 13:28:33 2008  commencing quadratic sieve (90-digit input)
Tue Feb 05 13:28:33 2008  using multiplier of 41
Tue Feb 05 13:28:33 2008  using 64kb Opteron sieve core
Tue Feb 05 13:28:33 2008  sieve interval: 18 blocks of size 65536
Tue Feb 05 13:28:33 2008  processing polynomials in batches of 6
Tue Feb 05 13:28:33 2008  using a sieve bound of 1582247 (60000 primes)
Tue Feb 05 13:28:33 2008  using large prime bound of 126579760 (26 bits)
Tue Feb 05 13:28:33 2008  using double large prime bound of 383933120608320 (42-49 bits)
Tue Feb 05 13:28:33 2008  using trial factoring cutoff of 49 bits
Tue Feb 05 13:28:33 2008  polynomial 'A' values have 12 factors
Tue Feb 05 14:42:32 2008  60432 relations (16460 full + 43972 combined from 631008 partial), need 60096
Tue Feb 05 14:42:33 2008  begin with 647467 relations
Tue Feb 05 14:42:34 2008  reduce to 144826 relations in 10 passes
Tue Feb 05 14:42:34 2008  attempting to read 144826 relations
Tue Feb 05 14:42:36 2008  recovered 144826 relations
Tue Feb 05 14:42:36 2008  recovered 123295 polynomials
Tue Feb 05 14:42:36 2008  attempting to build 60432 cycles
Tue Feb 05 14:42:36 2008  found 60432 cycles in 5 passes
Tue Feb 05 14:42:37 2008  distribution of cycle lengths:
Tue Feb 05 14:42:37 2008     length 1 : 16460
Tue Feb 05 14:42:37 2008     length 2 : 11957
Tue Feb 05 14:42:37 2008     length 3 : 10793
Tue Feb 05 14:42:37 2008     length 4 : 8024
Tue Feb 05 14:42:37 2008     length 5 : 5471
Tue Feb 05 14:42:37 2008     length 6 : 3456
Tue Feb 05 14:42:37 2008     length 7 : 2003
Tue Feb 05 14:42:37 2008     length 9+: 2268
Tue Feb 05 14:42:37 2008  largest cycle: 18 relations
Tue Feb 05 14:42:37 2008  matrix is 60000 x 60432 (14.8 MB) with weight 3642461 (60.27/col)
Tue Feb 05 14:42:37 2008  sparse part has weight 3642461 (60.27/col)
Tue Feb 05 14:42:38 2008  filtering completed in 3 passes
Tue Feb 05 14:42:38 2008  matrix is 55611 x 55675 (13.7 MB) with weight 3372205 (60.57/col)
Tue Feb 05 14:42:38 2008  sparse part has weight 3372205 (60.57/col)
Tue Feb 05 14:42:39 2008  saving the first 48 matrix rows for later
Tue Feb 05 14:42:39 2008  matrix is 55563 x 55675 (8.7 MB) with weight 2632003 (47.27/col)
Tue Feb 05 14:42:39 2008  sparse part has weight 1939874 (34.84/col)
Tue Feb 05 14:42:39 2008  matrix includes 64 packed rows
Tue Feb 05 14:42:39 2008  using block size 21845 for processor cache size 512 kB
Tue Feb 05 14:42:39 2008  commencing Lanczos iteration
Tue Feb 05 14:42:39 2008  memory use: 8.4 MB
Tue Feb 05 14:43:05 2008  lanczos halted after 880 iterations (dim = 55562)
Tue Feb 05 14:43:06 2008  recovered 18 nontrivial dependencies
Tue Feb 05 14:43:06 2008  prp43 factor: 1186280973757452857825332756781618820498731
Tue Feb 05 14:43:06 2008  prp48 factor: 404528197374300908699982328463045462331168395041
Tue Feb 05 14:43:06 2008  elapsed time 01:14:34

(2·10¹⁶³+1)/3 = (6)₁₆₂7_<163> = 7 · 61 · 167 · 34963 · 12614592942079272049_<20> · C135

C135 = P65 · P71

P65 = 10377754436587567376693516896966925177426777542616355517332761623_<65>

P71 = 20425799928742290584344313773322626491010687290873847923471967649372363_<71>

Number: n
N=211973935831355323693477966455996075420736602698565413687534168539153599729601192528535499470177455623893501702677635272385313443225149
  ( 135 digits)
SNFS difficulty: 163 digits.
Divisors found:

Tue Feb 05 14:44:10 2008  prp65 factor: 10377754436587567376693516896966925177426777542616355517332761623
Tue Feb 05 14:44:10 2008  prp71 factor: 20425799928742290584344313773322626491010687290873847923471967649372363
Tue Feb 05 14:44:10 2008  elapsed time 01:07:48 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 41.47 hours.
Scaled time: 72.75 units (timescale=1.754).
Factorization parameters were as follows:
name: KA_6_162_7
n: 211973935831355323693477966455996075420736602698565413687534168539153599729601192528535499470177455623893501702677635272385313443225149
type: snfs
skew: 0.44
deg: 5
c5: 125
c0: 2
m: 200000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2099990)
Primes: RFBsize:216816, AFBsize:216926, largePrimes:6940658 encountered
Relations: rels:6381595, finalFF:492593
Max relations in full relation-set: 28
Initial matrix: 433807 x 492593 with sparse part having weight 32470962.
Pruned matrix : 
Total sieving time: 41.26 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 41.47 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

9·10¹⁹⁹-1 = 8(9)₁₉₉_<200> = 311 · 18816601 · 7199849885356048147_<19> · 8780607192536057363_<19> · 6189868364159015753089_<22> · C131

C131 = P39 · P92

P39 = 653013029588688183402047290771742842951_<39>

P92 = 60185198005340312093913851920027593244762401225251579516624254991791230274129125334702673471_<92>

(11·10¹⁶⁵+7)/9 = 1(2)₁₆₄3_<166> = 2323037 · 3024071 · 801547104685055220907_<21> · 2244551866593860631050339_<25> · C107

C107 = P50 · P58

P50 = 22667491190849706134196427735425561647719849624523_<50>

P58 = 4266187260102382245262999179515923658804140846831092944231_<58>

Number: n
N=96703762136885993527051098298870383339158901947010897471096334946417565075450884442730993018763399928976813
  ( 107 digits)
Divisors found:

Tue Feb  5 21:58:19 2008  prp50 factor: 22667491190849706134196427735425561647719849624523
Tue Feb  5 21:58:19 2008  prp58 factor: 4266187260102382245262999179515923658804140846831092944231
Tue Feb  5 21:58:19 2008  elapsed time 00:31:25 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 10.14 hours.
Scaled time: 8.49 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_1_2_164_3
n: 96703762136885993527051098298870383339158901947010897471096334946417565075450884442730993018763399928976813
skew: 5982.01
# norm 2.22e+14
c5: 408000
c4: 39585968
c3: -38249412823790
c2: -4391565209106421
c1: 696703255789243605102
c0: 645439348323787340602296
# alpha -4.96
Y1: 248694786263
Y0: -188346099305469065669
# Murphy_E 1.38e-09
# M 51061564494728018280537336885306695758903469801669314827242486514533346876854629373845711032256659328639940
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 49/49
Sieved  special-q in [100000, 1600000)
Primes: RFBsize:183072, AFBsize:183292, largePrimes:7923702 encountered
Relations: rels:7188725, finalFF:454354
Max relations in full relation-set: 28
Initial matrix: 366442 x 454354 with sparse part having weight 31541384.
Pruned matrix : 317266 x 319162 with weight 16959885.
Total sieving time: 9.92 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,28,28,49,49,2.6,2.6,150000
total time: 10.14 hours.
 --------- CPU info (if available) ----------
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Total of 2 processors activated (12009.47 BogoMIPS).

Feb 4, 2008 (2nd)

By Jo Yeong Uk / GMP-ECM, GGNFS

(11·10¹⁴⁴+7)/9 = 1(2)₁₄₃3_<145> = 59 · 1669 · 51429901 · 2361395713_<10> · 65397750107_<11> · C112

C112 = P34 · P78

P34 = 4258603296735103039935301521943217_<34>

P78 = 366967307314766659198303919155557622909193203642497744426932236576610478647479_<78>

(11·10¹⁵⁶+7)/9 = 1(2)₁₅₅3_<157> = 12721 · 2742200326538945243417_<22> · 9541792824687531700463092793_<28> · C103

C103 = P41 · P63

P41 = 20014512109901815744898373231694000857379_<41>

P63 = 183465645941118388677264534427318636676528636593091062790132837_<63>

Number: 12223_156
N=3671975392439472899341330402417834604335376052564536472613853563638553912495032350819060859819301654223
  ( 103 digits)
Divisors found:
 r1=20014512109901815744898373231694000857379 (pp41)
 r2=183465645941118388677264534427318636676528636593091062790132837 (pp63)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.31 hours.
Scaled time: 9.87 units (timescale=1.858).
Factorization parameters were as follows:
name: 12223_156
n: 3671975392439472899341330402417834604335376052564536472613853563638553912495032350819060859819301654223
skew: 19530.82
# norm 1.35e+14
c5: 6720
c4: -442157698
c3: -8623263312341
c2: 181075102603430862
c1: 1613496398437236320040
c0: 174910907146950939185280
# alpha -6.11
Y1: 48802931441
Y0: -55912780045085853073
# Murphy_E 2.56e-09
# M 144302031692213904811710240983196039277303241981002758121166447200177541282832116968539726573935138066
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1560001)
Primes: RFBsize:135072, AFBsize:134658, largePrimes:4325792 encountered
Relations: rels:4231829, finalFF:317982
Max relations in full relation-set: 28
Initial matrix: 269812 x 317982 with sparse part having weight 25295169.
Pruned matrix : 235496 x 236909 with weight 15884839.
Polynomial selection time: 0.35 hours.
Total sieving time: 4.63 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 5.31 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)

(11·10¹⁷⁵+43)/9 = 1(2)₁₇₄7_<176> = 431 · 563 · 16290121 · 38995664297_<11> · 593004715928370319507_<21> · 34213955179215476404658449_<26> · C106

C106 = P47 · P59

P47 = 47531082292491978658661669522302345299666587893_<47>

P59 = 82221376817115875746030616826703371178580921798546057059393_<59>

Number: 12227_175
N=3908071027696326886864028499843206919992522378639674173594528479164089521830871500698729823982185555728949
  ( 106 digits)
Divisors found:
 r1=47531082292491978658661669522302345299666587893 (pp47)
 r2=82221376817115875746030616826703371178580921798546057059393 (pp59)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.32 hours.
Scaled time: 19.18 units (timescale=1.858).
Factorization parameters were as follows:
name: 12227_175
n: 3908071027696326886864028499843206919992522378639674173594528479164089521830871500698729823982185555728949
skew: 8608.29
# norm 1.20e+14
c5: 25260
c4: -60371188
c3: 5757318952065
c2: 46830095000041631
c1: -261301190147423580723
c0: 3535830573716278227215
# alpha -5.17
Y1: 25621186877
Y0: -172944140038548492006
# Murphy_E 1.75e-09
# M 2075970695538704841661361494941305006763486824834160907225439575126500475951541082025147569146320170113636
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1440001)
Primes: RFBsize:135072, AFBsize:135115, largePrimes:4655871 encountered
Relations: rels:4809611, finalFF:441492
Max relations in full relation-set: 28
Initial matrix: 270272 x 441492 with sparse part having weight 44629901.
Pruned matrix : 194914 x 196329 with weight 18507439.
Polynomial selection time: 0.49 hours.
Total sieving time: 9.52 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 10.32 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)

Feb 4, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(8·10¹⁶⁷-71)/9 = (8)₁₆₆1_<167> = 3 · 13 · 7480258613071537_<16> · C150

C150 = P34 · P117

P34 = 2269232521002778040596096495435919_<34>

P117 = 134272556782880983389435035962509777764315564283238280173555744073973109616249276693619292540182473602203459354521593_<117>

(11·10¹⁵⁹+43)/9 = 1(2)₁₅₈7_<160> = 3⁶ · 607 · 1523 · 9672317 · C144

C144 = P41 · P103

P41 = 25040024464232789848294795392827328171553_<41>

P103 = 7488050807888404363384367482738346838595043907027771100444640147357671594913324944576167521340548615683_<103>

Number: n
N=187500975418943751652660969335071540461164444315032750609349244011086201230476532801845590733194291631585853137616657120810227526386921690265699
  ( 144 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Feb 05 00:24:40 2008  prp41 factor: 25040024464232789848294795392827328171553
Tue Feb 05 00:24:40 2008  prp103 factor: 7488050807888404363384367482738346838595043907027771100444640147357671594913324944576167521340548615683
Tue Feb 05 00:24:40 2008  elapsed time 01:23:19 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 40.04 hours.
Scaled time: 57.97 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_1_2_158_7
n: 187500975418943751652660969335071540461164444315032750609349244011086201230476532801845590733194291631585853137616657120810227526386921690265699
skew: 2.08
deg: 5
c5: 11
c0: 430
m: 100000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2000001)
Primes: RFBsize:183072, AFBsize:182932, largePrimes:7315120 encountered
Relations: rels:6778458, finalFF:413850
Max relations in full relation-set: 28
Initial matrix: 366069 x 413850 with sparse part having weight 39217428.
Pruned matrix : 
Total sieving time: 39.82 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 40.04 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Feb 3, 2008 (4th)

By Kurt Beschorner

10⁸¹³+1 is divisible by 21765743514521277143440823504372166157_<38>

By Yousuke Koide

10¹¹³³+1 is divisible by 5571170781540045423292640754334163561_<37>

(10¹³²⁷-1)/9 is divisible by 32902513329012026560826807111_<29>

Feb 3, 2008 (3rd)

By Jo Yeong Uk / GGNFS

(11·10¹³⁶+7)/9 = 1(2)₁₃₅3_<137> = 95561 · 155465684301056887579729_<24> · C108

C108 = P44 · P65

P44 = 14334185432356752323140436045325276938680249_<44>

P65 = 57393396768433653752614517111796708118174950424989467951382669983_<65>

Number: 12223_136
N=822687591871552784709318643813197336735469821034016549030837174471470985203346819632076285577794861927265767
  ( 108 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=14334185432356752323140436045325276938680249 (pp44)
 r2=57393396768433653752614517111796708118174950424989467951382669983 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.35 hours.
Scaled time: 8.07 units (timescale=1.857).
Factorization parameters were as follows:
n: 822687591871552784709318643813197336735469821034016549030837174471470985203346819632076285577794861927265767
m: 1000000000000000000000000000
c5: 110
c0: 7
skew: 0.58
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1500001)
Primes: RFBsize:107126, AFBsize:107674, largePrimes:2376958 encountered
Relations: rels:2529390, finalFF:284184
Max relations in full relation-set: 28
Initial matrix: 214867 x 284184 with sparse part having weight 25136993.
Pruned matrix : 193207 x 194345 with weight 14316828.
Total sieving time: 4.15 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 4.35 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)

(11·10¹³⁸+7)/9 = 1(2)₁₃₇3_<139> = 623766815165969_<15> · 23752250570612018894611_<23> · C101

C101 = P39 · P63

P39 = 160798003756692938654694712820528450413_<39>

P63 = 513029679588668744253094982652790979172390866713850617213539769_<63>

Number: 12223_138
N=82494148345793731369441602124244699834884418764952216407190783233269739489161851992590938580119974597
  ( 101 digits)
Divisors found:
 r1=160798003756692938654694712820528450413 (pp39)
 r2=513029679588668744253094982652790979172390866713850617213539769 (pp63)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.18 hours.
Scaled time: 7.76 units (timescale=1.859).
Factorization parameters were as follows:
name: 12223_138
n: 82494148345793731369441602124244699834884418764952216407190783233269739489161851992590938580119974597
skew: 4243.25
# norm 1.19e+14
c5: 193680
c4: -67658172
c3: -9221234168102
c2: -47361928099406800
c1: 41132723755137780999
c0: 104857604310820431424095
# alpha -5.94
Y1: 43351291357
Y0: -13361886298864081646
# Murphy_E 2.87e-09
# M 71500888182725105628880026829625266678105175754627294008919100390854775685964105360002187732656023157
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [750000, 1350001)
Primes: RFBsize:114155, AFBsize:113911, largePrimes:3839474 encountered
Relations: rels:3720898, finalFF:269923
Max relations in full relation-set: 28
Initial matrix: 228148 x 269923 with sparse part having weight 21108901.
Pruned matrix : 202141 x 203345 with weight 13187397.
Polynomial selection time: 0.28 hours.
Total sieving time: 3.64 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,48,48,2.5,2.5,50000
total time: 4.18 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)

(11·10¹⁴²+7)/9 = 1(2)₁₄₁3_<143> = 41 · 154061 · 852989 · 641716583188361789950959757_<27> · C103

C103 = P51 · P53

P51 = 213109970184769549110217954567545220770332311910759_<51>

P53 = 16587584380176701656934488951246590820083044778169789_<53>

Number: 12223_142
N=3534979612696805971561202559424469132527119933396271700242344599515181935142280999950609689873517859851
  ( 103 digits)
Divisors found:
 r1=213109970184769549110217954567545220770332311910759 (pp51)
 r2=16587584380176701656934488951246590820083044778169789 (pp53)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.53 hours.
Scaled time: 10.28 units (timescale=1.858).
Factorization parameters were as follows:
name: 12223_142
n: 3534979612696805971561202559424469132527119933396271700242344599515181935142280999950609689873517859851
skew: 2679.82
# norm 5.30e+13
c5: 264600
c4: 1519439634
c3: 5152788085665
c2: -11953194132301114
c1: -25402458644324276290
c0: 28335371836441837330020
# alpha -5.47
Y1: 61721076197
Y0: -26616948120759083489
# Murphy_E 2.59e-09
# M 1548383572242134576146617681526396291714054299406984080533713325745441083028013889105891537464365554166
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1620001)
Primes: RFBsize:135072, AFBsize:134902, largePrimes:4460724 encountered
Relations: rels:4495194, finalFF:394216
Max relations in full relation-set: 28
Initial matrix: 270054 x 394216 with sparse part having weight 33311263.
Pruned matrix : 199211 x 200625 with weight 15737659.
Polynomial selection time: 0.35 hours.
Total sieving time: 4.89 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 5.53 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)

Feb 3, 2008 (2nd)

By Sinkiti Sibata / Msieve

(11·10¹²⁵+43)/9 = 1(2)₁₂₄7_<126> = 7³ · 47 · 503 · 9791 · 319485419022834938413_<21> · C94

C94 = P41 · P54

P41 = 26911423347030094859147806513779908366419_<41>

P54 = 179050464360592207024627576920634186756605854426645477_<54>

Sat Feb 02 08:18:48 2008  Msieve v. 1.30
Sat Feb 02 08:18:49 2008  random seeds: 9e0bea2a 4bbaab61
Sat Feb 02 08:18:49 2008  factoring 4818502846890221045374101350076711059884336292143407476048410706538319861125528494833125036863 (94 digits)
Sat Feb 02 08:18:49 2008  commencing quadratic sieve (94-digit input)
Sat Feb 02 08:18:50 2008  using multiplier of 2
Sat Feb 02 08:18:50 2008  using 64kb Pentium 2 sieve core
Sat Feb 02 08:18:50 2008  sieve interval: 18 blocks of size 65536
Sat Feb 02 08:18:50 2008  processing polynomials in batches of 6
Sat Feb 02 08:18:50 2008  using a sieve bound of 2057791 (76471 primes)
Sat Feb 02 08:18:50 2008  using large prime bound of 283975158 (28 bits)
Sat Feb 02 08:18:50 2008  using double large prime bound of 1644010566805608 (42-51 bits)
Sat Feb 02 08:18:50 2008  using trial factoring cutoff of 51 bits
Sat Feb 02 08:18:50 2008  polynomial 'A' values have 12 factors
Sun Feb 03 06:22:02 2008  76863 relations (18980 full + 57883 combined from 1103923 partial), need 76567
Sun Feb 03 06:22:22 2008  begin with 1122903 relations
Sun Feb 03 06:23:45 2008  reduce to 199427 relations in 10 passes
Sun Feb 03 06:23:46 2008  attempting to read 199427 relations
Sun Feb 03 06:24:11 2008  recovered 199427 relations
Sun Feb 03 06:24:11 2008  recovered 181755 polynomials
Sun Feb 03 06:24:36 2008  attempting to build 76863 cycles
Sun Feb 03 06:24:36 2008  found 76863 cycles in 6 passes
Sun Feb 03 06:24:41 2008  distribution of cycle lengths:
Sun Feb 03 06:24:41 2008     length 1 : 18980
Sun Feb 03 06:24:41 2008     length 2 : 13444
Sun Feb 03 06:24:41 2008     length 3 : 13097
Sun Feb 03 06:24:41 2008     length 4 : 10345
Sun Feb 03 06:24:41 2008     length 5 : 7787
Sun Feb 03 06:24:41 2008     length 6 : 5269
Sun Feb 03 06:24:42 2008     length 7 : 3401
Sun Feb 03 06:24:42 2008     length 9+: 4540
Sun Feb 03 06:24:42 2008  largest cycle: 20 relations
Sun Feb 03 06:24:43 2008  matrix is 76471 x 76863 with weight 4943542 (avg 64.32/col)
Sun Feb 03 06:24:48 2008  filtering completed in 3 passes
Sun Feb 03 06:24:48 2008  matrix is 72682 x 72746 with weight 4694355 (avg 64.53/col)
Sun Feb 03 06:24:51 2008  saving the first 48 matrix rows for later
Sun Feb 03 06:24:52 2008  matrix is 72634 x 72746 with weight 3670006 (avg 50.45/col)
Sun Feb 03 06:24:52 2008  matrix includes 64 packed rows
Sun Feb 03 06:24:52 2008  using block size 10922 for processor cache size 256 kB
Sun Feb 03 06:24:55 2008  commencing Lanczos iteration
Sun Feb 03 06:29:16 2008  lanczos halted after 1149 iterations (dim = 72632)
Sun Feb 03 06:29:17 2008  recovered 16 nontrivial dependencies
Sun Feb 03 06:32:11 2008  prp41 factor: 26911423347030094859147806513779908366419
Sun Feb 03 06:32:11 2008  prp54 factor: 179050464360592207024627576920634186756605854426645477
Sun Feb 03 06:32:11 2008  elapsed time 22:13:22

Feb 3, 2008

By Robert Backstrom / GGNFS, Msieve

(11·10¹³²+43)/9 = 1(2)₁₃₁7_<133> = 3³ · 83 · C129

C129 = P57 · P73

P57 = 111112771172331750872514090492110122437339906630826550009_<57>

P73 = 4908449645869942293694487080630525727438428859396006401801847501095827883_<73>

Number: n
N=545391442312459715404829193316475779661857305766274976449005900143785016609648470424909514601616341910853289702017948336556100947
  ( 129 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=111112771172331750872514090492110122437339906630826550009 (pp57)
 r2=4908449645869942293694487080630525727438428859396006401801847501095827883 (pp73)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 5.51 hours.
Scaled time: 7.21 units (timescale=1.309).
Factorization parameters were as follows:
name: KA_1_2_131_7
n: 545391442312459715404829193316475779661857305766274976449005900143785016609648470424909514601616341910853289702017948336556100947
skew: 0.52
deg: 5
c5: 1100
c0: 43
m: 100000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 500001)
Primes: RFBsize:148933, AFBsize:148846, largePrimes:5439382 encountered
Relations: rels:4852705, finalFF:336542
Max relations in full relation-set: 28
Initial matrix: 297846 x 336542 with sparse part having weight 16711281.
Pruned matrix : 259856 x 261409 with weight 10061932.
Total sieving time: 4.37 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.95 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,50000
total time: 5.51 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(11·10¹³⁷+43)/9 = 1(2)₁₃₆7_<138> = 7 · C137

C137 = P39 · P98

P39 = 826947682191349154287338776865934602857_<39>

P98 = 21114174253501663398552547882800994034080029605303708859438928706621453258063526161207848053837773_<98>

Number: n
N=17460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317461
  ( 137 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=826947682191349154287338776865934602857 (pp39)
 r2=21114174253501663398552547882800994034080029605303708859438928706621453258063526161207848053837773 (pp98)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.20 hours.
Scaled time: 12.62 units (timescale=1.753).
Factorization parameters were as follows:
name: KA_1_2_136_7
n: 17460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317461
type: snfs
skew: 0.52
deg: 5
c5: 1100
c0: 43
m: 1000000000000000000000000000
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1000000)
Primes: RFBsize:114155, AFBsize:114198, largePrimes:5398021 encountered
Relations: rels:4770513, finalFF:299953
Max relations in full relation-set: 28
Initial matrix: 228420 x 299953 with sparse part having weight 19344439.
Pruned matrix : 185538 x 186744 with weight 9834435.
Total sieving time: 6.31 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.67 hours.
Total square root time: 0.07 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.3,2.3,75000
total time: 7.20 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(11·10¹³³+43)/9 = 1(2)₁₃₂7_<134> = 1321 · 1410916038767_<13> · 3759336512783_<13> · C106

C106 = P37 · P69

P37 = 3516588143890561652644886771677592087_<37>

P69 = 496036320496666194477662303711920463713480656308118096409742336798941_<69>

Number: n
N=1744355443597675135882479103597911072800396043417938417736429887625152088132861173319540054833362331579867
  ( 106 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=3516588143890561652644886771677592087 (pp37)
 r2=496036320496666194477662303711920463713480656308118096409742336798941 (pp69)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 5.91 hours.
Scaled time: 7.74 units (timescale=1.309).
Factorization parameters were as follows:
name: KA_1_2_132_7
n: 1744355443597675135882479103597911072800396043417938417736429887625152088132861173319540054833362331579867
skew: 0.33
deg: 5
c5: 11000
c0: 43
m: 100000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 550001)
Primes: RFBsize:148933, AFBsize:149056, largePrimes:5686122 encountered
Relations: rels:5129599, finalFF:373496
Max relations in full relation-set: 28
Initial matrix: 298056 x 373496 with sparse part having weight 20625775.
Pruned matrix : 230995 x 232549 with weight 9849788.
Total sieving time: 5.01 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.68 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,75000
total time: 5.91 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(11·10¹⁴⁸+43)/9 = 1(2)₁₄₇7_<149> = 2237 · C145

C145 = P46 · P99

P46 = 5708590448834065059889081709749195794968604751_<46>

P99 = 957095567805688585006539301709267550428734463658167833478066966464619925304020149513216150426243521_<99>

Number: n
N=5463666616996970148512392589281279491382307654100233447573635325088163711319723836487359062236129737247305418963890130631301842745740823523568271
  ( 145 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=5708590448834065059889081709749195794968604751 (pp46)
 r2=957095567805688585006539301709267550428734463658167833478066966464619925304020149513216150426243521 (pp99)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 11.16 hours.
Scaled time: 20.27 units (timescale=1.817).
Factorization parameters were as follows:
name: KA_1_2_147_7
n: 5463666616996970148512392589281279491382307654100233447573635325088163711319723836487359062236129737247305418963890130631301842745740823523568271
skew: 0.33
deg: 5
c5: 11000
c0: 43
m: 100000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1900001)
Primes: RFBsize:183072, AFBsize:183037, largePrimes:7044436 encountered
Relations: rels:6450847, finalFF:440285
Max relations in full relation-set: 48
Initial matrix: 366176 x 440285 with sparse part having weight 39436571.
Pruned matrix : 321112 x 323006 with weight 23568462.
Total sieving time: 10.11 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.84 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 11.16 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(11·10¹⁴²+43)/9 = 1(2)₁₄₁7_<143> = 199 · 2711 · 25447 · C132

C132 = P55 · P78

P55 = 3068600121073799335852157386784751919947571513958188339_<55>

P78 = 290128701364190538984568387515170669387068553760927649832295688847493293426071_<78>

Number: n
N=890288968133139258467427941637942626811916485305684466174890492674520641988294022763275638082211998002722782842984474256989590786069
  ( 132 digits)
SNFS difficulty: 143 digits.
Divisors found:

Sun Feb  3 19:04:45 2008  prp55 factor: 3068600121073799335852157386784751919947571513958188339
Sun Feb  3 19:04:45 2008  prp78 factor: 290128701364190538984568387515170669387068553760927649832295688847493293426071
Sun Feb  3 19:04:45 2008  elapsed time 00:16:14 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-k8
Total time: 10.62 hours.
Scaled time: 8.91 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_1_2_141_7
n: 890288968133139258467427941637942626811916485305684466174890492674520641988294022763275638082211998002722782842984474256989590786069
type: snfs
deg: 5
c5: 1100
c0: 43
skew: 0.52
m: 10000000000000000000000000000
rlim: 2000000
alim: 2000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [100000, 1700001)
Primes: RFBsize:148933, AFBsize:148846, largePrimes:2743285 encountered
Relations: rels:2743528, finalFF:343108
Max relations in full relation-set: 28
Initial matrix: 297846 x 343108 with sparse part having weight 16612589.
Pruned matrix : 264132 x 265685 with weight 10944419.
Total sieving time: 10.12 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.39 hours.
Total time per square root: 0.00 hours, sqrts: 32.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,45,45,2.5,2.5,100000
total time: 10.62 hours.
 --------- CPU info (if available) ----------
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Total of 2 processors activated (12009.47 BogoMIPS).

Feb 2, 2008 (3rd)

By Sinkiti Sibata / Msieve, GGNFS

(11·10¹¹⁰+7)/9 = 1(2)₁₀₉3_<111> = 3 · 8874935947_<10> · C100

C100 = P36 · P65

P36 = 192974421658293224031417306264104681_<36>

P65 = 23788329512941257985749836483187483343956508948136539261231691863_<65>

Fri Feb  1 13:49:44 2008  Msieve v. 1.33
Fri Feb  1 13:49:44 2008  random seeds: a1488afa bb05cf89
Fri Feb  1 13:49:44 2008  factoring 4590539129976747396207516622062302388438943934694827013914981750655415827841212558189152724567910703 (100 digits)
Fri Feb  1 13:49:45 2008  searching for 15-digit factors
Fri Feb  1 13:49:47 2008  commencing quadratic sieve (100-digit input)
Fri Feb  1 13:49:48 2008  using multiplier of 23
Fri Feb  1 13:49:48 2008  using 64kb Pentium 4 sieve core
Fri Feb  1 13:49:48 2008  sieve interval: 18 blocks of size 65536
Fri Feb  1 13:49:48 2008  processing polynomials in batches of 6
Fri Feb  1 13:49:48 2008  using a sieve bound of 2751493 (99912 primes)
Fri Feb  1 13:49:48 2008  using large prime bound of 412723950 (28 bits)
Fri Feb  1 13:49:48 2008  using double large prime bound of 3222459040502850 (43-52 bits)
Fri Feb  1 13:49:48 2008  using trial factoring cutoff of 52 bits
Fri Feb  1 13:49:48 2008  polynomial 'A' values have 13 factors
Sat Feb  2 10:18:44 2008  100088 relations (23581 full + 76507 combined from 1507071 partial), need 100008
Sat Feb  2 10:18:50 2008  begin with 1530652 relations
Sat Feb  2 10:18:52 2008  reduce to 264655 relations in 12 passes
Sat Feb  2 10:18:52 2008  attempting to read 264655 relations
Sat Feb  2 10:19:02 2008  recovered 264655 relations
Sat Feb  2 10:19:02 2008  recovered 256120 polynomials
Sat Feb  2 10:19:02 2008  attempting to build 100088 cycles
Sat Feb  2 10:19:03 2008  found 100088 cycles in 6 passes
Sat Feb  2 10:19:03 2008  distribution of cycle lengths:
Sat Feb  2 10:19:03 2008     length 1 : 23581
Sat Feb  2 10:19:03 2008     length 2 : 16969
Sat Feb  2 10:19:03 2008     length 3 : 16869
Sat Feb  2 10:19:03 2008     length 4 : 13612
Sat Feb  2 10:19:03 2008     length 5 : 10500
Sat Feb  2 10:19:03 2008     length 6 : 7350
Sat Feb  2 10:19:03 2008     length 7 : 4635
Sat Feb  2 10:19:03 2008     length 9+: 6572
Sat Feb  2 10:19:03 2008  largest cycle: 20 relations
Sat Feb  2 10:19:03 2008  matrix is 99912 x 100088 (28.1 MB) with weight 6958780 (69.53/col)
Sat Feb  2 10:19:03 2008  sparse part has weight 6958780 (69.53/col)
Sat Feb  2 10:19:06 2008  filtering completed in 4 passes
Sat Feb  2 10:19:06 2008  matrix is 96049 x 96113 (27.1 MB) with weight 6726665 (69.99/col)
Sat Feb  2 10:19:06 2008  sparse part has weight 6726665 (69.99/col)
Sat Feb  2 10:19:07 2008  saving the first 48 matrix rows for later
Sat Feb  2 10:19:07 2008  matrix is 96001 x 96113 (17.4 MB) with weight 5308583 (55.23/col)
Sat Feb  2 10:19:07 2008  sparse part has weight 3978156 (41.39/col)
Sat Feb  2 10:19:07 2008  matrix includes 64 packed rows
Sat Feb  2 10:19:07 2008  using block size 21845 for processor cache size 512 kB
Sat Feb  2 10:19:08 2008  commencing Lanczos iteration
Sat Feb  2 10:19:08 2008  memory use: 16.5 MB
Sat Feb  2 10:20:46 2008  lanczos halted after 1520 iterations (dim = 95999)
Sat Feb  2 10:20:47 2008  recovered 16 nontrivial dependencies
Sat Feb  2 10:20:50 2008  prp36 factor: 192974421658293224031417306264104681
Sat Feb  2 10:20:50 2008  prp65 factor: 23788329512941257985749836483187483343956508948136539261231691863
Sat Feb  2 10:20:50 2008  elapsed time 20:31:06

(11·10¹¹²+43)/9 = 1(2)₁₁₁7_<113> = 1392541 · 171740189 · C98

C98 = P42 · P57

P42 = 143286201861700132912700962874088411962741_<42>

P57 = 356669421688691816769551532579943147017949354032325568303_<57>

Number: 12227_112
N=51105806753981743159739057597763445623761010676640079468814415944058025931144285169076386486598523
  ( 98 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=143286201861700132912700962874088411962741 (pp42)
 r2=356669421688691816769551532579943147017949354032325568303 (pp57)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.46 hours.
Scaled time: 1.66 units (timescale=0.676).
Factorization parameters were as follows:
name: 12227_112
n: 51105806753981743159739057597763445623761010676640079468814415944058025931144285169076386486598523
m: 10000000000000000000000
c5: 1100
c0: 43
skew: 0.52
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63799, largePrimes:2296912 encountered
Relations: rels:2612701, finalFF:434420
Max relations in full relation-set: 28
Initial matrix: 112964 x 434420 with sparse part having weight 37514997.
Pruned matrix : 67377 x 68005 with weight 5864456.
Total sieving time: 2.26 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.46 hours.
 --------- CPU info (if available) ----------

(11·10¹³⁸+43)/9 = 1(2)₁₃₇7_<139> = 3 · 353 · 3772770559_<10> · 5375963324383_<13> · 1780869062599870907_<19> · C95

C95 = P37 · P58

P37 = 7463409413579206909424210728917778139_<37>

P58 = 4281227127600524118339409264146075718886687783760343681913_<58>

Sat Feb  2 14:26:10 2008  Msieve v. 1.33
Sat Feb  2 14:26:10 2008  random seeds: 518df1e8 4f66404b
Sat Feb  2 14:26:10 2008  factoring 31952550845804420141668463672712528275349504043112878808043841079538101373805116809050521099907 (95 digits)
Sat Feb  2 14:26:11 2008  searching for 15-digit factors
Sat Feb  2 14:26:13 2008  commencing quadratic sieve (95-digit input)
Sat Feb  2 14:26:14 2008  using multiplier of 3
Sat Feb  2 14:26:14 2008  using 64kb Pentium 4 sieve core
Sat Feb  2 14:26:14 2008  sieve interval: 18 blocks of size 65536
Sat Feb  2 14:26:14 2008  processing polynomials in batches of 6
Sat Feb  2 14:26:14 2008  using a sieve bound of 2119673 (78824 primes)
Sat Feb  2 14:26:14 2008  using large prime bound of 309472258 (28 bits)
Sat Feb  2 14:26:14 2008  using double large prime bound of 1919194993237322 (43-51 bits)
Sat Feb  2 14:26:14 2008  using trial factoring cutoff of 51 bits
Sat Feb  2 14:26:14 2008  polynomial 'A' values have 12 factors
Sat Feb  2 20:59:00 2008  79041 relations (18875 full + 60166 combined from 1164620 partial), need 78920
Sat Feb  2 20:59:05 2008  begin with 1183495 relations
Sat Feb  2 20:59:06 2008  reduce to 207464 relations in 11 passes
Sat Feb  2 20:59:06 2008  attempting to read 207464 relations
Sat Feb  2 20:59:13 2008  recovered 207464 relations
Sat Feb  2 20:59:13 2008  recovered 192697 polynomials
Sat Feb  2 20:59:13 2008  attempting to build 79041 cycles
Sat Feb  2 20:59:13 2008  found 79041 cycles in 5 passes
Sat Feb  2 20:59:13 2008  distribution of cycle lengths:
Sat Feb  2 20:59:13 2008     length 1 : 18875
Sat Feb  2 20:59:13 2008     length 2 : 13735
Sat Feb  2 20:59:13 2008     length 3 : 13435
Sat Feb  2 20:59:13 2008     length 4 : 10830
Sat Feb  2 20:59:13 2008     length 5 : 8231
Sat Feb  2 20:59:13 2008     length 6 : 5366
Sat Feb  2 20:59:13 2008     length 7 : 3632
Sat Feb  2 20:59:13 2008     length 9+: 4937
Sat Feb  2 20:59:13 2008  largest cycle: 19 relations
Sat Feb  2 20:59:14 2008  matrix is 78824 x 79041 (21.5 MB) with weight 5328815 (67.42/col)
Sat Feb  2 20:59:14 2008  sparse part has weight 5328815 (67.42/col)
Sat Feb  2 20:59:15 2008  filtering completed in 3 passes
Sat Feb  2 20:59:15 2008  matrix is 75388 x 75452 (20.7 MB) with weight 5113466 (67.77/col)
Sat Feb  2 20:59:15 2008  sparse part has weight 5113466 (67.77/col)
Sat Feb  2 20:59:16 2008  saving the first 48 matrix rows for later
Sat Feb  2 20:59:16 2008  matrix is 75340 x 75452 (14.2 MB) with weight 4180469 (55.41/col)
Sat Feb  2 20:59:16 2008  sparse part has weight 3274785 (43.40/col)
Sat Feb  2 20:59:16 2008  matrix includes 64 packed rows
Sat Feb  2 20:59:16 2008  using block size 21845 for processor cache size 512 kB
Sat Feb  2 20:59:17 2008  commencing Lanczos iteration
Sat Feb  2 20:59:17 2008  memory use: 13.0 MB
Sat Feb  2 21:00:18 2008  lanczos halted after 1193 iterations (dim = 75337)
Sat Feb  2 21:00:18 2008  recovered 16 nontrivial dependencies
Sat Feb  2 21:00:22 2008  prp37 factor: 7463409413579206909424210728917778139
Sat Feb  2 21:00:22 2008  prp58 factor: 4281227127600524118339409264146075718886687783760343681913
Sat Feb  2 21:00:22 2008  elapsed time 06:34:12

Feb 2, 2008 (2nd)

By Jo Yeong Uk / GGNFS

(11·10¹³⁵+7)/9 = 1(2)₁₃₄3_<136> = 131 · 318423851 · 8863447521283_<13> · C112

C112 = P45 · P68

P45 = 146507265503071162570097163593367631761112907_<45>

P68 = 22563758847479551553339931144774084951879508530066949268898335852143_<68>

Number: 12223_135
N=3305754608214957636859188617439640563208150384163881738373873556942454204082790415027851957410195271119880909701
  ( 112 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=146507265503071162570097163593367631761112907 (pp45)
 r2=22563758847479551553339931144774084951879508530066949268898335852143 (pp68)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.57 hours.
Scaled time: 4.77 units (timescale=1.857).
Factorization parameters were as follows:
n: 3305754608214957636859188617439640563208150384163881738373873556942454204082790415027851957410195271119880909701
m: 1000000000000000000000000000
c5: 11
c0: 7
skew: 0.91
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1150001)
Primes: RFBsize:107126, AFBsize:107064, largePrimes:2237518 encountered
Relations: rels:2366180, finalFF:298235
Max relations in full relation-set: 28
Initial matrix: 214255 x 298235 with sparse part having weight 20597668.
Pruned matrix : 176349 x 177484 with weight 9366601.
Total sieving time: 2.43 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 2.57 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)

(11·10¹¹⁹+43)/9 = 1(2)₁₁₈7_<120> = 7 · 131 · C117

C117 = P31 · P39 · P48

P31 = 7726724306485600711748047366001_<31>

P39 = 125939710672765832787789653955253825423_<39>

P48 = 136969141012293087278356134180738215385520447897_<48>

Number: 12227_119
N=133284866109293590209620743971889010056948988246698170362292499697079849751605476796316490972979522597843208530231431
  ( 117 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=7726724306485600711748047366001 (pp31)
 r2=125939710672765832787789653955253825423 (pp39)
 r3=136969141012293087278356134180738215385520447897 (pp48)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.08 hours.
Scaled time: 2.01 units (timescale=1.860).
Factorization parameters were as follows:
n: 133284866109293590209620743971889010056948988246698170362292499697079849751605476796316490972979522597843208530231431
m: 1000000000000000000000000
c5: 11
c0: 430
skew: 2.08
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 480001)
Primes: RFBsize:49098, AFBsize:49742, largePrimes:1888339 encountered
Relations: rels:1934625, finalFF:187269
Max relations in full relation-set: 28
Initial matrix: 98905 x 187269 with sparse part having weight 16529964.
Pruned matrix : 80942 x 81500 with weight 4822120.
Total sieving time: 1.03 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 1.08 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)

Feb 2, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(11·10¹⁰²+43)/9 = 1(2)₁₀₁7_<103> = 3 · 5351 · 7417 · C95

C95 = P29 · P66

P29 = 15986555733012893316173285293_<29>

P66 = 642111998099621810502419011210481164093871271217524484541221231739_<66>

(11·10¹²²+43)/9 = 1(2)₁₂₁7_<123> = 1553 · 646855673 · 5495588970614054030497_<22> · C89

C89 = P30 · P60

P30 = 202819334939982598056638072887_<30>

P60 = 109156029776505315605230350032970862543603279732264658041597_<60>

(11·10¹⁰⁸+43)/9 = 1(2)₁₀₇7_<109> = 3 · 307 · 5179 · C102

C102 = P44 · P58

P44 = 52998473697593985191483510398970980470758279_<44>

P58 = 4834830709525647808402348659617169367180675927813342017607_<58>

Number: n
N=256238648191114710565285519387936251830970731466532285801786220981002210384462564243979166307059018353
  ( 102 digits)
SNFS difficulty: 109 digits.
Divisors found:
 r1=52998473697593985191483510398970980470758279 (pp44)
 r2=4834830709525647808402348659617169367180675927813342017607 (pp58)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.70 hours.
Scaled time: 1.29 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_2_107_7
n: 256238648191114710565285519387936251830970731466532285801786220981002210384462564243979166307059018353
skew: 0.33
deg: 5
c5: 11000
c0: 43
m: 1000000000000000000000
type: snfs
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 160001)
Primes: RFBsize:78498, AFBsize:78512, largePrimes:3833985 encountered
Relations: rels:3288688, finalFF:209248
Max relations in full relation-set: 48
Initial matrix: 157077 x 209248 with sparse part having weight 8669312.
Pruned matrix : 107179 x 108028 with weight 3135973.
Total sieving time: 0.60 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.03 hours.
Total square root time: 0.03 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,109,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000
total time: 0.70 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(5·10¹⁶⁴+1)/3 = 1(6)₁₆₃7_<165> = 29 · 51109 · 145869523 · 45231717026801_<14> · C137

C137 = P43 · P94

P43 = 4540862105110602564100033680942535811201803_<43>

P94 = 3753249345081429166561888673069600257378807334363856510196087848823616338912185173489836353563_<94>

Number: n
N=17042987722111448842955391614860266963453207743477456801387216880523122192828388238421867929811195976610704666895602314168554390251074089
  ( 137 digits)
SNFS difficulty: 165 digits.
Divisors found:

Sat Feb 02 12:46:52 2008  prp43 factor: 4540862105110602564100033680942535811201803
Sat Feb 02 12:46:52 2008  prp94 factor: 3753249345081429166561888673069600257378807334363856510196087848823616338912185173489836353563
Sat Feb 02 12:46:52 2008  elapsed time 01:14:11 (Msieve 1.33)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 49.04 hours.
Scaled time: 64.34 units (timescale=1.312).
Factorization parameters were as follows:
name: KA_1_6_163_7
n: 17042987722111448842955391614860266963453207743477456801387216880523122192828388238421867929811195976610704666895602314168554390251074089
skew: 1.15
deg: 5
c5: 1
c0: 2
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2000000)
Primes: RFBsize:230209, AFBsize:230077, largePrimes:7364021 encountered
Relations: rels:6905403, finalFF:556912
Max relations in full relation-set: 28
Initial matrix: 460350 x 556912 with sparse part having weight 41875479.
Pruned matrix : 387141 x 389506 with weight 26752549.
Total sieving time: 48.78 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 49.04 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(11·10¹¹⁰+43)/9 = 1(2)₁₀₉7_<111> = 51977 · C106

C106 = P47 · P59

P47 = 81184110247381809060406319688698040691781701091_<47>

P59 = 28964626395377574001973137610529281064629935087612238738761_<59>

Number: n
N=2351467422556558135756627397160709972145799530989134082810131831814499148127483737465075364530892937688251
  ( 106 digits)
SNFS difficulty: 111 digits.
Divisors found:

Sat Feb  2 12:50:25 2008  prp47 factor: 81184110247381809060406319688698040691781701091
Sat Feb  2 12:50:25 2008  prp59 factor: 28964626395377574001973137610529281064629935087612238738761
Sat Feb  2 12:50:25 2008  elapsed time 00:04:27 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-k8
Total time: 0.67 hours.
Scaled time: 0.56 units (timescale=0.836).
Factorization parameters were as follows:
name: KA_1_2_109_7
n: 2351467422556558135756627397160709972145799530989134082810131831814499148127483737465075364530892937688251
type: snfs
deg: 5
c5: 11
c0: 43
skew: 1.31
m: 10000000000000000000000
rlim: 1000000
alim: 1000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [100000, 160001)
Primes: RFBsize:78498, AFBsize:78392, largePrimes:1545266 encountered
Relations: rels:1538936, finalFF:190994
Max relations in full relation-set: 28
Initial matrix: 156955 x 190994 with sparse part having weight 6912098.
Pruned matrix : 119845 x 120693 with weight 3158427.
Total sieving time: 0.60 hours.
Total relation processing time: 0.03 hours.
Total matrix solve time: 0.04 hours, sqrts: 32.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.5,2.5,50000
total time: 0.67 hours.
 --------- CPU info (if available) ----------
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Total of 2 processors activated (12009.47 BogoMIPS).

(11·10¹²³+43)/9 = 1(2)₁₂₂7_<124> = 3² · 71 · 21179 · 38026953214673_<14> · C103

C103 = P36 · P67

P36 = 479001684843585031175534119002948761_<36>

P67 = 4958100159903010190304866660512588272578698548918562249510374124639_<67>

(11·10¹⁵¹+43)/9 = 1(2)₁₅₀7_<152> = 14454331 · 637792399301914965087547_<24> · 235218918106668005373009596143_<30> · C91

C91 = P42 · P49

P42 = 919097914080506766975348639423129323618987_<42>

P49 = 6132517724267022835952150979164863488281978181871_<49>

Number: n
N=5636384248435557042913746716336205772629431650068022004880943778426067540786043932194784677
  ( 91 digits)
Divisors found:
 r1=919097914080506766975348639423129323618987 (pp42)
 r2=6132517724267022835952150979164863488281978181871 (pp49)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.32 hours.
Scaled time: 4.80 units (timescale=1.445).
Factorization parameters were as follows:
name: KA_1_2_150_7
n:  5636384248435557042913746716336205772629431650068022004880943778426067540786043932194784677
m:  829092521266817765468
deg: 4
c4: 11928576
c3: 32904998720
c2: -68584145541624839
c1: -89054554649160018
c0: 84172890122121959585421
skew: 1635.250
type: gnfs
# adj. I(F,S) = 51.742
# E(F1,F2) = 1.402664e-04
# GGNFS version 0.77.1-20051202-athlon polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=58.00000000, seed=1201912733.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 700000
alim: 700000
lpbr: 27
lpba: 27
mfbr: 44
mfba: 44
rlambda: 2.4
alambda: 2.4
qintsize: 20000

type: gnfs
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 44/44
Sieved algebraic special-q in [100000, 600001)
Primes: RFBsize:56543, AFBsize:56816, largePrimes:2612032 encountered
Relations: rels:2297204, finalFF:127409
Max relations in full relation-set: 28
Initial matrix: 113435 x 127409 with sparse part having weight 9286207.
Pruned matrix : 107888 x 108519 with weight 6627776.
Total sieving time: 3.02 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.15 hours.
Total square root time: 0.07 hours, sqrts: 3.
Prototype def-par.txt line would be:
gnfs,90,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,700000,700000,27,27,44,44,2.4,2.4,40000
total time: 3.32 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(11·10¹⁴⁷+7)/9 = 1(2)₁₄₆3_<148> = 41 · 359 · 17987 · C139

C139 = P59 · P80

P59 = 60639450252175372852507882819631652825439122617058853904357_<59>

P80 = 76130359457876522538422881892238302321490455243664764661805980418638409324517663_<80>

Number: n
N=4616503145026132276328029386285299255606452544697679073230547318885072673351337200374052419135004823660330017098096533201835850513359157691
  ( 139 digits)
SNFS difficulty: 148 digits.
Divisors found:

Sat Feb 02 15:21:37 2008  prp59 factor: 60639450252175372852507882819631652825439122617058853904357
Sat Feb 02 15:21:37 2008  prp80 factor: 76130359457876522538422881892238302321490455243664764661805980418638409324517663
Sat Feb 02 15:21:37 2008  elapsed time 01:02:11 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 12.68 hours.
Scaled time: 22.27 units (timescale=1.756).
Factorization parameters were as follows:
name: KA_1_2_146_3
n: 4616503145026132276328029386285299255606452544697679073230547318885072673351337200374052419135004823660330017098096533201835850513359157691
type: snfs
skew: 0.36
deg: 5
c5: 1100
c0: 7
m: 100000000000000000000000000000
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1799990)
Primes: RFBsize:183072, AFBsize:182582, largePrimes:6521885 encountered
Relations: rels:5914180, finalFF:433290
Max relations in full relation-set: 28
Initial matrix: 365721 x 433290 with sparse part having weight 25005284.
Pruned matrix : 
Total sieving time: 12.49 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.3,2.3,100000
total time: 12.68 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(11·10¹²⁹+43)/9 = 1(2)₁₂₈7_<130> = 3 · 17 · 2269 · 8629 · 1012261 · C115

C115 = P33 · P82

P33 = 137168336280987058909192029624923_<33>

P82 = 8815331708024940951855441988686640906430791155889863737109891988891471546179563959_<82>

(11·10¹²⁰+43)/9 = 1(2)₁₁₉7_<121> = 3 · 2939 · C117

C117 = P53 · P65

P53 = 10360202665625776591605886682977757294938234539486161_<53>

P65 = 13380153130697716154258396236743209165877691612680584935690556371_<65>

Number: n
N=138621098131135558832054238655123309767746651040288331884112761962370672816402656484316913034163799730318954544881731
  ( 117 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=10360202665625776591605886682977757294938234539486161 (pp53)
 r2=13380153130697716154258396236743209165877691612680584935690556371 (pp65)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.28 hours.
Scaled time: 2.34 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_2_119_7
n: 138621098131135558832054238655123309767746651040288331884112761962370672816402656484316913034163799730318954544881731
skew: 1.31
deg: 5
c5: 11
c0: 43
m: 1000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 220001)
Primes: RFBsize:114155, AFBsize:113573, largePrimes:4315307 encountered
Relations: rels:3788011, finalFF:272120
Max relations in full relation-set: 48
Initial matrix: 227793 x 272120 with sparse part having weight 10596266.
Pruned matrix : 179876 x 181078 with weight 5024465.
Total sieving time: 1.10 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.09 hours.
Total square root time: 0.03 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,50000
total time: 1.28 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(11·10¹⁶⁷+7)/9 = 1(2)₁₆₆3_<168> = 3 · 41 · 79 · C164

C164 = P38 · P40 · P87

P38 = 14423979966512432432545987637860750601_<38>

P40 = 2524959991453561105199033616344355110857_<40>

P87 = 345365030444882216665762967853873494551988141411835789407073140545858646627934040752067_<87>

(11·10¹⁴⁸+7)/9 = 1(2)₁₄₇3_<149> = 17² · 1241573 · 1620767868131_<13> · C128

C128 = P61 · P67

P61 = 9977951392526419577166133150855561477582761570070861812038027_<61>

P67 = 2106288571161423902638665809382880013459521046170628246982291811907_<67>

Number: n
N=21016444981682612225056203512237555804076311423045693833897029194807082815809370173856574425843518830726347224042488806215387489
  ( 128 digits)
SNFS difficulty: 149 digits.
Divisors found:

Sat Feb  2 23:03:45 2008  prp61 factor: 9977951392526419577166133150855561477582761570070861812038027
Sat Feb  2 23:03:45 2008  prp67 factor: 2106288571161423902638665809382880013459521046170628246982291811907
Sat Feb  2 23:03:45 2008  elapsed time 00:35:31 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 21.00 hours.
Scaled time: 17.45 units (timescale=0.831).
Factorization parameters were as follows:
name: KA_1_2_147_3
n: 21016444981682612225056203512237555804076311423045693833897029194807082815809370173856574425843518830726347224042488806215387489
type: snfs
deg: 5
c5: 11000
c0: 7
skew: 0.23
m: 100000000000000000000000000000
rlim: 2500000
alim: 2500000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved  special-q in [100000, 3200001)
Primes: RFBsize:183072, AFBsize:182532, largePrimes:3031135 encountered
Relations: rels:3055901, finalFF:404994
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 20.86 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,2500000,2500000,26,26,45,45,2.5,2.5,100000
total time: 21.00 hours.
 --------- CPU info (if available) ----------
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Total of 2 processors activated (12009.47 BogoMIPS).

(11·10¹²⁶+43)/9 = 1(2)₁₂₅7_<127> = 3 · 149 · 163 · 142067 · 214141744783562320063_<21> · C96

C96 = P40 · P57

P40 = 1745478423811049629208332776515371425419_<40>

P57 = 315897374831811624279270914479096464615835238536442426593_<57>

Number: n
N=551392051907478892905276839856959560249645709930693432714313355558298115017072124938461681767467
  ( 96 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=1745478423811049629208332776515371425419 (pp40)
 r2=315897374831811624279270914479096464615835238536442426593 (pp57)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.72 hours.
Scaled time: 3.93 units (timescale=1.446).
Factorization parameters were as follows:
name: KA_1_2_125_7
n: 551392051907478892905276839856959560249645709930693432714313355558298115017072124938461681767467
skew: 0.83
deg: 5
c5: 110
c0: 43
m: 10000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 400001)
Primes: RFBsize:114155, AFBsize:114453, largePrimes:4691482 encountered
Relations: rels:4120461, finalFF:271046
Max relations in full relation-set: 28
Initial matrix: 228675 x 271046 with sparse part having weight 12982612.
Pruned matrix : 188205 x 189412 with weight 6833727.
Total sieving time: 2.23 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.35 hours.
Total square root time: 0.05 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,50000
total time: 2.72 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(11·10¹³¹+43)/9 = 1(2)₁₃₀7_<132> = 7 · 19 · C129

C129 = P32 · P48 · P50

P32 = 32415240075876389291454435280241_<32>

P48 = 772883054289567450015728285748118755690584982373_<48>

P50 = 36680521954763531909701891063601113368415398966683_<50>

Number: n
N=28349753841333173597883662813592007973807145936190394697664372879321221423868495390013541969278759
  ( 98 digits)
SNFS difficulty: 132 digits.
Divisors found:

Sun Feb  3 00:04:25 2008  prp48 factor: 772883054289567450015728285748118755690584982373
Sun Feb  3 00:04:25 2008  prp50 factor: 36680521954763531909701891063601113368415398966683
Sun Feb  3 00:04:25 2008  elapsed time 00:05:46 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 3.06 hours.
Scaled time: 2.56 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_1_2_130_7
n: 28349753841333173597883662813592007973807145936190394697664372879321221423868495390013541969278759
type: snfs
deg: 5
c5: 110
c0: 43
skew: 0.83
m: 100000000000000000000000000
rlim: 1500000
alim: 1500000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved  special-q in [100000, 550337)
Primes: RFBsize:114155, AFBsize:114453, largePrimes:1541470 encountered
Relations: rels:1615701, finalFF:252787
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 3.00 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1500000,1500000,25,25,44,44,2.5,2.5,50000
total time: 3.06 hours.
 --------- CPU info (if available) ----------
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Total of 2 processors activated (12009.47 BogoMIPS).

(11·10¹⁵⁸+43)/9 = 1(2)₁₅₇7_<159> = 71 · C157

C157 = P29 · P30 · P98

P29 = 73609322750518380920243244497_<29>

P30 = 699257274423233790983654844817_<30>

P98 = 33444292414172749749400378136524476926764366571801070725522241132909588873350783579759308359249013_<98>

(11·10¹³⁶+43)/9 = 1(2)₁₃₅7_<137> = 17327 · 677426430691_<12> · C121

C121 = P50 · P71

P50 = 15069402715240311151513397026733944991125470105653_<50>

P71 = 69098500671942225559710465911019554432414961727090137082577263863265187_<71>

Number: n
N=1041273133644800638436966964039937301980376146456499962236974820226681909664960757201914741690067877385787858958446802111
  ( 121 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=15069402715240311151513397026733944991125470105653 (pp50)
 r2=69098500671942225559710465911019554432414961727090137082577263863265187 (pp71)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.83 hours.
Scaled time: 7.01 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_2_135_7
n: 1041273133644800638436966964039937301980376146456499962236974820226681909664960757201914741690067877385787858958446802111
skew: 0.83
deg: 5
c5: 110
c0: 43
m: 1000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 650001)
Primes: RFBsize:148933, AFBsize:149531, largePrimes:5785695 encountered
Relations: rels:5177843, finalFF:352761
Max relations in full relation-set: 48
Initial matrix: 298531 x 352761 with sparse part having weight 20544999.
Pruned matrix : 252227 x 253783 with weight 11036455.
Total sieving time: 3.39 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.29 hours.
Total square root time: 0.06 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,75000
total time: 3.83 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Feb 1, 2008 (6th)

The factor table of 122...227 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Feb 1, 2008 (5th)

By Sinkiti Sibata / GGNFS, Msieve

(11·10¹²⁸+7)/9 = 1(2)₁₂₇3_<129> = 3 · 61 · 79 · 38841953 · 3001001404133_<13> · C104

C104 = P47 · P58

P47 = 17820426575258291271812216801778273828263811949_<47>

P58 = 4069927209397961264478571968552512687964124279931746688039_<58>

Number: 12223_128
N=72527839001722245343433093247741785957812868472563178292041549315582239211939650085232450024037863578011
  ( 104 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=17820426575258291271812216801778273828263811949 (pp47)
 r2=4069927209397961264478571968552512687964124279931746688039 (pp58)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 6.18 hours.
Scaled time: 4.18 units (timescale=0.676).
Factorization parameters were as follows:
name: 12223_128
n: 72527839001722245343433093247741785957812868472563178292041549315582239211939650085232450024037863578011
m: 10000000000000000000000000
c5: 11000
c0: 7
skew: 0.23
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1050001)
Primes: RFBsize:63951, AFBsize:63749, largePrimes:1505085 encountered
Relations: rels:1503095, finalFF:170416
Max relations in full relation-set: 28
Initial matrix: 127767 x 170416 with sparse part having weight 12944744.
Pruned matrix : 115378 x 116080 with weight 7079599.
Total sieving time: 5.82 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.22 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 6.18 hours.
 --------- CPU info (if available) ----------

(11·10¹²⁹+7)/9 = 1(2)₁₂₈3_<130> = 1459219821067_<13> · 82785343995961669807_<20> · C98

C98 = P47 · P51

P47 = 36382216950136191665275319616069319317105322207_<47>

P51 = 278090938993464323621253478672588687018603974937181_<51>

Number: 12223_129
N=10117564874327307322152950912916434067947268348447696910741179744918424161798658125524733589278467
  ( 98 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=36382216950136191665275319616069319317105322207 (pp47)
 r2=278090938993464323621253478672588687018603974937181 (pp51)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 5.73 hours.
Scaled time: 3.88 units (timescale=0.676).
Factorization parameters were as follows:
name: 12223_129
n: 10117564874327307322152950912916434067947268348447696910741179744918424161798658125524733589278467
m: 100000000000000000000000000
c5: 11
c0: 70
skew: 1.45
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1000001)
Primes: RFBsize:63951, AFBsize:63989, largePrimes:1484925 encountered
Relations: rels:1479962, finalFF:166211
Max relations in full relation-set: 28
Initial matrix: 128005 x 166211 with sparse part having weight 12291328.
Pruned matrix : 116824 x 117528 with weight 6896601.
Total sieving time: 5.39 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.22 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.73 hours.
 --------- CPU info (if available) ----------

(11·10¹⁴⁵+7)/9 = 1(2)₁₄₄3_<146> = 13 · 31 · 823 · 151593136619_<12> · 28621596899570201856329127192281_<32> · C97

C97 = P34 · P64

P34 = 1738141979248770825019597995643561_<34>

P64 = 4886373338108512536231001803679542238062728247725780926025401273_<64>

Thu Jan 31 09:05:46 2008  Msieve v. 1.30
Thu Jan 31 09:05:46 2008  random seeds: ed732f90 2131a286
Thu Jan 31 09:05:46 2008  factoring 8493210625248353223145884402754220986747232289349364818181442507813118382434252707555080903653153 (97 digits)
Thu Jan 31 09:05:47 2008  commencing quadratic sieve (97-digit input)
Thu Jan 31 09:05:48 2008  using multiplier of 1
Thu Jan 31 09:05:48 2008  using 64kb Pentium 2 sieve core
Thu Jan 31 09:05:48 2008  sieve interval: 18 blocks of size 65536
Thu Jan 31 09:05:48 2008  processing polynomials in batches of 6
Thu Jan 31 09:05:48 2008  using a sieve bound of 2404033 (88167 primes)
Thu Jan 31 09:05:48 2008  using large prime bound of 360604950 (28 bits)
Thu Jan 31 09:05:48 2008  using double large prime bound of 2527301234494800 (43-52 bits)
Thu Jan 31 09:05:48 2008  using trial factoring cutoff of 52 bits
Thu Jan 31 09:05:48 2008  polynomial 'A' values have 13 factors
Fri Feb 01 21:32:16 2008  88420 relations (21239 full + 67181 combined from 1335767 partial), need 88263
Fri Feb 01 21:32:44 2008  begin with 1357006 relations
Fri Feb 01 21:34:37 2008  reduce to 233037 relations in 12 passes
Fri Feb 01 21:34:38 2008  attempting to read 233037 relations
Fri Feb 01 21:35:21 2008  recovered 233037 relations
Fri Feb 01 21:35:21 2008  recovered 220181 polynomials
Fri Feb 01 21:35:54 2008  attempting to build 88420 cycles
Fri Feb 01 21:35:56 2008  found 88420 cycles in 6 passes
Fri Feb 01 21:36:02 2008  distribution of cycle lengths:
Fri Feb 01 21:36:02 2008     length 1 : 21239
Fri Feb 01 21:36:02 2008     length 2 : 15084
Fri Feb 01 21:36:02 2008     length 3 : 14823
Fri Feb 01 21:36:02 2008     length 4 : 12183
Fri Feb 01 21:36:02 2008     length 5 : 9263
Fri Feb 01 21:36:02 2008     length 6 : 6192
Fri Feb 01 21:36:02 2008     length 7 : 4006
Fri Feb 01 21:36:02 2008     length 9+: 5630
Fri Feb 01 21:36:02 2008  largest cycle: 18 relations
Fri Feb 01 21:36:10 2008  matrix is 88167 x 88420 with weight 5866985 (avg 66.35/col)
Fri Feb 01 21:36:58 2008  filtering completed in 3 passes
Fri Feb 01 21:36:58 2008  matrix is 84507 x 84571 with weight 5639170 (avg 66.68/col)
Fri Feb 01 21:37:03 2008  saving the first 48 matrix rows for later
Fri Feb 01 21:37:03 2008  matrix is 84459 x 84571 with weight 4459365 (avg 52.73/col)
Fri Feb 01 21:37:03 2008  matrix includes 64 packed rows
Fri Feb 01 21:37:04 2008  using block size 10922 for processor cache size 256 kB
Fri Feb 01 21:37:07 2008  commencing Lanczos iteration
Fri Feb 01 21:43:24 2008  lanczos halted after 1337 iterations (dim = 84459)
Fri Feb 01 21:43:25 2008  recovered 17 nontrivial dependencies
Fri Feb 01 21:57:06 2008  prp34 factor: 1738141979248770825019597995643561
Fri Feb 01 21:57:06 2008  prp64 factor: 4886373338108512536231001803679542238062728247725780926025401273
Fri Feb 01 21:57:06 2008  elapsed time 36:51:20

Feb 1, 2008 (4th)

By Jo Yeong Uk / GGNFS

(11·10¹²⁷+7)/9 = 1(2)₁₂₆3_<128> = 13 · 41 · 39930894669768828456551609_<26> · C99

C99 = P39 · P61

P39 = 131553635963448102867023745823633166713_<39>

P61 = 4365269589315262899723003685730075290012150262832120397531843_<61>

Number: 12223_127
N=574267086435090699768103539203445300361508173374549994005694693376903137493747861523667279345142059
  ( 99 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=131553635963448102867023745823633166713 (pp39)
 r2=4365269589315262899723003685730075290012150262832120397531843 (pp61)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.18 hours.
Scaled time: 4.05 units (timescale=1.859).
Factorization parameters were as follows:
n: 574267086435090699768103539203445300361508173374549994005694693376903137493747861523667279345142059
m: 10000000000000000000000000
c5: 1100
c0: 7
skew: 0.36
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 950001)
Primes: RFBsize:78498, AFBsize:78502, largePrimes:1568919 encountered
Relations: rels:1614187, finalFF:218469
Max relations in full relation-set: 28
Initial matrix: 157067 x 218469 with sparse part having weight 11091121.
Pruned matrix : 130554 x 131403 with weight 5278948.
Total sieving time: 2.10 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 2.18 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)

(11·10¹³⁰+7)/9 = 1(2)₁₂₉3_<131> = 31 · 857 · 109891 · C121

C121 = P52 · P69

P52 = 6368333907666863327198144994659776908553310493558001_<52>

P69 = 657384875534192380051162907704171430655174054549731898566209496449859_<69>

Number: 12223_130
N=4186446393251757937089321095384294030882377489367556216227186001816279187420481326563415495130071266809768698299004771859
  ( 121 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=6368333907666863327198144994659776908553310493558001 (pp52)
 r2=657384875534192380051162907704171430655174054549731898566209496449859 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.93 hours.
Scaled time: 3.60 units (timescale=1.860).
Factorization parameters were as follows:
n: 4186446393251757937089321095384294030882377489367556216227186001816279187420481326563415495130071266809768698299004771859
m: 100000000000000000000000000
c5: 11
c0: 7
skew: 0.91
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 900001)
Primes: RFBsize:78498, AFBsize:78392, largePrimes:1557066 encountered
Relations: rels:1615830, finalFF:230414
Max relations in full relation-set: 28
Initial matrix: 156955 x 230414 with sparse part having weight 11524693.
Pruned matrix : 122946 x 123794 with weight 5035615.
Total sieving time: 1.87 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 1.93 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)

(11·10¹³²+7)/9 = 1(2)₁₃₁3_<133> = 17 · 41 · 241 · 249729043237740918459457607_<27> · C101

C101 = P35 · P67

P35 = 15627040354064215471639879571774527_<35>

P67 = 1864466429448898434587464768488764084002767058127712202281064401391_<67>

Number: 12223_132
N=29136092131795957409269524543599123164049664084769673527820555195490040265768211379642590850877167057
  ( 101 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=15627040354064215471639879571774527 (pp35)
 r2=1864466429448898434587464768488764084002767058127712202281064401391 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.19 hours.
Scaled time: 5.93 units (timescale=1.858).
Factorization parameters were as follows:
n: 29136092131795957409269524543599123164049664084769673527820555195490040265768211379642590850877167057
m: 100000000000000000000000000
c5: 1100
c0: 7
skew: 0.36
type: snfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [600000, 1250001)
Primes: RFBsize:92938, AFBsize:92875, largePrimes:1687326 encountered
Relations: rels:1749659, finalFF:237564
Max relations in full relation-set: 28
Initial matrix: 185880 x 237564 with sparse part having weight 13207043.
Pruned matrix : 163716 x 164709 with weight 7305591.
Total sieving time: 3.08 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1200000,1200000,25,25,46,46,2.2,2.2,50000
total time: 3.19 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)

(11·10¹³³+7)/9 = 1(2)₁₃₂3_<134> = 13² · 216967 · 274877791810536202415819_<24> · C103

C103 = P49 · P54

P49 = 7288838851121349921757605985046744807118531852797_<49>

P54 = 166368762117567129996632571508461763704342293538361807_<54>

Number: 12223_133
N=1212635096935489162985899520225286878375226922845226590025671623905132630667309062931776714979850924179
  ( 103 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=7288838851121349921757605985046744807118531852797 (pp49)
 r2=166368762117567129996632571508461763704342293538361807 (pp54)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.81 hours.
Scaled time: 7.07 units (timescale=1.858).
Factorization parameters were as follows:
n: 1212635096935489162985899520225286878375226922845226590025671623905132630667309062931776714979850924179
m: 1000000000000000000000000000
c5: 11
c0: 700
skew: 2.29
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1400001)
Primes: RFBsize:107126, AFBsize:106864, largePrimes:2327353 encountered
Relations: rels:2474302, finalFF:297230
Max relations in full relation-set: 28
Initial matrix: 214057 x 297230 with sparse part having weight 23663112.
Pruned matrix : 186367 x 187501 with weight 11941864.
Total sieving time: 3.64 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 3.81 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)

Feb 1, 2008 (3rd)

By Robert Backstrom / GGNFS, GMP-ECM, Msieve

(11·10¹⁴⁰+7)/9 = 1(2)₁₃₉3_<141> = 3 · 3461 · 1095607588589_<13> · 834558173034127_<15> · 4419964196853031_<16> · C94

C94 = P47 · P48

P47 = 23791675036360545008892228841804329617387361131_<47>

P48 = 122425505136829100536474798340818755144635369207_<48>

Number: n
N=2912707834377726580270175322931490941526698320396340756910726140921366521664757928917626093117
  ( 94 digits)
Divisors found:
 r1=23791675036360545008892228841804329617387361131 (pp47)
 r2=122425505136829100536474798340818755144635369207 (pp48)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.46 hours.
Scaled time: 8.16 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_1_2_139_3
n:  2912707834377726580270175322931490941526698320396340756910726140921366521664757928917626093117
m:  4536326114264324860543
deg: 4
c4: 6878280
c3: 33377034
c2: -62303463404508495
c1: -64779800640570195830
c0: -1496909709532791612456
skew: 1635.250
type: gnfs
# adj. I(F,S) = 54.762
# E(F1,F2) = 4.865863e-05
# GGNFS version 0.77.1-20051202-athlon polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1201707937.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [100000, 940001)
Primes: RFBsize:92938, AFBsize:92957, largePrimes:1797298 encountered
Relations: rels:1838774, finalFF:224475
Max relations in full relation-set: 48
Initial matrix: 185979 x 224475 with sparse part having weight 15141846.
Pruned matrix : 161730 x 162723 with weight 8462261.
Polynomial selection time: 0.17 hours.
Total sieving time: 4.09 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.12 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,93,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 4.46 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

6·10¹⁶⁶-1 = 5(9)₁₆₆_<167> = 1415744095201_<13> · 12712979409464320156621733_<26> · C130

C130 = P35 · P38 · P58

P35 = 37154591566665333519909747568949477_<35>

P38 = 64960406415076577673529410226373905391_<38>

P58 = 1381204303898828183886023860415270650257402155513930927929_<58>

Number: n
N=89723592923520817279753844783907710962661690251065459520368194642257369051521960751508285565239
  ( 95 digits)
Divisors found:
 r1=64960406415076577673529410226373905391 (pp38)
 r2=1381204303898828183886023860415270650257402155513930927929 (pp58)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.46 hours.
Scaled time: 9.34 units (timescale=1.446).
Factorization parameters were as follows:
name: KA_5_9_166
n:  89723592923520817279753844783907710962661690251065459520368194642257369051521960751508285565239
m:  5984868794652303062657
deg: 4
c4: 69933960
c3: 104353378371
c2: 1096699571646412484
c1: -848692618763956120
c0: -668297857122058317044800
skew: 1635.250
type: gnfs
# adj. I(F,S) = 55.465
# E(F1,F2) = 3.088979e-05
# GGNFS version 0.77.1-20051202-athlon polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1201785727.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 26
lpba: 26
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 50000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [100000, 1000001)
Primes: RFBsize:92938, AFBsize:93074, largePrimes:2445364 encountered
Relations: rels:2348038, finalFF:215671
Max relations in full relation-set: 28
Initial matrix: 186089 x 215671 with sparse part having weight 14207860.
Pruned matrix : 168592 x 169586 with weight 9112248.
Total sieving time: 5.83 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.42 hours.
Total square root time: 0.10 hours, sqrts: 3.
Prototype def-par.txt line would be:
gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,26,26,45,45,2.4,2.4,60000
total time: 6.46 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(5·10¹⁶⁶-17)/3 = 1(6)₁₆₅1_<167> = 313 · 713279355969704807587_<21> · C143

C143 = P43 · P101

P43 = 6906530378904595777299619718427335413392823_<43>

P101 = 10808982929600989913554744120661733333612409183010564466357031082357367707270870872976077015961379497_<101>

Number: n
N=74652568968350432571858162428041298959592617781581769536102339784684274263627848893862771900886916705702120332595381912452867047041224239150031
  ( 143 digits)
SNFS difficulty: 166 digits.
Divisors found:

Fri Feb  1 15:09:29 2008  prp43 factor: 6906530378904595777299619718427335413392823
Fri Feb  1 15:09:29 2008  prp101 factor: 10808982929600989913554744120661733333612409183010564466357031082357367707270870872976077015961379497
Fri Feb  1 15:09:29 2008  elapsed time 00:49:24 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 46.58 hours.
Scaled time: 39.13 units (timescale=0.840).
Factorization parameters were as follows:
name: KA_1_6_165_1
n: 74652568968350432571858162428041298959592617781581769536102339784684274263627848893862771900886916705702120332595381912452867047041224239150031
type: snfs
deg: 5
c5: 50
c0: -17
skew: 0.81
m: 1000000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3000469)
Primes: RFBsize:216816, AFBsize:217226, largePrimes:5601777 encountered
Relations: rels:5457799, finalFF:447969
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 46.40 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 46.58 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

(11·10¹²⁶+7)/9 = 1(2)₁₂₅3_<127> = 47 · C125

C125 = P34 · P39 · P54

P34 = 2028013358477151338981105966488181_<34>

P39 = 100997020886744923001474572087204796497_<39>

P54 = 126961762538913698290780642666257974194325729545261037_<54>

Number: n
N=12822759782960615911248464548662628250867681715191527970142640677251818434976713082328187389
  ( 92 digits)
Divisors found:
 r1=100997020886744923001474572087204796497 (pp39)
 r2=126961762538913698290780642666257974194325729545261037 (pp54)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.79 hours.
Scaled time: 5.48 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_1_2_125_3
n:  12822759782960615911248464548662628250867681715191527970142640677251818434976713082328187389
m:  828222499879303485153
deg: 4
c4: 27251688
c3: 116985641150
c2: -35161021028079089
c1: -401192335890363161
c0: 14492918840677471284545
skew: 1635.250
type: gnfs
# adj. I(F,S) = 52.000
# E(F1,F2) = 1.265408e-04
# GGNFS version 0.77.1-20051202-athlon polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=58.00000000, seed=1201825203.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 700000
alim: 700000
lpbr: 26
lpba: 26
mfbr: 44
mfba: 44
rlambda: 2.4
alambda: 2.4
qintsize: 50000

type: gnfs
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 44/44
Sieved algebraic special-q in [100000, 650001)
Primes: RFBsize:56543, AFBsize:56107, largePrimes:2044474 encountered
Relations: rels:1905213, finalFF:138257
Max relations in full relation-set: 28
Initial matrix: 112725 x 138257 with sparse part having weight 10597229.
Pruned matrix : 104195 x 104822 with weight 6271740.
Total sieving time: 3.55 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.13 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,91,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,700000,700000,26,26,44,44,2.4,2.4,40000
total time: 3.79 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

7·10¹⁹²+3 = 7(0)₁₉₁3_<193> = 31 · 1105109 · 1243211 · 4470822866051487481_<19> · 5290673163123042490177645270463_<31> · C130

C130 = P39 · P92

P39 = 360922089125386739265100361213804922199_<39>

P92 = 19251941213231301805507821363673906075280686340797762406923312617295075302212157369103874171_<92>

9·10¹⁶⁵+7 = 9(0)₁₆₄7_<166> = 43 · 23131 · 1418088383_<10> · 35942958881_<11> · C141

C141 = P45 · P47 · P49

P45 = 316632999964816314980011979278660259022505001_<45>

P47 = 74603769316589492099122294657235536113237612649_<47>

P49 = 7515287056062349794626336991939024137322161656577_<49>

Number: n
N=177526225727465427375076325956215494327313122747943829679376540302091740288043953526266170975409861004259333830654434655259996183735344107473
  ( 141 digits)
SNFS difficulty: 165 digits.
Divisors found:

Fri Feb 01 18:19:06 2008  prp45 factor: 316632999964816314980011979278660259022505001
Fri Feb 01 18:19:06 2008  prp47 factor: 74603769316589492099122294657235536113237612649
Fri Feb 01 18:19:06 2008  prp49 factor: 7515287056062349794626336991939024137322161656577
Fri Feb 01 18:19:06 2008  elapsed time 01:04:51 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 40.01 hours.
Scaled time: 73.18 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_9_0_164_7
n: 177526225727465427375076325956215494327313122747943829679376540302091740288043953526266170975409861004259333830654434655259996183735344107473
skew: 0.95
deg: 5
c5: 9
c0: 7
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3000791)
Primes: RFBsize:230209, AFBsize:230717, largePrimes:7426505 encountered
Relations: rels:6885081, finalFF:513570
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 39.83 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 40.01 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Feb 1, 2008 (2nd)

By Yousuke Koide

(10¹⁴¹⁷-1)/9 is divisible by 57691258324093633641909137807790199_<35>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 1, 2008

By Robert Backstrom / GGNFS, Msieve

(4·10¹⁶⁵+41)/9 = (4)₁₆₄9_<165> = 5849891987_<10> · 12569892767983_<14> · C142

C142 = P70 · P73

P70 = 1281570790751209261870606118509601319231489235378717382008982025914249_<70>

P73 = 4716235264308885999918029689628367436288591731976079138987327132460971981_<73>

Number: n
N=6044189357049077446644490449750213711247494210862836335124304401771018375433568259682738692991215544680682817617072084546641347382952697657269
  ( 142 digits)
SNFS difficulty: 165 digits.
Divisors found:

Fri Feb 01 03:34:11 2008  prp70 factor: 1281570790751209261870606118509601319231489235378717382008982025914249
Fri Feb 01 03:34:11 2008  prp73 factor: 4716235264308885999918029689628367436288591731976079138987327132460971981
Fri Feb 01 03:34:11 2008  elapsed time 01:59:28 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 60.53 hours.
Scaled time: 106.11 units (timescale=1.753).
Factorization parameters were as follows:
name: KA_4_164_9
n: 6044189357049077446644490449750213711247494210862836335124304401771018375433568259682738692991215544680682817617072084546641347382952697657269
type: snfs
skew: 1.59
deg: 5
c5: 4
c0: 41
m: 1000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2900119)
Primes: RFBsize:230209, AFBsize:230843, largePrimes:7459245 encountered
Relations: rels:6912771, finalFF:514265
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 60.28 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 60.53 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

January 2008

Jan 31, 2008 (3rd)

By Sinkiti Sibata / GGNFS

(11·10¹⁰⁷+7)/9 = 1(2)₁₀₆3_<108> = 3² · 41 · C105

C105 = P46 · P60

P46 = 1292550447331944890025042849241722436631493391_<46>

P60 = 256257336153707341238146911505259598651293150772733923813137_<60>

Number: 12223_107
N=331225534477566997892201144233664558867810900331225534477566997892201144233664558867810900331225534477567
  ( 105 digits)
SNFS difficulty: 108 digits.
Divisors found:
 r1=1292550447331944890025042849241722436631493391 (pp46)
 r2=256257336153707341238146911505259598651293150772733923813137 (pp60)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.02 hours.
Scaled time: 1.37 units (timescale=0.676).
Factorization parameters were as follows:
name: 12223_107
n: 331225534477566997892201144233664558867810900331225534477566997892201144233664558867810900331225534477567
m: 1000000000000000000000
c5: 1100
c0: 7
skew: 0.36
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:64124, largePrimes:2429252 encountered
Relations: rels:3033429, finalFF:718930
Max relations in full relation-set: 28
Initial matrix: 113289 x 718930 with sparse part having weight 53214391.
Pruned matrix : 57627 x 58257 with weight 4923663.
Total sieving time: 1.84 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,108,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.02 hours.
 --------- CPU info (if available) ----------

(11·10¹¹¹+7)/9 = 1(2)₁₁₀3_<112> = 1666104019_<10> · C102

C102 = P39 · P64

P39 = 235975824491022308928990780915762844819_<39>

P64 = 3108712443286375789320997869432868788061093950925051865679921143_<64>

Number: 12223_111
N=733580981910002956557433418100543110341193062221538415376826614702633534804661090144229597601266108117
  ( 102 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=235975824491022308928990780915762844819 (pp39)
 r2=3108712443286375789320997869432868788061093950925051865679921143 (pp64)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.79 hours.
Scaled time: 1.21 units (timescale=0.676).
Factorization parameters were as follows:
name: 12223_111
n: 733580981910002956557433418100543110341193062221538415376826614702633534804661090144229597601266108117
m: 10000000000000000000000
c5: 110
c0: 7
skew: 0.58
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:64059, largePrimes:2021282 encountered
Relations: rels:2053022, finalFF:193864
Max relations in full relation-set: 28
Initial matrix: 113224 x 193864 with sparse part having weight 15557092.
Pruned matrix : 89133 x 89763 with weight 4789183.
Total sieving time: 1.58 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,112,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.79 hours.
 --------- CPU info (if available) ----------

(11·10¹¹⁴+7)/9 = 1(2)₁₁₃3_<115> = 151 · 122621323170953_<15> · C98

C98 = P43 · P55

P43 = 6707176161219300156417206391262616855238919_<43>

P55 = 9841640960702845903948148581547115321867466062969048439_<55>

Number: 12223_114
N=66009619638905539253901637431935754347497426208831751373830011892396353837800790236691341428997441
  ( 98 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=6707176161219300156417206391262616855238919 (pp43)
 r2=9841640960702845903948148581547115321867466062969048439 (pp55)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.23 hours.
Scaled time: 1.51 units (timescale=0.676).
Factorization parameters were as follows:
name: 12223_114
n: 66009619638905539253901637431935754347497426208831751373830011892396353837800790236691341428997441
m: 100000000000000000000000
c5: 11
c0: 70
skew: 1.45
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63989, largePrimes:2303070 encountered
Relations: rels:2648109, finalFF:464927
Max relations in full relation-set: 28
Initial matrix: 113152 x 464927 with sparse part having weight 38989712.
Pruned matrix : 65830 x 66459 with weight 5847898.
Total sieving time: 2.03 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.23 hours.
 --------- CPU info (if available) ----------

Jan 31, 2008 (2nd)

By Jo Yeong Uk / GMP-ECM, GGNFS

(11·10¹⁴⁹+7)/9 = 1(2)₁₄₈3_<150> = 3 · 5455414187_<10> · C139

C139 = P31 · P109

P31 = 2490019097316894784751546161679_<31>

P109 = 2999152258909011442964542293733101419514316878763530379221746764878442585998011725357379568000480610857964417_<109>

(11·10¹⁵⁰+7)/9 = 1(2)₁₄₉3_<151> = 14281 · 81937 · 44143109464746506290891_<23> · C119

C119 = P32 · P33 · P55

P32 = 68241356669473223079132276622237_<32>

P33 = 151148305752490290170716101146479_<33>

P55 = 2294022325606514181685656134858589548523107480053902263_<55>

Thu Jan 31 18:17:58 2008  
Thu Jan 31 18:17:58 2008  
Thu Jan 31 18:17:58 2008  Msieve v. 1.32
Thu Jan 31 18:17:58 2008  random seeds: 83626f43 2e9ca7e0
Thu Jan 31 18:17:58 2008  factoring 156547195729448570330739228648254921953631297430761643676132908131266366819040570422331 (87 digits)
Thu Jan 31 18:17:59 2008  no P-1/P+1/ECM available, skipping
Thu Jan 31 18:17:59 2008  commencing quadratic sieve (86-digit input)
Thu Jan 31 18:17:59 2008  using multiplier of 3
Thu Jan 31 18:17:59 2008  using 32kb Intel Core sieve core
Thu Jan 31 18:17:59 2008  sieve interval: 19 blocks of size 32768
Thu Jan 31 18:17:59 2008  processing polynomials in batches of 11
Thu Jan 31 18:17:59 2008  using a sieve bound of 1474127 (56333 primes)
Thu Jan 31 18:17:59 2008  using large prime bound of 117930160 (26 bits)
Thu Jan 31 18:17:59 2008  using double large prime bound of 338006235664960 (41-49 bits)
Thu Jan 31 18:17:59 2008  using trial factoring cutoff of 49 bits
Thu Jan 31 18:17:59 2008  polynomial 'A' values have 11 factors
Thu Jan 31 18:56:57 2008  56548 relations (15649 full + 40899 combined from 592255 partial), need 56429
Thu Jan 31 18:56:57 2008  begin with 607904 relations
Thu Jan 31 18:56:57 2008  reduce to 135305 relations in 10 passes
Thu Jan 31 18:56:57 2008  attempting to read 135305 relations
Thu Jan 31 18:56:58 2008  recovered 135305 relations
Thu Jan 31 18:56:58 2008  recovered 114562 polynomials
Thu Jan 31 18:56:58 2008  attempting to build 56548 cycles
Thu Jan 31 18:56:58 2008  found 56548 cycles in 5 passes
Thu Jan 31 18:56:59 2008  distribution of cycle lengths:
Thu Jan 31 18:56:59 2008     length 1 : 15649
Thu Jan 31 18:56:59 2008     length 2 : 10984
Thu Jan 31 18:56:59 2008     length 3 : 10147
Thu Jan 31 18:56:59 2008     length 4 : 7618
Thu Jan 31 18:56:59 2008     length 5 : 5079
Thu Jan 31 18:56:59 2008     length 6 : 3170
Thu Jan 31 18:56:59 2008     length 7 : 1835
Thu Jan 31 18:56:59 2008     length 9+: 2066
Thu Jan 31 18:56:59 2008  largest cycle: 20 relations
Thu Jan 31 18:56:59 2008  matrix is 56333 x 56548 with weight 3176684 (avg 56.18/col)
Thu Jan 31 18:56:59 2008  filtering completed in 3 passes
Thu Jan 31 18:56:59 2008  matrix is 51951 x 52015 with weight 2948955 (avg 56.69/col)
Thu Jan 31 18:57:00 2008  saving the first 48 matrix rows for later
Thu Jan 31 18:57:00 2008  matrix is 51903 x 52015 with weight 2312723 (avg 44.46/col)
Thu Jan 31 18:57:00 2008  matrix includes 64 packed rows
Thu Jan 31 18:57:00 2008  using block size 20806 for processor cache size 4096 kB
Thu Jan 31 18:57:01 2008  commencing Lanczos iteration
Thu Jan 31 18:57:11 2008  lanczos halted after 822 iterations (dim = 51901)
Thu Jan 31 18:57:11 2008  recovered 16 nontrivial dependencies
Thu Jan 31 18:57:11 2008  prp32 factor: 68241356669473223079132276622237
Thu Jan 31 18:57:11 2008  prp55 factor: 2294022325606514181685656134858589548523107480053902263
Thu Jan 31 18:57:11 2008  elapsed time 00:39:13

(11·10¹²²+7)/9 = 1(2)₁₂₁3_<123> = 3 · 41 · 15619 · 1095251 · C110

C110 = P38 · P73

P38 = 48431758142731886716282698692789115637_<38>

P73 = 1199355541668143121502827815414108595405173439839162449118989915332245617_<73>

Number: 12223_122
N=58086897521216703275912831000039986472494161953461626501002431196310592545468815762540152169182614030699413029
  ( 110 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=48431758142731886716282698692789115637 (pp38)
 r2=1199355541668143121502827815414108595405173439839162449118989915332245617 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.53 hours.
Scaled time: 2.85 units (timescale=1.857).
Factorization parameters were as follows:
n: 58086897521216703275912831000039986472494161953461626501002431196310592545468815762540152169182614030699413029
m: 1000000000000000000000000
c5: 1100
c0: 7
skew: 0.36
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [400000, 720001)
Primes: RFBsize:63951, AFBsize:64124, largePrimes:1449343 encountered
Relations: rels:1472423, finalFF:194913
Max relations in full relation-set: 28
Initial matrix: 128142 x 194913 with sparse part having weight 9661941.
Pruned matrix : 101275 x 101979 with weight 3961287.
Total sieving time: 1.48 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,800000,800000,25,25,45,45,2.2,2.2,40000
total time: 1.53 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)

Jan 31, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(85·10¹⁹⁵+41)/9 = 9(4)₁₉₄9_<196> = 11 · 251 · 2161031 · 27117551 · 1356870133_<10> · 1739134559_<10> · 25433652459414927499870617826399_<32> · C129

C129 = P34 · P96

P34 = 7002080819084472935961485898736537_<34>

P96 = 138896476007643400498736213707955873126885773149612346584374896337109150206915149170156100613749_<96>

(11·10¹³⁴+7)/9 = 1(2)₁₃₃3_<135> = 3² · 1909319 · 112657579 · 12870442303_<11> · 35009213055361_<14> · C96

C96 = P45 · P51

P45 = 250936660198033341179351798590647701228125319_<45>

P51 = 558378674753209903140848242317261829328091333759211_<51>

Number: n
N=140117679768374411977764694698883397854653689968283909022051675788789766936274055898866478563309
  ( 96 digits)
Divisors found:
 r1=250936660198033341179351798590647701228125319 (pp45)
 r2=558378674753209903140848242317261829328091333759211 (pp51)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.95 hours.
Scaled time: 10.00 units (timescale=1.438).
Factorization parameters were as follows:
name: KA_1_2_133_3
n:  140117679768374411977764694698883397854653689968283909022051675788789766936274055898866478563309
m:  7035295626774042355948
deg: 4
c4: 57195720
c3: 96456981219
c2: -312182490713950436
c1: -140354032571367830
c0: 208626920336365938460725
skew: 1635.250
type: gnfs
# adj. I(F,S) = 54.220
# E(F1,F2) = 3.549845e-05
# GGNFS version 0.77.1-20051202-athlon polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1201709066.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [100000, 1060001)
Primes: RFBsize:92938, AFBsize:92678, largePrimes:1805383 encountered
Relations: rels:1837680, finalFF:208790
Max relations in full relation-set: 28
Initial matrix: 185697 x 208790 with sparse part having weight 14018467.
Pruned matrix : 172473 x 173465 with weight 9746709.
Total sieving time: 6.36 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.47 hours.
Total square root time: 0.03 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,95,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 6.95 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(11·10¹¹³+7)/9 = 1(2)₁₁₂3_<114> = 3 · 332779 · C108

C108 = P49 · P59

P49 = 2619324426169291429122454074993428764646076844357_<49>

P59 = 46739462714767849044740338669006128168735950121361654313347_<59>

Number: n
N=122425816354820288361767842143707207307975385287956093205222507251781935581093580847171067707820327426732879
  ( 108 digits)
SNFS difficulty: 114 digits.
Divisors found:
 r1=2619324426169291429122454074993428764646076844357 (pp49)
 r2=46739462714767849044740338669006128168735950121361654313347 (pp59)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.28 hours.
Scaled time: 1.86 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_1_2_112_3
n: 122425816354820288361767842143707207307975385287956093205222507251781935581093580847171067707820327426732879
skew: 0.23
deg: 5
c5: 11000
c0: 7
m: 10000000000000000000000
type: snfs
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 200001)
Primes: RFBsize:78498, AFBsize:78252, largePrimes:4124095 encountered
Relations: rels:3582159, finalFF:227837
Max relations in full relation-set: 28
Initial matrix: 156817 x 227837 with sparse part having weight 11132713.
Pruned matrix : 101119 x 101967 with weight 3888696.
Total sieving time: 1.12 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.07 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,114,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000
total time: 1.28 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(11·10¹¹⁷+7)/9 = 1(2)₁₁₆3_<118> = 23 · 41 · 49742129 · C107

C107 = P30 · P78

P30 = 199547644984836153697911566023_<30>

P78 = 130577246643745005872051606673712223079810458974387218354742399714928811490183_<78>

Jan 30, 2008 (4th)

By Sinkiti Sibata / PRIMO

10²⁷³⁰+9 is prime.

Jan 30, 2008 (3rd)

By Tyler Cadigan / GGNFS, Msieve

9·10¹⁷⁰+7 = 9(0)₁₆₉7_<171> = 11593 · C167

C167 = P45 · P51 · P72

P45 = 647317419452212964571902174202614495944617659_<45>

P51 = 439565483361516384512985467534108059954554466647701_<51>

P72 = 272838590381901265341010790500512053115606212399648275844615354818716361_<72>

Number: 90007_170
N=77633054429397049943931682912102130596049340119037350125075476580695247131889933580608988182523936858449064090399378935564564823600448546536703182955231605279047701199
  ( 167 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=647317419452212964571902174202614495944617659
 r2=439565483361516384512985467534108059954554466647701
 r3=272838590381901265341010790500512053115606212399648275844615354818716361
Version: 
Total time: 93.71 hours.
Scaled time: 242.25 units (timescale=2.585).
Factorization parameters were as follows:
n: 77633054429397049943931682912102130596049340119037350125075476580695247131889933580608988182523936858449064090399378935564564823600448546536703182955231605279047701199
m: 10000000000000000000000000000000000
c5: 9
c4: 0
c3: 0
c2: 0
c1: 0
c0: 7
skew: 0.95
type: snfs
Y1: 1
Y0: -10000000000000000000000000000000000
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 7700001)
Primes: rational ideals filtering, algebraic ideals filtering, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 745800 x 746047
Total sieving time: 93.71 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 93.71 hours.
 --------- CPU info (if available) ----------

Jan 30, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(32·10¹⁶⁷-23)/9 = 3(5)₁₆₆3_<168> = 11 · 5867 · 8724407193127_<13> · C150

C150 = P47 · P104

P47 = 35370681682761663696088257679173159323507380621_<47>

P104 = 17853334356291297197483708874035153373989805242165023362167712280044355742973131910508838734976772818507_<104>

Number: n
N=631484606492292083872367262096114628708262907358211747146704361754234279408840465950023789885761252373596395216832756065677361490571843403991001952847
  ( 150 digits)
SNFS difficulty: 168 digits.
Divisors found:

Wed Jan 30 04:47:13 2008  prp47 factor: 35370681682761663696088257679173159323507380621
Wed Jan 30 04:47:13 2008  prp104 factor: 17853334356291297197483708874035153373989805242165023362167712280044355742973131910508838734976772818507
Wed Jan 30 04:47:13 2008  elapsed time 01:47:22 (Msieve 1.33)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 75.58 hours.
Scaled time: 99.02 units (timescale=1.310).
Factorization parameters were as follows:
name: KA_3_5_166_3
n: 631484606492292083872367262096114628708262907358211747146704361754234279408840465950023789885761252373596395216832756065677361490571843403991001952847
skew: 0.75
deg: 5
c5: 100
c0: -23
m: 2000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3600133)
Primes: RFBsize:230209, AFBsize:230357, largePrimes:7604437 encountered
Relations: rels:7042468, finalFF:511197
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 75.25 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 75.58 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

8·10¹⁶⁴-1 = 7(9)₁₆₄_<165> = 12954394367_<11> · 506888062514609_<15> · C141

C141 = P51 · P90

P51 = 136719084005415749015513821637101935561368136069713_<51>

P90 = 891110722536656448479198244649382601120593416934422175200192460737138401437174420855050241_<90>

Number: n
N=121831841732615858077060884495408980012801655561808302844196831596094254357569474806622403580182271741991617248312179184985155377588893450833
  ( 141 digits)
SNFS difficulty: 165 digits.
Divisors found:

Wed Jan 30 06:26:42 2008  prp51 factor: 136719084005415749015513821637101935561368136069713
Wed Jan 30 06:26:42 2008  prp90 factor: 891110722536656448479198244649382601120593416934422175200192460737138401437174420855050241
Wed Jan 30 06:26:42 2008  elapsed time 00:50:07 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 30.94 hours.
Scaled time: 56.59 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_7_9_164
n: 121831841732615858077060884495408980012801655561808302844196831596094254357569474806622403580182271741991617248312179184985155377588893450833
skew: 1.05
deg: 5
c5: 4
c0: -5
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2199990)
Primes: RFBsize:230209, AFBsize:230262, largePrimes:7266385 encountered
Relations: rels:6749996, finalFF:527344
Max relations in full relation-set: 28
Initial matrix: 460535 x 527344 with sparse part having weight 44818095.
Pruned matrix : 
Total sieving time: 30.78 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 30.94 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(88·10¹⁸⁴-7)/9 = 9(7)₁₈₄_<185> = 6277698227_<10> · 177693190297546087_<18> · 242984284590355995633538751051_<30> · C129

C129 = P33 · P97

P33 = 319127484177447982424141312841577_<33>

P97 = 1130385423636183718748628040572882785884593902791426607982038309444292046269569228004421072395199_<97>

Jan 30, 2008

The factor table of 122...223 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Jan 29, 2008 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(28·10¹⁹⁰-1)/9 = 3(1)₁₉₀_<191> = 83 · 197 · 306898684974258906701022611_<27> · 3903025884228757387157019754586401_<34> · C127

C127 = P42 · P85

P42 = 566411654175336073779051055434185692429273_<42>

P85 = 2804416823774290398535475890197371140903510729229348762350392625035735079960933230587_<85>

8·10¹⁶⁶-1 = 7(9)₁₆₆_<167> = 3099809 · 66319073 · 769195169 · C144

C144 = P71 · P74

P71 = 36016936302058360187537361721146449943796609862852885565964670381174623_<71>

P74 = 14046667079478560713957129015435981397074694852066792830046818073901232961_<74>

Number: n
N=505917913457799458734266811971710885068794540173797125115673787463148323314430390867563858141920290003653553739065318013688362034376483144348703
  ( 144 digits)
SNFS difficulty: 167 digits.
Divisors found:

Tue Jan 29 15:17:36 2008  prp71 factor: 36016936302058360187537361721146449943796609862852885565964670381174623
Tue Jan 29 15:17:36 2008  prp74 factor: 14046667079478560713957129015435981397074694852066792830046818073901232961
Tue Jan 29 15:17:36 2008  elapsed time 01:05:44 (Msieve 1.33, sqrts: 5)

Version: GGNFS-0.77.1-20050930-k8
Total time: 47.31 hours.
Scaled time: 39.65 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_7_9_166
n: 505917913457799458734266811971710885068794540173797125115673787463148323314430390867563858141920290003653553739065318013688362034376483144348703
type: snfs
deg: 5
c5: 5
c0: -2
skew: 0.83
m: 2000000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3000317)
Primes: RFBsize:216816, AFBsize:216391, largePrimes:5650975 encountered
Relations: rels:5543339, finalFF:475811
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 47.14 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 47.31 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

2·10²⁰⁰-7 = 1(9)₁₉₉3_<201> = 1301 · 77494184407_<11> · 29804123292653_<14> · 19122300006570627091_<20> · 348311486605878509660662409_<27> · C127

C127 = P36 · P92

P36 = 182349040760987799564918359076342409_<36>

P92 = 54801926834354290860267834669391833266360484125455715191587135759479195271787329085245083573_<92>

5·10¹⁶⁵+9 = 5(0)₁₆₄9_<166> = 521 · 291041 · 51554521 · 247260059 · C142

C142 = P34 · P47 · P62

P34 = 2818939442454687157524932103668483_<34>

P47 = 54054662364681162784830736490034092875986992681_<47>

P62 = 16976121589164324923231167526328949052941343024340689600524177_<62>

Number: n
N=917638520764052206896551340018795507931530546527901174784162865815188938411283681136417866187149051462548537
  ( 108 digits)
Divisors found:

Tue Jan 29 22:25:04 2008  prp47 factor: 54054662364681162784830736490034092875986992681
Tue Jan 29 22:25:04 2008  prp62 factor: 16976121589164324923231167526328949052941343024340689600524177
Tue Jan 29 22:25:04 2008  elapsed time 00:34:55 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 10.53 hours.
Scaled time: 6.85 units (timescale=0.651).
Factorization parameters were as follows:
name: KA_5_0_164_9
n: 917638520764052206896551340018795507931530546527901174784162865815188938411283681136417866187149051462548537
skew: 12661.24
# norm 8.65e+14
c5: 38640
c4: 1501673822
c3: -9563743305193
c2: 326542209276603545
c1: -784249620915261605303
c0: -3465551045340897498365887
# alpha -5.89
Y1: 180905640823
Y0: -473288130946733068878
# Murphy_E 1.29e-09
# M 615124226853032890747798413252407572674371891804947226660272403689813790259428441717994802080173114188169006
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved  special-q in [100000, 1600253)
Primes: RFBsize:183072, AFBsize:182897, largePrimes:4231691 encountered
Relations: rels:4183086, finalFF:395397
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 10.38 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 10.53 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

(5·10¹⁶⁷+31)/9 = (5)₁₆₆9_<167> = 7 · 139 · 599 · 266019989 · 23813862167_<11> · 1214077141347307_<16> · C128

C128 = P34 · P94

P34 = 3086469830114575503416081453035859_<34>

P94 = 4015460952029460285580689768666475042854516300138580007649352832352944445338548114829366485943_<94>

8·10¹⁶⁶-3 = 7(9)₁₆₅7_<167> = 73 · 263 · 4871 · 38923 · 10018333847_<11> · 23260492026164711_<17> · C128

C128 = P29 · P46 · P54

P29 = 18999269464663877966125576661_<29>

P46 = 5307586564792536865694064565220881786182872779_<46>

P54 = 935273344920036478019602994707096223631982392496166617_<54>

Number: n
N=4964044239906161870476855656801449522869998195582208895845589159358843507206718978911380698097818643
  ( 100 digits)
Divisors found:
 r1=5307586564792536865694064565220881786182872779 (pp46)
 r2=935273344920036478019602994707096223631982392496166617 (pp54)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.17 hours.
Scaled time: 7.63 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_7_9_165_7
n: 4964044239906161870476855656801449522869998195582208895845589159358843507206718978911380698097818643
skew: 11740.72
# norm 9.09e+13
c5: 18900
c4: -286790748
c3: -9341293608541
c2: 21518992260573429
c1: 507960725404261725909
c0: -1621065082208637890886413
# alpha -5.89
Y1: 14187730073
Y0: -12130433167648029208
# Murphy_E 3.39e-09
# M 2833834172188564969898722875963018176226523725892070100671241162145110381032161315411329682313695471
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 800001)
Primes: RFBsize:135072, AFBsize:135007, largePrimes:3475063 encountered
Relations: rels:3445984, finalFF:390014
Max relations in full relation-set: 48
Initial matrix: 270160 x 390014 with sparse part having weight 22376727.
Pruned matrix : 161780 x 163194 with weight 7262992.
Total sieving time: 3.89 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.10 hours.
Total square root time: 0.08 hours, sqrts: 3.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 4.17 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jan 29, 2008

By Alban Nonymous / Jan 24, 2008

10¹²⁶⁸+1 is divisible by 1068836516672887538001262066480057_<34>

10¹³⁷⁶+1 is divisible by 8316321056168357161591149746561_<31>

10¹³⁹³+1 is divisible by 2313690662340499476839285921303291_<34>

10¹⁴⁹⁶+1 is divisible by 3112019096332789739503121888657089_<34>

10¹⁵¹³+1 is divisible by 9788270089405071134464024815801247_<34>

10¹⁶⁷⁸+1 is divisible by 204080546955445025527141472026009_<33>

10¹⁷⁰⁹+1 is divisible by 830662208135423938663117541699_<30>

10¹⁷⁴⁵+1 is divisible by 5038152633461836859451917395541171_<34>

10¹⁷⁹²+1 is divisible by 8803929888324104650587958648444417_<34>

10¹⁸³⁹+1 is divisible by 2397103947161858599012200785150611_<34>

10¹⁸⁶²+1 is divisible by 123202615416316140277937805321161_<33>

References: Factorizations of numbers of the form 10ⁿ+1 (Alfred Reich)

Jan 28, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(2·10¹⁶⁴+7)/9 = (2)₁₆₃3_<164> = 59 · 697437560875820935427_<21> · C141

C141 = P48 · P93

P48 = 544113926826738557075513436540781338666336584873_<48>

P93 = 992522360499429901684593984914140940525360628309658561254022439588152781604125217695717239207_<93>

Number: n
N=540045239034688628751879697373871298969883014741235343144711185616205145128356800782052470756952541880048918185633946948049410617464398715711
  ( 141 digits)
SNFS difficulty: 165 digits.
Divisors found:

Mon Jan 28 03:37:34 2008  prp48 factor: 544113926826738557075513436540781338666336584873
Mon Jan 28 03:37:34 2008  prp93 factor: 992522360499429901684593984914140940525360628309658561254022439588152781604125217695717239207
Mon Jan 28 03:37:34 2008  elapsed time 00:57:20 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 37.52 hours.
Scaled time: 68.41 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_2_163_3
n: 540045239034688628751879697373871298969883014741235343144711185616205145128356800782052470756952541880048918185633946948049410617464398715711
skew: 2.04
deg: 5
c5: 1
c0: 35
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2516603)
Primes: RFBsize:250150, AFBsize:249871, largePrimes:7416724 encountered
Relations: rels:6907833, finalFF:557563
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 37.37 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 37.52 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

7·10¹⁹³-3 = 6(9)₁₉₂7_<194> = 135391 · 308941571 · 784047751 · 6463670201813352033221_<22> · 32665964050477191352790761_<26> · C125

C125 = P36 · P42 · P47

P36 = 569756699704183297346120295651615869_<36>

P42 = 296810751027062020613622711817064044961881_<42>

P47 = 59778586616800168827028392336187139434362916103_<47>

Mon Jan 28 09:08:45 2008  
Mon Jan 28 09:08:45 2008  
Mon Jan 28 09:08:45 2008  Msieve v. 1.33
Mon Jan 28 09:08:45 2008  random seeds: eaf4fd80 85d2fd47
Mon Jan 28 09:08:45 2008  factoring 17742927189068736669754163160818939750150478560748635115421055932744873894014336636069743 (89 digits)
Mon Jan 28 09:08:46 2008  searching for 15-digit factors
Mon Jan 28 09:08:47 2008  commencing quadratic sieve (89-digit input)
Mon Jan 28 09:08:47 2008  using multiplier of 23
Mon Jan 28 09:08:47 2008  using 64kb Opteron sieve core
Mon Jan 28 09:08:47 2008  sieve interval: 15 blocks of size 65536
Mon Jan 28 09:08:47 2008  processing polynomials in batches of 7
Mon Jan 28 09:08:47 2008  using a sieve bound of 1543813 (58667 primes)
Mon Jan 28 09:08:47 2008  using large prime bound of 123505040 (26 bits)
Mon Jan 28 09:08:47 2008  using double large prime bound of 367309670191840 (42-49 bits)
Mon Jan 28 09:08:47 2008  using trial factoring cutoff of 49 bits
Mon Jan 28 09:08:47 2008  polynomial 'A' values have 11 factors
Mon Jan 28 10:14:23 2008  58789 relations (15537 full + 43252 combined from 619377 partial), need 58763
Mon Jan 28 10:14:24 2008  begin with 634913 relations
Mon Jan 28 10:14:24 2008  reduce to 142871 relations in 9 passes
Mon Jan 28 10:14:24 2008  attempting to read 142871 relations
Mon Jan 28 10:14:26 2008  recovered 142871 relations
Mon Jan 28 10:14:26 2008  recovered 122497 polynomials
Mon Jan 28 10:14:26 2008  attempting to build 58789 cycles
Mon Jan 28 10:14:26 2008  found 58789 cycles in 6 passes
Mon Jan 28 10:14:27 2008  distribution of cycle lengths:
Mon Jan 28 10:14:27 2008     length 1 : 15537
Mon Jan 28 10:14:27 2008     length 2 : 11431
Mon Jan 28 10:14:27 2008     length 3 : 10411
Mon Jan 28 10:14:27 2008     length 4 : 7960
Mon Jan 28 10:14:27 2008     length 5 : 5547
Mon Jan 28 10:14:27 2008     length 6 : 3403
Mon Jan 28 10:14:27 2008     length 7 : 2090
Mon Jan 28 10:14:27 2008     length 9+: 2410
Mon Jan 28 10:14:27 2008  largest cycle: 18 relations
Mon Jan 28 10:14:27 2008  matrix is 58667 x 58789 (14.5 MB) with weight 3552843 (60.43/col)
Mon Jan 28 10:14:27 2008  sparse part has weight 3552843 (60.43/col)
Mon Jan 28 10:14:28 2008  filtering completed in 3 passes
Mon Jan 28 10:14:28 2008  matrix is 54808 x 54872 (13.6 MB) with weight 3353779 (61.12/col)
Mon Jan 28 10:14:28 2008  sparse part has weight 3353779 (61.12/col)
Mon Jan 28 10:14:29 2008  saving the first 48 matrix rows for later
Mon Jan 28 10:14:29 2008  matrix is 54760 x 54872 (10.2 MB) with weight 2800225 (51.03/col)
Mon Jan 28 10:14:29 2008  sparse part has weight 2340902 (42.66/col)
Mon Jan 28 10:14:29 2008  matrix includes 64 packed rows
Mon Jan 28 10:14:29 2008  using block size 21845 for processor cache size 512 kB
Mon Jan 28 10:14:29 2008  commencing Lanczos iteration
Mon Jan 28 10:14:29 2008  memory use: 9.1 MB
Mon Jan 28 10:14:58 2008  lanczos halted after 868 iterations (dim = 54760)
Mon Jan 28 10:14:58 2008  recovered 18 nontrivial dependencies
Mon Jan 28 10:14:59 2008  prp42 factor: 296810751027062020613622711817064044961881
Mon Jan 28 10:14:59 2008  prp47 factor: 59778586616800168827028392336187139434362916103
Mon Jan 28 10:14:59 2008  elapsed time 01:06:14

8·10¹⁶⁶-7 = 7(9)₁₆₅3_<167> = 189105069674903884763_<21> · C147

C147 = P46 · P102

P46 = 1522772221419401839524691150172700628024852433_<46>

P102 = 277812555442990950898376801343060528596613057168376742703741533699762175389406425410348927877185643467_<102>

Number: n
N=423045242190124065978268840790986080931372264092805157767902165882183318614229422370170273292031889136860171886007619487987078786024585708825505211
  ( 147 digits)
SNFS difficulty: 167 digits.
Divisors found:

Mon Jan 28 11:47:25 2008  prp46 factor: 1522772221419401839524691150172700628024852433
Mon Jan 28 11:47:25 2008  prp102 factor: 277812555442990950898376801343060528596613057168376742703741533699762175389406425410348927877185643467
Mon Jan 28 11:47:25 2008  elapsed time 02:35:34 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 73.65 hours.
Scaled time: 129.10 units (timescale=1.753).
Factorization parameters were as follows:
name: KA_7_9_165_3
n: 423045242190124065978268840790986080931372264092805157767902165882183318614229422370170273292031889136860171886007619487987078786024585708825505211
type: snfs
skew: 1.23
deg: 5
c5: 5
c0: -14
m: 2000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3300001)
Primes: RFBsize:230209, AFBsize:230867, largePrimes:7595197 encountered
Relations: rels:7039683, finalFF:510104
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 73.33 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.6,2.6,100000
total time: 73.65 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(14·10¹⁷⁹-41)/9 = 1(5)₁₇₈1_<180> = 11 · 4208178866231_<13> · 15619110457642458343_<20> · 351430029612999360197_<21> · C126

C126 = P35 · P92

P35 = 20107693569497065346641840555374563_<35>

P92 = 30446770005100168171382797846562982573356796889366415814698830439233930405861605026830253107_<92>

5·10¹⁶⁴-9 = 4(9)₁₆₃1_<165> = 2671 · 77632909 · 12338521168499_<14> · C141

C141 = P34 · P49 · P59

P34 = 4339455695928017012813559346271651_<34>

P49 = 2130438876068504052547916867650293287718131453411_<49>

P59 = 21138920651137598568207584663615217929520666173979820026871_<59>

Number: n
N=45035178353310875346083151105578272111290713326972753456419802659112470613730247332180443661058076304606981
  ( 107 digits)
Divisors found:

Mon Jan 28 16:51:00 2008  prp49 factor: 2130438876068504052547916867650293287718131453411
Mon Jan 28 16:51:00 2008  prp59 factor: 21138920651137598568207584663615217929520666173979820026871
Mon Jan 28 16:51:00 2008  elapsed time 00:37:13 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 8.58 hours.
Scaled time: 7.17 units (timescale=0.836).
Factorization parameters were as follows:
name: KA_4_9_163_1
n: 45035178353310875346083151105578272111290713326972753456419802659112470613730247332180443661058076304606981
skew: 8115.52
# norm 1.71e+15
c5: 154560
c4: 307703758
c3: 145805345482189
c2: -157159415040315452
c1: -3632690209768005682794
c0: -1184546233994452070467176
# alpha -7.03
Y1: 323870616509
Y0: -196286607975166774105
# Murphy_E 1.51e-09
# M 37232403993864362254878977070445837812503056159276185148333904982476946194988434481797403305406657484158305
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved  special-q in [100000, 1300289)
Primes: RFBsize:183072, AFBsize:183409, largePrimes:4088051 encountered
Relations: rels:4006302, finalFF:403691
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 8.44 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 8.58 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

Jan 27, 2008 (3rd)

By Bruce Dodson

(10³⁸¹-1)/9 is divisible by 82548590511975869997227448819484483748713764399174373_<53>, cofactor is prime.

References: The ECMNET Project (Paul Zimmermann)

Jan 27, 2008 (2nd)

By Sinkiti Sibata / PFGW

(43·10¹⁰⁷³²-7)/9, (43·10¹⁵⁹⁷²-7)/9 and (43·10¹⁸¹¹⁴-7)/9 are PRPs.

Jan 27, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

4·10¹⁶⁴-3 = 3(9)₁₆₃7_<165> = 21347 · 59377 · 1751822150967709_<16> · 3934065255006277_<16> · C125

C125 = P36 · P89

P36 = 618354792441051937903025593120469857_<36>

P89 = 74051794299396180801895939838809464335023542105428143074269478481756813823421500448195263_<89>

(46·10¹⁷⁷-1)/9 = 5(1)₁₇₇_<178> = 17 · 23920583 · 143176470892200291319_<21> · 2722757562808167831264949_<25> · C125

C125 = P33 · P93

P33 = 181438620433318013127689602298557_<33>

P93 = 177698711659907069705725103293869509281941495123735028737953271728984627792031730189561210103_<93>

9·10¹⁶⁷-7 = 8(9)₁₆₆3_<168> = 4102069211_<10> · C159

C159 = P73 · P87

P73 = 1475840225808026944863592821406727235005191165802606042142091249608358711_<73>

P87 = 148662072304606973843025284582176600459246392524700966245732210436802333527066765202333_<87>

Number: n
N=219401466359120384914441659331622622883141792996919768450976533267468558077432204495293680211871978578374113151939210418163761206222124856293654573347958072763
  ( 159 digits)
SNFS difficulty: 167 digits.
Divisors found:

Sun Jan 27 14:19:56 2008  prp73 factor: 1475840225808026944863592821406727235005191165802606042142091249608358711
Sun Jan 27 14:19:56 2008  prp87 factor: 148662072304606973843025284582176600459246392524700966245732210436802333527066765202333
Sun Jan 27 14:19:56 2008  elapsed time 01:34:48 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 92.12 hours.
Scaled time: 77.29 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_8_9_166_3
n: 219401466359120384914441659331622622883141792996919768450976533267468558077432204495293680211871978578374113151939210418163761206222124856293654573347958072763
type: snfs
deg: 5
c5: 900
c0: -7
skew: 0.38
m: 1000000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5900001)
Primes: RFBsize:216816, AFBsize:216321, largePrimes:6047622 encountered
Relations: rels:5989690, finalFF:470608
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 91.85 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 92.12 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

7·10¹⁹⁰+1 = 7(0)₁₈₉1_<191> = 29 · 18168419302228497779_<20> · 102557119002802823101_<21> · 73316966906831314464051823_<26> · C125

C125 = P39 · P86

P39 = 355098879311614202406460897590438184483_<39>

P86 = 49758043313543013512337916205691953866857075376389549242886554315519833104914284256879_<86>

Jan 26, 2008 (3rd)

By Sinkiti Sibata / PRIMO

(7·10²²²⁷-1)/3 is prime.

Jan 26, 2008 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

8·10¹⁸⁴-9 = 7(9)₁₈₃1_<185> = 17 · 41 · 53881 · 525199 · 19560201548737_<14> · 47291522362212610363688449301629559_<35> · C124

C124 = P38 · P87

P38 = 16036893578982114464326470006735731329_<38>

P87 = 273414034698599650866625624274832254903897139353621479873467317551382470700435628639391_<87>

3·10¹⁶⁶-7 = 2(9)₁₆₅3_<167> = 25411 · 4718927 · 954512749 · C147

C147 = P54 · P93

P54 = 611255532829942634147397320551746694935812453256656449_<54>

P93 = 428796965068732802120208918501494985696065115728677764830252574676814510715480757019757325969_<93>

Number: n
N=262104517358950568229392646975475073832192212584139002189008516545530131509021579305206164560915839602751144638772767618539909590293230081939024081
  ( 147 digits)
SNFS difficulty: 166 digits.
Divisors found:

Sat Jan 26 19:52:25 2008  prp54 factor: 611255532829942634147397320551746694935812453256656449
Sat Jan 26 19:52:25 2008  prp93 factor: 428796965068732802120208918501494985696065115728677764830252574676814510715480757019757325969
Sat Jan 26 19:52:25 2008  elapsed time 01:02:35 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 65.89 hours.
Scaled time: 55.08 units (timescale=0.836).
Factorization parameters were as follows:
name: KA_2_9_165_3
n: 262104517358950568229392646975475073832192212584139002189008516545530131509021579305206164560915839602751144638772767618539909590293230081939024081
type: snfs
deg: 5
c5: 30
c0: -7
skew: 0.75
m: 1000000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4125767)
Primes: RFBsize:216816, AFBsize:216451, largePrimes:5784372 encountered
Relations: rels:5641483, finalFF:469726
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 65.66 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 65.89 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

Jan 26, 2008

By Robert Backstrom / GMP-ECM

(5·10¹⁷⁷-17)/3 = 1(6)₁₇₆1_<178> = 11 · 187325868787_<12> · 388369379195020879_<18> · 379285042374911888951809_<24> · C124

C124 = P34 · P90

P34 = 8697916583198815476581493494469319_<34>

P90 = 631295035191337832585938232859170493922975996573273470112711910425120192821369762271447597_<90>

Jan 25, 2008 (4th)

By Yousuke Koide

10¹¹⁰³+1 is divisible by 28335885146165932870615739992009_<32>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 25, 2008 (3rd)

By Sinkiti Sibata / PRIMO

(2·10²⁷⁵⁹+61)/9 is prime.

Jan 25, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(16·10¹⁶⁷-1)/3 = 5(3)₁₆₇_<168> = 41 · 1867 · C163

C163 = P50 · P56 · P58

P50 = 40597113862788129876743745080216984123131298311427_<50>

P56 = 90647476731104016968844622707762569866503500594961277609_<56>

P58 = 1893301042298636909272719039593617589762226489198375358373_<58>

Number: n
N=6967396936958121589785796090419393749374022931445168763417682382501382592829677627252973118911692598447141407675458650676490696347777618108264639154158011853284039
  ( 163 digits)
SNFS difficulty: 168 digits.
Divisors found:

Fri Jan 25 16:25:02 2008  prp50 factor: 40597113862788129876743745080216984123131298311427
Fri Jan 25 16:25:02 2008  prp56 factor: 90647476731104016968844622707762569866503500594961277609
Fri Jan 25 16:25:02 2008  prp58 factor: 1893301042298636909272719039593617589762226489198375358373
Fri Jan 25 16:25:02 2008  elapsed time 01:52:38 (Msieve 1.33)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 65.44 hours.
Scaled time: 85.59 units (timescale=1.308).
Factorization parameters were as follows:
name: KA_5_3_167
n: 6967396936958121589785796090419393749374022931445168763417682382501382592829677627252973118911692598447141407675458650676490696347777618108264639154158011853284039
skew: 0.46
deg: 5
c5: 50
c0: -1
m: 2000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3002683)
Primes: RFBsize:230209, AFBsize:230262, largePrimes:7515348 encountered
Relations: rels:6996341, finalFF:506931
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 65.16 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 65.44 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

8·10¹⁶⁶+9 = 8(0)₁₆₅9_<167> = 19 · 233 · C164

C164 = P39 · P125

P39 = 247318002448511232349795071846013961161_<39>

P125 = 73067581878550869883137762289663789192178328142338528983715149951558468070091483340423029109213779504121706037391601196627747_<125>

Number: n
N=18070928393946238988028009939010616670431443415405466455839168737293878473006550711542805511633160153602891348543031398238084481590241698667269030946464874632934267
  ( 164 digits)
SNFS difficulty: 166 digits.
Divisors found:

Fri Jan 25 17:43:51 2008  prp39 factor: 247318002448511232349795071846013961161
Fri Jan 25 17:43:51 2008  prp125 factor: 73067581878550869883137762289663789192178328142338528983715149951558468070091483340423029109213779504121706037391601196627747
Fri Jan 25 17:43:51 2008  elapsed time 01:14:29 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 38.49 hours.
Scaled time: 70.60 units (timescale=1.834).
Factorization parameters were as follows:
name: KA_8_0_165_9
n: 18070928393946238988028009939010616670431443415405466455839168737293878473006550711542805511633160153602891348543031398238084481590241698667269030946464874632934267
skew: 0.65
deg: 5
c5: 80
c0: 9
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2800001)
Primes: RFBsize:250150, AFBsize:249916, largePrimes:7433182 encountered
Relations: rels:6924228, finalFF:559097
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 38.31 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 38.49 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jan 25, 2008

By Robert Backstrom / GMP-ECM

(28·10¹⁷⁹-1)/9 = 3(1)₁₇₉_<180> = 17 · 158980370820846386325091_<24> · 130636323549165510465523960184309_<33> · C123

C123 = P34 · P90

P34 = 7681520532229285847327407805697901_<34>

P90 = 114712818212665930084237933685466980822542837060511859279956130473398076525563656416693357_<90>

Jan 24, 2008

By Robert Backstrom / GGNFS, Msieve

3·10¹⁶⁵-7 = 2(9)₁₆₄3_<166> = 389 · 72612871 · 4893118907011_<13> · C143

C143 = P43 · P45 · P55

P43 = 9586550427068758139277418251508130186850823_<43>

P45 = 763966565598162182661254838642609221002481461_<45>

P55 = 2963709019423440832352969589339376348532317934047934059_<55>

Number: n
N=21705623988186509688790428902323610401675410826005059910283930842779622114834229639699870079593155974739505331652907856358417153429937020853777
  ( 143 digits)
SNFS difficulty: 165 digits.
Divisors found:

Thu Jan 24 15:26:22 2008  prp43 factor: 9586550427068758139277418251508130186850823
Thu Jan 24 15:26:22 2008  prp45 factor: 763966565598162182661254838642609221002481461
Thu Jan 24 15:26:22 2008  prp55 factor: 2963709019423440832352969589339376348532317934047934059
Thu Jan 24 15:26:22 2008  elapsed time 02:15:02 (Msieve 1.33, sqrts: 6)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 49.56 hours.
Scaled time: 86.88 units (timescale=1.753).
Factorization parameters were as follows:
name: KA_2_9_164_3
n: 21705623988186509688790428902323610401675410826005059910283930842779622114834229639699870079593155974739505331652907856358417153429937020853777
type: snfs
skew: 1.18
deg: 5
c5: 3
c0: -7
m: 1000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2400109)
Primes: RFBsize:230209, AFBsize:229717, largePrimes:7315297 encountered
Relations: rels:6790830, finalFF:500470
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 49.24 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 49.56 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jan 23, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

7·10¹⁶⁴+1 = 7(0)₁₆₃1_<165> = 1493 · 4603 · 119429 · 79514415457_<11> · C143

C143 = P61 · P82

P61 = 4011137403054399824497281514214954974908736320403030763817761_<61>

P82 = 2674077881194096559726374285341983014251581688108917524458192840920208139039746043_<82>

Number: n
N=10726093807938100380941104602089661772874937656392292672836679543626950747738348408334379189320094232984694581540360379030131023025802572869723
  ( 143 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=4011137403054399824497281514214954974908736320403030763817761 (pp61)
 r2=2674077881194096559726374285341983014251581688108917524458192840920208139039746043 (pp82)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 51.39 hours.
Scaled time: 93.99 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_7_0_163_1
n: 10726093807938100380941104602089661772874937656392292672836679543626950747738348408334379189320094232984694581540360379030131023025802572869723
skew: 1.07
deg: 5
c5: 7
c0: 10
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3400001)
Primes: RFBsize:250150, AFBsize:250406, largePrimes:7753552 encountered
Relations: rels:7254296, finalFF:580211
Max relations in full relation-set: 48
Initial matrix: 500621 x 580211 with sparse part having weight 54263099.
Pruned matrix : 464913 x 467480 with weight 37063090.
Total sieving time: 48.91 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 2.16 hours.
Total square root time: 0.14 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 51.39 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(4·10¹⁶⁵-31)/9 = (4)₁₆₄1_<165> = 3² · 7 · 79 · 337 · 29959 · 213283087187_<12> · C143

C143 = P43 · P101

P43 = 1430726570423886205441057904508188264305283_<43>

P101 = 28985417905225412247112454549094232344842096588627794290356131149243691637467494402561338794411644631_<101>

Number: n
N=41470207551846257950116491850868348405236653748523626812527085979082127700219902135132902454773983973407894491568655258286753201587180691885573
  ( 143 digits)
SNFS difficulty: 165 digits.
Divisors found:

Wed Jan 23 16:28:15 2008  prp43 factor: 1430726570423886205441057904508188264305283
Wed Jan 23 16:28:15 2008  prp101 factor: 28985417905225412247112454549094232344842096588627794290356131149243691637467494402561338794411644631
Wed Jan 23 16:28:15 2008  elapsed time 00:55:20 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-k8
Total time: 49.93 hours.
Scaled time: 41.89 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_4_164_1
n: 41470207551846257950116491850868348405236653748523626812527085979082127700219902135132902454773983973407894491568655258286753201587180691885573
type: snfs
deg: 5
c5: 4
c0: -31
skew: 1.51
m: 1000000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 100000)
Primes: RFBsize:216816, AFBsize:217657, largePrimes:5723795 encountered
Relations: rels:5649683, finalFF:500595
Max relations in full relation-set: 28
Initial matrix: 434537 x 500595 with sparse part having weight 44325199.
Pruned matrix : 409247 x 411483 with weight 32710677.
Total sieving time: 47.78 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 1.96 hours.
Total square root time: 0.00 hours, sqrts: 32.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 49.93 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

Jan 23, 2008

By JMB / GGNFS, Msieve

(8·10¹⁸¹+7)/3 = 2(6)₁₈₀9_<182> = 73 · 383 · 1063 · 73679 · 808737119 · 238190255383_<12> · 28997879660064605217042319409_<29> · C121

C121 = P49 · P73

P49 = 1081148321083352502456169169103040048126155984589_<49>

P73 = 2016448909088811437437590767002243563539760000671212660803839912919962279_<73>

Jan 22, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve

2·10¹⁶⁴+9 = 2(0)₁₆₃9_<165> = 11 · 17 · 19 · 2124275874910691323_<19> · C143

C143 = P62 · P81

P62 = 67130200642296191884709171155818744379421413745297802772910633_<62>

P81 = 394735263859854699241113017883444812425244047937865162764408227983060854002018867_<81>

Number: n
N=26498657463501774710786304364562173257102193262370047211443501109678795224636984084060517451881873318073703378052692450542514081851319770912811
  ( 143 digits)
SNFS difficulty: 165 digits.
Divisors found:

Tue Jan 22 22:48:01 2008  prp62 factor: 67130200642296191884709171155818744379421413745297802772910633
Tue Jan 22 22:48:01 2008  prp81 factor: 394735263859854699241113017883444812425244047937865162764408227983060854002018867
Tue Jan 22 22:48:01 2008  elapsed time 00:36:37 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-k8
Total time: 30.93 hours.
Scaled time: 25.89 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_2_0_163_9
n: 26498657463501774710786304364562173257102193262370047211443501109678795224636984084060517451881873318073703378052692450542514081851319770912811
type: snfs
deg: 5
c5: 1
c0: 45
skew: 2.14
m: 1000000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 100000)
Primes: RFBsize:216816, AFBsize:216986, largePrimes:5519473 encountered
Relations: rels:5435506, finalFF:523534
Max relations in full relation-set: 28
Initial matrix: 433866 x 523534 with sparse part having weight 39663812.
Pruned matrix : 365732 x 367965 with weight 25276057.
Total sieving time: 29.39 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.38 hours.
Total square root time: 0.01 hours, sqrts: 32.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 30.93 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

Jan 22, 2008 (3rd)

By Jo Yeong Uk / GMP-ECM

(2·10¹⁶⁵+7)/9 = (2)₁₆₄3_<165> = 1867 · 11462603 · 4855604094401_<13> · C142

C142 = P36 · P107

P36 = 135175420835923295308837910165690077_<36>

P107 = 15820453108988154482791229654640228746372406550518557422884079078297050679566535405743149235122673945634099_<107>

Jan 22, 2008 (2nd)

By JMB / GMP-ECM

6·10¹⁶⁷-1 = 5(9)₁₆₇_<168> = 173 · 1559 · 8623 · 92761 · 1458366583_<10> · 919553016868249730947567_<24> · C121

C121 = P34 · P87

P34 = 7293628624498449156699219017293493_<34>

P87 = 284346639497725940029917594329688361811266078086355525897345582582328575687665394870903_<87>

Jan 22, 2008

By Yousuke Koide

(10¹⁷²⁹-1)/9 is divisible by 940468712658622180120548555277_<30>

(10¹⁹¹⁷-1)/9 is divisible by 1510552624688788386453049_<25>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 21, 2008

By Robert Backstrom / GGNFS, Msieve

(86·10¹⁶⁶+31)/9 = 9(5)₁₆₅9_<167> = 3 · 5524823 · 25729399 · 191756229961403_<15> · 170453805976796449_<18> · C121

C121 = P43 · P79

P43 = 4207775080549597799925358625476582357997273_<43>

P79 = 1629213400252065933172781543589693668667463228952759374791851515131060589281919_<79>

Number: n
N=6855363546478120852508823668140569336220438309449632211103825793414564211312811099648902774037863458800459081558030206887
  ( 121 digits)
SNFS difficulty: 167 digits.
Divisors found:

Mon Jan 21 21:03:17 2008  prp43 factor: 4207775080549597799925358625476582357997273
Mon Jan 21 21:03:17 2008  prp79 factor: 1629213400252065933172781543589693668667463228952759374791851515131060589281919
Mon Jan 21 21:03:17 2008  elapsed time 02:50:05 (Msieve 1.33)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 117.31 hours.
Scaled time: 153.56 units (timescale=1.309).
Factorization parameters were as follows:
name: KA_9_5_165_9
n: 6855363546478120852508823668140569336220438309449632211103825793414564211312811099648902774037863458800459081558030206887
skew: 0.51
deg: 5
c5: 860
c0: 31
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5110037)
Primes: RFBsize:230209, AFBsize:230038, largePrimes:7978220 encountered
Relations: rels:7387955, finalFF:484643
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 116.89 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 117.31 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jan 20, 2008 (2nd)

By Sinkiti Sibata / PFGW

8·10¹³⁴⁴⁷-9 is PRP.

Jan 20, 2008

By Robert Backstrom / GGNFS, Msieve

8·10¹⁵⁸+9 = 8(0)₁₅₇9_<159> = 43 · 133397260513579219_<18> · 167167903992258454388890478299_<30> · C111

C111 = P49 · P63

P49 = 2033479913775371639587434065835085127837961461819_<49>

P63 = 410281407262533748598335324491991573466072616789247908444678817_<63>

Number: n
N=834299000663855262700697358741077630803654699409180671446600595711970677159208132513234866970546095185263588123
  ( 111 digits)
Divisors found:

Sun Jan 20 13:47:42 2008  prp49 factor: 2033479913775371639587434065835085127837961461819
Sun Jan 20 13:47:42 2008  prp63 factor: 410281407262533748598335324491991573466072616789247908444678817
Sun Jan 20 13:47:42 2008  elapsed time 00:38:14 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 17.62 hours.
Scaled time: 14.80 units (timescale=0.840).
Factorization parameters were as follows:
name: n
n: 834299000663855262700697358741077630803654699409180671446600595711970677159208132513234866970546095185263588123
skew: 58678.97
# norm 7.16e+15
c5: 1080
c4: 182319978
c3: 218777671087271
c2: 720093217709119301
c1: -192584130922452106377951
c0: 1924021866441673318910186961
# alpha -6.76
Y1: 160325997587
Y0: -3780758800577929514024
# Murphy_E 8.64e-10
# M 33078737459182277151461009133502300498047025913472764694038857216187874729045379963943227488355847412005621263
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1099990)
Primes: RFBsize:230209, AFBsize:230298, largePrimes:8164286 encountered
Relations: rels:9063518, finalFF:1450544
Max relations in full relation-set: 28
Initial matrix: 460588 x 1450544 with sparse part having weight 132062689.
Pruned matrix : 
Total sieving time: 17.36 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 17.62 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

8·10¹⁶⁵+9 = 8(0)₁₆₄9_<166> = 3089 · C163

C163 = P72 · P91

P72 = 314438682222884322729688296198134025767975025422514323112159291576842309_<72>

P91 = 8236374989606056257892776904055137083699957579463131990199160763315628777145426750588217509_<91>

Number: n
N=2589834898025250890255746196179993525412754936872774360634509550016186468112657818064098413726124959533829718355454839753965684687601165425704111362900615085788281
  ( 163 digits)
SNFS difficulty: 165 digits.
Divisors found:

Sun Jan 20 15:06:59 2008  prp72 factor: 314438682222884322729688296198134025767975025422514323112159291576842309
Sun Jan 20 15:06:59 2008  prp91 factor: 8236374989606056257892776904055137083699957579463131990199160763315628777145426750588217509
Sun Jan 20 15:06:59 2008  elapsed time 00:53:55 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 32.69 hours.
Scaled time: 59.79 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_8_0_164_9
n: 2589834898025250890255746196179993525412754936872774360634509550016186468112657818064098413726124959533829718355454839753965684687601165425704111362900615085788281
skew: 1.02
deg: 5
c5: 8
c0: 9
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2399990)
Primes: RFBsize:250150, AFBsize:250351, largePrimes:7431294 encountered
Relations: rels:6960850, finalFF:588566
Max relations in full relation-set: 28
Initial matrix: 500566 x 588566 with sparse part having weight 45969560.
Pruned matrix : 
Total sieving time: 32.52 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 32.69 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

8·10¹⁶²+9 = 8(0)₁₆₁9_<163> = 4339 · 31891930524271969_<17> · C143

C143 = P44 · P100

P44 = 21467718354271832026587974954408013867919721_<44>

P100 = 2692983165965493372324419233124120624401536996288557907855362716504013533241417008457888322335917819_<100>

Number: n
N=57812204139742489271285991377047918106956344241296136018020163264497892626415364960802382490255087006871059445557673759660623134031508745408499
  ( 143 digits)
SNFS difficulty: 162 digits.
Divisors found:

Sun Jan 20 17:58:22 2008  prp44 factor: 21467718354271832026587974954408013867919721
Sun Jan 20 17:58:22 2008  prp100 factor: 2692983165965493372324419233124120624401536996288557907855362716504013533241417008457888322335917819
Sun Jan 20 17:58:22 2008  elapsed time 01:03:41 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 39.20 hours.
Scaled time: 32.89 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_8_0_161_9
n: 57812204139742489271285991377047918106956344241296136018020163264497892626415364960802382490255087006871059445557673759660623134031508745408499
type: snfs
deg: 5
c5: 25
c0: 9
skew: 0.82
m: 200000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3700187)
Primes: RFBsize:216816, AFBsize:216596, largePrimes:5557225 encountered
Relations: rels:5370833, finalFF:450084
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 39.08 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 39.20 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

8·10¹⁵³+9 = 8(0)₁₅₂9_<154> = 47 · 61 · C151

C151 = P53 · P98

P53 = 48895464172194500888865555728935598425504411122071941_<53>

P98 = 57068140361452359856128021667726448531461834024720351768797284045710734038067945628429182751862647_<98>

Number: n
N=2790373212417160795256365538890826648064178583885594698290896407394489012905476107429368678060690617370073247296825950470875479595395884199511684687827
  ( 151 digits)
SNFS difficulty: 153 digits.
Divisors found:

Mon Jan 21 00:02:56 2008  prp53 factor: 48895464172194500888865555728935598425504411122071941
Mon Jan 21 00:02:56 2008  prp98 factor: 57068140361452359856128021667726448531461834024720351768797284045710734038067945628429182751862647
Mon Jan 21 00:02:56 2008  elapsed time 00:50:57 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 21.84 hours.
Scaled time: 38.38 units (timescale=1.757).
Factorization parameters were as follows:
name: KA_8_0_152_9
n: 2790373212417160795256365538890826648064178583885594698290896407394489012905476107429368678060690617370073247296825950470875479595395884199511684687827
type: snfs
skew: 0.51
deg: 5
c5: 250
c0: 9
m: 2000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1199990)
Primes: RFBsize:216816, AFBsize:216231, largePrimes:6128293 encountered
Relations: rels:5616787, finalFF:504996
Max relations in full relation-set: 28
Initial matrix: 433114 x 504996 with sparse part having weight 23765859.
Pruned matrix : 
Total sieving time: 21.68 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 21.84 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jan 19, 2008 (5th)

By Kurt Beschorner / Jan 11, 2008

10⁷²³+1 is divisible by 1432840997383099816903558298765841755281_<40>

By Yousuke Koide / Jan 19, 2008

(10¹⁵¹⁹-1)/9 is divisible by 1949428804182808888625531087089_<31>

By Yousuke Koide / Jan 10, 2008

10¹⁰⁷⁶+1 is divisible by 2943022282018927015773940725270857_<34>

By Yousuke Koide / Jan 14, 2008

10¹⁰⁸⁸+1 is divisible by 6618913490111218105668231761297491201_<37>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 19, 2008 (4th)

By Sinkiti Sibata / PRIMO

8·10²⁸⁶⁵-9 is prime.

Jan 19, 2008 (3rd)

By Robert Backstrom / GGNFS

8·10¹³⁵+9 = 8(0)₁₃₄9_<136> = C136

C136 = P68 · P69

P68 = 14801185105213067737040565827661608911957391220799504238072333395727_<68>

P69 = 540497260397233405983441758896201567297916533811770073388400426116967_<69>

Number: n
N=8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 136 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=14801185105213067737040565827661608911957391220799504238072333395727 (pp68)
 r2=540497260397233405983441758896201567297916533811770073388400426116967 (pp69)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.58 hours.
Scaled time: 6.27 units (timescale=1.752).
Factorization parameters were as follows:
name: KA_8_0_134_9
n: 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
type: snfs
skew: 1.02
deg: 5
c5: 8
c0: 9
m: 1000000000000000000000000000
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 520001)
Primes: RFBsize:114155, AFBsize:114197, largePrimes:4737996 encountered
Relations: rels:4119531, finalFF:278781
Max relations in full relation-set: 28
Initial matrix: 228417 x 278781 with sparse part having weight 12620096.
Pruned matrix : 181742 x 182948 with weight 6381214.
Total sieving time: 3.06 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.35 hours.
Total square root time: 0.05 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.3,2.3,75000
total time: 3.58 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jan 19, 2008 (2nd)

By Jo Yeong Uk / GGNFS

8·10¹⁶¹+9 = 8(0)₁₆₀9_<162> = 7 · 361469 · 2281823 · 93410043703_<11> · 104070924106063664505185233829029_<33> · C107

C107 = P42 · P65

P42 = 379610134970967214429953242481364208742167_<42>

P65 = 37547251435502570973405299828344898136743364461002377728913347569_<65>

Number: 80009_161
N=14253317185219973460389890832990183114112816437488046262223139768008252805218662703888332623114842777242023
  ( 107 digits)
Divisors found:
 r1=379610134970967214429953242481364208742167 (pp42)
 r2=37547251435502570973405299828344898136743364461002377728913347569 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.59 hours.
Scaled time: 22.76 units (timescale=2.150).
Factorization parameters were as follows:
name: 80009_161
n: 14253317185219973460389890832990183114112816437488046262223139768008252805218662703888332623114842777242023
skew: 17252.92
# norm 1.36e+15
c5: 25740
c4: 1525971078
c3: -78399570652366
c2: -924627151537472927
c1: 5307909918257896333150
c0: -6383666319595918601313427
# alpha -6.14
Y1: 1794392251
Y0: -223183169083949077020
# Murphy_E 1.50e-09
# M 3259513081427069279902873066038332939958046926443042510831308470696793387168947203008701013843850761293813
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1440001)
Primes: RFBsize:135072, AFBsize:134778, largePrimes:4529531 encountered
Relations: rels:4544044, finalFF:350991
Max relations in full relation-set: 28
Initial matrix: 269934 x 350991 with sparse part having weight 32490968.
Pruned matrix : 221679 x 223092 with weight 18081436.
Polynomial selection time: 0.55 hours.
Total sieving time: 9.69 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 10.59 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)

8·10¹⁵⁷+9 = 8(0)₁₅₆9_<158> = 11489 · 716402649541_<12> · 10593937852386983_<17> · C126

C126 = P40 · P87

P40 = 3790480017172792738294451504361484879367_<40>

P87 = 242046575091074164088712317063624793945838546238186463919115736744802008317537350438981_<87>

Number: 80009_157
N=917472706107830464548023335426499676786648020601531299604889262480796085192109512368398576216119494573875335431375851279405027
  ( 126 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=3790480017172792738294451504361484879367 (pp40)
 r2=242046575091074164088712317063624793945838546238186463919115736744802008317537350438981 (pp87)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 22.81 hours.
Scaled time: 49.09 units (timescale=2.152).
Factorization parameters were as follows:
n: 917472706107830464548023335426499676786648020601531299604889262480796085192109512368398576216119494573875335431375851279405027
m: 20000000000000000000000000000000
c5: 25
c0: 9
skew: 0.82
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2900001)
Primes: RFBsize:216816, AFBsize:216596, largePrimes:5641343 encountered
Relations: rels:5610183, finalFF:554682
Max relations in full relation-set: 28
Initial matrix: 433476 x 554682 with sparse part having weight 45050664.
Pruned matrix : 370085 x 372316 with weight 28747141.
Total sieving time: 21.92 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.77 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 22.81 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)

Jan 19, 2008

By Sinkiti Sibata / GGNFS

8·10¹⁶⁹-9 = 7(9)₁₆₈1_<170> = 41 · 311 · 6744493062860975247569_<22> · 153259559622294960992443672324849_<33> · C112

C112 = P37 · P76

P37 = 4793749476605961545931498988840397341_<37>

P76 = 1266174380191027066904884727886512981316500532551514322249230638281825634221_<76>

Number: 79991_169
N=6069722772332613766716520417588435051267558844262481968159500137499985223028918430208947236222098739972967006361
  ( 112 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=4793749476605961545931498988840397341 (pp37)
 r2=1266174380191027066904884727886512981316500532551514322249230638281825634221 (pp76)
Version: GGNFS-0.77.1-20060513-k8
Total time: 146.83 hours.
Scaled time: 292.79 units (timescale=1.994).
Factorization parameters were as follows:
name: 79991_169
n: 6069722772332613766716520417588435051267558844262481968159500137499985223028918430208947236222098739972967006361
m: 10000000000000000000000000000000000
c5: 4
c0: -45
skew: 1.62
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 7300001)
Primes: RFBsize:412849, AFBsize:412326, largePrimes:6069244 encountered
Relations: rels:6343174, finalFF:937345
Max relations in full relation-set: 28
Initial matrix: 825239 x 937345 with sparse part having weight 55828427.
Pruned matrix : 731366 x 735556 with weight 41378296.
Total sieving time: 140.28 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 6.01 hours.
Time per square root: 0.26 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 146.83 hours.
 --------- CPU info (if available) ----------

Jan 18, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve

(82·10¹⁶⁶+71)/9 = 9(1)₁₆₅9_<167> = 3 · 7 · 103 · 3559 · 657277553 · C152

C152 = P59 · P94

P59 = 13107171807510682605279428504965984440896588003160354566801_<59>

P94 = 1373817494916889709450680140394462103187938380492405920907074652881504931172026794650480415619_<94>

Number: n
N=18006861938039607305322991457173802411519321448085804024087657304778709212270954053562588283400455269971589526621315846889887965055791590110119179264819
  ( 152 digits)
SNFS difficulty: 167 digits.
Divisors found:

Sat Jan 19 00:19:19 2008  prp59 factor: 13107171807510682605279428504965984440896588003160354566801
Sat Jan 19 00:19:19 2008  prp94 factor: 1373817494916889709450680140394462103187938380492405920907074652881504931172026794650480415619
Sat Jan 19 00:19:19 2008  elapsed time 01:14:13 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 69.08 hours.
Scaled time: 57.96 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_9_1_165_9
n: 18006861938039607305322991457173802411519321448085804024087657304778709212270954053562588283400455269971589526621315846889887965055791590110119179264819
type: snfs
deg: 5
c5: 820
c0: 71
skew: 0.61
m: 1000000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5502187)
Primes: RFBsize:216816, AFBsize:217798, largePrimes:5905376 encountered
Relations: rels:5864793, finalFF:364046
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 68.91 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 69.08 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

Jan 18, 2008 (3rd)

By matsui / GMP-ECM

(5·10²⁰⁰+7)/3 = 1(6)₁₉₉9_<201> = 13 · C200

C200 = P43 · C157

P43 = 1715594718690854847659598110202544048758877_<43>

C157 = [7472926257488112167078933876668962989538550274994875554580903056006003718702207791126018309714959671296814070741865292739422577672509829862325988145378354069_<157>]

Jan 18, 2008 (2nd)

By Sinkiti Sibata / GGNFS

8·10¹⁴⁴+9 = 8(0)₁₄₃9_<145> = 17 · 5659 · C140

C140 = P49 · P92

P49 = 1783403562694297290006912071546504111216735779123_<49>

P92 = 46628531887385325172139496576332321929456019180371596843235469372553694072124836083262715161_<92>

Number: 80009_144
N=83157489891167635104934357556417159548039042441503903204681766680872737856407804330426286082554598089456669750423583464133135141315759383803
  ( 140 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=1783403562694297290006912071546504111216735779123 (pp49)
 r2=46628531887385325172139496576332321929456019180371596843235469372553694072124836083262715161 (pp92)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 17.72 hours.
Scaled time: 11.96 units (timescale=0.675).
Factorization parameters were as follows:
name: 80009_144
n: 83157489891167635104934357556417159548039042441503903204681766680872737856407804330426286082554598089456669750423583464133135141315759383803
m: 100000000000000000000000000000
c5: 4
c0: 45
skew: 1.62
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2350001)
Primes: RFBsize:100021, AFBsize:100108, largePrimes:2772356 encountered
Relations: rels:2756638, finalFF:246870
Max relations in full relation-set: 28
Initial matrix: 200193 x 246870 with sparse part having weight 25827334.
Pruned matrix : 187239 x 188303 with weight 17819215.
Total sieving time: 16.37 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.10 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 17.72 hours.
 --------- CPU info (if available) ----------

Jan 18, 2008

By Jo Yeong Uk / Msieve

8·10¹⁴²+9 = 8(0)₁₄₁9_<143> = 3329 · 29281922233_<11> · 1795510682849862934729054445135297_<34> · C96

C96 = P33 · P63

P33 = 627552504355594804282068645958259_<33>

P63 = 728347356775380943407963675027056892979696390562810902400314219_<63>

Fri Jan 18 00:19:37 2008  
Fri Jan 18 00:19:37 2008  
Fri Jan 18 00:19:37 2008  Msieve v. 1.32
Fri Jan 18 00:19:37 2008  random seeds: 181d3ee3 28f57196
Fri Jan 18 00:19:37 2008  factoring 457076207785168212371453509113670437822360245086692204469952475655630982399330567850785958184721 (96 digits)
Fri Jan 18 00:19:38 2008  no P-1/P+1/ECM available, skipping
Fri Jan 18 00:19:38 2008  commencing quadratic sieve (96-digit input)
Fri Jan 18 00:19:38 2008  using multiplier of 41
Fri Jan 18 00:19:38 2008  using 32kb Intel Core sieve core
Fri Jan 18 00:19:38 2008  sieve interval: 36 blocks of size 32768
Fri Jan 18 00:19:38 2008  processing polynomials in batches of 6
Fri Jan 18 00:19:38 2008  using a sieve bound of 2265589 (83442 primes)
Fri Jan 18 00:19:38 2008  using large prime bound of 339838350 (28 bits)
Fri Jan 18 00:19:38 2008  using double large prime bound of 2271382337631900 (43-52 bits)
Fri Jan 18 00:19:38 2008  using trial factoring cutoff of 52 bits
Fri Jan 18 00:19:38 2008  polynomial 'A' values have 13 factors
Fri Jan 18 04:56:17 2008  84020 relations (20540 full + 63480 combined from 1255479 partial), need 83538
Fri Jan 18 04:56:17 2008  begin with 1276019 relations
Fri Jan 18 04:56:18 2008  reduce to 218047 relations in 13 passes
Fri Jan 18 04:56:18 2008  attempting to read 218047 relations
Fri Jan 18 04:56:20 2008  recovered 218047 relations
Fri Jan 18 04:56:20 2008  recovered 204713 polynomials
Fri Jan 18 04:56:21 2008  attempting to build 84020 cycles
Fri Jan 18 04:56:21 2008  found 84020 cycles in 6 passes
Fri Jan 18 04:56:21 2008  distribution of cycle lengths:
Fri Jan 18 04:56:21 2008     length 1 : 20540
Fri Jan 18 04:56:21 2008     length 2 : 14920
Fri Jan 18 04:56:21 2008     length 3 : 14308
Fri Jan 18 04:56:21 2008     length 4 : 11504
Fri Jan 18 04:56:21 2008     length 5 : 8432
Fri Jan 18 04:56:21 2008     length 6 : 5715
Fri Jan 18 04:56:21 2008     length 7 : 3656
Fri Jan 18 04:56:21 2008     length 9+: 4945
Fri Jan 18 04:56:21 2008  largest cycle: 22 relations
Fri Jan 18 04:56:21 2008  matrix is 83442 x 84020 with weight 5533587 (avg 65.86/col)
Fri Jan 18 04:56:22 2008  filtering completed in 4 passes
Fri Jan 18 04:56:22 2008  matrix is 79418 x 79482 with weight 5234465 (avg 65.86/col)
Fri Jan 18 04:56:23 2008  saving the first 48 matrix rows for later
Fri Jan 18 04:56:23 2008  matrix is 79370 x 79482 with weight 4121997 (avg 51.86/col)
Fri Jan 18 04:56:23 2008  matrix includes 64 packed rows
Fri Jan 18 04:56:23 2008  using block size 31792 for processor cache size 4096 kB
Fri Jan 18 04:56:25 2008  commencing Lanczos iteration
Fri Jan 18 04:56:52 2008  lanczos halted after 1256 iterations (dim = 79365)
Fri Jan 18 04:56:52 2008  recovered 15 nontrivial dependencies
Fri Jan 18 04:56:53 2008  prp33 factor: 627552504355594804282068645958259
Fri Jan 18 04:56:53 2008  prp63 factor: 728347356775380943407963675027056892979696390562810902400314219
Fri Jan 18 04:56:53 2008  elapsed time 04:37:16

Jan 17, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

7·10¹⁶⁴+9 = 7(0)₁₆₃9_<165> = 4967 · 340656502544310619_<18> · C144

C144 = P50 · P95

P50 = 12939677343964955884740014469294611585657994552577_<50>

P95 = 31971554264779842589165734337945281912004539206121203124090877304667512724759902380130148456029_<95>

Number: n
N=413701596371317891466218325717451870444516473623608643198379811850920699346023699901441617183278752045530834118946731942880940904318389213136733
  ( 144 digits)
SNFS difficulty: 165 digits.
Divisors found:

Thu Jan 17 05:01:38 2008  prp50 factor: 12939677343964955884740014469294611585657994552577
Thu Jan 17 05:01:38 2008  prp95 factor: 31971554264779842589165734337945281912004539206121203124090877304667512724759902380130148456029
Thu Jan 17 05:01:38 2008  elapsed time 01:15:29 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 50.52 hours.
Scaled time: 92.41 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_7_0_163_9
n: 413701596371317891466218325717451870444516473623608643198379811850920699346023699901441617183278752045530834118946731942880940904318389213136733
skew: 1.67
deg: 5
c5: 7
c0: 90
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3200001)
Primes: RFBsize:250150, AFBsize:250726, largePrimes:7700483 encountered
Relations: rels:7192174, finalFF:570722
Max relations in full relation-set: 28
Initial matrix: 500942 x 570722 with sparse part having weight 52231117.
Pruned matrix : 
Total sieving time: 50.35 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 50.52 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

8·10¹³⁸+9 = 8(0)₁₃₇9_<139> = C139

C139 = P55 · P85

P55 = 2546678620364651588556275988984437932502588301075923203_<55>

P85 = 3141346511502304521005861647877216134965756685545711187785868781031519564330138156803_<85>

Number: n
N=8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 139 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=2546678620364651588556275988984437932502588301075923203 (pp55)
 r2=3141346511502304521005861647877216134965756685545711187785868781031519564330138156803 (pp85)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.84 hours.
Scaled time: 7.00 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_8_0_137_9
n: 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
skew: 0.51
deg: 5
c5: 250
c0: 9
m: 2000000000000000000000000000
type: snfs
rlim: 2200000
alim: 2200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 600001)
Primes: RFBsize:162662, AFBsize:162140, largePrimes:5837421 encountered
Relations: rels:5298457, finalFF:413705
Max relations in full relation-set: 48
Initial matrix: 324869 x 413705 with sparse part having weight 21736846.
Pruned matrix : 244542 x 246230 with weight 9611405.
Total sieving time: 3.39 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.25 hours.
Total square root time: 0.10 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,2200000,2200000,28,28,48,48,2.5,2.5,75000
total time: 3.84 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(68·10¹⁶⁶+13)/9 = 7(5)₁₆₅7_<167> = 23 · 2477 · 47387 · 270272371 · C150

C150 = P35 · P57 · P59

P35 = 17985186201587473669314610148901419_<35>

P57 = 397989410018895033644398024474036815977092109203982240519_<57>

P59 = 14466558893742234502005420987466649404111592901097703772811_<59>

Number: n
N=5757537239124070718550706302077403581327869498093808787670412687981204498446980968064332802066081638503147134728909
  ( 115 digits)
SNFS difficulty: 168 digits.
Divisors found:

Thu Jan 17 18:45:16 2008  prp57 factor: 397989410018895033644398024474036815977092109203982240519
Thu Jan 17 18:45:16 2008  prp59 factor: 14466558893742234502005420987466649404111592901097703772811
Thu Jan 17 18:45:16 2008  elapsed time 02:21:00 (Msieve 1.33)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 92.58 hours.
Scaled time: 162.30 units (timescale=1.753).
Factorization parameters were as follows:
name: KA_7_5_165_7
n: 5757537239124070718550706302077403581327869498093808787670412687981204498446980968064332802066081638503147134728909

# n: 103550379308220275542310045522274995058308499116008352769830405684729022693055150581242133006534481024514566056854884998045901353617827387408730421871

type: snfs
skew: 0.91
deg: 5
c5: 85
c0: 52
m: 2000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4100263)
Primes: RFBsize:230209, AFBsize:229927, largePrimes:7782959 encountered
Relations: rels:7221963, finalFF:514347
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 92.26 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.6,2.6,100000
total time: 92.58 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

8·10¹⁷¹+9 = 8(0)₁₇₀9_<172> = 1609 · 47441 · 179947 · 2675683 · 717143003 · 8834088052212443456467_<22> · 113402724882979773257549023_<27> · C96

C96 = P47 · P49

P47 = 66045585799722886585090670007395970328026662921_<47>

P49 = 4587394211090038825215575348339222477208606014167_<49>

Number: n
N=302977137965699242280736032700812694716266941721901019359481957770507344407132716999451859601807
  ( 96 digits)
Divisors found:
 r1=66045585799722886585090670007395970328026662921 (pp47)
 r2=4587394211090038825215575348339222477208606014167 (pp49)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.94 hours.
Scaled time: 9.03 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_8_0_170_9
n:  302977137965699242280736032700812694716266941721901019359481957770507344407132716999451859601807
m:  10512455641630070932636
deg: 4
c4: 24808080
c3: 107490494716
c2: 237883365092106694
c1: -567116283863032245
c0: -93029552726751959402373
skew: 1635.250
type: gnfs
# adj. I(F,S) = 54.436
# E(F1,F2) = 3.324346e-05
# GGNFS version 0.77.1-20051202-athlon polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1200539918.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [100000, 1060001)
Primes: RFBsize:92938, AFBsize:93341, largePrimes:1857869 encountered
Relations: rels:1936762, finalFF:252332
Max relations in full relation-set: 48
Initial matrix: 186357 x 252332 with sparse part having weight 18488619.
Pruned matrix : 154570 x 155565 with weight 8634865.
Total sieving time: 4.69 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.11 hours.
Total square root time: 0.06 hours, sqrts: 3.
Prototype def-par.txt line would be:
gnfs,95,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 4.94 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(83·10¹⁶⁶+61)/9 = 9(2)₁₆₅9_<167> = 3 · 131 · 3571 · 20201 · C157

C157 = P78 · P79

P78 = 934362002948337010399886026756338182492289458726612819250096628684686778943023_<78>

P79 = 3481489941299881313436648358877533150389619165412918752742979918506381341113641_<79>

Number: n
N=3252971914797445349054660398728776863568519850605226649656754557340236386460735898302316013890979678288381293137596702958878519747398343478609039579707076743
  ( 157 digits)
SNFS difficulty: 167 digits.
Divisors found:

Thu Jan 17 19:55:51 2008  prp78 factor: 934362002948337010399886026756338182492289458726612819250096628684686778943023
Thu Jan 17 19:55:51 2008  prp79 factor: 3481489941299881313436648358877533150389619165412918752742979918506381341113641
Thu Jan 17 19:55:51 2008  elapsed time 01:31:24 (Msieve 1.33)

Version: GGNFS-0.77.1-20050930-k8
Total time: 119.15 hours.
Scaled time: 99.73 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_9_2_165_9
n: 3252971914797445349054660398728776863568519850605226649656754557340236386460735898302316013890979678288381293137596702958878519747398343478609039579707076743
type: snfs
deg: 5
c5: 830
c0: 61
skew: 0.59
m: 1000000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 8900713)
Primes: RFBsize:216816, AFBsize:216337, largePrimes:6552860 encountered
Relations: rels:6849372, finalFF:293088
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 118.83 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 119.15 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

Jan 17, 2008 (2nd)

By Sinkiti Sibata / Msieve, GGNFS

8·10¹²⁶+9 = 8(0)₁₂₅9_<127> = 401 · 389297 · 232424285281_<12> · 9781973560753067_<16> · C92

C92 = P46 · P46

P46 = 2728784228720769076664362884053977424213249851_<46>

P46 = 8260139316381217641035166733618289230331842561_<46>

Wed Jan 16 20:51:56 2008  Msieve v. 1.30
Wed Jan 16 20:51:56 2008  random seeds: cfffcf7b 8fc00eba
Wed Jan 16 20:51:56 2008  factoring 22540137893577421722479220457850357073538436377154439147119377080504418319859512970688708411 (92 digits)
Wed Jan 16 20:51:57 2008  commencing quadratic sieve (92-digit input)
Wed Jan 16 20:51:57 2008  using multiplier of 1
Wed Jan 16 20:51:57 2008  using 64kb Pentium 4 sieve core
Wed Jan 16 20:51:57 2008  sieve interval: 18 blocks of size 65536
Wed Jan 16 20:51:57 2008  processing polynomials in batches of 6
Wed Jan 16 20:51:57 2008  using a sieve bound of 1787701 (66803 primes)
Wed Jan 16 20:51:57 2008  using large prime bound of 187708605 (27 bits)
Wed Jan 16 20:51:57 2008  using double large prime bound of 780317810587350 (42-50 bits)
Wed Jan 16 20:51:57 2008  using trial factoring cutoff of 50 bits
Wed Jan 16 20:51:57 2008  polynomial 'A' values have 12 factors
Thu Jan 17 03:35:28 2008  67110 relations (16704 full + 50406 combined from 841445 partial), need 66899
Thu Jan 17 03:35:31 2008  begin with 858149 relations
Thu Jan 17 03:35:33 2008  reduce to 171422 relations in 10 passes
Thu Jan 17 03:35:33 2008  attempting to read 171422 relations
Thu Jan 17 03:35:38 2008  recovered 171422 relations
Thu Jan 17 03:35:38 2008  recovered 153847 polynomials
Thu Jan 17 03:35:39 2008  attempting to build 67110 cycles
Thu Jan 17 03:35:39 2008  found 67110 cycles in 6 passes
Thu Jan 17 03:35:39 2008  distribution of cycle lengths:
Thu Jan 17 03:35:39 2008     length 1 : 16704
Thu Jan 17 03:35:39 2008     length 2 : 12264
Thu Jan 17 03:35:39 2008     length 3 : 11271
Thu Jan 17 03:35:39 2008     length 4 : 8988
Thu Jan 17 03:35:39 2008     length 5 : 6855
Thu Jan 17 03:35:39 2008     length 6 : 4505
Thu Jan 17 03:35:39 2008     length 7 : 2786
Thu Jan 17 03:35:39 2008     length 9+: 3737
Thu Jan 17 03:35:39 2008  largest cycle: 23 relations
Thu Jan 17 03:35:39 2008  matrix is 66803 x 67110 with weight 4164343 (avg 62.05/col)
Thu Jan 17 03:35:41 2008  filtering completed in 3 passes
Thu Jan 17 03:35:41 2008  matrix is 63419 x 63483 with weight 3955932 (avg 62.31/col)
Thu Jan 17 03:35:41 2008  saving the first 48 matrix rows for later
Thu Jan 17 03:35:41 2008  matrix is 63371 x 63483 with weight 3075316 (avg 48.44/col)
Thu Jan 17 03:35:41 2008  matrix includes 64 packed rows
Thu Jan 17 03:35:42 2008  using block size 21845 for processor cache size 512 kB
Thu Jan 17 03:35:42 2008  commencing Lanczos iteration
Thu Jan 17 03:36:22 2008  lanczos halted after 1003 iterations (dim = 63369)
Thu Jan 17 03:36:22 2008  recovered 17 nontrivial dependencies
Thu Jan 17 03:36:23 2008  prp46 factor: 2728784228720769076664362884053977424213249851
Thu Jan 17 03:36:23 2008  prp46 factor: 8260139316381217641035166733618289230331842561
Thu Jan 17 03:36:23 2008  elapsed time 06:44:27

8·10¹²¹+9 = 8(0)₁₂₀9_<122> = 107 · 17321 · C116

C116 = P56 · P61

P56 = 39837349575609258121788494808572654717964321457787972441_<56>

P61 = 1083534667380804556636556284146554026394969807509139591856667_<61>

Number: 80009_121
N=43165149321740613063824529351492192233834246905733249089350240402903503769126882337738156966828122310608860618114147
  ( 116 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=39837349575609258121788494808572654717964321457787972441 (pp56)
 r2=1083534667380804556636556284146554026394969807509139591856667 (pp61)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.09 hours.
Scaled time: 1.41 units (timescale=0.675).
Factorization parameters were as follows:
name: 80009_121
n: 43165149321740613063824529351492192233834246905733249089350240402903503769126882337738156966828122310608860618114147
m: 2000000000000000000000000
c5: 5
c0: 18
skew: 1.29
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63758, largePrimes:1975769 encountered
Relations: rels:1935048, finalFF:135159
Max relations in full relation-set: 28
Initial matrix: 112922 x 135159 with sparse part having weight 10397305.
Pruned matrix : 104434 x 105062 with weight 6434318.
Total sieving time: 1.80 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.09 hours.
 --------- CPU info (if available) ----------

8·10¹¹⁷+9 = 8(0)₁₁₆9_<118> = 570407 · 540758209 · 1090020499081_<13> · C92

C92 = P31 · P61

P31 = 8959752026870266003989106938343_<31>

P61 = 2655653222978175541447519201124671928388493948927052821291921_<61>

Wed Jan 16 21:03:16 2008  Msieve v. 1.30
Wed Jan 16 21:03:16 2008  random seeds: 2dab32f1 b486c163
Wed Jan 16 21:03:16 2008  factoring 23793994347243262779610066748319237664501818933229988395230398510229558410776055302151026903 (92 digits)
Wed Jan 16 21:03:17 2008  commencing quadratic sieve (92-digit input)
Wed Jan 16 21:03:18 2008  using multiplier of 7
Wed Jan 16 21:03:18 2008  using 64kb Pentium 2 sieve core
Wed Jan 16 21:03:18 2008  sieve interval: 18 blocks of size 65536
Wed Jan 16 21:03:18 2008  processing polynomials in batches of 6
Wed Jan 16 21:03:18 2008  using a sieve bound of 1777823 (67059 primes)
Wed Jan 16 21:03:18 2008  using large prime bound of 186671415 (27 bits)
Wed Jan 16 21:03:18 2008  using double large prime bound of 772573811846445 (42-50 bits)
Wed Jan 16 21:03:18 2008  using trial factoring cutoff of 50 bits
Wed Jan 16 21:03:18 2008  polynomial 'A' values have 12 factors
Thu Jan 17 09:34:51 2008  67313 relations (18203 full + 49110 combined from 814645 partial), need 67155
Thu Jan 17 09:34:59 2008  begin with 832848 relations
Thu Jan 17 09:35:08 2008  reduce to 165375 relations in 10 passes
Thu Jan 17 09:35:08 2008  attempting to read 165375 relations
Thu Jan 17 09:35:23 2008  recovered 165375 relations
Thu Jan 17 09:35:23 2008  recovered 140039 polynomials
Thu Jan 17 09:35:35 2008  attempting to build 67313 cycles
Thu Jan 17 09:35:36 2008  found 67313 cycles in 5 passes
Thu Jan 17 09:35:39 2008  distribution of cycle lengths:
Thu Jan 17 09:35:39 2008     length 1 : 18203
Thu Jan 17 09:35:39 2008     length 2 : 12779
Thu Jan 17 09:35:39 2008     length 3 : 11589
Thu Jan 17 09:35:39 2008     length 4 : 9025
Thu Jan 17 09:35:39 2008     length 5 : 6318
Thu Jan 17 09:35:39 2008     length 6 : 4096
Thu Jan 17 09:35:39 2008     length 7 : 2477
Thu Jan 17 09:35:39 2008     length 9+: 2826
Thu Jan 17 09:35:39 2008  largest cycle: 18 relations
Thu Jan 17 09:35:40 2008  matrix is 67059 x 67313 with weight 3998972 (avg 59.41/col)
Thu Jan 17 09:35:45 2008  filtering completed in 3 passes
Thu Jan 17 09:35:45 2008  matrix is 62553 x 62617 with weight 3752163 (avg 59.92/col)
Thu Jan 17 09:35:47 2008  saving the first 48 matrix rows for later
Thu Jan 17 09:35:48 2008  matrix is 62505 x 62617 with weight 2858139 (avg 45.64/col)
Thu Jan 17 09:35:48 2008  matrix includes 64 packed rows
Thu Jan 17 09:35:48 2008  using block size 10922 for processor cache size 256 kB
Thu Jan 17 09:35:50 2008  commencing Lanczos iteration
Thu Jan 17 09:38:48 2008  lanczos halted after 990 iterations (dim = 62503)
Thu Jan 17 09:38:49 2008  recovered 16 nontrivial dependencies
Thu Jan 17 09:39:30 2008  prp31 factor: 8959752026870266003989106938343
Thu Jan 17 09:39:30 2008  prp61 factor: 2655653222978175541447519201124671928388493948927052821291921
Thu Jan 17 09:39:30 2008  elapsed time 12:36:14

8·10¹³³+9 = 8(0)₁₃₂9_<134> = 89 · 683 · 48247 · 28063523 · C117

C117 = P57 · P61

P57 = 419570597518623739301843398921438222427110769704939738021_<57>

P61 = 2316656939278359599773662465108090166954145351342952510252907_<61>

Number: 80009_133
N=972001136258687370985823047469769423820780268765457967270853419909277049455757306026026401291609436357811577033677047
  ( 117 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=419570597518623739301843398921438222427110769704939738021 (pp57)
 r2=2316656939278359599773662465108090166954145351342952510252907 (pp61)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 6.79 hours.
Scaled time: 4.59 units (timescale=0.675).
Factorization parameters were as follows:
name: 80009_133
n: 972001136258687370985823047469769423820780268765457967270853419909277049455757306026026401291609436357811577033677047
m: 200000000000000000000000000
c5: 250
c0: 9
skew: 0.51
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:63828, largePrimes:1528267 encountered
Relations: rels:1544425, finalFF:190502
Max relations in full relation-set: 28
Initial matrix: 142393 x 190502 with sparse part having weight 13662880.
Pruned matrix : 125537 x 126312 with weight 7340552.
Total sieving time: 6.39 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.27 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 6.79 hours.
 --------- CPU info (if available) ----------

Jan 17, 2008

By Jo Yeong Uk / GGNFS, GMP-ECM

8·10¹³⁴+9 = 8(0)₁₃₃9_<135> = 59 · 16301584241_<11> · C123

C123 = P41 · P83

P41 = 28571873631885209731492091721987844825451_<41>

P83 = 29111825682462786935908160354061235293752365551347558913693510861695423975494302961_<83>

Number: 80009_134
N=831779404592797152588463117329260488018172917231409494936913348568290837598995454362795783479947855559771496090953957460411
  ( 123 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=28571873631885209731492091721987844825451 (pp41)
 r2=29111825682462786935908160354061235293752365551347558913693510861695423975494302961 (pp83)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.83 hours.
Scaled time: 6.03 units (timescale=2.130).
Factorization parameters were as follows:
n: 831779404592797152588463117329260488018172917231409494936913348568290837598995454362795783479947855559771496090953957460411
m: 1000000000000000000000000000
c5: 4
c0: 45
skew: 1.62
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1200001)
Primes: RFBsize:107126, AFBsize:107233, largePrimes:2282220 encountered
Relations: rels:2420613, finalFF:301201
Max relations in full relation-set: 28
Initial matrix: 214423 x 301201 with sparse part having weight 21861579.
Pruned matrix : 178535 x 179671 with weight 10032422.
Total sieving time: 2.69 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 2.83 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)

8·10¹⁴¹+9 = 8(0)₁₄₀9_<142> = 389 · 32563 · C135

C135 = P55 · P81

P55 = 4990867357422239873844609760866802279933879758965510129_<55>

P81 = 126543531026932811719775808439501974442746850624376305592456058350578392937456103_<81>

Number: 80009_141
N=631561978295267382421119685178985059375115210720259331979527602692569760165128194845080609807825952886897433624217622994919004939367287
  ( 135 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=4990867357422239873844609760866802279933879758965510129 (pp55)
 r2=126543531026932811719775808439501974442746850624376305592456058350578392937456103 (pp81)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.10 hours.
Scaled time: 13.13 units (timescale=2.152).
Factorization parameters were as follows:
n: 631561978295267382421119685178985059375115210720259331979527602692569760165128194845080609807825952886897433624217622994919004939367287
m: 20000000000000000000000000000
c5: 5
c0: 18
skew: 1.29
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:113902, largePrimes:3363009 encountered
Relations: rels:3471113, finalFF:400013
Max relations in full relation-set: 28
Initial matrix: 228123 x 400013 with sparse part having weight 33816000.
Pruned matrix : 169664 x 170868 with weight 12859155.
Total sieving time: 5.93 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.10 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)

8·10¹⁵⁸+9 = 8(0)₁₅₇9_<159> = 43 · 133397260513579219_<18> · C141

C141 = P30 · C111

P30 = 167167903992258454388890478299_<30>

C111 = [834299000663855262700697358741077630803654699409180671446600595711970677159208132513234866970546095185263588123_<111>]

8·10¹⁶¹+9 = 8(0)₁₆₀9_<162> = 7 · 361469 · 2281823 · 93410043703_<11> · C139

C139 = P33 · C107

P33 = 104070924106063664505185233829029_<33>

C107 = [14253317185219973460389890832990183114112816437488046262223139768008252805218662703888332623114842777242023_<107>]

8·10¹⁴³+9 = 8(0)₁₄₂9_<144> = 7 · 383 · C141

C141 = P69 · P72

P69 = 341296326661470018931101663238896398460963020877249035438454385737449_<69>

P72 = 874302175383230664843059392215687849285838943004522735011833597504969961_<72>

Number: 80009_143
N=298396120850428944423722491607609101081685938082804923535994032077582991421111525550167847817978366281238343901529280119358448340171577769489
  ( 141 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=341296326661470018931101663238896398460963020877249035438454385737449 (pp69)
 r2=874302175383230664843059392215687849285838943004522735011833597504969961 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 7.48 hours.
Scaled time: 16.07 units (timescale=2.150).
Factorization parameters were as follows:
n: 298396120850428944423722491607609101081685938082804923535994032077582991421111525550167847817978366281238343901529280119358448340171577769489
m: 100000000000000000000000000000
c5: 2
c0: 225
skew: 2.57
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1250001)
Primes: RFBsize:114155, AFBsize:113882, largePrimes:3338731 encountered
Relations: rels:3372927, finalFF:333484
Max relations in full relation-set: 28
Initial matrix: 228102 x 333484 with sparse part having weight 29484204.
Pruned matrix : 191664 x 192868 with weight 13878389.
Total sieving time: 7.28 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 7.48 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)

Jan 16, 2008 (4th)

By Jo Yeong Uk / GGNFS, GMP-ECM

(64·10¹⁷³-1)/9 = 7(1)₁₇₃_<174> = 3² · 1383089 · 2544133 · 4732520529573831035803_<22> · C139

C139 = P61 · P79

P61 = 1909861565401470161137659936941982422346862092020573206552679_<61>

P79 = 2484337649409539669664989360715143924562307337363563977630662091731238984022991_<79>

Number: 71111_173
N=4744740992087112195864762816440374455308257317012861173239758256887368325321090061827164414472315846815098000336885604806637133029988642889
  ( 139 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=1909861565401470161137659936941982422346862092020573206552679 (pp61)
 r2=2484337649409539669664989360715143924562307337363563977630662091731238984022991 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 130.26 hours.
Scaled time: 279.55 units (timescale=2.146).
Factorization parameters were as follows:
n: 4744740992087112195864762816440374455308257317012861173239758256887368325321090061827164414472315846815098000336885604806637133029988642889
m: 200000000000000000000000000000000000
c5: 1
c0: -50
skew: 2.19
type: snfs
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [4500000, 6500001)
Primes: RFBsize:602489, AFBsize:602205, largePrimes:10863804 encountered
Relations: rels:11191485, finalFF:1513162
Max relations in full relation-set: 28
Initial matrix: 1204758 x 1513162 with sparse part having weight 89597218.
Pruned matrix : 913804 x 919891 with weight 49944003.
Total sieving time: 124.75 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 5.25 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,50,50,2.6,2.6,100000
total time: 130.26 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)

8·10¹¹⁵+9 = 8(0)₁₁₄9_<116> = 23 · 164754409 · 1219038421_<10> · C98

C98 = P45 · P53

P45 = 562467957547373531345562723972322221908786381_<45>

P53 = 30790016732270191561933012796406982113872329442024087_<53>

Number: 80009_115
N=17318397824249470808770799132908237419565642366974059924207959257121120487219216176994046339559147
  ( 98 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=562467957547373531345562723972322221908786381 (pp45)
 r2=30790016732270191561933012796406982113872329442024087 (pp53)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.61 hours.
Scaled time: 1.31 units (timescale=2.147).
Factorization parameters were as follows:
n: 17318397824249470808770799132908237419565642366974059924207959257121120487219216176994046339559147
m: 200000000000000000000000
c5: 1
c0: 36
skew: 2.05
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 390001)
Primes: RFBsize:49098, AFBsize:49231, largePrimes:1769889 encountered
Relations: rels:1784790, finalFF:176199
Max relations in full relation-set: 28
Initial matrix: 98393 x 176199 with sparse part having weight 13245210.
Pruned matrix : 77376 x 77931 with weight 3716378.
Total sieving time: 0.57 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.61 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)

8·10¹⁴²+9 = 8(0)₁₄₁9_<143> = 3329 · 29281922233_<11> · C129

C129 = P34 · C96

P34 = 1795510682849862934729054445135297_<34>

C96 = [457076207785168212371453509113670437822360245086692204469952475655630982399330567850785958184721_<96>]

8·10¹⁷⁵+9 = 8(0)₁₇₄9_<176> = 29 · 9907 · 828349 · 149397358667_<12> · 3432767866354222343_<19> · 75056191036086198203_<20> · C115

C115 = P30 · P86

P30 = 266890443093272218468549330943_<30>

P86 = 32721226544458263861906681169586495852149103259513363783751003948859549712960564477403_<86>

Jan 16, 2008 (3rd)

By Jo Yeong Uk / GGNFS, GMP-ECM

8·10¹⁶⁴-9 = 7(9)₁₆₃1_<165> = 7 · 41 · 1143403361_<10> · 261891714717420247_<18> · 11046278788929908087_<20> · C117

C117 = P39 · P79

P39 = 308636832720759777975330569373913552783_<39>

P79 = 2730380120299666574824672795496309223735144601900062623583012669777090797192599_<79>

Number: 79991_164
N=842695872453016151605622018022638106849233137887964461947572705754837909988138005741669220163798173899089414403453017
  ( 117 digits)
Divisors found:
 r1=308636832720759777975330569373913552783 (pp39)
 r2=2730380120299666574824672795496309223735144601900062623583012669777090797192599 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 32.49 hours.
Scaled time: 69.91 units (timescale=2.152).
Factorization parameters were as follows:
name: 79991_164
n: 842695872453016151605622018022638106849233137887964461947572705754837909988138005741669220163798173899089414403453017
skew: 39822.29
# norm 1.28e+16
c5: 53100
c4: -1234949190
c3: -584057431279291
c2: 113539236838916353
c1: 172914044835050143787073
c0: 1186521124802802637136030280
# alpha -5.74
Y1: 3702589636013
Y0: -27549615417740198203969
# Murphy_E 4.20e-10
# M 398711343419018151458526581075477856479282773180178871103100914140391572713644277776727739442770855281441383627371216
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 3825001)
Primes: RFBsize:315948, AFBsize:317384, largePrimes:7631001 encountered
Relations: rels:7736677, finalFF:795523
Max relations in full relation-set: 28
Initial matrix: 633411 x 795523 with sparse part having weight 61742503.
Pruned matrix : 492974 x 496205 with weight 35425385.
Polynomial selection time: 1.75 hours.
Total sieving time: 29.00 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.41 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000
total time: 32.49 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)

7·10¹⁶¹-9 = 6(9)₁₆₀1_<162> = 31 · 238529 · 16165785424707406853881795571381_<32> · C124

C124 = P34 · P91

P34 = 1154734515303355813588848626575829_<34>

P91 = 5071263789375496111006719685471610072718773087775179235920085143775708329815366365895324241_<91>

Jan 16, 2008 (2nd)

By Robert Backstrom / GMP-ECM

8·10¹⁵⁶-9 = 7(9)₁₅₅1_<157> = 13001 · C153

C153 = P34 · P120

P34 = 1295988165151587695336675852925431_<34>

P120 = 474801621105532083834700125189778681342962201400810891482867919304452802278015894667986382020302929101025045361916944761_<120>

Jan 16, 2008

The factor table of 800...009 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Jan 15, 2008 (4th)

By Jo Yeong Uk / GMP-ECM

8·10¹⁸⁰-9 = 7(9)₁₇₉1_<181> = C181

C181 = P39 · C142

P39 = 826115977894170609050375729157582021497_<39>

C142 = [9683870320959750397301131599191235511655411576027658067144718311274518875633720728729028560156827649352670707054841461900759820696819277771503_<142>]

8·10¹⁹⁵-9 = 7(9)₁₉₄1_<196> = 3889 · 15610275261869941441_<20> · 435897677914358674687851179_<27> · 1045513792226296340499906371_<28> · C120

C120 = P32 · P89

P32 = 19119580804026448034824934992231_<32>

P89 = 15123377562818027057411188140424291585847836807190418568871815626881749196170735312717121_<89>

Jan 15, 2008 (3rd)

By matsui / GMP-ECM

(14·10¹⁹³-41)/9 = 1(5)₁₉₂1_<194> = 11 · 331 · C190

C190 = P32 · C158

P32 = 62526939757042506698769902098831_<32>

C158 = [68327837135788697792225797137899512369957580856225051975788498022627748463669114687246453722274284444945237019649575567790089868646790503352013257536766804281_<158>]

(8·10¹⁹⁵-53)/9 = (8)₁₉₄3_<195> = 23 · 29 · C193

C193 = P33 · C160

P33 = 144590681557580521442564517528323_<33>

C160 = [9216824939736569669228358640580173977056399699297573655614497386963756277829507934369338603231828859333521137520519483912139878643422967809749001298287897524163_<160>]

Jan 15, 2008 (2nd)

By Sinkiti Sibata / GGNFS

8·10¹⁵¹-9 = 7(9)₁₅₀1_<152> = 81001 · 1259231 · 1739471 · 87802863301_<11> · C124

C124 = P47 · P78

P47 = 30791592289433442832144020953926711999042958399_<47>

P78 = 166777008939323811795992782279128050360042974145183252503836734575392545775709_<78>

Number: 79991_151
N=5135329662510855451262747808996030428811545227752914475018951225716569545596080341020197792116773744210930101595349671729891
  ( 124 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=30791592289433442832144020953926711999042958399 (pp47)
 r2=166777008939323811795992782279128050360042974145183252503836734575392545775709 (pp78)
Version: GGNFS-0.77.1-20060513-k8
Total time: 21.10 hours.
Scaled time: 42.15 units (timescale=1.998).
Factorization parameters were as follows:
name: 79991_151
n: 5135329662510855451262747808996030428811545227752914475018951225716569545596080341020197792116773744210930101595349671729891
m: 2000000000000000000000000000000
c5: 5
c0: -18
skew: 1.29
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:176263, largePrimes:5423196 encountered
Relations: rels:5343061, finalFF:492291
Max relations in full relation-set: 28
Initial matrix: 352631 x 492291 with sparse part having weight 42349212.
Pruned matrix : 286234 x 288061 with weight 22574991.
Total sieving time: 19.86 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.98 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 21.10 hours.
 --------- CPU info (if available) ----------

8·10¹⁵²-9 = 7(9)₁₅₁1_<153> = 7 · 17 · 4660787009_<10> · 138804112174759_<15> · C128

C128 = P49 · P79

P49 = 8716632273706955002066316578892953673433856501001_<49>

P79 = 1192154963555103648416832707448716501053570407831671868210179818737805091325919_<79>

Number: 79991_152
N=10391576430584355190373677199759407351446517692328060162305724930882541948962841610590261491446581131649370344311873473040744919
  ( 128 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=8716632273706955002066316578892953673433856501001 (pp49)
 r2=1192154963555103648416832707448716501053570407831671868210179818737805091325919 (pp79)
Version: GGNFS-0.77.1-20060513-k8
Total time: 25.77 hours.
Scaled time: 51.56 units (timescale=2.001).
Factorization parameters were as follows:
name: 79991_152
n: 10391576430584355190373677199759407351446517692328060162305724930882541948962841610590261491446581131649370344311873473040744919
m: 2000000000000000000000000000000
c5: 25
c0: -9
skew: 0.82
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176228, largePrimes:5853695 encountered
Relations: rels:6051618, finalFF:728881
Max relations in full relation-set: 28
Initial matrix: 352594 x 728881 with sparse part having weight 65846116.
Pruned matrix : 233861 x 235687 with weight 30991348.
Total sieving time: 24.73 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.78 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 25.77 hours.
 --------- CPU info (if available) ----------

Jan 15, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(71·10¹⁶⁶-17)/9 = 7(8)₁₆₅7_<167> = 134850917 · C159

C159 = P42 · P117

P42 = 651848668311457681434595316282892913713581_<42>

P117 = 897460106491496446614435004796283119759388322955462991597812172002637625312740762585824492525266076716658116988493431_<117>

Number: n
N=585008175279140956000239055763253644681473607546093949727378486339020511732144089823941567181844887928265915232069863409893526262701564638888505955720633986411
  ( 159 digits)
SNFS difficulty: 167 digits.
Divisors found:

Tue Jan 15 05:36:06 2008  prp42 factor: 651848668311457681434595316282892913713581
Tue Jan 15 05:36:06 2008  prp117 factor: 897460106491496446614435004796283119759388322955462991597812172002637625312740762585824492525266076716658116988493431
Tue Jan 15 05:36:06 2008  elapsed time 03:06:55 (Msieve 1.32)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 124.47 hours.
Scaled time: 162.43 units (timescale=1.305).
Factorization parameters were as follows:
name: KA_7_8_165_7
n: 585008175279140956000239055763253644681473607546093949727378486339020511732144089823941567181844887928265915232069863409893526262701564638888505955720633986411
skew: 0.47
deg: 5
c5: 710
c0: -17
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5001307)
Primes: RFBsize:230209, AFBsize:229783, largePrimes:8029739 encountered
Relations: rels:7472162, finalFF:393297
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 124.03 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 124.47 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

2·10¹⁶⁵-3 = 1(9)₁₆₄7_<166> = 53 · 71881 · 238245737904007_<15> · C145

C145 = P37 · P52 · P57

P37 = 1403781958927021896724841424949479359_<37>

P52 = 2551589809127749396488652666886417210600862321179209_<52>

P57 = 615183048749711493044799857844699363803138896771654939937_<57>

Number: n
N=1569694797937903300551110733526778314018254369305286389639105161479391032809561453871065828543212923908169833
  ( 109 digits)
Divisors found:

Tue Jan 15 14:40:26 2008  prp52 factor: 2551589809127749396488652666886417210600862321179209
Tue Jan 15 14:40:26 2008  prp57 factor: 615183048749711493044799857844699363803138896771654939937
Tue Jan 15 14:40:26 2008  elapsed time 00:47:23 (Msieve 1.32)

Version: GGNFS-0.77.1-20050930-k8
Total time: 11.42 hours.
Scaled time: 9.56 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_1_9_164_7
n: 1569694797937903300551110733526778314018254369305286389639105161479391032809561453871065828543212923908169833
skew: 8306.36
# norm 2.76e+14
c5: 66240
c4: -3742036824
c3: -9666955114689
c2: 233645416862500981
c1: 389670328960034369953
c0: -1807187513145699342603261
# alpha -5.10
Y1: 357931261909
Y0: -473088827202633755566
# Murphy_E 1.24e-09
# M 794377935712316731005078895413010160819638922615293091642026246376800976490609919453234209027858723238419702
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 2800001)
Primes: RFBsize:230209, AFBsize:230661, largePrimes:7168024 encountered
Relations: rels:6884920, finalFF:517695
Max relations in full relation-set: 28
Initial matrix: 460952 x 517695 with sparse part having weight 37788957.
Pruned matrix : 413293 x 415661 with weight 25450233.
Total sieving time: 11.25 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 11.42 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

8·10¹⁴⁹-9 = 7(9)₁₄₈1_<150> = 41 · 387128561 · C140

C140 = P42 · P47 · P52

P42 = 506448962913497763293952892565556348977959_<42>

P47 = 51909484898783796991431617515193618122604873161_<47>

P52 = 1917204817158045773364919500838723218822870408926609_<52>

Number: n
N=50402365228617734335016222043145796714084216637046821048037371523707138598899480824205970221639614758238464126637047456747868817464881438991
  ( 140 digits)
SNFS difficulty: 150 digits.
Divisors found:

Tue Jan 15 21:21:09 2008  prp42 factor: 506448962913497763293952892565556348977959
Tue Jan 15 21:21:09 2008  prp47 factor: 51909484898783796991431617515193618122604873161
Tue Jan 15 21:21:09 2008  prp52 factor: 1917204817158045773364919500838723218822870408926609
Tue Jan 15 21:21:09 2008  elapsed time 00:47:51 (Msieve 1.32)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 14.51 hours.
Scaled time: 19.05 units (timescale=1.313).
Factorization parameters were as follows:
name: KA_7_9_148_1
n: 50402365228617734335016222043145796714084216637046821048037371523707138598899480824205970221639614758238464126637047456747868817464881438991
skew: 1.62
deg: 5
c5: 4
c0: -45
m: 1000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 799990)
Primes: RFBsize:203362, AFBsize:203002, largePrimes:6263890 encountered
Relations: rels:5792386, finalFF:494582
Max relations in full relation-set: 28
Initial matrix: 406428 x 494582 with sparse part having weight 27219008.
Pruned matrix : 
Total sieving time: 14.35 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 14.51 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jan 14, 2008 (6th)

By Irvine

10³⁷⁵+1 is divisible by 4709825349852110182615878875374419529306990314325041101342026868334001_<70>, cofactor is prime.

Reference: The Cunningham Project (Sam Wagstaff)

Jan 14, 2008 (5th)

By Yousuke Koide

(10¹²⁷⁹-1)/9 is divisible by 2320223789459953862122440032213_<31>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 14, 2008 (4th)

By Jo Yeong Uk / Msieve, GGNFS

8·10¹⁵⁸-9 = 7(9)₁₅₇1_<159> = 7 · 4323841 · 4714903 · 462997341128773543_<18> · 410562561244534563981430142949031_<33> · C95

C95 = P47 · P48

P47 = 46763860302718914140271163284841847599644741791_<47>

P48 = 630639651843465146374746113429199687582690077977_<48>

Sun Jan 13 22:37:33 2008  
Sun Jan 13 22:37:33 2008  
Sun Jan 13 22:37:33 2008  Msieve v. 1.32
Sun Jan 13 22:37:33 2008  random seeds: 22de54b1 e3793a1d
Sun Jan 13 22:37:33 2008  factoring 29491144580163096639800559468991908217808992070869327114070748537704128510842764288695820636807 (95 digits)
Sun Jan 13 22:37:34 2008  no P-1/P+1/ECM available, skipping
Sun Jan 13 22:37:34 2008  commencing quadratic sieve (95-digit input)
Sun Jan 13 22:37:34 2008  using multiplier of 23
Sun Jan 13 22:37:34 2008  using 32kb Intel Core sieve core
Sun Jan 13 22:37:34 2008  sieve interval: 36 blocks of size 32768
Sun Jan 13 22:37:34 2008  processing polynomials in batches of 6
Sun Jan 13 22:37:34 2008  using a sieve bound of 2117419 (78824 primes)
Sun Jan 13 22:37:34 2008  using large prime bound of 309143174 (28 bits)
Sun Jan 13 22:37:34 2008  using double large prime bound of 1915522827320368 (43-51 bits)
Sun Jan 13 22:37:34 2008  using trial factoring cutoff of 51 bits
Sun Jan 13 22:37:34 2008  polynomial 'A' values have 12 factors
Mon Jan 14 02:03:04 2008  79124 relations (19503 full + 59621 combined from 1162555 partial), need 78920
Mon Jan 14 02:03:05 2008  begin with 1182058 relations
Mon Jan 14 02:03:06 2008  reduce to 205345 relations in 12 passes
Mon Jan 14 02:03:06 2008  attempting to read 205345 relations
Mon Jan 14 02:03:07 2008  recovered 205345 relations
Mon Jan 14 02:03:07 2008  recovered 189496 polynomials
Mon Jan 14 02:03:08 2008  attempting to build 79124 cycles
Mon Jan 14 02:03:08 2008  found 79122 cycles in 5 passes
Mon Jan 14 02:03:08 2008  distribution of cycle lengths:
Mon Jan 14 02:03:08 2008     length 1 : 19503
Mon Jan 14 02:03:08 2008     length 2 : 13950
Mon Jan 14 02:03:08 2008     length 3 : 13238
Mon Jan 14 02:03:08 2008     length 4 : 10765
Mon Jan 14 02:03:08 2008     length 5 : 8092
Mon Jan 14 02:03:08 2008     length 6 : 5469
Mon Jan 14 02:03:08 2008     length 7 : 3396
Mon Jan 14 02:03:08 2008     length 9+: 4709
Mon Jan 14 02:03:08 2008  largest cycle: 21 relations
Mon Jan 14 02:03:08 2008  matrix is 78824 x 79122 with weight 5358756 (avg 67.73/col)
Mon Jan 14 02:03:08 2008  filtering completed in 3 passes
Mon Jan 14 02:03:08 2008  matrix is 75111 x 75175 with weight 5115448 (avg 68.05/col)
Mon Jan 14 02:03:10 2008  saving the first 48 matrix rows for later
Mon Jan 14 02:03:10 2008  matrix is 75063 x 75175 with weight 4227524 (avg 56.24/col)
Mon Jan 14 02:03:10 2008  matrix includes 64 packed rows
Mon Jan 14 02:03:10 2008  using block size 30070 for processor cache size 4096 kB
Mon Jan 14 02:03:12 2008  commencing Lanczos iteration
Mon Jan 14 02:03:40 2008  lanczos halted after 1188 iterations (dim = 75062)
Mon Jan 14 02:03:40 2008  recovered 17 nontrivial dependencies
Mon Jan 14 02:03:41 2008  prp47 factor: 46763860302718914140271163284841847599644741791
Mon Jan 14 02:03:41 2008  prp48 factor: 630639651843465146374746113429199687582690077977
Mon Jan 14 02:03:41 2008  elapsed time 03:26:08

8·10¹⁵⁴-9 = 7(9)₁₅₃1_<155> = 41 · 59281 · 547957391 · 12119965852433_<14> · C127

C127 = P39 · P89

P39 = 461939553236586484114536733702650233023_<39>

P89 = 10728951295727690102209746621884683736435695534177888595486933153914001471840926288450159_<89>

Number: 79991_154
N=4956126968245544840829612126947542016537069480457201107807317941718490806281289773378008927417668578515244674558217734871400657
  ( 127 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=461939553236586484114536733702650233023 (pp39)
 r2=10728951295727690102209746621884683736435695534177888595486933153914001471840926288450159 (pp89)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 18.01 hours.
Scaled time: 38.75 units (timescale=2.151).
Factorization parameters were as follows:
n: 4956126968245544840829612126947542016537069480457201107807317941718490806281289773378008927417668578515244674558217734871400657
m: 10000000000000000000000000000000
c5: 4
c0: -45
skew: 1.62
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:216516, largePrimes:5592938 encountered
Relations: rels:5575870, finalFF:574005
Max relations in full relation-set: 28
Initial matrix: 433396 x 574005 with sparse part having weight 43815050.
Pruned matrix : 340472 x 342702 with weight 27481926.
Total sieving time: 17.33 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.57 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 18.01 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)

3·10¹⁶⁴+1 = 3(0)₁₆₃1_<165> = 7 · 153643579 · 3358957632992895950040793_<25> · C131

C131 = P37 · P94

P37 = 9126754553793380350961701881130062943_<37>

P94 = 9098879264948989983429360562774153133639098883364585761384303273204226621258077428446473075683_<94>

Jan 14, 2008 (3rd)

By Sinkiti Sibata / GGNFS

8·10¹⁴⁵-9 = 7(9)₁₄₄1_<146> = 31 · 3769 · 7489 · 279971682391_<12> · C126

C126 = P55 · P71

P55 = 7742337301078104200488978966281420202696958368400348371_<55>

P71 = 42178597070720342821424007221144098406947930977765023595765919575211661_<71>

Number: 79991_145
N=326560925407781770767774075639791745382030213521430418350721109651781264744036225782582623040049517265875742904382248461554231
  ( 126 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=7742337301078104200488978966281420202696958368400348371 (pp55)
 r2=42178597070720342821424007221144098406947930977765023595765919575211661 (pp71)
Version: GGNFS-0.77.1-20060513-k8
Total time: 13.98 hours.
Scaled time: 27.74 units (timescale=1.985).
Factorization parameters were as follows:
name: 79991_145
n: 326560925407781770767774075639791745382030213521430418350721109651781264744036225782582623040049517265875742904382248461554231
m: 100000000000000000000000000000
c5: 8
c0: -9
skew: 1.02
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2150001)
Primes: RFBsize:100021, AFBsize:99978, largePrimes:2778825 encountered
Relations: rels:2779522, finalFF:267636
Max relations in full relation-set: 28
Initial matrix: 200064 x 267636 with sparse part having weight 27367024.
Pruned matrix : 181507 x 182571 with weight 16750604.
Total sieving time: 13.45 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.36 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 13.98 hours.
 --------- CPU info (if available) ----------

8·10¹⁴⁸-9 = 7(9)₁₄₇1_<149> = 23 · 2351 · 5417 · 18204143 · 1811121196799_<13> · 1947542272318766199929_<22> · C100

C100 = P37 · P64

P37 = 1698869895271211983854184427647893889_<37>

P64 = 2503720935946036989300856832502895816091759303149812092199359903_<64>

Sat Jan 12 20:55:23 2008  Msieve v. 1.30
Sat Jan 12 20:55:23 2008  random seeds: 45d02a07 42588f3f
Sat Jan 12 20:55:23 2008  factoring 4253496124238984707734842877964977170209510988448548351661975134912047668525960763545100431865332767 (100 digits)
Sat Jan 12 20:55:24 2008  commencing quadratic sieve (100-digit input)
Sat Jan 12 20:55:24 2008  using multiplier of 3
Sat Jan 12 20:55:24 2008  using 64kb Pentium 4 sieve core
Sat Jan 12 20:55:24 2008  sieve interval: 18 blocks of size 65536
Sat Jan 12 20:55:24 2008  processing polynomials in batches of 6
Sat Jan 12 20:55:24 2008  using a sieve bound of 2704027 (98824 primes)
Sat Jan 12 20:55:24 2008  using large prime bound of 405604050 (28 bits)
Sat Jan 12 20:55:24 2008  using double large prime bound of 3123087099560100 (43-52 bits)
Sat Jan 12 20:55:24 2008  using trial factoring cutoff of 52 bits
Sat Jan 12 20:55:24 2008  polynomial 'A' values have 13 factors
Sun Jan 13 07:55:59 2008  9287 relations (6915 full + 2372 combined from 447278 partial), need 98920
Sun Jan 13 07:55:59 2008  elapsed time 11:00:36
Sun Jan 13 08:10:19 2008  
Sun Jan 13 08:10:19 2008  
Sun Jan 13 08:10:19 2008  Msieve v. 1.30
Sun Jan 13 08:10:19 2008  random seeds: 8ded5200 352a1059
Sun Jan 13 08:10:19 2008  factoring 4253496124238984707734842877964977170209510988448548351661975134912047668525960763545100431865332767 (100 digits)
Sun Jan 13 08:10:20 2008  commencing quadratic sieve (100-digit input)
Sun Jan 13 08:10:20 2008  using multiplier of 3
Sun Jan 13 08:10:20 2008  using 64kb Pentium 4 sieve core
Sun Jan 13 08:10:20 2008  sieve interval: 18 blocks of size 65536
Sun Jan 13 08:10:20 2008  processing polynomials in batches of 6
Sun Jan 13 08:10:20 2008  using a sieve bound of 2704027 (98824 primes)
Sun Jan 13 08:10:20 2008  using large prime bound of 405604050 (28 bits)
Sun Jan 13 08:10:20 2008  using double large prime bound of 3123087099560100 (43-52 bits)
Sun Jan 13 08:10:20 2008  using trial factoring cutoff of 52 bits
Sun Jan 13 08:10:20 2008  polynomial 'A' values have 13 factors
Sun Jan 13 08:10:22 2008  restarting with 6915 full and 447278 partial relations
Mon Jan 14 09:57:41 2008  98999 relations (23067 full + 75932 combined from 1497061 partial), need 98920
Mon Jan 14 09:57:47 2008  begin with 1520128 relations
Mon Jan 14 09:57:50 2008  reduce to 263703 relations in 11 passes
Mon Jan 14 09:57:50 2008  attempting to read 263703 relations
Mon Jan 14 09:58:00 2008  recovered 263703 relations
Mon Jan 14 09:58:00 2008  recovered 255071 polynomials
Mon Jan 14 09:58:01 2008  attempting to build 98999 cycles
Mon Jan 14 09:58:01 2008  found 98999 cycles in 6 passes
Mon Jan 14 09:58:01 2008  distribution of cycle lengths:
Mon Jan 14 09:58:01 2008     length 1 : 23067
Mon Jan 14 09:58:01 2008     length 2 : 16643
Mon Jan 14 09:58:01 2008     length 3 : 16544
Mon Jan 14 09:58:01 2008     length 4 : 13575
Mon Jan 14 09:58:01 2008     length 5 : 10481
Mon Jan 14 09:58:01 2008     length 6 : 7268
Mon Jan 14 09:58:01 2008     length 7 : 4607
Mon Jan 14 09:58:01 2008     length 9+: 6814
Mon Jan 14 09:58:01 2008  largest cycle: 21 relations
Mon Jan 14 09:58:02 2008  matrix is 98824 x 98999 with weight 6671927 (avg 67.39/col)
Mon Jan 14 09:58:04 2008  filtering completed in 3 passes
Mon Jan 14 09:58:04 2008  matrix is 95182 x 95246 with weight 6452945 (avg 67.75/col)
Mon Jan 14 09:58:05 2008  saving the first 48 matrix rows for later
Mon Jan 14 09:58:05 2008  matrix is 95134 x 95246 with weight 5001470 (avg 52.51/col)
Mon Jan 14 09:58:05 2008  matrix includes 64 packed rows
Mon Jan 14 09:58:05 2008  using block size 21845 for processor cache size 512 kB
Mon Jan 14 09:58:07 2008  commencing Lanczos iteration
Mon Jan 14 09:59:41 2008  lanczos halted after 1506 iterations (dim = 95134)
Mon Jan 14 09:59:41 2008  recovered 18 nontrivial dependencies
Mon Jan 14 09:59:43 2008  prp37 factor: 1698869895271211983854184427647893889
Mon Jan 14 09:59:43 2008  prp64 factor: 2503720935946036989300856832502895816091759303149812092199359903
Mon Jan 14 09:59:43 2008  elapsed time 25:49:24

8·10¹⁴⁴-9 = 7(9)₁₄₃1_<145> = 41 · 356977 · 12418519760749442070754470311_<29> · C110

C110 = P34 · P77

P34 = 1202396689032442891861982410658929_<34>

P77 = 36605664115474603832272688375093831327326195191011201019483886504026399481577_<77>

Number: 79991_144
N=44014529332280370913945784430768068918614841536502394721741885965309300374132997959530907498071104444566051033
  ( 110 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=1202396689032442891861982410658929 (pp34)
 r2=36605664115474603832272688375093831327326195191011201019483886504026399481577 (pp77)
Version: GGNFS-0.77.1-20060513-k8
Total time: 15.54 hours.
Scaled time: 30.96 units (timescale=1.992).
Factorization parameters were as follows:
name: 79991_144
n: 44014529332280370913945784430768068918614841536502394721741885965309300374132997959530907498071104444566051033
m: 100000000000000000000000000000
c5: 4
c0: -45
skew: 1.62
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2350001)
Primes: RFBsize:100021, AFBsize:100108, largePrimes:2834967 encountered
Relations: rels:2856600, finalFF:275497
Max relations in full relation-set: 28
Initial matrix: 200193 x 275497 with sparse part having weight 29783015.
Pruned matrix : 180481 x 181545 with weight 17934606.
Total sieving time: 14.99 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.35 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 15.54 hours.
 --------- CPU info (if available) ----------

Jan 14, 2008 (2nd)

By Robert Backstrom / GGNFS, GMP-ECM, Msieve

(2·10¹⁶³-11)/9 = (2)₁₆₂1_<163> = 17 · 37877640361436692050097_<23> · C139

C139 = P64 · P76

P64 = 2220078767826668361325983014056277664531569885622229234531374787_<64>

P76 = 1554487611393771714900494781481020302062202220737078357519127682939670142767_<76>

Number: n
N=3451084940904905586708196728200554661963901726244208158350060888692051925846967926091130062961315383616227129749369913889451806441074215629
  ( 139 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=2220078767826668361325983014056277664531569885622229234531374787 (pp64)
 r2=1554487611393771714900494781481020302062202220737078357519127682939670142767 (pp76)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 38.74 hours.
Scaled time: 70.85 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_2_162_1
n: 3451084940904905586708196728200554661963901726244208158350060888692051925846967926091130062961315383616227129749369913889451806441074215629
skew: 0.71
deg: 5
c5: 125
c0: -22
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2600001)
Primes: RFBsize:216816, AFBsize:216697, largePrimes:7455704 encountered
Relations: rels:6931886, finalFF:513994
Max relations in full relation-set: 48
Initial matrix: 433578 x 513994 with sparse part having weight 52499854.
Pruned matrix : 395935 x 398166 with weight 33837805.
Total sieving time: 36.93 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.57 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 38.74 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

8·10¹⁶⁰-9 = 7(9)₁₅₉1_<161> = 31 · 57073 · C155

C155 = P39 · P117

P39 = 162324131850327948485434438093621716953_<39>

P117 = 278557273407351934069599866763595027872975703442508848781459154897177077473859196381772941462840739464361826004563169_<117>

8·10¹⁶⁵-9 = 7(9)₁₆₄1_<166> = 281 · C164

C164 = P29 · P136

P29 = 18039899370116253132365185259_<29>

P136 = 1578154639645101849715900601142746848194561974023738373087552898239995805944710078341227436286841880064814566233260954631456666425083629_<136>

5·10¹⁶²-1 = 4(9)₁₆₂_<163> = 7898189142101_<13> · 456514351349672851_<18> · C133

C133 = P46 · P87

P46 = 7739832354657573536230860093069953953660396661_<46>

P87 = 179166366257503162309509372277349334970926729613420475526494728627218732934704149702509_<87>

Number: n
N=1386717638426251931934033806378717686203165786751271889807208433424201191175011460788311942354451703713581361177260630054458086922449
  ( 133 digits)
SNFS difficulty: 162 digits.
Divisors found:

Mon Jan 14 10:32:34 2008  prp46 factor: 7739832354657573536230860093069953953660396661
Mon Jan 14 10:32:34 2008  prp87 factor: 179166366257503162309509372277349334970926729613420475526494728627218732934704149702509
Mon Jan 14 10:32:34 2008  elapsed time 00:57:29 (Msieve 1.32)

Version: GGNFS-0.77.1-20050930-k8
Total time: 39.69 hours.
Scaled time: 33.26 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_4_9_162
n: 1386717638426251931934033806378717686203165786751271889807208433424201191175011460788311942354451703713581361177260630054458086922449
type: snfs
deg: 5
c5: 500
c0: -1
skew: 0.29
m: 100000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3700000)
Primes: RFBsize:216816, AFBsize:216391, largePrimes:5827763 encountered
Relations: rels:5828091, finalFF:514396
Max relations in full relation-set: 28
Initial matrix: 433273 x 514396 with sparse part having weight 53218789.
Pruned matrix : 400490 x 402720 with weight 39410526.
Total sieving time: 39.57 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 39.69 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

8·10¹⁵⁵-9 = 7(9)₁₅₄1_<156> = 89 · 39076948619_<11> · 17285468921447286611_<20> · C125

C125 = P33 · P92

P33 = 630937457078491523522125157973689_<33>

P92 = 21091713323420107009957029361942912268853049172167108976864637180884556752573488461477765719_<92>

Jan 14, 2008

By matsui / GMP-ECM

5·10¹⁹⁰-9 = 4(9)₁₈₉1_<191> = 61 · 409 · C187

C187 = P32 · P155

P32 = 47568134021252279670958230004481_<32>

P155 = 42130900895096262260841447387806243682255781771378005956259860699611715275397274609349024640992587587106601079256289499605009903500893334162184491530113339_<155>

(34·10¹⁹⁷-43)/9 = 3(7)₁₉₆3_<198> = 11 · 433 · C194

C194 = P30 · C165

P30 = 175552370499658335275248396363_<30>

C165 = [451803018305522330975120918157248100722684575456134658825674860937758490095206379652486712157977804105105296752082281189878524588429897592043870795445824300265839717_<165>]

Jan 13, 2008 (3rd)

By matsui / GMP-ECM

(73·10²⁰⁰-1)/9 = 8(1)₂₀₀_<201> = 487 · C199

C199 = P36 · C164

P36 = 116587695911853113400792854475193411_<36>

C164 = [14285606062277732309168156983256445884072165236631874368716790782839231122943523363577821850787245917630279558418605214545784622225512312628692589974007175489848523_<164>]

Jan 13, 2008 (2nd)

By Sinkiti Sibata / GGNFS, Msieve

8·10¹³⁴-9 = 7(9)₁₃₃1_<135> = 7 · 41 · 2991559 · 51611423 · C119

C119 = P51 · P68

P51 = 547886259883585498357025117689672145168225517346471_<51>

P68 = 32951430664648770389924301340174201074562936491053050907418208102919_<68>

Number: 79991_134
N=18053636104667704643286239945614946302235180121774908791993905279361217947079393873400776543238916285526231963749448849
  ( 119 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=547886259883585498357025117689672145168225517346471 (pp51)
 r2=32951430664648770389924301340174201074562936491053050907418208102919 (pp68)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.77 hours.
Scaled time: 11.57 units (timescale=2.004).
Factorization parameters were as follows:
name: 79991_134
n: 18053636104667704643286239945614946302235180121774908791993905279361217947079393873400776543238916285526231963749448849
m: 1000000000000000000000000000
c5: 4
c0: -45
skew: 1.62
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:64108, largePrimes:1539429 encountered
Relations: rels:1553166, finalFF:188124
Max relations in full relation-set: 28
Initial matrix: 142670 x 188124 with sparse part having weight 14083615.
Pruned matrix : 127526 x 128303 with weight 7818342.
Total sieving time: 5.59 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.77 hours.
 --------- CPU info (if available) ----------

8·10¹²⁷-9 = 7(9)₁₂₆1_<128> = 379 · 162668538905134917251_<21> · C106

C106 = P42 · P64

P42 = 657946460633670262464217847012752777057361_<42>

P64 = 1972225892515966800861803327069244574222166958428213389132029239_<64>

Number: 79991_127
N=1297619045550961749053867427793399261073676933317173039733022282273362765727795424832044173656449032178279
  ( 106 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=657946460633670262464217847012752777057361 (pp42)
 r2=1972225892515966800861803327069244574222166958428213389132029239 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.10 hours.
Scaled time: 6.18 units (timescale=1.996).
Factorization parameters were as follows:
name: 79991_127
n: 1297619045550961749053867427793399261073676933317173039733022282273362765727795424832044173656449032178279
m: 20000000000000000000000000
c5: 25
c0: -9
skew: 0.82
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:63951, AFBsize:63968, largePrimes:1468206 encountered
Relations: rels:1493823, finalFF:197352
Max relations in full relation-set: 28
Initial matrix: 127983 x 197352 with sparse part having weight 9951716.
Pruned matrix : 104345 x 105048 with weight 4227563.
Total sieving time: 2.98 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 3.10 hours.
 --------- CPU info (if available) ----------

8·10¹⁶²-9 = 7(9)₁₆₁1_<163> = 103 · 885679 · 27972713 · 20174793473_<11> · 128513348641_<12> · 6739247979073_<13> · 1849901488629672000658219697_<28> · C86

C86 = P32 · P55

P32 = 29004454390043890346738171836159_<32>

P55 = 3343949795648324158059774855467139266458728235931156713_<55>

Sun Jan 13 08:25:03 2008  Msieve v. 1.30
Sun Jan 13 08:25:03 2008  random seeds: 4905ce6d 0961e9c8
Sun Jan 13 08:25:03 2008  factoring 96989439330478405638385934491360121476455014414443770871154615953823073607951988985367 (86 digits)
Sun Jan 13 08:25:04 2008  commencing quadratic sieve (86-digit input)
Sun Jan 13 08:25:04 2008  using multiplier of 1
Sun Jan 13 08:25:04 2008  using 64kb Pentium 2 sieve core
Sun Jan 13 08:25:04 2008  sieve interval: 9 blocks of size 65536
Sun Jan 13 08:25:05 2008  processing polynomials in batches of 12
Sun Jan 13 08:25:05 2008  using a sieve bound of 1466767 (56000 primes)
Sun Jan 13 08:25:05 2008  using large prime bound of 117341360 (26 bits)
Sun Jan 13 08:25:05 2008  using double large prime bound of 334974615074720 (41-49 bits)
Sun Jan 13 08:25:05 2008  using trial factoring cutoff of 49 bits
Sun Jan 13 08:25:05 2008  polynomial 'A' values have 11 factors
Sun Jan 13 14:10:11 2008  56141 relations (16063 full + 40078 combined from 585521 partial), need 56096
Sun Jan 13 14:10:16 2008  begin with 601584 relations
Sun Jan 13 14:10:23 2008  reduce to 133024 relations in 9 passes
Sun Jan 13 14:10:23 2008  attempting to read 133024 relations
Sun Jan 13 14:10:32 2008  recovered 133024 relations
Sun Jan 13 14:10:32 2008  recovered 109251 polynomials
Sun Jan 13 14:10:58 2008  attempting to build 56141 cycles
Sun Jan 13 14:10:58 2008  found 56141 cycles in 5 passes
Sun Jan 13 14:11:02 2008  distribution of cycle lengths:
Sun Jan 13 14:11:02 2008     length 1 : 16063
Sun Jan 13 14:11:02 2008     length 2 : 11348
Sun Jan 13 14:11:02 2008     length 3 : 9829
Sun Jan 13 14:11:02 2008     length 4 : 7247
Sun Jan 13 14:11:02 2008     length 5 : 4933
Sun Jan 13 14:11:02 2008     length 6 : 3080
Sun Jan 13 14:11:02 2008     length 7 : 1688
Sun Jan 13 14:11:02 2008     length 9+: 1953
Sun Jan 13 14:11:02 2008  largest cycle: 20 relations
Sun Jan 13 14:11:04 2008  matrix is 56000 x 56141 with weight 3038483 (avg 54.12/col)
Sun Jan 13 14:11:08 2008  filtering completed in 4 passes
Sun Jan 13 14:11:09 2008  matrix is 51087 x 51151 with weight 2800152 (avg 54.74/col)
Sun Jan 13 14:11:11 2008  saving the first 48 matrix rows for later
Sun Jan 13 14:11:12 2008  matrix is 51039 x 51151 with weight 2114035 (avg 41.33/col)
Sun Jan 13 14:11:12 2008  matrix includes 64 packed rows
Sun Jan 13 14:11:12 2008  using block size 10922 for processor cache size 256 kB
Sun Jan 13 14:11:14 2008  commencing Lanczos iteration
Sun Jan 13 14:13:38 2008  lanczos halted after 809 iterations (dim = 51034)
Sun Jan 13 14:13:39 2008  recovered 15 nontrivial dependencies
Sun Jan 13 14:14:05 2008  prp32 factor: 29004454390043890346738171836159
Sun Jan 13 14:14:05 2008  prp55 factor: 3343949795648324158059774855467139266458728235931156713
Sun Jan 13 14:14:05 2008  elapsed time 05:49:02

8·10¹⁴⁷-9 = 7(9)₁₄₆1_<148> = 71569 · 15914071 · 77519441 · 211293311 · 3128994342837361_<16> · C105

C105 = P45 · P60

P45 = 757574316234139695166249827153995203794288161_<45>

P60 = 180907822053975968030490364262581021587417735195779858011279_<60>

Number: 79991_147
N=137051119593948261370044705690083652684958246482044222007487026886745761271810395403932044275256914167919
  ( 105 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=757574316234139695166249827153995203794288161 (pp45)
 r2=180907822053975968030490364262581021587417735195779858011279 (pp60)
Version: GGNFS-0.77.1-20060513-k8
Total time: 21.13 hours.
Scaled time: 42.15 units (timescale=1.995).
Factorization parameters were as follows:
name: 79991_147
n: 137051119593948261370044705690083652684958246482044222007487026886745761271810395403932044275256914167919
m: 200000000000000000000000000000
c5: 25
c0: -9
skew: 0.82
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 3050001)
Primes: RFBsize:114155, AFBsize:114087, largePrimes:2932834 encountered
Relations: rels:2973016, finalFF:311516
Max relations in full relation-set: 28
Initial matrix: 228306 x 311516 with sparse part having weight 33697415.
Pruned matrix : 204714 x 205919 with weight 20792624.
Total sieving time: 20.36 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.57 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 21.13 hours.
 --------- CPU info (if available) ----------

Jan 13, 2008

By Jo Yeong Uk / GGNFS

8·10¹³⁶-9 = 7(9)₁₃₅1_<137> = 17 · 4337 · 31319 · 22064536663081199635553_<23> · C106

C106 = P45 · P61

P45 = 414874359200499062591640749476962066365515367_<45>

P61 = 3784707754227857968375340111961975566863294728841184192955991_<61>

Number: 79991_136
N=1570178204296442471478760889548334038176734874175207254303092147557263103549956249477642039440313865213697
  ( 106 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=414874359200499062591640749476962066365515367 (pp45)
 r2=3784707754227857968375340111961975566863294728841184192955991 (pp61)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.02 hours.
Scaled time: 6.42 units (timescale=2.126).
Factorization parameters were as follows:
n: 1570178204296442471478760889548334038176734874175207254303092147557263103549956249477642039440313865213697
m: 2000000000000000000000000000
c5: 5
c0: -18
skew: 1.29
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1250001)
Primes: RFBsize:107126, AFBsize:106673, largePrimes:2293144 encountered
Relations: rels:2442022, finalFF:309970
Max relations in full relation-set: 28
Initial matrix: 213865 x 309970 with sparse part having weight 23128338.
Pruned matrix : 176160 x 177293 with weight 10368683.
Total sieving time: 2.88 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 3.02 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)

8·10¹⁴⁰-9 = 7(9)₁₃₉1_<141> = 7 · 2445390769_<10> · 37242387217387908233_<20> · C112

C112 = P33 · P79

P33 = 388536296915994985391902206726511_<33>

P79 = 3229792119842628898676018383831983166364802105671842667810158223564146032892279_<79>

Number: 79991_140
N=1254891470052116520828269206319513146161103905631639479267954114925778079057809127052812483177258998970076508569
  ( 112 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=388536296915994985391902206726511 (pp33)
 r2=3229792119842628898676018383831983166364802105671842667810158223564146032892279 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.41 hours.
Scaled time: 11.62 units (timescale=2.148).
Factorization parameters were as follows:
n: 1254891470052116520828269206319513146161103905631639479267954114925778079057809127052812483177258998970076508569
m: 20000000000000000000000000000
c5: 1
c0: -36
skew: 2.05
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1100001)
Primes: RFBsize:114155, AFBsize:114197, largePrimes:3313249 encountered
Relations: rels:3414814, finalFF:399605
Max relations in full relation-set: 28
Initial matrix: 228416 x 399605 with sparse part having weight 33303166.
Pruned matrix : 167030 x 168236 with weight 12188509.
Total sieving time: 5.25 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 5.41 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)

8·10¹⁶¹-9 = 7(9)₁₆₀1_<162> = 29 · 199 · 571 · 1692365724601_<13> · C144

C144 = P33 · P111

P33 = 428383815004193749871857607077279_<33>

P111 = 334869450332200636093078292799339933789697545275221769023019937305594987180395275406031737563279818152065360169_<111>

8·10¹⁵⁸-9 = 7(9)₁₅₇1_<159> = 7 · 4323841 · 4714903 · 462997341128773543_<18> · C128

C128 = P33 · C95

P33 = 410562561244534563981430142949031_<33>

C95 = [29491144580163096639800559468991908217808992070869327114070748537704128510842764288695820636807_<95>]

8·10¹⁵⁰-9 = 7(9)₁₄₉1_<151> = 193 · 247601 · 3624571477934606884159_<22> · C122

C122 = P53 · P69

P53 = 96315157891755373030439425392135709447474977307786081_<53>

P69 = 479544565961051555887991852543525630193846540227492360552478340319353_<69>

Number: 79991_150
N=46187410586671979793763904423352571432961215465785614036273142323402790039945056505520163118222449815563959534158948325593
  ( 122 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=96315157891755373030439425392135709447474977307786081 (pp53)
 r2=479544565961051555887991852543525630193846540227492360552478340319353 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.20 hours.
Scaled time: 24.03 units (timescale=2.146).
Factorization parameters were as follows:
n: 46187410586671979793763904423352571432961215465785614036273142323402790039945056505520163118222449815563959534158948325593
m: 2000000000000000000000000000000
c5: 1
c0: -36
skew: 2.05
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:176388, largePrimes:5294283 encountered
Relations: rels:5193470, finalFF:481776
Max relations in full relation-set: 28
Initial matrix: 352754 x 481776 with sparse part having weight 38435562.
Pruned matrix : 281271 x 283098 with weight 21037307.
Total sieving time: 10.76 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.34 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 11.20 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)

Jan 12, 2008 (8th)

By Sinkiti Sibata / GGNFS, Msieve

8·10¹¹⁵-9 = 7(9)₁₁₄1_<116> = 31 · C115

C115 = P34 · P39 · P43

P34 = 1952641829846445891880391633628571_<34>

P39 = 183792537662905341244235989253778248189_<39>

P43 = 7190810275475399982758739592384651846401319_<43>

Number: 79991_115
N=2580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161
  ( 115 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=1952641829846445891880391633628571 (pp34)
 r2=183792537662905341244235989253778248189 (pp39)
 r3=7190810275475399982758739592384651846401319 (pp43)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1.28 hours.
Scaled time: 2.57 units (timescale=2.003).
Factorization parameters were as follows:
name: 79991_115
n: 2580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161
m: 100000000000000000000000
c5: 8
c0: -9
skew: 1.02
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 450001)
Primes: RFBsize:49098, AFBsize:64008, largePrimes:2120520 encountered
Relations: rels:2265866, finalFF:291540
Max relations in full relation-set: 28
Initial matrix: 113171 x 291540 with sparse part having weight 22877031.
Pruned matrix : 73769 x 74398 with weight 3980313.
Total sieving time: 1.19 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.28 hours.
 --------- CPU info (if available) ----------

8·10¹¹³-9 = 7(9)₁₁₂1_<114> = 60281424871_<11> · C104

C104 = P48 · P56

P48 = 390808792124933992905008532836460473489137122991_<48>

P56 = 33958003771356934218524016876132944905551552683170456031_<56>

Number: 79991_113
N=13271086436857956665003795278321466204613927762908668489758134204339053238368831986794926070452804708721
  ( 104 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=390808792124933992905008532836460473489137122991 (pp48)
 r2=33958003771356934218524016876132944905551552683170456031 (pp56)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.88 hours.
Scaled time: 1.27 units (timescale=0.675).
Factorization parameters were as follows:
name:79991_113
n: 13271086436857956665003795278321466204613927762908668489758134204339053238368831986794926070452804708721
m: 20000000000000000000000
c5: 250
c0: -9
skew: 0.51
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:63828, largePrimes:2133195 encountered
Relations: rels:2279375, finalFF:293525
Max relations in full relation-set: 28
Initial matrix: 112993 x 293525 with sparse part having weight 23279201.
Pruned matrix : 72949 x 73577 with weight 4016180.
Total sieving time: 1.70 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.88 hours.
 --------- CPU info (if available) ----------

8·10¹²¹-9 = 7(9)₁₂₀1_<122> = 19 · 16931 · C117

C117 = P53 · P64

P53 = 66190937999157259563309327452865130078561271454954931_<53>

P64 = 3757121508638448333172650338258137145904700516674921367147594549_<64>

Number: 79991_121
N=248687396833587719816344357438395468915629692031744946205807472434556357227011181607080130187852242383171323856271119
  ( 117 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=66190937999157259563309327452865130078561271454954931 (pp53)
 r2=3757121508638448333172650338258137145904700516674921367147594549 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.07 hours.
Scaled time: 4.17 units (timescale=2.010).
Factorization parameters were as follows:
name: 79991_121
n: 248687396833587719816344357438395468915629692031744946205807472434556357227011181607080130187852242383171323856271119
m: 2000000000000000000000000
c5: 5
c0: -18
skew: 1.29
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63758, largePrimes:1984467 encountered
Relations: rels:1952225, finalFF:141050
Max relations in full relation-set: 28
Initial matrix: 112922 x 141050 with sparse part having weight 10926246.
Pruned matrix : 102413 x 103041 with weight 6162277.
Total sieving time: 1.93 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.07 hours.
 --------- CPU info (if available) ----------

Jan 12, 2008 (7th)

By Robert Backstrom / GMP-ECM

8·10¹⁰⁸-9 = 7(9)₁₀₇1_<109> = 11897 · 6595030913_<10> · 74285794073_<11> · C85

C85 = P32 · P54

P32 = 10784808302586663079660355798191_<32>

P54 = 127267493166302734542256662357223329760676931011149417_<54>

Jan 12, 2008 (6th)

By Jo Yeong Uk / GMP-ECM, Msieve, GGNFS

8·10¹⁹¹-9 = 7(9)₁₉₀1_<192> = C192

C192 = P34 · C159

P34 = 2838215384488977187840273748749501_<34>

C159 = [281867262214153842659280716998882524780880662933308691584296839537167821919759679358142157019600539866645046737600020701546566244595946561032467565638861495491_<159>]

8·10¹²⁶-9 = 7(9)₁₂₅1_<127> = 23 · C126

C126 = P39 · P88

P39 = 217581248286592871920703441696601910487_<39>

P88 = 1598603233024812172766526043763336942138049668499189186436388071437141249364595430510791_<88>

Number: 79991_126
N=347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217
  ( 126 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=217581248286592871920703441696601910487 (pp39)
 r2=1598603233024812172766526043763336942138049668499189186436388071437141249364595430510791 (pp88)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.48 hours.
Scaled time: 3.18 units (timescale=2.151).
Factorization parameters were as follows:
n: 347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217
m: 20000000000000000000000000
c5: 5
c0: -18
skew: 1.29
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [400000, 720001)
Primes: RFBsize:63951, AFBsize:63758, largePrimes:1391980 encountered
Relations: rels:1386131, finalFF:169407
Max relations in full relation-set: 28
Initial matrix: 127775 x 169407 with sparse part having weight 8164693.
Pruned matrix : 109759 x 110461 with weight 4063548.
Total sieving time: 1.42 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,800000,800000,25,25,45,45,2.2,2.2,40000
total time: 1.48 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)

8·10¹³⁷-9 = 7(9)₁₃₆1_<138> = 281 · 45259 · 6783449 · 146011951 · C116

C116 = P31 · P34 · P52

P31 = 9029523373784041010808525557981_<31>

P34 = 1221423363891302373996983840134301_<34>

P52 = 5758491037866755216905701730446521364185825908289891_<52>

Sat Jan 12 21:44:58 2008  
Sat Jan 12 21:44:58 2008  
Sat Jan 12 21:44:58 2008  Msieve v. 1.28
Sat Jan 12 21:44:58 2008  random seeds: 5b6f6980 09f90c48
Sat Jan 12 21:44:58 2008  factoring 7033555494409129235621750952426445415239612600830862521555814673561206967670680651191 (85 digits)
Sat Jan 12 21:44:58 2008  commencing quadratic sieve (85-digit input)
Sat Jan 12 21:44:58 2008  using multiplier of 7
Sat Jan 12 21:44:58 2008  using 32kb Intel Core sieve core
Sat Jan 12 21:44:58 2008  sieve interval: 12 blocks of size 32768
Sat Jan 12 21:44:58 2008  processing polynomials in batches of 17
Sat Jan 12 21:44:58 2008  using a sieve bound of 1434241 (54480 primes)
Sat Jan 12 21:44:58 2008  using large prime bound of 116173521 (26 bits)
Sat Jan 12 21:44:58 2008  using double large prime bound of 328997602795950 (41-49 bits)
Sat Jan 12 21:44:58 2008  using trial factoring cutoff of 49 bits
Sat Jan 12 21:44:58 2008  polynomial 'A' values have 11 factors
Sat Jan 12 22:09:30 2008  54635 relations (15866 full + 38769 combined from 573370 partial), need 54576
Sat Jan 12 22:09:30 2008  begin with 589236 relations
Sat Jan 12 22:09:31 2008  reduce to 128767 relations in 9 passes
Sat Jan 12 22:09:31 2008  attempting to read 128767 relations
Sat Jan 12 22:09:32 2008  recovered 128767 relations
Sat Jan 12 22:09:32 2008  recovered 108972 polynomials
Sat Jan 12 22:09:32 2008  attempting to build 54635 cycles
Sat Jan 12 22:09:32 2008  found 54635 cycles in 5 passes
Sat Jan 12 22:09:32 2008  distribution of cycle lengths:
Sat Jan 12 22:09:32 2008     length 1 : 15866
Sat Jan 12 22:09:32 2008     length 2 : 11089
Sat Jan 12 22:09:32 2008     length 3 : 9652
Sat Jan 12 22:09:32 2008     length 4 : 6995
Sat Jan 12 22:09:32 2008     length 5 : 4741
Sat Jan 12 22:09:32 2008     length 6 : 2779
Sat Jan 12 22:09:32 2008     length 7 : 1683
Sat Jan 12 22:09:32 2008     length 9+: 1830
Sat Jan 12 22:09:32 2008  largest cycle: 17 relations
Sat Jan 12 22:09:32 2008  matrix is 54480 x 54635 with weight 2902839 (avg 53.13/col)
Sat Jan 12 22:09:32 2008  filtering completed in 3 passes
Sat Jan 12 22:09:32 2008  matrix is 49839 x 49903 with weight 2674857 (avg 53.60/col)
Sat Jan 12 22:09:33 2008  saving the first 48 matrix rows for later
Sat Jan 12 22:09:33 2008  matrix is 49791 x 49903 with weight 2017488 (avg 40.43/col)
Sat Jan 12 22:09:33 2008  matrix includes 64 packed rows
Sat Jan 12 22:09:33 2008  commencing Lanczos iteration
Sat Jan 12 22:10:15 2008  lanczos halted after 789 iterations
Sat Jan 12 22:10:15 2008  recovered 15 nontrivial dependencies
Sat Jan 12 22:10:16 2008  prp34 factor: 1221423363891302373996983840134301
Sat Jan 12 22:10:16 2008  prp52 factor: 5758491037866755216905701730446521364185825908289891
Sat Jan 12 22:10:16 2008  elapsed time 00:25:18

8·10¹⁴⁶-9 = 7(9)₁₄₅1_<147> = 7² · 74209 · 233102762089_<12> · 458430639997432973730641_<24> · C106

C106 = P34 · P72

P34 = 2237064275354436560413927703682193_<34>

P72 = 920317772467855578861737276438457302528107277025704935144084694913195343_<72>

Jan 12, 2008 (5th)

By matsui / GMP-ECM

5·10²⁰⁰-9 = 4(9)₁₉₉1_<201> = 79 · C199

C199 = P34 · C166

P34 = 4565579173849692757873296750073841_<34>

C166 = [1386267477366716881025736493978991704108086368524410882780963548849099077745191410286959757712217661501763612288987394960172120415770934106869087379738850488433099369_<166>]

Jan 12, 2008 (4th)

By Sinkiti Sibata / GGNFS

(46·10¹⁸⁶-1)/9 = 5(1)₁₈₆_<187> = 73 · C185

C185 = P40 · P43 · P43 · P61

P40 = 2825392120613905556303145902353338583991_<40>

P43 = 1414261240340299364785702351487807687732347_<43>

P43 = 1940352243663463704570905682634709845035983_<43>

P61 = 9030327814966384090537560378864803219811293177354264381962277_<61>

Number: 51111_186
N=70015220700152207001522070015220700152207001522070015220700152207001522070015220700152207001522070015220700152207001522070015220700152207001522070015220700152207001522070015220700152207
  ( 185 digits)
SNFS difficulty: 187 digits.
Divisors found:
 r1=2825392120613905556303145902353338583991 (pp40)
 r2=1414261240340299364785702351487807687732347 (pp43)
 r3=1940352243663463704570905682634709845035983 (pp43)
 r4=9030327814966384090537560378864803219811293177354264381962277 (pp61)
Version: GGNFS-0.77.1-20060513-k8
Total time: 826.01 hours.
Scaled time: 1644.60 units (timescale=1.991).
Factorization parameters were as follows:
name: 51111_186
n: 70015220700152207001522070015220700152207001522070015220700152207001522070015220700152207001522070015220700152207001522070015220700152207001522070015220700152207001522070015220700152207
m: 10000000000000000000000000000000000000
c5: 460
c0: -1
skew: 0.29
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 13200001)
Primes: RFBsize:501962, AFBsize:501266, largePrimes:6770607 encountered
Relations: rels:7281007, finalFF:1163691
Max relations in full relation-set: 28
Initial matrix: 1003295 x 1163691 with sparse part having weight 97320435.
Pruned matrix : 873987 x 879067 with weight 77783757.
Total sieving time: 811.78 hours.
Total relation processing time: 0.72 hours.
Matrix solve time: 13.15 hours.
Time per square root: 0.37 hours.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 826.01 hours.
 --------- CPU info (if available) ----------

Jan 12, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(67·10¹⁶⁶+23)/9 = 7(4)₁₆₅7_<167> = 83 · 199 · C163

C163 = P81 · P83

P81 = 367004643653966872365696265950784599299328674117914006464687180669547532610783737_<81>

P83 = 12280882187472171359124427810998046557688853247533252193235475312651380187494652843_<83>

Number: n
N=4507140790969573436123051670669276772079944568895346881664009471722736843521489643666794481107007594868586574102103556604979381512650266055848183353178206965214291
  ( 163 digits)
SNFS difficulty: 167 digits.
Divisors found:

Sat Jan 12 06:34:13 2008  prp81 factor: 367004643653966872365696265950784599299328674117914006464687180669547532610783737
Sat Jan 12 06:34:13 2008  prp83 factor: 12280882187472171359124427810998046557688853247533252193235475312651380187494652843
Sat Jan 12 06:34:13 2008  elapsed time 01:13:19 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 60.51 hours.
Scaled time: 110.67 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_7_4_165_7
n: 4507140790969573436123051670669276772079944568895346881664009471722736843521489643666794481107007594868586574102103556604979381512650266055848183353178206965214291
skew: 0.51
deg: 5
c5: 670
c0: 23
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4100000)
Primes: RFBsize:250150, AFBsize:249316, largePrimes:7893359 encountered
Relations: rels:7379758, finalFF:577015
Max relations in full relation-set: 28
Initial matrix: 499533 x 577015 with sparse part having weight 63713644.
Pruned matrix : 468271 x 470832 with weight 45026970.
Total sieving time: 60.30 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 60.51 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

4·10¹⁶⁴+7 = 4(0)₁₆₃7_<165> = 11 · 37 · 43 · 6449 · 238291 · 18515813 · C144

C144 = P69 · P76

P69 = 196948146026549213753598998945340356169909690257113074987708892318543_<69>

P76 = 4078518408615435716369982093154238241123860446542160172985649100147392724947_<76>

Number: n
N=803256639111961948349569451134375723264862953628626206118805410285163427541196501369025854991877728369841645329293165617105583432513049506792221
  ( 144 digits)
SNFS difficulty: 165 digits.
Divisors found:

Sat Jan 12 07:34:52 2008  prp69 factor: 196948146026549213753598998945340356169909690257113074987708892318543
Sat Jan 12 07:34:52 2008  prp76 factor: 4078518408615435716369982093154238241123860446542160172985649100147392724947
Sat Jan 12 07:34:52 2008  elapsed time 01:31:42 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 39.02 hours.
Scaled time: 68.52 units (timescale=1.756).
Factorization parameters were as follows:
name: KA_4_0_163_7
n: 803256639111961948349569451134375723264862953628626206118805410285163427541196501369025854991877728369841645329293165617105583432513049506792221
type: snfs
skew: 1.77
deg: 5
c5: 2
c0: 35
m: 1000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1900000)
Primes: RFBsize:230209, AFBsize:229267, largePrimes:7099618 encountered
Relations: rels:6578698, finalFF:504591
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 38.81 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 39.02 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jan 12, 2008 (2nd)

By Sinkiti Sibata / PFGW

7·10¹³¹⁴⁵+9 = 7(0)₁₃₁₄₄9_<13146> is PRP.

7·10¹⁶⁶⁴⁶+9 = 7(0)₁₆₆₄₅9_<16647> is PRP.

7·10²⁰⁸⁹¹+9 = 7(0)₂₀₈₉₀9_<20892> is PRP.

Jan 12, 2008

The factor table of 799...991 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Jan 11, 2008

By Robert Backstrom / GGNFS, Msieve

(5·10¹⁶³-17)/3 = 1(6)₁₆₂1_<164> = 11 · 47 · 579620986471812630953_<21> · C140

C140 = P59 · P82

P59 = 33002739048257539876683509719350404697818409337940816248091_<59>

P82 = 1685249160148384416019014327429980236270130559391192098286783927630082498099632571_<82>

Number: n
N=55617838263672310701551004098935263046156702544564899044762593157589752112781293997694541379125158139575071938101345124582616379953880171961
  ( 140 digits)
SNFS difficulty: 164 digits.
Divisors found:

Fri Jan 11 08:30:33 2008  prp59 factor: 33002739048257539876683509719350404697818409337940816248091
Fri Jan 11 08:30:33 2008  prp82 factor: 1685249160148384416019014327429980236270130559391192098286783927630082498099632571
Fri Jan 11 08:30:33 2008  elapsed time 00:50:42 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-k8
Total time: 38.98 hours.
Scaled time: 32.67 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_1_6_162_1
n: 55617838263672310701551004098935263046156702544564899044762593157589752112781293997694541379125158139575071938101345124582616379953880171961
type: snfs
deg: 5
c5: 8
c0: -85
skew: 1.60
m: 500000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3600001)
Primes: RFBsize:216816, AFBsize:216871, largePrimes:5732678 encountered
Relations: rels:5698376, finalFF:511733
Max relations in full relation-set: 28
Initial matrix: 433752 x 511733 with sparse part having weight 49865175.
Pruned matrix : 401349 x 403581 with weight 36480624.
Total sieving time: 36.68 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 2.19 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 38.98 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

(14·10¹⁶¹-41)/9 = 1(5)₁₆₀1_<162> = 11 · 79 · 2411 · 2528269 · 298614421769978987_<18> · C131

C131 = P49 · P83

P49 = 1237731289012386762849485097499340001383842403737_<49>

P83 = 79452599632851028607355803437954089119988633926215410442037070045079459127725856399_<83>

Number: n
N=98340968558953790892585585889392535669496255284578280374020149122636303507627134972206826846954930393394612505752654421559042963063
  ( 131 digits)
SNFS difficulty: 162 digits.
Divisors found:

Fri Jan 11 22:44:54 2008  prp49 factor: 1237731289012386762849485097499340001383842403737
Fri Jan 11 22:44:54 2008  prp83 factor: 79452599632851028607355803437954089119988633926215410442037070045079459127725856399
Fri Jan 11 22:44:54 2008  elapsed time 00:58:45 (Msieve 1.32)

Version: GGNFS-0.77.1-20050930-k8
Total time: 40.38 hours.
Scaled time: 33.84 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_1_5_160_1
n: 98340968558953790892585585889392535669496255284578280374020149122636303507627134972206826846954930393394612505752654421559042963063
type: snfs
deg: 5
c5: 140
c0: -41
skew: 0.78
m: 100000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3900001)
Primes: RFBsize:216816, AFBsize:216922, largePrimes:5786060 encountered
Relations: rels:5738816, finalFF:470992
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 40.25 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 40.38 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

Jan 10, 2008 (4th)

By matsui / GMP-ECM

(55·10¹⁸³-1)/9 = 6(1)₁₈₃_<184> = 3³ · 7 · 29 · C181

C181 = P31 · C150

P31 = 1814486819606228803034309724019_<31>

C150 = [614478313503825526186774142080138780423238442508754732017910702305971084132729055650327224394349460485381313575366771621956040706591459972940854945749_<150>]

Jan 10, 2008 (3rd)

By Jo Yeong Uk / GGNFS

(86·10¹⁷¹+31)/9 = 9(5)₁₇₀9_<172> = 11 · 17 · 1381 · 10267 · 37781 · 215134273 · 6394987531_<10> · 148336234710094457893_<21> · C120

C120 = P43 · P78

P43 = 1096966381258354525082396230206423839135069_<43>

P78 = 426102195310162589018569755129159308229685168412082711285523685052681229610341_<78>

Number: 95559_171
N=467419783235629658103214304014991608228915825261793443002931643083874160506685464483702892779307242690217664321338148529
  ( 120 digits)
Divisors found:
 r1=1096966381258354525082396230206423839135069 (pp43)
 r2=426102195310162589018569755129159308229685168412082711285523685052681229610341 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 48.00 hours.
Scaled time: 103.06 units (timescale=2.147).
Factorization parameters were as follows:
name: 95559_171
n: 467419783235629658103214304014991608228915825261793443002931643083874160506685464483702892779307242690217664321338148529
skew: 34824.01
# norm 1.82e+16
c5: 30660
c4: -7605601439
c3: -528135056994814
c2: 12643616123032503853
c1: -80969674776601688470101
c0: 4409842209862057154181171
# alpha -4.95
Y1: 1049506019249
Y0: -108799574192722567741550
# Murphy_E 2.79e-10
# M 391493396307864520630205026286345938563037358745772478822904461270085767891754310654812573400414010370216518282741011494
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4800001)
Primes: RFBsize:315948, AFBsize:316768, largePrimes:7779738 encountered
Relations: rels:7883829, finalFF:717826
Max relations in full relation-set: 28
Initial matrix: 632799 x 717826 with sparse part having weight 68095105.
Pruned matrix : 566163 x 569390 with weight 50169037.
Total sieving time: 45.46 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 2.17 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000
total time: 48.00 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406450)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4809.83 BogoMIPS (lpj=2404916)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)

Jan 10, 2008 (2nd)

By Yousuke Koide

(10¹⁰¹⁹-1)/9 is divisible by 19546240918513258853789109982103832107_<38>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 10, 2008

By Kurt Beschorner / Jan 3, 2008

10⁵⁰⁶+1 is divisible by 69691163546816853278309618463969524441_<38>

Reference: Factorizations of numbers of the form 10ⁿ+1 (Alfred Reich)

Jan 9, 2008 (2nd)

By Sinkiti Sibata / GGNFS

7·10¹⁶¹+9 = 7(0)₁₆₀9_<162> = 15371116800042997500203_<23> · 57118997757210264206905876447_<29> · C111

C111 = P54 · P58

P54 = 139490464604623382674750512013106688318266001541875221_<54>

P58 = 5715674892138940064628738708170977544099888345108701283569_<58>

Number: 70009_161
N=797282146233441389637438465879864974174079631931857291117873335595617292138291581776356920378174414625935543749
  ( 111 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=139490464604623382674750512013106688318266001541875221 (pp54)
 r2=5715674892138940064628738708170977544099888345108701283569 (pp58)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 89.61 hours.
Scaled time: 60.58 units (timescale=0.676).
Factorization parameters were as follows:
name: 70009_161
n: 797282146233441389637438465879864974174079631931857291117873335595617292138291581776356920378174414625935543749
m: 100000000000000000000000000000000
c5: 70
c0: 9
skew: 0.66
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4350001)
Primes: RFBsize:315948, AFBsize:316621, largePrimes:5728840 encountered
Relations: rels:5815604, finalFF:721506
Max relations in full relation-set: 28
Initial matrix: 632637 x 721506 with sparse part having weight 43287861.
Pruned matrix : 561950 x 565177 with weight 30874466.
Total sieving time: 75.81 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 13.19 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 89.61 hours.
 --------- CPU info (if available) ----------

Jan 9, 2008

By Robert Backstrom / GGNFS, Msieve

4·10¹⁶³+9 = 4(0)₁₆₂9_<164> = 7 · 1303 · 257837 · 959561 · 5915543 · C142

C142 = P66 · P76

P66 = 878200471969328827561876462072079282958405245015115821377184281733_<66>

P76 = 3412018883530127490227807989559980166714774210829016758904628027464337410663_<76>

Number: n
N=2996436593884420368599350071793146725644507391872863126806932222472234937356674817826792539332714575692570318811933890006862102836684710318979
  ( 142 digits)
SNFS difficulty: 165 digits.
Divisors found:

Wed Jan 09 05:18:19 2008  prp66 factor: 878200471969328827561876462072079282958405245015115821377184281733
Wed Jan 09 05:18:19 2008  prp76 factor: 3412018883530127490227807989559980166714774210829016758904628027464337410663
Wed Jan 09 05:18:19 2008  elapsed time 01:27:31 (Msieve 1.32)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 52.44 hours.
Scaled time: 68.75 units (timescale=1.311).
Factorization parameters were as follows:
name: KA_4_0_162_9
n: 2996436593884420368599350071793146725644507391872863126806932222472234937356674817826792539332714575692570318811933890006862102836684710318979
skew: 2.95
deg: 5
c5: 1
c0: 225
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2500213)
Primes: RFBsize:230209, AFBsize:229862, largePrimes:7327517 encountered
Relations: rels:6805231, finalFF:503679
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 52.15 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 52.44 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

5·10¹⁶⁴+3 = 5(0)₁₆₃3_<165> = 557 · 217837300066202477_<18> · C145

C145 = P64 · P82

P64 = 1196687247426772242533735797290481529635161715296376005028120547_<64>

P82 = 3443514377361480174374528664126918435300112338137700545497427175846407441531435641_<82>

Number: n
N=4120809741719225186741054484135263928241671284276174640242932170788013428862000974905621445274870595945310435532020747550508457434928692920215627
  ( 145 digits)
SNFS difficulty: 165 digits.
Divisors found:

Wed Jan  9 16:25:56 2008  prp64 factor: 1196687247426772242533735797290481529635161715296376005028120547
Wed Jan  9 16:25:56 2008  prp82 factor: 3443514377361480174374528664126918435300112338137700545497427175846407441531435641
Wed Jan  9 16:25:56 2008  elapsed time 00:57:08 (Msieve 1.32)

Version: GGNFS-0.77.1-20050930-k8
Total time: 38.58 hours.
Scaled time: 32.37 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_5_0_163_3
n: 4120809741719225186741054484135263928241671284276174640242932170788013428862000974905621445274870595945310435532020747550508457434928692920215627
type: snfs
deg: 5
c5: 1
c0: 6
skew: 1.43
m: 1000000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3800001)
Primes: RFBsize:216816, AFBsize:216821, largePrimes:5658666 encountered
Relations: rels:5541692, finalFF:429370
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 38.47 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 38.58 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

(73·10¹⁶⁴-1)/9 = 8(1)₁₆₄_<165> = 61 · 373 · 3620158294151899_<16> · C145

C145 = P67 · P79

P67 = 1043995987473037595727834603195896693955428946648402327832492964027_<67>

P79 = 9432249792339282259291436913130955217924127892296499942188495834211334121986719_<79>

Number: n
N=9847230936045602785233094889585613069848563625548151842425600774026787507620946164685576203283969203986063171766643656802199995825880290238757413
  ( 145 digits)
SNFS difficulty: 166 digits.
Divisors found:

Wed Jan 09 19:08:01 2008  prp67 factor: 1043995987473037595727834603195896693955428946648402327832492964027
Wed Jan 09 19:08:01 2008  prp79 factor: 9432249792339282259291436913130955217924127892296499942188495834211334121986719
Wed Jan 09 19:08:01 2008  elapsed time 01:57:05 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 74.89 hours.
Scaled time: 131.21 units (timescale=1.752).
Factorization parameters were as follows:
name: KA_8_1_164
n: 9847230936045602785233094889585613069848563625548151842425600774026787507620946164685576203283969203986063171766643656802199995825880290238757413
type: snfs
skew: 0.67
deg: 5
c5: 73
c0: -10
m: 1000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3500269)
Primes: RFBsize:230209, AFBsize:230027, largePrimes:7684684 encountered
Relations: rels:7147678, finalFF:483126
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 74.61 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 74.89 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jan 8, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

(52·10¹⁶¹-7)/9 = 5(7)₁₆₁_<162> = 67 · 211 · 399657043 · 41884981582841233_<17> · C133

C133 = P57 · P76

P57 = 303583120466432755281692462570253330795169293513976483517_<57>

P76 = 8042297897793284514496513202115956001841463193178478887769004032896132968527_<76>

Number: n
N=2441505891532717595222421523167960460997180306913825571010358957513150181867983231904207917169754437950011734144951653882157895269459
  ( 133 digits)
SNFS difficulty: 162 digits.
Divisors found:

Tue Jan  8 23:59:06 2008  prp57 factor: 303583120466432755281692462570253330795169293513976483517
Tue Jan  8 23:59:06 2008  prp76 factor: 8042297897793284514496513202115956001841463193178478887769004032896132968527
Tue Jan  8 23:59:06 2008  elapsed time 00:57:39 (Msieve 1.32)

Version: GGNFS-0.77.1-20050930-k8
Total time: 43.17 hours.
Scaled time: 36.18 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_5_7_161
n: 2441505891532717595222421523167960460997180306913825571010358957513150181867983231904207917169754437950011734144951653882157895269459
type: snfs
deg: 5
c5: 520
c0: -7
skew: 0.42
m: 100000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4000001)
Primes: RFBsize:216816, AFBsize:217161, largePrimes:5742071 encountered
Relations: rels:5648051, finalFF:422567
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 43.05 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 43.17 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

Jan 8, 2008 (2nd)

By matsui / GMP-ECM

(4·10¹⁹²-7)/3 = 1(3)₁₉₁1_<193> = 53 · 113 · C189

C189 = P39 · C151

P39 = 208077415143242929300081213865119997527_<39>

C151 = [1069940136279591667980810496981378274903150054006469796842841376740519957678800554460072994496458619358697351060409992237703368110891340267099632894977_<151>]

Jan 8, 2008

By Robert Backstrom / GGNFS, Msieve

7·10¹⁶⁶+9 = 7(0)₁₆₅9_<167> = 21991 · 972833 · 1082531 · C151

C151 = P68 · P84

P68 = 21801158658206841112555253752829902500472040092585365034962893355053_<68>

P84 = 138642011235137555584320880412798358499970719485097366270743949931671229392787022521_<84>

Number: n
N=3022556483630129261598847253569879921858042829617050352190156557137315012023902736896851269624585181616682870685916160325557846898137814787523960148613
  ( 151 digits)
SNFS difficulty: 166 digits.
Divisors found:

Tue Jan 08 02:23:48 2008  prp68 factor: 21801158658206841112555253752829902500472040092585365034962893355053
Tue Jan 08 02:23:48 2008  prp84 factor: 138642011235137555584320880412798358499970719485097366270743949931671229392787022521
Tue Jan 08 02:23:48 2008  elapsed time 01:22:44 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 48.47 hours.
Scaled time: 88.50 units (timescale=1.826).
Factorization parameters were as follows:
name: KA_7_0_165_9
n: 3022556483630129261598847253569879921858042829617050352190156557137315012023902736896851269624585181616682870685916160325557846898137814787523960148613
skew: 0.66
deg: 5
c5: 70
c0: 9
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3200001)
Primes: RFBsize:250150, AFBsize:250721, largePrimes:7669339 encountered
Relations: rels:7156943, finalFF:567239
Max relations in full relation-set: 28
Initial matrix: 500939 x 567239 with sparse part having weight 51971046.
Pruned matrix : 
Total sieving time: 48.24 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 48.47 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(4·10¹⁶⁷-7)/3 = 1(3)₁₆₆1_<168> = 11 · 1453 · 65789 · 65585573 · C151

C151 = P41 · P110

P41 = 44513060255051568150273475384941022348961_<41>

P110 = 43434155511436613056459493128340863687385119966755835981223737071050592042248993684052667503664574707092147821_<110>

Number: n
N=1933387181407858117653716396964261130297665698862132685796900976269788635641054996450601322919821997858497612243316173533210563965043659752396057763981
  ( 151 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=44513060255051568150273475384941022348961 (pp41)
 r2=43434155511436613056459493128340863687385119966755835981223737071050592042248993684052667503664574707092147821 (pp110)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 44.09 hours.
Scaled time: 80.15 units (timescale=1.818).
Factorization parameters were as follows:
name: KA_1_3_166_1
n: 1933387181407858117653716396964261130297665698862132685796900976269788635641054996450601322919821997858497612243316173533210563965043659752396057763981
skew: 0.89
deg: 5
c5: 25
c0: -14
m: 2000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2800001)
Primes: RFBsize:250150, AFBsize:250081, largePrimes:7547303 encountered
Relations: rels:7067753, finalFF:589532
Max relations in full relation-set: 48
Initial matrix: 500295 x 589532 with sparse part having weight 48687984.
Pruned matrix : 435661 x 438226 with weight 31937138.
Total sieving time: 42.02 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 1.71 hours.
Total square root time: 0.17 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 44.09 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jan 7, 2008 (2nd)

By Jo Yeong Uk / GGNFS

7·10¹⁶³+9 = 7(0)₁₆₂9_<164> = 10463 · 17394388742849265431_<20> · 21685605887741051661689_<23> · C119

C119 = P35 · P84

P35 = 18751242705828780547597219322844983_<35>

P84 = 945869076252608429463531219474556440073685963101828788499278956282259958157147275519_<84>

Number: 70009_163
N=17736220616750730441171459656279219097305026284234519209128657392107895275988306959156196633013809260456105154427871177
  ( 119 digits)
Divisors found:
 r1=18751242705828780547597219322844983 (pp35)
 r2=945869076252608429463531219474556440073685963101828788499278956282259958157147275519 (pp84)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 38.06 hours.
Scaled time: 81.90 units (timescale=2.152).
Factorization parameters were as follows:
name: 70009_163
n: 17736220616750730441171459656279219097305026284234519209128657392107895275988306959156196633013809260456105154427871177
skew: 221395.86
# norm 1.00e+16
c5: 900
c4: -368936484
c3: -64515235009570
c2: -6637800111968368825
c1: 1003631229460161110538300
c0: 64280742149364474007670220864
# alpha -5.48
Y1: 2264490571433
Y0: -114531360207998065534985
# Murphy_E 3.62e-10
# M 13078825261663832417425027932008595424256843732315959701340945098020013622714623701968577018374575816455494749105625740
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4125001)
Primes: RFBsize:315948, AFBsize:315634, largePrimes:7634260 encountered
Relations: rels:7677465, finalFF:728561
Max relations in full relation-set: 28
Initial matrix: 631658 x 728561 with sparse part having weight 60105103.
Pruned matrix : 551454 x 554676 with weight 40275843.
Polynomial selection time: 2.27 hours.
Total sieving time: 33.75 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.72 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000
total time: 38.06 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406450)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4809.83 BogoMIPS (lpj=2404916)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)

Jan 7, 2008

By Robert Backstrom / GGNFS, Msieve

7·10¹⁵⁹+9 = 7(0)₁₅₈9_<160> = 47 · 71 · 92371871 · 102843119 · C141

C141 = P64 · P77

P64 = 4231538071496958890327182029936342614194854003919814193922731887_<64>

P77 = 52182946885757635675346604057724856979445602984378050368353799424430749322239_<77>

Number: n
N=220814126429987102417525345115212994015254781641465598720037588384391899194205728399759788601386125925513113788312586671462061961060563534993
  ( 141 digits)
SNFS difficulty: 160 digits.
Divisors found:

Mon Jan  7 10:52:24 2008  prp64 factor: 4231538071496958890327182029936342614194854003919814193922731887
Mon Jan  7 10:52:24 2008  prp77 factor: 52182946885757635675346604057724856979445602984378050368353799424430749322239
Mon Jan  7 10:52:24 2008  elapsed time 00:47:28 (Msieve 1.32)

Version: GGNFS-0.77.1-20050930-k8
Total time: 37.69 hours.
Scaled time: 31.55 units (timescale=0.837).
Factorization parameters were as follows:
name: KA_7_0_158_9
n: 220814126429987102417525345115212994015254781641465598720037588384391899194205728399759788601386125925513113788312586671462061961060563534993
type: snfs
deg: 5
c5: 7
c0: 90
skew: 1.66
m: 100000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3600000)
Primes: RFBsize:216816, AFBsize:217356, largePrimes:5850727 encountered
Relations: rels:5857858, finalFF:519585
Max relations in full relation-set: 28
Initial matrix: 434238 x 519585 with sparse part having weight 53804158.
Pruned matrix : 399638 x 401873 with weight 39322056.
Total sieving time: 37.57 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 37.69 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

Jan 6, 2008 (5th)

By Jo Yeong Uk / GGNFS

7·10¹⁵²+9 = 7(0)₁₅₁9_<153> = 1926832847437_<13> · 6720374834881_<13> · 63639889190749_<14> · C114

C114 = P44 · P71

P44 = 77865850690669784859431617592698851037196011_<44>

P71 = 10908977710449886619312815188508141739609220654946251183378377187561523_<71>

Number: 70009_152
N=849436829589735592329176864706011392830693305217572069249710802758273465640411056591506419610722308940760472684753
  ( 114 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=77865850690669784859431617592698851037196011 (pp44)
 r2=10908977710449886619312815188508141739609220654946251183378377187561523 (pp71)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 17.38 hours.
Scaled time: 37.41 units (timescale=2.153).
Factorization parameters were as follows:
n: 849436829589735592329176864706011392830693305217572069249710802758273465640411056591506419610722308940760472684753
m: 1000000000000000000000000000000
c5: 700
c0: 9
skew: 0.42
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2300001)
Primes: RFBsize:176302, AFBsize:176233, largePrimes:5591809 encountered
Relations: rels:5524453, finalFF:488152
Max relations in full relation-set: 28
Initial matrix: 352603 x 488152 with sparse part having weight 45172811.
Pruned matrix : 301081 x 302908 with weight 25623922.
Total sieving time: 16.80 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.45 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 17.38 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406450)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4809.83 BogoMIPS (lpj=2404916)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)

Jan 6, 2008 (4th)

By Sibata / GGNFS

7·10¹⁷⁸+9 = 7(0)₁₇₇9_<179> = 2521 · 956113 · 1743745060873_<13> · 425228655272117_<15> · 1456142266504809349962840467_<28> · C116

C116 = P47 · P70

P47 = 13724946734647014417463514389532708012499306431_<47>

P70 = 1959728831003640657417517089713455927810208846008120710768293127210569_<70>

Number: 70009_178
N=26897173819877028591110438652440673484340131396511460906841522339126291846561419391159526937917846026688166192869239
  ( 116 digits)
Divisors found:
 r1=13724946734647014417463514389532708012499306431 (pp47)
 r2=1959728831003640657417517089713455927810208846008120710768293127210569 (pp70)
Version: GGNFS-0.77.1-20060513-k8
Total time: 46.23 hours.
Scaled time: 92.32 units (timescale=1.997).
Factorization parameters were as follows:
name: 70009_178
n: 26897173819877028591110438652440673484340131396511460906841522339126291846561419391159526937917846026688166192869239
skew: 65128.70
# norm 2.59e+16
c5: 75240
c4: -13181039364
c3: -658562293775890
c2: 51710009653767333541
c1: 1420986165414594796991522
c0: -33687414893484683332845870465
# alpha -6.85
Y1: 2035177406489
Y0: -12901908954921655902182
# Murphy_E 4.88e-10
# M 8982289048165742481213259840673138009408130390316621262097418188889777156561626476495961720222603100592888454691430
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 3510001)
Primes: RFBsize:315948, AFBsize:315985, largePrimes:7448433 encountered
Relations: rels:7438490, finalFF:727459
Max relations in full relation-set: 28
Initial matrix: 632017 x 727459 with sparse part having weight 54906751.
Pruned matrix : 548769 x 551993 with weight 34635393.
Total sieving time: 42.35 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 3.15 hours.
Time per square root: 0.41 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 46.23 hours.
 --------- CPU info (if available) ----------

Jan 6, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve

7·10¹⁴⁶+9 = 7(0)₁₄₅9_<147> = 1904249 · C141

C141 = P50 · P92

P50 = 29348460735839486849597048687491482266220440029873_<50>

P92 = 12525324190779213411439080213347337398023495842703998477149462377348409081784748884226366817_<92>

Number: n
N=367598985216744238804904190575917330139073198935643395375289681128885980772472507534466343424625666076232677554248420243361031041633735924241
  ( 141 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=29348460735839486849597048687491482266220440029873 (pp50)
 r2=12525324190779213411439080213347337398023495842703998477149462377348409081784748884226366817 (pp92)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 11.17 hours.
Scaled time: 14.57 units (timescale=1.305).
Factorization parameters were as follows:
name: KA_7_0_145_9
n: 367598985216744238804904190575917330139073198935643395375289681128885980772472507534466343424625666076232677554248420243361031041633735924241
skew: 0.66
deg: 5
c5: 70
c0: 9
m: 100000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:203362, AFBsize:203847, largePrimes:6878552 encountered
Relations: rels:6404033, finalFF:539587
Max relations in full relation-set: 28
Initial matrix: 407277 x 539587 with sparse part having weight 31365500.
Pruned matrix : 292139 x 294239 with weight 15013733.
Total sieving time: 9.38 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 1.42 hours.
Total square root time: 0.17 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 11.17 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁵⁷+9 = 7(0)₁₅₆9_<158> = 79 · 96857225721671_<14> · C142

C142 = P54 · P89

P54 = 643687030404506197051806584898109829074806677658713563_<54>

P89 = 14212293404416947433671925044120391584277610010545822637985641678790000790685720922856627_<89>

Number: n
N=9148268936726694531651576219628786925034862262185737873387878910253280521430132640027051308022147551977228490456289749680469055617015909332001
  ( 142 digits)
SNFS difficulty: 157 digits.
Divisors found:

Sun Jan 06 15:50:12 2008  prp54 factor: 643687030404506197051806584898109829074806677658713563
Sun Jan 06 15:50:12 2008  prp89 factor: 14212293404416947433671925044120391584277610010545822637985641678790000790685720922856627
Sun Jan 06 15:50:12 2008  elapsed time 00:47:37 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 21.73 hours.
Scaled time: 39.50 units (timescale=1.818).
Factorization parameters were as follows:
name: KA_7_0_156_9
n: 9148268936726694531651576219628786925034862262185737873387878910253280521430132640027051308022147551977228490456289749680469055617015909332001
skew: 0.42
deg: 5
c5: 700
c0: 9
m: 10000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1599990)
Primes: RFBsize:203362, AFBsize:203497, largePrimes:7016855 encountered
Relations: rels:6475989, finalFF:479308
Max relations in full relation-set: 28
Initial matrix: 406927 x 479308 with sparse part having weight 42290325.
Pruned matrix : 
Total sieving time: 21.58 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 21.73 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(5·10¹⁶⁷-17)/3 = 1(6)₁₆₆1_<168> = 11 · 103 · 57165172409_<11> · C154

C154 = P55 · P100

P55 = 1432799642868764623313581007575666255213214630794733651_<55>

P100 = 1795981494721534844168356589654494543435236348703608448307880333492214100092285485025785978171053563_<100>

Number: n
N=2573281644235925201154863504962616769184191842715562123978441074187952616988817531559698378059022788805862098468838043405885073260394546721714390639548513
  ( 154 digits)
SNFS difficulty: 167 digits.
Divisors found:

Sun Jan  6 18:26:05 2008  prp55 factor: 1432799642868764623313581007575666255213214630794733651
Sun Jan  6 18:26:05 2008  prp100 factor: 1795981494721534844168356589654494543435236348703608448307880333492214100092285485025785978171053563
Sun Jan  6 18:26:05 2008  elapsed time 01:17:38 (Msieve 1.32)

Version: GGNFS-0.77.1-20050930-k8
Total time: 54.16 hours.
Scaled time: 45.44 units (timescale=0.839).
Factorization parameters were as follows:
name: KA_1_6_166_1
n: 2573281644235925201154863504962616769184191842715562123978441074187952616988817531559698378059022788805862098468838043405885073260394546721714390639548513
type: snfs
deg: 5
c5: 500
c0: -17
skew: 0.51
m: 1000000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4700001)
Primes: RFBsize:216816, AFBsize:215811, largePrimes:5752099 encountered
Relations: rels:5651567, finalFF:380784
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 54.03 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 54.16 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

Jan 6, 2008 (2nd)

By Maksym Voznyy / PRIMO

(61·10²¹¹⁶-7)/9 is prime.

(61·10²¹⁸⁰-7)/9 is prime.

(61·10¹⁷⁸⁷⁸-7)/9 is PRP.

(61·10²²⁰⁹³-7)/9 is PRP.

Jan 6, 2008

By Paul Zimmermann

(10³³³-1)/9 is divisible by 378910432397861194405369041242690342635541471617136043289_<57>, cofactor is prime.

Jan 5, 2008 (3rd)

By Jo Yeong Uk / GGNFS

7·10¹⁴¹+9 = 7(0)₁₄₀9_<142> = 17627 · 98299 · C133

C133 = P39 · P95

P39 = 101414229444075792057935393801590219007_<39>

P95 = 39835625472292178795478811905988720116944029945084978719281689145836957513895091630614531075119_<95>

Number: 70009_141
N=4039899261695309109005048398359631685685486063939556024524503957895943660252833528639281309585610432411465854402366497268246378586833
  ( 133 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=101414229444075792057935393801590219007 (pp39)
 r2=39835625472292178795478811905988720116944029945084978719281689145836957513895091630614531075119 (pp95)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.92 hours.
Scaled time: 14.86 units (timescale=2.146).
Factorization parameters were as follows:
n: 4039899261695309109005048398359631685685486063939556024524503957895943660252833528639281309585610432411465854402366497268246378586833
m: 10000000000000000000000000000
c5: 70
c0: 9
skew: 0.66
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1200001)
Primes: RFBsize:114155, AFBsize:114417, largePrimes:3355192 encountered
Relations: rels:3424431, finalFF:361194
Max relations in full relation-set: 28
Initial matrix: 228640 x 361194 with sparse part having weight 32688347.
Pruned matrix : 183772 x 184979 with weight 14082163.
Total sieving time: 6.73 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.92 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406450)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4809.83 BogoMIPS (lpj=2404916)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)

7·10¹⁴²+9 = 7(0)₁₄₁9_<143> = 113 · 337 · 614934441575413662824970403_<27> · C112

C112 = P38 · P75

P38 = 19435116457349819947354128996919945157_<38>

P75 = 153806160331310217740660239181144108766898224889935222716697800849639765959_<75>

Number: 70009_142
N=2989240637896832248093598836643841444086092572084139927456736533426375053444720175992103186377912235052595510563
  ( 112 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=19435116457349819947354128996919945157 (pp38)
 r2=153806160331310217740660239181144108766898224889935222716697800849639765959 (pp75)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 7.54 hours.
Scaled time: 16.22 units (timescale=2.152).
Factorization parameters were as follows:
n: 2989240637896832248093598836643841444086092572084139927456736533426375053444720175992103186377912235052595510563
m: 10000000000000000000000000000
c5: 700
c0: 9
skew: 0.42
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1250001)
Primes: RFBsize:114155, AFBsize:114082, largePrimes:3285538 encountered
Relations: rels:3277670, finalFF:296280
Max relations in full relation-set: 28
Initial matrix: 228305 x 296280 with sparse part having weight 26224627.
Pruned matrix : 203393 x 204598 with weight 14737735.
Total sieving time: 7.32 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 7.54 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406450)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4809.83 BogoMIPS (lpj=2404916)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)

Jan 5, 2008 (2nd)

By Sinkiti Sibata / Msieve, GGNFS

7·10¹⁴⁹+9 = 7(0)₁₄₈9_<150> = 17 · 131 · 449 · 619 · 859 · 907 · 3347 · 43481 · 3089727089_<10> · 1140505032437_<13> · 3687919471679_<13> · C93

C93 = P45 · P49

P45 = 239837507703455294015342234963512005413275037_<45>

P49 = 3200142279977988684517610934831971048558705274893_<49>

Fri Jan  4 14:41:22 2008  Msieve v. 1.30
Fri Jan  4 14:41:22 2008  random seeds: 89fffcd3 bf362a6f
Fri Jan  4 14:41:22 2008  factoring 767514148726373849421756982578139971558958367374633360077892901949480634454258309618499746041 (93 digits)
Fri Jan  4 14:41:23 2008  commencing quadratic sieve (93-digit input)
Fri Jan  4 14:41:23 2008  using multiplier of 1
Fri Jan  4 14:41:23 2008  using 64kb Pentium 4 sieve core
Fri Jan  4 14:41:23 2008  sieve interval: 18 blocks of size 65536
Fri Jan  4 14:41:23 2008  processing polynomials in batches of 6
Fri Jan  4 14:41:23 2008  using a sieve bound of 1956883 (72780 primes)
Fri Jan  4 14:41:23 2008  using large prime bound of 244610375 (27 bits)
Fri Jan  4 14:41:23 2008  using double large prime bound of 1256766767596625 (42-51 bits)
Fri Jan  4 14:41:23 2008  using trial factoring cutoff of 51 bits
Fri Jan  4 14:41:23 2008  polynomial 'A' values have 12 factors
Fri Jan  4 22:12:21 2008  73205 relations (18541 full + 54664 combined from 996755 partial), need 72876
Fri Jan  4 22:12:25 2008  begin with 1015296 relations
Fri Jan  4 22:12:27 2008  reduce to 187278 relations in 10 passes
Fri Jan  4 22:12:27 2008  attempting to read 187278 relations
Fri Jan  4 22:12:34 2008  recovered 187278 relations
Fri Jan  4 22:12:34 2008  recovered 167179 polynomials
Fri Jan  4 22:12:34 2008  attempting to build 73205 cycles
Fri Jan  4 22:12:34 2008  found 73205 cycles in 6 passes
Fri Jan  4 22:12:34 2008  distribution of cycle lengths:
Fri Jan  4 22:12:34 2008     length 1 : 18541
Fri Jan  4 22:12:34 2008     length 2 : 13029
Fri Jan  4 22:12:34 2008     length 3 : 12466
Fri Jan  4 22:12:34 2008     length 4 : 9874
Fri Jan  4 22:12:34 2008     length 5 : 7323
Fri Jan  4 22:12:34 2008     length 6 : 5045
Fri Jan  4 22:12:34 2008     length 7 : 2957
Fri Jan  4 22:12:34 2008     length 9+: 3970
Fri Jan  4 22:12:34 2008  largest cycle: 21 relations
Fri Jan  4 22:12:35 2008  matrix is 72780 x 73205 with weight 4304451 (avg 58.80/col)
Fri Jan  4 22:12:37 2008  filtering completed in 4 passes
Fri Jan  4 22:12:37 2008  matrix is 68783 x 68847 with weight 4056821 (avg 58.93/col)
Fri Jan  4 22:12:37 2008  saving the first 48 matrix rows for later
Fri Jan  4 22:12:37 2008  matrix is 68735 x 68847 with weight 3005294 (avg 43.65/col)
Fri Jan  4 22:12:37 2008  matrix includes 64 packed rows
Fri Jan  4 22:12:37 2008  using block size 21845 for processor cache size 512 kB
Fri Jan  4 22:12:38 2008  commencing Lanczos iteration
Fri Jan  4 22:13:22 2008  lanczos halted after 1088 iterations (dim = 68733)
Fri Jan  4 22:13:22 2008  recovered 15 nontrivial dependencies
Fri Jan  4 22:13:23 2008  prp45 factor: 239837507703455294015342234963512005413275037
Fri Jan  4 22:13:23 2008  prp49 factor: 3200142279977988684517610934831971048558705274893
Fri Jan  4 22:13:23 2008  elapsed time 07:32:01

7·10¹¹⁹+9 = 7(0)₁₁₈9_<120> = 31991 · C116

C116 = P44 · P73

P44 = 12429111900259089222404905377487364334851383_<44>

P73 = 1760476070227298881000250830892187832585839053412152708131162759974648953_<73>

Number: 70009_119
N=21881154074583476602794535963239661154699759307305179581757369260104404363727298302647619643024600668938138851551999
  ( 116 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=12429111900259089222404905377487364334851383 (pp44)
 r2=1760476070227298881000250830892187832585839053412152708131162759974648953 (pp73)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.00 hours.
Scaled time: 4.04 units (timescale=2.016).
Factorization parameters were as follows:
name: 70009_119
n: 21881154074583476602794535963239661154699759307305179581757369260104404363727298302647619643024600668938138851551999
m: 1000000000000000000000000
c5: 7
c0: 90
skew: 1.67
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64083, largePrimes:2159262 encountered
Relations: rels:2257962, finalFF:227231
Max relations in full relation-set: 28
Initial matrix: 113247 x 227231 with sparse part having weight 20803966.
Pruned matrix : 89761 x 90391 with weight 5658124.
Total sieving time: 1.87 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.00 hours.
 --------- CPU info (if available) ----------

Jan 5, 2008

By Robert Backstrom / GGNFS, GMP-ECM, Msieve

7·10¹³⁷+9 = 7(0)₁₃₆9_<138> = 260202808401992767_<18> · C121

C121 = P55 · P67

P55 = 1529173935702381764254152743534663932887976167416684647_<55>

P67 = 1759256536718344842192906040610542540050982219751847395727987528241_<67>

Number: n
N=2690209242163733079058961856013706690488883800070139975077938579898447635548085461020149959227339603250033223472503615927
  ( 121 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=1529173935702381764254152743534663932887976167416684647 (pp55)
 r2=1759256536718344842192906040610542540050982219751847395727987528241 (pp67)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.64 hours.
Scaled time: 8.43 units (timescale=1.817).
Factorization parameters were as follows:
name: KA_7_0_136_9
n: 2690209242163733079058961856013706690488883800070139975077938579898447635548085461020149959227339603250033223472503615927
skew: 0.42
deg: 5
c5: 700
c0: 9
m: 1000000000000000000000000000
type: snfs
rlim: 2200000
alim: 2200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 700001)
Primes: RFBsize:162662, AFBsize:162645, largePrimes:6524001 encountered
Relations: rels:6138409, finalFF:570651
Max relations in full relation-set: 48
Initial matrix: 325375 x 570651 with sparse part having weight 34157269.
Pruned matrix : 163092 x 164782 with weight 16077087.
Total sieving time: 4.22 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.20 hours.
Total square root time: 0.10 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,2200000,2200000,28,28,48,48,2.5,2.5,75000
total time: 4.64 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

7·10¹⁶²+9 = 7(0)₁₆₁9_<163> = 23 · 39293 · C157

C157 = P33 · P125

P33 = 296777596371098420029084738265707_<33>

P125 = 26099002118993499083959038032360499646655560409399625783207929493736469419962227821932572864657403345682890557765228381684833_<125>

4·10¹⁶⁷-9 = 3(9)₁₆₆1_<168> = 43 · 443 · 3803 · 8363 · C156

C156 = P50 · P107

P50 = 42090948879771092306041949813824861415659616231911_<50>

P107 = 15685944386992125078642922951658875275870814395996579224833998729276744713659512994944344360612430130357121_<107>

Number: n
N=660236283323817840290544661230842159865224455940162022712927557130000768016670936364065296896675298786703649800998664393561639053390956010241141686786288231
  ( 156 digits)
SNFS difficulty: 167 digits.
Divisors found:

Sat Jan  5 07:57:07 2008  prp50 factor: 42090948879771092306041949813824861415659616231911
Sat Jan  5 07:57:07 2008  prp107 factor: 15685944386992125078642922951658875275870814395996579224833998729276744713659512994944344360612430130357121
Sat Jan  5 07:57:07 2008  elapsed time 01:13:32 (Msieve 1.32)

Version: GGNFS-0.77.1-20050930-k8
Total time: 108.68 hours.
Scaled time: 91.07 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_3_9_166_1
n: 660236283323817840290544661230842159865224455940162022712927557130000768016670936364065296896675298786703649800998664393561639053390956010241141686786288231
type: snfs
deg: 5
c5: 25
c0: -18
skew: 0.94
m: 2000000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 8200447)
Primes: RFBsize:216816, AFBsize:216551, largePrimes:6419024 encountered
Relations: rels:6664364, finalFF:480851
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 108.48 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 108.68 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

5·10¹⁶¹+9 = 5(0)₁₆₀9_<162> = 19 · 499 · 81412523 · 290804753657827_<15> · C136

C136 = P49 · P87

P49 = 2886044097090709483188406135551437413159237776161_<49>

P87 = 771827378327791401197721327141510578461690263003677335551724101499521451664262614805569_<87>

Number: n
N=2227527849195920167072818742245789804891947494234442788537785061825357198187109192712412964898187206347293193995545098532526760958240609
  ( 136 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=2886044097090709483188406135551437413159237776161 (pp49)
 r2=771827378327791401197721327141510578461690263003677335551724101499521451664262614805569 (pp87)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 26.60 hours.
Scaled time: 48.65 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_5_0_160_9
n: 2227527849195920167072818742245789804891947494234442788537785061825357198187109192712412964898187206347293193995545098532526760958240609
skew: 0.71
deg: 5
c5: 50
c0: 9
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1800001)
Primes: RFBsize:216816, AFBsize:215821, largePrimes:7227690 encountered
Relations: rels:6738236, finalFF:537059
Max relations in full relation-set: 48
Initial matrix: 432702 x 537059 with sparse part having weight 46858226.
Pruned matrix : 354338 x 356565 with weight 27479185.
Total sieving time: 25.31 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.09 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 26.60 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(55·10¹⁶⁶-1)/9 = 6(1)₁₆₆_<167> = 181 · 201007 · C160

C160 = P48 · P113

P48 = 120497742595657450620499053585177186485899649981_<48>

P113 = 13939638538030391821504360100234375955821869881112474237487787326972602160821849566450875175021582057328890814793_<113>

Number: n
N=1679694976432092896000986170298599345420424491720406293294233454751764399703600413660619639537885616394138141834622650400292843519374730307792835204884596968933
  ( 160 digits)
SNFS difficulty: 167 digits.
Divisors found:

Sat Jan 05 18:06:27 2008  recovered 43 nontrivial dependencies
...
Sat Jan 05 19:46:20 2008  reading relations for dependency 7
...
Sat Jan 05 20:02:44 2008  prp48 factor: 120497742595657450620499053585177186485899649981
Sat Jan 05 20:02:44 2008  prp113 factor: 13939638538030391821504360100234375955821869881112474237487787326972602160821849566450875175021582057328890814793
Sat Jan 05 20:02:44 2008  elapsed time 03:57:05 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 85.32 hours.
Scaled time: 149.14 units (timescale=1.748).
Factorization parameters were as follows:
name: KA_6_1_166
n: 1679694976432092896000986170298599345420424491720406293294233454751764399703600413660619639537885616394138141834622650400292843519374730307792835204884596968933
type: snfs
skew: 0.28
deg: 5
c5: 550
c0: -1
m: 1000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3900307)
Primes: RFBsize:230209, AFBsize:229923, largePrimes:7742476 encountered
Relations: rels:7182048, finalFF:512843
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 85.01 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.6,2.6,100000
total time: 85.32 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁵³+9 = 7(0)₁₅₂9_<154> = 229 · 383 · 8814412231_<10> · 659762031526680767195090417_<27> · C113

C113 = P33 · P81

P33 = 104956686158012241596645982785813_<33>

P81 = 130759423488435528873829580092903272449089541268530772072226531544627524905762137_<81>

Jan 4, 2008 (5th)

By Robert Backstrom / GGNFS, Msieve

2·10¹⁶⁷-1 = 1(9)₁₆₇_<168> = 4909 · 16729 · 76379 · C155

C155 = P55 · P101

P55 = 2075226395886463745978813668503914095832906194613111381_<55>

P101 = 15364821936988404978129042011260705176086625946572656434503802043499982149928090393044705627002582341_<101>

Number: n
N=31885484051733722430122978922374052186415647731414717844225369532026181178111894309739525314658565183166345642115120914615241018237573142523944303656722921
  ( 155 digits)
SNFS difficulty: 167 digits.
Divisors found:

Sat Jan 05 01:30:35 2008  prp55 factor: 2075226395886463745978813668503914095832906194613111381
Sat Jan 05 01:30:35 2008  prp101 factor: 15364821936988404978129042011260705176086625946572656434503802043499982149928090393044705627002582341
Sat Jan 05 01:30:35 2008  elapsed time 02:45:45 (Msieve 1.32)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 68.62 hours.
Scaled time: 89.89 units (timescale=1.310).
Factorization parameters were as follows:
name: KA_1_9_167
n: 31885484051733722430122978922374052186415647731414717844225369532026181178111894309739525314658565183166345642115120914615241018237573142523944303656722921
skew: 0.35
deg: 5
c5: 200
c0: -1
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3101069)
Primes: RFBsize:230209, AFBsize:229657, largePrimes:7516432 encountered
Relations: rels:6973016, finalFF:484541
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 68.25 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 68.62 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jan 4, 2008 (4th)

By Jo Yeong Uk / GGNFS

7·10¹⁶⁸-9 = 6(9)₁₆₇1_<169> = 9843923 · 117894475991_<12> · 1261779092388631_<16> · 27635543446430167_<17> · C120

C120 = P52 · P69

P52 = 1537937361615581169410967292004327295366166873569433_<52>

P69 = 112472511207691888590129843674497489028548891319841138462050561658307_<69>

Number: 69991_168
N=172975677141036546015229400354180589109448912005422828633671122239020593886199741604134349538195365917741806140785729931
  ( 120 digits)
Divisors found:
 r1=1537937361615581169410967292004327295366166873569433 (pp52)
 r2=112472511207691888590129843674497489028548891319841138462050561658307 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 45.59 hours.
Scaled time: 97.92 units (timescale=2.148).
Factorization parameters were as follows:
name: 69991_168
n: 172975677141036546015229400354180589109448912005422828633671122239020593886199741604134349538195365917741806140785729931
skew: 67391.34
# norm 5.09e+16
c5: 17280
c4: -30345414866
c3: -366826887495445
c2: 155289263798816555595
c1: 1928173509479924180946865
c0: -5273396086403893411410733594
# alpha -6.54
Y1: 1609298589041
Y0: -100020889963331680840305
# Murphy_E 2.83e-10
# M 2243431063636352947101853464256196889266586342162306354589158668527910371904618647504604110166117078652154422036894215
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4500001)
Primes: RFBsize:315948, AFBsize:316323, largePrimes:7733678 encountered
Relations: rels:7843528, finalFF:762917
Max relations in full relation-set: 28
Initial matrix: 632354 x 762917 with sparse part having weight 66957880.
Pruned matrix : 527399 x 530624 with weight 44323563.
Polynomial selection time: 2.69 hours.
Total sieving time: 40.77 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.78 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000
total time: 45.59 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406450)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4809.83 BogoMIPS (lpj=2404916)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)

Jan 4, 2008 (3rd)

By Robert Backstrom / GMP-ECM

7·10¹²⁷+9 = 7(0)₁₂₆9_<128> = 44879 · C124

C124 = P32 · P37 · P56

P32 = 75697857002716999529892478650803_<32>

P37 = 1098672696747497143987400806595400953_<37>

P56 = 18754390384244538050938832102972339330160248332842058469_<56>

7·10¹³⁴+9 = 7(0)₁₃₃9_<135> = 1373 · 5167 · 3601349599733_<13> · C116

C116 = P31 · P86

P31 = 1439181583139272216526486427199_<31>

P86 = 19037423273913052788182876625430173418517933868978126334120252095713816138227879752697_<86>

Jan 4, 2008 (2nd)

By Sinkiti Sibata / Msieve, GGNFS

7·10¹⁴⁸+9 = 7(0)₁₄₇9_<149> = 854417 · 1403083059087052553974969_<25> · 47025413165450464962041376031_<29> · C91

C91 = P40 · P51

P40 = 9370251329536055623552717563916135025857_<40>

P51 = 132513742186678071112443165485840454095701370690399_<51>

Fri Jan  4 08:23:13 2008  Msieve v. 1.30
Fri Jan  4 08:23:13 2008  random seeds: 2a1795f6 2f265fbe
Fri Jan  4 08:23:13 2008  factoring 1241687068906518298633710848308113944954223996000579428139069580827675959567636029806646943 (91 digits)
Fri Jan  4 08:23:14 2008  commencing quadratic sieve (90-digit input)
Fri Jan  4 08:23:14 2008  using multiplier of 2
Fri Jan  4 08:23:14 2008  using 64kb Pentium 4 sieve core
Fri Jan  4 08:23:14 2008  sieve interval: 18 blocks of size 65536
Fri Jan  4 08:23:14 2008  processing polynomials in batches of 6
Fri Jan  4 08:23:14 2008  using a sieve bound of 1652503 (62277 primes)
Fri Jan  4 08:23:14 2008  using large prime bound of 145420264 (27 bits)
Fri Jan  4 08:23:14 2008  using double large prime bound of 492861412574344 (42-49 bits)
Fri Jan  4 08:23:14 2008  using trial factoring cutoff of 49 bits
Fri Jan  4 08:23:14 2008  polynomial 'A' values have 12 factors
Fri Jan  4 12:29:01 2008  62747 relations (16982 full + 45765 combined from 694116 partial), need 62373
Fri Jan  4 12:29:04 2008  begin with 711098 relations
Fri Jan  4 12:29:05 2008  reduce to 152534 relations in 10 passes
Fri Jan  4 12:29:05 2008  attempting to read 152534 relations
Fri Jan  4 12:29:10 2008  recovered 152534 relations
Fri Jan  4 12:29:10 2008  recovered 128623 polynomials
Fri Jan  4 12:29:10 2008  attempting to build 62747 cycles
Fri Jan  4 12:29:10 2008  found 62747 cycles in 5 passes
Fri Jan  4 12:29:10 2008  distribution of cycle lengths:
Fri Jan  4 12:29:10 2008     length 1 : 16982
Fri Jan  4 12:29:10 2008     length 2 : 12077
Fri Jan  4 12:29:10 2008     length 3 : 10920
Fri Jan  4 12:29:10 2008     length 4 : 8357
Fri Jan  4 12:29:10 2008     length 5 : 5867
Fri Jan  4 12:29:10 2008     length 6 : 3794
Fri Jan  4 12:29:10 2008     length 7 : 2182
Fri Jan  4 12:29:10 2008     length 9+: 2568
Fri Jan  4 12:29:10 2008  largest cycle: 19 relations
Fri Jan  4 12:29:11 2008  matrix is 62277 x 62747 with weight 3737470 (avg 59.56/col)
Fri Jan  4 12:29:12 2008  filtering completed in 3 passes
Fri Jan  4 12:29:12 2008  matrix is 57933 x 57997 with weight 3465014 (avg 59.74/col)
Fri Jan  4 12:29:13 2008  saving the first 48 matrix rows for later
Fri Jan  4 12:29:13 2008  matrix is 57885 x 57997 with weight 2675909 (avg 46.14/col)
Fri Jan  4 12:29:13 2008  matrix includes 64 packed rows
Fri Jan  4 12:29:13 2008  using block size 21845 for processor cache size 512 kB
Fri Jan  4 12:29:13 2008  commencing Lanczos iteration
Fri Jan  4 12:29:46 2008  lanczos halted after 916 iterations (dim = 57883)
Fri Jan  4 12:29:46 2008  recovered 17 nontrivial dependencies
Fri Jan  4 12:29:47 2008  prp40 factor: 9370251329536055623552717563916135025857
Fri Jan  4 12:29:47 2008  prp51 factor: 132513742186678071112443165485840454095701370690399
Fri Jan  4 12:29:47 2008  elapsed time 04:06:34

7·10¹²⁰+9 = 7(0)₁₁₉9_<121> = 3613 · C118

C118 = P30 · P43 · P45

P30 = 830640561618524856111311045749_<30>

P43 = 5267270292924611350420925089608485692597297_<43>

P45 = 442824191940348923348965981442994565437113881_<45>

Number: 70009_120
N=1937448104068641018544146138942706891779684472737337392748408524771657902020481594243011347910323830611680044284528093
  ( 118 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=830640561618524856111311045749 (pp30)
 r2=5267270292924611350420925089608485692597297 (pp43)
 r3=442824191940348923348965981442994565437113881 (pp45)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.11 hours.
Scaled time: 4.22 units (timescale=2.003).
Factorization parameters were as follows:
name: 70009_120
n: 1937448104068641018544146138942706891779684472737337392748408524771657902020481594243011347910323830611680044284528093
m: 1000000000000000000000000
c5: 7
c0: 9
skew: 1.05
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63908, largePrimes:1993457 encountered
Relations: rels:1958903, finalFF:135849
Max relations in full relation-set: 28
Initial matrix: 113072 x 135849 with sparse part having weight 10934243.
Pruned matrix : 104688 x 105317 with weight 6771158.
Total sieving time: 1.96 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.11 hours.
 --------- CPU info (if available) ----------

Jan 4, 2008

By JMB / GGNFS / Dec 30, 2007

7·10¹⁵⁶-9 = 6(9)₁₅₅1_<157> = 2260571 · 21161214882893_<14> · 625086523594801_<15> · C123

C123 = P35 · P89

P35 = 15854608314307477257889614412447463_<35>

P89 = 14765346313638338741527800132362791570551309344130945927519948485674768514606278097831519_<89>

Number: 7*10^156-9
N=234098782427839665196883000012361900130395680636725922006376080346982807010226027831376517657752445555625517266741812986297
( 123 digits)
SNFS difficulty: 156 digits.
Divisors found:
r1=15854608314307477257889614412447463 (pp35)
r2=14765346313638338741527800132362791570551309344130945927519948485674768514606278097831519
(pp89)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 42.32 hours.

Jan 3, 2008 (2nd)

By matsui / GGNFS

3·10¹⁶⁵+1 = 3(0)₁₆₄1_<166> = 116891557 · 518126347 · 1922556849772274468793737_<25> · C125

C125 = P40 · P86

P40 = 1996780824920828139624227695148118615121_<40>

P86 = 12903063841818771390850986103947680780972868837668201185568690923523136035069365410047_<86>

N=25764590462072996269405677531284515063243873374651180669095169968451099335117503157111422341924469479276733945373461939520687
  ( 125 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=1996780824920828139624227695148118615121 (pp40)
 r2=12903063841818771390850986103947680780972868837668201185568690923523136035069365410047 (pp86)

Version: GGNFS-0.77.1-20060513-pentium4
Total time: 71.33 hours.
Scaled time: 92.01 units (timescale=1.290).
Factorization parameters were as follows:
n: 25764590462072996269405677531284515063243873374651180669095169968451099335117503157111422341924469479276733945373461939520687
m: 1000000000000000000000000000000000
c5: 3
c0: 1
skew: 0.8
type: snfs

Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 4800001)
Primes: RFBsize:348513, AFBsize:348501, largePrimes:5801459 encountered
Relations: rels:5977721, finalFF:817358
Max relations in full relation-set: 28
Initial matrix: 697079 x 817358 with sparse part having weight 44467712.
Pruned matrix : 598008 x 601557 with weight 30414881.
Total sieving time: 59.58 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 11.37 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 71.33 hours.

Jan 3, 2008

The factor table of 700...009 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Jan 2, 2008 (3rd)

By Sinkiti Sibata / PFGW

(19·10¹⁰⁸¹⁹+11)/3 and (19·10¹⁶⁰³⁶+11)/3 are PRPs.

Jan 2, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve

(2·10¹⁶⁶-17)/3 = (6)₁₆₅1_<166> = 3842906236981734253_<19> · C148

C148 = P64 · P85

P64 = 1100602829068959264051293759364233221830412643879055222397047131_<64>

P85 = 1576225422633670819910453271096401900701665607593218926957327204082110519610002697627_<85>

Number: n
N=1734798159401034080171951805732663587453115538866372203257419337379268789106327611243635763708787379629924381790161230793926643180172168189060858137
  ( 148 digits)
SNFS difficulty: 166 digits.
Divisors found:

Wed Jan  2 20:49:51 2008  prp64 factor: 1100602829068959264051293759364233221830412643879055222397047131
Wed Jan  2 20:49:51 2008  prp85 factor: 1576225422633670819910453271096401900701665607593218926957327204082110519610002697627
Wed Jan  2 20:49:51 2008  elapsed time 01:07:33 (Msieve 1.32)

Version: GGNFS-0.77.1-20050930-k8
Total time: 70.81 hours.
Scaled time: 59.62 units (timescale=0.842).
Factorization parameters were as follows:
name: KA_6_165_1
n: 1734798159401034080171951805732663587453115538866372203257419337379268789106327611243635763708787379629924381790161230793926643180172168189060858137
type: snfs
deg: 5
c5: 20
c0: -17
skew: 0.97
m: 1000000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5600001)
Primes: RFBsize:216816, AFBsize:216481, largePrimes:5965439 encountered
Relations: rels:5938781, finalFF:342850
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 70.66 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 70.81 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

3·10¹⁶⁷+1 = 3(0)₁₆₆1_<168> = 13² · 23 · 11240783 · C157

C157 = P48 · P110

P48 = 107653808874199343653823320575009810381715666999_<48>

P110 = 63779447095061318423367850224578695523579815789150289866244003646649681085810329261922617536898003393691354119_<110>

Number: n
N=6866100407673839710882458256002676877960427288936869306360920082777722078076735615102261401273652713425168105724751281057680269387071669463168216273591018881
  ( 157 digits)
SNFS difficulty: 167 digits.
Divisors found:

Wed Jan 02 22:42:17 2008  prp48 factor: 107653808874199343653823320575009810381715666999
Wed Jan 02 22:42:17 2008  prp110 factor: 63779447095061318423367850224578695523579815789150289866244003646649681085810329261922617536898003393691354119
Wed Jan 02 22:42:17 2008  elapsed time 01:12:16 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 48.99 hours.
Scaled time: 89.01 units (timescale=1.817).
Factorization parameters were as follows:
name: KA_3_0_166_1
n: 6866100407673839710882458256002676877960427288936869306360920082777722078076735615102261401273652713425168105724751281057680269387071669463168216273591018881
skew: 0.32
deg: 5
c5: 300
c0: 1
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3400000)
Primes: RFBsize:250150, AFBsize:250021, largePrimes:7702844 encountered
Relations: rels:7199778, finalFF:579094
Max relations in full relation-set: 28
Initial matrix: 500237 x 579094 with sparse part having weight 53234607.
Pruned matrix : 463022 x 465587 with weight 36385180.
Total sieving time: 48.80 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 48.99 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Jan 2, 2008

By Jo Yeong Uk / GGNFS

(73·10¹⁶⁶-1)/9 = 8(1)₁₆₆_<167> = 3 · 19 · 213287 · 4111361 · 5929768853_<10> · 3669810243913628169910801_<25> · C119

C119 = P55 · P64

P55 = 8223492567479697862048124640209449367402873621875410421_<55>

P64 = 9068131722716584529229143545406928460604605774689721826341970753_<64>

Number: 81111_166
N=74571713822686701323900979192571029758253172648119389362012248244916093237432632041053581859169646820908120119853417013
  ( 119 digits)
Divisors found:
 r1=8223492567479697862048124640209449367402873621875410421 (pp55)
 r2=9068131722716584529229143545406928460604605774689721826341970753 (pp64)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 38.36 hours.
Scaled time: 82.33 units (timescale=2.146).
Factorization parameters were as follows:
name: 81111_166
n: 74571713822686701323900979192571029758253172648119389362012248244916093237432632041053581859169646820908120119853417013
skew: 63934.65
# norm 5.02e+16
c5: 44700
c4: -8672528716
c3: -1167204485490759
c2: -23508456169732693191
c1: 1360412238556341935907211
c0: -4184003940301627376220420525
# alpha -6.83
Y1: 4470191423393
Y0: -69896334002934700208002
# Murphy_E 3.51e-10
# M 46104542136265429012421759151830318936477223069350986501594276445394325180456204984475629741637253392362953793618722669
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4125001)
Primes: RFBsize:315948, AFBsize:316441, largePrimes:7685412 encountered
Relations: rels:7784882, finalFF:771369
Max relations in full relation-set: 28
Initial matrix: 632470 x 771369 with sparse part having weight 64136043.
Pruned matrix : 516540 x 519766 with weight 40029222.
Polynomial selection time: 2.27 hours.
Total sieving time: 34.13 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.63 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000
total time: 38.36 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init)
Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406450)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4809.83 BogoMIPS (lpj=2404916)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)

Jan 1, 2008 (3rd)

By Bruce Dodson

10²⁷⁸+1 is divisible by 538978365796508304569088931293097537674917585678041_<51>

(10³³³-1)/9 is divisible by 2391225903192434229494639627847286709185128947978708401_<55>

References: Factoring and Prime Identification (Torbjörn Granlund), The ECMNET Project (Paul Zimmermann)

Jan 1, 2008 (2nd)

By Sinkiti Sibata / PFGW

(2·10²⁵⁰⁵+61)/9 is prime.

Jan 1, 2008

By matsui / GGNFS

(5·10¹⁶⁸+7)/3 = 1(6)₁₆₇9_<169> = 331935313 · 683366047897543_<15> · 154074768697553552249_<21> · C125

C125 = P60 · P66

P60 = 389150024577353540408352254416982467679044312048033653164543_<60>

P66 = 122544354335196425279257869050817022387231657467995884738591164013_<66>

N=47688138501357609774618672532490299817298311966335834818528738503217271683915586390382658927785128435204674599608535389191059
  ( 125 digits)
SNFS difficulty: 169 digits.
Divisors found:
 r1=389150024577353540408352254416982467679044312048033653164543 (pp60)
 r2=122544354335196425279257869050817022387231657467995884738591164013 (pp66)

Version: GGNFS-0.77.1-20060513-pentium4
Total time: 230.78 hours.
Scaled time: 292.87 units (timescale=1.269).
Factorization parameters were as follows:
n: 47688138501357609774618672532490299817298311966335834818528738503217271683915586390382658927785128435204674599608535389191059
m: 5000000000000000000000000000000000
c5: 8
c0: 35
skew: 1.34
type: snfs

Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 7300001)
Primes: RFBsize:412849, AFBsize:413746, largePrimes:6138486 encountered
Relations: rels:6454072, finalFF:972179
Max relations in full relation-set: 28
Initial matrix: 826660 x 972179 with sparse part having weight 59419918.
Pruned matrix : 704813 x 709010 with weight 42613207.
Total sieving time: 211.34 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 18.83 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 230.78 hours.

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