News <2007>

December 2007

Dec 31, 2007

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(2·10¹⁶⁶+7)/9 = (2)₁₆₅3_<166> = 3² · 13 · 19 · 2203 · 92591638837_<11> · C148

C148 = P62 · P87

P62 = 10579117484643669985321526488483937482639067300717328050482541_<62>

P87 = 463246679702034732206614919683068341832261226156838899536755186335885948793861377955651_<87>

Number: n
N=4900741048938921529386312376049753422014062526470395527666102273448608728036064841441443726000645540939103525055300397035584580148478781490647789191
  ( 148 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Dec 31 10:05:46 2007  prp62 factor: 10579117484643669985321526488483937482639067300717328050482541
Mon Dec 31 10:05:46 2007  prp87 factor: 463246679702034732206614919683068341832261226156838899536755186335885948793861377955651
Mon Dec 31 10:05:46 2007  elapsed time 01:19:50 (Msieve 1.32)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 48.46 hours.
Scaled time: 63.48 units (timescale=1.310).
Factorization parameters were as follows:
name: KA_2_165_3
n: 4900741048938921529386312376049753422014062526470395527666102273448608728036064841441443726000645540939103525055300397035584580148478781490647789191
skew: 0.81
deg: 5
c5: 20
c0: 7
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2200000)
Primes: RFBsize:230209, AFBsize:229397, largePrimes:7279611 encountered
Relations: rels:6773272, finalFF:518245
Max relations in full relation-set: 28
Initial matrix: 459672 x 518245 with sparse part having weight 38557490.
Pruned matrix : 415223 x 417585 with weight 27293794.
Total sieving time: 45.28 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 48.46 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁵⁴-9 = 6(9)₁₅₃1_<155> = 24187568437147_<14> · 357505542381274647193_<21> · C121

C121 = P35 · P86

P35 = 87307807817705591131142443529365687_<35>

P86 = 92719261960991305708767306625668063796197431975684064005420378748486361040936361668683_<86>

7·10¹⁶⁵-9 = 6(9)₁₆₄1_<166> = 449 · 96293 · 193732283 · C150

C150 = P60 · P91

P60 = 119720935477183205712026361015748167111027951799849560997421_<60>

P91 = 6980473515066820668028752248342210383473908035017528053560574089914810233581451339796380341_<91>

Number: n
N=835708819297501087161209256684919312616575197394475766671782482860339428847159691345411763978143923133144396640238950619922829764501373132545436100561
  ( 150 digits)
SNFS difficulty: 165 digits.
Divisors found:

Mon Dec 31 23:17:09 2007  prp60 factor: 119720935477183205712026361015748167111027951799849560997421
Mon Dec 31 23:17:09 2007  prp91 factor: 6980473515066820668028752248342210383473908035017528053560574089914810233581451339796380341
Mon Dec 31 23:17:09 2007  elapsed time 02:16:22 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 58.35 hours.
Scaled time: 102.75 units (timescale=1.761).
Factorization parameters were as follows:
name: KA_6_9_164_1
n: 835708819297501087161209256684919312616575197394475766671782482860339428847159691345411763978143923133144396640238950619922829764501373132545436100561
type: snfs
skew: 1.05
deg: 5
c5: 7
c0: -9
m: 1000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2800001)
Primes: RFBsize:230209, AFBsize:230717, largePrimes:7456900 encountered
Relations: rels:6921697, finalFF:489538
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 58.10 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 58.35 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(7·10¹⁶⁴-61)/9 = (7)₁₆₃1_<164> = 67 · 16943 · 608743 · 4855817 · 723493411 · 103466618887166809_<18> · C120

C120 = P39 · P40 · P43

P39 = 200987859740178940829671987628842189511_<39>

P40 = 1524315768672965057529391990531835488823_<40>

P43 = 1010681974438265260089808346426272470700763_<43>

Tue Jan 01 00:33:37 2008  
Tue Jan 01 00:33:37 2008  
Tue Jan 01 00:33:37 2008  Msieve v. 1.32
Tue Jan 01 00:33:37 2008  random seeds: 670f8060 b722816b
Tue Jan 01 00:33:37 2008  factoring 203134806920325175654885525513483664774580080235041609363980893235812401418296893 (81 digits)
Tue Jan 01 00:33:37 2008  searching for 15-digit factors
Tue Jan 01 00:33:38 2008  commencing quadratic sieve (80-digit input)
Tue Jan 01 00:33:38 2008  using multiplier of 5
Tue Jan 01 00:33:38 2008  using 64kb Opteron sieve core
Tue Jan 01 00:33:38 2008  sieve interval: 6 blocks of size 65536
Tue Jan 01 00:33:38 2008  processing polynomials in batches of 17
Tue Jan 01 00:33:38 2008  using a sieve bound of 1305691 (50294 primes)
Tue Jan 01 00:33:38 2008  using large prime bound of 129263409 (26 bits)
Tue Jan 01 00:33:38 2008  using trial factoring cutoff of 27 bits
Tue Jan 01 00:33:38 2008  polynomial 'A' values have 10 factors
Tue Jan 01 00:51:33 2008  50454 relations (25765 full + 24689 combined from 273397 partial), need 50390
Tue Jan 01 00:51:34 2008  begin with 299162 relations
Tue Jan 01 00:51:34 2008  reduce to 72049 relations in 2 passes
Tue Jan 01 00:51:34 2008  attempting to read 72049 relations
Tue Jan 01 00:51:35 2008  recovered 72049 relations
Tue Jan 01 00:51:35 2008  recovered 62785 polynomials
Tue Jan 01 00:51:35 2008  attempting to build 50454 cycles
Tue Jan 01 00:51:35 2008  found 50454 cycles in 1 passes
Tue Jan 01 00:51:35 2008  distribution of cycle lengths:
Tue Jan 01 00:51:35 2008     length 1 : 25765
Tue Jan 01 00:51:35 2008     length 2 : 24689
Tue Jan 01 00:51:35 2008  largest cycle: 2 relations
Tue Jan 01 00:51:35 2008  matrix is 50294 x 50454 with weight 1538986 (avg 30.50/col)
Tue Jan 01 00:51:35 2008  filtering completed in 4 passes
Tue Jan 01 00:51:35 2008  matrix is 42992 x 43056 with weight 1286275 (avg 29.87/col)
Tue Jan 01 00:51:35 2008  saving the first 48 matrix rows for later
Tue Jan 01 00:51:35 2008  matrix is 42944 x 43056 with weight 1002106 (avg 23.27/col)
Tue Jan 01 00:51:35 2008  matrix includes 64 packed rows
Tue Jan 01 00:51:35 2008  commencing Lanczos iteration
Tue Jan 01 00:52:18 2008  lanczos halted after 680 iterations (dim = 42920)
Tue Jan 01 00:52:18 2008  recovered 6 nontrivial dependencies
Tue Jan 01 00:52:18 2008  prp39 factor: 200987859740178940829671987628842189511
Tue Jan 01 00:52:18 2008  prp43 factor: 1010681974438265260089808346426272470700763
Tue Jan 01 00:52:18 2008  elapsed time 00:18:41

Dec 30, 2007 (2nd)

By Sinkiti Sibata / PFGW

(2·10²⁴⁴²+7)/9 is prime.

Dec 30, 2007

By Robert Backstrom / GGNFS, Msieve

(28·10¹⁶³+17)/9 = 3(1)₁₆₂3_<164> = 3 · 11 · 113 · 5227723 · 5474506657_<10> · C144

C144 = P54 · P90

P54 = 568254104215421080733918790780653788490645701320935561_<54>

P90 = 513006657969163357232705769402175646798527021065255936378677850134407454699737691808031507_<90>

Number: n
N=291518138880813831877316139677912045506082513260025572748734915030214053671271873482644565087545343430540161717571420952814494855357103004720427
  ( 144 digits)
SNFS difficulty: 164 digits.
Divisors found:

Sun Dec 30 22:22:57 2007  prp54 factor: 568254104215421080733918790780653788490645701320935561
Sun Dec 30 22:22:57 2007  prp90 factor: 513006657969163357232705769402175646798527021065255936378677850134407454699737691808031507
Sun Dec 30 22:22:57 2007  elapsed time 00:55:31 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 35.78 hours.
Scaled time: 54.81 units (timescale=1.532).
Factorization parameters were as follows:
name: KA_3_1_162_3
n: 291518138880813831877316139677912045506082513260025572748734915030214053671271873482644565087545343430540161717571420952814494855357103004720427
skew: 0.45
deg: 5
c5: 875
c0: 17
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2600000)
Primes: RFBsize:216816, AFBsize:216531, largePrimes:7351213 encountered
Relations: rels:6806772, finalFF:496921
Max relations in full relation-set: 28
Initial matrix: 433413 x 496921 with sparse part having weight 48938966.
Pruned matrix : 
Total sieving time: 35.60 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 35.78 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(89·10¹⁶¹+1)/9 = 9(8)₁₆₀9_<162> = 11 · 151 · 54497 · 4734857424467_<13> · 29333719355391524558753_<23> · C119

C119 = P50 · P70

P50 = 24068764486818214538179925119843116225195355366201_<50>

P70 = 3267965275130364758731306727795381662655553549388276194815369559709367_<70>

Number: n
N=78655886558212839023556857120942142003924560409165078599494695301264178096244478079634342453626033940099746525414904767
  ( 119 digits)
SNFS difficulty: 162 digits.
Divisors found:

Sun Dec 30 22:54:11 2007  prp50 factor: 24068764486818214538179925119843116225195355366201
Sun Dec 30 22:54:11 2007  prp70 factor: 3267965275130364758731306727795381662655553549388276194815369559709367
Sun Dec 30 22:54:11 2007  elapsed time 01:13:42 (Msieve 1.32)

Version: GGNFS-0.77.1-20050930-k8
Total time: 37.56 hours.
Scaled time: 31.47 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_9_8_160_9
n: 78655886558212839023556857120942142003924560409165078599494695301264178096244478079634342453626033940099746525414904767
type: snfs
deg: 5
c5: 890
c0: 1
skew: 0.22
m: 100000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3600001)
Primes: RFBsize:216816, AFBsize:217061, largePrimes:5646354 encountered
Relations: rels:5529662, finalFF:441875
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 37.45 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 37.56 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

Dec 29, 2007 (2nd)

By Robert Backstrom / GMP-ECM

2·10¹⁶³+3 = 2(0)₁₆₂3_<164> = 166140237444137244767_<21> · C144

C144 = P39 · P105

P39 = 190635692847477990579123632346869310511_<39>

P105 = 631467424737264651495425260061946168071504561817690296672097889180937084893277408137330615731353547645619_<105>

7·10¹⁵³-9 = 6(9)₁₅₂1_<154> = 137945979054044323691_<21> · C134

C134 = P33 · P101

P33 = 772167558584103691869638283989203_<33>

P101 = 65716956589780721844302884925214520835046088468765165698360498247128407329527151604691722545317100967_<101>

Dec 29, 2007

By Jo Yeong Uk / GGNFS

7·10¹⁴⁸-9 = 6(9)₁₄₇1_<149> = 7354479179_<10> · 18371504286793171_<17> · C123

C123 = P55 · P69

P55 = 2814258676699625279171724231993155814622006129842908123_<55>

P69 = 184093046599172102452699913165893938014185229449403497478166109476613_<69>

Number: 69991_148
N=518085453711788532865190630641573477595982123762441212022596337954685562506751479459950679549038087281476496982221376227399
  ( 123 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=2814258676699625279171724231993155814622006129842908123 (pp55)
 r2=184093046599172102452699913165893938014185229449403497478166109476613 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 15.54 hours.
Scaled time: 33.21 units (timescale=2.137).
Factorization parameters were as follows:
n: 518085453711788532865190630641573477595982123762441212022596337954685562506751479459950679549038087281476496982221376227399
m: 1000000000000000000000000000000
c5: 7
c0: -900
skew: 2.64
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2200001)
Primes: RFBsize:176302, AFBsize:175703, largePrimes:5573819 encountered
Relations: rels:5511681, finalFF:495649
Max relations in full relation-set: 28
Initial matrix: 352073 x 495649 with sparse part having weight 44562981.
Pruned matrix : 293821 x 295645 with weight 24414844.
Total sieving time: 15.02 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.40 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 15.54 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

Dec 28, 2007 (4th)

By Sinkiti Sibata / GGNFS

3·10¹⁷¹+1 = 3(0)₁₇₀1_<172> = 59 · 2421821 · 1600388452377973_<16> · 19226964394318121967711782431_<29> · C120

C120 = P42 · P79

P42 = 454231567465961238949597490091615349190531_<42>

P79 = 1502151578223577638654775137097332901436078950967469661170957656557872845681903_<79>

Number: 30001_171
N=682324665947963157631469728271325158696221411931460030747532541936673539403173263878033566456941819939868757489765660493
  ( 120 digits)
Divisors found:
 r1=454231567465961238949597490091615349190531 (pp42)
 r2=1502151578223577638654775137097332901436078950967469661170957656557872845681903 (pp79)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 72.45 hours.
Scaled time: 143.38 units (timescale=1.979).
Factorization parameters were as follows:
name: 30001_171
n: 682324665947963157631469728271325158696221411931460030747532541936673539403173263878033566456941819939868757489765660493
skew: 44071.04
# norm 1.16e+16
c5: 49080
c4: -8193826874
c3: -490521821772937
c2: 13679562189223828075
c1: 268407340291989159886011
c0: -3575626527912292763955712170
# alpha -5.23
Y1: 1376995663549
Y0: -106811371197497656583221
# Murphy_E 2.89e-10
# M 516601066594921290271387127147345628955044795772215321251305996854853784465683210678704718808492261730386730080006420124
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4350001)
Primes: RFBsize:315948, AFBsize:316211, largePrimes:7704182 encountered
Relations: rels:7780725, finalFF:757685
Max relations in full relation-set: 32
Initial matrix: 632244 x 757685 with sparse part having weight 71595438.
Pruned matrix : 531677 x 534902 with weight 46827802.
Total sieving time: 67.50 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 4.05 hours.
Time per square root: 0.47 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 72.45 hours.
 --------- CPU info (if available) ----------

Dec 28, 2007 (3rd)

By Jo Yeong Uk / GGNFS

7·10¹⁴⁰-9 = 6(9)₁₃₉1_<141> = 26003 · 49967046113187701_<17> · C120

C120 = P49 · P72

P49 = 3072384756632832193294930209979933326902287322161_<49>

P72 = 175353850256855514724412620180648233024414774451978568104314670271200777_<72>

Number: 70009_140
N=538754496546039129594575511841279608916142932610183608764794445522735349555460282454684421134028742368503726717312519097
  ( 120 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=3072384756632832193294930209979933326902287322161 (pp49)
 r2=175353850256855514724412620180648233024414774451978568104314670271200777 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.12 hours.
Scaled time: 13.11 units (timescale=2.144).
Factorization parameters were as follows:
n: 538754496546039129594575511841279608916142932610183608764794445522735349555460282454684421134028742368503726717312519097
m: 10000000000000000000000000000
c5: 7
c0: -9
skew: 1.05
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:113992, largePrimes:3368951 encountered
Relations: rels:3483950, finalFF:405792
Max relations in full relation-set: 28
Initial matrix: 228213 x 405792 with sparse part having weight 35387880.
Pruned matrix : 168806 x 170011 with weight 13391873.
Total sieving time: 5.95 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.12 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

7·10¹⁴⁴-9 = 6(9)₁₄₃1_<145> = 1487 · 3084617 · 6753139867_<10> · C126

C126 = P55 · P72

P55 = 2066420873807475272508154570496764559275489805725499291_<55>

P72 = 109360704402145490620976185805347880615820804660378980898198273592328057_<72>

Number: 69991_144
N=225985242350882492390817091181539241057870132922821577330562232474083020570409647436082746217322496695164359587616913392907587
  ( 126 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=2066420873807475272508154570496764559275489805725499291 (pp55)
 r2=109360704402145490620976185805347880615820804660378980898198273592328057 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.14 hours.
Scaled time: 21.75 units (timescale=2.144).
Factorization parameters were as follows:
n: 225985242350882492390817091181539241057870132922821577330562232474083020570409647436082746217322496695164359587616913392907587
m: 100000000000000000000000000000
c5: 7
c0: -90
skew: 1.67
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1450001)
Primes: RFBsize:114155, AFBsize:114352, largePrimes:3482197 encountered
Relations: rels:3539168, finalFF:329576
Max relations in full relation-set: 28
Initial matrix: 228573 x 329576 with sparse part having weight 32251907.
Pruned matrix : 200812 x 202018 with weight 16980012.
Total sieving time: 9.89 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 10.14 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

Dec 28, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

7·10¹⁸⁶-9 = 6(9)₁₈₅1_<187> = 1882873212211_<13> · 5833979226117373_<16> · 47533639674475314086029_<23> · 22494947546032604356359491_<26> · C111

C111 = P43 · P69

P43 = 2515472027805282686708792675704535850836383_<43>

P69 = 236922626264959098658721156310440198919184175106191358028227502394681_<69>

Number: n
N=595972239123669791995895721145326920898097780541200339694452957278131466762170631342974085756411616949220478823
  ( 111 digits)
Divisors found:
 r1=2515472027805282686708792675704535850836383 (pp43)
 r2=236922626264959098658721156310440198919184175106191358028227502394681 (pp69)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.07 hours.
Scaled time: 33.44 units (timescale=1.753).
Factorization parameters were as follows:
name: KA_6_9_185_1
n: 595972239123669791995895721145326920898097780541200339694452957278131466762170631342974085756411616949220478823
skew: 7691.60
# norm 7.39e+14
c5: 65280
c4: -3707517143
c3: -59981266406565
c2: 195444948138712791
c1: 464656384627185252258
c0: -666305598531814435117600
# alpha -4.72
Y1: 299854219969
Y0: -1556288568485250579843
# Murphy_E 8.93e-10
# M 261347015577692975215738963466108609772390237867217698520093975466862424241959027489401092781747038850578899133
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 100000)
Primes: RFBsize:230209, AFBsize:229965, largePrimes:7449706 encountered
Relations: rels:7280948, finalFF:562779
Max relations in full relation-set: 28
Initial matrix: 460254 x 562779 with sparse part having weight 47426767.
Pruned matrix : 375082 x 377447 with weight 27995113.
Total sieving time: 16.82 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.45 hours.
Total square root time: 0.65 hours, sqrts: 4.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 19.07 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁵⁸-9 = 6(9)₁₅₇1_<159> = 665507 · 4787893769_<10> · C144

C144 = P34 · P110

P34 = 4551229532797823713440523924237357_<34>

P110 = 48269429654485286004700435874371392955763120608188765913835335149678303496468383067863156974558912669025897961_<110>

5·10¹⁶⁷+3 = 5(0)₁₆₆3_<168> = 7 · 773 · 8329 · C161

C161 = P68 · P93

P68 = 66986389608208370945649030468786635518218514529828739674619854324867_<68>

P93 = 165620097981775245286549676152338224696848100622028775546996783901831190108848495803829997811_<93>

Number: n
N=11094292410356841480689529799258319926065860290596351278048063092974674681508936485819419666883219858321891974475405828661656232743521548965580379379979492866137
  ( 161 digits)
SNFS difficulty: 167 digits.
Divisors found:

Fri Dec 28 08:58:01 2007  prp68 factor: 66986389608208370945649030468786635518218514529828739674619854324867
Fri Dec 28 08:58:01 2007  prp93 factor: 165620097981775245286549676152338224696848100622028775546996783901831190108848495803829997811
Fri Dec 28 08:58:01 2007  elapsed time 01:10:29 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 46.34 hours.
Scaled time: 84.62 units (timescale=1.826).
Factorization parameters were as follows:
name: KA_5_0_166_3
n: 11094292410356841480689529799258319926065860290596351278048063092974674681508936485819419666883219858321891974475405828661656232743521548965580379379979492866137
skew: 0.36
deg: 5
c5: 500
c0: 3
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3200000)
Primes: RFBsize:250150, AFBsize:249916, largePrimes:7647488 encountered
Relations: rels:7156043, finalFF:585019
Max relations in full relation-set: 28
Initial matrix: 500132 x 585019 with sparse part having weight 52070590.
Pruned matrix : 452893 x 455457 with weight 34748113.
Total sieving time: 46.16 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 46.34 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Dec 28, 2007

By Sinkiti Sibata / PFGW

7·10¹²⁷⁵⁵-9 and 7·10¹⁵¹⁴²-9 are PRPs.

Dec 27, 2007 (5th)

By Yousuke Koide

(10¹⁸⁰⁹-1)/9 is divisible by 23016857713231589991096649713043507_<35>

(10¹⁸⁶³-1)/9 is divisible by 7506789884668978259450285467_<28>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 27, 2007 (4th)

By Jo Yeong Uk / GGNFS, GMP-ECM

7·10¹³⁷-9 = 6(9)₁₃₆1_<138> = 9041 · 162129560783_<12> · C123

C123 = P50 · P73

P50 = 63195768153342995547599618615921084920365446753767_<50>

P73 = 7556685842419476053247753995520570438772601000514461987314342496480958991_<73>

Number: 69991_137
N=477550566505190610831339497667016508356659514844638240871039919937869611141038512390547786684479527858687496804388001769097
  ( 123 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=63195768153342995547599618615921084920365446753767 (pp50)
 r2=7556685842419476053247753995520570438772601000514461987314342496480958991 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.07 hours.
Scaled time: 8.67 units (timescale=2.130).
Factorization parameters were as follows:
n: 477550566505190610831339497667016508356659514844638240871039919937869611141038512390547786684479527858687496804388001769097
m: 1000000000000000000000000000
c5: 700
c0: -9
skew: 0.42
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1450001)
Primes: RFBsize:107126, AFBsize:107093, largePrimes:2316731 encountered
Relations: rels:2429777, finalFF:264060
Max relations in full relation-set: 28
Initial matrix: 214287 x 264060 with sparse part having weight 22014166.
Pruned matrix : 198204 x 199339 with weight 13643617.
Total sieving time: 3.87 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 4.07 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

7·10¹⁶²-9 = 6(9)₁₆₁1_<163> = 859 · 118247 · 2662639391_<10> · 68628329971_<11> · C135

C135 = P30 · P105

P30 = 436977788659416077831566216483_<30>

P105 = 863057237779628902143622988929371538585971609219344275040457451654589439284920068001169478963439353329509_<105>

Dec 27, 2007 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

5·10¹⁷¹-9 = 4(9)₁₇₀1_<172> = 7 · 41 · C170

C170 = P43 · P128

P43 = 1363684689367687199660001585916252959225073_<43>

P128 = 12775389298778802140820274185385735600606854567622114532762344954306460995067145385939039085787137146377153359945100703455866041_<128>

7·10¹⁴³-9 = 6(9)₁₄₂1_<144> = 97 · 317 · 571 · C137

C137 = P68 · P70

P68 = 11669963674208858774803484401760836297661604636382205067928038771673_<68>

P70 = 3416342715437805134104596866257027736379971208960481691857755728114273_<70>

Number: n
N=39868595387807238075146492882117277574103046308113959709594872989761346018457223189921629162943461946194596677613254006978940667499388729
  ( 137 digits)
SNFS difficulty: 143 digits.
Divisors found:

Thu Dec 27 16:03:21 2007  prp68 factor: 11669963674208858774803484401760836297661604636382205067928038771673
Thu Dec 27 16:03:21 2007  prp70 factor: 3416342715437805134104596866257027736379971208960481691857755728114273
Thu Dec 27 16:03:21 2007  elapsed time 00:58:19 (Msieve 1.32)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 10.12 hours.
Scaled time: 13.24 units (timescale=1.309).
Factorization parameters were as follows:
name: KA_6_9_142_1
n: 39868595387807238075146492882117277574103046308113959709594872989761346018457223189921629162943461946194596677613254006978940667499388729
skew: 0.26
deg: 5
c5: 7000
c0: -9
m: 10000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1100001)
Primes: RFBsize:203362, AFBsize:202857, largePrimes:6879960 encountered
Relations: rels:6390626, finalFF:531267
Max relations in full relation-set: 28
Initial matrix: 406287 x 531267 with sparse part having weight 31643740.
Pruned matrix : 
Total sieving time: 9.91 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 10.12 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁹⁴-9 = 6(9)₁₉₃1_<195> = 59 · 503 · 19009 · 4546319117_<10> · 3201890183553739545421_<22> · 3663534177803835316717_<22> · 5453825411908180414535101_<25> · C109

C109 = P47 · P62

P47 = 52063286361231377503035962252713421659616793211_<47>

P62 = 81944416344344076297954674797070896167668217005498046483209993_<62>

Number: n
N=4266295613839554521455940618914223009809176846224270626203668901679911671717662492929960969596044736169757523
  ( 109 digits)
Divisors found:

Thu Dec 27 21:14:40 2007  prp47 factor: 52063286361231377503035962252713421659616793211
Thu Dec 27 21:14:40 2007  prp62 factor: 81944416344344076297954674797070896167668217005498046483209993
Thu Dec 27 21:14:40 2007  elapsed time 01:21:04 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 15.97 hours.
Scaled time: 28.00 units (timescale=1.753).
Factorization parameters were as follows:
name: KA_6_9_193_1
n: 4266295613839554521455940618914223009809176846224270626203668901679911671717662492929960969596044736169757523
skew: 20303.21
# norm 3.02e+15
c5: 64260
c4: -5524240892
c3: 33370301956429
c2: 2960552805759545129
c1: 13268125763144698600299
c0: -427943730192357035630844
# alpha -6.40
Y1: 410046852743
Y0: -581336125346552761433
# Murphy_E 1.18e-09
# M 835049287715849898352208609708011149328452835128639575533350171456753898162996679714302558410477726301170271
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:230209, AFBsize:229921, largePrimes:6992043 encountered
Relations: rels:6742934, finalFF:579789
Max relations in full relation-set: 28
Initial matrix: 460216 x 579789 with sparse part having weight 39572835.
Pruned matrix : 350884 x 353249 with weight 18553288.
Total sieving time: 15.64 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,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 15.97 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁰⁸-9 = 6(9)₁₀₇1_<109> = 404321 · 378807857 · C95

C95 = P46 · P50

P46 = 2663967441313171836581746263544242756268412123_<46>

P50 = 17156308633252668896929507566790813539577265672261_<50>

Number: n
N=45703847612105192551412600444051943138121632548159102877835632289400552214113597792942597220103
  ( 95 digits)
Divisors found:
 r1=2663967441313171836581746263544242756268412123 (pp46)
 r2=17156308633252668896929507566790813539577265672261 (pp50)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.81 hours.
Scaled time: 8.43 units (timescale=1.754).
Factorization parameters were as follows:
name: KA_6_9_107_1
n:  45703847612105192551412600444051943138121632548159102877835632289400552214113597792942597220103
m:  5492465041505502450157
deg: 4
c4: 50220792
c3: 473490998762
c2: -150320131923816106
c1: -1840155014132418213
c0: 240325391527681110358680
skew: 1635.250
type: gnfs
# adj. I(F,S) = 54.908
# E(F1,F2) = 4.085225e-05
# GGNFS version 0.77.1-20050930-k8 polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1198729570.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved  special-q in [100000, 100000)
Primes: RFBsize:92938, AFBsize:92993, largePrimes:1857627 encountered
Relations: rels:1908164, finalFF:212612
Max relations in full relation-set: 28
Initial matrix: 186005 x 212612 with sparse part having weight 16282353.
Pruned matrix : 174218 x 175212 with weight 11293718.
Total sieving time: 4.41 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.30 hours.
Total square root time: 0.04 hours, sqrts: 14.
Prototype def-par.txt line would be:
gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 4.81 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁴⁵-9 = 6(9)₁₄₄1_<146> = 94261 · C141

C141 = P34 · P108

P34 = 1021695068102849396044532089064863_<34>

P108 = 726849841772289840962937682508573633040889067399121266108989206433699098743911136797514039693842951036128037_<108>

Dec 27, 2007 (2nd)

By Sinkiti Sibata / GGNFS

7·10¹¹³-9 = 6(9)₁₁₂1_<114> = 491 · 2423 · 4003873 · C102

C102 = P48 · P54

P48 = 184432465107840005841929350652158018855881137453_<48>

P54 = 796792925041443202307060294296189274485989498333919823_<54>

Number: 69991_113
N=146954483345879750650262027109056915485927149646071893433452883477538598863216027684838960521344430819
  ( 102 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=184432465107840005841929350652158018855881137453 (pp48)
 r2=796792925041443202307060294296189274485989498333919823 (pp54)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.40 hours.
Scaled time: 1.62 units (timescale=0.675).
Factorization parameters were as follows:
name: 69991_113
n: 146954483345879750650262027109056915485927149646071893433452883477538598863216027684838960521344430819
m: 10000000000000000000000
c5: 7000
c0: -9
skew: 0.26
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63823, largePrimes:2223893 encountered
Relations: rels:2457553, finalFF:359535
Max relations in full relation-set: 28
Initial matrix: 112989 x 359535 with sparse part having weight 31384555.
Pruned matrix : 71414 x 72042 with weight 5203701.
Total sieving time: 2.19 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.40 hours.
 --------- CPU info (if available) ----------

7·10¹³⁵-9 = 6(9)₁₃₄1_<136> = 3673 · 255019 · 84498497 · 15088353311_<11> · C109

C109 = P37 · P73

P37 = 2619090469168430611738435623980583053_<37>

P73 = 2238016293251830424874207565385593578321653128229251831899397482529153343_<73>

Number: 69991_135
N=5861567143499528535945249491745181774451528037501922335500468042836092047603598088439983509779689035584096179
  ( 109 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=2619090469168430611738435623980583053 (pp37)
 r2=2238016293251830424874207565385593578321653128229251831899397482529153343 (pp73)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.83 hours.
Scaled time: 13.67 units (timescale=2.003).
Factorization parameters were as follows:
name: 69991_135
n: 5861567143499528535945249491745181774451528037501922335500468042836092047603598088439983509779689035584096179
m: 1000000000000000000000000000
c5: 7
c0: -9
skew: 1.05
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1225001)
Primes: RFBsize:78498, AFBsize:63908, largePrimes:1579365 encountered
Relations: rels:1604122, finalFF:195607
Max relations in full relation-set: 28
Initial matrix: 142472 x 195607 with sparse part having weight 16386599.
Pruned matrix : 126424 x 127200 with weight 8919279.
Total sieving time: 6.60 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 6.83 hours.
 --------- CPU info (if available) ----------

7·10¹⁴⁷-9 = 6(9)₁₄₆1_<148> = 44253346650419_<14> · 640263926981563_<15> · 2384930862846177191492797_<25> · C96

C96 = P36 · P60

P36 = 345533806013666402094028972113839143_<36>

P60 = 299796493353162488095487968396822078060268288441471385866693_<60>

Number: 69991_147
N=103589823377869076072607851794326081481578050618794143412322232850520425835300380055682643364099
  ( 96 digits)
Divisors found:
 r1=345533806013666402094028972113839143 (pp36)
 r2=299796493353162488095487968396822078060268288441471385866693 (pp60)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 11.00 hours.
Scaled time: 7.42 units (timescale=0.675).
Factorization parameters were as follows:
name: 69991_147
n:  103589823377869076072607851794326081481578050618794143412322232850520425835300380055682643364099
m:  7455843658268344282957
deg: 4
c4: 33522000
c3: 140814788
c2: 77276617925738599
c1: 69424401729227304416
c0: 2357246899800669557952
skew: 1635.250
type: gnfs
# adj. I(F,S) = 55.016
# E(F1,F2) = 2.812171e-05
# GGNFS version 0.77.1-20060513-pentium4 polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1198709841.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1500001)
Primes: RFBsize:92938, AFBsize:92936, largePrimes:1911524 encountered
Relations: rels:2002935, finalFF:233843
Max relations in full relation-set: 28
Initial matrix: 185950 x 233843 with sparse part having weight 21496159.
Pruned matrix : 166071 x 167064 with weight 13108251.
Polynomial selection time: 0.17 hours.
Total sieving time: 9.92 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.72 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,95,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 11.00 hours.
 --------- CPU info (if available) ----------

Dec 27, 2007

By Sinkiti Sibata / GGNFS

7·10¹³³-9 = 6(9)₁₃₂1_<134> = 449 · 1493 · 90917 · 94389114492319_<14> · C110

C110 = P44 · P66

P44 = 85173022756831337810382828011673697322037311_<44>

P66 = 142864005459473961587757841830261127716190760624346731496837517471_<66>

Number: 69991_133
N=12168159188131852215584768023354461103145336764833774484034596076561291835579447472592128168069219417276360481
  ( 110 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=85173022756831337810382828011673697322037311 (pp44)
 r2=142864005459473961587757841830261127716190760624346731496837517471 (pp66)
Version: GGNFS-0.77.1-20060513-k8
Total time: 8.35 hours.
Scaled time: 16.72 units (timescale=2.003).
Factorization parameters were as follows:
name: 69991_133
n: 12168159188131852215584768023354461103145336764833774484034596076561291835579447472592128168069219417276360481
m: 100000000000000000000000000
c5: 7000
c0: -9
skew: 0.26
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1375001)
Primes: RFBsize:78498, AFBsize:63823, largePrimes:1568311 encountered
Relations: rels:1565951, finalFF:168189
Max relations in full relation-set: 28
Initial matrix: 142389 x 168189 with sparse part having weight 15197800.
Pruned matrix : 134600 x 135375 with weight 10638770.
Total sieving time: 8.08 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 8.35 hours.
 --------- CPU info (if available) ----------

Dec 26, 2007 (6th)

By Sinkiti Sibata / PRIMO

(2·10²⁹⁷⁸-17)/3 is prime.

Dec 26, 2007 (5th)

By Sinkiti Sibata / GGNFS

7·10¹¹⁸-9 = 6(9)₁₁₇1_<119> = 29 · 281 · 479 · 564899 · C107

C107 = P34 · P74

P34 = 1984136958064167375045366373528421_<34>

P74 = 15999844291278446970836451631567805232288393575182670206207520554418064299_<74>

Number: 69991_118
N=31745882381597551712985680104483070892222684616727431250512197757342182638804213346559326046812565481941879
  ( 107 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=1984136958064167375045366373528421 (pp34)
 r2=15999844291278446970836451631567805232288393575182670206207520554418064299 (pp74)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.24 hours.
Scaled time: 4.45 units (timescale=1.991).
Factorization parameters were as follows:
name: 69991_118
n: 31745882381597551712985680104483070892222684616727431250512197757342182638804213346559326046812565481941879
m: 100000000000000000000000
c5: 7000
c0: -9
skew: 0.26
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63823, largePrimes:2167506 encountered
Relations: rels:2281489, finalFF:242097
Max relations in full relation-set: 28
Initial matrix: 112989 x 242097 with sparse part having weight 22238741.
Pruned matrix : 87145 x 87773 with weight 5534433.
Total sieving time: 2.10 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,118,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.24 hours.
 --------- CPU info (if available) ----------

7·10¹²²-9 = 6(9)₁₂₁1_<123> = 83 · 13523 · 244861 · 1071691642724939_<16> · C97

C97 = P44 · P53

P44 = 82895830946665960950649287503567133316049651_<44>

P53 = 28669805558837951631417683899953649248910278323675131_<53>

Number: 69991_122
N=2376607354879214865611819176528989671083739593311572594941837848584100495761234335579813189929281
  ( 97 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=82895830946665960950649287503567133316049651 (pp44)
 r2=28669805558837951631417683899953649248910278323675131 (pp53)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.38 hours.
Scaled time: 6.77 units (timescale=2.003).
Factorization parameters were as follows:
name: 69991_122
n: 2376607354879214865611819176528989671083739593311572594941837848584100495761234335579813189929281
m: 1000000000000000000000000
c5: 700
c0: -9
skew: 0.42
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:63803, largePrimes:2446192 encountered
Relations: rels:2891407, finalFF:532620
Max relations in full relation-set: 28
Initial matrix: 112969 x 532620 with sparse part having weight 52760048.
Pruned matrix : 76482 x 77110 with weight 9438717.
Total sieving time: 3.23 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.38 hours.
 --------- CPU info (if available) ----------

7·10¹³²-9 = 6(9)₁₃₁1_<133> = 1292567 · 190646486287_<12> · C116

C116 = P41 · P76

P41 = 10653299394346279999189253853948866948741_<41>

P76 = 2666441366915221621544897168193843156735547511317187784920639757035112567619_<76>

Number: 69991_132
N=28406398199217797464553546226922521246087029329926717717175210835294924586217098258316437679183181636843102569417679
  ( 116 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=10653299394346279999189253853948866948741 (pp41)
 r2=2666441366915221621544897168193843156735547511317187784920639757035112567619 (pp76)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.77 hours.
Scaled time: 11.49 units (timescale=1.991).
Factorization parameters were as follows:
name: 69991_132
n: 28406398199217797464553546226922521246087029329926717717175210835294924586217098258316437679183181636843102569417679
m: 100000000000000000000000000
c5: 700
c0: -9
skew: 0.42
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1150001)
Primes: RFBsize:63951, AFBsize:63803, largePrimes:1538473 encountered
Relations: rels:1545151, finalFF:170046
Max relations in full relation-set: 28
Initial matrix: 127822 x 170046 with sparse part having weight 14925657.
Pruned matrix : 117194 x 117897 with weight 8533990.
Total sieving time: 5.57 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,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.77 hours.
 --------- CPU info (if available) ----------

Dec 26, 2007 (4th)

By Jo Yeong Uk / GGNFS, GMP-ECM

7·10¹¹⁷-9 = 6(9)₁₁₆1_<118> = C118

C118 = P48 · P70

P48 = 965127703405741647531200158987421082342396773977_<48>

P70 = 7252926193392239386243000349720048960099140101219877063658000208088783_<70>

Number: 69991_117
N=6999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
  ( 118 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=965127703405741647531200158987421082342396773977 (pp48)
 r2=7252926193392239386243000349720048960099140101219877063658000208088783 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.05 hours.
Scaled time: 2.25 units (timescale=2.145).
Factorization parameters were as follows:
n: 6999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
m: 100000000000000000000000
c5: 700
c0: -9
skew: 0.42
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 450001)
Primes: RFBsize:49098, AFBsize:49186, largePrimes:1878131 encountered
Relations: rels:1929377, finalFF:194599
Max relations in full relation-set: 28
Initial matrix: 98352 x 194599 with sparse part having weight 16935639.
Pruned matrix : 78199 x 78754 with weight 4525630.
Total sieving time: 1.00 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 1.05 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

7·10¹⁵²-9 = 6(9)₁₅₁1_<153> = 642738965504016239_<18> · C136

C136 = P32 · P104

P32 = 12499425996572633795685838286539_<32>

P104 = 87131128901653143200613872829832683606052695848751370614553206443217691319643034696885938619060585421771_<104>

Dec 26, 2007 (3rd)

By matsui / GGNFS

2·10¹⁶⁷+9 = 2(0)₁₆₆9_<168> = 47 · 184481867 · 10008810089_<11> · 118729587401_<12> · 10440234088181_<14> · C124

C124 = P61 · P63

P61 = 6290280740566369228935563961231140837620944228695383054749943_<61>

P63 = 295567569227359507343672924451640185453395509237894904088703543_<63>

N=1859202988246876566381452884068131590659953240147645274080909534187043414526270082207047941221587915349634178688954923148049
  ( 124 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=6290280740566369228935563961231140837620944228695383054749943 (pp61)
 r2=295567569227359507343672924451640185453395509237894904088703543 (pp63)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 127.80 hours.
Scaled time: 166.65 units (timescale=1.304).
Factorization parameters were as follows:
n: 1859202988246876566381452884068131590659953240147645274080909534187043414526270082207047941221587915349634178688954923148049
m: 1000000000000000000000000000000000
c5: 200
c0: 9
skew: 0.54
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 5450001)
Primes: RFBsize:380800, AFBsize:380082, largePrimes:5892464 encountered
Relations: rels:6135246, finalFF:894339
Max relations in full relation-set: 28
Initial matrix: 760947 x 894339 with sparse part having weight 44957251.
Pruned matrix : 648054 x 651922 with weight 30819584.
Total sieving time: 114.05 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 13.26 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 127.80 hours.

Dec 26, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(22·10¹⁶⁶-1)/3 = 7(3)₁₆₆_<167> = 13 · 2501184977_<10> · C157

C157 = P47 · P111

P47 = 20970006021949093438264942952242363969867903567_<47>

P111 = 107550815343039437975417504676624224363468612606306698519306645404641567204160857189344675377069667152654245399_<111>

Number: n
N=2255341245409071967907084403148340605774006950236708152769712418205381307006397248573287358922524681798311083347365571924927256446185523776892981730485438233
  ( 157 digits)
SNFS difficulty: 167 digits.
Divisors found:

Wed Dec 26 05:26:18 2007  prp47 factor: 20970006021949093438264942952242363969867903567
Wed Dec 26 05:26:18 2007  prp111 factor: 107550815343039437975417504676624224363468612606306698519306645404641567204160857189344675377069667152654245399
Wed Dec 26 05:26:18 2007  elapsed time 02:18:47 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 78.83 hours.
Scaled time: 138.12 units (timescale=1.752).
Factorization parameters were as follows:
name: KA_7_3_166
n: 2255341245409071967907084403148340605774006950236708152769712418205381307006397248573287358922524681798311083347365571924927256446185523776892981730485438233
type: snfs
skew: 0.34
deg: 5
c5: 220
c0: -1
m: 1000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3500001)
Primes: RFBsize:230209, AFBsize:230048, largePrimes:7684784 encountered
Relations: rels:7152361, finalFF:475660
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 78.54 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.6,2.6,100000
total time: 78.83 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹²⁰-9 = 6(9)₁₁₉1_<121> = 197 · 419 · C116

C116 = P52 · P65

P52 = 1323129079639263647678527821934298050401138159281717_<52>

P65 = 64093734415499366088944419295581630353010019359658087508532919861_<65>

Number: n
N=84804283827823074034139781689543631804029414971590564917679270198563173134002883345650145984517160752577444483481337
  ( 116 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=1323129079639263647678527821934298050401138159281717 (pp52)
 r2=64093734415499366088944419295581630353010019359658087508532919861 (pp65)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.47 hours.
Scaled time: 2.59 units (timescale=1.755).
Factorization parameters were as follows:
name: KA_6_9_119_1
n: 84804283827823074034139781689543631804029414971590564917679270198563173134002883345650145984517160752577444483481337
type: snfs
skew: 1.05
deg: 5
c5: 7
c0: -9
m: 1000000000000000000000000
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 220001)
Primes: RFBsize:78498, AFBsize:78361, largePrimes:4117883 encountered
Relations: rels:3508482, finalFF:209284
Max relations in full relation-set: 28
Initial matrix: 156925 x 209284 with sparse part having weight 9419779.
Pruned matrix : 113353 x 114201 with weight 3874739.
Total sieving time: 1.28 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.10 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.4,2.4,50000
total time: 1.47 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(8·10¹⁶⁶-17)/9 = (8)₁₆₅7_<166> = 4083907 · 43094378617_<11> · C149

C149 = P41 · P51 · P58

P41 = 38584081030692973979026508694832853174717_<41>

P51 = 418114217260780904751406897239535819468897448269121_<51>

P58 = 3130746579328069205359019081831876161205414051790095798089_<58>

Number: n
N=1309009655457622967425044640452475241525607022021852781211536044491653424923374629964185236322257748149509769
  ( 109 digits)
Divisors found:

Thu Dec 27 01:08:55 2007  prp51 factor: 418114217260780904751406897239535819468897448269121
Thu Dec 27 01:08:55 2007  prp58 factor: 3130746579328069205359019081831876161205414051790095798089
Thu Dec 27 01:08:55 2007  elapsed time 00:56:09 (Msieve 1.32)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 14.81 hours.
Scaled time: 19.34 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_8_165_7
n: 1309009655457622967425044640452475241525607022021852781211536044491653424923374629964185236322257748149509769
skew: 17293.45
# norm 1.67e+15
c5: 69840
c4: 7463998242
c3: -78994172254267
c2: -2236017190191479429
c1: 14571241816633004474387
c0: 2943605098409076728592987
# alpha -6.80
Y1: 379170613327
Y0: -451398307899860421580
# Murphy_E 1.27e-09
# M 913262407536112418797141648337235351640361187128809490900940893449426725706506274192425043867981484896313502
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1500000)
Primes: RFBsize:230209, AFBsize:230668, largePrimes:6776674 encountered
Relations: rels:6460557, finalFF:550004
Max relations in full relation-set: 28
Initial matrix: 460957 x 550004 with sparse part having weight 33437232.
Pruned matrix : 373838 x 376206 with weight 17048281.
Total sieving time: 13.36 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 14.81 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 26, 2007

By Yousuke Koide

(10¹⁷⁹¹-1)/9 is divisible by 430713366297695220680641963_<27>

(10¹⁸²⁷-1)/9 is divisible by 223755556979749662730993077361_<30>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 25, 2007 (6th)

By Bruce Dodson

(10³⁰¹-1)/9 is divisible by 1141240390081433457327371568501745249133720840602413587_<55>, cofactor is prime.

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 25, 2007 (5th)

By Yousuke Koide

(10¹⁷⁰⁷-1)/9 is divisible by 75920820144562528214807220511_<29>

(10¹⁷¹³-1)/9 is divisible by 21378384423167366346901350575839_<32>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 25, 2007 (4th)

By Robert Backstrom / GGNFS, Msieve

(4·10¹⁶⁷-13)/9 = (4)₁₆₆3_<167> = 7 · 199 · 178417 · C159

C159 = P73 · P87

P73 = 1485476151933583531111398308948380526129750464603540854114915552692816459_<73>

P87 = 120382802341518563935422558643399557108880046309548748111160170924304751890414156384017_<87>

Number: n
N=178825781981260185544919324400362315519182373617989035689700410480589420542722308843419223897366923093762619358223783664573201072908733661591929401830902135803
  ( 159 digits)
SNFS difficulty: 167 digits.
Divisors found:

prp73 factor: 1485476151933583531111398308948380526129750464603540854114915552692816459
prp87 factor: 120382802341518563935422558643399557108880046309548748111160170924304751890414156384017
elapsed time 02:46:27 (Msieve 1.32)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 82.93 hours.
Scaled time: 108.55 units (timescale=1.309).
Factorization parameters were as follows:
name: KA_4_166_3
n: 178825781981260185544919324400362315519182373617989035689700410480589420542722308843419223897366923093762619358223783664573201072908733661591929401830902135803
skew: 1.01
deg: 5
c5: 25
c0: -26
m: 2000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3900397)
Primes: RFBsize:230209, AFBsize:230867, largePrimes:7730813 encountered
Relations: rels:7172093, finalFF:452321
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 82.63 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 82.93 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 25, 2007 (3rd)

By Sinkiti Sibata / GGNFS

(4·10¹⁶¹+41)/9 = (4)₁₆₀9_<161> = 18094688609_<11> · 26999490049546734407_<20> · C131

C131 = P57 · P75

P57 = 661800895912546464100385070921509481515371228023099756833_<57>

P75 = 137462252416217059157918563636603097318468429817984026396850545706670319831_<75>

Number: 44449_161
N=90972641803209054654671943300688174982440708379689549892031878497530778160414254242799972773189906368931128996322659002194437655223
  ( 131 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=661800895912546464100385070921509481515371228023099756833 (pp57)
 r2=137462252416217059157918563636603097318468429817984026396850545706670319831 (pp75)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 83.42 hours.
Scaled time: 166.08 units (timescale=1.991).
Factorization parameters were as follows:
name: 44449_161
n: 90972641803209054654671943300688174982440708379689549892031878497530778160414254242799972773189906368931128996322659002194437655223
m: 100000000000000000000000000000000
c5: 40
c0: 41
skew: 1
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4950001)
Primes: RFBsize:315948, AFBsize:314247, largePrimes:6029218 encountered
Relations: rels:6254224, finalFF:838574
Max relations in full relation-set: 32
Initial matrix: 630261 x 838574 with sparse part having weight 63869247.
Pruned matrix : 474489 x 477704 with weight 46325545.
Total sieving time: 79.60 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 3.37 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 83.42 hours.
 --------- CPU info (if available) ----------

Dec 25, 2007 (2nd)

By Jo Yeong Uk / GGNFS

9·10¹⁸¹-7 = 8(9)₁₈₀3_<182> = 3613 · 3761 · 17011 · 2340581 · 730684027 · 15300750882422633_<17> · 979400478501517858241_<21> · C119

C119 = P53 · P66

P53 = 16940272774462961564775996098870506033529998386074873_<53>

P66 = 896797988999442350354441292775914106811664777578919757946243069497_<66>

Number: 89993_181
N=15192002557240387749167059448579590970166470920242453316132075745911229316132758666921505340614262736034804889184448881
  ( 119 digits)
Divisors found:
 r1=16940272774462961564775996098870506033529998386074873 (pp53)
 r2=896797988999442350354441292775914106811664777578919757946243069497 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 38.34 hours.
Scaled time: 82.16 units (timescale=2.143).
Factorization parameters were as follows:
name: 89993_181
n: 15192002557240387749167059448579590970166470920242453316132075745911229316132758666921505340614262736034804889184448881
skew: 98114.36
# norm 2.21e+16
c5: 31560
c4: -1924665624
c3: -412313060325580
c2: 47672706443648087839
c1: 1442560992222373548243522
c0: -146358796049818815151457984880
# alpha -6.24
Y1: 3744248581117
Y0: -54512483709568246234133
# Murphy_E 3.34e-10
# M 5312090155304946753032180946674168126337529924282533139667763695347823533748345268463219266442595271493810276031748175
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4125001)
Primes: RFBsize:315948, AFBsize:316143, largePrimes:7687286 encountered
Relations: rels:7809081, finalFF:793940
Max relations in full relation-set: 28
Initial matrix: 632175 x 793940 with sparse part having weight 66592823.
Pruned matrix : 496253 x 499477 with weight 40203065.
Polynomial selection time: 2.37 hours.
Total sieving time: 34.05 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.57 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000
total time: 38.34 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

Dec 25, 2007

The factor table of 699...991 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Dec 24, 2007

By Robert Backstrom / GGNFS, Msieve

(64·10¹⁶⁹-1)/9 = 7(1)₁₆₉_<170> = 191 · 227 · 23599 · C161

C161 = P68 · P94

P68 = 11931889546918933708321958997600760626322617766055953766899623909449_<68>

P94 = 5824724856908681664958265245672136436260835730449256750908837269949436735995268697884565220373_<94>

Number: n
N=69499973633827580647471586447132751857395021337483909114981344631924934491933816608111087357431841283281168537224630080843910275596154330028617514385574482004477
  ( 161 digits)
SNFS difficulty: 171 digits.
Divisors found:

Mon Dec 24 19:01:19 2007  prp68 factor: 11931889546918933708321958997600760626322617766055953766899623909449
Mon Dec 24 19:01:19 2007  prp94 factor: 5824724856908681664958265245672136436260835730449256750908837269949436735995268697884565220373
Mon Dec 24 19:01:19 2007  elapsed time 01:27:33 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 72.40 hours.
Scaled time: 131.56 units (timescale=1.817).
Factorization parameters were as follows:
name: KA_7_1_169
n: 69499973633827580647471586447132751857395021337483909114981344631924934491933816608111087357431841283281168537224630080843910275596154330028617514385574482004477
skew: 0.35
deg: 5
c5: 1
c0: -5
m: 20000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4900001)
Primes: RFBsize:250150, AFBsize:249616, largePrimes:7898818 encountered
Relations: rels:7354029, finalFF:555685
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 72.21 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 72.40 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Dec 23, 2007 (5th)

By matsui / GGNFS

3·10¹⁶⁶+1 = 3(0)₁₆₅1_<167> = 19² · 31 · 373 · 193939 · 23755628747941_<14> · 447212374355192497_<18> · C124

C124 = P45 · P79

P45 = 625649191871122082626948379908529671729699051_<45>

P79 = 5575285937796913330137969587393113913079322142661733106598322245299860531890319_<79>

N=3488173141433069844672322710287029279310821431486754226005972594141095952219346638593373912893212468814594969707770010387269
  ( 124 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=625649191871122082626948379908529671729699051 (pp45)
 r2=5575285937796913330137969587393113913079322142661733106598322245299860531890319 (pp79)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 108.27 hours.
Scaled time: 184.28 units (timescale=1.702).
Factorization parameters were as follows:
n: 3488173141433069844672322710287029279310821431486754226005972594141095952219346638593373912893212468814594969707770010387269
m: 1000000000000000000000000000000000
c5: 30
c0: 1
skew: 0.51
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 5200001)
Primes: RFBsize:348513, AFBsize:347321, largePrimes:5907563 encountered
Relations: rels:6145608, finalFF:870306
Max relations in full relation-set: 28
Initial matrix: 695901 x 870306 with sparse part having weight 52151957.
Pruned matrix : 553239 x 556782 with weight 35119544.
Total sieving time: 103.81 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 4.08 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 108.27 hours.

Dec 23, 2007 (4th)

By Sinkiti Sibata / GGNFS

(22·10¹⁶¹-1)/3 = 7(3)₁₆₁_<162> = 73 · 34653533 · 22935196665910109914667553700279_<32> · C122

C122 = P53 · P69

P53 = 15456307151502000419816734779747252856782558221670037_<53>

P69 = 817754305715924564199835791161046377202886980231427415903294669859419_<69>

Number: 73333_161
N=12639461723608598020994817140915197006312553495483248231488432539680347420405192366902367090348663282604229103442194528503
  ( 122 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=15456307151502000419816734779747252856782558221670037 (pp53)
 r2=817754305715924564199835791161046377202886980231427415903294669859419 (pp69)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 94.57 hours.
Scaled time: 64.40 units (timescale=0.681).
Factorization parameters were as follows:
name: 73333_161
n: 12639461723608598020994817140915197006312553495483248231488432539680347420405192366902367090348663282604229103442194528503
m: 100000000000000000000000000000000
c5: 220
c0: -1
skew: 0.34
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4550001)
Primes: RFBsize:315948, AFBsize:315952, largePrimes:5839234 encountered
Relations: rels:5995706, finalFF:784221
Max relations in full relation-set: 32
Initial matrix: 631967 x 784221 with sparse part having weight 49430510.
Pruned matrix : 512955 x 516178 with weight 33232195.
Total sieving time: 82.14 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 11.76 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 94.57 hours.
 --------- CPU info (if available) ----------

5·10¹⁶⁷+9 = 5(0)₁₆₆9_<168> = 17 · 1989241 · 4503242489106295715733929_<25> · 13375753468061863141381463203_<29> · C108

C108 = P33 · P75

P33 = 247594231851496673861477854899257_<33>

P75 = 991401494836260862208699840210242066186026283682422229091025681417922365483_<75>

Number: 50009_167
N=245465291570409554408333235492955931297544893177855395881640586610749416809020286506572455808735126099146131
  ( 108 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=247594231851496673861477854899257 (pp33)
 r2=991401494836260862208699840210242066186026283682422229091025681417922365483 (pp75)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 148.51 hours.
Scaled time: 295.68 units (timescale=1.991).
Factorization parameters were as follows:
name: 50009_167
n: 245465291570409554408333235492955931297544893177855395881640586610749416809020286506572455808735126099146131
m: 1000000000000000000000000000000000
c5: 500
c0: 9
skew: 0.45
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 7250001)
Primes: RFBsize:380800, AFBsize:380707, largePrimes:6144009 encountered
Relations: rels:6397329, finalFF:900175
Max relations in full relation-set: 32
Initial matrix: 761574 x 900175 with sparse part having weight 67509735.
Pruned matrix : 652300 x 656171 with weight 49587514.
Total sieving time: 142.12 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 5.80 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 148.51 hours.
 --------- CPU info (if available) ----------

Dec 23, 2007 (3rd)

By Jo Yeong Uk / GGNFS

2·10¹⁸⁷+9 = 2(0)₁₈₆9_<188> = 61 · 149 · 283 · 70663 · 2939271579080203_<16> · 4012670006992512529_<19> · 5937247290902120471857247_<25> · C118

C118 = P48 · P70

P48 = 875378053458562890900671686629987206094799966703_<48>

P70 = 1795070177818256857278501924746661172178297270528928854534971402770967_<70>

Number: 20009_187
N=1571365038080062045688276537552192603928436205005459284020038961717757775228192637376787221670115377779946873535111801
  ( 118 digits)
Divisors found:
 r1=875378053458562890900671686629987206094799966703 (pp48)
 r2=1795070177818256857278501924746661172178297270528928854534971402770967 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 33.41 hours.
Scaled time: 71.01 units (timescale=2.125).
Factorization parameters were as follows:
name: 20009_187
n: 1571365038080062045688276537552192603928436205005459284020038961717757775228192637376787221670115377779946873535111801
skew: 86841.90
# norm 2.08e+16
c5: 18720
c4: 8005758744
c3: -417143604761414
c2: -54242084718394161427
c1: 1422581424753045528714126
c0: 43918391624543280113635161840
# alpha -6.35
Y1: 1252807503029
Y0: -38440854919115622102169
# Murphy_E 3.88e-10
# M 1529114244625491084620152441929551187310300433953474676067635486861415835076684651925957412555777624572292435341208442
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 100
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 3975001)
Primes: RFBsize:315948, AFBsize:316044, largePrimes:7583161 encountered
Relations: rels:7616240, finalFF:734012
Max relations in full relation-set: 28
Initial matrix: 632072 x 734011 with sparse part having weight 59496583.
Pruned matrix : 544994 x 548218 with weight 38635632.
Total sieving time: 31.36 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.72 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000
total time: 33.41 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

Dec 23, 2007 (2nd)

By Robert Backstrom / GMP-ECM

(13·10¹⁶⁵-31)/9 = 1(4)₁₆₄1_<166> = 11 · 499 · 1319876500333999_<16> · C147

C147 = P40 · P107

P40 = 1994429019434361543756357833325269071763_<40>

P107 = 99966786327320553004552683264048083299808115979086757765172472797852861187379110833799751735350193567159837_<107>

Dec 23, 2007

By Yousuke Koide

(10¹⁴⁶⁵-1)/9 is divisible by 750351062900043426795315702791_<30>

(10¹⁵⁴⁷-1)/9 is divisible by 223088287829064817231566124802627_<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 22, 2007

By Robert Backstrom / GGNFS, Msieve

5·10¹⁵³+9 = 5(0)₁₅₂9_<154> = 113 · 283 · C150

C150 = P64 · P86

P64 = 9652395741655011049538026702985684108326820233080272800634433481_<64>

P86 = 16198321181881033533347435589236482009169983223746311965676775774243157661743075509891_<86>

Number: n
N=156352606397948653804058913662090747052753369398667875793489477469589418055598986835110541292723349698239469651959098158166296632164858188185997060571
  ( 150 digits)
SNFS difficulty: 154 digits.
Divisors found:

Sat Dec 22 17:46:28 2007  prp64 factor: 9652395741655011049538026702985684108326820233080272800634433481
Sat Dec 22 17:46:28 2007  prp86 factor: 16198321181881033533347435589236482009169983223746311965676775774243157661743075509891
Sat Dec 22 17:46:28 2007  elapsed time 00:41:58 (Msieve 1.31)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 20.36 hours.
Scaled time: 35.68 units (timescale=1.752).
Factorization parameters were as follows:
name: KA_5_0_152_9
n: 156352606397948653804058913662090747052753369398667875793489477469589418055598986835110541292723349698239469651959098158166296632164858188185997060571
type: snfs
skew: 1.41
deg: 5
c5: 8
c0: 45
m: 5000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1200000)
Primes: RFBsize:216816, AFBsize:215956, largePrimes:6188331 encountered
Relations: rels:5704176, finalFF:531554
Max relations in full relation-set: 28
Initial matrix: 432837 x 531554 with sparse part having weight 24767036.
Pruned matrix : 
Total sieving time: 20.20 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 20.36 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 21, 2007 (3rd)

By Yousuke Koide

(10¹³³⁹-1)/9 is divisible by 5775107139441156343356533814929_<31>

(10¹³⁵¹-1)/9 is divisible by 1782854636817021657923017573_<28>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 21, 2007 (2nd)

By NFSNet

(10²³⁹-1)/9 = (1)₂₃₉_<239> = 479 · 142847911 · C228

C228 = P54 · P81 · P94

P54 = 383155477843726029783939406113226468701730728790004161_<54>

P81 = 128780300340244872385688233345188210841783983757299260103530718169486826135819357_<81>

P94 = 3290967632861131703281828943635774383301940171982919699073443165222894023742681701403432993547_<94>

Reference: NFSNet current status

Dec 21, 2007

By Robert Backstrom / GGNFS, Msieve

5·10¹⁶³+9 = 5(0)₁₆₂9_<164> = 470209 · 29802628633_<11> · C148

C148 = P39 · P44 · P66

P39 = 994274499440732115855225384785607465089_<39>

P44 = 20388243227799757288129029804812187656347787_<44>

P66 = 176010423833552850724204320884474640196768850687932515195507552179_<66>

Number: n
N=3567997124893726715042848190931992165491965877318560254922568110615225565901811932175902351214161088571608357164392386147216979036661072219279275697
  ( 148 digits)
SNFS difficulty: 164 digits.
Divisors found:

Fri Dec 21 19:06:29 2007  prp39 factor: 994274499440732115855225384785607465089
Fri Dec 21 19:06:29 2007  prp44 factor: 20388243227799757288129029804812187656347787
Fri Dec 21 19:06:29 2007  prp66 factor: 176010423833552850724204320884474640196768850687932515195507552179
Fri Dec 21 19:06:29 2007  elapsed time 01:29:29 (Msieve 1.31)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 46.82 hours.
Scaled time: 61.47 units (timescale=1.313).
Factorization parameters were as follows:
name: KA_5_0_162_9
n: 3567997124893726715042848190931992165491965877318560254922568110615225565901811932175902351214161088571608357164392386147216979036661072219279275697
skew: 1.41
deg: 5
c5: 8
c0: 45
m: 500000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2200000)
Primes: RFBsize:230209, AFBsize:229217, largePrimes:7357077 encountered
Relations: rels:6869781, finalFF:531314
Max relations in full relation-set: 28
Initial matrix: 459491 x 531314 with sparse part having weight 41024110.
Pruned matrix : 405664 x 408025 with weight 28167530.
Total sieving time: 46.52 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 46.82 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 20, 2007 (2nd)

By Sinkiti Sibata / GGNFS

5·10¹⁵⁷+9 = 5(0)₁₅₆9_<158> = 1097 · 14897 · 26348627 · 158905115827_<12> · 230706227803_<12> · C121

C121 = P59 · P63

P59 = 25360542995799645970199393340105446955335067305527210019419_<59>

P63 = 124896659843040259553684977555818906011332891068066978344194417_<63>

Number: 50009_157
N=3167447111981185564662038922263931214905167097009116697762326586042626329656257920880146946528001824003871576052481383723
  ( 121 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=25360542995799645970199393340105446955335067305527210019419 (pp59)
 r2=124896659843040259553684977555818906011332891068066978344194417 (pp63)
Version: GGNFS-0.77.1-20060513-k8
Total time: 49.75 hours.
Scaled time: 99.65 units (timescale=2.003).
Factorization parameters were as follows:
name: 50009_157
n: 3167447111981185564662038922263931214905167097009116697762326586042626329656257920880146946528001824003871576052481383723
m: 10000000000000000000000000000000
c5: 500
c0: 9
skew: 0.45
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3200001)
Primes: RFBsize:216816, AFBsize:216721, largePrimes:5704293 encountered
Relations: rels:5645688, finalFF:500017
Max relations in full relation-set: 28
Initial matrix: 433604 x 500017 with sparse part having weight 46100082.
Pruned matrix : 406183 x 408415 with weight 34369135.
Total sieving time: 46.98 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.40 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 49.75 hours.
 --------- CPU info (if available) ----------

Dec 20, 2007

By Robert Backstrom / GGNFS, Msieve

5·10¹⁵⁹+9 = 5(0)₁₅₈9_<160> = 158855819 · C152

C152 = P51 · P101

P51 = 595062504831659452988979151082530531460782679178587_<51>

P101 = 52893741733194472069753410091559437984333289639309186156142766882448531546650531764689412803138414753_<101>

Number: n
N=31475082445673582785154379519455941365295532548291479331959504738066913368782543622150851143828731889261167071254720609258890289690930364974543362494011
  ( 152 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=595062504831659452988979151082530531460782679178587 (pp51)
 r2=52893741733194472069753410091559437984333289639309186156142766882448531546650531764689412803138414753 (pp101)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 20.39 hours.
Scaled time: 37.07 units (timescale=1.818).
Factorization parameters were as follows:
name: KA_5_0_158_9
n: 31475082445673582785154379519455941365295532548291479331959504738066913368782543622150851143828731889261167071254720609258890289690930364974543362494011
skew: 1.78
deg: 5
c5: 1
c0: 18
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:216816, AFBsize:216936, largePrimes:6939749 encountered
Relations: rels:6405566, finalFF:494197
Max relations in full relation-set: 48
Initial matrix: 433819 x 494197 with sparse part having weight 37620448.
Pruned matrix : 385615 x 387848 with weight 23915069.
Total sieving time: 19.02 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 1.08 hours.
Total square root time: 0.14 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 20.39 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

8·10¹⁶³-7 = 7(9)₁₆₂3_<164> = 1511 · 9661 · 321227 · 564463 · C146

C146 = P42 · P104

P42 = 725182024346650930487852356735252779350207_<42>

P104 = 41678193707764674563769995598226622228791564423366352341260784993112394124120101447997247395973034963569_<104>

Number: n
N=30224276884108635845705620161872665740218373338594605309453520593775179206533817870115077142218894679107820860767648488655970203393799663737608783
  ( 146 digits)
SNFS difficulty: 165 digits.
Divisors found:

Thu Dec 20 18:40:55 2007  prp42 factor: 725182024346650930487852356735252779350207
Thu Dec 20 18:40:55 2007  prp104 factor: 41678193707764674563769995598226622228791564423366352341260784993112394124120101447997247395973034963569
Thu Dec 20 18:40:55 2007  elapsed time 02:14:03 (Msieve 1.31)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 113.19 hours.
Scaled time: 198.19 units (timescale=1.751).
Factorization parameters were as follows:
name: KA_7_9_162_3
n: 30224276884108635845705620161872665740218373338594605309453520593775179206533817870115077142218894679107820860767648488655970203393799663737608783
type: snfs
skew: 0.49
deg: 5
c5: 2
c0: -175
m: 1000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4400001)
Primes: RFBsize:230209, AFBsize:231247, largePrimes:7814161 encountered
Relations: rels:7249012, finalFF:516556
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 112.81 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 113.19 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 19, 2007 (5th)

By Yousuke Koide

(10¹²⁴⁹-1)/9 is divisible by 3859327619352771895471324837_<28>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 19, 2007 (4th)

By Jo Yeong Uk / GMP-ECM

5·10¹⁶²+9 = 5(0)₁₆₁9_<163> = 7 · 29² · 271229879065601402201623_<24> · C136

C136 = P35 · P101

P35 = 64374435181365818315554180691915647_<35>

P101 = 48643521375868913517679138570941692047144478517809618044912143356711058007954967110653981808106775647_<101>

Dec 19, 2007 (3rd)

By matsui / GGNFS

(7·10¹⁶⁶+11)/9 = (7)₁₆₅9_<166> = 3 · 40361 · 205111360920457_<15> · 12389475956090072848518619_<26> · C122

C122 = P47 · P75

P47 = 55943227542338151602426973986475076889992624589_<47>

P75 = 451837410354294038053223198387566184140151017305302109616973764868158183999_<75>

N=25277243059591087751933230830792917038072519013701850924280163483893165455099071542202433152586138066004172655689993751411
  ( 122 
digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=55943227542338151602426973986475076889992624589 (pp47)
 r2=451837410354294038053223198387566184140151017305302109616973764868158183999 (pp75)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 10.74 hours.
Scaled time: 18.27 units (timescale=1.701).
Factorization parameters were as follows:
n: 25277243059591087751933230830792917038072519013701850924280163483893165455099071542202433152586138066004172655689993751411
m: 1000000000000000000000000000000000
c5: 70
c0: 11
skew: 0.69
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 6000001)
Primes: , , largePrimes:5871705 encountered
Relations: rels:5969485, finalFF:743203
Max relations in full relation-set: 28
Initial matrix: 696897 x 743203 with sparse part having weight 52810271.
Pruned matrix : 665688 x 669236 with weight 44065470.
Total sieving time: 2.91 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 7.59 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 10.74 hours.

Dec 19, 2007 (2nd)

By Sinkiti Sibata / GGNFS

5·10¹⁵⁶+9 = 5(0)₁₅₅9_<157> = 7 · 37447 · 28194483512088014904108943_<26> · C126

C126 = P62 · P64

P62 = 74881270812473695723895111402915691073452855235176557355117707_<62>

P64 = 9034780048660293802053456177468412100175147936351538480358818021_<64>

Number: 50009_156
N=676535811554865734658433221423933641105523804759318323019495315982034160190227630983735165481246914074639192835621689847797847
  ( 126 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=74881270812473695723895111402915691073452855235176557355117707 (pp62)
 r2=9034780048660293802053456177468412100175147936351538480358818021 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 32.37 hours.
Scaled time: 64.84 units (timescale=2.003).
Factorization parameters were as follows:
name: 50009_156
n: 676535811554865734658433221423933641105523804759318323019495315982034160190227630983735165481246914074639192835621689847797847
m: 10000000000000000000000000000000
c5: 50
c0: 9
skew: 0.71
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:215821, largePrimes:5559380 encountered
Relations: rels:5479029, finalFF:518470
Max relations in full relation-set: 28
Initial matrix: 432702 x 518470 with sparse part having weight 40228570.
Pruned matrix : 380168 x 382395 with weight 26863487.
Total sieving time: 30.33 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.72 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 32.37 hours.
 --------- CPU info (if available) ----------

Dec 19, 2007

By Robert Backstrom / GGNFS, Msieve

5·10¹⁴⁷+9 = 5(0)₁₄₆9_<148> = C148

C148 = P40 · P108

P40 = 5849697884884838262743075248501338289883_<40>

P108 = 854744996817632047461743936663945403195159505305631899758967978986218123868623742456524092166116733189586923_<108>

Number: n
N=5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 148 digits)
SNFS difficulty: 149 digits.
Divisors found:

Wed Dec 19 02:59:00 2007  prp40 factor: 5849697884884838262743075248501338289883
Wed Dec 19 02:59:00 2007  prp108 factor: 854744996817632047461743936663945403195159505305631899758967978986218123868623742456524092166116733189586923
Wed Dec 19 02:59:00 2007  elapsed time 00:54:34 (Msieve 1.31)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 12.29 hours.
Scaled time: 16.07 units (timescale=1.308).
Factorization parameters were as follows:
name: KA_5_0_146_9
n: 5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
skew: 2.24
deg: 5
c5: 4
c0: 225
m: 500000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1500001)
Primes: RFBsize:203362, AFBsize:203297, largePrimes:6971350 encountered
Relations: rels:6423924, finalFF:479679
Max relations in full relation-set: 28
Initial matrix: 406723 x 479679 with sparse part having weight 30923173.
Pruned matrix : 
Total sieving time: 12.09 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 12.29 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 18, 2007 (4th)

By Jo Yeong Uk / GGNFS, GMP-ECM

5·10¹⁶⁴+9 = 5(0)₁₆₃9_<165> = C165

C165 = P79 · P86

P79 = 6673964901781837641922867159706054031558290898862034367879686441388466755506249_<79>

P86 = 74917984640061309718805919117074967560324362619058281263115508699855177428830489506241_<86>

Number: 50009_164
N=500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 165 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=6673964901781837641922867159706054031558290898862034367879686441388466755506249 (pp79)
 r2=74917984640061309718805919117074967560324362619058281263115508699855177428830489506241 (pp86)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 39.42 hours.
Scaled time: 84.59 units (timescale=2.146).
Factorization parameters were as follows:
n: 500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
m: 1000000000000000000000000000000000
c5: 1
c0: 18
skew: 1.78
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [2500000, 4600001)
Primes: RFBsize:348513, AFBsize:348406, largePrimes:6566352 encountered
Relations: rels:6735729, finalFF:809660
Max relations in full relation-set: 28
Initial matrix: 696986 x 809660 with sparse part having weight 54958042.
Pruned matrix : 606950 x 610498 with weight 38013089.
Total sieving time: 37.13 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 2.13 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,49,49,2.5,2.5,100000
total time: 39.42 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

5·10¹⁸⁵+9 = 5(0)₁₈₄9_<186> = C186

C186 = P42 · C144

P42 = 862676558302067280404855791214660371447819_<42>

C144 = [579591499488646557153454224836516440632324855138225561082733176963781513205559091433257936622764264592554118739834167338788722441133338317646011_<144>]

Dec 18, 2007 (3rd)

By Sinkiti Sibata / GGNFS

5·10¹⁵⁴+9 = 5(0)₁₅₃9_<155>= 829 · 15683 · 56596823 · 44630287349_<11> · C130

C130 = P58 · P72

P58 = 6547416756766895807011708792092633881889587619560266369321_<58>

P72 = 232538362293215384924110022839616818354212477256510811617282792627275661_<72>

Number: 50009_154
N=1522525569869729691381144278511493679974899677541911790344380065429203883992934588841549407329972980911637269126252640383900396181
  ( 130 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=6547416756766895807011708792092633881889587619560266369321 (pp58)
 r2=232538362293215384924110022839616818354212477256510811617282792627275661 (pp72)
Version: GGNFS-0.77.1-20060513-k8
Total time: 32.09 hours.
Scaled time: 64.08 units (timescale=1.997).
Factorization parameters were as follows:
name: 50009_154
n: 1522525569869729691381144278511493679974899677541911790344380065429203883992934588841549407329972980911637269126252640383900396181
m: 10000000000000000000000000000000
c5: 1
c0: 18
skew: 1.78
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:216936, largePrimes:5911757 encountered
Relations: rels:6144438, finalFF:787955
Max relations in full relation-set: 28
Initial matrix: 433819 x 787955 with sparse part having weight 63391684.
Pruned matrix : 273376 x 275609 with weight 35731953.
Total sieving time: 30.69 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.09 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 32.09 hours.
 --------- CPU info (if available) ----------

Dec 18, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

5·10¹⁶³+3 = 5(0)₁₆₂3_<164> = 29 · 227 · 1372379 · 3452401427_<10> · C145

C145 = P58 · P87

P58 = 1652368488234263596749387089016071429414818510198454291329_<58>

P87 = 970161182233720701578804573039325030395254397715312007695070136323727969873955547645013_<87>

Number: n
N=1603063766031098986258777513442487052832641665579047108880335847996162488378285630331639750683924926169543565709805927302627011252569149775992277
  ( 145 digits)
SNFS difficulty: 164 digits.
Divisors found:

Tue Dec 18 13:14:30 2007  prp58 factor: 1652368488234263596749387089016071429414818510198454291329
Tue Dec 18 13:14:30 2007  prp87 factor: 970161182233720701578804573039325030395254397715312007695070136323727969873955547645013
Tue Dec 18 13:14:30 2007  elapsed time 01:41:34 (Msieve 1.31)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 65.55 hours.
Scaled time: 85.80 units (timescale=1.309).
Factorization parameters were as follows:
name: KA_5_0_162_3
n: 1603063766031098986258777513442487052832641665579047108880335847996162488378285630331639750683924926169543565709805927302627011252569149775992277
skew: 1.13
deg: 5
c5: 8
c0: 15
m: 500000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100001)
Primes: RFBsize:230209, AFBsize:229672, largePrimes:7196433 encountered
Relations: rels:6672971, finalFF:503221
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 65.18 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 65.55 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

5·10¹⁴⁵+9 = 5(0)₁₄₄9_<146> = 480587 · 664114531 · 173304257326374916002763_<24> · C108

C108 = P40 · P69

P40 = 8011859098238196250376857716817447795633_<40>

P69 = 112826851275727796887800559483225541997057785219800577879840211604843_<69>

Number: n
N=903952834919007588982726744512079025688319216306952508354097362135326614270017939800842749245239175617050619
  ( 108 digits)
SNFS difficulty: 145 digits.
Divisors found:

Tue Dec 18 15:02:49 2007  prp40 factor: 8011859098238196250376857716817447795633
Tue Dec 18 15:02:49 2007  prp69 factor: 112826851275727796887800559483225541997057785219800577879840211604843
Tue Dec 18 15:02:49 2007  elapsed time 00:24:54 (Msieve 1.31)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.79 hours.
Scaled time: 8.75 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_5_0_144_9
n: 903952834919007588982726744512079025688319216306952508354097362135326614270017939800842749245239175617050619
skew: 1.12
deg: 5
c5: 5
c0: 9
m: 100000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 900000)
Primes: RFBsize:183072, AFBsize:182621, largePrimes:6411156 encountered
Relations: rels:5849768, finalFF:448390
Max relations in full relation-set: 28
Initial matrix: 365759 x 448390 with sparse part having weight 26854576.
Pruned matrix : 294774 x 296666 with weight 13333677.
Total sieving time: 4.67 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 4.79 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Dec 18, 2007

By Yousuke Koide

(10¹¹⁷¹-1)/9 is divisible by 822720687271610738727673132529_<30>, cofactor is prime

(10¹¹⁹³-1)/9 is divisible by 14202873041760299228830573_<26>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 17, 2007 (3rd)

By Yousuke Koide

(10¹⁵⁰⁹-1)/9 is divisible by 276617318087890951973712854116609_<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 17, 2007 (2nd)

By Sinkiti Sibata / GGNFS

5·10¹¹⁶+9 = 5(0)₁₁₅9_<117> = 5647 · 14738747 · C106

C106 = P37 · P70

P37 = 1770527491110016131038045568525078001_<37>

P70 = 3393039989462346591698405537211579666741526697212892785900831616289301_<70>

Number: 50009_116
N=6007470579778724082070197662126840225249465868554753560298389981872307218603794018676645158186753206767301
  ( 106 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=1770527491110016131038045568525078001 (pp37)
 r2=3393039989462346591698405537211579666741526697212892785900831616289301 (pp70)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.65 hours.
Scaled time: 1.11 units (timescale=0.674).
Factorization parameters were as follows:
name: 50009_116
n: 6007470579778724082070197662126840225249465868554753560298389981872307218603794018676645158186753206767301
m: 100000000000000000000000
c5: 50
c0: 9
skew: 0.71
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:64058, largePrimes:1928320 encountered
Relations: rels:1872426, finalFF:132412
Max relations in full relation-set: 28
Initial matrix: 113221 x 132412 with sparse part having weight 9758667.
Pruned matrix : 104806 x 105436 with weight 6199905.
Total sieving time: 1.39 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.65 hours.
 --------- CPU info (if available) ----------

5·10¹³⁷+9 = 5(0)₁₃₆9_<138> = 97 · 1506773568889_<13> · 226074463554510734010057673_<27> · C98

C98 = P38 · P60

P38 = 54141127725421474038977984368371957931_<38>

P60 = 279493344149482372551112704180571406141518303948937390507771_<60>

Number: 50009_137
N=15132084844002305813551973140721593577879529754928485014234706791511561393412085501945537540581801
  ( 98 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=54141127725421474038977984368371957931 (pp38)
 r2=279493344149482372551112704180571406141518303948937390507771 (pp60)
Version: GGNFS-0.77.1-20060513-k8
Total time: 12.19 hours.
Scaled time: 24.20 units (timescale=1.985).
Factorization parameters were as follows:
name: 50009_137
n: 15132084844002305813551973140721593577879529754928485014234706791511561393412085501945537540581801
m: 1000000000000000000000000000
c5: 500
c0: 9
skew: 0.45
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1975001)
Primes: RFBsize:78498, AFBsize:64083, largePrimes:1684652 encountered
Relations: rels:1727895, finalFF:191071
Max relations in full relation-set: 28
Initial matrix: 142648 x 191071 with sparse part having weight 20882416.
Pruned matrix : 131206 x 131983 with weight 12913225.
Total sieving time: 11.87 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 12.19 hours.
 --------- CPU info (if available) ----------

5·10¹⁵¹+9 = 5(0)₁₅₀9_<152> = 17 · 43 · 107 · C147

C147 = P48 · P100

P48 = 334673882571236023305008947620488003064113918729_<48>

P100 = 1910060078664050756982889449663405594416053618701081486519366050468241477476722382784210606901891513_<100>

Number: 50009_151
N=639247222470818364294207141669969443982765894882186736898628175460577623790224631473976245573212984389582827262615543935461600419346177940856846977
  ( 147 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=334673882571236023305008947620488003064113918729 (pp48)
 r2=1910060078664050756982889449663405594416053618701081486519366050468241477476722382784210606901891513 (pp100)
Version: GGNFS-0.77.1-20060513-k8
Total time: 20.92 hours.
Scaled time: 41.16 units (timescale=1.967).
Factorization parameters were as follows:
name 50009_151
n: 639247222470818364294207141669969443982765894882186736898628175460577623790224631473976245573212984389582827262615543935461600419346177940856846977
m: 1000000000000000000000000000000
c5: 50
c0: 9
skew: 0.71
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:175768, largePrimes:5442675 encountered
Relations: rels:5368300, finalFF:498395
Max relations in full relation-set: 28
Initial matrix: 352135 x 498395 with sparse part having weight 42380181.
Pruned matrix : 282161 x 283985 with weight 22301234.
Total sieving time: 19.66 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 1.00 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 20.92 hours.
 --------- CPU info (if available) ----------

Dec 17, 2007

By Jo Yeong Uk / GGNFS

5·10¹³⁸+9 = 5(0)₁₃₇9_<139> = 7 · 67 · 24062444319260058179401_<23> · C114

C114 = P45 · P69

P45 = 946212734975879332729540202137182929419049849_<45>

P69 = 468240129107916666081642626977725725851067323112806555638980157404389_<69>

Number: 50009_138
N=443054773188660674408303607729086637392367280159933140054775228028741936788471173247150308418917853949686442387261
  ( 114 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=946212734975879332729540202137182929419049849 (pp45)
 r2=468240129107916666081642626977725725851067323112806555638980157404389 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.63 hours.
Scaled time: 9.87 units (timescale=2.129).
Factorization parameters were as follows:
n: 443054773188660674408303607729086637392367280159933140054775228028741936788471173247150308418917853949686442387261
m: 10000000000000000000000000000
c5: 1
c0: 180
skew: 2.83
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1000001)
Primes: RFBsize:107126, AFBsize:107118, largePrimes:2193538 encountered
Relations: rels:2294860, finalFF:267501
Max relations in full relation-set: 28
Initial matrix: 214308 x 267501 with sparse part having weight 20336589.
Pruned matrix : 188484 x 189619 with weight 11495582.
Total sieving time: 4.48 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 4.63 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

5·10¹⁴⁹+9 = 5(0)₁₄₈9_<150> = 614655261608425773017_<21> · C129

C129 = P43 · P87

P43 = 1292831320258423031896200514838978324604313_<43>

P87 = 629211332393361618328576188689966621539549657057208953485058442782747222654866355168729_<87>

Number: 50009_149
N=813464117579671160481609861465604632683977337341874220218641873074098242561055665721518223145604420413125413994385245321276128177
  ( 129 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=1292831320258423031896200514838978324604313 (pp43)
 r2=629211332393361618328576188689966621539549657057208953485058442782747222654866355168729 (pp87)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.28 hours.
Scaled time: 24.19 units (timescale=2.145).
Factorization parameters were as follows:
n: 813464117579671160481609861465604632683977337341874220218641873074098242561055665721518223145604420413125413994385245321276128177
m: 1000000000000000000000000000000
c5: 1
c0: 18
skew: 1.78
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1650001)
Primes: RFBsize:135072, AFBsize:134903, largePrimes:3896038 encountered
Relations: rels:4055635, finalFF:434303
Max relations in full relation-set: 28
Initial matrix: 270042 x 434303 with sparse part having weight 42347910.
Pruned matrix : 218215 x 219629 with weight 20005906.
Total sieving time: 10.98 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.22 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 11.28 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

Dec 16, 2007 (4th)

By Sinkiti Sibata / GGNFS

5·10¹²¹+9 = 5(0)₁₂₀9_<122> = 401 · C120

C120 = P39 · P81

P39 = 234394740470022334833839226247804877881_<39>

P81 = 531958520279564508033197824266783726238632647326464705045488524626649705389905089_<81>

Number: 50009_121
N=124688279301745635910224438902743142144638403990024937655860349127182044887780548628428927680798004987531172069825436409
  ( 120 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=234394740470022334833839226247804877881 (pp39)
 r2=531958520279564508033197824266783726238632647326464705045488524626649705389905089 (pp81)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.07 hours.
Scaled time: 4.13 units (timescale=1.992).
Factorization parameters were as follows:
name: 50009_121
n: 124688279301745635910224438902743142144638403990024937655860349127182044887780548628428927680798004987531172069825436409
m: 1000000000000000000000000
c5: 50
c0: 9
skew: 0.71
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64058, largePrimes:2256398 encountered
Relations: rels:2489942, finalFF:350248
Max relations in full relation-set: 28
Initial matrix: 113221 x 350248 with sparse part having weight 32201932.
Pruned matrix : 75006 x 75636 with weight 5986172.
Total sieving time: 1.95 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.07 hours.
 --------- CPU info (if available) ----------

5·10¹⁰⁷+9 = 5(0)₁₀₆9_<108> = 19 · C107

C107 = P35 · P73

P35 = 22161612064368328651072431710802457_<35>

P73 = 1187449243189082427047892522175799526276103441537325771419337450292326123_<73>

Number: 50009_107
N=26315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684211
  ( 107 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=22161612064368328651072431710802457 (pp35)
 r2=1187449243189082427047892522175799526276103441537325771419337450292326123 (pp73)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.95 hours.
Scaled time: 1.31 units (timescale=0.674).
Factorization parameters were as follows:
name: 50009_107
n: 26315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684211
m: 1000000000000000000000
c5: 500
c0: 9
skew: 0.45
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:64083, largePrimes:2414537 encountered
Relations: rels:2970085, finalFF:672208
Max relations in full relation-set: 28
Initial matrix: 113248 x 672208 with sparse part having weight 51031416.
Pruned matrix : 58155 x 58785 with weight 4968824.
Total sieving time: 1.78 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,107,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.95 hours.
 --------- CPU info (if available) ----------

5·10¹¹⁴+9 = 5(0)₁₁₃9_<115> = 7 · 83 · 463 · 48623 · C105

C105 = P38 · P67

P38 = 70541614319082877066125526339209355501_<38>

P67 = 5419082164403195929289385747756719945734828037540124137574223619561_<67>

Number: 50009_114
N=382270804004751115685801549224284849574629336415081490606549481511433152190319400016180865627738226555061
  ( 105 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=70541614319082877066125526339209355501 (pp38)
 r2=5419082164403195929289385747756719945734828037540124137574223619561 (pp67)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.67 hours.
Scaled time: 1.13 units (timescale=0.674).
Factorization parameters were as follows:
name: 50009_114
n: 382270804004751115685801549224284849574629336415081490606549481511433152190319400016180865627738226555061
m: 100000000000000000000000
c5: 1
c0: 18
skew: 1.78
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:63888, largePrimes:2196933 encountered
Relations: rels:2439165, finalFF:379789
Max relations in full relation-set: 28
Initial matrix: 113053 x 379789 with sparse part having weight 30408564.
Pruned matrix : 65611 x 66240 with weight 4277422.
Total sieving time: 1.50 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:
snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.67 hours.
 --------- CPU info (if available) ----------

Dec 16, 2007 (3rd)

By Robert Backstrom / GMP-ECM

5·10¹⁰²+9 = 5(0)₁₀₁9_<103> = 7 · 23 · 7001 · C97

C97 = P41 · P57

P41 = 31854706908327006451053849450780933259103_<41>

P57 = 139254884403520782870512217316445103008038584589836414223_<57>

Dec 16, 2007 (2nd)

By Jo Yeong Uk / GGNFS

5·10¹³³+9 = 5(0)₁₃₂9_<134> = C134

C134 = P55 · P80

P55 = 1808856091842673778141469519200801928271629226769243833_<55>

P80 = 27641778815618891492508230793764960546620767858028425576294203682615206075499473_<80>

Number: 50009_133
N=50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 134 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=1808856091842673778141469519200801928271629226769243833 (pp55)
 r2=27641778815618891492508230793764960546620767858028425576294203682615206075499473 (pp80)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.70 hours.
Scaled time: 5.79 units (timescale=2.145).
Factorization parameters were as follows:
n: 50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
m: 1000000000000000000000000000
c5: 1
c0: 180
skew: 2.83
type: snfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [600000, 1150001)
Primes: RFBsize:92938, AFBsize:92784, largePrimes:1635992 encountered
Relations: rels:1676140, finalFF:218361
Max relations in full relation-set: 28
Initial matrix: 185786 x 218361 with sparse part having weight 11337457.
Pruned matrix : 170705 x 171697 with weight 7105532.
Total sieving time: 2.59 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1200000,1200000,25,25,46,46,2.2,2.2,50000
total time: 2.70 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

5·10¹²⁶+9 = 5(0)₁₂₅9_<127> = 7 · 541 · C124

C124 = P62 · P62

P62 = 18583998288422002372740046473239078846323774567438627504014367_<62>

P62 = 71045331073170059497410700220270620432737612295639886159776421_<62>

Number: 50009_126
N=1320306311064166886717718510694481119619751782413519936625297068919989437549511486664906258251914444151043041985740691840507
  ( 124 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=18583998288422002372740046473239078846323774567438627504014367 (pp62)
 r2=71045331073170059497410700220270620432737612295639886159776421 (pp62)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.52 hours.
Scaled time: 3.25 units (timescale=2.136).
Factorization parameters were as follows:
n: 1320306311064166886717718510694481119619751782413519936625297068919989437549511486664906258251914444151043041985740691840507
m: 10000000000000000000000000
c5: 50
c0: 9
skew: 0.71
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [400000, 720001)
Primes: RFBsize:63951, AFBsize:64058, largePrimes:1387334 encountered
Relations: rels:1376239, finalFF:164736
Max relations in full relation-set: 28
Initial matrix: 128074 x 164736 with sparse part having weight 7959278.
Pruned matrix : 112535 x 113239 with weight 4175510.
Total sieving time: 1.46 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,800000,800000,25,25,45,45,2.2,2.2,40000
total time: 1.52 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

5·10¹²⁹+9 = 5(0)₁₂₈9_<130> = 1283 · 6673 · 421483 · C118

C118 = P35 · P36 · P48

P35 = 55851141761388119444538473036013289_<35>

P36 = 188165401070611685235607528162110379_<36>

P48 = 131847024827184141097638546699400890537611235187_<48>

Number: 50009_129
N=1385613673935590348953591613436489741829549505362287644707221680889335587698736375275354448321494087870618987366346297
  ( 118 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=55851141761388119444538473036013289 (pp35)
 r2=188165401070611685235607528162110379 (pp36)
 r3=131847024827184141097638546699400890537611235187 (pp48)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.96 hours.
Scaled time: 4.16 units (timescale=2.127).
Factorization parameters were as follows:
n: 1385613673935590348953591613436489741829549505362287644707221680889335587698736375275354448321494087870618987366346297
m: 100000000000000000000000000
c5: 1
c0: 18
skew: 1.78
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 900001)
Primes: RFBsize:78498, AFBsize:78486, largePrimes:1556493 encountered
Relations: rels:1609896, finalFF:225323
Max relations in full relation-set: 28
Initial matrix: 157051 x 225323 with sparse part having weight 11609462.
Pruned matrix : 126069 x 126918 with weight 5246803.
Total sieving time: 1.89 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 1.96 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

Dec 16, 2007

By Sinkiti Sibata / PRIMO

(2·10²⁴⁰³+1)/3 is prime.

Dec 15, 2007 (4th)

By matsui / GGNFS

(5·10¹⁶⁶+7)/3 = 1(6)₁₆₅9_<167> = 38609 · 75787 · 156630091583671031730558418871436461_<36> · C122

C122 = P52 · P71

P52 = 2264388869748319451290164995673979200391552839732379_<52>

P71 = 16059767993409165566619664888931389674520944070045699328877175122292297_<71>

N=36365559895016016644306948036519971789440001831406469011965021801985852343260659678682774063764231328439857717070493184563
  ( 122 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=2264388869748319451290164995673979200391552839732379 (pp52)
 r2=16059767993409165566619664888931389674520944070045699328877175122292297 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 125.39 hours.
Scaled time: 238.73 units (timescale=1.904).
Factorization parameters were as follows:
n: 36365559895016016644306948036519971789440001831406469011965021801985852343260659678682774063764231328439857717070493184563
m: 1000000000000000000000000000000000
c5: 50
c0: 7
skew: 0.67
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 6400001)
Primes: RFBsize:348513, AFBsize:349596, largePrimes:6068375 encountered
Relations: rels:6296703, finalFF:852370
Max relations in full relation-set: 28
Initial matrix: 698174 x 852370 with sparse part having weight 63956552.
Pruned matrix : 581570 x 585124 with weight 46821531.
Total sieving time: 110.75 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 14.13 hours.
Time per square root: 0.35 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 125.39 hours.

Dec 15, 2007 (3rd)

By Yousuke Koide

(10¹³⁷⁵-1)/9 is divisible by 584213416911071661540509773751_<30>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 15, 2007 (2nd)

The factor table of 500...009 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Dec 15, 2007

By Alfred Reich

10¹⁸¹³+1 is divisible by 1341949101412826358472947603971939_<34>

10¹⁹⁶⁶+1 is divisible by 4955902500081447124888466401899581_<34>

Reference: Factorizations of numbers of the form 10ⁿ+1 (Alfred Reich)

Dec 14, 2007 (4th)

By Yousuke Koide

(10¹³¹⁵-1)/9 is divisible by 155872807295141767753013971998423271_<36>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 14, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(2·10²³⁶²+43)/9 is prime.

Dec 14, 2007 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(5·10¹⁶³+31)/9 = (5)₁₆₂9_<163> = 3² · 11503 · 2014594707737_<13> · C146

C146 = P35 · P44 · P68

P35 = 30188843843595259209660847329747917_<35>

P44 = 35971250079769021640351453407071430175983319_<44>

P68 = 24529244107054551003240215672832228187869914838761899129142536396667_<68>

Number: n
N=882347574042559821772402450073629885235585583487871518473855136881851884014580940306573631458996102973759197773
  ( 111 digits)
Divisors found:

Fri Dec 14 06:00:23 2007  prp44 factor: 35971250079769021640351453407071430175983319
Fri Dec 14 06:00:23 2007  prp68 factor: 24529244107054551003240215672832228187869914838761899129142536396667
Fri Dec 14 06:00:23 2007  elapsed time 01:21:20 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 23.38 hours.
Scaled time: 40.42 units (timescale=1.729).
Factorization parameters were as follows:
name: KA_5_162_9
n: 882347574042559821772402450073629885235585583487871518473855136881851884014580940306573631458996102973759197773
skew: 19044.42
# norm 6.38e+15
c5: 111600
c4: 14885090508
c3: 145705138135436
c2: -5337155657782209549
c1: 9745908703860354342290
c0: 107907444208141710319877800
# alpha -6.45
Y1: 212966576537
Y0: -1512145107533754160601
# Murphy_E 8.60e-10
# M 496213671955529285371696094504443999209726698467323627075527118570036745236814734332119703037015817317104508841
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1200001)
Primes: RFBsize:230209, AFBsize:230305, largePrimes:6818981 encountered
Relations: rels:6507373, finalFF:543771
Max relations in full relation-set: 28
Initial matrix: 460599 x 543771 with sparse part having weight 35789432.
Pruned matrix : 
Total sieving time: 23.12 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 23.38 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(4·10¹⁶¹+23)/9 = (4)₁₆₀7_<161> = 13³ · 132253376785665958621_<21> · C138

C138 = P39 · P99

P39 = 208122669820059734018270507907490349851_<39>

P99 = 734955876882058340201805409936009321630527412736093444708338848258488834565508219522142315629339181_<99>

5·10¹⁵²-9 = 4(9)₁₅₁1_<153> = 19 · 199 · 1451 · 94201 · C141

C141 = P52 · P90

P52 = 2456042554669170698593684758425118153245909492210089_<52>

P90 = 393916809814646016551948100067256455621282070935459752206741992118247884075792950119651649_<90>

Number: n
N=967476447904293055909635216958020112332090895404733428215992995669631565708561959491679428666082918940760232731437093604988438320239803286761
  ( 141 digits)
SNFS difficulty: 152 digits.
Divisors found:

Fri Dec 14 22:19:20 2007  prp52 factor: 2456042554669170698593684758425118153245909492210089
Fri Dec 14 22:19:20 2007  prp90 factor: 393916809814646016551948100067256455621282070935459752206741992118247884075792950119651649
Fri Dec 14 22:19:20 2007  elapsed time 01:04:26 (Msieve 1.30)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 22.64 hours.
Scaled time: 29.75 units (timescale=1.314).
Factorization parameters were as follows:
name: KA_4_9_151_1
n: 967476447904293055909635216958020112332090895404733428215992995669631565708561959491679428666082918940760232731437093604988438320239803286761
skew: 0.45
deg: 5
c5: 500
c0: -9
m: 1000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1100000)
Primes: RFBsize:203362, AFBsize:203297, largePrimes:6755039 encountered
Relations: rels:6230916, finalFF:474146
Max relations in full relation-set: 28
Initial matrix: 406726 x 474146 with sparse part having weight 31631044.
Pruned matrix : 349533 x 351630 with weight 19468857.
Total sieving time: 22.45 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 22.64 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 14, 2007

By Jo Yeong Uk / GGNFS

5·10¹⁵⁸-9 = 4(9)₁₅₇1_<159> = 192370543578919_<15> · 255761895497279_<15> · 6553146809446631_<16> · C115

C115 = P36 · P79

P36 = 916954738515527411860196269384889891_<36>

P79 = 1691210995646724198680462578472437912581425581533448011756847939729769453981971_<79>

Number: 49991_158
N=1550763936287826755654564895336804649264066034246143513988755304298815619485742512321951624878705182064449334155161
  ( 115 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=916954738515527411860196269384889891 (pp36)
 r2=1691210995646724198680462578472437912581425581533448011756847939729769453981971 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 25.62 hours.
Scaled time: 54.41 units (timescale=2.124).
Factorization parameters were as follows:
n: 1550763936287826755654564895336804649264066034246143513988755304298815619485742512321951624878705182064449334155161
m: 100000000000000000000000000000000
c5: 1
c0: -180
skew: 2.83
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3500001)
Primes: RFBsize:283146, AFBsize:282037, largePrimes:5639108 encountered
Relations: rels:5690607, finalFF:673567
Max relations in full relation-set: 28
Initial matrix: 565247 x 673567 with sparse part having weight 41646735.
Pruned matrix : 476541 x 479431 with weight 26834784.
Total sieving time: 24.40 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 1.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 25.62 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

(67·10¹⁶¹+23)/9 = 7(4)₁₆₀7_<162> = 3 · 11 · 1399 · 1523 · 87433 · 21320365267_<11> · 40377356857463_<14> · C126

C126 = P37 · P89

P37 = 6578288242353527353007952811929293213_<37>

P89 = 21383556043195314533903891888116589234987504067784812619439791414098469151797015018035563_<89>

Dec 13, 2007

By Sinkiti Sibata / PRIMO

(2·10²¹⁷⁵-17)/3 is prime.

Dec 12, 2007

By Sinkiti Sibata / PFGW

2·10¹²⁹⁸⁴-7 and 2·10¹³⁶¹⁴-7 are PRP.

Dec 11, 2007 (2nd)

By Yousuke Koide

10¹¹²¹+1 is divisible by 69849282640264627005884025897913761023_<38>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 11, 2007

By Robert Backstrom / GGNFS, Msieve

5·10¹⁵⁵-9 = 4(9)₁₅₄1_<156> = 52249831 · C148

C148 = P68 · P81

P68 = 12577330540482969770037590027834896246509937898150565038352486568081_<68>

P81 = 760845786107138460535930299805308106874138122028043088814610693093595148504742881_<81>

Number: n
N=9569408942203085786057374998973680890948719049445346531360072724445749881946986584511632200303193325161185688811127446517482515876462834875006581361
  ( 148 digits)
SNFS difficulty: 155 digits.
Divisors found:

Tue Dec 11 14:10:53 2007  prp68 factor: 12577330540482969770037590027834896246509937898150565038352486568081
Tue Dec 11 14:10:53 2007  prp81 factor: 760845786107138460535930299805308106874138122028043088814610693093595148504742881
Tue Dec 11 14:10:53 2007  elapsed time 01:06:58 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 25.92 hours.
Scaled time: 44.94 units (timescale=1.734).
Factorization parameters were as follows:
name: KA_4_9_154_1
n: 9569408942203085786057374998973680890948719049445346531360072724445749881946986584511632200303193325161185688811127446517482515876462834875006581361
type: snfs
skew: 1.12
deg: 5
c5: 5
c0: -9
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1200000)
Primes: RFBsize:216816, AFBsize:216491, largePrimes:6390484 encountered
Relations: rels:5934433, finalFF:556300
Max relations in full relation-set: 28
Initial matrix: 433373 x 556300 with sparse part having weight 28717637.
Pruned matrix : 323054 x 325284 with weight 14040928.
Total sieving time: 25.73 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,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 25.92 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 10, 2007 (5th)

By Sinkiti Sibata / PFGW

(8·10¹⁰⁷¹⁷-11)/3, (8·10¹⁴⁶⁷³-11)/3, (8·10¹⁶⁷⁵⁴-11)/3 and (8·10¹⁷⁶⁰⁶-11)/3 are PRP.

Dec 10, 2007 (4th)

By suberi / GMP-ECM

(16·10¹⁷⁶-61)/9 = 1(7)₁₇₅1_<177> = 3 · 5261 · C173

C173 = P36 · C137

P36 = 817155339792930387676948727914630841_<36>

C137 = [13784254841763201401763506838527012403768451779816402753683122065119425484587917320413953839479488490114718629521019279324075409499402757_<137>]

Dec 10, 2007 (3rd)

By Jo Yeong Uk / GGNFS

5·10¹⁶⁶-9 = 4(9)₁₆₅1_<167> = 41 · 89 · 809 · 16811 · 1289694079831_<13> · 47803986587156910009154269051461_<32> · C113

C113 = P48 · P65

P48 = 423642819486377500810088159556192139680472557229_<48>

P65 = 38574774798609590656685912133706632252046886635615382500322326219_<65>

Number: 49991_166
N=16341926356735026827094185515432260422814688809284832362536839593066759444529868046049647268284701680004884687151
  ( 113 digits)
Divisors found:
 r1=423642819486377500810088159556192139680472557229 (pp48)
 r2=38574774798609590656685912133706632252046886635615382500322326219 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 20.00 hours.
Scaled time: 42.48 units (timescale=2.124).
Factorization parameters were as follows:
name: 49991_166
n: 16341926356735026827094185515432260422814688809284832362536839593066759444529868046049647268284701680004884687151
skew: 27295.93
# norm 2.18e+15
c5: 33120
c4: 4441313622
c3: -62567391423243
c2: -2850563779112809232
c1: 20403393653491258023492
c0: 412100355487556686774922021
# alpha -5.81
Y1: 642727557923
Y0: -3456530699039931079782
# Murphy_E 7.71e-10
# M 1551685654449727006542580819033466558148370987093910726938703232431161248973769563550852895364742766086059152787
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1400000, 2380001)
Primes: RFBsize:203362, AFBsize:203153, largePrimes:7633589 encountered
Relations: rels:7513780, finalFF:534371
Max relations in full relation-set: 28
Initial matrix: 406594 x 534371 with sparse part having weight 51341064.
Pruned matrix : 315342 x 317438 with weight 31467716.
Polynomial selection time: 1.06 hours.
Total sieving time: 18.10 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.58 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000
total time: 20.00 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Dec 10, 2007 (2nd)

By Sinkiti Sibata / GGNFS

4·10¹⁷⁹+9 = 4(0)₁₇₈9_<180> = C180

C180 = P45 · P135

P45 = 921163045658547580756150590548571589420901651_<45>

P135 = 434233659160780244149695889605425366477201748488030257510308420904369547799589597822903126508104998452818212276951470860768875906012659_<135>

Number: 40009_179
N=400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 180 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=921163045658547580756150590548571589420901651 (pp45)
 r2=434233659160780244149695889605425366477201748488030257510308420904369547799589597822903126508104998452818212276951470860768875906012659 (pp135)
Version: GGNFS-0.77.1-20060513-k8
Total time: 514.08 hours.
Scaled time: 1025.58 units (timescale=1.995).
Factorization parameters were as follows:
name: 40009_179
n: 400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
m: 1000000000000000000000000000000000000
c5: 2
c0: 45
skew: 1.86
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 9400001)
Primes: RFBsize:501962, AFBsize:502481, largePrimes:6588779 encountered
Relations: rels:7085432, finalFF:1174582
Max relations in full relation-set: 28
Initial matrix: 1004508 x 1174582 with sparse part having weight 72170055.
Pruned matrix : 861753 x 866839 with weight 54190298.
Total sieving time: 503.52 hours.
Total relation processing time: 0.48 hours.
Matrix solve time: 9.74 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 514.08 hours.
 --------- CPU info (if available) ----------

Dec 10, 2007

By Robert Backstrom / GGNFS, Msieve

5·10¹⁴⁶-9 = 4(9)₁₄₅1_<147> = 41 · 59 · 5970268730389741_<16> · C128

C128 = P59 · P69

P59 = 89514634314987140562070529941642327551603414368208045052321_<59>

P69 = 386764152467374483050690533716910166621405836972248541038074724385249_<69>

Number: n
N=34621051674262958248832730437816687088862152041094871343262841750725698980225021240368058000790564138392180385545468782765612929
  ( 128 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=89514634314987140562070529941642327551603414368208045052321 (pp59)
 r2=386764152467374483050690533716910166621405836972248541038074724385249 (pp69)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.86 hours.
Scaled time: 12.82 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_4_9_145_1
n: 34621051674262958248832730437816687088862152041094871343262841750725698980225021240368058000790564138392180385545468782765612929
skew: 0.71
deg: 5
c5: 50
c0: -9
m: 100000000000000000000000000000
type: snfs
rlim: 1800000
alim: 1800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:135072, AFBsize:134503, largePrimes:6508918 encountered
Relations: rels:5845525, finalFF:310973
Max relations in full relation-set: 28
Initial matrix: 269640 x 310973 with sparse part having weight 24290713.
Pruned matrix : 244308 x 245720 with weight 16377793.
Total sieving time: 7.07 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 1.51 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.5,2.5,100000
total time: 8.86 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

4·10¹⁵⁴+9 = 4(0)₁₅₃9_<155> = 17 · 13913 · 1396989572897_<13> · 61059519554988608394921409_<26> · C112

C112 = P56 · P56

P56 = 42618868918024524866536599051397923694814520254443166653_<56>

P56 = 46520226216352324323002797548303105981922548494168073941_<56>

Number: n
N=1982639423151567720765887757879743509716301779332394742489381947815103365988434494345777849480504756361889489473
  ( 112 digits)
SNFS difficulty: 155 digits.
Divisors found:

Mon Dec 10 21:43:43 2007  prp56 factor: 42618868918024524866536599051397923694814520254443166653
Mon Dec 10 21:43:43 2007  prp56 factor: 46520226216352324323002797548303105981922548494168073941
Mon Dec 10 21:43:43 2007  elapsed time 01:00:47 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 24.01 hours.
Scaled time: 31.77 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_4_0_153_9
n: 1982639423151567720765887757879743509716301779332394742489381947815103365988434494345777849480504756361889489473
skew: 1.86
deg: 5
c5: 2
c0: 45
m: 10000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1200000)
Primes: RFBsize:203362, AFBsize:203302, largePrimes:6863368 encountered
Relations: rels:6330906, finalFF:483438
Max relations in full relation-set: 28
Initial matrix: 406729 x 483438 with sparse part having weight 36996653.
Pruned matrix : 344289 x 346386 with weight 21435247.
Total sieving time: 23.83 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 24.01 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 9, 2007 (2nd)

By Yousuke Koide

(10¹¹⁷⁷-1)/9 is divisible by 15112598396753272691345143612337643317_<38>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 9, 2007

By Jo Yeong Uk / GGNFS

5·10¹⁵⁴-9 = 4(9)₁₅₃1_<155> = 20431 · 52699109 · 32997845429069_<14> · 307535008641326161_<18> · C112

C112 = P35 · P78

P35 = 29858758013316752254424575775237339_<35>

P78 = 153258730444147188544171970047926818140030968120876657797177159787574781970379_<78>

Number: 49991_154
N=4576115345759931963273148602487874485867641118618536902522504884305530749801301398793635737836618902146792781481
  ( 112 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=29858758013316752254424575775237339 (pp35)
 r2=153258730444147188544171970047926818140030968120876657797177159787574781970379 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 16.32 hours.
Scaled time: 34.73 units (timescale=2.128).
Factorization parameters were as follows:
n: 4576115345759931963273148602487874485867641118618536902522504884305530749801301398793635737836618902146792781481
m: 10000000000000000000000000000000
c5: 1
c0: -18
skew: 1.78
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2500001)
Primes: RFBsize:216816, AFBsize:216936, largePrimes:5614449 encountered
Relations: rels:5616644, finalFF:590726
Max relations in full relation-set: 28
Initial matrix: 433819 x 590726 with sparse part having weight 45178149.
Pruned matrix : 324617 x 326850 with weight 28243374.
Total sieving time: 15.65 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.55 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 16.32 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

4·10¹⁶⁶+9 = 4(0)₁₆₅9_<167> = 95273 · 8165188054910845523309_<22> · 14974400622659504557368769453_<29> · C112

C112 = P50 · P63

P50 = 16787178947577077116058498947766265186683375867777_<50>

P63 = 204548731765952768246248790510940164302339098214505480636361977_<63>

Number: 40009_166
N=3433796163654992834720717303856461988726115533311254786924829579654454831482818646616432841788029058212662315129
  ( 112 digits)
Divisors found:
 r1=16787178947577077116058498947766265186683375867777 (pp50)
 r2=204548731765952768246248790510940164302339098214505480636361977 (pp63)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 17.28 hours.
Scaled time: 37.04 units (timescale=2.144).
Factorization parameters were as follows:
name: 40009_166
n: 3433796163654992834720717303856461988726115533311254786924829579654454831482818646616432841788029058212662315129
skew: 32399.49
# norm 4.04e+15
c5: 43260
c4: -2582623147
c3: -129295358935911
c2: -427069562025293841
c1: 24893025188825634820574
c0: -213047928497871312783824304
# alpha -6.19
Y1: 8847912799
Y0: -2398488377529493938175
# Murphy_E 7.74e-10
# M 1450873548697470902964069406047257719289617562836590192062108198415984904995949699924035264821588859357326623899
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1400000, 2240001)
Primes: RFBsize:203362, AFBsize:203291, largePrimes:7436972 encountered
Relations: rels:7186524, finalFF:474824
Max relations in full relation-set: 28
Initial matrix: 406739 x 474824 with sparse part having weight 42851975.
Pruned matrix : 354327 x 356424 with weight 28562696.
Polynomial selection time: 0.94 hours.
Total sieving time: 15.41 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.68 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000
total time: 17.28 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Dec 8, 2007 (3rd)

By matsui / GMP-ECM

(37·10¹⁷⁸-1)/9 = 4(1)₁₇₈_<179> = 7 · 137 · C176

C176 = P33 · C144

P33 = 256606801414902925624321820940911_<33>

C144 = [167059987357085613333034797110824057589025658340318711449285988164500386196628719375549643795216399404461119111310119558935462349796606422281239_<144>]

Dec 8, 2007 (2nd)

By Jo Yeong Uk / GGNFS

5·10¹⁶²-9 = 4(9)₁₆₁1_<163> = C163

C163 = P44 · P56 · P64

P44 = 68385977371361886229008858431010504877885471_<44>

P56 = 10358845079111018892823016494495871163939965326959587059_<56>

P64 = 7058161771042422170571387133040680162138563583374078964992316019_<64>

Number: 49991_162
N=4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
  ( 163 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=68385977371361886229008858431010504877885471 (pp44)
 r2=10358845079111018892823016494495871163939965326959587059 (pp56)
 r3=7058161771042422170571387133040680162138563583374078964992316019 (pp64)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 48.82 hours.
Scaled time: 104.66 units (timescale=2.144).
Factorization parameters were as follows:
n: 4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
m: 500000000000000000000000000000000
c5: 4
c0: -225
skew: 2.24
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [2500000, 5100001)
Primes: RFBsize:348513, AFBsize:348286, largePrimes:6727746 encountered
Relations: rels:6971731, finalFF:855302
Max relations in full relation-set: 28
Initial matrix: 696863 x 855302 with sparse part having weight 63866792.
Pruned matrix : 578415 x 581963 with weight 45564381.
Total sieving time: 46.21 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 2.42 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,49,49,2.5,2.5,100000
total time: 48.82 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

5·10¹⁵¹-9 = 4(9)₁₅₀1_<152> = 41 · 71 · 5849 · 301673 · 2377056670405894456247259031_<28> · C112

C112 = P34 · P78

P34 = 7216593624182899656979319751461431_<34>

P78 = 567463522224990994815587976391783657930851218965846028456860191438113244343673_<78>

Number: 49991_151
N=4095153636445241190206816689343683703674815019630873708328681246983802788485970229898316586832416033236168376063
  ( 112 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=7216593624182899656979319751461431 (pp34)
 r2=567463522224990994815587976391783657930851218965846028456860191438113244343673 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 12.78 hours.
Scaled time: 27.42 units (timescale=2.146).
Factorization parameters were as follows:
n: 4095153636445241190206816689343683703674815019630873708328681246983802788485970229898316586832416033236168376063
m: 1000000000000000000000000000000
c5: 50
c0: -9
skew: 0.71
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:175768, largePrimes:5401564 encountered
Relations: rels:5292212, finalFF:469027
Max relations in full relation-set: 28
Initial matrix: 352135 x 469027 with sparse part having weight 39728717.
Pruned matrix : 293297 x 295121 with weight 22323023.
Total sieving time: 12.29 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.38 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 12.78 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Dec 8, 2007

By Robert Backstrom / GMP-ECM

5·10¹⁵⁷-9 = 4(9)₁₅₆1_<158> = 23 · 47 · 32993 · C151

C151 = P41 · P110

P41 = 64414577002263313514982818321328963237311_<41>

P110 = 21763981302826500962913776820417810329105314486317929333032864905086682541577240814547337472885523445053489457_<110>

Dec 7, 2007 (4th)

By Jo Yeong Uk / GGNFS

5·10¹⁴⁸-9 = 4(9)₁₄₇1_<149> = 29 · 79² · 109 · 752100379 · C133

C133 = P34 · P99

P34 = 3528305141284807144178302848697901_<34>

P99 = 955101178320483387652564653901091192062550077009781733001890240341202021273986351553940732976675729_<99>

Number: 49991_148
N=3369888397915338921258428641420141674023216060199260547003287810058336759881465047437666734012844616469309629039403567538331159944829
  ( 133 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=3528305141284807144178302848697901 (pp34)
 r2=955101178320483387652564653901091192062550077009781733001890240341202021273986351553940732976675729 (pp99)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.19 hours.
Scaled time: 21.63 units (timescale=2.123).
Factorization parameters were as follows:
n: 3369888397915338921258428641420141674023216060199260547003287810058336759881465047437666734012844616469309629039403567538331159944829
m: 1000000000000000000000000000000
c5: 1
c0: -180
skew: 2.83
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1575001)
Primes: RFBsize:135072, AFBsize:134763, largePrimes:3725528 encountered
Relations: rels:3800513, finalFF:378509
Max relations in full relation-set: 28
Initial matrix: 269899 x 378509 with sparse part having weight 33652982.
Pruned matrix : 230441 x 231854 with weight 17271651.
Total sieving time: 9.90 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 10.19 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Dec 7, 2007 (3rd)

By Jo Yeong Uk / GGNFS

8·10¹⁸⁶-7 = 7(9)₁₈₅3_<187> = C187

C187 = P59 · P129

P59 = 23673718891878340687652156651068165346397873316066209701723_<59>

P129 = 337927472930521778199552160468265760927553690616358987625083967033589270515553679435711873302636879244937694756967161283401298491_<129>

Number: 79993_186
N=7999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 187 digits)
SNFS difficulty: 187 digits.
Divisors found:
 r1=23673718891878340687652156651068165346397873316066209701723 (pp59)
 r2=337927472930521778199552160468265760927553690616358987625083967033589270515553679435711873302636879244937694756967161283401298491 (pp129)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 403.36 hours.
Scaled time: 859.97 units (timescale=2.132).
Factorization parameters were as follows:
n: 7999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
m: 20000000000000000000000000000000000000
c5: 5
c0: -14
skew: 1.23
type: snfs
Factor base limits: 12000000/12000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [6000000, 12600001)
Primes: RFBsize:788060, AFBsize:788254, largePrimes:11493077 encountered
Relations: rels:12030057, finalFF:1799960
Max relations in full relation-set: 28
Initial matrix: 1576379 x 1799960 with sparse part having weight 101413617.
Pruned matrix : 1375471 x 1383416 with weight 74538419.
Total sieving time: 389.01 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 13.95 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,12000000,12000000,28,28,50,50,2.6,2.6,100000
total time: 403.36 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Dec 7, 2007 (2nd)

By Sinkiti Sibata / PFGW

5·10¹⁰⁸²⁰-9 and 5·10¹⁴⁵⁹²-9 are PRP.

Dec 7, 2007

By Yousuke Koide

(10¹⁰⁹³-1)/9 is divisible by 199506195135220536755902065305293_<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 6, 2007 (5th)

By Jo Yeong Uk / GMP-ECM

5·10¹⁹⁹-9 = 4(9)₁₉₈1_<200> = C200

C200 = P34 · P167

P34 = 1224112416041742410052808832168959_<34>

P167 = 40845921783620723265274965609618243098936302659169196754666765677273901878095642440080026040452661066087357309697423682859960350348666458327845592281510888305426519049_<167>

Dec 6, 2007 (4th)

By Robert Backstrom / GGNFS, Msieve

(16·10¹⁶²-7)/9 = 1(7)₁₆₂_<163>= 149 · 12918999672424547147_<20> · C141

C141 = P53 · P89

P53 = 42410911175907381021122531054551380413053150932223867_<53>

P89 = 21776331263493214068135261250146977053996751440377507135716102961789622007528024777905477_<89>

Number: n
N=923554050953145651757115932207095054219542878393925009149107585156454700784480736260600830105563687523730018039673296026246046433409929419559
  ( 141 digits)
SNFS difficulty: 163 digits.
Divisors found:

Thu Dec 06 08:21:53 2007  prp53 factor: 42410911175907381021122531054551380413053150932223867
Thu Dec 06 08:21:53 2007  prp89 factor: 21776331263493214068135261250146977053996751440377507135716102961789622007528024777905477
Thu Dec 06 08:21:53 2007  elapsed time 02:06:15 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 67.27 hours.
Scaled time: 88.59 units (timescale=1.317).
Factorization parameters were as follows:
name: KA_1_7_162
n: 923554050953145651757115932207095054219542878393925009149107585156454700784480736260600830105563687523730018039673296026246046433409929419559
skew: 0.67
deg: 5
c5: 50
c0: -7
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2600000)
Primes: RFBsize:216816, AFBsize:217591, largePrimes:7393862 encountered
Relations: rels:6850636, finalFF:494540
Max relations in full relation-set: 28
Initial matrix: 434472 x 494540 with sparse part having weight 50632783.
Pruned matrix : 
Total sieving time: 67.01 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 67.27 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

4·10¹⁵²+9 = 4(0)₁₅₁9_<153> = 26713 · 1234873 · 1996467668952176494127953_<25> · C118

C118 = P41 · P78

P41 = 35974049014171230767387935670841612478177_<41>

P78 = 168835367899724431687288680957130059518243845115630566914418157002167566445961_<78>

Number: n
N=6073691800150318752219511984753628781476739145121835518994745689916081064629478208333175321810209710086068549562293097
  ( 118 digits)
SNFS difficulty: 152 digits.
Divisors found:

Thu Dec 06 16:08:51 2007  prp41 factor: 35974049014171230767387935670841612478177
Thu Dec 06 16:08:51 2007  prp78 factor: 168835367899724431687288680957130059518243845115630566914418157002167566445961
Thu Dec 06 16:08:51 2007  elapsed time 00:47:53 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 22.03 hours.
Scaled time: 31.99 units (timescale=1.452).
Factorization parameters were as follows:
name: KA_4_0_151_9
n: 6073691800150318752219511984753628781476739145121835518994745689916081064629478208333175321810209710086068549562293097
skew: 0.94
deg: 5
c5: 25
c0: 18
m: 2000000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1200000)
Primes: RFBsize:148933, AFBsize:148625, largePrimes:7017509 encountered
Relations: rels:6462685, finalFF:361511
Max relations in full relation-set: 28
Initial matrix: 297622 x 361511 with sparse part having weight 34777349.
Pruned matrix : 266133 x 267685 with weight 22914288.
Total sieving time: 21.83 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 22.03 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(34·10¹⁶¹-7)/9 = 3(7)₁₆₁_<162> = 197 · 9371 · 110183 · 694182710171_<12> · C139

C139 = P58 · P82

P58 = 2616862112205494779410765284481436663033222318232195981387_<58>

P82 = 1022386293766035950048848925429858897403553614981437089485799152210536157188516281_<82>

Number: n
N=2675443956194536316022798734239381743434700299393259205203764910786567960718170468410719273526054038360896452757923210295394590633222461747
  ( 139 digits)
SNFS difficulty: 162 digits.
Divisors found:

Thu Dec 06 23:56:31 2007  prp58 factor: 2616862112205494779410765284481436663033222318232195981387
Thu Dec 06 23:56:31 2007  prp82 factor: 1022386293766035950048848925429858897403553614981437089485799152210536157188516281
Thu Dec 06 23:56:31 2007  elapsed time 02:44:21 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 69.26 hours.
Scaled time: 83.04 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_3_7_161
n: 2675443956194536316022798734239381743434700299393259205203764910786567960718170468410719273526054038360896452757923210295394590633222461747
type: snfs
skew: 0.46
deg: 5
c5: 340
c0: -7
m: 100000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3000001)
Primes: RFBsize:230209, AFBsize:229397, largePrimes:7454855 encountered
Relations: rels:6893700, finalFF:514080
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 68.95 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 69.26 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Dec 6, 2007 (3rd)

By Sinkiti Sibata / GGNFS

5·10¹⁴³-9 = 4(9)₁₄₂1_<144> = 17 · C143

C143 = P60 · P84

P60 = 285720265191441664337755675562698371459936363289423581013937_<60>

P84 = 102939022145228428989427304065983196665834399279521532082685405829806319911074359479_<84>

Number: 49991_143
N=29411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823
  ( 143 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=285720265191441664337755675562698371459936363289423581013937 (pp60)
 r2=102939022145228428989427304065983196665834399279521532082685405829806319911074359479 (pp84)
Version: GGNFS-0.77.1-20060513-k8
Total time: 11.80 hours.
Scaled time: 23.49 units (timescale=1.991).
Factorization parameters were as follows:
name: 49991_143
n: 29411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823
m: 50000000000000000000000000000
c5: 8
c0: -45
skew: 1.41
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1950001)
Primes: RFBsize:100021, AFBsize:99898, largePrimes:2740628 encountered
Relations: rels:2726242, finalFF:266126
Max relations in full relation-set: 28
Initial matrix: 199984 x 266126 with sparse part having weight 25911863.
Pruned matrix : 180593 x 181656 with weight 15619042.
Total sieving time: 11.27 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.36 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 11.80 hours.
 --------- CPU info (if available) ----------

5·10¹³⁵-9 = 4(9)₁₃₄1_<136> = 7 · 23 · 79 · 17536644897128650802233_<23> · C110

C110 = P46 · P65

P46 = 1719936531432379284578110469620659745107108719_<46>

P65 = 13033411521941582112132234407177385128654436282436915981843640207_<65>

Number: 49991_135
N=22416640605779012272061571478739422204655514974373750892597086537285582773909365228492465712874266775868664833
  ( 110 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=1719936531432379284578110469620659745107108719 (pp46)
 r2=13033411521941582112132234407177385128654436282436915981843640207 (pp65)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.81 hours.
Scaled time: 11.61 units (timescale=2.000).
Factorization parameters were as follows:
name: 49991_135
n: 22416640605779012272061571478739422204655514974373750892597086537285582773909365228492465712874266775868664833
m: 1000000000000000000000000000
c5: 5
c0: -9
skew: 1.12
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:63763, largePrimes:1597471 encountered
Relations: rels:1658522, finalFF:230632
Max relations in full relation-set: 28
Initial matrix: 142327 x 230632 with sparse part having weight 17325623.
Pruned matrix : 115642 x 116417 with weight 7445126.
Total sieving time: 5.63 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.81 hours.
 --------- CPU info (if available) ----------

5·10¹⁴²-9 = 4(9)₁₄₁1_<143> = 2339 · 7678802901535212851801_<22> · C118

C118 = P30 · P44 · P46

P30 = 117630389300918643864328074179_<30>

P44 = 13290764272933581140590846123083681578082559_<44>

P46 = 1780642654590329845797643787582718386220435529_<46>

Number: 49991_142
N=2783852765203771242392062028278372201075337622567765162596504687226524568762724852814366472811671739409898543364743269
  ( 118 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=117630389300918643864328074179 (pp30)
 r2=13290764272933581140590846123083681578082559 (pp44)
 r3=1780642654590329845797643787582718386220435529 (pp46)
Version: GGNFS-0.77.1-20060513-k8
Total time: 15.52 hours.
Scaled time: 30.95 units (timescale=1.994).
Factorization parameters were as follows:
name: 49991_142
n: 2783852765203771242392062028278372201075337622567765162596504687226524568762724852814366472811671739409898543364743269
m: 10000000000000000000000000000
c5: 500
c0: -9
skew: 0.45
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2350001)
Primes: RFBsize:100021, AFBsize:99988, largePrimes:2795102 encountered
Relations: rels:2767439, finalFF:225205
Max relations in full relation-set: 28
Initial matrix: 200076 x 225205 with sparse part having weight 24651803.
Pruned matrix : 193526 x 194590 with weight 19788059.
Total sieving time: 14.86 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.47 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 15.52 hours.
 --------- CPU info (if available) ----------

Dec 6, 2007 (2nd)

By Sinkiti Sibata / PFGW

(22·10¹¹⁴³¹-7)/3 and (22·10¹²⁹²⁷-7)/3 are PRP.

Dec 6, 2007

By Robert Backstrom / GGNFS, Msieve 1.30

9·10¹⁶¹+7 = 9(0)₁₆₀7_<162> = 32742491009_<11> · 15305913553837_<14> · C139

C139 = P61 · P78

P61 = 2871374186022696036738055549847702632759229312163023359543043_<61>

P78 = 625434371370412843235342091358846490870084281799111208724718685614180061274753_<78>

Number: n
N=1795856109004335763698691572087419453798364220434114608269312678179761222742470512062548832927933855893213113194030583971753238970152693379
  ( 139 digits)
SNFS difficulty: 161 digits.
Divisors found:

Thu Dec 06 02:15:29 2007  prp61 factor: 2871374186022696036738055549847702632759229312163023359543043
Thu Dec 06 02:15:29 2007  prp78 factor: 625434371370412843235342091358846490870084281799111208724718685614180061274753
Thu Dec 06 02:15:29 2007  elapsed time 01:54:10 (Msieve 1.30)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 65.06 hours.
Scaled time: 84.97 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_9_0_160_7
n: 1795856109004335763698691572087419453798364220434114608269312678179761222742470512062548832927933855893213113194030583971753238970152693379
skew: 0.60
deg: 5
c5: 90
c0: 7
m: 100000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2300001)
Primes: RFBsize:230209, AFBsize:230767, largePrimes:7363359 encountered
Relations: rels:6836918, finalFF:495414
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 64.81 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 65.06 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 5, 2007 (3rd)

By Jo Yeong Uk / GMP-ECM

5·10¹⁵³-9 = 4(9)₁₅₂1_<154> = 7² · 31 · 233 · 367 · 190668767 · 15049933389679_<14> · C125

C125 = P36 · P89

P36 = 394436722224962502210435443374249441_<36>

P89 = 34009384186180731129927406696605787600972387399376193654041569409619395347174902797719823_<89>

Dec 5, 2007 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS

5·10¹²³-9 = 4(9)₁₂₂1_<124> = 7 · 31 · 103668634195146479_<18> · C105

C105 = P33 · P72

P33 = 529652772019323584350569475910017_<33>

P72 = 419634942345057429532843777824194673588852290057980851002408093562224161_<72>

5·10¹²⁴-9 = 4(9)₁₂₃1_<125> = 112834510063289823811_<21> · C105

C105 = P45 · P60

P45 = 449489779543195000651111258759942012797389869_<45>

P60 = 985844086264210902762592892891295128151928079697441377159249_<60>

Number: n
N=443126840998862673372330594167340785125969505774279345379238258715809495060385177703056868837181152248381
  ( 105 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=449489779543195000651111258759942012797389869 (pp45)
 r2=985844086264210902762592892891295128151928079697441377159249 (pp60)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.96 hours.
Scaled time: 2.60 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_4_9_123_1
n: 443126840998862673372330594167340785125969505774279345379238258715809495060385177703056868837181152248381
skew: 1.78
deg: 5
c5: 1
c0: -18
m: 10000000000000000000000000
type: snfs
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 250001)
Primes: RFBsize:63951, AFBsize:63888, largePrimes:4613515 encountered
Relations: rels:4003172, finalFF:210650
Max relations in full relation-set: 48
Initial matrix: 127906 x 210650 with sparse part having weight 17161578.
Pruned matrix : 98518 x 99221 with weight 4907911.
Total sieving time: 1.71 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.10 hours.
Total square root time: 0.06 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000
total time: 1.96 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 5, 2007

By Sinkiti Sibata / GGNFS

5·10¹²⁸-9 = 4(9)₁₂₇1_<129> = 17981 · 3843931457165509_<16> · C109

C109 = P45 · P64

P45 = 942477006562110761447064968719904363145782491_<45>

P64 = 7675554588296651640866311850875593032012524032228064348193639269_<64>

Number: 49991_128
N=7234033712081902712464612958999569631054058842077060936513763588440193920136568538523951971389190729990239079
  ( 109 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=942477006562110761447064968719904363145782491 (pp45)
 r2=7675554588296651640866311850875593032012524032228064348193639269 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.04 hours.
Scaled time: 6.11 units (timescale=2.010).
Factorization parameters were as follows:
name: 49991_128
n: 7234033712081902712464612958999569631054058842077060936513763588440193920136568538523951971389190729990239079
m: 50000000000000000000000000
c5: 8
c0: -45
skew: 1.41
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:63951, AFBsize:63928, largePrimes:1408145 encountered
Relations: rels:1391646, finalFF:160862
Max relations in full relation-set: 28
Initial matrix: 127944 x 160862 with sparse part having weight 8338899.
Pruned matrix : 116420 x 117123 with weight 4694100.
Total sieving time: 2.90 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 3.04 hours.
 --------- CPU info (if available) ----------

5·10¹²⁹-9 = 4(9)₁₂₈1_<130> = 7 · 399271 · C124

C124 = P37 · P88

P37 = 1719378230348833617587044366277777273_<37>

P88 = 1040477691594168476615746126692780490295108691699389255395317590980581957687501917021311_<88>

Number: 49991_129
N=1788974692090620870822788818335702532150558678906592979991749248720078056543765297969835739921721623372882793176278052464903
  ( 124 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=1719378230348833617587044366277777273 (pp37)
 r2=1040477691594168476615746126692780490295108691699389255395317590980581957687501917021311 (pp88)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.02 hours.
Scaled time: 6.07 units (timescale=2.010).
Factorization parameters were as follows:
name: 49991_129
n: 1788974692090620870822788818335702532150558678906592979991749248720078056543765297969835739921721623372882793176278052464903
m: 100000000000000000000000000
c5: 1
c0: -18
skew: 1.78
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:63951, AFBsize:63888, largePrimes:1400726 encountered
Relations: rels:1379152, finalFF:155356
Max relations in full relation-set: 28
Initial matrix: 127906 x 155356 with sparse part having weight 8163928.
Pruned matrix : 118614 x 119317 with weight 4886712.
Total sieving time: 2.88 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 3.02 hours.
 --------- CPU info (if available) ----------

5·10¹³¹-9 = 4(9)₁₃₀1_<132> = 41 · 5547391 · C124

C124 = P60 · P64

P60 = 331708005539959846200945699830264904120183676134446346135329_<60>

P64 = 6627373043733457754101972925473022695394088807721914419175039809_<64>

Number: 49991_131
N=2198352694306118352775557233934329691552518925057765344324838864814459845991060504289533496412119129734953277157126876312161
  ( 124 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=331708005539959846200945699830264904120183676134446346135329 (pp60)
 r2=6627373043733457754101972925473022695394088807721914419175039809 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.40 hours.
Scaled time: 8.73 units (timescale=1.985).
Factorization parameters were as follows:
name: 49991_131
n: 2198352694306118352775557233934329691552518925057765344324838864814459845991060504289533496412119129734953277157126876312161
m: 100000000000000000000000000
c5: 50
c0: -9
skew: 0.71
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64058, largePrimes:1540929 encountered
Relations: rels:1578173, finalFF:205413
Max relations in full relation-set: 28
Initial matrix: 128074 x 205413 with sparse part having weight 14981903.
Pruned matrix : 107027 x 107731 with weight 6295031.
Total sieving time: 4.24 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.40 hours.
 --------- CPU info (if available) ----------

5·10¹³³-9 = 4(9)₁₃₂1_<134> = 1388981393_<10> · C125

C125 = P46 · P79

P46 = 4580943858133272901234098370518760018593679951_<46>

P79 = 7858119105566310646465581070947787541968136461241464994014105774627915529998537_<79>

Number: 49991_133
N=35997602453123718699088433361036392227609920185590275938275294088118860783040021616761859674530571627319128529175336476231687
  ( 125 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=4580943858133272901234098370518760018593679951 (pp46)
 r2=7858119105566310646465581070947787541968136461241464994014105774627915529998537 (pp79)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.68 hours.
Scaled time: 9.29 units (timescale=1.985).
Factorization parameters were as follows:
name: 49991_133
n: 35997602453123718699088433361036392227609920185590275938275294088118860783040021616761859674530571627319128529175336476231687
m: 500000000000000000000000000
c5: 8
c0: -45
skew: 1.41
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 925001)
Primes: RFBsize:78498, AFBsize:63928, largePrimes:1457680 encountered
Relations: rels:1439431, finalFF:160358
Max relations in full relation-set: 28
Initial matrix: 142491 x 160358 with sparse part having weight 10506246.
Pruned matrix : 136383 x 137159 with weight 7567068.
Total sieving time: 4.48 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 4.68 hours.
 --------- CPU info (if available) ----------

5·10¹³⁴-9 = 4(9)₁₃₃1_<135> = 19 · 4294946301634720547509_<22> · C112

C112 = P40 · P72

P40 = 7661951585715267309757814664269644345249_<40>

P72 = 799685573994862057768981025766325851378881906722550433228529476184746329_<72>

Number: 49991_134
N=6127152151743557074542844552870042019610302481794247517939862406771161342106351861871786326029301318444361340921
  ( 112 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=7661951585715267309757814664269644345249 (pp40)
 r2=799685573994862057768981025766325851378881906722550433228529476184746329 (pp72)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.82 hours.
Scaled time: 11.55 units (timescale=1.986).
Factorization parameters were as follows:
name: 49991_134
n: 6127152151743557074542844552870042019610302481794247517939862406771161342106351861871786326029301318444361340921
m: 1000000000000000000000000000
c5: 1
c0: -18
skew: 1.78
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:63888, largePrimes:1619441 encountered
Relations: rels:1697010, finalFF:245323
Max relations in full relation-set: 28
Initial matrix: 142453 x 245323 with sparse part having weight 18456007.
Pruned matrix : 112751 x 113527 with weight 7450413.
Total sieving time: 5.64 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.82 hours.
 --------- CPU info (if available) ----------

Dec 4, 2007 (5th)

By Jo Yeong Uk / GGNFS

5·10¹¹⁸-9 = 4(9)₁₁₇1_<119> = C119

C119 = P60 · P60

P60 = 113451761893099661361741916560523265424931846016438394824059_<60>

P60 = 440715940992725025596348804318707127294139212236448645152949_<60>

Number: 49991_118
N=49999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
  ( 119 digits)
SNFS difficulty: 120 digits.
Divisors found:

r1=113451761893099661361741916560523265424931846016438394824059
(pp60)

r2=440715940992725025596348804318707127294139212236448645152949
(pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.74 hours.
Scaled time: 1.58 units (timescale=2.145).
Factorization parameters were as follows:
n:
49999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
m: 1000000000000000000000000
c5: 1
c0: -180
skew: 2.83
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 420001)
Primes: RFBsize:49098, AFBsize:49121,
largePrimes:1721640 encountered
Relations: rels:1663175, finalFF:113797
Max relations in full relation-set: 28
Initial matrix: 98283 x 113797 with sparse part having
weight 8423002.
Pruned matrix : 92995 x 93550 with weight 5618322.
Total sieving time: 0.68 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.74 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz
stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz
stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz
stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz
stepping 07
Memory: 8167512k/8912896k available (2114k kernel
code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine..
4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine..
4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine..
4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine..
4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Dec 4, 2007 (4th)

By Robert Backstrom / GMP-ECM

5·10¹¹³-9 = 4(9)₁₁₂1_<114> = 23 · 263 · 200041 · 2035289 · C99

C99 = P30 · P69

P30 = 443952373522730358003023095039_<30>

P69 = 457303931730390724716183370178707280616570660476664818059347925723369_<69>

Dec 4, 2007 (3rd)

By matsui / GMP-ECM

(4·10¹⁸⁵-13)/9 = (4)₁₈₄3_<185> = 7 · 1451 · C181

C181 = P33 · C149

P33 = 164277524510786827843488693745099_<33>

C149 = [26636298892028694012587941153238062628591187075841112023861911522751253412947765247273184353075516238787560153594780836262462832930974948643067577301_<149>]

Dec 4, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

4·10¹⁶¹+9 = 4(0)₁₆₀9_<162> = 4051 · 127235411 · 1969369859_<10> · C141

C141 = P40 · P102

P40 = 3315928709727846416041854024938819789689_<40>

P102 = 118838532278963278232537809676524506390734233220677222531873601915306217550488799630909789562805027619_<102>

Number: n
N=394060101005733730854944506185225543063987154654543968918320787847903391279563079348777846305919632986249125213107544098370152142181416420491
  ( 141 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Dec 04 13:47:12 2007  prp40 factor: 3315928709727846416041854024938819789689
Tue Dec 04 13:47:12 2007  prp102 factor: 118838532278963278232537809676524506390734233220677222531873601915306217550488799630909789562805027619
Tue Dec 04 13:47:12 2007  elapsed time 01:05:12 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 31.49 hours.
Scaled time: 45.35 units (timescale=1.440).
Factorization parameters were as follows:
name: KA_4_0_160_9
n: 394060101005733730854944506185225543063987154654543968918320787847903391279563079348777846305919632986249125213107544098370152142181416420491
skew: 0.74
deg: 5
c5: 40
c0: 9
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:203362, AFBsize:203082, largePrimes:7092138 encountered
Relations: rels:6575017, finalFF:473191
Max relations in full relation-set: 28
Initial matrix: 406511 x 473191 with sparse part having weight 37652625.
Pruned matrix : 356677 x 358773 with weight 25275013.
Total sieving time: 31.28 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 31.49 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Dec 4, 2007

The factor table of 499...991 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Dec 3, 2007 (3rd)

By Yousuke Koide

(10¹⁰¹⁹-1)/9 is divisible by 1164875952920329463736875905335015089_<37>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 3, 2007 (2nd)

By Robert Backstrom / GMP-ECM

(64·10²³⁴+53)/9 = 7(1)₂₃₃7_<235> = 13 · 1181 · 7451 · 1471598307214747_<16> · 3052073285905649_<16> · 172548225862787861_<18> · 2699321912890730492306803_<25> · C155

C155 = P47 · P109

P47 = 26652891282185821045577962549160542412294508503_<47>

P109 = 1114899980065870331232905973592925067977812491581216317251152807767466063464285258166500582274270472922906037_<109>

Dec 3, 2007

By Jo Yeong Uk / GGNFS

(4·10¹⁸⁷-1)/3 = 1(3)₁₈₇_<188> = 13² · 71 · 641 · 4354373 · C174

C174 = P52 · P122

P52 = 5361712371792973170896785910460906141853462256912209_<52>

P122 = 74251719049861199442807051707488431927072858194646024738993713156188070400742301801156540569317981596338173399436320309791_<122>

Number: 13333_187
N=398116360656536779984902594959659524762886894764740907788961498125477543559005946143561502786041981375439529374284451922273986560056748206834695296451854204990252061970138319
  ( 174 digits)
SNFS difficulty: 187 digits.
Divisors found:
 r1=5361712371792973170896785910460906141853462256912209 (pp52)
 r2=74251719049861199442807051707488431927072858194646024738993713156188070400742301801156540569317981596338173399436320309791 (pp122)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 361.56 hours.
Scaled time: 773.01 units (timescale=2.138).
Factorization parameters were as follows:
n: 398116360656536779984902594959659524762886894764740907788961498125477543559005946143561502786041981375439529374284451922273986560056748206834695296451854204990252061970138319
m: 20000000000000000000000000000000000000
c5: 25
c0: -2
skew: 0.6
type: snfs
Factor base limits: 12000000/12000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [6000000, 11900001)
Primes: RFBsize:788060, AFBsize:788149, largePrimes:11393019 encountered
Relations: rels:11956011, finalFF:1824015
Max relations in full relation-set: 28
Initial matrix: 1576273 x 1824015 with sparse part having weight 91057329.
Pruned matrix : 1349070 x 1357015 with weight 64635248.
Total sieving time: 348.71 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 12.46 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,12000000,12000000,28,28,50,50,2.6,2.6,100000
total time: 361.56 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Jo Yeong Uk completed factorizations up to n=200 of 133...33. Congratulations!

Dec 2, 2007

By Sinkiti Sibata / PFGW

2·10¹³⁵⁶¹+9, 2·10¹⁵⁹⁵⁵+9, (23·10¹³⁰⁹²-11)/3, (17·10¹¹⁰⁴⁶+7)/3, (17·10¹⁵⁴⁴⁸+7)/3, (17·10¹⁶⁶²⁸+7)/3, (17·10¹⁶⁹¹⁸+7)/3 and (17·10¹⁸⁷³⁴+7)/3 are PRP.

Dec 1, 2007 (5th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

4·10¹⁶⁰+9 = 4(0)₁₅₉9_<161> = 277 · 138637 · 247609 · 15173733529_<11> · C138

C138 = P62 · P76

P62 = 60797126856307127135595444344471160234256633836042739865882569_<62>

P76 = 4559940072470123498850798447077277366305328269178339465898539108054593612449_<76>

Number: n
N=277231255043124412962563195334423003572989349824918726484343257938458321577544020345163333731927265082665578558503965730046567209330501481
  ( 138 digits)
SNFS difficulty: 160 digits.
Divisors found:

Sat Dec 01 14:19:53 2007  prp62 factor: 60797126856307127135595444344471160234256633836042739865882569
Sat Dec 01 14:19:53 2007  prp76 factor: 4559940072470123498850798447077277366305328269178339465898539108054593612449
Sat Dec 01 14:19:53 2007  elapsed time 01:19:11

Version: GGNFS-0.77.1-20051202-athlon
Total time: 27.74 hours.
Scaled time: 40.22 units (timescale=1.450).
Factorization parameters were as follows:
name: KA_4_0_159_9
n: 277231255043124412962563195334423003572989349824918726484343257938458321577544020345163333731927265082665578558503965730046567209330501481
skew: 1.18
deg: 5
c5: 4
c0: 9
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1500000)
Primes: RFBsize:203362, AFBsize:203477, largePrimes:7032527 encountered
Relations: rels:6512477, finalFF:474011
Max relations in full relation-set: 28
Initial matrix: 406903 x 474011 with sparse part having weight 35734018.
Pruned matrix : 354822 x 356920 with weight 23455777.
Total sieving time: 27.55 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 27.74 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 3400+

4·10¹⁵¹+9 = 4(0)₁₅₀9_<152> = 7 · 131 · 197 · 1531 · 47933 · 2296496011_<10> · 1404598779340570579_<19> · C111

C111 = P31 · P81

P31 = 6104431168415592413869608635611_<31>

P81 = 153232696611883288817148088275635599149717352290249536018399392505789557880036813_<81>

4·10¹⁵⁷+9 = 4(0)₁₅₆9_<158> = 7 · 87972114341735599736283329579_<29> · C128

C128 = P53 · P76

P53 = 22156740177008454467142813185853133375535106690625343_<53>

P76 = 2931642819433829612544003364072511581602586787125479620745479951967818422771_<76>

Number: n
N=64955648241987874447117430039138259202002854155007541960018688539768478636343303641089348405672723770075499054458421913940885453
  ( 128 digits)
SNFS difficulty: 157 digits.
Divisors found:

Sat Dec 01 21:40:37 2007  prp53 factor: 22156740177008454467142813185853133375535106690625343
Sat Dec 01 21:40:37 2007  prp76 factor: 2931642819433829612544003364072511581602586787125479620745479951967818422771
Sat Dec 01 21:40:37 2007  elapsed time 01:33:31 (Msieve 1.30)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 37.39 hours.
Scaled time: 48.71 units (timescale=1.303).
Factorization parameters were as follows:
name: KA_4_0_156_9
n: 64955648241987874447117430039138259202002854155007541960018688539768478636343303641089348405672723770075499054458421913940885453
skew: 0.94
deg: 5
c5: 25
c0: 18
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1600001)
Primes: RFBsize:216816, AFBsize:216551, largePrimes:7116928 encountered
Relations: rels:6581195, finalFF:473861
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 37.16 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 37.39 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

4·10¹⁶²+9 = 4(0)₁₆₁9_<163> = 13 · C162

C162 = P77 · P86

P77 = 14484959608208348655122569360348676482871487639034491862149522347733039174529_<77>

P86 = 21242193006733989503775579532646316990712184952355071124010335682117913659526189758317_<86>

Number: n
N=307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307693
  ( 162 digits)
SNFS difficulty: 162 digits.
Divisors found:

Sun Dec 02 00:56:26 2007  prp77 factor: 14484959608208348655122569360348676482871487639034491862149522347733039174529
Sun Dec 02 00:56:26 2007  prp86 factor: 21242193006733989503775579532646316990712184952355071124010335682117913659526189758317
Sun Dec 02 00:56:26 2007  elapsed time 01:38:38 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 57.08 hours.
Scaled time: 75.52 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_4_0_161_9
n: 307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307693
skew: 0.94
deg: 5
c5: 25
c0: 18
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2800000)
Primes: RFBsize:216816, AFBsize:216551, largePrimes:7515407 encountered
Relations: rels:6986522, finalFF:507662
Max relations in full relation-set: 28
Initial matrix: 433431 x 507662 with sparse part having weight 54891344.
Pruned matrix : 403528 x 405759 with weight 36508693.
Total sieving time: 56.79 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 57.08 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 1, 2007 (4th)

By Yousuke Koide

10¹⁴⁹⁷+1 is divisible by 7016092401376747085885131800303253_<34>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 1, 2007 (3rd)

By Robert Backstrom / GGNFS

4·10¹⁵⁵+9 = 4(0)₁₅₄9_<156> = 1975423 · 3095912878954409_<16> · C134

C134 = P65 · P70

P65 = 34448312105302906122201979845692525321041884536529688865372252369_<65>

P70 = 1898642540091341888277141518857734481586769553402869501770427156234223_<70>

Number: n
N=65405030797471631024897797203292080268700559470205742591870217011703486438834669678697175888566047633668436172058302458077017630624287
  ( 134 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=34448312105302906122201979845692525321041884536529688865372252369 (pp65)
 r2=1898642540091341888277141518857734481586769553402869501770427156234223 (pp70)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 26.75 hours.
Scaled time: 32.02 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_4_0_154_9
n: 65405030797471631024897797203292080268700559470205742591870217011703486438834669678697175888566047633668436172058302458077017630624287
type: snfs
skew: 1.17
deg: 5
c5: 4
c0: 9
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:216816, AFBsize:216936, largePrimes:6166954 encountered
Relations: rels:5660881, finalFF:507771
Max relations in full relation-set: 28
Initial matrix: 433816 x 507771 with sparse part having weight 24265495.
Pruned matrix : 362409 x 364642 with weight 13836447.
Total sieving time: 24.20 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.29 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 26.75 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Dec 1, 2007 (2nd)

By Sinkiti Sibata / Msieve

4·10¹⁷²+9 = 4(0)₁₇₁9_<173> = 379417 · 2183353693_<10> · 369214042069_<12> · 10392906827609765461_<20> · 1432364659536702101368956541_<28> · C100

C100 = P45 · P56

P45 = 521485688834094616003641826229481656646415453_<45>

P56 = 16846429736694498814138730507079319979241737624177166277_<56>

Thu Nov 29 14:35:06 2007  Msieve v. 1.30
Thu Nov 29 14:35:06 2007  random seeds: 5e6160f2 130a07ab
Thu Nov 29 14:35:06 2007  factoring 8785172015635305902166850873310561627369223602890592020277003775916249170381081979472941403203278481 (100 digits)
Thu Nov 29 14:35:06 2007  commencing quadratic sieve (100-digit input)
Thu Nov 29 14:35:07 2007  using multiplier of 1
Thu Nov 29 14:35:07 2007  using 64kb Pentium 4 sieve core
Thu Nov 29 14:35:07 2007  sieve interval: 18 blocks of size 65536
Thu Nov 29 14:35:07 2007  processing polynomials in batches of 6
Thu Nov 29 14:35:07 2007  using a sieve bound of 2825051 (102331 primes)
Thu Nov 29 14:35:07 2007  using large prime bound of 423757650 (28 bits)
Thu Nov 29 14:35:07 2007  using double large prime bound of 3379182069851550 (43-52 bits)
Thu Nov 29 14:35:07 2007  using trial factoring cutoff of 52 bits
Thu Nov 29 14:35:07 2007  polynomial 'A' values have 13 factors
Sat Dec  1 08:30:49 2007  102586 relations (23428 full + 79158 combined from 1560356 partial), need 102427
Sat Dec  1 08:30:56 2007  begin with 1583784 relations
Sat Dec  1 08:30:59 2007  reduce to 275743 relations in 14 passes
Sat Dec  1 08:30:59 2007  attempting to read 275743 relations
Sat Dec  1 08:31:11 2007  recovered 275743 relations
Sat Dec  1 08:31:11 2007  recovered 267629 polynomials
Sat Dec  1 08:31:11 2007  attempting to build 102586 cycles
Sat Dec  1 08:31:11 2007  found 102586 cycles in 5 passes
Sat Dec  1 08:31:11 2007  distribution of cycle lengths:
Sat Dec  1 08:31:11 2007     length 1 : 23428
Sat Dec  1 08:31:11 2007     length 2 : 17036
Sat Dec  1 08:31:11 2007     length 3 : 16856
Sat Dec  1 08:31:11 2007     length 4 : 14145
Sat Dec  1 08:31:11 2007     length 5 : 11048
Sat Dec  1 08:31:11 2007     length 6 : 7584
Sat Dec  1 08:31:11 2007     length 7 : 5024
Sat Dec  1 08:31:11 2007     length 9+: 7465
Sat Dec  1 08:31:11 2007  largest cycle: 20 relations
Sat Dec  1 08:31:12 2007  matrix is 102331 x 102586 with weight 6915312 (avg 67.41/col)
Sat Dec  1 08:31:15 2007  filtering completed in 3 passes
Sat Dec  1 08:31:15 2007  matrix is 98799 x 98863 with weight 6691681 (avg 67.69/col)
Sat Dec  1 08:31:16 2007  saving the first 48 matrix rows for later
Sat Dec  1 08:31:16 2007  matrix is 98751 x 98863 with weight 5212412 (avg 52.72/col)
Sat Dec  1 08:31:16 2007  matrix includes 64 packed rows
Sat Dec  1 08:31:16 2007  using block size 21845 for processor cache size 512 kB
Sat Dec  1 08:31:17 2007  commencing Lanczos iteration
Sat Dec  1 08:32:59 2007  lanczos halted after 1563 iterations (dim = 98750)
Sat Dec  1 08:32:59 2007  recovered 16 nontrivial dependencies
Sat Dec  1 08:33:01 2007  prp45 factor: 521485688834094616003641826229481656646415453
Sat Dec  1 08:33:01 2007  prp56 factor: 16846429736694498814138730507079319979241737624177166277
Sat Dec  1 08:33:01 2007  elapsed time 41:57:55

Dec 1, 2007

By Sinitiki Sibata / PFGW

4·10¹⁹⁶⁷⁹-9 is PRP.

November 2007

Nov 30, 2007 (3rd)

By Alfred Reich

10¹⁶⁵⁵+1 is divisible by 18802215938788787651629737655497612041_<38>

10¹⁸¹³+1 is divisible by 1341949101412826358472947603971939_<34>

Reference: Factorizations of numbers of the form 10ⁿ+1 (Alfred Reich)

Nov 30, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM

(19·10¹⁶¹-1)/9 = 2(1)₁₆₁_<162> = 727717 · 384816673 · 674074250329_<12> · C136

C136 = P35 · P101

P35 = 14467529402478870760723338650411987_<35>

P101 = 77302329134119121600032539311233102902267933504106572342606708487422816772928441334860645111491619777_<101>

Nov 30, 2007

By Bruce Dodson

10²⁴²+1 is divisible by 209363088773816814667969748813613304559806235889961_<51> and cofactor is prime.

Reference: Factoring and Prime Identification (Torbjörn Granlund)

Nov 29, 2007

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

4·10¹⁵⁸+9 = 4(0)₁₅₇9_<159> = 29 · 617 · C155

C155 = P59 · P97

P59 = 16694516335098246170350962150521377733606416852014894432101_<59>

P97 = 1339069098410419305684551449267723355927167683871174848884295909043052511734794797656249685854513_<97>

Number: n
N=22355110937238026043704241882300340915441792879897166489688705080198960487341418431788967752752473034147431956631084781758229475213770748337338624042921813
  ( 155 digits)
SNFS difficulty: 160 digits.
Divisors found:

Thu Nov 29 08:24:10 2007  prp59 factor: 16694516335098246170350962150521377733606416852014894432101
Thu Nov 29 08:24:10 2007  prp97 factor: 1339069098410419305684551449267723355927167683871174848884295909043052511734794797656249685854513
Thu Nov 29 08:24:10 2007  elapsed time 01:05:46 (Msieve 1.30)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 33.00 hours.
Scaled time: 43.14 units (timescale=1.307).
Factorization parameters were as follows:
name: KA_4_0_157_9
n: 22355110937238026043704241882300340915441792879897166489688705080198960487341418431788967752752473034147431956631084781758229475213770748337338624042921813
skew: 2.95
deg: 5
c5: 1
c0: 225
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
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: 48/48
Sieved  special-q in [100000, 1450000)
Primes: RFBsize:216816, AFBsize:216371, largePrimes:7014483 encountered
Relations: rels:6490308, finalFF:490288
Max relations in full relation-set: 28
Initial matrix: 433251 x 490288 with sparse part having weight 34015211.
Pruned matrix : 387237 x 389467 with weight 22902473.
Total sieving time: 31.53 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 1.22 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 33.00 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

4·10¹⁵³+9 = 4(0)₁₅₂9_<154> = 211 · 499 · 823 · 7213 · 5983931 · 20484293 · C128

C128 = P34 · P95

P34 = 1674567153955540249123309372823653_<34>

P95 = 31178204285060110569074580607563260199102302136786304734413870091585370032227633400052324234081_<95>

Nov 28, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

4·10¹⁷¹+9 = 4(0)₁₇₀9_<172> = 4727579 · 42758299609_<11> · 70786206663533_<14> · 52842317195285609_<17> · 1749706642519018677552131_<25> · C100

C100 = P44 · P57

P44 = 13309174465738976322573197980572388901369971_<44>

P57 = 227171538029579664285228640378502521594404174584065064527_<57>

Number: n
N=30234656332859324703546336715738054258309704996708157961949684440936332
94526234496732144750815118717
  ( 100 digits)
Divisors found:

Wed Nov 28 06:36:31 2007  recovered 43 nontrivial dependencies
...
Wed Nov 28 07:11:14 2007  reading relations for dependency 7
...
Wed Nov 28 07:16:43 2007  prp44 factor: 
13309174465738976322573197980572388901369971
Wed Nov 28 07:16:43 2007  prp57 factor: 
227171538029579664285228640378502521594404174584065064527
Wed Nov 28 07:16:43 2007  elapsed time 00:53:58 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.30 hours.
Scaled time: 7.53 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_4_0_170_9
n: 
3023465633285932470354633671573805425830970499670815796194968444093633294
526234496732144750815118717
skew: 13066.21
# norm 1.20e+14
c5: 13380
c4: -91502224
c3: -7858450792205
c2: -14686422473786386
c1: -36147477295763868464
c0: 769155274794014273908275
# alpha -6.05
Y1: 15220904303
Y0: -11770923922825153852
# Murphy_E 3.35e-09
# M 
9956905416872819849530372527310632673808913467304665376913463743595106352
33511921121477064551418045
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved  special-q in [100000, 800000)
Primes: RFBsize:135072, AFBsize:134812, largePrimes:3453555 encountered
Relations: rels:3414232, finalFF:377182
Max relations in full relation-set: 28
Initial matrix: 269962 x 377182 with sparse part having weight 19839270.
Pruned matrix : 171344 x 172757 with weight 6919700.
Total sieving time: 6.15 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,
26,48,48,2.5,2.5,100000
total time: 6.30 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(2·10¹⁶⁷+7)/9 = (2)₁₆₆3_<167> = 17 · 22549 · 56437 · 85331 · C152

C152 = P58 · P94

P58 = 2871978723164024191549374139558544135462013900057318167591_<58>

P94 = 4191401889447764303388864665063780609861896939555630361153238115797687072530286019054001194603_<94>

Number: n
N=12037617046723468605626924896371158078923549938485194482958855970507181664139302569091093571951782614912001181491026391397577812391492441451368958711373
  ( 152 digits)
SNFS difficulty: 167 digits.
Divisors found:

Wed Nov 28 16:26:47 2007  prp58 factor: 2871978723164024191549374139558544135462013900057318167591
Wed Nov 28 16:26:47 2007  prp94 factor: 4191401889447764303388864665063780609861896939555630361153238115797687072530286019054001194603
Wed Nov 28 16:26:47 2007  elapsed time 01:44:43 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 74.04 hours.
Scaled time: 106.55 units (timescale=1.439).
Factorization parameters were as follows:
name: KA_2_166_3
n: 12037617046723468605626924896371158078923549938485194482958855970507181664139302569091093571951782614912001181491026391397577812391492441451368958711373
skew: 0.51
deg: 5
c5: 200
c0: 7
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3700001)
Primes: RFBsize:216816, AFBsize:216921, largePrimes:7734112 encountered
Relations: rels:7208772, finalFF:447988
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 73.76 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 74.04 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Nov 28, 2007

By JMB / GMP-ECM

4·10¹⁶⁵+9 = 4(0)₁₆₄9_<166> = 19 · 1877 · 8893 · 11427643437022285783_<20> · 128867463506675408316022657357_<30> · C109

C109 = P39 · P71

P39 = 467807742471873906594101709631462254293_<39>

P71 = 18307391061578173853638901084078048550027933080852242492899530687116597_<71>

Nov 27, 2007 (4th)

By Robert Backstrom / GGNFS, Msieve

(5·10¹⁶²-23)/9 = (5)₁₆₁3_<162> = 916781 · 51222224362217_<14> · C143

C143 = P53 · P90

P53 = 88251067479212923009474772487688631800999197025093157_<53>

P90 = 134055145824349829678858500491427751894659830463832718793400933405117679808822762144065977_<90>

Number: n
N=11830509720080425325375598472836094119415647645200888882018736825250641
682747740385363305803723965653576539279961713632444852447675173179219389
  ( 143 digits)
SNFS difficulty: 162 digits.
Divisors found:

Wed Nov 28 01:46:13 2007  prp53 factor: 
88251067479212923009474772487688631800999197025093157
Wed Nov 28 01:46:13 2007  prp90 factor: 
1340551458243498296788585004914277518946598304638327187934009334051176798
08822762144065977
Wed Nov 28 01:46:13 2007  elapsed time 01:49:31 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 57.66 hours.
Scaled time: 76.39 units (timescale=1.325).
Factorization parameters were as follows:
name: KA_5_161_3
n: 
1183050972008042532537559847283609411941564764520088888201873682525064168
2747740385363305803723965653576539279961713632444852447675173179219389
skew: 0.54
deg: 5
c5: 500
c0: -23
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2700000)
Primes: RFBsize:216816, AFBsize:216551, largePrimes:7434136 encountered
Relations: rels:6877587, finalFF:488281
Max relations in full relation-set: 28
Initial matrix: 433433 x 488281 with sparse part having weight 51570740.
Pruned matrix : 409705 x 411936 with weight 36845788.
Total sieving time: 57.40 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 57.66 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 27, 2007 (3rd)

By Sinkiti Sibata / GGNFS

4·10¹⁴¹+9 = 4(0)₁₄₀9_<142> = 3264208176022063_<16> · 1989887208412614157281179_<25> · C102

C102 = P38 · P65

P38 = 12560245906602427344287633654384461339_<38>

P65 = 49029282824428429410597115467691293631272803877265436025347251103_<65>

Number: 40009_141
N=615819848899179877938710121407036005167041262827473023425282772740726134822493088078335262461028606917
  ( 102 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=12560245906602427344287633654384461339 (pp38)
 r2=49029282824428429410597115467691293631272803877265436025347251103 (pp65)
Version: GGNFS-0.77.1-20060513-k8
Total time: 8.54 hours.
Scaled time: 17.10 units (timescale=2.003).
Factorization parameters were as follows:
name: 40009_141
n: 615819848899179877938710121407036005167041262827473023425282772740726134822493088078335262461028606917
m: 10000000000000000000000000000
c5: 40
c0: 9
skew: 0.74
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1550001)
Primes: RFBsize:100021, AFBsize:99568, largePrimes:2682501 encountered
Relations: rels:2667799, finalFF:280425
Max relations in full relation-set: 28
Initial matrix: 199656 x 280425 with sparse part having weight 23554506.
Pruned matrix : 173823 x 174885 with weight 12458201.
Total sieving time: 8.15 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.25 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 8.54 hours.
 --------- CPU info (if available) ----------

4·10¹³⁵+9 = 4(0)₁₃₄9_<136> = 4432543729_<10> · 350104414826237_<15> · C112

C112 = P32 · P34 · P47

P32 = 50076108520827966913691944342129_<32>

P34 = 4390119913201648970056724078503841_<34>

P47 = 11724718391352138352586053521568560187634367997_<47>

Number: 40009_135
N=25775635121078719114580793852241494535899517591251721059647750320822687095
16545156309460784839303831716228099533
  ( 112 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=50076108520827966913691944342129 (pp32)
 r2=4390119913201648970056724078503841 (pp34)
 r3=11724718391352138352586053521568560187634367997 (pp47)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.32 hours.
Scaled time: 12.66 units (timescale=2.003).
Factorization parameters were as follows:
name: 40009_135
n:
2577563512107871911458079385224149453589951759125172105964775032082268709516
545156309460784839303831716228099533
m: 1000000000000000000000000000
c5: 4
c0: 9
skew: 1.18
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:64053, largePrimes:1576550 encountered
Relations: rels:1619234, finalFF:212791
Max relations in full relation-set: 28
Initial matrix: 142615 x 212791 with sparse part having weight 15765979.
Pruned matrix : 120857 x 121634 with weight 7446674.
Total sieving time: 6.12 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 6.32 hours.
 --------- CPU info (if available) ----------

Nov 27, 2007 (2nd)

By Sinkiti Sibata / GGNFS

4·10¹⁴⁵+9 = 4(0)₁₄₄9_<146> = 7 · 23 · 16196138573250129419_<20> · 270390616492056889150461299_<27> · C98

C98 = P40 · P59

P40 = 1605173021880918410125104138533069730893_<40>

P59 = 35343468163557001022907513872788192718182385124531802470493_<59>

Number: 40009_145
N=56732381595848825220588411669623668386053143977130622031227669941751645504214351435599936083040249
  ( 98 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=1605173021880918410125104138533069730893 (pp40)
 r2=35343468163557001022907513872788192718182385124531802470493 (pp59)
Version: GGNFS-0.77.1-20060513-k8
Total time: 11.67 hours.
Scaled time: 23.46 units (timescale=2.010).
Factorization parameters were as follows:
name: 40009_145
n: 56732381595848825220588411669623668386053143977130622031227669941751645504214351435599936083040249
m: 100000000000000000000000000000
c5: 4
c0: 9
skew: 1.18
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1950001)
Primes: RFBsize:100021, AFBsize:100078, largePrimes:2670477 encountered
Relations: rels:2616911, finalFF:229148
Max relations in full relation-set: 28
Initial matrix: 200163 x 229148 with sparse part having weight 21999475.
Pruned matrix : 191898 x 192962 with weight 16653697.
Total sieving time: 11.09 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 11.67 hours.
 --------- CPU info (if available) ----------

Nov 27, 2007

By Robert Backstrom / GGNFS, Msieve

4·10¹³⁷+9 = 4(0)₁₃₆9_<138> = 47 · 210996161 · 27663076039007_<14> · C115

C115 = P48 · P68

P48 = 144128879329630272184991648078450696106391196441_<48>

P68 = 10116635425360137333667412655105196323996222926944429943963917753921_<68>

Number: n
N=1458099326443594054045323972411079454526604785894103274387642346249087765340142012336087436548886974989376608995161
  ( 115 digits)
SNFS difficulty: 137 digits.
Divisors found:

Tue Nov 27 03:12:55 2007  prp48 factor: 144128879329630272184991648078450696106391196441
Tue Nov 27 03:12:55 2007  prp68 factor: 10116635425360137333667412655105196323996222926944429943963917753921
Tue Nov 27 03:12:55 2007  elapsed time 00:26:19 (Msieve 1.30)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 6.20 hours.
Scaled time: 8.01 units (timescale=1.293).
Factorization parameters were as follows:
name: KA_4_0_136_9
n: 1458099326443594054045323972411079454526604785894103274387642346249087765340142012336087436548886974989376608995161
skew: 0.94
deg: 5
c5: 25
c0: 18
m: 2000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 800000)
Primes: RFBsize:114155, AFBsize:113992, largePrimes:6288087 encountered
Relations: rels:5665178, finalFF:314490
Max relations in full relation-set: 28
Initial matrix: 228211 x 314490 with sparse part having weight 25079773.
Pruned matrix : 185311 x 186516 with weight 11952601.
Total sieving time: 6.00 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,75000
total time: 6.20 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

4·10¹⁴⁶+9 = 4(0)₁₄₅9_<147> = 220681 · 486209806553_<12> · C130

C130 = P39 · P91

P39 = 764412203911204700836054966106935734613_<39>

P91 = 4876898556751362048961362794806390789746536739262210158192817562689449702712780913893826501_<91>

Number: n
N=3727960774017682077509562283847137837199147716353152979632032702775892834651891935886292568866270350371012428874815801170002379113
  ( 130 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=764412203911204700836054966106935734613 (pp39)
 r2=4876898556751362048961362794806390789746536739262210158192817562689449702712780913893826501 (pp91)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 10.26 hours.
Scaled time: 12.27 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_4_0_145_9
n: 3727960774017682077509562283847137837199147716353152979632032702775892834651891935886292568866270350371012428874815801170002379113
type: snfs
skew: 0.74
deg: 5
c5: 40
c0: 9
m: 100000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1150001)
Primes: RFBsize:148933, AFBsize:148405, largePrimes:5927738 encountered
Relations: rels:5289921, finalFF:359602
Max relations in full relation-set: 28
Initial matrix: 297405 x 359602 with sparse part having weight 20581544.
Pruned matrix : 247886 x 249437 with weight 11630633.
Total sieving time: 8.79 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 1.21 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 10.26 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Nov 26, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(10²¹⁵³+53)/9 is prime.

Nov 26, 2007 (2nd)

By Sinkiti Sibata / GGNFS, Msieve

4·10¹²⁶+9 = 4(0)₁₂₅9_<127> = 13² · 1093 · 157478185310284045321_<21> · C102

C102 = P32 · P70

P32 = 51219530045909995936125110786993_<32>

P70 = 2684708475243401264102954877320619544959453611256556529626076156285909_<70>

Number: 40009_126
N=137509506412238603536864415063538192494400116628332569921903945385237808208535294351993306538906381637
  ( 102 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=51219530045909995936125110786993 (pp32)
 r2=2684708475243401264102954877320619544959453611256556529626076156285909 (pp70)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.80 hours.
Scaled time: 5.61 units (timescale=2.003).
Factorization parameters were as follows:
name: 40009_126
n: 137509506412238603536864415063538192494400116628332569921903945385237808208535294351993306538906381637
m: 10000000000000000000000000
c5: 40
c0: 9
skew: 0.74
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:63733, largePrimes:2383131 encountered
Relations: rels:2755788, finalFF:468753
Max relations in full relation-set: 28
Initial matrix: 112898 x 468753 with sparse part having weight 45593086.
Pruned matrix : 76412 x 77040 with weight 8664530.
Total sieving time: 2.66 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.80 hours.
 --------- CPU info (if available) ----------

4·10¹²⁸+9 = 4(0)₁₂₇9_<129> = 1993 · 51913 · 1430797079340329352472921_<25> · C97

C97 = P48 · P50

P48 = 181803558476376236283955641729897094029004670893_<48>

P50 = 14862646249026576411818998493115073085499220973317_<50>

Number: 40009_128
N=2702081976448597109558698566520468643612755318410534419392185730772033180107476795736942719562081
  ( 97 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=181803558476376236283955641729897094029004670893 (pp48)
 r2=14862646249026576411818998493115073085499220973317 (pp50)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.78 hours.
Scaled time: 7.55 units (timescale=1.997).
Factorization parameters were as follows:
name: 40009_128
n: 2702081976448597109558698566520468643612755318410534419392185730772033180107476795736942719562081
m: 20000000000000000000000000
c5: 125
c0: 9
skew: 0.59
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:63951, AFBsize:64093, largePrimes:1557590 encountered
Relations: rels:1625431, finalFF:234022
Max relations in full relation-set: 28
Initial matrix: 128110 x 234022 with sparse part having weight 14826718.
Pruned matrix : 98552 x 99256 with weight 5347992.
Total sieving time: 3.66 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 3.78 hours.
 --------- CPU info (if available) ----------

4·10¹²⁹+9 = 4(0)₁₂₈9_<130> = 19 · 13921 · 42456366769_<11> · 1961107985919825167_<19> · C96

C96 = P32 · P64

P32 = 90496029963707513725625363116699_<32>

P64 = 2007068038467510110982557191892561779029831762757164209225700983_<64>

Number: 40009_129
N=181631689348355459790962688701929834427428033812142412776081374439007954060590809771261908015117
  ( 96 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=90496029963707513725625363116699 (pp32)
 r2=2007068038467510110982557191892561779029831762757164209225700983 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.35 hours.
Scaled time: 8.78 units (timescale=2.016).
Factorization parameters were as follows:
name: 40009_129
n: 181631689348355459790962688701929834427428033812142412776081374439007954060590809771261908015117
m: 100000000000000000000000000
c5: 2
c0: 45
skew: 1.86
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64093, largePrimes:1536620 encountered
Relations: rels:1564442, finalFF:196332
Max relations in full relation-set: 28
Initial matrix: 128109 x 196332 with sparse part having weight 14524685.
Pruned matrix : 109268 x 109972 with weight 6465733.
Total sieving time: 4.20 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.35 hours.
 --------- CPU info (if available) ----------

4·10¹³³+9 = 4(0)₁₃₂9_<134> = 7 · 14039910954930703_<17> · C117

C117 = P54 · P64

P54 = 212045331507039776360742002829387808898620546351104409_<54>

P64 = 1919414992157459171757261776221197366678153779688615271444343881_<64>

Number: 40009_133
N=407002988311610582561227888701054777787770001367652789611232968795378225157190752222575768698744823864819960731271329
  ( 117 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=212045331507039776360742002829387808898620546351104409 (pp54)
 r2=1919414992157459171757261776221197366678153779688615271444343881 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.87 hours.
Scaled time: 11.73 units (timescale=1.997).
Factorization parameters were as follows:
name: 40009_133
n: 407002988311610582561227888701054777787770001367652789611232968795378225157190752222575768698744823864819960731271329
m: 200000000000000000000000000
c5: 125
c0: 9
skew: 0.59
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:64093, largePrimes:1612445 encountered
Relations: rels:1679680, finalFF:236889
Max relations in full relation-set: 28
Initial matrix: 142657 x 236889 with sparse part having weight 18018688.
Pruned matrix : 114736 x 115513 with weight 7558893.
Total sieving time: 5.69 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.87 hours.
 --------- CPU info (if available) ----------

4·10¹⁴⁷+9 = 4(0)₁₄₆9_<148> = 19 · 4057594903_<10> · 44338326960703_<14> · 256008644002393841860575255628769_<33> · C91

C91 = P39 · P53

P39 = 404664799012214157417672549706061106703_<39>

P53 = 11295575051062064761509401409725052595688718501423797_<53>

Mon Nov 26 07:03:06 2007  Msieve v. 1.28
Mon Nov 26 07:03:06 2007  random seeds: 806018b8 fde7d0ee
Mon Nov 26 07:03:06 2007  factoring 4570921607765411105037991565791212407235592613498883380616910429784125813855670791040411291 (91 digits)
Mon Nov 26 07:03:07 2007  commencing quadratic sieve (91-digit input)
Mon Nov 26 07:03:07 2007  using multiplier of 3
Mon Nov 26 07:03:07 2007  using 64kb Pentium 2 sieve core
Mon Nov 26 07:03:07 2007  sieve interval: 18 blocks of size 65536
Mon Nov 26 07:03:07 2007  processing polynomials in batches of 6
Mon Nov 26 07:03:07 2007  using a sieve bound of 1719869 (64508 primes)
Mon Nov 26 07:03:07 2007  using large prime bound of 165107424 (27 bits)
Mon Nov 26 07:03:07 2007  using double large prime bound of 619412223763104 (42-50 bits)
Mon Nov 26 07:03:07 2007  using trial factoring cutoff of 50 bits
Mon Nov 26 07:03:07 2007  polynomial 'A' values have 12 factors
Mon Nov 26 18:54:49 2007  64777 relations (16555 full + 48222 combined from 769817 partial), need 64604
Mon Nov 26 18:54:55 2007  begin with 786372 relations
Mon Nov 26 18:55:11 2007  reduce to 163091 relations in 10 passes
Mon Nov 26 18:55:11 2007  attempting to read 163091 relations
Mon Nov 26 18:55:23 2007  recovered 163091 relations
Mon Nov 26 18:55:23 2007  recovered 145695 polynomials
Mon Nov 26 18:55:45 2007  attempting to build 64777 cycles
Mon Nov 26 18:55:45 2007  found 64777 cycles in 6 passes
Mon Nov 26 18:55:48 2007  distribution of cycle lengths:
Mon Nov 26 18:55:48 2007     length 1 : 16555
Mon Nov 26 18:55:48 2007     length 2 : 11833
Mon Nov 26 18:55:48 2007     length 3 : 11147
Mon Nov 26 18:55:48 2007     length 4 : 8679
Mon Nov 26 18:55:48 2007     length 5 : 6323
Mon Nov 26 18:55:48 2007     length 6 : 4272
Mon Nov 26 18:55:48 2007     length 7 : 2648
Mon Nov 26 18:55:48 2007     length 9+: 3320
Mon Nov 26 18:55:48 2007  largest cycle: 18 relations
Mon Nov 26 18:55:49 2007  matrix is 64508 x 64777 with weight 4021806 (avg 62.09/col)
Mon Nov 26 18:55:53 2007  filtering completed in 3 passes
Mon Nov 26 18:55:53 2007  matrix is 61073 x 61137 with weight 3812110 (avg 62.35/col)
Mon Nov 26 18:55:56 2007  saving the first 48 matrix rows for later
Mon Nov 26 18:55:56 2007  matrix is 61025 x 61137 with weight 3042466 (avg 49.76/col)
Mon Nov 26 18:55:56 2007  matrix includes 64 packed rows
Mon Nov 26 18:55:56 2007  using block size 10922 for processor cache size 256 kB
Mon Nov 26 18:55:58 2007  commencing Lanczos iteration
Mon Nov 26 18:59:10 2007  lanczos halted after 966 iterations
Mon Nov 26 18:59:11 2007  recovered 16 nontrivial dependencies
Mon Nov 26 18:59:37 2007  prp39 factor: 404664799012214157417672549706061106703
Mon Nov 26 18:59:37 2007  prp53 factor: 11295575051062064761509401409725052595688718501423797
Mon Nov 26 18:59:37 2007  elapsed time 11:56:31

Nov 26, 2007

By Robert Backstrom / GGNFS, Msieve

4·10¹¹⁰+9 = 4(0)₁₀₉9_<111> = 113 · 2393 · 251419167001_<12> · C94

C94 = P36 · P59

P36 = 165181848872234857617062189249532241_<36>

P59 = 35618706443028798016568330143685321380313564206887456692761_<59>

Number: n
N=5883563784696880916434650652243177524072887965464968204171469084560963632896817817164100807401
  ( 94 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=165181848872234857617062189249532241 (pp36)
 r2=35618706443028798016568330143685321380313564206887456692761 (pp59)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.95 hours.
Scaled time: 1.13 units (timescale=1.193).
Factorization parameters were as follows:
name: KA_4_0_109_9
n: 5883563784696880916434650652243177524072887965464968204171469084560963632896817817164100807401
type: snfs
skew: 1.18
deg: 5
c5: 4
c0: 9
m: 10000000000000000000000
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 160001)
Primes: RFBsize:63951, AFBsize:64053, largePrimes:3675896 encountered
Relations: rels:3189891, finalFF:232392
Max relations in full relation-set: 28
Initial matrix: 128068 x 232392 with sparse part having weight 9272010.
Pruned matrix : 64275 x 64979 with weight 2367167.
Total sieving time: 0.80 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.04 hours.
Total square root time: 0.04 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.4,2.4,50000
total time: 0.95 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

4·10¹¹⁹+9 = 4(0)₁₁₈9_<120> = 59011 · C115

C115 = P44 · P72

P44 = 10299709529696676595537272509874674618354731_<44>

P72 = 658115379703367141596436109463234164314654145602057711013672694021719049_<72>

Number: n
N=6778397247970717323888766501160800528714985341715951263323787090542441239768856653844198539255393062310416701970819
  ( 115 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=10299709529696676595537272509874674618354731 (pp44)
 r2=658115379703367141596436109463234164314654145602057711013672694021719049 (pp72)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.09 hours.
Scaled time: 2.49 units (timescale=1.194).
Factorization parameters were as follows:
name: KA_4_0_118_9
n: 6778397247970717323888766501160800528714985341715951263323787090542441239768856653844198539255393062310416701970819
type: snfs
skew: 1.86
deg: 5
c5: 2
c0: 45
m: 1000000000000000000000000
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 240001)
Primes: RFBsize:78498, AFBsize:78531, largePrimes:4067301 encountered
Relations: rels:3437845, finalFF:191917
Max relations in full relation-set: 28
Initial matrix: 157094 x 191917 with sparse part having weight 8634183.
Pruned matrix : 126308 x 127157 with weight 4290229.
Total sieving time: 1.70 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.17 hours.
Total square root time: 0.12 hours, sqrts: 5.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.4,2.4,50000
total time: 2.09 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(52·10¹⁶⁴-7)/9 = 5(7)₁₆₄_<165> = 29 · 7019 · 6320886474787_<13> · C147

C147 = P52 · P96

P52 = 1253831070899856312688601931720582966577047750139261_<52>

P96 = 358154634908081150423440098044503617839531497495445248785010282856127665013429077944232929344361_<96>

Number: n
N=449065409434546449622971187681183740755523201415900451788832840460807324862141335905611317885561982939064087542226259352648468932390312211175057221
  ( 147 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Nov 26 16:37:58 2007  prp52 factor: 1253831070899856312688601931720582966577047750139261
Mon Nov 26 16:37:58 2007  prp96 factor: 358154634908081150423440098044503617839531497495445248785010282856127665013429077944232929344361
Mon Nov 26 16:37:58 2007  elapsed time 02:02:22 (Msieve 1.30)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 108.78 hours.
Scaled time: 140.77 units (timescale=1.294).
Factorization parameters were as follows:
name: KA_5_7_164
n: 449065409434546449622971187681183740755523201415900451788832840460807324862141335905611317885561982939064087542226259352648468932390312211175057221
skew: 1.06
deg: 5
c5: 26
c0: -35
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3600001)
Primes: RFBsize:230209, AFBsize:230477, largePrimes:7720364 encountered
Relations: rels:7181991, finalFF:477241
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 108.43 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,166,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 108.78 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

4·10¹³¹+9 = 4(0)₁₃₀9_<132> = 619 · 194167 · 14543527 · C117

C117 = P44 · P73

P44 = 80094272947449979071432758202536808045156517_<44>

P73 = 2857082077051308573674020837361541499660528541802562865615658481450429087_<73>

Number: n
N=228835911712614820963407007506081825552432657431830205371716856226255647416792245683256227303671261195144781724409979
  ( 117 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=80094272947449979071432758202536808045156517 (pp44)
 r2=2857082077051308573674020837361541499660528541802562865615658481450429087 (pp73)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.68 hours.
Scaled time: 4.40 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_4_0_130_9
n: 228835911712614820963407007506081825552432657431830205371716856226255647416792245683256227303671261195144781724409979
type: snfs
skew: 0.74
deg: 5
c5: 40
c0: 9
m: 100000000000000000000000000
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 460001)
Primes: RFBsize:114155, AFBsize:113572, largePrimes:4179030 encountered
Relations: rels:3531412, finalFF:259869
Max relations in full relation-set: 28
Initial matrix: 227794 x 259869 with sparse part having weight 7780095.
Pruned matrix : 168810 x 170012 with weight 4136104.
Total sieving time: 3.28 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.26 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.2,2.2,50000
total time: 3.68 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

4·10¹¹⁷+9 = 4(0)₁₁₆9_<118> = 163890451 · 119008224119929_<15> · C96

C96 = P34 · P63

P34 = 1049848161996414833607686052033851_<34>

P63 = 195345258444219449654150537877637812726731604913236518703820721_<63>

Number: n
N=205082860532378423488589379837991228596967004928112301824211634341274075328421533654926527226571
  ( 96 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=1049848161996414833607686052033851 (pp34)
 r2=195345258444219449654150537877637812726731604913236518703820721 (pp63)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.75 hours.
Scaled time: 2.09 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_4_0_116_9
n: 205082860532378423488589379837991228596967004928112301824211634341274075328421533654926527226571
type: snfs
skew: 0.94
deg: 5
c5: 25
c0: 18
m: 200000000000000000000000
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 220001)
Primes: RFBsize:78498, AFBsize:78241, largePrimes:3946046 encountered
Relations: rels:3317892, finalFF:182434
Max relations in full relation-set: 28
Initial matrix: 156803 x 182434 with sparse part having weight 7590913.
Pruned matrix : 131548 x 132396 with weight 4205854.
Total sieving time: 1.36 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.18 hours.
Total square root time: 0.11 hours, sqrts: 5.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.4,2.4,50000
total time: 1.75 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Nov 25, 2007 (5th)

By Jo Yeong Uk / GGNFS

4·10¹¹⁸+9 = 4(0)₁₁₇9_<119> = C119

C119 = P52 · P68

P52 = 3728574790867178284745181738866780429302431068160529_<52>

P68 = 10727959674558907354142285722781332734722136495462711094331511744121_<68>

Number: 40009_118
N=40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 119 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=3728574790867178284745181738866780429302431068160529 (pp52)
 r2=10727959674558907354142285722781332734722136495462711094331511744121 (pp68)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.90 hours.
Scaled time: 1.93 units (timescale=2.144).
Factorization parameters were as follows:
n: 40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
m: 1000000000000000000000000
c5: 1
c0: 225
skew: 2.95
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 450001)
Primes: RFBsize:49098, AFBsize:49111, largePrimes:1886445 encountered
Relations: rels:1942478, finalFF:199895
Max relations in full relation-set: 28
Initial matrix: 98273 x 199895 with sparse part having weight 17093793.
Pruned matrix : 77103 x 77658 with weight 4340439.
Total sieving time: 0.85 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.90 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Nov 25, 2007 (4th)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(4·10¹⁶⁴-7)/3 = 1(3)₁₆₃1_<165> = 983 · 6424123 · 8002014907_<10> · C145

C145 = P41 · P44 · P61

P41 = 38845079894049413226636666173926767146741_<41>

P44 = 37241278615967782300259863150917251444291063_<44>

P61 = 1823943632731313508599180109626448102079347834135801509470639_<61>

Number: n
N=67925993006367260173084306432034998810393910129667030593595794518859702769290352728359242093103768599257
  ( 104 digits)
Divisors found:

Mon Nov 26 00:08:03 2007  prp44 factor: 37241278615967782300259863150917251444291063
Mon Nov 26 00:08:03 2007  prp61 factor: 1823943632731313508599180109626448102079347834135801509470639
Mon Nov 26 00:08:03 2007  elapsed time 01:07:26 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 18.97 hours.
Scaled time: 22.69 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_1_3_163_1
n: 67925993006367260173084306432034998810393910129667030593595794518859702769290352728359242093103768599257
skew: 14548.83
# norm 4.31e+14
c5: 15540
c4: 662881441
c3: -30284510564936
c2: -70420841882984262
c1: 1380105811745476751310
c0: 213375504826872901606500
# alpha -5.63
Y1: 56183257309
Y0: -84745088989414396159
# Murphy_E 1.94e-09
# M 35605800172212779601640616997983630603863264454095218451097658761114576612953147801228187028086397273557
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved  special-q in [100000, 1200000)
Primes: RFBsize:169511, AFBsize:169993, largePrimes:4092500 encountered
Relations: rels:4001895, finalFF:381407
Max relations in full relation-set: 28
Initial matrix: 339591 x 381407 with sparse part having weight 23210863.
Pruned matrix : 297455 x 299216 with weight 14265146.
Total sieving time: 18.76 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 18.97 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Nov 25, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(22·10²¹⁵⁹-31)/9 is prime.

Nov 25, 2007 (2nd)

By matsui / GMP-ECM

(5·10¹⁸⁷-23)/9 = (5)₁₈₆3_<187> = 3 · C187

C187 = P34 · C154

P34 = 1249569676018218532056891295863517_<34>

C154 = [1481991670726852801036337564124989580909663768841067210637083024250974479404992726846367777814579781927851301822010278319654383652691909116064846052888903_<154>]

Nov 25, 2007

The factor table of 400...009 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Nov 24, 2007 (4th)

By matsui / GMP-ECM

(2·10¹⁸⁹+61)/9 = (2)₁₈₈9_<189> = 31 · 107 · C185

C185 = P36 · C149

P36 = 927349548463379812942637190276565777_<36>

C149 = [72243462018069324109887983093635000589160560432323063168326829250562665832911989665414796383191130798805708121654081515508917870686847094978760612881_<149>]

Nov 24, 2007 (3rd)

By Sinkiti Sibata / GGNFS

4·10¹⁵⁹-9 = 3(9)₁₅₈1_<160> = 13 · 199 · 2130173 · 64929089 · 24131072597_<11> · 952589489681209_<15> · C117

C117 = P44 · P73

P44 = 74079493501806378527450601403663790436099271_<44>

P73 = 6564912794659200412500871081575072082513907943647734630671406825808638043_<73>

Number: 39991_159
N=486325414711881789179913696860213450928824568538724820830782157801328627106326427776063177946853247455134006055166653
  ( 117 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=74079493501806378527450601403663790436099271 (pp44)
 r2=6564912794659200412500871081575072082513907943647734630671406825808638043 (pp73)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 77.01 hours.
Scaled time: 51.98 units (timescale=0.675).
Factorization parameters were as follows:
name: 39991_159
n: 486325414711881789179913696860213450928824568538724820830782157801328627106326427776063177946853247455134006055166653
m: 100000000000000000000000000000000
c5: 2
c0: -45
skew: 1.86
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3900001)
Primes: RFBsize:283146, AFBsize:283407, largePrimes:5742291 encountered
Relations: rels:5806571, finalFF:681486
Max relations in full relation-set: 28
Initial matrix: 566618 x 681486 with sparse part having weight 45436461.
Pruned matrix : 483086 x 485983 with weight 31035378.
Total sieving time: 66.61 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 9.87 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 77.01 hours.
 --------- CPU info (if available) ----------

Nov 24, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

(32·10¹⁶²-23)/9 = 3(5)₁₆₁3_<163> = 79 · 353 · 10831 · 2304545063_<10> · C145

C145 = P59 · P87

P59 = 11418294572176870102030727526262175468766886077048774464453_<59>

P87 = 447353324129822631187220179321823753744991839539223628912706731724334093004388243879691_<87>

Number: n
N=5108012032756833801090420940354909442473568947558897114792618109230650012286452899825548147198860702329357055515312908368542021336328083488124023
  ( 145 digits)
SNFS difficulty: 163 digits.
Divisors found:

Sat Nov 24 02:02:22 2007  prp59 factor: 11418294572176870102030727526262175468766886077048774464453
Sat Nov 24 02:02:22 2007  prp87 factor: 447353324129822631187220179321823753744991839539223628912706731724334093004388243879691
Sat Nov 24 02:02:22 2007  elapsed time 01:45:11 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 44.69 hours.
Scaled time: 59.13 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_3_5_161_3
n: 5108012032756833801090420940354909442473568947558897114792618109230650012286452899825548147198860702329357055515312908368542021336328083488124023
skew: 0.75
deg: 5
c5: 100
c0: -23
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100000)
Primes: RFBsize:216816, AFBsize:217116, largePrimes:7231197 encountered
Relations: rels:6696431, finalFF:498681
Max relations in full relation-set: 28
Initial matrix: 433996 x 498681 with sparse part having weight 44598884.
Pruned matrix : 388932 x 391165 with weight 29632951.
Total sieving time: 44.45 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 44.69 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 24, 2007

By Yousuke Koide

10¹⁷⁴⁹+1 is divisible by 1107787169378395599401257233239538397_<37>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 22, 2007 (3rd)

By Robert Backstrom / GGNFS

(5·10¹⁶¹-41)/9 = (5)₁₆₀1_<161> = 3² · 68196269 · 15233617008611_<14> · C139

C139 = P50 · P90

P50 = 16440538531421432078827696011643851667074412930711_<50>

P90 = 361414271751827151353177663968973256352972286750998069364546030733668065300904591141591911_<90>

Number: n
N=5941845260541530719336256541742219880917628765154081949520232045063493647492461579811333302877434609513809414777144042637306700263481078721
  ( 139 digits)
SNFS difficulty: 161 digits.
Divisors found:

Thu Nov 22 18:28:14 2007  prp50 factor: 16440538531421432078827696011643851667074412930711
Thu Nov 22 18:28:14 2007  prp90 factor: 361414271751827151353177663968973256352972286750998069364546030733668065300904591141591911
Thu Nov 22 18:28:14 2007  elapsed time 02:27:05 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 48.96 hours.
Scaled time: 58.56 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_5_160_1
n: 5941845260541530719336256541742219880917628765154081949520232045063493647492461579811333302877434609513809414777144042637306700263481078721
type: snfs
skew: 0.96
deg: 5
c5: 50
c0: -41
m: 100000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100000)
Primes: RFBsize:250150, AFBsize:250567, largePrimes:7178290 encountered
Relations: rels:6709445, finalFF:607497
Max relations in full relation-set: 28
Initial matrix: 500782 x 607497 with sparse part having weight 34954359.
Pruned matrix : 408203 x 410770 with weight 20239156.
Total sieving time: 48.70 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.3,2.3,100000
total time: 48.96 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Nov 22, 2007 (2nd)

By Jo Yeong Uk / GGNFS

8·10¹⁸¹-7 = 7(9)₁₈₀3_<182> = C182

C182 = P48 · P135

P48 = 216148982655435929699114314027715477553384103519_<48>

P135 = 370115089218478356758654535607364677329573694364240237802979699121028544430300307143621280593966654455367748978194923424449434078433447_<135>

Number: 79993_181
N=79999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 182 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=216148982655435929699114314027715477553384103519 (pp48)
 r2=370115089218478356758654535607364677329573694364240237802979699121028544430300307143621280593966654455367748978194923424449434078433447 (pp135)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 248.23 hours.
Scaled time: 529.98 units (timescale=2.135).
Factorization parameters were as follows:
n: 79999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
m: 2000000000000000000000000000000000000
c5: 5
c0: -14
skew: 1.23
type: snfs
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [5000000, 9100001)
Primes: RFBsize:664579, AFBsize:665480, largePrimes:11067378 encountered
Relations: rels:11387297, finalFF:1536217
Max relations in full relation-set: 28
Initial matrix: 1330124 x 1536217 with sparse part having weight 93212688.
Pruned matrix : 1143509 x 1150223 with weight 64319333.
Total sieving time: 238.30 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 9.59 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000
total time: 248.23 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 22, 2007

By Yousuke Koide

10¹⁰⁷⁹+1 is divisible by 12872791513686398145408033283561_<32>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 21, 2007 (2nd)

By Robert Backstrom / GGNFS

2·10¹⁶²+9 = 2(0)₁₆₁9_<163> = 11 · 113 · 2081 · 2657 · C153

C153 = P47 · P107

P47 = 27122851242050836906551105038309233622985323233_<47>

P107 = 10729015936115722072912979992395528159519097329221924474233456905349010539193520511048503243582233656097483_<107>

Number: n
N=291001503208859535061564265651302436861094295924708253361979542649323701281159624158760359646784825637743314939558512723565886104522114020560808112722539
  ( 153 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=27122851242050836906551105038309233622985323233 (pp47)
 r2=10729015936115722072912979992395528159519097329221924474233456905349010539193520511048503243582233656097483 (pp107)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 36.87 hours.
Scaled time: 48.12 units (timescale=1.305).
Factorization parameters were as follows:
name: KA_2_0_161_9
n: 291001503208859535061564265651302436861094295924708253361979542649323701281159624158760359646784825637743314939558512723565886104522114020560808112722539
skew: 1.08
deg: 5
c5: 25
c0: 36
m: 200000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1550001)
Primes: RFBsize:230209, AFBsize:230472, largePrimes:7089581 encountered
Relations: rels:6599696, finalFF:530658
Max relations in full relation-set: 28
Initial matrix: 460745 x 530658 with sparse part having weight 35163360.
Pruned matrix : 401897 x 404264 with weight 22662170.
Total sieving time: 33.35 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 3.15 hours.
Total square root time: 0.12 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 36.87 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 21, 2007

By Sinkiti Sibata / GGNFS

4·10¹⁵¹-9 = 3(9)₁₅₀1_<152> = 31 · 5519 · 371213 · 1158569 · 54827975693_<11> · 85431185431_<11> · C114

C114 = P48 · P66

P48 = 683451293547552766493247508223331705485919834283_<48>

P66 = 169811308556460662649467994337463527761352643619555931552038754243_<66>

Number: 39991_151
N=116057758491915655173344214309582763419377248961382375191490426117901521122776418083702863212981536767552323112769
  ( 114 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=683451293547552766493247508223331705485919834283 (pp48)
 r2=169811308556460662649467994337463527761352643619555931552038754243 (pp66)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 27.46 hours.
Scaled time: 18.54 units (timescale=0.675).
Factorization parameters were as follows:
name: 39991_151
n: 116057758491915655173344214309582763419377248961382375191490426117901521122776418083702863212981536767552323112769
m: 1000000000000000000000000000000
c5: 40
c0: -9
skew: 0.74
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:175758, largePrimes:5240539 encountered
Relations: rels:5083135, finalFF:433587
Max relations in full relation-set: 28
Initial matrix: 352127 x 433587 with sparse part having weight 34832429.
Pruned matrix : 302527 x 304351 with weight 21729699.
Total sieving time: 23.97 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.16 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 27.46 hours.
 --------- CPU info (if available) ----------

4·10¹⁸⁵+3 = 4(0)₁₈₄3_<186> = 59 · C184

C184 = P68 · P117

P68 = 11020580464970018963281153740355391062570795450373519356122648057289_<68>

P117 = 615181844413636911986288389296689173200938369983514842349545281535581167010170014581500501046126500380108078763742353_<117>

Number: 40003_185
N=6779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661017
  ( 184 digits)
SNFS difficulty: 185 digits.
Divisors found:
 r1=11020580464970018963281153740355391062570795450373519356122648057289 (pp68)
 r2=615181844413636911986288389296689173200938369983514842349545281535581167010170014581500501046126500380108078763742353 (pp117)
Version: GGNFS-0.77.1-20060513-k8
Total time: 676.35 hours.
Scaled time: 1350.68 units (timescale=1.997).
Factorization parameters were as follows:
name: 40003_185
n: 6779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661017
m: 10000000000000000000000000000000000000
c5: 4
c0: 3
skew: 0.94
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 11400001)
Primes: RFBsize:501962, AFBsize:502056, largePrimes:6651477 encountered
Relations: rels:7134496, finalFF:1151991
Max relations in full relation-set: 28
Initial matrix: 1004085 x 1151991 with sparse part having weight 85952580.
Pruned matrix : 882609 x 887693 with weight 67545486.
Total sieving time: 663.68 hours.
Total relation processing time: 0.62 hours.
Matrix solve time: 11.72 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,185,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 676.35 hours.
 --------- CPU info (if available) ----------

Nov 20, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

4·10¹⁶¹-9 = 3(9)₁₆₀1_<162> = 53 · C160

C160 = P41 · P120

P41 = 21806825430466113390135407080568754712841_<41>

P120 = 346092091000860392504443010316442896408178789678554842890548184933093473061870388053493738110298874615414662714544919267_<120>

Number: n
N=7547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547
  ( 160 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Nov 20 21:05:11 2007  prp41 factor: 21806825430466113390135407080568754712841
Tue Nov 20 21:05:11 2007  prp120 factor: 346092091000860392504443010316442896408178789678554842890548184933093473061870388053493738110298874615414662714544919267
Tue Nov 20 21:05:11 2007  elapsed time 01:33:02 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 32.27 hours.
Scaled time: 42.73 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_3_9_160_1
n: 7547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547
skew: 0.74
deg: 5
c5: 40
c0: -9
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1600000)
Primes: RFBsize:216816, AFBsize:216336, largePrimes:7059026 encountered
Relations: rels:6542964, finalFF:512046
Max relations in full relation-set: 28
Initial matrix: 433219 x 512046 with sparse part having weight 41365043.
Pruned matrix : 370773 x 373003 with weight 24932021.
Total sieving time: 32.05 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 32.27 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 20, 2007 (2nd)

By matsui / GMP-ECM

(2·10¹⁸⁶-17)/3 = (6)₁₈₅1_<186> = 577 · C184

C184 = P35 · C149

P35 = 56045655546039900196398563598407527_<35>

C149 = [20615362435591879186624607699826768353984778680961983009624827499187120028491903918962048793936194257434728540858949740169821440639266289814167775059_<149>]

Nov 20, 2007

By JMB / GMP-ECM

9·10²⁰⁰+7 = 9(0)₁₉₉7_<201> = 16363 · 1185871 · 11041256557141927631_<20> · C172

C172 = P40 · P133

P40 = 1129520353150946514870638937980393951891_<40>

P133 = 3719029026601584878459985815308542356310526920113885973087730339593263375620616238307141131837874615521876099561714963205165591240279_<133>

Nov 19, 2007 (2nd)

By Robert Backstrom / GGNFS, GMP-ECM, Msieve

4·10¹⁴⁷-9 = 3(9)₁₄₆1_<148> = 13 · 89 · 6167403400563579766175239_<25> · C120

C120 = P43 · P77

P43 = 9859117276170965916528849893551257536137453_<43>

P77 = 56857301497661450675385390309929156870609092238968154609890852061865551467889_<77>

Number: n
N=560562803472055342614818809179881640621418269258805647401713026165934061851143305328751575837660941339806278907419746717
  ( 120 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=9859117276170965916528849893551257536137453 (pp43)
 r2=56857301497661450675385390309929156870609092238968154609890852061865551467889 (pp77)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 16.03 hours.
Scaled time: 19.11 units (timescale=1.192).
Factorization parameters were as follows:
name: KA_3_9_146_1
n: 560562803472055342614818809179881640621418269258805647401713026165934061851143305328751575837660941339806278907419746717
type: snfs
skew: 0.94
deg: 5
c5: 25
c0: -18
m: 200000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1800001)
Primes: RFBsize:148933, AFBsize:148625, largePrimes:6504113 encountered
Relations: rels:5821520, finalFF:335213
Max relations in full relation-set: 28
Initial matrix: 297622 x 335213 with sparse part having weight 24954157.
Pruned matrix : 280576 x 282128 with weight 18024050.
Total sieving time: 13.38 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 2.30 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 16.03 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

2·10¹⁵⁸+9 = 2(0)₁₅₇9_<159> = 11 · 41 · 97 · 4773739 · 7061641 · C141

C141 = P34 · P107

P34 = 3675342336556885802003207981173427_<34>

P107 = 36899426515186775228625677333483856599631170454625200580800988523050776047130897857948345990003506238466139_<107>

(14·10¹⁶⁶-41)/9 = 1(5)₁₆₅1_<167> = 17 · 2011 · C162

C162 = P32 · P40 · P45 · P47

P32 = 35081134283933574559653611257097_<32>

P40 = 2728630078335383137189177941861782066861_<40>

P45 = 126411714129835466690844912764467931579339687_<45>

P47 = 37602690897693034145575177417896418231525935887_<47>

Number: n
N=12970326457624057370940093292765884024967210652070161540053382611780691229396033766335056809054710948583510049684525069811157738709
  ( 131 digits)
SNFS difficulty: 167 digits.
Divisors found:

Mon Nov 19 08:29:02 2007  prp40 factor: 2728630078335383137189177941861782066861
Mon Nov 19 08:29:02 2007  prp45 factor: 126411714129835466690844912764467931579339687
Mon Nov 19 08:29:02 2007  prp47 factor: 37602690897693034145575177417896418231525935887
Mon Nov 19 08:29:02 2007  elapsed time 03:38:46 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 212.15 hours.
Scaled time: 254.37 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_1_5_165_1

n: 12970326457624057370940093292765884024967210652070161540053382611780691229396033766335056809054710948583510049684525069811157738709

# n: 455013764166366032572485317680859846010341812839838405111754630577574971642892197488974041464754308817841739712626306945785109999577487218988374398325549347867773

type: snfs
skew: 0.78
deg: 5
c5: 140
c0: -41
m: 1000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3400001)
Primes: RFBsize:250150, AFBsize:250097, largePrimes:7703762 encountered
Relations: rels:7182168, finalFF:528137
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 211.32 hours.
Total relation processing time: 0.83 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.6,2.6,100000
total time: 212.15 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Nov 19, 2007

By Jo Yeong Uk / GGNFS

2·10¹⁵³+9 = 2(0)₁₅₂9_<154> = 7 · 23 · 41 · 83 · 3482753797249_<13> · 36236576853259787647_<20> · C116

C116 = P52 · P64

P52 = 2959271181514799226974060568985564239580538542286449_<52>

P64 = 9774340558371489481440431760860958181256487808303078991400909109_<64>

Number: 20009_153
N=28924924332700020078102154409371603648546043054508471127824139389385626667861861974281623089899076036621178091363941
  ( 116 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=2959271181514799226974060568985564239580538542286449 (pp52)
 r2=9774340558371489481440431760860958181256487808303078991400909109 (pp64)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 13.75 hours.
Scaled time: 29.35 units (timescale=2.134).
Factorization parameters were as follows:
n: 28924924332700020078102154409371603648546043054508471127824139389385626667861861974281623089899076036621178091363941
m: 10000000000000000000000000000000
c5: 1
c0: 450
skew: 3.39
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2300001)
Primes: RFBsize:216816, AFBsize:216826, largePrimes:5458908 encountered
Relations: rels:5374729, finalFF:530472
Max relations in full relation-set: 28
Initial matrix: 433706 x 530472 with sparse part having weight 36351069.
Pruned matrix : 358650 x 360882 with weight 22220315.
Total sieving time: 13.03 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.61 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 13.75 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 18, 2007 (5th)

By Robert Backstrom / GGNFS, Msieve

2·10¹⁶¹+9 = 2(0)₁₆₀9_<162> = 89 · C160

C160 = P74 · P86

P74 = 34658477847360659014058595102069167012530568460007500101714626375633760287_<74>

P86 = 64838133432541527475079803698431770081537553848180889286332859833318730119895305215663_<86>

Number: n
N=2247191011235955056179775280898876404494382022471910112359550561797752808988764044943820224719101123595505617977528089887640449438202247191011235955056179775281
  ( 160 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=34658477847360659014058595102069167012530568460007500101714626375633760287 (pp74)
 r2=64838133432541527475079803698431770081537553848180889286332859833318730119895305215663 (pp86)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 44.07 hours.
Scaled time: 58.35 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_2_0_160_9
n: 2247191011235955056179775280898876404494382022471910112359550561797752808988764044943820224719101123595505617977528089887640449438202247191011235955056179775281
skew: 0.85
deg: 5
c5: 20
c0: 9
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:216816, AFBsize:216651, largePrimes:7001649 encountered
Relations: rels:6463003, finalFF:491333
Max relations in full relation-set: 48
Initial matrix: 433534 x 491333 with sparse part having weight 39251584.
Pruned matrix : 388274 x 390505 with weight 25421104.
Total sieving time: 39.34 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 4.37 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 44.07 hours.
 --------- CPU info (if available) ----------

2·10¹⁵⁴+9 = 2(0)₁₅₃9_<155> = 11 · 139 · 123307 · C147

C147 = P57 · P90

P57 = 830079215274331883817516423026643554541585944243418276953_<57>

P90 = 127795405115706014236248092068937621366157768320616692605819506501989361071666161673603051_<90>

Number: n
N=106080309594110586696617947039119018304385493129409072262824490186120714311071268289763648455730854269029413911116146625540532880538725457703783603
  ( 147 digits)
SNFS difficulty: 155 digits.
Divisors found:

Sun Nov 18 21:03:15 2007  prp57 factor: 830079215274331883817516423026643554541585944243418276953
Sun Nov 18 21:03:15 2007  prp90 factor: 127795405115706014236248092068937621366157768320616692605819506501989361071666161673603051
Sun Nov 18 21:03:15 2007  elapsed time 00:52:25 (Msieve 1.29)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 17.88 hours.
Scaled time: 23.42 units (timescale=1.310).
Factorization parameters were as follows:
name: KA_2_0_153_9
n: 106080309594110586696617947039119018304385493129409072262824490186120714311071268289763648455730854269029413911116146625540532880538725457703783603
skew: 2.14
deg: 5
c5: 1
c0: 45
m: 10000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 750000)
Primes: RFBsize:203362, AFBsize:203572, largePrimes:6377392 encountered
Relations: rels:5863802, finalFF:471912
Max relations in full relation-set: 28
Initial matrix: 406998 x 471912 with sparse part having weight 26578410.
Pruned matrix : 347290 x 349388 with weight 15627841.
Total sieving time: 17.71 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 17.88 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 18, 2007 (4th)

By Jo Yeong Uk / GGNFS

4·10¹⁴¹-9 = 3(9)₁₄₀1_<142> = 13 · 191 · 20359 · 195319 · 12420177806754397_<17> · C113

C113 = P36 · P78

P36 = 163736308730108767707475962968700893_<36>

P78 = 199209262950089812594969876563503547961581096151892699792833892052250192212997_<78>

Number: 39991_141
N=32617789380293323671116887710598264533701832802595148777896193264079821368295646222589206276954325334265840106321
  ( 113 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=163736308730108767707475962968700893 (pp36)
 r2=199209262950089812594969876563503547961581096151892699792833892052250192212997 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.44 hours.
Scaled time: 11.55 units (timescale=2.123).
Factorization parameters were as follows:
n: 32617789380293323671116887710598264533701832802595148777896193264079821368295646222589206276954325334265840106321
m: 20000000000000000000000000000
c5: 5
c0: -36
skew: 1.48
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1100001)
Primes: RFBsize:114155, AFBsize:113572, largePrimes:3187730 encountered
Relations: rels:3200509, finalFF:325241
Max relations in full relation-set: 28
Initial matrix: 227794 x 325241 with sparse part having weight 26244758.
Pruned matrix : 187279 x 188481 with weight 12048136.
Total sieving time: 5.27 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 5.44 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 18, 2007 (3rd)

By Sinkiti Sibata / GGNFS, Msieve

2·10¹⁴⁸+9 = 2(0)₁₄₇9_<149> = 11 · 17 · 41 · 89819 · C140

C140 = P33 · P45 · P63

P33 = 609146353706828448793174289718131_<33>

P45 = 150327116082360350342458857196514705709372161_<45>

P63 = 317159220689745360562169219217954642762236170568071499368229363_<63>

Number: 20009_148
N=29042655068025427477641936744710994528214215510409132260749261322213369262621494629040875043696308199191832070407911191359581261140499285033
  ( 140 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=609146353706828448793174289718131 (pp33)
 r2=150327116082360350342458857196514705709372161 (pp45)
 r3=317159220689745360562169219217954642762236170568071499368229363 (pp63)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 20.82 hours.
Scaled time: 14.06 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_148
n: 29042655068025427477641936744710994528214215510409132260749261322213369262621494629040875043696308199191832070407911191359581261140499285033
m: 200000000000000000000000000000
c5: 125
c0: 18
skew: 0.68
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2650001)
Primes: RFBsize:114155, AFBsize:113727, largePrimes:2759008 encountered
Relations: rels:2717014, finalFF:256815
Max relations in full relation-set: 28
Initial matrix: 227948 x 256815 with sparse part having weight 24576686.
Pruned matrix : 218819 x 220022 with weight 19196213.
Total sieving time: 19.03 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.53 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 20.82 hours.
 --------- CPU info (if available) ----------

4·10¹¹⁷-9 = 3(9)₁₁₆1_<118> = 13 · 9973 · 214363 · 581922332049027043_<18> · C90

C90 = P42 · P48

P42 = 531991308851942132115845825480210110671439_<42>

P48 = 464912723832181683082293085018597257414298049209_<48>

Sat Nov 17 15:56:48 2007  Msieve v. 1.28
Sat Nov 17 15:56:48 2007  random seeds: 515dd9e0 50f90094
Sat Nov 17 15:56:48 2007  factoring 247329528453403843265964841503467900787215031507298040842564825634927508129438170852841751 (90 digits)
Sat Nov 17 15:56:49 2007  commencing quadratic sieve (89-digit input)
Sat Nov 17 15:56:49 2007  using multiplier of 1
Sat Nov 17 15:56:49 2007  using 64kb Pentium 2 sieve core
Sat Nov 17 15:56:49 2007  sieve interval: 18 blocks of size 65536
Sat Nov 17 15:56:49 2007  processing polynomials in batches of 6
Sat Nov 17 15:56:49 2007  using a sieve bound of 1575281 (59464 primes)
Sat Nov 17 15:56:49 2007  using large prime bound of 126022480 (26 bits)
Sat Nov 17 15:56:49 2007  using double large prime bound of 380896014563600 (42-49 bits)
Sat Nov 17 15:56:49 2007  using trial factoring cutoff of 49 bits
Sat Nov 17 15:56:49 2007  polynomial 'A' values have 11 factors
Sat Nov 17 23:25:48 2007  59782 relations (15877 full + 43905 combined from 635165 partial), need 59560
Sat Nov 17 23:25:52 2007  begin with 651042 relations
Sat Nov 17 23:25:54 2007  reduce to 146575 relations in 9 passes
Sat Nov 17 23:25:54 2007  attempting to read 146575 relations
Sat Nov 17 23:26:02 2007  recovered 146575 relations
Sat Nov 17 23:26:02 2007  recovered 123038 polynomials
Sat Nov 17 23:26:14 2007  attempting to build 59782 cycles
Sat Nov 17 23:26:14 2007  found 59782 cycles in 5 passes
Sat Nov 17 23:26:16 2007  distribution of cycle lengths:
Sat Nov 17 23:26:16 2007     length 1 : 15877
Sat Nov 17 23:26:16 2007     length 2 : 11295
Sat Nov 17 23:26:17 2007     length 3 : 10499
Sat Nov 17 23:26:17 2007     length 4 : 7977
Sat Nov 17 23:26:17 2007     length 5 : 5541
Sat Nov 17 23:26:17 2007     length 6 : 3771
Sat Nov 17 23:26:17 2007     length 7 : 2219
Sat Nov 17 23:26:17 2007     length 9+: 2603
Sat Nov 17 23:26:17 2007  largest cycle: 19 relations
Sat Nov 17 23:26:18 2007  matrix is 59464 x 59782 with weight 3654625 (avg 61.13/col)
Sat Nov 17 23:26:21 2007  filtering completed in 3 passes
Sat Nov 17 23:26:21 2007  matrix is 55555 x 55619 with weight 3417406 (avg 61.44/col)
Sat Nov 17 23:26:23 2007  saving the first 48 matrix rows for later
Sat Nov 17 23:26:23 2007  matrix is 55507 x 55619 with weight 2798607 (avg 50.32/col)
Sat Nov 17 23:26:23 2007  matrix includes 64 packed rows
Sat Nov 17 23:26:23 2007  using block size 10922 for processor cache size 256 kB
Sat Nov 17 23:26:26 2007  commencing Lanczos iteration
Sat Nov 17 23:29:02 2007  lanczos halted after 879 iterations
Sat Nov 17 23:29:03 2007  recovered 17 nontrivial dependencies
Sat Nov 17 23:29:33 2007  prp42 factor: 531991308851942132115845825480210110671439
Sat Nov 17 23:29:33 2007  prp48 factor: 464912723832181683082293085018597257414298049209
Sat Nov 17 23:29:33 2007  elapsed time 07:32:45

4·10¹⁰⁵-9 = 3(9)₁₀₄1_<106> = 13 · 4049 · 230177683 · C93

C93 = P34 · P59

P34 = 5089468623085822110371775885182959_<34>

P59 = 64868403116863325702101470038639463824085108816719708634719_<59>

Number: 39991_105
N=330145702292958441592211172106378607837842790909434221456259170903001863735703019123414553521
  ( 93 digits)
SNFS difficulty: 105 digits.
Divisors found:
 r1=5089468623085822110371775885182959 (pp34)
 r2=64868403116863325702101470038639463824085108816719708634719 (pp59)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.24 hours.
Scaled time: 0.84 units (timescale=0.675).
Factorization parameters were as follows:
name: 39991_105
n: 330145702292958441592211172106378607837842790909434221456259170903001863735703019123414553521
m: 1000000000000000000000
c5: 4
c0: -9
skew: 1.18
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 450001)
Primes: RFBsize:49098, AFBsize:64053, largePrimes:2165320 encountered
Relations: rels:2447143, finalFF:427386
Max relations in full relation-set: 28
Initial matrix: 113215 x 427386 with sparse part having weight 29087007.
Pruned matrix : 55181 x 55811 with weight 3194505.
Total sieving time: 1.11 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,105,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.24 hours.
 --------- CPU info (if available) ----------

4·10¹²³-9 = 3(9)₁₂₂1_<124> = 13 · 15601 · 14877774143167099699747_<23> · C97

C97 = P48 · P49

P48 = 470762130228440485791543763322013994572073144603_<48>

P49 = 2815948587112211304623095233966680241651606098227_<49>

Number: 39991_123
N=1325641955482711805978372001349693249395454462809784497501309555808926827572054827616211192918881
  ( 97 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=470762130228440485791543763322013994572073144603 (pp48)
 r2=2815948587112211304623095233966680241651606098227 (pp49)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.60 hours.
Scaled time: 1.75 units (timescale=0.675).
Factorization parameters were as follows:
name: 39991_123
n: 1325641955482711805978372001349693249395454462809784497501309555808926827572054827616211192918881
m: 2000000000000000000000000
c5: 125
c0: -9
skew: 0.59
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:64093, largePrimes:2072753 encountered
Relations: rels:2079058, finalFF:159271
Max relations in full relation-set: 28
Initial matrix: 113257 x 159271 with sparse part having weight 13679756.
Pruned matrix : 100109 x 100739 with weight 6360731.
Total sieving time: 2.31 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.60 hours.
 --------- CPU info (if available) ----------

Nov 18, 2007 (2nd)

By Yousuke Koide

(10¹⁶⁸³-1)/9 is divisible by 2597072697640403933361917807092159369_<37>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 18, 2007

By Robert Backstrom / GGNFS

4·10¹⁰⁹-9 = 3(9)₁₀₈1_<110> = 53 · C108

C108 = P49 · P59

P49 = 7969641884935205730310904257533114365615152149547_<49>

P59 = 94698982969196667127271104615127284069462500623071914214001_<59>

Number: n
N=754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547
  ( 108 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=7969641884935205730310904257533114365615152149547 (pp49)
 r2=94698982969196667127271104615127284069462500623071914214001 (pp59)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.96 hours.
Scaled time: 1.15 units (timescale=1.192).
Factorization parameters were as follows:
name: KA_3_9_108_1
n: 754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547
type: snfs
skew: 1.86
deg: 5
c5: 2
c0: -45
m: 10000000000000000000000
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 160001)
Primes: RFBsize:63951, AFBsize:64093, largePrimes:3342545 encountered
Relations: rels:2790483, finalFF:160806
Max relations in full relation-set: 28
Initial matrix: 128109 x 160806 with sparse part having weight 5905277.
Pruned matrix : 96382 x 97086 with weight 2618908.
Total sieving time: 0.81 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.08 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.4,2.4,50000
total time: 0.96 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

4·10¹²¹-9 = 3(9)₁₂₀1_<122> = 31 · C121

C121 = P48 · P73

P48 = 207550763771542349075740138245104441965655783933_<48>

P73 = 6216901143594248208194826668257714111385850652570251799400319368993225117_<73>

Number: n
N=1290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161
  ( 121 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=207550763771542349075740138245104441965655783933 (pp48)
 r2=6216901143594248208194826668257714111385850652570251799400319368993225117 (pp73)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.55 hours.
Scaled time: 2.05 units (timescale=1.318).
Factorization parameters were as follows:
name: KA_3_9_120_1
n: 1290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161
skew: 0.74
deg: 5
c5: 40
c0: -9
m: 1000000000000000000000000
type: snfs
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 200001)
Primes: RFBsize:63951, AFBsize:63733, largePrimes:4298910 encountered
Relations: rels:3675690, finalFF:181805
Max relations in full relation-set: 48
Initial matrix: 127751 x 181805 with sparse part having weight 12806423.
Pruned matrix : 102487 x 103189 with weight 4549576.
Total sieving time: 1.36 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.10 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000
total time: 1.55 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 17, 2007 (4th)

By Jo Yeong Uk / GGNFS

(4·10¹⁹⁵-1)/3 = 1(3)₁₉₅_<196> = 919 · 2815092622300365139319_<22> · 1616772208578912506305058572743036521_<37> · C135

C135 = P49 · P86

P49 = 9750955237361634372618257316599424244951087381213_<49>

P86 = 32691476708214933835165765723715218661077209696240370449876399876944717064876363130561_<86>

Number: 13333_195
N=318773126025054291670957797550571273589430793561728712537650216394184484148701462662385921621852455278537160766090492754352887897550493
  ( 135 digits)
Divisors found:
 r1=9750955237361634372618257316599424244951087381213 (pp49)
 r2=32691476708214933835165765723715218661077209696240370449876399876944717064876363130561 (pp86)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 386.78 hours.
Scaled time: 823.45 units (timescale=2.129).
Factorization parameters were as follows:
name: 13333_195
n: 318773126025054291670957797550571273589430793561728712537650216394184484148701462662385921621852455278537160766090492754352887897550493
skew: 131671.97
# norm 3.05e+18
c5: 197280
c4: -307423178886
c3: -58612697870847169
c2: 3978958100881520574793
c1: 213561147801238145597164433
c0: -11098269473779960898804283038595
# alpha -5.90
Y1: 773059969233563
Y0: -69451436841457195078837658
# Murphy_E 4.23e-11
# M 56576599863178588454020620146065243601482425869774777937223046811868572601341632692068072510368265616104157355536434726657596047407882
type: gnfs
rlim: 12000000
alim: 12000000
lpbr: 28
lpba: 28
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 12000000/12000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 51/51
Sieved algebraic special-q in [6000000, 11600001)
Primes: RFBsize:788060, AFBsize:788407, largePrimes:12637468 encountered
Relations: rels:13248927, finalFF:1826316
Max relations in full relation-set: 28
Initial matrix: 1576544 x 1826316 with sparse part having weight 125344949.
Pruned matrix : 1341143 x 1349089 with weight 79768099.
Polynomial selection time: 23.32 hours.
Total sieving time: 349.55 hours.
Total relation processing time: 0.39 hours.
Matrix solve time: 13.52 hours.
Time per square root: 0.67 hours.
Prototype def-par.txt line would be:
gnfs,134,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,12000000,12000000,28,28,51,51,2.6,2.6,100000
total time: 386.78 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

4·10¹³¹-9 = 3(9)₁₃₀1_<132> = 83 · 157 · 43427 · 89517934664444970329_<20> · C103

C103 = P37 · P67

P37 = 2706709430006427754108248781033420387_<37>

P67 = 2917230383237813120633073932480522042054906957099018520221291471441_<67>

Number: 39991_131
N=7896094987811053945775833802148765097844972873029553301959921686999250192636341021809147450036357667667
  ( 103 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=2706709430006427754108248781033420387 (pp37)
 r2=2917230383237813120633073932480522042054906957099018520221291471441 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.06 hours.
Scaled time: 4.43 units (timescale=2.145).
Factorization parameters were as follows:
n: 7896094987811053945775833802148765097844972873029553301959921686999250192636341021809147450036357667667
m: 200000000000000000000000000
c5: 5
c0: -36
skew: 1.48
type: snfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [600000, 1000001)
Primes: RFBsize:92938, AFBsize:92554, largePrimes:1605182 encountered
Relations: rels:1657757, finalFF:229082
Max relations in full relation-set: 28
Initial matrix: 185559 x 229082 with sparse part having weight 10774169.
Pruned matrix : 157627 x 158618 with weight 5983307.
Total sieving time: 1.97 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1200000,1200000,25,25,46,46,2.2,2.2,50000
total time: 2.06 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 17, 2007 (3rd)

By Robert Backstrom / GGNFS

2·10¹⁵²+9 = 2(0)₁₅₁9_<153> = 11 · 5689 · C148

C148 = P69 · P80

P69 = 246315360411796404596074328483957549191621049813614560388841748191993_<69>

P80 = 12975075126577197804004996961447593348172069718738575880540661517804485822477547_<80>

Number: n
N=3195960306172997331373144345547228303424471468064366640566324166253855127119321178030968855366816344141005768708352642260183128525543712747087681171
  ( 148 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=246315360411796404596074328483957549191621049813614560388841748191993 (pp69)
 r2=12975075126577197804004996961447593348172069718738575880540661517804485822477547 (pp80)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 16.67 hours.
Scaled time: 14.62 units (timescale=0.877).
Factorization parameters were as follows:
name: KA_2_0_151_9
n: 3195960306172997331373144345547228303424471468064366640566324166253855127119321178030968855366816344141005768708352642260183128525543712747087681171
skew: 0.54
deg: 5
c5: 200
c0: 9
m: 1000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 650001)
Primes: RFBsize:203362, AFBsize:203482, largePrimes:6183842 encountered
Relations: rels:5700058, finalFF:479667
Max relations in full relation-set: 28
Initial matrix: 406909 x 479667 with sparse part having weight 26262880.
Pruned matrix : 339138 x 341236 with weight 14609906.
Total sieving time: 14.71 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.47 hours.
Total square root time: 0.32 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 16.67 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 17, 2007 (2nd)

By Sinkiti Sibata / GGNFS

2·10¹⁴⁷+9 = 2(0)₁₄₆9_<148> = 7 · 188393823755666606087_<21> · C127

C127 = P35 · P92

P35 = 48974472633629490212445941599538267_<35>

P92 = 30966742771240142891864085906864765198542074244953818306582481386219016872212029624089901403_<92>

Number: 20009_147
N=1516579896402744219014433937457116142826101612462661029810181639049330302450011786700883958686428599152590539537076162355488601
  ( 127 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=48974472633629490212445941599538267 (pp35)
 r2=30966742771240142891864085906864765198542074244953818306582481386219016872212029624089901403 (pp92)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 17.87 hours.
Scaled time: 12.06 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_147
n: 1516579896402744219014433937457116142826101612462661029810181639049330302450011786700883958686428599152590539537076162355488601
m: 100000000000000000000000000000
c5: 200
c0: 9
skew: 0.54
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2350001)
Primes: RFBsize:114155, AFBsize:114287, largePrimes:2723540 encountered
Relations: rels:2681399, finalFF:265609
Max relations in full relation-set: 28
Initial matrix: 228507 x 265609 with sparse part having weight 23794062.
Pruned matrix : 215996 x 217202 with weight 17271817.
Total sieving time: 16.25 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.37 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 17.87 hours.
 --------- CPU info (if available) ----------

Nov 17, 2007

The factor table of 399...991 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Nov 16, 2007 (3rd)

By Jo Yeong Uk / GGNFS, GMP-ECM

2·10¹⁴⁹+9 = 2(0)₁₄₈9_<150> = 467 · 1867 · 4621 · 108421 · C135

C135 = P40 · P96

P40 = 1863452397272640607861076350654167212689_<40>

P96 = 245697714723845525541313190866322224591579633478192557941408979790414184607140661966923663278569_<96>

Number: 20009_149
N=457845995506559311920071361063861840226353200596349254744820183599147637255647440000439776818147406947190006280979032862128666078562041
  ( 135 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=1863452397272640607861076350654167212689 (pp40)
 r2=245697714723845525541313190866322224591579633478192557941408979790414184607140661966923663278569 (pp96)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 9.32 hours.
Scaled time: 19.79 units (timescale=2.123).
Factorization parameters were as follows:
n: 457845995506559311920071361063861840226353200596349254744820183599147637255647440000439776818147406947190006280979032862128666078562041
m: 1000000000000000000000000000000
c5: 1
c0: 45
skew: 2.14
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1500001)
Primes: RFBsize:135072, AFBsize:135163, largePrimes:3697267 encountered
Relations: rels:3741082, finalFF:354567
Max relations in full relation-set: 28
Initial matrix: 270299 x 354567 with sparse part having weight 30900567.
Pruned matrix : 237134 x 238549 with weight 17237573.
Total sieving time: 9.00 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.25 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 9.32 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

2·10¹⁹¹+9 = 2(0)₁₉₀9_<192> = C192

C192 = P45 · C148

P45 = 139787422364207720750158040677389843257571643_<45>

C148 = [1430743886806296706788516093667434949145159858014350886258366962866810355411884866166709798529837275207436439253831768696683312353651987615427655563_<148>]

2·10¹³⁷+9 = 2(0)₁₃₆9_<138> = 1747 · 187546628295101_<15> · 17157672728274349_<17> · 1099656391248576163177704783751416330647_<40> · 32352842794331493715586477085068987078828228518142150588757859949_<65>

C104 = P40 · P65

P40 = 1099656391248576163177704783751416330647_<40>

P65 = 32352842794331493715586477085068987078828228518142150588757859949_<65>

Number: 20009_137
N=35577010353847071166627381630160508224933719406788362654288006111043429068247910493731177879457902557003
  ( 104 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=1099656391248576163177704783751416330647 (pp40)
 r2=32352842794331493715586477085068987078828228518142150588757859949 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 8.22 hours.
Scaled time: 5.55 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_137
n: 35577010353847071166627381630160508224933719406788362654288006111043429068247910493731177879457902557003
m: 1000000000000000000000000000
c5: 200
c0: 9
skew: 0.54
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1225001)
Primes: RFBsize:78498, AFBsize:63988, largePrimes:1552634 encountered
Relations: rels:1574611, finalFF:193594
Max relations in full relation-set: 28
Initial matrix: 142551 x 193594 with sparse part having weight 15125767.
Pruned matrix : 126553 x 127329 with weight 8216971.
Total sieving time: 7.78 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 8.22 hours.
 --------- CPU info (if available) ----------

Nov 16, 2007

By Robert Backstrom / GGNFS, Msieve

2·10¹⁴⁶+9 = 2(0)₁₄₅9_<147> = 11 · 19 · 443 · C142

C142 = P43 · P99

P43 = 5697591929599718777554446090898432894508443_<43>

P99 = 379130428884937776481991873307188799908650024737963391395977785501700705423478684413792248504210049_<99>

Number: n
N=2160130471880501582295570652467409031505502932377115577780897966237160724507760268720230701934396837568989166945683519284564787713177875943707
  ( 142 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=5697591929599718777554446090898432894508443 (pp43)
 r2=379130428884937776481991873307188799908650024737963391395977785501700705423478684413792248504210049 (pp99)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.11 hours.
Scaled time: 10.69 units (timescale=1.318).
Factorization parameters were as follows:
name: KA_2_0_145_9
n: 2160130471880501582295570652467409031505502932377115577780897966237160724507760268720230701934396837568989166945683519284564787713177875943707
skew: 0.85
deg: 5
c5: 20
c0: 9
m: 100000000000000000000000000000
type: snfs
rlim: 2200000
alim: 2200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 850001)
Primes: RFBsize:162662, AFBsize:162600, largePrimes:6215071 encountered
Relations: rels:5583240, finalFF:372600
Max relations in full relation-set: 48
Initial matrix: 325329 x 372600 with sparse part having weight 24152920.
Pruned matrix : 286219 x 287909 with weight 14211438.
Total sieving time: 6.19 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.66 hours.
Total square root time: 0.10 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2200000,2200000,28,28,48,48,2.5,2.5,100000
total time: 8.11 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

2·10¹⁶⁷-9 = 1(9)₁₆₆1_<168> = 11 · 25693999 · C159

C159 = P51 · P54 · P56

P51 = 213778048882883699682952867750597400299228114685941_<51>

P54 = 253294029617274149322595661355934135791715095080163601_<54>

P56 = 13068253350533572176578369071664035808002504957074122959_<56>

Number: n
N=707628975225622987615972826254806883824577800513582250010277426328933141866387485335318251478947211830209140203586766770644842719181945240138828454917359567819
  ( 159 digits)
SNFS difficulty: 167 digits.
Divisors found:

Fri Nov 16 05:59:23 2007  prp51 factor: 213778048882883699682952867750597400299228114685941
Fri Nov 16 05:59:23 2007  prp54 factor: 253294029617274149322595661355934135791715095080163601
Fri Nov 16 05:59:23 2007  prp56 factor: 13068253350533572176578369071664035808002504957074122959
Fri Nov 16 05:59:23 2007  elapsed time 01:49:33 (Msieve 1.29)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 62.94 hours.
Scaled time: 82.45 units (timescale=1.310).
Factorization parameters were as follows:
name: KA_1_9_166_1
n: 707628975225622987615972826254806883824577800513582250010277426328933141866387485335318251478947211830209140203586766770644842719181945240138828454917359567819
skew: 0.54
deg: 5
c5: 200
c0: -9
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2600001)
Primes: RFBsize:230209, AFBsize:230472, largePrimes:7397646 encountered
Relations: rels:6871280, finalFF:499906
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 62.61 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 62.94 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 15, 2007 (4th)

By Sinkiti Sibata / GGNFS

2·10¹³³+9 = 2(0)₁₃₂9_<134> = 41 · 106261 · 138657907177600053240515967083_<30> · C98

C98 = P30 · P68

P30 = 337482959187671618348715804443_<30>

P68 = 98101523251692854700293015379351134705420468393200528633582388590261_<68>

Number: 20009_133
N=33107592367799477994531315875696566699102396778630104307460969147141634839210559134468289330329623
  ( 98 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=337482959187671618348715804443 (pp30)
 r2=98101523251692854700293015379351134705420468393200528633582388590261 (pp68)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 5.55 hours.
Scaled time: 3.75 units (timescale=0.676).
Factorization parameters were as follows:
name: 20009_133
n: 33107592367799477994531315875696566699102396778630104307460969147141634839210559134468289330329623
m: 200000000000000000000000000
c5: 125
c0: 18
skew: 0.68
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 925001)
Primes: RFBsize:78498, AFBsize:63828, largePrimes:1467588 encountered
Relations: rels:1461357, finalFF:170545
Max relations in full relation-set: 28
Initial matrix: 142392 x 170545 with sparse part having weight 10197756.
Pruned matrix : 131765 x 132540 with weight 6330275.
Total sieving time: 5.15 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.55 hours.
 --------- CPU info (if available) ----------

2·10¹³⁶+9 = 2(0)₁₃₅9_<137> = 11 · 626113 · 1638117457_<10> · 14068805453502347862038393_<26> · C96

C96 = P37 · P59

P37 = 7479989621822215707304648726870274177_<37>

P59 = 16845400134770192015265810071674311005731257071385123440419_<59>

Number: 20009_136
N=126003418183523590081005231307316729274954208236469757844274078817776161403684503808348053760163
  ( 96 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=7479989621822215707304648726870274177 (pp37)
 r2=16845400134770192015265810071674311005731257071385123440419 (pp59)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 7.86 hours.
Scaled time: 5.31 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_136
n: 126003418183523590081005231307316729274954208236469757844274078817776161403684503808348053760163
m: 1000000000000000000000000000
c5: 20
c0: 9
skew: 0.85
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1150001)
Primes: RFBsize:78498, AFBsize:63843, largePrimes:1536871 encountered
Relations: rels:1552675, finalFF:189444
Max relations in full relation-set: 28
Initial matrix: 142408 x 189444 with sparse part having weight 14166681.
Pruned matrix : 126873 x 127649 with weight 7809355.
Total sieving time: 7.43 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 7.86 hours.
 --------- CPU info (if available) ----------

Nov 15, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

(2·10¹⁶⁷+1)/3 = (6)₁₆₆7_<167> = 67 · 163 · 154247 · 105057409 · C150

C150 = P44 · P45 · P62

P44 = 35110383512037779258731687752743501077616849_<44>

P45 = 144490044053633250534088853071686157579676183_<45>

P62 = 74255636529996781604025069037975869335914287473493040697234147_<62>

Number: n
N=376706333569452881833796963898895894903820904576725150866190626909505248384898760572288876235614404361232252029198354520001692450611622477750149560949
  ( 150 digits)
SNFS difficulty: 167 digits.
Divisors found:

Thu Nov 15 11:40:38 2007  prp44 factor: 35110383512037779258731687752743501077616849
Thu Nov 15 11:40:38 2007  prp45 factor: 144490044053633250534088853071686157579676183
Thu Nov 15 11:40:38 2007  prp62 factor: 74255636529996781604025069037975869335914287473493040697234147
Thu Nov 15 11:40:38 2007  elapsed time 03:04:59 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 61.61 hours.
Scaled time: 81.70 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_6_166_7
n: 376706333569452881833796963898895894903820904576725150866190626909505248384898760572288876235614404361232252029198354520001692450611622477750149560949
skew: 0.35
deg: 5
c5: 200
c0: 1
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2850000)
Primes: RFBsize:250150, AFBsize:249566, largePrimes:7551318 encountered
Relations: rels:7059925, finalFF:577979
Max relations in full relation-set: 28
Initial matrix: 499781 x 577979 with sparse part having weight 49191823.
Pruned matrix : 444384 x 446946 with weight 33215771.
Total sieving time: 61.30 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 61.61 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 15, 2007 (2nd)

By Jo Yeong Uk / GGNFS

2·10¹³⁸+9 = 2(0)₁₃₇9_<139> = 11² · 41 · 9034909729_<10> · C125

C125 = P30 · P38 · P58

P30 = 799755820751262322119275375033_<30>

P38 = 20766309102022228980253099855875658537_<38>

P58 = 2686706507069958673687375702336773298121688744721734859241_<58>

Number: 20009_138
N=44620758746381241841688897721867317475788276748995108314229042673027347676487429597124584059980824714622578162566104956058761
  ( 125 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=799755820751262322119275375033 (pp30)
 r2=20766309102022228980253099855875658537 (pp38)
 r3=2686706507069958673687375702336773298121688744721734859241 (pp58)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.74 hours.
Scaled time: 10.09 units (timescale=2.126).
Factorization parameters were as follows:
n: 44620758746381241841688897721867317475788276748995108314229042673027347676487429597124584059980824714622578162566104956058761
m: 10000000000000000000000000000
c5: 1
c0: 450
skew: 3.39
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1000001)
Primes: RFBsize:107126, AFBsize:106598, largePrimes:2324281 encountered
Relations: rels:2569529, finalFF:387303
Max relations in full relation-set: 28
Initial matrix: 213788 x 387303 with sparse part having weight 31262275.
Pruned matrix : 152381 x 153513 with weight 10650969.
Total sieving time: 4.62 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 4.74 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

2·10¹⁴¹+9 = 2(0)₁₄₀9_<142> = 7 · 29 · 84089 · 1843241 · C128

C128 = P39 · P45 · P45

P39 = 193589288637298059074525377001965216949_<39>

P45 = 468214580957084640590379178323139739604088747_<45>

P45 = 701271823576894703710295051061370970173632749_<45>

Number: 20009_141
N=63564209137520160828475746211489351888520291688068698024161891639200326972468705608592258442484833328985146148995415235418800347
  ( 128 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=193589288637298059074525377001965216949 (pp39)
 r2=468214580957084640590379178323139739604088747 (pp45)
 r3=701271823576894703710295051061370970173632749 (pp45)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.50 hours.
Scaled time: 11.67 units (timescale=2.123).
Factorization parameters were as follows:
n: 63564209137520160828475746211489351888520291688068698024161891639200326972468705608592258442484833328985146148995415235418800347
m: 10000000000000000000000000000
c5: 20
c0: 9
skew: 0.85
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1100001)
Primes: RFBsize:114155, AFBsize:113962, largePrimes:3318316 encountered
Relations: rels:3434745, finalFF:413798
Max relations in full relation-set: 28
Initial matrix: 228184 x 413798 with sparse part having weight 34667463.
Pruned matrix : 162968 x 164172 with weight 12380892.
Total sieving time: 5.34 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 5.50 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 15, 2007

By JMB / GMP-ECM

9·10¹⁷⁸+7 = 9(0)₁₇₇7_<179> = 149 · C177

C177 = P35 · C143

P35 = 34477381911603229695013790339605181_<35>

C143 = [17519510245477803843772234672206519263441432562534062592219996721821259842723144120268391140425192935308257597913633559158414046764815248848903_<143>]

Nov 14, 2007 (3rd)

By Jo Yeong Uk / GGNFS, Msieve

2·10¹⁵¹+9 = 2(0)₁₅₀9_<152> = C152

C152 = P64 · P88

P64 = 5361545627942898041009151470006806437953024698709373565545033283_<64>

P88 = 3730267610848168946728870898319835513379653329283710892077298113553792162530729021571523_<88>

Number: 20009_151
N=20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 152 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=5361545627942898041009151470006806437953024698709373565545033283 (pp64)
 r2=3730267610848168946728870898319835513379653329283710892077298113553792162530729021571523 (pp88)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.44 hours.
Scaled time: 24.53 units (timescale=2.145).
Factorization parameters were as follows:
n: 20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
m: 1000000000000000000000000000000
c5: 20
c0: 9
skew: 0.85
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:176393, largePrimes:5255231 encountered
Relations: rels:5101022, finalFF:437517
Max relations in full relation-set: 28
Initial matrix: 352762 x 437517 with sparse part having weight 35441926.
Pruned matrix : 301643 x 303470 with weight 21914347.
Total sieving time: 10.89 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.44 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 11.44 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

2·10¹¹⁵+9 = 2(0)₁₁₄9_<116> = 2549 · C112

C112 = P34 · P36 · P43

P34 = 3610985855871191931623417922834769_<34>

P36 = 347349964829672312277520077897474727_<36>

P43 = 6255573247015228068683536228478645049008707_<43>

Number: 20009_115
N=7846214201647704982346018046292663789721459395841506473126716359356610435464888191447626520204001569242840329541
  ( 112 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=3610985855871191931623417922834769 (pp34)
 r2=347349964829672312277520077897474727 (pp36)
 r3=6255573247015228068683536228478645049008707 (pp43)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.64 hours.
Scaled time: 1.37 units (timescale=2.143).
Factorization parameters were as follows:
n: 7846214201647704982346018046292663789721459395841506473126716359356610435464888191447626520204001569242840329541
m: 100000000000000000000000
c5: 2
c0: 9
skew: 1.35
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 390001)
Primes: RFBsize:49098, AFBsize:48886, largePrimes:1863902 encountered
Relations: rels:1959876, finalFF:245084
Max relations in full relation-set: 28
Initial matrix: 98049 x 245084 with sparse part having weight 19250215.
Pruned matrix : 66805 x 67359 with weight 3521221.
Total sieving time: 0.60 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,115,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.64 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

2·10¹²⁸+9 = 2(0)₁₂₇9_<129> = 11 · 19 · 41 · 3628268961937_<13> · C112

C112 = P30 · P82

P30 = 838738174203331430476288994347_<30>

P82 = 7669622162401410990558076424963758890890607406854931844023679051213111668308932099_<82>

Number: 20009_128
N=6432804889321966154737940019106072881085761416381139523418545975573334342986996964229572138342044269550217844353
  ( 112 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=838738174203331430476288994347 (pp30)
 r2=7669622162401410990558076424963758890890607406854931844023679051213111668308932099 (pp82)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.75 hours.
Scaled time: 3.75 units (timescale=2.146).
Factorization parameters were as follows:
n: 6432804889321966154737940019106072881085761416381139523418545975573334342986996964229572138342044269550217844353
m: 100000000000000000000000000
c5: 1
c0: 450
skew: 3.39
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 850001)
Primes: RFBsize:78498, AFBsize:78411, largePrimes:1572335 encountered
Relations: rels:1653001, finalFF:250088
Max relations in full relation-set: 28
Initial matrix: 156973 x 250088 with sparse part having weight 11746162.
Pruned matrix : 112238 x 113086 with weight 4590998.
Total sieving time: 1.69 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 1.75 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

2·10¹²⁹+9 = 2(0)₁₂₈9_<130> = 7³ · 163 · 4507 · C121

C121 = P41 · P80

P41 = 82003635083982433094568610504258544735069_<41>

P80 = 96789357905979190059916421135822880484975096215801511141201084498141280349953947_<80>

Number: 20009_129
N=7937079185734887593874167046697325195980474197859232432137387602376763124415823530918175646633742048331470586833465867343
  ( 121 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=82003635083982433094568610504258544735069 (pp41)
 r2=96789357905979190059916421135822880484975096215801511141201084498141280349953947 (pp80)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.72 hours.
Scaled time: 3.68 units (timescale=2.139).
Factorization parameters were as follows:
n: 7937079185734887593874167046697325195980474197859232432137387602376763124415823530918175646633742048331470586833465867343
m: 100000000000000000000000000
c5: 1
c0: 45
skew: 2.14
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 850001)
Primes: RFBsize:78498, AFBsize:78411, largePrimes:1567044 encountered
Relations: rels:1646980, finalFF:248901
Max relations in full relation-set: 28
Initial matrix: 156973 x 248901 with sparse part having weight 11659733.
Pruned matrix : 112684 x 113532 with weight 4605631.
Total sieving time: 1.66 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 1.72 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

2·10¹⁴³+9 = 2(0)₁₄₂9_<144> = 41 · 67 · 3331649 · 14935649 · 82226933119967_<14> · 1277854822563168097967_<22> · C92

C92 = P39 · P53

P39 = 378442673724566134246810453283328526129_<39>

P53 = 36795294718689337041099821264332695452995703051552587_<53>

Wed Nov 14 21:20:40 2007  
Wed Nov 14 21:20:40 2007  
Wed Nov 14 21:20:40 2007  Msieve v. 1.28
Wed Nov 14 21:20:40 2007  random seeds: 3b93c2a8 eb1b55fc
Wed Nov 14 21:20:40 2007  factoring 13924909713824200219224541074202380892627126993472216666474137256898926894158453179847045723 (92 digits)
Wed Nov 14 21:20:41 2007  commencing quadratic sieve (91-digit input)
Wed Nov 14 21:20:41 2007  using multiplier of 3
Wed Nov 14 21:20:41 2007  using 32kb Intel Core sieve core
Wed Nov 14 21:20:41 2007  sieve interval: 36 blocks of size 32768
Wed Nov 14 21:20:41 2007  processing polynomials in batches of 6
Wed Nov 14 21:20:41 2007  using a sieve bound of 1753547 (65732 primes)
Wed Nov 14 21:20:41 2007  using large prime bound of 177108247 (27 bits)
Wed Nov 14 21:20:41 2007  using double large prime bound of 702796695147472 (42-50 bits)
Wed Nov 14 21:20:41 2007  using trial factoring cutoff of 50 bits
Wed Nov 14 21:20:41 2007  polynomial 'A' values have 12 factors
Wed Nov 14 22:27:23 2007  66322 relations (17638 full + 48684 combined from 795835 partial), need 65828
Wed Nov 14 22:27:23 2007  begin with 813473 relations
Wed Nov 14 22:27:24 2007  reduce to 163711 relations in 11 passes
Wed Nov 14 22:27:24 2007  attempting to read 163711 relations
Wed Nov 14 22:27:25 2007  recovered 163711 relations
Wed Nov 14 22:27:25 2007  recovered 140908 polynomials
Wed Nov 14 22:27:25 2007  attempting to build 66322 cycles
Wed Nov 14 22:27:25 2007  found 66322 cycles in 5 passes
Wed Nov 14 22:27:25 2007  distribution of cycle lengths:
Wed Nov 14 22:27:25 2007     length 1 : 17638
Wed Nov 14 22:27:25 2007     length 2 : 12531
Wed Nov 14 22:27:25 2007     length 3 : 11404
Wed Nov 14 22:27:25 2007     length 4 : 8950
Wed Nov 14 22:27:25 2007     length 5 : 6342
Wed Nov 14 22:27:25 2007     length 6 : 4034
Wed Nov 14 22:27:25 2007     length 7 : 2526
Wed Nov 14 22:27:25 2007     length 9+: 2897
Wed Nov 14 22:27:25 2007  largest cycle: 17 relations
Wed Nov 14 22:27:25 2007  matrix is 65732 x 66322 with weight 3973198 (avg 59.91/col)
Wed Nov 14 22:27:26 2007  filtering completed in 3 passes
Wed Nov 14 22:27:26 2007  matrix is 61414 x 61478 with weight 3685100 (avg 59.94/col)
Wed Nov 14 22:27:27 2007  saving the first 48 matrix rows for later
Wed Nov 14 22:27:27 2007  matrix is 61366 x 61478 with weight 2818330 (avg 45.84/col)
Wed Nov 14 22:27:27 2007  matrix includes 64 packed rows
Wed Nov 14 22:27:27 2007  using block size 24591 for processor cache size 4096 kB
Wed Nov 14 22:27:28 2007  commencing Lanczos iteration
Wed Nov 14 22:27:44 2007  lanczos halted after 972 iterations
Wed Nov 14 22:27:44 2007  recovered 16 nontrivial dependencies
Wed Nov 14 22:27:45 2007  prp39 factor: 378442673724566134246810453283328526129
Wed Nov 14 22:27:45 2007  prp53 factor: 36795294718689337041099821264332695452995703051552587
Wed Nov 14 22:27:45 2007  elapsed time 01:07:05

Nov 14, 2007 (2nd)

By matsuix / GMP-ECM

(79·10¹⁸⁸-7)/9 = 8(7)₁₈₈_<189> = 17 · 293 · C186

C186 = P32 · C154

P32 = 21765125120660595551469602307679_<32>

C154 = [8096678074753473185944039706917079992623437626274897607442886516416138091715794569583278042469134900566577085836441842147205791368296429713363394770501523_<154>]

Nov 14, 2007

By Sinkiti Sibata / Msieve, GGNFS

2·10¹¹³+9 = 2(0)₁₁₂9_<114> = 29 · 41 · 43 · 66063586712481298029647_<23> · C86

C86 = P30 · P57

P30 = 126503094686428494316629112361_<30>

P57 = 468076014118751200598434885891146498395685059990909881001_<57>

Tue Nov 13 19:16:24 2007  
Tue Nov 13 19:16:24 2007  Msieve v. 1.28
Tue Nov 13 19:16:24 2007  random seeds: 79b93950 914c419f
Tue Nov 13 19:16:24 2007  factoring 59213064334510423889180281278137633024927225091119261905297311496666472844090768153361 (86 digits)
Tue Nov 13 19:16:25 2007  commencing quadratic sieve (86-digit input)
Tue Nov 13 19:16:25 2007  using multiplier of 1
Tue Nov 13 19:16:25 2007  using 64kb Pentium 2 sieve core
Tue Nov 13 19:16:25 2007  sieve interval: 8 blocks of size 65536
Tue Nov 13 19:16:25 2007  processing polynomials in batches of 13
Tue Nov 13 19:16:25 2007  using a sieve bound of 1450331 (55667 primes)
Tue Nov 13 19:16:25 2007  using large prime bound of 116026480 (26 bits)
Tue Nov 13 19:16:25 2007  using double large prime bound of 328248542117840 (41-49 bits)
Tue Nov 13 19:16:25 2007  using trial factoring cutoff of 49 bits
Tue Nov 13 19:16:25 2007  polynomial 'A' values have 11 factors
Wed Nov 14 00:52:54 2007  55802 relations (15557 full + 40245 combined from 585823 partial), need 55763
Wed Nov 14 00:52:57 2007  begin with 601380 relations
Wed Nov 14 00:52:59 2007  reduce to 134103 relations in 9 passes
Wed Nov 14 00:52:59 2007  attempting to read 134103 relations
Wed Nov 14 00:53:05 2007  recovered 134103 relations
Wed Nov 14 00:53:05 2007  recovered 113504 polynomials
Wed Nov 14 00:53:06 2007  attempting to build 55802 cycles
Wed Nov 14 00:53:06 2007  found 55802 cycles in 5 passes
Wed Nov 14 00:53:09 2007  distribution of cycle lengths:
Wed Nov 14 00:53:09 2007     length 1 : 15557
Wed Nov 14 00:53:09 2007     length 2 : 10981
Wed Nov 14 00:53:09 2007     length 3 : 9922
Wed Nov 14 00:53:09 2007     length 4 : 7142
Wed Nov 14 00:53:09 2007     length 5 : 4933
Wed Nov 14 00:53:09 2007     length 6 : 3153
Wed Nov 14 00:53:09 2007     length 7 : 1922
Wed Nov 14 00:53:09 2007     length 9+: 2192
Wed Nov 14 00:53:09 2007  largest cycle: 17 relations
Wed Nov 14 00:53:10 2007  matrix is 55667 x 55802 with weight 2940878 (avg 52.70/col)
Wed Nov 14 00:53:15 2007  filtering completed in 3 passes
Wed Nov 14 00:53:15 2007  matrix is 51377 x 51441 with weight 2736176 (avg 53.19/col)
Wed Nov 14 00:53:17 2007  saving the first 48 matrix rows for later
Wed Nov 14 00:53:17 2007  matrix is 51329 x 51441 with weight 2040428 (avg 39.67/col)
Wed Nov 14 00:53:17 2007  matrix includes 64 packed rows
Wed Nov 14 00:53:17 2007  using block size 5461 for processor cache size 128 kB
Wed Nov 14 00:53:18 2007  commencing Lanczos iteration
Wed Nov 14 00:55:31 2007  lanczos halted after 813 iterations
Wed Nov 14 00:55:32 2007  recovered 17 nontrivial dependencies
Wed Nov 14 00:55:33 2007  prp30 factor: 126503094686428494316629112361
Wed Nov 14 00:55:33 2007  prp57 factor: 468076014118751200598434885891146498395685059990909881001
Wed Nov 14 00:55:33 2007  elapsed time 05:39:09

2·10¹²⁴+9 = 2(0)₁₂₃9_<125> = 11 · 7699 · 530843 · C114

C114 = P50 · P65

P50 = 12933342699273453806862343859989698555609089656801_<50>

P65 = 34397439116451164611055979433447141435329163111083759614363162267_<65>

Number: 20009_124
N=444873868070456791285157294883334653826114223009391544914693262254988985036803067248867103876557666800384103127867
  ( 114 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=12933342699273453806862343859989698555609089656801 (pp50)
 r2=34397439116451164611055979433447141435329163111083759614363162267 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.57 hours.
Scaled time: 1.74 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_124
n: 444873868070456791285157294883334653826114223009391544914693262254988985036803067248867103876557666800384103127867
m: 10000000000000000000000000
c5: 1
c0: 45
skew: 2.14
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:63918, largePrimes:2172125 encountered
Relations: rels:2319136, finalFF:277481
Max relations in full relation-set: 28
Initial matrix: 113080 x 277481 with sparse part having weight 24656124.
Pruned matrix : 81390 x 82019 with weight 5386144.
Total sieving time: 2.35 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.57 hours.
 --------- CPU info (if available) ----------

2·10¹³¹+9 = 2(0)₁₃₀9_<132> = 23 · 5816239007_<10> · 74887441003_<11> · C110

C110 = P50 · P60

P50 = 57062021722090451670266439953685372616833385097687_<50>

P60 = 349867635331476129784259517594411816903548623239985088658229_<60>

Number: 20009_131
N=19964154607141111700061809502715420631256369551377576495671386457041725733903887371073728671212925530921416323
  ( 110 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=57062021722090451670266439953685372616833385097687 (pp50)
 r2=349867635331476129784259517594411816903548623239985088658229 (pp60)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 4.46 hours.
Scaled time: 3.01 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_131
n: 19964154607141111700061809502715420631256369551377576495671386457041725733903887371073728671212925530921416323
m: 100000000000000000000000000
c5: 20
c0: 9
skew: 0.85
type: snfs

Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:63951, AFBsize:63843, largePrimes:1417127 encountered
Relations: rels:1397458, finalFF:156815
Max relations in full relation-set: 28
Initial matrix: 127861 x 156815 with sparse part having weight 9252290.
Pruned matrix : 118504 x 119207 with weight 5490939.
Total sieving time: 4.16 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.46 hours.
 --------- CPU info (if available) ----------

2·10¹³²+9 = 2(0)₁₃₁9_<133> = 11 · 17 · 338993 · 2059033 · 22755127841_<11> · 113606374765035095179_<21> · C88

C88 = P41 · P47

P41 = 64553585691076468757776709697760029089923_<41>

P47 = 91818881868322405255423164024086685058772234099_<47>

Number: 20009_132
N=5927238058745577841908105029284969199323891268952962791663876711778527940853004477884377
  ( 88 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=64553585691076468757776709697760029089923 (pp41)
 r2=91818881868322405255423164024086685058772234099 (pp47)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 4.49 hours.
Scaled time: 3.03 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_132
n: 5927238058745577841908105029284969199323891268952962791663876711778527940853004477884377
m: 100000000000000000000000000
c5: 200
c0: 9
skew: 0.54
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:63951, AFBsize:63988, largePrimes:1398569 encountered
Relations: rels:1367313, finalFF:147644
Max relations in full relation-set: 28
Initial matrix: 128004 x 147644 with sparse part having weight 8145619.
Pruned matrix : 122053 x 122757 with weight 5454428.
Total sieving time: 4.18 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.49 hours.
 --------- CPU info (if available) ----------

2·10¹²¹+9 = 2(0)₁₂₀9_<122> = 47 · 25022303 · 6042247621_<10> · C103

C103 = P50 · P54

P50 = 23276367811865773221842316006407580116078609884723_<50>

P54 = 120918048180665503779004167358585435298916357823336103_<54>

Number: 20009_121
N=2814532964546077252871970629316708556510168734465584891122419326288554907143692044303039418256114054469
  ( 103 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=23276367811865773221842316006407580116078609884723 (pp50)
 r2=120918048180665503779004167358585435298916357823336103 (pp54)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.13 hours.
Scaled time: 1.44 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_121
n: 2814532964546077252871970629316708556510168734465584891122419326288554907143692044303039418256114054469
m: 1000000000000000000000000
c5: 20
c0: 9
skew: 0.85
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63843, largePrimes:2088965 encountered
Relations: rels:2160713, finalFF:219066
Max relations in full relation-set: 28
Initial matrix: 113008 x 219066 with sparse part having weight 18684530.
Pruned matrix : 87485 x 88114 with weight 4996495.
Total sieving time: 1.91 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.13 hours.
 --------- CPU info (if available) ----------

Nov 13, 2007 (5th)

By Jo Yeong Uk / GMP-ECM

2·10¹⁴⁴+9 = 2(0)₁₄₃9_<145> = 11 · 42923 · C139

C139 = P33 · P107

P33 = 128461577505546794238270375795409_<33>

P107 = 32974179012994192473352789524852599153449785137428491442089586166492685253837254412846376457647278813227617_<107>

Nov 13, 2007 (4th)

By Sinkiti Sibata / GGNFS

2·10¹⁰⁹+9 = 2(0)₁₀₈9_<110> = 23 · 95905845140127483764287_<23> · C85

C85 = P42 · P44

P42 = 748402279230484392743519946043122325419467_<42>

P44 = 12114959912210466897728207722918366529921027_<44>

Number: 20009_109
N=9066863611084262532391767761617834512428564112384343014130227238186317203834158432609
  ( 85 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=748402279230484392743519946043122325419467 (pp42)
 r2=12114959912210466897728207722918366529921027 (pp44)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.20 hours.
Scaled time: 0.81 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_109
n: 9066863611084262532391767761617834512428564112384343014130227238186317203834158432609
m: 10000000000000000000000
c5: 1
c0: 45
skew: 2.14
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 450001)
Primes: RFBsize:49098, AFBsize:63918, largePrimes:1920083 encountered
Relations: rels:1935524, finalFF:195943
Max relations in full relation-set: 28
Initial matrix: 113080 x 195943 with sparse part having weight 13085661.
Pruned matrix : 82364 x 82993 with weight 3462543.
Total sieving time: 1.04 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.20 hours.
 --------- CPU info (if available) ----------

2·10¹¹²+9 = 2(0)₁₁₁9_<113> = 11 · 83 · 10859 · 4136577279787441_<16> · C90

C90 = P31 · P59

P31 = 9206018018107001474355735891329_<31>

P59 = 52973226058227628382351941365777895979723862883622018652443_<59>

Number: 20009_112
N=487672473569298877322950209283462946924937198672763413701237098246837153702239074068366747
  ( 90 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=9206018018107001474355735891329 (pp31)
 r2=52973226058227628382351941365777895979723862883622018652443 (pp59)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.05 hours.
Scaled time: 1.38 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_112
n: 487672473569298877322950209283462946924937198672763413701237098246837153702239074068366747
m: 10000000000000000000000
c5: 200
c0: 9
skew: 0.54
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:63988, largePrimes:2409465 encountered
Relations: rels:3030076, finalFF:735233
Max relations in full relation-set: 28
Initial matrix: 113151 x 735233 with sparse part having weight 52489673.
Pruned matrix : 56354 x 56983 with weight 4802576.
Total sieving time: 1.89 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,112,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.05 hours.
 --------- CPU info (if available) ----------

2·10¹⁴²+9 = 2(0)₁₄₁9_<143> = 11 · 449 · 183695312580749129_<18> · 470754046684836857_<18> · 237679956825681386323_<21> · C84

C84 = P35 · P49

P35 = 36136781193374500273671200283243499_<35>

P49 = 5452012051103151492998305179171168472959562758251_<49>

Tue Nov 13 17:25:38 2007  Msieve v. 1.28
Tue Nov 13 17:25:38 2007  random seeds: 101e150d 418d085c
Tue Nov 13 17:25:38 2007  factoring 197018166554355499780407837997782804306340474278893940041682769225414512357104360249 (84 digits)
Tue Nov 13 17:25:39 2007  commencing quadratic sieve (83-digit input)
Tue Nov 13 17:25:40 2007  using multiplier of 29
Tue Nov 13 17:25:40 2007  using 64kb Pentium 2 sieve core
Tue Nov 13 17:25:40 2007  sieve interval: 6 blocks of size 65536
Tue Nov 13 17:25:40 2007  processing polynomials in batches of 17
Tue Nov 13 17:25:40 2007  using a sieve bound of 1392707 (53151 primes)
Tue Nov 13 17:25:40 2007  using large prime bound of 121165509 (26 bits)
Tue Nov 13 17:25:40 2007  using double large prime bound of 354880447655010 (41-49 bits)
Tue Nov 13 17:25:40 2007  using trial factoring cutoff of 49 bits
Tue Nov 13 17:25:40 2007  polynomial 'A' values have 11 factors
Tue Nov 13 21:04:22 2007  53343 relations (15805 full + 37538 combined from 575786 partial), need 53247
Tue Nov 13 21:04:28 2007  begin with 591591 relations
Tue Nov 13 21:04:31 2007  reduce to 124728 relations in 11 passes
Tue Nov 13 21:04:31 2007  attempting to read 124728 relations
Tue Nov 13 21:04:40 2007  recovered 124728 relations
Tue Nov 13 21:04:40 2007  recovered 100888 polynomials
Tue Nov 13 21:04:54 2007  attempting to build 53343 cycles
Tue Nov 13 21:04:55 2007  found 53343 cycles in 5 passes
Tue Nov 13 21:04:57 2007  distribution of cycle lengths:
Tue Nov 13 21:04:57 2007     length 1 : 15805
Tue Nov 13 21:04:57 2007     length 2 : 10899
Tue Nov 13 21:04:57 2007     length 3 : 9489
Tue Nov 13 21:04:57 2007     length 4 : 6716
Tue Nov 13 21:04:57 2007     length 5 : 4439
Tue Nov 13 21:04:57 2007     length 6 : 2729
Tue Nov 13 21:04:57 2007     length 7 : 1532
Tue Nov 13 21:04:57 2007     length 9+: 1734
Tue Nov 13 21:04:57 2007  largest cycle: 17 relations
Tue Nov 13 21:04:57 2007  matrix is 53151 x 53343 with weight 2794558 (avg 52.39/col)
Tue Nov 13 21:04:59 2007  filtering completed in 3 passes
Tue Nov 13 21:04:59 2007  matrix is 48275 x 48339 with weight 2547868 (avg 52.71/col)
Tue Nov 13 21:05:01 2007  saving the first 48 matrix rows for later
Tue Nov 13 21:05:01 2007  matrix is 48227 x 48339 with weight 1924721 (avg 39.82/col)
Tue Nov 13 21:05:01 2007  matrix includes 64 packed rows
Tue Nov 13 21:05:02 2007  commencing Lanczos iteration
Tue Nov 13 21:09:26 2007  lanczos halted after 764 iterations
Tue Nov 13 21:09:27 2007  recovered 17 nontrivial dependencies
Tue Nov 13 21:09:49 2007  prp35 factor: 36136781193374500273671200283243499
Tue Nov 13 21:09:49 2007  prp49 factor: 5452012051103151492998305179171168472959562758251
Tue Nov 13 21:09:49 2007  elapsed time 03:44:11

Nov 13, 2007 (3rd)

By matsuix / GMP-ECM

2·10¹⁷⁷+3 = 2(0)₁₇₆3_<178> = 19 · 23 · 107 · C173

C173 = P30 · C144

P30 = 221303620588838744540899263379_<30>

C144 = [193275258075082552732257542798544930147975742565477273667881259410088142299640908729176984976444019569373369657540183408799360677960504958362823_<144>]

Nov 13, 2007 (2nd)

By JMB / GMP-ECM

9·10¹⁷⁹+7 = 9(0)₁₇₈7_<180> = 367699 · 313009111137872717_<18> · C157

C157 = P34 · P124

P34 = 1707358559977705545311234918697001_<34>

P124 = 4580030236511827524816894288626065240922568714998170751384355667293248449614016116415020750898340461128531874477462326513929_<124>

Nov 13, 2007

The factor table of 200...009 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Nov 12, 2007 (5th)

By Yousuke Koide

(10¹³⁰⁹-1)/9 is divisible by 1163807225003295831984120638730881_<34>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 12, 2007 (4th)

By matsuix / GMP-ECM

6·10¹⁹⁴-1 = 5(9)₁₉₄_<195> = 19 · C194

C194 = P30 · P164

P30 = 552558220648518327302187386107_<30>

P164 = 57150443497805430547760194830899991379283534240795388543593799035627131426642721828037543684764910233345763252213386580962086660768427630404724977220097501462854303_<164>

Nov 12, 2007 (3rd)

By Jo Yeong Uk / GGNFS

(8·10¹⁷⁸+7)/3 = 2(6)₁₇₇9_<179> = C179

C179 = P78 · P101

P78 = 767662720421063505818715038954728721321787934050897941208611795952414246856909_<78>

P101 = 34737477745486953572334913721147854658092970596516908814796404141305652988617311793270855849086732641_<101>

Number: 26669_178
N=26666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
  ( 179 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=767662720421063505818715038954728721321787934050897941208611795952414246856909 (pp78)
 r2=34737477745486953572334913721147854658092970596516908814796404141305652988617311793270855849086732641 (pp101)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 229.96 hours.
Scaled time: 491.89 units (timescale=2.139).
Factorization parameters were as follows:
n: 26666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
m: 1000000000000000000000000000000000000
c5: 2
c0: 175
skew: 2.45
type: snfs
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [5000000, 8800001)
Primes: RFBsize:664579, AFBsize:665250, largePrimes:11139695 encountered
Relations: rels:11517589, finalFF:1584544
Max relations in full relation-set: 28
Initial matrix: 1329894 x 1584544 with sparse part having weight 95324120.
Pruned matrix : 1095649 x 1102362 with weight 62665643.
Total sieving time: 220.70 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 8.91 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000
total time: 229.96 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 12, 2007 (2nd)

By Robert Backstrom / GMP-ECM

2·10¹⁶⁵+3 = 2(0)₁₆₄3_<166> = 94136405394950299_<17> · C149

C149 = P36 · P113

P36 = 838305023383274289860418539450587157_<36>

P113 = 25343717347214324824522098723663613215893017202640604427624247481323908812513490062007103784101162836271292998421_<113>

Nov 12, 2007

By JMB / GMP-ECM, Msieve

9·10¹⁷⁷+7 = 9(0)₁₇₆7_<178> = 153438528657199_<15> · 32667044190772508911_<20> · C145

C145 = P33 · P112

P33 = 231363885166211856645528826109773_<33>

P112 = 7760731807961019750154843183467424612751080704744319434512584619725381829268383039969389480897051376995338032131_<112>

9·10¹⁸²+7 = 9(0)₁₈₁7_<183> = 681997 · 5371290194501118001753_<22> · 15159963126712966411921_<23> · C134

C134 = P37 · P41 · P57

P37 = 6744944339966240521048365048076011509_<37>

P41 = 19234654468418325743668292529120757280653_<41>

P57 = 124916706233941797813783021695951936693773474351449547931_<57>

9·10¹⁹¹+7 = 9(0)₁₉₀7_<192> = 19² · 71 · 223 · 5348430907_<10> · 7081217033400011183081_<22> · 4467601201156530952852184773_<28> · C126

C126 = P32 · P38 · P58

P32 = 16211565179348756515840607697259_<32>

P38 = 21676057655573837315308075461982724731_<38>

P58 = 2648244977702149059480307274983753320329588866774945947601_<58>

Nov 11, 2007 (4th)

By Robert Backstrom / GGNFS, Msieve

(17·10¹⁶⁵-71)/9 = 1(8)₁₆₄1_<166> = 3² · 11 · 19 · 239 · 2301857 · C154

C154 = P52 · P103

P52 = 1104452615085621808528281839929327507501092871162291_<52>

P103 = 1652700990864867075451213479344319367803780935121458431710865579015107058129083254411956069524400585357_<103>

Number: n
N=1825329931315300800903828355172001996656416128933119005508117804769257585582659512383777143680106332212925711617403703267839837227789771348804185345172887
  ( 154 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Nov 12 01:18:09 2007  prp52 factor: 1104452615085621808528281839929327507501092871162291
Mon Nov 12 01:18:09 2007  prp103 factor: 1652700990864867075451213479344319367803780935121458431710865579015107058129083254411956069524400585357
Mon Nov 12 01:18:09 2007  elapsed time 01:38:44 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 45.96 hours.
Scaled time: 60.94 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_1_8_164_1
n: 1825329931315300800903828355172001996656416128933119005508117804769257585582659512383777143680106332212925711617403703267839837227789771348804185345172887
skew: 1.33
deg: 5
c5: 17
c0: -71
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100000)
Primes: RFBsize:250150, AFBsize:249087, largePrimes:7336079 encountered
Relations: rels:6862148, finalFF:583606
Max relations in full relation-set: 28
Initial matrix: 499302 x 583606 with sparse part having weight 42516043.
Pruned matrix : 429944 x 432504 with weight 26149440.
Total sieving time: 45.69 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,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 45.96 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 11, 2007 (3rd)

By matsuix / GMP-ECM

4·10¹⁷⁶+7 = 4(0)₁₇₅7_<177> = 11 · 37 · C174

C174 = P37 · C138

P37 = 7135210354090040619550238567081980993_<37>

C138 = [137739594774192223139709541988016487305378968971069153072936288397790444184230544651923302551708474913403317389091953092751175896905333457_<138>]

(14·10¹⁹⁶-41)/9 = 1(5)₁₉₅1_<197> = 43 · C195

C195 = P29 · C167

P29 = 12991941439670998826484083573_<29>

C167 = [27844730337109139843652566781414443973010019917901912124608905800374293093913322511112990355973246182909621326436655829024147474787381586660026718061075677175452115209_<167>]

Nov 11, 2007 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

9·10¹⁶³+7 = 9(0)₁₆₂7_<164> = 47 · 349 · 859 · 58211 · C153

C153 = P33 · P42 · P78

P33 = 818470811192938112676337938572201_<33>

P42 = 873583190755642325776044428797599382814221_<42>

P78 = 153466481365034760327052932409167822889494591377902353931701362171082781011161_<78>

Number: n
N=134065738464908389294733191862713080806437886653151154389264336165712868499470848705785633116618319074552541740190520581
  ( 120 digits)
SNFS difficulty: 163 digits.
Divisors found:

Sun Nov 11 08:08:38 2007  prp42 factor: 873583190755642325776044428797599382814221
Sun Nov 11 08:08:38 2007  prp78 factor: 153466481365034760327052932409167822889494591377902353931701362171082781011161
Sun Nov 11 08:08:38 2007  elapsed time 01:40:59 (Msieve 1.29)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 63.94 hours.
Scaled time: 83.51 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_9_0_162_7

n: 134065738464908389294733191862713080806437886653151154389264336165712868499470848705785633116618319074552541740190520581

# n: 109728893714553854980742941642496184479539542626049635609986238428007354105418652745423356276793313693697545479480233833467867898192710425178858044968781

skew: 0.16
deg: 5
c5: 9000
c0: 7
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
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: 48/48
Sieved  special-q in [100000, 2950001)
Primes: RFBsize:216816, AFBsize:217011, largePrimes:7516572 encountered
Relations: rels:6969287, finalFF:457940
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 63.56 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,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 63.94 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 11, 2007

By JMB / GMP-ECM

9·10¹⁸³+7 = 9(0)₁₈₂7_<184> = 59 · 5879009045374855927_<19> · C164

C164 = P35 · P129

P35 = 81464545498575947436007410472506863_<35>

P129 = 318506082558980426195556346049653444619519149682263511747011957601975589600934055977483795167502851069663481908650764978825371373_<129>

9·10¹⁶⁴+7 = 9(0)₁₆₃7_<165> = 883 · 24573393591862132649_<20> · C143

C143 = P34 · P110

P34 = 2564993881968404917452325855647781_<34>

P110 = 16170756423913671663934778083625100661998605305949217253030068605305369307115708420697061171260255444165225841_<110>

9·10¹⁷³+7 = 9(0)₁₇₂7_<174> = 19 · 647 · 224401 · C165

C165 = P31 · P134

P31 = 4204449134966651726234511502249_<31>

P134 = 77598037366254001837116882823105292830227805356149887771917581121716866409828186604482406682111147355193961123945624774784312354859251_<134>

9·10¹⁶⁹+7 = 9(0)₁₆₈7_<170> = 2111 · 1429958609_<10> · C158

C158 = P32 · P126

P32 = 56769904881370799699375018291651_<32>

P126 = 525185398197314224568248713026766256427182001005757531713576174925963787257959304880282840700874560113146274753741218461103843_<126>

Nov 10, 2007 (2nd)

By Sinkiti Sibata / PFGW

(23·10¹⁰⁵⁹⁸+7)/3, (23·10¹²⁴⁶⁵+7)/3, (23·10¹⁵⁸⁷⁵+7)/3 and (23·10¹⁸⁸⁹⁵+7)/3 are PRPs. There is no other PRP of the form (23·10ⁿ+7)/3 (10001≤n≤20000).

Nov 10, 2007

By matsuix / GMP-ECM

6·10¹⁶⁶-1 = 5(9)₁₆₆_<167> = 1415744095201_<13> · C155

C155 = P26 · C130

P26 = 12712979409464320156621733_<26>

C130 = [3333643448967159954626524687734330724615407100378702091659234658746271899362005594705868470962976554854259399799326518042378430003_<130>]

Nov 9, 2007

By matsuix / GMP-ECM

(55·10¹⁸⁰-1)/9 = 6(1)₁₈₀_<181> = 3 · 23 · C179

C179 = P30 · P150

P30 = 101498619902504222710961733499_<30>

P150 = 872591447867335155263871338215982008049920291961559255672354899684344056901549523294371067281499223907198249217989811855244487724718971598186664829281_<150>

Nov 8, 2007 (2nd)

By matsuix / GMP-ECM

(8·10¹⁷⁴-53)/9 = (8)₁₇₃3_<174> = 2309 · C171

C171 = P29 · C143

P29 = 28200513448768426338019164149_<29>

C143 = [13651064825355236966422593727849148145450828300351719858603135500864608496173059635187685618753649483887590160393912399962653031892990513454363_<143>]

Nov 8, 2007

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

9·10¹⁵³+7 = 9(0)₁₅₂7_<154> = 907 · 1567 · 51635332541907318461_<20> · C129

C129 = P61 · P68

P61 = 4772486568530653705948719675085861919871051034726502704647793_<61>

P68 = 25696533054533355691086868666739471157508323084478430890473067987511_<68>

Number: n
N=122636358860564412039100336767082272939485086621808173675665794174642554988798630986018211854909258720752103550308799860577713223
  ( 129 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=4772486568530653705948719675085861919871051034726502704647793 (pp61)
 r2=25696533054533355691086868666739471157508323084478430890473067987511 (pp68)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 26.78 hours.
Scaled time: 35.54 units (timescale=1.327).
Factorization parameters were as follows:
name: KA_9_0_152_7
n: 122636358860564412039100336767082272939485086621808173675665794174642554988798630986018211854909258720752103550308799860577713223
skew: 0.24
deg: 5
c5: 9000
c0: 7
m: 1000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:183072, AFBsize:183101, largePrimes:6782121 encountered
Relations: rels:6200134, finalFF:427533
Max relations in full relation-set: 48
Initial matrix: 366240 x 427533 with sparse part having weight 38208097.
Pruned matrix : 321175 x 323070 with weight 23509586.
Total sieving time: 23.39 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 3.08 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 26.78 hours.
 --------- CPU info (if available) ----------

Cywin on AMD 64 3200+

(67·10¹⁶⁵+23)/9 = 7(4)₁₆₄7_<166> = 11 · 17 · 113417 · C159

C159 = P76 · P84

P76 = 3436383816970356938534318813689175226044935882855602276600499748816862981373_<76>

P84 = 102143530795393078870771512077719961217354103402463760765008945031833455587257908841_<84>

Number: n
N=351004376233502067423634322257777917760418568213229144337614952819956323425302295053639519584815678512598105002812461856105588319194641309439952033732715018693
  ( 159 digits)
SNFS difficulty: 166 digits.
Divisors found:

Thu Nov 08 15:26:03 2007  prp76 factor: 3436383816970356938534318813689175226044935882855602276600499748816862981373
Thu Nov 08 15:26:03 2007  prp84 factor: 102143530795393078870771512077719961217354103402463760765008945031833455587257908841
Thu Nov 08 15:26:03 2007  elapsed time 02:17:33 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 81.97 hours.
Scaled time: 98.04 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_7_4_164_7
n: 351004376233502067423634322257777917760418568213229144337614952819956323425302295053639519584815678512598105002812461856105588319194641309439952033732715018693
type: snfs
skew: 0.81
deg: 5
c5: 67
c0: 23
m: 1000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2600000)
Primes: RFBsize:250150, AFBsize:249876, largePrimes:7471694 encountered
Relations: rels:6998321, finalFF:574667
Max relations in full relation-set: 28
Initial matrix: 500091 x 574667 with sparse part having weight 41672522.
Pruned matrix : 442380 x 444944 with weight 28636697.
Total sieving time: 81.66 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 81.97 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(71·10¹⁶⁵-17)/9 = 7(8)₁₆₄7_<166> = 3 · 11 · 79 · 467 · 1619 · 377387 · C152

C152 = P31 · P41 · P81

P31 = 1719997418393992940622623083871_<31>

P41 = 38022766744779558259291504973562443163143_<41>

P81 = 162163322041498669991056527746571842965333158652283809975565132898038976089503147_<81>

Nov 7, 2007 (4th)

By Jo Yeong Uk / GGNFS

9·10¹⁶⁰+7 = 9(0)₁₅₉7_<161> = 193 · 233 · 43499 · 1514405906081012721338467999_<28> · C125

C125 = P58 · P67

P58 = 9539345889759064940903674568760087065552798466254478738629_<58>

P67 = 3184850972645850020285709503660847208668237617514389096861847478007_<67>

Number: 90007_160
N=30381395035404349559261482175363386501616068379879041925147514635035093035613293267212425275525857274850151785739806178832403
  ( 125 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=9539345889759064940903674568760087065552798466254478738629 (pp58)
 r2=3184850972645850020285709503660847208668237617514389096861847478007 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 30.91 hours.
Scaled time: 66.06 units (timescale=2.137).
Factorization parameters were as follows:
n: 30381395035404349559261482175363386501616068379879041925147514635035093035613293267212425275525857274850151785739806178832403
m: 100000000000000000000000000000000
c5: 9
c0: 7
skew: 0.95
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3800001)
Primes: RFBsize:283146, AFBsize:283337, largePrimes:5671469 encountered
Relations: rels:5709779, finalFF:661423
Max relations in full relation-set: 28
Initial matrix: 566547 x 661423 with sparse part having weight 42662144.
Pruned matrix : 495804 x 498700 with weight 29440637.
Total sieving time: 29.54 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.24 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 30.91 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 7, 2007 (3rd)

By Sinkiti Sibata / PFGW

9·10¹⁵⁷¹⁰+7, 9·10¹⁶⁴⁵³+7, 9·10¹⁷⁴⁸⁸+7 and 9·10¹⁸¹⁰⁹+7 are PRPs. There is no other PRP of the form 9·10ⁿ+7 (10001≤n≤20000).

Nov 7, 2007 (2nd)

By Sinkiti Sibata / Msieve, GGNFS

9·10¹²¹+7 = 9(0)₁₂₀7_<122> = 71 · 10733 · 14298301 · 13437563210843_<14> · C96

C96 = P47 · P50

P47 = 46754707307478264058557236237372093839004268587_<47>

P50 = 13147183761460396406902731745730328931732164333889_<50>

Mon Nov 05 07:44:28 2007  
Mon Nov 05 07:44:28 2007  Msieve v. 1.28
Mon Nov 05 07:44:28 2007  random seeds: cd76d0a4 bee9a5b5
Mon Nov 05 07:44:28 2007  factoring 614692728684711966341285537593488278848176917343378079725035602868779219670052351614028502244843 (96 digits)
Mon Nov 05 07:44:29 2007  commencing quadratic sieve (96-digit input)
Mon Nov 05 07:44:30 2007  using multiplier of 11
Mon Nov 05 07:44:30 2007  using 64kb Pentium 2 sieve core
Mon Nov 05 07:44:30 2007  sieve interval: 18 blocks of size 65536
Mon Nov 05 07:44:30 2007  processing polynomials in batches of 6
Mon Nov 05 07:44:30 2007  using a sieve bound of 2297747 (84706 primes)
Mon Nov 05 07:44:30 2007  using large prime bound of 344662050 (28 bits)
Mon Nov 05 07:44:30 2007  using double large prime bound of 2329744160961150 (43-52 bits)
Mon Nov 05 07:44:30 2007  using trial factoring cutoff of 52 bits
Mon Nov 05 07:44:30 2007  polynomial 'A' values have 13 factors
Tue Nov 06 21:50:05 2007  85254 relations (21080 full + 64174 combined from 1274004 partial), need 84802
Tue Nov 06 21:50:26 2007  begin with 1295084 relations
Tue Nov 06 21:53:11 2007  reduce to 222278 relations in 12 passes
Tue Nov 06 21:53:12 2007  attempting to read 222278 relations
Tue Nov 06 21:53:48 2007  recovered 222278 relations
Tue Nov 06 21:53:48 2007  recovered 207893 polynomials
Tue Nov 06 21:56:08 2007  attempting to build 85254 cycles
Tue Nov 06 21:56:15 2007  found 85254 cycles in 6 passes
Tue Nov 06 21:56:21 2007  distribution of cycle lengths:
Tue Nov 06 21:56:21 2007     length 1 : 21080
Tue Nov 06 21:56:21 2007     length 2 : 14945
Tue Nov 06 21:56:21 2007     length 3 : 14297
Tue Nov 06 21:56:21 2007     length 4 : 11531
Tue Nov 06 21:56:21 2007     length 5 : 8635
Tue Nov 06 21:56:21 2007     length 6 : 5795
Tue Nov 06 21:56:21 2007     length 7 : 3728
Tue Nov 06 21:56:21 2007     length 9+: 5243
Tue Nov 06 21:56:21 2007  largest cycle: 20 relations
Tue Nov 06 21:56:42 2007  matrix is 84706 x 85254 with weight 5719147 (avg 67.08/col)
Tue Nov 06 21:57:55 2007  filtering completed in 3 passes
Tue Nov 06 21:57:55 2007  matrix is 80583 x 80647 with weight 5410769 (avg 67.09/col)
Tue Nov 06 21:57:59 2007  saving the first 48 matrix rows for later
Tue Nov 06 21:58:00 2007  matrix is 80535 x 80647 with weight 4352733 (avg 53.97/col)
Tue Nov 06 21:58:00 2007  matrix includes 64 packed rows
Tue Nov 06 21:58:00 2007  using block size 10922 for processor cache size 256 kB
Tue Nov 06 21:58:03 2007  commencing Lanczos iteration
Tue Nov 06 22:04:03 2007  lanczos halted after 1275 iterations
Tue Nov 06 22:04:05 2007  recovered 15 nontrivial dependencies
Tue Nov 06 23:20:29 2007  prp47 factor: 46754707307478264058557236237372093839004268587
Tue Nov 06 23:20:29 2007  prp50 factor: 13147183761460396406902731745730328931732164333889
Tue Nov 06 23:20:29 2007  elapsed time 39:36:01

9·10¹⁶⁶-7 = 8(9)₁₆₅3_<167> = 42709 · 1578482099_<10> · C154

C154 = P39 · P115

P39 = 326236852168633890020751838911718198217_<39>

P115 = 4092139473970466337231565660348581447470351547418909019180227591362356350317132972423887166170348215102482040007519_<115>

Number: 89993_166
N=1335006700623134276833509278792951544459029456753960978279183880064673180289547757171082237750647795330058324252033450827327369675772426590179731812393623
  ( 154 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=326236852168633890020751838911718198217 (pp39)
 r2=4092139473970466337231565660348581447470351547418909019180227591362356350317132972423887166170348215102482040007519 (pp115)
Version: GGNFS-0.77.1-20060513-k8
Total time: 124.14 hours.
Scaled time: 248.65 units (timescale=2.003).
Factorization parameters were as follows:
name: 89993_166
n: 1335006700623134276833509278792951544459029456753960978279183880064673180289547757171082237750647795330058324252033450827327369675772426590179731812393623
m: 1000000000000000000000000000000000
c5: 90
c0: -7
skew: 0.6
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 6400001)
Primes: RFBsize:348513, AFBsize:349111, largePrimes:5986344 encountered
Relations: rels:6137431, finalFF:783376
Max relations in full relation-set: 28
Initial matrix: 697691 x 783376 with sparse part having weight 60293050.
Pruned matrix : 635609 x 639161 with weight 46938360.
Total sieving time: 117.98 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 5.62 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 124.14 hours.
 --------- CPU info (if available) ----------

Nov 7, 2007

By Robert Backstrom / GGNFS, Msieve

9·10¹⁵⁴+7 = 9(0)₁₅₃7_<155> = C155

C155 = P75 · P81

P75 = 342774283579171568600971909894532466448184589420657720323497289127488139607_<75>

P81 = 262563454469922156375323276959104849917481523961677799993943153957816466910677201_<81>

Number: n
N=90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
  ( 155 digits)
SNFS difficulty: 155 digits.
Divisors found:

Wed Nov 07 02:43:42 2007  prp75 factor: 342774283579171568600971909894532466448184589420657720323497289127488139607
Wed Nov 07 02:43:42 2007  prp81 factor: 262563454469922156375323276959104849917481523961677799993943153957816466910677201
Wed Nov 07 02:43:42 2007  elapsed time 01:08:12 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 31.83 hours.
Scaled time: 38.16 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_9_0_153_7
n: 90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
type: snfs
skew: 1.51
deg: 5
c5: 9
c0: 70
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1350000)
Primes: RFBsize:216816, AFBsize:217291, largePrimes:6508656 encountered
Relations: rels:6015638, finalFF:533595
Max relations in full relation-set: 28
Initial matrix: 434171 x 533595 with sparse part having weight 29453920.
Pruned matrix : 345128 x 347362 with weight 15856430.
Total sieving time: 31.59 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 31.83 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Nov 6, 2007 (7th)

By JMB / GGNFS

9·10¹⁵²+7 = 9(0)₁₅₁7_<153> = 4761397 · 170458908643_<12> · 49688519499466733076979_<23> · C113

C113 = P39 · P74

P39 = 703840987201156095759020645169329337871_<39>

P74 = 31707193373284828223436939712373236806907701314756561688871528206762760813_<74>

Nov 6, 2007 (6th)

By Jo Yeong Uk / GGNFS, GMP-ECM

9·10¹⁵⁰+7 = 9(0)₁₄₉7_<151> = 19732343 · 326052556279_<12> · C133

C133 = P39 · P94

P39 = 589499724724831441087810448027951375963_<39>

P94 = 2372972128635709558872684003447910854760650370032899324921933688620430554494554451055042317237_<94>

Number: 90007_150
N=1398866416610448089159839440560263500294515545943113810621260052431416451996375989188510257329362504846021037950153661991966102374231
  ( 133 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=589499724724831441087810448027951375963 (pp39)
 r2=2372972128635709558872684003447910854760650370032899324921933688620430554494554451055042317237 (pp94)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 12.90 hours.
Scaled time: 27.68 units (timescale=2.146).
Factorization parameters were as follows:
n: 1398866416610448089159839440560263500294515545943113810621260052431416451996375989188510257329362504846021037950153661991966102374231
m: 1000000000000000000000000000000
c5: 9
c0: 7
skew: 0.95
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:176458, largePrimes:5458981 encountered
Relations: rels:5399088, finalFF:508783
Max relations in full relation-set: 28
Initial matrix: 352824 x 508783 with sparse part having weight 43914106.
Pruned matrix : 281114 x 282942 with weight 22700108.
Total sieving time: 12.40 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.39 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 12.90 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹⁶²+7 = 9(0)₁₆₁7_<163> = 5675476123_<10> · 19653188594940718862107501_<26> · C128

C128 = P36 · P93

P36 = 688903506523745903246622831283151599_<36>

P93 = 117124780898551182812517761055884645674869174813318998257172923202640159324081908982573296791_<93>

Nov 6, 2007 (5th)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

9·10¹⁶⁴-7 = 8(9)₁₆₃3_<165> = 19 · 1847353 · C158

C158 = P40 · P56 · P63

P40 = 5195304037384876588643582502770703788863_<40>

P56 = 44521045988937219971985542168110282187182538753337627749_<56>

P63 = 110856890051938744122912238100452821884732080214861054731598977_<63>

Number: n
N=4935464700192921827044022834990668957767855479530538704420183216532608252538248713711246307900524500214451242775212773
  ( 118 digits)
SNFS difficulty: 165 digits.
Divisors found:

Tue Nov 06 10:24:21 2007  prp56 factor: 44521045988937219971985542168110282187182538753337627749
Tue Nov 06 10:24:21 2007  prp63 factor: 110856890051938744122912238100452821884732080214861054731598977
Tue Nov 06 10:24:21 2007  elapsed time 01:29:30 (Msieve 1.29)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 64.39 hours.
Scaled time: 84.09 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_8_9_163_3
n: 4935464700192921827044022834990668957767855479530538704420183216532608252538248713711246307900524500214451242775212773

# n: 25641239683282826264048301029977258784524896461386415561816513169184004869328396388038224934470250706081392645243448898305618334648776412862933585172092747099

skew: 1.51
deg: 5
c5: 9
c0: -70
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3200000)
Primes: RFBsize:216816, AFBsize:217291, largePrimes:7651039 encountered
Relations: rels:7167373, finalFF:504847
Max relations in full relation-set: 28
Initial matrix: 434171 x 504847 with sparse part having weight 46676546.
Pruned matrix : 406046 x 408280 with weight 34115092.
Total sieving time: 64.06 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 64.39 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(2·10¹⁶⁶+1)/3 = (6)₁₆₅7_<166> = 132420593 · C158

C158 = P36 · P123

P36 = 472608263478122255214913213813840403_<36>

P123 = 106525087996081326022960925559747436760122308821013875848798824526842994763515192581889447596719018370039169071680038462873_<123>

Nov 6, 2007 (4th)

By matsuix / GMP-ECM

(19·10¹⁶⁵-1)/9 = 2(1)₁₆₅_<166> = 97 · 28030207 · 678175727 · 28933389748066579_<17> · C131

C131 = P40 · P92

P40 = 1004850910964957079601987123021515538751_<40>

P92 = 39379469642482560582795123873781476067047647244625665707647850841194751914774629866823998323_<92>

Nov 6, 2007 (3rd)

By Sinkiti Sibata / GGNFS

9·10¹³³+7 = 9(0)₁₃₂7_<134> = 5881 · 26930082287_<11> · 176964956297383872307_<21> · C100

C100 = P44 · P57

P44 = 25264976655443100325796147326226279933324489_<44>

P57 = 127100563245798676374051740186784449244832505678728530547_<57>

Number: 90007_133
N=3211192763298772886403404485557143401237610375947392799399813124253179761582114633674548555499665483
  ( 100 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=25264976655443100325796147326226279933324489 (pp44)
 r2=127100563245798676374051740186784449244832505678728530547 (pp57)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 8.81 hours.
Scaled time: 5.96 units (timescale=0.676).
Factorization parameters were as follows:
name: 90007_133
n: 3211192763298772886403404485557143401237610375947392799399813124253179761582114633674548555499665483
m: 100000000000000000000000000
c5: 9000
c0: 7
skew: 0.24
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1300001)
Primes: RFBsize:78498, AFBsize:63803, largePrimes:1571280 encountered
Relations: rels:1590409, finalFF:190659
Max relations in full relation-set: 28
Initial matrix: 142368 x 190659 with sparse part having weight 15771459.
Pruned matrix : 127262 x 128037 with weight 8863354.
Total sieving time: 8.34 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.32 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 8.81 hours.
 --------- CPU info (if available) ----------

9·10¹¹⁷+7 = 9(0)₁₁₆7_<118> = 47 · 443867 · C111

C111 = P41 · P71

P41 = 17471857037357853190634584935442902072067_<41>

P71 = 24691798610564857752888526692177153472802870226100236461016311059115929_<71>

Number: 90007_117
N=431411575319020471390006657639299562083696817558297724701797533850110074663442648073275160198696667283265655243
  ( 111 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=17471857037357853190634584935442902072067 (pp41)
 r2=24691798610564857752888526692177153472802870226100236461016311059115929 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.78 hours.
Scaled time: 1.88 units (timescale=0.676).
Factorization parameters were as follows:
name: 90007_117
n: 431411575319020471390006657639299562083696817558297724701797533850110074663442648073275160198696667283265655243
m: 100000000000000000000000
c5: 900
c0: 7
skew: 0.38
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:63823, largePrimes:2291621 encountered
Relations: rels:2546258, finalFF:364912
Max relations in full relation-set: 28
Initial matrix: 112985 x 364912 with sparse part having weight 33871287.
Pruned matrix : 74587 x 75215 with weight 6217223.
Total sieving time: 2.55 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.78 hours.
 --------- CPU info (if available) ----------

Nov 6, 2007 (2nd)

By JMB / GGNFS

9·10¹⁸⁴+7 = 9(0)₁₈₃7_<185> = 617 · 3725507 · 159746791 · 1198459567_<10> · 80746431532206891622049_<23> · 666062407088402900138543_<24> · C112

C112 = P53 · P60

P53 = 11636058351571852705216457129789359016330456971195199_<53>

P60 = 326792650541123463809952364790176505238645003791330917413293_<60>

Nov 6, 2007

By Torbjörn Granlund

(10⁸⁴³-1)/9 is divisible by 769166959867961874063651865987632601_<36>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 5, 2007 (5th)

By JMB / GMP-ECM, Msieve

9·10¹⁴⁷+7 = 9(0)₁₄₆7_<148> = 25951 · 1738969 · 197021917 · 92978880982634662097_<20> · C110

C110 = P30 · P40 · P41

P30 = 102931531869565976194616134711_<30>

P40 = 2005256885602141410291462050850625780121_<40>

P41 = 52744753108364828721861464937342277420987_<41>

9·10¹⁵¹+7 = 9(0)₁₅₀7_<152> = 269 · 21613 · 67791928153_<11> · 44970969250703_<14> · 383031576676808952277813_<24> · C98

C98 = P40 · P58

P40 = 6810025963958582438251862479127272552967_<40>

P58 = 1946621858651143417424307752923064400610721325684111628979_<58>

Nov 5, 2007 (4th)

By Sinkiti Sibata / GGNFS

9·10¹²⁰+7 = 9(0)₁₁₉7_<121> = 29 · 281 · 386471 · 142583653 · C104

C104 = P33 · P71

P33 = 266099299493114096677875328801409_<33>

P71 = 75319566589929176165358361692126958829966221213822132241587381268023129_<71>

Number: 90007_120
N=20042483907705114278411372506196732936640720090441885904393246630974136265348532459246920117086459788761
  ( 104 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=266099299493114096677875328801409 (pp33)
 r2=75319566589929176165358361692126958829966221213822132241587381268023129 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.09 hours.
Scaled time: 1.41 units (timescale=0.676).
Factorization parameters were as follows:
name: 90007_120
n: 20042483907705114278411372506196732936640720090441885904393246630974136265348532459246920117086459788761
m: 1000000000000000000000000
c5: 9
c0: 7
skew: 0.95
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63908, largePrimes:2006815 encountered
Relations: rels:1988282, finalFF:148363
Max relations in full relation-set: 28
Initial matrix: 113070 x 148363 with sparse part having weight 12012483.
Pruned matrix : 101019 x 101648 with weight 6176663.
Total sieving time: 1.81 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.09 hours.
 --------- CPU info (if available) ----------

9·10¹²⁶+7 = 9(0)₁₂₅7_<127> = 18386461 · 1742218293047_<13> · C108

C108 = P32 · P77

P32 = 13822662893206118250744627949841_<32>

P77 = 20325913755563927082639117313372686004914219990075373791674260136282142256981_<77>

Number: 90007_126
N=280958253839541308962636479299682207592405666050712699120756569825329538777009922534463258852005274600090021
  ( 108 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=13822662893206118250744627949841 (pp32)
 r2=20325913755563927082639117313372686004914219990075373791674260136282142256981 (pp77)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 3.97 hours.
Scaled time: 2.69 units (timescale=0.676).
Factorization parameters were as follows:
name: 90007_126
n: 280958253839541308962636479299682207592405666050712699120756569825329538777009922534463258852005274600090021
m: 10000000000000000000000000
c5: 90
c0: 7
skew: 0.6
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:49098, AFBsize:64083, largePrimes:2196928 encountered
Relations: rels:2262442, finalFF:171270
Max relations in full relation-set: 28
Initial matrix: 113248 x 171270 with sparse part having weight 16894508.
Pruned matrix : 103160 x 103790 with weight 7851326.
Total sieving time: 3.61 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.22 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.97 hours.
 --------- CPU info (if available) ----------

Nov 5, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

4·10¹⁶¹-3 = 3(9)₁₆₀7_<162> = 13 · 71 · 738953 · 17948851 · 743599950371757358081470341_<27> · C119

C119 = P43 · P77

P43 = 2846805213519635781879812334100609838888539_<43>

P77 = 15435038486874269067278126927452408807037060575563649377214970000125309743587_<77>

Number: n
N=43940548035309899548763925751595996999472868799993550808813202591598052489814547810338118021293899624001452203163049393
  ( 119 digits)
SNFS difficulty: 161 digits.
Divisors found:

Mon Nov 05 02:38:02 2007  prp43 factor: 2846805213519635781879812334100609838888539
Mon Nov 05 02:38:02 2007  prp77 factor: 15435038486874269067278126927452408807037060575563649377214970000125309743587
Mon Nov 05 02:38:02 2007  elapsed time 01:17:03 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 33.21 hours.
Scaled time: 43.87 units (timescale=1.321).
Factorization parameters were as follows:
name: KA_3_9_160_7
n: 43940548035309899548763925751595996999472868799993550808813202591598052489814547810338118021293899624001452203163049393
skew: 0.60
deg: 5
c5: 40
c0: -3
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:216816, AFBsize:215821, largePrimes:7042289 encountered
Relations: rels:6514886, finalFF:501112
Max relations in full relation-set: 28
Initial matrix: 432703 x 501112 with sparse part having weight 40819259.
Pruned matrix : 378693 x 380920 with weight 25477509.
Total sieving time: 33.00 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 33.21 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

9·10¹¹¹+7 = 9(0)₁₁₀7_<112> = 131 · 859 · C107

C107 = P33 · P35 · P40

P33 = 682916690512923260407060455419117_<33>

P35 = 51118310350528656363520883890560151_<35>

P40 = 2291046123805509364111583138403788910949_<40>

9·10¹²⁷+7 = 9(0)₁₂₆7_<128> = 344206321 · C120

C120 = P35 · P85

P35 = 33157853781215682395478284485540807_<35>

P85 = 7885645618034098004254139912968642957732499669205257892740457352566043261860258601681_<85>

9·10¹³⁵+7 = 9(0)₁₃₄7_<136> = 1002121 · 14760091 · C123

C123 = P54 · P70

P54 = 588447254183867044277609191468715934421424931568990421_<54>

P70 = 1034012456449314522976535796820781617144073180839915839118262268905897_<70>

Number: n
N=608461790789514535341427955241331643019831322889419400572308896788480722510373845551247628493647294880837405891288543412637
  ( 123 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=588447254183867044277609191468715934421424931568990421 (pp54)
 r2=1034012456449314522976535796820781617144073180839915839118262268905897 (pp70)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.84 hours.
Scaled time: 6.28 units (timescale=1.297).
Factorization parameters were as follows:
name: KA_9_0_134_7
n: 608461790789514535341427955241331643019831322889419400572308896788480722510373845551247628493647294880837405891288543412637
skew: 0.95
deg: 5
c5: 9
c0: 7
m: 1000000000000000000000000000
type: snfs
rlim: 2400000
alim: 2400000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 440001)
Primes: RFBsize:176302, AFBsize:176458, largePrimes:5339208 encountered
Relations: rels:4827042, finalFF:398527
Max relations in full relation-set: 48
Initial matrix: 352824 x 398527 with sparse part having weight 16282983.
Pruned matrix : 297861 x 299689 with weight 9125460.
Total sieving time: 3.68 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.99 hours.
Total square root time: 0.04 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,2400000,2400000,28,28,48,48,2.5,2.5,75000
total time: 4.84 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

9·10¹⁴³+7 = 9(0)₁₄₂7_<144> = 67 · 14449 · C138

C138 = P32 · P107

P32 = 16764671435106466291549252481783_<32>

P107 = 55454254267525152340965490394347806129765919513362592966669387843539324159605808600050322487693263291392363_<107>

Nov 5, 2007 (2nd)

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

9·10¹⁰⁸+7 = 9(0)₁₀₇7_<109> = 37871 · 3406331833_<10> · 88079868587_<11> · C84

C84 = P33 · P52

P33 = 144064331776620889004606685503461_<33>

P52 = 5498138252554114429604456503865744400402842973430807_<52>

Mon Nov  5 01:24:55 2007  
Mon Nov  5 01:24:55 2007  
Mon Nov  5 01:24:55 2007  Msieve v. 1.28
Mon Nov  5 01:24:55 2007  random seeds: 152d9442 e6816ec9
Mon Nov  5 01:24:55 2007  factoring 792085613369686554167223683559223742655367466905587896034275024581697823391242523027 (84 digits)
Mon Nov  5 01:24:55 2007  commencing quadratic sieve (84-digit input)
Mon Nov  5 01:24:55 2007  using multiplier of 43
Mon Nov  5 01:24:55 2007  using 32kb Intel Core sieve core
Mon Nov  5 01:24:55 2007  sieve interval: 12 blocks of size 32768
Mon Nov  5 01:24:55 2007  processing polynomials in batches of 17
Mon Nov  5 01:24:55 2007  using a sieve bound of 1401067 (53824 primes)
Mon Nov  5 01:24:55 2007  using large prime bound of 119090695 (26 bits)
Mon Nov  5 01:24:55 2007  using double large prime bound of 344017052465110 (41-49 bits)
Mon Nov  5 01:24:55 2007  using trial factoring cutoff of 49 bits
Mon Nov  5 01:24:55 2007  polynomial 'A' values have 11 factors
Mon Nov  5 01:43:23 2007  54205 relations (16445 full + 37760 combined from 563337 partial), need 53920
Mon Nov  5 01:43:23 2007  begin with 579782 relations
Mon Nov  5 01:43:24 2007  reduce to 124756 relations in 9 passes
Mon Nov  5 01:43:24 2007  attempting to read 124756 relations
Mon Nov  5 01:43:25 2007  recovered 124756 relations
Mon Nov  5 01:43:25 2007  recovered 99117 polynomials
Mon Nov  5 01:43:25 2007  attempting to build 54205 cycles
Mon Nov  5 01:43:25 2007  found 54205 cycles in 5 passes
Mon Nov  5 01:43:25 2007  distribution of cycle lengths:
Mon Nov  5 01:43:25 2007     length 1 : 16445
Mon Nov  5 01:43:25 2007     length 2 : 11224
Mon Nov  5 01:43:25 2007     length 3 : 9837
Mon Nov  5 01:43:25 2007     length 4 : 6662
Mon Nov  5 01:43:25 2007     length 5 : 4386
Mon Nov  5 01:43:25 2007     length 6 : 2611
Mon Nov  5 01:43:25 2007     length 7 : 1468
Mon Nov  5 01:43:25 2007     length 9+: 1572
Mon Nov  5 01:43:25 2007  largest cycle: 15 relations
Mon Nov  5 01:43:25 2007  matrix is 53824 x 54205 with weight 2718225 (avg 50.15/col)
Mon Nov  5 01:43:25 2007  filtering completed in 3 passes
Mon Nov  5 01:43:25 2007  matrix is 48768 x 48832 with weight 2453195 (avg 50.24/col)
Mon Nov  5 01:43:26 2007  saving the first 48 matrix rows for later
Mon Nov  5 01:43:26 2007  matrix is 48720 x 48832 with weight 1746320 (avg 35.76/col)
Mon Nov  5 01:43:26 2007  matrix includes 64 packed rows
Mon Nov  5 01:43:26 2007  commencing Lanczos iteration
Mon Nov  5 01:44:06 2007  lanczos halted after 771 iterations
Mon Nov  5 01:44:07 2007  recovered 17 nontrivial dependencies
Mon Nov  5 01:44:07 2007  prp33 factor: 144064331776620889004606685503461
Mon Nov  5 01:44:07 2007  prp52 factor: 5498138252554114429604456503865744400402842973430807
Mon Nov  5 01:44:07 2007  elapsed time 00:19:12

9·10¹³¹+7 = 9(0)₁₃₀7_<132> = 38921 · 632971 · 968437 · 83275116371_<11> · 274255609394142444443_<21> C85

C85 = P40 · P45

P40 = 2288057282169860293574275141471863042313_<40>

P45 = 721881101657780564083407600404226856588479089_<45>

Mon Nov  5 01:45:50 2007  
Mon Nov  5 01:45:50 2007  
Mon Nov  5 01:45:50 2007  Msieve v. 1.28
Mon Nov  5 01:45:50 2007  random seeds: 72177c0e 693b4483
Mon Nov  5 01:45:50 2007  factoring 1651705311508886027462420179604336574242886949428131140156014177945487040201122692857 (85 digits)
Mon Nov  5 01:45:50 2007  commencing quadratic sieve (84-digit input)
Mon Nov  5 01:45:50 2007  using multiplier of 5
Mon Nov  5 01:45:50 2007  using 32kb Intel Core sieve core
Mon Nov  5 01:45:50 2007  sieve interval: 12 blocks of size 32768
Mon Nov  5 01:45:50 2007  processing polynomials in batches of 17
Mon Nov  5 01:45:50 2007  using a sieve bound of 1413031 (54118 primes)
Mon Nov  5 01:45:50 2007  using large prime bound of 118694604 (26 bits)
Mon Nov  5 01:45:50 2007  using double large prime bound of 341960341070040 (41-49 bits)
Mon Nov  5 01:45:50 2007  using trial factoring cutoff of 49 bits
Mon Nov  5 01:45:50 2007  polynomial 'A' values have 11 factors
Mon Nov  5 02:05:58 2007  54588 relations (16316 full + 38272 combined from 571175 partial), need 54214
Mon Nov  5 02:05:58 2007  begin with 587491 relations
Mon Nov  5 02:05:58 2007  reduce to 126754 relations in 10 passes
Mon Nov  5 02:05:58 2007  attempting to read 126754 relations
Mon Nov  5 02:05:59 2007  recovered 126754 relations
Mon Nov  5 02:05:59 2007  recovered 102596 polynomials
Mon Nov  5 02:05:59 2007  attempting to build 54588 cycles
Mon Nov  5 02:05:59 2007  found 54588 cycles in 5 passes
Mon Nov  5 02:05:59 2007  distribution of cycle lengths:
Mon Nov  5 02:05:59 2007     length 1 : 16316
Mon Nov  5 02:05:59 2007     length 2 : 11199
Mon Nov  5 02:05:59 2007     length 3 : 9830
Mon Nov  5 02:05:59 2007     length 4 : 6838
Mon Nov  5 02:05:59 2007     length 5 : 4545
Mon Nov  5 02:05:59 2007     length 6 : 2670
Mon Nov  5 02:05:59 2007     length 7 : 1519
Mon Nov  5 02:05:59 2007     length 9+: 1671
Mon Nov  5 02:05:59 2007  largest cycle: 18 relations
Mon Nov  5 02:05:59 2007  matrix is 54118 x 54588 with weight 2840617 (avg 52.04/col)
Mon Nov  5 02:06:00 2007  filtering completed in 3 passes
Mon Nov  5 02:06:00 2007  matrix is 49044 x 49108 with weight 2553112 (avg 51.99/col)
Mon Nov  5 02:06:00 2007  saving the first 48 matrix rows for later
Mon Nov  5 02:06:00 2007  matrix is 48996 x 49108 with weight 1908309 (avg 38.86/col)
Mon Nov  5 02:06:00 2007  matrix includes 64 packed rows
Mon Nov  5 02:06:00 2007  commencing Lanczos iteration
Mon Nov  5 02:06:41 2007  lanczos halted after 776 iterations
Mon Nov  5 02:06:42 2007  recovered 16 nontrivial dependencies
Mon Nov  5 02:06:42 2007  prp40 factor: 2288057282169860293574275141471863042313
Mon Nov  5 02:06:42 2007  prp45 factor: 721881101657780564083407600404226856588479089
Mon Nov  5 02:06:42 2007  elapsed time 00:20:52

9·10¹¹²+7 = 9(0)₁₁₁7_<113> = 1706363 · 6132851 · 14021233 · C93

C93 = P45 · P49

P45 = 366287276724937330096345104351579811913585089_<45>

P49 = 1674559682769946750885495255184227109771029382647_<49>

Number: 90007_112
N=613369905915178755561126474140880398319161319784569225022227103519115609390857587884174550583
  ( 93 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=366287276724937330096345104351579811913585089 (pp45)
 r2=1674559682769946750885495255184227109771029382647 (pp49)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.89 hours.
Scaled time: 1.90 units (timescale=2.119).
Factorization parameters were as follows:
n: 613369905915178755561126474140880398319161319784569225022227103519115609390857587884174550583
m: 10000000000000000000000
c5: 900
c0: 7
skew: 0.38
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 360001)
Primes: RFBsize:30757, AFBsize:30859, largePrimes:1047627 encountered
Relations: rels:958703, finalFF:81871
Max relations in full relation-set: 28
Initial matrix: 61680 x 81871 with sparse part having weight 4265106.
Pruned matrix : 57019 x 57391 with weight 2165245.
Total sieving time: 0.86 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,112,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.89 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹¹⁴+7 = 9(0)₁₁₃7_<115> = 653 · 4287299 · 249763385813_<12> · C95

C95 = P42 · P54

P42 = 115630510169949718409527011290812428381853_<42>

P54 = 111312603505914666012718121697883345483669372301240129_<54>

Number: 90007_114
N=12871133131734246468791789551870388883140990287398533490691419410177257253759609146868658979037
  ( 95 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=115630510169949718409527011290812428381853 (pp42)
 r2=111312603505914666012718121697883345483669372301240129 (pp54)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.90 hours.
Scaled time: 1.93 units (timescale=2.145).
Factorization parameters were as follows:
n: 12871133131734246468791789551870388883140990287398533490691419410177257253759609146868658979037
m: 100000000000000000000000
c5: 9
c0: 70
skew: 1.51
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 420001)
Primes: RFBsize:49098, AFBsize:49341, largePrimes:1898932 encountered
Relations: rels:2001615, finalFF:245554
Max relations in full relation-set: 28
Initial matrix: 98503 x 245554 with sparse part having weight 19808415.
Pruned matrix : 69060 x 69616 with weight 3831506.
Total sieving time: 0.85 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.90 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹⁴⁶+7 = 9(0)₁₄₅7_<147> = 23 · 4271 · 437543 · 5421833 · 8849681 · C123

C123 = P35 · P89

P35 = 23988971368700909013664451648647553_<35>

P89 = 18191938657561789126660465345836496511300044062263632583171015546703249344891910371448337_<89>

9·10¹³²+7 = 9(0)₁₃₁7_<133> = 491 · 85117573 · C123

C123 = P51 · P73

P51 = 139221663158686554389864242499707408798312738177711_<51>

P73 = 1546802865177850881667388439251649501422697254868710734255734319160698559_<73>

Number: 90007_132
N=215348467468682007507192912246188645535589219763134333352082775267400780424803384796810560313123800212289002220311443618449
  ( 123 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=139221663158686554389864242499707408798312738177711 (pp51)
 r2=1546802865177850881667388439251649501422697254868710734255734319160698559 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.77 hours.
Scaled time: 8.02 units (timescale=2.125).
Factorization parameters were as follows:
n: 215348467468682007507192912246188645535589219763134333352082775267400780424803384796810560313123800212289002220311443618449
m: 100000000000000000000000000
c5: 900
c0: 7
skew: 0.38
type: snfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [600000, 1350001)
Primes: RFBsize:92938, AFBsize:92634, largePrimes:1721351 encountered
Relations: rels:1789708, finalFF:239139
Max relations in full relation-set: 28
Initial matrix: 185636 x 239139 with sparse part having weight 15179814.
Pruned matrix : 164618 x 165610 with weight 8472390.
Total sieving time: 3.64 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1200000,1200000,25,25,46,46,2.2,2.2,50000
total time: 3.77 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹⁴⁰+7 = 9(0)₁₃₉7_<141> = 151 · 160910339138441_<15> · C125

C125 = P33 · P46 · P48

P33 = 119266962910373522768317901849023_<33>

P46 = 1073502048919627741496999269090973341811523617_<46>

P48 = 289306754986378993892936910082750693641415226647_<48>

Number: 90007_140
N=37040906958342008436196962352631290237631464821269784853671653578621103961679404648708146669704204687383872089120977255061577
  ( 125 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=119266962910373522768317901849023 (pp33)
 r2=1073502048919627741496999269090973341811523617 (pp46)
 r3=289306754986378993892936910082750693641415226647 (pp48)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.15 hours.
Scaled time: 13.17 units (timescale=2.142).
Factorization parameters were as follows:
n: 37040906958342008436196962352631290237631464821269784853671653578621103961679404648708146669704204687383872089120977255061577
m: 10000000000000000000000000000
c5: 9
c0: 7
skew: 0.95
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:113992, largePrimes:3368728 encountered
Relations: rels:3487641, finalFF:407793
Max relations in full relation-set: 28
Initial matrix: 228211 x 407793 with sparse part having weight 35263251.
Pruned matrix : 168183 x 169388 with weight 13199446.
Total sieving time: 5.98 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.15 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 5, 2007

The factor table of 900...007 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Nov 4, 2007 (3rd)

By Sinkiti Sibata / PFGW

9·10¹⁰⁸⁵⁵-7 is PRP. It is the only PRP of the form 9·10ⁿ-7 (10001≤n≤20000).

Nov 4, 2007 (2nd)

By Jo Yeong Uk / GGNFS

9·10¹⁶⁰+1 = 9(0)₁₅₉1_<161> = 196668336511615844317373683402996797341833_<42> · C120

C120 = P52 · P69

P52 = 1739150909232723432175836807853304310816643860207313_<52>

P69 = 263130261241924464291801141224892605010946153371020043305094966475369_<69>

Number: 90001_160
N=457623233085536978487969224809644797039838287759370817200669676684400841774026444495529209155367065867115087869248173497
  ( 120 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=1739150909232723432175836807853304310816643860207313 (pp52)
 r2=263130261241924464291801141224892605010946153371020043305094966475369 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 27.70 hours.
Scaled time: 59.42 units (timescale=2.145).
Factorization parameters were as follows:
n: 457623233085536978487969224809644797039838287759370817200669676684400841774026444495529209155367065867115087869248173497
m: 100000000000000000000000000000000
c5: 9
c0: 1
skew: 0.64
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:282992, largePrimes:5669639 encountered
Relations: rels:5735722, finalFF:684749
Max relations in full relation-set: 28
Initial matrix: 566202 x 684749 with sparse part having weight 43062449.
Pruned matrix : 470596 x 473491 with weight 28108258.
Total sieving time: 26.39 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.17 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 27.70 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 4, 2007

By Sinkiti Sibata / GGNFS

9·10¹⁶¹-7 = 8(9)₁₆₀3_<162> = 53 · 710382599 · 3193863019_<10> · 14169121763_<11> · C132

C132 = P39 · P93

P39 = 637003641965194182950788890954509239897_<39>

P93 = 829226536019218470577471928756725407087718463007725782007729866451066972588969963334914455291_<93>

Number: 89993_161
N=528220323458424440646483477713402912362372432295144177626701835540702260229176792484870656015751898878654984062057672951330199945027
  ( 132 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=637003641965194182950788890954509239897 (pp39)
 r2=829226536019218470577471928756725407087718463007725782007729866451066972588969963334914455291 (pp93)
Version: GGNFS-0.77.1-20060513-k8
Total time: 72.73 hours.
Scaled time: 146.18 units (timescale=2.010).
Factorization parameters were as follows:
name: 89993_161
n: 528220323458424440646483477713402912362372432295144177626701835540702260229176792484870656015751898878654984062057672951330199945027
m: 100000000000000000000000000000000
c5: 90
c0: -7
skew: 0.6
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4550001)
Primes: RFBsize:315948, AFBsize:316641, largePrimes:5828768 encountered
Relations: rels:5947621, finalFF:747210
Max relations in full relation-set: 28
Initial matrix: 632656 x 747210 with sparse part having weight 48277826.
Pruned matrix : 546815 x 550042 with weight 33888020.
Total sieving time: 68.82 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 3.49 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 72.73 hours.
 --------- CPU info (if available) ----------

Nov 3, 2007 (2nd)

By suberi / GGNFS

3·10¹⁵⁸-7 = 2(9)₁₅₇3_<159> = 17 · 41 · 47 · 3041 · 841123744137979613_<18> · C133

C133 = P51 · P83

P51 = 263885431718243596975433066048441779693678318105769_<51>

P83 = 13567470651611743221749122292261888185172901056388384006891037144978168857382893251_<83>

Number: 29993_158
N=3580257850225164627404836853606844290357386870515998826943797062408011849614535981097388373034324355416498626742076743203763054265019
  ( 133 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=263885431718243596975433066048441779693678318105769 (pp51)
 r2=13567470651611743221749122292261888185172901056388384006891037144978168857382893251 (pp83)
Version: GGNFS-0.77.1-20060722-k8
Total time: 49.54 hours.
Scaled time: 72.72 units (timescale=1.468).
Factorization parameters were as follows:
n: 3580257850225164627404836853606844290357386870515998826943797062408011849614535981097388373034324355416498626742076743203763054265019
m: 10000000000000000000000000000000
c5: 3000
c0: -7
skew: 0.3
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3300001)
Primes: RFBsize:283146, AFBsize:283037, largePrimes:5584207 encountered
Relations: rels:5598336, finalFF:647691
Max relations in full relation-set: 32
Initial matrix: 566250 x 647691 with sparse part having weight 39597994.
Pruned matrix : 499206 x 502101 with weight 26364073.
Total sieving time: 45.55 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.63 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 49.54 hours.
 --------- CPU info (if available) ----------

Nov 3, 2007

By Jo Yeong Uk / GGNFS

(8·10¹⁶⁰+1)/9 = (8)₁₅₉9_<160> = 3 · 825027643337_<12> · 4496569364490716593_<19> · C129

C129 = P45 · P85

P45 = 584055110117804933562252574038305701305028939_<45>

P85 = 1367485081849265048121060885327005302341443223828135540212293179914394095612984131937_<85>

Number: 88889_160
N=798686650063927990314125701018237249713184766388387794727385204591609598499027731309396698824991490472673979526416377225579124843
  ( 129 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=584055110117804933562252574038305701305028939 (pp45)
 r2=1367485081849265048121060885327005302341443223828135540212293179914394095612984131937 (pp85)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 27.65 hours.
Scaled time: 59.31 units (timescale=2.145).
Factorization parameters were as follows:
n: 798686650063927990314125701018237249713184766388387794727385204591609598499027731309396698824991490472673979526416377225579124843
m: 200000000000000000000000000000000
c5: 1
c0: 4
skew: 1.32
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:282707, largePrimes:5654427 encountered
Relations: rels:5714441, finalFF:680834
Max relations in full relation-set: 28
Initial matrix: 565917 x 680834 with sparse part having weight 42328056.
Pruned matrix : 473624 x 476517 with weight 27571459.
Total sieving time: 26.35 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.16 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 27.65 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 2, 2007 (6th)

By Sinkiti Sibata / GGNFS

9·10¹⁵⁹-7 = 8(9)₁₅₈3_<160> = 18104666690449826252281753693_<29> · C132

C132 = P56 · P77

P56 = 22392329597836817510288640646341074175512979619336814351_<56>

P77 = 22199985850784836127380389132731731977501124190563051137404670084573603137251_<77>

Number: 89993_159
N=497109400238087848582031566032851660055020853947195342757531373490526734611539481118145584113295135923191327086633995939773759489101
  ( 132 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=22392329597836817510288640646341074175512979619336814351 (pp56)
 r2=22199985850784836127380389132731731977501124190563051137404670084573603137251 (pp77)
Version: GGNFS-0.77.1-20060513-k8
Total time: 59.23 hours.
Scaled time: 118.63 units (timescale=2.003).
Factorization parameters were as follows:
name: 89993_159
n: 497109400238087848582031566032851660055020853947195342757531373490526734611539481118145584113295135923191327086633995939773759489101
m: 100000000000000000000000000000000
c5: 9
c0: -70
skew: 1.51
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3900001)
Primes: RFBsize:283146, AFBsize:284062, largePrimes:5877832 encountered
Relations: rels:6049555, finalFF:771663
Max relations in full relation-set: 28
Initial matrix: 567272 x 771663 with sparse part having weight 50943228.
Pruned matrix : 418651 x 421551 with weight 36252838.
Total sieving time: 56.43 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 2.38 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 59.23 hours.
 --------- CPU info (if available) ----------

Nov 2, 2007 (5th)

By Robert Backstrom / GGNFS, Msieve

6·10¹⁶⁷+7 = 6(0)₁₆₆7_<168> = 157 · C166

C166 = P47 · P120

P47 = 30141491732912660764138607233343720887304110987_<47>

P120 = 126790541251891655395868197515952259522258968043055404184000880238481113593670765322134091338218303304135490412872342073_<120>

Number: n
N=3821656050955414012738853503184713375796178343949044585987261146496815286624203821656050955414012738853503184713375796178343949044585987261146496815286624203821656051
  ( 166 digits)
SNFS difficulty: 168 digits.
Divisors found:

Fri Nov 02 11:53:15 2007  prp47 factor: 30141491732912660764138607233343720887304110987
Fri Nov 02 11:53:15 2007  prp120 factor: 126790541251891655395868197515952259522258968043055404184000880238481113593670765322134091338218303304135490412872342073
Fri Nov 02 11:53:15 2007  elapsed time 05:00:20 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 142.75 hours.
Scaled time: 170.45 units (timescale=1.194).
Factorization parameters were as follows:
name: KA_6_0_166_7
n: 3821656050955414012738853503184713375796178343949044585987261146496815286624203821656050955414012738853503184713375796178343949044585987261146496815286624203821656051
type: snfs
skew: 0.82
deg: 5
c5: 75
c0: 28
m: 2000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5000213)
Primes: RFBsize:250150, AFBsize:250046, largePrimes:8066210 encountered
Relations: rels:7523828, finalFF:472612
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 142.32 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.6,2.6,100000
total time: 142.75 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

3·10¹⁶⁰-1 = 2(9)₁₆₀_<161> = 3119 · 62171 · 716003 · 80479894854409_<14> · C133

C133 = P59 · P75

P59 = 22773127470380768369771978355584433053642892841637684786821_<59>

P75 = 117894381311324651726376382743763178993218466198694259251340381195966953253_<75>

Number: n
N=2684823773644472499695314004905933113030245860446596390581560505765323424678107700978354714731235290256104741769394425383100177478713
  ( 133 digits)
SNFS difficulty: 160 digits.
Divisors found:

Fri Nov 02 21:39:00 2007  prp59 factor: 22773127470380768369771978355584433053642892841637684786821
Fri Nov 02 21:39:00 2007  prp75 factor: 117894381311324651726376382743763178993218466198694259251340381195966953253
Fri Nov 02 21:39:00 2007  elapsed time 01:07:33 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 28.18 hours.
Scaled time: 37.37 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_2_9_160
n: 2684823773644472499695314004905933113030245860446596390581560505765323424678107700978354714731235290256104741769394425383100177478713
skew: 0.95
deg: 5
c5: 3
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1400000)
Primes: RFBsize:216816, AFBsize:216846, largePrimes:7002342 encountered
Relations: rels:6502743, finalFF:523807
Max relations in full relation-set: 28
Initial matrix: 433727 x 523807 with sparse part having weight 39790411.
Pruned matrix : 360363 x 362595 with weight 22732739.
Total sieving time: 27.98 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 28.18 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 2, 2007 (4th)

By matsui / GMP-ECM

(5·10¹⁶⁶+7)/3 = 1(6)₁₆₅9_<167> = 38609 · 75787 · C157

C157 = P36 · C122

P36 = 156630091583671031730558418871436461_<36>

C122 = [36365559895016016644306948036519971789440001831406469011965021801985852343260659678682774063764231328439857717070493184563_<122>]

Nov 2, 2007 (3rd)

By Jo Yeong Uk / GGNFS, GMP-ECM

2·10¹⁶⁰-3 = 1(9)₁₅₉7_<161> = 15073 · 1023361 · 2269267633_<10> · 51894756337_<11> · C131

C131 = P49 · P82

P49 = 1244702530203678363132386159041482385491409469399_<49>

P82 = 8845587159376599603050287573778844195307606321990000300773593282138846596884883531_<82>

Number: 19997_160
N=11010124718413221462280367876462346322453582439931705506709272261862462870251427913507922600641649990825847478334158897252623567869
  ( 131 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=1244702530203678363132386159041482385491409469399 (pp49)
 r2=8845587159376599603050287573778844195307606321990000300773593282138846596884883531 (pp82)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 25.76 hours.
Scaled time: 54.81 units (timescale=2.128).
Factorization parameters were as follows:
n: 11010124718413221462280367876462346322453582439931705506709272261862462870251427913507922600641649990825847478334158897252623567869
m: 100000000000000000000000000000000
c5: 2
c0: -3
skew: 1.08
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3500001)
Primes: RFBsize:283146, AFBsize:283187, largePrimes:5679964 encountered
Relations: rels:5762216, finalFF:699117
Max relations in full relation-set: 28
Initial matrix: 566398 x 699117 with sparse part having weight 43937665.
Pruned matrix : 457329 x 460224 with weight 27759676.
Total sieving time: 24.56 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 1.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 25.76 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

(7·10¹⁶¹+11)/9 = (7)₁₆₀9_<161> = 13 · 1181 · 188695951 · 13069034534977941833_<20> · C130

C130 = P34 · P96

P34 = 6012553105775282745767182262190667_<34>

P96 = 341662463922226905047290637587563518265187529653427259070665961826179127070588201628147242777463_<96>

Nov 2, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

9·10¹⁶⁰-7 = 8(9)₁₅₉3_<161> = 619 · 31247 · 201823 · C149

C149 = P44 · P44 · P61

P44 = 44832592826645189491277561661890927333335849_<44>

P44 = 58928729369518409469720209631759471783420671_<44>

P61 = 8726738097012509717654043907256703264726239277870739541104253_<61>

Number: n
N=23055411367586615082003261341128857444920360386517972549304906315835176876756217183769848071125522085298104115328957218756792728520856138498005089787
  ( 149 digits)
SNFS difficulty: 160 digits.
Divisors found:

Fri Nov 02 05:43:45 2007  prp44 factor: 44832592826645189491277561661890927333335849
Fri Nov 02 05:43:45 2007  prp44 factor: 58928729369518409469720209631759471783420671
Fri Nov 02 05:43:45 2007  prp61 factor: 8726738097012509717654043907256703264726239277870739541104253
Fri Nov 02 05:43:45 2007  elapsed time 01:21:01 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 35.14 hours.
Scaled time: 50.08 units (timescale=1.425).
Factorization parameters were as follows:
name: KA_8_9_159_3
n: 23055411367586615082003261341128857444920360386517972549304906315835176876756217183769848071125522085298104115328957218756792728520856138498005089787
skew: 0.95
deg: 5
c5: 9
c0: -7
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1800179)
Primes: RFBsize:203362, AFBsize:203517, largePrimes:7126574 encountered
Relations: rels:6588475, finalFF:452122
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 34.95 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 35.14 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Nov 2, 2007

By Jo Yeong Uk / GGNFS, GMP-ECM

(4·10¹⁹⁰-31)/9 = (4)₁₈₉1_<190> = C190

C190 = P89 · P101

P89 = 56633002372177889917787382603024134082794402810604184699423290284260806567232850743196879_<89>

P101 = 78477994425170505252478126430623716163551522942533133685072386085630247384183834818134344179505629079_<101>

Number: 44441_190
N=4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441
  ( 190 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=56633002372177889917787382603024134082794402810604184699423290284260806567232850743196879 (pp89)
 r2=78477994425170505252478126430623716163551522942533133685072386085630247384183834818134344179505629079 (pp101)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 506.30 hours.
Scaled time: 1086.00 units (timescale=2.145).
Factorization parameters were as follows:
n: 4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441
m: 100000000000000000000000000000000000000
c5: 4
c0: -31
skew: 1.51
type: snfs
Factor base limits: 13000000/13000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 51/51
Sieved algebraic special-q in [6500000, 14600001)
Primes: RFBsize:849252, AFBsize:849764, largePrimes:12825340 encountered
Relations: rels:13582667, finalFF:1936815
Max relations in full relation-set: 28
Initial matrix: 1699080 x 1936815 with sparse part having weight 144996551.
Pruned matrix : 1492822 x 1501381 with weight 111522440.
Total sieving time: 485.19 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 20.54 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,13000000,13000000,28,28,51,51,2.6,2.6,100000
total time: 506.30 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific ro2utine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

P89 is the biggest factor which was found in our tables so far. Congratulations!

I was surprized that two P89s had been found continuously from the same near-repdigit sequence.

(5·10¹⁶⁰-23)/9 = (5)₁₅₉3_<160> = 3 · 47 · 36583 · 391183217 · 13416202562095777_<17> · C129

C129 = P36 · P93

P36 = 557467334877805199211719058269920279_<36>

P93 = 368128820889923730632432710032916764064373628070399222255862045362828218454119475627959989141_<93>

Nov 1, 2007 (5th)

By matsui / Msieve

(5·10¹⁷³+7)/3 = 1(6)₁₇₂9_<174> = 79 · 141073 · 154543 · 165887 · 63473899 · 133660440077_<12> · 1862230537518772176753410725489813_<34> · C104

C104 = P43 · P61

P43 = 5917523119420196943705339866721088586618339_<43>

P61 = 6239425363430810864236794554166498878991514867897846161057107_<61>

Nov 1, 2007 (4th)

By Robert Backstrom / GMP-ECM, GGNFS

9·10¹⁵⁴-7 = 8(9)₁₅₃3_<155> = 31 · 59 · 3116155837_<10> · C143

C143 = P34 · P47 · P63

P34 = 3792154237087773328323098510929643_<34>

P47 = 13515254733080096925398066307959108515533417271_<47>

P63 = 308105468835983009135964692963347948427570307230290780677274397_<63>

prp34 factors: 3792154237087773328323098510929643
prp47 factor:  13515254733080096925398066307959108515533417271 (pp47)
prp63 factor:  308105468835983009135964692963347948427570307230290780677274397 (pp63)

GMP-ECM 6.0.1 [powered by GMP 4.1.4] [ECM]
Input number is 15791000075873905536643005674835499743042023035608132996665252198463383016350684288596800392658129485982981128379660782197197761083905185830441 (143 digits)
Using B1=1030000, B2=875663603, polynomial Dickson(3), sigma=1277051764
Step 1 took 15188ms
Step 2 took 8703ms
********** Factor found in step 2: 3792154237087773328323098510929643
Found probable prime factor of 34 digits: 3792154237087773328323098510929643
Composite cofactor 4164123895973381665684521031919367758331000757893159498628020621881612855280700051156426496919521695565910587 has 109 digits

Number: n
N=4164123895973381665684521031919367758331000757893159498628020621881612855280700051156426496919521695565910587
  ( 109 digits)
Divisors found:
 r1=13515254733080096925398066307959108515533417271 (pp47)
 r2=308105468835983009135964692963347948427570307230290780677274397 (pp63)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 15.47 hours.
Scaled time: 20.19 units (timescale=1.305).
Factorization parameters were as follows:
name: KA_8_9_153_3
n: 4164123895973381665684521031919367758331000757893159498628020621881612855280700051156426496919521695565910587
skew: 13433.88
# norm 5.58e+14
c5: 62340
c4: -1730045296
c3: -31252455735533
c2: 59780409705258362
c1: 594864083607926757768
c0: 4226538018654160771217904
# alpha -5.88
Y1: 54837503413
Y0: -582038343536829418255
# Murphy_E 1.28e-09
# M 775188593700025757374907442535572328332511394125380113220895912641476417303724565829169862375221504000062036
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:230209, AFBsize:230238, largePrimes:6848426 encountered
Relations: rels:6590432, finalFF:586768
Max relations in full relation-set: 28
Initial matrix: 460530 x 586768 with sparse part having weight 36842357.
Pruned matrix : 341921 x 344287 with weight 16084571.
Total sieving time: 13.36 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 1.49 hours.
Total square root time: 0.31 hours, sqrts: 2.
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: 15.47 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 1, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(85·10²⁹⁶⁰-31)/9 is prime.

Nov 1, 2007 (2nd)

By Sinkiti Sibata / GGNFS

9·10¹⁵²-7 = 8(9)₁₅₁3_<153> = 27487 · 2387449 · 5618769997_<10> · C133

C133 = P44 · P89

P44 = 75820868126956676281536230696860571433120407_<44>

P89 = 32192229601894986931087007258474395061004652068487123300133829248970334366365297350334109_<89>

Number: 89993_152
N=2440842795357990826312342895539487490184328387705207959270387795925092533977126288036775251949678234292518146093908937568969876062363
  ( 133 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=75820868126956676281536230696860571433120407 (pp44)
 r2=32192229601894986931087007258474395061004652068487123300133829248970334366365297350334109 (pp89)
Version: GGNFS-0.77.1-20060513-k8
Total time: 37.53 hours.
Scaled time: 72.25 units (timescale=1.925).
Factorization parameters were as follows:
name: 89993_152
n: 2440842795357990826312342895539487490184328387705207959270387795925092533977126288036775251949678234292518146093908937568969876062363
m: 1000000000000000000000000000000
c5: 900
c0: -7
skew: 0.38
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2500001)
Primes: RFBsize:176302, AFBsize:175703, largePrimes:5892665 encountered
Relations: rels:5985872, finalFF:583936
Max relations in full relation-set: 28
Initial matrix: 352069 x 583936 with sparse part having weight 61282735.
Pruned matrix : 277434 x 279258 with weight 33988858.
Total sieving time: 35.96 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.27 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 37.53 hours.
 --------- CPU info (if available) ----------

Nov 1, 2007

By Yousuke Koide

(10¹²⁶⁵-1)/9 is divisible by 7973059286225484515918622191263721_<34>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

October 2007

Oct 31, 2007 (5th)

By Robert Backstrom / GGNFS, Msieve

9·10¹⁵⁷-7 = 8(9)₁₅₆3_<158> = 23 · 64057787 · C149

C149 = P73 · P76

P73 = 8547312778918799179387612593474476828728823510172134540253167241939987973_<73>

P76 = 7146824962215572093535969278319248184705372720242480746696150650147917691641_<76>

Number: n
N=61086148328241023456170774434462215920080438294417426293679106525704877121001087183439811795314562241854476205041713894715231040563014033617462633693
  ( 149 digits)
SNFS difficulty: 157 digits.
Divisors found:

Thu Nov 01 00:37:53 2007  prp73 factor: 8547312778918799179387612593474476828728823510172134540253167241939987973
Thu Nov 01 00:37:53 2007  prp76 factor: 7146824962215572093535969278319248184705372720242480746696150650147917691641
Thu Nov 01 00:37:53 2007  elapsed time 01:22:09 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 37.30 hours.
Scaled time: 49.46 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_8_9_156_3
n: 61086148328241023456170774434462215920080438294417426293679106525704877121001087183439811795314562241854476205041713894715231040563014033617462633693
skew: 0.38
deg: 5
c5: 900
c0: -7
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1900000)
Primes: RFBsize:216816, AFBsize:216321, largePrimes:7229719 encountered
Relations: rels:6721021, finalFF:520151
Max relations in full relation-set: 28
Initial matrix: 433201 x 520151 with sparse part having weight 46044664.
Pruned matrix : 368182 x 370412 with weight 28093041.
Total sieving time: 37.05 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 37.30 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 31, 2007 (4th)

By Jo Yeong Uk / GGNFS, Msieve

9·10¹⁵⁰-7 = 8(9)₁₄₉3_<151> = 859 · 352963277 · 18139634852382632412042997_<26> · C115

C115 = P41 · P74

P41 = 55504280314514112186236174411054189440309_<41>

P74 = 29482533885016913889484106257918099812603456906714576053691076225565509087_<74>

Number: 89993_150
N=1636406825136139563104533988910623283706494518193323744963557735997068458160508983884811204786788623931439183587883
  ( 115 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=55504280314514112186236174411054189440309 (pp41)
 r2=29482533885016913889484106257918099812603456906714576053691076225565509087 (pp74)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 12.99 hours.
Scaled time: 27.87 units (timescale=2.146).
Factorization parameters were as follows:
n: 1636406825136139563104533988910623283706494518193323744963557735997068458160508983884811204786788623931439183587883
m: 1000000000000000000000000000000
c5: 9
c0: -7
skew: 0.95
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:176458, largePrimes:5472027 encountered
Relations: rels:5419693, finalFF:513988
Max relations in full relation-set: 28
Initial matrix: 352824 x 513988 with sparse part having weight 44556647.
Pruned matrix : 279117 x 280945 with weight 22936374.
Total sieving time: 12.50 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.38 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 12.99 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹⁵³-7 = 8(9)₁₅₂3_<154> = 235483 · 15771126802857831503737789_<26> · 2469438507084583723424410362013_<31> · C93

C93 = P35 · P59

P35 = 29916323560200857306637278521712341_<35>

P59 = 32803016936544339453376593485631195739277624165372655627383_<59>

Wed Oct 31 08:32:17 2007  
Wed Oct 31 08:32:17 2007  
Wed Oct 31 08:32:17 2007  Msieve v. 1.28
Wed Oct 31 08:32:17 2007  random seeds: 78b84c31 5c438943
Wed Oct 31 08:32:17 2007  factoring 981345668424409173005139032359911659122268552148212314853518231679477196677844688222808633603 (93 digits)
Wed Oct 31 08:32:17 2007  commencing quadratic sieve (93-digit input)
Wed Oct 31 08:32:18 2007  using multiplier of 3
Wed Oct 31 08:32:18 2007  using 32kb Intel Core sieve core
Wed Oct 31 08:32:18 2007  sieve interval: 36 blocks of size 32768
Wed Oct 31 08:32:18 2007  processing polynomials in batches of 6
Wed Oct 31 08:32:18 2007  using a sieve bound of 1953863 (72941 primes)
Wed Oct 31 08:32:18 2007  using large prime bound of 244232875 (27 bits)
Wed Oct 31 08:32:18 2007  using double large prime bound of 1253277823035125 (42-51 bits)
Wed Oct 31 08:32:18 2007  using trial factoring cutoff of 51 bits
Wed Oct 31 08:32:18 2007  polynomial 'A' values have 12 factors
Wed Oct 31 09:57:24 2007  73505 relations (19333 full + 54172 combined from 979953 partial), need 73037
Wed Oct 31 09:57:24 2007  begin with 999286 relations
Wed Oct 31 09:57:24 2007  reduce to 184209 relations in 11 passes
Wed Oct 31 09:57:24 2007  attempting to read 184209 relations
Wed Oct 31 09:57:26 2007  recovered 184209 relations
Wed Oct 31 09:57:26 2007  recovered 160186 polynomials
Wed Oct 31 09:57:26 2007  attempting to build 73505 cycles
Wed Oct 31 09:57:26 2007  found 73505 cycles in 6 passes
Wed Oct 31 09:57:26 2007  distribution of cycle lengths:
Wed Oct 31 09:57:26 2007     length 1 : 19333
Wed Oct 31 09:57:26 2007     length 2 : 13661
Wed Oct 31 09:57:26 2007     length 3 : 12554
Wed Oct 31 09:57:26 2007     length 4 : 9800
Wed Oct 31 09:57:26 2007     length 5 : 7114
Wed Oct 31 09:57:26 2007     length 6 : 4591
Wed Oct 31 09:57:26 2007     length 7 : 2825
Wed Oct 31 09:57:26 2007     length 9+: 3627
Wed Oct 31 09:57:26 2007  largest cycle: 18 relations
Wed Oct 31 09:57:26 2007  matrix is 72941 x 73505 with weight 4546757 (avg 61.86/col)
Wed Oct 31 09:57:27 2007  filtering completed in 3 passes
Wed Oct 31 09:57:27 2007  matrix is 68316 x 68380 with weight 4231949 (avg 61.89/col)
Wed Oct 31 09:57:28 2007  saving the first 48 matrix rows for later
Wed Oct 31 09:57:28 2007  matrix is 68268 x 68380 with weight 3299116 (avg 48.25/col)
Wed Oct 31 09:57:28 2007  matrix includes 64 packed rows
Wed Oct 31 09:57:28 2007  using block size 27352 for processor cache size 4096 kB
Wed Oct 31 09:57:29 2007  commencing Lanczos iteration
Wed Oct 31 09:57:50 2007  lanczos halted after 1081 iterations
Wed Oct 31 09:57:50 2007  recovered 15 nontrivial dependencies
Wed Oct 31 09:57:50 2007  prp35 factor: 29916323560200857306637278521712341
Wed Oct 31 09:57:50 2007  prp59 factor: 32803016936544339453376593485631195739277624165372655627383
Wed Oct 31 09:57:50 2007  elapsed time 01:25:33

Oct 31, 2007 (3rd)

By Sinkiti Sibata / GGNFS

9·10¹⁴⁸-7 = 8(9)₁₄₇3_<149> = 53 · 839 · 3833 · 5333122741489_<13> · 380397540317863012963011373_<27> · C102

C102 = P48 · P55

P48 = 185048077381378285528736195447051909587258335893_<48>

P55 = 1406572115111896750750738223467919885903244947129739803_<55>

Number: 89993_148
N=260283465599715195282875769247700889484368036515112348257395053869878284353005891464605690479865649079
  ( 102 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=185048077381378285528736195447051909587258335893 (pp48)
 r2=1406572115111896750750738223467919885903244947129739803 (pp55)
Version: GGNFS-0.77.1-20060513-k8
Total time: 30.10 hours.
Scaled time: 59.93 units (timescale=1.991).
Factorization parameters were as follows:
name: 89993_148
n: 260283465599715195282875769247700889484368036515112348257395053869878284353005891464605690479865649079
m: 100000000000000000000000000000
c5: 9000
c0: -7
skew: 0.24
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 4250001)
Primes: RFBsize:114155, AFBsize:114082, largePrimes:3049998 encountered
Relations: rels:3108836, finalFF:263510
Max relations in full relation-set: 28
Initial matrix: 228304 x 263510 with sparse part having weight 32994625.
Pruned matrix : 218898 x 220103 with weight 26198623.
Total sieving time: 29.21 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.62 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 30.10 hours.
 --------- CPU info (if available) ----------

Oct 31, 2007 (2nd)

By matsui / GMP-ECM, Msieve

(5·10¹⁹⁸+7)/3 = 1(6)₁₉₇9_<199> = 2671 · 2222089 · 43446912661062564370891697_<26> · 151432609261393100562428907767_<30> · C134

C134 = P38 · P43 · P53

P38 = 78356711420850326025452572618724188949_<38>

P43 = 5527668366912659164266442169275274462403349_<43>

P53 = 98540986433720343595658132228977073747961703420580549_<53>

(5·10¹⁷³+7)/3 = 1(6)₁₇₂9_<174> = 79 · 141073 · 154543 · 165887 · 63473899 · 133660440077_<12> · C137

C137 = P34 · C104

P34 = 1862230537518772176753410725489813_<34>

C104 = [36921943839998587914228808236155511843378747795412617433005313650028624835179704262350945849262592485273_<104>]

Oct 31, 2007

By Womack

(10³⁰⁹-1)/9 is divisible by 5294796903161592416528456780680376286484870226446771978908657527791_<67> and the cofactor is prime.

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 30, 2007 (5th)

By Tyler Cadigan / Msieve, GGNFS

(64·10¹⁶³-1)/9 = 7(1)₁₆₃_<164> = 637330387763_<12> · 10957735036324101653_<20> · C134

C134 = P61 · P73

P61 = 5153208161696653721426359516088698419315495201808470280932923_<61>

P73 = 1975942751788253995617036939102852461531533982770011785041254696010379563_<73>

Mon Oct 29 19:58:09 2007  
Mon Oct 29 19:58:09 2007  
Mon Oct 29 19:58:09 2007  Msieve v. 1.29
Mon Oct 29 19:58:09 2007  random seeds: 79db1e80 385338a0
Mon Oct 29 19:58:09 2007  factoring 10182444315560575705513301530834416904561566048028307675788338594283441380448622210798637965512347107701350195485846065970978973052649 (134 digits)
Mon Oct 29 19:58:10 2007  commencing number field sieve (133-digit input)
Mon Oct 29 19:58:10 2007  R0: -400000000000000000000000000000000
Mon Oct 29 19:58:10 2007  R1:  1
Mon Oct 29 19:58:10 2007  A0: -2
Mon Oct 29 19:58:10 2007  A1:  0
Mon Oct 29 19:58:10 2007  A2:  0
Mon Oct 29 19:58:10 2007  A3:  0
Mon Oct 29 19:58:10 2007  A4:  0
Mon Oct 29 19:58:10 2007  A5:  125
Mon Oct 29 19:58:10 2007  size score = 2.442337e-011, Murphy alpha = 0.284179, combined = 2.221603e-011
Mon Oct 29 20:01:42 2007  restarting with 5837456 relations
Mon Oct 29 20:01:48 2007  factor base loaded:
Mon Oct 29 20:01:48 2007  348513 rational ideals (max prime = 4999999)
Mon Oct 29 20:01:48 2007  316326 algebraic ideals (max prime = 4499969)
Mon Oct 29 20:01:48 2007  added 15854 free relations
Mon Oct 29 20:01:48 2007  
Mon Oct 29 20:01:48 2007  commencing relation filtering
Mon Oct 29 20:01:48 2007  commencing duplicate removal, pass 1
Mon Oct 29 20:01:52 2007  error -14 reading relation 62058
Mon Oct 29 20:06:03 2007  found 79763 hash collisions in 5853309 relations
Mon Oct 29 20:06:03 2007  commencing duplicate removal, pass 2
Mon Oct 29 20:09:59 2007  found 17169 duplicates and 5836140 unique relations
Mon Oct 29 20:09:59 2007  memory use: 37.8 MB
Mon Oct 29 20:10:05 2007  ignoring smallest 282973 rational and 283029 algebraic ideals
Mon Oct 29 20:10:05 2007  filtering ideals above 3997355
Mon Oct 29 20:10:05 2007  need 962203 more relations than ideals
Mon Oct 29 20:10:05 2007  commencing singleton removal, pass 1
Mon Oct 29 20:14:14 2007  relations with 0 large ideals: 103993
Mon Oct 29 20:14:14 2007  relations with 1 large ideals: 760328
Mon Oct 29 20:14:14 2007  relations with 2 large ideals: 2000058
Mon Oct 29 20:14:14 2007  relations with 3 large ideals: 1934872
Mon Oct 29 20:14:14 2007  relations with 4 large ideals: 844689
Mon Oct 29 20:14:14 2007  relations with 5 large ideals: 173568
Mon Oct 29 20:14:14 2007  relations with 6 large ideals: 17913
Mon Oct 29 20:14:14 2007  relations with 7+ large ideals: 719
Mon Oct 29 20:14:14 2007  5836140 relations and about 5716455 large ideals
Mon Oct 29 20:14:14 2007  commencing singleton removal, pass 2
Mon Oct 29 20:18:32 2007  found 3032525 singletons
Mon Oct 29 20:18:32 2007  current dataset: 2803615 relations and about 2113481 large ideals
Mon Oct 29 20:18:32 2007  commencing singleton removal, pass 3
Mon Oct 29 20:22:13 2007  found 448303 singletons
Mon Oct 29 20:22:13 2007  current dataset: 2355312 relations and about 1639581 large ideals
Mon Oct 29 20:22:13 2007  commencing singleton removal, final pass
Mon Oct 29 20:26:10 2007  memory use: 77.5 MB
Mon Oct 29 20:26:10 2007  commencing in-memory singleton removal
Mon Oct 29 20:26:11 2007  begin with 2355312 relations and 1708927 unique ideals
Mon Oct 29 20:26:17 2007  reduce to 2069330 relations and 1416639 ideals in 11 passes
Mon Oct 29 20:26:17 2007  max relations containing the same ideal: 35
Mon Oct 29 20:26:18 2007  dataset has 15.3% excess relations
Mon Oct 29 20:26:22 2007  ignoring smallest 256574 rational and 256498 algebraic ideals
Mon Oct 29 20:26:22 2007  filtering ideals above 3597619
Mon Oct 29 20:26:22 2007  need 611282 more relations than ideals
Mon Oct 29 20:26:22 2007  commencing singleton removal, final pass
Mon Oct 29 20:29:45 2007  memory use: 93.6 MB
Mon Oct 29 20:29:45 2007  commencing in-memory singleton removal
Mon Oct 29 20:29:46 2007  begin with 2355312 relations and 1761848 unique ideals
Mon Oct 29 20:29:53 2007  reduce to 2068928 relations and 1469137 ideals in 11 passes
Mon Oct 29 20:29:53 2007  max relations containing the same ideal: 35
Mon Oct 29 20:29:54 2007  dataset has 6.0% excess relations
Mon Oct 29 20:29:54 2007  relations with 0 large ideals: 68851
Mon Oct 29 20:29:54 2007  relations with 1 large ideals: 298085
Mon Oct 29 20:29:54 2007  relations with 2 large ideals: 616837
Mon Oct 29 20:29:54 2007  relations with 3 large ideals: 631687
Mon Oct 29 20:29:54 2007  relations with 4 large ideals: 341963
Mon Oct 29 20:29:54 2007  relations with 5 large ideals: 94801
Mon Oct 29 20:29:54 2007  relations with 6 large ideals: 15793
Mon Oct 29 20:29:54 2007  relations with 7+ large ideals: 911
Mon Oct 29 20:29:54 2007  commencing 2-way merge
Mon Oct 29 20:30:00 2007  reduce to 1298002 relation sets and 698213 unique ideals
Mon Oct 29 20:30:00 2007  ignored 2 oversize relation sets
Mon Oct 29 20:30:00 2007  commencing full merge
Mon Oct 29 20:30:59 2007  found 664054 cycles, need 590413
Mon Oct 29 20:31:00 2007  weight of 590413 cycles is about 38798316 (65.71/cycle)
Mon Oct 29 20:31:00 2007  distribution of cycle lengths:
Mon Oct 29 20:31:00 2007  1 relations: 100601
Mon Oct 29 20:31:00 2007  2 relations: 68982
Mon Oct 29 20:31:00 2007  3 relations: 62992
Mon Oct 29 20:31:00 2007  4 relations: 55520
Mon Oct 29 20:31:00 2007  5 relations: 50346
Mon Oct 29 20:31:00 2007  6 relations: 44152
Mon Oct 29 20:31:00 2007  7 relations: 39232
Mon Oct 29 20:31:00 2007  8 relations: 34235
Mon Oct 29 20:31:00 2007  9 relations: 30168
Mon Oct 29 20:31:00 2007  10+ relations: 104185
Mon Oct 29 20:31:00 2007  heaviest cycle: 17 relations
Mon Oct 29 20:31:00 2007  commencing cycle optimization
Mon Oct 29 20:31:02 2007  start with 3228434 relations
Mon Oct 29 20:31:22 2007  pruned 92753 relations
Mon Oct 29 20:31:22 2007  distribution of cycle lengths:
Mon Oct 29 20:31:22 2007  1 relations: 100601
Mon Oct 29 20:31:22 2007  2 relations: 70333
Mon Oct 29 20:31:22 2007  3 relations: 65309
Mon Oct 29 20:31:22 2007  4 relations: 56690
Mon Oct 29 20:31:22 2007  5 relations: 52216
Mon Oct 29 20:31:22 2007  6 relations: 45474
Mon Oct 29 20:31:22 2007  7 relations: 40433
Mon Oct 29 20:31:22 2007  8 relations: 35072
Mon Oct 29 20:31:22 2007  9 relations: 30464
Mon Oct 29 20:31:22 2007  10+ relations: 93821
Mon Oct 29 20:31:22 2007  heaviest cycle: 17 relations
Mon Oct 29 20:31:25 2007  
Mon Oct 29 20:31:25 2007  commencing linear algebra
Mon Oct 29 20:31:27 2007  read 590413 cycles
Mon Oct 29 20:31:31 2007  cycles contain 1626805 unique relations
Mon Oct 29 20:35:42 2007  read 1626805 relations
Mon Oct 29 20:35:52 2007  using 32 quadratic characters above 134216228
Mon Oct 29 20:38:40 2007  read 590413 cycles
Mon Oct 29 20:40:52 2007  filtering completed in 3 passes
Mon Oct 29 20:40:53 2007  matrix is 585116 x 585316 with weight 52706044 (avg 90.05/col)
Mon Oct 29 20:42:11 2007  read 585316 cycles
Mon Oct 29 20:44:43 2007  matrix is 585116 x 585316 with weight 52706044 (avg 90.05/col)
Mon Oct 29 20:44:43 2007  saving the first 48 matrix rows for later
Mon Oct 29 20:44:44 2007  matrix is 585068 x 585316 with weight 39821171 (avg 68.03/col)
Mon Oct 29 20:44:44 2007  matrix includes 64 packed rows
Mon Oct 29 20:44:44 2007  using block size 21845 for processor cache size 512 kB
Mon Oct 29 20:44:55 2007  commencing Lanczos iteration
Mon Oct 29 23:39:22 2007  lanczos halted after 9254 iterations (dim = 585068)
Mon Oct 29 23:39:40 2007  recovered 51 nontrivial dependencies
Mon Oct 29 23:39:49 2007  
Mon Oct 29 23:39:49 2007  commencing square root phase
Mon Oct 29 23:39:49 2007  reading relations for dependency 1
Mon Oct 29 23:40:38 2007  read 292046 cycles
Mon Oct 29 23:40:40 2007  cycles contain 983974 unique relations
Mon Oct 29 23:45:16 2007  read 983974 relations
Mon Oct 29 23:45:37 2007  multiplying 1554024 relations
Mon Oct 29 23:58:13 2007  multiply complete, coefficients have about 43.64 million bits
Mon Oct 29 23:58:15 2007  initial square root is modulo 1843111
Tue Oct 30 00:16:39 2007  prp61 factor: 5153208161696653721426359516088698419315495201808470280932923
Tue Oct 30 00:16:39 2007  prp73 factor: 1975942751788253995617036939102852461531533982770011785041254696010379563
Tue Oct 30 00:16:39 2007  elapsed time 04:18:30

Oct 30, 2007 (4th)

By Sinkiti Sibata / GGNFS

(8·10¹⁶⁹+7)/3 = 2(6)₁₆₈9_<170> = 29 · 2731 · 3853 · 6101 · C158

C158 = P39 · P119

P39 = 662045957785193703483721009542997210001_<39>

P119 = 21635197395131458368660666363246008064391683714979718942359200843611409545192525720721351020928312546549349492289471827_<119>

Number: 26669_169
N=14323494981331534264770233164626933360731902226623376107836718853298476108817106742366885509525113696497209270753439876022351249265426627408162506926892141827
  ( 158 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=662045957785193703483721009542997210001 (pp39)
 r2=21635197395131458368660666363246008064391683714979718942359200843611409545192525720721351020928312546549349492289471827 (pp119)
Version: GGNFS-0.77.1-20060513-k8
Total time: 139.76 hours.
Scaled time: 279.94 units (timescale=2.003).
Factorization parameters were as follows:
name: 26669_169
n: 14323494981331534264770233164626933360731902226623376107836718853298476108817106742366885509525113696497209270753439876022351249265426627408162506926892141827
m: 10000000000000000000000000000000000
c5: 4
c0: 35
skew: 1.54
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 7100001)
Primes: RFBsize:412849, AFBsize:412831, largePrimes:6055936 encountered
Relations: rels:6345700, finalFF:951274
Max relations in full relation-set: 28
Initial matrix: 825744 x 951274 with sparse part having weight 56560583.
Pruned matrix : 721298 x 725490 with weight 40805496.
Total sieving time: 133.63 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 5.58 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 139.76 hours.
 --------- CPU info (if available) ----------

Oct 30, 2007 (3rd)

By Jo Yeong Uk / GGNFS

9·10¹⁴³-7 = 8(9)₁₄₂3_<144> = 1777 · 1725179 · 133421887 · C127

C127 = P39 · P89

P39 = 156872632499525723095280260098133461577_<39>

P89 = 14026414070177028542787457357907396822775755157120560213926799915579235133672913797156429_<89>

Number: 89993_143
N=2200360499717057804285186354000826515700652096122032856111785933419856092599249419038475136935920236563158160790423597130028533
  ( 127 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=156872632499525723095280260098133461577 (pp39)
 r2=14026414070177028542787457357907396822775755157120560213926799915579235133672913797156429 (pp89)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 9.59 hours.
Scaled time: 20.58 units (timescale=2.146).
Factorization parameters were as follows:
n: 2200360499717057804285186354000826515700652096122032856111785933419856092599249419038475136935920236563158160790423597130028533
m: 100000000000000000000000000000
c5: 9
c0: -700
skew: 2.39
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1400001)
Primes: RFBsize:114155, AFBsize:114082, largePrimes:3411338 encountered
Relations: rels:3448077, finalFF:323928
Max relations in full relation-set: 28
Initial matrix: 228301 x 323928 with sparse part having weight 30228512.
Pruned matrix : 199683 x 200888 with weight 15655341.
Total sieving time: 9.35 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 9.59 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹⁴⁴-7 = 8(9)₁₄₃3_<145> = 30380069764762946805547503800941_<32> · C114

C114 = P40 · P74

P40 = 5793759319832245415885975057146558926953_<40>

P74 = 51132060310818176689028811056072205332653270314035794978186101297841513141_<74>

Number: 89993_144
N=296246850968027270505132871619611111688006744457888000889843536883278888233053939988057668145613936858002808589373
  ( 114 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=5793759319832245415885975057146558926953 (pp40)
 r2=51132060310818176689028811056072205332653270314035794978186101297841513141 (pp74)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 8.87 hours.
Scaled time: 19.03 units (timescale=2.146).
Factorization parameters were as follows:
n: 296246850968027270505132871619611111688006744457888000889843536883278888233053939988057668145613936858002808589373
m: 100000000000000000000000000000
c5: 9
c0: -70
skew: 1.51
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1350001)
Primes: RFBsize:114155, AFBsize:114417, largePrimes:3343512 encountered
Relations: rels:3328593, finalFF:281277
Max relations in full relation-set: 28
Initial matrix: 228636 x 281277 with sparse part having weight 25879845.
Pruned matrix : 211599 x 212806 with weight 16431801.
Total sieving time: 8.61 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 8.87 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹⁵³-7 = 8(9)₁₅₂3_<154> = 235483 · 15771126802857831503737789_<26> · C124

C124 = P31 · C93

P31 = 2469438507084583723424410362013_<31>

C93 = [981345668424409173005139032359911659122268552148212314853518231679477196677844688222808633603_<93>]

9·10¹⁴⁶-7 = 8(9)₁₄₅3_<147> = 19 · 307 · 2243 · 17371526793899_<14> · 28598478520519_<14> · C114

C114 = P44 · P70

P44 = 64299853807288749095977974116352073454267827_<44>

P70 = 2153427995281495420234041605616327252058426335937525315582533212837981_<70>

Number: 89993_146
N=138465105281123041720280097879537854129018147941456341438827168511391802940627666355587781402709904235851131937287
  ( 114 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=64299853807288749095977974116352073454267827 (pp44)
 r2=2153427995281495420234041605616327252058426335937525315582533212837981 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.37 hours.
Scaled time: 22.21 units (timescale=2.143).
Factorization parameters were as follows:
n: 138465105281123041720280097879537854129018147941456341438827168511391802940627666355587781402709904235851131937287
m: 100000000000000000000000000000
c5: 90
c0: -7
skew: 0.6
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1575001)
Primes: RFBsize:135072, AFBsize:135493, largePrimes:3715295 encountered
Relations: rels:3729829, finalFF:320257
Max relations in full relation-set: 28
Initial matrix: 270632 x 320257 with sparse part having weight 29075311.
Pruned matrix : 251639 x 253056 with weight 19777051.
Total sieving time: 10.00 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 10.37 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 30, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

8·10¹⁶⁷-7 = 7(9)₁₆₆3_<168> = 15137 · C164

C164 = P41 · P123

P41 = 70835644003123593484318087394932806885707_<41>

P123 = 746102215179633311919695276118227149695996068322953673178010306203699906940184998267472539948678240767141330911324215957227_<123>

Number: n
N=52850630904406421351654885380194226068573693598467331703772213780802008323974367444011362885644447380590605800356741758604743344123670476316311025962872431789654489
  ( 164 digits)
SNFS difficulty: 167 digits.
Divisors found:

Tue Oct 30 07:24:05 2007  prp41 factor: 70835644003123593484318087394932806885707
Tue Oct 30 07:24:05 2007  prp123 factor: 746102215179633311919695276118227149695996068322953673178010306203699906940184998267472539948678240767141330911324215957227
Tue Oct 30 07:24:05 2007  elapsed time 02:09:23 (Msieve 1.28)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 78.72 hours.
Scaled time: 102.80 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_7_9_166_3
n: 52850630904406421351654885380194226068573693598467331703772213780802008323974367444011362885644447380590605800356741758604743344123670476316311025962872431789654489
skew: 0.78
deg: 5
c5: 25
c0: -7
m: 2000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3100001)
Primes: RFBsize:216816, AFBsize:216906, largePrimes:7450046 encountered
Relations: rels:6889776, finalFF:446877
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 78.46 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 78.72 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

9·10¹⁴¹-7 = 8(9)₁₄₀3_<142> = 2467639565737_<13> · C130

C130 = P62 · P68

P62 = 53727058137272382231521263461791395461691665958866250660772681_<62>

P68 = 67884046657300958448660911774042029705347021611364740350454114167369_<68>

Number: n
N=3647210121350119518190235337345061800537587608749415529958760713265023919457085448117350162821494933357724078360429982102496846289
  ( 130 digits)
SNFS difficulty: 141 digits.
Divisors found:

Tue Oct 30 09:24:32 2007  prp62 factor: 53727058137272382231521263461791395461691665958866250660772681
Tue Oct 30 09:24:32 2007  prp68 factor: 67884046657300958448660911774042029705347021611364740350454114167369
Tue Oct 30 09:24:32 2007  elapsed time 00:50:42 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.66 hours.
Scaled time: 9.64 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_8_9_140_3
n: 3647210121350119518190235337345061800537587608749415529958760713265023919457085448117350162821494933357724078360429982102496846289
skew: 0.60
deg: 5
c5: 90
c0: -7
m: 10000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 9500000)
Primes: RFBsize:148933, AFBsize:149225, largePrimes:6523890 encountered
Relations: rels:5928439, finalFF:382643
Max relations in full relation-set: 28
Initial matrix: 298225 x 382643 with sparse part having weight 26922338.
Pruned matrix : 236427 x 237982 with weight 14528939.
Total sieving time: 6.49 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 6.66 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Oct 30, 2007

By matsui / GMP-ECM

(5·10¹⁸¹+7)/3 = 1(6)₁₈₀9_<182> = 19 · 167393 · C175

C175 = P38 · P138

P38 = 15723245803923831841763637804116393807_<38>

P138 = 333284910953414496865344254925662573105861000375900329621890909608385992777196180707248922993978075855583628204941899412869920935091825201_<138>

Oct 29, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve 1.28, GMP-ECM

9·10¹⁸⁴-7 = 8(9)₁₈₃3_<185> = 31 · 311 · 22091 · 37100458201_<11> · 1275537910469_<13> · 282209150413571_<15> · 480434327015263_<15> · 14873984820428774119490711269_<29> · C97

C97 = P39 · P58

P39 = 593474640229445793717454630072648349617_<39>

P58 = 7461012807353624814862644671648910980191120545663272451503_<58>

Number: n
N=4427921891591479845215021556692579780756319432292202349671112615670635805041615039103114621124351
  ( 97 digits)
Divisors found:
 r1=593474640229445793717454630072648349617 (pp39)
 r2=7461012807353624814862644671648910980191120545663272451503 (pp58)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.00 hours.
Scaled time: 11.63 units (timescale=1.453).
Factorization parameters were as follows:
name: n
n:  4427921891591479845215021556692579780756319432292202349671112615670635805041615039103114621124351
m:  13069795307958322129988
deg: 4
c4: 151748640
c3: 1255715867918
c2: -263120823138764827
c1: -4731771597968022768
c0: 240860015889048958069487
skew: 1635.250
type: gnfs
# adj. I(F,S) = 55.565
# E(F1,F2) = 2.428134e-05
# GGNFS version 0.77.1-20051202-athlon polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1193586766.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [100000, 1180001)
Primes: RFBsize:92938, AFBsize:92740, largePrimes:1863035 encountered
Relations: rels:1930390, finalFF:234741
Max relations in full relation-set: 28
Initial matrix: 185753 x 234741 with sparse part having weight 16859853.
Pruned matrix : 163671 x 164663 with weight 9437558.
Polynomial selection time: 0.17 hours.
Total sieving time: 7.24 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.44 hours.
Total square root time: 0.06 hours, sqrts: 2.
Prototype def-par.txt line would be:
gnfs,96,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 8.00 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

9·10¹⁴⁰-7 = 8(9)₁₃₉3_<141> = 47 · 109 · 167 · 617 · C133

C133 = P33 · P101

P33 = 153337616869490449763658859895879_<33>

P101 = 11119053224090329768606633153477332542273472771580149117582678104067239138069306589653736225297573611_<101>

(89·10¹⁶⁴+1)/9 = 9(8)₁₆₃9_<165> = 17 · 19597 · 7888299157_<10> · C150

C150 = P42 · P109

P42 = 270666531521708051044165587427652002648199_<42>

P109 = 1390244075564748945696789150673380726874059327867465501106095914306348058416858266414264460951086291348664927_<109>

Number: n
N=376292541901713990156240140280107136920403712406844501532612508891705603189038511185276004611331447762586551055990351376936771061312168024647111016473
  ( 150 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Oct 29 21:17:16 2007  prp42 factor: 270666531521708051044165587427652002648199
Mon Oct 29 21:17:16 2007  prp109 factor: 1390244075564748945696789150673380726874059327867465501106095914306348058416858266414264460951086291348664927
Mon Oct 29 21:17:16 2007  elapsed time 02:10:55 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 74.57 hours.
Scaled time: 98.88 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_9_8_163_9
n: 376292541901713990156240140280107136920403712406844501532612508891705603189038511185276004611331447762586551055990351376936771061312168024647111016473
skew: 0.65
deg: 5
c5: 89
c0: 10
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3500000)
Primes: RFBsize:250150, AFBsize:249266, largePrimes:7709961 encountered
Relations: rels:7186570, finalFF:561747
Max relations in full relation-set: 28
Initial matrix: 499481 x 561747 with sparse part having weight 51822639.
Pruned matrix : 473183 x 475744 with weight 37331802.
Total sieving time: 74.27 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 74.57 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

9·10¹⁴⁵-7 = 8(9)₁₄₄3_<146> = 97 · 3307 · 3767 · C137

C137 = P29 · P108

P29 = 88689612345000909646591931059_<29>

P108 = 839785174596700619416492075514766572936766799231731694119293012984478206119418982501449042954689673043155839_<108>

Oct 29, 2007 (2nd)

By Jo Yeong Uk / GGNFS, GMP-ECM

9·10¹³⁸-7 = 8(9)₁₃₇3_<139> = 113 · 1039 · 21012038995387387919_<20> · C115

C115 = P55 · P60

P55 = 8324111480329451493669984302302012442668075809611357389_<55>

P60 = 438270694932342412379485394874876095508458992349269934992589_<60>

Number: 89993_138
N=3648214123178278233256210719479595987622179900672256982789110923572726048983147685427800495148109948692769945390121
  ( 115 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=8324111480329451493669984302302012442668075809611357389 (pp55)
 r2=438270694932342412379485394874876095508458992349269934992589 (pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.25 hours.
Scaled time: 13.42 units (timescale=2.146).
Factorization parameters were as follows:
n: 3648214123178278233256210719479595987622179900672256982789110923572726048983147685427800495148109948692769945390121
m: 10000000000000000000000000000
c5: 9
c0: -700
skew: 2.39
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:114082, largePrimes:3249074 encountered
Relations: rels:3266483, finalFF:322988
Max relations in full relation-set: 28
Initial matrix: 228301 x 322988 with sparse part having weight 26878127.
Pruned matrix : 191188 x 192393 with weight 12738220.
Total sieving time: 6.06 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.25 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹⁴⁹-7 = 8(9)₁₄₈3_<150> = C150

C150 = P38 · P42 · P72

P38 = 35794409962129142828512220689799871821_<38>

P42 = 123028439265110134626156384131454479013793_<42>

P72 = 204372184460583650412981392697490828081020379007054396748321776875537981_<72>

Number: 89993_149
N=899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 150 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=35794409962129142828512220689799871821 (pp38)
 r2=123028439265110134626156384131454479013793 (pp42)
 r3=204372184460583650412981392697490828081020379007054396748321776875537981 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 12.84 hours.
Scaled time: 27.54 units (timescale=2.146).
Factorization parameters were as follows:
n: 899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
m: 1000000000000000000000000000000
c5: 9
c0: -70
skew: 1.51
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:176833, largePrimes:5402800 encountered
Relations: rels:5281314, finalFF:455491
Max relations in full relation-set: 28
Initial matrix: 353199 x 455491 with sparse part having weight 38566153.
Pruned matrix : 301756 x 303585 with weight 22658433.
Total sieving time: 12.29 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.44 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 12.84 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹³⁹-7 = 8(9)₁₃₈3_<140> = 31 · 34319 · C134

C134 = P41 · P93

P41 = 95880034599375142177521603584056943225357_<41>

P93 = 882303513756038409718500891576339947944242061119473046440639355414422699311396515924957852941_<93>

Number: 89993_139
N=84595291426079224430368205705670422384290090413567580828451088412418964760421434942931076456284443207891048784224670054864746228224937
  ( 134 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=95880034599375142177521603584056943225357 (pp41)
 r2=882303513756038409718500891576339947944242061119473046440639355414422699311396515924957852941 (pp93)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.16 hours.
Scaled time: 13.12 units (timescale=2.129).
Factorization parameters were as follows:
n: 84595291426079224430368205705670422384290090413567580828451088412418964760421434942931076456284443207891048784224670054864746228224937
m: 10000000000000000000000000000
c5: 9
c0: -70
skew: 1.51
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:114417, largePrimes:3350084 encountered
Relations: rels:3437732, finalFF:383556
Max relations in full relation-set: 28
Initial matrix: 228636 x 383556 with sparse part having weight 32672853.
Pruned matrix : 174534 x 175741 with weight 12890921.
Total sieving time: 5.98 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.16 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹⁹⁷-7 = 8(9)₁₉₆3_<198> = C198

C198 = P33 · C166

P33 = 104572749495411191273052631155941_<33>

C166 = [8606448662225270711938618675616267002791985751466136050473524371365139986511632740091624538638242280156899111248894398265050813422371895877062117828590480106511274373_<166>]

Oct 29, 2007

By Sinkiti Sibata / GGNFS

9·10¹³⁷-7 = 8(9)₁₃₆3_<138> = 227 · 2521 · C133

C133 = P39 · P94

P39 = 221091843902924979644001926922716807503_<39>

P94 = 7113299338479217992920918313593338363891253403625902931023690166695268837106428754985186805093_<94>

Number: 89993_137
N=1572692466977826783651687062158048603186973912526844986693274293293165602769336690740510985256881840120083807034129173969493261012779
  ( 133 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=221091843902924979644001926922716807503 (pp39)
 r2=7113299338479217992920918313593338363891253403625902931023690166695268837106428754985186805093 (pp94)
Version: GGNFS-0.77.1-20060513-k8
Total time: 13.09 hours.
Scaled time: 26.31 units (timescale=2.010).
Factorization parameters were as follows:
name: 89993_137
n: 1572692466977826783651687062158048603186973912526844986693274293293165602769336690740510985256881840120083807034129173969493261012779
m: 1000000000000000000000000000
c5: 900
c0: -7
skew: 0.38
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 2125001)
Primes: RFBsize:78498, AFBsize:63823, largePrimes:1683910 encountered
Relations: rels:1718050, finalFF:173211
Max relations in full relation-set: 28
Initial matrix: 142385 x 173211 with sparse part having weight 19269917.
Pruned matrix : 135154 x 135929 with weight 13734266.
Total sieving time: 12.78 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 13.09 hours.
 --------- CPU info (if available) ----------

Oct 28, 2007 (5th)

By JMB / GMP-ECM

(2·10¹⁶⁴+43)/9 = (2)₁₆₃7_<164> = 3³ · 17² · 2309 · 631311078642593_<15> · C142

C142 = P36 · P106

P36 = 212146409889374522698249183584805409_<36>

P106 = 9209220022038251514752208083059669039690403032046144718649809261395595313649005423325208968370329688568373_<106>

Oct 28, 2007 (4th)

By Robert Backstrom / GGNFS, GMP-ECM

9·10¹²⁰-7 = 8(9)₁₁₉3_<121> = C121

C121 = P56 · P66

P56 = 20354029401725849662526304753223971301497103511422609997_<56>

P66 = 442172889817918611600780346173978409068598975005735222119428696669_<66>

Number: n
N=8999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 121 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=20354029401725849662526304753223971301497103511422609997 (pp56)
 r2=442172889817918611600780346173978409068598975005735222119428696669 (pp66)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.55 hours.
Scaled time: 2.24 units (timescale=1.442).
Factorization parameters were as follows:
name: KA_8_9_119_3
n: 8999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
skew: 0.95
deg: 5
c5: 9
c0: -7
m: 1000000000000000000000000
type: snfs
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 250001)
Primes: RFBsize:78498, AFBsize:78361, largePrimes:4232731 encountered
Relations: rels:3638568, finalFF:200786
Max relations in full relation-set: 28
Initial matrix: 156923 x 200786 with sparse part having weight 10194178.
Pruned matrix : 122805 x 123653 with weight 4620848.
Total sieving time: 1.31 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.13 hours.
Total square root time: 0.05 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000
total time: 1.55 hours.
 --------- CPU info (if available) ----------

9·10¹²⁴-7 = 8(9)₁₂₃3_<125> = 31 · 83 · 859 · C119

C119 = P39 · P80

P39 = 514997239710717504843060243797163586321_<39>

P80 = 79068710858248681348102914984733040362741538735234491408794076224567905858038519_<80>

Number: n
N=40720167839482908161995686376886870777262039256956475117488995374641379744069220665756646323172444933890807512599498599
  ( 119 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=514997239710717504843060243797163586321 (pp39)
 r2=79068710858248681348102914984733040362741538735234491408794076224567905858038519 (pp80)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.17 hours.
Scaled time: 3.15 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_8_9_123_3
n: 40720167839482908161995686376886870777262039256956475117488995374641379744069220665756646323172444933890807512599498599
skew: 1.51
deg: 5
c5: 9
c0: -70
m: 10000000000000000000000000
type: snfs
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 350001)
Primes: RFBsize:78498, AFBsize:78806, largePrimes:4616754 encountered
Relations: rels:3996538, finalFF:211076
Max relations in full relation-set: 28
Initial matrix: 157368 x 211076 with sparse part having weight 12304449.
Pruned matrix : 125655 x 126505 with weight 5315318.
Total sieving time: 1.90 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.16 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000
total time: 2.17 hours.
 --------- CPU info (if available) ----------

9·10¹²³-7 = 8(9)₁₂₂3_<124> = 283 · 449 · 18553 · C115

C115 = P33 · P83

P33 = 335087805245091568482853093222231_<33>

P83 = 11392970303565490307790042441076114728020253883982388272289002974166360045042039653_<83>

Oct 28, 2007 (3rd)

By Sinkiti Sibata / GGNFS

9·10¹⁰³-7 = 8(9)₁₀₂3_<104> = 8969263 · 22129553 · C90

C90 = P34 · P57

P34 = 3138341068996635669510657500009591_<34>

P57 = 144481741911394492878214372456463812416287949515103488657_<57>

Number: 89993_103
N=453432984360701811730662361842066998814076709622439235119159164702296684015661335059709287
  ( 90 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=3138341068996635669510657500009591 (pp34)
 r2=144481741911394492878214372456463812416287949515103488657 (pp57)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1.16 hours.
Scaled time: 2.33 units (timescale=2.010).
Factorization parameters were as follows:
name: 89993_103
n: 453432984360701811730662361842066998814076709622439235119159164702296684015661335059709287
m: 100000000000000000000
c5: 9000
c0: -7
skew: 0.24
type: snfs
Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [250000, 350001)
Primes: RFBsize:37706, AFBsize:41552, largePrimes:1383872 encountered
Relations: rels:1489916, finalFF:267931
Max relations in full relation-set: 28
Initial matrix: 79325 x 267931 with sparse part having weight 10896930.
Pruned matrix : 39729 x 40189 with weight 1773397.
Total sieving time: 1.10 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,103,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000
total time: 1.16 hours.
 --------- CPU info (if available) ----------

9·10¹¹⁰-7 = 8(9)₁₀₉3_<111> = 19 · 41551595117_<11> · C100

C100 = P29 · P71

P29 = 41281949109330068117018801413_<29>

P71 = 27614743514922133541815936402538216668321370424896711617313719193012707_<71>

Number: 89993_110
N=1139990436450218045364874916232246048513796723724260459114263780638570351214091539941676577618554991
  ( 100 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=41281949109330068117018801413 (pp29)
 r2=27614743514922133541815936402538216668321370424896711617313719193012707 (pp71)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1.60 hours.
Scaled time: 3.20 units (timescale=2.003).
Factorization parameters were as follows:
name: 89993_110
n: 1139990436450218045364874916232246048513796723724260459114263780638570351214091539941676577618554991
m: 10000000000000000000000
c5: 9
c0: -7
skew: 0.95
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 450001)
Primes: RFBsize:49098, AFBsize:63908, largePrimes:2384591 encountered
Relations: rels:2925739, finalFF:659504
Max relations in full relation-set: 28
Initial matrix: 113070 x 659504 with sparse part having weight 48577546.
Pruned matrix : 58429 x 59058 with weight 4920438.
Total sieving time: 1.50 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.60 hours.
 --------- CPU info (if available) ----------

9·10¹³³-7 = 8(9)₁₃₂3_<134> = 264101 · 534617 · C123

C123 = P39 · P85

P39 = 182955127132944612210518087078849494903_<39>

P85 = 3484055901363921062151806188107621607898929991774539197434850631713521731052250641243_<85>

Number: 89993_133
N=637425890372322111870552134461924960577827615567570996460983077035726280509113823885139408501711796643783835904368410084429
  ( 123 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=182955127132944612210518087078849494903 (pp39)
 r2=3484055901363921062151806188107621607898929991774539197434850631713521731052250641243 (pp85)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.85 hours.
Scaled time: 13.77 units (timescale=2.010).
Factorization parameters were as follows:
name: 89993_133
n: 637425890372322111870552134461924960577827615567570996460983077035726280509113823885139408501711796643783835904368410084429
m: 100000000000000000000000000
c5: 9000
c0: -7
skew: 0.24
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1225001)
Primes: RFBsize:78498, AFBsize:63803, largePrimes:1569153 encountered
Relations: rels:1588445, finalFF:190481
Max relations in full relation-set: 28
Initial matrix: 142368 x 190481 with sparse part having weight 15782385.
Pruned matrix : 127348 x 128123 with weight 8890552.
Total sieving time: 6.62 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 6.85 hours.
 --------- CPU info (if available) ----------

9·10¹²²-7 = 8(9)₁₂₁3_<123> = 53 · 4483 · 916879 · 2468335253078521_<16> · C97

C97 = P38 · P59

P38 = 21496643135387952418448986201888231937_<38>

P59 = 77859405334185056592558073314508609031087592802266287870129_<59>

Number: 89993_122
N=1673715851202497322218396988251980025978426972094963254178577242866898726074527843954613286109873
  ( 97 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=21496643135387952418448986201888231937 (pp38)
 r2=77859405334185056592558073314508609031087592802266287870129 (pp59)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.78 hours.
Scaled time: 5.54 units (timescale=1.991).
Factorization parameters were as follows:
name: 89993_122
n: 1673715851202497322218396988251980025978426972094963254178577242866898726074527843954613286109873
m: 1000000000000000000000000
c5: 900
c0: -7
skew: 0.38
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:63823, largePrimes:2113012 encountered
Relations: rels:2116801, finalFF:142981
Max relations in full relation-set: 28
Initial matrix: 112985 x 142981 with sparse part having weight 12791337.
Pruned matrix : 105117 x 105745 with weight 7557577.
Total sieving time: 2.61 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.78 hours.
 --------- CPU info (if available) ----------

9·10¹²⁷-7 = 8(9)₁₂₆3_<128> = 16927 · 2815289 · 34549727 · C110

C110 = P53 · P58

P53 = 18928495665651195086151678397725759673977330546366127_<53>

P58 = 2887877797068484257309586094965034801453924030197429437839_<58>

Number: 89993_127
N=54663182364741125803462775792405445851485144937413141458737770402786616920134187641356901510330757177881679553
  ( 110 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=18928495665651195086151678397725759673977330546366127 (pp53)
 r2=2887877797068484257309586094965034801453924030197429437839 (pp58)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.41 hours.
Scaled time: 8.86 units (timescale=2.010).
Factorization parameters were as follows:
name: 89993_127
n: 54663182364741125803462775792405445851485144937413141458737770402786616920134187641356901510330757177881679553
m: 10000000000000000000000000
c5: 900
c0: -7
skew: 0.38
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:63823, largePrimes:1546280 encountered
Relations: rels:1577253, finalFF:198015
Max relations in full relation-set: 28
Initial matrix: 127838 x 198015 with sparse part having weight 14562521.
Pruned matrix : 108690 x 109393 with weight 6383787.
Total sieving time: 4.25 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.41 hours.
 --------- CPU info (if available) ----------

9·10¹¹⁹-7 = 8(9)₁₁₈3_<120> = 61 · 823 · 1004981 · 1446682233738538319_<19> · C92

C92 = P41 · P51

P41 = 45567990874948473844291875103339917072403_<41>

P51 = 270596365668481699029128282701225154281973286874043_<51>

Number: 89993_119
N=12330532721575594545992327055219422353381614259277089538199489555365772207883504963972335329
  ( 92 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=45567990874948473844291875103339917072403 (pp41)
 r2=270596365668481699029128282701225154281973286874043 (pp51)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.11 hours.
Scaled time: 4.20 units (timescale=1.991).
Factorization parameters were as follows:
name: 89993_119
n: 12330532721575594545992327055219422353381614259277089538199489555365772207883504963972335329
m: 1000000000000000000000000
c5: 9
c0: -70
skew: 1.51
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64228, largePrimes:1981105 encountered
Relations: rels:1934715, finalFF:128846
Max relations in full relation-set: 28
Initial matrix: 113390 x 128846 with sparse part having weight 9933260.
Pruned matrix : 107064 x 107694 with weight 6957791.
Total sieving time: 1.96 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.11 hours.
 --------- CPU info (if available) ----------

Oct 28, 2007 (2nd)

By Sinkiti Sibata / PRIMO

(5·10²⁸⁴⁷+1)/3 is prime.

Oct 28, 2007

The factor table of 899...993 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Oct 27, 2007

By Yousuke Koide

10¹¹²¹+1 is divisible by 162578197086018239450239785966343_<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 26, 2007 (3rd)

By Sinkiti Sibata / GGNFS

(8·10¹⁶³+7)/3 = 2(6)₁₆₂9_<164> = 17 · 9672675193889_<13> · 2132690377238720580097964644733_<31> · C119

C119 = P32 · P88

P32 = 16241366780245493793149978382913_<32>

P88 = 4681907431777497416749516436722604837221873429043948077027598629819267084782903500320897_<88>

Number: 26669_163
N=76040575830655542110535543314902372731075646666123180911982484874925096768258162409352851616275001258339376508641632961
  ( 119 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=16241366780245493793149978382913 (pp32)
 r2=4681907431777497416749516436722604837221873429043948077027598629819267084782903500320897 (pp88)
Version: GGNFS-0.77.1-20060513-k8
Total time: 89.67 hours.
Scaled time: 179.08 units (timescale=1.997).
Factorization parameters were as follows:
name: 26669_163
n: 76040575830655542110535543314902372731075646666123180911982484874925096768258162409352851616275001258339376508641632961
m: 200000000000000000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 5150001)
Primes: RFBsize:315948, AFBsize:316791, largePrimes:5926048 encountered
Relations: rels:6075527, finalFF:765961
Max relations in full relation-set: 28
Initial matrix: 632805 x 765961 with sparse part having weight 56904865.
Pruned matrix : 534793 x 538021 with weight 40888773.
Total sieving time: 85.28 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 3.92 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 89.67 hours.
 --------- CPU info (if available) ----------

Oct 26, 2007 (2nd)

By Jo Yeong Uk / Msieve, GGNFS

(82·10¹⁶¹+71)/9 = 9(1)₁₆₀9_<162> = 11 · 23 · 3748991 · 2671832954149_<13> · 5966029856099_<13> · 302592140766530934908888222616061079_<36> · C93

C93 = P40 · P53

P40 = 3850694069121437110112555389391787483611_<40>

P53 = 51718395086698620503380784735167544390948057134540087_<53>

Fri Oct 26 00:04:24 2007  
Fri Oct 26 00:04:24 2007  
Fri Oct 26 00:04:24 2007  Msieve v. 1.28
Fri Oct 26 00:04:24 2007  random seeds: bb05f469 520cf979
Fri Oct 26 00:04:24 2007  factoring 199151717224829651201838246240894378459227321597236742980797132267408631739729758957535014157 (93 digits)
Fri Oct 26 00:04:24 2007  commencing quadratic sieve (92-digit input)
Fri Oct 26 00:04:24 2007  using multiplier of 53
Fri Oct 26 00:04:24 2007  using 32kb Intel Core sieve core
Fri Oct 26 00:04:24 2007  sieve interval: 36 blocks of size 32768
Fri Oct 26 00:04:24 2007  processing polynomials in batches of 6
Fri Oct 26 00:04:24 2007  using a sieve bound of 1879931 (70588 primes)
Fri Oct 26 00:04:24 2007  using large prime bound of 219951927 (27 bits)
Fri Oct 26 00:04:24 2007  using double large prime bound of 1037982177167364 (42-50 bits)
Fri Oct 26 00:04:24 2007  using trial factoring cutoff of 50 bits
Fri Oct 26 00:04:24 2007  polynomial 'A' values have 12 factors
Fri Oct 26 01:38:35 2007  70852 relations (18438 full + 52414 combined from 913373 partial), need 70684
Fri Oct 26 01:38:35 2007  begin with 931811 relations
Fri Oct 26 01:38:36 2007  reduce to 176982 relations in 10 passes
Fri Oct 26 01:38:36 2007  attempting to read 176982 relations
Fri Oct 26 01:38:37 2007  recovered 176982 relations
Fri Oct 26 01:38:37 2007  recovered 157867 polynomials
Fri Oct 26 01:38:38 2007  attempting to build 70852 cycles
Fri Oct 26 01:38:38 2007  found 70852 cycles in 5 passes
Fri Oct 26 01:38:38 2007  distribution of cycle lengths:
Fri Oct 26 01:38:38 2007     length 1 : 18438
Fri Oct 26 01:38:38 2007     length 2 : 13138
Fri Oct 26 01:38:38 2007     length 3 : 12424
Fri Oct 26 01:38:38 2007     length 4 : 9444
Fri Oct 26 01:38:38 2007     length 5 : 6893
Fri Oct 26 01:38:38 2007     length 6 : 4449
Fri Oct 26 01:38:38 2007     length 7 : 2721
Fri Oct 26 01:38:38 2007     length 9+: 3345
Fri Oct 26 01:38:38 2007  largest cycle: 17 relations
Fri Oct 26 01:38:38 2007  matrix is 70588 x 70852 with weight 4361172 (avg 61.55/col)
Fri Oct 26 01:38:38 2007  filtering completed in 3 passes
Fri Oct 26 01:38:38 2007  matrix is 66408 x 66472 with weight 4123761 (avg 62.04/col)
Fri Oct 26 01:38:39 2007  saving the first 48 matrix rows for later
Fri Oct 26 01:38:39 2007  matrix is 66360 x 66472 with weight 3167656 (avg 47.65/col)
Fri Oct 26 01:38:39 2007  matrix includes 64 packed rows
Fri Oct 26 01:38:39 2007  using block size 26588 for processor cache size 4096 kB
Fri Oct 26 01:38:41 2007  commencing Lanczos iteration
Fri Oct 26 01:39:01 2007  lanczos halted after 1051 iterations
Fri Oct 26 01:39:01 2007  recovered 17 nontrivial dependencies
Fri Oct 26 01:39:01 2007  prp40 factor: 3850694069121437110112555389391787483611
Fri Oct 26 01:39:01 2007  prp53 factor: 51718395086698620503380784735167544390948057134540087
Fri Oct 26 01:39:01 2007  elapsed time 01:34:37

10¹⁶⁰-3 = (9)₁₅₉7_<160> = 13 · 383 · 52771123082243438120761219452533939_<35> · C122

C122 = P55 · P68

P55 = 3104829324566476660204837376960208819056316254480075411_<55>

P68 = 12258118210972106300910696745912453876036288591144435630300652094167_<68>

Number: 99997_160
N=38059364885428552053660274073288904257094149099533297652419641952424130876827819709343439432012909374053370298093233227637
  ( 122 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=3104829324566476660204837376960208819056316254480075411 (pp55)
 r2=12258118210972106300910696745912453876036288591144435630300652094167 (pp68)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.28 hours.
Scaled time: 51.72 units (timescale=2.130).
Factorization parameters were as follows:
n: 38059364885428552053660274073288904257094149099533297652419641952424130876827819709343439432012909374053370298093233227637
m: 100000000000000000000000000000000
c5: 1
c0: -3
skew: 1.25
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3400001)
Primes: RFBsize:283146, AFBsize:282992, largePrimes:5668831 encountered
Relations: rels:5757196, finalFF:705905
Max relations in full relation-set: 28
Initial matrix: 566202 x 705905 with sparse part having weight 43019303.
Pruned matrix : 449468 x 452363 with weight 26383924.
Total sieving time: 23.17 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.99 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 24.28 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 26, 2007

By Robert Backstrom / GGNFS, Msieve

(68·10¹⁵⁹+13)/9 = 7(5)₁₅₈7_<160> = 3 · 11 · 4815673 · 4744027650700422249483517_<25> · C128

C128 = P43 · P85

P43 = 1817556499049832315979311388016701905830557_<43>

P85 = 5513918500405508167982559945335390530223566166104141567423964571081382710408776663717_<85>

Number: n
N=10021858405643136835110663638106493348996711376408485617314301858636084358685512690994172006148128480343234388008600600371800369
  ( 128 digits)
SNFS difficulty: 161 digits.
Divisors found:

Fri Oct 26 04:07:36 2007  prp43 factor: 1817556499049832315979311388016701905830557
Fri Oct 26 04:07:36 2007  prp85 factor: 5513918500405508167982559945335390530223566166104141567423964571081382710408776663717
Fri Oct 26 04:07:36 2007  elapsed time 01:12:41 (Msieve 1.28)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 35.05 hours.
Scaled time: 45.84 units (timescale=1.308).
Factorization parameters were as follows:
name: KA_7_5_158_7
n: 10021858405643136835110663638106493348996711376408485617314301858636084358685512690994172006148128480343234388008600600371800369
skew: 1.14
deg: 5
c5: 34
c0: 65
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700001)
Primes: RFBsize:216816, AFBsize:216756, largePrimes:7052915 encountered
Relations: rels:6510490, finalFF:471406
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 34.83 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 35.05 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 25, 2007 (4th)

By Robert Backstrom / GGNFS, Msieve

(8·10¹⁶⁷+7)/3 = 2(6)₁₆₆9_<168> = 13 · C167

C167 = P41 · P127

P41 = 13118854935330807737302880871625861715191_<41>

P127 = 1563613639600265717122264555652120246875230542463041437585843162802180545583168901897596747095254252168082117302855188658610343_<127>

Number: n
N=20512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820513
  ( 167 digits)
SNFS difficulty: 167 digits.
Divisors found:

Fri Oct 26 00:52:24 2007  prp41 factor: 13118854935330807737302880871625861715191
Fri Oct 26 00:52:24 2007  prp127 factor: 1563613639600265717122264555652120246875230542463041437585843162802180545583168901897596747095254252168082117302855188658610343
Fri Oct 26 00:52:24 2007  elapsed time 02:20:14 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 68.58 hours.
Scaled time: 82.23 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_2_6_166_9
n: 20512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820513
type: snfs
skew: 0.78
deg: 5
c5: 25
c0: 7
m: 2000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2800001)
Primes: RFBsize:250150, AFBsize:250196, largePrimes:7501352 encountered
Relations: rels:7006091, finalFF:549114
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 68.27 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.6,2.6,100000
total time: 68.58 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Oct 25, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(26·10²⁶⁸⁸-11)/3 is prime.

Oct 25, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM

(46·10¹⁶¹-1)/9 = 5(1)₁₆₁_<162> = 17 · 29 · 47 · 724447 · 855857254801063_<15> · 3172216729960337_<16> · C122

C122 = P31 · P91

P31 = 8979918563026048055214325630447_<31>

P91 = 1248899066404055568679090185969582597135314562972683825422549780576518206214842043840714379_<91>

(82·10¹⁶¹+71)/9 = 9(1)₁₆₀9_<162> = 11 · 23 · 3748991 · 2671832954149_<13> · 5966029856099_<13> · C128

C128 = P36 · C93

P36 = 302592140766530934908888222616061079_<36>

C93 = [199151717224829651201838246240894378459227321597236742980797132267408631739729758957535014157_<93>]

Oct 25, 2007

By Robert Backstrom / GGNFS, Msieve

10¹⁶⁶+9 = 1(0)₁₆₅9_<167> = 6841 · 3298055297_<10> · C153

C153 = P47 · P106

P47 = 96175707342105206747325741564689382490429756801_<47>

P106 = 4608473425480966721109597553701118029210118730372926247354918207318621993190226935764939329385047887076817_<106>

Number: n
N=443223191462926543459909958595746661943719852080722467101166627816472353539797980148447621698392127726651524401212365554604364053039646401916272115182417
  ( 153 digits)
SNFS difficulty: 166 digits.
Divisors found:

Thu Oct 25 15:40:05 2007  prp47 factor: 96175707342105206747325741564689382490429756801
Thu Oct 25 15:40:05 2007  prp106 factor: 4608473425480966721109597553701118029210118730372926247354918207318621993190226935764939329385047887076817
Thu Oct 25 15:40:05 2007  elapsed time 01:54:23 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 62.44 hours.
Scaled time: 82.79 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_1_0_165_9
n: 443223191462926543459909958595746661943719852080722467101166627816472353539797980148447621698392127726651524401212365554604364053039646401916272115182417
skew: 0.98
deg: 5
c5: 10
c0: 9
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2900000)
Primes: RFBsize:250150, AFBsize:250021, largePrimes:7553576 encountered
Relations: rels:7043754, finalFF:563405
Max relations in full relation-set: 28
Initial matrix: 500238 x 563405 with sparse part having weight 49550458.
Pruned matrix : 457419 x 459984 with weight 35024031.
Total sieving time: 62.12 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 62.44 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 24, 2007 (5th)

By Jo Yeong Uk / GGNFS, GMP-ECM

(10¹⁶⁰+11)/3 = (3)₁₅₉7_<160> = 2357 · 3547 · 6483784428566166293003_<22> · C131

C131 = P65 · P66

P65 = 98546042989459507145454598033560826513496496641717463749658701161_<65>

P66 = 624008085251487858816186117499534910163524917199921025095545919941_<66>

Number: 33337_160
N=61493527594963435585105940425622344176908261835783977623937353322902951931684135308791965353024017933025951725442269952202949751501
  ( 131 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=98546042989459507145454598033560826513496496641717463749658701161 (pp65)
 r2=624008085251487858816186117499534910163524917199921025095545919941 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.41 hours.
Scaled time: 51.96 units (timescale=2.129).
Factorization parameters were as follows:
n: 61493527594963435585105940425622344176908261835783977623937353322902951931684135308791965353024017933025951725442269952202949751501
m: 100000000000000000000000000000000
c5: 1
c0: 11
skew: 1.62
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3400001)
Primes: RFBsize:283146, AFBsize:283048, largePrimes:5715875 encountered
Relations: rels:5844133, finalFF:739067
Max relations in full relation-set: 28
Initial matrix: 566258 x 739067 with sparse part having weight 45560931.
Pruned matrix : 423383 x 426278 with weight 27548907.
Total sieving time: 23.43 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.85 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 24.41 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(28·10¹⁵⁹-1)/9 = 3(1)₁₅₉_<160> = 3³ · 97 · 717667 · 31119047 · 4319493713_<10> · C134

C134 = P51 · P83

P51 = 691407189640250229701631872793975317289967702892453_<51>

P83 = 17810004148297787657731990085303963501623195591076357396769870762158063825273702029_<83>

Number: 31111_159
N=12313964915655771746286044453350809950290851202515862861599384612499767983759056219534341024515693473314812267723013626438858554887137
  ( 134 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=691407189640250229701631872793975317289967702892453 (pp51)
 r2=17810004148297787657731990085303963501623195591076357396769870762158063825273702029 (pp83)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 31.18 hours.
Scaled time: 66.89 units (timescale=2.145).
Factorization parameters were as follows:
n: 12313964915655771746286044453350809950290851202515862861599384612499767983759056219534341024515693473314812267723013626438858554887137
m: 100000000000000000000000000000000
c5: 14
c0: -5
skew: 0.81
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3800001)
Primes: RFBsize:283146, AFBsize:284317, largePrimes:5680047 encountered
Relations: rels:5727480, finalFF:670051
Max relations in full relation-set: 28
Initial matrix: 567529 x 670051 with sparse part having weight 43786702.
Pruned matrix : 489700 x 492601 with weight 29899843.
Total sieving time: 29.75 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.29 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 31.18 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(2·10¹⁶²+43)/9 = (2)₁₆₁7_<162> = 79 · 3074539183721_<13> · 92026938157876922867_<20> · C127

C127 = P31 · P97

P31 = 7374950638373593966200740279443_<31>

P97 = 1348050841856743517595672702299157137569123136816328878609841055467622001119053294651183847225613_<97>

(4·10¹⁶²-13)/9 = (4)₁₆₁3_<162> = 4795407827859115566133901_<25> · C137

C137 = P30 · P108

P30 = 732132950352080637131122456739_<30>

P108 = 126590752328295613964062194725925454032813432338962666501971716450553063422318328708874925852644810865626637_<108>

(5·10¹⁶²-41)/9 = (5)₁₆₁1_<162> = 17 · 7802477 · 1221834755184846949_<19> · C136

C136 = P29 · P107

P29 = 74150969555284684198040824859_<29>

P107 = 46229241501927787031803827366761897615314009076339630433468603502437500587889723061122144734719131912055229_<107>

3·10¹⁶³-7 = 2(9)₁₆₂3_<164> = 41 · 43 · 73 · 433163734125755498123_<21> · C138

C138 = P33 · P105

P33 = 984803325251956195887249668731139_<33>

P105 = 546442521935781460110773913223987286991730594097092602213887622250012599971203648826978554376441175284731_<105>

Oct 24, 2007 (4th)

By Sinkiti Sibata / GGNFS

(8·10¹⁵⁸+7)/3 = 2(6)₁₅₇9_<159> = 453968096244493_<15> · C144

C144 = P56 · P88

P56 = 77025991204399032295102167879033530984020107406191788251_<56>

P88 = 7626163354920877208117873161490105884353828530163763489424107667430447229492870343004083_<88>

Number: 26669_158
N=587412791499445703414789501643028537938176365461039166386707531445737063824203352653873977007985725071863227998012464875392047576593221164428833
  ( 144 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=77025991204399032295102167879033530984020107406191788251 (pp56)
 r2=7626163354920877208117873161490105884353828530163763489424107667430447229492870343004083 (pp88)
Version: GGNFS-0.77.1-20060513-k8
Total time: 59.71 hours.
Scaled time: 118.95 units (timescale=1.992).
Factorization parameters were as follows:
name: 26669_158
n: 587412791499445703414789501643028537938176365461039166386707531445737063824203352653873977007985725071863227998012464875392047576593221164428833
m: 20000000000000000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3900001)
Primes: RFBsize:283146, AFBsize:284107, largePrimes:5971981 encountered
Relations: rels:6202849, finalFF:822675
Max relations in full relation-set: 28
Initial matrix: 567319 x 822675 with sparse part having weight 58139262.
Pruned matrix : 388038 x 390938 with weight 44121525.
Total sieving time: 56.94 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 2.38 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 59.71 hours.
 --------- CPU info (if available) ----------

Oct 24, 2007 (3rd)

By Robert Backstrom / GGNFS

(8·10¹⁵²+7)/3 = 2(6)₁₅₁9_<153> = 61 · C151

C151 = P39 · P113

P39 = 421869844046731851658147807645650077819_<39>

P113 = 10362401487434351205807812414291785916154078462280535061673815273435490140412383670255796593884378838685001402691_<113>

Number: n
N=4371584699453551912568306010928961748633879781420765027322404371584699453551912568306010928961748633879781420765027322404371584699453551912568306010929
  ( 151 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=421869844046731851658147807645650077819 (pp39)
 r2=10362401487434351205807812414291785916154078462280535061673815273435490140412383670255796593884378838685001402691 (pp113)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 16.95 hours.
Scaled time: 22.10 units (timescale=1.304).
Factorization parameters were as follows:
name: KA_2_6_151_9
n: 4371584699453551912568306010928961748633879781420765027322404371584699453551912568306010928961748633879781420765027322404371584699453551912568306010929
skew: 0.78
deg: 5
c5: 25
c0: 7
m: 2000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 750001)
Primes: RFBsize:203362, AFBsize:203182, largePrimes:6399966 encountered
Relations: rels:5939023, finalFF:511751
Max relations in full relation-set: 28
Initial matrix: 406608 x 511751 with sparse part having weight 27504928.
Pruned matrix : 311614 x 313711 with weight 13508229.
Total sieving time: 15.13 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.56 hours.
Total square root time: 0.09 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 16.95 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 24, 2007 (2nd)

By Kurt Beschorner

10⁷⁵³+1 is divisible by 1756473376297178637489284481878718601_<37>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 24, 2007

By Yousuke Koide

10¹³⁷¹+1 is divisible by 127539278618607069275328998039143_<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 23, 2007

By Sinkiti Sibata / GGNFS

(8·10¹⁴⁶+7)/3 = 2(6)₁₄₅9_<147> = 2167165829_<10> · C138

C138 = P64 · P74

P64 = 4143397241869544226241437570296544113990642586158773224155313511_<64>

P74 = 29697508503653602939343659106341885529158177653874575739404674525553127951_<74>

Number: 26669_146
N=123048574824435673891693992129047484472249246906461197560099895182809596923866349254192982509723148032649543343582622844440699543102045961
  ( 138 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=4143397241869544226241437570296544113990642586158773224155313511 (pp64)
 r2=29697508503653602939343659106341885529158177653874575739404674525553127951 (pp74)
Version: GGNFS-0.77.1-20060513-k8
Total time: 19.70 hours.
Scaled time: 39.37 units (timescale=1.998).
Factorization parameters were as follows:
name: 26669_146
n: 123048574824435673891693992129047484472249246906461197560099895182809596923866349254192982509723148032649543343582622844440699543102045961
m: 200000000000000000000000000000
c5: 5
c0: 14
skew: 1.23
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2850001)
Primes: RFBsize:114155, AFBsize:114392, largePrimes:2877121 encountered
Relations: rels:2886374, finalFF:288594
Max relations in full relation-set: 28
Initial matrix: 228612 x 288594 with sparse part having weight 30123579.
Pruned matrix : 210472 x 211679 with weight 20270448.
Total sieving time: 18.98 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.51 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 19.70 hours.
 --------- CPU info (if available) ----------

Oct 23, 2007 (2nd)

By Jo Yeong Uk / GGNFS

(8·10¹⁶⁵+7)/3 = 2(6)₁₆₄9_<166> = 73 · 9803 · 19961 · 3844331 · 12325751 · 106692540971_<12> · 5524900734469672569379_<22> · C109

C109 = P33 · P36 · P42

P33 = 161800001655869356136898432615667_<33>

P36 = 226209579099872731684276944664364189_<36>

P42 = 182609076402191723318653867302508477992533_<42>

Number: 26669_165
N=6683621898604490720408773048442746311375034340493821379268599844292684440397247763706382879797337575415946579
  ( 109 digits)
Divisors found:
 r1=161800001655869356136898432615667 (pp33)
 r2=226209579099872731684276944664364189 (pp36)
 r3=182609076402191723318653867302508477992533 (pp42)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 14.55 hours.
Scaled time: 30.77 units (timescale=2.114).
Factorization parameters were as follows:
name: 26669_165
n: 6683621898604490720408773048442746311375034340493821379268599844292684440397247763706382879797337575415946579
skew: 30844.34
# norm 3.88e+15
c5: 32640
c4: -6377134016
c3: 10966983900756
c2: 6023277967525827220
c1: 20338186144994372135593
c0: -322736910701913843682752030
# alpha -6.58
Y1: 391238345143
Y0: -728218088733067565453
# Murphy_E 1.05e-09
# M 2458195276530130644457672644483945265068481024582090432931298737948038172243268879673145326804447368387365992
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1200000, 1920001)
Primes: RFBsize:176302, AFBsize:175803, largePrimes:7512919 encountered
Relations: rels:7327983, finalFF:490794
Max relations in full relation-set: 28
Initial matrix: 352190 x 490794 with sparse part having weight 47989971.
Pruned matrix : 258659 x 260483 with weight 27043110.
Polynomial selection time: 0.68 hours.
Total sieving time: 13.24 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.38 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000
total time: 14.55 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 23, 2007

By Robert Backstrom / GGNFS, Msieve

(64·10¹⁶⁰+53)/9 = 7(1)₁₅₉7_<161> = 23 · 191 · 114769 · 748180586440778137_<18> · C135

C135 = P43 · P92

P43 = 2272678914182122391159400004256881975433059_<43>

P92 = 82948234356112188698160244749473598135682577177508948629769483777144299322248884566566919647_<92>

Number: n
N=188514703189773269056083345014625106760612761414432617373683190484568696824418797686302626998621689259459609264199987578100566480410173
  ( 135 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Oct 23 03:14:29 2007  prp43 factor: 2272678914182122391159400004256881975433059
Tue Oct 23 03:14:29 2007  prp92 factor: 82948234356112188698160244749473598135682577177508948629769483777144299322248884566566919647
Tue Oct 23 03:14:29 2007  elapsed time 01:10:32 (Msieve 1.28)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 38.03 hours.
Scaled time: 49.78 units (timescale=1.309).
Factorization parameters were as follows:
name: KA_7_1_159_7
n: 188514703189773269056083345014625106760612761414432617373683190484568696824418797686302626998621689259459609264199987578100566480410173
skew: 1.93
deg: 5
c5: 2
c0: 53
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:216816, AFBsize:216946, largePrimes:7083358 encountered
Relations: rels:6573818, finalFF:499435
Max relations in full relation-set: 28
Initial matrix: 433827 x 499435 with sparse part having weight 36087703.
Pruned matrix : 381360 x 383593 with weight 23854377.
Total sieving time: 37.83 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 38.03 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(8·10¹⁶⁰+7)/3 = 2(6)₁₅₉9_<161> = 49843 · C156

C156 = P70 · P86

P70 = 8206529381083043352109674031409945933677801693490815409442456291123149_<70>

P86 = 65193609889480326298653585942015762338033823753726962763716880835878142163048859303067_<86>

Number: n
N=535013275016886356492720475626801490011970922028502832226524620642149683339017849380387750871068488386868099164710524379886175925740157427656173718810397983
  ( 156 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Oct 23 23:09:38 2007  prp70 factor: 8206529381083043352109674031409945933677801693490815409442456291123149
Tue Oct 23 23:09:38 2007  prp86 factor: 65193609889480326298653585942015762338033823753726962763716880835878142163048859303067
Tue Oct 23 23:09:38 2007  elapsed time 01:04:53 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 36.34 hours.
Scaled time: 52.83 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_2_6_159_9
n: 535013275016886356492720475626801490011970922028502832226524620642149683339017849380387750871068488386868099164710524379886175925740157427656173718810397983
skew: 1.95
deg: 5
c5: 1
c0: 28
m: 200000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1800000)
Primes: RFBsize:203362, AFBsize:203227, largePrimes:7259162 encountered
Relations: rels:6779635, finalFF:504684
Max relations in full relation-set: 28
Initial matrix: 406653 x 504684 with sparse part having weight 41751576.
Pruned matrix : 337714 x 339811 with weight 26445618.
Total sieving time: 36.12 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 36.34 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Oct 22, 2007 (4th)

By Sinkiti Sibata / PRIMO

(85·10²⁵⁸⁰-13)/9 is prime.

Oct 22, 2007 (3rd)

By Jo Yeong Uk / GGNFS

(8·10¹⁵⁴+7)/3 = 2(6)₁₅₃9_<155> = 17224619 · 55682718131_<11> · 46415095754141034190321569677_<29> · C108

C108 = P35 · P73

P35 = 63976167233321490585818587278762619_<35>

P73 = 9363133420441845598841194850047950471022696892436041111098985547200676067_<73>

Number: 26669_154
N=599017389534088974031064754543587991849505713299448734373260781981910865693172098475924868395465908007539473
  ( 108 digits)
Divisors found:
 r1=63976167233321490585818587278762619 (pp35)
 r2=9363133420441845598841194850047950471022696892436041111098985547200676067 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.65 hours.
Scaled time: 22.83 units (timescale=2.144).
Factorization parameters were as follows:
name: 26669_154
n: 599017389534088974031064754543587991849505713299448734373260781981910865693172098475924868395465908007539473
skew: 21354.62
# norm 6.78e+14
c5: 32400
c4: 104238510
c3: -63159803819065
c2: 42231149150739894
c1: 10386860579266260178521
c0: 1573011234854712440644311
# alpha -5.93
Y1: 268163654693
Y0: -450172247251438281950
# Murphy_E 1.31e-09
# M 353372238522770296188352642033280019967747150736232710020604793608863613888916745569090484185353683588909139
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1440001)
Primes: RFBsize:135072, AFBsize:135004, largePrimes:4543413 encountered
Relations: rels:4565506, finalFF:355041
Max relations in full relation-set: 28
Initial matrix: 270157 x 355041 with sparse part having weight 33355043.
Pruned matrix : 221309 x 222723 with weight 18208925.
Polynomial selection time: 0.60 hours.
Total sieving time: 9.69 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 10.65 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹⁵⁷+7)/3 = 2(6)₁₅₆9_<158>= 71 · 73 · 4423 · 17761 · 463849 · 131698991 · C133

C133 = P48 · P85

P48 = 272730925941823417805548362043843409679870198107_<48>

P85 = 3931060343889521523931450002903303012283257053146040409429479768292617881055891882137_<85>

Number: 26669_157
N=1072121727522171991711117449162947893294510889614725272405934873471024006838246193709580176818241416588454805181432061281055284514659
  ( 133 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=272730925941823417805548362043843409679870198107 (pp48)
 r2=3931060343889521523931450002903303012283257053146040409429479768292617881055891882137 (pp85)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 19.84 hours.
Scaled time: 42.45 units (timescale=2.140).
Factorization parameters were as follows:
n: 1072121727522171991711117449162947893294510889614725272405934873471024006838246193709580176818241416588454805181432061281055284514659
m: 20000000000000000000000000000000
c5: 25
c0: 7
skew: 0.78
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2700001)
Primes: RFBsize:216816, AFBsize:216906, largePrimes:5656803 encountered
Relations: rels:5671985, finalFF:600758
Max relations in full relation-set: 28
Initial matrix: 433786 x 600758 with sparse part having weight 46380712.
Pruned matrix : 331528 x 333760 with weight 28777533.
Total sieving time: 19.11 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.61 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 19.84 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 22, 2007 (2nd)

By Sinkiti Sibata / GGNFS

(8·10¹⁵⁰+7)/3 = 2(6)₁₄₉9_<151> = 19 · 19173023 · 221211127 · C134

C134 = P52 · P83

P52 = 3153611510488812690844381411841100171038865591531757_<52>

P83 = 10493234479791580568317662070396265616908097303633122206670593944661297064473922083_<83>

Number: 26669_150
N=33091585037728817063066885723269305783539863851825906597312108108442540229578000079303679297783978010391230631520577621957205438089831
  ( 134 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=3153611510488812690844381411841100171038865591531757 (pp52)
 r2=10493234479791580568317662070396265616908097303633122206670593944661297064473922083 (pp83)
Version: GGNFS-0.77.1-20060513-k8
Total time: 21.11 hours.
Scaled time: 42.22 units (timescale=2.000).
Factorization parameters were as follows:
name: 26669_150
n: 33091585037728817063066885723269305783539863851825906597312108108442540229578000079303679297783978010391230631520577621957205438089831
m: 1000000000000000000000000000000
c5: 8
c0: 7
skew: 0.97
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:176343, largePrimes:5664697 encountered
Relations: rels:5756890, finalFF:642726
Max relations in full relation-set: 28
Initial matrix: 352710 x 642726 with sparse part having weight 56826393.
Pruned matrix : 241016 x 242843 with weight 25378288.
Total sieving time: 20.10 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.75 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 21.11 hours.
 --------- CPU info (if available) ----------

(8·10¹⁴³+7)/3 = 2(6)₁₄₂9_<144> = 13² · 3517 · 62776679931694823_<17> · C121

C121 = P47 · P75

P47 = 20021116406067209554446200468334668005750140859_<47>

P75 = 356962853960238997946851914156890231498548267914175830313090442617598040829_<75>

Number: 26669_143
N=7146794851779914387843228963979571845388741890295760803609820465560862056129003230767892770563281325758005179009183132111
  ( 121 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=20021116406067209554446200468334668005750140859 (pp47)
 r2=356962853960238997946851914156890231498548267914175830313090442617598040829 (pp75)
Version: GGNFS-0.77.1-20060513-k8
Total time: 17.14 hours.
Scaled time: 34.23 units (timescale=1.997).
Factorization parameters were as follows:
nama: 26669_143
n: 7146794851779914387843228963979571845388741890295760803609820465560862056129003230767892770563281325758005179009183132111
m: 20000000000000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2550001)
Primes: RFBsize:100021, AFBsize:100373, largePrimes:2900939 encountered
Relations: rels:2943333, finalFF:278741
Max relations in full relation-set: 28
Initial matrix: 200460 x 278741 with sparse part having weight 32014645.
Pruned matrix : 180795 x 181861 with weight 19476116.
Total sieving time: 16.50 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.43 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 17.14 hours.
 --------- CPU info (if available) ----------

Oct 22, 2007

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(13·10¹⁶⁵-1)/3 = 4(3)₁₆₅_<166> = 7 · 801331 · C159

C159 = P77 · P83

P77 = 20581230672475861430727158263255086663302501457153191742856250309416063163917_<77>

P83 = 37535376232092446430954426168419670162044288493908322073297750728833564783295676597_<83>

Number: n
N=772524236610862487060961848534025324889524577294050832451318642418200528394692853574389419127735753449721834821125875633937845433469588781189106148455031750449
  ( 159 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Oct 22 02:26:02 2007  prp77 factor: 20581230672475861430727158263255086663302501457153191742856250309416063163917
Mon Oct 22 02:26:02 2007  prp83 factor: 37535376232092446430954426168419670162044288493908322073297750728833564783295676597
Mon Oct 22 02:26:02 2007  elapsed time 02:07:00 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 54.52 hours.
Scaled time: 65.37 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_4_3_165
n: 772524236610862487060961848534025324889524577294050832451318642418200528394692853574389419127735753449721834821125875633937845433469588781189106148455031750449
type: snfs
skew: 0.60
deg: 5
c5: 13
c0: -1
m: 1000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2300001)
Primes: RFBsize:250150, AFBsize:249271, largePrimes:7324010 encountered
Relations: rels:6828395, finalFF:550183
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 54.23 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 54.52 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(8·10¹⁶²+7)/3 = 2(6)₁₆₁9_<163> = 23 · 2417 · C158

C158 = P38 · P121

P38 = 13758431094795674099921153836784941879_<38>

P121 = 3486545464024582803252161746345501308393073883180459970373351716778246003294776444321266822336985947908508412928696412621_<121>

Oct 21, 2007 (5th)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(2·10¹⁶⁵+1)/3 = (6)₁₆₄7_<165> = 1907 · 25763 · 1950089 · C151

C151 = P38 · P54 · P61

P38 = 11159480313913593484408359509139419441_<38>

P54 = 145144015245287700460200196670856548838130894793891909_<54>

P61 = 4295998076553065365533511361350566844970496455322403010819807_<61>

prp38 factor: 11159480313913593484408359509139419441
prp54 factor: 145144015245287700460200196670856548838130894793891909
prp61 factor: 4295998076553065365533511361350566844970496455322403010819807

GMP-ECM 6.0.1 [powered by GMP 4.1.4] [ECM]
Input number is 6958364614900921735999678821358908199403904875839651413675026093315854699909592774863910249349186886963352504343210374853320078119407677971416772426283 (151 digits)
Using B1=1361500, B2=1303162716, polynomial Dickson(6), sigma=52991453
Step 1 took 19547ms
Step 2 took 9719ms
********** Factor found in step 2: 11159480313913593484408359509139419441
Found probable prime factor of 38 digits: 11159480313913593484408359509139419441
Composite cofactor 623538410316944757090120947223253498225421302104017860093686064012093871425660741494485547326568250544542234241563 has 114 digits

Number: n
N=623538410316944757090120947223253498225421302104017860093686064012093871425660741494485547326568250544542234241563
  ( 114 digits)
SNFS difficulty: 165 digits.
Divisors found:

Sun Oct 21 14:25:53 2007  prp54 factor: 145144015245287700460200196670856548838130894793891909
Sun Oct 21 14:25:53 2007  prp61 factor: 4295998076553065365533511361350566844970496455322403010819807
Sun Oct 21 14:25:53 2007  elapsed time 01:41:00 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 43.08 hours.
Scaled time: 62.64 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_6_164_7

n: 623538410316944757090120947223253498225421302104017860093686064012093871425660741494485547326568250544542234241563

# n: 6958364614900921735999678821358908199403904875839651413675026093315854699909592774863910249349186886963352504343210374853320078119407677971416772426283

skew: 0.87
deg: 5
c5: 2
c0: 1
m: 1000000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2300001)
Primes: RFBsize:203362, AFBsize:203032, largePrimes:7214058 encountered
Relations: rels:6650540, finalFF:426929
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 42.87 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 43.08 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(8·10¹⁶⁵-53)/9 = (8)₁₆₄3_<165> = 6403993 · C159

C159 = P45 · P114

P45 = 350982021485651168585060151283338980210340619_<45>

P114 = 395468373808917744465660761189260784883193175621159446317143996419722368165129799067011823208112320581081097991649_<114>

Number: n
N=138802289273097095654053477086700264801802389366897947716196580616013928948530844566645979920479127458273125671575357575951268043061397613783914018783107490731
  ( 159 digits)
SNFS difficulty: 165 digits.
Divisors found:

Sun Oct 21 20:17:38 2007  prp45 factor: 350982021485651168585060151283338980210340619
Sun Oct 21 20:17:38 2007  prp114 factor: 395468373808917744465660761189260784883193175621159446317143996419722368165129799067011823208112320581081097991649
Sun Oct 21 20:17:38 2007  elapsed time 01:35:15 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 47.74 hours.
Scaled time: 63.31 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_8_164_3
n: 138802289273097095654053477086700264801802389366897947716196580616013928948530844566645979920479127458273125671575357575951268043061397613783914018783107490731
skew: 1.46
deg: 5
c5: 8
c0: -53
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2200000)
Primes: RFBsize:250150, AFBsize:250051, largePrimes:7311231 encountered
Relations: rels:6818524, finalFF:565781
Max relations in full relation-set: 28
Initial matrix: 500266 x 565781 with sparse part having weight 42203089.
Pruned matrix : 447352 x 449917 with weight 27775961.
Total sieving time: 47.50 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 47.74 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 21, 2007 (4th)

By anonymous / GMP-ECM

(5·10¹⁹⁰+7)/3 = 1(6)₁₈₉9_<191> = 983 · 3110537 · 4168826771_<10> · 54213944958939972267302651_<26> · C146

C146 = P29 · P117

P29 = 95241712200343898401070633893_<29>

P117 = 253225715089880357003437152506851618536597279889801230013665252373632182359449182088181293413579341092522759275175463_<117>

Oct 21, 2007 (3rd)

By Sinkiti Sibata / GGNFS

(8·10¹³⁰+7)/3 = 2(6)₁₂₉9_<131> = 359 · C128

C128 = P33 · P96

P33 = 682633639211723545834566164085833_<33>

P96 = 108814456650602300245382079887888010720933070751698732192617045113744525935607329203942293274227_<96>

Number: 26669_130
N=74280408542246982358402971216341689879294336118848653667595171773444753946146703806870937790157845868152274837511606313834726091
  ( 128 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=682633639211723545834566164085833 (pp33)
 r2=108814456650602300245382079887888010720933070751698732192617045113744525935607329203942293274227 (pp96)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.74 hours.
Scaled time: 7.43 units (timescale=1.987).
Factorization parameters were as follows:
name: 26669_130
n: 74280408542246982358402971216341689879294336118848653667595171773444753946146703806870937790157845868152274837511606313834726091
m: 100000000000000000000000000
c5: 8
c0: 7
skew: 0.97
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:63951, AFBsize:64073, largePrimes:1455357 encountered
Relations: rels:1452260, finalFF:170662
Max relations in full relation-set: 28
Initial matrix: 128089 x 170662 with sparse part having weight 10762332.
Pruned matrix : 114592 x 115296 with weight 5636879.
Total sieving time: 3.59 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 3.74 hours.
 --------- CPU info (if available) ----------

(8·10¹³³+7)/3 = 2(6)₁₃₂9_<134> = 73 · 523 · 30253 · 694831 · 1145213 · C113

C113 = P42 · P72

P42 = 133271547249140168413145147446888048704353_<42>

P72 = 217707224173432323868406589757746873580273750494054826756936569259268393_<72>

Number: 26669_133
N=29014178612908736597074844178599916279879417120217498603765526981626610191279580281530698625258572423340334414729
  ( 113 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=133271547249140168413145147446888048704353 (pp42)
 r2=217707224173432323868406589757746873580273750494054826756936569259268393 (pp72)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.92 hours.
Scaled time: 13.77 units (timescale=1.988).
Factorization parameters were as follows:
name: 26669_133
n: 29014178612908736597074844178599916279879417120217498603765526981626610191279580281530698625258572423340334414729
m: 200000000000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1225001)
Primes: RFBsize:78498, AFBsize:64168, largePrimes:1593511 encountered
Relations: rels:1626248, finalFF:203055
Max relations in full relation-set: 28
Initial matrix: 142732 x 203055 with sparse part having weight 17060245.
Pruned matrix : 124557 x 125334 with weight 8832672.
Total sieving time: 6.72 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,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 6.92 hours.
 --------- CPU info (if available) ----------

(8·10¹⁰³+7)/3 = 2(6)₁₀₂9_<104> = 6641346161_<10> · C94

C94 = P44 · P50

P44 = 50628118279694776375171982905395943152916717_<44>

P50 = 79308699618830633011348707020263138933756280563537_<50>

Number: 26669_103
N=4015250224910941314607779057861800657715583674522859533065478269484027075195044432297987948029
  ( 94 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=50628118279694776375171982905395943152916717 (pp44)
 r2=79308699618830633011348707020263138933756280563537 (pp50)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1.18 hours.
Scaled time: 2.36 units (timescale=1.995).
Factorization parameters were as follows:
name: 26669_103
n: 4015250224910941314607779057861800657715583674522859533065478269484027075195044432297987948029
m: 200000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [250000, 350001)
Primes: RFBsize:37706, AFBsize:41542, largePrimes:1391765 encountered
Relations: rels:1503988, finalFF:273193
Max relations in full relation-set: 28
Initial matrix: 79314 x 273193 with sparse part having weight 11183859.
Pruned matrix : 40266 x 40726 with weight 1829275.
Total sieving time: 1.13 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,103,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000
total time: 1.18 hours.
 --------- CPU info (if available) ----------

(8·10¹⁰⁴+7)/3 = 2(6)₁₀₃9_<105> = 76561 · C100

C100 = P33 · P67

P33 = 733945223005884153559250475665329_<33>

P67 = 4745669469153279016048570235521763800475125498182552663288629329901_<67>

Number: 26669_104
N=3483061436849919236512933042497703356365077084503424284775103076849396777297405554612226416408702429
  ( 100 digits)
SNFS difficulty: 105 digits.
Divisors found:
 r1=733945223005884153559250475665329 (pp33)
 r2=4745669469153279016048570235521763800475125498182552663288629329901 (pp67)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1.96 hours.
Scaled time: 3.87 units (timescale=1.977).
Factorization parameters were as follows:
name: 26669_104
n: 3483061436849919236512933042497703356365077084503424284775103076849396777297405554612226416408702429
m: 1000000000000000000000
c5: 4
c0: 35
skew: 1.54
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 450001)
Primes: RFBsize:49098, AFBsize:64193, largePrimes:2081424 encountered
Relations: rels:2253638, finalFF:328853
Max relations in full relation-set: 28
Initial matrix: 113355 x 328853 with sparse part having weight 22829670.
Pruned matrix : 62492 x 63122 with weight 3004338.
Total sieving time: 1.88 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,105,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.96 hours.
 --------- CPU info (if available) ----------

(8·10¹³⁴+7)/3 = 2(6)₁₃₃9_<135> = 148654243 · 1262823917_<10> · C118

C118 = P41 · P77

P41 = 37620956682884538589371868827603031738343_<41>

P77 = 37758852612331776616795032844299692308607656131997210191374930427924942519293_<77>

Number: 26669_134
N=1420524158523955469338558698249232537056327868898328355704847871904688048016727899141317771917491175737048611605351499
  ( 118 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=37620956682884538589371868827603031738343 (pp41)
 r2=37758852612331776616795032844299692308607656131997210191374930427924942519293 (pp77)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.82 hours.
Scaled time: 11.68 units (timescale=2.007).
Factorization parameters were as follows:
name: 26669_134
n: 1420524158523955469338558698249232537056327868898328355704847871904688048016727899141317771917491175737048611605351499
m: 1000000000000000000000000000
c5: 4
c0: 35
skew: 1.54
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:64193, largePrimes:1541556 encountered
Relations: rels:1560889, finalFF:192289
Max relations in full relation-set: 28
Initial matrix: 142755 x 192289 with sparse part having weight 14621950.
Pruned matrix : 126409 x 127186 with weight 7901050.
Total sieving time: 5.64 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.82 hours.
 --------- CPU info (if available) ----------

(8·10¹⁴²+7)/3 = 2(6)₁₄₁9_<143> = 3064708476607_<13> · 4187678852923_<13> · C118

C118 = P40 · P78

P40 = 9788973638568650061780766529522450169529_<40>

P78 = 212260427653808834797575069001986356489959724932965465429439372027648665816401_<78>

Number: 26669_142
N=2077811730814442779423909735030670832942412279493881032584070517296902178699768133028182972994685705973158369638645129
  ( 118 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=9788973638568650061780766529522450169529 (pp40)
 r2=212260427653808834797575069001986356489959724932965465429439372027648665816401 (pp78)
Version: GGNFS-0.77.1-20060513-k8
Total time: 10.11 hours.
Scaled time: 20.14 units (timescale=1.992).
Factorization parameters were as follows:
name: 26669_142
n: 2077811730814442779423909735030670832942412279493881032584070517296902178699768133028182972994685705973158369638645129
m: 20000000000000000000000000000
c5: 25
c0: 7
skew: 0.78
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1750001)
Primes: RFBsize:100021, AFBsize:99418, largePrimes:2798512 encountered
Relations: rels:2847765, finalFF:330698
Max relations in full relation-set: 28
Initial matrix: 199503 x 330698 with sparse part having weight 30315932.
Pruned matrix : 162985 x 164046 with weight 13847017.
Total sieving time: 9.75 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 10.11 hours.
 --------- CPU info (if available) ----------

Oct 21, 2007 (2nd)

By Jo Yeong Uk / GGNFS

(8·10¹³⁹+7)/3 = 2(6)₁₃₈9_<140> = 1768103158425827_<16> · 27452760668249467_<17> · C108

C108 = P40 · P69

P40 = 1241873230306512944129120625376444423573_<40>

P69 = 442382402449578672496474001239726150208458221956431612701743308645417_<69>

Number: 26669_139
N=549382863160814110758042194456932311882676877376245309068323886591250711707365842143014691420858830013214941
  ( 108 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=1241873230306512944129120625376444423573 (pp40)
 r2=442382402449578672496474001239726150208458221956431612701743308645417 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.56 hours.
Scaled time: 11.90 units (timescale=2.140).
Factorization parameters were as follows:
n: 549382863160814110758042194456932311882676877376245309068323886591250711707365842143014691420858830013214941
m: 10000000000000000000000000000
c5: 4
c0: 35
skew: 1.54
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1100001)
Primes: RFBsize:114155, AFBsize:114442, largePrimes:3315311 encountered
Relations: rels:3411950, finalFF:393858
Max relations in full relation-set: 28
Initial matrix: 228661 x 393858 with sparse part having weight 33230335.
Pruned matrix : 169036 x 170243 with weight 12385404.
Total sieving time: 5.40 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 5.56 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹⁴¹+7)/3 = 2(6)₁₄₀9_<142> = 29 · 73 · 1339806917806153_<16> · 92415619460291259403_<20> · C104

C104 = P39 · P65

P39 = 502212812269744236328154953897511547463_<39>

P65 = 20256877015611825323436706422598519488570631957881652952297498821_<65>

Number: 26669_141
N=10173263173812758517105524274113209930018018460702750505221307224574470950799246504255661100980128041123
  ( 104 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=502212812269744236328154953897511547463 (pp39)
 r2=20256877015611825323436706422598519488570631957881652952297498821 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.21 hours.
Scaled time: 13.22 units (timescale=2.127).
Factorization parameters were as follows:
n: 10173263173812758517105524274113209930018018460702750505221307224574470950799246504255661100980128041123
m: 20000000000000000000000000000
c5: 5
c0: 14
skew: 1.23
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:114392, largePrimes:3261056 encountered
Relations: rels:3266559, finalFF:311634
Max relations in full relation-set: 28
Initial matrix: 228612 x 311634 with sparse part having weight 26294993.
Pruned matrix : 196110 x 197317 with weight 13252279.
Total sieving time: 6.01 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.21 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹⁵¹+7)/3 = 2(6)₁₅₀9_<152> = 83 · 191 · 222531925376261959597_<21> · 87151965549522581150273_<23> · C104

C104 = P37 · P68

P37 = 2151824979439633304570135127360335431_<37>

P68 = 40307031630293129082698941368209006104445744505208908458146567077043_<68>

Number: 26669_151
N=86733677509128161765261668212148242470942103656896529718188268435982587405152137619461718298337699610533
  ( 104 digits)
Divisors found:
 r1=2151824979439633304570135127360335431 (pp37)
 r2=40307031630293129082698941368209006104445744505208908458146567077043 (pp68)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.74 hours.
Scaled time: 12.28 units (timescale=2.138).
Factorization parameters were as follows:
name: 26669_151
n: 86733677509128161765261668212148242470942103656896529718188268435982587405152137619461718298337699610533
skew: 11778.21
# norm 6.95e+14
c5: 62160
c4: 1496130332
c3: -45556222412128
c2: -74626143902162469
c1: 113505084408824096690
c0: -1919290235623806504596725
# alpha -6.68
Y1: 4648483103
Y0: -67442740130436131592
# Murphy_E 2.11e-09
# M 56184838726415761082613399246235419642783909465629485767916514734753284656665661743230574578593360749961
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1620001)
Primes: RFBsize:135072, AFBsize:135343, largePrimes:4346551 encountered
Relations: rels:4257071, finalFF:317428
Max relations in full relation-set: 28
Initial matrix: 270499 x 317428 with sparse part having weight 25317400.
Pruned matrix : 238627 x 240043 with weight 16192467.
Polynomial selection time: 0.39 hours.
Total sieving time: 5.00 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 5.74 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 21, 2007

By Yousuke Koide

10¹⁰⁷³+1 is divisible by 588831771788611721102815421599303_<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 20, 2007 (5th)

By Jo Yeong Uk / GGNFS

(8·10¹³⁷+7)/3 = 2(6)₁₃₆9_<138> = 13 · 773 · 56401 · 23192382931_<11> · 887752643993_<12> · C107

C107 = P36 · P72

P36 = 225827415705440762247969188163076931_<36>

P72 = 101191741405873712462631199841067741763362688081142783407044807587961997_<72>

Number: 26669_137
N=22851869452421705492448224919086710644084493570019228618031253647076457659430866698743479971878791015391207
  ( 107 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=225827415705440762247969188163076931 (pp36)
 r2=101191741405873712462631199841067741763362688081142783407044807587961997 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.05 hours.
Scaled time: 6.48 units (timescale=2.122).
Factorization parameters were as follows:
n: 22851869452421705492448224919086710644084493570019228618031253647076457659430866698743479971878791015391207
m: 2000000000000000000000000000
c5: 25
c0: 7
skew: 0.78
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1250001)
Primes: RFBsize:107126, AFBsize:106423, largePrimes:2289110 encountered
Relations: rels:2432530, finalFF:305349
Max relations in full relation-set: 28
Initial matrix: 213613 x 305349 with sparse part having weight 22381011.
Pruned matrix : 177541 x 178673 with weight 10158100.
Total sieving time: 2.91 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 3.05 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 20, 2007 (4th)

By Sinkiti Sibata / GGNFS

8·10¹⁶²-7 = 7(9)₁₆₁3_<163> = 494213 · 388509891553534266757079_<24> · C134

C134 = P59 · P76

P59 = 16147676136454049333700128338546853224145331776821755134693_<59>

P76 = 2580261432154997404112328929704725753375527855692727120431726388111826233063_<76>

Number: 79993_162
N=41665225953822000619568717595040558356062958012654461159308411510245494930736049031230987938063485411773501288539791869984896374954659
  ( 134 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=16147676136454049333700128338546853224145331776821755134693 (pp59)
 r2=2580261432154997404112328929704725753375527855692727120431726388111826233063 (pp76)
Version: GGNFS-0.77.1-20060513-k8
Total time: 61.95 hours.
Scaled time: 124.03 units (timescale=2.002).
Factorization parameters were as follows:
name: 79993_162
n: 41665225953822000619568717595040558356062958012654461159308411510245494930736049031230987938063485411773501288539791869984896374954659
m: 200000000000000000000000000000000
c5: 25
c0: -7
skew: 0.78
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4150001)
Primes: RFBsize:315948, AFBsize:315706, largePrimes:5839925 encountered
Relations: rels:6045274, finalFF:823077
Max relations in full relation-set: 28
Initial matrix: 631718 x 823077 with sparse part having weight 47717456.
Pruned matrix : 473657 x 476879 with weight 31143738.
Total sieving time: 59.04 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 2.51 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 61.95 hours.
 --------- CPU info (if available) ----------

(8·10¹¹¹+7)/3 = 2(6)₁₁₀9_<112> = 2145389 · 1377179399_<10> · C96

C96 = P35 · P62

P35 = 18106717789925267749261242702101927_<35>

P62 = 49846243240205443718855673321344571054539531011124970246880177_<62>

Number: 26669_111
N=902551859238370029090835659332155419008692464984287175991403902356426578709847092352072009801079
  ( 96 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=18106717789925267749261242702101927 (pp35)
 r2=49846243240205443718855673321344571054539531011124970246880177 (pp62)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1.44 hours.
Scaled time: 2.88 units (timescale=2.004).
Factorization parameters were as follows:
name: 26669_111
n: 902551859238370029090835659332155419008692464984287175991403902356426578709847092352072009801079
m: 20000000000000000000000
c5: 5
c0: 14
skew: 1.23
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 450001)
Primes: RFBsize:49098, AFBsize:63943, largePrimes:2241963 encountered
Relations: rels:2551561, finalFF:441249
Max relations in full relation-set: 28
Initial matrix: 113106 x 441249 with sparse part having weight 35014615.
Pruned matrix : 62074 x 62703 with weight 4765126.
Total sieving time: 1.35 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,112,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.44 hours.
 --------- CPU info (if available) ----------

(8·10¹²³+7)/3 = 2(6)₁₂₂9_<124> = 1229019557_<10> · 379092951201193_<15> · C100

C100 = P49 · P52

P49 = 2898545393005568842248882069535618909163031509171_<49>

P52 = 1974622690311058776335153117537051940589078496100539_<52>

Number: 26669_123
N=5723533501925381515361880891681341029181435487375163222371432533464834744116374151471404911716543169
  ( 100 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=2898545393005568842248882069535618909163031509171 (pp49)
 r2=1974622690311058776335153117537051940589078496100539 (pp52)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.84 hours.
Scaled time: 5.61 units (timescale=1.980).
Factorization parameters were as follows:
name: 26669_123
n: 5723533501925381515361880891681341029181435487375163222371432533464834744116374151471404911716543169
m: 2000000000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:64168, largePrimes:2114570 encountered
Relations: rels:2123330, finalFF:147078
Max relations in full relation-set: 28
Initial matrix: 113332 x 147078 with sparse part having weight 13374411.
Pruned matrix : 104524 x 105154 with weight 7551198.
Total sieving time: 2.67 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.84 hours.
 --------- CPU info (if available) ----------

(8·10¹²⁸+7)/3 = 2(6)₁₂₇9_<129> = 419 · 16311689 · 7428034067_<10> · C109

C109 = P45 · P65

P45 = 351941064731415296526137239470932854807364819_<45>

P65 = 14924917745215309816252937894497602188907340265178654448165423583_<65>

Number: 26669_128
N=5252691442279870184066566890500076729558621086294228055364583650241045931829029287346821680267717975147126477
  ( 109 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=351941064731415296526137239470932854807364819 (pp45)
 r2=14924917745215309816252937894497602188907340265178654448165423583 (pp65)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.50 hours.
Scaled time: 8.89 units (timescale=1.977).
Factorization parameters were as follows:
name: 26669_128
n: 5252691442279870184066566890500076729558621086294228055364583650241045931829029287346821680267717975147126477
m: 20000000000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64168, largePrimes:1486278 encountered
Relations: rels:1489312, finalFF:175012
Max relations in full relation-set: 28
Initial matrix: 128185 x 175012 with sparse part having weight 12253287.
Pruned matrix : 114089 x 114793 with weight 6318497.
Total sieving time: 4.34 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.50 hours.
 --------- CPU info (if available) ----------

Oct 20, 2007 (3rd)

By Jo Yeong Uk / GGNFS

6·10¹⁵⁷+7 = 6(0)₁₅₆7_<158> = 29575545858739133328361799_<26> · C133

C133 = P54 · P79

P54 = 909973554507637615273149646490856241896005712528152743_<54>

P79 = 2229408796486527839879415799102804165173602971152320543487096830961582839982551_<79>

Number: 60007_157
N=2028703046989440216492418523064717588124374356914471327996618052411940079032641598918868315472019544767523143015305980889826382787393
  ( 133 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=909973554507637615273149646490856241896005712528152743 (pp54)
 r2=2229408796486527839879415799102804165173602971152320543487096830961582839982551 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 31.18 hours.
Scaled time: 66.81 units (timescale=2.143).
Factorization parameters were as follows:
n: 2028703046989440216492418523064717588124374356914471327996618052411940079032641598918868315472019544767523143015305980889826382787393
m: 20000000000000000000000000000000
c5: 75
c0: 28
skew: 0.82
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3800001)
Primes: RFBsize:283146, AFBsize:283092, largePrimes:5685473 encountered
Relations: rels:5694522, finalFF:634310
Max relations in full relation-set: 28
Initial matrix: 566304 x 634310 with sparse part having weight 42093593.
Pruned matrix : 518113 x 521008 with weight 30976126.
Total sieving time: 29.55 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.48 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 31.18 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹²⁰+7)/3 = 2(6)₁₁₉9_<121> = C121

C121 = P61 · P61

P61 = 1060471105842071452080239329331029536565351505210275149416401_<61>

P61 = 2514605680415204721631917533968366670395835407292136222935069_<61>

Number: 26669_120
N=2666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
  ( 121 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=1060471105842071452080239329331029536565351505210275149416401 (pp61)
 r2=2514605680415204721631917533968366670395835407292136222935069 (pp61)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.89 hours.
Scaled time: 1.88 units (timescale=2.115).
Factorization parameters were as follows:
n: 2666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
m: 2000000000000000000000000
c5: 1
c0: 28
skew: 1.95
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 450001)
Primes: RFBsize:49098, AFBsize:49156, largePrimes:1800198 encountered
Relations: rels:1786914, finalFF:141902
Max relations in full relation-set: 28
Initial matrix: 98318 x 141902 with sparse part having weight 11624596.
Pruned matrix : 86828 x 87383 with weight 5098835.
Total sieving time: 0.84 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.89 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹²⁹+7)/3 = 2(6)₁₂₈9_<130> = C130

C130 = P34 · P97

P34 = 1638212584355948805449002823879881_<34>

P97 = 1627790368681026216200316702373859265165289584295147399375933455475170245176591783551889658852549_<97>

Number: 26669_129
N=2666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
  ( 130 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=1638212584355948805449002823879881 (pp34)
 r2=1627790368681026216200316702373859265165289584295147399375933455475170245176591783551889658852549 (pp97)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.97 hours.
Scaled time: 4.23 units (timescale=2.142).
Factorization parameters were as follows:
n: 2666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
m: 100000000000000000000000000
c5: 4
c0: 35
skew: 1.54
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 900001)
Primes: RFBsize:78498, AFBsize:78746, largePrimes:1495528 encountered
Relations: rels:1503818, finalFF:187166
Max relations in full relation-set: 28
Initial matrix: 157308 x 187166 with sparse part having weight 9227172.
Pruned matrix : 142970 x 143820 with weight 5564851.
Total sieving time: 1.90 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 1.97 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(16·10¹⁵⁹-61)/9 = 1(7)₁₅₈1_<160> = 7 · 11 · 139 · 283 · 1123 · 5563 · 11321 · 1123247 · 11160628967_<11> · C126

C126 = P48 · P79

P48 = 188771796820566483431209728112718047569192774367_<48>

P79 = 3506798873133264834251861643109592173565728384191166286258478470759285819773297_<79>

Number: 17771_159
N=661984724369704169532858342692717943247722809774460911744787521251800997758672407790754400607584194600473401375243866412677999
  ( 126 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=188771796820566483431209728112718047569192774367 (pp48)
 r2=3506798873133264834251861643109592173565728384191166286258478470759285819773297 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 29.47 hours.
Scaled time: 63.21 units (timescale=2.145).
Factorization parameters were as follows:
n: 661984724369704169532858342692717943247722809774460911744787521251800997758672407790754400607584194600473401375243866412677999
m: 200000000000000000000000000000000
c5: 1
c0: -1220
skew: 4.14
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3700001)
Primes: RFBsize:283146, AFBsize:282548, largePrimes:5712059 encountered
Relations: rels:5803604, finalFF:708737
Max relations in full relation-set: 28
Initial matrix: 565758 x 708737 with sparse part having weight 44615649.
Pruned matrix : 451837 x 454729 with weight 28540403.
Total sieving time: 28.30 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 1.04 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 29.47 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹⁰⁶+7)/3 = 2(6)₁₀₅9_<107> = 38933 · C102

C102 = P31 · P72

P31 = 4246217137079532440315775172579_<31>

P72 = 161305309862279566253022081601447659781689908478972816016415808296252467_<72>

Number: 26669_106
N=684937371039135609037748610861394361253092920316098596734561083570920983912533497718302382725879502393
  ( 102 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=4246217137079532440315775172579 (pp31)
 r2=161305309862279566253022081601447659781689908478972816016415808296252467 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.46 hours.
Scaled time: 0.97 units (timescale=2.131).
Factorization parameters were as follows:
n: 684937371039135609037748610861394361253092920316098596734561083570920983912533497718302382725879502393
m: 2000000000000000000000
c5: 5
c0: 14
skew: 1.23
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 260001)
Primes: RFBsize:30757, AFBsize:30719, largePrimes:1032267 encountered
Relations: rels:965725, finalFF:100183
Max relations in full relation-set: 28
Initial matrix: 61541 x 100183 with sparse part having weight 4259001.
Pruned matrix : 47943 x 48314 with weight 1440203.
Total sieving time: 0.43 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,107,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.46 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹¹⁴+7)/3 = 2(6)₁₁₃9_<115> = 19 · 59 · 131 · 1613 · 172841183 · C98

C98 = P38 · P61

P38 = 15049466556427553742046054404910545751_<38>

P61 = 4328018617649452918247261765466850080785970021940189130656211_<61>

Number: 26669_114
N=65134371441911253580479783239297921264158773495625664468264260314515100006542227915558640767809461
  ( 98 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=15049466556427553742046054404910545751 (pp38)
 r2=4328018617649452918247261765466850080785970021940189130656211 (pp61)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.67 hours.
Scaled time: 1.44 units (timescale=2.143).
Factorization parameters were as follows:
n: 65134371441911253580479783239297921264158773495625664468264260314515100006542227915558640767809461
m: 100000000000000000000000
c5: 4
c0: 35
skew: 1.54
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 390001)
Primes: RFBsize:49098, AFBsize:49236, largePrimes:1810475 encountered
Relations: rels:1862920, finalFF:208249
Max relations in full relation-set: 28
Initial matrix: 98398 x 208249 with sparse part having weight 15809065.
Pruned matrix : 71479 x 72034 with weight 3436955.
Total sieving time: 0.63 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,115,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.67 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹²¹+7)/3 = 2(6)₁₂₀9_<122> = 1201 · 130987 · 356098343 · C105

C105 = P34 · P72

P34 = 2613842632420286549810407132723579_<34>

P72 = 182116015280402325835265886158642537928794970041065896876634298939239171_<72>

Number: 26669_121
N=476022604786419945107592660920030371584869577656015528481440710159671902378490644477488507224323312113009
  ( 105 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=2613842632420286549810407132723579 (pp34)
 r2=182116015280402325835265886158642537928794970041065896876634298939239171 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.03 hours.
Scaled time: 2.21 units (timescale=2.145).
Factorization parameters were as follows:
n: 476022604786419945107592660920030371584869577656015528481440710159671902378490644477488507224323312113009
m: 2000000000000000000000000
c5: 5
c0: 14
skew: 1.23
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 480001)
Primes: RFBsize:49098, AFBsize:49101, largePrimes:1853503 encountered
Relations: rels:1867932, finalFF:158603
Max relations in full relation-set: 28
Initial matrix: 98264 x 158603 with sparse part having weight 13988463.
Pruned matrix : 85087 x 85642 with weight 5253077.
Total sieving time: 0.97 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 1.03 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹²²+7)/3 = 2(6)₁₂₁9_<123> = 71 · C121

C121 = P32 · P89

P32 = 41145387625225226433684691675373_<32>

P89 = 91282857238129608087362318513711416984201527885327331838828175050639169331657601989276343_<89>

Number: 26669_122
N=3755868544600938967136150234741784037558685446009389671361502347417840375586854460093896713615023474178403755868544600939
  ( 121 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=41145387625225226433684691675373 (pp32)
 r2=91282857238129608087362318513711416984201527885327331838828175050639169331657601989276343 (pp89)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.01 hours.
Scaled time: 2.16 units (timescale=2.140).
Factorization parameters were as follows:
n: 3755868544600938967136150234741784037558685446009389671361502347417840375586854460093896713615023474178403755868544600939
m: 2000000000000000000000000
c5: 25
c0: 7
skew: 0.78
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:63951, AFBsize:63568, largePrimes:1347942 encountered
Relations: rels:1344158, finalFF:170026
Max relations in full relation-set: 28
Initial matrix: 127582 x 170026 with sparse part having weight 7333871.
Pruned matrix : 103697 x 104398 with weight 3449577.
Total sieving time: 0.96 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,800000,800000,25,25,45,45,2.2,2.2,40000
total time: 1.01 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹³⁶+7)/3 = 2(6)₁₃₅9_<137> = C137

C137 = P58 · P79

P58 = 5964796989232317289442216128587619639536748687234582636411_<58>

P79 = 4470674645726497105263584854203238916337233478995531171674915681021609495628279_<79>

Number: 26669_136
N=26666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
  ( 137 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=5964796989232317289442216128587619639536748687234582636411 (pp58)
 r2=4470674645726497105263584854203238916337233478995531171674915681021609495628279 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.34 hours.
Scaled time: 7.05 units (timescale=2.115).
Factorization parameters were as follows:
n: 26666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
m: 2000000000000000000000000000
c5: 5
c0: 14
skew: 1.23
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1300001)
Primes: RFBsize:107126, AFBsize:107483, largePrimes:2282771 encountered
Relations: rels:2388130, finalFF:269548
Max relations in full relation-set: 28
Initial matrix: 214674 x 269548 with sparse part having weight 20402502.
Pruned matrix : 193656 x 194793 with weight 11687881.
Total sieving time: 3.16 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 3.34 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 20, 2007 (2nd)

By Sinkiti Sibata / PRIMO

(19·10²⁴⁵⁰-1)/9 is prime.

Oct 20, 2007

The factor table of 266...669 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Oct 19, 2007 (4th)

By anonymous / GMP-ECM

(5·10¹⁹⁷+7)/3 = 1(6)₁₉₆9_<198> = 83 · C196

C196 = P32 · P165

P32 = 15064399083367851403807447165139_<32>

P165 = 133296530276542123994572514856391958946944378887295148756651456417065116602615650106241786028692598529148978098311741021285646641176103363192439421156437978817430437_<165>

Oct 19, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

(7·10¹⁶⁵-61)/9 = (7)₁₆₄1_<165> = 3 · 24320321 · C158

C158 = P43 · P56 · P60

P43 = 2761925283898534955675154755036172189749839_<43>

P56 = 31324884696363766525451707222706492435165921240617655521_<56>

P60 = 123214995686345230412614529840111656059539641564894743216343_<60>

Number: n
N=10660190680018543310314829284500778557127566665722021483978737750182625437355833389668633866274185248593522234318340586839263316436459011345255650994872117817
  ( 158 digits)
SNFS difficulty: 165 digits.
Divisors found:

Fri Oct 19 11:07:36 2007  prp43 factor: 2761925283898534955675154755036172189749839
Fri Oct 19 11:07:36 2007  prp56 factor: 31324884696363766525451707222706492435165921240617655521
Fri Oct 19 11:07:36 2007  prp60 factor: 123214995686345230412614529840111656059539641564894743216343
Fri Oct 19 11:07:36 2007  elapsed time 01:47:49 (Msieve 1.28)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 68.73 hours.
Scaled time: 89.90 units (timescale=1.308).
Factorization parameters were as follows:
name: KA_7_164_1
n: 10660190680018543310314829284500778557127566665722021483978737750182625437355833389668633866274185248593522234318340586839263316436459011345255650994872117817
skew: 1.54
deg: 5
c5: 7
c0: -61
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2700000)
Primes: RFBsize:216816, AFBsize:217077, largePrimes:7393191 encountered
Relations: rels:6842637, finalFF:458263
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 68.48 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 68.73 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 19, 2007 (2nd)

By Sinkiti Sibata / GGNFS

8·10¹⁵⁷-7 = 7(9)₁₅₆3_<158> = 857 · 3270705001345087307_<19> · C137

C137 = P45 · P92

P45 = 578713235026034382304696193140789480917763057_<45>

P92 = 49317877250812105191907662188584024853530218296906864974832385857053714133780682125502798451_<92>

Number: 79993_157
N=28540908288434340243572900615340141426849017077515115869543700976161255377143717419668797504442722574263007547983496570507801448444624707
  ( 137 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=578713235026034382304696193140789480917763057 (pp45)
 r2=49317877250812105191907662188584024853530218296906864974832385857053714133780682125502798451 (pp92)
Version: GGNFS-0.77.1-20060513-k8
Total time: 32.59 hours.
Scaled time: 64.80 units (timescale=1.988).
Factorization parameters were as follows:
name: 79993_157
n: 28540908288434340243572900615340141426849017077515115869543700976161255377143717419668797504442722574263007547983496570507801448444624707
m: 20000000000000000000000000000000
c5: 25
c0: -7
skew: 0.78
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:216906, largePrimes:5533011 encountered
Relations: rels:5442369, finalFF:511459
Max relations in full relation-set: 28
Initial matrix: 433786 x 511459 with sparse part having weight 38990519.
Pruned matrix : 385864 x 388096 with weight 26569740.
Total sieving time: 30.52 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 1.78 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 32.59 hours.
 --------- CPU info (if available) ----------

Oct 19, 2007

By Yousuke Koide

10¹²⁴⁰+1 is divisible by 15595203791066837732161767737921_<32>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 17, 2007 (5th)

By suberi / PRIMO

(49·10²³⁴⁰+23)/9 is prime.

(49·10²⁴⁵⁴+23)/9 is prime.

Oct 17, 2007 (4th)

By Jo Yeong Uk / GGNFS

6·10¹⁴⁷+7 = 6(0)₁₄₆7_<148> = 31 · 74460874157397706814885857_<26> · C121

C121 = P34 · P87

P34 = 3757810852757300286714196049398151_<34>

P87 = 691713910870677076891814665811219671401933953308716939722566516154829814248796350852671_<87>

Number: 60007_147
N=2599330041273026231158261182959552205625966726296449796273234752243784692588394514029060595219631994321473925185220811321
  ( 121 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=3757810852757300286714196049398151 (pp34)
 r2=691713910870677076891814665811219671401933953308716939722566516154829814248796350852671 (pp87)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 13.31 hours.
Scaled time: 28.42 units (timescale=2.135).
Factorization parameters were as follows:
n: 2599330041273026231158261182959552205625966726296449796273234752243784692588394514029060595219631994321473925185220811321
m: 200000000000000000000000000000
c5: 75
c0: 28
skew: 0.82
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1800001)
Primes: RFBsize:135072, AFBsize:134748, largePrimes:3940451 encountered
Relations: rels:4092560, finalFF:408421
Max relations in full relation-set: 28
Initial matrix: 269886 x 408421 with sparse part having weight 41102101.
Pruned matrix : 230332 x 231745 with weight 21474737.
Total sieving time: 12.95 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.27 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 13.31 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

6·10¹⁴⁹+7 = 6(0)₁₄₈7_<150> = 25747 · 436150417 · 2488433141_<10> · 314768938357_<12> · C116

C116 = P45 · P72

P45 = 288204824127944521231161772400113432086544229_<45>

P72 = 236684181525452140035337569045008331845614114346156387833169766487401841_<72>

Number: 60007_149
N=68213522910409429827571176132944362685370905642562309751882399036574081305064117581575728647981845432390542542525589
  ( 116 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=288204824127944521231161772400113432086544229 (pp45)
 r2=236684181525452140035337569045008331845614114346156387833169766487401841 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.33 hours.
Scaled time: 24.17 units (timescale=2.133).
Factorization parameters were as follows:
n: 68213522910409429827571176132944362685370905642562309751882399036574081305064117581575728647981845432390542542525589
m: 1000000000000000000000000000000
c5: 3
c0: 35
skew: 1.63
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1650001)
Primes: RFBsize:135072, AFBsize:135283, largePrimes:3745970 encountered
Relations: rels:3742941, finalFF:304925
Max relations in full relation-set: 28
Initial matrix: 270420 x 304925 with sparse part having weight 27971216.
Pruned matrix : 258210 x 259626 with weight 21031729.
Total sieving time: 10.95 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 11.33 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 17, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

8·10¹⁶⁰-7 = 7(9)₁₅₉3_<161> = 179 · 2341 · C156

C156 = P74 · P83

P74 = 16454596943744503209146711864636020997566170732129357607128813577870908913_<74>

P83 = 11602412280012005744956049762841701654854199246869403531853864740606458920710587799_<83>

Number: n
N=190913017642749242910564410472533582793009719859010736470829684110548182866033949107362321884120571116292278284360166953433928584212925288576958230618152487
  ( 156 digits)
SNFS difficulty: 160 digits.
Divisors found:

Thu Oct 18 14:19:06 2007  prp74 factor: 16454596943744503209146711864636020997566170732129357607128813577870908913
Thu Oct 18 14:19:06 2007  prp83 factor: 11602412280012005744956049762841701654854199246869403531853864740606458920710587799
Thu Oct 18 14:19:06 2007  elapsed time 01:30:26 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 44.43 hours.
Scaled time: 53.27 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_7_9_159_3
n: 190913017642749242910564410472533582793009719859010736470829684110548182866033949107362321884120571116292278284360166953433928584212925288576958230618152487
type: snfs
skew: 0.97
deg: 5
c5: 8
c0: -7
m: 100000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1900000)
Primes: RFBsize:230209, AFBsize:229842, largePrimes:6910058 encountered
Relations: rels:6394628, finalFF:542880
Max relations in full relation-set: 28
Initial matrix: 460116 x 542880 with sparse part having weight 33147572.
Pruned matrix : 389747 x 392111 with weight 20148312.
Total sieving time: 44.19 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 44.43 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Oct 17, 2007 (2nd)

By Sinkiti Sibata / GGNFS

8·10¹⁵⁶-7 = 7(9)₁₅₅3_<157> = 181 · 909281 · C149

C149 = P41 · P49 · P61

P41 = 10904285406759073728471842840772332558593_<41>

P49 = 1088070887339914750056094304772577853777226365141_<49>

P61 = 4096933317053668078876000501612735226248308616390449901334401_<61>

Number: 79993_156
N=48608620467846913541870107667669010851819834748797120444766932935980545031569810354864742533717415158103700184799645686904547817062501954598199593813
  ( 149 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=10904285406759073728471842840772332558593 (pp41)
 r2=1088070887339914750056094304772577853777226365141 (pp49)
 r3=4096933317053668078876000501612735226248308616390449901334401 (pp61)
Version: GGNFS-0.77.1-20060513-k8
Total time: 40.39 hours.
Scaled time: 80.67 units (timescale=1.997).
Factorization parameters were as follows:
name: 79993_156
n: 48608620467846913541870107667669010851819834748797120444766932935980545031569810354864742533717415158103700184799645686904547817062501954598199593813
m: 20000000000000000000000000000000
c5: 5
c0: -14
skew: 1.23
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2800001)
Primes: RFBsize:216816, AFBsize:217381, largePrimes:5747043 encountered
Relations: rels:5780210, finalFF:606107
Max relations in full relation-set: 28
Initial matrix: 434262 x 606107 with sparse part having weight 50764657.
Pruned matrix : 345539 x 347774 with weight 31579083.
Total sieving time: 38.37 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.68 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 40.39 hours.
 --------- CPU info (if available) ----------

Oct 18, 2007

By Sinkiti Sibata / PRIMO

(8·10²³⁰⁸+7)/3 is prime.

Oct 17, 2007 (3rd)

By Jo Yeong Uk / GGNFS

(4·10¹⁸⁸-31)/9 = (4)₁₈₇1_<188> = C188

C188 = P89 · P100

P89 = 13495944323227175196168775505661471275310792953928331944840120875227820565323694150016861_<89>

P100 = 3293170405864330551260159426012918407131606691963604942513292260623991525800017750997167920521516781_<100>

Number: 44441_188
N=44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441
  ( 188 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=13495944323227175196168775505661471275310792953928331944840120875227820565323694150016861 (pp89)
 r2=3293170405864330551260159426012918407131606691963604942513292260623991525800017750997167920521516781 (pp100)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 506.97 hours.
Scaled time: 1079.34 units (timescale=2.129).
Factorization parameters were as follows:
n: 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441
m: 100000000000000000000000000000000000000
c5: 1
c0: -775
skew: 3.78
type: snfs
Factor base limits: 13000000/13000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 51/51
Sieved algebraic special-q in [6500000, 14600001)
Primes: RFBsize:849252, AFBsize:849399, largePrimes:12866508 encountered
Relations: rels:13641443, finalFF:1950967
Max relations in full relation-set: 28
Initial matrix: 1698715 x 1950967 with sparse part having weight 145829012.
Pruned matrix : 1480381 x 1488938 with weight 111459556.
Total sieving time: 484.73 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 21.67 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,13000000,13000000,28,28,51,51,2.6,2.6,100000
total time: 506.97 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

P89 is the largest factor found by GGNFS in our tables so far. Congratulations!

Oct 17, 2007 (2nd)

By Robert Backstrom / GGNFS

8·10¹⁵⁸-7 = 7(9)₁₅₇3_<159> = 13 · 67 · C156

C156 = P75 · P82

P75 = 346176468096559273822741304052813207109273708583996031665987163333529663757_<75>

P82 = 2653226273941471985206044635089360508906271929143252016829426314360757542050928219_<82>

Number: n
N=918484500574052812858783008036739380022962112514351320321469575200918484500574052812858783008036739380022962112514351320321469575200918484500574052812858783
  ( 156 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=346176468096559273822741304052813207109273708583996031665987163333529663757 (pp75)
 r2=2653226273941471985206044635089360508906271929143252016829426314360757542050928219 (pp82)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 41.09 hours.
Scaled time: 53.30 units (timescale=1.297).
Factorization parameters were as follows:
name: KA_7_9_157_3
n: 918484500574052812858783008036739380022962112514351320321469575200918484500574052812858783008036739380022962112514351320321469575200918484500574052812858783
skew: 0.49
deg: 5
c5: 250
c0: -7
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1700001)
Primes: RFBsize:216816, AFBsize:217701, largePrimes:7120715 encountered
Relations: rels:6580353, finalFF:493138
Max relations in full relation-set: 48
Initial matrix: 434583 x 493138 with sparse part having weight 42370582.
Pruned matrix : 389862 x 392098 with weight 27989624.
Total sieving time: 36.05 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 4.66 hours.
Total square root time: 0.16 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 41.09 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 17, 2007

By Sinkiti Sibata / GGNFS

8·10¹⁵⁵-7 = 7(9)₁₅₄3_<156> = 17 · 29 · 43 · 671189 · 25898947 · C139

C139 = P33 · P107

P33 = 152487428057225842444645257923753_<33>

P107 = 14236841024808958548325101138045141061138828604047990755202358992513725161786539507007143495539941593140193_<107>

Number: 79993_155
N=2170939271532717501787887771947025467482753556964582820892856569651806507508303518706699363818037448964912725918478477349824220002633704329
  ( 139 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=152487428057225842444645257923753 (pp33)
 r2=14236841024808958548325101138045141061138828604047990755202358992513725161786539507007143495539941593140193 (pp107)
Version: GGNFS-0.77.1-20060513-k8
Total time: 32.46 hours.
Scaled time: 64.57 units (timescale=1.989).
Factorization parameters were as follows:
name: 79993_155
n: 2170939271532717501787887771947025467482753556964582820892856569651806507508303518706699363818037448964912725918478477349824220002633704329
m: 10000000000000000000000000000000
c5: 8
c0: -7
skew: 0.97
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:216531, largePrimes:5864311 encountered
Relations: rels:6046107, finalFF:741412
Max relations in full relation-set: 28
Initial matrix: 433412 x 741412 with sparse part having weight 59974965.
Pruned matrix : 286069 x 288300 with weight 35055031.
Total sieving time: 30.74 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.41 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 32.46 hours.
 --------- CPU info (if available) ----------

Oct 16, 2007 (5th)

By Sinkiti Sibata / PRIMO

(13·10²²¹⁵+23)/9 is prime.

Oct 16, 2007 (4th)

By suberi / PRIMO

(32·10²⁴⁸⁸-41)/9 is prime.

6·10²⁷⁴⁹+7 is prime.

(55·10²⁶⁸⁴+17)/9 is prime.

Oct 16, 2007 (3rd)

By Sinkiti Sibata / GGNFS, Msieve

8·10¹⁵⁴-7 = 7(9)₁₅₃3_<155> = 2356867 · 603555989507_<12> · C137

C137 = P33 · P105

P33 = 113351694760778508277044308809837_<33>

P105 = 496145811653311910056803679142753059087314051602854121158090203147254006251607995277425635648201231426581_<105>

Number: 79993_154
N=56238968599364916192824354906296195040092106248699331349662875284930630365782995510575903116148472404164256027791590822905326605756077297
  ( 137 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=113351694760778508277044308809837 (pp33)
 r2=496145811653311910056803679142753059087314051602854121158090203147254006251607995277425635648201231426581 (pp105)
Version: GGNFS-0.77.1-20060513-k8
Total time: 32.35 hours.
Scaled time: 64.79 units (timescale=2.003).
Factorization parameters were as follows:
name: 79993_154
n: 56238968599364916192824354906296195040092106248699331349662875284930630365782995510575903116148472404164256027791590822905326605756077297
m: 10000000000000000000000000000000
c5: 4
c0: -35
skew: 1.54
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:216906, largePrimes:5878753 encountered
Relations: rels:6079432, finalFF:757874
Max relations in full relation-set: 28
Initial matrix: 433786 x 757874 with sparse part having weight 61304584.
Pruned matrix : 284596 x 286828 with weight 35456047.
Total sieving time: 30.84 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.20 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 32.35 hours.
 --------- CPU info (if available) ----------

8·10¹⁵¹-7 = 7(9)₁₅₀3_<152> = 23 · 107 · 5569 · 6029 · 5676941659286357_<16> · 21788576409750498214905595223_<29> · C97

C97 = P31 · P67

P31 = 5423671886025109442120246388749_<31>

P67 = 1443175595670302296287530288340641513337370692964945259930652789367_<67>

Sun Oct 14 13:22:15 2007  Msieve v. 1.28
Sun Oct 14 13:22:15 2007  random seeds: bb320d00 c465a215
Sun Oct 14 13:22:15 2007  factoring 7827310904834559223584755757587750335344461821449169367211160089090463613553875031305565495631883 (97 digits)
Sun Oct 14 13:22:16 2007  commencing quadratic sieve (97-digit input)
Sun Oct 14 13:22:17 2007  using multiplier of 2
Sun Oct 14 13:22:17 2007  using 64kb Pentium 2 sieve core
Sun Oct 14 13:22:17 2007  sieve interval: 18 blocks of size 65536
Sun Oct 14 13:22:17 2007  processing polynomials in batches of 6
Sun Oct 14 13:22:17 2007  using a sieve bound of 2395621 (88235 primes)
Sun Oct 14 13:22:17 2007  using large prime bound of 359343150 (28 bits)
Sun Oct 14 13:22:17 2007  using double large prime bound of 2511405435485700 (43-52 bits)
Sun Oct 14 13:22:17 2007  using trial factoring cutoff of 52 bits
Sun Oct 14 13:22:17 2007  polynomial 'A' values have 13 factors
Tue Oct 16 05:45:50 2007  88486 relations (21837 full + 66649 combined from 1318373 partial), need 88331
Tue Oct 16 05:46:24 2007  begin with 1340210 relations
Tue Oct 16 05:49:03 2007  reduce to 229420 relations in 11 passes
Tue Oct 16 05:49:04 2007  attempting to read 229420 relations
Tue Oct 16 05:49:50 2007  recovered 229420 relations
Tue Oct 16 05:49:51 2007  recovered 215053 polynomials
Tue Oct 16 05:51:40 2007  attempting to build 88486 cycles
Tue Oct 16 05:51:49 2007  found 88486 cycles in 6 passes
Tue Oct 16 05:51:55 2007  distribution of cycle lengths:
Tue Oct 16 05:51:55 2007     length 1 : 21837
Tue Oct 16 05:51:55 2007     length 2 : 15474
Tue Oct 16 05:51:55 2007     length 3 : 15081
Tue Oct 16 05:51:55 2007     length 4 : 12029
Tue Oct 16 05:51:55 2007     length 5 : 8894
Tue Oct 16 05:51:55 2007     length 6 : 6072
Tue Oct 16 05:51:55 2007     length 7 : 3868
Tue Oct 16 05:51:55 2007     length 9+: 5231
Tue Oct 16 05:51:55 2007  largest cycle: 19 relations
Tue Oct 16 05:52:26 2007  matrix is 88235 x 88486 with weight 5849695 (avg 66.11/col)
Tue Oct 16 05:53:30 2007  filtering completed in 3 passes
Tue Oct 16 05:53:30 2007  matrix is 83979 x 84043 with weight 5585692 (avg 66.46/col)
Tue Oct 16 05:53:34 2007  saving the first 48 matrix rows for later
Tue Oct 16 05:53:35 2007  matrix is 83931 x 84043 with weight 4343397 (avg 51.68/col)
Tue Oct 16 05:53:35 2007  matrix includes 64 packed rows
Tue Oct 16 05:53:35 2007  using block size 10922 for processor cache size 256 kB
Tue Oct 16 05:53:38 2007  commencing Lanczos iteration
Tue Oct 16 05:59:52 2007  lanczos halted after 1329 iterations
Tue Oct 16 05:59:53 2007  recovered 18 nontrivial dependencies
Tue Oct 16 06:24:18 2007  prp31 factor: 5423671886025109442120246388749
Tue Oct 16 06:24:18 2007  prp67 factor: 1443175595670302296287530288340641513337370692964945259930652789367
Tue Oct 16 06:24:18 2007  elapsed time 41:02:03

8·10¹⁵²-7 = 7(9)₁₅₁3_<153> = 13 · 18307 · 4639298979169_<13> · 238372349228810543_<18> · C118

C118 = P33 · P86

P33 = 132196018950577432404812799228403_<33>

P86 = 22993381145741293920904930229003616713749210764279783545611429634014833752788402278923_<86>

Number: 79993_152
N=3039633449680265926335230629866243286215279582467641725078699207006615408808046094193646027979410320642927781189849969
  ( 118 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=132196018950577432404812799228403 (pp33)
 r2=22993381145741293920904930229003616713749210764279783545611429634014833752788402278923 (pp86)
Version: GGNFS-0.77.1-20060513-k8
Total time: 21.25 hours.
Scaled time: 42.02 units (timescale=1.978).
Factorization parameters were as follows:
name: 79993_152
n: 3039633449680265926335230629866243286215279582467641725078699207006615408808046094193646027979410320642927781189849969
m: 2000000000000000000000000000000
c5: 25
c0: -7
skew: 0.78
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:175903, largePrimes:5420804 encountered
Relations: rels:5333741, finalFF:489141
Max relations in full relation-set: 28
Initial matrix: 352269 x 489141 with sparse part having weight 41279494.
Pruned matrix : 285474 x 287299 with weight 22202017.
Total sieving time: 20.13 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.86 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 21.25 hours.
 --------- CPU info (if available) ----------

Oct 16, 2007 (2nd)

By Bryan Koen / GGNFS

(23·10¹⁷⁰+1)/3 = 7(6)₁₆₉7_<171> = 13 · 461 · 1289 · 10909069 · 3428780111_<10> · 5783988689_<10> · 1475103520971674381_<19> · C120

C120 = P50 · P71

P50 = 28622256358095202962667644344453285032065134088263_<50>

P71 = 10864963237661550249466184242559236733294008124794269198135353057048507_<71>

Number: 76667_170
N=310979763109628948369420398838169134459778745943966806045542931361213579741500676681882065931657868642085688329210373341
  ( 120 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=28622256358095202962667644344453285032065134088263 (pp50)
 r2=10864963237661550249466184242559236733294008124794269198135353057048507 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 96.07 hours.
Scaled time: 214.23 units (timescale=2.230).
Factorization parameters were as follows:
n: 310979763109628948369420398838169134459778745943966806045542931361213579741500676681882065931657868642085688329210373341
m: 10000000000000000000000000000000000
c5: 23
c0: 1
skew: 0.53
type: snfs

Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 6700001)
Primes: RFBsize:412849, AFBsize:412891, largePrimes:5994447 encountered
Relations: rels:6291016, finalFF:958381
Max relations in full relation-set: 28
Initial matrix: 825805 x 958381 with sparse part having weight 51452736.
Pruned matrix : 711926 x 716119 with weight 36381718.
Total sieving time: 83.92 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 11.78 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 96.07 hours.
 --------- CPU info (if available) ----------

Oct 16, 2007

By Robert Backstrom / GGNFS, Msieve

6·10¹⁶⁴+7 = 6(0)₁₆₃7_<165> = 29 · 127031 · C159

C159 = P61 · P98

P61 = 1770843922137685855971883220866292296403759900031873711559753_<61>

P98 = 91973613665363851062774584215016713526677170996970636469854370682108828520625054063548519257625981_<98>

Number: n
N=162870914756349183297370530516716120610255601470072876590807728442066408443879704628167058868877784108630556918091402614458213973835873350490879364499406742693
  ( 159 digits)
SNFS difficulty: 165 digits.
Divisors found:

Tue Oct 16 01:56:00 2007  prp61 factor: 1770843922137685855971883220866292296403759900031873711559753
Tue Oct 16 01:56:00 2007  prp98 factor: 91973613665363851062774584215016713526677170996970636469854370682108828520625054063548519257625981
Tue Oct 16 01:56:00 2007  elapsed time 01:28:26 (Msieve 1.28)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 53.90 hours.
Scaled time: 70.50 units (timescale=1.308).
Factorization parameters were as follows:
name: KA_6_0_163_7
n: 162870914756349183297370530516716120610255601470072876590807728442066408443879704628167058868877784108630556918091402614458213973835873350490879364499406742693
skew: 1.63
deg: 5
c5: 3
c0: 35
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2700001)
Primes: RFBsize:216816, AFBsize:216606, largePrimes:7411428 encountered
Relations: rels:6890615, finalFF:484135
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 53.63 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 53.90 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

6·10¹⁸⁵+7 = 6(0)₁₈₄7_<186> = 9109 · 486119 · 10533650783_<11> · 7198232528923_<13> · 6020878659975871147_<19> · 57715737637649789572192595701_<29> · C106

C106 = P44 · P63

P44 = 15856940822896359383771402356889784989979289_<44>

P63 = 324309472250677628769264887001027044666888119049640084725461111_<63>

Number: n
N=5142556109783744147491364117529179269926062940937525300905943350583234457373321719669183987601774864930079
  ( 106 digits)
Divisors found:

Wed Oct 17 00:32:49 2007  prp44 factor: 15856940822896359383771402356889784989979289
Wed Oct 17 00:32:49 2007  prp63 factor: 324309472250677628769264887001027044666888119049640084725461111
Wed Oct 17 00:32:49 2007  elapsed time 00:52:18 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.70 hours.
Scaled time: 12.65 units (timescale=1.454).
Factorization parameters were as follows:
name: n
n: 5142556109783744147491364117529179269926062940937525300905943350583234457373321719669183987601774864930079
skew: 21313.42
# norm 5.43e+14
c5: 9000
c4: -76048988
c3: 12119061025586
c2: -340898511045832731
c1: -5046737451005388060230
c0: -9154601256957836199856000
# alpha -6.42
Y1: 5525266307
Y0: -224588401435796917287
# Murphy_E 1.76e-09
# M 241119437529606858479298978826451053129591147004948447723988093141534466268833497155997142159084665980338
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved  special-q in [100000, 1300000)
Primes: RFBsize:183072, AFBsize:182920, largePrimes:4087871 encountered
Relations: rels:4028528, finalFF:410738
Max relations in full relation-set: 28
Initial matrix: 366075 x 410738 with sparse part having weight 23343007.
Pruned matrix : 317878 x 319772 with weight 13914370.
Total sieving time: 8.54 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 8.70 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Oct 15, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(86·10²¹⁰⁷+13)/9 is prime.

Oct 15, 2007 (2nd)

By Sinkiti Sibata / GGNFS

8·10¹⁴⁶-7 = 7(9)₁₄₅3_<147> = 13 · 1046365087_<10> · 19154907071_<11> · C127

C127 = P52 · P76

P52 = 1580183000642280038370796123881094831961607470495009_<52>

P76 = 1943014132025684712297993803987711508705879519397502794606730636362479155677_<76>

Number: 79993_146
N=3070317901434701737005636645958802200607040503016177760156771811800164613700248026172643912484812419742745714980450551562516093
  ( 127 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=1580183000642280038370796123881094831961607470495009 (pp52)
 r2=1943014132025684712297993803987711508705879519397502794606730636362479155677 (pp76)
Version: GGNFS-0.77.1-20060513-k8
Total time: 19.55 hours.
Scaled time: 39.02 units (timescale=1.996).
Factorization parameters were as follows:
name: 79993_146
n: 3070317901434701737005636645958802200607040503016177760156771811800164613700248026172643912484812419742745714980450551562516093
m: 200000000000000000000000000000
c5: 5
c0: -14
skew: 1.23
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2850001)
Primes: RFBsize:114155, AFBsize:114392, largePrimes:2881812 encountered
Relations: rels:2895290, finalFF:293370
Max relations in full relation-set: 28
Initial matrix: 228612 x 293370 with sparse part having weight 30568649.
Pruned matrix : 209081 x 210288 with weight 20114196.
Total sieving time: 18.83 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.52 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 19.55 hours.
 --------- CPU info (if available) ----------

Oct 15, 2007

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

6·10¹⁸⁸+7 = 6(0)₁₈₇7_<189> = 17 · 199 · 257 · 3463 · 16649 · 96059 · 61883693 · 90624285000529213_<17> · 454041790607190733_<18> · 517371257791985827755390629_<27> · C101

C101 = P49 · P53

P49 = 3525119596170058088736272803183372325772469391249_<49>

P53 = 26831479803562967544394299568098567920660248574603957_<53>

Number: n
N=94584175249780957684016168054931694295712083157601963382080588311931355733585636495867363625056572293
  ( 101 digits)
Divisors found:
 r1=3525119596170058088736272803183372325772469391249 (pp49)
 r2=26831479803562967544394299568098567920660248574603957 (pp53)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.98 hours.
Scaled time: 9.14 units (timescale=1.309).
Factorization parameters were as follows:
name: n
n: 94584175249780957684016168054931694295712083157601963382080588311931355733585636495867363625056572293
skew: 7737.01
# norm 9.79e+13
c5: 78000
c4: -297470066
c3: -15863340244548
c2: 7080761517578508
c1: 414301049080350364575
c0: -367453236957540790697550
# alpha -5.80
Y1: 14831016739
Y0: -16471952224750940243
# Murphy_E 2.86e-09
# M 1155531281704554954285740779202815785221773336456573589977276941683087980735395064780088119878136440
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:135072, AFBsize:135064, largePrimes:3586849 encountered
Relations: rels:3583146, finalFF:407778
Max relations in full relation-set: 48
Initial matrix: 270216 x 407778 with sparse part having weight 25913894.
Pruned matrix : 153604 x 155019 with weight 8586650.
Total sieving time: 6.41 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.35 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 6.98 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

8·10¹⁴²-7 = 7(9)₁₄₁3_<143> = 2857 · C140

C140 = P66 · P75

P66 = 170295424162300840230361627660073534692518109605861209895558110069_<66>

P75 = 164428376204146486985826323441216525770957734599964780155385367813374589421_<75>

Number: n
N=28001400070003500175008750437521876093804690234511725586279313965698284914245712285614280714035701785089254462723136156807840392019600980049
  ( 140 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=170295424162300840230361627660073534692518109605861209895558110069 (pp66)
 r2=164428376204146486985826323441216525770957734599964780155385367813374589421 (pp75)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.72 hours.
Scaled time: 9.22 units (timescale=1.194).
Factorization parameters were as follows:
name: KA_7_9_141_3
n: 28001400070003500175008750437521876093804690234511725586279313965698284914245712285614280714035701785089254462723136156807840392019600980049
type: snfs
skew: 0.65
deg: 5
c5: 25
c0: -7
m: 20000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 850001)
Primes: RFBsize:148933, AFBsize:148500, largePrimes:5611558 encountered
Relations: rels:4989427, finalFF:361392
Max relations in full relation-set: 28
Initial matrix: 297497 x 361392 with sparse part having weight 17904087.
Pruned matrix : 240103 x 241654 with weight 9277622.
Total sieving time: 6.20 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 1.13 hours.
Total square root time: 0.19 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 7.72 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

5·10¹⁶⁵-1 = 4(9)₁₆₅_<166> = 428440364567_<12> · C155

C155 = P67 · P88

P67 = 4418255297469253568147847349351285035723609901981851222353873612047_<67>

P88 = 2641367423527036890767831864312306241956122491114136519637229891724953923688971860336151_<88>

Number: n
N=11670235611561044253628931909394969161619544523964876135974702959832102611543850287772225137109509941642444928668610984199652981246175861323416965983211097
  ( 155 digits)
SNFS difficulty: 165 digits.
Divisors found:

Mon Oct 15 22:21:57 2007  prp67 factor: 4418255297469253568147847349351285035723609901981851222353873612047
Mon Oct 15 22:21:57 2007  prp88 factor: 2641367423527036890767831864312306241956122491114136519637229891724953923688971860336151
Mon Oct 15 22:21:57 2007  elapsed time 01:18:34 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 44.16 hours.
Scaled time: 64.21 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_4_9_165
n: 11670235611561044253628931909394969161619544523964876135974702959832102611543850287772225137109509941642444928668610984199652981246175861323416965983211097
skew: 0.72
deg: 5
c5: 5
c0: -1
m: 1000000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2400000)
Primes: RFBsize:203362, AFBsize:203387, largePrimes:7325021 encountered
Relations: rels:6796373, finalFF:457305
Max relations in full relation-set: 28
Initial matrix: 406814 x 457305 with sparse part having weight 40727776.
Pruned matrix : 379736 x 381834 with weight 30695175.
Total sieving time: 43.93 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 44.16 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

8·10¹⁶⁸-7 = 7(9)₁₆₇3_<169> = 889051 · 3504811485997_<13> · 212811322817407_<15> · 15345355832599422733596083704019_<32> · C105

C105 = P33 · P73

P33 = 350969010395558715534644431751677_<33>

P73 = 2240052427411472440287076912394101922396296096003376631991190413937458559_<73>

Oct 14, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

6·10¹⁴⁶+7 = 6(0)₁₄₅7_<147> = 4357 · C144

C144 = P62 · P83

P62 = 11418173072097254220419104341228272288444055633023768296587371_<62>

P83 = 12060548760877474653322042621937488929340653264886088872424357570501388208759630481_<83>

Number: n
N=137709433096167087445490016066100527886160201973835207711728253385356896947440899701629561624971310534771631856782189579986229056690383291255451
  ( 144 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=11418173072097254220419104341228272288444055633023768296587371 (pp62)
 r2=12060548760877474653322042621937488929340653264886088872424357570501388208759630481 (pp83)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 14.29 hours.
Scaled time: 17.06 units (timescale=1.194).
Factorization parameters were as follows:
name: KA_6_0_145_7
n: 137709433096167087445490016066100527886160201973835207711728253385356896947440899701629561624971310534771631856782189579986229056690383291255451
type: snfs
skew: 0.65
deg: 5
c5: 60
c0: 7
m: 100000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:148933, AFBsize:148615, largePrimes:6235655 encountered
Relations: rels:5562121, finalFF:337505
Max relations in full relation-set: 28
Initial matrix: 297615 x 337505 with sparse part having weight 22977078.
Pruned matrix : 271076 x 272628 with weight 15819578.
Total sieving time: 11.99 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 1.85 hours.
Total square root time: 0.22 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 14.29 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

6·10¹⁴⁸+7 = 6(0)₁₄₇7_<149> = 4549 · 787609 · 12956873023_<11> · C130

C130 = P40 · P90

P40 = 9540749344069170990484839035782631826167_<40>

P90 = 135469633078895411887709169907086398273346654936908113597527218378494142638547322866052347_<90>

Number: n
N=1292481812938762669912955974480348284084579994249280402316109378518340638209958112361129835839479159506743055281672649662826363949
  ( 130 digits)
SNFS difficulty: 149 digits.
Divisors found:

Sun Oct 14 07:28:32 2007  prp40 factor: 9540749344069170990484839035782631826167
Sun Oct 14 07:28:32 2007  prp90 factor: 135469633078895411887709169907086398273346654936908113597527218378494142638547322866052347
Sun Oct 14 07:28:32 2007  elapsed time 00:56:42 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 15.17 hours.
Scaled time: 17.95 units (timescale=1.183).
Factorization parameters were as follows:
name: KA_6_0_147_7
n: 1292481812938762669912955974480348284084579994249280402316109378518340638209958112361129835839479159506743055281672649662826363949
skew: 0.52
deg: 5
c5: 375
c0: 14
m: 200000000000000000000000000000
type: snfs
rlim: 1800000
alim: 1800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1850000)
Primes: RFBsize:135072, AFBsize:135288, largePrimes:6951878 encountered
Relations: rels:6272499, finalFF:315014
Max relations in full relation-set: 28
Initial matrix: 270426 x 315014 with sparse part having weight 39437700.
Pruned matrix : 259998 x 261414 with weight 27086460.
Total sieving time: 14.94 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.5,2.5,100000
total time: 15.17 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

8·10¹⁵³-7 = 7(9)₁₅₂3_<154> = 73 · 246833 · 540901 · C141

C141 = P38 · P104

P38 = 45503821118476645834178831665898714663_<38>

P104 = 18038409980107755666629933064361219737535695629711907649346771548449394176944215804284623352754129419979_<104>

Oct 14, 2007

By Sinkiti Sibata / GGNFS, Msieve

8·10¹³⁷-7 = 7(9)₁₃₆3_<138> = 73 · 9964781 · C130

C130 = P48 · P82

P48 = 141316153943199860951746141560760739245162925887_<48>

P82 = 7782292667443130880016248231198064453618474981570509859512503079754219269452839403_<82>

Number: 79993_137
N=1099763668623428964057555400254567520253691063597981621885075953108843075523576896430442484976881173696051081207012566599402325461
  ( 130 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=141316153943199860951746141560760739245162925887 (pp48)
 r2=7782292667443130880016248231198064453618474981570509859512503079754219269452839403 (pp82)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.78 hours.
Scaled time: 13.49 units (timescale=1.990).
Factorization parameters were as follows:
name: 79993_137
n: 1099763668623428964057555400254567520253691063597981621885075953108843075523576896430442484976881173696051081207012566599402325461
m: 2000000000000000000000000000
c5: 25
c0: -7
skew: 0.78
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1225001)
Primes: RFBsize:78498, AFBsize:63568, largePrimes:1548308 encountered
Relations: rels:1559004, finalFF:182026
Max relations in full relation-set: 28
Initial matrix: 142130 x 182026 with sparse part having weight 14809823.
Pruned matrix : 129678 x 130452 with weight 8882231.
Total sieving time: 6.56 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 6.78 hours.
 --------- CPU info (if available) ----------

8·10¹⁶⁵-7 = 7(9)₁₆₄3_<166> = 2381 · 5443 · 9170957 · 1193913161057723_<16> · 18720100338778545677_<20> · 221092714624829016465471979_<27> · C92

C92 = P38 · P54

P38 = 14107017695779960660551276385083916411_<38>

P54 = 965577295039246891714130651139286441420217189730013597_<54>

Sat Oct 13 14:10:21 2007  Msieve v. 1.28
Sat Oct 13 14:10:21 2007  random seeds: d891a068 1d65775f
Sat Oct 13 14:10:21 2007  factoring 13621415987762003925737115669456429853506846533116955465249119119459261411157655645041440367 (92 digits)
Sat Oct 13 14:10:22 2007  commencing quadratic sieve (91-digit input)
Sat Oct 13 14:10:22 2007  using multiplier of 7
Sat Oct 13 14:10:22 2007  using 64kb Pentium 2 sieve core
Sat Oct 13 14:10:22 2007  sieve interval: 18 blocks of size 65536
Sat Oct 13 14:10:22 2007  processing polynomials in batches of 6
Sat Oct 13 14:10:22 2007  using a sieve bound of 1753547 (65651 primes)
Sat Oct 13 14:10:22 2007  using large prime bound of 177108247 (27 bits)
Sat Oct 13 14:10:22 2007  using double large prime bound of 702796695147472 (42-50 bits)
Sat Oct 13 14:10:22 2007  using trial factoring cutoff of 50 bits
Sat Oct 13 14:10:22 2007  polynomial 'A' values have 12 factors
Sun Oct 14 04:42:53 2007  66323 relations (17390 full + 48933 combined from 797713 partial), need 65747
Sun Oct 14 04:43:12 2007  begin with 815103 relations
Sun Oct 14 04:43:18 2007  reduce to 165651 relations in 10 passes
Sun Oct 14 04:43:18 2007  attempting to read 165651 relations
Sun Oct 14 04:43:40 2007  recovered 165651 relations
Sun Oct 14 04:43:40 2007  recovered 143802 polynomials
Sun Oct 14 04:44:26 2007  attempting to build 66323 cycles
Sun Oct 14 04:44:27 2007  found 66323 cycles in 5 passes
Sun Oct 14 04:44:31 2007  distribution of cycle lengths:
Sun Oct 14 04:44:31 2007     length 1 : 17390
Sun Oct 14 04:44:31 2007     length 2 : 12238
Sun Oct 14 04:44:31 2007     length 3 : 11622
Sun Oct 14 04:44:31 2007     length 4 : 8894
Sun Oct 14 04:44:31 2007     length 5 : 6300
Sun Oct 14 04:44:31 2007     length 6 : 4157
Sun Oct 14 04:44:31 2007     length 7 : 2532
Sun Oct 14 04:44:31 2007     length 9+: 3190
Sun Oct 14 04:44:32 2007  largest cycle: 19 relations
Sun Oct 14 04:44:33 2007  matrix is 65651 x 66323 with weight 3988888 (avg 60.14/col)
Sun Oct 14 04:44:40 2007  filtering completed in 4 passes
Sun Oct 14 04:44:40 2007  matrix is 61409 x 61473 with weight 3690038 (avg 60.03/col)
Sun Oct 14 04:44:44 2007  saving the first 48 matrix rows for later
Sun Oct 14 04:44:44 2007  matrix is 61361 x 61473 with weight 2824181 (avg 45.94/col)
Sun Oct 14 04:44:44 2007  matrix includes 64 packed rows
Sun Oct 14 04:44:44 2007  using block size 10922 for processor cache size 256 kB
Sun Oct 14 04:44:47 2007  commencing Lanczos iteration
Sun Oct 14 04:49:15 2007  lanczos halted after 972 iterations
Sun Oct 14 04:49:16 2007  recovered 17 nontrivial dependencies
Sun Oct 14 04:50:10 2007  prp38 factor: 14107017695779960660551276385083916411
Sun Oct 14 04:50:10 2007  prp54 factor: 965577295039246891714130651139286441420217189730013597
Sun Oct 14 04:50:10 2007  elapsed time 14:39:49

8·10¹³¹-7 = 7(9)₁₃₀3_<132> = 149 · 281 · 376313501619021334931_<21> · C107

C107 = P44 · P64

P44 = 37274544353516647698335148848851846484864657_<44>

P64 = 1362182369130717145175925548652388406862572932354777517395196191_<64>

Number: 79993_131
N=50774727135741302668281681978154025666220800077589563173122909846534600529922377074914069545651920596921487
  ( 107 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=37274544353516647698335148848851846484864657 (pp44)
 r2=1362182369130717145175925548652388406862572932354777517395196191 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.40 hours.
Scaled time: 8.79 units (timescale=1.999).
Factorization parameters were as follows:
name: 79993_131
n: 50774727135741302668281681978154025666220800077589563173122909846534600529922377074914069545651920596921487
m: 200000000000000000000000000
c5: 5
c0: -14
skew: 1.23
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:63943, largePrimes:1469981 encountered
Relations: rels:1455868, finalFF:158326
Max relations in full relation-set: 28
Initial matrix: 127959 x 158326 with sparse part having weight 11756685.
Pruned matrix : 119410 x 120113 with weight 7188237.
Total sieving time: 4.24 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.40 hours.
 --------- CPU info (if available) ----------

6·10¹⁵⁰+7 = 6(0)₁₄₉7_<151> = 13 · 1021 · 51377866217_<11> · 38690659722181_<14> · 13553397374370467_<17> · C107

C107 = P44 · P63

P44 = 75896163172818350563639937211446513525782697_<44>

P63 = 221071096062905112755419151133504653865878416206951105384644033_<63>

Number: 60007_150
N=16778447979584046870105927524867093522623211025234406911205125926978020882062201070003687860376291055697001
  ( 107 digits)
Divisors found:
 r1=75896163172818350563639937211446513525782697 (pp44)
 r2=221071096062905112755419151133504653865878416206951105384644033 (pp63)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 19.13 hours.
Scaled time: 12.93 units (timescale=0.676).
Factorization parameters were as follows:
name: 60007_150
n: 16778447979584046870105927524867093522623211025234406911205125926978020882062201070003687860376291055697001
skew: 36403.92
# norm 2.09e+14
c5: 2100
c4: -112214840
c3: -13116197646990
c2: 123037965666033289
c1: 5760329507112287712094
c0: 1238462310613528311780792
# alpha -5.17
Y1: 120696764773
Y0: -380634342801918434537
# Murphy_E 1.56e-09
# M 13741135059811030920870521422422840200370178162132655706061264578222105542413703524686047496399343377873432
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2300001)
Primes: RFBsize:183072, AFBsize:183420, largePrimes:4395571 encountered
Relations: rels:4422833, finalFF:421465
Max relations in full relation-set: 28
Initial matrix: 366571 x 421465 with sparse part having weight 30675596.
Pruned matrix : 323362 x 325258 with weight 19810409.
Total sieving time: 15.47 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 3.20 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 19.13 hours.
 --------- CPU info (if available) ----------

8·10¹³⁴-7 = 7(9)₁₃₃3_<135> = 13 · 31 · 43 · 379 · 398471 · 16515812627621261_<17> · C107

C107 = P41 · P66

P41 = 48003731369287073342189922196135629754309_<41>

P66 = 385572109653783210030204978859579938448033879962204411809558451037_<66>

Number: 79993_134
N=18508899975309508283025996892062552559124843281306774880121900716696676128531676413045071788063922916268433
  ( 107 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=48003731369287073342189922196135629754309 (pp41)
 r2=385572109653783210030204978859579938448033879962204411809558451037 (pp66)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.87 hours.
Scaled time: 11.71 units (timescale=1.996).
Factorization parameters were as follows:
name: 79993_134
n: 18508899975309508283025996892062552559124843281306774880121900716696676128531676413045071788063922916268433
m: 1000000000000000000000000000
c5: 4
c0: -35
skew: 1.54
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:64193, largePrimes:1523402 encountered
Relations: rels:1537466, finalFF:188576
Max relations in full relation-set: 28
Initial matrix: 142755 x 188576 with sparse part having weight 13498820.
Pruned matrix : 126954 x 127731 with weight 7386006.
Total sieving time: 5.68 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.87 hours.
 --------- CPU info (if available) ----------

8·10¹³⁶-7 = 7(9)₁₃₅3_<137> = 163 · 269 · 22407799279_<11> · 81876428270723_<14> · C108

C108 = P42 · P67

P42 = 110918576820312746668279691257635716599183_<42>

P67 = 8965772596523034939022478706473281787255547555025279231551238868629_<67>

Number: 79993_136
N=994470736500895131291624755886395172525421692165650373010779297212968520824895570611922816043828312385730107
  ( 108 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=110918576820312746668279691257635716599183 (pp42)
 r2=8965772596523034939022478706473281787255547555025279231551238868629 (pp67)
Version: GGNFS-0.77.1-20060513-k8
Total time: 7.91 hours.
Scaled time: 15.72 units (timescale=1.988).
Factorization parameters were as follows:
name: 79993_136
n: 994470736500895131291624755886395172525421692165650373010779297212968520824895570611922816043828312385730107
m: 2000000000000000000000000000
c5: 5
c0: -14
skew: 1.23
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1375001)
Primes: RFBsize:78498, AFBsize:63943, largePrimes:1589559 encountered
Relations: rels:1610836, finalFF:189841
Max relations in full relation-set: 28
Initial matrix: 142506 x 189841 with sparse part having weight 16890095.
Pruned matrix : 128981 x 129757 with weight 9843551.
Total sieving time: 7.67 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 7.91 hours.
 --------- CPU info (if available) ----------

Oct 13, 2007 (6th)

By Robert Backstrom / Msieve, GGNFS

8·10¹¹⁰-7 = 7(9)₁₀₉3_<111> = 13 · 30197 · 69511273067394199277_<20> · C86

C86 = P43 · P43

P43 = 3412752588243064179197971634430268240789861_<43>

P43 = 8590585972779452282610598329176427275489929_<43>

Sat Oct 13 14:21:54 2007  Msieve v. 1.28
Sat Oct 13 14:21:54 2007  random seeds: 71c0a470 a1018f8f
Sat Oct 13 14:21:54 2007  factoring 29317544513127637059005073107012633156477405810349541305000972214868654912800710809869 (86 digits)
Sat Oct 13 14:21:54 2007  commencing quadratic sieve (85-digit input)
Sat Oct 13 14:21:54 2007  using multiplier of 1
Sat Oct 13 14:21:54 2007  using 64kb Opteron sieve core
Sat Oct 13 14:21:54 2007  sieve interval: 7 blocks of size 65536
Sat Oct 13 14:21:54 2007  processing polynomials in batches of 15
Sat Oct 13 14:21:54 2007  using a sieve bound of 1442579 (55333 primes)
Sat Oct 13 14:21:54 2007  using large prime bound of 115406320 (26 bits)
Sat Oct 13 14:21:54 2007  using double large prime bound of 325097179907280 (41-49 bits)
Sat Oct 13 14:21:54 2007  using trial factoring cutoff of 49 bits
Sat Oct 13 14:21:54 2007  polynomial 'A' values have 11 factors
Sat Oct 13 14:54:41 2007  55598 relations (16566 full + 39032 combined from 566706 partial), need 55429
Sat Oct 13 14:54:42 2007  begin with 583272 relations
Sat Oct 13 14:54:43 2007  reduce to 129047 relations in 9 passes
Sat Oct 13 14:54:43 2007  attempting to read 129047 relations
Sat Oct 13 14:54:44 2007  recovered 129047 relations
Sat Oct 13 14:54:44 2007  recovered 103401 polynomials
Sat Oct 13 14:54:45 2007  attempting to build 55598 cycles
Sat Oct 13 14:54:45 2007  found 55598 cycles in 5 passes
Sat Oct 13 14:54:45 2007  distribution of cycle lengths:
Sat Oct 13 14:54:45 2007     length 1 : 16566
Sat Oct 13 14:54:46 2007     length 2 : 11426
Sat Oct 13 14:54:46 2007     length 3 : 9845
Sat Oct 13 14:54:46 2007     length 4 : 7055
Sat Oct 13 14:54:46 2007     length 5 : 4727
Sat Oct 13 14:54:46 2007     length 6 : 2766
Sat Oct 13 14:54:46 2007     length 7 : 1568
Sat Oct 13 14:54:46 2007     length 9+: 1645
Sat Oct 13 14:54:46 2007  largest cycle: 19 relations
Sat Oct 13 14:54:46 2007  matrix is 55333 x 55598 with weight 2843187 (avg 51.14/col)
Sat Oct 13 14:54:47 2007  filtering completed in 3 passes
Sat Oct 13 14:54:47 2007  matrix is 49684 x 49748 with weight 2566866 (avg 51.60/col)
Sat Oct 13 14:54:48 2007  saving the first 48 matrix rows for later
Sat Oct 13 14:54:48 2007  matrix is 49636 x 49748 with weight 1895227 (avg 38.10/col)
Sat Oct 13 14:54:48 2007  matrix includes 64 packed rows
Sat Oct 13 14:54:48 2007  commencing Lanczos iteration
Sat Oct 13 14:56:13 2007  lanczos halted after 786 iterations
Sat Oct 13 14:56:13 2007  recovered 16 nontrivial dependencies
Sat Oct 13 14:56:14 2007  prp43 factor: 3412752588243064179197971634430268240789861
Sat Oct 13 14:56:14 2007  prp43 factor: 8590585972779452282610598329176427275489929
Sat Oct 13 14:56:14 2007  elapsed time 00:34:20

8·10¹⁰³-7 = 7(9)₁₀₂3_<104> = 281 · 9903493 · 76751663 · C87

C87 = P35 · P53

P35 = 11645958539351398837968999925860551_<35>

P53 = 32161199219947116795810535309580815458905862060506117_<53>

Sat Oct 13 14:18:15 2007  Msieve v. 1.28
Sat Oct 13 14:18:15 2007  random seeds: fd6310c0 0e9f8101
Sat Oct 13 14:18:15 2007  factoring 374547992691324672010178946818039861713393421705423703090741037387853600337071824490467 (87 digits)
Sat Oct 13 14:18:15 2007  commencing quadratic sieve (87-digit input)
Sat Oct 13 14:18:15 2007  using multiplier of 7
Sat Oct 13 14:18:15 2007  using 64kb Athlon XP sieve core
Sat Oct 13 14:18:15 2007  sieve interval: 10 blocks of size 65536
Sat Oct 13 14:18:15 2007  processing polynomials in batches of 11
Sat Oct 13 14:18:15 2007  using a sieve bound of 1483429 (56667 primes)
Sat Oct 13 14:18:15 2007  using large prime bound of 118674320 (26 bits)
Sat Oct 13 14:18:15 2007  using double large prime bound of 341855144981120 (42-49 bits)
Sat Oct 13 14:18:15 2007  using trial factoring cutoff of 49 bits
Sat Oct 13 14:18:15 2007  polynomial 'A' values have 11 factors
Sat Oct 13 15:27:24 2007  56771 relations (15604 full + 41167 combined from 595942 partial), need 56763
Sat Oct 13 15:27:25 2007  begin with 611546 relations
Sat Oct 13 15:27:25 2007  reduce to 136916 relations in 9 passes
Sat Oct 13 15:27:25 2007  attempting to read 136916 relations
Sat Oct 13 15:27:27 2007  recovered 136916 relations
Sat Oct 13 15:27:27 2007  recovered 116979 polynomials
Sat Oct 13 15:27:28 2007  attempting to build 56771 cycles
Sat Oct 13 15:27:28 2007  found 56771 cycles in 6 passes
Sat Oct 13 15:27:28 2007  distribution of cycle lengths:
Sat Oct 13 15:27:28 2007     length 1 : 15604
Sat Oct 13 15:27:28 2007     length 2 : 10981
Sat Oct 13 15:27:28 2007     length 3 : 9938
Sat Oct 13 15:27:28 2007     length 4 : 7431
Sat Oct 13 15:27:28 2007     length 5 : 5307
Sat Oct 13 15:27:28 2007     length 6 : 3290
Sat Oct 13 15:27:28 2007     length 7 : 1927
Sat Oct 13 15:27:28 2007     length 9+: 2293
Sat Oct 13 15:27:28 2007  largest cycle: 20 relations
Sat Oct 13 15:27:29 2007  matrix is 56667 x 56771 with weight 3278330 (avg 57.75/col)
Sat Oct 13 15:27:30 2007  filtering completed in 4 passes
Sat Oct 13 15:27:30 2007  matrix is 52445 x 52509 with weight 3068265 (avg 58.43/col)
Sat Oct 13 15:27:31 2007  saving the first 48 matrix rows for later
Sat Oct 13 15:27:31 2007  matrix is 52397 x 52509 with weight 2467820 (avg 47.00/col)
Sat Oct 13 15:27:31 2007  matrix includes 64 packed rows
Sat Oct 13 15:27:31 2007  using block size 10922 for processor cache size 256 kB
Sat Oct 13 15:27:32 2007  commencing Lanczos iteration
Sat Oct 13 15:28:04 2007  lanczos halted after 830 iterations
Sat Oct 13 15:28:04 2007  recovered 18 nontrivial dependencies
Sat Oct 13 15:28:05 2007  prp35 factor: 11645958539351398837968999925860551
Sat Oct 13 15:28:05 2007  prp53 factor: 32161199219947116795810535309580815458905862060506117
Sat Oct 13 15:28:05 2007  elapsed time 01:09:50

8·10¹¹⁹-7 = 7(9)₁₁₈3_<120> = 31 · C119

C119 = P41 · P78

P41 = 65850038351296212647890397578950381287521_<41>

P78 = 391897290556327270259798161999635360467060860906617319029511693859070848809543_<78>

Number: n
N=25806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903
  ( 119 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=65850038351296212647890397578950381287521 (pp41)
 r2=391897290556327270259798161999635360467060860906617319029511693859070848809543 (pp78)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.48 hours.
Scaled time: 1.94 units (timescale=1.313).
Factorization parameters were as follows:
name: KA_7_9_118_3
n: 25806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903
skew: 1.54
deg: 5
c5: 4
c0: -35
m: 1000000000000000000000000
type: snfs
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 200001)
Primes: RFBsize:63951, AFBsize:64193, largePrimes:4027991 encountered
Relations: rels:3391987, finalFF:155362
Max relations in full relation-set: 48
Initial matrix: 128208 x 155362 with sparse part having weight 9403022.
Pruned matrix : 112183 x 112888 with weight 4664374.
Total sieving time: 1.28 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.12 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000
total time: 1.48 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 13, 2007 (5th)

By Sinkiti Sibata / GGNFS

6·10¹³⁴+7 = 6(0)₁₃₃7_<135> = 193 · 863 · 23603 · 100586824269101_<15> · C112

C112 = P35 · P77

P35 = 16080745011300179212403283434151191_<35>

P77 = 94355816472667095064977591820097467102390568492729306979142286831385089101801_<77>

Number: 60007_134
N=1517311825029996661504435096321997519435645891033130360977335775340869413282472959239396871158506225871024394991
  ( 112 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=16080745011300179212403283434151191 (pp35)
 r2=94355816472667095064977591820097467102390568492729306979142286831385089101801 (pp77)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.83 hours.
Scaled time: 11.61 units (timescale=1.992).
Factorization parameters were as follows:
name: 60007_134
n: 1517311825029996661504435096321997519435645891033130360977335775340869413282472959239396871158506225871024394991
m: 1000000000000000000000000000
c5: 3
c0: 35
skew: 1.63
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:63993, largePrimes:1532434 encountered
Relations: rels:1543630, finalFF:184907
Max relations in full relation-set: 28
Initial matrix: 142556 x 184907 with sparse part having weight 13770867.
Pruned matrix : 128299 x 129075 with weight 7860258.
Total sieving time: 5.62 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.83 hours.
 --------- CPU info (if available) ----------

8·10¹⁰²-7 = 7(9)₁₀₁3_<103> = 2599231 · C97

C97 = P36 · P62

P36 = 123290814675728514277867589716453613_<36>

P62 = 24964012229434350382875423100742889170251821341837628816240131_<62>

Number: 79993_102
N=3077833405341810712476113127305730040923642415776050685760519168938813056630980470762313930543303
  ( 97 digits)
SNFS difficulty: 102 digits.
Divisors found:
 r1=123290814675728514277867589716453613 (pp36)
 r2=24964012229434350382875423100742889170251821341837628816240131 (pp62)
Version: GGNFS-0.77.1-20060513-k8
Total time: 0.89 hours.
Scaled time: 1.79 units (timescale=1.999).
Factorization parameters were as follows:
name: 79993_102
n: 3077833405341810712476113127305730040923642415776050685760519168938813056630980470762313930543303
m: 200000000000000000000
c5: 25
c0: -7
skew: 0.78
type: snfs
Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [250000, 310001)
Primes: RFBsize:37706, AFBsize:41317, largePrimes:1576393 encountered
Relations: rels:1849951, finalFF:427438
Max relations in full relation-set: 28
Initial matrix: 79087 x 427438 with sparse part having weight 15779526.
Pruned matrix : 37970 x 38429 with weight 2534723.
Total sieving time: 0.84 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,102,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000
total time: 0.89 hours.
 --------- CPU info (if available) ----------

8·10¹¹³-7 = 7(9)₁₁₂3_<114> = 43 · 73 · 947 · 138185209 · C100

C100 = P34 · P67

P34 = 1766907794190056087078782907983423_<34>

P67 = 1102232585621228023273179280338960623464028098584925315433259382103_<67>

Number: 79993_113
N=1947543346544406138446494012197593494161099060936009527105845848444968706122941158047420354746878569
  ( 100 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=1766907794190056087078782907983423 (pp34)
 r2=1102232585621228023273179280338960623464028098584925315433259382103 (pp67)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.01 hours.
Scaled time: 7.94 units (timescale=1.983).
Factorization parameters were as follows:
name: 79993_113
n: 1947543346544406138446494012197593494161099060936009527105845848444968706122941158047420354746878569
m: 20000000000000000000000
c5: 250
c0: -7
skew: 0.49
type: snfs
n: 1947543346544406138446494012197593494161099060936009527105845848444968706122941158047420354746878569
m: 20000000000000000000000
c5: 250
c0: -7
skew: 0.49
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64168, largePrimes:2727503 encountered
Relations: rels:3846323, finalFF:1205129
Max relations in full relation-set: 28
Initial matrix: 113332 x 1205129 with sparse part having weight 90876931.
Pruned matrix : 49293 x 49923 with weight 10051860.
Total sieving time: 3.88 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 4.01 hours.
 --------- CPU info (if available) ----------

8·10¹²⁸-7 = 7(9)₁₂₇3_<129> = 13 · 4458931 · 28353751 · 344697087446640263047_<21> · C94

C94 = P39 · P55

P39 = 212705206095827642161365792695450030873_<39>

P55 = 6638800655743115255251905310435410068403132728886029351_<55>

Number: 79993_128
N=1412107461708955027069290923954737312907713787250726572515699054670309444073066843051334153423
  ( 94 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=212705206095827642161365792695450030873 (pp39)
 r2=6638800655743115255251905310435410068403132728886029351 (pp55)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 5.28 hours.
Scaled time: 3.57 units (timescale=0.676).
Factorization parameters were as follows:
name: 79993_128
n: 1412107461708955027069290923954737312907713787250726572515699054670309444073066843051334153423
m: 20000000000000000000000000
c5: 250
c0: -7
skew: 0.49
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64168, largePrimes:1487851 encountered
Relations: rels:1489577, finalFF:174328
Max relations in full relation-set: 28
Initial matrix: 128185 x 174328 with sparse part having weight 12264098.
Pruned matrix : 114449 x 115153 with weight 6368258.
Total sieving time: 4.96 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.28 hours.
 --------- CPU info (if available) ----------

8·10¹¹⁴-7 = 7(9)₁₁₃3_<115> = 230904677 · C107

C107 = P48 · P59

P48 = 587132704218609332602624273840988912804671457773_<48>

P59 = 59009370997911180303851532975515874983963222792974758349433_<59>

Number: 79993_114
N=34646331568242768854785908039446078435215064959468101202644760634276801591160494336803753871126655437992709
  ( 107 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=587132704218609332602624273840988912804671457773 (pp48)
 r2=59009370997911180303851532975515874983963222792974758349433 (pp59)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.32 hours.
Scaled time: 6.61 units (timescale=1.994).
Factorization parameters were as follows:
name: 79993_114
n: 34646331568242768854785908039446078435215064959468101202644760634276801591160494336803753871126655437992709
m: 100000000000000000000000
c5: 4
c0: -35
skew: 1.54
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64193, largePrimes:2486912 encountered
Relations: rels:3148089, finalFF:767372
Max relations in full relation-set: 28
Initial matrix: 113355 x 767372 with sparse part having weight 60310023.
Pruned matrix : 62081 x 62711 with weight 6647029.
Total sieving time: 3.20 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.32 hours.
 --------- CPU info (if available) ----------

Oct 13, 2007 (4th)

The factor table of 799...993 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Oct 13, 2007 (3rd)

By Robert Backstrom / GGNFS

6·10¹⁴⁴+7 = 6(0)₁₄₃7_<145> = 13 · 61 · 6217 · C139

C139 = P47 · P92

P47 = 17996214744046724344420417956846958165765495333_<47>

P92 = 67626362611447967176376164281940047499923797596474846813424537050089499416597128887441863259_<92>

Number: n
N=1217018543914390047546886146495361840910930266662961521321860634744135035509558565062115612299270539368420113178667855558559788368588670247
  ( 139 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=17996214744046724344420417956846958165765495333 (pp47)
 r2=67626362611447967176376164281940047499923797596474846813424537050089499416597128887441863259 (pp92)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.95 hours.
Scaled time: 11.51 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_6_0_143_7
n: 1217018543914390047546886146495361840910930266662961521321860634744135035509558565062115612299270539368420113178667855558559788368588670247
skew: 1.63
deg: 5
c5: 3
c0: 35
m: 100000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:148933, AFBsize:148840, largePrimes:6333809 encountered
Relations: rels:5693227, finalFF:347656
Max relations in full relation-set: 28
Initial matrix: 297838 x 347656 with sparse part having weight 22955213.
Pruned matrix : 259683 x 261236 with weight 14197561.
Total sieving time: 6.15 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.51 hours.
Total square root time: 0.13 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 7.95 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Oct 13, 2007 (2nd)

By Sinkiti Sibata / GGNFS

6·10¹³²+7 = 6(0)₁₃₁7_<133> = 13 · 31 · 59 · 2090009 · 148913261947_<12> · C111

C111 = P55 · P57

P55 = 1983329501828473727548585254782922572449329984672734213_<55>

P57 = 408806495210391060163003461145989705978462625906890077609_<57>

Number: 60007_132
N=810797982489869232300976179328579352721883380713949594003733868807533449400899968769781243999195835893799536717
  ( 111 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=1983329501828473727548585254782922572449329984672734213 (pp55)
 r2=408806495210391060163003461145989705978462625906890077609 (pp57)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 7.78 hours.
Scaled time: 5.26 units (timescale=0.676).
Factorization parameters were as follows:
name: 60007_132
n: 810797982489869232300976179328579352721883380713949594003733868807533449400899968769781243999195835893799536717
m: 100000000000000000000000000
c5: 600
c0: 7
skew: 0.41
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1250001)
Primes: RFBsize:63951, AFBsize:63523, largePrimes:1533110 encountered
Relations: rels:1528629, finalFF:158241
Max relations in full relation-set: 28
Initial matrix: 127540 x 158241 with sparse part having weight 14199593.
Pruned matrix : 119830 x 120531 with weight 9182188.
Total sieving time: 7.35 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 7.78 hours.
 --------- CPU info (if available) ----------

6·10¹⁶⁷-7 = 5(9)₁₆₆3_<168> = 86004929922823687_<17> · 117124643630091042473553137641_<30> · C122

C122 = P55 · P68

P55 = 1422924018199617086667469983408773956446337923324187259_<55>

P68 = 41859873490837916408900575837828799444368507615420908476733092182981_<68>

Number: 59993_167
N=59563419388910720197810859969956349938363680093704772757910598946408447555545711050233081537114891883517241917857936839079
  ( 122 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=1422924018199617086667469983408773956446337923324187259 (pp55)
 r2=41859873490837916408900575837828799444368507615420908476733092182981 (pp68)
Version: GGNFS-0.77.1-20060513-k8
Total time: 154.80 hours.
Scaled time: 308.82 units (timescale=1.995).
Factorization parameters were as follows:
name: 59993_167
n: 59563419388910720197810859969956349938363680093704772757910598946408447555545711050233081537114891883517241917857936839079
m: 1000000000000000000000000000000000
c5: 600
c0: -7
skew: 0.41
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 7450001)
Primes: RFBsize:380800, AFBsize:380567, largePrimes:6136257 encountered
Relations: rels:6361592, finalFF:867619
Max relations in full relation-set: 28
Initial matrix: 761433 x 867619 with sparse part having weight 66909828.
Pruned matrix : 680057 x 683928 with weight 51296332.
Total sieving time: 147.94 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 6.30 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 154.80 hours.
 --------- CPU info (if available) ----------

Oct 13, 2007

By Jo Yeong Uk / GMP-ECM, GGNFS

6·10¹⁹³+7 = 6(0)₁₉₂7_<194> = C194

C194 = P37 · C157

P37 = 9431867921209970677263227064224760463_<37>

C157 = [6361412235753920282712594389572541485300199982510262458997768914548898435588007324833733189857362507423842664895526461468007039663923961796686299905053607689_<157>]

6·10¹⁴⁰+7 = 6(0)₁₃₉7_<141> = 17 · 25765322537_<11> · 29151135776457323_<17> · C113

C113 = P52 · P61

P52 = 6123908191785128062611453979386707666992816396823857_<52>

P61 = 7673307351852464227438937019759901799643665911557369118867853_<61>

Number: 60007_140
N=46990629750094353640929945031801720386834025557110371526615491443551271997160943220584424618795094865880900769021
  ( 113 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=6123908191785128062611453979386707666992816396823857 (pp52)
 r2=7673307351852464227438937019759901799643665911557369118867853 (pp61)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.19 hours.
Scaled time: 13.10 units (timescale=2.117).
Factorization parameters were as follows:
n: 46990629750094353640929945031801720386834025557110371526615491443551271997160943220584424618795094865880900769021
m: 10000000000000000000000000000
c5: 6
c0: 7
skew: 1.03
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:114412, largePrimes:3206977 encountered
Relations: rels:3155190, finalFF:262058
Max relations in full relation-set: 28
Initial matrix: 228633 x 262058 with sparse part having weight 22384343.
Pruned matrix : 214081 x 215288 with weight 15710541.
Total sieving time: 5.95 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.19 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

6·10¹⁸³+7 = 6(0)₁₈₂7_<184> = C184

C184 = P37 · P148

P37 = 4646109535270935651861373920553944113_<37>

P148 = 1291403044730436574664225203953221354301912479271324672689780038042977651172600578097674193944368819808698887156719580132180993397271065994090189239_<148>

6·10¹⁶⁰+7 = 6(0)₁₅₉7_<161> = 4229 · 482513 · 19099104039013_<14> · C139

C139 = P34 · P105

P34 = 2891475901086594031773677024975431_<34>

P105 = 532441594081401683367165802963920698884830621397625778059323292338660459693626121501287829706854904467897_<105>

Oct 12, 2007 (3rd)

By Jo Yeong Uk / GGNFS

6·10¹⁵²+7 = 6(0)₁₅₁7_<153> = C153

C153 = P43 · P111

P43 = 1840685266806508095129806305318544351784701_<43>

P111 = 325965557947322722135583311765356705447166321685192963549916970963466614546316438202055770474848508291355137107_<111>

Number: 60007_152
N=600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
  ( 153 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=1840685266806508095129806305318544351784701 (pp43)
 r2=325965557947322722135583311765356705447166321685192963549916970963466614546316438202055770474848508291355137107 (pp111)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 20.05 hours.
Scaled time: 42.60 units (timescale=2.125).
Factorization parameters were as follows:
n: 600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
m: 2000000000000000000000000000000
c5: 75
c0: 28
skew: 0.82
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2500001)
Primes: RFBsize:176302, AFBsize:175743, largePrimes:5716294 encountered
Relations: rels:5680786, finalFF:487419
Max relations in full relation-set: 28
Initial matrix: 352111 x 487419 with sparse part having weight 48790712.
Pruned matrix : 305178 x 307002 with weight 29072127.
Total sieving time: 19.36 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.56 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 20.05 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 12, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

(89·10¹⁶³+1)/9 = 9(8)₁₆₂9_<164> = 3² · 11 · 191 · 44453 · 169823791 · C147

C147 = P71 · P77

P71 = 53555495404586983124284868689499027110767249977749056417262621184569457_<71>

P77 = 12935263718227109600388586097547759844207588321745878007455274683392359947511_<77>

Number: n
N=692754456618632700742588855519739501284878125239435320459568642724351039203120317771928341708484604722354579869380134021593082789437079791653771527
  ( 147 digits)
SNFS difficulty: 164 digits.
Divisors found:

Fri Oct 12 07:40:24 2007  prp71 factor: 53555495404586983124284868689499027110767249977749056417262621184569457
Fri Oct 12 07:40:24 2007  prp77 factor: 12935263718227109600388586097547759844207588321745878007455274683392359947511
Fri Oct 12 07:40:24 2007  elapsed time 01:36:36 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 40.85 hours.
Scaled time: 58.50 units (timescale=1.432).
Factorization parameters were as follows:
name: KA_9_8_162_9
n: 692754456618632700742588855519739501284878125239435320459568642724351039203120317771928341708484604722354579869380134021593082789437079791653771527
skew: 0.10
deg: 5
c5: 89000
c0: 1
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100001)
Primes: RFBsize:203362, AFBsize:202807, largePrimes:7209972 encountered
Relations: rels:6664266, finalFF:448066
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 40.59 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 40.85 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

6·10¹⁴⁵+7 = 6(0)₁₄₄7_<146> = 163 · C144

C144 = P64 · P80

P64 = 3919572055477532086753025839329335485817252963822084748594102007_<64>

P80 = 93912844131744392068992466757974562467028071947951869170587151041083038337579227_<80>

Number: n
N=368098159509202453987730061349693251533742331288343558282208588957055214723926380368098159509202453987730061349693251533742331288343558282208589
  ( 144 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=3919572055477532086753025839329335485817252963822084748594102007 (pp64)
 r2=93912844131744392068992466757974562467028071947951869170587151041083038337579227 (pp80)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 11.95 hours.
Scaled time: 14.29 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_6_0_144_7
n: 368098159509202453987730061349693251533742331288343558282208588957055214723926380368098159509202453987730061349693251533742331288343558282208589
type: snfs
skew: 1.03
deg: 5
c5: 6
c0: 7
m: 100000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:148933, AFBsize:149160, largePrimes:6126432 encountered
Relations: rels:5452417, finalFF:336584
Max relations in full relation-set: 28
Initial matrix: 298159 x 336584 with sparse part having weight 21730162.
Pruned matrix : 270315 x 271869 with weight 14890622.
Total sieving time: 9.92 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 1.75 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 11.95 hours.
 --------- CPU info (if available) ----------

6·10¹³⁸+7 = 6(0)₁₃₇7_<139> = 13 · C138

C138 = P52 · P86

P52 = 8786475728072227386487041599685529123701731718444931_<52>

P86 = 52528280487235138475680678891847720293425922478509734700005290994634833797311729822369_<86>

Number: n
N=461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461539
  ( 138 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=8786475728072227386487041599685529123701731718444931 (pp52)
 r2=52528280487235138475680678891847720293425922478509734700005290994634833797311729822369 (pp86)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.79 hours.
Scaled time: 8.84 units (timescale=1.302).
Factorization parameters were as follows:
name: KA_6_0_137_3
n: 461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461539
skew: 0.26
deg: 5
c5: 6000
c0: 7
m: 1000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 750001)
Primes: RFBsize:114155, AFBsize:114432, largePrimes:6211466 encountered
Relations: rels:5545647, finalFF:312486
Max relations in full relation-set: 48
Initial matrix: 228654 x 312486 with sparse part having weight 29654727.
Pruned matrix : 190499 x 191706 with weight 12900013.
Total sieving time: 5.71 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.83 hours.
Total square root time: 0.08 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,75000
total time: 6.79 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(25·10¹⁶⁴-7)/9 = 2(7)₁₆₄_<165> = 109 · 233 · 98429 · 3605093 · C149

C149 = P69 · P81

P69 = 202665523211650989063300380086943340369476928178393708116016987186139_<69>

P81 = 152088249235178053009249905689353519859990659090201830262384603581442406000454727_<81>

Number: n
N=30823044605591338486772528468080215864221880056493623390494021588481356096730350429012600680064293390882554678466909555819589219907302066966191429053
  ( 149 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=202665523211650989063300380086943340369476928178393708116016987186139 (pp69)
 r2=152088249235178053009249905689353519859990659090201830262384603581442406000454727 (pp81)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 63.84 hours.
Scaled time: 83.38 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_2_7_164
n: 30823044605591338486772528468080215864221880056493623390494021588481356096730350429012600680064293390882554678466909555819589219907302066966191429053
skew: 1.23
deg: 5
c5: 5
c0: -14
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2800001)
Primes: RFBsize:216816, AFBsize:217381, largePrimes:7523615 encountered
Relations: rels:7019729, finalFF:495769
Max relations in full relation-set: 28
Initial matrix: 434262 x 495769 with sparse part having weight 44468095.
Pruned matrix : 406710 x 408945 with weight 32940913.
Total sieving time: 58.95 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 4.48 hours.
Total square root time: 0.14 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 63.84 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 12, 2007

By Sinkiti Sibata / GGNFS

6·10¹¹⁴+7 = 6(0)₁₁₃7_<115> = 13 · 23 · 294199 · 314707 · 2354837 · C95

C95 = P32 · P64

P32 = 13963735493801662655038504422019_<32>

P64 = 6591283660858015718799436869882276779748116589270476529805242367_<64>

Number: 60007_114
N=92038941604838034885826953995277077283508823907453477048445035739217774475488560068977546478973
  ( 95 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=13963735493801662655038504422019 (pp32)
 r2=6591283660858015718799436869882276779748116589270476529805242367 (pp64)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.60 hours.
Scaled time: 1.08 units (timescale=0.676).
Factorization parameters were as follows:
name: 60007_114
n: 92038941604838034885826953995277077283508823907453477048445035739217774475488560068977546478973
m: 100000000000000000000000
c5: 3
c0: 35
skew: 1.63
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:63993, largePrimes:2069865 encountered
Relations: rels:2160911, finalFF:246690
Max relations in full relation-set: 28
Initial matrix: 113156 x 246690 with sparse part having weight 18938825.
Pruned matrix : 79136 x 79765 with weight 3921681.
Total sieving time: 1.41 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.60 hours.
 --------- CPU info (if available) ----------

6·10¹¹⁶+7 = 6(0)₁₁₅7_<117> = 1433 · C114

C114 = P46 · P68

P46 = 4260569836341526184189932091009434032922764443_<46>

P68 = 98273714505283129560284285927238795172266087521311216860992588389453_<68>

Number: 60007_116
N=418702023726448011165387299371946964410327983251919050942079553384508025122121423586880669923237962316817864619679
  ( 114 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=4260569836341526184189932091009434032922764443 (pp46)
 r2=98273714505283129560284285927238795172266087521311216860992588389453 (pp68)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.17 hours.
Scaled time: 1.47 units (timescale=0.676).
Factorization parameters were as follows:
name: 60007_116
n: 418702023726448011165387299371946964410327983251919050942079553384508025122121423586880669923237962316817864619679
m: 100000000000000000000000
c5: 60
c0: 7
skew: 0.65
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63883, largePrimes:2216313 encountered
Relations: rels:2423409, finalFF:333688
Max relations in full relation-set: 28
Initial matrix: 113048 x 333688 with sparse part having weight 30159400.
Pruned matrix : 73820 x 74449 with weight 5302920.
Total sieving time: 1.96 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.17 hours.
 --------- CPU info (if available) ----------

6·10¹¹⁷+7 = 6(0)₁₁₆7_<118> = 31 · 2602909783189_<13> · C104

C104 = P39 · P65

P39 = 761007481197519851161967935908199514911_<39>

P65 = 97710562768479463816800500502385687103003804418987111582005841643_<65>

Number: 60007_117
N=74358469258832718774436183724553279940996020408249446899718017650687200724318637458592452381540883238773
  ( 104 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=761007481197519851161967935908199514911 (pp39)
 r2=97710562768479463816800500502385687103003804418987111582005841643 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.20 hours.
Scaled time: 1.49 units (timescale=0.676).
Factorization parameters were as follows:
name: 60007_117
n: 74358469258832718774436183724553279940996020408249446899718017650687200724318637458592452381540883238773
m: 100000000000000000000000
c5: 600
c0: 7
skew: 0.41
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63523, largePrimes:1980594 encountered
Relations: rels:1938172, finalFF:128803
Max relations in full relation-set: 28
Initial matrix: 112687 x 128803 with sparse part having weight 10218920.
Pruned matrix : 106545 x 107172 with weight 7132342.
Total sieving time: 1.89 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.20 hours.
 --------- CPU info (if available) ----------

6·10¹²⁷+7 = 6(0)₁₂₆7_<128> = 197 · 9720031 · 266168660299_<12> · C108

C108 = P43 · P65

P43 = 3583617409332378966987419272264607655669797_<43>

P65 = 32850260496263134596383389203484134247046587543608521946389524867_<65>

Number: 60007_127
N=117722765415512284233525269842016058687696108332067481812522215595485313176760239621795561889746921472341999
  ( 108 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=3583617409332378966987419272264607655669797 (pp43)
 r2=32850260496263134596383389203484134247046587543608521946389524867 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 5.28 hours.
Scaled time: 3.57 units (timescale=0.676).
Factorization parameters were as follows:
name: 60007_127
n: 117722765415512284233525269842016058687696108332067481812522215595485313176760239621795561889746921472341999
m: 10000000000000000000000000
c5: 600
c0: 7
skew: 0.41
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:63523, largePrimes:1506649 encountered
Relations: rels:1516333, finalFF:181202
Max relations in full relation-set: 28
Initial matrix: 127540 x 181202 with sparse part having weight 12751877.
Pruned matrix : 111515 x 112216 with weight 6223089.
Total sieving time: 4.97 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.28 hours.
 --------- CPU info (if available) ----------

Oct 11, 2007 (4th)

By Sinkiti Sibata / Msieve

6·10¹⁵⁵+7 = 6(0)₁₅₄7_<156> = 30253 · 8290186057_<10> · 93174093649657_<14> · 47369174977499761_<17> · 7846580404504329797862521_<25> · C86

C86 = P41 · P46

P41 = 11519704348754539604022205034624081555611_<41>

P46 = 5996609457515185443760101854342559834794121041_<46>

Thu Oct 11 07:46:13 2007  Msieve v. 1.28
Thu Oct 11 07:46:13 2007  random seeds: a4efa528 11c3b45d
Thu Oct 11 07:46:13 2007  factoring 69079168045520282358058872569745380341436008514853935086936756082097682617184706711051 (86 digits)
Thu Oct 11 07:46:14 2007  commencing quadratic sieve (86-digit input)
Thu Oct 11 07:46:14 2007  using multiplier of 11
Thu Oct 11 07:46:14 2007  using 64kb Pentium 2 sieve core
Thu Oct 11 07:46:14 2007  sieve interval: 9 blocks of size 65536
Thu Oct 11 07:46:14 2007  processing polynomials in batches of 12
Thu Oct 11 07:46:14 2007  using a sieve bound of 1470947 (55891 primes)
Thu Oct 11 07:46:14 2007  using large prime bound of 117675760 (26 bits)
Thu Oct 11 07:46:14 2007  using double large prime bound of 336694943593840 (41-49 bits)
Thu Oct 11 07:46:14 2007  using trial factoring cutoff of 49 bits
Thu Oct 11 07:46:14 2007  polynomial 'A' values have 11 factors
Thu Oct 11 13:23:21 2007  56030 relations (15871 full + 40159 combined from 586780 partial), need 55987
Thu Oct 11 13:23:28 2007  begin with 602651 relations
Thu Oct 11 13:23:29 2007  reduce to 133601 relations in 10 passes
Thu Oct 11 13:23:29 2007  attempting to read 133601 relations
Thu Oct 11 13:23:38 2007  recovered 133601 relations
Thu Oct 11 13:23:38 2007  recovered 112180 polynomials
Thu Oct 11 13:23:39 2007  attempting to build 56030 cycles
Thu Oct 11 13:23:39 2007  found 56030 cycles in 6 passes
Thu Oct 11 13:23:42 2007  distribution of cycle lengths:
Thu Oct 11 13:23:42 2007     length 1 : 15871
Thu Oct 11 13:23:42 2007     length 2 : 11072
Thu Oct 11 13:23:42 2007     length 3 : 9884
Thu Oct 11 13:23:42 2007     length 4 : 7361
Thu Oct 11 13:23:42 2007     length 5 : 4850
Thu Oct 11 13:23:42 2007     length 6 : 3171
Thu Oct 11 13:23:42 2007     length 7 : 1783
Thu Oct 11 13:23:42 2007     length 9+: 2038
Thu Oct 11 13:23:42 2007  largest cycle: 20 relations
Thu Oct 11 13:23:42 2007  matrix is 55891 x 56030 with weight 3116041 (avg 55.61/col)
Thu Oct 11 13:23:47 2007  filtering completed in 3 passes
Thu Oct 11 13:23:47 2007  matrix is 51400 x 51464 with weight 2897239 (avg 56.30/col)
Thu Oct 11 13:23:49 2007  saving the first 48 matrix rows for later
Thu Oct 11 13:23:49 2007  matrix is 51352 x 51464 with weight 2270531 (avg 44.12/col)
Thu Oct 11 13:23:49 2007  matrix includes 64 packed rows
Thu Oct 11 13:23:49 2007  using block size 5461 for processor cache size 128 kB
Thu Oct 11 13:23:51 2007  commencing Lanczos iteration
Thu Oct 11 13:26:11 2007  lanczos halted after 814 iterations
Thu Oct 11 13:26:12 2007  recovered 16 nontrivial dependencies
Thu Oct 11 13:26:13 2007  prp41 factor: 11519704348754539604022205034624081555611
Thu Oct 11 13:26:13 2007  prp46 factor: 5996609457515185443760101854342559834794121041
Thu Oct 11 13:26:13 2007  elapsed time 05:40:00

6·10¹⁰⁴+7 = 6(0)₁₀₃7_<105> = 8629566092175419113_<19> · C86

C86 = P39 · P48

P39 = 312703414298744945585964596618843105759_<39>

P48 = 222346177668355476515021026054869613681073668721_<48>

Thu Oct 11 08:00:35 2007  Msieve v. 1.26
Thu Oct 11 08:00:35 2007  random seeds: 35251e1c b1bd4346
Thu Oct 11 08:00:35 2007  factoring 69528408913170114020623970508248965547977728760224458789292141359530747384979933264239 (86 digits)
Thu Oct 11 08:00:36 2007  commencing quadratic sieve (86-digit input)
Thu Oct 11 08:00:36 2007  using multiplier of 31
Thu Oct 11 08:00:36 2007  using 64kb Pentium 2 sieve core
Thu Oct 11 08:00:36 2007  sieve interval: 9 blocks of size 65536
Thu Oct 11 08:00:36 2007  processing polynomials in batches of 12
Thu Oct 11 08:00:36 2007  using a sieve bound of 1470947 (55662 primes)
Thu Oct 11 08:00:36 2007  using large prime bound of 117675760 (26 bits)
Thu Oct 11 08:00:36 2007  using double large prime bound of 336694943593840 (41-49 bits)
Thu Oct 11 08:00:36 2007  using trial factoring cutoff of 49 bits
Thu Oct 11 08:00:36 2007  polynomial 'A' values have 11 factors
Thu Oct 11 13:29:42 2007  55839 relations (15809 full + 40030 combined from 583377 partial), need 55758
Thu Oct 11 13:29:51 2007  begin with 599186 relations
Thu Oct 11 13:29:54 2007  reduce to 132538 relations in 10 passes
Thu Oct 11 13:29:54 2007  attempting to read 132538 relations
Thu Oct 11 13:30:03 2007  recovered 132538 relations
Thu Oct 11 13:30:03 2007  recovered 110467 polynomials
Thu Oct 11 13:30:16 2007  attempting to build 55839 cycles
Thu Oct 11 13:30:16 2007  found 55838 cycles in 5 passes
Thu Oct 11 13:30:18 2007  distribution of cycle lengths:
Thu Oct 11 13:30:18 2007     length 1 : 15809
Thu Oct 11 13:30:18 2007     length 2 : 11217
Thu Oct 11 13:30:18 2007     length 3 : 9985
Thu Oct 11 13:30:18 2007     length 4 : 7192
Thu Oct 11 13:30:18 2007     length 5 : 4922
Thu Oct 11 13:30:18 2007     length 6 : 3106
Thu Oct 11 13:30:18 2007     length 7 : 1762
Thu Oct 11 13:30:18 2007     length 9+: 1845
Thu Oct 11 13:30:18 2007  largest cycle: 18 relations
Thu Oct 11 13:30:19 2007  matrix is 55662 x 55838 with weight 3139688 (avg 56.23/col)
Thu Oct 11 13:30:22 2007  filtering completed in 3 passes
Thu Oct 11 13:30:22 2007  matrix is 50880 x 50944 with weight 2899893 (avg 56.92/col)
Thu Oct 11 13:30:24 2007  saving the first 48 matrix rows for later
Thu Oct 11 13:30:24 2007  matrix is 50832 x 50944 with weight 2295297 (avg 45.06/col)
Thu Oct 11 13:30:24 2007  matrix includes 64 packed rows
Thu Oct 11 13:30:24 2007  using block size 10922 for processor cache size 256 kB
Thu Oct 11 13:30:25 2007  commencing Lanczos iteration
Thu Oct 11 13:33:05 2007  lanczos halted after 805 iterations
Thu Oct 11 13:33:06 2007  recovered 17 nontrivial dependencies
Thu Oct 11 13:33:21 2007  prp39 factor: 312703414298744945585964596618843105759
Thu Oct 11 13:33:21 2007  prp48 factor: 222346177668355476515021026054869613681073668721
Thu Oct 11 13:33:21 2007  elapsed time 05:32:46

Oct 11, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(4·10¹⁶²+23)/9 = (4)₁₆₁7_<162> = 3 · 191537 · 36201871247_<11> · C146

C146 = P68 · P79

P68 = 14267717847005813507700165288034158445726684150241889062913896709923_<68>

P79 = 1497469599792136047698907928447361359099204601762726546842329109356470216353817_<79>

Number: n
N=21365473734302912529054906948237323508436428295729914712019667578602171034133803699777503768069330971332086852316622127836560860767947345582826091
  ( 146 digits)
SNFS difficulty: 162 digits.
Divisors found:

Thu Oct 11 07:49:06 2007  prp68 factor: 14267717847005813507700165288034158445726684150241889062913896709923
Thu Oct 11 07:49:06 2007  prp79 factor: 1497469599792136047698907928447361359099204601762726546842329109356470216353817
Thu Oct 11 07:49:06 2007  elapsed time 02:07:31 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 67.17 hours.
Scaled time: 80.33 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_4_161_7
n: 21365473734302912529054906948237323508436428295729914712019667578602171034133803699777503768069330971332086852316622127836560860767947345582826091
type: snfs
skew: 1.13
deg: 5
c5: 25
c0: 46
m: 200000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2900000)
Primes: RFBsize:230209, AFBsize:229862, largePrimes:7394863 encountered
Relations: rels:6833492, finalFF:510861
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 66.85 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 67.17 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

6·10¹⁰⁶+7 = 6(0)₁₀₅7_<107> = C107

C107 = P33 · P74

P33 = 660354883413107731466749453206421_<33>

P74 = 90860235166103760559298389079671871752970399872818769276787670766575373867_<74>

Number: n
N=60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
  ( 107 digits)
SNFS difficulty: 106 digits.
Divisors found:
 r1=660354883413107731466749453206421 (pp33)
 r2=90860235166103760559298389079671871752970399872818769276787670766575373867 (pp74)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.81 hours.
Scaled time: 0.97 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_6_0_105_7
n: 60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
type: snfs
skew: 0.65
deg: 5
c5: 60
c0: 7
m: 1000000000000000000000
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 200001)
Primes: RFBsize:41538, AFBsize:41547, largePrimes:2680462 encountered
Relations: rels:2220524, finalFF:111084
Max relations in full relation-set: 28
Initial matrix: 83152 x 111084 with sparse part having weight 5499964.
Pruned matrix : 67479 x 67958 with weight 2313666.
Total sieving time: 0.68 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.04 hours.
Total square root time: 0.04 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,106,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.4,2.4,50000
total time: 0.81 hours.
 --------- CPU info (if available) ----------

6·10¹¹²+7 = 6(0)₁₁₁7_<113> = 43 · C112

C112 = P29 · P32 · P52

P29 = 42037675529382231904791550999_<29>

P32 = 14936485810428385363892834492251_<32>

P52 = 2222264100043128899370105966054617650050692155163401_<52>

N = 6*10^112+7 : c112

prp29 factor: 42037675529382231904791550999
prp32 factor: 14936485810428385363892834492251
prp52 factor: 2222264100043128899370105966054617650050692155163401

GMP-ECM 6.0.1 [powered by GMP 4.1.4] [ECM]
Input number is 1395348837209302325581395348837209302325581395348837209302325581395348837209302325581395348837209302325581395349 (112 digits)
Using B1=87500, B2=26096911, polynomial x^2, sigma=730686625
Step 1 took 1203ms
Step 2 took 953ms
********** Factor found in step 2: 42037675529382231904791550999
Found probable prime factor of 29 digits: 42037675529382231904791550999
Composite cofactor 33192816197318600608605463828793223988644935250050070386447688396465987039773305651 has 83 digits

Thu Oct 11 14:51:32 2007  
Thu Oct 11 14:51:32 2007  
Thu Oct 11 14:51:32 2007  Msieve v. 1.28
Thu Oct 11 14:51:32 2007  random seeds: 409cfc00 e37a735e
Thu Oct 11 14:51:32 2007  factoring 33192816197318600608605463828793223988644935250050070386447688396465987039773305651 (83 digits)
Thu Oct 11 14:51:32 2007  commencing quadratic sieve (83-digit input)
Thu Oct 11 14:51:33 2007  using multiplier of 1
Thu Oct 11 14:51:33 2007  using 64kb Athlon XP sieve core
Thu Oct 11 14:51:33 2007  sieve interval: 6 blocks of size 65536
Thu Oct 11 14:51:33 2007  processing polynomials in batches of 17
Thu Oct 11 14:51:33 2007  using a sieve bound of 1369321 (52647 primes)
Thu Oct 11 14:51:33 2007  using large prime bound of 121869569 (26 bits)
Thu Oct 11 14:51:33 2007  using trial factoring cutoff of 27 bits
Thu Oct 11 14:51:33 2007  polynomial 'A' values have 10 factors
Thu Oct 11 15:25:57 2007  52751 relations (26020 full + 26731 combined from 283185 partial), need 52743
Thu Oct 11 15:25:58 2007  begin with 309205 relations
Thu Oct 11 15:25:58 2007  reduce to 76065 relations in 2 passes
Thu Oct 11 15:25:58 2007  attempting to read 76065 relations
Thu Oct 11 15:25:59 2007  recovered 76065 relations
Thu Oct 11 15:25:59 2007  recovered 69714 polynomials
Thu Oct 11 15:25:59 2007  attempting to build 52751 cycles
Thu Oct 11 15:25:59 2007  found 52751 cycles in 1 passes
Thu Oct 11 15:25:59 2007  distribution of cycle lengths:
Thu Oct 11 15:25:59 2007     length 1 : 26020
Thu Oct 11 15:25:59 2007     length 2 : 26731
Thu Oct 11 15:25:59 2007  largest cycle: 2 relations
Thu Oct 11 15:25:59 2007  matrix is 52647 x 52751 with weight 1646722 (avg 31.22/col)
Thu Oct 11 15:26:00 2007  filtering completed in 4 passes
Thu Oct 11 15:26:00 2007  matrix is 46089 x 46153 with weight 1415834 (avg 30.68/col)
Thu Oct 11 15:26:00 2007  saving the first 48 matrix rows for later
Thu Oct 11 15:26:01 2007  matrix is 46041 x 46153 with weight 1132687 (avg 24.54/col)
Thu Oct 11 15:26:01 2007  matrix includes 64 packed rows
Thu Oct 11 15:26:01 2007  commencing Lanczos iteration
Thu Oct 11 15:27:17 2007  lanczos halted after 730 iterations
Thu Oct 11 15:27:18 2007  recovered 10 nontrivial dependencies
Thu Oct 11 15:27:18 2007  prp32 factor: 14936485810428385363892834492251
Thu Oct 11 15:27:18 2007  prp52 factor: 2222264100043128899370105966054617650050692155163401
Thu Oct 11 15:27:18 2007  elapsed time 00:35:46

(55·10¹⁶⁴-1)/9 = 6(1)₁₆₄_<165> = 13 · 863 · 19751 · C157

C157 = P46 · P112

P46 = 2039347963490980778560349082035680167389362879_<46>

P112 = 1352339114250697693044223701395926133298449563024538791688249501380572686573552852589778414243811182815085121861_<112>

Number: n
N=2757890018596357122830957296003083613878567247312881325398578877625921784561272606907739980779742968471198081644196023138538802706004178942492698464864797819
  ( 157 digits)
SNFS difficulty: 166 digits.
Divisors found:

Thu Oct 11 23:37:55 2007  prp46 factor: 2039347963490980778560349082035680167389362879
Thu Oct 11 23:37:55 2007  prp112 factor: 1352339114250697693044223701395926133298449563024538791688249501380572686573552852589778414243811182815085121861
Thu Oct 11 23:37:55 2007  elapsed time 01:27:35 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 46.45 hours.
Scaled time: 61.40 units (timescale=1.322).
Factorization parameters were as follows:
name: KA_6_1_164
n: 2757890018596357122830957296003083613878567247312881325398578877625921784561272606907739980779742968471198081644196023138538802706004178942492698464864797819
skew: 0.71
deg: 5
c5: 11
c0: -2
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2200000)
Primes: RFBsize:250150, AFBsize:250187, largePrimes:7389826 encountered
Relations: rels:6945502, finalFF:606876
Max relations in full relation-set: 28
Initial matrix: 500404 x 606876 with sparse part having weight 45655180.
Pruned matrix : 414282 x 416848 with weight 26923583.
Total sieving time: 46.18 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 46.45 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 11, 2007 (2nd)

By Yousuke Koide

10¹⁰⁰⁹+1 is divisible by 873234964696345278371172272680705837_<36>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 11, 2007

The factor table of 600...007 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Oct 10, 2007 (2nd)

By Sinkiti Sibata / PRIMO

(28·10²²⁰⁷+53)/9 is prime.

Oct 10, 2007

By Jo Yeong Uk / GGNFS

(8·10¹⁵⁹-53)/9 = (8)₁₅₈3_<159> = 480451 · 4208429 · 104033087 · 13728238483_<11> · C129

C129 = P42 · P87

P42 = 316712295015730221860570435349138324870013_<42>

P87 = 971912454296354051931961805793739631984439234627451326067513307017004518364331228609949_<87>

Number: 88883_159
N=307816623954569300455053980011477723245374843831649497265306543156045707790951139583730144537538886277612234831260348782103559337
  ( 129 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=316712295015730221860570435349138324870013 (pp42)
 r2=971912454296354051931961805793739631984439234627451326067513307017004518364331228609949 (pp87)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 36.09 hours.
Scaled time: 76.93 units (timescale=2.132).
Factorization parameters were as follows:
n: 307816623954569300455053980011477723245374843831649497265306543156045707790951139583730144537538886277612234831260348782103559337
m: 100000000000000000000000000000000
c5: 4
c0: -265
skew: 2.31
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4100001)
Primes: RFBsize:283146, AFBsize:282842, largePrimes:5712676 encountered
Relations: rels:5728756, finalFF:637907
Max relations in full relation-set: 28
Initial matrix: 566052 x 637907 with sparse part having weight 44270840.
Pruned matrix : 519131 x 522025 with weight 33004800.
Total sieving time: 34.34 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.60 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 36.09 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 9, 2007 (5th)

By Sinkiti Sibata / GGNFS

6·10¹⁶³-7 = 5(9)₁₆₂3_<164> = 30339296027748931253_<20> · C145

C145 = P50 · P96

P50 = 15909833358959093262353180001154624082529476187767_<50>

P96 = 124302573471643865966793637908816400185876720580733444177989495780776161055978026073936417281843_<96>

Number: 59993_163
N=1977633230023623206564389103658481345270454210925237336059189627833971133619728015943405220774679827442341511985530665001766489444666368027814581
  ( 145 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=15909833358959093262353180001154624082529476187767 (pp50)
 r2=124302573471643865966793637908816400185876720580733444177989495780776161055978026073936417281843 (pp96)
Version: GGNFS-0.77.1-20060513-k8
Total time: 95.21 hours.
Scaled time: 190.23 units (timescale=1.998).
Factorization parameters were as follows:
name: 59993_163
n: 1977633230023623206564389103658481345270454210925237336059189627833971133619728015943405220774679827442341511985530665001766489444666368027814581
m: 200000000000000000000000000000000
c5: 375
c0: -14
skew: 0.52
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 5350001)
Primes: RFBsize:315948, AFBsize:315866, largePrimes:5944123 encountered
Relations: rels:6092944, finalFF:763528
Max relations in full relation-set: 28
Initial matrix: 631880 x 763528 with sparse part having weight 59643557.
Pruned matrix : 535995 x 539218 with weight 43398744.
Total sieving time: 90.70 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 4.03 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 95.21 hours.
 --------- CPU info (if available) ----------

Oct 9, 2007 (4th)

By Sinkiti Sibata / PRIMO

(8·10²⁰⁷³-11)/3 is prime.

Oct 9, 2007 (3rd)

By suberi / PRIMO

5·10²⁷³³+9 is prime.

Oct 9, 2007 (2nd)

By Jo Yeong Uk / GGNFS

(8·10¹⁵⁹-17)/9 = (8)₁₅₈7_<159> = 229 · 800509 · 4884721 · 262148354051_<12> · C133

C133 = P41 · P93

P41 = 31689588497279916590736503849012575753313_<41>

P93 = 119492948637304780639682337876688171145045603197808488844094715899024113564434226339292816029_<93>

Number: 88887_159
N=3786682370642793460441992233699759761247607307411975413165317553691947475895090384189590618511490509963186182014264349114253796254077
  ( 133 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=31689588497279916590736503849012575753313 (pp41)
 r2=119492948637304780639682337876688171145045603197808488844094715899024113564434226339292816029 (pp93)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 31.11 hours.
Scaled time: 66.71 units (timescale=2.144).
Factorization parameters were as follows:
n: 3786682370642793460441992233699759761247607307411975413165317553691947475895090384189590618511490509963186182014264349114253796254077
m: 100000000000000000000000000000000
c5: 4
c0: -85
skew: 1.84
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3800001)
Primes: RFBsize:283146, AFBsize:283447, largePrimes:5649191 encountered
Relations: rels:5661375, finalFF:639116
Max relations in full relation-set: 28
Initial matrix: 566657 x 639116 with sparse part having weight 40954229.
Pruned matrix : 512428 x 515325 with weight 29660434.
Total sieving time: 29.57 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.40 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 31.11 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 9, 2007

By Robert Backstrom / GGNFS, Msieve

4·10¹⁶²+3 = 4(0)₁₆₁3_<163> = 7 · 16111 · 898857769272037_<15> · C143

C143 = P47 · P96

P47 = 52633384675921297349532423419308829377260438229_<47>

P96 = 749699425654555588156813979006319175064153379838686656191939648186729452596767342041598941114643_<96>

Number: n
N=39459218261793484031429986564259843918054327571537121376310544925094790528770124732699157255927616425625128819829539343779063155819583908887247
  ( 143 digits)
SNFS difficulty: 162 digits.
Divisors found:

Tue Oct 09 03:46:58 2007  prp47 factor: 52633384675921297349532423419308829377260438229
Tue Oct 09 03:46:58 2007  prp96 factor: 749699425654555588156813979006319175064153379838686656191939648186729452596767342041598941114643
Tue Oct 09 03:46:58 2007  elapsed time 01:16:25 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 36.15 hours.
Scaled time: 52.53 units (timescale=1.453).
Factorization parameters were as follows:
name: KA_4_0_161_3
n: 39459218261793484031429986564259843918054327571537121376310544925094790528770124732699157255927616425625128819829539343779063155819583908887247
skew: 0.75
deg: 5
c5: 25
c0: 6
m: 200000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1900000)
Primes: RFBsize:203362, AFBsize:202562, largePrimes:7139160 encountered
Relations: rels:6577562, finalFF:434257
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 35.92 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 36.15 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Oct 8, 2007 (4th)

By Bryan Koen / GMP-ECM

(23·10¹⁷³+1)/3 = 7(6)₁₇₂7_<174> = 11 · 19 · 41 · C170

C170 = P30 · P141

P30 = 357911945978650040346202809163_<30>

P141 = 249977110919930838083661846538618118461822803550100409862996457896163981755684629971850878837293997356705743192000800069352481784564014480361_<141>

Oct 8, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(31·10²¹⁷⁷+23)/9 is prime.

Oct 8, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

(73·10¹⁵⁹-1)/9 = 8(1)₁₅₉_<160> = 2657 · 105091757 · 340002075499_<12> · C137

C137 = P68 · P69

P68 = 85748085121300963152030695599342054561573492952495448497507158243159_<68>

P69 = 996355092269813964638397829269428609707014906515819237429532829639679_<69>

Number: n
N=85435541262993683107759178811222508432637694938946198668249661730703724787996850375797180518678700584591827296195920977054636644636705961
  ( 137 digits)
SNFS difficulty: 161 digits.
Divisors found:

Mon Oct 08 11:11:00 2007  prp68 factor: 85748085121300963152030695599342054561573492952495448497507158243159
Mon Oct 08 11:11:00 2007  prp69 factor: 996355092269813964638397829269428609707014906515819237429532829639679
Mon Oct 08 11:11:01 2007  elapsed time 01:25:31 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 45.89 hours.
Scaled time: 60.85 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_8_1_159
n: 85435541262993683107759178811222508432637694938946198668249661730703724787996850375797180518678700584591827296195920977054636644636705961
skew: 0.67
deg: 5
c5: 73
c0: -10
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100000)
Primes: RFBsize:250150, AFBsize:250101, largePrimes:7499050 encountered
Relations: rels:7084336, finalFF:634136
Max relations in full relation-set: 28
Initial matrix: 500316 x 634136 with sparse part having weight 48027068.
Pruned matrix : 392586 x 395151 with weight 27479275.
Total sieving time: 45.64 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 45.89 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

6·10¹⁶⁴-7 = 5(9)₁₆₃3_<165> = 17 · 302404974167609_<15> · C150

C150 = P51 · P99

P51 = 604857162810389628774661784293336029351376392407791_<51>

P99 = 192957014318376632131120220747611805227589329088927241976832631934622388748514730334494973730320991_<99>

Number: n
N=116711432224977017360883726082633787948846053120532190717761735193932640441906310777526105200497999505680676600497638929152987804613749651905799240881
  ( 150 digits)
SNFS difficulty: 165 digits.
Divisors found:

Mon Oct 08 17:31:28 2007  prp51 factor: 604857162810389628774661784293336029351376392407791
Mon Oct 08 17:31:28 2007  prp99 factor: 192957014318376632131120220747611805227589329088927241976832631934622388748514730334494973730320991
Mon Oct 08 17:31:28 2007  elapsed time 01:42:50 (Msieve 1.28)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 53.19 hours.
Scaled time: 63.34 units (timescale=1.191).
Factorization parameters were as follows:
name: KA_5_9_163_3
n: 116711432224977017360883726082633787948846053120532190717761735193932640441906310777526105200497999505680676600497638929152987804613749651905799240881
skew: 1.63
deg: 5
c5: 3
c0: -35
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2600000)
Primes: RFBsize:216816, AFBsize:216606, largePrimes:7376363 encountered
Relations: rels:6846162, finalFF:475104
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 52.94 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 53.19 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 8, 2007

By Jo Yeong Uk / GGNFS

(5·10¹⁵⁹-41)/9 = (5)₁₅₈1_<159> = 203232471011_<12> · 30634761442301959_<17> · C131

C131 = P66 · P66

P66 = 140302918730839359783997803266247889954113331203299846460516096197_<66>

P66 = 635994249340914371879827621457572197377938193794948288296614712167_<66>

Number: 55551_159
N=89231849478559493177495087019280828859221907790013794337807829144866668300309536154113542379040143520122806007729736339743638328899
  ( 131 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=140302918730839359783997803266247889954113331203299846460516096197 (pp66)
 r2=635994249340914371879827621457572197377938193794948288296614712167 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 27.76 hours.
Scaled time: 59.39 units (timescale=2.139).
Factorization parameters were as follows:
n: 89231849478559493177495087019280828859221907790013794337807829144866668300309536154113542379040143520122806007729736339743638328899
m: 100000000000000000000000000000000
c5: 1
c0: -82
skew: 2.41
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:282833, largePrimes:5618340 encountered
Relations: rels:5637592, finalFF:646613
Max relations in full relation-set: 28
Initial matrix: 566045 x 646613 with sparse part having weight 40570327.
Pruned matrix : 501999 x 504893 with weight 27943297.
Total sieving time: 26.39 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.23 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 27.76 hours.
 --------- CPU info (if available) ----------

Oct 7, 2007 (5th)

By Sinkiti Sibata / PRIMO

(17·10²⁰⁶⁸-53)/9 is prime.

Oct 7, 2007 (4th)

By Yousuke Koide

10¹⁰⁰⁷+1 is divisible by 80130271534233515728987750894609_<32>

10¹⁰⁵⁴+1 is divisible by 111276132074930025328712302045364981_<36>

10¹⁶⁰⁵+1 is divisible by 4298338634928851216299618775086771_<34>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 7, 2007 (3rd)

By Sinkiti Sibata / GGNFS

6·10¹⁶¹-7 = 5(9)₁₆₀3_<162> = 59 · 4889 · 22063 · 61949 · 56338169 · 5137570679_<10> · C130

C130 = P32 · P99

P32 = 25632208522320555148392302355173_<32>

P99 = 205132168410612051871480238620927190554253620898540807301677670565578241342961193951890988344739443_<99>

Number: 59993_161
N=5257990515336585603900960324981397066212063936330995720178877708548412575128763722465208456773985220196118351156898540333928188639
  ( 130 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=25632208522320555148392302355173 (pp32)
 r2=205132168410612051871480238620927190554253620898540807301677670565578241342961193951890988344739443 (pp99)
Version: GGNFS-0.77.1-20060513-k8
Total time: 67.83 hours.
Scaled time: 134.98 units (timescale=1.990).
Factorization parameters were as follows:
name: 59993_161
n: 5257990515336585603900960324981397066212063936330995720178877708548412575128763722465208456773985220196118351156898540333928188639
m: 100000000000000000000000000000000
c5: 60
c0: -7
skew: 0.65
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4350001)
Primes: RFBsize:315948, AFBsize:316366, largePrimes:5776158 encountered
Relations: rels:5879966, finalFF:735887
Max relations in full relation-set: 28
Initial matrix: 632381 x 735887 with sparse part having weight 44476895.
Pruned matrix : 553498 x 556723 with weight 31162467.
Total sieving time: 64.08 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.36 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 67.83 hours.
 --------- CPU info (if available) ----------

Oct 7, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM

10¹⁹²+9 = 1(0)₁₉₁9_<193> = C193

C193 = P48 · P145

P48 = 325208379747671632800443572929049811907718391209_<48>

P145 = 3074951515012920315894112276452006313835272802228418099697777887803931547784516799444634005241238767287033369894773351997005678938044816110863201_<145>

Oct 7, 2007

By suberi / PRIMO

(13·10²⁰⁷⁹-7)/3 is prime.

(13·10²¹²⁰-7)/3 is prime.

(13·10²²⁶⁰-7)/3 is prime.

(13·10²⁴²³-7)/3 is prime.

Oct 6, 2007 (4th)

By Jo Yeong Uk / GGNFS

(4·10¹⁵⁹+41)/9 = (4)₁₅₈9_<159> = 3709 · 3456197 · 40995079027450649_<17> · C132

C132 = P48 · P85

P48 = 218551920024031168927773697661809538745109102567_<48>

P85 = 3869686706115428835860198962763376764473465747888783930870949253002451781545174371711_<85>

Number: 44449_159
N=845727459512995808632831376766004857195411667709864917200855795181161872981252627569069291871505578807711339836312388193111282282137
  ( 132 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=218551920024031168927773697661809538745109102567 (pp48)
 r2=3869686706115428835860198962763376764473465747888783930870949253002451781545174371711 (pp85)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 27.95 hours.
Scaled time: 59.92 units (timescale=2.144).
Factorization parameters were as follows:
n: 845727459512995808632831376766004857195411667709864917200855795181161872981252627569069291871505578807711339836312388193111282282137
m: 100000000000000000000000000000000
c5: 2
c0: 205
skew: 2.52
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:283793, largePrimes:5629726 encountered
Relations: rels:5660465, finalFF:657003
Max relations in full relation-set: 28
Initial matrix: 567004 x 657003 with sparse part having weight 41479342.
Pruned matrix : 495662 x 498561 with weight 28049677.
Total sieving time: 26.61 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 27.95 hours.
 --------- CPU info (if available) ----------

Oct 6, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

2·10¹⁶¹+3 = 2(0)₁₆₀3_<162> = 1645747984609139286241_<22> · C141

C141 = P44 · P97

P44 = 23143371269685496536153160328427093498540901_<44>

P97 = 5250976096680145607463471043357442149484478476541758912748098433643075952275139383190561991897383_<97>

Number: n
N=121525289333712574060203929849274253650679147008067862136662858454750139437642287196603579159652285468795971038414619211834083134495020362083
  ( 141 digits)
SNFS difficulty: 161 digits.
Divisors found:

Sat Oct 06 11:57:55 2007  prp44 factor: 23143371269685496536153160328427093498540901
Sat Oct 06 11:57:55 2007  prp97 factor: 5250976096680145607463471043357442149484478476541758912748098433643075952275139383190561991897383
Sat Oct 06 11:57:55 2007  elapsed time 01:40:44 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 43.82 hours.
Scaled time: 63.63 units (timescale=1.452).
Factorization parameters were as follows:
name: KA_2_0_160_3
n: 121525289333712574060203929849274253650679147008067862136662858454750139437642287196603579159652285468795971038414619211834083134495020362083
skew: 0.68
deg: 5
c5: 20
c0: 3
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2300000)
Primes: RFBsize:203362, AFBsize:203062, largePrimes:7438144 encountered
Relations: rels:6924431, finalFF:458969
Max relations in full relation-set: 28
Initial matrix: 406490 x 458969 with sparse part having weight 41917861.
Pruned matrix : 379962 x 382058 with weight 31649775.
Total sieving time: 43.56 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 43.82 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

2·10¹⁶⁰-9 = 1(9)₁₅₉1_<161> = 158642813009799873789292199_<27> · C135

C135 = P48 · P87

P48 = 514829968216555250825419476063055331353216130401_<48>

P87 = 244875747315362559771904473968778705005860870814895857896156971504755878896463497536209_<87>

Number: n
N=126069373207373321436708046654043582257956838503880528523913166513739523221993375991519276144852178818516438085011957703665140363189809
  ( 135 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=514829968216555250825419476063055331353216130401 (pp48)
 r2=244875747315362559771904473968778705005860870814895857896156971504755878896463497536209 (pp87)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 39.32 hours.
Scaled time: 46.99 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_1_9_159_1
n: 126069373207373321436708046654043582257956838503880528523913166513739523221993375991519276144852178818516438085011957703665140363189809
type: snfs
skew: 1.35
deg: 5
c5: 2
c0: -9
m: 100000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1600001)
Primes: RFBsize:230209, AFBsize:230337, largePrimes:6544960 encountered
Relations: rels:6024747, finalFF:519640
Max relations in full relation-set: 28
Initial matrix: 460611 x 519640 with sparse part having weight 28682777.
Pruned matrix : 405415 x 407782 with weight 18445497.
Total sieving time: 35.33 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 3.68 hours.
Total square root time: 0.09 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 39.32 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Oct 6, 2007 (2nd)

By Sinkiti Sibata / GGNFS

6·10¹⁶⁰-7 = 5(9)₁₅₉3_<161> = 110893837864780114169227_<24> · 53482456690377432712639319435401_<32> · C107

C107 = P51 · P56

P51 = 125543951754463483312651367167081146619879782542807_<51>

P56 = 80581749745901679359607613279455998414547734638470247237_<56>

Number: 59993_160
N=10116551302389730489061629792753496443305947169260756466085450095805957750759395081955491468661781825974259
  ( 107 digits)
Divisors found:
 r1=125543951754463483312651367167081146619879782542807 (pp51)
 r2=80581749745901679359607613279455998414547734638470247237 (pp56)
Version: GGNFS-0.77.1-20060513-k8
Total time: 16.09 hours.
Scaled time: 31.66 units (timescale=1.968).
Factorization parameters were as follows:
name: 59993_160
n: 10116551302389730489061629792753496443305947169260756466085450095805957750759395081955491468661781825974259
skew: 8717.48
# norm 7.18e+14
c5: 34200
c4: 3446830450
c3: -49450344917839
c2: -282207816974048745
c1: 293743109705688382953
c0: -105852972657943776101076
# alpha -6.04
Y1: 1982489113
Y0: -196879813041941649923
# Murphy_E 1.63e-09
# M 8200850302644055184453131829831345367830490194178486463399401491964831823878780279463907218481306105711361
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2300001)
Primes: RFBsize:183072, AFBsize:182207, largePrimes:4770558 encountered
Relations: rels:5287342, finalFF:797494
Max relations in full relation-set: 28
Initial matrix: 365359 x 797494 with sparse part having weight 66842766.
Pruned matrix : 198399 x 200289 with weight 27225588.
Total sieving time: 15.17 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.58 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 16.09 hours.
 --------- CPU info (if available) ----------

6·10¹⁴⁸-7 = 5(9)₁₄₇3_<149> = 17 · 5261 · 7069 · 20877877 · 4124979457_<10> · C124

C124 = P46 · P78

P46 = 2202754157836179317307651152968047629805882079_<46>

P78 = 500267040879752050179524392513061490125276212618093746534715313369595549802451_<78>

Number: 59993_148
N=1101965304326275718376569832258079442992217073921951287705392731002575698336321117095630581548488817660192266002626251175629
  ( 124 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=2202754157836179317307651152968047629805882079 (pp46)
 r2=500267040879752050179524392513061490125276212618093746534715313369595549802451 (pp78)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 38.13 hours.
Scaled time: 25.82 units (timescale=0.677).
Factorization parameters were as follows:
name: 59993_148
n: 1101965304326275718376569832258079442992217073921951287705392731002575698336321117095630581548488817660192266002626251175629
m: 200000000000000000000000000000
c5: 375
c0: -14
skew: 0.52
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 4550001)
Primes: RFBsize:114155, AFBsize:114432, largePrimes:3074783 encountered
Relations: rels:3142613, finalFF:260671
Max relations in full relation-set: 28
Initial matrix: 228653 x 260671 with sparse part having weight 33256669.
Pruned matrix : 220290 x 221497 with weight 26947508.
Total sieving time: 35.67 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 2.06 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 38.13 hours.
 --------- CPU info (if available) ----------

Oct 6, 2007

By Bryan Koen / GGNFS

(61·10¹⁶⁹-7)/9 = 6(7)₁₆₉_<170> = 679517 · 2099650316119_<13> · 462133680259364512974037301324911_<33> · C120

C120 = P38 · P82

P38 = 56540095809527061398275309610361450221_<38>

P82 = 1818092044741429958746153841013907596909769895723120119363711217697392274661650529_<82>

Number: 67777_169
N=102795098400219410634465090516194534805474053557213593780153631997610268197607479386423556429973192979895429973931816909
  ( 120 digits)
Divisors found:
 r1=56540095809527061398275309610361450221 (pp38)
 r2=1818092044741429958746153841013907596909769895723120119363711217697392274661650529 (pp82)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 57.70 hours.
Scaled time: 129.60 units (timescale=2.246).
Factorization parameters were as follows:
name: 67777_169
n: 102795098400219410634465090516194534805474053557213593780153631997610268197607479386423556429973192979895429973931816909
skew: 105558.47
# norm 5.86e+015
c5: 3420
c4: -855817826
c3: -172975041238792
c2: 10097144255620342185
c1: 454824918396171751978112
c0: 4817673992078805183239899869
# alpha -4.79
Y1: 1203809206333
Y0: -124620494456053891335838
# Murphy_E 3.13e-010
# M 19860790920966959294374370574608201829699352757127470678651745225926909610626249915480516469649586859101696560082650191
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4350001)
Primes: RFBsize:315948, AFBsize:316478, largePrimes:7651281 encountered
Relations: rels:7683310, finalFF:711142
Max relations in full relation-set: 28
Initial matrix: 632504 x 711142 with sparse part having weight 59334766.
Pruned matrix : 568876 x 572102 with weight 42656010.
Total sieving time: 48.21 hours.
Total relation processing time: 0.50 hours.
Matrix solve time: 8.60 hours.
Time per square root: 0.39 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 57.70 hours.
 --------- CPU info (if available) ----------

Oct 5, 2007 (4th)

By Jo Yeong Uk / PRIMO

(55·10²⁰¹⁵+17)/9 is prime.

Oct 5, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

6·10¹⁵¹-7 = 5(9)₁₅₀3_<152> = 38049083 · C145

C145 = P45 · P100

P45 = 163890451242523530323685961374784914589069397_<45>

P100 = 9621735296463067319406359609200658570446718765888423723850749029550679811036943776234172558145948143_<100>

Number: n
N=1576910539473448019759109569079496607053578663117847018809888269843454571559582658010444036193986593579666558586970413978176556843695812590279771
  ( 145 digits)
SNFS difficulty: 151 digits.
Divisors found:

Fri Oct 05 09:28:44 2007  prp45 factor: 163890451242523530323685961374784914589069397
Fri Oct 05 09:28:44 2007  prp100 factor: 9621735296463067319406359609200658570446718765888423723850749029550679811036943776234172558145948143
Fri Oct 05 09:28:44 2007  elapsed time 00:54:09 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.99 hours.
Scaled time: 26.51 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_5_9_150_3
n: 1576910539473448019759109569079496607053578663117847018809888269843454571559582658010444036193986593579666558586970413978176556843695812590279771
skew: 0.65
deg: 5
c5: 60
c0: -7
m: 1000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 900000)
Primes: RFBsize:216816, AFBsize:216901, largePrimes:6806958 encountered
Relations: rels:6383461, finalFF:576223
Max relations in full relation-set: 28
Initial matrix: 433784 x 576223 with sparse part having weight 36816750.
Pruned matrix : 309229 x 311461 with weight 17215851.
Total sieving time: 19.80 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 19.99 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 5, 2007 (2nd)

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

6·10¹⁵⁹-7 = 5(9)₁₅₈3_<160> = 13 · 46099251251888935727327_<23> · 24879066220185916328457524320554279793687_<41> · C96

C96 = P41 · P56

P41 = 17014311483120697384989356382969398497597_<41>

P56 = 23651874787979709585009977994193399030605069949949286937_<56>

Thu Oct  4 21:37:14 2007  
Thu Oct  4 21:37:14 2007  
Thu Oct  4 21:37:14 2007  Msieve v. 1.28
Thu Oct  4 21:37:14 2007  random seeds: 1a77d3d5 9d0329b9
Thu Oct  4 21:37:14 2007  factoring 402420364802456082600245272138853200856277707189366407172983739323623291446802112677069257990389 (96 digits)
Thu Oct  4 21:37:14 2007  commencing quadratic sieve (96-digit input)
Thu Oct  4 21:37:14 2007  using multiplier of 1
Thu Oct  4 21:37:14 2007  using 32kb Intel Core sieve core
Thu Oct  4 21:37:14 2007  sieve interval: 36 blocks of size 32768
Thu Oct  4 21:37:14 2007  processing polynomials in batches of 6
Thu Oct  4 21:37:14 2007  using a sieve bound of 2248781 (83529 primes)
Thu Oct  4 21:37:14 2007  using large prime bound of 337317150 (28 bits)
Thu Oct  4 21:37:14 2007  using double large prime bound of 2241140878991550 (43-51 bits)
Thu Oct  4 21:37:14 2007  using trial factoring cutoff of 51 bits
Thu Oct  4 21:37:14 2007  polynomial 'A' values have 12 factors
Fri Oct  5 02:05:05 2007  83793 relations (19127 full + 64666 combined from 1276886 partial), need 83625
Fri Oct  5 02:05:06 2007  begin with 1296013 relations
Fri Oct  5 02:05:07 2007  reduce to 225145 relations in 12 passes
Fri Oct  5 02:05:07 2007  attempting to read 225145 relations
Fri Oct  5 02:05:08 2007  recovered 225145 relations
Fri Oct  5 02:05:08 2007  recovered 213597 polynomials
Fri Oct  5 02:05:09 2007  attempting to build 83793 cycles
Fri Oct  5 02:05:09 2007  found 83793 cycles in 6 passes
Fri Oct  5 02:05:09 2007  distribution of cycle lengths:
Fri Oct  5 02:05:09 2007     length 1 : 19127
Fri Oct  5 02:05:09 2007     length 2 : 13665
Fri Oct  5 02:05:09 2007     length 3 : 13753
Fri Oct  5 02:05:09 2007     length 4 : 11694
Fri Oct  5 02:05:09 2007     length 5 : 8929
Fri Oct  5 02:05:09 2007     length 6 : 6357
Fri Oct  5 02:05:09 2007     length 7 : 4300
Fri Oct  5 02:05:09 2007     length 9+: 5968
Fri Oct  5 02:05:09 2007  largest cycle: 20 relations
Fri Oct  5 02:05:09 2007  matrix is 83529 x 83793 with weight 5817253 (avg 69.42/col)
Fri Oct  5 02:05:10 2007  filtering completed in 4 passes
Fri Oct  5 02:05:10 2007  matrix is 80599 x 80663 with weight 5617583 (avg 69.64/col)
Fri Oct  5 02:05:11 2007  saving the first 48 matrix rows for later
Fri Oct  5 02:05:11 2007  matrix is 80551 x 80663 with weight 4705622 (avg 58.34/col)
Fri Oct  5 02:05:11 2007  matrix includes 64 packed rows
Fri Oct  5 02:05:11 2007  using block size 32265 for processor cache size 4096 kB
Fri Oct  5 02:05:14 2007  commencing Lanczos iteration
Fri Oct  5 02:05:49 2007  lanczos halted after 1276 iterations
Fri Oct  5 02:05:49 2007  recovered 17 nontrivial dependencies
Fri Oct  5 02:05:50 2007  prp41 factor: 17014311483120697384989356382969398497597
Fri Oct  5 02:05:50 2007  prp56 factor: 23651874787979709585009977994193399030605069949949286937
Fri Oct  5 02:05:50 2007  elapsed time 04:28:36

(5·10¹⁶¹-23)/9 = (5)₁₆₀3_<161> = 181 · 9377 · 59980747 · 1556391950309252260727_<22> · C126

C126 = P30 · P97

P30 = 204200339305081254682089876323_<30>

P97 = 1717108343637436044836379289726170911481645229487158423846189656851215623920488863042590355402187_<97>

6·10¹⁸⁵-7 = 5(9)₁₈₄3_<186> = 1259 · 105094819 · 18234595094684519_<17> · 496645177774564607081_<21> · 91097916289552225379407273_<26> · C112

C112 = P43 · P70

P43 = 1567828725851495950483147060696472797473131_<43>

P70 = 3505861909643653215337674382799814173297028903124851463841838321295469_<70>

Number: 59993_185
N=5496591010807901243959700004966756355343953965432332097077840850790392390952200017975624837864532764649639543439
  ( 112 digits)
Divisors found:
 r1=1567828725851495950483147060696472797473131 (pp43)
 r2=3505861909643653215337674382799814173297028903124851463841838321295469 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 17.45 hours.
Scaled time: 37.14 units (timescale=2.129).
Factorization parameters were as follows:
name: 59993_185
n: 5496591010807901243959700004966756355343953965432332097077840850790392390952200017975624837864532764649639543439
skew: 31918.14
# norm 4.35e+15
c5: 49500
c4: 1148015948
c3: -102222124732255
c2: -6099585714717477637
c1: 33741417547897847981555
c0: 598316031826581667570223049
# alpha -6.53
Y1: 598253464301
Y0: -2565057913790794214018
# Murphy_E 7.81e-10
# M 3628664822376311219602672466853507363069765951502221673628741042021637214537904922189021557595578069943077896990
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1400000, 2240001)
Primes: RFBsize:203362, AFBsize:203437, largePrimes:7582629 encountered
Relations: rels:7467623, finalFF:565840
Max relations in full relation-set: 28
Initial matrix: 406880 x 565840 with sparse part having weight 52660477.
Pruned matrix : 291699 x 293797 with weight 29738311.
Polynomial selection time: 0.94 hours.
Total sieving time: 15.79 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.47 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000
total time: 17.45 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Oct 5, 2007

By Sinkiti Sibata / GGNFS

6·10¹⁴²-7 = 5(9)₁₄₁3_<143> = 353 · 85223 · 1064743 · 17170804432778660568577_<23> · C108

C108 = P32 · P76

P32 = 42191759522915775604583057626823_<32>

P76 = 2585572109501371476246882696300039865583164290410873961325438433783561473999_<76>

Number: 59993_142
N=109089836673239920516770319965068209364823641145718230527163887975622905277416393899382401902254788759475177
  ( 108 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=42191759522915775604583057626823 (pp32)
 r2=2585572109501371476246882696300039865583164290410873961325438433783561473999 (pp76)
Version: GGNFS-0.77.1-20060513-k8
Total time: 17.01 hours.
Scaled time: 34.09 units (timescale=2.004).
Factorization parameters were as follows:
name: 59993_142
n: 109089836673239920516770319965068209364823641145718230527163887975622905277416393899382401902254788759475177
m: 10000000000000000000000000000
c5: 600
c0: -7
skew: 0.41
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2550001)
Primes: RFBsize:100021, AFBsize:99733, largePrimes:2907987 encountered
Relations: rels:2943976, finalFF:268434
Max relations in full relation-set: 28
Initial matrix: 199820 x 268434 with sparse part having weight 31091401.
Pruned matrix : 182446 x 183509 with weight 19802614.
Total sieving time: 16.40 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 17.01 hours.
 --------- CPU info (if available) ----------

6·10¹⁵²-7 = 5(9)₁₅₁3_<153> = 19 · 79 · 317 · 683 · 194723 · C139

C139 = P61 · P79

P61 = 2422519199645591483038400362598333261141854085321449290981587_<61>

P79 = 3913867442685506786621678329983313608259562954908441460080566565534765765237163_<79>

Number: 59993_152
N=9481419024773431796374859861929423222068324195372690108617292629460624268055670298332904077189122625243218702260577584276221851166121117681
  ( 139 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=2422519199645591483038400362598333261141854085321449290981587 (pp61)
 r2=3913867442685506786621678329983313608259562954908441460080566565534765765237163 (pp79)
Version: GGNFS-0.77.1-20060513-k8
Total time: 30.48 hours.
Scaled time: 59.79 units (timescale=1.962).
Factorization parameters were as follows:
name: 59993_152
n: 9481419024773431796374859861929423222068324195372690108617292629460624268055670298332904077189122625243218702260577584276221851166121117681
m: 1000000000000000000000000000000
c5: 600
c0: -7
skew: 0.41
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2300001)
Primes: RFBsize:176302, AFBsize:175743, largePrimes:5726784 encountered
Relations: rels:5711566, finalFF:522112
Max relations in full relation-set: 28
Initial matrix: 352111 x 522112 with sparse part having weight 50262752.
Pruned matrix : 292470 x 294294 with weight 27860308.
Total sieving time: 28.94 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,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 30.48 hours.
 --------- CPU info (if available) ----------

Oct 4, 2007 (10th)

By Jo Yeong Uk / GGNFS

6·10¹⁴⁵-7 = 5(9)₁₄₄3_<146> = 1766550377_<10> · 157012037513_<12> · 4348276733443_<13> · C113

C113 = P36 · P78

P36 = 208622310195879907337278472254444759_<36>

P78 = 238459345830976112102219160803088310324167412809493635059788300420093626611189_<78>

Number: 59993_145
N=49747939615056500626663559867471926285149195969519260672945306537946404080535869032470347651193685603727971808451
  ( 113 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=208622310195879907337278472254444759 (pp36)
 r2=238459345830976112102219160803088310324167412809493635059788300420093626611189 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.31 hours.
Scaled time: 21.94 units (timescale=2.128).
Factorization parameters were as follows:
n: 49747939615056500626663559867471926285149195969519260672945306537946404080535869032470347651193685603727971808451
m: 100000000000000000000000000000
c5: 6
c0: -7
skew: 1.03
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1450001)
Primes: RFBsize:114155, AFBsize:114412, largePrimes:3499162 encountered
Relations: rels:3558668, finalFF:328093
Max relations in full relation-set: 28
Initial matrix: 228633 x 328093 with sparse part having weight 33496163.
Pruned matrix : 202020 x 203227 with weight 17855809.
Total sieving time: 10.03 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 10.31 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Oct 4, 2007 (9th)

By Robert Backstrom / GGNFS, Msieve

(17·10¹⁶¹-71)/9 = 1(8)₁₆₀1_<162> = 7 · 11 · 523 · 12553 · 892039002817_<12> · C141

C141 = P70 · P71

P70 = 5517382888130356012700422947230695246102802588279510829603153154612691_<70>

P71 = 75918829205014441614543498027493064480460216213141344861042989326442621_<71>

Number: n
N=418873249142637799821007491061910714467071107673848593381389819578321584166718844538758955967710943384855248756160831082732301629584089903111
  ( 141 digits)
SNFS difficulty: 162 digits.
Divisors found:

Thu Oct 04 19:17:06 2007  prp70 factor: 5517382888130356012700422947230695246102802588279510829603153154612691
Thu Oct 04 19:17:06 2007  prp71 factor: 75918829205014441614543498027493064480460216213141344861042989326442621
Thu Oct 04 19:17:06 2007  elapsed time 01:24:27 (Msieve 1.26)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 56.52 hours.
Scaled time: 73.71 units (timescale=1.304).
Factorization parameters were as follows:
name: KA_1_8_160_1
n: 418873249142637799821007491061910714467071107673848593381389819578321584166718844538758955967710943384855248756160831082732301629584089903111
skew: 0.84
deg: 5
c5: 170
c0: -71
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2300000)
Primes: RFBsize:216816, AFBsize:216842, largePrimes:7378545 encountered
Relations: rels:6867652, finalFF:491420
Max relations in full relation-set: 28
Initial matrix: 433725 x 491420 with sparse part having weight 41722542.
Pruned matrix : 394644 x 396876 with weight 30589920.
Total sieving time: 55.53 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.74 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 56.52 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 4, 2007 (8th)

By Sinkiti Sibata / GGNFS

6·10¹³²-7 = 5(9)₁₃₁3_<133> = 17 · 31397 · 60607 · 17658261422573_<14> · C110

C110 = P45 · P65

P45 = 157220545256202605499721340161299887750890477_<45>

P65 = 66808873437291415726408144788722762650560407722248850407211168531_<65>

Number: 59993_132
N=10503727509763587149462644038115572609411003558019047308296016303974338616397089884714139804160694574969979287
  ( 110 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=157220545256202605499721340161299887750890477 (pp45)
 r2=66808873437291415726408144788722762650560407722248850407211168531 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 8.23 hours.
Scaled time: 5.57 units (timescale=0.677).
Factorization parameters were as follows:
name: 59993_132
n: 10503727509763587149462644038115572609411003558019047308296016303974338616397089884714139804160694574969979287
m: 100000000000000000000000000
c5: 600
c0: -7
skew: 0.41
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1300001)
Primes: RFBsize:63951, AFBsize:63523, largePrimes:1546399 encountered
Relations: rels:1543966, finalFF:157068
Max relations in full relation-set: 28
Initial matrix: 127540 x 157068 with sparse part having weight 14736218.
Pruned matrix : 120366 x 121067 with weight 9730311.
Total sieving time: 7.77 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 8.23 hours.
 --------- CPU info (if available) ----------

Oct 4, 2007 (7th)

By Jo Yeong Uk / GMP-ECM

6·10¹⁵⁹-7 = 5(9)₁₅₈3_<160> = 13 · 46099251251888935727327_<23> · C137

C137 = P41 · C96

P41 = 24879066220185916328457524320554279793687_<41>

C96 = [402420364802456082600245272138853200856277707189366407172983739323623291446802112677069257990389_<96>]

Oct 4, 2007 (6th)

By Sinkiti Sibata / GGNFS

6·10¹³⁵-7 = 5(9)₁₃₄3_<136> = 13 · 414413481743_<12> · 36564792200396563_<17> · C107

C107 = P43 · P65

P43 = 1126059761985818701739729351936313997694323_<43>

P65 = 27048891575232108774848633209666793723302095208678124558846257723_<65>

Number: 59993_135
N=30458668409186085102726075004708104994463090774955003534458454777954452719667825900945750528186059032006529
  ( 107 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=1126059761985818701739729351936313997694323 (pp43)
 r2=27048891575232108774848633209666793723302095208678124558846257723 (pp65)
Version: GGNFS-0.77.1-20060513-k8
Total time: 7.79 hours.
Scaled time: 15.48 units (timescale=1.986).
Factorization parameters were as follows:
name: 59993_135
n: 30458668409186085102726075004708104994463090774955003534458454777954452719667825900945750528186059032006529
m: 1000000000000000000000000000
c5: 6
c0: -7
skew: 1.03
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1375001)
Primes: RFBsize:78498, AFBsize:63888, largePrimes:1589402 encountered
Relations: rels:1605693, finalFF:183280
Max relations in full relation-set: 28
Initial matrix: 142452 x 183280 with sparse part having weight 16657071.
Pruned matrix : 130634 x 131410 with weight 10249543.
Total sieving time: 7.56 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 7.79 hours.
 --------- CPU info (if available) ----------

Oct 4, 2007 (5th)

By Robert Backstrom / GGNFS, Msieve

(73·10¹⁵⁸-1)/9 = 8(1)₁₅₈_<159> = 26530558669965200379377507_<26> · C134

C134 = P54 · P81

P54 = 212107814191998704725420221052699981457889085100997601_<54>

P81 = 144137600146936537044461384043301075248536512091523845543692062426638973343118573_<81>

Number: n
N=30572711310047020199673079420220032560072723217483618025140594148989783940701088253778438397676150664410526395099842238233630731543373
  ( 134 digits)
SNFS difficulty: 159 digits.
Divisors found:

Thu Oct 04 16:13:30 2007  prp54 factor: 212107814191998704725420221052699981457889085100997601
Thu Oct 04 16:13:30 2007  prp81 factor: 144137600146936537044461384043301075248536512091523845543692062426638973343118573
Thu Oct 04 16:13:30 2007  elapsed time 01:50:08 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 50.48 hours.
Scaled time: 60.38 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_8_1_158
n: 30572711310047020199673079420220032560072723217483618025140594148989783940701088253778438397676150664410526395099842238233630731543373
type: snfs
skew: 0.11
deg: 5
c5: 73000
c0: -1
m: 10000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100000)
Primes: RFBsize:230209, AFBsize:230497, largePrimes:7060727 encountered
Relations: rels:6539168, finalFF:541829
Max relations in full relation-set: 28
Initial matrix: 460773 x 541829 with sparse part having weight 34927383.
Pruned matrix : 393656 x 396023 with weight 22051476.
Total sieving time: 50.21 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,159,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 50.48 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Oct 4, 2007 (4th)

By Jo Yeong Uk / PRIMO

(38·10²⁰⁴³+61)/9 is prime.

Oct 4, 2007 (3rd)

By Jo Yeong Uk / GGNFS, GMP-ECM

6·10¹³¹-7 = 5(9)₁₃₀3_<132> = 53 · 169607 · C125

C125 = P59 · P67

P59 = 12872498163753083570298872692434111691304047437203023579603_<59>

P67 = 5185238891853061753866196726218370889062130742679403097113868915761_<67>

Number: 59993_131
N=66746978113999611310097449475596804199185887107943546740850741408746145779182529734944412560401843507037523259931310684822883
  ( 125 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=12872498163753083570298872692434111691304047437203023579603 (pp59)
 r2=5185238891853061753866196726218370889062130742679403097113868915761 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.84 hours.
Scaled time: 6.06 units (timescale=2.135).
Factorization parameters were as follows:
n: 66746978113999611310097449475596804199185887107943546740850741408746145779182529734944412560401843507037523259931310684822883
m: 100000000000000000000000000
c5: 60
c0: -7
skew: 0.65
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 1100001)
Primes: RFBsize:78498, AFBsize:78436, largePrimes:1617139 encountered
Relations: rels:1662134, finalFF:216620
Max relations in full relation-set: 28
Initial matrix: 157001 x 216620 with sparse part having weight 13625699.
Pruned matrix : 135783 x 136632 with weight 6867620.
Total sieving time: 2.75 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 2.84 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

(86·10¹⁵⁸+31)/9 = 9(5)₁₅₇9_<159> = 7² · 1657 · 48530561 · 369122094120620012071_<21> · C126

C126 = P49 · P78

P49 = 3016236812826278990601156748919149544847529142617_<49>

P78 = 217814388128186210847141219564082430746842862444289701637257172552121621783169_<78>

Number: 95559_158
N=656979775835466476708907333677417137270421517155228763448205475015038680910810608163311078289165054665585517079132773251213273
  ( 126 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=3016236812826278990601156748919149544847529142617 (pp49)
 r2=217814388128186210847141219564082430746842862444289701637257172552121621783169 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 36.34 hours.
Scaled time: 76.82 units (timescale=2.114).
Factorization parameters were as follows:
n: 656979775835466476708907333677417137270421517155228763448205475015038680910810608163311078289165054665585517079132773251213273
m: 100000000000000000000000000000000
c5: 43
c0: 1550
skew: 2.05
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4100001)
Primes: RFBsize:283146, AFBsize:282493, largePrimes:5699146 encountered
Relations: rels:5718310, finalFF:642706
Max relations in full relation-set: 28
Initial matrix: 565705 x 642706 with sparse part having weight 43053754.
Pruned matrix : 513370 x 516262 with weight 31561464.
Total sieving time: 34.80 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.38 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 36.34 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

6·10¹⁴¹-7 = 5(9)₁₄₀3_<142> = 13 · 1447583 · 84331879 · C127

C127 = P37 · P90

P37 = 6476031936152650611823116269070611627_<37>

P90 = 583799427952449996104077409330623614593075799711097271574870756751412606331718775669681999_<90>

Oct 4, 2007 (2nd)

By Sinkiti Sibata / Msieve, GGNFS

6·10¹²⁷-7 = 5(9)₁₂₆3_<128> = 343127 · 582525896334758811474813322548179_<33> · C90

C90 = P42 · P48

P42 = 538379064288744086953750328027856177081161_<42>

P48 = 557561730154771569560097260837268094018249256461_<48>

Wed Oct 03 15:19:24 2007  Msieve v. 1.26
Wed Oct 03 15:19:24 2007  random seeds: ee28c423 6aa74c56
Wed Oct 03 15:19:24 2007  factoring 300179562563939145447468893460840371948057004209201877467016267991673377504711137500631221 (90 digits)
Wed Oct 03 15:19:25 2007  commencing quadratic sieve (90-digit input)
Wed Oct 03 15:19:26 2007  using multiplier of 5
Wed Oct 03 15:19:26 2007  using 64kb Pentium 2 sieve core
Wed Oct 03 15:19:26 2007  sieve interval: 18 blocks of size 65536
Wed Oct 03 15:19:26 2007  processing polynomials in batches of 6
Wed Oct 03 15:19:26 2007  using a sieve bound of 1579619 (60000 primes)
Wed Oct 03 15:19:26 2007  using large prime bound of 126369520 (26 bits)
Wed Oct 03 15:19:26 2007  using double large prime bound of 382786039401520 (42-49 bits)
Wed Oct 03 15:19:26 2007  using trial factoring cutoff of 49 bits
Wed Oct 03 15:19:26 2007  polynomial 'A' values have 12 factors
Thu Oct 04 01:00:41 2007  60563 relations (16228 full + 44335 combined from 633835 partial), need 60096
Thu Oct 04 01:00:52 2007  begin with 650063 relations
Thu Oct 04 01:01:24 2007  reduce to 146669 relations in 10 passes
Thu Oct 04 01:01:24 2007  attempting to read 146669 relations
Thu Oct 04 01:01:38 2007  recovered 146669 relations
Thu Oct 04 01:01:38 2007  recovered 124245 polynomials
Thu Oct 04 01:02:13 2007  attempting to build 60563 cycles
Thu Oct 04 01:02:14 2007  found 60563 cycles in 6 passes
Thu Oct 04 01:02:17 2007  distribution of cycle lengths:
Thu Oct 04 01:02:17 2007     length 1 : 16228
Thu Oct 04 01:02:17 2007     length 2 : 11907
Thu Oct 04 01:02:17 2007     length 3 : 10599
Thu Oct 04 01:02:17 2007     length 4 : 8065
Thu Oct 04 01:02:17 2007     length 5 : 5670
Thu Oct 04 01:02:17 2007     length 6 : 3510
Thu Oct 04 01:02:18 2007     length 7 : 2163
Thu Oct 04 01:02:18 2007     length 9+: 2421
Thu Oct 04 01:02:18 2007  largest cycle: 19 relations
Thu Oct 04 01:02:20 2007  matrix is 60000 x 60563 with weight 3581602 (avg 59.14/col)
Thu Oct 04 01:02:25 2007  filtering completed in 3 passes
Thu Oct 04 01:02:25 2007  matrix is 55899 x 55963 with weight 3306276 (avg 59.08/col)
Thu Oct 04 01:02:28 2007  saving the first 48 matrix rows for later
Thu Oct 04 01:02:28 2007  matrix is 55851 x 55963 with weight 2583325 (avg 46.16/col)
Thu Oct 04 01:02:28 2007  matrix includes 64 packed rows
Thu Oct 04 01:02:28 2007  using block size 10922 for processor cache size 256 kB
Thu Oct 04 01:02:29 2007  commencing Lanczos iteration
Thu Oct 04 01:06:36 2007  lanczos halted after 885 iterations
Thu Oct 04 01:06:37 2007  recovered 17 nontrivial dependencies
Thu Oct 04 01:07:05 2007  prp42 factor: 538379064288744086953750328027856177081161
Thu Oct 04 01:07:05 2007  prp48 factor: 557561730154771569560097260837268094018249256461
Thu Oct 04 01:07:05 2007  elapsed time 09:47:41

6·10¹²³-7 = 5(9)₁₂₂3_<124> = 13² · 1660493 · C116

C116 = P45 · P71

P45 = 419726743015322283340796841866026105998611897_<45>

P71 = 50940224585810878707118381444742680923300871417714179798205170107648957_<71>

Number: 59993_123
N=21380974553871444688254468890053067115588260258501612679604952428097769224215962068469171433819236054429504159841429
  ( 116 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=419726743015322283340796841866026105998611897 (pp45)
 r2=50940224585810878707118381444742680923300871417714179798205170107648957 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 3.06 hours.
Scaled time: 2.07 units (timescale=0.677).
Factorization parameters were as follows:
name: 59993_123
n: 21380974553871444688254468890053067115588260258501612679604952428097769224215962068469171433819236054429504159841429
m: 2000000000000000000000000
c5: 375
c0: -14
skew: 0.52
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:64283, largePrimes:2107214 encountered
Relations: rels:2116210, finalFF:152007
Max relations in full relation-set: 28
Initial matrix: 113447 x 152007 with sparse part having weight 13697410.
Pruned matrix : 103414 x 104045 with weight 7180122.
Total sieving time: 2.74 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.06 hours.
 --------- CPU info (if available) ----------

6·10¹²⁸-7 = 5(9)₁₂₇3_<129> = 47 · 157 · 8893 · C121

C121 = P35 · P42 · P46

P35 = 45062760365254252417196977668457049_<35>

P42 = 107331866482129355939909099089742932497167_<42>

P46 = 1890422922086710862023492300837255153472513593_<46>

Number: 59993_128
N=9143352172651724671661080561054985575066639417445336126160095189610799042575211729177505031243824903769647139905342227519
  ( 121 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=45062760365254252417196977668457049 (pp35)
 r2=107331866482129355939909099089742932497167 (pp42)
 r3=1890422922086710862023492300837255153472513593 (pp46)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 5.27 hours.
Scaled time: 3.57 units (timescale=0.677).
Factorization parameters were as follows:
name: 59993_128
n: 9143352172651724671661080561054985575066639417445336126160095189610799042575211729177505031243824903769647139905342227519
m: 20000000000000000000000000
c5: 375
c0: -14
skew: 0.52
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64283, largePrimes:1484571 encountered
Relations: rels:1488026, finalFF:176006
Max relations in full relation-set: 28
Initial matrix: 128300 x 176006 with sparse part having weight 12189392.
Pruned matrix : 113811 x 114516 with weight 6184426.
Total sieving time: 4.96 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.27 hours.
 --------- CPU info (if available) ----------

(37·10¹⁶¹-1)/9 = 4(1)₁₆₁_<162> = 3 · 41 · 1307 · 2075820356295079_<16> · 1262790142328673659357_<22> · C120

C120 = P38 · P83

P38 = 37343365815058483964552266720070550859_<38>

P83 = 26124266598228484286956693574306899716358742145356317706463821362063741663610307863_<83>

Number: 41111_161
N=975568044227759770362488001375467674400042183142302355527744077810832923409238855463500596189094164000811015620989104317
  ( 120 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=37343365815058483964552266720070550859 (pp38)
 r2=26124266598228484286956693574306899716358742145356317706463821362063741663610307863 (pp83)
Version: GGNFS-0.77.1-20060513-k8
Total time: 73.17 hours.
Scaled time: 146.20 units (timescale=1.998).
Factorization parameters were as follows:
name: 41111_161
n: 975568044227759770362488001375467674400042183142302355527744077810832923409238855463500596189094164000811015620989104317
m: 100000000000000000000000000000000
c5: 370
c0: -1
skew: 0.31
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4550001)
Primes: RFBsize:315948, AFBsize:315496, largePrimes:5801398 encountered
Relations: rels:5906549, finalFF:737188
Max relations in full relation-set: 28
Initial matrix: 631511 x 737188 with sparse part having weight 47432370.
Pruned matrix : 551065 x 554286 with weight 33711664.
Total sieving time: 69.23 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.52 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 73.17 hours.
 --------- CPU info (if available) ----------

Oct 4, 2007

By Robert Backstrom / Msieve, GGNFS

6·10¹⁵⁵-7 = 5(9)₁₅₄3_<156> = 9151759 · 44509450084691841113_<20> · 1276610766484719268151_<22> · 1340426558177838497399939_<25> · C84

C84 = P36 · P49

P36 = 217264834889735630458321389261532721_<36>

P49 = 3961899731258636703690742682913482426977474823891_<49>

Wed Oct 03 15:36:33 2007  Msieve v. 1.26
Wed Oct 03 15:36:33 2007  random seeds: 965c87cc d2ef83b1
Wed Oct 03 15:36:33 2007  factoring 860781490961595669697733605784670171336258336753794416470408536041356301000209037411 (84 digits)
Wed Oct 03 15:36:34 2007  commencing quadratic sieve (84-digit input)
Wed Oct 03 15:36:34 2007  using multiplier of 1
Wed Oct 03 15:36:34 2007  using 64kb Opteron sieve core
Wed Oct 03 15:36:34 2007  sieve interval: 6 blocks of size 65536
Wed Oct 03 15:36:34 2007  processing polynomials in batches of 17
Wed Oct 03 15:36:34 2007  using a sieve bound of 1409117 (53799 primes)
Wed Oct 03 15:36:34 2007  using large prime bound of 119774945 (26 bits)
Wed Oct 03 15:36:34 2007  using trial factoring cutoff of 27 bits
Wed Oct 03 15:36:34 2007  polynomial 'A' values have 11 factors
Wed Oct 03 16:07:49 2007  54021 relations (27210 full + 26811 combined from 284568 partial), need 53895
Wed Oct 03 16:07:50 2007  begin with 311778 relations
Wed Oct 03 16:07:50 2007  reduce to 77387 relations in 2 passes
Wed Oct 03 16:07:50 2007  attempting to read 77387 relations
Wed Oct 03 16:07:51 2007  recovered 77387 relations
Wed Oct 03 16:07:51 2007  recovered 71517 polynomials
Wed Oct 03 16:07:51 2007  attempting to build 54021 cycles
Wed Oct 03 16:07:51 2007  found 54021 cycles in 1 passes
Wed Oct 03 16:07:51 2007  distribution of cycle lengths:
Wed Oct 03 16:07:51 2007     length 1 : 27210
Wed Oct 03 16:07:51 2007     length 2 : 26811
Wed Oct 03 16:07:51 2007  largest cycle: 2 relations
Wed Oct 03 16:07:51 2007  matrix is 53799 x 54021 with weight 1755888 (avg 32.50/col)
Wed Oct 03 16:07:51 2007  filtering completed in 4 passes
Wed Oct 03 16:07:51 2007  matrix is 46702 x 46766 with weight 1491481 (avg 31.89/col)
Wed Oct 03 16:07:52 2007  saving the first 48 matrix rows for later
Wed Oct 03 16:07:52 2007  matrix is 46654 x 46766 with weight 1088600 (avg 23.28/col)
Wed Oct 03 16:07:52 2007  matrix includes 64 packed rows
Wed Oct 03 16:07:52 2007  commencing Lanczos iteration
Wed Oct 03 16:08:46 2007  lanczos halted after 739 iterations
Wed Oct 03 16:08:47 2007  recovered 6 nontrivial dependencies
Wed Oct 03 16:08:47 2007  prp36 factor: 217264834889735630458321389261532721
Wed Oct 03 16:08:47 2007  prp49 factor: 3961899731258636703690742682913482426977474823891
Wed Oct 03 16:08:47 2007  elapsed time 00:32:14

(31·10¹⁵⁸-13)/9 = 3(4)₁₅₇3_<159> = 7 · 127 · 78148787 · 4740691519332947_<16> · C133

C133 = P41 · P92

P41 = 58339351804238222158586791687727596860143_<41>

P92 = 17926350607259622695271137524190494788700231091726771361636249626207975716925845807554474581_<92>

Number: n
N=1045811674643038618720970610503378607430945162952929917680418191298320275906164719144573731068294405811697968071724804081565705525083
  ( 133 digits)
SNFS difficulty: 159 digits.
Divisors found:

Thu Oct 04 02:14:25 2007  prp41 factor: 58339351804238222158586791687727596860143
Thu Oct 04 02:14:25 2007  prp92 factor: 17926350607259622695271137524190494788700231091726771361636249626207975716925845807554474581
Thu Oct 04 02:14:25 2007  elapsed time 01:06:27 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 42.50 hours.
Scaled time: 61.62 units (timescale=1.450).
Factorization parameters were as follows:
name: KA_3_4_157_3
n: 1045811674643038618720970610503378607430945162952929917680418191298320275906164719144573731068294405811697968071724804081565705525083
skew: 0.21
deg: 5
c5: 31000
c0: -13
m: 10000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1800000)
Primes: RFBsize:183072, AFBsize:182522, largePrimes:7262660 encountered
Relations: rels:6751741, finalFF:444988
Max relations in full relation-set: 28
Initial matrix: 365661 x 444988 with sparse part having weight 40908464.
Pruned matrix : 320686 x 322578 with weight 26986987.
Total sieving time: 42.25 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 42.50 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(82·10¹⁶⁰-1)/9 = 9(1)₁₆₀_<161> = 1183282325293_<13> · 1398206145473_<13> · C137

C137 = P59 · P79

P59 = 22056688036771319510990392077888123590637483193298813665679_<59>

P79 = 2496729301249539633152615904948407043950273202114296465618776682890249002888781_<79>

Number: n
N=55069579309927136700780310410936392743026521929117229883721627958613372143091384300827504395420854995614166408956523800756004310953847299
  ( 137 digits)
SNFS difficulty: 161 digits.
Divisors found:

Thu Oct 04 02:36:45 2007  prp59 factor: 22056688036771319510990392077888123590637483193298813665679
Thu Oct 04 02:36:45 2007  prp79 factor: 2496729301249539633152615904948407043950273202114296465618776682890249002888781
Thu Oct 04 02:36:45 2007  elapsed time 01:27:51 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 36.40 hours.
Scaled time: 48.16 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_9_1_160
n: 55069579309927136700780310410936392743026521929117229883721627958613372143091384300827504395420854995614166408956523800756004310953847299
skew: 0.41
deg: 5
c5: 82
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:250150, AFBsize:250142, largePrimes:7161867 encountered
Relations: rels:6671064, finalFF:562452
Max relations in full relation-set: 28
Initial matrix: 500360 x 562452 with sparse part having weight 39726103.
Pruned matrix : 448099 x 450664 with weight 25765807.
Total sieving time: 36.16 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 36.40 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

6·10¹³³-7 = 5(9)₁₃₂3_<134> = 419 · C132

C132 = P39 · P40 · P53

P39 = 803784771613572434432727851402219930947_<39>

P40 = 8211994164161688590117664996602372379877_<40>

P53 = 21694458850171435203820744840123411555745339465862013_<53>

Number: n
N=143198090692124105011933174224343675417661097852028639618138424821002386634844868735083532219570405727923627684964200477326968973747
  ( 132 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=803784771613572434432727851402219930947 (pp39)
 r2=8211994164161688590117664996602372379877 (pp40)
 r3=21694458850171435203820744840123411555745339465862013 (pp53)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.50 hours.
Scaled time: 6.52 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_5_9_132_3
n: 143198090692124105011933174224343675417661097852028639618138424821002386634844868735083532219570405727923627684964200477326968973747
skew: 0.52
deg: 5
c5: 375
c0: -14
m: 200000000000000000000000000
type: snfs
rlim: 1200000
alim: 1200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 550001)
Primes: RFBsize:92938, AFBsize:93099, largePrimes:5807271 encountered
Relations: rels:5166926, finalFF:262402
Max relations in full relation-set: 28
Initial matrix: 186103 x 262402 with sparse part having weight 21646923.
Pruned matrix : 153360 x 154354 with weight 9710538.
Total sieving time: 3.84 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.40 hours.
Total square root time: 0.12 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,48,48,2.5,2.5,75000
total time: 4.50 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

6·10¹⁴⁰-7 = 5(9)₁₃₉3_<141> = 118447393 · C133

C133 = P39 · P95

P39 = 488302592269751645844131141513207371459_<39>

P95 = 10373772369705551105830529941865993946904275182321723727108870993322153016866124697921503890739_<95>

Number: n
N=5065539939743545052105958972013845842938898621432723301896564325396338609157906919910005955133178828173955673300466815677403723018201
  ( 133 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=488302592269751645844131141513207371459 (pp39)
 r2=10373772369705551105830529941865993946904275182321723727108870993322153016866124697921503890739 (pp95)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.15 hours.
Scaled time: 9.46 units (timescale=1.322).
Factorization parameters were as follows:
name: KA_5_9_139_3
n: 5065539939743545052105958972013845842938898621432723301896564325396338609157906919910005955133178828173955673300466815677403723018201
skew: 1.03
deg: 5
c5: 6
c0: -7
m: 10000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 850001)
Primes: RFBsize:114155, AFBsize:114412, largePrimes:6395094 encountered
Relations: rels:5722594, finalFF:311875
Max relations in full relation-set: 48
Initial matrix: 228633 x 311875 with sparse part having weight 33205990.
Pruned matrix : 195644 x 196851 with weight 15042093.
Total sieving time: 5.86 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 1.01 hours.
Total square root time: 0.04 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000
total time: 7.15 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 3, 2007 (5th)

By suberi / PRIMO

(13·10²⁵⁶³+41)/9 is prime.

(13·10²⁶⁴¹+41)/9 is prime.

Oct 3, 2007 (4th)

By Robert Backstrom / GMP-ECM, Msieve

6·10¹²⁵-7 = 5(9)₁₂₄3_<126> = 23 · 3623 · 10966621 · C114

C114 = P38 · P77

P38 = 50636596327829583320839536142290785563_<38>

P77 = 12966349985343467300064590701602747532440337222241547532187032604088384653879_<77>

6·10¹⁵⁷-7 = 5(9)₁₅₆3_<158> = 53 · 97 · 739 · 1091 · 519487 · 709369890512947561_<18> · 1398747574182377711176049107_<28> · C98

C98 = P35 · P64

P35 = 22320341571287862440791180961911537_<35>

P64 = 1258191770139023959637271001787399781177095229292345787867966729_<64>

Wed Oct 03 16:19:38 2007  Msieve v. 1.26
Wed Oct 03 16:19:38 2007  random seeds: b8709f30 80cbbce4
Wed Oct 03 16:19:38 2007  factoring 28083270071686319089592401973395533416884243987372294079591744321397845903861895820202049357252473 (98 digits)
Wed Oct 03 16:19:38 2007  commencing quadratic sieve (98-digit input)
Wed Oct 03 16:19:38 2007  using multiplier of 1
Wed Oct 03 16:19:38 2007  using 64kb Opteron sieve core
Wed Oct 03 16:19:38 2007  sieve interval: 18 blocks of size 65536
Wed Oct 03 16:19:38 2007  processing polynomials in batches of 6
Wed Oct 03 16:19:38 2007  using a sieve bound of 2473301 (90543 primes)
Wed Oct 03 16:19:38 2007  using large prime bound of 370995150 (28 bits)
Wed Oct 03 16:19:38 2007  using double large prime bound of 2659884601469100 (43-52 bits)
Wed Oct 03 16:19:38 2007  using trial factoring cutoff of 52 bits
Wed Oct 03 16:19:38 2007  polynomial 'A' values have 13 factors
Wed Oct 03 23:18:45 2007  90718 relations (21893 full + 68825 combined from 1364772 partial), need 90639
Wed Oct 03 23:18:47 2007  begin with 1386665 relations
Wed Oct 03 23:18:48 2007  reduce to 237587 relations in 12 passes
Wed Oct 03 23:18:48 2007  attempting to read 237587 relations
Wed Oct 03 23:18:52 2007  recovered 237587 relations
Wed Oct 03 23:18:52 2007  recovered 225257 polynomials
Wed Oct 03 23:18:52 2007  attempting to build 90718 cycles
Wed Oct 03 23:18:53 2007  found 90718 cycles in 6 passes
Wed Oct 03 23:18:53 2007  distribution of cycle lengths:
Wed Oct 03 23:18:53 2007     length 1 : 21893
Wed Oct 03 23:18:53 2007     length 2 : 15660
Wed Oct 03 23:18:53 2007     length 3 : 15243
Wed Oct 03 23:18:53 2007     length 4 : 12310
Wed Oct 03 23:18:53 2007     length 5 : 9641
Wed Oct 03 23:18:53 2007     length 6 : 6118
Wed Oct 03 23:18:53 2007     length 7 : 4176
Wed Oct 03 23:18:53 2007     length 9+: 5677
Wed Oct 03 23:18:53 2007  largest cycle: 19 relations
Wed Oct 03 23:18:53 2007  matrix is 90543 x 90718 with weight 6047781 (avg 66.67/col)
Wed Oct 03 23:18:54 2007  filtering completed in 3 passes
Wed Oct 03 23:18:54 2007  matrix is 86539 x 86603 with weight 5807038 (avg 67.05/col)
Wed Oct 03 23:18:55 2007  saving the first 48 matrix rows for later
Wed Oct 03 23:18:55 2007  matrix is 86491 x 86603 with weight 4591383 (avg 53.02/col)
Wed Oct 03 23:18:55 2007  matrix includes 64 packed rows
Wed Oct 03 23:18:55 2007  using block size 21845 for processor cache size 512 kB
Wed Oct 03 23:18:55 2007  commencing Lanczos iteration
Wed Oct 03 23:20:21 2007  lanczos halted after 1370 iterations
Wed Oct 03 23:20:21 2007  recovered 17 nontrivial dependencies
Wed Oct 03 23:20:22 2007  prp35 factor: 22320341571287862440791180961911537
Wed Oct 03 23:20:22 2007  prp64 factor: 1258191770139023959637271001787399781177095229292345787867966729
Wed Oct 03 23:20:22 2007  elapsed time 07:00:44

Oct 3, 2007 (3rd)

By Sinkiti Sibata / Msieve v. 1.26, GGNFS

6·10¹⁵³-7 = 5(9)₁₅₂3_<154> = 13 · 139747 · 41191413729044567_<17> · 28576336929599376517741_<23> · 1025244729230700913218569_<25> · C85

C85 = P42 · P43

P42 = 356746994819799697074718391780142365509993_<42>

P43 = 7671217220429161293573234558957602035904237_<43>

Wed Oct 03 14:47:30 2007  Msieve v. 1.26
Wed Oct 03 14:47:30 2007  random seeds: 460178a0 145787d5
Wed Oct 03 14:47:30 2007  factoring 2736683689998000234925592599907106848522357423838373040075488018168277701797414540341 (85 digits)
Wed Oct 03 14:47:30 2007  commencing quadratic sieve (85-digit input)
Wed Oct 03 14:47:31 2007  using multiplier of 21
Wed Oct 03 14:47:31 2007  using 64kb Pentium 2 sieve core
Wed Oct 03 14:47:31 2007  sieve interval: 6 blocks of size 65536
Wed Oct 03 14:47:31 2007  processing polynomials in batches of 17
Wed Oct 03 14:47:31 2007  using a sieve bound of 1425547 (54412 primes)
Wed Oct 03 14:47:31 2007  using large prime bound of 116894854 (26 bits)
Wed Oct 03 14:47:31 2007  using double large prime bound of 332683806537686 (41-49 bits)
Wed Oct 03 14:47:31 2007  using trial factoring cutoff of 49 bits
Wed Oct 03 14:47:31 2007  polynomial 'A' values have 11 factors
Wed Oct 03 19:20:05 2007  54584 relations (15772 full + 38812 combined from 574026 partial), need 54508
Wed Oct 03 19:20:07 2007  begin with 589798 relations
Wed Oct 03 19:20:09 2007  reduce to 128585 relations in 11 passes
Wed Oct 03 19:20:09 2007  attempting to read 128585 relations
Wed Oct 03 19:20:14 2007  recovered 128585 relations
Wed Oct 03 19:20:14 2007  recovered 109292 polynomials
Wed Oct 03 19:20:15 2007  attempting to build 54584 cycles
Wed Oct 03 19:20:15 2007  found 54584 cycles in 5 passes
Wed Oct 03 19:20:19 2007  distribution of cycle lengths:
Wed Oct 03 19:20:19 2007     length 1 : 15772
Wed Oct 03 19:20:19 2007     length 2 : 11077
Wed Oct 03 19:20:19 2007     length 3 : 9717
Wed Oct 03 19:20:19 2007     length 4 : 6987
Wed Oct 03 19:20:19 2007     length 5 : 4720
Wed Oct 03 19:20:19 2007     length 6 : 2838
Wed Oct 03 19:20:19 2007     length 7 : 1656
Wed Oct 03 19:20:19 2007     length 9+: 1817
Wed Oct 03 19:20:19 2007  largest cycle: 17 relations
Wed Oct 03 19:20:20 2007  matrix is 54412 x 54584 with weight 2905977 (avg 53.24/col)
Wed Oct 03 19:20:22 2007  filtering completed in 3 passes
Wed Oct 03 19:20:22 2007  matrix is 49748 x 49812 with weight 2673600 (avg 53.67/col)
Wed Oct 03 19:20:24 2007  saving the first 48 matrix rows for later
Wed Oct 03 19:20:24 2007  matrix is 49700 x 49812 with weight 1993341 (avg 40.02/col)
Wed Oct 03 19:20:24 2007  matrix includes 64 packed rows
Wed Oct 03 19:20:24 2007  commencing Lanczos iteration
Wed Oct 03 19:25:55 2007  lanczos halted after 787 iterations
Wed Oct 03 19:25:56 2007  recovered 19 nontrivial dependencies
Wed Oct 03 19:25:59 2007  prp42 factor: 356746994819799697074718391780142365509993
Wed Oct 03 19:25:59 2007  prp43 factor: 7671217220429161293573234558957602035904237
Wed Oct 03 19:25:59 2007  elapsed time 04:38:29

8·10¹⁶⁰-3 = 7(9)₁₅₉7_<161> = 43² · 431 · 48859 · 4647456722639_<13> · 626627965062020591_<18> · C120

C120 = P47 · P74

P47 = 14692417462058974457446490078935236626410262041_<47>

P74 = 48018970537507694295810504240418883922125431142142818767721221650978656473_<74>

Number: 79997_160
N=705514761235373466365712554295053490555390684232165126019501416207453667149193594120119006252562816485365473350050841393
  ( 120 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=14692417462058974457446490078935236626410262041 (pp47)
 r2=48018970537507694295810504240418883922125431142142818767721221650978656473 (pp74)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 60.89 hours.
Scaled time: 41.22 units (timescale=0.677).
Factorization parameters were as follows:
name: 79997_160
n: 705514761235373466365712554295053490555390684232165126019501416207453667149193594120119006252562816485365473350050841393
m: 100000000000000000000000000000000
c5: 8
c0: -3
skew: 0.82
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3500001)
Primes: RFBsize:283146, AFBsize:283367, largePrimes:5694153 encountered
Relations: rels:5794190, finalFF:713570
Max relations in full relation-set: 28
Initial matrix: 566578 x 713570 with sparse part having weight 44691099.
Pruned matrix : 447630 x 450526 with weight 27726964.
Total sieving time: 52.59 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 7.83 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 60.89 hours.
 --------- CPU info (if available) ----------

Oct 3, 2007 (2nd)

By Jo Yeong Uk / GGNFS

6·10¹¹¹-7 = 5(9)₁₁₀3_<112> = 13 · 2423 · C108

C108 = P51 · P57

P51 = 360964079692659801539218828060656161476910423250161_<51>

P57 = 527704135252280213728502010679882140961843051369612566587_<57>

Number: 59993_111
N=190482237531350201593701387345630020000634940791771167338645671291152100066668783135972570557795485570970507
  ( 108 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=360964079692659801539218828060656161476910423250161 (pp51)
 r2=527704135252280213728502010679882140961843051369612566587 (pp57)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.71 hours.
Scaled time: 1.53 units (timescale=2.145).
Factorization parameters were as follows:
n: 190482237531350201593701387345630020000634940791771167338645671291152100066668783135972570557795485570970507
m: 10000000000000000000000
c5: 60
c0: -7
skew: 0.65
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 320001)
Primes: RFBsize:30757, AFBsize:30694, largePrimes:1074870 encountered
Relations: rels:1007128, finalFF:101389
Max relations in full relation-set: 28
Initial matrix: 61518 x 101389 with sparse part having weight 4955758.
Pruned matrix : 50735 x 51106 with weight 1760939.
Total sieving time: 0.68 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.71 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

6·10¹²²-7 = 5(9)₁₂₁3_<123> = 29 · C122

C122 = P38 · P84

P38 = 68004493287578401111324018574258290351_<38>

P84 = 304239531422152873078652750157120871113171209374964566110469309352350285844274312067_<84>

Number: 59993_122
N=20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517
  ( 122 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=68004493287578401111324018574258290351 (pp38)
 r2=304239531422152873078652750157120871113171209374964566110469309352350285844274312067 (pp84)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.52 hours.
Scaled time: 3.26 units (timescale=2.144).
Factorization parameters were as follows:
n: 20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517
m: 2000000000000000000000000
c5: 75
c0: -28
skew: 0.82
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [400000, 720001)
Primes: RFBsize:63951, AFBsize:63523, largePrimes:1389910 encountered
Relations: rels:1372098, finalFF:158574
Max relations in full relation-set: 28
Initial matrix: 127540 x 158574 with sparse part having weight 7799698.
Pruned matrix : 114540 x 115241 with weight 4337757.
Total sieving time: 1.46 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,800000,800000,25,25,45,45,2.2,2.2,40000
total time: 1.52 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

6·10¹³⁷-7 = 5(9)₁₃₆3_<138> = C138

C138 = P44 · P95

P44 = 11930304707794017951010060929038611787637529_<44>

P95 = 50292093512751817677191069598755399434481984540235534607565516222232375080068547729293970178017_<95>

Number: 59993_137
N=599999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 138 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=11930304707794017951010060929038611787637529 (pp44)
 r2=50292093512751817677191069598755399434481984540235534607565516222232375080068547729293970178017 (pp95)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.81 hours.
Scaled time: 10.24 units (timescale=2.129).
Factorization parameters were as follows:
n: 599999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
m: 2000000000000000000000000000
c5: 75
c0: -28
skew: 0.82
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1600001)
Primes: RFBsize:107126, AFBsize:106878, largePrimes:2399412 encountered
Relations: rels:2552130, finalFF:267534
Max relations in full relation-set: 28
Initial matrix: 214070 x 267534 with sparse part having weight 24798377.
Pruned matrix : 197717 x 198851 with weight 15730218.
Total sieving time: 4.58 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 4.81 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

6·10¹³⁰-7 = 5(9)₁₂₉3_<131> = 3581 · 11927683 · 77492399487775327777_<20> · C101

C101 = P41 · P60

P41 = 41741913374238084153759348799228096820219_<41>

P60 = 434269551129510598310111242531747787622152307167204480286557_<60>

Number: 59993_130
N=18127241984317287948259696060358425132269108005734409737154495900535745003233991139307777121631495983
  ( 101 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=41741913374238084153759348799228096820219 (pp41)
 r2=434269551129510598310111242531747787622152307167204480286557 (pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.61 hours.
Scaled time: 5.60 units (timescale=2.145).
Factorization parameters were as follows:
n: 18127241984317287948259696060358425132269108005734409737154495900535745003233991139307777121631495983
m: 100000000000000000000000000
c5: 6
c0: -7
skew: 1.03
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 1050001)
Primes: RFBsize:78498, AFBsize:78516, largePrimes:1562106 encountered
Relations: rels:1575211, finalFF:190100
Max relations in full relation-set: 28
Initial matrix: 157080 x 190100 with sparse part having weight 11252053.
Pruned matrix : 145006 x 145855 with weight 6877487.
Total sieving time: 2.51 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 2.61 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Oct 3, 2007

The factor table of 599...993 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Oct 2, 2007 (3rd)

By Jo Yeong Uk / GGNFS

4·10¹⁵⁸+7 = 4(0)₁₅₇7_<159> = 11 · 37 · 12007 · 64184521 · 801992267819_<12> · C133

C133 = P47 · P86

P47 = 40168232933255472863199410867005086259141899511_<47>

P86 = 39586568659768781756154959633375249919813838935426658359620291935490219828230564916987_<86>

Number: 40007_158
N=1590122510953903345542624420568097263521630484531474875782839648114082015795534996005269615326322770371113782601521530538607210893357
  ( 133 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=40168232933255472863199410867005086259141899511 (pp47)
 r2=39586568659768781756154959633375249919813838935426658359620291935490219828230564916987 (pp86)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.50 hours.
Scaled time: 52.33 units (timescale=2.136).
Factorization parameters were as follows:
n: 1590122510953903345542624420568097263521630484531474875782839648114082015795534996005269615326322770371113782601521530538607210893357
m: 100000000000000000000000000000000
c5: 1
c0: 175
skew: 2.81
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3400001)
Primes: RFBsize:283146, AFBsize:283052, largePrimes:5731305 encountered
Relations: rels:5871089, finalFF:749665
Max relations in full relation-set: 28
Initial matrix: 566262 x 749665 with sparse part having weight 45967150.
Pruned matrix : 415205 x 418100 with weight 27576167.
Total sieving time: 23.50 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.87 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 24.50 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Oct 2, 2007 (2nd)

By Sinkiti Sibata / GGNFS

(5·10¹⁶¹+7)/3 = 1(6)₁₆₀9_<162> = 570049 · 111524293 · 148946655411315836615893811933_<30> · C119

C119 = P59 · P60

P59 = 19431998449239836919883891499392364284154878753810288198627_<59>

P60 = 905771934729220258028194158863173230204066471520265077490687_<60>

Number: 16669_161
N=17600958831023174839925978092753242124486597026417452012549969280102392991960434543098921399672637559438776334598686749
  ( 119 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=19431998449239836919883891499392364284154878753810288198627 (pp59)
 r2=905771934729220258028194158863173230204066471520265077490687 (pp60)
Version: GGNFS-0.77.1-20060513-k8
Total time: 73.18 hours.
Scaled time: 146.44 units (timescale=2.001).
Factorization parameters were as follows:
name: 16669_161
n: 17600958831023174839925978092753242124486597026417452012549969280102392991960434543098921399672637559438776334598686749
m: 100000000000000000000000000000000
c5: 50
c0: 7
skew: 0.67
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4550001)
Primes: RFBsize:315948, AFBsize:316881, largePrimes:5795306 encountered
Relations: rels:5901400, finalFF:737692
Max relations in full relation-set: 28
Initial matrix: 632894 x 737692 with sparse part having weight 45414630.
Pruned matrix : 553191 x 556419 with weight 32190862.
Total sieving time: 69.32 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.47 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 73.18 hours.
 --------- CPU info (if available) ----------

Oct 2, 2007

By Robert Backstrom / GGNFS, Msieve

(4·10¹⁶¹-7)/3 = 1(3)₁₆₀1_<162> = 11 · 11124606089_<11> · 100299923063_<12> · C140

C140 = P45 · P95

P45 = 866216913035861859660556067350054626872174933_<45>

P95 = 12541057250108172132778787912475915358164724857304431753382275697071209996577378790384734808091_<95>

Number: n
N=10863275897394715416026646238743388383563411275697039333548489540819916417179198180218113482105248693668875830361857053271903904435535782903
  ( 140 digits)
SNFS difficulty: 161 digits.
Divisors found:

prp45 factor: 866216913035861859660556067350054626872174933
prp95 factor: 12541057250108172132778787912475915358164724857304431753382275697071209996577378790384734808091
elapsed time 02:26:08 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 40.30 hours.
Scaled time: 48.24 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_1_3_160_1
n: 10863275897394715416026646238743388383563411275697039333548489540819916417179198180218113482105248693668875830361857053271903904435535782903
type: snfs
skew: 0.71
deg: 5
c5: 40
c0: -7
m: 100000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:250150, AFBsize:249831, largePrimes:6771115 encountered
Relations: rels:6304352, finalFF:590349
Max relations in full relation-set: 28
Initial matrix: 500047 x 590349 with sparse part having weight 31375036.
Pruned matrix : 415114 x 417678 with weight 17906321.
Total sieving time: 40.07 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.3,2.3,100000
total time: 40.30 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

5·10¹⁶¹-1 = 4(9)₁₆₁_<162> = 23 · 5039 · 5503 · 121219311137_<12> · C142

C142 = P69 · P74

P69 = 205172085665013628136788854347422145538579372307983152097920947502671_<69>

P74 = 31521596990625887572504276079879084677165618298704568194646451128941172807_<74>

Number: n
N=6467351798058730387628097619584464793561004208531537922182496075642274563849187638841619505437822847268801141316782851382812647988076505067497
  ( 142 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Oct 02 05:21:23 2007  prp69 factor: 205172085665013628136788854347422145538579372307983152097920947502671
Tue Oct 02 05:21:23 2007  prp74 factor: 31521596990625887572504276079879084677165618298704568194646451128941172807
Tue Oct 02 05:21:23 2007  elapsed time 01:18:32 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 29.84 hours.
Scaled time: 43.39 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_4_9_161
n: 6467351798058730387628097619584464793561004208531537922182496075642274563849187638841619505437822847268801141316782851382812647988076505067497
skew: 0.46
deg: 5
c5: 50
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1600000)
Primes: RFBsize:203362, AFBsize:203587, largePrimes:7032000 encountered
Relations: rels:6494307, finalFF:456833
Max relations in full relation-set: 28
Initial matrix: 407014 x 456833 with sparse part having weight 35481673.
Pruned matrix : 369264 x 371363 with weight 25332214.
Total sieving time: 29.63 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 29.84 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(28·10¹⁶⁰-1)/9 = 3(1)₁₆₀_<161> = 53 · 113 · 367 · 10608547 · 331545143 · C139

C139 = P51 · P88

P51 = 633091035242735539801967600647466189684568802167457_<51>

P88 = 6356680828325396531036158080960100862662205508268214943170736874990151494680541613194001_<88>

Number: n
N=4024357646312174958831474608222302299118450594684435034315875112537932079099180653597254994891579763036098222505425488832273115077429825457
  ( 139 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Oct 02 06:04:18 2007  prp51 factor: 633091035242735539801967600647466189684568802167457
Tue Oct 02 06:04:18 2007  prp88 factor: 6356680828325396531036158080960100862662205508268214943170736874990151494680541613194001
Tue Oct 02 06:04:18 2007  elapsed time 01:22:53 (Msieve 1.26)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 34.41 hours.
Scaled time: 44.59 units (timescale=1.296).
Factorization parameters were as follows:
name: KA_3_1_160
n: 4024357646312174958831474608222302299118450594684435034315875112537932079099180653597254994891579763036098222505425488832273115077429825457
skew: 0.51
deg: 5
c5: 28
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:216816, AFBsize:216531, largePrimes:7070916 encountered
Relations: rels:6546532, finalFF:488128
Max relations in full relation-set: 28
Initial matrix: 433413 x 488128 with sparse part having weight 35567073.
Pruned matrix : 391277 x 393508 with weight 24641110.
Total sieving time: 33.14 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 1.06 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 34.41 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁶¹-3 = 6(9)₁₆₀7_<162> = 11759927 · 890858477521139_<15> · C140

C140 = P52 · P89

P52 = 5434034586523956104106766412088428719802308238404951_<52>

P89 = 12295955952110120403085408303775786006169912054674465432621806697568821168788407881446399_<89>

Number: n
N=66816649918141495127926394200224912688873813650781970983701894207994243406438544537584681883365367975168764122211116754043488833134562721449
  ( 140 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Oct 02 11:41:36 2007  prp52 factor: 5434034586523956104106766412088428719802308238404951
Tue Oct 02 11:41:36 2007  prp89 factor: 12295955952110120403085408303775786006169912054674465432621806697568821168788407881446399
Tue Oct 02 11:41:36 2007  elapsed time 02:02:16 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 53.37 hours.
Scaled time: 70.61 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_6_9_160_7
n: 66816649918141495127926394200224912688873813650781970983701894207994243406438544537584681883365367975168764122211116754043488833134562721449
skew: 0.53
deg: 5
c5: 70
c0: -3
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2500000)
Primes: RFBsize:250150, AFBsize:249361, largePrimes:7482224 encountered
Relations: rels:6975734, finalFF:559949
Max relations in full relation-set: 28
Initial matrix: 499578 x 559949 with sparse part having weight 47483613.
Pruned matrix : 454399 x 456960 with weight 33007219.
Total sieving time: 53.09 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 53.37 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 1, 2007 (3rd)

By Jo Yeong Uk / GGNFS

2·10¹⁵⁸-7 = 1(9)₁₅₇3_<159> = 953 · 25057 · 2414090848213589432916932990633_<31> · C121

C121 = P53 · P69

P53 = 31571248495465350553236417278124057355578453451578557_<53>

P69 = 109891134207565565423460471928953710097707635400211726467910976480493_<69>

Number: 19993_158
N=3469400305515585275088518477571852718127951025814114467282749380810057951257353312433363378995962611612031180850967588601
  ( 121 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=31571248495465350553236417278124057355578453451578557 (pp53)
 r2=109891134207565565423460471928953710097707635400211726467910976480493 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 34.21 hours.
Scaled time: 72.22 units (timescale=2.111).
Factorization parameters were as follows:
n: 3469400305515585275088518477571852718127951025814114467282749380810057951257353312433363378995962611612031180850967588601
m: 100000000000000000000000000000000
c5: 1
c0: -350
skew: 3.23
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4000001)
Primes: RFBsize:283146, AFBsize:283727, largePrimes:5808005 encountered
Relations: rels:5905005, finalFF:708062
Max relations in full relation-set: 28
Initial matrix: 566937 x 708062 with sparse part having weight 48034519.
Pruned matrix : 464821 x 467719 with weight 33043298.
Total sieving time: 32.81 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.26 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 34.21 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Oct 2, 2007 (2nd)

By Jo Yeong Uk / PRIMO

4·10²⁰³⁸+9 is prime!

Oct 1, 2007

By Sinkiti Sibata / GGNFS

(5·10¹⁵⁹+7)/3 = 1(6)₁₅₈9_<160> = 61 · 139 · 22354882834663_<14> · C142

C142 = P50 · P93

P50 = 20633650419206281386733031458970921470010125270621_<50>

P93 = 426143283646225856200448242499018567906598044643963243984154881765936470251951711802769440857_<93>

Number: 16669_159
N=8792891543248889413056523663055605397019366650336981625335329343284007000558823348485757194490519250667301471004607262229383740155945979162197
  ( 142 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=20633650419206281386733031458970921470010125270621 (pp50)
 r2=426143283646225856200448242499018567906598044643963243984154881765936470251951711802769440857 (pp93)
Version: GGNFS-0.77.1-20060513-k8
Total time: 40.03 hours.
Scaled time: 77.81 units (timescale=1.944).
Factorization parameters were as follows:
name: 16669_159
n: 8792891543248889413056523663055605397019366650336981625335329343284007000558823348485757194490519250667301471004607262229383740155945979162197
m: 100000000000000000000000000000000
c5: 1
c0: 14
skew: 1.7
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3300001)
Primes: RFBsize:283146, AFBsize:283092, largePrimes:5781861 encountered
Relations: rels:5963802, finalFF:786585
Max relations in full relation-set: 28
Initial matrix: 566302 x 786585 with sparse part having weight 46911389.
Pruned matrix : 388163 x 391058 with weight 28940900.
Total sieving time: 37.70 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 2.02 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 40.03 hours.
 --------- CPU info (if available) ----------

(5·10¹⁵⁴+7)/3 = 1(6)₁₅₃9_<155> = 17² · 211 · 89227 · 3642209 · 34988803 · C131

C131 = P64 · P67

P64 = 3039500772684756067905656547847651710767202885317667360748022141_<64>

P67 = 7908169219491322981400916567456394408788268380654149703529298881099_<67>

Number: 16669_154
N=24036886453165680508340850848781676496510660976142667106365241496273418489191071703314462061843335352040879870593174633908578412959
  ( 131 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=3039500772684756067905656547847651710767202885317667360748022141 (pp64)
 r2=7908169219491322981400916567456394408788268380654149703529298881099 (pp67)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 35.56 hours.
Scaled time: 24.07 units (timescale=0.677).
Factorization parameters were as follows:
name: 16669_154
n: 24036886453165680508340850848781676496510660976142667106365241496273418489191071703314462061843335352040879870593174633908578412959
m: 10000000000000000000000000000000
c5: 1
c0: 14
skew: 1.7
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2400001)
Primes: RFBsize:216816, AFBsize:216671, largePrimes:5670953 encountered
Relations: rels:5752856, finalFF:662121
Max relations in full relation-set: 28
Initial matrix: 433551 x 662121 with sparse part having weight 48626390.
Pruned matrix : 281115 x 283346 with weight 30459459.
Total sieving time: 31.66 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 3.54 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 35.56 hours.
 --------- CPU info (if available) ----------

September 2007

Sep 30, 2007 (4th)

By Jo Yeong Uk / GGNFS

(5·10¹⁶²+7)/3 = 1(6)₁₆₁9_<163> = 26605422918850732566241_<23> · 63779260936918673666795069_<26> · C114

C114 = P56 · P59

P56 = 12345841030073355518195566173708094971913700674342341749_<56>

P59 = 79557003995848246810709883183266502089230667106521497802989_<59>

Number: 16669_162
N=982198124161653180383430896087817726373941018203689950840839374285322703169061071123818762648082907378560911687761
  ( 114 digits)
Divisors found:
 r1=12345841030073355518195566173708094971913700674342341749 (pp56)
 r2=79557003995848246810709883183266502089230667106521497802989 (pp59)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.98 hours.
Scaled time: 53.55 units (timescale=2.144).
Factorization parameters were as follows:
name: 16669_162
n: 982198124161653180383430896087817726373941018203689950840839374285322703169061071123818762648082907378560911687761
skew: 79581.38
# norm 1.52e+16
c5: 14400
c4: -5104766820
c3: -426663243207224
c2: 28085394149617420745
c1: 790358088000437855793756
c0: -30202005118332397627600032105
# alpha -6.65
Y1: 1156683005687
Y0: -9263415975208444237468
# Murphy_E 5.69e-10
# M 282687440591493322167609652050488048787882302796981977330370789227978501143302103505532468545998949397979264317724
type: gnfs
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1800000, 3075001)
Primes: RFBsize:256726, AFBsize:255796, largePrimes:7643428 encountered
Relations: rels:7673917, finalFF:699431
Max relations in full relation-set: 28
Initial matrix: 512600 x 699431 with sparse part having weight 61343989.
Pruned matrix : 366077 x 368704 with weight 35631843.
Polynomial selection time: 1.18 hours.
Total sieving time: 22.62 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.87 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000
total time: 24.98 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Sep 30, 2007 (3rd)

By Sinkiti Sibata / GGNFS

(5·10¹⁶⁰+7)/3 = 1(6)₁₅₉9_<161> = 79 · 22979881 · 8218427297_<10> · 120437201921_<12> · 576732416278247_<15> · C116

C116 = P55 · P61

P55 = 4977320437750921565229473834967340708864912661751976709_<55>

P61 = 3231130839822657913824785584822600613852060607675347893277881_<61>

Number: 16669_160
N=16082373566096614517840744716684819770544179685787058568186342091536319780818203204639102366383712317368525176873629
  ( 116 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=4977320437750921565229473834967340708864912661751976709 (pp55)
 r2=3231130839822657913824785584822600613852060607675347893277881 (pp61)
Version: GGNFS-0.77.1-20060513-k8
Total time: 48.41 hours.
Scaled time: 96.57 units (timescale=1.995).
Factorization parameters were as follows:
name: 16669_160
n: 16082373566096614517840744716684819770544179685787058568186342091536319780818203204639102366383712317368525176873629
m: 100000000000000000000000000000000
c5: 5
c0: 7
skew: 1.07
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3500001)
Primes: RFBsize:283146, AFBsize:282597, largePrimes:5621726 encountered
Relations: rels:5644743, finalFF:651649
Max relations in full relation-set: 28
Initial matrix: 565808 x 651649 with sparse part having weight 40725051.
Pruned matrix : 498172 x 501065 with weight 27770530.
Total sieving time: 45.45 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 2.62 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 48.41 hours.
 --------- CPU info (if available) ----------

Sep 30, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

(5·10¹⁶⁴+7)/3 = 1(6)₁₆₃9_<165> = 13 · 191 · 111667 · C156

C156 = P59 · P98

P59 = 26302708085062711351718348313317723934590092763062351780943_<59>

P98 = 22853183997916580633609069137995891297392038889869322628145873448439676832765537008398620936667403_<98>

Number: n
N=601100627511426222646761161680965546206801796708529971231335989315691212650463737172222577853390145565689747467684178070804876373058548212170868388304701029
  ( 156 digits)
SNFS difficulty: 165 digits.
Divisors found:

Linear algebra by Msieve 1.26:

Sun Sep 30 03:05:26 2007  commencing square root phase
Sun Sep 30 03:05:26 2007  reading relations for dependency 1
Sun Sep 30 03:05:27 2007  read 217366 cycles
Sun Sep 30 03:05:27 2007  cycles contain 795544 unique relations
Sun Sep 30 03:06:01 2007  read 795544 relations
Sun Sep 30 03:06:08 2007  multiplying 1142918 relations
Sun Sep 30 03:08:47 2007  multiply complete, coefficients have about 24.09 million bits
Sun Sep 30 03:08:48 2007  initial square root is modulo 8296751
Sun Sep 30 03:15:04 2007  prp59 factor: 26302708085062711351718348313317723934590092763062351780943
Sun Sep 30 03:15:04 2007  prp98 factor: 22853183997916580633609069137995891297392038889869322628145873448439676832765537008398620936667403
Sun Sep 30 03:15:04 2007  elapsed time 01:26:28

Version: GGNFS-0.77.1-20051202-athlon
Total time: 40.61 hours.
Scaled time: 53.77 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_1_6_163_9
n: 601100627511426222646761161680965546206801796708529971231335989315691212650463737172222577853390145565689747467684178070804876373058548212170868388304701029
skew: 1.70
deg: 5
c5: 1
c0: 14
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1900000)
Primes: RFBsize:250150, AFBsize:250091, largePrimes:7227599 encountered
Relations: rels:6752702, finalFF:576673
Max relations in full relation-set: 28
Initial matrix: 500305 x 576673 with sparse part having weight 39570403.
Pruned matrix : 436717 x 439282 with weight 24359944.
Total sieving time: 40.39 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 40.61 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(5·10¹⁶³+7)/3 = 1(6)₁₆₂9_<164> = 19 · 932483 · 3338407 · C150

C150 = P36 · P115

P36 = 179096204859467232396164279888334937_<36>

P115 = 1573361650372442894213033131277538811100419125034880034126626043409760465523866973561143332026778461515089011520283_<115>

Number: n
N=281783100453132491764192749729106318410556661674307444387519334626303961635821594561083163050656636337622215383852258673518554659375130169219873027171
  ( 150 digits)
SNFS difficulty: 164 digits.
Divisors found:

Linear algebra using Msieve 1.26:

Sun Sep 30 18:13:20 2007  commencing square root phase
Sun Sep 30 18:13:20 2007  reading relations for dependency 1
Sun Sep 30 18:13:21 2007  read 238377 cycles
Sun Sep 30 18:13:21 2007  cycles contain 836180 unique relations
Sun Sep 30 18:13:57 2007  read 836180 relations
Sun Sep 30 18:14:04 2007  multiplying 1175696 relations
Sun Sep 30 18:16:39 2007  multiply complete, coefficients have about 28.40 million bits
Sun Sep 30 18:16:40 2007  initial square root is modulo 143457841
Sun Sep 30 18:22:25 2007  prp36 factor: 179096204859467232396164279888334937
Sun Sep 30 18:22:25 2007  prp115 factor: 1573361650372442894213033131277538811100419125034880034126626043409760465523866973561143332026778461515089011520283
Sun Sep 30 18:22:25 2007  elapsed time 01:32:22

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 65.07 hours.
Scaled time: 79.39 units (timescale=1.220).
Factorization parameters were as follows:
name: KA_1_6_162_9
n: 281783100453132491764192749729106318410556661674307444387519334626303961635821594561083163050656636337622215383852258673518554659375130169219873027171
skew: 0.45
deg: 5
c5: 8
c0: 35
m: 500000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3100000)
Primes: RFBsize:216816, AFBsize:217636, largePrimes:7586330 encountered
Relations: rels:7073916, finalFF:488697
Max relations in full relation-set: 28
Initial matrix: 434517 x 488697 with sparse part having weight 43843717.
Pruned matrix : 412969 x 415205 with weight 33648580.
Total sieving time: 64.61 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.20 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 65.07 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(55·10¹⁵⁸-1)/9 = 6(1)₁₅₈_<159> = 13 · 23 · 5763827 · 1559789123863_<13> · C138

C138 = P59 · P80

P59 = 15010258650299280272276491101329623983515589707475827317847_<59>

P80 = 15145513101806035552114587951495643112100912817276775268355705388408504954678887_<80>

Number: n
N=227338069049605129053211193199122381737271351068558536526884137163254204545481577681925791011163714893896017433744000903964174094369196289
  ( 138 digits)
SNFS difficulty: 160 digits.
Divisors found:

Linear algebra using Msieve 1.26:

Sun Sep 30 21:00:47 2007  commencing square root phase
Sun Sep 30 21:00:47 2007  reading relations for dependency 1
Sun Sep 30 21:00:47 2007  read 187803 cycles
Sun Sep 30 21:00:48 2007  cycles contain 698085 unique relations
Sun Sep 30 21:01:15 2007  read 698085 relations
Sun Sep 30 21:01:20 2007  multiplying 993110 relations
Sun Sep 30 21:03:51 2007  multiply complete, coefficients have about 26.43 million bits
Sun Sep 30 21:03:52 2007  initial square root is modulo 38909441
Sun Sep 30 21:09:48 2007  prp59 factor: 15010258650299280272276491101329623983515589707475827317847
Sun Sep 30 21:09:48 2007  prp80 factor: 15145513101806035552114587951495643112100912817276775268355705388408504954678887
Sun Sep 30 21:09:48 2007  elapsed time 01:03:31

Version: GGNFS-0.77.1-20051202-athlon
Total time: 29.89 hours.
Scaled time: 43.28 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_6_1_158
n: 227338069049605129053211193199122381737271351068558536526884137163254204545481577681925791011163714893896017433744000903964174094369196289
skew: 0.56
deg: 5
c5: 88
c0: -5
m: 50000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1600000)
Primes: RFBsize:183072, AFBsize:183537, largePrimes:7075458 encountered
Relations: rels:6528000, finalFF:420262
Max relations in full relation-set: 28
Initial matrix: 366675 x 420262 with sparse part having weight 36710081.
Pruned matrix : 330856 x 332753 with weight 26194028.
Total sieving time: 29.67 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 29.89 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Sep 30, 2007

By Bruce Dodson

(10³³⁹-1)/9 is divisible by 777734075184513369134763199249605543798943174359980119_<54>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 29, 2007 (5th)

By Yousuke Koide

10¹⁰⁷⁵+1 is divisible by 17749774754658825560922224895404476651_<38>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 29, 2007 (4th)

By suberi / PRIMO

6·10²⁵⁹³+7 is prime!

(55·10²⁹⁶⁹+71)/9 is prime!

Sep 29, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

(2·10¹⁶⁵-17)/3 = (6)₁₆₄1_<165> = 24310071773347_<14> · C152

C152 = P50 · P102

P50 = 51734164323600805573653584774564809428106146895381_<50>

P102 = 530084446675280350994104791959744914314598013435184675057749458635575389733945696768078005752479641723_<102>

Number: n
N=27423475869683962390491718591322401700236139951798106363550172466967761626634044630890142340664811630560708218722793851241742987522268137155303643581463
  ( 152 digits)
SNFS difficulty: 165 digits.
Divisors found:

Linear algebra using Msieve 1.26:

...
Sat Sep 29 12:41:06 2007  commencing square root phase
Sat Sep 29 12:41:06 2007  reading relations for dependency 1
Sat Sep 29 12:41:06 2007  read 242194 cycles
Sat Sep 29 12:41:07 2007  cycles contain 838445 unique relations
Sat Sep 29 12:41:38 2007  read 838445 relations
Sat Sep 29 12:41:44 2007  multiplying 1189934 relations
Sat Sep 29 12:44:18 2007  multiply complete, coefficients have about 26.63 million bits
Sat Sep 29 12:44:18 2007  initial square root is modulo 44576321
Sat Sep 29 12:50:18 2007  prp50 factor: 51734164323600805573653584774564809428106146895381
Sat Sep 29 12:50:18 2007  prp102 factor: 530084446675280350994104791959744914314598013435184675057749458635575389733945696768078005752479641723
Sat Sep 29 12:50:18 2007  elapsed time 01:33:37

Version: GGNFS-0.77.1-20051202-athlon
Total time: 63.87 hours.
Scaled time: 92.54 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_6_164_1
n: 27423475869683962390491718591322401700236139951798106363550172466967761626634044630890142340664811630560708218722793851241742987522268137155303643581463
skew: 1.53
deg: 5
c5: 2
c0: -17
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3300000)
Primes: RFBsize:216816, AFBsize:216686, largePrimes:7771552 encountered
Relations: rels:7297268, finalFF:503771
Max relations in full relation-set: 28
Initial matrix: 433567 x 503771 with sparse part having weight 49944999.
Pruned matrix : 407928 x 410159 with weight 37183923.
Total sieving time: 63.60 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 63.87 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

5·10¹⁶⁷-7 = 4(9)₁₆₆3_<168> = 13 · C167

C167 = P47 · P121

P47 = 27166347444900583109731812696436491851217550133_<47>

P121 = 1415778788059272495359858060016860902525618476647398886043545011620987173109239480930954828521246215935467936088821001417_<121>

Number: n
N=38461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461
  ( 167 digits)
SNFS difficulty: 167 digits.
Divisors found:

Linear algebra by Msieve 1.26:

Sat Sep 29 23:21:09 2007  commencing square root phase
Sat Sep 29 23:21:09 2007  reading relations for dependency 1
Sat Sep 29 23:21:09 2007  read 257497 cycles
Sat Sep 29 23:21:10 2007  cycles contain 895173 unique relations
Sat Sep 29 23:22:06 2007  read 895173 relations
Sat Sep 29 23:22:16 2007  multiplying 1259610 relations
Sat Sep 29 23:29:41 2007  multiply complete, coefficients have about 37.13 milli on bits
Sat Sep 29 23:29:43 2007  initial square root is modulo 214451
Sat Sep 29 23:41:15 2007  prp47 factor: 27166347444900583109731812696436491851217550133
Sat Sep 29 23:41:15 2007  prp121 factor: 1415778788059272495359858060016860902525618476647398886043545011620987173109239480930954828521246215935467936088821001417
Sat Sep 29 23:41:15 2007  elapsed time 02:44:57

Version: GGNFS-0.77.1-20051202-athlon
Total time: 199.44 hours.
Scaled time: 238.33 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_4_9_166_3
n: 38461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461
type: snfs
skew: 1.00
deg: 5
c5: 500
c0: -7
m: 1000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3300000)
Primes: RFBsize:250150, AFBsize:249951, largePrimes:7696642 encountered
Relations: rels:7217894, finalFF:566646
Max relations in full relation-set: 28
Initial matrix: 500167 x 566646 with sparse part having weight 45760093.
Pruned matrix : 461435 x 463999 with weight 34043459.
Total sieving time: 198.86 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,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.6,2.6,100000
total time: 199.44 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Sep 29, 2007 (2nd)

By Jo Yeong Uk / GGNFS

(5·10¹⁵⁵+7)/3 = 1(6)₁₅₄9_<156> = 59 · 3975371759544157964120556169_<28> · C126

C126 = P50 · P77

P50 = 12183673828219514815541105378476410328653530357743_<50>

P77 = 58323116951920764556691672750208036680903493856562686440783028131664900724273_<77>

Number: 16669_155
N=710589833587302941718597558350764196066850853049176811985093853269458721857536326881047933687224985740262132968074713493595839
  ( 126 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=12183673828219514815541105378476410328653530357743 (pp50)
 r2=58323116951920764556691672750208036680903493856562686440783028131664900724273 (pp77)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 18.11 hours.
Scaled time: 38.82 units (timescale=2.143).
Factorization parameters were as follows:
n: 710589833587302941718597558350764196066850853049176811985093853269458721857536326881047933687224985740262132968074713493595839
m: 10000000000000000000000000000000
c5: 5
c0: 7
skew: 1.07
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:216351, largePrimes:5702060 encountered
Relations: rels:5761249, finalFF:638372
Max relations in full relation-set: 28
Initial matrix: 433232 x 638372 with sparse part having

目次