News and updates, November 2008

Since June 16, 2000

English text only.

News and updates, November 2008	2008-12-04(Thu) 23:21

October November December

News and updates, November 2008

Nov 30, 2008 (10th): By Jo Yeong Uk / GGNFS
(11·10¹³⁹+1)/3 = 3(6)₁₃₈7_<140> = 17 · 37 · 167 · 3550454911_<10> · 577793052509_<12> · 18481830371284369_<17> · C97
C97 = P48 · P50
P48 = 186684117639574787528989733088753211050056946911_<48>
P50 = 49316885889471914935083459467994951356728795737709_<50>

Number: 36667_139 N=9206679327007660850305599792616297445143259412106374422712579360327352603261588284466462493766899 ( 97 digits) Divisors found: r1=186684117639574787528989733088753211050056946911 (pp48) r2=49316885889471914935083459467994951356728795737709 (pp50) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.36 hours. Scaled time: 5.62 units (timescale=2.385). Factorization parameters were as follows: name: 36667_139 n: 9206679327007660850305599792616297445143259412106374422712579360327352603261588284466462493766899 skew: 1735.67 # norm 2.03e+13 c5: 592440 c4: -2146536287 c3: -4150159948542 c2: 6245351775971518 c1: 7030137616889093286 c0: -19054775817785412320 # alpha -5.87 Y1: 13808501069 Y0: -1730988725850774993 # Murphy_E 5.15e-09 # M 9026319937559876238802573127597355132016530503268299678618003208170456302899329542892731471298988 type: gnfs rlim: 1000000 alim: 1000000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [500000, 850001) Primes: RFBsize:78498, AFBsize:79035, largePrimes:4094354 encountered Relations: rels:3942403, finalFF:241663 Max relations in full relation-set: 28 Initial matrix: 157611 x 241663 with sparse part having weight 21027438. Pruned matrix : 125329 x 126181 with weight 8294614. Polynomial selection time: 0.18 hours. Total sieving time: 2.04 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.05 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: gnfs,96,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1000000,1000000,26,26,49,49,2.5,2.5,50000 total time: 2.36 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Nov 30, 2008 (9th): By Erik Branger / GGNFS, Msieve
(11·10¹¹⁹+1)/3 = 3(6)₁₁₈7_<120> = 7 · 157 · 401 · 22478800580953_<14> · C101
C101 = P50 · P52
P50 = 12991913767799353249814912229358520152908976070653_<50>
P52 = 2848938679148128690045374612108836831282623299109037_<52>

Number: 36667_119 N=37013165649240677352188638468717285587168893121133951533421728005342231052746388846355743968062791161 ( 101 digits) SNFS difficulty: 121 digits. Divisors found: r1=12991913767799353249814912229358520152908976070653 r2=2848938679148128690045374612108836831282623299109037 Version: Total time: 1.93 hours. Scaled time: 1.52 units (timescale=0.788). Factorization parameters were as follows: n: 37013165649240677352188638468717285587168893121133951533421728005342231052746388846355743968062791161 m: 1000000000000000000000000 deg: 5 c5: 11 c0: 10 skew: 0.98 type: snfs lss: 1 rlim: 730000 alim: 730000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 730000/730000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [365000, 565001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 69857 x 70095 Total sieving time: 1.93 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000 total time: 1.93 hours. --------- CPU info (if available) ----------
Nov 30, 2008 (8th): By Sinkiti Sibata / Msieve, GGNFS
(11·10¹¹⁴+1)/3 = 3(6)₁₁₃7_<115> = 4084686562950884396339324671_<28> · C87
C87 = P44 · P44
P44 = 21099559767919706148965388700117758588600401_<44>
P44 = 42544095972337002803163257909814208720366277_<44>

Sun Nov 30 17:56:41 2008 Msieve v. 1.38 Sun Nov 30 17:56:41 2008 random seeds: 43c7e764 2d8bf80a Sun Nov 30 17:56:41 2008 factoring 897661695740436635978921665840942462701571152708113448971815635450427880352253509077077 (87 digits) Sun Nov 30 17:56:42 2008 searching for 15-digit factors Sun Nov 30 17:56:43 2008 commencing quadratic sieve (87-digit input) Sun Nov 30 17:56:43 2008 using multiplier of 1 Sun Nov 30 17:56:43 2008 using 32kb Intel Core sieve core Sun Nov 30 17:56:43 2008 sieve interval: 22 blocks of size 32768 Sun Nov 30 17:56:43 2008 processing polynomials in batches of 10 Sun Nov 30 17:56:43 2008 using a sieve bound of 1499123 (56997 primes) Sun Nov 30 17:56:43 2008 using large prime bound of 119929840 (26 bits) Sun Nov 30 17:56:43 2008 using double large prime bound of 348392707234640 (42-49 bits) Sun Nov 30 17:56:43 2008 using trial factoring cutoff of 49 bits Sun Nov 30 17:56:43 2008 polynomial 'A' values have 11 factors Sun Nov 30 18:50:59 2008 57411 relations (15553 full + 41858 combined from 607010 partial), need 57093 Sun Nov 30 18:50:59 2008 begin with 622563 relations Sun Nov 30 18:51:00 2008 reduce to 138886 relations in 10 passes Sun Nov 30 18:51:00 2008 attempting to read 138886 relations Sun Nov 30 18:51:01 2008 recovered 138886 relations Sun Nov 30 18:51:01 2008 recovered 118621 polynomials Sun Nov 30 18:51:02 2008 attempting to build 57411 cycles Sun Nov 30 18:51:02 2008 found 57411 cycles in 5 passes Sun Nov 30 18:51:02 2008 distribution of cycle lengths: Sun Nov 30 18:51:02 2008 length 1 : 15553 Sun Nov 30 18:51:02 2008 length 2 : 11104 Sun Nov 30 18:51:02 2008 length 3 : 10158 Sun Nov 30 18:51:02 2008 length 4 : 7663 Sun Nov 30 18:51:02 2008 length 5 : 5261 Sun Nov 30 18:51:02 2008 length 6 : 3377 Sun Nov 30 18:51:02 2008 length 7 : 1937 Sun Nov 30 18:51:02 2008 length 9+: 2358 Sun Nov 30 18:51:02 2008 largest cycle: 17 relations Sun Nov 30 18:51:02 2008 matrix is 56997 x 57411 (13.3 MB) with weight 3247632 (56.57/col) Sun Nov 30 18:51:02 2008 sparse part has weight 3247632 (56.57/col) Sun Nov 30 18:51:02 2008 filtering completed in 4 passes Sun Nov 30 18:51:02 2008 matrix is 52859 x 52923 (12.3 MB) with weight 3006031 (56.80/col) Sun Nov 30 18:51:02 2008 sparse part has weight 3006031 (56.80/col) Sun Nov 30 18:51:03 2008 saving the first 48 matrix rows for later Sun Nov 30 18:51:03 2008 matrix is 52811 x 52923 (7.8 MB) with weight 2373089 (44.84/col) Sun Nov 30 18:51:03 2008 sparse part has weight 1733530 (32.76/col) Sun Nov 30 18:51:03 2008 matrix includes 64 packed rows Sun Nov 30 18:51:03 2008 using block size 21169 for processor cache size 1024 kB Sun Nov 30 18:51:03 2008 commencing Lanczos iteration Sun Nov 30 18:51:03 2008 memory use: 7.7 MB Sun Nov 30 18:51:20 2008 lanczos halted after 837 iterations (dim = 52811) Sun Nov 30 18:51:20 2008 recovered 17 nontrivial dependencies Sun Nov 30 18:51:21 2008 prp44 factor: 21099559767919706148965388700117758588600401 Sun Nov 30 18:51:21 2008 prp44 factor: 42544095972337002803163257909814208720366277 Sun Nov 30 18:51:21 2008 elapsed time 00:54:40
(11·10¹¹²+1)/3 = 3(6)₁₁₁7_<113> = 37 · 53 · 6053 · 121254179151355849_<18> · C89
C89 = P37 · P53
P37 = 2344658050851003644637589698792718697_<37>
P53 = 10865430383019248585841901328692422403234007461482983_<53>

Sun Nov 30 18:57:49 2008 Msieve v. 1.38 Sun Nov 30 18:57:49 2008 random seeds: 1760b75c 1e4aa34b Sun Nov 30 18:57:49 2008 factoring 25475718823507185358250712731480185849953749457460003767658389018952004744064201971433151 (89 digits) Sun Nov 30 18:57:50 2008 searching for 15-digit factors Sun Nov 30 18:57:52 2008 commencing quadratic sieve (89-digit input) Sun Nov 30 18:57:52 2008 using multiplier of 31 Sun Nov 30 18:57:52 2008 using 32kb Intel Core sieve core Sun Nov 30 18:57:52 2008 sieve interval: 30 blocks of size 32768 Sun Nov 30 18:57:52 2008 processing polynomials in batches of 7 Sun Nov 30 18:57:52 2008 using a sieve bound of 1544489 (58667 primes) Sun Nov 30 18:57:52 2008 using large prime bound of 123559120 (26 bits) Sun Nov 30 18:57:52 2008 using double large prime bound of 367599255202560 (42-49 bits) Sun Nov 30 18:57:52 2008 using trial factoring cutoff of 49 bits Sun Nov 30 18:57:52 2008 polynomial 'A' values have 11 factors Sun Nov 30 20:01:08 2008 59023 relations (16122 full + 42901 combined from 619206 partial), need 58763 Sun Nov 30 20:01:09 2008 begin with 635328 relations Sun Nov 30 20:01:10 2008 reduce to 142320 relations in 10 passes Sun Nov 30 20:01:10 2008 attempting to read 142320 relations Sun Nov 30 20:01:12 2008 recovered 142320 relations Sun Nov 30 20:01:12 2008 recovered 120307 polynomials Sun Nov 30 20:01:12 2008 attempting to build 59023 cycles Sun Nov 30 20:01:12 2008 found 59023 cycles in 6 passes Sun Nov 30 20:01:12 2008 distribution of cycle lengths: Sun Nov 30 20:01:12 2008 length 1 : 16122 Sun Nov 30 20:01:12 2008 length 2 : 11639 Sun Nov 30 20:01:12 2008 length 3 : 10383 Sun Nov 30 20:01:12 2008 length 4 : 7676 Sun Nov 30 20:01:12 2008 length 5 : 5403 Sun Nov 30 20:01:12 2008 length 6 : 3358 Sun Nov 30 20:01:12 2008 length 7 : 2090 Sun Nov 30 20:01:12 2008 length 9+: 2352 Sun Nov 30 20:01:12 2008 largest cycle: 20 relations Sun Nov 30 20:01:12 2008 matrix is 58667 x 59023 (14.4 MB) with weight 3551446 (60.17/col) Sun Nov 30 20:01:12 2008 sparse part has weight 3551446 (60.17/col) Sun Nov 30 20:01:13 2008 filtering completed in 3 passes Sun Nov 30 20:01:13 2008 matrix is 54455 x 54518 (13.4 MB) with weight 3299267 (60.52/col) Sun Nov 30 20:01:13 2008 sparse part has weight 3299267 (60.52/col) Sun Nov 30 20:01:13 2008 saving the first 48 matrix rows for later Sun Nov 30 20:01:13 2008 matrix is 54407 x 54518 (10.2 MB) with weight 2772385 (50.85/col) Sun Nov 30 20:01:13 2008 sparse part has weight 2337636 (42.88/col) Sun Nov 30 20:01:13 2008 matrix includes 64 packed rows Sun Nov 30 20:01:13 2008 using block size 21807 for processor cache size 1024 kB Sun Nov 30 20:01:14 2008 commencing Lanczos iteration Sun Nov 30 20:01:14 2008 memory use: 9.0 MB Sun Nov 30 20:01:35 2008 lanczos halted after 862 iterations (dim = 54404) Sun Nov 30 20:01:36 2008 recovered 15 nontrivial dependencies Sun Nov 30 20:01:36 2008 prp37 factor: 2344658050851003644637589698792718697 Sun Nov 30 20:01:36 2008 prp53 factor: 10865430383019248585841901328692422403234007461482983 Sun Nov 30 20:01:36 2008 elapsed time 01:03:47
(11·10¹¹⁶+1)/3 = 3(6)₁₁₅7_<117> = 5923 · C113
C113 = P43 · P71
P43 = 1306986629179934599512414769208909338753123_<43>
P71 = 47365110316386599844519000083508998721829561294653165381499167296421523_<71>

Number: 36667_116 N=61905565873149867747200180088918903708706173673251167764083516236141594912488040970229050593730654510664640666329 ( 113 digits) SNFS difficulty: 118 digits. Divisors found: r1=1306986629179934599512414769208909338753123 (pp43) r2=47365110316386599844519000083508998721829561294653165381499167296421523 (pp71) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.39 hours. Scaled time: 4.79 units (timescale=2.003). Factorization parameters were as follows: name: 36667_116 n: 61905565873149867747200180088918903708706173673251167764083516236141594912488040970229050593730654510664640666329 m: 200000000000000000000000 deg: 5 c5: 55 c0: 16 skew: 0.78 type: snfs lss: 1 rlim: 650000 alim: 650000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 650000/650000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [325000, 575001) Primes: RFBsize:52831, AFBsize:52923, largePrimes:1703942 encountered Relations: rels:1982042, finalFF:430957 Max relations in full relation-set: 28 Initial matrix: 105821 x 430957 with sparse part having weight 20615305. Pruned matrix : 61853 x 62446 with weight 3879059. Total sieving time: 2.30 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.01 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,118,5,0,0,0,0,0,0,0,0,650000,650000,25,25,45,45,2.2,2.2,50000 total time: 2.39 hours. --------- CPU info (if available) ----------
(34·10¹⁵⁰-61)/9 = 3(7)₁₄₉1_<151> = 3 · 389 · 30137 · 38659272836953_<14> · 67606737734777_<14> · 100407816699053448695811907_<27> · C90
C90 = P43 · P48
P43 = 1973252236706869812819161804219996164666783_<43>
P48 = 207430084791366627386951998914230244772682187809_<48>

Sun Nov 30 20:11:43 2008 Msieve v. 1.38 Sun Nov 30 20:11:43 2008 random seeds: d7427efc dffe20ca Sun Nov 30 20:11:43 2008 factoring 409311878774859856196618058713465886648346234120836517657865266347085566045370911909848447 (90 digits) Sun Nov 30 20:11:43 2008 searching for 15-digit factors Sun Nov 30 20:11:45 2008 commencing quadratic sieve (90-digit input) Sun Nov 30 20:11:45 2008 using multiplier of 7 Sun Nov 30 20:11:45 2008 using 32kb Intel Core sieve core Sun Nov 30 20:11:45 2008 sieve interval: 36 blocks of size 32768 Sun Nov 30 20:11:45 2008 processing polynomials in batches of 6 Sun Nov 30 20:11:45 2008 using a sieve bound of 1573717 (60000 primes) Sun Nov 30 20:11:45 2008 using large prime bound of 125897360 (26 bits) Sun Nov 30 20:11:45 2008 using double large prime bound of 380215566683840 (42-49 bits) Sun Nov 30 20:11:45 2008 using trial factoring cutoff of 49 bits Sun Nov 30 20:11:45 2008 polynomial 'A' values have 12 factors Sun Nov 30 21:34:45 2008 60440 relations (16042 full + 44398 combined from 633475 partial), need 60096 Sun Nov 30 21:34:45 2008 begin with 649517 relations Sun Nov 30 21:34:46 2008 reduce to 147373 relations in 10 passes Sun Nov 30 21:34:46 2008 attempting to read 147373 relations Sun Nov 30 21:34:48 2008 recovered 147373 relations Sun Nov 30 21:34:48 2008 recovered 127487 polynomials Sun Nov 30 21:34:48 2008 attempting to build 60440 cycles Sun Nov 30 21:34:48 2008 found 60439 cycles in 5 passes Sun Nov 30 21:34:48 2008 distribution of cycle lengths: Sun Nov 30 21:34:48 2008 length 1 : 16042 Sun Nov 30 21:34:48 2008 length 2 : 11565 Sun Nov 30 21:34:48 2008 length 3 : 10681 Sun Nov 30 21:34:48 2008 length 4 : 8203 Sun Nov 30 21:34:48 2008 length 5 : 5747 Sun Nov 30 21:34:48 2008 length 6 : 3601 Sun Nov 30 21:34:48 2008 length 7 : 2155 Sun Nov 30 21:34:48 2008 length 9+: 2445 Sun Nov 30 21:34:48 2008 largest cycle: 20 relations Sun Nov 30 21:34:48 2008 matrix is 60000 x 60439 (14.8 MB) with weight 3629462 (60.05/col) Sun Nov 30 21:34:48 2008 sparse part has weight 3629462 (60.05/col) Sun Nov 30 21:34:49 2008 filtering completed in 3 passes Sun Nov 30 21:34:49 2008 matrix is 56097 x 56161 (13.7 MB) with weight 3376905 (60.13/col) Sun Nov 30 21:34:49 2008 sparse part has weight 3376905 (60.13/col) Sun Nov 30 21:34:49 2008 saving the first 48 matrix rows for later Sun Nov 30 21:34:49 2008 matrix is 56049 x 56161 (8.8 MB) with weight 2662129 (47.40/col) Sun Nov 30 21:34:49 2008 sparse part has weight 1959855 (34.90/col) Sun Nov 30 21:34:49 2008 matrix includes 64 packed rows Sun Nov 30 21:34:49 2008 using block size 22464 for processor cache size 1024 kB Sun Nov 30 21:34:50 2008 commencing Lanczos iteration Sun Nov 30 21:34:50 2008 memory use: 8.5 MB Sun Nov 30 21:35:10 2008 lanczos halted after 888 iterations (dim = 56047) Sun Nov 30 21:35:10 2008 recovered 16 nontrivial dependencies Sun Nov 30 21:35:10 2008 prp43 factor: 1973252236706869812819161804219996164666783 Sun Nov 30 21:35:10 2008 prp48 factor: 207430084791366627386951998914230244772682187809 Sun Nov 30 21:35:10 2008 elapsed time 01:23:27
(11·10¹⁴³-17)/3 = 3(6)₁₄₂1_<144> = 59 · 103 · 197 · 219076802827792599331905203_<27> · C112
C112 = P37 · P75
P37 = 5820795363380476217942633647955613143_<37>
P75 = 240180222166092282236882706207457733262537991553564219984716625310194297761_<75>

Number: 36661_143 N=1398039923560082634828910420072859904457691715505441275759702220737789195249611934079696273591083487191067072823 ( 112 digits) SNFS difficulty: 145 digits. Divisors found: r1=5820795363380476217942633647955613143 (pp37) r2=240180222166092282236882706207457733262537991553564219984716625310194297761 (pp75) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 22.85 hours. Scaled time: 10.81 units (timescale=0.473). Factorization parameters were as follows: name: 36661_143 n: 1398039923560082634828910420072859904457691715505441275759702220737789195249611934079696273591083487191067072823 m: 50000000000000000000000000000 deg: 5 c5: 88 c0: -425 skew: 1.37 type: snfs lss: 1 rlim: 1860000 alim: 1860000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1860000/1860000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [930000, 2730001) Primes: RFBsize:139249, AFBsize:139409, largePrimes:4151418 encountered Relations: rels:4312026, finalFF:326401 Max relations in full relation-set: 28 Initial matrix: 278725 x 326401 with sparse part having weight 36068468. Pruned matrix : 262731 x 264188 with weight 27157932. Total sieving time: 20.04 hours. Total relation processing time: 0.25 hours. Matrix solve time: 2.47 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1860000,1860000,26,26,49,49,2.3,2.3,100000 total time: 22.85 hours. --------- CPU info (if available) ----------
(11·10¹²³+1)/3 = 3(6)₁₂₂7_<124> = 17 · 233 · 420319 · C115
C115 = P49 · P66
P49 = 9794999209502002672388914985834215568969898339847_<49>
P66 = 224844961786526402678113350024342711554948949791525830477913909179_<66>

Number: 36667_123 N=2202356222959534112779755467971839504883156015757536029981701961576441194628114329686083870245406553784502034755613 ( 115 digits) SNFS difficulty: 125 digits. Divisors found: r1=9794999209502002672388914985834215568969898339847 (pp49) r2=224844961786526402678113350024342711554948949791525830477913909179 (pp66) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.84 hours. Scaled time: 5.64 units (timescale=1.985). Factorization parameters were as follows: name: 36667_123 n: 2202356222959534112779755467971839504883156015757536029981701961576441194628114329686083870245406553784502034755613 m: 5000000000000000000000000 deg: 5 c5: 88 c0: 25 skew: 0.78 type: snfs lss: 1 rlim: 860000 alim: 860000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 860000/860000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [430000, 680001) Primes: RFBsize:68342, AFBsize:68636, largePrimes:2725883 encountered Relations: rels:2864348, finalFF:412312 Max relations in full relation-set: 28 Initial matrix: 137045 x 412312 with sparse part having weight 29982948. Pruned matrix : 86555 x 87304 with weight 5897482. Total sieving time: 2.70 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.04 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,860000,860000,26,26,46,46,2.3,2.3,50000 total time: 2.84 hours. --------- CPU info (if available) ----------
Nov 30, 2008 (7th): By Robert Backstrom / Msieve, GGNFS
(11·10¹¹¹+1)/3 = 3(6)₁₁₀7_<112> = 19 · 4479173856329141155090247729_<28> · C83
C83 = P40 · P43
P40 = 5224631191091294072933327702528080958339_<40>
P43 = 8246397610153091399492664950103852314306803_<43>

Sun Nov 30 20:26:18 2008 Sun Nov 30 20:26:18 2008 Sun Nov 30 20:26:18 2008 Msieve v. 1.38 Sun Nov 30 20:26:18 2008 random seeds: 2bc1f670 7511cf85 Sun Nov 30 20:26:18 2008 factoring 43084386168146546835721754466890151824910052764435983250283044114671565568707280217 (83 digits) Sun Nov 30 20:26:18 2008 searching for 15-digit factors Sun Nov 30 20:26:19 2008 commencing quadratic sieve (83-digit input) Sun Nov 30 20:26:19 2008 using multiplier of 5 Sun Nov 30 20:26:19 2008 using 64kb Opteron sieve core Sun Nov 30 20:26:19 2008 sieve interval: 6 blocks of size 65536 Sun Nov 30 20:26:19 2008 processing polynomials in batches of 17 Sun Nov 30 20:26:19 2008 using a sieve bound of 1368167 (52647 primes) Sun Nov 30 20:26:19 2008 using large prime bound of 121766863 (26 bits) Sun Nov 30 20:26:19 2008 using trial factoring cutoff of 27 bits Sun Nov 30 20:26:19 2008 polynomial 'A' values have 11 factors Sun Nov 30 20:42:41 2008 52814 relations (27081 full + 25733 combined from 279284 partial), need 52743 Sun Nov 30 20:42:41 2008 begin with 306365 relations Sun Nov 30 20:42:41 2008 reduce to 75332 relations in 2 passes Sun Nov 30 20:42:41 2008 attempting to read 75332 relations Sun Nov 30 20:42:42 2008 recovered 75332 relations Sun Nov 30 20:42:42 2008 recovered 68175 polynomials Sun Nov 30 20:42:42 2008 attempting to build 52814 cycles Sun Nov 30 20:42:42 2008 found 52814 cycles in 1 passes Sun Nov 30 20:42:42 2008 distribution of cycle lengths: Sun Nov 30 20:42:42 2008 length 1 : 27081 Sun Nov 30 20:42:42 2008 length 2 : 25733 Sun Nov 30 20:42:42 2008 largest cycle: 2 relations Sun Nov 30 20:42:42 2008 matrix is 52647 x 52814 (7.2 MB) with weight 1683721 (31.88/col) Sun Nov 30 20:42:42 2008 sparse part has weight 1683721 (31.88/col) Sun Nov 30 20:42:42 2008 filtering completed in 3 passes Sun Nov 30 20:42:42 2008 matrix is 37904 x 37965 (5.7 MB) with weight 1347008 (35.48/col) Sun Nov 30 20:42:42 2008 sparse part has weight 1347008 (35.48/col) Sun Nov 30 20:42:43 2008 saving the first 48 matrix rows for later Sun Nov 30 20:42:43 2008 matrix is 37856 x 37965 (3.8 MB) with weight 1039465 (27.38/col) Sun Nov 30 20:42:43 2008 sparse part has weight 762472 (20.08/col) Sun Nov 30 20:42:43 2008 matrix includes 64 packed rows Sun Nov 30 20:42:43 2008 using block size 15186 for processor cache size 1024 kB Sun Nov 30 20:42:43 2008 commencing Lanczos iteration Sun Nov 30 20:42:43 2008 memory use: 4.3 MB Sun Nov 30 20:42:49 2008 lanczos halted after 600 iterations (dim = 37854) Sun Nov 30 20:42:49 2008 recovered 17 nontrivial dependencies Sun Nov 30 20:42:49 2008 prp40 factor: 5224631191091294072933327702528080958339 Sun Nov 30 20:42:49 2008 prp43 factor: 8246397610153091399492664950103852314306803 Sun Nov 30 20:42:49 2008 elapsed time 00:16:31
(34·10¹³³-61)/9 = 3(7)₁₃₂1_<134> = 153962383 · 105954652313_<12> · 242858635321_<12> · 161803335731828507203_<21> · C83
C83 = P41 · P43
P41 = 26799939804329649021518979639474619438057_<41>
P43 = 2199008524395165291774974383767263037749039_<43>

Sun Nov 30 21:30:16 2008 Sun Nov 30 21:30:16 2008 Sun Nov 30 21:30:16 2008 Msieve v. 1.38 Sun Nov 30 21:30:16 2008 random seeds: e4438188 325b217a Sun Nov 30 21:30:16 2008 factoring 58933296082998196336578171305363661582019073412603463167509046878466276668371777223 (83 digits) Sun Nov 30 21:30:16 2008 searching for 15-digit factors Sun Nov 30 21:30:17 2008 commencing quadratic sieve (83-digit input) Sun Nov 30 21:30:17 2008 using multiplier of 23 Sun Nov 30 21:30:17 2008 using 64kb Opteron sieve core Sun Nov 30 21:30:17 2008 sieve interval: 6 blocks of size 65536 Sun Nov 30 21:30:17 2008 processing polynomials in batches of 17 Sun Nov 30 21:30:17 2008 using a sieve bound of 1375981 (52647 primes) Sun Nov 30 21:30:17 2008 using large prime bound of 122462309 (26 bits) Sun Nov 30 21:30:17 2008 using trial factoring cutoff of 27 bits Sun Nov 30 21:30:17 2008 polynomial 'A' values have 11 factors Sun Nov 30 21:46:50 2008 52756 relations (27452 full + 25304 combined from 276041 partial), need 52743 Sun Nov 30 21:46:51 2008 begin with 303493 relations Sun Nov 30 21:46:51 2008 reduce to 74861 relations in 2 passes Sun Nov 30 21:46:51 2008 attempting to read 74861 relations Sun Nov 30 21:46:51 2008 recovered 74861 relations Sun Nov 30 21:46:51 2008 recovered 68059 polynomials Sun Nov 30 21:46:51 2008 attempting to build 52756 cycles Sun Nov 30 21:46:51 2008 found 52756 cycles in 1 passes Sun Nov 30 21:46:51 2008 distribution of cycle lengths: Sun Nov 30 21:46:51 2008 length 1 : 27452 Sun Nov 30 21:46:51 2008 length 2 : 25304 Sun Nov 30 21:46:51 2008 largest cycle: 2 relations Sun Nov 30 21:46:51 2008 matrix is 52647 x 52756 (7.3 MB) with weight 1691578 (32.06/col) Sun Nov 30 21:46:51 2008 sparse part has weight 1691578 (32.06/col) Sun Nov 30 21:46:52 2008 filtering completed in 3 passes Sun Nov 30 21:46:52 2008 matrix is 37816 x 37879 (5.7 MB) with weight 1347132 (35.56/col) Sun Nov 30 21:46:52 2008 sparse part has weight 1347132 (35.56/col) Sun Nov 30 21:46:52 2008 saving the first 48 matrix rows for later Sun Nov 30 21:46:52 2008 matrix is 37768 x 37879 (3.6 MB) with weight 1000452 (26.41/col) Sun Nov 30 21:46:52 2008 sparse part has weight 712309 (18.80/col) Sun Nov 30 21:46:52 2008 matrix includes 64 packed rows Sun Nov 30 21:46:52 2008 using block size 15151 for processor cache size 1024 kB Sun Nov 30 21:46:53 2008 commencing Lanczos iteration Sun Nov 30 21:46:53 2008 memory use: 4.2 MB Sun Nov 30 21:46:58 2008 lanczos halted after 599 iterations (dim = 37768) Sun Nov 30 21:46:58 2008 recovered 18 nontrivial dependencies Sun Nov 30 21:46:58 2008 prp41 factor: 26799939804329649021518979639474619438057 Sun Nov 30 21:46:58 2008 prp43 factor: 2199008524395165291774974383767263037749039 Sun Nov 30 21:46:58 2008 elapsed time 00:16:42
(34·10¹⁰⁹-61)/9 = 3(7)₁₀₈1_<110> = 355457 · C105
C105 = P33 · P73
P33 = 102274718124055259233175468223737_<33>
P73 = 1039156707415436687110020687405007603981945643618063760550394061953391619_<73>

Number: n N=106279459337635150743346671405480206544751623340594721099254699662062577970831289798140922186868672660203 ( 105 digits) SNFS difficulty: 111 digits. Divisors found: r1=102274718124055259233175468223737 (pp33) r2=1039156707415436687110020687405007603981945643618063760550394061953391619 (pp73) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.91 hours. Scaled time: 1.65 units (timescale=1.817). Factorization parameters were as follows: name: KA_3_7_108_1 n: 106279459337635150743346671405480206544751623340594721099254699662062577970831289798140922186868672660203 type: snfs skew: 1.78 deg: 5 c5: 17 c0: -305 m: 10000000000000000000000 rlim: 500000 alim: 500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [100000, 200001) Primes: RFBsize:41538, AFBsize:41418, largePrimes:4212687 encountered Relations: rels:3752838, finalFF:255574 Max relations in full relation-set: 48 Initial matrix: 83021 x 255574 with sparse part having weight 23447240. Pruned matrix : 53378 x 53857 with weight 2927628. Total sieving time: 0.84 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.01 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,500000,500000,28,28,56,56,2.5,2.5,50000 total time: 0.91 hours. --------- CPU info (if available) ----------
Nov 30, 2008 (6th): By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38
(34·10¹⁵¹-61)/9 = 3(7)₁₅₀1_<152> = 31 · 85413659 · 2512923666807739522019_<22> · 552414667069372497692778901_<27> · C95
C95 = P40 · P55
P40 = 4219687194429644317151362254455770822763_<40>
P55 = 2435693468651238851330439053636574682409976561582029267_<55>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2347407703 Step 1 took 8636ms Step 2 took 404ms ********** Factor found in step 2: 4219687194429644317151362254455770822763 Found probable prime factor of 40 digits: 4219687194429644317151362254455770822763 Probable prime cofactor 2435693468651238851330439053636574682409976561582029267 has 55 digits
(11·10¹¹⁰+1)/3 = 3(6)₁₀₉7_<111> = 1730988986761_<13> · C99
C99 = P39 · P61
P39 = 190853932462516980462149362837947703859_<39>
P61 = 1109879967768032011225337624689665807633302433866174800966433_<61>

SNFS difficulty: 111 digits. Divisors found: r1=190853932462516980462149362837947703859 (pp39) r2=1109879967768032011225337624689665807633302433866174800966433 (pp61) Version: Msieve-1.38 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.403). Factorization parameters were as follows: n: 211824956409900504611721650005430185338299024638751288343886051876340119698931368923094866483564947 m: 10000000000000000000000 deg: 5 c5: 11 c0: 1 skew: 0.62 type: snfs lss: 1 rlim: 500000 alim: 500000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [250000, 350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 54411 x 54621 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,500000,500000,25,25,46,46,2.3,2.3,50000 total time: 0.30 hours.
Nov 30, 2008 (5th): Factorizations of 366...667 and Factorizations of 377...771 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.
Nov 30, 2008 (4th): By Sinkiti Sibata / Msieve, GGNFS
(11·10¹⁴⁸-17)/3 = 3(6)₁₄₇1_<149> = 127 · 6053 · 3527767 · 12713377 · 33380182777_<11> · 55504775997620393_<17> · C102
C102 = P43 · P60
P43 = 2948246018368709645486068483619884355791607_<43>
P60 = 194694387041111373270642545173578018166065623787751820262767_<60>

Sat Nov 29 19:58:25 2008 Msieve v. 1.38 Sat Nov 29 19:58:25 2008 random seeds: 0bb27454 e6c455c6 Sat Nov 29 19:58:25 2008 factoring 574006951392693106963739100431843481150210144630008572838701316332226314859054721325873107493033196569 (102 digits) Sat Nov 29 19:58:26 2008 searching for 15-digit factors Sat Nov 29 19:58:28 2008 commencing quadratic sieve (102-digit input) Sat Nov 29 19:58:28 2008 using multiplier of 1 Sat Nov 29 19:58:28 2008 using 32kb Intel Core sieve core Sat Nov 29 19:58:28 2008 sieve interval: 36 blocks of size 32768 Sat Nov 29 19:58:28 2008 processing polynomials in batches of 6 Sat Nov 29 19:58:28 2008 using a sieve bound of 3272219 (117500 primes) Sat Nov 29 19:58:28 2008 using large prime bound of 490832850 (28 bits) Sat Nov 29 19:58:28 2008 using double large prime bound of 4402308790788150 (44-52 bits) Sat Nov 29 19:58:28 2008 using trial factoring cutoff of 52 bits Sat Nov 29 19:58:28 2008 polynomial 'A' values have 13 factors Sun Nov 30 09:52:49 2008 117762 relations (28907 full + 88855 combined from 1739700 partial), need 117596 Sun Nov 30 09:52:52 2008 begin with 1768607 relations Sun Nov 30 09:52:53 2008 reduce to 305866 relations in 11 passes Sun Nov 30 09:52:53 2008 attempting to read 305866 relations Sun Nov 30 09:52:59 2008 recovered 305866 relations Sun Nov 30 09:52:59 2008 recovered 294831 polynomials Sun Nov 30 09:52:59 2008 attempting to build 117762 cycles Sun Nov 30 09:52:59 2008 found 117762 cycles in 6 passes Sun Nov 30 09:52:59 2008 distribution of cycle lengths: Sun Nov 30 09:52:59 2008 length 1 : 28907 Sun Nov 30 09:53:00 2008 length 2 : 20776 Sun Nov 30 09:53:00 2008 length 3 : 19574 Sun Nov 30 09:53:00 2008 length 4 : 16039 Sun Nov 30 09:53:00 2008 length 5 : 12143 Sun Nov 30 09:53:00 2008 length 6 : 7941 Sun Nov 30 09:53:00 2008 length 7 : 5284 Sun Nov 30 09:53:00 2008 length 9+: 7098 Sun Nov 30 09:53:00 2008 largest cycle: 19 relations Sun Nov 30 09:53:00 2008 matrix is 117500 x 117762 (33.6 MB) with weight 8326328 (70.70/col) Sun Nov 30 09:53:00 2008 sparse part has weight 8326328 (70.70/col) Sun Nov 30 09:53:02 2008 filtering completed in 4 passes Sun Nov 30 09:53:02 2008 matrix is 112064 x 112128 (32.2 MB) with weight 7980133 (71.17/col) Sun Nov 30 09:53:02 2008 sparse part has weight 7980133 (71.17/col) Sun Nov 30 09:53:03 2008 saving the first 48 matrix rows for later Sun Nov 30 09:53:03 2008 matrix is 112016 x 112128 (22.2 MB) with weight 6586527 (58.74/col) Sun Nov 30 09:53:03 2008 sparse part has weight 5144383 (45.88/col) Sun Nov 30 09:53:03 2008 matrix includes 64 packed rows Sun Nov 30 09:53:03 2008 using block size 43690 for processor cache size 1024 kB Sun Nov 30 09:53:04 2008 commencing Lanczos iteration Sun Nov 30 09:53:04 2008 memory use: 20.1 MB Sun Nov 30 09:54:49 2008 lanczos halted after 1774 iterations (dim = 112012) Sun Nov 30 09:54:49 2008 recovered 14 nontrivial dependencies Sun Nov 30 09:54:50 2008 prp43 factor: 2948246018368709645486068483619884355791607 Sun Nov 30 09:54:50 2008 prp60 factor: 194694387041111373270642545173578018166065623787751820262767 Sun Nov 30 09:54:50 2008 elapsed time 13:56:25
(11·10¹⁴⁷-17)/3 = 3(6)₁₄₆1_<148> = 7 · 20753 · 36857 · C138
C138 = P55 · P83
P55 = 8842698700184589568599008652313694532003883719628427533_<55>
P83 = 77443985378298208181284593151571674690130665279220978504034704045989491535203645511_<83>

Number: 36661_147 N=684813828841791925548542636326045013960593236516865610758561616214614337734306773754040675593517862354982976147348950128332745010084254363 ( 138 digits) SNFS difficulty: 148 digits. Divisors found: r1=8842698700184589568599008652313694532003883719628427533 (pp55) r2=77443985378298208181284593151571674690130665279220978504034704045989491535203645511 (pp83) Version: GGNFS-0.77.1-20060513-k8 Total time: 19.10 hours. Scaled time: 37.43 units (timescale=1.960). Factorization parameters were as follows: name: 36661_147 n: 684813828841791925548542636326045013960593236516865610758561616214614337734306773754040675593517862354982976147348950128332745010084254363 m: 200000000000000000000000000000 deg: 5 c5: 275 c0: -136 skew: 0.87 type: snfs lss: 1 rlim: 2100000 alim: 2100000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1050000, 2550001) Primes: RFBsize:155805, AFBsize:155548, largePrimes:4285623 encountered Relations: rels:4471418, finalFF:407942 Max relations in full relation-set: 28 Initial matrix: 311420 x 407942 with sparse part having weight 41248728. Pruned matrix : 275681 x 277302 with weight 25234510. Total sieving time: 17.84 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.96 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000 total time: 19.10 hours. --------- CPU info (if available) ----------
Nov 30, 2008 (3rd): By Wataru Sakai /
(29·10¹⁹⁸+61)/9 = 3(2)₁₉₇9_<199> = C199
C199 = P34 · P80 · P86
P34 = 2095371728411637326523016514560361_<34>
P80 = 74843311724277390714103497997979276379695056502313658840857218754233651055714689_<80>
P86 = 20546668414495269636043870873401510005927188389041146706716965258195301264107264535501_<86>

Number: 32229_198 N=3222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229 ( 199 digits) SNFS difficulty: 200 digits. Divisors found: r1=2095371728411637326523016514560361 r2=74843311724277390714103497997979276379695056502313658840857218754233651055714689 r3=20546668414495269636043870873401510005927188389041146706716965258195301264107264535501 Version: Total time: 1037.76 hours. Scaled time: 2075.52 units (timescale=2.000). Factorization parameters were as follows: n: 3222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229 m: 5000000000000000000000000000000000000000 deg: 5 c5: 232 c0: 1525 skew: 1.46 type: snfs lss: 1 rlim: 15600000 alim: 15600000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6Factor base limits: 15600000/15600000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [7800000, 19100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 3123383 x 3123631 Total sieving time: 1037.76 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,200,5,0,0,0,0,0,0,0,0,15600000,15600000,29,29,56,56,2.6,2.6,100000 total time: 1037.76 hours. --------- CPU info (if available) ----------
Nov 30, 2008 (2nd): By Robert Backstrom / GGNFS
(11·10¹⁴⁹-17)/3 = 3(6)₁₄₈1_<150> = 113 · 2789 · C145
C145 = P52 · P93
P52 = 1749531190763715955891758353574118748596593649502417_<52>
P93 = 665001742324150244386503948550084957227608454300070908441392564284028975306968875042947440769_<93>

Number: n N=1163441290108316384109084255360555744174067739782605706573760591282017111048355793038601924331893839155299316425358366359200863908041600429838673 ( 145 digits) SNFS difficulty: 151 digits. Divisors found: r1=1749531190763715955891758353574118748596593649502417 (pp52) r2=665001742324150244386503948550084957227608454300070908441392564284028975306968875042947440769 (pp93) Version: GGNFS-0.77.1-20051202-athlon Total time: 12.50 hours. Scaled time: 22.78 units (timescale=1.822). Factorization parameters were as follows: name: KA_3_6_148_1 n: 1163441290108316384109084255360555744174067739782605706573760591282017111048355793038601924331893839155299316425358366359200863908041600429838673 type: snfs skew: 1.73 deg: 5 c5: 11 c0: -170 m: 1000000000000000000000000000000 rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [100000, 900001) Primes: RFBsize:148933, AFBsize:149101, largePrimes:9843134 encountered Relations: rels:8711625, finalFF:409868 Max relations in full relation-set: 48 Initial matrix: 298099 x 409868 with sparse part having weight 47976057. Pruned matrix : 244058 x 245612 with weight 21718722. Total sieving time: 11.67 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.50 hours. Total square root time: 0.13 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,56,56,2.5,2.5,100000 total time: 12.50 hours. --------- CPU info (if available) ----------
Nov 30, 2008: By Serge Batalov / Msieve-1.38
(11·10¹⁵⁹-17)/3 = 3(6)₁₅₈1_<160> = 7 · C159
C159 = P43 · P116
P43 = 9605698962417846290315464856568118961559197_<43>
P116 = 54531120104733736426800532979622712211483081760295270849348053571911942643371024243440985426930821251996580938007759_<116>

SNFS difficulty: 161 digits. Divisors found: r1=9605698962417846290315464856568118961559197 (pp43) r2=54531120104733736426800532979622712211483081760295270849348053571911942643371024243440985426930821251996580938007759 (pp116) Version: Msieve-1.38 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.552). Factorization parameters were as follows: n: 523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523 m: 100000000000000000000000000000000 deg: 5 c5: 11 c0: -170 skew: 1.73 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1700000, 3000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 617903 x 618145 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,52,52,2.4,2.4,100000 total time: 17.00 hours.
Nov 29, 2008 (4th): By Sinkiti Sibata / GGNFS, Msieve
(29·10¹⁶¹-11)/9 = 3(2)₁₆₀1_<162> = 3² · 107 · 12829059953513_<14> · 378530381329301986746325121_<27> · C119
C119 = P40 · P80
P40 = 2546623150563877412685398371793679334001_<40>
P80 = 27056333382115000182457185576833611392251799115728017548960989369903042621465479_<80>

Number: 32221_161 N=68902284960268310691160272909882658392427741164950225050125505847630985571103442660751760239191044441082947519332451479 ( 119 digits) SNFS difficulty: 163 digits. Divisors found: r1=2546623150563877412685398371793679334001 (pp40) r2=27056333382115000182457185576833611392251799115728017548960989369903042621465479 (pp80) Version: GGNFS-0.77.1-20060513-nocona Total time: 55.10 hours. Scaled time: 141.29 units (timescale=2.564). Factorization parameters were as follows: name: 32221_161 n: 68902284960268310691160272909882658392427741164950225050125505847630985571103442660751760239191044441082947519332451479 m: 200000000000000000000000000000000 deg: 5 c5: 145 c0: -176 skew: 1.04 type: snfs lss: 1 rlim: 3700000 alim: 3700000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3700000/3700000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1850000, 3550001) Primes: RFBsize:263397, AFBsize:262673, largePrimes:9228731 encountered Relations: rels:9590220, finalFF:635440 Max relations in full relation-set: 28 Initial matrix: 526137 x 635440 with sparse part having weight 70868979. Pruned matrix : 480579 x 483273 with weight 51758556. Total sieving time: 52.00 hours. Total relation processing time: 0.15 hours. Matrix solve time: 2.75 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3700000,3700000,27,27,51,51,2.4,2.4,100000 total time: 55.10 hours. --------- CPU info (if available) ----------
(11·10¹³⁵-17)/3 = 3(6)₁₃₄1_<136> = 7 · 643 · 98953 · 1598539 · C121
C121 = P54 · P68
P54 = 463899733528641667300807588409536956588227985148592021_<54>
P68 = 11101613225813972447215283066867552276042114840195309698943540163023_<68>

Number: 36661_135 N=5150035417193145851355521736539756677829975768640092551076918709929398652640501243150621028631411539736512996373257039483 ( 121 digits) SNFS difficulty: 136 digits. Divisors found: r1=463899733528641667300807588409536956588227985148592021 (pp54) r2=11101613225813972447215283066867552276042114840195309698943540163023 (pp68) Version: GGNFS-0.77.1-20060513-k8 Total time: 6.75 hours. Scaled time: 13.32 units (timescale=1.972). Factorization parameters were as follows: name: 36661_135 n: 5150035417193145851355521736539756677829975768640092551076918709929398652640501243150621028631411539736512996373257039483 m: 1000000000000000000000000000 deg: 5 c5: 11 c0: -17 skew: 1.09 type: snfs lss: 1 rlim: 1300000 alim: 1300000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [650000, 1175001) Primes: RFBsize:100021, AFBsize:100129, largePrimes:3397345 encountered Relations: rels:3539165, finalFF:431299 Max relations in full relation-set: 28 Initial matrix: 200215 x 431299 with sparse part having weight 37332250. Pruned matrix : 146610 x 147675 with weight 10914158. Total sieving time: 6.42 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.18 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000 total time: 6.75 hours. --------- CPU info (if available) ----------
(11·10¹²⁰-17)/3 = 3(6)₁₁₉1_<121> = 277 · 6048409 · 233162350530541_<15> · C97
C97 = P49 · P49
P49 = 2105127696207944911022798679968833991726314291117_<49>
P49 = 4458755319605430079360836851668789221417006597841_<49>

Sat Nov 29 07:45:04 2008 Msieve v. 1.38 Sat Nov 29 07:45:04 2008 random seeds: 3c84e488 28be6288 Sat Nov 29 07:45:04 2008 factoring 9386249313915898130261757082745844486257562853489685991325229137610986951325811514789997817678397 (97 digits) Sat Nov 29 07:45:05 2008 searching for 15-digit factors Sat Nov 29 07:45:07 2008 commencing quadratic sieve (97-digit input) Sat Nov 29 07:45:07 2008 using multiplier of 13 Sat Nov 29 07:45:07 2008 using 32kb Intel Core sieve core Sat Nov 29 07:45:07 2008 sieve interval: 36 blocks of size 32768 Sat Nov 29 07:45:07 2008 processing polynomials in batches of 6 Sat Nov 29 07:45:07 2008 using a sieve bound of 2433061 (89412 primes) Sat Nov 29 07:45:07 2008 using large prime bound of 364959150 (28 bits) Sat Nov 29 07:45:07 2008 using double large prime bound of 2582495835375450 (43-52 bits) Sat Nov 29 07:45:07 2008 using trial factoring cutoff of 52 bits Sat Nov 29 07:45:07 2008 polynomial 'A' values have 13 factors Sat Nov 29 13:54:17 2008 89905 relations (21674 full + 68231 combined from 1343247 partial), need 89508 Sat Nov 29 13:54:22 2008 begin with 1364921 relations Sat Nov 29 13:54:23 2008 reduce to 235606 relations in 10 passes Sat Nov 29 13:54:23 2008 attempting to read 235606 relations Sat Nov 29 13:54:27 2008 recovered 235606 relations Sat Nov 29 13:54:27 2008 recovered 222456 polynomials Sat Nov 29 13:54:27 2008 attempting to build 89905 cycles Sat Nov 29 13:54:28 2008 found 89905 cycles in 6 passes Sat Nov 29 13:54:28 2008 distribution of cycle lengths: Sat Nov 29 13:54:28 2008 length 1 : 21674 Sat Nov 29 13:54:28 2008 length 2 : 15506 Sat Nov 29 13:54:28 2008 length 3 : 15138 Sat Nov 29 13:54:28 2008 length 4 : 12293 Sat Nov 29 13:54:28 2008 length 5 : 9307 Sat Nov 29 13:54:28 2008 length 6 : 6256 Sat Nov 29 13:54:28 2008 length 7 : 4136 Sat Nov 29 13:54:28 2008 length 9+: 5595 Sat Nov 29 13:54:28 2008 largest cycle: 20 relations Sat Nov 29 13:54:28 2008 matrix is 89412 x 89905 (24.4 MB) with weight 6028665 (67.06/col) Sat Nov 29 13:54:28 2008 sparse part has weight 6028665 (67.06/col) Sat Nov 29 13:54:29 2008 filtering completed in 3 passes Sat Nov 29 13:54:29 2008 matrix is 85386 x 85449 (23.2 MB) with weight 5736383 (67.13/col) Sat Nov 29 13:54:29 2008 sparse part has weight 5736383 (67.13/col) Sat Nov 29 13:54:30 2008 saving the first 48 matrix rows for later Sat Nov 29 13:54:30 2008 matrix is 85338 x 85449 (14.2 MB) with weight 4515452 (52.84/col) Sat Nov 29 13:54:30 2008 sparse part has weight 3212893 (37.60/col) Sat Nov 29 13:54:30 2008 matrix includes 64 packed rows Sat Nov 29 13:54:30 2008 using block size 34179 for processor cache size 1024 kB Sat Nov 29 13:54:30 2008 commencing Lanczos iteration Sat Nov 29 13:54:30 2008 memory use: 13.8 MB Sat Nov 29 13:55:24 2008 lanczos halted after 1350 iterations (dim = 85336) Sat Nov 29 13:55:24 2008 recovered 17 nontrivial dependencies Sat Nov 29 13:55:24 2008 prp49 factor: 2105127696207944911022798679968833991726314291117 Sat Nov 29 13:55:24 2008 prp49 factor: 4458755319605430079360836851668789221417006597841 Sat Nov 29 13:55:24 2008 elapsed time 06:10:20
(11·10¹³⁴-17)/3 = 3(6)₁₃₃1_<135> = 10093 · 24133 · 8598394367382957958478995153_<28> · C99
C99 = P42 · P58
P42 = 108612463794649131001183112199859161618563_<42>
P58 = 1611917530744212293292156513540070557954192544839381684071_<58>

Number: 36661_134 N=175074334447915985220800658956999547881339884018263365077774518425860165827877515202679577075009973 ( 99 digits) SNFS difficulty: 136 digits. Divisors found: r1=108612463794649131001183112199859161618563 (pp42) r2=1611917530744212293292156513540070557954192544839381684071 (pp58) Version: GGNFS-0.77.1-20060513-k8 Total time: 5.99 hours. Scaled time: 12.03 units (timescale=2.010). Factorization parameters were as follows: name: 36661_134 n: 175074334447915985220800658956999547881339884018263365077774518425860165827877515202679577075009973 m: 1000000000000000000000000000 deg: 5 c5: 11 c0: -170 skew: 1.73 type: snfs lss: 1 rlim: 1300000 alim: 1300000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [650000, 1175001) Primes: RFBsize:100021, AFBsize:99724, largePrimes:3190511 encountered Relations: rels:3153954, finalFF:278438 Max relations in full relation-set: 28 Initial matrix: 199810 x 278438 with sparse part having weight 23194464. Pruned matrix : 175657 x 176720 with weight 11268879. Total sieving time: 5.57 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.26 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000 total time: 5.99 hours. --------- CPU info (if available) ----------
(11·10¹⁴⁴-17)/3 = 3(6)₁₄₃1_<145> = 157 · 10136260877_<11> · C133
C133 = P61 · P72
P61 = 5065705850886976495988343132418566289486969861509620415150181_<61>
P72 = 454835161040530031250813026453337616614594591416830701515656087243041929_<72>

Number: 36661_144 N=2304061136472133163799949453218864216324962170621676146520944921910783356238101620691422131265770593846200318144699849557627814939149 ( 133 digits) SNFS difficulty: 146 digits. Divisors found: r1=5065705850886976495988343132418566289486969861509620415150181 (pp61) r2=454835161040530031250813026453337616614594591416830701515656087243041929 (pp72) Version: GGNFS-0.77.1-20060513-nocona Total time: 15.29 hours. Scaled time: 39.21 units (timescale=2.564). Factorization parameters were as follows: name: 36661_144 n: 2304061136472133163799949453218864216324962170621676146520944921910783356238101620691422131265770593846200318144699849557627814939149 m: 100000000000000000000000000000 deg: 5 c5: 11 c0: -170 skew: 1.73 type: snfs lss: 1 rlim: 1900000 alim: 1900000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1900000/1900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [950000, 2250001) Primes: RFBsize:142029, AFBsize:142163, largePrimes:4461462 encountered Relations: rels:5018508, finalFF:688348 Max relations in full relation-set: 28 Initial matrix: 284257 x 688348 with sparse part having weight 77522317. Pruned matrix : 203776 x 205261 with weight 29271991. Total sieving time: 14.79 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.35 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000 total time: 15.29 hours. --------- CPU info (if available) ----------
(11·10¹⁶⁰-17)/3 = 3(6)₁₅₉1_<161> = 21766998733_<11> · 629345781923007387639337_<24> · 146878709199615825406227598069_<30> · C98
C98 = P45 · P53
P45 = 957664442926109750412572273548012986189861349_<45>
P53 = 19028797420494901463586438810592233217404823016337961_<53>

Sat Nov 29 14:03:27 2008 Msieve v. 1.38 Sat Nov 29 14:03:27 2008 random seeds: 27020444 ac7423e9 Sat Nov 29 14:03:27 2008 factoring 18223202681252044003716422527687772043697950467962637572786101774796419825519335769749720315369389 (98 digits) Sat Nov 29 14:03:28 2008 searching for 15-digit factors Sat Nov 29 14:03:29 2008 commencing quadratic sieve (98-digit input) Sat Nov 29 14:03:30 2008 using multiplier of 13 Sat Nov 29 14:03:30 2008 using 32kb Intel Core sieve core Sat Nov 29 14:03:30 2008 sieve interval: 36 blocks of size 32768 Sat Nov 29 14:03:30 2008 processing polynomials in batches of 6 Sat Nov 29 14:03:30 2008 using a sieve bound of 2457703 (90588 primes) Sat Nov 29 14:03:30 2008 using large prime bound of 368655450 (28 bits) Sat Nov 29 14:03:30 2008 using double large prime bound of 2629766418374550 (43-52 bits) Sat Nov 29 14:03:30 2008 using trial factoring cutoff of 52 bits Sat Nov 29 14:03:30 2008 polynomial 'A' values have 13 factors Sat Nov 29 19:47:07 2008 91084 relations (22967 full + 68117 combined from 1341174 partial), need 90684 Sat Nov 29 19:47:09 2008 begin with 1364141 relations Sat Nov 29 19:47:11 2008 reduce to 234288 relations in 10 passes Sat Nov 29 19:47:11 2008 attempting to read 234288 relations Sat Nov 29 19:47:14 2008 recovered 234288 relations Sat Nov 29 19:47:14 2008 recovered 219976 polynomials Sat Nov 29 19:47:15 2008 attempting to build 91084 cycles Sat Nov 29 19:47:15 2008 found 91084 cycles in 6 passes Sat Nov 29 19:47:15 2008 distribution of cycle lengths: Sat Nov 29 19:47:15 2008 length 1 : 22967 Sat Nov 29 19:47:15 2008 length 2 : 16339 Sat Nov 29 19:47:15 2008 length 3 : 15478 Sat Nov 29 19:47:15 2008 length 4 : 12139 Sat Nov 29 19:47:15 2008 length 5 : 8966 Sat Nov 29 19:47:15 2008 length 6 : 6133 Sat Nov 29 19:47:15 2008 length 7 : 3870 Sat Nov 29 19:47:15 2008 length 9+: 5192 Sat Nov 29 19:47:15 2008 largest cycle: 20 relations Sat Nov 29 19:47:15 2008 matrix is 90588 x 91084 (24.4 MB) with weight 6028326 (66.18/col) Sat Nov 29 19:47:15 2008 sparse part has weight 6028326 (66.18/col) Sat Nov 29 19:47:16 2008 filtering completed in 3 passes Sat Nov 29 19:47:16 2008 matrix is 85968 x 86032 (23.1 MB) with weight 5709069 (66.36/col) Sat Nov 29 19:47:16 2008 sparse part has weight 5709069 (66.36/col) Sat Nov 29 19:47:17 2008 saving the first 48 matrix rows for later Sat Nov 29 19:47:17 2008 matrix is 85920 x 86032 (14.3 MB) with weight 4507429 (52.39/col) Sat Nov 29 19:47:17 2008 sparse part has weight 3219825 (37.43/col) Sat Nov 29 19:47:17 2008 matrix includes 64 packed rows Sat Nov 29 19:47:17 2008 using block size 34412 for processor cache size 1024 kB Sat Nov 29 19:47:18 2008 commencing Lanczos iteration Sat Nov 29 19:47:18 2008 memory use: 13.8 MB Sat Nov 29 19:48:11 2008 lanczos halted after 1360 iterations (dim = 85918) Sat Nov 29 19:48:11 2008 recovered 17 nontrivial dependencies Sat Nov 29 19:48:12 2008 prp45 factor: 957664442926109750412572273548012986189861349 Sat Nov 29 19:48:12 2008 prp53 factor: 19028797420494901463586438810592233217404823016337961 Sat Nov 29 19:48:12 2008 elapsed time 05:44:45
(11·10¹⁴²-17)/3 = 3(6)₁₄₁1_<143> = 53 · 7852775608472349923_<19> · 2209134768103327026461_<22> · C101
C101 = P36 · P65
P36 = 485358917513402248806445046758915291_<36>
P65 = 82165054748679947348480555740015151916804192014196841159896556469_<65>

Number: 36661_142 N=39879542030248730305952505549511479412491993196918291201620186809045469006365085989027975256569067479 ( 101 digits) Divisors found: r1=485358917513402248806445046758915291 (pp36) r2=82165054748679947348480555740015151916804192014196841159896556469 (pp65) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 9.38 hours. Scaled time: 4.44 units (timescale=0.473). Factorization parameters were as follows: name: 36661_142 n: 39879542030248730305952505549511479412491993196918291201620186809045469006365085989027975256569067479 skew: 2082.32 # norm 1.23e+14 c5: 694260 c4: 3381224247 c3: -23801353228510 c2: -9926089970119084 c1: 21900716397827144332 c0: 6005824574800108133350 # alpha -5.93 Y1: 18094922549 Y0: -8950447478689257681 # Murphy_E 3.20e-09 # M 22311532077896101791765456491507583033848276516459723976941369835133769069388259434247533295035075598 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1500001) Primes: RFBsize:135072, AFBsize:135291, largePrimes:4019335 encountered Relations: rels:4151080, finalFF:480080 Max relations in full relation-set: 28 Initial matrix: 270451 x 480080 with sparse part having weight 37267957. Pruned matrix : 158606 x 160022 with weight 13822330. Total sieving time: 8.40 hours. Total relation processing time: 0.33 hours. Matrix solve time: 0.52 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 9.38 hours. --------- CPU info (if available) ----------
(11·10¹⁴⁰-17)/3 = 3(6)₁₃₉1_<141> = 19937 · 85087 · 38421740169819971_<17> · C115
C115 = P46 · P70
P46 = 4310159630862946677025293676143401052048035549_<46>
P70 = 1305202882733129400361734021700020844652399098566959423983108286773661_<70>

Number: 36661_140 N=5625632775242278895503641449999420022802034367450748010214474861781619745325974560260325834412849046572994244874889 ( 115 digits) SNFS difficulty: 141 digits. Divisors found: r1=4310159630862946677025293676143401052048035549 (pp46) r2=1305202882733129400361734021700020844652399098566959423983108286773661 (pp70) Version: GGNFS-0.77.1-20060513-k8 Total time: 8.34 hours. Scaled time: 16.51 units (timescale=1.979). Factorization parameters were as follows: name: 36661_140 n: 5625632775242278895503641449999420022802034367450748010214474861781619745325974560260325834412849046572994244874889 m: 10000000000000000000000000000 deg: 5 c5: 11 c0: -17 skew: 1.09 type: snfs lss: 1 rlim: 1570000 alim: 1570000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1570000/1570000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [785000, 1485001) Primes: RFBsize:119057, AFBsize:119011, largePrimes:3601073 encountered Relations: rels:3633049, finalFF:338910 Max relations in full relation-set: 28 Initial matrix: 238133 x 338910 with sparse part having weight 29665582. Pruned matrix : 207023 x 208277 with weight 14398096. Total sieving time: 7.81 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.35 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000 total time: 8.34 hours. --------- CPU info (if available) ----------
(11·10¹⁴⁵-17)/3 = 3(6)₁₄₄1_<146> = 64879 · 184043 · 5941489091849_<13> · C123
C123 = P55 · P69
P55 = 2408472121547289871373542292920092592599029191777402247_<55>
P69 = 214590776583004188735108491680326897863212133273819137444936868883071_<69>

Number: 36661_145 N=516835902941348589508791970092043654132499949138794905474603269728655539745759808332443712734409744644426855368404775660537 ( 123 digits) SNFS difficulty: 146 digits. Divisors found: r1=2408472121547289871373542292920092592599029191777402247 (pp55) r2=214590776583004188735108491680326897863212133273819137444936868883071 (pp69) Version: GGNFS-0.77.1-20060513-nocona Total time: 16.26 hours. Scaled time: 41.87 units (timescale=2.575). Factorization parameters were as follows: name: 36661_145 n: 516835902941348589508791970092043654132499949138794905474603269728655539745759808332443712734409744644426855368404775660537 m: 100000000000000000000000000000 deg: 5 c5: 11 c0: -17 skew: 1.09 type: snfs lss: 1 rlim: 1900000 alim: 1900000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1900000/1900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [950000, 2250001) Primes: RFBsize:142029, AFBsize:142108, largePrimes:4619974 encountered Relations: rels:5424522, finalFF:914310 Max relations in full relation-set: 28 Initial matrix: 284202 x 914310 with sparse part having weight 103851334. Pruned matrix : 196007 x 197492 with weight 31950170. Total sieving time: 15.71 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.38 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000 total time: 16.26 hours. --------- CPU info (if available) ----------
Nov 29, 2008 (3rd): By Serge Batalov / Msieve-1.38, GMP-ECM, GMP-ECM 6.2.1
(34·10¹⁷¹-7)/9 = 3(7)₁₇₁_<172> = 3 · 117917 · 471774240006282373987_<21> · C146
C146 = P67 · P80
P67 = 1872405935270522689357066301818617011650603001455113126945903699221_<67>
P80 = 12089393077978057072487459330648278729512042675916075725904232034926240219356201_<80>

SNFS difficulty: 173 digits. Divisors found: r1=1872405935270522689357066301818617011650603001455113126945903699221 (pp67) r2=12089393077978057072487459330648278729512042675916075725904232034926240219356201 (pp80) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.561). Factorization parameters were as follows: n: 22636251353024486990443569623606952139781589234140446733973661409451373214880172157489920365589050835529237199414251961233190439964627012965219421 m: 20000000000000000000000000000000000 deg: 5 c5: 85 c0: -56 skew: 0.92 type: snfs lss: 1 rlim: 5400000 alim: 5400000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5400000/5400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2700000, 6600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1025183 x 1025425 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,173,5,0,0,0,0,0,0,0,0,5400000,5400000,27,27,52,52,2.4,2.4,100000 total time: 60.00 hours.
(11·10¹³⁷-17)/3 = 3(6)₁₃₆1_<138> = 457 · 25282613101_<11> · 70540502984696358345035712479_<29> · C96
C96 = P30 · P67
P30 = 225068055414946500455101512413_<30>
P67 = 1998853021220465571838973633604944432837054563410179737705368297499_<67>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3848341359 Step 1 took 20041ms Step 2 took 8402ms ********** Factor found in step 2: 225068055414946500455101512413 Found probable prime factor of 30 digits: 225068055414946500455101512413 Probable prime cofactor 1998853021220465571838973633604944432837054563410179737705368297499 has 67 digits
(11·10¹⁷⁸-17)/3 = 3(6)₁₇₇1_<179> = 419 · 875323 · 160850805730055940026013323_<27> · C144
C144 = P32 · P113
P32 = 25564389165499286775537881549053_<32>
P113 = 24312544101470344889522583008595898850613862866972797747589406600656397524145120318815543370098395903890481926987_<113>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4102962534 Step 1 took 19473ms Step 2 took 13973ms ********** Factor found in step 2: 25564389165499286775537881549053 Found probable prime factor of 32 digits: 25564389165499286775537881549053 Probable prime cofactor 24312544101470344889522583008595898850613862866972797747589406600656397524145120318815543370098395903890481926987 has 113 digits
(11·10¹¹⁹-17)/3 = 3(6)₁₁₈1_<120> = 95339 · 106454485737497_<15> · C101
C101 = P33 · P69
P33 = 201591097540583059899592638756229_<33>
P69 = 179211354572697613407122682853275301429002320329115019253778195188123_<69>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1995292405 Step 1 took 17977ms Step 2 took 8827ms ********** Factor found in step 2: 201591097540583059899592638756229 Found probable prime factor of 33 digits: 201591097540583059899592638756229 Probable prime cofactor 179211354572697613407122682853275301429002320329115019253778195188123 has 69 digits
(11·10¹⁹⁹-17)/3 = 3(6)₁₉₈1_<200> = 47 · 167 · 809 · 897231271 · C184
C184 = P33 · P152
P33 = 620849510886121014996653223133973_<33>
P152 = 10366158259157309433389410520769455172640438054800073452130936958194069123240087142681724227125048990871767365225139184688088979862324552054539230787287_<152>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3437716281 Step 1 took 29551ms Step 2 took 19011ms ********** Factor found in step 2: 620849510886121014996653223133973 Found probable prime factor of 33 digits: 620849510886121014996653223133973 Probable prime cofactor 10366158259157309433389410520769455172640438054800073452130936958194069123240087142681724227125048990871767365225139184688088979862324552054539230787287 has 152 digits
(11·10¹²⁶-17)/3 = 3(6)₁₂₅1_<127> = 2387939232349009_<16> · C112
C112 = P53 · P60
P53 = 14087763858732627321101608034056487645098264034924687_<53>
P60 = 108994879691177420849768695576009997842287982075496976611867_<60>

SNFS difficulty: 127 digits. Divisors found: r1=14087763858732627321101608034056487645098264034924687 (pp53) r2=108994879691177420849768695576009997842287982075496976611867 (pp60) Version: Msieve-1.38 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.554). Factorization parameters were as follows: n: 1535494126900280097634966453816017651318018197457135481071718189164248955722438293136152218641345776503775460629 m: 10000000000000000000000000 deg: 5 c5: 110 c0: -17 skew: 0.69 type: snfs lss: 1 rlim: 980000 alim: 980000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 980000/980000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [490000, 740001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 130283 x 130515 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,980000,980000,26,26,49,49,2.4,2.4,50000 total time: 2.00 hours.
(11·10¹⁸³-17)/3 = 3(6)₁₈₂1_<184> = 7² · C182
C182 = P31 · P152
P31 = 3223571118646144467773535158267_<31>
P152 = 23213364687364694423071285117959366924827885485071481831459700304705661130344587728525748337616731300987146031291571492942419541892201351763828235946767_<152>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1551405898 Step 1 took 28124ms Step 2 took 18519ms ********** Factor found in step 2: 3223571118646144467773535158267 Found probable prime factor of 31 digits: 3223571118646144467773535158267 Probable prime cofactor 23213364687364694423071285117959366924827885485071481831459700304705661130344587728525748337616731300987146031291571492942419541892201351763828235946767 has 152 digits
(11·10¹⁹⁷-17)/3 = 3(6)₁₉₆1_<198> = 155539 · 23359738123_<11> · C183
C183 = P38 · P145
P38 = 27255285980819546400270342287438245231_<38>
P145 = 3702656423765222191449953291983165896174333193450106467327364998558250919653147210340654247030518342692904270634997845089652018632377252248552123_<145>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2963924375 Step 1 took 30017ms Step 2 took 18759ms ********** Factor found in step 2: 27255285980819546400270342287438245231 Found probable prime factor of 38 digits: 27255285980819546400270342287438245231 Probable prime cofactor 3702656423765222191449953291983165896174333193450106467327364998558250919653147210340654247030518342692904270634997845089652018632377252248552123 has 145 digits
(11·10¹⁶²-17)/3 = 3(6)₁₆₁1_<163> = 229 · 6461041 · 6240128181383599_<16> · 87674584682570693_<17> · C121
C121 = P33 · P88
P33 = 731052435518075457940546324433539_<33>
P88 = 6196089676534327845925392116638898810470739385870543386025115721853192452315915758888913_<88>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2785932908 Step 1 took 22539ms Step 2 took 10481ms ********** Factor found in step 2: 731052435518075457940546324433539 Found probable prime factor of 33 digits: 731052435518075457940546324433539 Probable prime cofactor 6196089676534327845925392116638898810470739385870543386025115721853192452315915758888913 has 88 digits
(11·10¹³⁶-17)/3 = 3(6)₁₃₅1_<137> = 31 · C136
C136 = P36 · P45 · P56
P36 = 110448053390064403764987276605352253_<36>
P45 = 169097178743797369834770845207818629319141307_<45>
P56 = 63330848811647738103769089974633221625010035821186883861_<56>

SNFS difficulty: 137 digits. Divisors found: r1=110448053390064403764987276605352253 (pp36) r2=169097178743797369834770845207818629319141307 (pp45) r3=63330848811647738103769089974633221625010035821186883861 (pp56) Version: Msieve-1.38 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.558). Factorization parameters were as follows: n: 1182795698924731182795698924731182795698924731182795698924731182795698924731182795698924731182795698924731182795698924731182795698924731 m: 1000000000000000000000000000 deg: 5 c5: 110 c0: -17 skew: 0.69 type: snfs lss: 1 rlim: 1350000 alim: 1350000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1350000/1350000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [675000, 1200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 204242 x 204484 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1350000,1350000,26,26,49,49,2.3,2.3,75000 total time: 2.40 hours.
(11·10¹⁷⁷-17)/3 = 3(6)₁₇₆1_<178> = 7 · 103 · 151 · C173
C173 = P31 · P142
P31 = 5556832887851812076162476070701_<31>
P142 = 6060826921814296872914390472209730923182376228115283211788582114118810150036488088797677147810237162263095022865241892934485730623618870717791_<142>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3024729889 Step 1 took 24813ms Step 2 took 17166ms ********** Factor found in step 2: 5556832887851812076162476070701 Found probable prime factor of 31 digits: 5556832887851812076162476070701 Probable prime cofactor 6060826921814296872914390472209730923182376228115283211788582114118810150036488088797677147810237162263095022865241892934485730623618870717791 has 142 digits
(11·10¹⁷¹-17)/3 = 3(6)₁₇₀1_<172> = 7 · 83 · 89 · 37879493 · C160
C160 = P38 · C122
P38 = 83385999899891719865878511313987222461_<38>
C122 = [22449568247593753184083167533291975290884854540034547605076554357224725377782546501707146485392713868517979960233913402073_<122>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=718240080 Step 1 took 24841ms Step 2 took 16811ms ********** Factor found in step 2: 83385999899891719865878511313987222461 Found probable prime factor of 38 digits: 83385999899891719865878511313987222461 Composite cofactor 22449568247593753184083167533291975290884854540034547605076554357224725377782546501707146485392713868517979960233913402073 has 122 digits
(11·10¹⁷⁵-17)/3 = 3(6)₁₇₄1_<176> = 29201 · 2933501 · 588474961 · 32750153572057_<14> · C143
C143 = P40 · P104
P40 = 1109870810744795934280775949391017001109_<40>
P104 = 20011226434218264569802564557860035959581832711691655219245543666648061801344742292178573885646208347277_<104>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2854008978 Step 1 took 19162ms Step 2 took 13841ms ********** Factor found in step 2: 1109870810744795934280775949391017001109 Found probable prime factor of 40 digits: 1109870810744795934280775949391017001109 Probable prime cofactor 20011226434218264569802564557860035959581832711691655219245543666648061801344742292178573885646208347277 has 104 digits
(11·10¹⁶⁵-17)/3 = 3(6)₁₆₄1_<166> = 7 · 179 · 649915076007329393_<18> · 2371711292610209065707512288131_<31> · C115
C115 = P32 · P83
P32 = 26297757323118614671519055263267_<32>
P83 = 72191025851228490858060062036302772473383497526433611076929831488505843922709835817_<83>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2265542806 Step 1 took 12957ms Step 2 took 11043ms ********** Factor found in step 2: 26297757323118614671519055263267 Found probable prime factor of 32 digits: 26297757323118614671519055263267 Probable prime cofactor 72191025851228490858060062036302772473383497526433611076929831488505843922709835817 has 83 digits
(11·10¹⁵⁶-17)/3 = 3(6)₁₅₅1_<157> = 1619 · 2520183811697_<13> · C141
C141 = P39 · P103
P39 = 384665774755265922540245230014640845803_<39>
P103 = 2336193530902535449760773143184500147895336647884600817095444483766385399109723704479196726601653355909_<103>

SNFS difficulty: 157 digits. Divisors found: r1=384665774755265922540245230014640845803 (pp39) r2=2336193530902535449760773143184500147895336647884600817095444483766385399109723704479196726601653355909 (pp103) Version: Msieve-1.38 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.316). Factorization parameters were as follows: n: 898653694542864079694322256023889802504426131617625176516182040256382815496843564561485283796472486632464351154376228436806719058721147899927 m: 10000000000000000000000000000000 deg: 5 c5: 110 c0: -17 skew: 0.69 type: snfs lss: 1 rlim: 2900000 alim: 2900000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 2900000/2900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1450000, 2350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 538024 x 538266 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,52,52,2.4,2.4,100000 total time: 16.00 hours.
Nov 29, 2008 (2nd): By Erik Branger / GGNFS, Msieve
(11·10¹⁰⁹-17)/3 = 3(6)₁₀₈1_<110> = 103 · C108
C108 = P32 · P76
P32 = 55686128876513198408165347351459_<32>
P76 = 6392742002332402976749775654819971481286309835724565111795563996899029411793_<76>

Number: 36661_109 N=355987055016181229773462783171521035598705501618122977346278317152103559870550161812297734627831715210355987 ( 108 digits) SNFS difficulty: 111 digits. Divisors found: r1=55686128876513198408165347351459 r2=6392742002332402976749775654819971481286309835724565111795563996899029411793 Version: Total time: 1.33 hours. Scaled time: 1.04 units (timescale=0.784). Factorization parameters were as follows: n: 355987055016181229773462783171521035598705501618122977346278317152103559870550161812297734627831715210355987 m: 10000000000000000000000 deg: 5 c5: 11 c0: -170 skew: 1.73 type: snfs lss: 1 rlim: 500000 alim: 500000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [250000, 400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 46578 x 46805 Total sieving time: 1.33 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000 total time: 1.33 hours. --------- CPU info (if available) ----------
(11·10¹¹⁰-17)/3 = 3(6)₁₀₉1_<111> = 19 · 43 · 359 · 3413 · 6037 · C98
C98 = P32 · P66
P32 = 80031387200864474276826335774639_<32>
P66 = 758118538179302738564118749660544653553657027889141216006719903893_<66>

Number: 36661_110 N=60673278273181134471086551243482531992281681325714658104638326655668739103398066074480921786769627 ( 98 digits) SNFS difficulty: 111 digits. Divisors found: r1=80031387200864474276826335774639 r2=758118538179302738564118749660544653553657027889141216006719903893 Version: Total time: 0.92 hours. Scaled time: 0.72 units (timescale=0.792). Factorization parameters were as follows: n: 60673278273181134471086551243482531992281681325714658104638326655668739103398066074480921786769627 m: 10000000000000000000000 deg: 5 c5: 11 c0: -17 skew: 1.09 type: snfs lss: 1 rlim: 500000 alim: 500000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [250000, 350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 49726 x 49945 Total sieving time: 0.92 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000 total time: 0.92 hours. --------- CPU info (if available) ----------
(11·10¹²³-17)/3 = 3(6)₁₂₂1_<124> = 7 · 23070065599136107_<17> · C107
C107 = P42 · P65
P42 = 668886617714639215408779843398589318361601_<42>
P65 = 33944706176884080583579775103068072235776993030794292237369985689_<65>

Number: 36661_123 N=22705159703973214452236063687756023515217752056680576539032965607066094137200662015975910403773494297128089 ( 107 digits) SNFS difficulty: 125 digits. Divisors found: r1=668886617714639215408779843398589318361601 r2=33944706176884080583579775103068072235776993030794292237369985689 Version: Total time: 3.21 hours. Scaled time: 2.53 units (timescale=0.787). Factorization parameters were as follows: n: 22705159703973214452236063687756023515217752056680576539032965607066094137200662015975910403773494297128089 m: 5000000000000000000000000 deg: 5 c5: 88 c0: -425 skew: 1.37 type: snfs lss: 1 rlim: 860000 alim: 860000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 860000/860000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [430000, 780001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 136821 x 137069 Total sieving time: 3.21 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,860000,860000,26,26,46,46,2.3,2.3,50000 total time: 3.21 hours. --------- CPU info (if available) ----------
(11·10¹³²-17)/3 = 3(6)₁₃₁1_<133> = 199 · C131
C131 = P59 · P72
P59 = 23458969553533159486261373436846041377784456048254245377789_<59>
P72 = 785433503141268669465977030069961182458200542220187279043681975728135151_<72>

Number: 36661_132 N=18425460636515912897822445561139028475711892797319932998324958123953098827470686767169179229480737018425460636515912897822445561139 ( 131 digits) SNFS difficulty: 133 digits. Divisors found: r1=23458969553533159486261373436846041377784456048254245377789 r2=785433503141268669465977030069961182458200542220187279043681975728135151 Version: Total time: 4.67 hours. Scaled time: 3.69 units (timescale=0.789). Factorization parameters were as follows: n: 18425460636515912897822445561139028475711892797319932998324958123953098827470686767169179229480737018425460636515912897822445561139 m: 200000000000000000000000000 deg: 5 c5: 275 c0: -136 skew: 0.87 type: snfs lss: 1 rlim: 1200000 alim: 1200000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [600000, 1050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 181650 x 181898 Total sieving time: 4.67 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,133,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,47,47,2.3,2.3,75000 total time: 4.67 hours. --------- CPU info (if available) ----------
Nov 29, 2008: By Robert Backstrom / GMP-ECM, Msieve, GGNFS
(11·10¹⁰¹-17)/3 = 3(6)₁₀₀1_<102> = 138913373 · C94
C94 = P32 · P63
P32 = 15362996616432738906443983605163_<32>
P63 = 171811187227657721764594149916169855418000979165505985718980539_<63>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 2639534688043797386351468599547047688969921324037439265596600743879904684674719306302256922857 (94 digits) Using B1=1200000, B2=1426326730, polynomial Dickson(6), sigma=1460276515 Step 1 took 7406ms Step 2 took 3875ms ********** Factor found in step 2: 15362996616432738906443983605163 Found probable prime factor of 32 digits: 15362996616432738906443983605163 Probable prime cofactor 171811187227657721764594149916169855418000979165505985718980539 has 63 digits
(11·10¹¹⁶-17)/3 = 3(6)₁₁₅1_<117> = 53 · 3461 · 84201513116637056621653_<23> · C89
C89 = P35 · P54
P35 = 73977684816291194925607695803441513_<35>
P54 = 320902669571158779992693858038181395877039064352464353_<54>

Sat Nov 29 04:02:03 2008 Sat Nov 29 04:02:03 2008 Sat Nov 29 04:02:03 2008 Msieve v. 1.38 Sat Nov 29 04:02:03 2008 random seeds: 46a032e0 bae8cfdf Sat Nov 29 04:02:03 2008 factoring 23739636546241623339183677581442267087364438127319553630046719804948907173444660052886089 (89 digits) Sat Nov 29 04:02:04 2008 searching for 15-digit factors Sat Nov 29 04:02:04 2008 commencing quadratic sieve (89-digit input) Sat Nov 29 04:02:05 2008 using multiplier of 1 Sat Nov 29 04:02:05 2008 using 64kb Opteron sieve core Sat Nov 29 04:02:05 2008 sieve interval: 15 blocks of size 65536 Sat Nov 29 04:02:05 2008 processing polynomials in batches of 7 Sat Nov 29 04:02:05 2008 using a sieve bound of 1542239 (58667 primes) Sat Nov 29 04:02:05 2008 using large prime bound of 123379120 (26 bits) Sat Nov 29 04:02:05 2008 using double large prime bound of 366635860574400 (42-49 bits) Sat Nov 29 04:02:05 2008 using trial factoring cutoff of 49 bits Sat Nov 29 04:02:05 2008 polynomial 'A' values have 11 factors Sat Nov 29 04:46:12 2008 58992 relations (15923 full + 43069 combined from 620929 partial), need 58763 Sat Nov 29 04:46:12 2008 begin with 636852 relations Sat Nov 29 04:46:13 2008 reduce to 142375 relations in 12 passes Sat Nov 29 04:46:13 2008 attempting to read 142375 relations Sat Nov 29 04:46:14 2008 recovered 142375 relations Sat Nov 29 04:46:14 2008 recovered 117564 polynomials Sat Nov 29 04:46:14 2008 attempting to build 58992 cycles Sat Nov 29 04:46:14 2008 found 58992 cycles in 5 passes Sat Nov 29 04:46:14 2008 distribution of cycle lengths: Sat Nov 29 04:46:14 2008 length 1 : 15923 Sat Nov 29 04:46:14 2008 length 2 : 11484 Sat Nov 29 04:46:14 2008 length 3 : 10494 Sat Nov 29 04:46:14 2008 length 4 : 7817 Sat Nov 29 04:46:14 2008 length 5 : 5387 Sat Nov 29 04:46:14 2008 length 6 : 3465 Sat Nov 29 04:46:14 2008 length 7 : 2026 Sat Nov 29 04:46:14 2008 length 9+: 2396 Sat Nov 29 04:46:14 2008 largest cycle: 16 relations Sat Nov 29 04:46:14 2008 matrix is 58667 x 58992 (14.0 MB) with weight 3438927 (58.29/col) Sat Nov 29 04:46:14 2008 sparse part has weight 3438927 (58.29/col) Sat Nov 29 04:46:15 2008 filtering completed in 3 passes Sat Nov 29 04:46:15 2008 matrix is 54349 x 54413 (13.0 MB) with weight 3197994 (58.77/col) Sat Nov 29 04:46:15 2008 sparse part has weight 3197994 (58.77/col) Sat Nov 29 04:46:15 2008 saving the first 48 matrix rows for later Sat Nov 29 04:46:15 2008 matrix is 54301 x 54413 (8.9 MB) with weight 2565338 (47.15/col) Sat Nov 29 04:46:15 2008 sparse part has weight 2018746 (37.10/col) Sat Nov 29 04:46:15 2008 matrix includes 64 packed rows Sat Nov 29 04:46:15 2008 using block size 21765 for processor cache size 1024 kB Sat Nov 29 04:46:16 2008 commencing Lanczos iteration Sat Nov 29 04:46:16 2008 memory use: 8.4 MB Sat Nov 29 04:46:35 2008 lanczos halted after 860 iterations (dim = 54297) Sat Nov 29 04:46:35 2008 recovered 13 nontrivial dependencies Sat Nov 29 04:46:35 2008 prp35 factor: 73977684816291194925607695803441513 Sat Nov 29 04:46:35 2008 prp54 factor: 320902669571158779992693858038181395877039064352464353 Sat Nov 29 04:46:35 2008 elapsed time 00:44:32
(11·10¹³⁰-17)/3 = 3(6)₁₂₉1_<131> = 83 · 109 · 26529247 · 80947637321_<11> · 381304712411819489_<18> · C91
C91 = P35 · P57
P35 = 26119835504853257224991747510790013_<35>
P57 = 189493854350681751333427226811128589700254398242977884057_<57>

Sat Nov 29 04:56:17 2008 Sat Nov 29 04:56:17 2008 Sat Nov 29 04:56:17 2008 Msieve v. 1.38 Sat Nov 29 04:56:17 2008 random seeds: c7f8ab60 3c0d8e28 Sat Nov 29 04:56:17 2008 factoring 4949548304820429075400004912874089555561546276186079877477197022930758447185728135187522741 (91 digits) Sat Nov 29 04:56:17 2008 searching for 15-digit factors Sat Nov 29 04:56:18 2008 commencing quadratic sieve (91-digit input) Sat Nov 29 04:56:18 2008 using multiplier of 29 Sat Nov 29 04:56:18 2008 using 64kb Opteron sieve core Sat Nov 29 04:56:18 2008 sieve interval: 18 blocks of size 65536 Sat Nov 29 04:56:18 2008 processing polynomials in batches of 6 Sat Nov 29 04:56:18 2008 using a sieve bound of 1716263 (64706 primes) Sat Nov 29 04:56:18 2008 using large prime bound of 164761248 (27 bits) Sat Nov 29 04:56:18 2008 using double large prime bound of 617076512625696 (42-50 bits) Sat Nov 29 04:56:18 2008 using trial factoring cutoff of 50 bits Sat Nov 29 04:56:18 2008 polynomial 'A' values have 12 factors Sat Nov 29 06:06:22 2008 65132 relations (17203 full + 47929 combined from 761920 partial), need 64802 Sat Nov 29 06:06:23 2008 begin with 779123 relations Sat Nov 29 06:06:24 2008 reduce to 162114 relations in 10 passes Sat Nov 29 06:06:24 2008 attempting to read 162114 relations Sat Nov 29 06:06:26 2008 recovered 162114 relations Sat Nov 29 06:06:26 2008 recovered 141428 polynomials Sat Nov 29 06:06:27 2008 attempting to build 65132 cycles Sat Nov 29 06:06:27 2008 found 65132 cycles in 5 passes Sat Nov 29 06:06:27 2008 distribution of cycle lengths: Sat Nov 29 06:06:27 2008 length 1 : 17203 Sat Nov 29 06:06:27 2008 length 2 : 12059 Sat Nov 29 06:06:27 2008 length 3 : 11019 Sat Nov 29 06:06:27 2008 length 4 : 8801 Sat Nov 29 06:06:27 2008 length 5 : 6314 Sat Nov 29 06:06:27 2008 length 6 : 4210 Sat Nov 29 06:06:27 2008 length 7 : 2421 Sat Nov 29 06:06:27 2008 length 9+: 3105 Sat Nov 29 06:06:27 2008 largest cycle: 19 relations Sat Nov 29 06:06:27 2008 matrix is 64706 x 65132 (15.8 MB) with weight 3894254 (59.79/col) Sat Nov 29 06:06:27 2008 sparse part has weight 3894254 (59.79/col) Sat Nov 29 06:06:28 2008 filtering completed in 3 passes Sat Nov 29 06:06:28 2008 matrix is 60808 x 60872 (14.9 MB) with weight 3650160 (59.96/col) Sat Nov 29 06:06:28 2008 sparse part has weight 3650160 (59.96/col) Sat Nov 29 06:06:28 2008 saving the first 48 matrix rows for later Sat Nov 29 06:06:28 2008 matrix is 60760 x 60872 (8.7 MB) with weight 2777885 (45.63/col) Sat Nov 29 06:06:28 2008 sparse part has weight 1912037 (31.41/col) Sat Nov 29 06:06:28 2008 matrix includes 64 packed rows Sat Nov 29 06:06:28 2008 using block size 24348 for processor cache size 1024 kB Sat Nov 29 06:06:29 2008 commencing Lanczos iteration Sat Nov 29 06:06:29 2008 memory use: 8.9 MB Sat Nov 29 06:06:50 2008 lanczos halted after 962 iterations (dim = 60758) Sat Nov 29 06:06:50 2008 recovered 16 nontrivial dependencies Sat Nov 29 06:06:51 2008 prp35 factor: 26119835504853257224991747510790013 Sat Nov 29 06:06:51 2008 prp57 factor: 189493854350681751333427226811128589700254398242977884057 Sat Nov 29 06:06:51 2008 elapsed time 01:10:34
(11·10¹²⁸-17)/3 = 3(6)₁₂₇1_<129> = 19 · C128
C128 = P64 · P65
P64 = 1090272986019580928374762912685367956622743722256057747557165627_<64>
P65 = 17700379502650997404470878861782680291067945187883910993616729797_<65>

Number: n N=19298245614035087719298245614035087719298245614035087719298245614035087719298245614035087719298245614035087719298245614035087719 ( 128 digits) SNFS difficulty: 131 digits. Divisors found: r1=1090272986019580928374762912685367956622743722256057747557165627 (pp64) r2=17700379502650997404470878861782680291067945187883910993616729797 (pp65) Version: GGNFS-0.77.1-20051202-athlon Total time: 2.84 hours. Scaled time: 5.16 units (timescale=1.816). Factorization parameters were as follows: name: KA_3_6_127_1 n: 19298245614035087719298245614035087719298245614035087719298245614035087719298245614035087719298245614035087719298245614035087719 type: snfs skew: 2.74 deg: 5 c5: 11 c0: -1700 m: 100000000000000000000000000 rlim: 800000 alim: 800000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [100000, 550001) Primes: RFBsize:63951, AFBsize:63749, largePrimes:6492214 encountered Relations: rels:5659445, finalFF:184434 Max relations in full relation-set: 48 Initial matrix: 127767 x 184434 with sparse part having weight 26352058. Pruned matrix : 116709 x 117411 with weight 12205227. Total sieving time: 2.63 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.09 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,28,28,56,56,2.5,2.5,50000 total time: 2.84 hours. --------- CPU info (if available) ----------
(10¹⁷⁰+11)/3 = (3)₁₆₉7_<170> = 37 · 163 · 1291 · 23038909286259871_<17> · C147
C147 = P47 · P101
P47 = 11678389683627973847213584321368447993233911399_<47>
P101 = 15911762839346654192692129977862432931562688321822699857420110352345615549508686305420162237407946893_<101>

Number: n N=185823766991360923710679129196544755596402591828367442331733798414239140090653102165527343177897437971975078078955898882605783639735498740459333307 ( 147 digits) SNFS difficulty: 170 digits. Divisors found: Sat Nov 29 17:02:34 2008 prp47 factor: 11678389683627973847213584321368447993233911399 Sat Nov 29 17:02:34 2008 prp101 factor: 15911762839346654192692129977862432931562688321822699857420110352345615549508686305420162237407946893 Sat Nov 29 17:02:34 2008 elapsed time 05:16:03 (Msieve 1.38) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 46.56 hours. Scaled time: 60.72 units (timescale=1.304). Factorization parameters were as follows: name: KA_3_169_7 n: 185823766991360923710679129196544755596402591828367442331733798414239140090653102165527343177897437971975078078955898882605783639735498740459333307 type: snfs skew: 1.62 deg: 5 c5: 1 c0: 11 m: 10000000000000000000000000000000000 rlim: 6000000 alim: 6000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 1900001) Primes: RFBsize:412849, AFBsize:412887, largePrimes:14693738 encountered Relations: rels:13330852, finalFF:847863 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 46.08 hours. Total relation processing time: 0.48 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,56,56,2.5,2.5,100000 total time: 46.56 hours. --------- CPU info (if available) ----------
Nov 28, 2008 (8th): By Erik Branger / GGNFS; Msieve
(32·10¹⁴⁹+31)/9 = 3(5)₁₄₈9_<150> = 23 · 1192127 · 3454681 · 5814839 · C129
C129 = P44 · P86
P44 = 36079668826573699943490114729420937250109313_<44>
P86 = 17891589284599087776495371368847733054140180147919739353006755447057290876475925057937_<86>

Number: 35559_149 N=645522616169409752919180544786267715281071636514574448021532325578189047306661052443515232321172943154564141276747304249108267281 ( 129 digits) SNFS difficulty: 151 digits. Divisors found: r1=36079668826573699943490114729420937250109313 r2=17891589284599087776495371368847733054140180147919739353006755447057290876475925057937 Version: Total time: 24.26 hours. Scaled time: 19.26 units (timescale=0.794). Factorization parameters were as follows: n: 645522616169409752919180544786267715281071636514574448021532325578189047306661052443515232321172943154564141276747304249108267281 m: 1000000000000000000000000000000 deg: 5 c5: 16 c0: 155 skew: 1.57 type: snfs lss: 1 rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1150000, 1850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 332704 x 332952 Total sieving time: 24.26 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 24.26 hours. --------- CPU info (if available) ----------
Nov 28, 2008 (7th): By Sinkiti Sibata / GGNFS
(32·10¹⁵⁸+31)/9 = 3(5)₁₅₇9_<159> = 1847 · 3271 · 782689767414187_<15> · C137
C137 = P57 · P81
P57 = 728383830613617901512898035711531200163111814922121405509_<57>
P81 = 103230986344316631452156190293703543504210710933180145720843938503614168819071729_<81>

Number: 35559_158 N=75191781271495427961526192435963176611571086648507863294028382067951511505660654447069167461791164580416202384221687140995631470166755061 ( 137 digits) SNFS difficulty: 160 digits. Divisors found: r1=728383830613617901512898035711531200163111814922121405509 (pp57) r2=103230986344316631452156190293703543504210710933180145720843938503614168819071729 (pp81) Version: GGNFS-0.77.1-20050930-nocona Total time: 61.27 hours. Scaled time: 61.94 units (timescale=1.011). Factorization parameters were as follows: name: 35559_158 n: 75191781271495427961526192435963176611571086648507863294028382067951511505660654447069167461791164580416202384221687140995631470166755061 m: 40000000000000000000000000000000 deg: 5 c5: 125 c0: 124 skew: 1.00 type: snfs lss: 1 rlim: 3300000 alim: 3300000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3300000/3300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1650000, 3350001) Primes: RFBsize:236900, AFBsize:237133, largePrimes:10009512 encountered Relations: rels:11723424, finalFF:1603464 Max relations in full relation-set: 28 Initial matrix: 474099 x 1603464 with sparse part having weight 209003057. Pruned matrix : 327083 x 329517 with weight 65552425. Total sieving time: 59.47 hours. Total relation processing time: 0.20 hours. Matrix solve time: 1.51 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3300000,3300000,27,27,51,51,2.4,2.4,100000 total time: 61.27 hours. --------- CPU info (if available) ----------
(32·10¹⁵⁵+13)/9 = 3(5)₁₅₄7_<156> = 3 · 9745711663_<10> · 836420183209442561075511309839_<30> · C116
C116 = P41 · P75
P41 = 23094872044969571779279121773911112181383_<41>
P75 = 629553425817664516608346615262883641525165764299729025538826136158686426449_<75>

Number: 35557_155 N=14539455814731205321210177525875969087182313619367490212466311977932541637996102085909142345349193136322821376598967 ( 116 digits) SNFS difficulty: 156 digits. Divisors found: r1=23094872044969571779279121773911112181383 (pp41) r2=629553425817664516608346615262883641525165764299729025538826136158686426449 (pp75) Version: GGNFS-0.77.1-20060513-k8 Total time: 25.53 hours. Scaled time: 50.99 units (timescale=1.997). Factorization parameters were as follows: name: 35557_155 n: 14539455814731205321210177525875969087182313619367490212466311977932541637996102085909142345349193136322821376598967 m: 20000000000000000000000000000000 deg: 5 c5: 1 c0: 13 skew: 1.67 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1400000, 2100001) Primes: RFBsize:203362, AFBsize:202632, largePrimes:7931710 encountered Relations: rels:8033044, finalFF:597631 Max relations in full relation-set: 28 Initial matrix: 406058 x 597631 with sparse part having weight 61275731. Pruned matrix : 323038 x 325132 with weight 32326940. Total sieving time: 23.64 hours. Total relation processing time: 0.18 hours. Matrix solve time: 1.53 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 25.53 hours. --------- CPU info (if available) ----------
Nov 28, 2008 (6th): By Jo Yeong Uk / GGNFS
(32·10¹⁵⁷+31)/9 = 3(5)₁₅₆9_<158> = 3² · 13 · 3343 · 314771 · 107802232591_<12> · 11902574766281436363312409_<26> · C111
C111 = P47 · P64
P47 = 34721041154083197424198540840683236213110001909_<47>
P64 = 6482299664938003634923870800254260917289099912150023501829586029_<64>

Number: 35559_157 N=225072193439412145701799215959772861124655915684613894776517073007926147419114083683529204169407787632869729361 ( 111 digits) Divisors found: r1=34721041154083197424198540840683236213110001909 (pp47) r2=6482299664938003634923870800254260917289099912150023501829586029 (pp64) Version: GGNFS-0.77.1-20050930-nocona Total time: 15.38 hours. Scaled time: 36.67 units (timescale=2.384). Factorization parameters were as follows: name: 35559_157 n: 225072193439412145701799215959772861124655915684613894776517073007926147419114083683529204169407787632869729361 skew: 28795.49 # norm 1.13e+16 c5: 46800 c4: 1274979120 c3: -523803857097587 c2: -954455472874104530 c1: 68225153952563267555272 c0: 198863934818240337723728640 # alpha -6.89 Y1: 444567509023 Y0: -1369034617122522968939 # Murphy_E 9.23e-10 # M 11475828137743923857118331731015828543479728004221583302539558888654103715022607496554975749211705474898107198 type: gnfs rlim: 2100000 alim: 2100000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [1050000, 1950001) Primes: RFBsize:155805, AFBsize:155375, largePrimes:8686731 encountered Relations: rels:8631688, finalFF:456376 Max relations in full relation-set: 28 Initial matrix: 311259 x 456376 with sparse part having weight 50491100. Pruned matrix : 250053 x 251673 with weight 27602004. Polynomial selection time: 0.84 hours. Total sieving time: 13.96 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.35 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000 total time: 15.38 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Nov 28, 2008 (5th): By Tyler Cadigan / GGNFS, Msieve
(43·10¹⁹²-7)/9 = 4(7)₁₉₂_<193> = 4451 · 5827 · 940903127 · 12835951153_<11> · 2701303725402363678544195517_<28> · C139
C139 = P54 · P86
P54 = 135427060717739009170914297860127597169429975010164729_<54>
P86 = 41693801642367404962648784775123910677444951042004634952791915483103489484160391387347_<86>

Number: 47777_192 N=5646469006574256973282355219285673016714439033035136874206463329954028779275555920105596499863540512205308966627980373468257697311316283963 ( 139 digits) SNFS difficulty: 195 digits. Divisors found: r1=135427060717739009170914297860127597169429975010164729 r2=41693801642367404962648784775123910677444951042004634952791915483103489484160391387347 Version: Total time: 593.99 hours. Scaled time: 1495.67 units (timescale=2.518). Factorization parameters were as follows: n: 5646469006574256973282355219285673016714439033035136874206463329954028779275555920105596499863540512205308966627980373468257697311316283963 m: 500000000000000000000000000000000000000 deg: 5 c5: 172 c0: -875 Y0: 500000000000000000000000000000000000000 Y1: -1 skew: 1.38 type: snfs lss: 1 rlim: 12800000 alim: 12800000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 qintsize: 1000000 Factor base limits: 12800000/12800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6400000, 1 ) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2014456 x 2014704 Total sieving time: 593.99 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,195,5,0,0,0,0,0,0,0,0,12800000,12800000,28,28,55,55,2.5,2.5,100000 total time: 593.99 hours. --------- CPU info (if available) ----------
Nov 28, 2008 (4th): By Serge Batalov / Msieve-1.38+pol51 gnfs
8·10¹⁸⁵+9 = 8(0)₁₈₄9_<186> = 7 · 24329 · 53381 · 25502165263849_<14> · 1303028394848660857467715486468010946754987_<43> · C121
C121 = P38 · P84
P38 = 11958203612381011725704592874030579567_<38>
P84 = 221454293090384742218717863326746087344454398748013997486958446978047338608032823703_<84>

Number: 80009_185 N=2648195527610722149244619035624215921962390457850886740531905304699190651782516458062408766925167070534368118892625076601 ( 121 digits) Divisors found: r1=11958203612381011725704592874030579567 (pp38) r2=221454293090384742218717863326746087344454398748013997486958446978047338608032823703 (pp84) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.315). Factorization parameters were as follows: name: 80009_185 n: 2648195527610722149244619035624215921962390457850886740531905304699190651782516458062408766925167070534368118892625076601 skew: 97324.20 # norm 6.02e+16 c5: 31560 c4: -20257094952 c3: -869302950855308 c2: 173746730595733330327 c1: 2705646423516967148423142 c0: -146634980995403207875729446336 # alpha -6.61 Y1: 4019354345677 Y0: -153025594366465211457007 # Murphy_E 2.66e-10 # M 2084414786921268954617093831981252894697800350894014333202808952118001393556414218128011869192530578591410857486809023958 type: gnfs rlim: 5200000 alim: 5200000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5200000/5200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [2600000, 4700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 699597 x 699839 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 1.70 hours. Time per square root: 0.50 hours. Prototype def-par.txt line would be: gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5200000,5200000,27,27,52,52,2.5,2.5,100000 total time: 70.00 hours.
(32·10¹⁶³+31)/9 = 3(5)₁₆₂9_<164> = 3 · 13 · 33533 · 13815635357301430349027_<23> · C136
C136 = P52 · P84
P52 = 7298831326676946646025396317875694511838180349179983_<52>
P84 = 269616373803723615329708115913185862970918638097728700348675818639575345943982545577_<84>

SNFS difficulty: 165 digits. Divisors found: r1=7298831326676946646025396317875694511838180349179983 (pp52) r2=269616373803723615329708115913185862970918638097728700348675818639575345943982545577 (pp84) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.310). Factorization parameters were as follows: n: 1967884435303659598974407641705651605895826214331689001349496161987105599499654836345057185351290971556047757091915941837674076873585191 m: 400000000000000000000000000000000 deg: 5 c5: 125 c0: 124 skew: 1.00 type: snfs lss: 1 rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2000000, 3800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 751201 x 751443 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,52,52,2.4,2.4,100000 total time: 32.00 hours.
(32·10¹⁷²+13)/9 = 3(5)₁₇₁7_<173> = 37 · 2987983 · 15505397 · C158
C158 = P46 · P112
P46 = 3223320654117369921102155773727518551111001831_<46>
P112 = 6434891389908080526697096790304309578136358069732443055338000019495154297132988986043062674697587170436074188981_<112>

SNFS difficulty: 173 digits. Divisors found: r1=3223320654117369921102155773727518551111001831 (pp46) r2=6434891389908080526697096790304309578136358069732443055338000019495154297132988986043062674697587170436074188981 (pp112) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.729). Factorization parameters were as follows: n: 20741718324092745817932403403493671875317896729662839811155637583900644726621173514191415102199691204642649327958919643967405329532734416609470589959731024211 m: 20000000000000000000000000000000000 deg: 5 c5: 100 c0: 13 skew: 0.66 type: snfs lss: 1 rlim: 5500000 alim: 5500000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2750000, 6150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1033757 x 1033999 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,173,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,52,52,2.4,2.4,100000 total time: 52.00 hours.
Nov 28, 2008 (3rd): By Markus Tervooren / GGNFS
(32·10¹⁶⁰+31)/9 = 3(5)₁₅₉9_<161> = 3 · 43 · 139 · 20629781705287_<14> · 2019091759073720141_<19> · C125
C125 = P41 · P84
P41 = 49505366525422020814016668476770343965501_<41>
P84 = 961612254795298853587706824117737416378847326019848732349508624487390819019261139067_<84>

N=47604967128978778980308853599287784927336120234905235004022738211686430159655031390012816340428481995268348789459939011327567 ( 125 digits) SNFS difficulty: 161 digits. Divisors found: r1=49505366525422020814016668476770343965501 (pp41) r2=961612254795298853587706824117737416378847326019848732349508624487390819019261139067 (pp84) Version: GGNFS-0.77.1-20060722-nocona Total time: 30.26 hours. Scaled time: 46.29 units (timescale=1.530). Factorization parameters were as follows: n: 47604967128978778980308853599287784927336120234905235004022738211686430159655031390012816340428481995268348789459939011327567 m: 200000000000000000000000000000000 deg: 5 c5: 1 c0: 31 skew: 1.99 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 qintsize: 5000 type: snfs rlambda: 2.4 alambda: 2.4 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1700000, 1985001) Primes: RFBsize:243539, AFBsize:243245, largePrimes:10208774 encountered Relations: rels:12323629, finalFF:1513653 Max relations in full relation-set: 32 Initial matrix: 486848 x 1513653 with sparse part having weight 217147940. Pruned matrix : 344986 x 347484 with weight 86395308. Total sieving time: 27.94 hours. Total relation processing time: 0.09 hours. Matrix solve time: 2.14 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 30.26 hours. --------- CPU info (if available) ---------- Intel(R) Xeon(R) CPU E5335 @ 2.00GHz stepping 0b Intel(R) Xeon(R) CPU E5335 @ 2.00GHz stepping 0b Intel(R) Xeon(R) CPU E5335 @ 2.00GHz stepping 0b Memory: 16428772k/17825792k available (1928k kernel code, 343260k reserved, 867k data, 176k init) Calibrating delay using timer specific routine.. 3993.74 BogoMIPS (lpj=7987498) Calibrating delay using timer specific routine.. 3990.12 BogoMIPS (lpj=7980241) Calibrating delay using timer specific routine.. 3990.13 BogoMIPS (lpj=7980276) Calibrating delay using timer specific routine.. 3990.04 BogoMIPS (lpj=7980080)
Nov 28, 2008 (2nd): By Robert Backstrom / GGNFS, Msieve
(29·10¹⁶⁶-11)/9 = 3(2)₁₆₅1_<167> = 7 · 31 · 53 · 35251 · 497346601 · 213701737408337603_<18> · C132
C132 = P62 · P71
P62 = 18906556686684146433835881345695559366409569958898328591881699_<62>
P71 = 39552031510187221770337793580470173334223496149600838342975909506856043_<71>

Number: n N=747792725820872276182403763957411243471551527733257813413020576660548430228202239146613462924753798426754801343957204384310879257057 ( 132 digits) SNFS difficulty: 167 digits. Divisors found: Fri Nov 28 03:42:05 2008 prp62 factor: 18906556686684146433835881345695559366409569958898328591881699 Fri Nov 28 03:42:05 2008 prp71 factor: 39552031510187221770337793580470173334223496149600838342975909506856043 Fri Nov 28 03:42:05 2008 elapsed time 02:47:08 (Msieve 1.38) Version: GGNFS-0.77.1-20050930-k8 Total time: 44.06 hours. Scaled time: 36.96 units (timescale=0.839). Factorization parameters were as follows: name: KA_3_2_165_1 n: 747792725820872276182403763957411243471551527733257813413020576660548430228202239146613462924753798426754801343957204384310879257057 type: snfs skew: 0.52 deg: 5 c5: 290 c0: -11 m: 1000000000000000000000000000000000 rlim: 5400000 alim: 5400000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 5400000/5400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 2200001) Primes: RFBsize:374362, AFBsize:373593, largePrimes:15524089 encountered Relations: rels:14102407, finalFF:767427 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 43.53 hours. Total relation processing time: 0.53 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5400000,5400000,28,28,56,56,2.5,2.5,100000 total time: 44.06 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(32·10¹⁵¹+13)/9 = 3(5)₁₅₀7_<152> = 37 · 2137 · 10781 · 158906947 · C135
C135 = P56 · P79
P56 = 35286918260832971119796069080905050350002961841266080149_<56>
P79 = 7438503322170209816946556791363220387621438800981627959820246469138811695379971_<79>

Number: n N=262481858712354698059517611967957792929674054710118423170194967391373575737986775226844972214369983360318353897435684826276256295295679 ( 135 digits) SNFS difficulty: 152 digits. Divisors found: Fri Nov 28 13:16:03 2008 prp56 factor: 35286918260832971119796069080905050350002961841266080149 Fri Nov 28 13:16:03 2008 prp79 factor: 7438503322170209816946556791363220387621438800981627959820246469138811695379971 Fri Nov 28 13:16:03 2008 elapsed time 00:30:14 (Msieve 1.38) Version: GGNFS-0.77.1-20050930-k8 Total time: 12.47 hours. Scaled time: 10.43 units (timescale=0.836). Factorization parameters were as follows: name: KA_3_5_150_7 n: 262481858712354698059517611967957792929674054710118423170194967391373575737986775226844972214369983360318353897435684826276256295295679 type: snfs skew: 1.05 deg: 5 c5: 10 c0: 13 m: 2000000000000000000000000000000 rlim: 2400000 alim: 2400000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 700001) Primes: RFBsize:176302, AFBsize:176888, largePrimes:10574079 encountered Relations: rels:9335262, finalFF:404813 Max relations in full relation-set: 28 Initial matrix: 353256 x 404813 with sparse part having weight 34304116. Pruned matrix : 315684 x 317514 with weight 23782300. Total sieving time: 12.27 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,28,28,56,56,2.5,2.5,100000 total time: 12.47 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(28·10¹⁷⁹+71)/9 = 3(1)₁₇₈9_<180> = 41 · C178
C178 = P78 · P101
P78 = 463075775995206321032650596711128078474740747807397760979408995670133078825749_<78>
P101 = 16386250963897014588548079794123952353280585186116441103459154761169411054261602389191949558824062491_<101>

Number: n N=7588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880759 ( 178 digits) SNFS difficulty: 181 digits. Divisors found: Fri Nov 28 18:24:07 2008 prp78 factor: 463075775995206321032650596711128078474740747807397760979408995670133078825749 Fri Nov 28 18:24:08 2008 prp101 factor: 16386250963897014588548079794123952353280585186116441103459154761169411054261602389191949558824062491 Fri Nov 28 18:24:08 2008 elapsed time 04:22:22 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 31.62 hours. Scaled time: 64.66 units (timescale=2.045). Factorization parameters were as follows: name: KA_3_1_178_9 n: 7588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880758807588075880759 type: snfs skew: 1.91 deg: 5 c5: 14 c0: 355 m: 1000000000000000000000000000000000000 rlim: 8000000 alim: 8000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 2100001) Primes: RFBsize:539777, AFBsize:539736, largePrimes:16473243 encountered Relations: rels:15646828, finalFF:1184593 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 31.20 hours. Total relation processing time: 0.42 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,181,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,56,56,2.5,2.5,100000 total time: 31.62 hours. --------- CPU info (if available) ----------
Nov 28, 2008: Factorizations of 366...661 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.
Nov 27, 2008 (4th): By Jo Yeong Uk / GGNFS
(32·10¹⁵⁰+31)/9 = 3(5)₁₄₉9_<151> = 7 · 15073 · 920219 · 4319202413_<10> · 265240094732112281_<18> · C113
C113 = P43 · P70
P43 = 9328504925290444441822005205016085050202529_<43>
P70 = 3426602734277911210608358720760753470015484796145599102726577084452023_<70>

Number: 35559_150 N=31965080483725198765375891316094958518982027309305547961910175720694233352383936555933314648188090942893133766167 ( 113 digits) SNFS difficulty: 151 digits. Divisors found: r1=9328504925290444441822005205016085050202529 (pp43) r2=3426602734277911210608358720760753470015484796145599102726577084452023 (pp70) Version: GGNFS-0.77.1-20050930-nocona Total time: 9.37 hours. Scaled time: 22.29 units (timescale=2.379). Factorization parameters were as follows: n: 31965080483725198765375891316094958518982027309305547961910175720694233352383936555933314648188090942893133766167 m: 2000000000000000000000000000000 deg: 5 c5: 1 c0: 31 skew: 1.99 type: snfs lss: 1 rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1000000, 1600001) Primes: RFBsize:148933, AFBsize:148876, largePrimes:6640709 encountered Relations: rels:6470040, finalFF:365507 Max relations in full relation-set: 28 Initial matrix: 297873 x 365507 with sparse part having weight 36847502. Pruned matrix : 270279 x 271832 with weight 24272165. Total sieving time: 8.90 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.37 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000 total time: 9.37 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
(32·10¹⁵⁹+31)/9 = 3(5)₁₅₈9_<160> = 71 · 4099 · 2686673839_<10> · 2236273950894083539_<19> · 142399011313204411709_<21> · C107
C107 = P42 · P65
P42 = 691801292122926124619142949686718950073469_<42>
P65 = 20641578597385298121235556805106391775954256529093190003746261231_<65>

Number: 35559_159 N=14279870745128086325073949925715343467378244321563381991867004239842949568432183034744786374363261516380339 ( 107 digits) Divisors found: r1=691801292122926124619142949686718950073469 (pp42) r2=20641578597385298121235556805106391775954256529093190003746261231 (pp65) Version: GGNFS-0.77.1-20050930-nocona Total time: 9.48 hours. Scaled time: 22.54 units (timescale=2.378). Factorization parameters were as follows: name: 35559_159 n: 14279870745128086325073949925715343467378244321563381991867004239842949568432183034744786374363261516380339 skew: 6610.55 # norm 1.46e+14 c5: 25440 c4: -137352764 c3: 14140130325568 c2: 11186446944255427 c1: -256581559691255668326 c0: 88625683951583427259919 # alpha -5.09 Y1: 6223772741 Y0: -223790397110437034630 # Murphy_E 1.59e-09 # M 11583433849997306632283936826464805133153048936625287091066066575029620600574454972810926420293069935986582 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 51 mfba: 51 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 51/51 Sieved algebraic special-q in [900000, 1450001) Primes: RFBsize:135072, AFBsize:134928, largePrimes:5377820 encountered Relations: rels:5449762, finalFF:384816 Max relations in full relation-set: 28 Initial matrix: 270076 x 384816 with sparse part having weight 38468322. Pruned matrix : 215248 x 216662 with weight 19235135. Polynomial selection time: 0.55 hours. Total sieving time: 8.62 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.18 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,51,51,2.6,2.6,50000 total time: 9.48 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Nov 27, 2008 (3rd): By Sinkiti Sibata / GGNFS
(32·10¹⁴²+31)/9 = 3(5)₁₄₁9_<143> = 3 · 64561841 · 104257759 · 377994599 · C118
C118 = P37 · P82
P37 = 1213740532142468235120515988563847529_<37>
P82 = 3837871883887678543854926447937643139346902671587478192888671244047886126346297597_<82>

Number: 35559_142 N=4658180662644448017979591182199206192957275439326873380189147999176379892124261928899928390307204730058222534367087813 ( 118 digits) SNFS difficulty: 143 digits. Divisors found: r1=1213740532142468235120515988563847529 (pp37) r2=3837871883887678543854926447937643139346902671587478192888671244047886126346297597 (pp82) Version: GGNFS-0.77.1-20060513-k8 Total time: 10.65 hours. Scaled time: 21.34 units (timescale=2.003). Factorization parameters were as follows: name: 35559_142 n: 4658180662644448017979591182199206192957275439326873380189147999176379892124261928899928390307204730058222534367087813 m: 20000000000000000000000000000 deg: 5 c5: 100 c0: 31 skew: 0.79 type: snfs lss: 1 rlim: 1730000 alim: 1730000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1730000/1730000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [865000, 1765001) Primes: RFBsize:130213, AFBsize:130606, largePrimes:3697321 encountered Relations: rels:3696975, finalFF:308074 Max relations in full relation-set: 28 Initial matrix: 260883 x 308074 with sparse part having weight 26725119. Pruned matrix : 243807 x 245175 with weight 18265017. Total sieving time: 9.84 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.61 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,1730000,1730000,26,26,48,48,2.3,2.3,100000 total time: 10.65 hours. --------- CPU info (if available) ----------
(32·10¹⁴⁷+13)/9 = 3(5)₁₄₆7_<148> = 577 · 3003359 · 455596076143783_<15> · C124
C124 = P38 · P42 · P45
P38 = 72519105901762960424586887146043201269_<38>
P42 = 237393285754289721684399278650422527285701_<42>
P45 = 261591459190022276610663797779771133402539237_<45>

Number: 35557_147 N=4503440539192284694080254631636649733208049606510396053663091715437410543570581827078424255488049582122601901054604325523853 ( 124 digits) SNFS difficulty: 148 digits. Divisors found: r1=72519105901762960424586887146043201269 (pp38) r2=237393285754289721684399278650422527285701 (pp42) r3=261591459190022276610663797779771133402539237 (pp45) Version: GGNFS-0.77.1-20050930-nocona Total time: 19.05 hours. Scaled time: 19.22 units (timescale=1.009). Factorization parameters were as follows: name: 35557_147 n: 4503440539192284694080254631636649733208049606510396053663091715437410543570581827078424255488049582122601901054604325523853 m: 200000000000000000000000000000 deg: 5 c5: 100 c0: 13 skew: 0.66 type: snfs lss: 1 rlim: 2100000 alim: 2100000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1050000, 2750001) Primes: RFBsize:155805, AFBsize:156147, largePrimes:4692420 encountered Relations: rels:5382227, finalFF:751102 Max relations in full relation-set: 28 Initial matrix: 312016 x 751102 with sparse part having weight 87947570. Pruned matrix : 224954 x 226578 with weight 36935309. Total sieving time: 18.48 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.43 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000 total time: 19.05 hours. --------- CPU info (if available) ----------
(32·10¹³⁸+13)/9 = 3(5)₁₃₇7_<139> = 151 · 239070938762608352011_<21> · C116
C116 = P35 · P82
P35 = 38286075216383022257640191847520543_<35>
P82 = 2572544443884594548631930409137038593963600087065351749783286536175566198407004759_<82>

Number: 35557_138 N=98492630076053819893362066775404397948947703796013667845436549228724048750081144551122623075631307653019377351264137 ( 116 digits) SNFS difficulty: 140 digits. Divisors found: r1=38286075216383022257640191847520543 (pp35) r2=2572544443884594548631930409137038593963600087065351749783286536175566198407004759 (pp82) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 11.96 hours. Scaled time: 5.64 units (timescale=0.472). Factorization parameters were as follows: name: 35557_138 n: 98492630076053819893362066775404397948947703796013667845436549228724048750081144551122623075631307653019377351264137 m: 4000000000000000000000000000 deg: 5 c5: 125 c0: 52 skew: 0.84 type: snfs lss: 1 rlim: 1510000 alim: 1510000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1510000/1510000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [755000, 1730001) Primes: RFBsize:114886, AFBsize:114462, largePrimes:3597792 encountered Relations: rels:3646300, finalFF:319530 Max relations in full relation-set: 28 Initial matrix: 229414 x 319530 with sparse part having weight 29910094. Pruned matrix : 203028 x 204239 with weight 15985370. Total sieving time: 10.78 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.94 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1510000,1510000,26,26,48,48,2.3,2.3,75000 total time: 11.96 hours. --------- CPU info (if available) ----------
(32·10¹⁴³+13)/9 = 3(5)₁₄₂7_<144> = 3² · 43 · 136300339079_<12> · C130
C130 = P54 · P77
P54 = 129540884783737232563732791036117978164375414441872727_<54>
P77 = 52034658491669865443373273867237919313125763903812941156376897881115098465367_<77>

Number: 35557_143 N=6740615700430520249355904501258211265810098697425404834449623922044888793184621364778853022916598827039769466350315646703231345809 ( 130 digits) SNFS difficulty: 145 digits. Divisors found: r1=129540884783737232563732791036117978164375414441872727 (pp54) r2=52034658491669865443373273867237919313125763903812941156376897881115098465367 (pp77) Version: GGNFS-0.77.1-20060513-k8 Total time: 17.48 hours. Scaled time: 34.27 units (timescale=1.960). Factorization parameters were as follows: name: 35557_143 n: 6740615700430520249355904501258211265810098697425404834449623922044888793184621364778853022916598827039769466350315646703231345809 m: 40000000000000000000000000000 deg: 5 c5: 125 c0: 52 skew: 0.84 type: snfs lss: 1 rlim: 1830000 alim: 1830000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1830000/1830000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [915000, 2415001) Primes: RFBsize:137166, AFBsize:136949, largePrimes:4152822 encountered Relations: rels:4421422, finalFF:440986 Max relations in full relation-set: 28 Initial matrix: 274181 x 440986 with sparse part having weight 48070702. Pruned matrix : 226240 x 227674 with weight 23821835. Total sieving time: 16.49 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.74 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1830000,1830000,26,26,49,49,2.3,2.3,100000 total time: 17.48 hours. --------- CPU info (if available) ----------
(32·10¹⁴⁴+13)/9 = 3(5)₁₄₃7_<145> = 1562829649_<10> · C136
C136 = P53 · P84
P53 = 21343091280175666099265930659020264876344915006263847_<53>
P84 = 106595410233811335107263401150127469936167809467849002202851268941550486159081360419_<84>

Number: 35557_144 N=2275075570668006667408416664582715217962668403122646130164091579475502742753222207109250686832570806669892884503086078549022687216471893 ( 136 digits) SNFS difficulty: 146 digits. Divisors found: r1=21343091280175666099265930659020264876344915006263847 (pp53) r2=106595410233811335107263401150127469936167809467849002202851268941550486159081360419 (pp84) Version: GGNFS-0.77.1-20060513-k8 Total time: 14.18 hours. Scaled time: 27.80 units (timescale=1.960). Factorization parameters were as follows: name: 35557_144 n: 2275075570668006667408416664582715217962668403122646130164091579475502742753222207109250686832570806669892884503086078549022687216471893 m: 100000000000000000000000000000 deg: 5 c5: 16 c0: 65 skew: 1.32 type: snfs lss: 1 rlim: 1910000 alim: 1910000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1910000/1910000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [955000, 2055001) Primes: RFBsize:142718, AFBsize:142665, largePrimes:4190102 encountered Relations: rels:4488048, finalFF:534806 Max relations in full relation-set: 28 Initial matrix: 285447 x 534806 with sparse part having weight 51597395. Pruned matrix : 216011 x 217502 with weight 20112430. Total sieving time: 13.43 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.53 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1910000,1910000,26,26,49,49,2.3,2.3,100000 total time: 14.18 hours. --------- CPU info (if available) ----------
Nov 27, 2008 (2nd): By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38
(32·10²⁰¹+13)/9 = 3(5)₂₀₀7_<202> = 71 · C200
C200 = P35 · P165
P35 = 64499300335345945772569335465848633_<35>
P165 = 776415356460893542572148430011329803890783961378327293176367619348587721447168535503721077213200924311601722917814388070780548658836862919766647808745906924624959499_<165>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2420471301 Step 1 took 35354ms Step 2 took 21406ms ********** Factor found in step 2: 64499300335345945772569335465848633 Found probable prime factor of 35 digits: 64499300335345945772569335465848633 Probable prime cofactor 776415356460893542572148430011329803890783961378327293176367619348587721447168535503721077213200924311601722917814388070780548658836862919766647808745906924624959499 has 165 digits
(32·10¹⁸⁹+13)/9 = 3(5)₁₈₈7_<190> = 19 · 107 · C187
C187 = P39 · P148
P39 = 843460198256475257121613143362568122851_<39>
P148 = 2073506955858448830349465499436664370903520495707406284060409753621333767261713347013056871399165319114052676049692680217196117332798366844122275079_<148>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3643605157 Step 1 took 28189ms Step 2 took 19369ms ********** Factor found in step 2: 843460198256475257121613143362568122851 Found probable prime factor of 39 digits: 843460198256475257121613143362568122851 Probable prime cofactor 2073506955858448830349465499436664370903520495707406284060409753621333767261713347013056871399165319114052676049692680217196117332798366844122275079 has 148 digits
(32·10¹⁶⁸+13)/9 = 3(5)₁₆₇7_<169> = 2293 · C166
C166 = P68 · P98
P68 = 34830569746839257317899826291328772117731947319522284446012964814699_<68>
P98 = 44518737073861990630104024619714585669202122565337947057601576528643764758484259563116570090807251_<98>

SNFS difficulty: 170 digits. Divisors found: r1=34830569746839257317899826291328772117731947319522284446012964814699 (pp68) r2=44518737073861990630104024619714585669202122565337947057601576528643764758484259563116570090807251 (pp98) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.949). Factorization parameters were as follows: n: 1550612976692348694093133691912584193438968842370499588118428066094878131511363085719823617773901245336046906042544943547996317294180355671851528807481707612540582449 m: 4000000000000000000000000000000000 deg: 5 c5: 125 c0: 52 skew: 0.84 type: snfs lss: 1 rlim: 4800000 alim: 4800000 lpbr: 27 lpba: 27 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 53/53 Sieved rational special-q in [2400000, 5400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 924774 x 925016 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,53,53,2.5,2.5,200000 total time: 60.00 hours.
(32·10¹⁶¹+31)/9 = 3(5)₁₆₀9_<162> = 19 · 47692016535428836243_<20> · C141
C141 = P66 · P76
P66 = 110241649022448520071238394292360412717056973196080358021493292843_<66>
P76 = 3559282679293368344699238534100485608179773689995381905642703269366099354989_<76>

SNFS difficulty: 162 digits. Divisors found: r1=110241649022448520071238394292360412717056973196080358021493292843 (pp66) r2=3559282679293368344699238534100485608179773689995381905642703269366099354989 (pp76) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.729). Factorization parameters were as follows: n: 392381191902339709749372813102397984185725242296439646480483642273917995502467744884092300496990794306058047534341998381451290475411990043727 m: 200000000000000000000000000000000 deg: 5 c5: 10 c0: 31 skew: 1.25 type: snfs lss: 1 rlim: 3600000 alim: 3600000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1800000, 3100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 689147 x 689389 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3600000,3600000,27,27,52,52,2.4,2.4,100000 total time: 19.00 hours.
Nov 27, 2008: By Robert Backstrom / GGNFS, Msieve
(14·10¹⁷⁵-23)/9 = 1(5)₁₇₄3_<176> = 13 · 7573 · C171
C171 = P43 · P128
P43 = 2038700949876497258819164740062522064954709_<43>
P128 = 77503388727423169575714188322817654539111949909475491882640338731051584806905658501368959790339414055676600291226770718963064333_<128>

Number: n N=158006232217245025907379003906139783599178819038848089422498507405413519238951696366195243786687072042941579452869562469456831004434332045582540762786372188194451498294097 ( 171 digits) SNFS difficulty: 176 digits. Divisors found: Thu Nov 27 04:51:58 2008 prp43 factor: 2038700949876497258819164740062522064954709 Thu Nov 27 04:51:58 2008 prp128 factor: 77503388727423169575714188322817654539111949909475491882640338731051584806905658501368959790339414055676600291226770718963064333 Thu Nov 27 04:51:59 2008 elapsed time 03:36:08 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 19.92 hours. Scaled time: 40.86 units (timescale=2.051). Factorization parameters were as follows: name: KA_1_5_174_3 n: 158006232217245025907379003906139783599178819038848089422498507405413519238951696366195243786687072042941579452869562469456831004434332045582540762786372188194451498294097 type: snfs skew: 1.10 deg: 5 c5: 14 c0: -23 m: 100000000000000000000000000000000000 rlim: 7500000 alim: 7500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 7500000/7500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 3800001) Primes: RFBsize:508261, AFBsize:508901, largePrimes:18196504 encountered Relations: rels:17583392, finalFF:1197106 Max relations in full relation-set: 28 Initial matrix: 1017230 x 1197106 with sparse part having weight 109758757. Pruned matrix : Total sieving time: 19.33 hours. Total relation processing time: 0.59 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,176,5,0,0,0,0,0,0,0,0,7500000,7500000,28,28,56,56,2.5,2.5,100000 total time: 19.92 hours. --------- CPU info (if available) ----------
9·10¹⁶⁷+1 = 9(0)₁₆₆1_<168> = 65011 · 331853765402124003677_<21> · C143
C143 = P55 · P88
P55 = 7113900758268929663283411570479354669535798745893423331_<55>
P88 = 5864096533496964606518020454924687639490103035820928855353490102504942263905443892896093_<88>

Number: n N=41716600776206258411222477166102973461160042517623071486739187464549952517470294390048761365003310345273758999726780709270940796628119644945783 ( 143 digits) SNFS difficulty: 167 digits. Divisors found: Thu Nov 27 10:01:19 2008 prp55 factor: 7113900758268929663283411570479354669535798745893423331 Thu Nov 27 10:01:19 2008 prp88 factor: 5864096533496964606518020454924687639490103035820928855353490102504942263905443892896093 Thu Nov 27 10:01:19 2008 elapsed time 02:38:18 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 31.92 hours. Scaled time: 57.87 units (timescale=1.813). Factorization parameters were as follows: name: KA_9_0_166_1 n: 41716600776206258411222477166102973461160042517623071486739187464549952517470294390048761365003310345273758999726780709270940796628119644945783 type: snfs skew: 0.26 deg: 5 c5: 900 c0: 1 m: 1000000000000000000000000000000000 rlim: 5500000 alim: 5500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 1850001) Primes: RFBsize:380800, AFBsize:379512, largePrimes:14682360 encountered Relations: rels:13224417, finalFF:760889 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 31.46 hours. Total relation processing time: 0.45 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,56,56,2.5,2.5,100000 total time: 31.92 hours. --------- CPU info (if available) ----------
(29·10¹⁶²-11)/9 = 3(2)₁₆₁1_<163> = 893147 · 19471057 · 746734138448512777471322756059_<30> · C120
C120 = P53 · P67
P53 = 46463222638182568129303288420608644739547623874362397_<53>
P67 = 5340324918609786317635870057618451405996157273164823665163903114313_<67>

Number: n N=248128705653600704252183940981166727591290446648117130564206869724052667609229038959837362742059371119512152905479688261 ( 120 digits) SNFS difficulty: 163 digits. Divisors found: Thu Nov 27 22:04:17 2008 prp53 factor: 46463222638182568129303288420608644739547623874362397 Thu Nov 27 22:04:17 2008 prp67 factor: 5340324918609786317635870057618451405996157273164823665163903114313 Thu Nov 27 22:04:17 2008 elapsed time 02:32:33 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 42.18 hours. Scaled time: 61.20 units (timescale=1.451). Factorization parameters were as follows: name: KA_3_2_161_1 n: 248128705653600704252183940981166727591290446648117130564206869724052667609229038959837362742059371119512152905479688261 type: snfs skew: 0.33 deg: 5 c5: 2900 c0: -11 m: 100000000000000000000000000000000 rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 1800001) Primes: RFBsize:315948, AFBsize:316467, largePrimes:14976512 encountered Relations: rels:13784661, finalFF:723023 Max relations in full relation-set: 28 Initial matrix: 632482 x 723023 with sparse part having weight 64151002. Pruned matrix : 558893 x 562119 with weight 45340058. Total sieving time: 41.44 hours. Total relation processing time: 0.73 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.5,2.5,100000 total time: 42.18 hours. --------- CPU info (if available) ----------
Nov 26, 2008 (6th): By Robert Backstrom / GGNFS, Msieve
(31·10¹⁶²+41)/9 = 3(4)₁₆₁9_<163> = 4829107 · 227519218577615844600233_<24> · C133
C133 = P64 · P69
P64 = 4497256276942913708784333111919888344610032022987466112890666921_<64>
P69 = 697086435613153702704174629418486140293389147332010155586147216393899_<69>

Number: n N=3134976348133017753986237508264591675227397506931118169753747860898160990515607185310712968530556574409882478282528797528962745514979 ( 133 digits) SNFS difficulty: 163 digits. Divisors found: Thu Nov 27 01:18:58 2008 prp64 factor: 4497256276942913708784333111919888344610032022987466112890666921 Thu Nov 27 01:18:58 2008 prp69 factor: 697086435613153702704174629418486140293389147332010155586147216393899 Thu Nov 27 01:18:58 2008 elapsed time 02:47:55 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 46.31 hours. Scaled time: 93.82 units (timescale=2.026). Factorization parameters were as follows: name: KA_3_4_161_9 n: 3134976348133017753986237508264591675227397506931118169753747860898160990515607185310712968530556574409882478282528797528962745514979 type: snfs skew: 0.42 deg: 5 c5: 3100 c0: 41 m: 100000000000000000000000000000000 rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 2400001) Primes: RFBsize:315948, AFBsize:316018, largePrimes:15816324 encountered Relations: rels:14466655, finalFF:677553 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 45.67 hours. Total relation processing time: 0.63 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.5,2.5,100000 total time: 46.31 hours. --------- CPU info (if available) ----------
Nov 26, 2008 (5th): By Jo Yeong Uk / GGNFS
(28·10¹⁶⁵+71)/9 = 3(1)₁₆₄9_<166> = 1753 · 6055958639980063027_<19> · 965316807436900108524947_<24> · C120
C120 = P35 · P85
P35 = 70439990548456091885222669101231123_<35>
P85 = 4309843978488043509530024860013260980329590471359429014805762306586306512837214055029_<85>

Number: 31119_165 N=303585369110018185007471879360898991168929903700924426959244422935273048194869215246139424974107724672809347382969467567 ( 120 digits) Divisors found: r1=70439990548456091885222669101231123 (pp35) r2=4309843978488043509530024860013260980329590471359429014805762306586306512837214055029 (pp85) Version: GGNFS-0.77.1-20050930-nocona Total time: 40.96 hours. Scaled time: 97.08 units (timescale=2.370). Factorization parameters were as follows: name: 31119_165 n: 303585369110018185007471879360898991168929903700924426959244422935273048194869215246139424974107724672809347382969467567 skew: 33667.21 # norm 1.82e+16 c5: 32340 c4: -23522374526 c3: 310860150727100 c2: 20865714667004567049 c1: -32102243520844357032692 c0: -2872046884747467271572696700 # alpha -5.20 Y1: 976166667797 Y0: -98743561855902881885457 # Murphy_E 2.75e-10 # M 153187704591743685195168053080016067196268183713315786138378510697769178895803432423620387704969606083977056054982934738 type: gnfs rlim: 4200000 alim: 4200000 lpbr: 27 lpba: 27 mfbr: 53 mfba: 53 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4200000/4200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 53/53 Sieved algebraic special-q in [2100000, 4400001) Primes: RFBsize:296314, AFBsize:297542, largePrimes:9896798 encountered Relations: rels:10038568, finalFF:728716 Max relations in full relation-set: 28 Initial matrix: 593938 x 728716 with sparse part having weight 78608378. Pruned matrix : 495863 x 498896 with weight 56165481. Polynomial selection time: 2.65 hours. Total sieving time: 35.87 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.08 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4200000,4200000,27,27,53,53,2.4,2.4,100000 total time: 40.96 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Nov 26, 2008 (4th): By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1
(32·10¹⁰⁵+13)/9 = 3(5)₁₀₄7_<106> = 6943591 · 11775493 · C92
C92 = P35 · P58
P35 = 16322666212462824649542261200640023_<35>
P58 = 2664116050279468052227828533131936012933075971887327880993_<58>

SNFS difficulty: 106 digits. Divisors found: r1=16322666212462824649542261200640023 (pp35) r2=2664116050279468052227828533131936012933075971887327880993 (pp58) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.565). Factorization parameters were as follows: n: 43485477039976584910743136045130133133538428294391933903186090881596753760752964623976782839 m: 200000000000000000000000000 deg: 4 c4: 20 c0: 13 skew: 0.90 type: snfs lss: 1 rlim: 420000 alim: 420000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 420000/420000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [210000, 270001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 38130 x 38343 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,106,4,0,0,0,0,0,0,0,0,420000,420000,25,25,46,46,2.2,2.2,20000 total time: 0.50 hours.
(32·10¹⁷⁰+13)/9 = 3(5)₁₆₉7_<171> = 3² · 7 · 5540993 · 12984208595306517726286012309466401_<35> · C128
C128 = P29 · P99
P29 = 79463930140396661143010131997_<29>
P99 = 987174192828764409699802414185584254672009061795451677369777853855095127393439210182651571314227959_<99>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4231249235 Step 1 took 27069ms Step 2 took 20682ms ********** Factor found in step 2: 79463930140396661143010131997 Found probable prime factor of 29 digits: 79463930140396661143010131997
(32·10¹⁵⁰+13)/9 = 3(5)₁₄₉7_<151> = 34178423 · C144
C144 = P52 · P92
P52 = 2431428001729590940164509177974037642037881794664501_<52>
P92 = 42785246111212653779850385352873604265492028686791920253084903971196032603178702127108172759_<92>

SNFS difficulty: 151 digits. Divisors found: r1=2431428001729590940164509177974037642037881794664501 (pp52) r2=42785246111212653779850385352873604265492028686791920253084903971196032603178702127108172759 (pp92) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.950). Factorization parameters were as follows: n: 104029245455694534401296266815925227315360792262286517887485784688063447384788805368684083392482899388177024889520372416116318636338357552528259 m: 2000000000000000000000000000000 deg: 5 c5: 1 c0: 13 skew: 1.67 type: snfs lss: 1 rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1150000, 1750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 289384 x 289626 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,52,52,2.4,2.4,200000 total time: 10.00 hours.
(32·10¹⁷⁶+31)/9 = 3(5)₁₇₅9_<177> = 857 · 1303 · C171
C171 = P40 · P131
P40 = 3660718354755801093405249716097352669909_<40>
P131 = 86979301255766846910552733876279826203666396318195941678536718624178967053141838401347217342937724437358746417149543025182392182581_<131>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3906121173 Step 1 took 24827ms Step 2 took 17271ms ********** Factor found in step 2: 3660718354755801093405249716097352669909 Found probable prime factor of 40 digits: 3660718354755801093405249716097352669909 Probable prime cofactor 86979301255766846910552733876279826203666396318195941678536718624178967053141838401347217342937724437358746417149543025182392182581 has 131 digits
(32·10¹⁵⁹+13)/9 = 3(5)₁₅₈7_<160> = 23 · 59 · 489677 · C151
C151 = P61 · P91
P61 = 1232966069094936177518596294215111397980392397178880244356891_<61>
P91 = 4339770769793435292184566514528285478018485043899804024027687412872122711201864678555927143_<91>

SNFS difficulty: 161 digits. Divisors found: r1=1232966069094936177518596294215111397980392397178880244356891 (pp61) r2=4339770769793435292184566514528285478018485043899804024027687412872122711201864678555927143 (pp91) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.949). Factorization parameters were as follows: n: 5350790106805317102401796263181789103694200689326538071352094150203217297960148837249875002658694735842746643525823775285104514761742272980566285992413 m: 100000000000000000000000000000000 deg: 5 c5: 16 c0: 65 skew: 1.32 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1700000, 2900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 503048 x 503290 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,52,52,2.5,2.5,200000 total time: 22.00 hours.
(32·10¹⁵³+13)/9 = 3(5)₁₅₂7_<154> = 19 · 218143 · 70572269 · C140
C140 = P42 · P98
P42 = 403967241451444975239778660111155267040127_<42>
P98 = 30090704578648225872257958579041618055553664570878690395590884572436070064354330906165968391395267_<98>

SNFS difficulty: 155 digits. Divisors found: r1=403967241451444975239778660111155267040127 (pp42) r2=30090704578648225872257958579041618055553664570878690395590884572436070064354330906165968391395267 (pp98) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.723). Factorization parameters were as follows: n: 12155658921966888698616208655832446688236837622138948118055634331019789700340514206626868868857159960301790182378014050733043219562806878909 m: 4000000000000000000000000000000 deg: 5 c5: 125 c0: 52 skew: 0.84 type: snfs lss: 1 rlim: 2700000 alim: 2700000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 2700000/2700000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1350000, 2250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 563951 x 564193 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,2700000,2700000,27,27,52,52,2.5,2.5,100000 total time: 13.00 hours.
(32·10²⁰⁰+31)/9 = 3(5)₁₉₉9_<201> = 47 · 18951629 · 486479627 · 3127490721447603892747013_<25> · C159
C159 = P31 · P128
P31 = 4028141074602949806622803794063_<31>
P128 = 65132493605364354978645976959047691248910542452002211669809096765307018582702503470064768992992787394098368670588376753466133461_<128>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=251454589 Step 1 took 24715ms Step 2 took 16344ms ********** Factor found in step 2: 4028141074602949806622803794063 Found probable prime factor of 31 digits: 4028141074602949806622803794063 Probable prime cofactor 65132493605364354978645976959047691248910542452002211669809096765307018582702503470064768992992787394098368670588376753466133461 has 128 digits
Nov 26, 2008 (3rd): By Erik Branger / GGNFS, Msieve
8·10¹⁶⁸+3 = 8(0)₁₆₇3_<169> = 11 · 7508952959070127_<16> · 67190157772167649_<17> · C136
C136 = P50 · P87
P50 = 13469805809745432155725685004278020183984235651737_<50>
P87 = 107016544227351834704803055140285312688017262106116130497648324056315093035478326557023_<87>

Number: 80003_168 N=1441492069172462733055271981772212297398850822494070561575278242939498872337270030684777421160455311668790312909413094797598647699498951 ( 136 digits) SNFS difficulty: 170 digits. Divisors found: r1=13469805809745432155725685004278020183984235651737 r2=107016544227351834704803055140285312688017262106116130497648324056315093035478326557023 Version: Total time: 78.19 hours. Scaled time: 61.54 units (timescale=0.787). Factorization parameters were as follows: n: 1441492069172462733055271981772212297398850822494070561575278242939498872337270030684777421160455311668790312909413094797598647699498951 m: 10000000000000000000000000000000000 deg: 5 c5: 2 c0: 75 skew: 2.06 type: snfs lss: 1 rlim: 4800000 alim: 4800000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2400000, 4400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 809243 x 809491 Total sieving time: 78.19 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,52,52,2.4,2.4,100000 total time: 78.19 hours. --------- CPU info (if available) ----------
(32·10¹³⁶+31)/9 = 3(5)₁₃₅9_<137> = 3 · 496891 · 1122571 · 4761415135792806704700849085613258322433_<40> · C85
C85 = P35 · P50
P35 = 92123373788344372285635615769596739_<35>
P50 = 48440139168210650866664274877353596332333457620279_<50>

Tue Nov 25 20:57:27 2008 Msieve v. 1.38 Tue Nov 25 20:57:27 2008 random seeds: cf745a60 a52fd4cc Tue Nov 25 20:57:27 2008 factoring 4462469046952490638354343160769488971248707524461871437573226959519017881746418670181 (85 digits) Tue Nov 25 20:57:28 2008 searching for 15-digit factors Tue Nov 25 20:57:30 2008 commencing quadratic sieve (85-digit input) Tue Nov 25 20:57:30 2008 using multiplier of 1 Tue Nov 25 20:57:30 2008 using 64kb Pentium 4 sieve core Tue Nov 25 20:57:30 2008 sieve interval: 6 blocks of size 65536 Tue Nov 25 20:57:30 2008 processing polynomials in batches of 17 Tue Nov 25 20:57:30 2008 using a sieve bound of 1434241 (54676 primes) Tue Nov 25 20:57:30 2008 using large prime bound of 116173521 (26 bits) Tue Nov 25 20:57:30 2008 using double large prime bound of 328997602795950 (41-49 bits) Tue Nov 25 20:57:30 2008 using trial factoring cutoff of 49 bits Tue Nov 25 20:57:30 2008 polynomial 'A' values have 11 factors Tue Nov 25 21:50:59 2008 54899 relations (15846 full + 39053 combined from 576302 partial), need 54772 Tue Nov 25 21:51:02 2008 begin with 592148 relations Tue Nov 25 21:51:02 2008 reduce to 130381 relations in 10 passes Tue Nov 25 21:51:02 2008 attempting to read 130381 relations Tue Nov 25 21:51:06 2008 recovered 130381 relations Tue Nov 25 21:51:06 2008 recovered 111038 polynomials Tue Nov 25 21:51:07 2008 attempting to build 54899 cycles Tue Nov 25 21:51:07 2008 found 54899 cycles in 5 passes Tue Nov 25 21:51:07 2008 distribution of cycle lengths: Tue Nov 25 21:51:07 2008 length 1 : 15846 Tue Nov 25 21:51:07 2008 length 2 : 10901 Tue Nov 25 21:51:07 2008 length 3 : 9452 Tue Nov 25 21:51:07 2008 length 4 : 7155 Tue Nov 25 21:51:07 2008 length 5 : 4909 Tue Nov 25 21:51:07 2008 length 6 : 2926 Tue Nov 25 21:51:07 2008 length 7 : 1730 Tue Nov 25 21:51:07 2008 length 9+: 1980 Tue Nov 25 21:51:07 2008 largest cycle: 16 relations Tue Nov 25 21:51:07 2008 matrix is 54676 x 54899 (11.8 MB) with weight 2881914 (52.49/col) Tue Nov 25 21:51:07 2008 sparse part has weight 2881914 (52.49/col) Tue Nov 25 21:51:08 2008 filtering completed in 3 passes Tue Nov 25 21:51:08 2008 matrix is 49850 x 49914 (10.9 MB) with weight 2649803 (53.09/col) Tue Nov 25 21:51:08 2008 sparse part has weight 2649803 (53.09/col) Tue Nov 25 21:51:08 2008 saving the first 48 matrix rows for later Tue Nov 25 21:51:08 2008 matrix is 49802 x 49914 (6.4 MB) with weight 2011559 (40.30/col) Tue Nov 25 21:51:08 2008 sparse part has weight 1389929 (27.85/col) Tue Nov 25 21:51:08 2008 matrix includes 64 packed rows Tue Nov 25 21:51:08 2008 using block size 19965 for processor cache size 512 kB Tue Nov 25 21:51:09 2008 commencing Lanczos iteration Tue Nov 25 21:51:09 2008 memory use: 6.8 MB Tue Nov 25 21:51:32 2008 lanczos halted after 790 iterations (dim = 49799) Tue Nov 25 21:51:32 2008 recovered 15 nontrivial dependencies Tue Nov 25 21:51:34 2008 prp35 factor: 92123373788344372285635615769596739 Tue Nov 25 21:51:34 2008 prp50 factor: 48440139168210650866664274877353596332333457620279 Tue Nov 25 21:51:34 2008 elapsed time 00:54:07
(32·10¹⁴⁸+13)/9 = 3(5)₁₄₇7_<149> = 37 · 1015690043_<10> · 21788482138371211_<17> · 331676232498798305313287633537_<30> · C93
C93 = P38 · P55
P38 = 94903203682704040124208587387626991143_<38>
P55 = 1379502043103630182118926944969415246125508853045791327_<55>

Wed Nov 26 12:04:05 2008 Msieve v. 1.38 Wed Nov 26 12:04:05 2008 random seeds: ba40a840 d9ff2749 Wed Nov 26 12:04:05 2008 factoring 130919163377370183397007958071376655425247437752619741439878676248451252269473992284455216761 (93 digits) Wed Nov 26 12:04:06 2008 searching for 15-digit factors Wed Nov 26 12:04:07 2008 commencing quadratic sieve (93-digit input) Wed Nov 26 12:04:07 2008 using multiplier of 1 Wed Nov 26 12:04:07 2008 using 32kb Intel Core sieve core Wed Nov 26 12:04:07 2008 sieve interval: 36 blocks of size 32768 Wed Nov 26 12:04:07 2008 processing polynomials in batches of 6 Wed Nov 26 12:04:07 2008 using a sieve bound of 1885753 (70588 primes) Wed Nov 26 12:04:07 2008 using large prime bound of 220633101 (27 bits) Wed Nov 26 12:04:07 2008 using double large prime bound of 1043775707505921 (42-50 bits) Wed Nov 26 12:04:07 2008 using trial factoring cutoff of 50 bits Wed Nov 26 12:04:07 2008 polynomial 'A' values have 12 factors Wed Nov 26 13:42:50 2008 70721 relations (18727 full + 51994 combined from 909015 partial), need 70684 Wed Nov 26 13:42:51 2008 begin with 927742 relations Wed Nov 26 13:42:52 2008 reduce to 175950 relations in 10 passes Wed Nov 26 13:42:52 2008 attempting to read 175950 relations Wed Nov 26 13:42:54 2008 recovered 175950 relations Wed Nov 26 13:42:54 2008 recovered 151728 polynomials Wed Nov 26 13:42:54 2008 attempting to build 70721 cycles Wed Nov 26 13:42:54 2008 found 70721 cycles in 6 passes Wed Nov 26 13:42:54 2008 distribution of cycle lengths: Wed Nov 26 13:42:54 2008 length 1 : 18727 Wed Nov 26 13:42:54 2008 length 2 : 13332 Wed Nov 26 13:42:54 2008 length 3 : 12178 Wed Nov 26 13:42:54 2008 length 4 : 9387 Wed Nov 26 13:42:54 2008 length 5 : 6780 Wed Nov 26 13:42:54 2008 length 6 : 4296 Wed Nov 26 13:42:54 2008 length 7 : 2643 Wed Nov 26 13:42:54 2008 length 9+: 3378 Wed Nov 26 13:42:54 2008 largest cycle: 19 relations Wed Nov 26 13:42:55 2008 matrix is 70588 x 70721 (17.1 MB) with weight 4196924 (59.34/col) Wed Nov 26 13:42:55 2008 sparse part has weight 4196924 (59.34/col) Wed Nov 26 13:42:55 2008 filtering completed in 3 passes Wed Nov 26 13:42:55 2008 matrix is 66187 x 66251 (16.1 MB) with weight 3964446 (59.84/col) Wed Nov 26 13:42:55 2008 sparse part has weight 3964446 (59.84/col) Wed Nov 26 13:42:56 2008 saving the first 48 matrix rows for later Wed Nov 26 13:42:56 2008 matrix is 66139 x 66251 (9.5 MB) with weight 3022847 (45.63/col) Wed Nov 26 13:42:56 2008 sparse part has weight 2093712 (31.60/col) Wed Nov 26 13:42:56 2008 matrix includes 64 packed rows Wed Nov 26 13:42:56 2008 using block size 26500 for processor cache size 2048 kB Wed Nov 26 13:42:56 2008 commencing Lanczos iteration Wed Nov 26 13:42:56 2008 memory use: 9.7 MB Wed Nov 26 13:43:19 2008 lanczos halted after 1047 iterations (dim = 66133) Wed Nov 26 13:43:20 2008 recovered 13 nontrivial dependencies Wed Nov 26 13:43:20 2008 prp38 factor: 94903203682704040124208587387626991143 Wed Nov 26 13:43:20 2008 prp55 factor: 1379502043103630182118926944969415246125508853045791327 Wed Nov 26 13:43:20 2008 elapsed time 01:39:15
Nov 26, 2008 (2nd): By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(32·10¹⁴⁵+13)/9 = 3(5)₁₄₄7_<146> = 37 · 3197004779_<10> · 254681218216645409818996342939_<30> · C106
C106 = P34 · P72
P34 = 5229918696886448659761231433046467_<34>
P72 = 225668323907862446214856345291670054173175166345927281111241519005977043_<72>

GMP-ECM 6.0.1 [powered by GMP 4.1.4] [ECM] Input number is 1180226986500756972134059759800332242451110673451530099017680638918163275649167707645548036671643354257081 (106 digits) Using B1=882000, B2=702018447, polynomial Dickson(3), sigma=923708382 Step 1 took 8610ms Step 2 took 6406ms ********** Factor found in step 2: 5229918696886448659761231433046467 Found probable prime factor of 34 digits: 5229918696886448659761231433046467 Probable prime cofactor 225668323907862446214856345291670054173175166345927281111241519005977043 has 72 digits
(32·10¹⁶⁶-41)/9 = 3(5)₁₆₅1_<167> = 31 · 10531 · 5788583 · C155
C155 = P40 · P115
P40 = 9792135022795704973814420716717552208387_<40>
P115 = 1921438569531190489372181741560709835825907604892997957330053823094539017344979860619343704918741149830171856900671_<115>

Number: n N=18814985910856850738989493552015668813724344381955732627780744427450386269838098108337739752472791134671475386080902144478651310281628482623249021352127677 ( 155 digits) SNFS difficulty: 167 digits. Divisors found: Wed Nov 26 09:08:30 2008 prp40 factor: 9792135022795704973814420716717552208387 Wed Nov 26 09:08:30 2008 prp115 factor: 1921438569531190489372181741560709835825907604892997957330053823094539017344979860619343704918741149830171856900671 Wed Nov 26 09:08:30 2008 elapsed time 02:15:55 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 37.41 hours. Scaled time: 68.08 units (timescale=1.820). Factorization parameters were as follows: name: KA_3_5_165_1 n: 18814985910856850738989493552015668813724344381955732627780744427450386269838098108337739752472791134671475386080902144478651310281628482623249021352127677 type: snfs skew: 1.33 deg: 5 c5: 10 c0: -41 m: 2000000000000000000000000000000000 rlim: 5200000 alim: 5200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 5200000/5200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 2150001) Primes: RFBsize:361407, AFBsize:361403, largePrimes:15647474 encountered Relations: rels:14410609, finalFF:836059 Max relations in full relation-set: 28 Initial matrix: 722876 x 836059 with sparse part having weight 94388964. Pruned matrix : 631595 x 635273 with weight 62761233. Total sieving time: 36.91 hours. Total relation processing time: 0.49 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5200000,5200000,28,28,56,56,2.5,2.5,100000 total time: 37.41 hours. --------- CPU info (if available) ----------
(32·10¹⁵⁸+13)/9 = 3(5)₁₅₇7_<159> = 3 · 7 · 4889 · 6761 · 1812937883_<10> · 5326454155007_<13> · 29917160077671362567875821596807351_<35> · C94
C94 = P40 · P54
P40 = 6043839649643906935863300584811449219393_<40>
P54 = 293361275238573998016222754474394638893197836210505131_<54>

Number: n N=1773028506956992823270714966016153997533707382744774221590296026068158413217827561776171205483 ( 94 digits) Divisors found: r1=6043839649643906935863300584811449219393 (pp40) r2=293361275238573998016222754474394638893197836210505131 (pp54) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 6.60 hours. Scaled time: 8.65 units (timescale=1.310). Factorization parameters were as follows: name: KA_3_5_157_7 n: 1773028506956992823270714966016153997533707382744774221590296026068158413217827561776171205483 m: 3101524404745634812660 deg: 4 c4: 19160856 c3: 80284134 c2: -135811583081129561 c1: -160852531582126458026 c0: 1407163380862846602243 skew: 1635.250 type: gnfs # adj. I(F,S) = 55.938 # E(F1,F2) = 5.489594e-05 # GGNFS version 0.77.1-20060513-athlon-xp polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1227641341. # maxskew=2000.0 # These parameters should be manually set: rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 type: gnfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [100000, 880001) Primes: RFBsize:92938, AFBsize:93100, largePrimes:1766464 encountered Relations: rels:1793660, finalFF:209859 Max relations in full relation-set: 28 Initial matrix: 186117 x 209859 with sparse part having weight 12840070. Pruned matrix : 168779 x 169773 with weight 8560939. Polynomial selection time: 0.17 hours. Total sieving time: 5.89 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.40 hours. Total square root time: 0.04 hours, sqrts: 1. Prototype def-par.txt line would be: gnfs,93,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 6.60 hours. --------- CPU info (if available) ----------
(31·10¹⁶⁷+41)/9 = 3(4)₁₆₆9_<168> = 7⁴ · 23 · 107 · 443 · C159
C159 = P47 · P112
P47 = 82428469360546100817236547386728121355817832071_<47>
P112 = 1596373276554398260694282851868805545175066253459654053153617203305739262457720934111478909609962402182895680953_<112>

Number: n N=131586605714458804155816928144361334942782011803697417116828042223841300323604186069384933706935671232760809125303351106872422993136724453506518546845747243663 ( 159 digits) SNFS difficulty: 168 digits. Divisors found: Wed Nov 26 13:09:28 2008 prp47 factor: 82428469360546100817236547386728121355817832071 Wed Nov 26 13:09:28 2008 prp112 factor: 1596373276554398260694282851868805545175066253459654053153617203305739262457720934111478909609962402182895680953 Wed Nov 26 13:09:28 2008 elapsed time 03:20:59 (Msieve 1.38) Version: GGNFS-0.77.1-20050930-k8 Total time: 64.94 hours. Scaled time: 54.35 units (timescale=0.837). Factorization parameters were as follows: name: KA_3_4_166_9 n: 131586605714458804155816928144361334942782011803697417116828042223841300323604186069384933706935671232760809125303351106872422993136724453506518546845747243663 type: snfs skew: 0.42 deg: 5 c5: 3100 c0: 41 m: 1000000000000000000000000000000000 rlim: 5500000 alim: 5500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 3250001) Primes: RFBsize:380800, AFBsize:380784, largePrimes:16898141 encountered Relations: rels:15611597, finalFF:778444 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 64.09 hours. Total relation processing time: 0.85 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,56,56,2.5,2.5,100000 total time: 64.94 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
Nov 26, 2008: By Sinkiti Sibata / GGNFS, Msieve
(32·10¹²⁵+31)/9 = 3(5)₁₂₄9_<126> = 19 · 3067 · 134807213061289_<15> · C107
C107 = P42 · P65
P42 = 855863039493258726374436148063275096378011_<42>
P65 = 52883804346368337523551464619943154719770857071655107899081988477_<65>

Number: 35559_125 N=45261293527849611944009007470516564747912317071464403030095643688236704332954890087226456720792950338179247 ( 107 digits) SNFS difficulty: 126 digits. Divisors found: r1=855863039493258726374436148063275096378011 (pp42) r2=52883804346368337523551464619943154719770857071655107899081988477 (pp65) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.93 hours. Scaled time: 5.68 units (timescale=1.937). Factorization parameters were as follows: name: 35559_125 n: 45261293527849611944009007470516564747912317071464403030095643688236704332954890087226456720792950338179247 m: 20000000000000000000000000 deg: 5 c5: 1 c0: 31 skew: 1.99 type: snfs lss: 1 rlim: 900000 alim: 900000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 900000/900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [450000, 700001) Primes: RFBsize:71274, AFBsize:71376, largePrimes:2868761 encountered Relations: rels:3072916, finalFF:475953 Max relations in full relation-set: 28 Initial matrix: 142714 x 475953 with sparse part having weight 34254737. Pruned matrix : 85856 x 86633 with weight 6376451. Total sieving time: 2.80 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.04 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000 total time: 2.93 hours. --------- CPU info (if available) ----------
(32·10¹²⁸+31)/9 = 3(5)₁₂₇9_<129> = 25000147 · 4170310365607_<13> · 3288676168058609_<16> · C94
C94 = P46 · P48
P46 = 8411554247231991338364718226661881690595399127_<46>
P48 = 123281857069967884883915224017233748896454151597_<48>

Wed Nov 26 00:36:44 2008 Msieve v. 1.38 Wed Nov 26 00:36:44 2008 random seeds: 7e6bef0c f76e70b4 Wed Nov 26 00:36:44 2008 factoring 1036992028443535661266653954091510658049072752976818609735661966213284022836424574186379455819 (94 digits) Wed Nov 26 00:36:45 2008 searching for 15-digit factors Wed Nov 26 00:36:46 2008 commencing quadratic sieve (94-digit input) Wed Nov 26 00:36:47 2008 using multiplier of 3 Wed Nov 26 00:36:47 2008 using 32kb Intel Core sieve core Wed Nov 26 00:36:47 2008 sieve interval: 36 blocks of size 32768 Wed Nov 26 00:36:47 2008 processing polynomials in batches of 6 Wed Nov 26 00:36:47 2008 using a sieve bound of 1956287 (72941 primes) Wed Nov 26 00:36:47 2008 using large prime bound of 244535875 (27 bits) Wed Nov 26 00:36:47 2008 using double large prime bound of 1256078084807500 (42-51 bits) Wed Nov 26 00:36:47 2008 using trial factoring cutoff of 51 bits Wed Nov 26 00:36:47 2008 polynomial 'A' values have 12 factors Wed Nov 26 00:36:47 2008 restarting with 10856 full and 592550 partial relations Wed Nov 26 01:45:42 2008 73117 relations (18244 full + 54873 combined from 1001025 partial), need 73037 Wed Nov 26 01:45:44 2008 begin with 1019269 relations Wed Nov 26 01:45:45 2008 reduce to 187744 relations in 12 passes Wed Nov 26 01:45:45 2008 attempting to read 187744 relations Wed Nov 26 01:45:47 2008 recovered 187744 relations Wed Nov 26 01:45:47 2008 recovered 170550 polynomials Wed Nov 26 01:45:48 2008 attempting to build 73117 cycles Wed Nov 26 01:45:48 2008 found 73117 cycles in 5 passes Wed Nov 26 01:45:48 2008 distribution of cycle lengths: Wed Nov 26 01:45:48 2008 length 1 : 18244 Wed Nov 26 01:45:48 2008 length 2 : 13033 Wed Nov 26 01:45:48 2008 length 3 : 12520 Wed Nov 26 01:45:48 2008 length 4 : 10040 Wed Nov 26 01:45:48 2008 length 5 : 7217 Wed Nov 26 01:45:48 2008 length 6 : 4975 Wed Nov 26 01:45:48 2008 length 7 : 3133 Wed Nov 26 01:45:48 2008 length 9+: 3955 Wed Nov 26 01:45:48 2008 largest cycle: 18 relations Wed Nov 26 01:45:48 2008 matrix is 72941 x 73117 (18.6 MB) with weight 4579830 (62.64/col) Wed Nov 26 01:45:48 2008 sparse part has weight 4579830 (62.64/col) Wed Nov 26 01:45:49 2008 filtering completed in 3 passes Wed Nov 26 01:45:49 2008 matrix is 69223 x 69287 (17.7 MB) with weight 4366954 (63.03/col) Wed Nov 26 01:45:49 2008 sparse part has weight 4366954 (63.03/col) Wed Nov 26 01:45:49 2008 saving the first 48 matrix rows for later Wed Nov 26 01:45:49 2008 matrix is 69175 x 69287 (10.6 MB) with weight 3397331 (49.03/col) Wed Nov 26 01:45:49 2008 sparse part has weight 2369792 (34.20/col) Wed Nov 26 01:45:49 2008 matrix includes 64 packed rows Wed Nov 26 01:45:49 2008 using block size 27714 for processor cache size 1024 kB Wed Nov 26 01:45:50 2008 commencing Lanczos iteration Wed Nov 26 01:45:50 2008 memory use: 10.6 MB Wed Nov 26 01:46:21 2008 lanczos halted after 1096 iterations (dim = 69175) Wed Nov 26 01:46:21 2008 recovered 18 nontrivial dependencies Wed Nov 26 01:46:22 2008 prp46 factor: 8411554247231991338364718226661881690595399127 Wed Nov 26 01:46:22 2008 prp48 factor: 123281857069967884883915224017233748896454151597 Wed Nov 26 01:46:22 2008 elapsed time 01:09:38
(32·10¹²⁷+31)/9 = 3(5)₁₂₆9_<128> = 3 · 13 · 23 · 1857797 · 42403008773_<11> · C108
C108 = P50 · P58
P50 = 93598957773679097998335210590339756869624650269513_<50>
P58 = 5375874010147014698096140847150062199888070164109434270599_<58>

Number: 35559_127 N=503176204472369347528704149914346319811344140205384244788935122030122608807740644710994427251286623921948287 ( 108 digits) SNFS difficulty: 128 digits. Divisors found: r1=93598957773679097998335210590339756869624650269513 (pp50) r2=5375874010147014698096140847150062199888070164109434270599 (pp58) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.91 hours. Scaled time: 5.49 units (timescale=1.885). Factorization parameters were as follows: name: 35559_127 n: 503176204472369347528704149914346319811344140205384244788935122030122608807740644710994427251286623921948287 m: 20000000000000000000000000 deg: 5 c5: 100 c0: 31 skew: 0.79 type: snfs lss: 1 rlim: 970000 alim: 970000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 970000/970000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [485000, 735001) Primes: RFBsize:76350, AFBsize:76308, largePrimes:2524019 encountered Relations: rels:2393135, finalFF:184054 Max relations in full relation-set: 28 Initial matrix: 152722 x 184054 with sparse part having weight 12789703. Pruned matrix : 140139 x 140966 with weight 7598605. Total sieving time: 2.69 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.10 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,970000,970000,26,26,47,47,2.3,2.3,50000 total time: 2.91 hours. --------- CPU info (if available) ----------
(32·10¹²⁶+13)/9 = 3(5)₁₂₅7_<127> = 380191666015952176443593_<24> · C103
C103 = P32 · P72
P32 = 11501538774057476031056012458627_<32>
P72 = 813109299918853671165561790980638470245413633332066936422499433992993087_<72>

Number: 35557_126 N=9352008140563424847917023294566006210147916989237119692496652400268872388438878951389661139693484511549 ( 103 digits) SNFS difficulty: 127 digits. Divisors found: r1=11501538774057476031056012458627 (pp32) r2=813109299918853671165561790980638470245413633332066936422499433992993087 (pp72) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 3.65 hours. Scaled time: 1.73 units (timescale=0.473). Factorization parameters were as follows: name: 35557_126 n: 9352008140563424847917023294566006210147916989237119692496652400268872388438878951389661139693484511549 m: 20000000000000000000000000 deg: 5 c5: 10 c0: 13 skew: 1.05 type: snfs lss: 1 rlim: 930000 alim: 930000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 930000/930000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [465000, 765001) Primes: RFBsize:73474, AFBsize:73352, largePrimes:2549493 encountered Relations: rels:2483110, finalFF:230404 Max relations in full relation-set: 28 Initial matrix: 146892 x 230404 with sparse part having weight 17391688. Pruned matrix : 120843 x 121641 with weight 6495539. Total sieving time: 3.35 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.17 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,930000,930000,26,26,46,46,2.3,2.3,50000 total time: 3.65 hours. --------- CPU info (if available) ----------
(32·10¹³⁰+13)/9 = 3(5)₁₂₉7_<131> = 17 · 37 · 1777 · 100591304997342587_<18> · C108
C108 = P37 · P72
P37 = 1050271947861286918310443412512133053_<37>
P72 = 301097526163687219478040228435943897480969623432826469142619137934601839_<72>

Number: 35557_130 N=316234285300150577120637906765190725260228622770227425697921490435194156409281796327578461287310422146484467 ( 108 digits) SNFS difficulty: 131 digits. Divisors found: r1=1050271947861286918310443412512133053 (pp37) r2=301097526163687219478040228435943897480969623432826469142619137934601839 (pp72) Version: GGNFS-0.77.1-20060513-k8 Total time: 3.12 hours. Scaled time: 6.11 units (timescale=1.955). Factorization parameters were as follows: name: 35557_130 n: 316234285300150577120637906765190725260228622770227425697921490435194156409281796327578461287310422146484467 m: 200000000000000000000000000 deg: 5 c5: 1 c0: 13 skew: 1.67 type: snfs lss: 1 rlim: 1090000 alim: 1090000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1090000/1090000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [545000, 795001) Primes: RFBsize:84976, AFBsize:85103, largePrimes:2811907 encountered Relations: rels:2795363, finalFF:289791 Max relations in full relation-set: 28 Initial matrix: 170143 x 289791 with sparse part having weight 20768407. Pruned matrix : 128435 x 129349 with weight 6660177. Total sieving time: 2.93 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.08 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1090000,1090000,26,26,47,47,2.3,2.3,50000 total time: 3.12 hours. --------- CPU info (if available) ----------
(32·10¹³⁴+13)/9 = 3(5)₁₃₃7_<135> = 3² · 7 · 88560727 · 2289483979_<10> · C116
C116 = P49 · P67
P49 = 3196374879110325254657478673654847444267746688383_<49>
P67 = 8708240782305831710840887083343494810399416878830148384579837357001_<67>

Number: 35557_134 N=27834802077806407057659935627871990894848877408888265744552298958093842386798039849894726455952568910653769070419383 ( 116 digits) SNFS difficulty: 136 digits. Divisors found: r1=3196374879110325254657478673654847444267746688383 (pp49) r2=8708240782305831710840887083343494810399416878830148384579837357001 (pp67) Version: GGNFS-0.77.1-20060513-k8 Total time: 6.00 hours. Scaled time: 12.05 units (timescale=2.010). Factorization parameters were as follows: name: 35557_134 n: 27834802077806407057659935627871990894848877408888265744552298958093842386798039849894726455952568910653769070419383 m: 1000000000000000000000000000 deg: 5 c5: 16 c0: 65 skew: 1.32 type: snfs lss: 1 rlim: 1300000 alim: 1300000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [650000, 1175001) Primes: RFBsize:100021, AFBsize:100193, largePrimes:3501357 encountered Relations: rels:3766590, finalFF:544316 Max relations in full relation-set: 28 Initial matrix: 200278 x 544316 with sparse part having weight 44663294. Pruned matrix : 133071 x 134136 with weight 11084208. Total sieving time: 5.73 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.12 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000 total time: 6.00 hours. --------- CPU info (if available) ----------
(32·10¹³⁷+13)/9 = 3(5)₁₃₆7_<138> = 3 · 23 · 45337 · 145847851 · 159472373 · 9568191913142298047_<19> · C96
C96 = P44 · P52
P44 = 88546528817072023971206079968369863534097279_<44>
P52 = 5767912849452179312919971545551350229311180122030031_<52>

Wed Nov 26 05:14:00 2008 Msieve v. 1.38 Wed Nov 26 05:14:00 2008 random seeds: cf0e7240 51db047a Wed Nov 26 05:14:00 2008 factoring 510728661338377406183907643299278443750079883884964732152000041361727719148120748810880513385649 (96 digits) Wed Nov 26 05:14:00 2008 searching for 15-digit factors Wed Nov 26 05:14:02 2008 commencing quadratic sieve (96-digit input) Wed Nov 26 05:14:02 2008 using multiplier of 1 Wed Nov 26 05:14:02 2008 using 32kb Intel Core sieve core Wed Nov 26 05:14:02 2008 sieve interval: 36 blocks of size 32768 Wed Nov 26 05:14:02 2008 processing polynomials in batches of 6 Wed Nov 26 05:14:02 2008 using a sieve bound of 2265611 (83418 primes) Wed Nov 26 05:14:02 2008 using large prime bound of 339841650 (28 bits) Wed Nov 26 05:14:02 2008 using double large prime bound of 2271422065653900 (43-52 bits) Wed Nov 26 05:14:02 2008 using trial factoring cutoff of 52 bits Wed Nov 26 05:14:02 2008 polynomial 'A' values have 12 factors Wed Nov 26 09:51:26 2008 83756 relations (20168 full + 63588 combined from 1271970 partial), need 83514 Wed Nov 26 09:51:28 2008 begin with 1292138 relations Wed Nov 26 09:51:29 2008 reduce to 221157 relations in 13 passes Wed Nov 26 09:51:29 2008 attempting to read 221157 relations Wed Nov 26 09:51:33 2008 recovered 221157 relations Wed Nov 26 09:51:33 2008 recovered 206126 polynomials Wed Nov 26 09:51:33 2008 attempting to build 83756 cycles Wed Nov 26 09:51:33 2008 found 83756 cycles in 7 passes Wed Nov 26 09:51:33 2008 distribution of cycle lengths: Wed Nov 26 09:51:33 2008 length 1 : 20168 Wed Nov 26 09:51:33 2008 length 2 : 14206 Wed Nov 26 09:51:33 2008 length 3 : 13951 Wed Nov 26 09:51:33 2008 length 4 : 11416 Wed Nov 26 09:51:33 2008 length 5 : 8719 Wed Nov 26 09:51:33 2008 length 6 : 6047 Wed Nov 26 09:51:33 2008 length 7 : 3746 Wed Nov 26 09:51:33 2008 length 9+: 5503 Wed Nov 26 09:51:33 2008 largest cycle: 20 relations Wed Nov 26 09:51:34 2008 matrix is 83418 x 83756 (23.2 MB) with weight 5751541 (68.67/col) Wed Nov 26 09:51:34 2008 sparse part has weight 5751541 (68.67/col) Wed Nov 26 09:51:34 2008 filtering completed in 3 passes Wed Nov 26 09:51:34 2008 matrix is 79674 x 79736 (22.2 MB) with weight 5495801 (68.92/col) Wed Nov 26 09:51:34 2008 sparse part has weight 5495801 (68.92/col) Wed Nov 26 09:51:35 2008 saving the first 48 matrix rows for later Wed Nov 26 09:51:35 2008 matrix is 79626 x 79736 (16.3 MB) with weight 4608485 (57.80/col) Wed Nov 26 09:51:35 2008 sparse part has weight 3785457 (47.47/col) Wed Nov 26 09:51:35 2008 matrix includes 64 packed rows Wed Nov 26 09:51:35 2008 using block size 31894 for processor cache size 1024 kB Wed Nov 26 09:51:36 2008 commencing Lanczos iteration Wed Nov 26 09:51:36 2008 memory use: 14.4 MB Wed Nov 26 09:52:30 2008 lanczos halted after 1261 iterations (dim = 79624) Wed Nov 26 09:52:30 2008 recovered 16 nontrivial dependencies Wed Nov 26 09:52:32 2008 prp44 factor: 88546528817072023971206079968369863534097279 Wed Nov 26 09:52:32 2008 prp52 factor: 5767912849452179312919971545551350229311180122030031 Wed Nov 26 09:52:32 2008 elapsed time 04:38:32
(32·10¹²⁶+31)/9 = 3(5)₁₂₅9_<127> = 7 · 16476983 · C119
C119 = P51 · P68
P51 = 680997224473041479842187137587524564706549553049407_<51>
P68 = 45267487816196178055544763426310297914032845214592067327606904162777_<68>

Number: 35559_126 N=30827033561696818920547317912296682985467455294243365821760968493838218835810931402703270162258254920607002902651323239 ( 119 digits) SNFS difficulty: 127 digits. Divisors found: r1=680997224473041479842187137587524564706549553049407 (pp51) r2=45267487816196178055544763426310297914032845214592067327606904162777 (pp68) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 3.64 hours. Scaled time: 1.72 units (timescale=0.472). Factorization parameters were as follows: name: 35559_126 n: 30827033561696818920547317912296682985467455294243365821760968493838218835810931402703270162258254920607002902651323239 m: 20000000000000000000000000 deg: 5 c5: 10 c0: 31 skew: 1.25 type: snfs lss: 1 rlim: 930000 alim: 930000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 930000/930000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [465000, 765001) Primes: RFBsize:73474, AFBsize:73628, largePrimes:2612797 encountered Relations: rels:2582628, finalFF:264069 Max relations in full relation-set: 28 Initial matrix: 147168 x 264069 with sparse part having weight 19890177. Pruned matrix : 113591 x 114390 with weight 6088730. Total sieving time: 3.36 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.15 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,930000,930000,26,26,46,46,2.3,2.3,50000 total time: 3.64 hours. --------- CPU info (if available) ----------
(32·10¹³⁷+31)/9 = 3(5)₁₃₆9_<138> = 17² · 167 · 370663 · C128
C128 = P44 · P85
P44 = 13381285655013871857765308443020945443852381_<44>
P85 = 1485306483235108080529520897277681421570533714769036651190820055852516640157660621731_<85>

Number: 35559_137 N=19875310337413053710637590695530793527882282744921895395807157800777667144452785946358436075296632143126961352653038140244691511 ( 128 digits) SNFS difficulty: 138 digits. Divisors found: r1=13381285655013871857765308443020945443852381 (pp44) r2=1485306483235108080529520897277681421570533714769036651190820055852516640157660621731 (pp85) Version: GGNFS-0.77.1-20060513-k8 Total time: 7.53 hours. Scaled time: 14.94 units (timescale=1.985). Factorization parameters were as follows: name: 35559_137 n: 19875310337413053710637590695530793527882282744921895395807157800777667144452785946358436075296632143126961352653038140244691511 m: 2000000000000000000000000000 deg: 5 c5: 100 c0: 31 skew: 0.79 type: snfs lss: 1 rlim: 1420000 alim: 1420000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1420000/1420000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [710000, 1385001) Primes: RFBsize:108487, AFBsize:108634, largePrimes:3522102 encountered Relations: rels:3644702, finalFF:410418 Max relations in full relation-set: 28 Initial matrix: 217185 x 410418 with sparse part having weight 36113840. Pruned matrix : 168501 x 169650 with weight 12265564. Total sieving time: 7.10 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.26 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1420000,1420000,26,26,48,48,2.3,2.3,75000 total time: 7.53 hours. --------- CPU info (if available) ----------
(32·10¹³¹+31)/9 = 3(5)₁₃₀9_<132> = 266066510143035541_<18> · C115
C115 = P42 · P73
P42 = 844138519262383556289425467818988709704541_<42>
P73 = 1583082461247132173875334710522972730177912267910497115891734314149580039_<73>

Number: 35559_131 N=1336340884707403852333814649696063832094289430719468240561408485925328779819885140490430012885296587458038921257099 ( 115 digits) SNFS difficulty: 132 digits. Divisors found: r1=844138519262383556289425467818988709704541 (pp42) r2=1583082461247132173875334710522972730177912267910497115891734314149580039 (pp73) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 5.16 hours. Scaled time: 2.43 units (timescale=0.471). Factorization parameters were as follows: name: 35559_131 n: 1336340884707403852333814649696063832094289430719468240561408485925328779819885140490430012885296587458038921257099 m: 200000000000000000000000000 deg: 5 c5: 10 c0: 31 skew: 1.25 type: snfs lss: 1 rlim: 1130000 alim: 1130000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1130000/1130000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [565000, 965001) Primes: RFBsize:87884, AFBsize:88119, largePrimes:2834235 encountered Relations: rels:2738680, finalFF:224186 Max relations in full relation-set: 28 Initial matrix: 176069 x 224186 with sparse part having weight 17121575. Pruned matrix : 157598 x 158542 with weight 9354096. Total sieving time: 4.65 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.36 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,1130000,1130000,26,26,47,47,2.3,2.3,50000 total time: 5.16 hours. --------- CPU info (if available) ----------
Nov 25, 2008 (6th): By Sinkiti Sibata / Msieve, GGNFS
(32·10¹¹¹+31)/9 = 3(5)₁₁₀9_<112> = 83 · 479 · 221059673 · 213133327019_<12> · C88
C88 = P36 · P52
P36 = 487569966093755841400317894390408449_<36>
P52 = 3893104217967748849798424193291740807807864809580849_<52>

Tue Nov 25 16:11:38 2008 Msieve v. 1.38 Tue Nov 25 16:11:38 2008 random seeds: 4901283c 27d5cc06 Tue Nov 25 16:11:38 2008 factoring 1898160691553993157407449678245732393464881155578512112540299285983401084722145598193201 (88 digits) Tue Nov 25 16:11:39 2008 searching for 15-digit factors Tue Nov 25 16:11:41 2008 commencing quadratic sieve (88-digit input) Tue Nov 25 16:11:41 2008 using multiplier of 1 Tue Nov 25 16:11:41 2008 using 32kb Intel Core sieve core Tue Nov 25 16:11:41 2008 sieve interval: 24 blocks of size 32768 Tue Nov 25 16:11:41 2008 processing polynomials in batches of 9 Tue Nov 25 16:11:41 2008 using a sieve bound of 1508383 (57034 primes) Tue Nov 25 16:11:41 2008 using large prime bound of 120670640 (26 bits) Tue Nov 25 16:11:41 2008 using double large prime bound of 352275850752880 (42-49 bits) Tue Nov 25 16:11:41 2008 using trial factoring cutoff of 49 bits Tue Nov 25 16:11:41 2008 polynomial 'A' values have 11 factors Tue Nov 25 17:12:53 2008 57299 relations (14815 full + 42484 combined from 613221 partial), need 57130 Tue Nov 25 17:12:56 2008 begin with 628036 relations Tue Nov 25 17:12:56 2008 reduce to 140932 relations in 10 passes Tue Nov 25 17:12:56 2008 attempting to read 140932 relations Tue Nov 25 17:12:59 2008 recovered 140932 relations Tue Nov 25 17:12:59 2008 recovered 122059 polynomials Tue Nov 25 17:12:59 2008 attempting to build 57299 cycles Tue Nov 25 17:12:59 2008 found 57299 cycles in 5 passes Tue Nov 25 17:12:59 2008 distribution of cycle lengths: Tue Nov 25 17:12:59 2008 length 1 : 14815 Tue Nov 25 17:12:59 2008 length 2 : 11055 Tue Nov 25 17:12:59 2008 length 3 : 10130 Tue Nov 25 17:12:59 2008 length 4 : 7717 Tue Nov 25 17:12:59 2008 length 5 : 5412 Tue Nov 25 17:12:59 2008 length 6 : 3622 Tue Nov 25 17:12:59 2008 length 7 : 2122 Tue Nov 25 17:12:59 2008 length 9+: 2426 Tue Nov 25 17:12:59 2008 largest cycle: 20 relations Tue Nov 25 17:12:59 2008 matrix is 57034 x 57299 (13.4 MB) with weight 3274244 (57.14/col) Tue Nov 25 17:12:59 2008 sparse part has weight 3274244 (57.14/col) Tue Nov 25 17:13:00 2008 filtering completed in 3 passes Tue Nov 25 17:13:00 2008 matrix is 53372 x 53436 (12.5 MB) with weight 3072775 (57.50/col) Tue Nov 25 17:13:00 2008 sparse part has weight 3072775 (57.50/col) Tue Nov 25 17:13:00 2008 saving the first 48 matrix rows for later Tue Nov 25 17:13:00 2008 matrix is 53324 x 53436 (8.0 MB) with weight 2417387 (45.24/col) Tue Nov 25 17:13:00 2008 sparse part has weight 1766360 (33.06/col) Tue Nov 25 17:13:00 2008 matrix includes 64 packed rows Tue Nov 25 17:13:00 2008 using block size 21374 for processor cache size 2048 kB Tue Nov 25 17:13:00 2008 commencing Lanczos iteration Tue Nov 25 17:13:00 2008 memory use: 7.9 MB Tue Nov 25 17:13:17 2008 lanczos halted after 845 iterations (dim = 53320) Tue Nov 25 17:13:17 2008 recovered 14 nontrivial dependencies Tue Nov 25 17:13:18 2008 prp36 factor: 487569966093755841400317894390408449 Tue Nov 25 17:13:18 2008 prp52 factor: 3893104217967748849798424193291740807807864809580849 Tue Nov 25 17:13:18 2008 elapsed time 01:01:40
(32·10¹¹³+13)/9 = 3(5)₁₁₂7_<114> = 3 · 367 · 8039 · 260363 · 4472974792621_<13> · C89
C89 = P42 · P47
P42 = 722805190445538559579755657850210987340009_<42>
P47 = 47722275212804886755544319503545804388116823209_<47>

Tue Nov 25 17:21:51 2008 Msieve v. 1.38 Tue Nov 25 17:21:51 2008 random seeds: 73861c22 a47e1017 Tue Nov 25 17:21:51 2008 factoring 34493908223685840362451462065513046847262683445436352847040664541897484049027610225468881 (89 digits) Tue Nov 25 17:21:52 2008 searching for 15-digit factors Tue Nov 25 17:21:53 2008 commencing quadratic sieve (89-digit input) Tue Nov 25 17:21:53 2008 using multiplier of 1 Tue Nov 25 17:21:53 2008 using 32kb Intel Core sieve core Tue Nov 25 17:21:53 2008 sieve interval: 32 blocks of size 32768 Tue Nov 25 17:21:53 2008 processing polynomials in batches of 7 Tue Nov 25 17:21:53 2008 using a sieve bound of 1556083 (58841 primes) Tue Nov 25 17:21:53 2008 using large prime bound of 124486640 (26 bits) Tue Nov 25 17:21:53 2008 using double large prime bound of 372581168808240 (42-49 bits) Tue Nov 25 17:21:53 2008 using trial factoring cutoff of 49 bits Tue Nov 25 17:21:53 2008 polynomial 'A' values have 11 factors Tue Nov 25 18:01:21 2008 59297 relations (17170 full + 42127 combined from 608482 partial), need 58937 Tue Nov 25 18:01:23 2008 begin with 625652 relations Tue Nov 25 18:01:23 2008 reduce to 138778 relations in 10 passes Tue Nov 25 18:01:23 2008 attempting to read 138778 relations Tue Nov 25 18:01:26 2008 recovered 138778 relations Tue Nov 25 18:01:26 2008 recovered 102781 polynomials Tue Nov 25 18:01:26 2008 attempting to build 59297 cycles Tue Nov 25 18:01:26 2008 found 59297 cycles in 5 passes Tue Nov 25 18:01:26 2008 distribution of cycle lengths: Tue Nov 25 18:01:26 2008 length 1 : 17170 Tue Nov 25 18:01:26 2008 length 2 : 12193 Tue Nov 25 18:01:26 2008 length 3 : 10649 Tue Nov 25 18:01:26 2008 length 4 : 7548 Tue Nov 25 18:01:26 2008 length 5 : 4978 Tue Nov 25 18:01:26 2008 length 6 : 3084 Tue Nov 25 18:01:26 2008 length 7 : 1791 Tue Nov 25 18:01:26 2008 length 9+: 1884 Tue Nov 25 18:01:26 2008 largest cycle: 16 relations Tue Nov 25 18:01:26 2008 matrix is 58841 x 59297 (13.8 MB) with weight 3372407 (56.87/col) Tue Nov 25 18:01:26 2008 sparse part has weight 3372407 (56.87/col) Tue Nov 25 18:01:26 2008 filtering completed in 3 passes Tue Nov 25 18:01:26 2008 matrix is 53403 x 53467 (12.5 MB) with weight 3061639 (57.26/col) Tue Nov 25 18:01:26 2008 sparse part has weight 3061639 (57.26/col) Tue Nov 25 18:01:27 2008 saving the first 48 matrix rows for later Tue Nov 25 18:01:27 2008 matrix is 53355 x 53467 (8.5 MB) with weight 2428743 (45.43/col) Tue Nov 25 18:01:27 2008 sparse part has weight 1915838 (35.83/col) Tue Nov 25 18:01:27 2008 matrix includes 64 packed rows Tue Nov 25 18:01:27 2008 using block size 21386 for processor cache size 2048 kB Tue Nov 25 18:01:27 2008 commencing Lanczos iteration Tue Nov 25 18:01:27 2008 memory use: 8.0 MB Tue Nov 25 18:01:45 2008 lanczos halted after 846 iterations (dim = 53348) Tue Nov 25 18:01:45 2008 recovered 13 nontrivial dependencies Tue Nov 25 18:01:46 2008 prp42 factor: 722805190445538559579755657850210987340009 Tue Nov 25 18:01:46 2008 prp47 factor: 47722275212804886755544319503545804388116823209 Tue Nov 25 18:01:46 2008 elapsed time 00:39:55
(31·10¹⁴⁷+41)/9 = 3(4)₁₄₆9_<148> = 30619519171_<11> · C138
C138 = P38 · P50 · P50
P38 = 52645699521864232841037910835053332133_<38>
P50 = 26284555383594257254292409604368589956841814276767_<50>
P50 = 81293773300248697922814898301342394783351214050929_<50>

Number: 34449_147 N=112491787516595175094248525044692787688858788070759429119202756420202848274323231189071647765374520630627849399171887618027300225120326219 ( 138 digits) SNFS difficulty: 149 digits. Divisors found: r1=52645699521864232841037910835053332133 (pp38) r2=26284555383594257254292409604368589956841814276767 (pp50) r3=81293773300248697922814898301342394783351214050929 (pp50) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 39.23 hours. Scaled time: 18.52 units (timescale=0.472). Factorization parameters were as follows: name: 34449_147 n: 112491787516595175094248525044692787688858788070759429119202756420202848274323231189071647765374520630627849399171887618027300225120326219 m: 200000000000000000000000000000 deg: 5 c5: 775 c0: 328 skew: 0.84 type: snfs lss: 1 rlim: 2200000 alim: 2200000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1100000, 4100001) Primes: RFBsize:162662, AFBsize:163207, largePrimes:4709465 encountered Relations: rels:5141491, finalFF:384765 Max relations in full relation-set: 28 Initial matrix: 325936 x 384765 with sparse part having weight 47733275. Pruned matrix : 306013 x 307706 with weight 36858857. Total sieving time: 34.63 hours. Total relation processing time: 0.38 hours. Matrix solve time: 4.11 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,49,49,2.3,2.3,100000 total time: 39.23 hours. --------- CPU info (if available) ----------
(32·10¹²²+31)/9 = 3(5)₁₂₁9_<123> = 328781 · 2504008107923036641496791213_<28> · C90
C90 = P35 · P56
P35 = 42723292270746693182558544322045801_<35>
P56 = 10108816517969606422105778729319311803504197245858958103_<56>

Tue Nov 25 18:15:00 2008 Msieve v. 1.38 Tue Nov 25 18:15:00 2008 random seeds: d1551f0c 1ce83f3a Tue Nov 25 18:15:00 2008 factoring 431881922608567386526197281175982703937335426667558565328396228433888608545324127306075503 (90 digits) Tue Nov 25 18:15:01 2008 searching for 15-digit factors Tue Nov 25 18:15:03 2008 commencing quadratic sieve (90-digit input) Tue Nov 25 18:15:03 2008 using multiplier of 7 Tue Nov 25 18:15:03 2008 using 32kb Intel Core sieve core Tue Nov 25 18:15:03 2008 sieve interval: 36 blocks of size 32768 Tue Nov 25 18:15:03 2008 processing polynomials in batches of 6 Tue Nov 25 18:15:03 2008 using a sieve bound of 1584929 (59679 primes) Tue Nov 25 18:15:03 2008 using large prime bound of 126794320 (26 bits) Tue Nov 25 18:15:03 2008 using double large prime bound of 385105414448400 (42-49 bits) Tue Nov 25 18:15:03 2008 using trial factoring cutoff of 49 bits Tue Nov 25 18:15:03 2008 polynomial 'A' values have 12 factors Tue Nov 25 19:31:03 2008 60194 relations (15958 full + 44236 combined from 638107 partial), need 59775 Tue Nov 25 19:31:05 2008 begin with 654065 relations Tue Nov 25 19:31:05 2008 reduce to 146856 relations in 10 passes Tue Nov 25 19:31:05 2008 attempting to read 146856 relations Tue Nov 25 19:31:08 2008 recovered 146856 relations Tue Nov 25 19:31:08 2008 recovered 125328 polynomials Tue Nov 25 19:31:08 2008 attempting to build 60194 cycles Tue Nov 25 19:31:08 2008 found 60194 cycles in 5 passes Tue Nov 25 19:31:08 2008 distribution of cycle lengths: Tue Nov 25 19:31:08 2008 length 1 : 15958 Tue Nov 25 19:31:08 2008 length 2 : 11650 Tue Nov 25 19:31:08 2008 length 3 : 10547 Tue Nov 25 19:31:08 2008 length 4 : 8074 Tue Nov 25 19:31:08 2008 length 5 : 5654 Tue Nov 25 19:31:08 2008 length 6 : 3590 Tue Nov 25 19:31:08 2008 length 7 : 2148 Tue Nov 25 19:31:08 2008 length 9+: 2573 Tue Nov 25 19:31:08 2008 largest cycle: 20 relations Tue Nov 25 19:31:09 2008 matrix is 59679 x 60194 (14.7 MB) with weight 3625687 (60.23/col) Tue Nov 25 19:31:09 2008 sparse part has weight 3625687 (60.23/col) Tue Nov 25 19:31:09 2008 filtering completed in 3 passes Tue Nov 25 19:31:09 2008 matrix is 55677 x 55741 (13.7 MB) with weight 3363925 (60.35/col) Tue Nov 25 19:31:09 2008 sparse part has weight 3363925 (60.35/col) Tue Nov 25 19:31:09 2008 saving the first 48 matrix rows for later Tue Nov 25 19:31:09 2008 matrix is 55629 x 55741 (8.7 MB) with weight 2647142 (47.49/col) Tue Nov 25 19:31:09 2008 sparse part has weight 1945354 (34.90/col) Tue Nov 25 19:31:09 2008 matrix includes 64 packed rows Tue Nov 25 19:31:09 2008 using block size 22296 for processor cache size 2048 kB Tue Nov 25 19:31:10 2008 commencing Lanczos iteration Tue Nov 25 19:31:10 2008 memory use: 8.4 MB Tue Nov 25 19:31:28 2008 lanczos halted after 881 iterations (dim = 55626) Tue Nov 25 19:31:29 2008 recovered 16 nontrivial dependencies Tue Nov 25 19:31:29 2008 prp35 factor: 42723292270746693182558544322045801 Tue Nov 25 19:31:29 2008 prp56 factor: 10108816517969606422105778729319311803504197245858958103 Tue Nov 25 19:31:29 2008 elapsed time 01:16:29
(32·10¹¹⁹+13)/9 = 3(5)₁₁₈7_<120> = 3 · 207637403 · 1000206492930416143935716239_<28> · C84
C84 = P33 · P51
P33 = 640277981563769011474718630122289_<33>
P51 = 891296885887495874319183654447578766973756482284363_<51>

Tue Nov 25 16:25:35 2008 Msieve v. 1.38 Tue Nov 25 16:25:35 2008 random seeds: ac2b7704 f677277a Tue Nov 25 16:25:35 2008 factoring 570677771070118815842205302870178050917454543396455013477008232333098780244762466907 (84 digits) Tue Nov 25 16:25:38 2008 searching for 15-digit factors Tue Nov 25 16:25:42 2008 commencing quadratic sieve (84-digit input) Tue Nov 25 16:25:43 2008 using multiplier of 43 Tue Nov 25 16:25:43 2008 using 64kb Pentium 2 sieve core Tue Nov 25 16:25:43 2008 sieve interval: 6 blocks of size 65536 Tue Nov 25 16:25:43 2008 processing polynomials in batches of 17 Tue Nov 25 16:25:43 2008 using a sieve bound of 1407293 (53824 primes) Tue Nov 25 16:25:43 2008 using large prime bound of 119619905 (26 bits) Tue Nov 25 16:25:43 2008 using double large prime bound of 346773678658515 (41-49 bits) Tue Nov 25 16:25:43 2008 using trial factoring cutoff of 49 bits Tue Nov 25 16:25:43 2008 polynomial 'A' values have 11 factors Tue Nov 25 20:30:12 2008 53931 relations (16424 full + 37507 combined from 568412 partial), need 53920 Tue Nov 25 20:30:18 2008 begin with 584836 relations Tue Nov 25 20:30:20 2008 reduce to 124724 relations in 10 passes Tue Nov 25 20:30:20 2008 attempting to read 124724 relations Tue Nov 25 20:30:26 2008 recovered 124724 relations Tue Nov 25 20:30:26 2008 recovered 100563 polynomials Tue Nov 25 20:30:26 2008 attempting to build 53931 cycles Tue Nov 25 20:30:26 2008 found 53931 cycles in 4 passes Tue Nov 25 20:30:30 2008 distribution of cycle lengths: Tue Nov 25 20:30:30 2008 length 1 : 16424 Tue Nov 25 20:30:30 2008 length 2 : 11082 Tue Nov 25 20:30:30 2008 length 3 : 9630 Tue Nov 25 20:30:30 2008 length 4 : 6837 Tue Nov 25 20:30:30 2008 length 5 : 4320 Tue Nov 25 20:30:30 2008 length 6 : 2598 Tue Nov 25 20:30:30 2008 length 7 : 1463 Tue Nov 25 20:30:30 2008 length 9+: 1577 Tue Nov 25 20:30:30 2008 largest cycle: 18 relations Tue Nov 25 20:30:31 2008 matrix is 53824 x 53931 (11.3 MB) with weight 2739791 (50.80/col) Tue Nov 25 20:30:31 2008 sparse part has weight 2739791 (50.80/col) Tue Nov 25 20:30:35 2008 filtering completed in 3 passes Tue Nov 25 20:30:35 2008 matrix is 48144 x 48208 (10.2 MB) with weight 2482659 (51.50/col) Tue Nov 25 20:30:35 2008 sparse part has weight 2482659 (51.50/col) Tue Nov 25 20:30:37 2008 saving the first 48 matrix rows for later Tue Nov 25 20:30:37 2008 matrix is 48096 x 48208 (5.6 MB) with weight 1823977 (37.84/col) Tue Nov 25 20:30:37 2008 sparse part has weight 1189151 (24.67/col) Tue Nov 25 20:30:37 2008 matrix includes 64 packed rows Tue Nov 25 20:30:38 2008 using block size 5461 for processor cache size 128 kB Tue Nov 25 20:30:39 2008 commencing Lanczos iteration Tue Nov 25 20:30:39 2008 memory use: 6.2 MB Tue Nov 25 20:32:29 2008 lanczos halted after 762 iterations (dim = 48096) Tue Nov 25 20:32:30 2008 recovered 18 nontrivial dependencies Tue Nov 25 20:32:32 2008 prp33 factor: 640277981563769011474718630122289 Tue Nov 25 20:32:32 2008 prp51 factor: 891296885887495874319183654447578766973756482284363 Tue Nov 25 20:32:32 2008 elapsed time 04:06:57
(32·10¹²⁰+31)/9 = 3(5)₁₁₉9_<121> = 7 · 5807 · C116
C116 = P31 · P86
P31 = 3113032816097266174778764676807_<31>
P86 = 28097902683758787473437650239350518110448549347179343214543208493496692074850718804313_<86>

Number: 35559_120 N=87469693118048551146536336823920774325458327524799024712921733758654716119844413283366271139648098490874450922668591 ( 116 digits) SNFS difficulty: 121 digits. Divisors found: r1=3113032816097266174778764676807 (pp31) r2=28097902683758787473437650239350518110448549347179343214543208493496692074850718804313 (pp86) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.50 hours. Scaled time: 5.00 units (timescale=2.003). Factorization parameters were as follows: name: 35559_120 n: 87469693118048551146536336823920774325458327524799024712921733758654716119844413283366271139648098490874450922668591 m: 2000000000000000000000000 deg: 5 c5: 1 c0: 31 skew: 1.99 type: snfs lss: 1 rlim: 740000 alim: 740000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 740000/740000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [370000, 620001) Primes: RFBsize:59531, AFBsize:59539, largePrimes:1702979 encountered Relations: rels:1960859, finalFF:410760 Max relations in full relation-set: 28 Initial matrix: 119134 x 410760 with sparse part having weight 19379073. Pruned matrix : 67073 x 67732 with weight 3827093. Total sieving time: 2.41 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.02 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000 total time: 2.50 hours. --------- CPU info (if available) ----------
(32·10¹²⁴+13)/9 = 3(5)₁₂₃7_<125> = 31 · 37 · 111150343 · 3992206561597_<13> · C101
C101 = P41 · P61
P41 = 10402125562044091642484846822078823468091_<41>
P61 = 6715806088535023166394807724616174297101621140015673344377671_<61>

Number: 35557_124 N=69858658183281510532470852601943169332228650358787493281055371585330045221451803823211994604321396061 ( 101 digits) SNFS difficulty: 126 digits. Divisors found: r1=10402125562044091642484846822078823468091 (pp41) r2=6715806088535023166394807724616174297101621140015673344377671 (pp61) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 3.20 hours. Scaled time: 1.51 units (timescale=0.472). Factorization parameters were as follows: name: 35557_124 n: 69858658183281510532470852601943169332228650358787493281055371585330045221451803823211994604321396061 m: 10000000000000000000000000 deg: 5 c5: 16 c0: 65 skew: 1.32 type: snfs lss: 1 rlim: 890000 alim: 890000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 890000/890000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [445000, 695001) Primes: RFBsize:70555, AFBsize:70488, largePrimes:2519735 encountered Relations: rels:2495783, finalFF:266363 Max relations in full relation-set: 28 Initial matrix: 141107 x 266363 with sparse part having weight 18696002. Pruned matrix : 104070 x 104839 with weight 5169750. Total sieving time: 2.97 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.12 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000 total time: 3.20 hours. --------- CPU info (if available) ----------
(32·10¹¹³+31)/9 = 3(5)₁₁₂9_<114> = 6871 · 5101787 · C104
C104 = P31 · P73
P31 = 2169685434607141957872712202903_<31>
P73 = 4674858004238930698030761281227982249602384821440497976576836629122533589_<73>

Number: 35559_113 N=10142971320653820632723339542539382492089008306725584839857993969919889375979466051668360765372800808867 ( 104 digits) SNFS difficulty: 115 digits. Divisors found: r1=2169685434607141957872712202903 (pp31) r2=4674858004238930698030761281227982249602384821440497976576836629122533589 (pp73) Version: GGNFS-0.77.1-20060513-k8 Total time: 1.57 hours. Scaled time: 3.08 units (timescale=1.967). Factorization parameters were as follows: name: 35559_113 n: 10142971320653820632723339542539382492089008306725584839857993969919889375979466051668360765372800808867 m: 40000000000000000000000 deg: 5 c5: 125 c0: 124 skew: 1.00 type: snfs lss: 1 rlim: 580000 alim: 580000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 580000/580000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [290000, 440001) Primes: RFBsize:47588, AFBsize:47780, largePrimes:1340429 encountered Relations: rels:1372204, finalFF:195899 Max relations in full relation-set: 28 Initial matrix: 95434 x 195899 with sparse part having weight 9478162. Pruned matrix : 67455 x 67996 with weight 2513133. Total sieving time: 1.49 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.01 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,115,5,0,0,0,0,0,0,0,0,580000,580000,25,25,45,45,2.2,2.2,50000 total time: 1.57 hours. --------- CPU info (if available) ----------
9·10²¹³-1 = 8(9)₂₁₃_<214> = 293 · 31517 · 297630677 · 653240602737601_<15> · 2763180643414756163_<19> · 1880839632718006855987957867_<28> · 179481389251375241524195452694409_<33> · C106
C106 = P30 · P77
P30 = 240517498236320119968635920027_<30>
P77 = 22343541377353884509643293353805591669647127166940550303134256458298751571009_<77>

Mon Nov 24 00:11:51 2008 Msieve v. 1.38 Mon Nov 24 00:11:51 2008 random seeds: a24e6aa0 3eb03746 Mon Nov 24 00:11:51 2008 factoring 5374012673820858541660812441083032124477051306670520962378248708789456585274457770479061617280814335697243 (106 digits) Mon Nov 24 00:11:52 2008 searching for 15-digit factors Mon Nov 24 00:11:54 2008 commencing quadratic sieve (106-digit input) Mon Nov 24 00:11:54 2008 using multiplier of 3 Mon Nov 24 00:11:54 2008 using 32kb Intel Core sieve core Mon Nov 24 00:11:54 2008 sieve interval: 41 blocks of size 32768 Mon Nov 24 00:11:54 2008 processing polynomials in batches of 5 Mon Nov 24 00:11:54 2008 using a sieve bound of 4519019 (158667 primes) Mon Nov 24 00:11:54 2008 using large prime bound of 677852850 (29 bits) Mon Nov 24 00:11:54 2008 using double large prime bound of 7871251019049750 (45-53 bits) Mon Nov 24 00:11:54 2008 using trial factoring cutoff of 53 bits Mon Nov 24 00:11:54 2008 polynomial 'A' values have 14 factors Tue Nov 25 22:27:00 2008 158913 relations (37698 full + 121215 combined from 2331858 partial), need 158763 Tue Nov 25 22:27:03 2008 begin with 2369556 relations Tue Nov 25 22:27:06 2008 reduce to 417220 relations in 11 passes Tue Nov 25 22:27:06 2008 attempting to read 417220 relations Tue Nov 25 22:27:16 2008 recovered 417220 relations Tue Nov 25 22:27:16 2008 recovered 409284 polynomials Tue Nov 25 22:27:16 2008 attempting to build 158913 cycles Tue Nov 25 22:27:16 2008 found 158913 cycles in 6 passes Tue Nov 25 22:27:16 2008 distribution of cycle lengths: Tue Nov 25 22:27:16 2008 length 1 : 37698 Tue Nov 25 22:27:16 2008 length 2 : 27255 Tue Nov 25 22:27:16 2008 length 3 : 26726 Tue Nov 25 22:27:16 2008 length 4 : 21725 Tue Nov 25 22:27:16 2008 length 5 : 16730 Tue Nov 25 22:27:16 2008 length 6 : 11228 Tue Nov 25 22:27:16 2008 length 7 : 7302 Tue Nov 25 22:27:16 2008 length 9+: 10249 Tue Nov 25 22:27:16 2008 largest cycle: 20 relations Tue Nov 25 22:27:17 2008 matrix is 158667 x 158913 (42.9 MB) with weight 10612023 (66.78/col) Tue Nov 25 22:27:17 2008 sparse part has weight 10612023 (66.78/col) Tue Nov 25 22:27:20 2008 filtering completed in 3 passes Tue Nov 25 22:27:20 2008 matrix is 152562 x 152626 (41.4 MB) with weight 10241543 (67.10/col) Tue Nov 25 22:27:20 2008 sparse part has weight 10241543 (67.10/col) Tue Nov 25 22:27:21 2008 saving the first 48 matrix rows for later Tue Nov 25 22:27:21 2008 matrix is 152514 x 152626 (22.7 MB) with weight 7745078 (50.75/col) Tue Nov 25 22:27:21 2008 sparse part has weight 5042413 (33.04/col) Tue Nov 25 22:27:21 2008 matrix includes 64 packed rows Tue Nov 25 22:27:21 2008 using block size 43690 for processor cache size 1024 kB Tue Nov 25 22:27:22 2008 commencing Lanczos iteration Tue Nov 25 22:27:22 2008 memory use: 24.2 MB Tue Nov 25 22:30:07 2008 lanczos halted after 2415 iterations (dim = 152514) Tue Nov 25 22:30:08 2008 recovered 18 nontrivial dependencies Tue Nov 25 22:30:09 2008 prp30 factor: 240517498236320119968635920027 Tue Nov 25 22:30:09 2008 prp77 factor: 22343541377353884509643293353805591669647127166940550303134256458298751571009 Tue Nov 25 22:30:09 2008 elapsed time 46:18:18
Nov 25, 2008 (5th): By Serge Batalov / Msieve, GMP-ECM 6.2.1, Msieve-1.39, Msieve-1.39/QS, Msieve-1.38
(32·10¹³³+13)/9 = 3(5)₁₃₂7_<134> = 37 · 28229087 · 26252902873_<11> · 1807579431701_<13> · 672131425700807858561_<21> · C82
C82 = P40 · P42
P40 = 3701932676318776884096888982145290362881_<40>
P42 = 288304533842512763257586489293524587911771_<42>

Mon Nov 24 21:44:24 2008 Msieve v. 1.39 Mon Nov 24 21:44:24 2008 random seeds: 53b7fae1 4fe02420 Mon Nov 24 21:44:24 2008 factoring 1067283974562450657219633927845179417913759582844266707522004006708319194601372251 (82 digits) Mon Nov 24 21:44:25 2008 searching for 15-digit factors Mon Nov 24 21:44:25 2008 commencing quadratic sieve (82-digit input) Mon Nov 24 21:44:26 2008 using multiplier of 11 Mon Nov 24 21:44:26 2008 using 64kb Opteron sieve core Mon Nov 24 21:44:26 2008 sieve interval: 6 blocks of size 65536 Mon Nov 24 21:44:26 2008 processing polynomials in batches of 17 Mon Nov 24 21:44:26 2008 using a sieve bound of 1334341 (51074 primes) Mon Nov 24 21:44:26 2008 using large prime bound of 126762395 (26 bits) Mon Nov 24 21:44:26 2008 using trial factoring cutoff of 27 bits Mon Nov 24 21:44:26 2008 polynomial 'A' values have 10 factors Mon Nov 24 21:57:27 2008 51230 relations (26672 full + 24558 combined from 272144 partial), need 51170 Mon Nov 24 21:57:28 2008 begin with 298816 relations Mon Nov 24 21:57:28 2008 reduce to 72630 relations in 2 passes Mon Nov 24 21:57:28 2008 attempting to read 72630 relations Mon Nov 24 21:57:28 2008 recovered 72630 relations Mon Nov 24 21:57:28 2008 recovered 62674 polynomials Mon Nov 24 21:57:28 2008 attempting to build 51230 cycles Mon Nov 24 21:57:28 2008 found 51230 cycles in 1 passes Mon Nov 24 21:57:28 2008 distribution of cycle lengths: Mon Nov 24 21:57:28 2008 length 1 : 26672 Mon Nov 24 21:57:28 2008 length 2 : 24558 Mon Nov 24 21:57:28 2008 largest cycle: 2 relations Mon Nov 24 21:57:28 2008 matrix is 51074 x 51230 (7.6 MB) with weight 1577987 (30.80/col) Mon Nov 24 21:57:28 2008 sparse part has weight 1577987 (30.80/col) Mon Nov 24 21:57:29 2008 filtering completed in 3 passes Mon Nov 24 21:57:29 2008 matrix is 36236 x 36299 (5.9 MB) with weight 1256664 (34.62/col) Mon Nov 24 21:57:29 2008 sparse part has weight 1256664 (34.62/col) Mon Nov 24 21:57:29 2008 saving the first 48 matrix rows for later Mon Nov 24 21:57:29 2008 matrix is 36188 x 36299 (4.6 MB) with weight 1006135 (27.72/col) Mon Nov 24 21:57:29 2008 sparse part has weight 834315 (22.98/col) Mon Nov 24 21:57:29 2008 matrix includes 64 packed rows Mon Nov 24 21:57:29 2008 using block size 14519 for processor cache size 1024 kB Mon Nov 24 21:57:29 2008 commencing Lanczos iteration Mon Nov 24 21:57:29 2008 memory use: 4.3 MB Mon Nov 24 21:57:34 2008 lanczos halted after 573 iterations (dim = 36186) Mon Nov 24 21:57:34 2008 recovered 16 nontrivial dependencies Mon Nov 24 21:57:34 2008 prp40 factor: 3701932676318776884096888982145290362881 Mon Nov 24 21:57:34 2008 prp42 factor: 288304533842512763257586489293524587911771 Mon Nov 24 21:57:34 2008 elapsed time 00:13:10
(32·10¹²⁰+13)/9 = 3(5)₁₁₉7_<121> = 4937 · 12451 · 1016780899_<10> · 666585174041787950087_<21> · C83
C83 = P30 · P54
P30 = 750956733862170017094819057059_<30>
P54 = 113642862248618823692705891243347504507404736593836833_<54>

Factor found in step 2: 750956733862170017094819057059
(32·10¹⁵⁷+13)/9 = 3(5)₁₅₆7_<158> = 29 · 37 · 4001 · 10345641860816323_<17> · 1998968244836228509_<19> · 1730927190715608520160070713867_<31> · C87
C87 = P31 · P57
P31 = 1037983176934327212428494372699_<31>
P57 = 222898294402775465729776596045681470561860226927431308539_<57>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1740884508 Step 1 took 9068ms Step 2 took 7069ms ********** Factor found in step 2: 1037983176934327212428494372699 Found probable prime factor of 31 digits: 1037983176934327212428494372699 Probable prime cofactor 222898294402775465729776596045681470561860226927431308539 has 57 digits
(32·10¹¹²+31)/9 = 3(5)₁₁₁9_<113> = 3³ · C112
C112 = P36 · P76
P36 = 779171800996810039027022481680618939_<36>
P76 = 1690092513998630224825837674006645536944911498054409463644922048126340665503_<76>

SNFS difficulty: 113 digits. Divisors found: r1=779171800996810039027022481680618939 (pp36) r2=1690092513998630224825837674006645536944911498054409463644922048126340665503 (pp76) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.530). Factorization parameters were as follows: n: 1316872427983539094650205761316872427983539094650205761316872427983539094650205761316872427983539094650205761317 m: 20000000000000000000000 deg: 5 c5: 100 c0: 31 skew: 0.79 type: snfs lss: 1 rlim: 550000 alim: 550000 lpbr: 25 lpba: 25 mfbr: 47 mfba: 47 rlambda: 2.4 alambda: 2.4 Factor base limits: 550000/550000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved rational special-q in [275000, 375001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 70160 x 70392 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,113,5,0,0,0,0,0,0,0,0,550000,550000,25,25,47,47,2.4,2.4,50000 total time: 0.40 hours.
(32·10²⁰⁴+31)/9 = 3(5)₂₀₃9_<205> = 7 · C204
C204 = P32 · P173
P32 = 14637538698830902307625620189239_<32>
P173 = 34700950643913702365065874534902278676298261512243498500603317994747009402362554449670858232087763450045141503365706972462373562457470861965763765551899124491831749801274983_<173>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3260985831 Step 1 took 27673ms Step 2 took 17877ms ********** Factor found in step 2: 14637538698830902307625620189239 Found probable prime factor of 32 digits: 14637538698830902307625620189239 Probable prime cofactor 34700950643913702365065874534902278676298261512243498500603317994747009402362554449670858232087763450045141503365706972462373562457470861965763765551899124491831749801274983 has 173 digits
(32·10¹¹⁰+13)/9 = 3(5)₁₀₉7_<111> = 3 · 7 · 9887 · 1530281 · 20230061 · C92
C92 = P31 · P61
P31 = 7606386568876402013092015181731_<31>
P61 = 7272385101382534798671686555514012222568303439645131667835121_<61>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2507754419 Step 1 took 12573ms Step 2 took 9527ms ********** Factor found in step 2: 7606386568876402013092015181731 Found probable prime factor of 31 digits: 7606386568876402013092015181731 Probable prime cofactor 7272385101382534798671686555514012222568303439645131667835121 has 61 digits
(32·10¹⁹¹+13)/9 = 3(5)₁₉₀7_<192> = 3 · 397 · 11399 · 9912175103_<10> · 1107141154793_<13> · 34670318910569_<14> · 2487293749934501_<16> · 6876334367075809644387659601569_<31> · C103
C103 = P32 · P72
P32 = 29910520760937869999189622935359_<32>
P72 = 134552297455318840469145844020671821216847923472351025231267535414587713_<72>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3521872813 Step 1 took 10297ms Step 2 took 8073ms ********** Factor found in step 2: 29910520760937869999189622935359 Found probable prime factor of 32 digits: 29910520760937869999189622935359 Probable prime cofactor 134552297455318840469145844020671821216847923472351025231267535414587713 has 72 digits
(32·10¹⁰⁷+13)/9 = 3(5)₁₀₆7_<108> = 3² · 848868677 · C98
C98 = P27 · P72
P27 = 238802620593963929748934177_<27>
P72 = 194888118356224715493353351777762026261476308030109023440212914292340537_<72>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4219071836 Step 1 took 11769ms Step 2 took 7820ms ********** Factor found in step 2: 238802620593963929748934177 Found probable prime factor of 27 digits: 238802620593963929748934177 Probable prime cofactor 194888118356224715493353351777762026261476308030109023440212914292340537 has 72 digits
(32·10¹³⁸+31)/9 = 3(5)₁₃₇9_<139> = 7 · 29 · 28547 · 6549012698471_<13> · 318047692355660734589_<21> · C99
C99 = P35 · P65
P35 = 12106920853579459070424999289438561_<35>
P65 = 24330395648365789996989790128333355913417874067772163713318487061_<65>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1141709438 Step 1 took 10100ms Step 2 took 8013ms ********** Factor found in step 2: 12106920853579459070424999289438561 Found probable prime factor of 35 digits: 12106920853579459070424999289438561 Probable prime cofactor 24330395648365789996989790128333355913417874067772163713318487061 has 65 digits
(32·10¹⁰⁶+31)/9 = 3(5)₁₀₅9_<107> = 3 · 1821487 · C100
C100 = P28 · P73
P28 = 3571013824957159595463095741_<28>
P73 = 1822084889737849498179943594910491438357264930935924835236634397925820159_<73>

Factor found in step 2: 3571013824957159595463095741
(32·10¹¹⁶+31)/9 = 3(5)₁₁₅9_<117> = 491 · 175661008871473_<15> · C100
C100 = P43 · P58
P43 = 1726129193205343241018771466495207041016209_<43>
P58 = 2388236362175239596226223470142158679479256151585078511157_<58>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2138698920 Step 1 took 11101ms Step 2 took 8108ms ********** Factor found in step 2: 1726129193205343241018771466495207041016209 Found probable prime factor of 43 digits: 1726129193205343241018771466495207041016209 Probable prime cofactor 2388236362175239596226223470142158679479256151585078511157 has 58 digits
(32·10¹³²+13)/9 = 3(5)₁₃₁7_<133> = 148794791 · 2833366320968183379087743_<25> · C100
C100 = P30 · P71
P30 = 661868311318946194599394724447_<30>
P71 = 12742229569126623063338124721065029231175785715234648227686968662772787_<71>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3096332453 Step 1 took 10644ms Step 2 took 8337ms ********** Factor found in step 2: 661868311318946194599394724447 Found probable prime factor of 30 digits: 661868311318946194599394724447 Probable prime cofactor 12742229569126623063338124721065029231175785715234648227686968662772787 has 71 digits
(32·10¹⁴⁹+13)/9 = 3(5)₁₄₈7_<150> = 3 · 9234772121_<10> · 100360203094699379549_<21> · C120
C120 = P32 · P34 · P55
P32 = 25145039467698927171165751342183_<32>
P34 = 3767430535319777861990133738332443_<34>
P55 = 1349897908339817126731715201675741182458631650813620119_<55>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2310493951 Step 1 took 16384ms ********** Factor found in step 1: 25145039467698927171165751342183 Found probable prime factor of 32 digits: 25145039467698927171165751342183 Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=169416394 Step 1 took 15265ms Step 2 took 12202ms ********** Factor found in step 2: 3767430535319777861990133738332443 Found probable prime factor of 34 digits: 3767430535319777861990133738332443
(32·10¹⁴¹+31)/9 = 3(5)₁₄₀9_<142> = 383 · 5477 · 16602920627_<11> · 6586700235426342488768387_<25> · C101
C101 = P31 · P35 · P36
P31 = 3688852328182643226043829314643_<31>
P35 = 17459840163246399172064730922660979_<35>
P36 = 240647874318475240136761574757014533_<36>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1536110132 Step 1 took 10029ms Step 2 took 8096ms ********** Factor found in step 2: 3688852328182643226043829314643 Found probable prime factor of 31 digits: 3688852328182643226043829314643 Mon Nov 24 22:45:24 2008 Msieve v. 1.39 Mon Nov 24 22:45:24 2008 random seeds: 5e5c56b8 b847632e Mon Nov 24 22:45:25 2008 factoring 4201673421225585687652109078110886743277008789701716681609806135007807 (70 digits) Mon Nov 24 22:45:25 2008 searching for 15-digit factors Mon Nov 24 22:45:25 2008 commencing quadratic sieve (70-digit input) Mon Nov 24 22:45:25 2008 using multiplier of 23 Mon Nov 24 22:45:25 2008 using 64kb Opteron sieve core Mon Nov 24 22:45:25 2008 sieve interval: 6 blocks of size 65536 Mon Nov 24 22:45:25 2008 processing polynomials in batches of 17 Mon Nov 24 22:45:25 2008 using a sieve bound of 218287 (9781 primes) Mon Nov 24 22:45:25 2008 using large prime bound of 21392126 (24 bits) Mon Nov 24 22:45:25 2008 using trial factoring cutoff of 24 bits Mon Nov 24 22:45:25 2008 polynomial 'A' values have 9 factors Mon Nov 24 22:46:20 2008 10026 relations (4844 full + 5182 combined from 54427 partial), need 9877 Mon Nov 24 22:46:20 2008 begin with 59271 relations Mon Nov 24 22:46:20 2008 reduce to 14536 relations in 2 passes Mon Nov 24 22:46:20 2008 attempting to read 14536 relations Mon Nov 24 22:46:20 2008 recovered 14536 relations Mon Nov 24 22:46:20 2008 recovered 11729 polynomials Mon Nov 24 22:46:20 2008 attempting to build 10026 cycles Mon Nov 24 22:46:20 2008 found 10026 cycles in 1 passes Mon Nov 24 22:46:20 2008 distribution of cycle lengths: Mon Nov 24 22:46:20 2008 length 1 : 4844 Mon Nov 24 22:46:20 2008 length 2 : 5182 Mon Nov 24 22:46:20 2008 largest cycle: 2 relations Mon Nov 24 22:46:20 2008 matrix is 9781 x 10026 (1.4 MB) with weight 292831 (29.21/col) Mon Nov 24 22:46:20 2008 sparse part has weight 292831 (29.21/col) Mon Nov 24 22:46:20 2008 filtering completed in 3 passes Mon Nov 24 22:46:20 2008 matrix is 7725 x 7789 (1.2 MB) with weight 243518 (31.26/col) Mon Nov 24 22:46:20 2008 sparse part has weight 243518 (31.26/col) Mon Nov 24 22:46:20 2008 commencing Lanczos iteration Mon Nov 24 22:46:20 2008 memory use: 1.5 MB Mon Nov 24 22:46:20 2008 lanczos halted after 123 iterations (dim = 7717) Mon Nov 24 22:46:20 2008 recovered 59 nontrivial dependencies Mon Nov 24 22:46:20 2008 prp35 factor: 17459840163246399172064730922660979 Mon Nov 24 22:46:20 2008 prp36 factor: 240647874318475240136761574757014533 Mon Nov 24 22:46:20 2008 elapsed time 00:00:56
(32·10¹⁴⁸+13)/9 = 3(5)₁₄₇7_<149> = 37 · 1015690043_<10> · 21788482138371211_<17> · C122
C122 = P30 · C93
P30 = 331676232498798305313287633537_<30>
C93 = [130919163377370183397007958071376655425247437752619741439878676248451252269473992284455216761_<93>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1788152846 Step 1 took 15351ms Step 2 took 12352ms ********** Factor found in step 2: 331676232498798305313287633537 Found probable prime factor of 30 digits: 331676232498798305313287633537 Composite cofactor 130919163377370183397007958071376655425247437752619741439878676248451252269473992284455216761 has 93 digits
(32·10¹⁴⁵+13)/9 = 3(5)₁₄₄7_<146> = 37 · 3197004779_<10> · C135
C135 = P30 · C106
P30 = 254681218216645409818996342939_<30>
C106 = [1180226986500756972134059759800332242451110673451530099017680638918163275649167707645548036671643354257081_<106>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=905853048 Step 1 took 15690ms Step 2 took 12502ms ********** Factor found in step 2: 254681218216645409818996342939 Found probable prime factor of 30 digits: 254681218216645409818996342939 Composite cofactor 1180226986500756972134059759800332242451110673451530099017680638918163275649167707645548036671643354257081 has 106 digits
(32·10¹⁷⁶+13)/9 = 3(5)₁₇₅7_<177> = 3 · 7 · 9925220777_<10> · 2226740461727_<13> · 12954658312101283688035155697_<29> · C125
C125 = P36 · P89
P36 = 670617771284617422568164672853882771_<36>
P89 = 88181478626904046575951572845551494672796981698068302152918697596211551701623415862806429_<89>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=447520435 Step 1 took 13533ms ********** Factor found in step 1: 670617771284617422568164672853882771 Found probable prime factor of 36 digits: 670617771284617422568164672853882771 Probable prime cofactor 88181478626904046575951572845551494672796981698068302152918697596211551701623415862806429 has 89 digits
(32·10¹⁵⁸+13)/9 = 3(5)₁₅₇7_<159> = 3 · 7 · 4889 · 6761 · 1812937883_<10> · 5326454155007_<13> · C128
C128 = P35 · C94
P35 = 29917160077671362567875821596807351_<35>
C94 = [1773028506956992823270714966016153997533707382744774221590296026068158413217827561776171205483_<94>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2227927754 Step 1 took 13273ms Step 2 took 9689ms ********** Factor found in step 2: 29917160077671362567875821596807351 Found probable prime factor of 35 digits: 29917160077671362567875821596807351 Composite cofactor 1773028506956992823270714966016153997533707382744774221590296026068158413217827561776171205483 has 94 digits
(32·10¹³⁶+31)/9 = 3(5)₁₃₅9_<137> = 3 · 496891 · 1122571 · C125
C125 = P40 · C85
P40 = 4761415135792806704700849085613258322433_<40>
C85 = [4462469046952490638354343160769488971248707524461871437573226959519017881746418670181_<85>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1947702416 Step 1 took 15638ms Step 2 took 12168ms ********** Factor found in step 2: 4761415135792806704700849085613258322433 Found probable prime factor of 40 digits: 4761415135792806704700849085613258322433 Composite cofactor 4462469046952490638354343160769488971248707524461871437573226959519017881746418670181 has 85 digits
(32·10²⁰⁵+13)/9 = 3(5)₂₀₄7_<206> = 37 · 967379807683_<12> · 1184417920426891_<16> · C177
C177 = P33 · C145
P33 = 795593320256493401773149644687597_<33>
C145 = [1054174796839763600251173148992151267392532166265351897868569865399104713716754192260199669134941216435023948497548183846373245867966030763646021_<145>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3026039895 Step 1 took 31370ms Step 2 took 23237ms ********** Factor found in step 2: 795593320256493401773149644687597 Found probable prime factor of 33 digits: 795593320256493401773149644687597 Composite cofactor 1054174796839763600251173148992151267392532166265351897868569865399104713716754192260199669134941216435023948497548183846373245867966030763646021 has 145 digits
(32·10¹⁶⁶+13)/9 = 3(5)₁₆₅7_<167> = 37 · 71 · 1061 · 522009982599416239_<18> · C143
C143 = P33 · P110
P33 = 245652995118526324744360953023587_<33>
P110 = 99478938010092014586431984516395488503049535368699230296313702892077298924404182342090564617201312578520899767_<110>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3389241046 Step 1 took 18884ms Step 2 took 13969ms ********** Factor found in step 2: 245652995118526324744360953023587 Found probable prime factor of 33 digits: 245652995118526324744360953023587 Probable prime cofactor 99478938010092014586431984516395488503049535368699230296313702892077298924404182342090564617201312578520899767 has 110 digits
(32·10¹⁵⁵+13)/9 = 3(5)₁₅₄7_<156> = 3 · 9745711663_<10> · C146
C146 = P30 · C116
P30 = 836420183209442561075511309839_<30>
C116 = [14539455814731205321210177525875969087182313619367490212466311977932541637996102085909142345349193136322821376598967_<116>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3636140472 Step 1 took 19495ms Step 2 took 14178ms ********** Factor found in step 2: 836420183209442561075511309839 Found probable prime factor of 30 digits: 836420183209442561075511309839 Composite cofactor 14539455814731205321210177525875969087182313619367490212466311977932541637996102085909142345349193136322821376598967 has 116 digits
(32·10²⁰²+31)/9 = 3(5)₂₀₁9_<203> = 3² · 43 · 389 · 10429 · 1464390643_<10> · 164985366343084789_<18> · C167
C167 = P33 · P135
P33 = 466182519781633765887136567956083_<33>
P135 = 201069352542540042650344508717518021638710606851507419933772379949081681365191326619697562625614660401936804153516374403184966817798817_<135>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=430933424 Step 1 took 20917ms Step 2 took 13093ms ********** Factor found in step 2: 466182519781633765887136567956083 Found probable prime factor of 33 digits: 466182519781633765887136567956083 Probable prime cofactor 201069352542540042650344508717518021638710606851507419933772379949081681365191326619697562625614660401936804153516374403184966817798817 has 135 digits
(32·10¹⁸⁹+31)/9 = 3(5)₁₈₈9_<190> = 701 · 2383 · 2376873324384917_<16> · 4759383136642136198432852719_<28> · C141
C141 = P33 · P108
P33 = 333814150829410815649737373435823_<33>
P108 = 563642797085802332383830652856064364475273552193519508492141508999800002809776410596006504633051870472710537_<108>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1257938415 Step 1 took 14609ms Step 2 took 10712ms ********** Factor found in step 2: 333814150829410815649737373435823 Found probable prime factor of 33 digits: 333814150829410815649737373435823 Probable prime cofactor 563642797085802332383830652856064364475273552193519508492141508999800002809776410596006504633051870472710537 has 108 digits
(32·10¹⁷⁰+13)/9 = 3(5)₁₆₉7_<171> = 3² · 7 · 5540993 · C163
C163 = P35 · C128
P35 = 12984208595306517726286012309466401_<35>
C128 = [78444741095347397678580999552636074583338295133502838361927571852405256534421658239002539572952571276956284929552098180737904123_<128>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2815647174 Step 1 took 22088ms Step 2 took 13643ms ********** Factor found in step 2: 12984208595306517726286012309466401 Found probable prime factor of 35 digits: 12984208595306517726286012309466401 Composite cofactor 78444741095347397678580999552636074583338295133502838361927571852405256534421658239002539572952571276956284929552098180737904123 has 128 digits
(32·10¹⁷¹+31)/9 = 3(5)₁₇₀9_<172> = 23 · 769 · 17417 · 159589 · C158
C158 = P33 · P126
P33 = 107987834546806140945454007205523_<33>
P126 = 669733704346118779197931924293208612028416461194287929094971953976142368895751217073718031774189697036538650671648735737179543_<126>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3083652194 Step 1 took 19369ms Step 2 took 12661ms ********** Factor found in step 2: 107987834546806140945454007205523 Found probable prime factor of 33 digits: 107987834546806140945454007205523 Probable prime cofactor 669733704346118779197931924293208612028416461194287929094971953976142368895751217073718031774189697036538650671648735737179543 has 126 digits
(32·10¹⁹⁰+13)/9 = 3(5)₁₈₉7_<191> = 37 · 113 · 485964719904233782920111577_<27> · C161
C161 = P36 · C125
P36 = 699056118054564041970473612040807401_<36>
C125 = [25032862789153365018478740251724706852131249447149089422041868395151290097102441153373002551131680579832018686146524928049361_<125>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4191816949 Step 1 took 27021ms Step 2 took 20674ms ********** Factor found in step 2: 699056118054564041970473612040807401 Found probable prime factor of 36 digits: 699056118054564041970473612040807401 Composite cofactor 25032862789153365018478740251724706852131249447149089422041868395151290097102441153373002551131680579832018686146524928049361 has 125 digits
(32·10¹⁴³+31)/9 = 3(5)₁₄₂9_<144> = 19 · 59 · 1747 · 10253 · C134
C134 = P53 · P81
P53 = 23079352820141598249619821678406829423352705026772569_<53>
P81 = 767245531149285575267317899340707869952195439658557920669800614699184607306931801_<81>

SNFS difficulty: 145 digits. Divisors found: r1=23079352820141598249619821678406829423352705026772569 (pp53) r2=767245531149285575267317899340707869952195439658557920669800614699184607306931801 (pp81) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.729). Factorization parameters were as follows: n: 17707530313071302506770464821911341751421185586262790520373820609700536492625271455568848575873804968724781806697706346734440820566769 m: 40000000000000000000000000000 deg: 5 c5: 125 c0: 124 skew: 1.00 type: snfs lss: 1 rlim: 1830000 alim: 1830000 lpbr: 26 lpba: 26 mfbr: 50 mfba: 50 rlambda: 2.3 alambda: 2.3 Factor base limits: 1830000/1830000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 50/50 Sieved rational special-q in [915000, 2015001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 280603 x 280845 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1830000,1830000,26,26,50,50,2.3,2.3,100000 total time: 8.00 hours.
(32·10¹⁸⁵+31)/9 = 3(5)₁₈₄9_<186> = 17 · 347 · 4323883 · C176
C176 = P31 · P145
P31 = 3568420194938534766279266855287_<31>
P145 = 3906421938835330886237170731851398038761864173604013154645274793931398036626799143927453920469689066686149317964345952393979283699104118805078521_<145>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2825353847 Step 1 took 22174ms Step 2 took 14393ms ********** Factor found in step 2: 3568420194938534766279266855287 Found probable prime factor of 31 digits: 3568420194938534766279266855287 Probable prime cofactor 3906421938835330886237170731851398038761864173604013154645274793931398036626799143927453920469689066686149317964345952393979283699104118805078521 has 145 digits
(32·10¹⁸⁶+31)/9 = 3(5)₁₈₅9_<187> = 7² · 11888401325164912805825621_<26> · 6024171809472740969693719777_<28> · C133
C133 = P36 · P97
P36 = 426892186754019709687986691410122407_<36>
P97 = 2373407857358874412233536608360417319692140812876644426471548027819447985400508358165919646993389_<97>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4039017758 Step 1 took 13817ms Step 2 took 10652ms ********** Factor found in step 2: 426892186754019709687986691410122407 Found probable prime factor of 36 digits: 426892186754019709687986691410122407 Probable prime cofactor 2373407857358874412233536608360417319692140812876644426471548027819447985400508358165919646993389 has 97 digits
(32·10¹⁸¹+31)/9 = 3(5)₁₈₀9_<182> = 3 · 13² · 43 · 359 · 40039 · C171
C171 = P39 · P132
P39 = 372638789975169574957214534210894523011_<39>
P132 = 304484593113223482635726534234166940008636199680134144356572163201145489184394894990238818475119649638851178460186072715697294579669_<132>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=742742276 Step 1 took 24819ms Step 2 took 16777ms ********** Factor found in step 2: 372638789975169574957214534210894523011 Found probable prime factor of 39 digits: 372638789975169574957214534210894523011 Probable prime cofactor 304484593113223482635726534234166940008636199680134144356572163201145489184394894990238818475119649638851178460186072715697294579669 has 132 digits
(32·10¹⁸⁵+13)/9 = 3(5)₁₈₄7_<186> = 3 · 29 · 43 · 168832608157_<12> · C171
C171 = P33 · C139
P33 = 290495865583715280417753050377727_<33>
C139 = [1937864805353253318005736959102344995714626766253850408250067765460602155724470008087217876606783341886236558661754693541740125223893701443_<139>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3377039204 Step 1 took 24625ms Step 2 took 16884ms ********** Factor found in step 2: 290495865583715280417753050377727 Found probable prime factor of 33 digits: 290495865583715280417753050377727 Composite cofactor 1937864805353253318005736959102344995714626766253850408250067765460602155724470008087217876606783341886236558661754693541740125223893701443 has 139 digits
Nov 25, 2008 (4th): By Sinkiti Sibata / GGNFS
(31·10¹⁵¹+41)/9 = 3(4)₁₅₀9_<152> = 3² · 13 · 5813021873_<10> · C140
C140 = P50 · P91
P50 = 25159023166929253852356966287189982699044095992221_<50>
P91 = 2012971334982969607587578984544165589319626732300682305366828685278214905844400647139065009_<91>

Number: 34449_151 N=50644392451201039940486898811919837806947292225271785123798546055054166195530666819430997570993822590013111807604058720118930867542077294989 ( 140 digits) SNFS difficulty: 152 digits. Divisors found: r1=25159023166929253852356966287189982699044095992221 (pp50) r2=2012971334982969607587578984544165589319626732300682305366828685278214905844400647139065009 (pp91) Version: GGNFS-0.77.1-20060513-k8 Total time: 29.07 hours. Scaled time: 53.88 units (timescale=1.853). Factorization parameters were as follows: name: 34449_151 n: 50644392451201039940486898811919837806947292225271785123798546055054166195530666819430997570993822590013111807604058720118930867542077294989 m: 1000000000000000000000000000000 deg: 5 c5: 310 c0: 41 skew: 0.67 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:176735, largePrimes:7906736 encountered Relations: rels:7966289, finalFF:469567 Max relations in full relation-set: 28 Initial matrix: 353104 x 469567 with sparse part having weight 52765137. Pruned matrix : 314785 x 316614 with weight 32293031. Total sieving time: 27.06 hours. Total relation processing time: 0.20 hours. Matrix solve time: 1.63 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000 total time: 29.07 hours. --------- CPU info (if available) ----------
Nov 25, 2008 (3rd): By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(32·10¹⁶⁵-41)/9 = 3(5)₁₆₄1_<166> = 28933 · 77017 · 1481692160913415043336153_<25> · C133
C133 = P45 · P88
P45 = 952732027174124881625503241681651225883485593_<45>
P88 = 1130312827031637517531129402173147614032500164417042066514785305877661651415227444360379_<88>

GMP-ECM 6.0.1 [powered by GMP 4.1.4] [ECM] Input number is 1076885231038767992413352754329605253167257680508027092947125535368173098885445945137010069761323421743188297144152194724878946519747 (133 digits) Using B1=2114000, B2=2439300909, polynomial Dickson(6), sigma=2117395774 Step 1 took 28031ms Step 2 took 15469ms ********** Factor found in step 2: 952732027174124881625503241681651225883485593 Found probable prime factor of 45 digits: 952732027174124881625503241681651225883485593 Probable prime cofactor 1130312827031637517531129402173147614032500164417042066514785305877661651415227444360379 has 88 digits
(31·10¹⁶⁵+41)/9 = 3(4)₁₆₄9_<166> = 3571 · 21693282270189289_<17> · 1201928900749666965658298861489_<31> · C116
C116 = P44 · P72
P44 = 52360156332128908550551752115093402369791409_<44>
P72 = 706519827658752527682749389034573409857980191378297593467378048714187971_<72>

Number: n N=36993488627961056344488479201846311208466483880832964717932506627895049398002594345347037447623735419557550086941139 ( 116 digits) Divisors found: Tue Nov 25 04:40:41 2008 prp44 factor: 52360156332128908550551752115093402369791409 Tue Nov 25 04:40:41 2008 prp72 factor: 706519827658752527682749389034573409857980191378297593467378048714187971 Tue Nov 25 04:40:41 2008 elapsed time 00:49:14 (Msieve 1.38) Version: GGNFS-0.77.1-20050930-k8 Total time: 34.13 hours. Scaled time: 28.63 units (timescale=0.839). Factorization parameters were as follows: name: KA_3_4_164_9 n: 36993488627961056344488479201846311208466483880832964717932506627895049398002594345347037447623735419557550086941139 skew: 27554.71 # norm 2.12e+15 c5: 73080 c4: -270741138 c3: -118636966223308 c2: -1515144755494934221 c1: 37855017221866213730472 c0: 462963681614409640635618000 # alpha -5.09 Y1: 2124809634343 Y0: -13831376378547203326429 # Murphy_E 4.86e-10 # M 9599321862410283898123100379616895623818960450150469167051830326877405946979609366726360656345165674977990457946100 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved special-q in [100000, 2020001) Primes: RFBsize:315948, AFBsize:315804, largePrimes:6353259 encountered Relations: rels:6186586, finalFF:669899 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 33.85 hours. Total relation processing time: 0.28 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 34.13 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(31·10¹⁵⁸+41)/9 = 3(4)₁₅₇9_<159> = 17 · 341656622449638885049_<21> · C137
C137 = P51 · P87
P51 = 403369120592280214906680606143906456903218042215967_<51>
P87 = 147020458057331909160593920488882803957838848951345662283367806977244326092173137116359_<87>

Number: n N=59303512875660190239903873838592225362043522656415163955070689963128025148740225659345164492560895282613090072407941118087658052686704153 ( 137 digits) SNFS difficulty: 159 digits. Divisors found: Tue Nov 25 07:05:02 2008 prp51 factor: 403369120592280214906680606143906456903218042215967 Tue Nov 25 07:05:03 2008 prp87 factor: 147020458057331909160593920488882803957838848951345662283367806977244326092173137116359 Tue Nov 25 07:05:03 2008 elapsed time 01:23:00 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 32.75 hours. Scaled time: 67.17 units (timescale=2.051). Factorization parameters were as follows: name: KA_3_4_157_9 n: 59303512875660190239903873838592225362043522656415163955070689963128025148740225659345164492560895282613090072407941118087658052686704153 type: snfs skew: 0.27 deg: 5 c5: 31000 c0: 41 m: 10000000000000000000000000000000 rlim: 4000000 alim: 4000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 1750001) Primes: RFBsize:283146, AFBsize:283059, largePrimes:14395021 encountered Relations: rels:12895344, finalFF:596990 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 32.42 hours. Total relation processing time: 0.33 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,56,56,2.5,2.5,100000 total time: 32.75 hours. --------- CPU info (if available) ----------
Nov 25, 2008 (2nd): By Serge Batalov / ***Msieve-1.39-beta (and it's own poly. select!)***, GMP-ECM 6.2.1
(29·10¹⁹³+43)/9 = 3(2)₁₉₂7_<194> = 37 · 376545742538947_<15> · 5277015119215697866479228169_<28> · 12855017410089438631794603630041_<32> · C119
C119 = P55 · P64
P55 = 5149427821374870752051649514844128520721202945360567979_<55>
P64 = 6620884931864348748165073996244706685224112510911662888370567223_<64>

Number: 32227_193 N=34093769070263942955503177408570636568154822681818558606509181335014782811074308996491335063579593027737149761680752317 ( 119 digits) Divisors found: r1=5149427821374870752051649514844128520721202945360567979 (pp55) r2=6620884931864348748165073996244706685224112510911662888370567223 (pp64) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.950). Factorization parameters were as follows: name: 32227_193 n: 34093769070263942955503177408570636568154822681818558606509181335014782811074308996491335063579593027737149761680752317 Y0: -78144654374057956235581 Y1: 3845840165363 c0: -1871596898878390306911020084352 c1: -15959543399998484701121224 c2: 195713673571504411046 c3: 1015716197615315 c4: -3952249560 c5: 11700 skew: 142699.88 # norm 6.915e+16 # alpha -7.327632 # Murphy_E 2.169e-11 # M type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 4050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 618901 x 619149 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.5,2.5,100000 total time: 50.00 hours.
7·10¹⁷⁴+9 = 7(0)₁₇₃9_<175> = 2417 · 62141 · 24597884160931_<14> · 238162287627716653181_<21> · C133
C133 = P34 · P100
P34 = 1927956018365591441032402945607921_<34>
P100 = 4126437621140930568054372656781264192663859088452172703723803757169122245662645278492526385498425387_<100>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3558391417 Step 1 took 12353ms Step 2 took 9712ms ********** Factor found in step 2: 1927956018365591441032402945607921 Found probable prime factor of 34 digits: 1927956018365591441032402945607921 Probable prime cofactor 4126437621140930568054372656781264192663859088452172703723803757169122245662645278492526385498425387 has 100 digits
Nov 25, 2008: Factorizations of 355...557 and Factorizations of 355...559 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.
Nov 24, 2008 (6th): By Wataru Sakai / GGNFS
(13·10¹⁸¹+41)/9 = 1(4)₁₈₀9_<182> = 17 · 19 · C179
C179 = P50 · P130
P50 = 27562524394914669598711172166617269924884888204961_<50>
P130 = 1622479915196479736876798893912635377625993367732178502949268365993143847383362621642915177047839771381675513828189657496747215083_<130>

Number: 14449_181 N=44719642242862057103543171654626762985896112831097351221190230478156174750601995184038527691778465772273821809425524595803233574131406948744410044719642242862057103543171654626763 ( 179 digits) SNFS difficulty: 182 digits. Divisors found: r1=27562524394914669598711172166617269924884888204961 (pp50) r2=1622479915196479736876798893912635377625993367732178502949268365993143847383362621642915177047839771381675513828189657496747215083 (pp130) Version: GGNFS-0.77.1-20060722-nocona Total time: 351.70 hours. Scaled time: 697.77 units (timescale=1.984). Factorization parameters were as follows: n: 44719642242862057103543171654626762985896112831097351221190230478156174750601995184038527691778465772273821809425524595803233574131406948744410044719642242862057103543171654626763 m: 1000000000000000000000000000000000000 deg: 5 c5: 130 c0: 41 skew: 0.79 type: snfs lss: 1 rlim: 7600000 alim: 7600000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7600000/7600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3800000, 7100001) Primes: RFBsize:514565, AFBsize:513133, largePrimes:19008871 encountered Relations: rels:21296485, finalFF:2344194 Max relations in full relation-set: 32 Initial matrix: 1027765 x 2344193 with sparse part having weight 350900025. Pruned matrix : 721846 x 727048 with weight 202326012. Total sieving time: 336.70 hours. Total relation processing time: 0.39 hours. Matrix solve time: 14.25 hours. Time per square root: 0.35 hours. Prototype def-par.txt line would be: snfs,182,5,0,0,0,0,0,0,0,0,7600000,7600000,28,28,53,53,2.5,2.5,100000 total time: 351.70 hours. --------- CPU info (if available) ----------
Nov 24, 2008 (5th): By Jo Yeong Uk / GGNFS, Msieve
(32·10¹⁴⁷-41)/9 = 3(5)₁₄₆1_<148> = 1559 · 4523 · 6029 · 59237052585780701417_<20> · C118
C118 = P36 · P82
P36 = 577085991676888579048591258886894351_<36>
P82 = 2446557956931734686843641738363522287338694689153264217316360714289132931884914001_<82>

Number: 35551_147 N=1411874324770932570133784077882139868858237151608737458865903660716993942523655638259947462944967839507201267607708351 ( 118 digits) SNFS difficulty: 148 digits. Divisors found: r1=577085991676888579048591258886894351 (pp36) r2=2446557956931734686843641738363522287338694689153264217316360714289132931884914001 (pp82) Version: GGNFS-0.77.1-20050930-nocona Total time: 11.61 hours. Scaled time: 27.56 units (timescale=2.374). Factorization parameters were as follows: n: 1411874324770932570133784077882139868858237151608737458865903660716993942523655638259947462944967839507201267607708351 m: 200000000000000000000000000000 deg: 5 c5: 100 c0: -41 skew: 0.84 type: snfs lss: 1 rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [900000, 1800001) Primes: RFBsize:135072, AFBsize:134269, largePrimes:3907862 encountered Relations: rels:3974260, finalFF:333414 Max relations in full relation-set: 28 Initial matrix: 269405 x 333414 with sparse part having weight 32597540. Pruned matrix : 250682 x 252093 with weight 21205303. Total sieving time: 11.00 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.52 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,49,49,2.3,2.3,75000 total time: 11.61 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
(29·10¹⁶¹+43)/9 = 3(2)₁₆₀7_<162> = 3 · 127 · 1303 · 81017 · 2764441 · 723581991738401_<15> · C130
C130 = P41 · P44 · P46
P41 = 65731665480805222595720071261961910422471_<41>
P44 = 19465377701474799653076880016239617879270773_<44>
P46 = 3130238241711695725511513679546855990923798339_<46>

I used Serge Batalov's ECM result.Thanks for him to prevent wasting my resources. Mon Nov 24 20:15:36 2008 Mon Nov 24 20:15:36 2008 Mon Nov 24 20:15:36 2008 Msieve v. 1.34 Mon Nov 24 20:15:36 2008 random seeds: ab854081 b2e8a7f3 Mon Nov 24 20:15:36 2008 factoring 205755772979417104595082042547315417057596909369989234543823785687942743680835498075669 (87 digits) Mon Nov 24 20:15:37 2008 no P-1/P+1/ECM available, skipping Mon Nov 24 20:15:37 2008 commencing quadratic sieve (87-digit input) Mon Nov 24 20:15:37 2008 using multiplier of 13 Mon Nov 24 20:15:37 2008 using 32kb Intel Core sieve core Mon Nov 24 20:15:37 2008 sieve interval: 19 blocks of size 32768 Mon Nov 24 20:15:37 2008 processing polynomials in batches of 11 Mon Nov 24 20:15:37 2008 using a sieve bound of 1480243 (56155 primes) Mon Nov 24 20:15:37 2008 using large prime bound of 118419440 (26 bits) Mon Nov 24 20:15:37 2008 using double large prime bound of 340534638927600 (41-49 bits) Mon Nov 24 20:15:37 2008 using trial factoring cutoff of 49 bits Mon Nov 24 20:15:37 2008 polynomial 'A' values have 11 factors Mon Nov 24 20:51:07 2008 56540 relations (15918 full + 40622 combined from 591093 partial), need 56251 Mon Nov 24 20:51:07 2008 begin with 607011 relations Mon Nov 24 20:51:08 2008 reduce to 134507 relations in 10 passes Mon Nov 24 20:51:08 2008 attempting to read 134507 relations Mon Nov 24 20:51:09 2008 recovered 134507 relations Mon Nov 24 20:51:09 2008 recovered 112909 polynomials Mon Nov 24 20:51:09 2008 attempting to build 56540 cycles Mon Nov 24 20:51:09 2008 found 56540 cycles in 6 passes Mon Nov 24 20:51:09 2008 distribution of cycle lengths: Mon Nov 24 20:51:09 2008 length 1 : 15918 Mon Nov 24 20:51:09 2008 length 2 : 11285 Mon Nov 24 20:51:09 2008 length 3 : 10098 Mon Nov 24 20:51:09 2008 length 4 : 7501 Mon Nov 24 20:51:09 2008 length 5 : 4854 Mon Nov 24 20:51:09 2008 length 6 : 3068 Mon Nov 24 20:51:09 2008 length 7 : 1807 Mon Nov 24 20:51:09 2008 length 9+: 2009 Mon Nov 24 20:51:09 2008 largest cycle: 19 relations Mon Nov 24 20:51:09 2008 matrix is 56155 x 56540 (13.9 MB) with weight 3179419 (56.23/col) Mon Nov 24 20:51:09 2008 sparse part has weight 3179419 (56.23/col) Mon Nov 24 20:51:09 2008 filtering completed in 3 passes Mon Nov 24 20:51:09 2008 matrix is 51433 x 51497 (12.7 MB) with weight 2910899 (56.53/col) Mon Nov 24 20:51:09 2008 sparse part has weight 2910899 (56.53/col) Mon Nov 24 20:51:09 2008 saving the first 48 matrix rows for later Mon Nov 24 20:51:09 2008 matrix is 51385 x 51497 (8.4 MB) with weight 2277388 (44.22/col) Mon Nov 24 20:51:09 2008 sparse part has weight 1697155 (32.96/col) Mon Nov 24 20:51:09 2008 matrix includes 64 packed rows Mon Nov 24 20:51:09 2008 using block size 20598 for processor cache size 4096 kB Mon Nov 24 20:51:10 2008 commencing Lanczos iteration Mon Nov 24 20:51:10 2008 memory use: 7.5 MB Mon Nov 24 20:51:19 2008 lanczos halted after 814 iterations (dim = 51385) Mon Nov 24 20:51:19 2008 recovered 18 nontrivial dependencies Mon Nov 24 20:51:20 2008 prp41 factor: 65731665480805222595720071261961910422471 Mon Nov 24 20:51:20 2008 prp46 factor: 3130238241711695725511513679546855990923798339 Mon Nov 24 20:51:20 2008 elapsed time 00:35:44
Nov 24, 2008 (4th): By Erik Branger / GGNFS, Msieve
(31·10¹²⁹+23)/9 = 3(4)₁₂₈7_<130> = 3² · 113 · 1307 · 2023778357_<10> · C115
C115 = P40 · P75
P40 = 1808155721885738375046960285070261414171_<40>
P75 = 708147729052792909331890541107232260936223443052897711922138946192172196179_<75>

Number: 34447_129 N=1280441368227199028861108069600156146599223949765701089268336067031998884839311050344612389229259445048883382652609 ( 115 digits) SNFS difficulty: 131 digits. Divisors found: r1=1808155721885738375046960285070261414171 r2=708147729052792909331890541107232260936223443052897711922138946192172196179 Version: Total time: 5.59 hours. Scaled time: 11.52 units (timescale=2.061). Factorization parameters were as follows: n: 1280441368227199028861108069600156146599223949765701089268336067031998884839311050344612389229259445048883382652609 m: 100000000000000000000000000 deg: 5 c5: 31 c0: 230 skew: 1.49 type: snfs lss: 1 rlim: 1090000 alim: 1090000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3Factor base limits: 1090000/1090000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [545000, 1095001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 179344 x 179592 Total sieving time: 5.59 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1090000,1090000,26,26,47,47,2.3,2.3,50000 total time: 5.59 hours. --------- CPU info (if available) ----------
Nov 24, 2008 (3rd): By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38
(32·10¹⁸⁰-41)/9 = 3(5)₁₇₉1_<181> = 73 · 227 · 1693 · C174
C174 = P37 · C137
P37 = 1782454901553614650304098655062208111_<37>
C137 = [71102233465445408409612382583042372098046406252784713936200060362115527942842424757820993742113288336936350920262904289486346645532474047_<137>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1778025856 Step 1 took 25039ms Step 2 took 16297ms ********** Factor found in step 2: 1782454901553614650304098655062208111 Found probable prime factor of 37 digits: 1782454901553614650304098655062208111 Composite cofactor 71102233465445408409612382583042372098046406252784713936200060362115527942842424757820993742113288336936350920262904289486346645532474047 has 137 digits
(31·10¹⁷³+41)/9 = 3(4)₁₇₂9_<174> = 7 · 19 · 4691 · 7782742866519634973_<19> · C149
C149 = P32 · P117
P32 = 83377522136045683392304271789693_<32>
P117 = 850786214026242067189873714302933069285863191449712790626418410523447559037456956822189265479193369646179402708251047_<117>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=526494384 Step 1 took 20116ms Step 2 took 14285ms ********** Factor found in step 2: 83377522136045683392304271789693 Found probable prime factor of 32 digits: 83377522136045683392304271789693 Probable prime cofactor 850786214026242067189873714302933069285863191449712790626418410523447559037456956822189265479193369646179402708251047 has 117 digits
(32·10¹⁷⁸-41)/9 = 3(5)₁₇₇1_<179> = 28156920554652720527_<20> · 5210329393120129261464619_<25> · C135
C135 = P33 · P103
P33 = 125024948769124296559864649242229_<33>
P103 = 1938476088265407267608468946830297300218344442829662873259342913111548879306471757099239916369185285863_<103>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3121908314 Step 1 took 11952ms Step 2 took 9541ms ********** Factor found in step 2: 125024948769124296559864649242229 Found probable prime factor of 33 digits: 125024948769124296559864649242229 Probable prime cofactor 1938476088265407267608468946830297300218344442829662873259342913111548879306471757099239916369185285863 has 103 digits
(31·10¹⁹¹+41)/9 = 3(4)₁₉₀9_<192> = 7 · 19 · C190
C190 = P32 · P159
P32 = 16352608158325280068530540592321_<32>
P159 = 158372770134973853451453319258450143367925711568851708222095631882900541087769377379856401740310931607028215689622351972876314002803779729804456699654096482093_<159>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3712999241 Step 1 took 30616ms Step 2 took 19179ms ********** Factor found in step 2: 16352608158325280068530540592321 Found probable prime factor of 32 digits: 16352608158325280068530540592321 Probable prime cofactor 158372770134973853451453319258450143367925711568851708222095631882900541087769377379856401740310931607028215689622351972876314002803779729804456699654096482093 has 159 digits
(31·10¹⁹⁹+23)/9 = 3(4)₁₉₈7_<200> = 37 · 269 · 1171 · 2131 · 5335974706151_<13> · C177
C177 = P36 · P141
P36 = 587694556997297870644186569026808713_<36>
P141 = 442241408781365201047390169107407138612743617495375426139753485106195550727452708337636024716855229535778626601983057531826393257778505615673_<141>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1953325660 Step 1 took 28043ms Step 2 took 4695ms ********** Factor found in step 2: 587694556997297870644186569026808713 Found probable prime factor of 36 digits: 587694556997297870644186569026808713 Probable prime cofactor 442241408781365201047390169107407138612743617495375426139753485106195550727452708337636024716855229535778626601983057531826393257778505615673 has 141 digits
(32·10¹⁸⁷-41)/9 = 3(5)₁₈₆1_<188> = 3533 · 3739 · C181
C181 = P36 · P145
P36 = 827294513452956265618762024603598903_<36>
P145 = 3253480605332184680921640377891870384597854099985062122053939956180523797724675112907904366651740113627813901481730040593855626571502160884709191_<145>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3710936791 Step 1 took 28301ms Step 2 took 18753ms ********** Factor found in step 2: 827294513452956265618762024603598903 Found probable prime factor of 36 digits: 827294513452956265618762024603598903 Probable prime cofactor 3253480605332184680921640377891870384597854099985062122053939956180523797724675112907904366651740113627813901481730040593855626571502160884709191 has 145 digits
(31·10¹⁹²+23)/9 = 3(4)₁₉₁7_<193> = 3² · 232982699 · 5557520236851780468690203_<25> · C159
C159 = P41 · P118
P41 = 68847142672712911758410719469952112423811_<41>
P118 = 4293248525452453558473029420197389416256988299456207145251790401469095489360510382530193461098608464957750681137104549_<118>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1102381511 Step 1 took 24753ms Step 2 took 16493ms ********** Factor found in step 2: 68847142672712911758410719469952112423811 Found probable prime factor of 41 digits: 68847142672712911758410719469952112423811 Probable prime cofactor 4293248525452453558473029420197389416256988299456207145251790401469095489360510382530193461098608464957750681137104549 has 118 digits
(32·10¹⁹⁴-41)/9 = 3(5)₁₉₃1_<195> = 3 · 13 · 10067 · 157427 · 172969 · 6254734808027557837_<19> · 1569299852534710883524631_<25> · C136
C136 = P35 · P102
P35 = 10833599953333206062513961588376283_<35>
P102 = 312757454475848459879503203836292897307277646250554042188313990627705705745444626647351015419658382929_<102>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2633261084 Step 1 took 18932ms Step 2 took 13679ms ********** Factor found in step 2: 10833599953333206062513961588376283 Found probable prime factor of 35 digits: 10833599953333206062513961588376283 Probable prime cofactor 312757454475848459879503203836292897307277646250554042188313990627705705745444626647351015419658382929 has 102 digits
(31·10¹⁹⁴+23)/9 = 3(4)₁₉₃7_<195> = 67939 · 3215447 · 4483159 · C177
C177 = P35 · C143
P35 = 19142262145430902451199177266387881_<35>
C143 = [18373050867731199376514309341207865522577073846536752888979846972728248598440480445014355515199596125693843553423683088903672752641169831356221_<143>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2790789935 Step 1 took 28016ms Step 2 took 18710ms ********** Factor found in step 2: 19142262145430902451199177266387881 Found probable prime factor of 35 digits: 19142262145430902451199177266387881 Composite cofactor 18373050867731199376514309341207865522577073846536752888979846972728248598440480445014355515199596125693843553423683088903672752641169831356221 has 143 digits
(32·10²⁰³-41)/9 = 3(5)₂₀₂1_<204> = 3 · 7 · 61 · 22739 · 379837 · 536563509683722190583327839_<27> · C164
C164 = P33 · P132
P33 = 354102979541164110880003592212481_<33>
P132 = 169137144852597308225618316511538561476577202292669595418051665587776733341784913636767253699943916968786779942651786094067252427383_<132>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4180862736 Step 1 took 24856ms Step 2 took 16720ms ********** Factor found in step 2: 354102979541164110880003592212481 Found probable prime factor of 33 digits: 354102979541164110880003592212481 Probable prime cofactor 169137144852597308225618316511538561476577202292669595418051665587776733341784913636767253699943916968786779942651786094067252427383 has 132 digits
(32·10¹⁷⁰-41)/9 = 3(5)₁₆₉1_<171> = 3 · 13 · C169
C169 = P60 · P109
P60 = 998043704380098602044869755178934572557337371599512013922099_<60>
P109 = 9134679249814733560138714436517929988836887392421258951330673846471491717924198918470826456585941620511614291_<109>

SNFS difficulty: 171 digits. Divisors found: r1=998043704380098602044869755178934572557337371599512013922099 (pp60) r2=9134679249814733560138714436517929988836887392421258951330673846471491717924198918470826456585941620511614291 (pp109) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.950). Factorization parameters were as follows: n: 9116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809116809 m: 20000000000000000000000000000000000 deg: 5 c5: 1 c0: -41 skew: 2.10 type: snfs lss: 1 rlim: 5100000 alim: 5100000 lpbr: 27 lpba: 27 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 5100000/5100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [2550000, 4550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 962406 x 962647 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,54,54,2.5,2.5,200000 total time: 42.00 hours.
(26·10¹⁷⁵-71)/9 = 2(8)₁₇₄1_<176> = 3² · 7² · 51396937 · C166
C166 = P34 · C132
P34 = 5485541467765331185793932059381071_<34>
C132 = [232346165013524035407277568756740617921650712557593860807267789156818500888584376591986045173426639312451934844830078298810503320383_<132>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1753223694 Step 1 took 19425ms Step 2 took 12913ms ********** Factor found in step 2: 5485541467765331185793932059381071 Found probable prime factor of 34 digits: 5485541467765331185793932059381071 Composite cofactor 232346165013524035407277568756740617921650712557593860807267789156818500888584376591986045173426639312451934844830078298810503320383 has 132 digits
(29·10¹⁶⁶+43)/9 = 3(2)₁₆₅7_<167> = 13 · 37 · 61 · 139 · 577 · 52967429 · 80517401 · 84663716459138949752951_<23> · C119
C119 = P33 · P86
P33 = 761702925310844258565528121716823_<33>
P86 = 49786130187401782926117076264729435237188242647832592699115744065130471304676109804097_<86>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1084544580 Step 1 took 11941ms Step 2 took 9369ms ********** Factor found in step 2: 761702925310844258565528121716823 Found probable prime factor of 33 digits: 761702925310844258565528121716823 Probable prime cofactor 49786130187401782926117076264729435237188242647832592699115744065130471304676109804097 has 86 digits
(17·10¹⁶⁸+1)/9 = 1(8)₁₆₇9_<169> = 1722973771_<10> · 441744465139454537703640231879_<30> · C130
C130 = P38 · P92
P38 = 62067659878874716493548893843727505309_<38>
P92 = 39984462054234271226059897447734856516947654297265965031547710425930629429688197202520858369_<92>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3404844789 Step 1 took 14129ms Step 2 took 9713ms ********** Factor found in step 2: 62067659878874716493548893843727505309 Found probable prime factor of 38 digits: 62067659878874716493548893843727505309 Probable prime cofactor 39984462054234271226059897447734856516947654297265965031547710425930629429688197202520858369 has 92 digits
(22·10¹⁹⁸-13)/9 = 2(4)₁₉₇3_<199> = 761 · C196
C196 = P40 · C157
P40 = 1116164463888701212766808462545049455171_<40>
C157 = [2877844495788575168113607192129997691026661911215134817394216371163195475768528619368913071644015537645015736907890065295017724885610399161647249281604057553_<157>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2917915214 Step 1 took 32189ms Step 2 took 20917ms ********** Factor found in step 2: 1116164463888701212766808462545049455171 Found probable prime factor of 40 digits: 1116164463888701212766808462545049455171 Composite cofactor 2877844495788575168113607192129997691026661911215134817394216371163195475768528619368913071644015537645015736907890065295017724885610399161647249281604057553 has 157 digits
7·10¹⁶⁸+3 = 7(0)₁₆₇3_<169> = 341870677521159820404771314461_<30> · C140
C140 = P67 · P73
P67 = 5749965473293729696597801765242916256625281553550128309455278186337_<67>
P73 = 3560991610105122471722990488660298925687905168583791168409158735294004479_<73>

SNFS difficulty: 170 digits. Divisors found: r1=5749965473293729696597801765242916256625281553550128309455278186337 (pp67) r2=3560991610105122471722990488660298925687905168583791168409158735294004479 (pp73) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.723). Factorization parameters were as follows: n: 20475578808793101098067109352302136241947465332363736170498450833112663592480281217974216315890803341249803045346825107415291040669074603423 m: 5000000000000000000000000000000000 deg: 5 c5: 56 c0: 75 skew: 1.06 type: snfs lss: 1 rlim: 4800000 alim: 4800000 lpbr: 27 lpba: 27 mfbr: 53 mfba: 53 rlambda: 2.4 alambda: 2.4 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 53/53 Sieved rational special-q in [2400000, 4800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 917860 x 918102 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,53,53,2.4,2.4,100000 total time: 36.00 hours.
(17·10¹⁷⁰+1)/9 = 1(8)₁₆₉9_<171> = 3 · 7 · 23 · 37501 · 1307923 · 46512393772229041_<17> · C141
C141 = P37 · P104
P37 = 4807025903651954567691869159809598947_<37>
P104 = 35660637429904587067911820002302375560227157892722747763245437688750495106878532185673868322404000400823_<104>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3211483261 Step 1 took 14620ms Step 2 took 10677ms ********** Factor found in step 2: 4807025903651954567691869159809598947 Found probable prime factor of 37 digits: 4807025903651954567691869159809598947 Probable prime cofactor 35660637429904587067911820002302375560227157892722747763245437688750495106878532185673868322404000400823 has 104 digits
(26·10¹⁹⁸-71)/9 = 2(8)₁₉₇1_<199> = 281 · 7743557 · 15794094665352108651876851_<26> · 56141214127490815204720556917_<29> · C136
C136 = P34 · P102
P34 = 6672158345324570924911004640070319_<34>
P102 = 224409447889967492996585171782030978009865301467761627115443269401396865659446660091646883625181321541_<102>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=234056921 Step 1 took 16085ms Step 2 took 11441ms ********** Factor found in step 2: 6672158345324570924911004640070319 Found probable prime factor of 34 digits: 6672158345324570924911004640070319 Probable prime cofactor 224409447889967492996585171782030978009865301467761627115443269401396865659446660091646883625181321541 has 102 digits
4·10¹⁷²+7 = 4(0)₁₇₁7_<173> = 11 · 107 · 109 · 28109 · 4110437 · 37009237580533_<14> · C143
C143 = P45 · P99
P45 = 100305578557150326645901431665213886002442319_<45>
P99 = 726923004900429115307541442670226086141573640361924923419646985297364567603919585356657165361801089_<99>

SNFS difficulty: 172 digits. Divisors found: r1=100305578557150326645901431665213886002442319 (pp45) r2=726923004900429115307541442670226086141573640361924923419646985297364567603919585356657165361801089 (pp99) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.538). Factorization parameters were as follows: n: 72914432573039764485645880875045651008927003853729473970414449958165524809692232914487279677657403075526865507092416340315342944171122673885391 m: 20000000000000000000000000000000000 deg: 5 c5: 25 c0: 14 skew: 0.89 type: snfs lss: 1 rlim: 5300000 alim: 5300000 lpbr: 27 lpba: 27 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 5300000/5300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 53/53 Sieved rational special-q in [2650000, 4950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 965179 x 965421 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,172,5,0,0,0,0,0,0,0,0,5300000,5300000,27,27,53,53,2.5,2.5,100000 total time: 37.00 hours.
(14·10¹⁷⁰-23)/9 = 1(5)₁₆₉3_<171> = 3 · 691 · 22263472690475736337_<20> · C148
C148 = P28 · C120
P28 = 4140183215192466077295603949_<28>
C120 = [814092505380309124943551135799902484909003478048353721821331357008460909965452505234824673882421566041432715888319342397_<120>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2712233381 Step 1 took 14573ms ********** Factor found in step 1: 4140183215192466077295603949 Found probable prime factor of 28 digits: 4140183215192466077295603949 Composite cofactor 814092505380309124943551135799902484909003478048353721821331357008460909965452505234824673882421566041432715888319342397 has 120 digits
(67·10¹⁶⁹+23)/9 = 7(4)₁₆₈7_<170> = 7 · 11³ · 47 · 9634504347070848704094689_<25> · C140
C140 = P44 · P96
P44 = 36355850834570118053133951458400315996827161_<44>
P96 = 485349570832950084927284102664391171870708737358204755442100584286328162153818832105814831878757_<96>

SNFS difficulty: 171 digits. Divisors found: r1=36355850834570118053133951458400315996827161 (pp44) r2=485349570832950084927284102664391171870708737358204755442100584286328162153818832105814831878757 (pp96) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.728). Factorization parameters were as follows: n: 17645296599825356972196652946718116402721679125350513178441215898893463560972287693021794077117749728905327359821616360176301061848636518877 m: 10000000000000000000000000000000000 deg: 5 c5: 67 c0: 230 skew: 1.28 type: snfs lss: 1 rlim: 5100000 alim: 5100000 lpbr: 27 lpba: 27 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 5100000/5100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 53/53 Sieved rational special-q in [2550000, 5150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 954924 x 955166 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,53,53,2.5,2.5,100000 total time: 40.00 hours.
(8·10²⁰⁹+1)/9 = (8)₂₀₈9_<209> = 47 · 103 · 2237941 · 4609345901_<10> · 30497201569_<11> · 6734479233509927143_<19> · 20018060180487237540114636047_<29> · C132
C132 = P33 · P100
P33 = 287944218227248700481818032174301_<33>
P100 = 1503592325881574908416447589270613098491254186484255698064601081514562926755107233101700906147750381_<100>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1801430418 Step 1 took 15665ms Step 2 took 12740ms ********** Factor found in step 2: 287944218227248700481818032174301 Found probable prime factor of 33 digits: 287944218227248700481818032174301 Probable prime cofactor 1503592325881574908416447589270613098491254186484255698064601081514562926755107233101700906147750381 has 100 digits
(25·10¹⁷⁶-43)/9 = 2(7)₁₇₅3_<177> = 3 · 7 · 13 · 281 · C172
C172 = P35 · P138
P35 = 17117031548021844777195855517637263_<35>
P138 = 211543692732147083754486058627421714563422861284785083503461250666691057398802310212309971774486900777685438889359113718536082788821389067_<138>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=387572664 Step 1 took 24831ms Step 2 took 16880ms ********** Factor found in step 2: 17117031548021844777195855517637263 Found probable prime factor of 35 digits: 17117031548021844777195855517637263 Probable prime cofactor 211543692732147083754486058627421714563422861284785083503461250666691057398802310212309971774486900777685438889359113718536082788821389067 has 138 digits
Nov 24, 2008 (2nd): By Robert Backstrom / GGNFS, GMP-ECM, Msieve
(32·10¹⁵⁵-41)/9 = 3(5)₁₅₄1_<156> = 3² · 7 · 577 · 1458547 · 44654861 · 168236298229207179798289_<24> · C114
C114 = P49 · P66
P49 = 6589889674901733654324033821990327559794316422291_<49>
P66 = 135457821999390469099670401531267201792965530673937169973854234797_<66>

Number: n N=892652102578460163452218925109299370287832470891244205426080081902444565148626159311884218437879316318892518659927 ( 114 digits) Divisors found: r1=6589889674901733654324033821990327559794316422291 (pp49) r2=135457821999390469099670401531267201792965530673937169973854234797 (pp66) Version: GGNFS-0.77.1-20051202-athlon Total time: 31.44 hours. Scaled time: 64.30 units (timescale=2.045). Factorization parameters were as follows: name: KA_3_5_154_1 n: 892652102578460163452218925109299370287832470891244205426080081902444565148626159311884218437879316318892518659927 skew: 17881.72 # norm 1.65e+15 c5: 124740 c4: -3305249242 c3: -66180629234238 c2: 941123426736639434 c1: 18068018182754986939935 c0: 56736548028175370430747650 # alpha -4.71 Y1: 627207758323 Y0: -5901134905459535117853 # Murphy_E 5.87e-10 # M 875948648962425620048330212363563760145461037216438232018025505669232687984754761478672507962506218253364299892481 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [100000, 1700001) Primes: RFBsize:250150, AFBsize:250601, largePrimes:7261061 encountered Relations: rels:7091857, finalFF:612715 Max relations in full relation-set: 28 Initial matrix: 500833 x 612715 with sparse part having weight 46311257. Pruned matrix : 402233 x 404801 with weight 24686433. Total sieving time: 29.94 hours. Total relation processing time: 0.22 hours. Matrix solve time: 0.71 hours. Total square root time: 0.58 hours, sqrts: 3. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 31.44 hours. --------- CPU info (if available) ----------
(29·10¹⁵⁶+61)/9 = 3(2)₁₅₅9_<157> = 1583 · 13954570914080293172207179192384157_<35> · C120
C120 = P40 · P80
P40 = 1891857657521508354844909719281960503397_<40>
P80 = 77102707610175432125304673350243785044485094386824629693426617726158095364091947_<80>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 145867347807952268579412120037241313649196025306635310236169952952796714365773755203936139204221987693598990373913843959 (120 digits) Using B1=4516000, B2=8562077170, polynomial Dickson(6), sigma=3701885376 Step 1 took 59297ms Step 2 took 18375ms ********** Factor found in step 2: 1891857657521508354844909719281960503397 Found probable prime factor of 40 digits: 1891857657521508354844909719281960503397 Probable prime cofactor 77102707610175432125304673350243785044485094386824629693426617726158095364091947 has 80 digits
(31·10¹⁵²+23)/9 = 3(4)₁₅₁7_<153> = 107 · 677 · 487387 · C142
C142 = P62 · P81
P62 = 73614591348542831536038340486350437160072591338127130900413721_<62>
P81 = 132528380627864005990141182168512501174418120784716384110004695241628977470486099_<81>

Number: n N=9756022582004349047507364507499921946225366500848674640456733416082136242417803225035612096644979843850061570187862543328775065391426079364379 ( 142 digits) SNFS difficulty: 153 digits. Divisors found: r1=73614591348542831536038340486350437160072591338127130900413721 (pp62) r2=132528380627864005990141182168512501174418120784716384110004695241628977470486099 (pp81) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 29.59 hours. Scaled time: 38.64 units (timescale=1.306). Factorization parameters were as follows: name: KA_3_4_151_7 n: 9756022582004349047507364507499921946225366500848674640456733416082136242417803225035612096644979843850061570187862543328775065391426079364379 type: snfs skew: 0.38 deg: 5 c5: 3100 c0: 23 m: 1000000000000000000000000000000 rlim: 2400000 alim: 2400000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [100000, 1150001) Primes: RFBsize:176302, AFBsize:176014, largePrimes:12206874 encountered Relations: rels:11170380, finalFF:458117 Max relations in full relation-set: 28 Initial matrix: 352383 x 458117 with sparse part having weight 46424684. Pruned matrix : 296745 x 298570 with weight 28529175. Total sieving time: 26.27 hours. Total relation processing time: 0.42 hours. Matrix solve time: 2.66 hours. Total square root time: 0.25 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,28,28,56,56,2.5,2.5,100000 total time: 29.59 hours. --------- CPU info (if available) ----------
(32·10¹⁶⁰-41)/9 = 3(5)₁₅₉1_<161> = 47527409 · 1059981455713_<13> · 24745675942864343054205647_<26> · C116
C116 = P57 · P60
P57 = 163875404876858976588551599658128966517628862360417550081_<57>
P60 = 174041157702382505971591718344739887639052132484582251616929_<60>

Number: n N=28521065183715196355824844085452176849021322513407806760569274498363666847451583590806239126414388837306251084921249 ( 116 digits) Divisors found: Mon Nov 24 21:52:43 2008 prp57 factor: 163875404876858976588551599658128966517628862360417550081 Mon Nov 24 21:52:43 2008 prp60 factor: 174041157702382505971591718344739887639052132484582251616929 Mon Nov 24 21:52:43 2008 elapsed time 00:43:19 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 36.70 hours. Scaled time: 53.17 units (timescale=1.449). Factorization parameters were as follows: name: KA_3_5_159_1 n: 28521065183715196355824844085452176849021322513407806760569274498363666847451583590806239126414388837306251084921249 skew: 115436.32 # norm 1.36e+16 c5: 4800 c4: -783522220 c3: -300581098722771 c2: 10441071344211345536 c1: -17790501904306421094330 c0: -14839347986275999951931807367 # alpha -6.62 Y1: 1602120061993 Y0: -22635281731215525167408 # Murphy_E 5.30e-10 # M 3583062506374066250087638677111738450689527918815593869953971918521088312084087884886850189552142664315250577447483 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved special-q in [100000, 1720001) Primes: RFBsize:315948, AFBsize:316284, largePrimes:6170251 encountered Relations: rels:6123996, finalFF:749005 Max relations in full relation-set: 28 Initial matrix: 632311 x 749005 with sparse part having weight 34439405. Pruned matrix : 499348 x 502573 with weight 16557018. Total sieving time: 36.45 hours. Total relation processing time: 0.25 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 36.70 hours. --------- CPU info (if available) ----------
(31·10¹⁶¹+41)/9 = 3(4)₁₆₀9_<162> = 7 · 174672715331411159_<18> · C144
C144 = P50 · P95
P50 = 19271833543064282432963298327790989181455280173613_<50>
P95 = 14617497794949856808550674252675297489036964937095681265244845906085208668384217430630196277221_<95>

Number: n N=281705984320382834768168838574043320101246180179813501104002009710698781848409531013928771698738236445365657545494019832461744291094443157169473 ( 144 digits) SNFS difficulty: 162 digits. Divisors found: Mon Nov 24 23:56:29 2008 prp50 factor: 19271833543064282432963298327790989181455280173613 Mon Nov 24 23:56:29 2008 prp95 factor: 14617497794949856808550674252675297489036964937095681265244845906085208668384217430630196277221 Mon Nov 24 23:56:29 2008 elapsed time 01:55:56 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 30.90 hours. Scaled time: 56.45 units (timescale=1.827). Factorization parameters were as follows: name: KA_3_4_160_9 n: 281705984320382834768168838574043320101246180179813501104002009710698781848409531013928771698738236445365657545494019832461744291094443157169473 type: snfs skew: 0.67 deg: 5 c5: 310 c0: 41 m: 100000000000000000000000000000000 rlim: 4400000 alim: 4400000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 4400000/4400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 1800001) Primes: RFBsize:309335, AFBsize:309440, largePrimes:14840002 encountered Relations: rels:13480228, finalFF:698255 Max relations in full relation-set: 28 Initial matrix: 618842 x 698255 with sparse part having weight 80958662. Pruned matrix : 558849 x 562007 with weight 56988131. Total sieving time: 30.47 hours. Total relation processing time: 0.43 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4400000,4400000,28,28,56,56,2.5,2.5,100000 total time: 30.90 hours. --------- CPU info (if available) ----------
Nov 24, 2008: By Sinkiti Sibata / GGNFS
(31·10¹⁴⁶+41)/9 = 3(4)₁₄₅9_<147> = 587 · 3001 · 10030451 · C134
C134 = P30 · P50 · P55
P30 = 224989048861303607305990760947_<30>
P50 = 10690526136524945934822924019667842419697205995921_<50>
P55 = 8104648192327214100807766498210552641603797424899038771_<55>

Number: 34449_146 N=19493715659669137717634283501866598231174008195488279686946974479242646515513142646151978243163268222141919758885399329471406009037177 ( 134 digits) SNFS difficulty: 147 digits. Divisors found: r1=224989048861303607305990760947 (pp30) r2=10690526136524945934822924019667842419697205995921 (pp50) r3=8104648192327214100807766498210552641603797424899038771 (pp55) Version: GGNFS-0.77.1-20060513-k8 Total time: 22.19 hours. Scaled time: 43.77 units (timescale=1.972). Factorization parameters were as follows: name: 34449_146 n: 19493715659669137717634283501866598231174008195488279686946974479242646515513142646151978243163268222141919758885399329471406009037177 m: 100000000000000000000000000000 deg: 5 c5: 310 c0: 41 skew: 0.67 type: snfs lss: 1 rlim: 2000000 alim: 2000000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1000000, 2900001) Primes: RFBsize:148933, AFBsize:149232, largePrimes:4381484 encountered Relations: rels:4654922, finalFF:390109 Max relations in full relation-set: 28 Initial matrix: 298232 x 390109 with sparse part having weight 45287677. Pruned matrix : 267944 x 269499 with weight 29530201. Total sieving time: 20.88 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.02 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,49,49,2.3,2.3,100000 total time: 22.19 hours. --------- CPU info (if available) ----------
(32·10¹⁴⁸-41)/9 = 3(5)₁₄₇1_<149> = 73 · 7883 · 9419 · 16411 · 77309956598999_<14> · C121
C121 = P52 · P70
P52 = 4843514337760459572815534254707218514959785263884641_<52>
P70 = 1067473790535875080479232281288764753614270973659955842797287456129819_<70>

Number: 35551_148 N=5170324609644016527884881041706215829565526794526256285437584956636903529022585551794141982832094977765160463535536209979 ( 121 digits) SNFS difficulty: 150 digits. Divisors found: r1=4843514337760459572815534254707218514959785263884641 (pp52) r2=1067473790535875080479232281288764753614270973659955842797287456129819 (pp70) Version: GGNFS-0.77.1-20060513-k8 Total time: 23.00 hours. Scaled time: 45.79 units (timescale=1.991). Factorization parameters were as follows: name: 35551_148 n: 5170324609644016527884881041706215829565526794526256285437584956636903529022585551794141982832094977765160463535536209979 m: 400000000000000000000000000000 deg: 5 c5: 125 c0: -164 skew: 1.06 type: snfs lss: 1 rlim: 2200000 alim: 2200000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1100000, 1800001) Primes: RFBsize:162662, AFBsize:162616, largePrimes:7413483 encountered Relations: rels:7905348, finalFF:907301 Max relations in full relation-set: 28 Initial matrix: 325344 x 907301 with sparse part having weight 102751201. Pruned matrix : 217844 x 219534 with weight 33552730. Total sieving time: 21.78 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.91 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,49,49,2.4,2.4,100000 total time: 23.00 hours. --------- CPU info (if available) ----------
Nov 23, 2008 (7th): By Markus Tervooren / GGNFS
(79·10¹⁶⁸-7)/9 = 8(7)₁₆₈_<169> = 67 · 503 · 557 · 1205760657098941451_<19> · C144
C144 = P61 · P83
P61 = 7759395761065552324116951099007858595802868200287671942463351_<61>
P83 = 49980153610709556948637712835820984645682617068092949162535061366397670901309487461_<83>

N=387815792064344895618351800343352262605326578940255711093416077885722827353065727386705918821842903745588255225110877887373958010723171586541811 ( 144 digits) SNFS difficulty: 171 digits. Divisors found: r1=7759395761065552324116951099007858595802868200287671942463351 (pp61) r2=49980153610709556948637712835820984645682617068092949162535061366397670901309487461 (pp83) Version: GGNFS-0.77.1-20060722-nocona Total time: 67.86 hours. Scaled time: 137.82 units (timescale=2.031). Factorization parameters were as follows: n: 387815792064344895618351800343352262605326578940255711093416077885722827353065727386705918821842903745588255225110877887373958010723171586541811 m: 5000000000000000000000000000000000 deg: 5 c5: 632 c0: -175 skew: 0.77 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2500000, 7400001) Primes: RFBsize:348513, AFBsize:348556, largePrimes:10510580 encountered Relations: rels:11477264, finalFF:824020 Max relations in full relation-set: 32 Initial matrix: 697136 x 824020 with sparse part having weight 113502940. Pruned matrix : 630588 x 634137 with weight 91303413. Total sieving time: 61.15 hours. Total relation processing time: 0.30 hours. Matrix solve time: 6.27 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000 total time: 67.86 hours. --------- CPU info (if available) ----------
Nov 23, 2008 (6th): By Wataru Sakai / Msieve
(7·10¹⁹⁹-61)/9 = (7)₁₉₈1_<199> = C199
C199 = P54 · P73 · P74
P54 = 162977242689074237420617781730238377969785419608250633_<54>
P73 = 1078499033126045544619923456125343966895163031786125650645190344488551801_<73>
P74 = 44249544503388844859222475426113422020799712625769378619900612613079145387_<74>

Number: 77771_199 N=7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777771 ( 199 digits) SNFS difficulty: 200 digits. Divisors found: r1=162977242689074237420617781730238377969785419608250633 r2=1078499033126045544619923456125343966895163031786125650645190344488551801 r3=44249544503388844859222475426113422020799712625769378619900612613079145387 Version: Total time: 931.32 hours. Scaled time: 1842.15 units (timescale=1.978). Factorization parameters were as follows: n: 7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777771 m: 5000000000000000000000000000000000000000 deg: 5 c5: 112 c0: -305 skew: 1.22 type: snfs lss: 1 rlim: 15400000 alim: 15400000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 Factor base limits: 15400000/15400000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [7700000, 17600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 3166635 x 3166882 Total sieving time: 931.32 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,200,5,0,0,0,0,0,0,0,0,15400000,15400000,29,29,56,56,2.6,2.6,100000 total time: 931.32 hours. --------- CPU info (if available) ----------
Nov 23, 2008 (5th): By Kenji Ibusuki / GGNFS-0.77.1
(29·10¹⁹¹-11)/9 = 3(2)₁₉₀1_<192> = 3 · C192
C192 = P78 · P114
P78 = 234962048155245284311390320134874392608349302915475444887775014352507137133437_<78>
P114 = 457126622153211121929472840043706090744226808049801534743653872091775669361431051141638973630223980189775046870811_<114>

Number: 32221_191 N=107407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407 ( 192 digits) SNFS difficulty: 193 digits. Divisors found: r1=234962048155245284311390320134874392608349302915475444887775014352507137133437 (pp78) r2=457126622153211121929472840043706090744226808049801534743653872091775669361431051141638973630223980189775046870811 (pp114) Version: GGNFS-0.77.1 Total time: 665.59 hours. Scaled time: 1474.28 units (timescale=2.215). Factorization parameters were as follows: number: 32221_191 n: 107407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407 m: 200000000000000000000000000000000000000 type: snfs deg: 5 skew: 1.040 c0: -176 c5: 145 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.6 alambda: 2.6 qintsize: 10000 q0: 10000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Sieved special-q in [10000, 10420001) Relations: rels:16881690, finalFF:1351631 Initial matrix: 1203472 x 1351631 with sparse part having weight 178964056. Pruned matrix : 1169451 x 1175532 with weight 141697409. Total sieving time: 641.10 hours. Total relation processing time: 5.50 hours. Matrix solve time: 18.74 hours. Time per square root: 0.24 hours. Prototype def-par.txt line would be: snfs,193,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.6,2.6,100000 total time: 665.59 hours. --------- CPU info (if available) ----------
Nov 23, 2008 (4th): By Sinkiti Sibata / GGNFS
(31·10¹⁴³+41)/9 = 3(4)₁₄₂9_<144> = 7 · 233 · 1506781 · 512151545029_<12> · C123
C123 = P46 · P77
P46 = 2763241941388641272813974675010137882804144873_<46>
P77 = 99037048435115939648404395098604147324333042396077440279511597887787486342327_<77>

Number: 34449_143 N=273663325987250666193658535831565708877585280399160212059319626415796731264203768483627142893257335731842059187153779939471 ( 123 digits) SNFS difficulty: 145 digits. Divisors found: r1=2763241941388641272813974675010137882804144873 (pp46) r2=99037048435115939648404395098604147324333042396077440279511597887787486342327 (pp77) Version: GGNFS-0.77.1-20060513-k8 Total time: 21.55 hours. Scaled time: 42.13 units (timescale=1.955). Factorization parameters were as follows: name: 34449_143 n: 273663325987250666193658535831565708877585280399160212059319626415796731264203768483627142893257335731842059187153779939471 m: 50000000000000000000000000000 deg: 5 c5: 248 c0: 1025 skew: 1.33 type: snfs lss: 1 rlim: 1890000 alim: 1890000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1890000/1890000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [945000, 2845001) Primes: RFBsize:141338, AFBsize:141131, largePrimes:4261266 encountered Relations: rels:4491050, finalFF:353932 Max relations in full relation-set: 28 Initial matrix: 282536 x 353932 with sparse part having weight 41049959. Pruned matrix : 259250 x 260726 with weight 28392947. Total sieving time: 20.22 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.03 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1890000,1890000,26,26,49,49,2.3,2.3,100000 total time: 21.55 hours. --------- CPU info (if available) ----------
(31·10¹⁴²+41)/9 = 3(4)₁₄₁9_<143> = 3² · 17 · 809 · 3037 · C134
C134 = P51 · P84
P51 = 249013338986204435097585192153943981947080710065557_<51>
P84 = 367969504790916776725533016892666807229583043626074786102746866272342615210332238593_<84>

Number: 34449_142 N=91629315033086336258089934120092012703910322193113037170545087138342097380259920272842329508498424035340485686522479420891591595441301 ( 134 digits) SNFS difficulty: 144 digits. Divisors found: r1=249013338986204435097585192153943981947080710065557 (pp51) r2=367969504790916776725533016892666807229583043626074786102746866272342615210332238593 (pp84) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 22.54 hours. Scaled time: 10.66 units (timescale=0.473). Factorization parameters were as follows: name: 34449_142 n: 91629315033086336258089934120092012703910322193113037170545087138342097380259920272842329508498424035340485686522479420891591595441301 m: 20000000000000000000000000000 deg: 5 c5: 775 c0: 328 skew: 0.84 type: snfs lss: 1 rlim: 1790000 alim: 1790000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1790000/1790000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [895000, 2695001) Primes: RFBsize:134359, AFBsize:134584, largePrimes:4106423 encountered Relations: rels:4251420, finalFF:308391 Max relations in full relation-set: 28 Initial matrix: 269010 x 308391 with sparse part having weight 34555699. Pruned matrix : 256408 x 257817 with weight 26898094. Total sieving time: 20.05 hours. Total relation processing time: 0.26 hours. Matrix solve time: 2.15 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,144,5,0,0,0,0,0,0,0,0,1790000,1790000,26,26,49,49,2.3,2.3,100000 total time: 22.54 hours. --------- CPU info (if available) ----------
Nov 23, 2008 (3rd): By matsui / GMP-ECM
(26·10¹⁹⁴-71)/9 = 2(8)₁₉₃1_<195> = 127 · C193
C193 = P32 · P162
P32 = 11413826722781612615066149463171_<32>
P162 = 199294742752855759616595652474247599588531861457327919786234813849577319328816218083242071052288301464688708144297554003022214681904207255725793885068388792538693_<162>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] 2274715660542432195975503062117235345581802274715660542432195975503062117235345581802274715660542432195975503062117235345581802274715660542432195975503062117235345581802274715660542432195975503 = 11413826722781612615066149463171* 199294742752855759616595652474247599588531861457327919786234813849577319328816218083242071052288301464688708144297554003022214681904207255725793885068388792538693
Nov 23, 2008 (2nd): By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1
(31·10¹⁶⁶+41)/9 = 3(4)₁₆₅9_<167> = 3 · 1669 · C163
C163 = P69 · P95
P69 = 181349445677364300441878201566985382903693854106708508967491099295051_<69>
P95 = 37933713566617419532751041365089999565596259225341362011623253271472207437090733501918061961357_<95>

SNFS difficulty: 167 digits. Divisors found: r1=181349445677364300441878201566985382903693854106708508967491099295051 (pp69) r2=37933713566617419532751041365089999565596259225341362011623253271472207437090733501918061961357 (pp95) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.953). Factorization parameters were as follows: n: 6879257927789982912810953553913410114728269311852295674943967334620420300468233362181834320839713290282493398131504782193817544326831325033841510773805561103344207 m: 1000000000000000000000000000000000 deg: 5 c5: 310 c0: 41 skew: 0.67 type: snfs lss: 1 rlim: 4300000 alim: 4300000 lpbr: 27 lpba: 27 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 4300000/4300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 53/53 Sieved rational special-q in [2150000, 4750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 888968 x 889210 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,4300000,4300000,27,27,53,53,2.5,2.5,200000 total time: 50.00 hours.
9·10²¹³-1 = 8(9)₂₁₃_<214> = 293 · 31517 · 297630677 · 653240602737601_<15> · 2763180643414756163_<19> · 1880839632718006855987957867_<28> · C138
C138 = P33 · C106
P33 = 179481389251375241524195452694409_<33>
C106 = [5374012673820858541660812441083032124477051306670520962378248708789456585274457770479061617280814335697243_<106>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3144849970 Step 1 took 21095ms Step 2 took 13861ms ********** Factor found in step 2: 179481389251375241524195452694409 Found probable prime factor of 33 digits: 179481389251375241524195452694409 Composite cofactor 5374012673820858541660812441083032124477051306670520962378248708789456585274457770479061617280814335697243 has 106 digits
(32·10¹⁹⁶-41)/9 = 3(5)₁₉₅1_<197> = 31 · 73 · 11463757430011_<14> · 155869784726978437957_<21> · 84293380190754159708341_<23> · C138
C138 = P43 · P95
P43 = 2621005805007976677279163475247999795539713_<43>
P95 = 39799034734136717395774185493040870102947697545992386055866170111726118412127304962406603538947_<95>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=983927123 Step 1 took 18737ms Step 2 took 14050ms ********** Factor found in step 2: 2621005805007976677279163475247999795539713 Found probable prime factor of 43 digits: 2621005805007976677279163475247999795539713 Probable prime cofactor 39799034734136717395774185493040870102947697545992386055866170111726118412127304962406603538947 has 95 digits
Nov 23, 2008: By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(29·10¹⁶³+61)/9 = 3(2)₁₆₂9_<164> = 3 · 13 · 11518110473_<11> · C152
C152 = P59 · P94
P59 = 28968902095765974876176251537052725076837212300626871212011_<59>
P94 = 2476153740130391749632672210156842557311791559372719993391286077470404443761638984392106323937_<94>

Number: n N=71731455271902062683594372416193981301312252677751010734398503646894671594995286707459435462753685485581660198251757661434457299653547628447564971207307 ( 152 digits) SNFS difficulty: 164 digits. Divisors found: Sun Nov 23 02:19:40 2008 prp59 factor: 28968902095765974876176251537052725076837212300626871212011 Sun Nov 23 02:19:40 2008 prp94 factor: 2476153740130391749632672210156842557311791559372719993391286077470404443761638984392106323937 Sun Nov 23 02:19:40 2008 elapsed time 02:27:09 (Msieve 1.38) Version: GGNFS-0.77.1-20050930-k8 Total time: 45.02 hours. Scaled time: 37.68 units (timescale=0.837). Factorization parameters were as follows: name: KA_3_2_162_9 n: 71731455271902062683594372416193981301312252677751010734398503646894671594995286707459435462753685485581660198251757661434457299653547628447564971207307 type: snfs skew: 0.29 deg: 5 c5: 29000 c0: 61 m: 100000000000000000000000000000000 rlim: 4600000 alim: 4600000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 4600000/4600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 2350001) Primes: RFBsize:322441, AFBsize:321512, largePrimes:15532518 encountered Relations: rels:14047608, finalFF:643166 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 44.42 hours. Total relation processing time: 0.60 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,4600000,4600000,28,28,56,56,2.5,2.5,100000 total time: 45.02 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(31·10¹³¹+41)/9 = 3(4)₁₃₀9_<132> = 7 · 347 · 9920299856931027199537861_<25> · C104
C104 = P46 · P59
P46 = 1248935601417172450982864120557249528038055829_<46>
P59 = 11445290611232355952658107212384022849920784550095471386349_<59>

Number: n N=14294430912933799768877945621994775259320155089090998487296732530834015369018161723244761086025290478321 ( 104 digits) Divisors found: r1=1248935601417172450982864120557249528038055829 (pp46) r2=11445290611232355952658107212384022849920784550095471386349 (pp59) Version: GGNFS-0.77.1-20051202-athlon Total time: 7.75 hours. Scaled time: 15.85 units (timescale=2.045). Factorization parameters were as follows: name: KA_3_4_130_9 n: 14294430912933799768877945621994775259320155089090998487296732530834015369018161723244761086025290478321 skew: 3390.65 # norm 2.31e+13 c5: 91800 c4: 6859206 c3: -4725006547371 c2: -2699552177629954 c1: 27385722727592109576 c0: -21567600773132452286336 # alpha -4.55 Y1: 91767493427 Y0: -43497552812811424329 # Murphy_E 2.47e-09 # M 7075543479495724653964217112395499653546303942025095148589176977474698349047121752729839508576224373702 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [100000, 1000001) Primes: RFBsize:169511, AFBsize:169506, largePrimes:4076820 encountered Relations: rels:4026657, finalFF:415113 Max relations in full relation-set: 28 Initial matrix: 339097 x 415113 with sparse part having weight 23662065. Pruned matrix : 265650 x 267409 with weight 11101962. Polynomial selection time: 0.98 hours. Total sieving time: 6.36 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.20 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 7.75 hours. --------- CPU info (if available) ----------
(31·10¹⁵⁹+41)/9 = 3(4)₁₅₈9_<160> = 89 · 283 · 67447 · 110291 · 162901069 · C138
C138 = P33 · P105
P33 = 519200074012305510805012666334819_<33>
P105 = 217360863393650894273483985147045926746949619702827516312957917248727025467082747527790644449593568212041_<105>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 112853776361362171890036514539513706755461921707305238431624689696835446173126379474301045848075084708611487263335709392706447626493355579 (138 digits) Using B1=1428000, B2=2140044280, polynomial Dickson(6), sigma=3811119449 Step 1 took 15585ms Step 2 took 7162ms ********** Factor found in step 2: 519200074012305510805012666334819 Found probable prime factor of 33 digits: 519200074012305510805012666334819 Probable prime cofactor 217360863393650894273483985147045926746949619702827516312957917248727025467082747527790644449593568212041 has 105 digits
(32·10¹⁶⁸-41)/9 = 3(5)₁₆₇1_<169> = 67 · 91159 · C162
C162 = P40 · P123
P40 = 2071061672414038887327862478162760144139_<40>
P123 = 281086561073560727550682470459751650208883734024290695333856539193174433441099866200434115946299221513714137236518465529753_<123>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 582147603270119562384365247265284317160054042945065077461924499567273313587978157167009251435134830933511703358975297967247902845095416448111173892091701273067667 (162 digits) Using B1=2658000, B2=4281434440, polynomial Dickson(6), sigma=79681721 Step 1 took 53859ms Step 2 took 19406ms ********** Factor found in step 2: 2071061672414038887327862478162760144139 Found probable prime factor of 40 digits: 2071061672414038887327862478162760144139 Probable prime cofactor 281086561073560727550682470459751650208883734024290695333856539193174433441099866200434115946299221513714137236518465529753 has 123 digits
(32·10¹⁶²-41)/9 = 3(5)₁₆₁1_<163> = 23 · 29 · 1213 · 22133 · 16724402733491_<14> · 147843987594734310011684362061_<30> · C110
C110 = P47 · P64
P47 = 22564381405754882879509950206984140408804091429_<47>
P64 = 3558793866027322837892334872232527090837570341500904949191061183_<64>

Number: n N=80301982137501457226438683808161823698010328552916864791826396744849000596280781712481044585978795444664900507 ( 110 digits) Divisors found: r1=22564381405754882879509950206984140408804091429 (pp47) r2=3558793866027322837892334872232527090837570341500904949191061183 (pp64) Version: GGNFS-0.77.1-20051202-athlon Total time: 17.19 hours. Scaled time: 35.03 units (timescale=2.038). Factorization parameters were as follows: name: KA_3_5_161_1 n: 80301982137501457226438683808161823698010328552916864791826396744849000596280781712481044585978795444664900507 skew: 20941.36 # norm 3.03e+15 c5: 80160 c4: -178494500 c3: -208866880738614 c2: 1010698957953137416 c1: 26388170788187158703673 c0: 67057988088281024513967838 # alpha -6.73 Y1: 2999771929 Y0: -1000353997470729914547 # Murphy_E 1.09e-09 # M 51387382130815976307384603189548897007283674985944576533889534954907903830011786739793269560296316131041848063 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [100000, 1000001) Primes: RFBsize:230209, AFBsize:229814, largePrimes:6650753 encountered Relations: rels:6415890, finalFF:611905 Max relations in full relation-set: 28 Initial matrix: 460107 x 611905 with sparse part having weight 37008769. Pruned matrix : 312942 x 315306 with weight 13812048. Total sieving time: 16.59 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.29 hours. Total square root time: 0.11 hours, sqrts: 1. Prototype def-par.txt line would be: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 17.19 hours. --------- CPU info (if available) ----------
(29·10¹⁶⁸+43)/9 = 3(2)₁₆₇7_<169> = 23 · 701 · C165
C165 = P51 · P114
P51 = 977639558746409933281005872314517859936176961237157_<51>
P114 = 204423522793514430218662211232552454622248740088943549859241400069576142068391696971781870504041640804809998425557_<114>

Number: n N=199852522621238120834970056578938300702240415693247052175291336737717684191665460660064641953868524605980414452783118664158172934455264046531180439262061788886821449 ( 165 digits) SNFS difficulty: 169 digits. Divisors found: Sun Nov 23 17:05:15 2008 prp51 factor: 977639558746409933281005872314517859936176961237157 Sun Nov 23 17:05:15 2008 prp114 factor: 204423522793514430218662211232552454622248740088943549859241400069576142068391696971781870504041640804809998425557 Sun Nov 23 17:05:15 2008 elapsed time 03:41:45 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 60.15 hours. Scaled time: 110.02 units (timescale=1.829). Factorization parameters were as follows: name: KA_3_2_167_7 n: 199852522621238120834970056578938300702240415693247052175291336737717684191665460660064641953868524605980414452783118664158172934455264046531180439262061788886821449 type: snfs skew: 0.27 deg: 5 c5: 29000 c0: 43 m: 1000000000000000000000000000000000 rlim: 6000000 alim: 6000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 3400001) Primes: RFBsize:412849, AFBsize:412761, largePrimes:17173952 encountered Relations: rels:16036227, finalFF:897904 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 59.30 hours. Total relation processing time: 0.85 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,56,56,2.5,2.5,100000 total time: 60.15 hours. --------- CPU info (if available) ----------
(32·10¹⁵⁶-41)/9 = 3(5)₁₅₅1_<157> = 73 · 4871 · 7159 · 8814419 · 380665371239696891267261_<24> · C117
C117 = P36 · P82
P36 = 277097866660463929160851656157857587_<36>
P82 = 1502255740059705391542146623564628296144683429311981707835983561439257940088530651_<82>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 416271860748980805269299319690524959322893202639117708912412035001294381766873523256418067451244226313074070942399137 (117 digits) Using B1=2456000, B2=3567875230, polynomial Dickson(6), sigma=3741657175 Step 1 took 32438ms Step 2 took 11703ms ********** Factor found in step 2: 277097866660463929160851656157857587 Found probable prime factor of 36 digits: 277097866660463929160851656157857587 Probable prime cofactor 1502255740059705391542146623564628296144683429311981707835983561439257940088530651 has 82 digits
Nov 22, 2008 (10th): By Markus Tervooren / GGNFS
7·10¹⁶⁷-9 = 6(9)₁₆₆1_<168> = 1315096889_<10> · 2924704534089087990741564307_<28> · C132
C132 = P44 · P88
P44 = 32171713835165356860545627602731658117138163_<44>
P88 = 5656972847387801199256068528668241589373474506207018297434013731023661520263653791197559_<88>

N=181994511619460886722571958133515667928438683353276929634860147537918477950452863619794044389350713131234957248455222391689631344117 ( 132 digits) SNFS difficulty: 168 digits. Divisors found: r1=32171713835165356860545627602731658117138163 (pp44) r2=5656972847387801199256068528668241589373474506207018297434013731023661520263653791197559 (pp88) Version: GGNFS-0.77.1-20060722-nocona Total time: 76.94 hours. Scaled time: 157.33 units (timescale=2.045). Factorization parameters were as follows: n: 181994511619460886722571958133515667928438683353276929634860147537918477950452863619794044389350713131234957248455222391689631344117 m: 2000000000000000000000000000000000 deg: 5 c5: 175 c0: -72 skew: 0.84 type: snfs lss: 1 rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2250000, 5150001) Primes: RFBsize:315948, AFBsize:315881, largePrimes:10450786 encountered Relations: rels:11438283, finalFF:947465 Max relations in full relation-set: 32 Initial matrix: 631897 x 947465 with sparse part having weight 126994170. Pruned matrix : 515741 x 518964 with weight 79936325. Total sieving time: 72.97 hours. Total relation processing time: 0.21 hours. Matrix solve time: 3.65 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,52,52,2.4,2.4,100000 total time: 76.94 hours. --------- CPU info (if available) ----------
Nov 22, 2008 (9th): By Robert Backstrom / GGNFS, GMP-ECM, Msieve
(31·10¹³⁹+41)/9 = 3(4)₁₃₈9_<140> = 3 · 13² · 151 · 211 · 263887980827_<12> · 65802951844819631490175873_<26> · C96
C96 = P41 · P55
P41 = 17751030558599310472733314763851239959047_<41>
P55 = 6917724541519043115256611096093267885584506550050379251_<55>

Number: n N=122796739732476938843056250443218226969682997756544001036135289144535313607829770602408058533797 ( 96 digits) Divisors found: r1=17751030558599310472733314763851239959047 (pp41) r2=6917724541519043115256611096093267885584506550050379251 (pp55) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 9.83 hours. Scaled time: 12.88 units (timescale=1.310). Factorization parameters were as follows: name: KA_3_4_138_9 n: 122796739732476938843056250443218226969682997756544001036135289144535313607829770602408058533797 m: 7243743645372881631714 deg: 4 c4: 44599968 c3: 106520161388 c2: -859752888831163147 c1: -226792341741364904 c0: 453710617209311880093505 skew: 1635.250 type: gnfs # adj. I(F,S) = 56.152 # E(F1,F2) = 2.818535e-05 # GGNFS version 0.77.1-20060513-athlon-xp polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1227291941. # maxskew=2000.0 # These parameters should be manually set: rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 type: gnfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:92938, AFBsize:92030, largePrimes:1875231 encountered Relations: rels:1947293, finalFF:232210 Max relations in full relation-set: 28 Initial matrix: 185049 x 232210 with sparse part having weight 18482100. Pruned matrix : 164303 x 165292 with weight 10782603. Polynomial selection time: 0.17 hours. Total sieving time: 8.95 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.51 hours. Total square root time: 0.09 hours, sqrts: 2. Prototype def-par.txt line would be: gnfs,95,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 9.83 hours. --------- CPU info (if available) ----------
(31·10¹⁴⁸+41)/9 = 3(4)₁₄₇9_<149> = 3 · 5101 · 75389 · 4525837 · C133
C133 = P28 · P33 · P73
P28 = 7423689621961529739231158597_<28>
P33 = 702766731950884884431830689726431_<33>
P73 = 1264458890754132592520292456614107767172350023484547611212032793438177533_<73>

GMP-ECM 6.2.1 [powered by GMP 4.1.4] [ECM] Input number is 6596836416721928663206667563446461274548082634185610745446412601130224788147677008292567890044088794576244499948181477445864362643631 (133 digits) Using B1=68000, B2=20337252, polynomial x^2, sigma=1865824268 Step 1 took 906ms ********** Factor found in step 1: 7423689621961529739231158597 Found probable prime factor of 28 digits: 7423689621961529739231158597 Composite cofactor 888619642341522732989585178583008347765811867881469147602770976994452953369611679679482249149798980474723 has 105 digits GMP-ECM 6.2.1 [powered by GMP 4.1.4] [ECM] Input number is 888619642341522732989585178583008347765811867881469147602770976994452953369611679679482249149798980474723 (105 digits) Using B1=2118000, B2=2854078510, polynomial Dickson(6), sigma=2632614283 Step 1 took 20141ms Step 2 took 10594ms ********** Factor found in step 2: 702766731950884884431830689726431 Found probable prime factor of 33 digits: 702766731950884884431830689726431 Probable prime cofactor 1264458890754132592520292456614107767172350023484547611212032793438177533 has 73 digits
(31·10¹⁷⁶+23)/9 = 3(4)₁₇₅7_<177> = 61 · 127 · 6269 · 93623059 · 328309320318647_<15> · 202720502544193253155472756683183303_<36> · C112
C112 = P52 · P60
P52 = 2266172878279014315730607731434242315087398795693843_<52>
P60 = 502262330982835789656318035407776239301869911590546746313137_<60>

Number: n N=1138213272254499930643296820016032059483757432491990061526260841951018280753405751022578969878813592572060915491 ( 112 digits) Divisors found: r1=2266172878279014315730607731434242315087398795693843 (pp52) r2=502262330982835789656318035407776239301869911590546746313137 (pp60) Version: GGNFS-0.77.1-20051202-athlon Total time: 21.91 hours. Scaled time: 39.61 units (timescale=1.808). Factorization parameters were as follows: name: KA_3_4_175_7 n: 1138213272254499930643296820016032059483757432491990061526260841951018280753405751022578969878813592572060915491 skew: 53039.99 # norm 7.36e+15 c5: 17460 c4: 5859327786 c3: -118467216522632 c2: -13760853615378600227 c1: 187861473514694524755838 c0: 4487634284275327949310944367 # alpha -6.95 Y1: 227078131093 Y0: -2305860398873277449270 # Murphy_E 8.45e-10 # M 2024995312728739307273871443214848386906755758974582669400508108420435202603172697573663281195273174673215143 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:250150, AFBsize:249691, largePrimes:7037075 encountered Relations: rels:6984182, finalFF:754863 Max relations in full relation-set: 48 Initial matrix: 499918 x 754863 with sparse part having weight 51708575. Pruned matrix : 264371 x 266934 with weight 16537923. Polynomial selection time: 1.90 hours. Total sieving time: 19.21 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.46 hours. Total square root time: 0.14 hours, sqrts: 1. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 21.91 hours. --------- CPU info (if available) ----------
(31·10¹²⁷+41)/9 = 3(4)₁₂₆9_<128> = 3 · 13 · 5082719021_<10> · C117
C117 = P43 · P74
P43 = 9973580693615855217576522026614909705580359_<43>
P74 = 17422375492504637407894128118367596750344220464668292825505166710628246069_<74>

Number: n N=173763467848970278713974750561149146568806736167382405237857999467581269407965348000471968423452003995969697905358771 ( 117 digits) SNFS difficulty: 128 digits. Divisors found: Sat Nov 22 21:21:13 2008 prp43 factor: 9973580693615855217576522026614909705580359 Sat Nov 22 21:21:13 2008 prp74 factor: 17422375492504637407894128118367596750344220464668292825505166710628246069 Sat Nov 22 21:21:13 2008 elapsed time 00:09:04 (Msieve 1.38) Version: GGNFS-0.77.1-20050930-k8 Total time: 2.73 hours. Scaled time: 2.28 units (timescale=0.836). Factorization parameters were as follows: name: KA_3_4_126_9 n: 173763467848970278713974750561149146568806736167382405237857999467581269407965348000471968423452003995969697905358771 type: snfs skew: 0.42 deg: 5 c5: 3100 c0: 41 m: 10000000000000000000000000 rlim: 800000 alim: 800000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 550001) Primes: RFBsize:63951, AFBsize:63920, largePrimes:5985205 encountered Relations: rels:5100087, finalFF:107496 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 2.62 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,28,28,56,56,2.5,2.5,50000 total time: 2.73 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(31·10¹⁵⁷+23)/9 = 3(4)₁₅₆7_<158> = 37 · 5003 · C153
C153 = P39 · P115
P39 = 137062009031584687162325943108145597979_<39>
P115 = 1357593856795359123077509588134425961575969533810088621185776166177182280010278618966059027685150731758000076456763_<115>

Number: n N=186074541461309400545858670983596028569044759330587833486094529468505083136304403544059750335984595428928828888852874461509280617815496888053354173681977 ( 153 digits) SNFS difficulty: 158 digits. Divisors found: Sat Nov 22 22:31:01 2008 prp39 factor: 137062009031584687162325943108145597979 Sat Nov 22 22:31:01 2008 prp115 factor: 1357593856795359123077509588134425961575969533810088621185776166177182280010278618966059027685150731758000076456763 Sat Nov 22 22:31:01 2008 elapsed time 01:49:31 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 25.37 hours. Scaled time: 51.88 units (timescale=2.045). Factorization parameters were as follows: name: KA_3_4_156_7 n: 186074541461309400545858670983596028569044759330587833486094529468505083136304403544059750335984595428928828888852874461509280617815496888053354173681977 type: snfs skew: 0.38 deg: 5 c5: 3100 c0: 23 m: 10000000000000000000000000000000 rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 1400001) Primes: RFBsize:250150, AFBsize:249137, largePrimes:13233651 encountered Relations: rels:11691766, finalFF:516629 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 25.07 hours. Total relation processing time: 0.30 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,56,56,2.5,2.5,100000 total time: 25.37 hours. --------- CPU info (if available) ----------
Nov 22, 2008 (8th): By Serge Batalov / GMP-ECM 6.2.1
(32·10¹⁵²-41)/9 = 3(5)₁₅₁1_<153> = 3 · 13 · 1069 · 4057 · C145
C145 = P30 · P30 · P86
P30 = 177032885146535852618476212619_<30>
P30 = 183767390539545233362133693209_<30>
P86 = 64615655324137978437197139681674314373675816817502284960654218102416791281648499460663_<86>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=524982478 Step 1 took 18886ms Step 2 took 14066ms ********** Factor found in step 2: 183767390539545233362133693209 Found probable prime factor of 30 digits: 183767390539545233362133693209 Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1337943101 Step 1 took 19191ms Step 2 took 14563ms ********** Factor found in step 2: 177032885146535852618476212619 Found probable prime factor of 30 digits: 177032885146535852618476212619
Nov 22, 2008 (7th): By Sinkiti Sibata / GGNFS
(32·10¹¹⁵-41)/9 = 3(5)₁₁₄1_<116> = 1553881626764981_<16> · C101
C101 = P40 · P62
P40 = 1874364695456994437787812330948654894281_<40>
P62 = 12207744796954647002836007977637501893348342131034571999208491_<62>

Number: 35551_115 N=22881765858560605328444758333732016135351937111017680153991433819602314108836986599559243845282539971 ( 101 digits) SNFS difficulty: 116 digits. Divisors found: r1=1874364695456994437787812330948654894281 (pp40) r2=12207744796954647002836007977637501893348342131034571999208491 (pp62) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 1.63 hours. Scaled time: 0.77 units (timescale=0.473). Factorization parameters were as follows: name: 35551_115 n: 22881765858560605328444758333732016135351937111017680153991433819602314108836986599559243845282539971 m: 200000000000000000000000 deg: 5 c5: 1 c0: -41 skew: 2.10 type: snfs lss: 1 rlim: 610000 alim: 610000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 610000/610000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [305000, 455001) Primes: RFBsize:49861, AFBsize:49970, largePrimes:1339209 encountered Relations: rels:1376013, finalFF:204044 Max relations in full relation-set: 28 Initial matrix: 99895 x 204044 with sparse part having weight 8657884. Pruned matrix : 64281 x 64844 with weight 2194412. Total sieving time: 1.55 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.02 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,610000,610000,25,25,45,45,2.2,2.2,50000 total time: 1.63 hours. --------- CPU info (if available) ----------
(32·10¹³⁸-41)/9 = 3(5)₁₃₇1_<139> = 157 · 1854331 · C131
C131 = P43 · P88
P43 = 3614408098329054255724340417243253779450081_<43>
P88 = 3378962493146452219447414756610095654554526360880050718178161743928515403049413915028913_<88>

Number: 35551_138 N=12212949399178668390243576524554600576571890847483782236527906299510402361140498997671220687341868711013028609162572245802355191953 ( 131 digits) SNFS difficulty: 140 digits. Divisors found: r1=3614408098329054255724340417243253779450081 (pp43) r2=3378962493146452219447414756610095654554526360880050718178161743928515403049413915028913 (pp88) Version: GGNFS-0.77.1-20060513-k8 Total time: 8.53 hours. Scaled time: 16.67 units (timescale=1.955). Factorization parameters were as follows: name: 35551_138 n: 12212949399178668390243576524554600576571890847483782236527906299510402361140498997671220687341868711013028609162572245802355191953 m: 4000000000000000000000000000 deg: 5 c5: 125 c0: -164 skew: 1.06 type: snfs lss: 1 rlim: 1510000 alim: 1510000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1510000/1510000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [755000, 1430001) Primes: RFBsize:114886, AFBsize:114908, largePrimes:3334696 encountered Relations: rels:3259503, finalFF:260977 Max relations in full relation-set: 28 Initial matrix: 229860 x 260977 with sparse part having weight 20373065. Pruned matrix : 219199 x 220412 with weight 14602189. Total sieving time: 7.87 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.48 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1510000,1510000,26,26,48,48,2.3,2.3,75000 total time: 8.53 hours. --------- CPU info (if available) ----------
(31·10¹⁴¹+41)/9 = 3(4)₁₄₀9_<142> = 2143 · 21736275811319_<14> · C125
C125 = P36 · P90
P36 = 250844864487752569642988214862325027_<36>
P90 = 294785870231812031961140657885418584096523225421107367822479810640014905616838732440253811_<90>

Number: 34449_141 N=73945521671203103330866766193284634285998509123366560370612765483356140853530412183713691765269584991516030247771197457427897 ( 125 digits) SNFS difficulty: 142 digits. Divisors found: r1=250844864487752569642988214862325027 (pp36) r2=294785870231812031961140657885418584096523225421107367822479810640014905616838732440253811 (pp90) Version: GGNFS-0.77.1-20060513-k8 Total time: 15.03 hours. Scaled time: 29.39 units (timescale=1.955). Factorization parameters were as follows: name: 34449_141 n: 73945521671203103330866766193284634285998509123366560370612765483356140853530412183713691765269584991516030247771197457427897 m: 10000000000000000000000000000 deg: 5 c5: 310 c0: 41 skew: 0.67 type: snfs lss: 1 rlim: 1660000 alim: 1660000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1660000/1660000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [830000, 2130001) Primes: RFBsize:125335, AFBsize:125478, largePrimes:4027860 encountered Relations: rels:4257982, finalFF:408568 Max relations in full relation-set: 28 Initial matrix: 250880 x 408568 with sparse part having weight 45738650. Pruned matrix : 209515 x 210833 with weight 22135631. Total sieving time: 14.18 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.62 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,1660000,1660000,26,26,48,48,2.3,2.3,100000 total time: 15.03 hours. --------- CPU info (if available) ----------
Nov 22, 2008 (6th): By Wataru Sakai / GGNFS
9·10¹⁸⁵+7 = 9(0)₁₈₄7_<186> = 3260111 · C180
C180 = P89 · P92
P89 = 16002389063807038301896669024272082879641164981792275113754829766261058133472766404528443_<89>
P92 = 17251437819596683036560616627382651350704560527929204910892350271133158669382239777179811659_<92>

Number: 90007_185 N=276064219899261098778538522154613753948868612142347300444678110653287572110274772852826176777416474469734312727388730015634436986961486894157898304689625598637592400994935448516937 ( 180 digits) SNFS difficulty: 185 digits. Divisors found: r1=16002389063807038301896669024272082879641164981792275113754829766261058133472766404528443 r2=17251437819596683036560616627382651350704560527929204910892350271133158669382239777179811659 Version: Total time: 307.81 hours. Scaled time: 612.84 units (timescale=1.991). Factorization parameters were as follows: n: 276064219899261098778538522154613753948868612142347300444678110653287572110274772852826176777416474469734312727388730015634436986961486894157898304689625598637592400994935448516937 m: 10000000000000000000000000000000000000 deg: 5 c5: 9 c0: 7 skew: 0.95 type: snfs lss: 1 rlim: 10500000 alim: 10500000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.7 alambda: 2.7 Factor base limits: 10500000/10500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [5250000, 8150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1277949 x 1278197 Total sieving time: 307.81 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,185,5,0,0,0,0,0,0,0,0,10500000,10500000,28,28,55,55,2.7,2.7,100000 total time: 307.81 hours. --------- CPU info (if available) ----------
(29·10¹⁷⁷-11)/9 = 3(2)₁₇₆1_<178> = C178
C178 = P46 · P52 · P80
P46 = 4238791109846768319832989175973237807031692293_<46>
P52 = 9122678024342822606413342521202266190898888619350609_<52>
P80 = 83328032289291372193606565637887001304378576354453021528093000914205072237905433_<80>

Number: 32221_177 N=3222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221 ( 178 digits) SNFS difficulty: 179 digits. Divisors found: r1=4238791109846768319832989175973237807031692293 (pp46) r2=9122678024342822606413342521202266190898888619350609 (pp52) r3=83328032289291372193606565637887001304378576354453021528093000914205072237905433 (pp80) Version: GGNFS-0.77.1-20060722-nocona Total time: 216.80 hours. Scaled time: 436.41 units (timescale=2.013). Factorization parameters were as follows: n: 3222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221 m: 200000000000000000000000000000000000 deg: 5 c5: 725 c0: -88 skew: 0.66 type: snfs lss: 1 rlim: 6800000 alim: 6800000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 6800000/6800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3400000, 9900001) Primes: RFBsize:463872, AFBsize:464782, largePrimes:18589630 encountered Relations: rels:20197980, finalFF:1175338 Max relations in full relation-set: 32 Initial matrix: 928721 x 1175338 with sparse part having weight 172348679. Pruned matrix : 767940 x 772647 with weight 161025116. Total sieving time: 204.87 hours. Total relation processing time: 0.41 hours. Matrix solve time: 11.23 hours. Time per square root: 0.28 hours. Prototype def-par.txt line would be: snfs,179,5,0,0,0,0,0,0,0,0,6800000,6800000,28,28,53,53,2.5,2.5,100000 total time: 216.80 hours. --------- CPU info (if available) ----------
Nov 22, 2008 (5th): By Jo Yeong Uk / GGNFS
(29·10¹⁵⁷+43)/9 = 3(2)₁₅₆7_<158> = 37 · 18143 · 198323 · 120011103804224805681823546153_<30> · C118
C118 = P52 · P66
P52 = 3779316950432087251769608243853000617761392165509961_<52>
P66 = 533625819775685716703761578486849254082415913206193590187082495683_<66>

Number: 32227_157 N=2016741105866467140951604570336781152331001527925371904341000515480857002518308891930313959772708022278077300275998363 ( 118 digits) SNFS difficulty: 158 digits. Divisors found: r1=3779316950432087251769608243853000617761392165509961 (pp52) r2=533625819775685716703761578486849254082415913206193590187082495683 (pp66) Version: GGNFS-0.77.1-20050930-nocona Total time: 28.09 hours. Scaled time: 66.75 units (timescale=2.376). Factorization parameters were as follows: n: 2016741105866467140951604570336781152331001527925371904341000515480857002518308891930313959772708022278077300275998363 m: 10000000000000000000000000000000 deg: 5 c5: 2900 c0: 43 skew: 0.43 type: snfs lss: 1 rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1600000, 3400001) Primes: RFBsize:230209, AFBsize:230182, largePrimes:8236119 encountered Relations: rels:8439376, finalFF:550147 Max relations in full relation-set: 28 Initial matrix: 460458 x 550147 with sparse part having weight 61945056. Pruned matrix : 427466 x 429832 with weight 45595021. Total sieving time: 26.52 hours. Total relation processing time: 0.12 hours. Matrix solve time: 1.40 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,50,50,2.4,2.4,100000 total time: 28.09 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Nov 22, 2008 (4th): By Sinkiti Sibata / GGNFS, Msieve
(32·10¹²⁵-41)/9 = 3(5)₁₂₄1_<126> = 3 · 7 · C125
C125 = P49 · P76
P49 = 4101642359788017039736531885784855474095010630123_<49>
P76 = 4127911564696239905743837315670797719255008130849857537912706158500072765097_<76>

Number: 35551_125 N=16931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931 ( 125 digits) SNFS difficulty: 126 digits. Divisors found: r1=4101642359788017039736531885784855474095010630123 (pp49) r2=4127911564696239905743837315670797719255008130849857537912706158500072765097 (pp76) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 2.61 hours. Scaled time: 1.23 units (timescale=0.473). Factorization parameters were as follows: name: 35551_125 n: 16931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931 m: 20000000000000000000000000 deg: 5 c5: 1 c0: -41 skew: 2.10 type: snfs lss: 1 rlim: 900000 alim: 900000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 900000/900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [450000, 650001) Primes: RFBsize:71274, AFBsize:71351, largePrimes:2368602 encountered Relations: rels:2262222, finalFF:197699 Max relations in full relation-set: 28 Initial matrix: 142689 x 197699 with sparse part having weight 12662606. Pruned matrix : 119300 x 120077 with weight 5455752. Total sieving time: 2.36 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.15 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000 total time: 2.61 hours. --------- CPU info (if available) ----------
(32·10¹³²-41)/9 = 3(5)₁₃₁1_<133> = 73 · C131
C131 = P32 · P35 · P65
P32 = 53253233532503110182693787985653_<32>
P35 = 20444379394590998327962375579649849_<35>
P65 = 44736777108005239501416276185226616696706068766867655030020027971_<65>

Number: 35551_132 N=48706240487062404870624048706240487062404870624048706240487062404870624048706240487062404870624048706240487062404870624048706240487 ( 131 digits) SNFS difficulty: 133 digits. Divisors found: r1=53253233532503110182693787985653 (pp32) r2=20444379394590998327962375579649849 (pp35) r3=44736777108005239501416276185226616696706068766867655030020027971 (pp65) Version: GGNFS-0.77.1-20060513-k8 Total time: 6.33 hours. Scaled time: 12.59 units (timescale=1.991). Factorization parameters were as follows: name: 35551_132 n: 48706240487062404870624048706240487062404870624048706240487062404870624048706240487062404870624048706240487062404870624048706240487 m: 200000000000000000000000000 deg: 5 c5: 100 c0: -41 skew: 0.84 type: snfs lss: 1 rlim: 1180000 alim: 1180000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1180000/1180000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [590000, 1115001) Primes: RFBsize:91490, AFBsize:90768, largePrimes:3152382 encountered Relations: rels:3171737, finalFF:314254 Max relations in full relation-set: 28 Initial matrix: 182322 x 314254 with sparse part having weight 26946203. Pruned matrix : 151286 x 152261 with weight 9842261. Total sieving time: 6.01 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.17 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,133,5,0,0,0,0,0,0,0,0,1180000,1180000,26,26,47,47,2.3,2.3,75000 total time: 6.33 hours. --------- CPU info (if available) ----------
(32·10¹²¹-41)/9 = 3(5)₁₂₀1_<122> = 31 · 97 · 624613195527409379246773_<24> · C95
C95 = P46 · P49
P46 = 7302277230608177321336738676050278849209010349_<46>
P49 = 2592415258819787071229728638616500578052858667409_<49>

Fri Nov 21 23:38:37 2008 Msieve v. 1.38 Fri Nov 21 23:38:37 2008 random seeds: 0d4af2ec 94d26f7d Fri Nov 21 23:38:37 2008 factoring 18930534916760935971590741741646619489241142175356386448608577960372293068418528062763830015741 (95 digits) Fri Nov 21 23:38:37 2008 searching for 15-digit factors Fri Nov 21 23:38:39 2008 commencing quadratic sieve (95-digit input) Fri Nov 21 23:38:39 2008 using multiplier of 1 Fri Nov 21 23:38:39 2008 using 32kb Intel Core sieve core Fri Nov 21 23:38:39 2008 sieve interval: 36 blocks of size 32768 Fri Nov 21 23:38:39 2008 processing polynomials in batches of 6 Fri Nov 21 23:38:39 2008 using a sieve bound of 2125181 (78824 primes) Fri Nov 21 23:38:39 2008 using large prime bound of 310276426 (28 bits) Fri Nov 21 23:38:39 2008 using double large prime bound of 1928180890905122 (43-51 bits) Fri Nov 21 23:38:39 2008 using trial factoring cutoff of 51 bits Fri Nov 21 23:38:39 2008 polynomial 'A' values have 12 factors Sat Nov 22 02:33:35 2008 78924 relations (20057 full + 58867 combined from 1153943 partial), need 78920 Sat Nov 22 02:33:36 2008 begin with 1174000 relations Sat Nov 22 02:33:37 2008 reduce to 202550 relations in 9 passes Sat Nov 22 02:33:37 2008 attempting to read 202550 relations Sat Nov 22 02:33:40 2008 recovered 202550 relations Sat Nov 22 02:33:40 2008 recovered 182655 polynomials Sat Nov 22 02:33:40 2008 attempting to build 78924 cycles Sat Nov 22 02:33:40 2008 found 78924 cycles in 6 passes Sat Nov 22 02:33:40 2008 distribution of cycle lengths: Sat Nov 22 02:33:40 2008 length 1 : 20057 Sat Nov 22 02:33:40 2008 length 2 : 14148 Sat Nov 22 02:33:40 2008 length 3 : 13467 Sat Nov 22 02:33:40 2008 length 4 : 10622 Sat Nov 22 02:33:40 2008 length 5 : 7732 Sat Nov 22 02:33:40 2008 length 6 : 5123 Sat Nov 22 02:33:40 2008 length 7 : 3320 Sat Nov 22 02:33:40 2008 length 9+: 4455 Sat Nov 22 02:33:40 2008 largest cycle: 20 relations Sat Nov 22 02:33:40 2008 matrix is 78824 x 78924 (20.4 MB) with weight 5044100 (63.91/col) Sat Nov 22 02:33:40 2008 sparse part has weight 5044100 (63.91/col) Sat Nov 22 02:33:41 2008 filtering completed in 3 passes Sat Nov 22 02:33:41 2008 matrix is 74614 x 74678 (19.5 MB) with weight 4821220 (64.56/col) Sat Nov 22 02:33:41 2008 sparse part has weight 4821220 (64.56/col) Sat Nov 22 02:33:42 2008 saving the first 48 matrix rows for later Sat Nov 22 02:33:42 2008 matrix is 74566 x 74678 (12.6 MB) with weight 3859562 (51.68/col) Sat Nov 22 02:33:42 2008 sparse part has weight 2866657 (38.39/col) Sat Nov 22 02:33:42 2008 matrix includes 64 packed rows Sat Nov 22 02:33:42 2008 using block size 29871 for processor cache size 1024 kB Sat Nov 22 02:33:43 2008 commencing Lanczos iteration Sat Nov 22 02:33:43 2008 memory use: 12.1 MB Sat Nov 22 02:34:22 2008 lanczos halted after 1180 iterations (dim = 74564) Sat Nov 22 02:34:22 2008 recovered 16 nontrivial dependencies Sat Nov 22 02:34:23 2008 prp46 factor: 7302277230608177321336738676050278849209010349 Sat Nov 22 02:34:23 2008 prp49 factor: 2592415258819787071229728638616500578052858667409 Sat Nov 22 02:34:23 2008 elapsed time 02:55:46
(32·10¹²³-41)/9 = 3(5)₁₂₂1_<124> = 167 · 293 · 2268001 · 259137899539_<12> · 260503293345466609_<18> · C84
C84 = P42 · P43
P42 = 167982103839853336193445278263392698635919_<42>
P43 = 2825354631611978018062501736888645582464009_<43>

Fri Nov 21 21:28:02 2008 Msieve v. 1.38 Fri Nov 21 21:28:02 2008 random seeds: b8cb3a44 4d4e9d2a Fri Nov 21 21:28:02 2008 factoring 474609015111853860752833336137112158853448747727127472704320673550969428561212139271 (84 digits) Fri Nov 21 21:28:04 2008 searching for 15-digit factors Fri Nov 21 21:28:09 2008 commencing quadratic sieve (84-digit input) Fri Nov 21 21:28:10 2008 using multiplier of 15 Fri Nov 21 21:28:10 2008 using 64kb Pentium 2 sieve core Fri Nov 21 21:28:10 2008 sieve interval: 6 blocks of size 65536 Fri Nov 21 21:28:10 2008 processing polynomials in batches of 17 Fri Nov 21 21:28:10 2008 using a sieve bound of 1390619 (53529 primes) Fri Nov 21 21:28:10 2008 using large prime bound of 119593234 (26 bits) Fri Nov 21 21:28:10 2008 using double large prime bound of 346634530714364 (41-49 bits) Fri Nov 21 21:28:10 2008 using trial factoring cutoff of 49 bits Fri Nov 21 21:28:10 2008 polynomial 'A' values have 11 factors Sat Nov 22 01:02:21 2008 53629 relations (17104 full + 36525 combined from 561999 partial), need 53625 Sat Nov 22 01:02:31 2008 begin with 579103 relations Sat Nov 22 01:02:32 2008 reduce to 121584 relations in 10 passes Sat Nov 22 01:02:32 2008 attempting to read 121584 relations Sat Nov 22 01:02:37 2008 recovered 121584 relations Sat Nov 22 01:02:37 2008 recovered 93293 polynomials Sat Nov 22 01:02:38 2008 attempting to build 53629 cycles Sat Nov 22 01:02:38 2008 found 53629 cycles in 4 passes Sat Nov 22 01:02:41 2008 distribution of cycle lengths: Sat Nov 22 01:02:41 2008 length 1 : 17104 Sat Nov 22 01:02:41 2008 length 2 : 11333 Sat Nov 22 01:02:41 2008 length 3 : 9269 Sat Nov 22 01:02:41 2008 length 4 : 6572 Sat Nov 22 01:02:41 2008 length 5 : 4225 Sat Nov 22 01:02:41 2008 length 6 : 2400 Sat Nov 22 01:02:41 2008 length 7 : 1329 Sat Nov 22 01:02:41 2008 length 9+: 1397 Sat Nov 22 01:02:41 2008 largest cycle: 16 relations Sat Nov 22 01:02:42 2008 matrix is 53529 x 53629 (11.4 MB) with weight 2782077 (51.88/col) Sat Nov 22 01:02:42 2008 sparse part has weight 2782077 (51.88/col) Sat Nov 22 01:02:46 2008 filtering completed in 3 passes Sat Nov 22 01:02:46 2008 matrix is 47011 x 47075 (10.2 MB) with weight 2486567 (52.82/col) Sat Nov 22 01:02:46 2008 sparse part has weight 2486567 (52.82/col) Sat Nov 22 01:02:48 2008 saving the first 48 matrix rows for later Sat Nov 22 01:02:48 2008 matrix is 46963 x 47075 (6.2 MB) with weight 1901594 (40.39/col) Sat Nov 22 01:02:48 2008 sparse part has weight 1340469 (28.48/col) Sat Nov 22 01:02:48 2008 matrix includes 64 packed rows Sat Nov 22 01:02:48 2008 using block size 5461 for processor cache size 128 kB Sat Nov 22 01:02:49 2008 commencing Lanczos iteration Sat Nov 22 01:02:49 2008 memory use: 6.4 MB Sat Nov 22 01:04:39 2008 lanczos halted after 744 iterations (dim = 46954) Sat Nov 22 01:04:40 2008 recovered 14 nontrivial dependencies Sat Nov 22 01:04:41 2008 prp42 factor: 167982103839853336193445278263392698635919 Sat Nov 22 01:04:41 2008 prp43 factor: 2825354631611978018062501736888645582464009 Sat Nov 22 01:04:41 2008 elapsed time 03:36:39
(32·10¹¹¹-41)/9 = 3(5)₁₁₀1_<112> = 46560268009_<11> · C101
C101 = P51 · P51
P51 = 250725206151227572491375889110383529086023607868659_<51>
P51 = 304574822852910071162849414423941486520137105717021_<51>

Number: 35551_111 N=76364585248269496393816506554713280356615130143710070231171455531033722911050513054523245829788744839 ( 101 digits) SNFS difficulty: 112 digits. Divisors found: r1=250725206151227572491375889110383529086023607868659 (pp51) r2=304574822852910071162849414423941486520137105717021 (pp51) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 1.54 hours. Scaled time: 0.73 units (timescale=0.473). Factorization parameters were as follows: name: 35551_111 n: 76364585248269496393816506554713280356615130143710070231171455531033722911050513054523245829788744839 m: 20000000000000000000000 deg: 5 c5: 10 c0: -41 skew: 1.33 type: snfs lss: 1 rlim: 530000 alim: 530000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 530000/530000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [265000, 415001) Primes: RFBsize:43825, AFBsize:43507, largePrimes:1230717 encountered Relations: rels:1219885, finalFF:156266 Max relations in full relation-set: 28 Initial matrix: 87398 x 156266 with sparse part having weight 7026889. Pruned matrix : 64055 x 64555 with weight 2168146. Total sieving time: 1.46 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.02 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,112,5,0,0,0,0,0,0,0,0,530000,530000,25,25,45,45,2.2,2.2,50000 total time: 1.54 hours. --------- CPU info (if available) ----------
(31·10¹¹⁶+41)/9 = 3(4)₁₁₅9_<117> = 4159 · 5309 · 1265569807591063802657_<22> · C89
C89 = P38 · P51
P38 = 24351976690366456440494140268150735011_<38>
P51 = 506170946785176908374198765538995513913432276329177_<51>

Sat Nov 22 05:22:34 2008 Msieve v. 1.38 Sat Nov 22 05:22:34 2008 random seeds: 1a24b790 2ab2abb3 Sat Nov 22 05:22:34 2008 factoring 12326263097453348113695198957819947847469270526475883181784504535093721446219669534715947 (89 digits) Sat Nov 22 05:22:35 2008 searching for 15-digit factors Sat Nov 22 05:22:36 2008 commencing quadratic sieve (89-digit input) Sat Nov 22 05:22:36 2008 using multiplier of 3 Sat Nov 22 05:22:36 2008 using 32kb Intel Core sieve core Sat Nov 22 05:22:36 2008 sieve interval: 28 blocks of size 32768 Sat Nov 22 05:22:36 2008 processing polynomials in batches of 8 Sat Nov 22 05:22:36 2008 using a sieve bound of 1533107 (58333 primes) Sat Nov 22 05:22:36 2008 using large prime bound of 122648560 (26 bits) Sat Nov 22 05:22:36 2008 using double large prime bound of 362737408899600 (42-49 bits) Sat Nov 22 05:22:36 2008 using trial factoring cutoff of 49 bits Sat Nov 22 05:22:36 2008 polynomial 'A' values have 11 factors Sat Nov 22 06:30:13 2008 58550 relations (15565 full + 42985 combined from 620271 partial), need 58429 Sat Nov 22 06:30:14 2008 begin with 635836 relations Sat Nov 22 06:30:14 2008 reduce to 142791 relations in 11 passes Sat Nov 22 06:30:14 2008 attempting to read 142791 relations Sat Nov 22 06:30:16 2008 recovered 142791 relations Sat Nov 22 06:30:16 2008 recovered 123483 polynomials Sat Nov 22 06:30:16 2008 attempting to build 58550 cycles Sat Nov 22 06:30:16 2008 found 58550 cycles in 5 passes Sat Nov 22 06:30:16 2008 distribution of cycle lengths: Sat Nov 22 06:30:16 2008 length 1 : 15565 Sat Nov 22 06:30:16 2008 length 2 : 11170 Sat Nov 22 06:30:16 2008 length 3 : 10250 Sat Nov 22 06:30:16 2008 length 4 : 7878 Sat Nov 22 06:30:16 2008 length 5 : 5508 Sat Nov 22 06:30:16 2008 length 6 : 3522 Sat Nov 22 06:30:16 2008 length 7 : 2079 Sat Nov 22 06:30:16 2008 length 9+: 2578 Sat Nov 22 06:30:16 2008 largest cycle: 18 relations Sat Nov 22 06:30:17 2008 matrix is 58333 x 58550 (14.2 MB) with weight 3493391 (59.67/col) Sat Nov 22 06:30:17 2008 sparse part has weight 3493391 (59.67/col) Sat Nov 22 06:30:17 2008 filtering completed in 3 passes Sat Nov 22 06:30:17 2008 matrix is 54459 x 54523 (13.4 MB) with weight 3283171 (60.22/col) Sat Nov 22 06:30:17 2008 sparse part has weight 3283171 (60.22/col) Sat Nov 22 06:30:17 2008 saving the first 48 matrix rows for later Sat Nov 22 06:30:18 2008 matrix is 54411 x 54523 (9.4 MB) with weight 2678963 (49.13/col) Sat Nov 22 06:30:18 2008 sparse part has weight 2139290 (39.24/col) Sat Nov 22 06:30:18 2008 matrix includes 64 packed rows Sat Nov 22 06:30:18 2008 using block size 21809 for processor cache size 1024 kB Sat Nov 22 06:30:18 2008 commencing Lanczos iteration Sat Nov 22 06:30:18 2008 memory use: 8.7 MB Sat Nov 22 06:30:38 2008 lanczos halted after 861 iterations (dim = 54411) Sat Nov 22 06:30:38 2008 recovered 18 nontrivial dependencies Sat Nov 22 06:30:38 2008 prp38 factor: 24351976690366456440494140268150735011 Sat Nov 22 06:30:38 2008 prp51 factor: 506170946785176908374198765538995513913432276329177 Sat Nov 22 06:30:38 2008 elapsed time 01:08:04
Nov 22, 2008 (3rd): By Serge Batalov / GMP-ECM 6.2.1, GMP-ECM 6.2.1; Msieve-1.38
(31·10¹⁹⁹+41)/9 = 3(4)₁₉₈9_<200> = 3 · 13 · 211 · 4933314511_<10> · 108886162810849_<15> · C172
C172 = P30 · P143
P30 = 142018885622971503634552823639_<30>
P143 = 54867418150082322617178305566660740301855900348368997744658055286701238044662021541391733259709740789882218697925348449694048592355472049447861_<143>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1592717021 Step 1 took 24586ms Step 2 took 16761ms ********** Factor found in step 2: 142018885622971503634552823639 Found probable prime factor of 30 digits: 142018885622971503634552823639 Probable prime cofactor 54867418150082322617178305566660740301855900348368997744658055286701238044662021541391733259709740789882218697925348449694048592355472049447861 has 143 digits
(32·10¹³⁵-41)/9 = 3(5)₁₃₄1_<136> = 17 · 67 · 541 · 631 · 646855311531991_<15> · C113
C113 = P30 · P31 · P52
P30 = 395238694440067346506321051229_<30>
P31 = 4607584230616385795106992439653_<31>
P52 = 7762779182268771788520111353675163478851612794868937_<52>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=978761011 Step 1 took 56903ms Step 2 took 20658ms ********** Factor found in step 2: 4607584230616385795106992439653 Found probable prime factor of 31 digits: 4607584230616385795106992439653 Composite cofactor 3068150709226442954934260179839783913836305853892991916706470823431308919117773573 has 82 digits Fri Nov 21 11:32:35 2008 Msieve v. 1.38 Fri Nov 21 11:32:35 2008 random seeds: f61d4527 abcf05c9 Fri Nov 21 11:32:35 2008 factoring 3068150709226442954934260179839783913836305853892991916706470823431308919117773573 (82 digits) Fri Nov 21 11:32:35 2008 no P-1/P+1/ECM available, skipping Fri Nov 21 11:32:35 2008 commencing quadratic sieve (82-digit input) Fri Nov 21 11:32:35 2008 using multiplier of 13 Fri Nov 21 11:32:35 2008 using 64kb Opteron sieve core Fri Nov 21 11:32:35 2008 sieve interval: 6 blocks of size 65536 Fri Nov 21 11:32:35 2008 processing polynomials in batches of 17 Fri Nov 21 11:32:35 2008 using a sieve bound of 1339157 (51471 primes) Fri Nov 21 11:32:35 2008 using large prime bound of 125880758 (26 bits) Fri Nov 21 11:32:35 2008 using trial factoring cutoff of 27 bits Fri Nov 21 11:32:35 2008 polynomial 'A' values have 11 factors Fri Nov 21 11:46:18 2008 51761 relations (27110 full + 24651 combined from 267857 partial), need 51567 Fri Nov 21 11:46:18 2008 begin with 294967 relations Fri Nov 21 11:46:18 2008 reduce to 73333 relations in 2 passes Fri Nov 21 11:46:18 2008 attempting to read 73333 relations Fri Nov 21 11:46:18 2008 recovered 73333 relations Fri Nov 21 11:46:18 2008 recovered 64668 polynomials Fri Nov 21 11:46:19 2008 attempting to build 51761 cycles Fri Nov 21 11:46:19 2008 found 51761 cycles in 1 passes Fri Nov 21 11:46:19 2008 distribution of cycle lengths: Fri Nov 21 11:46:19 2008 length 1 : 27110 Fri Nov 21 11:46:19 2008 length 2 : 24651 Fri Nov 21 11:46:19 2008 largest cycle: 2 relations Fri Nov 21 11:46:19 2008 matrix is 51471 x 51761 (7.9 MB) with weight 1651481 (31.91/col) Fri Nov 21 11:46:19 2008 sparse part has weight 1651481 (31.91/col) Fri Nov 21 11:46:19 2008 filtering completed in 3 passes Fri Nov 21 11:46:19 2008 matrix is 36514 x 36576 (6.1 MB) with weight 1302933 (35.62/col) Fri Nov 21 11:46:19 2008 sparse part has weight 1302933 (35.62/col) Fri Nov 21 11:46:19 2008 saving the first 48 matrix rows for later Fri Nov 21 11:46:19 2008 matrix is 36466 x 36576 (4.2 MB) with weight 993167 (27.15/col) Fri Nov 21 11:46:19 2008 sparse part has weight 731232 (19.99/col) Fri Nov 21 11:46:19 2008 matrix includes 64 packed rows Fri Nov 21 11:46:19 2008 using block size 14630 for processor cache size 1024 kB Fri Nov 21 11:46:19 2008 commencing Lanczos iteration Fri Nov 21 11:46:19 2008 memory use: 4.1 MB Fri Nov 21 11:46:24 2008 lanczos halted after 578 iterations (dim = 36464) Fri Nov 21 11:46:24 2008 recovered 17 nontrivial dependencies Fri Nov 21 11:46:24 2008 prp30 factor: 395238694440067346506321051229 Fri Nov 21 11:46:24 2008 prp52 factor: 7762779182268771788520111353675163478851612794868937 Fri Nov 21 11:46:24 2008 elapsed time 00:13:49
(32·10¹³⁹-41)/9 = 3(5)₁₃₈1_<140> = C140
C140 = P51 · P89
P51 = 464526285610532197573410910418540500603849191853171_<51>
P89 = 76541536306873319748687998204768071820486616615213271404046353568746662919813194493399781_<89>

SNFS difficulty: 141 digits. Divisors found: r1=464526285610532197573410910418540500603849191853171 (pp51) r2=76541536306873319748687998204768071820486616615213271404046353568746662919813194493399781 (pp89) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.949). Factorization parameters were as follows: n: 35555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555551 m: 10000000000000000000000000000 deg: 5 c5: 16 c0: -205 skew: 1.67 type: snfs lss: 1 rlim: 1580000 alim: 1580000 lpbr: 25 lpba: 25 mfbr: 48 mfba: 48 rlambda: 2.4 alambda: 2.4 Factor base limits: 1580000/1580000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 48/48 Sieved rational special-q in [790000, 1590001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 220033 x 220275 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1580000,1580000,25,25,48,48,2.4,2.4,200000 total time: 4.50 hours.
(32·10¹⁵⁷-41)/9 = 3(5)₁₅₆1_<158> = 254050733 · C150
C150 = P29 · P121
P29 = 82152423305033592348298831619_<29>
P121 = 1703596103003294419723782049965196114125342318793393470606475103127644906981867365346338961594764303306093223734477470313_<121>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1517652325 Step 1 took 18518ms Step 2 took 14281ms ********** Factor found in step 2: 82152423305033592348298831619 Found probable prime factor of 29 digits: 82152423305033592348298831619 Probable prime cofactor 1703596103003294419723782049965196114125342318793393470606475103127644906981867365346338961594764303306093223734477470313 has 121 digits
(32·10¹⁵⁰-41)/9 = 3(5)₁₄₉1_<151> = 7229 · C147
C147 = P57 · P91
P57 = 151630060370265312596023804982270143882259787233401865167_<57>
P91 = 3243724314599321778834666368665223817246547329724430342376155329768224196716824187092053957_<91>

SNFS difficulty: 151 digits. Divisors found: r1=151630060370265312596023804982270143882259787233401865167 (pp57) r2=3243724314599321778834666368665223817246547329724430342376155329768224196716824187092053957 (pp91) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.952). Factorization parameters were as follows: n: 491846113647192634604448133290296798389203977805444121670432363474277985275356972687170501529334009621739598223205914449516607491431118488802815819 m: 2000000000000000000000000000000 deg: 5 c5: 1 c0: -41 skew: 2.10 type: snfs lss: 1 rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 53/53 Sieved rational special-q in [1150000, 1750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 350251 x 350493 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,53,53,2.5,2.5,200000 total time: 10.00 hours.
Nov 22, 2008 (2nd): By Erik Branger / GGNFS, Msieve
(31·10¹²⁵+41)/9 = 3(4)₁₂₄9_<126> = 7² · 487 · 1133565895591_<13> · C110
C110 = P42 · P68
P42 = 874649588582602018285507418779006331185511_<42>
P68 = 14558387529805029615527432457618027810773080096835070639069566035223_<68>

Number: 34449_125 N=12733487663370052831395840247528589876745259188248257431076297252867117599646478553622394464399720261573253953 ( 110 digits) SNFS difficulty: 126 digits. Divisors found: r1=874649588582602018285507418779006331185511 r2=14558387529805029615527432457618027810773080096835070639069566035223 Version: Total time: 2.26 hours. Scaled time: 4.52 units (timescale=1.997). Factorization parameters were as follows: n: 12733487663370052831395840247528589876745259188248257431076297252867117599646478553622394464399720261573253953 m: 10000000000000000000000000 deg: 5 c5: 31 c0: 41 skew: 1.06 type: snfs lss: 1 rlim: 900000 alim: 900000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3Factor base limits: 900000/900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [450000, 700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 121472 x 121697 Total sieving time: 2.26 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000 total time: 2.26 hours. --------- CPU info (if available) ----------
Nov 22, 2008: By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(32·10¹⁵⁴-41)/9 = 3(5)₁₅₃1_<155> = 19 · 1997 · 5903 · 48647 · 8841960503_<10> · 12814998923_<11> · 1194009122626689491_<19> · C104
C104 = P37 · P67
P37 = 7152201341862591428684838599721619649_<37>
P67 = 3372348398945690607950846917414070323884300578481012329068619483687_<67>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 24119714744167530175826743896080551920044617404588160851068750109106326746284237447175478123245774165863 (104 digits) Using B1=1766000, B2=2140281790, polynomial Dickson(6), sigma=647106178 Step 1 took 12632ms Step 2 took 5157ms ********** Factor found in step 2: 7152201341862591428684838599721619649 Found probable prime factor of 37 digits: 7152201341862591428684838599721619649 Probable prime cofactor 3372348398945690607950846917414070323884300578481012329068619483687 has 67 digits
(29·10¹⁶⁰+61)/9 = 3(2)₁₅₉9_<161> = 3 · 18658042499_<11> · 173087931043_<12> · 68198980432302694162763_<23> · C116
C116 = P46 · P71
P46 = 3392334564486724377686000326486270997623824929_<46>
P71 = 14375561255610661870862903525731472575001154792532546013717693189769037_<71>

Number: n N=48766713331304223297469209004162040855423177792331628693848084378802536364064355176272991837831834801871342032923373 ( 116 digits) Divisors found: Sat Nov 22 06:14:15 2008 prp46 factor: 3392334564486724377686000326486270997623824929 Sat Nov 22 06:14:15 2008 prp71 factor: 14375561255610661870862903525731472575001154792532546013717693189769037 Sat Nov 22 06:14:16 2008 elapsed time 00:37:16 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 33.08 hours. Scaled time: 67.65 units (timescale=2.045). Factorization parameters were as follows: name: KA_3_2_159_9 n: 48766713331304223297469209004162040855423177792331628693848084378802536364064355176272991837831834801871342032923373 skew: 40631.40 # norm 1.28e+16 c5: 48960 c4: -3677136100 c3: -580854246872754 c2: 4669045965929046074 c1: 201689939828851083322901 c0: -1049108959979503795077868296 # alpha -6.13 Y1: 3663644112433 Y0: -15836453313678855586037 # Murphy_E 4.96e-10 # M 5020676239017025116654576699585057370287755122455090683803015253454311247305124917305425540222722612575777110676580 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved special-q in [100000, 1900001) Primes: RFBsize:315948, AFBsize:316550, largePrimes:6201115 encountered Relations: rels:6010949, finalFF:652204 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 32.85 hours. Total relation processing time: 0.23 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 33.08 hours. --------- CPU info (if available) ----------
(32·10¹²⁸-41)/9 = 3(5)₁₂₇1_<129> = 3² · 13 · 2383 · 17203 · 44439431 · 12342097267987_<14> · C99
C99 = P45 · P54
P45 = 401832657422981661467753981794828719551127827_<45>
P54 = 336349426550456762380413783163560600207935723362612513_<54>

Number: n N=135156183893466024666977800451768589430551510931312422361412184461027826326223292573670614332699251 ( 99 digits) SNFS difficulty: 131 digits. Divisors found: r1=401832657422981661467753981794828719551127827 (pp45) r2=336349426550456762380413783163560600207935723362612513 (pp54) Version: GGNFS-0.77.1-20051202-athlon Total time: 2.24 hours. Scaled time: 4.58 units (timescale=2.045). Factorization parameters were as follows: name: KA_3_5_127_1 n: 135156183893466024666977800451768589430551510931312422361412184461027826326223292573670614332699251 type: snfs skew: 5.28 deg: 5 c5: 1 c0: -4100 m: 200000000000000000000000000 rlim: 800000 alim: 800000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [100000, 380001) Primes: RFBsize:63951, AFBsize:64074, largePrimes:5795056 encountered Relations: rels:4973051, finalFF:148600 Max relations in full relation-set: 28 Initial matrix: 128089 x 148600 with sparse part having weight 12143336. Pruned matrix : 120774 x 121478 with weight 8312350. Total sieving time: 2.07 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.04 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,28,28,56,56,2.5,2.5,50000 total time: 2.24 hours. --------- CPU info (if available) ----------
(32·10¹⁴⁰-41)/9 = 3(5)₁₃₉1_<141> = 3 · 13 · 23 · 73 · 1301 · 3109 · 2055125448574067128165337723_<28> · C102
C102 = P47 · P55
P47 = 81534190191088785562703437179631417594742467373_<47>
P55 = 8011540784187013965767181696517537757246380887244496561_<55>

Number: n N=653214490021568591153880136071698042579076844847058983336996288582169963418227578858397724804353204253 ( 102 digits) SNFS difficulty: 141 digits. Divisors found: r1=81534190191088785562703437179631417594742467373 (pp47) r2=8011540784187013965767181696517537757246380887244496561 (pp55) Version: GGNFS-0.77.1-20051202-athlon Total time: 4.74 hours. Scaled time: 6.86 units (timescale=1.448). Factorization parameters were as follows: name: KA_3_5_139_1 n: 653214490021568591153880136071698042579076844847058983336996288582169963418227578858397724804353204253 type: snfs skew: 2.10 deg: 5 c5: 1 c0: -41 m: 20000000000000000000000000000 rlim: 1200000 alim: 1200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [100000, 600001) Primes: RFBsize:92938, AFBsize:93090, largePrimes:7573396 encountered Relations: rels:6550842, finalFF:211514 Max relations in full relation-set: 28 Initial matrix: 186092 x 211514 with sparse part having weight 17096091. Pruned matrix : 174635 x 175629 with weight 12149381. Total sieving time: 3.84 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.64 hours. Total square root time: 0.10 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,56,56,2.5,2.5,100000 total time: 4.74 hours. --------- CPU info (if available) ----------
(31·10¹⁴⁰+41)/9 = 3(4)₁₃₉9_<141> = 59 · 10228703 · 221997037441_<12> · 247948902336703103_<18> · C104
C104 = P37 · P67
P37 = 1788847380174561304042465308411568243_<37>
P67 = 5796474718390466137267505980824046764103166906082630165666673013633_<67>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 10369008614240863352321120069636994460028391623281167738181012372516588639848686662393445079840448856819 (104 digits) Using B1=2156000, B2=2854157680, polynomial Dickson(6), sigma=3161595063 Step 1 took 22047ms Step 2 took 8375ms ********** Factor found in step 2: 1788847380174561304042465308411568243 Found probable prime factor of 37 digits: 1788847380174561304042465308411568243 Probable prime cofactor 5796474718390466137267505980824046764103166906082630165666673013633 has 67 digits
Nov 21, 2008 (10th): By Sinkiti Sibata / Msieve
(32·10¹⁴⁹-41)/9 = 3(5)₁₄₈1_<150> = 3 · 7 · 419 · 34729 · 533793222600156067_<18> · 1324836958983859085546653940413_<31> · C94
C94 = P41 · P53
P41 = 80114216324581510271381545232553255062473_<41>
P53 = 20536990094074404442694620736817421850163590286243607_<53>

Fri Nov 21 20:27:25 2008 Msieve v. 1.38 Fri Nov 21 20:27:25 2008 random seeds: 57771344 631fd988 Fri Nov 21 20:27:25 2008 factoring 1645304867052464418756468820263549672476733372189469658647398655789212312830417506743281860111 (94 digits) Fri Nov 21 20:27:25 2008 searching for 15-digit factors Fri Nov 21 20:27:27 2008 commencing quadratic sieve (94-digit input) Fri Nov 21 20:27:27 2008 using multiplier of 31 Fri Nov 21 20:27:27 2008 using 32kb Intel Core sieve core Fri Nov 21 20:27:27 2008 sieve interval: 36 blocks of size 32768 Fri Nov 21 20:27:27 2008 processing polynomials in batches of 6 Fri Nov 21 20:27:27 2008 using a sieve bound of 1986293 (74118 primes) Fri Nov 21 20:27:27 2008 using large prime bound of 256231797 (27 bits) Fri Nov 21 20:27:27 2008 using double large prime bound of 1366278931731603 (42-51 bits) Fri Nov 21 20:27:27 2008 using trial factoring cutoff of 51 bits Fri Nov 21 20:27:27 2008 polynomial 'A' values have 12 factors Fri Nov 21 20:27:27 2008 restarting with 338 full and 17985 partial relations Fri Nov 21 23:26:19 2008 74250 relations (18366 full + 55884 combined from 1032480 partial), need 74214 Fri Nov 21 23:26:20 2008 begin with 1050846 relations Fri Nov 21 23:26:21 2008 reduce to 191860 relations in 12 passes Fri Nov 21 23:26:21 2008 attempting to read 191860 relations Fri Nov 21 23:26:24 2008 recovered 191860 relations Fri Nov 21 23:26:24 2008 recovered 175246 polynomials Fri Nov 21 23:26:24 2008 attempting to build 74250 cycles Fri Nov 21 23:26:24 2008 found 74250 cycles in 5 passes Fri Nov 21 23:26:24 2008 distribution of cycle lengths: Fri Nov 21 23:26:24 2008 length 1 : 18366 Fri Nov 21 23:26:24 2008 length 2 : 13089 Fri Nov 21 23:26:24 2008 length 3 : 12660 Fri Nov 21 23:26:24 2008 length 4 : 10071 Fri Nov 21 23:26:24 2008 length 5 : 7558 Fri Nov 21 23:26:24 2008 length 6 : 5099 Fri Nov 21 23:26:24 2008 length 7 : 3181 Fri Nov 21 23:26:24 2008 length 9+: 4226 Fri Nov 21 23:26:24 2008 largest cycle: 21 relations Fri Nov 21 23:26:24 2008 matrix is 74118 x 74250 (19.6 MB) with weight 4844671 (65.25/col) Fri Nov 21 23:26:24 2008 sparse part has weight 4844671 (65.25/col) Fri Nov 21 23:26:25 2008 filtering completed in 3 passes Fri Nov 21 23:26:25 2008 matrix is 70475 x 70539 (18.8 MB) with weight 4640189 (65.78/col) Fri Nov 21 23:26:25 2008 sparse part has weight 4640189 (65.78/col) Fri Nov 21 23:26:25 2008 saving the first 48 matrix rows for later Fri Nov 21 23:26:26 2008 matrix is 70427 x 70539 (12.2 MB) with weight 3705494 (52.53/col) Fri Nov 21 23:26:26 2008 sparse part has weight 2781041 (39.43/col) Fri Nov 21 23:26:26 2008 matrix includes 64 packed rows Fri Nov 21 23:26:26 2008 using block size 28215 for processor cache size 1024 kB Fri Nov 21 23:26:26 2008 commencing Lanczos iteration Fri Nov 21 23:26:26 2008 memory use: 11.5 MB Fri Nov 21 23:27:02 2008 lanczos halted after 1116 iterations (dim = 70427) Fri Nov 21 23:27:02 2008 recovered 18 nontrivial dependencies Fri Nov 21 23:27:02 2008 prp41 factor: 80114216324581510271381545232553255062473 Fri Nov 21 23:27:02 2008 prp53 factor: 20536990094074404442694620736817421850163590286243607 Fri Nov 21 23:27:02 2008 elapsed time 02:59:37
Nov 21, 2008 (9th): By Robert Backstrom / GGNFS
(31·10¹⁰⁵+41)/9 = 3(4)₁₀₄9_<106> = 353 · 5431 · 128291 · C95
C95 = P36 · P59
P36 = 594693148785308211822209674660147831_<36>
P59 = 23549167060302104560864919762949010499061378501200898045083_<59>

Number: n N=14004528310362318666354244575991794858089633112257439635385050554676123620105734472655682664973 ( 95 digits) SNFS difficulty: 106 digits. Divisors found: r1=594693148785308211822209674660147831 (pp36) r2=23549167060302104560864919762949010499061378501200898045083 (pp59) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.64 hours. Scaled time: 1.30 units (timescale=2.045). Factorization parameters were as follows: name: KA_3_4_104_9 n: 14004528310362318666354244575991794858089633112257439635385050554676123620105734472655682664973 type: snfs skew: 1.06 deg: 5 c5: 31 c0: 41 m: 1000000000000000000000 rlim: 400000 alim: 400000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 400000/400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [100000, 160001) Primes: RFBsize:33860, AFBsize:34095, largePrimes:3193883 encountered Relations: rels:2701320, finalFF:112185 Max relations in full relation-set: 28 Initial matrix: 68020 x 112185 with sparse part having weight 7919858. Pruned matrix : 55163 x 55567 with weight 2392508. Total sieving time: 0.51 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.01 hours. Total square root time: 0.08 hours, sqrts: 5. Prototype def-par.txt line would be: snfs,106,5,0,0,0,0,0,0,0,0,400000,400000,28,28,56,56,2.5,2.5,50000 total time: 0.64 hours. --------- CPU info (if available) ----------
(32·10¹⁰⁷-41)/9 = 3(5)₁₀₆1_<108> = 3 · 7 · 53 · 323093 · C99
C99 = P43 · P57
P43 = 4969113507692915159830820858462998480110977_<43>
P57 = 198978356029457891142388803820629371983665753967882940507_<57>

Number: n N=988746036684509216134405657207346002014562016183139466236470434514002669418403739656765174448645339 ( 99 digits) SNFS difficulty: 108 digits. Divisors found: r1=4969113507692915159830820858462998480110977 (pp43) r2=198978356029457891142388803820629371983665753967882940507 (pp57) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.88 hours. Scaled time: 1.27 units (timescale=1.447). Factorization parameters were as follows: name: KA_3_5_106_1 n: 988746036684509216134405657207346002014562016183139466236470434514002669418403739656765174448645339 type: snfs skew: 0.84 deg: 5 c5: 100 c0: -41 m: 2000000000000000000000 rlim: 450000 alim: 450000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 450000/450000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [100000, 160001) Primes: RFBsize:37706, AFBsize:37550, largePrimes:3672853 encountered Relations: rels:3166359, finalFF:149304 Max relations in full relation-set: 28 Initial matrix: 75320 x 149304 with sparse part having weight 10857343. Pruned matrix : 56531 x 56971 with weight 2447010. Total sieving time: 0.79 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.02 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,108,5,0,0,0,0,0,0,0,0,450000,450000,28,28,56,56,2.5,2.5,50000 total time: 0.88 hours. --------- CPU info (if available) ----------
Nov 21, 2008 (8th): By Erik Branger / GGNFS, Msieve
(31·10¹¹²+41)/9 = 3(4)₁₁₁9_<113> = 3 · 163 · 21187 · C106
C106 = P48 · P59
P48 = 258792217686256918312919174969009069760596232037_<48>
P59 = 12846642731570680842788982699578386236853374596065485513239_<59>

Number: 34449_112 N=3324611162326209839139546875017259826094737883741500671780583556556842641231117669818215731165592479437843 ( 106 digits) SNFS difficulty: 114 digits. Divisors found: r1=258792217686256918312919174969009069760596232037 r2=12846642731570680842788982699578386236853374596065485513239 Version: Total time: 1.68 hours. Scaled time: 3.69 units (timescale=2.195). Factorization parameters were as follows: n: 3324611162326209839139546875017259826094737883741500671780583556556842641231117669818215731165592479437843 m: 20000000000000000000000 deg: 5 c5: 775 c0: 328 skew: 0.84 type: snfs lss: 1 rlim: 560000 alim: 560000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 560000/560000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [280000, 530001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 66642 x 66860 Total sieving time: 1.68 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,114,5,0,0,0,0,0,0,0,0,560000,560000,25,25,45,45,2.2,2.2,50000 total time: 1.68 hours. --------- CPU info (if available) ----------
(31·10¹⁵³+41)/9 = 3(4)₁₅₂9_<154> = 5835739554532332869_<19> · 50158851041600162665093_<23> · 4032687920589908329955267_<25> · C88
C88 = P41 · P47
P41 = 44486831924067687045714216542322079414577_<41>
P47 = 65591809150534983525158372279246902373496543283_<47>

Fri Nov 21 12:35:16 2008 Msieve v. 1.36 Fri Nov 21 12:35:16 2008 random seeds: 21ecf6b8 72b652fe Fri Nov 21 12:35:16 2008 factoring 2917971789275374742550279961408364217439585732684651363096861229810434025847121781636291 (88 digits) Fri Nov 21 12:35:17 2008 searching for 15-digit factors Fri Nov 21 12:35:18 2008 commencing quadratic sieve (88-digit input) Fri Nov 21 12:35:19 2008 using multiplier of 19 Fri Nov 21 12:35:19 2008 using 64kb Pentium 4 sieve core Fri Nov 21 12:35:19 2008 sieve interval: 13 blocks of size 65536 Fri Nov 21 12:35:19 2008 processing polynomials in batches of 8 Fri Nov 21 12:35:19 2008 using a sieve bound of 1517699 (57619 primes) Fri Nov 21 12:35:19 2008 using large prime bound of 121415920 (26 bits) Fri Nov 21 12:35:19 2008 using double large prime bound of 356201769813440 (42-49 bits) Fri Nov 21 12:35:19 2008 using trial factoring cutoff of 49 bits Fri Nov 21 12:35:19 2008 polynomial 'A' values have 11 factors Fri Nov 21 13:46:13 2008 58029 relations (16470 full + 41559 combined from 601969 partial), need 57715 Fri Nov 21 13:46:15 2008 begin with 618438 relations Fri Nov 21 13:46:16 2008 reduce to 137673 relations in 12 passes Fri Nov 21 13:46:16 2008 attempting to read 137673 relations Fri Nov 21 13:46:21 2008 recovered 137673 relations Fri Nov 21 13:46:21 2008 recovered 112399 polynomials Fri Nov 21 13:46:22 2008 attempting to build 58029 cycles Fri Nov 21 13:46:22 2008 found 58029 cycles in 5 passes Fri Nov 21 13:46:22 2008 distribution of cycle lengths: Fri Nov 21 13:46:22 2008 length 1 : 16470 Fri Nov 21 13:46:22 2008 length 2 : 11704 Fri Nov 21 13:46:22 2008 length 3 : 10218 Fri Nov 21 13:46:22 2008 length 4 : 7559 Fri Nov 21 13:46:22 2008 length 5 : 5181 Fri Nov 21 13:46:22 2008 length 6 : 3198 Fri Nov 21 13:46:22 2008 length 7 : 1770 Fri Nov 21 13:46:22 2008 length 9+: 1929 Fri Nov 21 13:46:22 2008 largest cycle: 19 relations Fri Nov 21 13:46:22 2008 matrix is 57619 x 58029 (13.8 MB) with weight 3380613 (58.26/col) Fri Nov 21 13:46:22 2008 sparse part has weight 3380613 (58.26/col) Fri Nov 21 13:46:23 2008 filtering completed in 3 passes Fri Nov 21 13:46:23 2008 matrix is 52792 x 52855 (12.6 MB) with weight 3099871 (58.65/col) Fri Nov 21 13:46:23 2008 sparse part has weight 3099871 (58.65/col) Fri Nov 21 13:46:23 2008 saving the first 48 matrix rows for later Fri Nov 21 13:46:23 2008 matrix is 52744 x 52855 (9.0 MB) with weight 2535635 (47.97/col) Fri Nov 21 13:46:23 2008 sparse part has weight 2054683 (38.87/col) Fri Nov 21 13:46:23 2008 matrix includes 64 packed rows Fri Nov 21 13:46:23 2008 using block size 21142 for processor cache size 512 kB Fri Nov 21 13:46:24 2008 commencing Lanczos iteration Fri Nov 21 13:46:24 2008 memory use: 8.3 MB Fri Nov 21 13:46:52 2008 lanczos halted after 836 iterations (dim = 52742) Fri Nov 21 13:46:53 2008 recovered 16 nontrivial dependencies Fri Nov 21 13:46:53 2008 prp41 factor: 44486831924067687045714216542322079414577 Fri Nov 21 13:46:53 2008 prp47 factor: 65591809150534983525158372279246902373496543283 Fri Nov 21 13:46:53 2008 elapsed time 01:11:37
Nov 21, 2008 (7th): By Sinkiti Sibata / GGNFS
(31·10¹⁴⁴+23)/9 = 3(4)₁₄₃7_<145> = 3 · 28081 · 12198479 · 74631544459542509715103237_<26> · C107
C107 = P45 · P63
P45 = 159211005704693000085823595910997363902059699_<45>
P63 = 282087708148123545945056068424813008842460110880541912155624277_<63>

Number: 34447_144 N=44911467711194671956311458873486555830635215692557289809449257051105516413906070946575439201768427467712623 ( 107 digits) SNFS difficulty: 146 digits. Divisors found: r1=159211005704693000085823595910997363902059699 (pp45) r2=282087708148123545945056068424813008842460110880541912155624277 (pp63) Version: GGNFS-0.77.1-20060513-k8 Total time: 21.60 hours. Scaled time: 42.60 units (timescale=1.972). Factorization parameters were as follows: name: 34447_144 n: 44911467711194671956311458873486555830635215692557289809449257051105516413906070946575439201768427467712623 m: 100000000000000000000000000000 deg: 5 c5: 31 c0: 230 skew: 1.49 type: snfs lss: 1 rlim: 1930000 alim: 1930000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1930000/1930000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [965000, 2865001) Primes: RFBsize:144125, AFBsize:144048, largePrimes:4340864 encountered Relations: rels:4606753, finalFF:371261 Max relations in full relation-set: 28 Initial matrix: 288238 x 371261 with sparse part having weight 43229078. Pruned matrix : 261658 x 263163 with weight 28833069. Total sieving time: 20.36 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.96 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1930000,1930000,26,26,49,49,2.3,2.3,100000 total time: 21.60 hours. --------- CPU info (if available) ----------
(32·10¹²⁶-41)/9 = 3(5)₁₂₅1_<127> = 409 · C124
C124 = P57 · P68
P57 = 171194598333615048222366566893522206348126341433869776357_<57>
P68 = 50780164511633549798402123157855699628021684842890883339859369480427_<68>

Number: 35551_126 N=8693289866883998913338766639500135832654170062483020918228742189622385221407226297201847324096712849769084487910893778864439 ( 124 digits) SNFS difficulty: 127 digits. Divisors found: r1=171194598333615048222366566893522206348126341433869776357 (pp57) r2=50780164511633549798402123157855699628021684842890883339859369480427 (pp68) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.84 hours. Scaled time: 5.41 units (timescale=1.902). Factorization parameters were as follows: name: 35551_126 n: 8693289866883998913338766639500135832654170062483020918228742189622385221407226297201847324096712849769084487910893778864439 m: 20000000000000000000000000 deg: 5 c5: 10 c0: -41 skew: 1.33 type: snfs lss: 1 rlim: 930000 alim: 930000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 930000/930000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [465000, 715001) Primes: RFBsize:73474, AFBsize:72978, largePrimes:2463207 encountered Relations: rels:2336543, finalFF:179494 Max relations in full relation-set: 28 Initial matrix: 146518 x 179494 with sparse part having weight 13010167. Pruned matrix : 134193 x 134989 with weight 7615669. Total sieving time: 2.63 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.10 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,930000,930000,26,26,46,46,2.3,2.3,50000 total time: 2.84 hours. --------- CPU info (if available) ----------
(32·10¹¹⁹-41)/9 = 3(5)₁₁₈1_<120> = 3² · 7 · 17 · 317 · 1109 · 1223 · 4241 · C105
C105 = P34 · P71
P34 = 5146035129801747950200491709940393_<34>
P71 = 35380153561359894771496352426470646393927511422671498242115915382113823_<71>

Number: 35551_119 N=182067513124538441101462579812715985235713896251223737793957929646967334531924025154370350419725671352439 ( 105 digits) SNFS difficulty: 121 digits. Divisors found: r1=5146035129801747950200491709940393 (pp34) r2=35380153561359894771496352426470646393927511422671498242115915382113823 (pp71) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 2.15 hours. Scaled time: 1.02 units (timescale=0.473). Factorization parameters were as follows: name: 35551_119 n: 182067513124538441101462579812715985235713896251223737793957929646967334531924025154370350419725671352439 m: 1000000000000000000000000 deg: 5 c5: 16 c0: -205 skew: 1.67 type: snfs lss: 1 rlim: 730000 alim: 730000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 730000/730000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [365000, 565001) Primes: RFBsize:58789, AFBsize:58897, largePrimes:1264545 encountered Relations: rels:1228338, finalFF:140700 Max relations in full relation-set: 28 Initial matrix: 117750 x 140700 with sparse part having weight 5817576. Pruned matrix : 103103 x 103755 with weight 3356003. Total sieving time: 2.00 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.08 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000 total time: 2.15 hours. --------- CPU info (if available) ----------
Nov 21, 2008 (6th): By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1
(32·10¹²⁷-41)/9 = 3(5)₁₂₆1_<128> = 401 · 2917 · 17987 · 3229901922977237_<16> · 2071025562653464453843_<22> · C81
C81 = P33 · P48
P33 = 400338547831239941807329391891749_<33>
P48 = 631052844269568196604006040863340283212860511491_<48>

Fri Nov 21 00:20:47 2008 Msieve v. 1.38 Fri Nov 21 00:20:47 2008 random seeds: b84c8010 b8809f02 Fri Nov 21 00:20:47 2008 factoring 252634779279652537693843677634751731140715269848712613595857696355762680242587759 (81 digits) Fri Nov 21 00:20:48 2008 no P-1/P+1/ECM available, skipping Fri Nov 21 00:20:48 2008 commencing quadratic sieve (81-digit input) Fri Nov 21 00:20:48 2008 using multiplier of 39 Fri Nov 21 00:20:48 2008 using 64kb Opteron sieve core Fri Nov 21 00:20:48 2008 sieve interval: 6 blocks of size 65536 Fri Nov 21 00:20:48 2008 processing polynomials in batches of 17 Fri Nov 21 00:20:48 2008 using a sieve bound of 1315507 (50588 primes) Fri Nov 21 00:20:48 2008 using large prime bound of 128919686 (26 bits) Fri Nov 21 00:20:48 2008 using trial factoring cutoff of 27 bits Fri Nov 21 00:20:48 2008 polynomial 'A' values have 10 factors Fri Nov 21 00:38:56 2008 50811 relations (26310 full + 24501 combined from 269737 partial), need 50684 Fri Nov 21 00:38:56 2008 begin with 296047 relations Fri Nov 21 00:38:57 2008 reduce to 72222 relations in 2 passes Fri Nov 21 00:38:57 2008 attempting to read 72222 relations Fri Nov 21 00:38:57 2008 recovered 72222 relations Fri Nov 21 00:38:57 2008 recovered 62442 polynomials Fri Nov 21 00:38:57 2008 attempting to build 50811 cycles Fri Nov 21 00:38:57 2008 found 50811 cycles in 1 passes Fri Nov 21 00:38:57 2008 distribution of cycle lengths: Fri Nov 21 00:38:57 2008 length 1 : 26310 Fri Nov 21 00:38:57 2008 length 2 : 24501 Fri Nov 21 00:38:57 2008 largest cycle: 2 relations Fri Nov 21 00:38:57 2008 matrix is 50588 x 50811 (7.6 MB) with weight 1577942 (31.06/col) Fri Nov 21 00:38:57 2008 sparse part has weight 1577942 (31.06/col) Fri Nov 21 00:38:58 2008 filtering completed in 3 passes Fri Nov 21 00:38:58 2008 matrix is 35841 x 35905 (5.9 MB) with weight 1254482 (34.94/col) Fri Nov 21 00:38:58 2008 sparse part has weight 1254482 (34.94/col) Fri Nov 21 00:38:58 2008 saving the first 48 matrix rows for later Fri Nov 21 00:38:58 2008 matrix is 35793 x 35905 (4.6 MB) with weight 1006660 (28.04/col) Fri Nov 21 00:38:58 2008 sparse part has weight 834359 (23.24/col) Fri Nov 21 00:38:58 2008 matrix includes 64 packed rows Fri Nov 21 00:38:58 2008 using block size 14362 for processor cache size 1024 kB Fri Nov 21 00:38:58 2008 commencing Lanczos iteration Fri Nov 21 00:38:58 2008 memory use: 4.2 MB Fri Nov 21 00:39:06 2008 lanczos halted after 567 iterations (dim = 35789) Fri Nov 21 00:39:06 2008 recovered 16 nontrivial dependencies Fri Nov 21 00:39:06 2008 prp33 factor: 400338547831239941807329391891749 Fri Nov 21 00:39:06 2008 prp48 factor: 631052844269568196604006040863340283212860511491 Fri Nov 21 00:39:06 2008 elapsed time 00:18:19
(31·10¹¹¹+41)/9 = 3(4)₁₁₀9_<112> = 88327 · C107
C107 = P50 · P57
P50 = 41454123728155760979248725791099159638505634915673_<50>
P57 = 940714774807484928843711276649544526402883573778713355119_<57>

SNFS difficulty: 112 digits. Divisors found: r1=41454123728155760979248725791099159638505634915673 (pp50) r2=940714774807484928843711276649544526402883573778713355119 (pp57) Version: Msieve-1.38 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.949). Factorization parameters were as follows: n: 38996506667773664275300241652546157397448622102465208197317291931622770437628861440380002088200034467880087 m: 10000000000000000000000 deg: 5 c5: 310 c0: 41 skew: 0.67 type: snfs lss: 1 rlim: 520000 alim: 520000 lpbr: 25 lpba: 25 mfbr: 47 mfba: 47 rlambda: 2.4 alambda: 2.4 Factor base limits: 520000/520000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved rational special-q in [260000, 360001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 90705 x 90947 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,112,5,0,0,0,0,0,0,0,0,520000,520000,25,25,47,47,2.4,2.4,50000 total time: 0.50 hours.
(31·10¹²⁴+41)/9 = 3(4)₁₂₃9_<125> = 3² · 95544360543089_<14> · 2649780403203617373383_<22> · C89
C89 = P29 · P60
P29 = 48404523956151107959172206679_<29>
P60 = 312302729254556267292136300344926518307355113530119444922057_<60>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2358009462 Step 1 took 11056ms ********** Factor found in step 1: 48404523956151107959172206679 Found probable prime factor of 29 digits: 48404523956151107959172206679 Probable prime cofactor 312302729254556267292136300344926518307355113530119444922057 has 60 digits
(32·10¹⁹⁷-41)/9 = 3(5)₁₉₆1_<198> = 3 · 7 · 47 · 139 · 1283 · 69001 · 7465399 · 52789594305359_<14> · 5704587641284886551_<19> · C146
C146 = P32 · P114
P32 = 25381539827219968939889818942099_<32>
P114 = 513038436540897283961126919502212025962143546345330531503056737906022207414185764428308211340282304133292693358681_<114>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2785240796 Step 1 took 83890ms Step 2 took 28611ms ********** Factor found in step 2: 25381539827219968939889818942099 Found probable prime factor of 32 digits: 25381539827219968939889818942099 Probable prime cofactor 513038436540897283961126919502212025962143546345330531503056737906022207414185764428308211340282304133292693358681 has 114 digits
(31·10¹¹⁸+41)/9 = 3(4)₁₁₇9_<119> = 3 · 349 · 7559 · 25033 · 142330839643_<12> · C97
C97 = P39 · P58
P39 = 667275628520032946456406704929974171499_<39>
P58 = 1830589570099598722655453913313123714527630752671977509873_<58>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4183339842 Step 1 took 11372ms Step 2 took 9026ms ********** Factor found in step 2: 667275628520032946456406704929974171499 Found probable prime factor of 39 digits: 667275628520032946456406704929974171499 Probable prime cofactor 1830589570099598722655453913313123714527630752671977509873 has 58 digits
(31·10¹¹⁷+41)/9 = 3(4)₁₁₆9_<118> = 2939 · 15300092001869737_<17> · C98
C98 = P35 · P64
P35 = 39060798498707080488288532923358921_<35>
P64 = 1961030909115423998982595692229352015289040401796279581247674883_<64>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=406823575 Step 1 took 13031ms ********** Factor found in step 1: 39060798498707080488288532923358921 Found probable prime factor of 35 digits: 39060798498707080488288532923358921 Probable prime cofactor 1961030909115423998982595692229352015289040401796279581247674883 has 64 digits
Nov 21, 2008 (5th): By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(29·10¹⁵²+43)/9 = 3(2)₁₅₁7_<153> = 3 · 40296437249_<11> · 17122663123552071584377558151_<29> · C114
C114 = P39 · P75
P39 = 220220544173356641441005461809174158519_<39>
P75 = 706868192209211965355505466528845063936170712012029710240294391113595495089_<75>

Number: n N=155666897947149516564762656348434456049373366190782014151391987567686593948726747795044131944426787108190772013191 ( 114 digits) Divisors found: r1=220220544173356641441005461809174158519 (pp39) r2=706868192209211965355505466528845063936170712012029710240294391113595495089 (pp75) Version: GGNFS-0.77.1-20051202-athlon Total time: 26.06 hours. Scaled time: 53.11 units (timescale=2.038). Factorization parameters were as follows: name: KA_3_2_151_7 n: 155666897947149516564762656348434456049373366190782014151391987567686593948726747795044131944426787108190772013191 skew: 40305.29 # norm 4.06e+15 c5: 33600 c4: 662166430 c3: -119500018998054 c2: -5194326731023833722 c1: 90592809296439845948331 c0: -5694511903865148553261982 # alpha -6.17 Y1: 1852807172777 Y0: -5409670490352917931165 # Murphy_E 6.68e-10 # M 23888537930743219166264097391624569843008903802972367072493419719091397771460949961003863560930060113166770635755 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:250150, AFBsize:250862, largePrimes:6935471 encountered Relations: rels:6699692, finalFF:603533 Max relations in full relation-set: 28 Initial matrix: 501089 x 603533 with sparse part having weight 37743944. Pruned matrix : 402062 x 404631 with weight 18813363. Polynomial selection time: 2.34 hours. Total sieving time: 22.66 hours. Total relation processing time: 0.21 hours. Matrix solve time: 0.69 hours. Total square root time: 0.16 hours, sqrts: 1. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 26.06 hours. --------- CPU info (if available) ----------
(29·10¹⁵¹+43)/9 = 3(2)₁₅₀7_<152> = 37 · 1759 · 15563627912986965137034736448411_<32> · C116
C116 = P54 · P62
P54 = 975096392303048933102454301118670269267371089773626501_<54>
P62 = 32623423650910648679172594020763946317343258487506521412621679_<62>

Number: n N=31810982706576934772998608605741160071516082639197877089858403102494412714121865479732665846484350034366517761515179 ( 116 digits) SNFS difficulty: 152 digits. Divisors found: Fri Nov 21 20:16:11 2008 prp54 factor: 975096392303048933102454301118670269267371089773626501 Fri Nov 21 20:16:11 2008 prp62 factor: 32623423650910648679172594020763946317343258487506521412621679 Fri Nov 21 20:16:11 2008 elapsed time 00:07:22 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 19.51 hours. Scaled time: 28.33 units (timescale=1.452). Factorization parameters were as follows: name: KA_3_2_150_7 n: 31810982706576934772998608605741160071516082639197877089858403102494412714121865479732665846484350034366517761515179 type: snfs skew: 0.68 deg: 5 c5: 290 c0: 43 m: 1000000000000000000000000000000 rlim: 2200000 alim: 2200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 1000001) Primes: RFBsize:162662, AFBsize:162100, largePrimes:10824027 encountered Relations: rels:9422016, finalFF:331070 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 19.24 hours. Total relation processing time: 0.28 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2200000,2200000,28,28,56,56,2.5,2.5,100000 total time: 19.51 hours. --------- CPU info (if available) ----------
(31·10¹⁶⁶+23)/9 = 3(4)₁₆₅7_<167> = 7 · 19 · 37 · 3191371129640080919489_<22> · 30931033777436558908625985247_<29> · C113
C113 = P38 · P76
P38 = 61798914931319480887285014377816703853_<38>
P76 = 1147395711679263505648383683460557746640664861931176587561400962806755863693_<76>

Number: n N=70907809978627579542331612890992534418293146708040921479541278492523484270210998457654446469974744522569415909129 ( 113 digits) Divisors found: Fri Nov 21 22:03:23 2008 prp38 factor: 61798914931319480887285014377816703853 Fri Nov 21 22:03:23 2008 prp76 factor: 1147395711679263505648383683460557746640664861931176587561400962806755863693 Fri Nov 21 22:03:23 2008 elapsed time 00:56:46 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 24.47 hours. Scaled time: 50.05 units (timescale=2.045). Factorization parameters were as follows: name: KA_3_4_165_7 n: 70907809978627579542331612890992534418293146708040921479541278492523484270210998457654446469974744522569415909129 skew: 32881.19 # norm 7.28e+15 c5: 83160 c4: -668967376 c3: -458058952759210 c2: 3172828514069222313 c1: 170324935437936606139530 c0: 758285338230349101156775464 # alpha -6.22 Y1: 1248999244049 Y0: -3856169760807240084551 # Murphy_E 6.59e-10 # M 31637108997680505828204905949716122300136356195570654326165134163816097965750691160478327792426738914491526610890 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved special-q in [100000, 1600001) Primes: RFBsize:250150, AFBsize:250251, largePrimes:6877052 encountered Relations: rels:6547858, finalFF:553182 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 24.23 hours. Total relation processing time: 0.24 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 24.47 hours. --------- CPU info (if available) ----------
(29·10¹⁵⁴+61)/9 = 3(2)₁₅₃9_<155> = 3 · 17 · 139 · 1155721321_<10> · C142
C142 = P66 · P76
P66 = 986372713677326998182527307992767279549974733724897913803676371177_<66>
P76 = 3987276352659791668600404809219191996642277325038493061533106729035862222933_<76>

Number: n N=3932940596154473397043411029640516430303803401489513592173945327232225973966600528391700714282673182011623756607136363687254410051134029602141 ( 142 digits) SNFS difficulty: 156 digits. Divisors found: Fri Nov 21 22:18:20 2008 prp66 factor: 986372713677326998182527307992767279549974733724897913803676371177 Fri Nov 21 22:18:20 2008 prp76 factor: 3987276352659791668600404809219191996642277325038493061533106729035862222933 Fri Nov 21 22:18:20 2008 elapsed time 01:37:29 (Msieve 1.38) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 21.20 hours. Scaled time: 27.66 units (timescale=1.305). Factorization parameters were as follows: name: KA_3_2_153_9 n: 3932940596154473397043411029640516430303803401489513592173945327232225973966600528391700714282673182011623756607136363687254410051134029602141 type: snfs skew: 1.84 deg: 5 c5: 29 c0: 610 m: 10000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 900001) Primes: RFBsize:216816, AFBsize:216747, largePrimes:11290316 encountered Relations: rels:9758502, finalFF:438402 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 20.89 hours. Total relation processing time: 0.31 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,56,56,2.5,2.5,100000 total time: 21.20 hours. --------- CPU info (if available) ----------
(32·10¹⁵¹-41)/9 = 3(5)₁₅₀1_<152> = 17 · 31 · 47 · 139 · 4091 · 32293129663_<11> · 4851519655528868117_<19> · 29189954590458934457859397_<26> · C87
C87 = P39 · P49
P39 = 180480728295344801238466336014947707069_<39>
P49 = 3058458065007834303252286311493510914433449868357_<49>

Fri Nov 21 22:15:27 2008 Fri Nov 21 22:15:27 2008 Fri Nov 21 22:15:28 2008 Msieve v. 1.38 Fri Nov 21 22:15:28 2008 random seeds: a89c3cd0 547fa8f3 Fri Nov 21 22:15:28 2008 factoring 551992739033384950060268575515588763406213000287167928339052156947081662679297048315633 (87 digits) Fri Nov 21 22:15:29 2008 searching for 15-digit factors Fri Nov 21 22:15:31 2008 commencing quadratic sieve (87-digit input) Fri Nov 21 22:15:31 2008 using multiplier of 1 Fri Nov 21 22:15:31 2008 using 32kb Intel Core sieve core Fri Nov 21 22:15:31 2008 sieve interval: 22 blocks of size 32768 Fri Nov 21 22:15:31 2008 processing polynomials in batches of 10 Fri Nov 21 22:15:32 2008 using a sieve bound of 1499123 (56843 primes) Fri Nov 21 22:15:32 2008 using large prime bound of 119929840 (26 bits) Fri Nov 21 22:15:32 2008 using double large prime bound of 348392707234640 (42-49 bits) Fri Nov 21 22:15:32 2008 using trial factoring cutoff of 49 bits Fri Nov 21 22:15:32 2008 polynomial 'A' values have 11 factors Fri Nov 21 22:48:17 2008 56958 relations (16178 full + 40780 combined from 596856 partial), need 56939 Fri Nov 21 22:48:17 2008 begin with 613034 relations Fri Nov 21 22:48:18 2008 reduce to 135437 relations in 9 passes Fri Nov 21 22:48:18 2008 attempting to read 135437 relations Fri Nov 21 22:48:20 2008 recovered 135437 relations Fri Nov 21 22:48:20 2008 recovered 110021 polynomials Fri Nov 21 22:48:20 2008 attempting to build 56958 cycles Fri Nov 21 22:48:20 2008 found 56958 cycles in 5 passes Fri Nov 21 22:48:20 2008 distribution of cycle lengths: Fri Nov 21 22:48:21 2008 length 1 : 16178 Fri Nov 21 22:48:21 2008 length 2 : 11310 Fri Nov 21 22:48:21 2008 length 3 : 9937 Fri Nov 21 22:48:21 2008 length 4 : 7424 Fri Nov 21 22:48:21 2008 length 5 : 5053 Fri Nov 21 22:48:21 2008 length 6 : 3174 Fri Nov 21 22:48:22 2008 length 7 : 1914 Fri Nov 21 22:48:22 2008 length 9+: 1968 Fri Nov 21 22:48:22 2008 largest cycle: 17 relations Fri Nov 21 22:48:22 2008 matrix is 56843 x 56958 (12.9 MB) with weight 3155406 (55.40/col) Fri Nov 21 22:48:22 2008 sparse part has weight 3155406 (55.40/col) Fri Nov 21 22:48:23 2008 filtering completed in 4 passes Fri Nov 21 22:48:23 2008 matrix is 52253 x 52317 (12.0 MB) with weight 2938923 (56.18/col) Fri Nov 21 22:48:23 2008 sparse part has weight 2938923 (56.18/col) Fri Nov 21 22:48:24 2008 saving the first 48 matrix rows for later Fri Nov 21 22:48:24 2008 matrix is 52205 x 52317 (7.7 MB) with weight 2303617 (44.03/col) Fri Nov 21 22:48:24 2008 sparse part has weight 1692532 (32.35/col) Fri Nov 21 22:48:24 2008 matrix includes 64 packed rows Fri Nov 21 22:48:24 2008 using block size 20926 for processor cache size 4096 kB Fri Nov 21 22:48:25 2008 commencing Lanczos iteration Fri Nov 21 22:48:25 2008 memory use: 7.6 MB Fri Nov 21 22:48:37 2008 lanczos halted after 828 iterations (dim = 52203) Fri Nov 21 22:48:38 2008 recovered 16 nontrivial dependencies Fri Nov 21 22:48:38 2008 prp39 factor: 180480728295344801238466336014947707069 Fri Nov 21 22:48:38 2008 prp49 factor: 3058458065007834303252286311493510914433449868357 Fri Nov 21 22:48:38 2008 elapsed time 00:33:10
(28·10¹⁵⁹+71)/9 = 3(1)₁₅₈9_<160> = 41 · 91084690499731_<14> · C144
C144 = P68 · P77
P68 = 23171439760163422371111675724153326581658778372287070365863549514077_<68>
P77 = 35952844688261045591447954066332986440191163322054061900169489973005924718257_<77>

Number: n N=833079174900552296204015274726708994720787603658384837712899528402125685009777275008418875429543491560512280381394998443766749291297875480403789 ( 144 digits) SNFS difficulty: 161 digits. Divisors found: Sat Nov 22 00:10:35 2008 prp68 factor: 23171439760163422371111675724153326581658778372287070365863549514077 Sat Nov 22 00:10:35 2008 prp77 factor: 35952844688261045591447954066332986440191163322054061900169489973005924718257 Sat Nov 22 00:10:35 2008 elapsed time 01:06:10 (Msieve 1.38) Version: GGNFS-0.77.1-20050930-k8 Total time: 21.41 hours. Scaled time: 17.94 units (timescale=0.838). Factorization parameters were as follows: name: KA_3_1_158_9 n: 833079174900552296204015274726708994720787603658384837712899528402125685009777275008418875429543491560512280381394998443766749291297875480403789 type: snfs skew: 1.91 deg: 5 c5: 14 c0: 355 m: 100000000000000000000000000000000 rlim: 4000000 alim: 4000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 1150001) Primes: RFBsize:283146, AFBsize:282603, largePrimes:13023992 encountered Relations: rels:11576174, finalFF:592990 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 21.08 hours. Total relation processing time: 0.33 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,56,56,2.5,2.5,100000 total time: 21.41 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(31·10¹⁴⁹+41)/9 = 3(4)₁₄₈9_<150> = 7 · 42824491 · 9158260301_<10> · 22224985260767827_<17> · 1112929878226468993_<19> · C97
C97 = P38 · P60
P38 = 22521545757000487584780938305372935523_<38>
P60 = 225220787774420230975891805254681225718909593400875653913409_<60>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 5072320277289301240298525799177849702522387783534603072805642037340932334501433151881909182127907 (97 digits) Using B1=1328000, B2=1426405900, polynomial Dickson(6), sigma=4224044251 Step 1 took 13875ms Step 2 took 5313ms ********** Factor found in step 2: 22521545757000487584780938305372935523 Found probable prime factor of 38 digits: 22521545757000487584780938305372935523 Probable prime cofactor 225220787774420230975891805254681225718909593400875653913409 has 60 digits
Nov 21, 2008 (4th): Factorizations of 344...449 and Factorizations of 355...551 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.
Nov 21, 2008 (3rd): By Sinkiti Sibata / Msieve
(31·10¹³²+23)/9 = 3(4)₁₃₁7_<133> = 3 · 2297 · 193937 · 113221838034086314271_<21> · C104
C104 = P42 · P63
P42 = 128001041209174255487204192912085552014267_<42>
P63 = 177841272808507424123091401292295891898695805385853038162258313_<63>

Thu Nov 20 05:27:39 2008 Msieve v. 1.38 Thu Nov 20 05:27:39 2008 random seeds: 06aef7d0 3491eb82 Thu Nov 20 05:27:39 2008 factoring 22763868089453759778600523391606177381637960434520514072517380420776039653079075638988500274654715351571 (104 digits) Thu Nov 20 05:27:40 2008 searching for 15-digit factors Thu Nov 20 05:27:42 2008 commencing quadratic sieve (104-digit input) Thu Nov 20 05:27:42 2008 using multiplier of 11 Thu Nov 20 05:27:42 2008 using 32kb Intel Core sieve core Thu Nov 20 05:27:42 2008 sieve interval: 36 blocks of size 32768 Thu Nov 20 05:27:42 2008 processing polynomials in batches of 6 Thu Nov 20 05:27:42 2008 using a sieve bound of 3650509 (129768 primes) Thu Nov 20 05:27:42 2008 using large prime bound of 547576350 (29 bits) Thu Nov 20 05:27:42 2008 using double large prime bound of 5360439540079200 (44-53 bits) Thu Nov 20 05:27:42 2008 using trial factoring cutoff of 53 bits Thu Nov 20 05:27:42 2008 polynomial 'A' values have 14 factors Fri Nov 21 11:27:11 2008 130009 relations (30765 full + 99244 combined from 1944400 partial), need 129864 Fri Nov 21 11:27:14 2008 begin with 1975165 relations Fri Nov 21 11:27:16 2008 reduce to 343309 relations in 13 passes Fri Nov 21 11:27:16 2008 attempting to read 343309 relations Fri Nov 21 11:27:24 2008 recovered 343309 relations Fri Nov 21 11:27:24 2008 recovered 336630 polynomials Fri Nov 21 11:27:25 2008 attempting to build 130009 cycles Fri Nov 21 11:27:25 2008 found 130009 cycles in 6 passes Fri Nov 21 11:27:25 2008 distribution of cycle lengths: Fri Nov 21 11:27:25 2008 length 1 : 30765 Fri Nov 21 11:27:25 2008 length 2 : 22047 Fri Nov 21 11:27:25 2008 length 3 : 21707 Fri Nov 21 11:27:25 2008 length 4 : 17738 Fri Nov 21 11:27:25 2008 length 5 : 13868 Fri Nov 21 11:27:25 2008 length 6 : 9322 Fri Nov 21 11:27:25 2008 length 7 : 6050 Fri Nov 21 11:27:25 2008 length 9+: 8512 Fri Nov 21 11:27:25 2008 largest cycle: 21 relations Fri Nov 21 11:27:26 2008 matrix is 129768 x 130009 (36.9 MB) with weight 9152557 (70.40/col) Fri Nov 21 11:27:26 2008 sparse part has weight 9152557 (70.40/col) Fri Nov 21 11:27:28 2008 filtering completed in 3 passes Fri Nov 21 11:27:28 2008 matrix is 124950 x 125013 (35.6 MB) with weight 8843121 (70.74/col) Fri Nov 21 11:27:28 2008 sparse part has weight 8843121 (70.74/col) Fri Nov 21 11:27:29 2008 saving the first 48 matrix rows for later Fri Nov 21 11:27:29 2008 matrix is 124902 x 125013 (22.0 MB) with weight 7005702 (56.04/col) Fri Nov 21 11:27:29 2008 sparse part has weight 5022897 (40.18/col) Fri Nov 21 11:27:29 2008 matrix includes 64 packed rows Fri Nov 21 11:27:29 2008 using block size 43690 for processor cache size 1024 kB Fri Nov 21 11:27:30 2008 commencing Lanczos iteration Fri Nov 21 11:27:30 2008 memory use: 21.4 MB Fri Nov 21 11:29:34 2008 lanczos halted after 1976 iterations (dim = 124902) Fri Nov 21 11:29:34 2008 recovered 18 nontrivial dependencies Fri Nov 21 11:29:35 2008 prp42 factor: 128001041209174255487204192912085552014267 Fri Nov 21 11:29:35 2008 prp63 factor: 177841272808507424123091401292295891898695805385853038162258313 Fri Nov 21 11:29:35 2008 elapsed time 30:01:56
Nov 21, 2008 (2nd): By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38
(29·10¹⁵⁸-11)/9 = 3(2)₁₅₇1_<159> = 3 · 17 · 599 · 3320365643961975314499641_<25> · C130
C130 = P37 · P94
P37 = 3113310324647811275855004400415874517_<37>
P94 = 1020352344078143226664091214916101776213040500244838288298165298571081699060386378588779843357_<94>

Run 58 out of 100: Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2684999099 Step 1 took 33625ms ********** Factor found in step 1: 3113310324647811275855004400415874517 Found probable prime factor of 37 digits: 3113310324647811275855004400415874517 Probable prime cofactor 1020352344078143226664091214916101776213040500244838288298165298571081699060386378588779843357 has 94 digits
(8·10²⁴¹+1)/9 = (8)₂₄₀9_<241> = 3 · 240542009 · 36048817474529_<14> · 2236835197411007_<16> · 619328809218826631987_<21> · 2307994439692107818518677103_<28> · C156
C156 = P30 · P126
P30 = 139271372194463204233517633963_<30>
P126 = 767348030659914881516899932516529213904508061822198690776663718238208342560952835364792234120627533932150190654837531132325483_<126>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3302111522 Step 1 took 26889ms Step 2 took 16389ms ********** Factor found in step 2: 139271372194463204233517633963 Found probable prime factor of 30 digits: 139271372194463204233517633963 Probable prime cofactor 767348030659914881516899932516529213904508061822198690776663718238208342560952835364792234120627533932150190654837531132325483 has 126 digits
4·10²³⁴+1 = 4(0)₂₃₃1_<235> = 101844481261409_<15> · 15083067110761453_<17> · 166470474810555341081321_<24> · 281722440676563078737805904561_<30> · C152
C152 = P35 · P117
P35 = 59520510316289955705069974366831129_<35>
P117 = 932840774605491827367365884272243625937825837089740051536226422913469229092335449597657018460854220557450573143028437_<117>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3553856087 Step 1 took 14589ms Step 2 took 10980ms ********** Factor found in step 2: 59520510316289955705069974366831129 Found probable prime factor of 35 digits: 59520510316289955705069974366831129 Probable prime cofactor 932840774605491827367365884272243625937825837089740051536226422913469229092335449597657018460854220557450573143028437 has 117 digits
(31·10¹⁵³+23)/9 = 3(4)₁₅₂7_<154> = 3 · 33179 · 20826677 · C142
C142 = P43 · P99
P43 = 8057751421933845833175419115668072017469321_<43>
P99 = 206205758933494869507949855300183014699121320329094444631862433555090877799400218997532783562912443_<99>

SNFS difficulty: 155 digits. Divisors found: r1=8057751421933845833175419115668072017469321 (pp43) r2=206205758933494869507949855300183014699121320329094444631862433555090877799400218997532783562912443 (pp99) Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.948). Factorization parameters were as follows: n: 1661554747257316118030711657236449112247555007148199909420522176066246632447220815227217524487168894168556200871108421492188390703937161661203 m: 5000000000000000000000000000000 deg: 5 c5: 248 c0: 575 skew: 1.18 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 53/53 Sieved rational special-q in [1400000, 2600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 625976 x 626218 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,53,53,2.5,2.5,100000 total time: 20.00 hours.
Nov 21, 2008: By Robert Backstrom / GGNFS, GMP-ECM
(28·10¹⁵⁵+71)/9 = 3(1)₁₅₄9_<156> = 3911 · 17762298559_<11> · 1654368234481259210641757_<25> · C118
C118 = P58 · P60
P58 = 5207543179028634894163598836860089001918725016663488946821_<58>
P60 = 519832559697601779512517512681427527642437186726029598257623_<60>

Number: n N=2707050500490241799888406019421296662760926921905251579321279923412603805121355417444843351066830762011792020904866483 ( 118 digits) SNFS difficulty: 156 digits. Divisors found: r1=5207543179028634894163598836860089001918725016663488946821 (pp58) r2=519832559697601779512517512681427527642437186726029598257623 (pp60) Version: GGNFS-0.77.1-20051202-athlon Total time: 15.17 hours. Scaled time: 27.73 units (timescale=1.828). Factorization parameters were as follows: name: KA_3_1_154_9 n: 2707050500490241799888406019421296662760926921905251579321279923412603805121355417444843351066830762011792020904866483 type: snfs skew: 1.20 deg: 5 c5: 28 c0: 71 m: 10000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [100000, 850001) Primes: RFBsize:216816, AFBsize:216157, largePrimes:11660197 encountered Relations: rels:10375245, finalFF:578312 Max relations in full relation-set: 48 Initial matrix: 433041 x 578312 with sparse part having weight 56231987. Pruned matrix : 323328 x 325557 with weight 28767447. Total sieving time: 13.85 hours. Total relation processing time: 0.24 hours. Matrix solve time: 1.02 hours. Total square root time: 0.05 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,56,56,2.5,2.5,100000 total time: 15.17 hours. --------- CPU info (if available) ----------
(29·10¹⁵⁹-11)/9 = 3(2)₁₅₈1_<160> = 113 · 127 · 439 · 647 · 2930064630617_<13> · C138
C138 = P32 · P107
P32 = 19376489485924470209262041162989_<32>
P107 = 13923622050520029560513560197456375374993934656664684892227903781263511730077220792928335238140859671738599_<107>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 269790916267887465351909992767559683801135115291189777213727431952734734185276613939457571274588620565285534217037470149479822257561512411 (138 digits) Using B1=800000, B2=696806892, polynomial Dickson(3), sigma=2305516098 Step 1 took 8563ms Step 2 took 3640ms ********** Factor found in step 2: 19376489485924470209262041162989 Found probable prime factor of 32 digits: 19376489485924470209262041162989 Probable prime cofactor 13923622050520029560513560197456375374993934656664684892227903781263511730077220792928335238140859671738599 has 107 digits
Nov 20, 2008 (9th): By Jo Yeong Uk / GGNFS
(31·10¹⁵¹+23)/9 = 3(4)₁₅₀7_<152> = 37 · 813097 · C145
C145 = P51 · P94
P51 = 661308922236046130574180250788845131268232439494137_<51>
P94 = 1731293583610207200485057312737901737674537238871160790344877979353997153175128440849742800979_<94>

Number: 34447_151 N=1144919893851448143248506550793977755336609200293360977756566474763688626241310607382552058279554506941891226915030963010478369654458116228360123 ( 145 digits) SNFS difficulty: 152 digits. Divisors found: r1=661308922236046130574180250788845131268232439494137 (pp51) r2=1731293583610207200485057312737901737674537238871160790344877979353997153175128440849742800979 (pp94) Version: GGNFS-0.77.1-20050930-nocona Total time: 11.38 hours. Scaled time: 27.00 units (timescale=2.373). Factorization parameters were as follows: n: 1144919893851448143248506550793977755336609200293360977756566474763688626241310607382552058279554506941891226915030963010478369654458116228360123 m: 1000000000000000000000000000000 deg: 5 c5: 310 c0: 23 skew: 0.59 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1200000, 1900001) Primes: RFBsize:176302, AFBsize:176064, largePrimes:7721639 encountered Relations: rels:7779627, finalFF:545693 Max relations in full relation-set: 28 Initial matrix: 352433 x 545693 with sparse part having weight 57523083. Pruned matrix : 282021 x 283847 with weight 27602538. Total sieving time: 10.80 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.45 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000 total time: 11.38 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Nov 20, 2008 (8th): By Robert Backstrom / Msieve
(31·10¹⁴¹+23)/9 = 3(4)₁₄₀7_<142> = 3 · 89 · 151 · 26064697 · 2350566219110645571032862479372843_<34> · C97
C97 = P43 · P54
P43 = 1549081274511290351303642137676399869628903_<43>
P54 = 900184644644614901232675640022748801919586985760172207_<54>

Thu Nov 20 16:38:07 2008 Thu Nov 20 16:38:07 2008 Thu Nov 20 16:38:07 2008 Msieve v. 1.38 Thu Nov 20 16:38:08 2008 random seeds: 9bc7b380 5b2b56c3 Thu Nov 20 16:38:08 2008 factoring 1394459176621573051639386763789651414147839796257994686093167116726624290897405719337770464498921 (97 digits) Thu Nov 20 16:38:09 2008 searching for 15-digit factors Thu Nov 20 16:38:10 2008 commencing quadratic sieve (97-digit input) Thu Nov 20 16:38:11 2008 using multiplier of 13 Thu Nov 20 16:38:11 2008 using 32kb Intel Core sieve core Thu Nov 20 16:38:11 2008 sieve interval: 36 blocks of size 32768 Thu Nov 20 16:38:11 2008 processing polynomials in batches of 6 Thu Nov 20 16:38:11 2008 using a sieve bound of 2334863 (85703 primes) Thu Nov 20 16:38:12 2008 using large prime bound of 350229450 (28 bits) Thu Nov 20 16:38:12 2008 using double large prime bound of 2397920528297850 (43-52 bits) Thu Nov 20 16:38:12 2008 using trial factoring cutoff of 52 bits Thu Nov 20 16:38:12 2008 polynomial 'A' values have 13 factors Thu Nov 20 20:11:57 2008 85990 relations (22065 full + 63925 combined from 1278641 partial), need 85799 Thu Nov 20 20:11:58 2008 begin with 1300706 relations Thu Nov 20 20:11:59 2008 reduce to 220755 relations in 11 passes Thu Nov 20 20:11:59 2008 attempting to read 220755 relations Thu Nov 20 20:12:02 2008 recovered 220755 relations Thu Nov 20 20:12:02 2008 recovered 205400 polynomials Thu Nov 20 20:12:03 2008 attempting to build 85990 cycles Thu Nov 20 20:12:03 2008 found 85990 cycles in 6 passes Thu Nov 20 20:12:03 2008 distribution of cycle lengths: Thu Nov 20 20:12:03 2008 length 1 : 22065 Thu Nov 20 20:12:04 2008 length 2 : 15290 Thu Nov 20 20:12:04 2008 length 3 : 14451 Thu Nov 20 20:12:04 2008 length 4 : 11510 Thu Nov 20 20:12:04 2008 length 5 : 8566 Thu Nov 20 20:12:04 2008 length 6 : 5640 Thu Nov 20 20:12:05 2008 length 7 : 3598 Thu Nov 20 20:12:05 2008 length 9+: 4870 Thu Nov 20 20:12:05 2008 largest cycle: 24 relations Thu Nov 20 20:12:05 2008 matrix is 85703 x 85990 (23.2 MB) with weight 5738545 (66.74/col) Thu Nov 20 20:12:05 2008 sparse part has weight 5738545 (66.74/col) Thu Nov 20 20:12:06 2008 filtering completed in 3 passes Thu Nov 20 20:12:06 2008 matrix is 81042 x 81106 (22.0 MB) with weight 5441103 (67.09/col) Thu Nov 20 20:12:07 2008 sparse part has weight 5441103 (67.09/col) Thu Nov 20 20:12:07 2008 saving the first 48 matrix rows for later Thu Nov 20 20:12:07 2008 matrix is 80994 x 81106 (14.4 MB) with weight 4384075 (54.05/col) Thu Nov 20 20:12:08 2008 sparse part has weight 3281672 (40.46/col) Thu Nov 20 20:12:08 2008 matrix includes 64 packed rows Thu Nov 20 20:12:08 2008 using block size 32442 for processor cache size 4096 kB Thu Nov 20 20:12:09 2008 commencing Lanczos iteration Thu Nov 20 20:12:09 2008 memory use: 13.4 MB Thu Nov 20 20:12:46 2008 lanczos halted after 1283 iterations (dim = 80993) Thu Nov 20 20:12:46 2008 recovered 17 nontrivial dependencies Thu Nov 20 20:12:47 2008 prp43 factor: 1549081274511290351303642137676399869628903 Thu Nov 20 20:12:47 2008 prp54 factor: 900184644644614901232675640022748801919586985760172207 Thu Nov 20 20:12:47 2008 elapsed time 03:34:39
Nov 20, 2008 (7th): By Serge Batalov / GMP-ECM 6.2.1
(31·10¹⁷⁶+23)/9 = 3(4)₁₇₅7_<177> = 61 · 127 · 6269 · 93623059 · 328309320318647_<15> · C147
C147 = P36 · C112
P36 = 202720502544193253155472756683183303_<36>
C112 = [1138213272254499930643296820016032059483757432491990061526260841951018280753405751022578969878813592572060915491_<112>]

Factor found in step 2: 202720502544193253155472756683183303
Nov 20, 2008 (6th): By Sinkiti Sibata / GGNFS
(31·10¹³⁵+23)/9 = 3(4)₁₃₄7_<136> = 3 · 53 · 14827 · 80153 · 175333 · C120
C120 = P55 · P65
P55 = 5320146285913004033923822786340081282766713399367469351_<55>
P65 = 19541673492807033009504105677720911572680933743819569639669768521_<65>

Number: 34447_135 N=103964561653281937615940698397888792368105511524925163767455307432152372393741558475751641975328714898867866571732099871 ( 120 digits) SNFS difficulty: 136 digits. Divisors found: r1=5320146285913004033923822786340081282766713399367469351 (pp55) r2=19541673492807033009504105677720911572680933743819569639669768521 (pp65) Version: GGNFS-0.77.1-20060513-k8 Total time: 7.27 hours. Scaled time: 14.60 units (timescale=2.010). Factorization parameters were as follows: name: 34447_135 n: 103964561653281937615940698397888792368105511524925163767455307432152372393741558475751641975328714898867866571732099871 m: 1000000000000000000000000000 deg: 5 c5: 31 c0: 23 skew: 0.94 type: snfs lss: 1 rlim: 1320000 alim: 1320000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1320000/1320000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [660000, 1335001) Primes: RFBsize:101433, AFBsize:101212, largePrimes:3455437 encountered Relations: rels:3558281, finalFF:377834 Max relations in full relation-set: 28 Initial matrix: 202710 x 377834 with sparse part having weight 34651730. Pruned matrix : 162371 x 163448 with weight 12239877. Total sieving time: 6.87 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.23 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1320000,1320000,26,26,48,48,2.3,2.3,75000 total time: 7.27 hours. --------- CPU info (if available) ----------
(31·10¹³⁶+23)/9 = 3(4)₁₃₅7_<137> = 7 · 37 · 191 · 76280803889_<11> · C121
C121 = P48 · P74
P48 = 230857778558202023809686931408875980413732116091_<48>
P74 = 39539054474929483767587850106894599968633750590814267323704018007244123137_<74>

Number: 34447_136 N=9127898282373957556699495805501989405108267715924648355714034125424503203800344076649701860823029148177829292694783097467 ( 121 digits) SNFS difficulty: 137 digits. Divisors found: r1=230857778558202023809686931408875980413732116091 (pp48) r2=39539054474929483767587850106894599968633750590814267323704018007244123137 (pp74) Version: GGNFS-0.77.1-20060513-k8 Total time: 6.15 hours. Scaled time: 12.09 units (timescale=1.967). Factorization parameters were as follows: name: 34447_136 n: 9127898282373957556699495805501989405108267715924648355714034125424503203800344076649701860823029148177829292694783097467 m: 1000000000000000000000000000 deg: 5 c5: 310 c0: 23 skew: 0.59 type: snfs lss: 1 rlim: 1370000 alim: 1370000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1370000/1370000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [685000, 1210001) Primes: RFBsize:104967, AFBsize:104854, largePrimes:3408938 encountered Relations: rels:3538159, finalFF:429663 Max relations in full relation-set: 28 Initial matrix: 209888 x 429663 with sparse part having weight 35074190. Pruned matrix : 151114 x 152227 with weight 10313401. Total sieving time: 5.80 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.18 hours. Time per square root: 0.08 h