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: 166666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666

目次