News and updates, June 2009

Jun 30, 2009 (3rd)

By Sinkiti Sibata / Msieve / Jun 30, 2009
(58·10¹⁴³-13)/9 = 6(4)₁₄₂3_<144> = 113 · 223 · 77023 · C135
C135 = P64 · P72
P64 = 1652337627292589379706191532069268484497360291057948743864303033_<64>
P72 = 200947660644812862508216274233245205166132877847788787856034118266055523_<72>

Number: 64443_143 N=332033380799846526477379417918328852033073705607452776566870643319489211252896617924602015943659826695384126147432305894890078475301259 ( 135 digits) SNFS difficulty: 146 digits. Divisors found: r1=1652337627292589379706191532069268484497360291057948743864303033 (pp64) r2=200947660644812862508216274233245205166132877847788787856034118266055523 (pp72) Version: Msieve-1.40 Total time: 10.20 hours. Scaled time: 26.14 units (timescale=2.564). Factorization parameters were as follows: name: 64443_143 n: 332033380799846526477379417918328852033073705607452776566870643319489211252896617924602015943659826695384126147432305894890078475301259 m: 50000000000000000000000000000 deg: 5 c5: 464 c0: -325 skew: 0.93 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, 2255001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 341670 x 341918 Total sieving time: 9.82 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.25 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,146.000,5,0,0,0,0,0,0,0,0,1910000,1910000,26,26,49,49,2.3,2.3,100000 total time: 10.20 hours. --------- CPU info (if available) ----------

(58·10¹⁵⁵-13)/9 = 6(4)₁₅₄3_<156> = 227 · 42416069 · 2974192430852304989290612183_<28> · C119
C119 = P38 · P81
P38 = 23571159999526622109100196347300471721_<38>
P81 = 954726968014034137402089586947817032218884506562192209056620458034761171420831227_<81>

Number: 64443_155 N=22504022118921734259662990204779762049959337208129694385777166920187136905382202309246021844159118798649720943027231667 ( 119 digits) SNFS difficulty: 156 digits. Divisors found: r1=23571159999526622109100196347300471721 (pp38) r2=954726968014034137402089586947817032218884506562192209056620458034761171420831227 (pp81) Version: Msieve-1.40 Total time: 25.30 hours. Scaled time: 51.56 units (timescale=2.038). Factorization parameters were as follows: name: 64443_155 n: 22504022118921734259662990204779762049959337208129694385777166920187136905382202309246021844159118798649720943027231667 m: 10000000000000000000000000000000 deg: 5 c5: 58 c0: -13 skew: 0.74 type: snfs lss: 1 rlim: 2900000 alim: 2900000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 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: 50/50 Sieved rational special-q in [1450000, 2450001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 527291 x 527539 Total sieving time: 24.05 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.99 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,156.000,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,100000 total time: 25.30 hours. --------- CPU info (if available) ----------

Jun 30, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jun 30, 2009
(58·10¹⁶¹-13)/9 = 6(4)₁₆₀3_<162> = 653319345451_<12> · C150
C150 = P52 · P99
P52 = 1575237244329951942400489897260475329452903303322367_<52>
P99 = 626201342405418301153045845166292234087621760837772895460574802045257424597728085044658561255896879_<99>

Number: 64443_161 N=986415677006427804635947990417506924988037544295951487502593886272837369809392052611588638503606484328606433676386764357014430239213162142871046192593 ( 150 digits) SNFS difficulty: 162 digits. Divisors found: r1=1575237244329951942400489897260475329452903303322367 r2=626201342405418301153045845166292234087621760837772895460574802045257424597728085044658561255896879 Version: Total time: 20.20 hours. Scaled time: 48.26 units (timescale=2.389). Factorization parameters were as follows: n: 986415677006427804635947990417506924988037544295951487502593886272837369809392052611588638503606484328606433676386764357014430239213162142871046192593 m: 100000000000000000000000000000000 deg: 5 c5: 580 c0: -13 skew: 0.47 type: snfs lss: 1 rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2000000, 3700001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9541464 Max relations in full relation-set: Initial matrix: Pruned matrix : 736941 x 737189 Total sieving time: 18.04 hours. Total relation processing time: 0.78 hours. Matrix solve time: 1.11 hours. Time per square root: 0.28 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,51,51,2.4,2.4,100000 total time: 20.20 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673802) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)

Jun 30, 2009

By Andreas Tete / Msieve v. 1.42, GGNFS / Jun 30, 2009
(58·10¹⁷¹-13)/9 = 6(4)₁₇₀3_<172> = 267800740964923_<15> · 136821051590356663_<18> · 23486273512771613646940357632313_<32> · C109
C109 = P49 · P61
P49 = 1680685663562710108755241113940108250558188502759_<49>
P61 = 4455743436763288668170528477507378349835514471314046357878921_<61>

Mon Jun 29 21:25:16 2009 Msieve v. 1.42 Mon Jun 29 21:25:16 2009 random seeds: bbef2658 2c483f2b Mon Jun 29 21:25:16 2009 factoring 7488704114681698263211093624793715429841463355073981832582681151912872857638281873870764124988601995996443039 (109 digits) Mon Jun 29 21:25:17 2009 searching for 15-digit factors Mon Jun 29 21:25:18 2009 commencing number field sieve (109-digit input) Mon Jun 29 21:25:18 2009 R0: -1200755848565647964360 Mon Jun 29 21:25:18 2009 R1: 277561682419 Mon Jun 29 21:25:18 2009 A0: 765270029707707158906661 Mon Jun 29 21:25:18 2009 A1: 4592249298769793133290 Mon Jun 29 21:25:18 2009 A2: -476743582276620277 Mon Jun 29 21:25:18 2009 A3: -11323319301534 Mon Jun 29 21:25:18 2009 A4: 354533780 Mon Jun 29 21:25:18 2009 A5: 3000 Mon Jun 29 21:25:18 2009 skew 32429.05, size 2.389419e-010, alpha -5.307571, combined = 1.238732e-009 Mon Jun 29 21:25:19 2009 Mon Jun 29 21:25:19 2009 commencing relation filtering Mon Jun 29 21:25:19 2009 commencing duplicate removal, pass 1 Mon Jun 29 21:26:31 2009 found 490481 hash collisions in 5342536 relations Mon Jun 29 21:26:45 2009 added 36477 free relations Mon Jun 29 21:26:45 2009 commencing duplicate removal, pass 2 Mon Jun 29 21:26:54 2009 found 476302 duplicates and 4902710 unique relations Mon Jun 29 21:26:54 2009 memory use: 41.3 MB Mon Jun 29 21:26:54 2009 reading rational ideals above 3080192 Mon Jun 29 21:26:54 2009 reading algebraic ideals above 3080192 Mon Jun 29 21:26:54 2009 commencing singleton removal, pass 1 Mon Jun 29 21:27:49 2009 relations with 0 large ideals: 119050 Mon Jun 29 21:27:49 2009 relations with 1 large ideals: 753244 Mon Jun 29 21:27:49 2009 relations with 2 large ideals: 1732248 Mon Jun 29 21:27:49 2009 relations with 3 large ideals: 1672371 Mon Jun 29 21:27:49 2009 relations with 4 large ideals: 570809 Mon Jun 29 21:27:49 2009 relations with 5 large ideals: 20278 Mon Jun 29 21:27:49 2009 relations with 6 large ideals: 34710 Mon Jun 29 21:27:49 2009 relations with 7+ large ideals: 0 Mon Jun 29 21:27:49 2009 4902710 relations and about 4779680 large ideals Mon Jun 29 21:27:49 2009 commencing singleton removal, pass 2 Mon Jun 29 21:28:47 2009 found 2126072 singletons Mon Jun 29 21:28:47 2009 current dataset: 2776638 relations and about 2200364 large ideals Mon Jun 29 21:28:47 2009 commencing singleton removal, pass 3 Mon Jun 29 21:29:34 2009 found 500480 singletons Mon Jun 29 21:29:34 2009 current dataset: 2276158 relations and about 1665007 large ideals Mon Jun 29 21:29:34 2009 commencing singleton removal, pass 4 Mon Jun 29 21:30:18 2009 found 148691 singletons Mon Jun 29 21:30:18 2009 current dataset: 2127467 relations and about 1512452 large ideals Mon Jun 29 21:30:18 2009 commencing singleton removal, final pass Mon Jun 29 21:31:04 2009 memory use: 33.3 MB Mon Jun 29 21:31:04 2009 commencing in-memory singleton removal Mon Jun 29 21:31:04 2009 begin with 2127467 relations and 1560650 unique ideals Mon Jun 29 21:31:06 2009 reduce to 1935741 relations and 1366206 ideals in 15 passes Mon Jun 29 21:31:06 2009 max relations containing the same ideal: 46 Mon Jun 29 21:31:07 2009 reading rational ideals above 720000 Mon Jun 29 21:31:07 2009 reading algebraic ideals above 720000 Mon Jun 29 21:31:07 2009 commencing singleton removal, final pass Mon Jun 29 21:31:52 2009 keeping 1670936 ideals with weight <= 20, new excess is 200601 Mon Jun 29 21:31:54 2009 memory use: 47.7 MB Mon Jun 29 21:31:54 2009 commencing in-memory singleton removal Mon Jun 29 21:31:54 2009 begin with 1946275 relations and 1670936 unique ideals Mon Jun 29 21:31:56 2009 reduce to 1927241 relations and 1600494 ideals in 10 passes Mon Jun 29 21:31:56 2009 max relations containing the same ideal: 20 Mon Jun 29 21:31:58 2009 removing 322019 relations and 274994 ideals in 47025 cliques Mon Jun 29 21:31:58 2009 commencing in-memory singleton removal Mon Jun 29 21:31:58 2009 begin with 1605222 relations and 1600494 unique ideals Mon Jun 29 21:31:59 2009 reduce to 1571407 relations and 1290716 ideals in 7 passes Mon Jun 29 21:31:59 2009 max relations containing the same ideal: 20 Mon Jun 29 21:32:00 2009 removing 241602 relations and 194577 ideals in 47025 cliques Mon Jun 29 21:32:00 2009 commencing in-memory singleton removal Mon Jun 29 21:32:00 2009 begin with 1329805 relations and 1290716 unique ideals Mon Jun 29 21:32:01 2009 reduce to 1304264 relations and 1069911 ideals in 8 passes Mon Jun 29 21:32:01 2009 max relations containing the same ideal: 20 Mon Jun 29 21:32:02 2009 relations with 0 large ideals: 17810 Mon Jun 29 21:32:02 2009 relations with 1 large ideals: 117111 Mon Jun 29 21:32:02 2009 relations with 2 large ideals: 310411 Mon Jun 29 21:32:02 2009 relations with 3 large ideals: 412635 Mon Jun 29 21:32:02 2009 relations with 4 large ideals: 296443 Mon Jun 29 21:32:02 2009 relations with 5 large ideals: 118042 Mon Jun 29 21:32:02 2009 relations with 6 large ideals: 27975 Mon Jun 29 21:32:02 2009 relations with 7+ large ideals: 3837 Mon Jun 29 21:32:02 2009 commencing 2-way merge Mon Jun 29 21:32:03 2009 reduce to 804300 relation sets and 569947 unique ideals Mon Jun 29 21:32:03 2009 commencing full merge Mon Jun 29 21:32:12 2009 memory use: 43.1 MB Mon Jun 29 21:32:12 2009 found 376706 cycles, need 346147 Mon Jun 29 21:32:12 2009 weight of 346147 cycles is about 24613171 (71.11/cycle) Mon Jun 29 21:32:12 2009 distribution of cycle lengths: Mon Jun 29 21:32:12 2009 1 relations: 36446 Mon Jun 29 21:32:12 2009 2 relations: 33802 Mon Jun 29 21:32:13 2009 3 relations: 34003 Mon Jun 29 21:32:13 2009 4 relations: 31923 Mon Jun 29 21:32:13 2009 5 relations: 30349 Mon Jun 29 21:32:13 2009 6 relations: 27713 Mon Jun 29 21:32:13 2009 7 relations: 25349 Mon Jun 29 21:32:13 2009 8 relations: 23008 Mon Jun 29 21:32:13 2009 9 relations: 20155 Mon Jun 29 21:32:13 2009 10+ relations: 83399 Mon Jun 29 21:32:13 2009 heaviest cycle: 18 relations Mon Jun 29 21:32:13 2009 commencing cycle optimization Mon Jun 29 21:32:13 2009 start with 2229788 relations Mon Jun 29 21:32:20 2009 pruned 77903 relations Mon Jun 29 21:32:20 2009 memory use: 56.0 MB Mon Jun 29 21:32:20 2009 distribution of cycle lengths: Mon Jun 29 21:32:20 2009 1 relations: 36446 Mon Jun 29 21:32:20 2009 2 relations: 34796 Mon Jun 29 21:32:20 2009 3 relations: 35589 Mon Jun 29 21:32:20 2009 4 relations: 33220 Mon Jun 29 21:32:20 2009 5 relations: 31692 Mon Jun 29 21:32:20 2009 6 relations: 28752 Mon Jun 29 21:32:20 2009 7 relations: 26007 Mon Jun 29 21:32:20 2009 8 relations: 23590 Mon Jun 29 21:32:20 2009 9 relations: 20541 Mon Jun 29 21:32:20 2009 10+ relations: 75514 Mon Jun 29 21:32:20 2009 heaviest cycle: 18 relations Mon Jun 29 21:32:21 2009 RelProcTime: 298 Mon Jun 29 21:32:21 2009 Mon Jun 29 21:32:21 2009 commencing linear algebra Mon Jun 29 21:32:21 2009 read 346147 cycles Mon Jun 29 21:32:21 2009 cycles contain 1137287 unique relations Mon Jun 29 21:32:57 2009 read 1137287 relations Mon Jun 29 21:32:58 2009 using 20 quadratic characters above 118112012 Mon Jun 29 21:33:06 2009 building initial matrix Mon Jun 29 21:33:22 2009 memory use: 126.8 MB Mon Jun 29 21:33:22 2009 read 346147 cycles Mon Jun 29 21:33:23 2009 matrix is 345913 x 346147 (97.7 MB) with weight 32532069 (93.98/col) Mon Jun 29 21:33:23 2009 sparse part has weight 23181247 (66.97/col) Mon Jun 29 21:33:28 2009 filtering completed in 3 passes Mon Jun 29 21:33:28 2009 matrix is 344348 x 344548 (97.4 MB) with weight 32420368 (94.10/col) Mon Jun 29 21:33:28 2009 sparse part has weight 23116687 (67.09/col) Mon Jun 29 21:33:29 2009 read 344548 cycles Mon Jun 29 21:33:30 2009 matrix is 344348 x 344548 (97.4 MB) with weight 32420368 (94.10/col) Mon Jun 29 21:33:30 2009 sparse part has weight 23116687 (67.09/col) Mon Jun 29 21:33:30 2009 saving the first 48 matrix rows for later Mon Jun 29 21:33:30 2009 matrix is 344300 x 344548 (93.4 MB) with weight 25498522 (74.01/col) Mon Jun 29 21:33:30 2009 sparse part has weight 22429237 (65.10/col) Mon Jun 29 21:33:30 2009 matrix includes 64 packed rows Mon Jun 29 21:33:30 2009 using block size 65536 for processor cache size 3072 kB Mon Jun 29 21:33:33 2009 commencing Lanczos iteration Mon Jun 29 21:33:33 2009 memory use: 91.0 MB Mon Jun 29 21:50:21 2009 lanczos halted after 5445 iterations (dim = 344300) Mon Jun 29 21:50:21 2009 recovered 30 nontrivial dependencies Mon Jun 29 21:50:22 2009 BLanczosTime: 1081 Mon Jun 29 21:50:22 2009 Mon Jun 29 21:50:22 2009 commencing square root phase Mon Jun 29 21:50:22 2009 reading relations for dependency 1 Mon Jun 29 21:50:22 2009 read 172326 cycles Mon Jun 29 21:50:22 2009 cycles contain 703698 unique relations Mon Jun 29 21:50:56 2009 read 703698 relations Mon Jun 29 21:50:59 2009 multiplying 567642 relations Mon Jun 29 21:52:27 2009 multiply complete, coefficients have about 22.77 million bits Mon Jun 29 21:52:28 2009 initial square root is modulo 3467819 Mon Jun 29 21:54:35 2009 sqrtTime: 253 Mon Jun 29 21:54:35 2009 prp49 factor: 1680685663562710108755241113940108250558188502759 Mon Jun 29 21:54:35 2009 prp61 factor: 4455743436763288668170528477507378349835514471314046357878921 Mon Jun 29 21:54:35 2009 elapsed time 00:29:19 total time ~ 11 hours

Jun 29, 2009 (4th)

By Sinkiti Sibata / Msieve, GGNFS / Jun 29, 2009
(58·10¹³³-13)/9 = 6(4)₁₃₂3_<134> = 3 · 7 · 1489 · 68003251 · 16251891980953498210510658603_<29> · C94
C94 = P46 · P48
P46 = 3332366710852869308417885511991106085178367213_<46>
P48 = 559609530053519556611176759097123548994837054123_<48>

Sun Jun 28 20:57:37 2009 Msieve v. 1.41 Sun Jun 28 20:57:37 2009 random seeds: a9bdadcc 57a2d679 Sun Jun 28 20:57:37 2009 factoring 1864824169026366881665848988133902606847100055810034881259952154184029473528657675188049669199 (94 digits) Sun Jun 28 20:57:38 2009 searching for 15-digit factors Sun Jun 28 20:57:39 2009 commencing quadratic sieve (94-digit input) Sun Jun 28 20:57:39 2009 using multiplier of 19 Sun Jun 28 20:57:39 2009 using 32kb Intel Core sieve core Sun Jun 28 20:57:39 2009 sieve interval: 36 blocks of size 32768 Sun Jun 28 20:57:39 2009 processing polynomials in batches of 6 Sun Jun 28 20:57:39 2009 using a sieve bound of 1986839 (74118 primes) Sun Jun 28 20:57:39 2009 using large prime bound of 256302231 (27 bits) Sun Jun 28 20:57:39 2009 using double large prime bound of 1366955142352932 (42-51 bits) Sun Jun 28 20:57:39 2009 using trial factoring cutoff of 51 bits Sun Jun 28 20:57:39 2009 polynomial 'A' values have 12 factors Sun Jun 28 23:52:08 2009 74244 relations (18184 full + 56060 combined from 1032634 partial), need 74214 Sun Jun 28 23:52:10 2009 begin with 1050818 relations Sun Jun 28 23:52:11 2009 reduce to 192288 relations in 11 passes Sun Jun 28 23:52:11 2009 attempting to read 192288 relations Sun Jun 28 23:52:13 2009 recovered 192288 relations Sun Jun 28 23:52:13 2009 recovered 175552 polynomials Sun Jun 28 23:52:14 2009 attempting to build 74244 cycles Sun Jun 28 23:52:14 2009 found 74244 cycles in 6 passes Sun Jun 28 23:52:14 2009 distribution of cycle lengths: Sun Jun 28 23:52:14 2009 length 1 : 18184 Sun Jun 28 23:52:14 2009 length 2 : 13292 Sun Jun 28 23:52:14 2009 length 3 : 12515 Sun Jun 28 23:52:14 2009 length 4 : 9850 Sun Jun 28 23:52:14 2009 length 5 : 7471 Sun Jun 28 23:52:14 2009 length 6 : 5174 Sun Jun 28 23:52:14 2009 length 7 : 3312 Sun Jun 28 23:52:14 2009 length 9+: 4446 Sun Jun 28 23:52:14 2009 largest cycle: 19 relations Sun Jun 28 23:52:14 2009 matrix is 74118 x 74244 (19.4 MB) with weight 4794826 (64.58/col) Sun Jun 28 23:52:14 2009 sparse part has weight 4794826 (64.58/col) Sun Jun 28 23:52:15 2009 filtering completed in 3 passes Sun Jun 28 23:52:15 2009 matrix is 70508 x 70572 (18.6 MB) with weight 4594906 (65.11/col) Sun Jun 28 23:52:15 2009 sparse part has weight 4594906 (65.11/col) Sun Jun 28 23:52:15 2009 saving the first 48 matrix rows for later Sun Jun 28 23:52:15 2009 matrix is 70460 x 70572 (12.0 MB) with weight 3588469 (50.85/col) Sun Jun 28 23:52:15 2009 sparse part has weight 2713229 (38.45/col) Sun Jun 28 23:52:15 2009 matrix includes 64 packed rows Sun Jun 28 23:52:15 2009 using block size 28228 for processor cache size 1024 kB Sun Jun 28 23:52:16 2009 commencing Lanczos iteration Sun Jun 28 23:52:16 2009 memory use: 11.4 MB Sun Jun 28 23:52:49 2009 lanczos halted after 1116 iterations (dim = 70458) Sun Jun 28 23:52:49 2009 recovered 16 nontrivial dependencies Sun Jun 28 23:52:50 2009 prp46 factor: 3332366710852869308417885511991106085178367213 Sun Jun 28 23:52:50 2009 prp48 factor: 559609530053519556611176759097123548994837054123 Sun Jun 28 23:52:50 2009 elapsed time 02:55:13

(58·10¹¹⁷-13)/9 = 6(4)₁₁₆3_<118> = C118
C118 = P45 · P73
P45 = 675790396195456442895915104432949740666991523_<45>
P73 = 9536158668020699116745173193884730385667768369512984877372857570707904041_<73>

Number: 64443_117 N=6444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443 ( 118 digits) SNFS difficulty: 119 digits. Divisors found: r1=675790396195456442895915104432949740666991523 (pp45) r2=9536158668020699116745173193884730385667768369512984877372857570707904041 (pp73) Version: Msieve-1.40 Total time: 1.62 hours. Scaled time: 3.37 units (timescale=2.085). Factorization parameters were as follows: name: 64443_117 n: 6444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443 m: 200000000000000000000000 deg: 5 c5: 725 c0: -52 skew: 0.59 type: snfs lss: 1 rlim: 680000 alim: 680000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 680000/680000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [340000, 590001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 80828 x 81054 Total sieving time: 1.56 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,119.000,5,0,0,0,0,0,0,0,0,680000,680000,25,25,45,45,2.2,2.2,50000 total time: 1.62 hours. --------- CPU info (if available) ----------

(58·10¹⁴⁴-13)/9 = 6(4)₁₄₃3_<145> = 970493 · C139
C139 = P37 · P103
P37 = 2093179992515501466190084387420835861_<37>
P103 = 3172389486725938777025473977276200607103207453371670538718534881764544597885610351738781046647527068891_<103>

Number: 64443_144 N=6640382202081256067219902095578684693701494440912448049027086691449031002227161292708390935786702680436071609423709851018445722374550300151 ( 139 digits) SNFS difficulty: 146 digits. Divisors found: r1=2093179992515501466190084387420835861 (pp37) r2=3172389486725938777025473977276200607103207453371670538718534881764544597885610351738781046647527068891 (pp103) Version: Msieve-1.40 Total time: 10.37 hours. Scaled time: 26.59 units (timescale=2.564). Factorization parameters were as follows: name: 64443_144 n: 6640382202081256067219902095578684693701494440912448049027086691449031002227161292708390935786702680436071609423709851018445722374550300151 m: 100000000000000000000000000000 deg: 5 c5: 29 c0: -65 skew: 1.18 type: snfs lss: 1 rlim: 1930000 alim: 1930000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1930000/1930000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [965000, 2265001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 342546 x 342794 Total sieving time: 9.86 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.26 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,146.000,5,0,0,0,0,0,0,0,0,1930000,1930000,26,26,49,49,2.3,2.3,100000 total time: 10.37 hours. --------- CPU info (if available) ----------

(58·10¹³⁶-13)/9 = 6(4)₁₃₅3_<137> = 3² · 58871741 · C129
C129 = P48 · P81
P48 = 235727953664055447319411949797137297749012365291_<48>
P81 = 515970662989061743281594639447232372573905136516236978628437287176925324434133117_<81>

Number: 64443_136 N=121628708537097515549276754481585550988894550055186814114440641854985974122295683886102397195294323420136221674852351099324442047 ( 129 digits) SNFS difficulty: 138 digits. Divisors found: r1=235727953664055447319411949797137297749012365291 (pp48) r2=515970662989061743281594639447232372573905136516236978628437287176925324434133117 (pp81) Version: Msieve-1.40 Total time: 5.51 hours. Scaled time: 14.12 units (timescale=2.564). Factorization parameters were as follows: name: 64443_136 n: 121628708537097515549276754481585550988894550055186814114440641854985974122295683886102397195294323420136221674852351099324442047 m: 2000000000000000000000000000 deg: 5 c5: 145 c0: -104 skew: 0.94 type: snfs lss: 1 rlim: 1430000 alim: 1430000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1430000/1430000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [715000, 1465001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 223069 x 223300 Total sieving time: 5.25 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.11 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,138.000,5,0,0,0,0,0,0,0,0,1430000,1430000,26,26,48,48,2.3,2.3,75000 total time: 5.51 hours. --------- CPU info (if available) ----------

(58·10¹³⁹-13)/9 = 6(4)₁₃₈3_<140> = 3 · 7 · 19 · 1231 · 1060570349_<10> · 1193524663_<10> · 83228320831_<11> · C106
C106 = P53 · P53
P53 = 32502218758975974264690934359203256203943891833157149_<53>
P53 = 38317707245925041958237144145989843140569750883793499_<53>

Number: 64443_139 N=1245410503249454513950936539400601771642350901839495372749797874484849665147960918528578908546230931574351 ( 106 digits) SNFS difficulty: 141 digits. Divisors found: r1=32502218758975974264690934359203256203943891833157149 (pp53) r2=38317707245925041958237144145989843140569750883793499 (pp53) Version: Msieve-1.40 Total time: 7.24 hours. Scaled time: 15.19 units (timescale=2.099). Factorization parameters were as follows: name: 64443_139 n: 1245410503249454513950936539400601771642350901839495372749797874484849665147960918528578908546230931574351 m: 10000000000000000000000000000 deg: 5 c5: 29 c0: -65 skew: 1.18 type: snfs lss: 1 rlim: 1600000 alim: 1600000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [800000, 1700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 237619 x 237853 Total sieving time: 6.89 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.19 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,141.000,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000 total time: 7.24 hours. --------- CPU info (if available) ----------

(58·10¹⁶²-13)/9 = 6(4)₁₆₁3_<163> = 498670553 · 868251372853531_<15> · 2403433417659585403_<19> · 1519135220149328937011_<22> · C100
C100 = P40 · P61
P40 = 3978007396055070106886225840980948818901_<40>
P61 = 1024783602569126724040280540933691019026235418901075033484997_<61>

Number: 64443_162 N=4076596750375945652022220384779745370572439383193580743868681381671398185956334119178766833053528297 ( 100 digits) Divisors found: r1=3978007396055070106886225840980948818901 (pp40) r2=1024783602569126724040280540933691019026235418901075033484997 (pp61) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 7.99 hours. Scaled time: 3.78 units (timescale=0.473). Factorization parameters were as follows: name: 64443_162 n: 4076596750375945652022220384779745370572439383193580743868681381671398185956334119178766833053528297 skew: 2809.15 # norm 1.60e+14 c5: 875880 c4: 4607514726 c3: -15446799894661 c2: 2133887816628030 c1: 514909499414304834 c0: -27061090266943223903321 # alpha -6.39 Y1: 32280451331 Y0: -5414619025710030114 # Murphy_E 3.38e-09 # M 3423235280954909331517329139689087262865239008060333048147151500659748101870819046725204686439576175 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1400001) Primes: RFBsize:135072, AFBsize:134813, largePrimes:3983622 encountered Relations: rels:4123288, finalFF:497538 Max relations in full relation-set: 28 Initial matrix: 269969 x 497538 with sparse part having weight 35933016. Pruned matrix : 142475 x 143888 with weight 12612276. Total sieving time: 7.22 hours. Total relation processing time: 0.29 hours. Matrix solve time: 0.37 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 7.99 hours. --------- CPU info (if available) ----------

Jun 29, 2009 (3rd)

By Dmitry Domanov / GGNFS/msieve 1.41, ECMNET / Jun 29, 2009
(58·10¹⁶⁷-13)/9 = 6(4)₁₆₆3_<168> = 907 · 9309593 · 616323772949751279227_<21> · 253974892032742945956761_<24> · 284996068419181591076316632267_<30> · C85
C85 = P39 · P46
P39 = 173896095349135933269424744970466539597_<39>
P46 = 9838278194508804532101741831512619052600114781_<46>

Number: 0011 N=1710838162983627990454857587732199143565178607498223962752146552456866980922081483257 ( 85 digits) Divisors found: r1=173896095349135933269424744970466539597 (pp39) r2=9838278194508804532101741831512619052600114781 (pp46) Version: Msieve v. 1.41 Total time: 1.39 hours. Scaled time: 2.76 units (timescale=1.976). Factorization parameters were as follows: name: 0011 n: 1710838162983627990454857587732199143565178607498223962752146552456866980922081483257 m: 25598906778006399254 deg: 4 c4: 3984036 c3: -6341237708 c2: -5106462467755171 c1: 19869950659843206 c0: 4617545228137607483265 skew: 1379.250 type: gnfs # adj. I(F,S) = 47.861 # E(F1,F2) = 1.101643e-003 # GGNFS version 0.77.1-VC8(Sat 01/17/2009) polyselect. # Options were: # lcd=1, enumLCD=12, maxS1=56.00000000, seed=1246215921. # maxskew=1500.0 # These parameters should be manually set: rlim: 550000 alim: 550000 lpbr: 24 lpba: 24 mfbr: 40 mfba: 40 rlambda: 1.9 alambda: 1.9 qintsize: 10000 type: gnfs Factor base limits: 550000/550000 Large primes per side: 3 Large prime bits: 24/24 Max factor residue bits: 40/40 Sieved algebraic special-q in [275000, 605001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 46853 x 47079 Polynomial selection time: 0.14 hours. Total sieving time: 1.23 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,84,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,550000,550000,24,24,40,40,1.9,1.9,10000 total time: 1.39 hours. --------- CPU info (if available) ----------

6·10²¹³+1 = 6(0)₂₁₂1_<214> = 887 · C211
C211 = P33 · C178
P33 = 710379914267074902446340727571899_<33>
C178 = [9522192505057989196554921686963471449090843139265281936834912784663455668678513277670521436604345942154664018593294330166634222414359055518446450597428054285995444333986164085477_<178>]

C211=P133*C178 C211=710379914267074902446340727571899<33>*9522192505057989196554921686963471449090843139265281936834912784663455668678513277670521436604345942154664018593294330166634222414359055518446450597428054285995444333986164085477<178>

Jun 29, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jun 29, 2009
(58·10¹³⁵-13)/9 = 6(4)₁₃₄3_<136> = 43 · 1605169 · C128
C128 = P41 · P88
P41 = 16684801071616165742858411059235412368987_<41>
P88 = 5595968120588461964689090820225357668914533447115863619998466725214360596278094821062067_<88>

Number: 64443_135 N=93367614895124271192721682764265688990546260157529228132197460921479794983326821827576953455389178168321310635080190055832916129 ( 128 digits) SNFS difficulty: 136 digits. Divisors found: r1=16684801071616165742858411059235412368987 r2=5595968120588461964689090820225357668914533447115863619998466725214360596278094821062067 Version: Total time: 2.32 hours. Scaled time: 5.53 units (timescale=2.389). Factorization parameters were as follows: n: 93367614895124271192721682764265688990546260157529228132197460921479794983326821827576953455389178168321310635080190055832916129 m: 1000000000000000000000000000 deg: 5 c5: 58 c0: -13 skew: 0.74 type: snfs lss: 1 rlim: 1400000 alim: 1400000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [700000, 1300001) Primes: rational ideals reading, algebraic ideals reading, Relations: 3643747 Max relations in full relation-set: Initial matrix: Pruned matrix : 195461 x 195709 Total sieving time: 2.04 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.07 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,26,26,48,48,2.3,2.3,50000 total time: 2.32 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673809) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672376) Calibrating delay using timer specific routine.. 5430.28 BogoMIPS (lpj=2715140)

Jun 29, 2009

By Robert Backstrom / GGNFS / Jun 29, 2009
(58·10¹⁴⁵-13)/9 = 6(4)₁₄₄3_<146> = 3² · 7 · 701 · 745210479281_<12> · 8730110436289447812154290169607_<31> · C99
C99 = P44 · P55
P44 = 81209611999697626708180466005454678658771007_<44>
P55 = 2761981658215742112136342325393296828876923189500830369_<55>

Number: n N=224299458813981879732712982352694968415152384821436552669343237460916892743989333004630031522311583 ( 99 digits) Divisors found: r1=81209611999697626708180466005454678658771007 (pp44) r2=2761981658215742112136342325393296828876923189500830369 (pp55) Version: GGNFS-0.77.1-20051202-athlon Total time: 4.02 hours. Scaled time: 7.33 units (timescale=1.823). Factorization parameters were as follows: n: 224299458813981879732712982352694968415152384821436552669343237460916892743989333004630031522311583 Y0: -14418171140978802868 Y1: 6052927273 c0: 10863423250545833835634935 c1: -878321344639862200188 c2: -38824411212279790 c3: 973149801761 c4: -49670352 c5: 360 skew: 22477.80 type: gnfs name: KA_6_4_144_3 rlim: 1800000 alim: 1800000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 10000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [900000, 1300001) Primes: RFBsize:135072, AFBsize:134465, largePrimes:10029840 encountered Relations: rels:8639337, finalFF:328863 Max relations in full relation-set: 48 Initial matrix: 269621 x 328863 with sparse part having weight 31872885. Pruned matrix : 227953 x 229365 with weight 16672392. Total sieving time: 3.22 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.37 hours. Total square root time: 0.17 hours, sqrts: 2. Prototype def-par.txt line would be: gnfs,98,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,28,28,56,56,2.5,2.5,100000 total time: 4.02 hours. --------- CPU info (if available) ----------

(58·10¹³⁰-13)/9 = 6(4)₁₂₉3_<131> = 3 · 23 · 233 · 191051625186109_<15> · C113
C113 = P37 · P76
P37 = 9787483305184856962017021595435426277_<37>
P76 = 2143673808252724180424039293341153908233557786918513112730116683447368346263_<76>

Number: n N=20981171610035582164419150272767266755882901911373431794670668008723701373071536696140282554060983673945944952851 ( 113 digits) SNFS difficulty: 131 digits. Divisors found: r1=9787483305184856962017021595435426277 (pp37) r2=2143673808252724180424039293341153908233557786918513112730116683447368346263 (pp76) Version: GGNFS-0.77.1-20051202-athlon Total time: 2.47 hours. Scaled time: 4.50 units (timescale=1.823). Factorization parameters were as follows: name: KA_6_4_129_3 n: 20981171610035582164419150272767266755882901911373431794670668008723701373071536696140282554060983673945944952851 m: 100000000000000000000000000 deg: 5 c5: 58 c0: -13 skew: 0.74 type: snfs lss: 1 rlim: 1200000 alim: 1200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.3 alambda: 2.3 qintsize: 20000 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [600000, 980001) Primes: RFBsize:92938, AFBsize:92609, largePrimes:4750730 encountered Relations: rels:4127468, finalFF:213711 Max relations in full relation-set: 48 Initial matrix: 185613 x 213711 with sparse part having weight 18258528. Pruned matrix : 174221 x 175213 with weight 11392735. Total sieving time: 2.07 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.17 hours. Total square root time: 0.16 hours, sqrts: 6. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,56,56,2.3,2.3,50000 total time: 2.47 hours. --------- CPU info (if available) ----------

Jun 28, 2009 (7th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jun 28, 2009
(58·10¹²⁸-13)/9 = 6(4)₁₂₇3_<129> = 61 · 154046456857541_<15> · C113
C113 = P56 · P58
P56 = 14261505825626082595820373781089104840019592878166331551_<56>
P58 = 4808820337208844827360136163259599581637949123534929470293_<58>

Number: 64443_128 N=68581019253493123466471220014200095653837774179925416620219999548337191520566357504095160518146710794723443114443 ( 113 digits) SNFS difficulty: 131 digits. Divisors found: r1=14261505825626082595820373781089104840019592878166331551 r2=4808820337208844827360136163259599581637949123534929470293 Version: Total time: 1.58 hours. Scaled time: 3.78 units (timescale=2.390). Factorization parameters were as follows: n: 68581019253493123466471220014200095653837774179925416620219999548337191520566357504095160518146710794723443114443 m: 100000000000000000000000000 deg: 5 c5: 29 c0: -650 skew: 1.86 type: snfs lss: 1 rlim: 1000000 alim: 1000000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [500000, 950001) Primes: rational ideals reading, algebraic ideals reading, Relations: 2835190 Max relations in full relation-set: Initial matrix: Pruned matrix : 156420 x 156668 Total sieving time: 1.38 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.05 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000 total time: 1.58 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673809) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672376) Calibrating delay using timer specific routine.. 5430.28 BogoMIPS (lpj=2715140)

Jun 28, 2009 (6th)

By Sinkiti Sibata / Msieve / Jun 28, 2009
(58·10¹¹⁴-13)/9 = 6(4)₁₁₃3_<115> = 43 · 47 · 89 · 563 · 16090520573459_<14> · C94
C94 = P38 · P57
P38 = 11253044703352173797806298790102967343_<38>
P57 = 351463824057779343280271448782487763478579276272297536337_<57>

Sun Jun 28 16:54:01 2009 Msieve v. 1.41 Sun Jun 28 16:54:01 2009 random seeds: ffdefb00 e3939988 Sun Jun 28 16:54:01 2009 factoring 3955038123733294154552830225937839027981089639074561881089832913509377721150125554052066842591 (94 digits) Sun Jun 28 16:54:01 2009 searching for 15-digit factors Sun Jun 28 16:54:03 2009 commencing quadratic sieve (94-digit input) Sun Jun 28 16:54:03 2009 using multiplier of 5 Sun Jun 28 16:54:03 2009 using 32kb Intel Core sieve core Sun Jun 28 16:54:03 2009 sieve interval: 36 blocks of size 32768 Sun Jun 28 16:54:03 2009 processing polynomials in batches of 6 Sun Jun 28 16:54:03 2009 using a sieve bound of 2025307 (75235 primes) Sun Jun 28 16:54:03 2009 using large prime bound of 271391138 (28 bits) Sun Jun 28 16:54:03 2009 using double large prime bound of 1515207662043732 (42-51 bits) Sun Jun 28 16:54:03 2009 using trial factoring cutoff of 51 bits Sun Jun 28 16:54:03 2009 polynomial 'A' values have 12 factors Sun Jun 28 20:42:43 2009 75336 relations (18180 full + 57156 combined from 1080234 partial), need 75331 Sun Jun 28 20:42:44 2009 begin with 1098414 relations Sun Jun 28 20:42:45 2009 reduce to 197110 relations in 9 passes Sun Jun 28 20:42:45 2009 attempting to read 197110 relations Sun Jun 28 20:42:48 2009 recovered 197110 relations Sun Jun 28 20:42:48 2009 recovered 183003 polynomials Sun Jun 28 20:42:48 2009 attempting to build 75336 cycles Sun Jun 28 20:42:49 2009 found 75336 cycles in 6 passes Sun Jun 28 20:42:49 2009 distribution of cycle lengths: Sun Jun 28 20:42:49 2009 length 1 : 18180 Sun Jun 28 20:42:49 2009 length 2 : 13127 Sun Jun 28 20:42:49 2009 length 3 : 12543 Sun Jun 28 20:42:49 2009 length 4 : 10283 Sun Jun 28 20:42:49 2009 length 5 : 7819 Sun Jun 28 20:42:49 2009 length 6 : 5228 Sun Jun 28 20:42:49 2009 length 7 : 3525 Sun Jun 28 20:42:49 2009 length 9+: 4631 Sun Jun 28 20:42:49 2009 largest cycle: 23 relations Sun Jun 28 20:42:49 2009 matrix is 75235 x 75336 (20.1 MB) with weight 4962914 (65.88/col) Sun Jun 28 20:42:49 2009 sparse part has weight 4962914 (65.88/col) Sun Jun 28 20:42:50 2009 filtering completed in 3 passes Sun Jun 28 20:42:50 2009 matrix is 72005 x 72069 (19.3 MB) with weight 4777877 (66.30/col) Sun Jun 28 20:42:50 2009 sparse part has weight 4777877 (66.30/col) Sun Jun 28 20:42:50 2009 saving the first 48 matrix rows for later Sun Jun 28 20:42:50 2009 matrix is 71957 x 72069 (12.2 MB) with weight 3788035 (52.56/col) Sun Jun 28 20:42:50 2009 sparse part has weight 2761797 (38.32/col) Sun Jun 28 20:42:50 2009 matrix includes 64 packed rows Sun Jun 28 20:42:50 2009 using block size 28827 for processor cache size 1024 kB Sun Jun 28 20:42:51 2009 commencing Lanczos iteration Sun Jun 28 20:42:51 2009 memory use: 11.7 MB Sun Jun 28 20:43:28 2009 lanczos halted after 1139 iterations (dim = 71951) Sun Jun 28 20:43:28 2009 recovered 13 nontrivial dependencies Sun Jun 28 20:43:29 2009 prp38 factor: 11253044703352173797806298790102967343 Sun Jun 28 20:43:29 2009 prp57 factor: 351463824057779343280271448782487763478579276272297536337 Sun Jun 28 20:43:29 2009 elapsed time 03:49:28

(55·10¹⁶⁸+53)/9 = 6(1)₁₆₇7_<169> = 3² · 23 · 8597 · 60736241 · 48550887541806695475431280614507_<32> · C124
C124 = P60 · P64
P60 = 409276563277414763663135352084046268821974277482384997407629_<60>
P64 = 2845384416537614405451040024545314866333284940268230907212204201_<64>

Number: 61117_168 N=1164549155203626829526840703770057776331666897044154747749189812937458891968038623377040295732783853980802775338775983249429 ( 124 digits) SNFS difficulty: 170 digits. Divisors found: r1=409276563277414763663135352084046268821974277482384997407629 (pp60) r2=2845384416537614405451040024545314866333284940268230907212204201 (pp64) Version: Msieve-1.40 Total time: 80.05 hours. Scaled time: 204.46 units (timescale=2.554). Factorization parameters were as follows: name: 61117_168 n: 1164549155203626829526840703770057776331666897044154747749189812937458891968038623377040295732783853980802775338775983249429 m: 5000000000000000000000000000000000 deg: 5 c5: 88 c0: 265 skew: 1.25 type: snfs lss: 1 rlim: 4900000 alim: 4900000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4900000/4900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2450000, 5750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1020457 x 1020705 Total sieving time: 77.37 hours. Total relation processing time: 0.16 hours. Matrix solve time: 2.40 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,170.000,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000 total time: 80.05 hours. --------- CPU info (if available) ----------

Jun 28, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / Jun 28, 2009
(19·10¹⁸⁵+11)/3 = 6(3)₁₈₄7_<186> = 23 · C185
C185 = P78 · P108
P78 = 273631349641806731525848462476809281476079559226376744837229076093340563539867_<78>
P108 = 100632591697200952849656764311882330854240620551378358640057703218893173694556069027234501070088318306649757_<108>

Number: n N=27536231884057971014492753623188405797101449275362318840579710144927536231884057971014492753623188405797101449275362318840579710144927536231884057971014492753623188405797101449275362319 ( 185 digits) SNFS difficulty: 186 digits. Divisors found: Sun Jun 28 17:31:53 2009 prp78 factor: 273631349641806731525848462476809281476079559226376744837229076093340563539867 Sun Jun 28 17:31:53 2009 prp108 factor: 100632591697200952849656764311882330854240620551378358640057703218893173694556069027234501070088318306649757 Sun Jun 28 17:31:53 2009 elapsed time 03:29:19 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 190.82 hours. Scaled time: 503.58 units (timescale=2.639). Factorization parameters were as follows: name: KA_6_3_184_7 n: 27536231884057971014492753623188405797101449275362318840579710144927536231884057971014492753623188405797101449275362318840579710144927536231884057971014492753623188405797101449275362319 m: 10000000000000000000000000000000000000 deg: 5 c5: 19 c0: 11 skew: 0.90 type: snfs lss: 1 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [4500000, 8500027) Primes: RFBsize:602489, AFBsize:603121, largePrimes:21076591 encountered Relations: rels:21063612, finalFF:1223628 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2072055 hash collisions in 22483145 relations Msieve: matrix is 1553384 x 1553632 (420.8 MB) Total sieving time: 190.28 hours. Total relation processing time: 0.54 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,56,56,2.5,2.5,100000 total time: 190.82 hours. --------- CPU info (if available) ----------

(58·10¹⁰¹-13)/9 = 6(4)₁₀₀3_<102> = 1069 · C99
C99 = P42 · P58
P42 = 378980653168484429716330805966707908641167_<42>
P58 = 1590709002596225501218237944810237612242622890947590032041_<58>

Number: n N=602847936804905934933998544849807712296019124831098638395177216505560752520528011641201538301631847 ( 99 digits) SNFS difficulty: 103 digits. Divisors found: r1=378980653168484429716330805966707908641167 (pp42) r2=1590709002596225501218237944810237612242622890947590032041 (pp58) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.35 hours. Scaled time: 0.64 units (timescale=1.829). Factorization parameters were as follows: name: KA_6_4_100_3 n: 602847936804905934933998544849807712296019124831098638395177216505560752520528011641201538301631847 m: 20000000000000000000000000 deg: 4 c4: 145 c0: -52 skew: 0.77 type: snfs lss: 1 rlim: 400000 alim: 400000 lpbr: 25 lpba: 25 mfbr: 43 mfba: 43 rlambda: 2.2 alambda: 2.2 qintsize: 10000 Factor base limits: 400000/400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved rational special-q in [200000, 260001) Primes: RFBsize:33860, AFBsize:33714, largePrimes:1034002 encountered Relations: rels:968213, finalFF:100967 Max relations in full relation-set: 48 Initial matrix: 67641 x 100967 with sparse part having weight 4053842. Pruned matrix : 52459 x 52861 with weight 1539494. Total sieving time: 0.31 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Total square root time: 0.02 hours, sqrts: 6. Prototype def-par.txt line would be: snfs,103,4,0,0,0,0,0,0,0,0,400000,400000,25,25,43,43,2.2,2.2,10000 total time: 0.35 hours. --------- CPU info (if available) ----------

Jun 28, 2009 (4th)

By Dmitry Domanov / ECMNET, GGNFS/msieve 1.41 / Jun 28, 2009
(2·10¹⁷²-17)/3 = (6)₁₇₁1_<172> = 17310897119749_<14> · C159
C159 = P34 · C126
P34 = 1198926844780485953297393643793523_<34>
C126 = [321215490763403568953802801349834582946542687658223456641360521873909777640871296136079965295434494691834967162688081300105243_<126>]

C159=P34*C126 C159=1198926844780485953297393643793523<34>*321215490763403568953802801349834582946542687658223456641360521873909777640871296136079965295434494691834967162688081300105243<126>

(56·10²⁰²+43)/9 = 6(2)₂₀₁7_<203> = 11 · C202
C202 = P60 · P143
P60 = 430270091015054667643764166187119702272619904315042374067203_<60>
P143 = 13146546261724103154134734048449804194958643080538462991695579386437701046476401588101268264567193940577012483460643381470898174364294389389619_<143>

Total sieving time: ~28 CPU-days Total postprocessing time: 32:20 hours prp60 factor: 430270091015054667643764166187119702272619904315042374067203 prp143 factor: 13146546261724103154134734048449804194958643080538462991695579386437701046476401588101268264567193940577012483460643381470898174364294389389619

Jun 28, 2009 (3rd)

By Wataru Sakai / Msieve / Jun 28, 2009
(47·10¹⁹¹+7)/9 = 5(2)₁₉₀3_<192> = 13 · 19 · C190
C190 = P90 · P101
P90 = 157199391414811481308413123039831010800549348549055356443631902777496014250523799578529659_<90>
P101 = 13449543220035923396736531400707244067808735111856700550761352132101359599419084915660120869479028651_<101>

Number: 52223_191 N=2114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260009 ( 190 digits) SNFS difficulty: 193 digits. Divisors found: r1=157199391414811481308413123039831010800549348549055356443631902777496014250523799578529659 r2=13449543220035923396736531400707244067808735111856700550761352132101359599419084915660120869479028651 Version: Total time: 619.85 hours. Scaled time: 1242.18 units (timescale=2.004). Factorization parameters were as follows: n: 2114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260009 m: 200000000000000000000000000000000000000 deg: 5 c5: 235 c0: 112 skew: 0.86 type: snfs lss: 1 rlim: 11900000 alim: 11900000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 11900000/11900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [5950000, 12350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2061084 x 2061332 Total sieving time: 619.85 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,193,5,0,0,0,0,0,0,0,0,11900000,11900000,28,28,55,55,2.5,2.5,100000 total time: 619.85 hours. --------- CPU info (if available) ----------

(53·10¹⁹¹-17)/9 = 5(8)₁₉₀7_<192> = 13 · 3077325253235247465155976615079042868201_<40> · C152
C152 = P38 · P42 · P73
P38 = 30955878554994429517866299495278628197_<38>
P42 = 260830264234883533140803293326399923032711_<42>
P73 = 1823120991418613541878724349970952485904020949548098505262099347038089097_<73>

Number: 58887_191 N=45299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299 ( 191 digits) SNFS difficulty: 193 digits. Divisors found: r1=30955878554994429517866299495278628197 r2=3077325253235247465155976615079042868201 r3=260830264234883533140803293326399923032711 r4=1823120991418613541878724349970952485904020949548098505262099347038089097 Version: Total time: 627.02 hours. Scaled time: 1254.04 units (timescale=2.000). Factorization parameters were as follows: n: 45299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299 m: 200000000000000000000000000000000000000 deg: 5 c5: 265 c0: -272 skew: 1.01 type: snfs lss: 1 rlim: 11900000 alim: 11900000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5Factor base limits: 11900000/11900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [5950000, 13050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2074170 x 2074418 Total sieving time: 627.02 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,193,5,0,0,0,0,0,0,0,0,11900000,11900000,28,28,55,55,2.5,2.5,100000 total time: 627.02 hours. --------- CPU info (if available) ----------

Jun 28, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.3, Msieve / Jun 28, 2009
(58·10¹¹⁹-13)/9 = 6(4)₁₁₈3_<120> = 877 · 2153 · 16433 · 124229663974013057_<18> · C93
C93 = P32 · P61
P32 = 31626202427768372681682563838197_<32>
P61 = 5286310259872520471610188001300077202533865033368128652932579_<61>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1236900711 Step 1 took 5784ms Step 2 took 4948ms ********** Factor found in step 2: 31626202427768372681682563838197 Found probable prime factor of 32 digits: 31626202427768372681682563838197 Probable prime cofactor 5286310259872520471610188001300077202533865033368128652932579 has 61 digits

(58·10¹⁶⁷-13)/9 = 6(4)₁₆₆3_<168> = 907 · 9309593 · 616323772949751279227_<21> · 253974892032742945956761_<24> · C114
C114 = P30 · C85
P30 = 284996068419181591076316632267_<30>
C85 = [1710838162983627990454857587732199143565178607498223962752146552456866980922081483257_<85>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=578427496 Step 1 took 2408ms ********** Factor found in step 1: 284996068419181591076316632267 Found probable prime factor of 30 digits: 284996068419181591076316632267 Composite cofactor 1710838162983627990454857587732199143565178607498223962752146552456866980922081483257 has 85 digits

(58·10¹⁷⁴-13)/9 = 6(4)₁₇₃3_<175> = 23 · 2003 · 109917710069_<12> · 2561799797279_<13> · C147
C147 = P29 · P119
P29 = 28060415355482968596031509529_<29>
P119 = 17703932477233971993285289597402034285856075678888714104981748648524578359619999237243122567152169494477870888624600693_<119>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=380138816 Step 1 took 3284ms Step 2 took 3172ms ********** Factor found in step 2: 28060415355482968596031509529 Found probable prime factor of 29 digits: 28060415355482968596031509529 Probable prime cofactor has 119 digits

(58·10¹⁷³-13)/9 = 6(4)₁₇₂3_<174> = 3636439 · C168
C168 = P28 · P34 · C106
P28 = 5201072681589129941159853013_<28>
P34 = 4151220228381396271312783062791689_<34>
C106 = [8208059208418425479971505016759308076623141385702515597077892607382839099391926518651326516913860567839841_<106>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=619016146 Step 1 took 3924ms Step 2 took 3676ms ********** Factor found in step 2: 4151220228381396271312783062791689 Found probable prime factor of 34 digits: 4151220228381396271312783062791689 Composite cofactor Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=4219703845 Step 1 took 3853ms Step 2 took 3548ms ********** Factor found in step 2: 5201072681589129941159853013 Found probable prime factor of 28 digits: 5201072681589129941159853013

(58·10¹⁵⁵-13)/9 = 6(4)₁₅₄3_<156> = 227 · 42416069 · C146
C146 = P28 · C119
P28 = 2974192430852304989290612183_<28>
C119 = [22504022118921734259662990204779762049959337208129694385777166920187136905382202309246021844159118798649720943027231667_<119>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=697347838 Step 1 took 9721ms Step 2 took 9808ms ********** Factor found in step 2: 2974192430852304989290612183 Found probable prime factor of 28 digits: 2974192430852304989290612183 Composite cofactor has 119 digits

(58·10¹¹²-13)/9 = 6(4)₁₁₁3_<113> = 3 · 31 · C111
C111 = P45 · P67
P45 = 652436120450225810366755666771025792484664531_<45>
P67 = 1062097872590924024217052162548785136776202179702201158841319923821_<67>

SNFS difficulty: 114 digits. Divisors found: r1=652436120450225810366755666771025792484664531 (pp45) r2=1062097872590924024217052162548785136776202179702201158841319923821 (pp67) Version: Msieve v. 1.42 Total time: 0.71 hours. Scaled time: 1.91 units (timescale=2.699). Factorization parameters were as follows: n: 692951015531660692951015531660692951015531660692951015531660692951015531660692951015531660692951015531660692951 m: 20000000000000000000000 deg: 5 c5: 725 c0: -52 skew: 0.59 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 : 57409 x 57635 Total sieving time: 0.67 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,114.000,5,0,0,0,0,0,0,0,0,560000,560000,25,25,45,45,2.2,2.2,50000 total time: 0.71 hours.

(58·10¹¹⁶-13)/9 = 6(4)₁₁₅3_<117> = C117
C117 = P56 · P62
P56 = 36666873968480742387982057101824145634673636068789484339_<56>
P62 = 17575658208507661253565689505378100610551179018660768260310137_<62>

SNFS difficulty: 118 digits. Divisors found: r1=36666873968480742387982057101824145634673636068789484339 (pp56) r2=17575658208507661253565689505378100610551179018660768260310137 (pp62) Version: Msieve v. 1.42 Total time: 0.72 hours. Scaled time: 1.97 units (timescale=2.739). Factorization parameters were as follows: n: 644444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443 m: 200000000000000000000000 deg: 5 c5: 145 c0: -104 skew: 0.94 type: snfs lss: 1 rlim: 670000 alim: 670000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 670000/670000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [335000, 585001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 70823 x 71049 Total sieving time: 0.67 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.02 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,118.000,5,0,0,0,0,0,0,0,0,670000,670000,25,25,45,45,2.2,2.2,50000 total time: 0.72 hours.

(58·10¹²²-13)/9 = 6(4)₁₂₁3_<123> = 63694693 · C116
C116 = P32 · P84
P32 = 20739698165441745472143977056603_<32>
P84 = 487842692297273949867459723857663010869242116718559328343030013911282591596902649517_<84>

SNFS difficulty: 124 digits. Divisors found: r1=20739698165441745472143977056603 (pp32) r2=487842692297273949867459723857663010869242116718559328343030013911282591596902649517 (pp84) Version: Msieve v. 1.42 Total time: 1.07 hours. Scaled time: 2.92 units (timescale=2.738). Factorization parameters were as follows: n: 10117710190461934473009304628321930124452353423611672709442911428185146358181590488935152642064613521952989779610751 m: 2000000000000000000000000 deg: 5 c5: 725 c0: -52 skew: 0.59 type: snfs lss: 1 rlim: 830000 alim: 830000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 830000/830000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [415000, 765001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 105540 x 105788 Total sieving time: 0.97 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.04 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,124.000,5,0,0,0,0,0,0,0,0,830000,830000,25,25,46,46,2.2,2.2,50000 total time: 1.07 hours.

(58·10¹⁵⁰-13)/9 = 6(4)₁₄₉3_<151> = 91520629 · 44412318343_<11> · 5279210260962477050762476446083_<31> · C102
C102 = P37 · P65
P37 = 9080338989895340087399783131537142371_<37>
P65 = 33074403639492669396853934308598204613343777969269022112121857233_<65>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1156783142 Step 1 took 6716ms Step 2 took 7148ms ********** Factor found in step 2: 9080338989895340087399783131537142371 Found probable prime factor of 37 digits: 9080338989895340087399783131537142371 Probable prime cofactor has 65 digits

(58·10¹⁴¹-13)/9 = 6(4)₁₄₀3_<142> = 439 · 3083 · 5531 · 297691 · 120686142884170765021_<21> · C107
C107 = P29 · P78
P29 = 44671237448007050301716904523_<29>
P78 = 536404836594779201210885696729897207146989810269196135430698329060421809691473_<78>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=288397723 Step 1 took 6948ms Step 2 took 264ms ********** Factor found in step 2: 44671237448007050301716904523 Found probable prime factor of 29 digits: 44671237448007050301716904523 Probable prime cofactor has 78 digits

(58·10¹⁹⁰-13)/9 = 6(4)₁₈₉3_<191> = 3² · 509² · 3547 · 1265377 · 12500658557_<11> · 189748339830808583554936738487_<30> · C136
C136 = P31 · P105
P31 = 8859562242390101042337256758079_<31>
P105 = 293023967158645378132168017909583983083045335220259236533576678613996132987368553614771402092617621838013_<105>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=60059875 Step 1 took 9684ms Step 2 took 9073ms ********** Factor found in step 2: 8859562242390101042337256758079 Found probable prime factor of 31 digits: 8859562242390101042337256758079 Probable prime cofactor has 105 digits

(58·10¹⁶⁴-13)/9 = 6(4)₁₆₃3_<165> = 634425495437_<12> · C154
C154 = P38 · C116
P38 = 34223943495856159696154680142313760883_<38>
C116 = [29680745593852382710885424670845104038289735607516074357223266600260200692718744499668077307158865998260008404416733_<116>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1920900515 Step 1 took 9293ms Step 2 took 9241ms ********** Factor found in step 2: 34223943495856159696154680142313760883 Found probable prime factor of 38 digits: 34223943495856159696154680142313760883 Composite cofactor has 116 digits

(58·10¹⁷²-13)/9 = 6(4)₁₇₁3_<173> = 3² · 31 · 41865383430599_<14> · C157
C157 = P34 · P123
P34 = 6908239763065591955895879222911977_<34>
P123 = 798654247269250625821363125778243854007703628918987098880286209849549880972564009269875503432979327263787634758461031670979_<123>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=526144718 Step 1 took 11613ms Step 2 took 10593ms ********** Factor found in step 2: 6908239763065591955895879222911977 Found probable prime factor of 34 digits: 6908239763065591955895879222911977 Probable prime cofactor has 123 digits

(58·10¹⁸³-13)/9 = 6(4)₁₈₂3_<184> = 25919 · 5252563412071_<13> · C167
C167 = P39 · P128
P39 = 961420063382696913845039546496705687743_<39>
P128 = 49235999353202946808007492839763276913494801029546625572470190315605759777492573030933345460372056027724551909999157757321602349_<128>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1633217857 Step 1 took 10608ms Step 2 took 10413ms ********** Factor found in step 2: 961420063382696913845039546496705687743 Found probable prime factor of 39 digits: 961420063382696913845039546496705687743 Probable prime cofactor has 128 digits

(58·10¹⁹⁶-13)/9 = 6(4)₁₉₅3_<197> = 3 · 23 · 257 · 24169 · C189
C189 = P30 · C160
P30 = 103847259321610372073924050253_<30>
C160 = [1447936609718760749360067535781392847535511656388177962890118978787031768606123874361301183998193725780863669969923596746060603885509742425909266190788773872803_<160>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2549112822 Step 1 took 12280ms Step 2 took 11289ms ********** Factor found in step 2: 103847259321610372073924050253 Found probable prime factor of 30 digits: 103847259321610372073924050253 Composite cofactor has 160 digits

(58·10¹⁹⁸-13)/9 = 6(4)₁₉₇3_<199> = 43 · 1117 · 19237 · 24821 · 2784569 · 59237954935041703_<17> · C163
C163 = P32 · P132
P32 = 11886551500859734818658620538271_<32>
P132 = 143315551274420434222213373947337563362940576038866710475231323622530913839047854154795199333394648781320634451598336144835705100237_<132>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=581503178 Step 1 took 10729ms Step 2 took 9936ms ********** Factor found in step 2: 11886551500859734818658620538271 Found probable prime factor of 32 digits: 11886551500859734818658620538271 Probable prime cofactor has 132 digits

Jun 28, 2009

Factorizations of 644...443 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Jun 27, 2009 (5th)

By Andreas Tete / Msieve v. 1.42, GGNFS / Jun 27, 2009
(47·10¹⁸⁴+7)/9 = 5(2)₁₈₃3_<185> = 37663 · 135409 · 1588687 · 1021756909_<10> · 15578211305893_<14> · 1203431099965687585292929_<25> · C123
C123 = P56 · P67
P56 = 58503555637351580708422043524842421283873937516824943479_<56>
P67 = 5751563245817234489103450552093888364306272232411751491982339846761_<67>

Fri Jun 26 23:31:17 2009 Msieve v. 1.42 Fri Jun 26 23:31:17 2009 random seeds: a6acf584 39c875ea Fri Jun 26 23:31:17 2009 factoring 336486900353415024147237600989002997396746148444863813675164649764209038471473839837535695797853611852188481025423346221519 (123 digits) Fri Jun 26 23:31:18 2009 searching for 15-digit factors Fri Jun 26 23:31:20 2009 commencing number field sieve (123-digit input) Fri Jun 26 23:31:20 2009 R0: -487824567839495206772299 Fri Jun 26 23:31:20 2009 R1: 14668679888561 Fri Jun 26 23:31:20 2009 A0: -50331570058330244910862222320 Fri Jun 26 23:31:20 2009 A1: 768380589069646930261796 Fri Jun 26 23:31:20 2009 A2: -8962274101419223348 Fri Jun 26 23:31:20 2009 A3: -707850425755693 Fri Jun 26 23:31:20 2009 A4: 2360485890 Fri Jun 26 23:31:20 2009 A5: 12180 Fri Jun 26 23:31:20 2009 skew 126238.69, size 9.298006e-012, alpha -5.586956, combined = 2.122476e-010 Fri Jun 26 23:31:20 2009 Fri Jun 26 23:31:20 2009 commencing relation filtering Fri Jun 26 23:31:20 2009 commencing duplicate removal, pass 1 Fri Jun 26 23:31:20 2009 error -15 reading relation 69 Fri Jun 26 23:31:20 2009 error -15 reading relation 27248 Fri Jun 26 23:33:01 2009 found 1043150 hash collisions in 8851963 relations Fri Jun 26 23:33:26 2009 added 58672 free relations Fri Jun 26 23:33:26 2009 commencing duplicate removal, pass 2 Fri Jun 26 23:34:11 2009 found 999794 duplicates and 7910840 unique relations Fri Jun 26 23:34:11 2009 memory use: 50.6 MB Fri Jun 26 23:34:11 2009 reading rational ideals above 6094848 Fri Jun 26 23:34:11 2009 reading algebraic ideals above 6094848 Fri Jun 26 23:34:11 2009 commencing singleton removal, pass 1 Fri Jun 26 23:35:56 2009 relations with 0 large ideals: 212256 Fri Jun 26 23:35:56 2009 relations with 1 large ideals: 1376046 Fri Jun 26 23:35:56 2009 relations with 2 large ideals: 2997314 Fri Jun 26 23:35:56 2009 relations with 3 large ideals: 2528754 Fri Jun 26 23:35:56 2009 relations with 4 large ideals: 716094 Fri Jun 26 23:35:56 2009 relations with 5 large ideals: 25114 Fri Jun 26 23:35:56 2009 relations with 6 large ideals: 55262 Fri Jun 26 23:35:56 2009 relations with 7+ large ideals: 0 Fri Jun 26 23:35:56 2009 7910840 relations and about 7542439 large ideals Fri Jun 26 23:35:56 2009 commencing singleton removal, pass 2 Fri Jun 26 23:37:42 2009 found 3526496 singletons Fri Jun 26 23:37:42 2009 current dataset: 4384344 relations and about 3347379 large ideals Fri Jun 26 23:37:42 2009 commencing singleton removal, pass 3 Fri Jun 26 23:38:55 2009 found 708171 singletons Fri Jun 26 23:38:55 2009 current dataset: 3676173 relations and about 2596928 large ideals Fri Jun 26 23:38:55 2009 commencing singleton removal, pass 4 Fri Jun 26 23:40:04 2009 found 188233 singletons Fri Jun 26 23:40:04 2009 current dataset: 3487940 relations and about 2404927 large ideals Fri Jun 26 23:40:04 2009 commencing singleton removal, final pass Fri Jun 26 23:41:13 2009 memory use: 53.4 MB Fri Jun 26 23:41:13 2009 commencing in-memory singleton removal Fri Jun 26 23:41:13 2009 begin with 3487940 relations and 2532650 unique ideals Fri Jun 26 23:41:17 2009 reduce to 3111783 relations and 2149870 ideals in 14 passes Fri Jun 26 23:41:17 2009 max relations containing the same ideal: 37 Fri Jun 26 23:41:18 2009 reading rational ideals above 720000 Fri Jun 26 23:41:18 2009 reading algebraic ideals above 720000 Fri Jun 26 23:41:18 2009 commencing singleton removal, final pass Fri Jun 26 23:42:25 2009 keeping 2757965 ideals with weight <= 20, new excess is 296631 Fri Jun 26 23:42:30 2009 memory use: 91.6 MB Fri Jun 26 23:42:30 2009 commencing in-memory singleton removal Fri Jun 26 23:42:30 2009 begin with 3123556 relations and 2757965 unique ideals Fri Jun 26 23:42:35 2009 reduce to 3089558 relations and 2666631 ideals in 13 passes Fri Jun 26 23:42:35 2009 max relations containing the same ideal: 20 Fri Jun 26 23:42:38 2009 removing 321434 relations and 282016 ideals in 39418 cliques Fri Jun 26 23:42:38 2009 commencing in-memory singleton removal Fri Jun 26 23:42:38 2009 begin with 2768124 relations and 2666631 unique ideals Fri Jun 26 23:42:41 2009 reduce to 2746885 relations and 2363049 ideals in 7 passes Fri Jun 26 23:42:41 2009 max relations containing the same ideal: 20 Fri Jun 26 23:42:43 2009 removing 240115 relations and 200697 ideals in 39418 cliques Fri Jun 26 23:42:43 2009 commencing in-memory singleton removal Fri Jun 26 23:42:43 2009 begin with 2506770 relations and 2363049 unique ideals Fri Jun 26 23:42:45 2009 reduce to 2492837 relations and 2148206 ideals in 7 passes Fri Jun 26 23:42:45 2009 max relations containing the same ideal: 20 Fri Jun 26 23:42:47 2009 relations with 0 large ideals: 13137 Fri Jun 26 23:42:47 2009 relations with 1 large ideals: 106816 Fri Jun 26 23:42:47 2009 relations with 2 large ideals: 367021 Fri Jun 26 23:42:47 2009 relations with 3 large ideals: 664916 Fri Jun 26 23:42:47 2009 relations with 4 large ideals: 697372 Fri Jun 26 23:42:47 2009 relations with 5 large ideals: 436442 Fri Jun 26 23:42:47 2009 relations with 6 large ideals: 165605 Fri Jun 26 23:42:47 2009 relations with 7+ large ideals: 41528 Fri Jun 26 23:42:47 2009 commencing 2-way merge Fri Jun 26 23:42:50 2009 reduce to 1533730 relation sets and 1189099 unique ideals Fri Jun 26 23:42:50 2009 commencing full merge Fri Jun 26 23:43:13 2009 memory use: 103.6 MB Fri Jun 26 23:43:14 2009 found 759285 cycles, need 713299 Fri Jun 26 23:43:14 2009 weight of 713299 cycles is about 50132409 (70.28/cycle) Fri Jun 26 23:43:14 2009 distribution of cycle lengths: Fri Jun 26 23:43:14 2009 1 relations: 81341 Fri Jun 26 23:43:14 2009 2 relations: 80416 Fri Jun 26 23:43:14 2009 3 relations: 79712 Fri Jun 26 23:43:14 2009 4 relations: 73116 Fri Jun 26 23:43:14 2009 5 relations: 67623 Fri Jun 26 23:43:14 2009 6 relations: 59640 Fri Jun 26 23:43:14 2009 7 relations: 52283 Fri Jun 26 23:43:14 2009 8 relations: 44735 Fri Jun 26 23:43:14 2009 9 relations: 38808 Fri Jun 26 23:43:14 2009 10+ relations: 135625 Fri Jun 26 23:43:14 2009 heaviest cycle: 18 relations Fri Jun 26 23:43:14 2009 commencing cycle optimization Fri Jun 26 23:43:16 2009 start with 4176779 relations Fri Jun 26 23:43:27 2009 pruned 122566 relations Fri Jun 26 23:43:27 2009 memory use: 108.8 MB Fri Jun 26 23:43:27 2009 distribution of cycle lengths: Fri Jun 26 23:43:27 2009 1 relations: 81341 Fri Jun 26 23:43:27 2009 2 relations: 82483 Fri Jun 26 23:43:27 2009 3 relations: 83177 Fri Jun 26 23:43:27 2009 4 relations: 75664 Fri Jun 26 23:43:27 2009 5 relations: 69884 Fri Jun 26 23:43:27 2009 6 relations: 60818 Fri Jun 26 23:43:27 2009 7 relations: 53164 Fri Jun 26 23:43:27 2009 8 relations: 44844 Fri Jun 26 23:43:27 2009 9 relations: 38867 Fri Jun 26 23:43:27 2009 10+ relations: 123057 Fri Jun 26 23:43:27 2009 heaviest cycle: 18 relations Fri Jun 26 23:43:28 2009 RelProcTime: 517 Fri Jun 26 23:43:28 2009 Fri Jun 26 23:43:28 2009 commencing linear algebra Fri Jun 26 23:43:28 2009 read 713299 cycles Fri Jun 26 23:43:30 2009 cycles contain 2252275 unique relations Fri Jun 26 23:44:06 2009 read 2252275 relations Fri Jun 26 23:44:10 2009 using 20 quadratic characters above 134214012 Fri Jun 26 23:44:24 2009 building initial matrix Fri Jun 26 23:45:01 2009 memory use: 262.0 MB Fri Jun 26 23:45:02 2009 read 713299 cycles Fri Jun 26 23:45:04 2009 matrix is 713058 x 713299 (201.5 MB) with weight 67363351 (94.44/col) Fri Jun 26 23:45:04 2009 sparse part has weight 47840390 (67.07/col) Fri Jun 26 23:45:19 2009 filtering completed in 3 passes Fri Jun 26 23:45:19 2009 matrix is 709979 x 710179 (201.1 MB) with weight 67172917 (94.59/col) Fri Jun 26 23:45:19 2009 sparse part has weight 47741684 (67.22/col) Fri Jun 26 23:45:21 2009 read 710179 cycles Fri Jun 26 23:45:22 2009 matrix is 709979 x 710179 (201.1 MB) with weight 67172917 (94.59/col) Fri Jun 26 23:45:22 2009 sparse part has weight 47741684 (67.22/col) Fri Jun 26 23:45:22 2009 saving the first 48 matrix rows for later Fri Jun 26 23:45:23 2009 matrix is 709931 x 710179 (194.0 MB) with weight 53262504 (75.00/col) Fri Jun 26 23:45:23 2009 sparse part has weight 46602145 (65.62/col) Fri Jun 26 23:45:23 2009 matrix includes 64 packed rows Fri Jun 26 23:45:23 2009 using block size 65536 for processor cache size 3072 kB Fri Jun 26 23:45:29 2009 commencing Lanczos iteration Fri Jun 26 23:45:29 2009 memory use: 191.5 MB Sat Jun 27 01:00:51 2009 lanczos halted after 11229 iterations (dim = 709931) Sat Jun 27 01:00:53 2009 recovered 32 nontrivial dependencies Sat Jun 27 01:00:53 2009 BLanczosTime: 4645 Sat Jun 27 01:00:53 2009 Sat Jun 27 01:00:53 2009 commencing square root phase Sat Jun 27 01:00:53 2009 reading relations for dependency 1 Sat Jun 27 01:00:54 2009 read 354935 cycles Sat Jun 27 01:00:55 2009 cycles contain 1379817 unique relations Sat Jun 27 01:01:45 2009 read 1379817 relations Sat Jun 27 01:01:53 2009 multiplying 1124500 relations Sat Jun 27 01:05:21 2009 multiply complete, coefficients have about 49.76 million bits Sat Jun 27 01:05:22 2009 initial square root is modulo 13925531 Sat Jun 27 01:09:52 2009 sqrtTime: 539 Sat Jun 27 01:09:52 2009 prp56 factor: 58503555637351580708422043524842421283873937516824943479 Sat Jun 27 01:09:52 2009 prp67 factor: 5751563245817234489103450552093888364306272232411751491982339846761 Sat Jun 27 01:09:52 2009 elapsed time 01:38:35 total time ~ 56 hours 40 minutes

Jun 27, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Jun 27, 2009
4·10²¹⁷-9 = 3(9)₂₁₆1_<218> = C218
C218 = P54 · P165
P54 = 153138923096637815337324392839746144304740150626975813_<54>
P165 = 261200739767238216403031051949070797540409290687764527939818984072695012732362463527871657040814436595996243277659214477992470411020857002428756477130421386528676107_<165>

Number: n N=39999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 ( 218 digits) SNFS difficulty: 217 digits. Divisors found: Sat Jun 27 16:32:05 2009 prp54 factor: 153138923096637815337324392839746144304740150626975813 Sat Jun 27 16:32:05 2009 prp165 factor: 261200739767238216403031051949070797540409290687764527939818984072695012732362463527871657040814436595996243277659214477992470411020857002428756477130421386528676107 Sat Jun 27 16:32:05 2009 elapsed time 62:55:06 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20050930-k8 Total time: 201.57 hours. Scaled time: 406.36 units (timescale=2.016). Factorization parameters were as follows: name: KA_3_9_216_1 n: 39999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 m: 1000000000000000000000000000000000000 deg: 6 c6: 40 c0: -9 skew: 0.78 type: snfs lss: 1 rlim: 30000000 alim: 30000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 30000000/30000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [15000000, 51099990) Primes: RFBsize:1857859, AFBsize:1857909, largePrimes:38359729 encountered Relations: rels:35364571, finalFF:1138388 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 9231841 hash collisions in 50553036 relations Msieve: matrix is 5454062 x 5454310 (1490.4 MB) Total sieving time: 200.07 hours. Total relation processing time: 1.49 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,217,6,0,0,0,0,0,0,0,0,30000000,30000000,29,29,58,58,2.6,2.6,100000 total time: 201.57 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3352056k/3407296k available (3119k kernel code, 53956k reserved, 1894k data, 424k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5661.68 BogoMIPS (lpj=2830844) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456) Total of 4 processors activated (22644.41 BogoMIPS).

Jun 27, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Jun 27, 2009
(14·10¹⁶⁹-17)/3 = 4(6)₁₆₈1_<170> = 215880244364499579382801212799_<30> · C141
C141 = P39 · P47 · P56
P39 = 164987940471911919931720360662845119279_<39>
P47 = 32526795988018253979416672362657704392943753593_<47>
P56 = 40281013844684900168945533327602460233451320127931079037_<56>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 216169232177971192501955249216876153564299586479509590522860815653381675214844760678296009204006289701356974365633658790823919329922476632539 (141 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5538504349 Step 1 took 4012ms Step 2 took 2371ms ********** Factor found in step 2: 164987940471911919931720360662845119279 Found probable prime factor of 39 digits: 164987940471911919931720360662845119279 Composite cofactor 1310212319516604554737041668268993579654865949023704998524458434780684269585853050111262206001535729941 has 103 digits Number: 46661_169 N=1310212319516604554737041668268993579654865949023704998524458434780684269585853050111262206001535729941 ( 103 digits) Divisors found: r1=32526795988018253979416672362657704392943753593 r2=40281013844684900168945533327602460233451320127931079037 Version: Total time: 3.63 hours. Scaled time: 8.68 units (timescale=2.390). Factorization parameters were as follows: name: 46661_169 n: 1310212319516604554737041668268993579654865949023704998524458434780684269585853050111262206001535729941 skew: 7580.79 # norm 2.17e+13 c5: 11640 c4: 80574174 c3: -2644906284335 c2: -10484031778600973 c1: 62593522390370734919 c0: -62150029590737475022585 # alpha -4.06 Y1: 57271184329 Y0: -40764009580135475262 # Murphy_E 2.53e-09 # M 1010454591132022271215501380240311892732052755553949690211722162287652266129439944490048921978649313790 type: gnfs rlim: 1500000 alim: 1500000 lpbr: 26 lpba: 26 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 50/50 Sieved algebraic special-q in [750000, 1400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4804835 Max relations in full relation-set: Initial matrix: Pruned matrix : 257647 x 257895 Polynomial selection time: 0.25 hours. Total sieving time: 2.93 hours. Total relation processing time: 0.29 hours. Matrix solve time: 0.13 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000 total time: 3.63 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672386) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5237.73 BogoMIPS (lpj=2618866)

Jun 27, 2009 (2nd)

By Dmitry Domanov / GGNFS/Msieve 1.41 / Jun 27, 2009
(16·10¹⁸⁴-7)/9 = 1(7)_184<185> = 4639 · 2208469987_<10> · 122889553861_<12> · 2043810257434261739_<19> · C142
C142 = P61 · P82
P61 = 3963965902151640309444352830053938422744024270549330775181009_<61>
P82 = 1742914757078340982220330559551431495030549136659252945881611664525081678798945299_<82>

N=6908854667415452929349067257832242713851174690747514804546818467887473298594120925395357875176704646282864437854825702195352929879995014626691 ( 142 digits) SNFS difficulty: 185 digits. Divisors found: r1=3963965902151640309444352830053938422744024270549330775181009 (pp61) r2=1742914757078340982220330559551431495030549136659252945881611664525081678798945299 (pp82) Version: Msieve v. 1.41 Total time: 203.60 hours. Scaled time: 404.75 units (timescale=1.988). Factorization parameters were as follows: n: 6908854667415452929349067257832242713851174690747514804546818467887473298594120925395357875176704646282864437854825702195352929879995014626691 m: 10000000000000000000000000000000000000 deg: 5 c5: 8 c0: -35 skew: 1.34 type: snfs lss: 1 rlim: 8800000 alim: 8800000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 8800000/8800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4400000, 7400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1652077 x 1652325 Total sieving time: 198.57 hours. Total relation processing time: 0.33 hours. Matrix solve time: 4.38 hours. Time per square root: 0.32 hours. Prototype def-par.txt line would be: snfs,185.000,5,0,0,0,0,0,0,0,0,8800000,8800000,28,28,54,54,2.5,2.5,100000 total time: 203.60 hours. --------- CPU info (if available) ----------

Jun 27, 2009

By Tyler Cadigan / PRIMO 3.0.7 / Jun 27, 2009
(10²⁹⁵²+17)/9 = (1)₂₉₅₁3_<2952> is prime.

Jun 26, 2009 (2nd)

By Dmitry Domanov / ECMNET / Jun 26, 2009
(8·10¹⁷⁴+7)/3 = 2(6)₁₇₃9_<175> = 9291193902637_<13> · 35960739752300141123644395023_<29> · C133
C133 = P42 · P92
P42 = 147246485091491533084862542850273174082841_<42>
P92 = 54203041264768699675736191181175423376382598279706791561135352844935913636053459860335938759_<92>

C133=P42*P92 C133=147246485091491533084862542850273174082841<42>*54203041264768699675736191181175423376382598279706791561135352844935913636053459860335938759<92>

Jun 26, 2009

By Robert Backstrom / GGNFS, Msieve / Jun 26, 2009
(35·10¹⁶⁷-17)/9 = 3(8)₁₆₆7_<168> = 3 · 219943721724751_<15> · 25906357094181540237749_<23> · C131
C131 = P57 · P74
P57 = 996244817379145944395119476840665614982629783547816089009_<57>
P74 = 22836013332760580540298944200610015633803921232860776910122536509987443319_<74>

Number: n N=22750259932363806506452932866536434963285158584917848593353721346670116012441195229750928624948194947776451081125903243713646380871 ( 131 digits) SNFS difficulty: 169 digits. Divisors found: Fri Jun 26 01:01:57 2009 prp57 factor: 996244817379145944395119476840665614982629783547816089009 Fri Jun 26 01:01:57 2009 prp74 factor: 22836013332760580540298944200610015633803921232860776910122536509987443319 Fri Jun 26 01:01:57 2009 elapsed time 01:14:28 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 49.98 hours. Scaled time: 132.95 units (timescale=2.660). Factorization parameters were as follows: name: KA_3_8_166_7 n: 22750259932363806506452932866536434963285158584917848593353721346670116012441195229750928624948194947776451081125903243713646380871 m: 5000000000000000000000000000000000 deg: 5 c5: 28 c0: -425 skew: 1.72 type: snfs lss: 1 rlim: 4800000 alim: 4800000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2400000, 5202913) Primes: RFBsize:335439, AFBsize:335322, largePrimes:16921186 encountered Relations: rels:16583215, finalFF:748495 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2030599 hash collisions in 18840257 relations Msieve: matrix is 793962 x 794210 (211.7 MB) Total sieving time: 49.54 hours. Total relation processing time: 0.44 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,4800000,4800000,28,28,56,56,2.4,2.4,100000 total time: 49.98 hours. --------- CPU info (if available) ----------

(85·10¹⁶⁸+41)/9 = 9(4)₁₆₇9_<169> = 7 · 30130007026272762236778552242458213_<35> · C134
C134 = P39 · P95
P39 = 646081469853325946280782791194467559557_<39>
P95 = 69309355117636896116388768379746577518566014665395648129726751071650431763506721291831801078927_<95>

Number: n N=44779490028988984693345170298727232692672656093119287564674642677206820719270872412399590798774417897156369411429035099199813230155339 ( 134 digits) SNFS difficulty: 170 digits. Divisors found: Fri Jun 26 12:38:16 2009 prp39 factor: 646081469853325946280782791194467559557 Fri Jun 26 12:38:16 2009 prp95 factor: 69309355117636896116388768379746577518566014665395648129726751071650431763506721291831801078927 Fri Jun 26 12:38:16 2009 elapsed time 01:40:25 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 45.19 hours. Scaled time: 120.22 units (timescale=2.660). Factorization parameters were as follows: name: KA_9_4_167_9 n: 44779490028988984693345170298727232692672656093119287564674642677206820719270872412399590798774417897156369411429035099199813230155339 m: 5000000000000000000000000000000000 deg: 5 c5: 136 c0: 205 skew: 1.09 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2500000, 4983701) Primes: RFBsize:348513, AFBsize:348092, largePrimes:16608879 encountered Relations: rels:15751124, finalFF:670651 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1838346 hash collisions in 18598297 relations Msieve: matrix is 800495 x 800743 (213.7 MB) Total sieving time: 44.69 hours. Total relation processing time: 0.50 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000 total time: 45.19 hours. --------- CPU info (if available) ----------

(32·10¹⁶⁸+31)/9 = 3(5)₁₆₇9_<169> = 7 · 61 · 39983209801_<11> · 111470331997295376701_<21> · C136
C136 = P61 · P76
P61 = 1073104304815526983816771184467768044461214238015586531509631_<61>
P76 = 1741007758140672565912344588362661612431195406392316590249384001939025425007_<76>

Number: n N=1868282919977985573733322020556574078433082808304869247090505648965219877477967805693204420862322587884350227847740147854847247088742417 ( 136 digits) SNFS difficulty: 170 digits. Divisors found: Fri Jun 26 12:41:03 2009 prp61 factor: 1073104304815526983816771184467768044461214238015586531509631 Fri Jun 26 12:41:03 2009 prp76 factor: 1741007758140672565912344588362661612431195406392316590249384001939025425007 Fri Jun 26 12:41:03 2009 elapsed time 01:41:17 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 45.35 hours. Scaled time: 120.14 units (timescale=2.649). Factorization parameters were as follows: name: KA_3_5_167_9 n: 1868282919977985573733322020556574078433082808304869247090505648965219877477967805693204420862322587884350227847740147854847247088742417 m: 4000000000000000000000000000000000 deg: 5 c5: 125 c0: 124 skew: 1.00 type: snfs lss: 1 rlim: 4800000 alim: 4800000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2400000, 4894117) Primes: RFBsize:335439, AFBsize:335383, largePrimes:15896129 encountered Relations: rels:14761745, finalFF:507282 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1791801 hash collisions in 17666333 relations Msieve: matrix is 827896 x 828144 (222.0 MB) Total sieving time: 44.92 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,170,5,0,0,0,0,0,0,0,0,4800000,4800000,28,28,56,56,2.4,2.4,100000 total time: 45.35 hours. --------- CPU info (if available) ----------

Jun 25, 2009 (2nd)

By matsui / GMP-ECM / Jun 25, 2009
(55·10¹⁹²+17)/9 = 6(1)₁₉₁3_<193> = 83 · C191
C191 = P37 · P155
P37 = 1554680079421055663241309632741999791_<37>
P155 = 47358839729650484514213082265957188539646153312865411770034607331778178504222288115743334089402845551750039467061001611721179865193092780024997006733901821_<155>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] 73627844712182061579651941097724230254350736278447121820615796519410977242302543507362784471218206157965194109772423025435073627844712182061579651941097724230254350736278447121820615796519411 = 1554680079421055663241309632741999791* 47358839729650484514213082265957188539646153312865411770034607331778178504222288115743334089402845551750039467061001611721179865193092780024997006733901821

(53·10¹⁹¹-17)/9 = 5(8)₁₉₀7_<192> = 13 · C191
C191 = P40 · C152
P40 = 3077325253235247465155976615079042868201_<40>
C152 = [14720298171771570716723886854991671208898715252902464943556125290604128965082355315462245187807878703850020843469774087345493414370248002017144961313499_<152>]

45299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299 = 3077325253235247465155976615079042868201* 14720298171771570716723886854991671208898715252902464943556125290604128965082355315462245187807878703850020843469774087345493414370248002017144961313499

Jun 25, 2009

By Jo Yeong Uk / GMP-ECM / Jun 25, 2009
(4·10¹⁷⁰-7)/3 = 1(3)₁₆₉1_<171> = 31 · 109789 · 9312411211130847248950201_<25> · C139
C139 = P40 · P100
P40 = 1502800256281439263857988805655344280607_<40>
P100 = 2799334573149479855515889170258387660810275368454048558247681468213445701259426026270237351262891687_<100>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 4206840713946531714695528183547906105304724835861710639562086194419321364323506470619518559763137831380386962778321740712084950551575614009 (139 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4784109703 Step 1 took 4633ms Step 2 took 4431ms ********** Factor found in step 2: 1502800256281439263857988805655344280607 Found probable prime factor of 40 digits: 1502800256281439263857988805655344280607 Probable prime cofactor 2799334573149479855515889170258387660810275368454048558247681468213445701259426026270237351262891687 has 100 digits

Jun 24, 2009 (6th)

By Serge Batalov / PFGW / Jun 23, 2009
(14·10²⁸¹⁷-17)/3 = 4(6)₂₈₁₆1_<2818> is prime.
(22·10³⁵²⁰-13)/9 = 2(4)₃₅₁₉3_<3521> is prime.

Jun 24, 2009 (5th)

By Robert Backstrom / GMP-ECM / Jun 24, 2009
(22·10¹⁶⁸-31)/9 = 2(4)₁₆₇1_<169> = 8873219 · 11099060621790018608384460043_<29> · C134
C134 = P42 · P92
P42 = 371200625538831365829940284569021747043127_<42>
P92 = 66865800468067413875508513185834603191397073474295317096215322040316133061063996555098731599_<92>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 24820626960901307166243457286366035083079281210552737892128741525214711320317507910090012420833207935695272455422603107378826450670073 (134 digits) Using B1=5878000, B2=11417264050, polynomial Dickson(12), sigma=4081711366 Step 1 took 72790ms ********** Factor found in step 1: 371200625538831365829940284569021747043127 Found probable prime factor of 42 digits: 371200625538831365829940284569021747043127 Probable prime cofactor 66865800468067413875508513185834603191397073474295317096215322040316133061063996555098731599 has 92 digits

Jun 24, 2009 (4th)

By Andreas Tete / Syd`s Database workers / Jun 24, 2009
6·10²⁰⁵+1 = 6(0)₂₀₄1_<206> = 31 · 47 · 107 · 321588220688443027059385703_<27> · C175
C175 = P32 · P143
P32 = 52608200965763511019049070037321_<32>
P143 = 22748582359849985239621437062492301500654660877058842699222608390850103339364205134046046593760422318845790606886535630528076929599435895212973_<143>

This factor is from Syd`s Database 52608200965763511019049070037321

Jun 24, 2009 (3rd)

By Jo Yeong Uk / GMP-ECM / Jun 24, 2009
(22·10¹⁶⁷-13)/9 = 2(4)₁₆₆3_<168> = 3 · 103 · 180519949 · 99146963869_<11> · 20757436223520443_<17> · C130
C130 = P42 · P89
P42 = 167490769827406767572595332518138087825351_<42>
P89 = 12713129747157146466674781904758060906332193817674471949615764473430324022539144529420019_<89>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 2129331888267055615375292847991745991122250793026866418237055157471572765868882564504408062284213491426581138168217340664995101669 (130 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1892633111 Step 1 took 9996ms Step 2 took 5101ms ********** Factor found in step 2: 167490769827406767572595332518138087825351 Found probable prime factor of 42 digits: 167490769827406767572595332518138087825351 Probable prime cofactor 12713129747157146466674781904758060906332193817674471949615764473430324022539144529420019 has 89 digits

(68·10¹⁶⁷+13)/9 = 7(5)₁₆₆7_<168> = 11 · 6133 · 3692624693_<10> · 3515568961760680937252533_<25> · C129
C129 = P40 · P90
P40 = 1277051303251277396745439863477632923199_<40>
P90 = 675556407842777457227772829257886093211284966360659547830383521551498877804611413980290869_<90>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 862720191055370426409187832685236228895646134693978735857012571110151934022354543430530334015543289916386083309198010532757969931 (129 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1210827030 Step 1 took 10042ms Step 2 took 5075ms ********** Factor found in step 2: 1277051303251277396745439863477632923199 Found probable prime factor of 40 digits: 1277051303251277396745439863477632923199 Probable prime cofactor 675556407842777457227772829257886093211284966360659547830383521551498877804611413980290869 has 90 digits

Jun 24, 2009 (2nd)

By Dmitry Domanov / ECMNET / Jun 24, 2009
10²¹⁷-9 = (9)₂₁₆1_<217> = 277 · 1597 · 209837 · 26201554231_<11> · 28091934741523_<14> · 6880830160720697642858093533_<28> · C155
C155 = P32 · P123
P32 = 63325093119323060926195351466951_<32>
P123 = 335898346710792594131217225602531441026219994792367522422800950405251569979293410168943832776047737138867077267300064073493_<123>

C155=P32*P123 C155=63325093119323060926195351466951<32>*335898346710792594131217225602531441026219994792367522422800950405251569979293410168943832776047737138867077267300064073493<123>

Jun 24, 2009

By Tyler Cadigan / GGNFS, Msieve / Jun 24, 2009
6·10¹⁸⁵+1 = 6(0)₁₈₄1_<186> = 19 · 167 · 3149035144740077_<16> · 30217523095511560432976100709_<29> · C139
C139 = P66 · P74
P66 = 123251687544331276107061304469530687861827519667502885428574726923_<66>
P74 = 16123225707827282939353513239821935387962162632669892472730626095154698983_<74>

Number: 60001_185 N=1987214777147857751405440882712878768498289240274665943254488411740605391914998115487412671203360049610514137987060572328808885079490819309 ( 139 digits) SNFS difficulty: 185 digits. Divisors found: r1=123251687544331276107061304469530687861827519667502885428574726923 (pp66) r2=16123225707827282939353513239821935387962162632669892472730626095154698983 (pp74) Version: Msieve v. 1.41 Total time: 216.99 hours. Scaled time: 550.28 units (timescale=2.536). Factorization parameters were as follows: n: 1987214777147857751405440882712878768498289240274665943254488411740605391914998115487412671203360049610514137987060572328808885079490819309 m: 10000000000000000000000000000000000000 deg: 5 c5: 6 c0: 1 skew: 0.70 type: snfs lss: 1 rlim: 8700000 alim: 8700000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 qintsize: 1000000 Factor base limits: 8700000/8700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4350000, 7350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1090015 x 1090262 Total sieving time: 213.24 hours. Total relation processing time: 0.47 hours. Matrix solve time: 2.48 hours. Time per square root: 0.79 hours. Prototype def-par.txt line would be: snfs,185.000,5,0,0,0,0,0,0,0,0,8700000,8700000,28,28,54,54,2.5,2.5,100000 total time: 216.99 hours. --------- CPU info (if available) ----------

Jun 23, 2009 (5th)

By Jo Yeong Uk / GGNFS, GMP-ECM 6.2.3, Msieve v1.39/YAFU 1.10 / Jun 23, 2009
(4·10¹⁷²-7)/3 = 1(3)₁₇₁1_<173> = 1979 · 13289227921_<11> · 162833506738538029_<18> · 11712824240851604859171398762414514649183_<41> · C102
C102 = P43 · P59
P43 = 5134015334759491232232164584639017885994807_<43>
P59 = 51776254296606631877254403452223499612447702177657692377141_<59>

Number: 13331_172 N=265820083535185443400012989979500246927574859540043887531215591340458372270487885471414380147411506787 ( 102 digits) Divisors found: r1=5134015334759491232232164584639017885994807 r2=51776254296606631877254403452223499612447702177657692377141 Version: Total time: 3.25 hours. Scaled time: 7.75 units (timescale=2.385). Factorization parameters were as follows: name: 13331_172 n: 265820083535185443400012989979500246927574859540043887531215591340458372270487885471414380147411506787 skew: 12643.51 # norm 3.65e+14 c5: 38880 c4: -845394138 c3: -33007101816765 c2: 73320781261222582 c1: 1557463663881869440290 c0: -4414460967845638019542375 # alpha -6.49 Y1: 12393727643 Y0: -23279481991745479608 # Murphy_E 2.72e-09 # M 141911435455571799952981958314235858806500151888383279234915351745234001551558863634711718448352602713 type: gnfs rlim: 1500000 alim: 1500000 lpbr: 26 lpba: 26 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 50/50 Sieved algebraic special-q in [750000, 1300001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4792695 Max relations in full relation-set: Initial matrix: Pruned matrix : 216449 x 216697 Polynomial selection time: 0.22 hours. Total sieving time: 2.65 hours. Total relation processing time: 0.26 hours. Matrix solve time: 0.09 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000 total time: 3.25 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673796) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672351) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

(89·10¹⁹⁴+1)/9 = 9(8)₁₉₃9_<195> = 19 · 787 · 1478629721_<10> · 1769297203_<10> · 2283368889277607_<16> · 38346165072677325477768700865603_<32> · C126
C126 = P34 · P43 · P49
P34 = 9097052437296664414776212359460597_<34>
P43 = 3374615834793386611677694152332672045296747_<43>
P49 = 9404503802431255949573827788376837390651779708209_<49>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 288709400214039153514611082816280322399269582988374671238906295467466961967639668368802541858848488578358621719840471080565431 (126 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6364061278 Step 1 took 4180ms ********** Factor found in step 1: 9097052437296664414776212359460597 Found probable prime factor of 34 digits: 9097052437296664414776212359460597 Composite cofactor 31736587450059131430259469757449683794651893754830576115125492366442558497351134990476896123 has 92 digits 06/23/09 22:31:38 v1.10 @ 조영욱-PC, starting SIQS on c92: 31736587450059131430259469757449683794651893754830576115125492366442558497351134990476896123 06/23/09 22:31:38 v1.10 @ 조영욱-PC, random seeds: 552356298, 3598319296 06/23/09 22:31:38 v1.10 @ 조영욱-PC, ==== sieve params ==== 06/23/09 22:31:38 v1.10 @ 조영욱-PC, n = 92 digits, 306 bits 06/23/09 22:31:38 v1.10 @ 조영욱-PC, factor base: 71746 primes (max prime = 1914439) 06/23/09 22:31:38 v1.10 @ 조영욱-PC, single large prime cutoff: 229732680 (120 * pmax) 06/23/09 22:31:38 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits 06/23/09 22:31:38 v1.10 @ 조영욱-PC, double large prime cutoff: 1122537872193945 06/23/09 22:31:38 v1.10 @ 조영욱-PC, using 16 large prime slices of factor base 06/23/09 22:31:38 v1.10 @ 조영욱-PC, buckets hold 1024 elements 06/23/09 22:31:38 v1.10 @ 조영욱-PC, sieve interval: 11 blocks of size 65536 06/23/09 22:31:38 v1.10 @ 조영욱-PC, polynomial A has ~ 12 factors 06/23/09 22:31:38 v1.10 @ 조영욱-PC, using multiplier of 3 06/23/09 22:31:38 v1.10 @ 조영욱-PC, using small prime variation correction of 17 bits 06/23/09 22:31:38 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning 06/23/09 22:31:38 v1.10 @ 조영욱-PC, trial factoring cutoff at 100 bits 06/23/09 22:31:38 v1.10 @ 조영욱-PC, ==== sieving started ==== 06/23/09 23:55:14 v1.10 @ 조영욱-PC, sieve time = 2424.8690, relation time = 833.1370, poly_time = 1757.1540 06/23/09 23:55:14 v1.10 @ 조영욱-PC, 71833 relations found: 19062 full + 52771 from 910631 partial, using 753626 polys (368 A polys) 06/23/09 23:55:14 v1.10 @ 조영욱-PC, on average, sieving found 1.23 rels/poly and 185.33 rels/sec 06/23/09 23:55:14 v1.10 @ 조영욱-PC, trial division touched 29908181 sieve locations out of 1086571937792 06/23/09 23:55:14 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ==== 06/23/09 23:55:15 v1.10 @ 조영욱-PC, begin with 929693 relations 06/23/09 23:55:15 v1.10 @ 조영욱-PC, reduce to 175623 relations in 10 passes 06/23/09 23:55:17 v1.10 @ 조영욱-PC, recovered 175623 relations 06/23/09 23:55:17 v1.10 @ 조영욱-PC, recovered 156791 polynomials 06/23/09 23:55:17 v1.10 @ 조영욱-PC, attempting to build 71833 cycles 06/23/09 23:55:17 v1.10 @ 조영욱-PC, found 71833 cycles in 5 passes 06/23/09 23:55:17 v1.10 @ 조영욱-PC, distribution of cycle lengths: 06/23/09 23:55:17 v1.10 @ 조영욱-PC, length 1 : 19062 06/23/09 23:55:17 v1.10 @ 조영욱-PC, length 2 : 14133 06/23/09 23:55:17 v1.10 @ 조영욱-PC, length 3 : 12724 06/23/09 23:55:17 v1.10 @ 조영욱-PC, length 4 : 9637 06/23/09 23:55:17 v1.10 @ 조영욱-PC, length 5 : 6676 06/23/09 23:55:17 v1.10 @ 조영욱-PC, length 6 : 4215 06/23/09 23:55:17 v1.10 @ 조영욱-PC, length 7 : 2381 06/23/09 23:55:17 v1.10 @ 조영욱-PC, length 9+: 3005 06/23/09 23:55:17 v1.10 @ 조영욱-PC, largest cycle: 21 relations 06/23/09 23:55:17 v1.10 @ 조영욱-PC, matrix is 71746 x 71833 (18.7 MB) with weight 4332676 (60.32/col) 06/23/09 23:55:17 v1.10 @ 조영욱-PC, sparse part has weight 4332676 (60.32/col) 06/23/09 23:55:18 v1.10 @ 조영욱-PC, filtering completed in 3 passes 06/23/09 23:55:18 v1.10 @ 조영욱-PC, matrix is 67865 x 67929 (17.9 MB) with weight 4138642 (60.93/col) 06/23/09 23:55:18 v1.10 @ 조영욱-PC, sparse part has weight 4138642 (60.93/col) 06/23/09 23:55:18 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later 06/23/09 23:55:18 v1.10 @ 조영욱-PC, matrix is 67817 x 67929 (12.2 MB) with weight 3300446 (48.59/col) 06/23/09 23:55:18 v1.10 @ 조영욱-PC, sparse part has weight 2517689 (37.06/col) 06/23/09 23:55:18 v1.10 @ 조영욱-PC, matrix includes 64 packed rows 06/23/09 23:55:18 v1.10 @ 조영욱-PC, using block size 27171 for processor cache size 4096 kB 06/23/09 23:55:18 v1.10 @ 조영욱-PC, commencing Lanczos iteration 06/23/09 23:55:18 v1.10 @ 조영욱-PC, memory use: 10.7 MB 06/23/09 23:55:39 v1.10 @ 조영욱-PC, lanczos halted after 1074 iterations (dim = 67814) 06/23/09 23:55:39 v1.10 @ 조영욱-PC, recovered 16 nontrivial dependencies 06/23/09 23:55:40 v1.10 @ 조영욱-PC, prp49 = 9404503802431255949573827788376837390651779708209 06/23/09 23:55:44 v1.10 @ 조영욱-PC, prp43 = 3374615834793386611677694152332672045296747 06/23/09 23:55:44 v1.10 @ 조영욱-PC, Lanczos elapsed time = 24.9760 seconds. 06/23/09 23:55:44 v1.10 @ 조영욱-PC, Sqrt elapsed time = 4.9760 seconds. 06/23/09 23:55:44 v1.10 @ 조영욱-PC, SIQS elapsed time = 5046.4850 seconds. 06/23/09 23:55:44 v1.10 @ 조영욱-PC, 06/23/09 23:55:44 v1.10 @ 조영욱-PC,

Jun 23, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Jun 23, 2009
5·10¹⁶⁹+9 = 5(0)₁₆₈9_<170> = 601 · 240050495558407698763546267_<27> · C141
C141 = P47 · P94
P47 = 41281411513583644762377184791184555905650687227_<47>
P94 = 8395341891024184763633786646465985958174272838380095043933734588514621669155826987694109067001_<94>

Number: n N=346571563400596869585973019313910592991068897473874180601102588897696004361669211747830725681790090285548632257724403837334518143947437896227 ( 141 digits) SNFS difficulty: 170 digits. Divisors found: Tue Jun 23 03:22:08 2009 prp47 factor: 41281411513583644762377184791184555905650687227 Tue Jun 23 03:22:08 2009 prp94 factor: 8395341891024184763633786646465985958174272838380095043933734588514621669155826987694109067001 Tue Jun 23 03:22:08 2009 elapsed time 01:53:33 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 34.53 hours. Scaled time: 92.22 units (timescale=2.671). Factorization parameters were as follows: name: KA_5_0_168_9 n: 346571563400596869585973019313910592991068897473874180601102588897696004361669211747830725681790090285548632257724403837334518143947437896227 m: 10000000000000000000000000000000000 deg: 5 c5: 1 c0: 18 skew: 1.78 type: snfs lss: 1 rlim: 4800000 alim: 4800000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2400000, 4312493) Primes: RFBsize:335439, AFBsize:335377, largePrimes:15839972 encountered Relations: rels:14929612, finalFF:644433 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1396892 hash collisions in 16096513 relations Msieve: matrix is 859768 x 860016 (230.2 MB) Total sieving time: 34.09 hours. Total relation processing time: 0.44 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,4800000,4800000,28,28,56,56,2.4,2.4,100000 total time: 34.53 hours. --------- CPU info (if available) ----------

(47·10¹⁶⁷+61)/9 = 5(2)₁₆₆9_<168> = 73 · 83 · 4889 · 2368801 · 17554369602202312039753_<23> · C132
C132 = P64 · P68
P64 = 5079837261726309477074870937453617318273958408771046998347443561_<64>
P68 = 83458532416670736671267228864304174336696566851849644029351322951463_<68>

Number: n N=423955762779197108748010664666559127694051691975812539877069526095525968365910818624458358288204930884391825958098258024391334879743 ( 132 digits) SNFS difficulty: 169 digits. Divisors found: Tue Jun 23 03:49:36 2009 prp64 factor: 5079837261726309477074870937453617318273958408771046998347443561 Tue Jun 23 03:49:36 2009 prp68 factor: 83458532416670736671267228864304174336696566851849644029351322951463 Tue Jun 23 03:49:36 2009 elapsed time 02:21:21 (Msieve 1.39 - dependency 4) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 74.52 hours. Scaled time: 198.22 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_2_166_9 n: 423955762779197108748010664666559127694051691975812539877069526095525968365910818624458358288204930884391825958098258024391334879743 m: 2000000000000000000000000000000000 deg: 5 c5: 1175 c0: 488 skew: 0.84 type: snfs lss: 1 rlim: 4800000 alim: 4800000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2400000, 6868387) Primes: RFBsize:335439, AFBsize:335523, largePrimes:18006057 encountered Relations: rels:18460657, finalFF:659503 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2776050 hash collisions in 21096983 relations Msieve: matrix is 847467 x 847715 (222.3 MB) Total sieving time: 73.33 hours. Total relation processing time: 1.19 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,4800000,4800000,28,28,56,56,2.4,2.4,100000 total time: 74.52 hours. --------- CPU info (if available) ----------

(23·10¹⁷¹-41)/9 = 2(5)₁₇₀1_<172> = 562003853 · C163
C163 = P43 · P120
P43 = 9819478707452999260663842216145669618164917_<43>
P120 = 463081680659769326936886310127931535214424803461949022560762005197836495742479612235092546488980256930797094956201310351_<120>

Number: n N=4547220703050154276354321641199772264827436255237836519878015063280278890820265525040013481109631388159816682885901060816313577045094663355547413934821467417155867 ( 163 digits) SNFS difficulty: 172 digits. Divisors found: Tue Jun 23 13:07:13 2009 prp43 factor: 9819478707452999260663842216145669618164917 Tue Jun 23 13:07:13 2009 prp120 factor: 463081680659769326936886310127931535214424803461949022560762005197836495742479612235092546488980256930797094956201310351 Tue Jun 23 13:07:13 2009 elapsed time 01:27:20 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 83.31 hours. Scaled time: 113.38 units (timescale=1.361). Factorization parameters were as follows: name: KA_2_5_170_1 n: 4547220703050154276354321641199772264827436255237836519878015063280278890820265525040013481109631388159816682885901060816313577045094663355547413934821467417155867 m: 10000000000000000000000000000000000 deg: 5 c5: 230 c0: -41 skew: 0.71 type: snfs lss: 1 rlim: 5200000 alim: 5200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 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 [2600000, 7388737) Primes: RFBsize:361407, AFBsize:360913, largePrimes:18867095 encountered Relations: rels:19622703, finalFF:765979 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2982267 hash collisions in 22477415 relations Msieve: matrix is 899270 x 899518 (235.4 MB) Total sieving time: 81.95 hours. Total relation processing time: 1.36 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,172,5,0,0,0,0,0,0,0,0,5200000,5200000,28,28,56,56,2.4,2.4,100000 total time: 83.31 hours. --------- CPU info (if available) ----------

Jun 23, 2009 (3rd)

By Dmitry Domanov / ECMNET / Jun 23, 2009
(2·10²³⁴+1)/3 = (6)₂₃₃7_<234> = 11393 · 25339 · C226
C226 = P39 · P187
P39 = 729812897211517853487632354670094565923_<39>
P187 = 3164241616437046679403827475768447797264211271061761553933740453597778289635577612191476954130503242628832673837317052776146482706548181034700795185780339672202760023332942933779133885627_<187>

C226=P39*P187 C226=729812897211517853487632354670094565923<39>*3164241616437046679403827475768447797264211271061761553933740453597778289635577612191476954130503242628832673837317052776146482706548181034700795185780339672202760023332942933779133885627<187>

Jun 23, 2009 (2nd)

By Serge Batalov / Msieve-1.42 / Jun 23, 2009
(49·10¹⁶⁷-13)/9 = 5(4)₁₆₆3_<168> = 3 · 59 · 1105171 · 403536238013_<12> · 374925660096668543699_<21> · C128
C128 = P60 · P69
P60 = 154366586188854324678105391045950947662796027385267558778367_<60>
P69 = 119170789977225348190653974594475835745955100338192207667847653826801_<69>

SNFS difficulty: 169 digits. Divisors found: r1=154366586188854324678105391045950947662796027385267558778367 (pp60) r2=119170789977225348190653974594475835745955100338192207667847653826801 (pp69) Version: Msieve-1.42 Total time: 28.81 hours. Scaled time: 82.02 units (timescale=2.847). Factorization parameters were as follows: n: 18395988022213213815357754832451835276664855589756973035375079343242696253657629170109553860881160095980243731307550988163613967 m: 2000000000000000000000000000000000 deg: 5 c5: 1225 c0: -104 skew: 0.61 type: snfs lss: 1 rlim: 4700000 alim: 4700000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4700000/4700000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2350000, 5450001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 914075 x 914323 Total sieving time: 27.23 hours. Total relation processing time: 0.13 hours. Matrix solve time: 1.28 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,169.000,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.4,2.4,100000 total time: 28.81 hours.

Jun 23, 2009

By Serge Batalov / PFGW / Jun 22, 2009
(16·10³⁰¹⁰-7)/9 = 1(7)_3010<3011> is prime.
(16·10¹⁷⁸³⁹-7)/9 = 1(7)_17839<17840> is PRP.
(52·10⁹⁰¹⁵-43)/9 = 5(7)₉₀₁₄3_<9016> is prime.

Jun 22, 2009 (4th)

By Dmitry Domanov / ECMNET / Jun 22, 2009
(89·10¹⁸⁵+1)/9 = 9(8)₁₈₄9_<186> = 11 · 1987 · 616943 · C176
C176 = P29 · P148
P29 = 40940401384167441808899155767_<29>
P148 = 1791264866192661432732845062852095165264741708650930105086935795122598812517413884118459537265905771919543758665292146582186543306950429077800614017_<148>

[2009-06-21 02:52:13 GMT] a: Factor found! / (probable) 40940401384167441808899155767 B1: 11000000 sigma: 2019692168 (found in step 2) [2009-06-21 02:52:13 GMT] a: Co-factor: / (Probable) 1791264866192661432732845062852095165264741708650930105086935795122598812517413884118459537265905771919543758665292146582186543306950429077800614017

(89·10¹⁹⁴+1)/9 = 9(8)₁₉₃9_<195> = 19 · 787 · 1478629721_<10> · 1769297203_<10> · 2283368889277607_<16> · C158
C158 = P32 · C126
P32 = 38346165072677325477768700865603_<32>
C126 = [288709400214039153514611082816280322399269582988374671238906295467466961967639668368802541858848488578358621719840471080565431_<126>]

[2009-06-21 00:32:28 GMT] a: Factor found! / (probable) 38346165072677325477768700865603 B1: 11000000 sigma: 2792758941 (found in step 2) [2009-06-21 00:32:28 GMT] a: Co-factor: / (Composite) 288709400214039153514611082816280322399269582988374671238906295467466961967639668368802541858848488578358621719840471080565431

(46·10¹⁸⁴+71)/9 = 5(1)₁₈₃9_<185> = 31 · C184
C184 = P36 · C149
P36 = 109950766165990238619142052692775317_<36>
C149 = [14995307238006754970142095290739002827809014572111810162500899017717459167125063659570942091364689704175545066490272917015118441624190530505317102797_<149>]

C184=P36*C149 C184=109950766165990238619142052692775317<36>*14995307238006754970142095290739002827809014572111810162500899017717459167125063659570942091364689704175545066490272917015118441624190530505317102797<149>

(89·10¹⁹⁹+1)/9 = 9(8)₁₉₈9_<200> = 3² · 11 · 29 · 173 · 421 · 3013553 · C186
C186 = P35 · P151
P35 = 75505703827954394348190142512190813_<35>
P151 = 2078392237191109696799707468604509557501015179027375428569828921512009119409343165258187588687754438966150764624796567341773480588321102772113091935307_<151>

C186=P35*P151 C186=75505703827954394348190142512190813<35>*2078392237191109696799707468604509557501015179027375428569828921512009119409343165258187588687754438 966150764624796567341773480588321102772113091935307<151>

Jun 22, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Jun 22, 2009
(34·10¹⁶⁷-43)/9 = 3(7)₁₆₆3_<168> = 11 · 79 · 2212123 · 688065433235990265046158859_<27> · C132
C132 = P53 · P80
P53 = 11607192724957470109727382625443317990290621072844033_<53>
P80 = 24606532827049850789319866486334883175438181692662700048777546004311547846632257_<80>

Number: n N=285612768816560198153005074423318240175774326559723692726855192453231155131923257812510152266159767651064662586228076782756067772481 ( 132 digits) SNFS difficulty: 169 digits. Divisors found: Mon Jun 22 05:13:22 2009 prp53 factor: 11607192724957470109727382625443317990290621072844033 Mon Jun 22 05:13:22 2009 prp80 factor: 24606532827049850789319866486334883175438181692662700048777546004311547846632257 Mon Jun 22 05:13:22 2009 elapsed time 01:22:41 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 39.08 hours. Scaled time: 100.64 units (timescale=2.575). Factorization parameters were as follows: name: KA_3_7_166_3 n: 285612768816560198153005074423318240175774326559723692726855192453231155131923257812510152266159767651064662586228076782756067772481 m: 2000000000000000000000000000000000 deg: 5 c5: 425 c0: -172 skew: 0.83 type: snfs lss: 1 rlim: 4600000 alim: 4600000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 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 [2300000, 4535147) Primes: RFBsize:322441, AFBsize:321656, largePrimes:15842237 encountered Relations: rels:14942542, finalFF:595563 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1561562 hash collisions in 16410559 relations Msieve: matrix is 845581 x 845829 (229.1 MB) Total sieving time: 38.59 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,169,5,0,0,0,0,0,0,0,0,4600000,4600000,28,28,56,56,2.4,2.4,100000 total time: 39.08 hours. --------- CPU info (if available) ----------

(19·10¹⁶⁹+71)/9 = 2(1)₁₆₈9_<170> = 17 · 29 · 157 · 401 · 1202690777_<10> · 11917016737_<11> · C143
C143 = P34 · P109
P34 = 5953901394817602332266795990080373_<34>
P109 = 7970709470626566079289325522510715490264808474915393724092566519897218412184343046077211774275868043748116947_<109>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 47456818234849384485919149010234197237043999182472042017612061274694520497973354897231898436283664885858051334911013044250936917790809933381231 (143 digits) Using B1=1792000, B2=2140281790, polynomial Dickson(6), sigma=4224226140 Step 1 took 24913ms Step 2 took 8362ms ********** Factor found in step 2: 5953901394817602332266795990080373 Found probable prime factor of 34 digits: 5953901394817602332266795990080373 Probable prime cofactor 7970709470626566079289325522510715490264808474915393724092566519897218412184343046077211774275868043748116947 has 109 digits

Jun 22, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Jun 22, 2009
(4·10¹⁷²-7)/3 = 1(3)₁₇₁1_<173> = 1979 · 13289227921_<11> · 162833506738538029_<18> · C142
C142 = P41 · C102
P41 = 11712824240851604859171398762414514649183_<41>
C102 = [265820083535185443400012989979500246927574859540043887531215591340458372270487885471414380147411506787_<102>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4085455744 Step 1 took 42653ms Step 2 took 14897ms ********** Factor found in step 2: 11712824240851604859171398762414514649183 Found probable prime factor of 41 digits: 11712824240851604859171398762414514649183 Composite cofactor 265820083535185443400012989979500246927574859540043887531215591340458372270487885471414380147411506787 has 102 digits

Jun 22, 2009

By Jo Yeong Uk / GMP-ECM / Jun 21, 2009
(13·10¹⁶⁷-7)/3 = 4(3)₁₆₆1_<168> = 5959318178397209_<16> · 10739075572896235220891_<23> · C130
C130 = P39 · P92
P39 = 278840979899609144669916444484675755961_<39>
P92 = 24282982392014604316378653148216272453420429843296842734094382957632012796139059509470390809_<92>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 6771090605074307069591549228648573420714999216153608492489545679884278552852674684314455216639986692541470079887690700098181362449 (130 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3881612235 Step 1 took 4274ms Step 2 took 5819ms ********** Factor found in step 2: 278840979899609144669916444484675755961 Found probable prime factor of 39 digits: 278840979899609144669916444484675755961 Probable prime cofactor 24282982392014604316378653148216272453420429843296842734094382957632012796139059509470390809 has 92 digits

(41·10¹⁶⁷+13)/9 = 4(5)₁₆₆7_<168> = 430279 · 338623573 · 18003240719_<11> · 7832365170209_<13> · C131
C131 = P35 · P96
P35 = 38994801836476403223875236485088157_<35>
P96 = 568622021797804765367548597934605439349622589855711387016954054617774589676260150974346419105693_<96>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 22173303059861962649674962465807468961083598829975529901522059915208172285205905279352766464136854475819255274008388042078205577801 (131 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3093000109 Step 1 took 4196ms ********** Factor found in step 1: 38994801836476403223875236485088157 Found probable prime factor of 35 digits: 38994801836476403223875236485088157 Probable prime cofactor 568622021797804765367548597934605439349622589855711387016954054617774589676260150974346419105693 has 96 digits

Jun 21, 2009

By Serge Batalov / PFGW / Jun 20, 2009
(2·10³⁹⁶⁰⁶+1)/3 = (6)₃₉₆₀₅7_<39606> is PRP.

Jun 20, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / Jun 20, 2009
9·10¹⁶⁸+1 = 9(0)₁₆₇1_<169> = 193 · 183122333 · 1365503329_<10> · 70195540469_<11> · C139
C139 = P54 · P85
P54 = 803534758897924386932162437579226018617463265776195233_<54>
P85 = 3306259477416131198963892436083070510480940866548861316188259476731788862020584275713_<85>

Number: n N=2656694412039548462553232526428776317534088841928298827414634961259564708940735214813108191929447902768879073075808499186281445628188276129 ( 139 digits) SNFS difficulty: 170 digits. Divisors found: Sat Jun 20 12:49:06 2009 prp54 factor: 803534758897924386932162437579226018617463265776195233 Sat Jun 20 12:49:06 2009 prp85 factor: 3306259477416131198963892436083070510480940866548861316188259476731788862020584275713 Sat Jun 20 12:49:06 2009 elapsed time 01:55:16 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 43.37 hours. Scaled time: 112.12 units (timescale=2.585). Factorization parameters were as follows: name: KA_9_0_167_1 n: 2656694412039548462553232526428776317534088841928298827414634961259564708940735214813108191929447902768879073075808499186281445628188276129 m: 5000000000000000000000000000000000 deg: 5 c5: 72 c0: 25 skew: 0.81 type: snfs lss: 1 rlim: 4800000 alim: 4800000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2400000, 4868657) Primes: RFBsize:335439, AFBsize:335327, largePrimes:16134981 encountered Relations: rels:15152762, finalFF:557837 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1660784 hash collisions in 16908306 relations Msieve: matrix is 905009 x 905257 (241.5 MB) Total sieving time: 42.92 hours. Total relation processing time: 0.45 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,4800000,4800000,28,28,56,56,2.4,2.4,100000 total time: 43.37 hours. --------- CPU info (if available) ----------

Jun 20, 2009 (4th)

By Andreas Tete / Syd`s Database / Jun 20, 2009
2·10¹⁷⁶-9 = 1(9)₁₇₅1_<177> = 977 · 30422398200031601_<17> · C157
C157 = P27 · C131
P27 = 671851302766021349481441049_<27>
C131 = [10015412055048508505562981822117361493985212600568876345607115690865494900174994593465034317095895575473501050630145079867266172367_<131>]

this faktor is from the database http://factordb.com/search.php 671851302766021349481441049

Jun 20, 2009 (3rd)

By Dmitry Domanov / ECMNET / Jun 20, 2009
(2·10²⁴⁸+1)/3 = (6)₂₄₇7_<248> = 163 · 44179 · C241
C241 = P35 · C207
P35 = 41158940460267795191725127905610171_<35>
C207 = [224926729683557925143732786282199759731260062609772664415477620172801666485846605924960352715932697003118406528404722564383235862597511428194310219734798101447346433956246920912393774411884500256114875326201_<207>]

C241=P35*C207 C241=41158940460267795191725127905610171<35>*224926729683557925143732786282199759731260062609772664415477620172801666485846605924960352715932697003118406528404722564383235862597511428194310219734798101447346433956246920912393774411884500256114875326201<207>

Jun 20, 2009 (2nd)

By Jo Yeong Uk / GMP-ECM / Jun 20, 2009
(2·10²⁴⁵+1)/3 = (6)₂₄₄7_<245> = 23 · 153669121 · 869061193254415949_<18> · 38056099737006898261987_<23> · 39366916868321772201193201_<26> · 143367365426738090002045861251553483338881_<42> · C129
C129 = P43 · P86
P43 = 6214754527728988809452793868940752428182767_<43>
P86 = 16259754221608044527762712435800332789719768404154926526062152292523869431586832367349_<86>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 101050381168499134820535981759329661173475719716918113615492884413715003106991408503990025473220959006588553102747390264655274683 (129 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=69261048 Step 1 took 10110ms Step 2 took 5103ms ********** Factor found in step 2: 6214754527728988809452793868940752428182767 Found probable prime factor of 43 digits: 6214754527728988809452793868940752428182767 Probable prime cofactor 16259754221608044527762712435800332789719768404154926526062152292523869431586832367349 has 86 digits

Jun 20, 2009

By Wataru Sakai / GMP-ECM 6.2.1 / Jun 20, 2009
(19·10²⁰²+11)/3 = 6(3)₂₀₁7_<203> = 54127212709_<11> · 2197913408641_<13> · 64728150351148599673_<20> · 82174869021302388567870545099_<29> · C132
C132 = P40 · P92
P40 = 2453756815506768300255949590474181892893_<40>
P92 = 40788935163953970485133759532334003772942726766052495834782985563446394535091642055266233843_<92>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=463793176 Step 1 took 38271ms ********** Factor found in step 1: 2453756815506768300255949590474181892893 Found probable prime factor of 40 digits: 2453756815506768300255949590474181892893 Probable prime cofactor 40788935163953970485133759532334003772942726766052495834782985563446394535091642055266233843 has 92 digits

Jun 19, 2009 (3rd)

By Dmitry Domanov / ECMNET, ggnfs/msieve 1.41, GMP-ECM 6.2.3 / Jun 18, 2009
(13·10¹⁷⁷-31)/9 = 1(4)₁₇₆1_<178> = 11 · 29 · 348544794317_<12> · 1148063635439185721_<19> · C146
C146 = P44 · P102
P44 = 25033842181419094771095940168167426214644379_<44>
P102 = 452020454928961964652287587071087355520379293916864910615544580991786263169013953137748282195897806913_<102>

C146=P44*P102 C146=25033842181419094771095940168167426214644379<44>*452020454928961964652287587071087355520379293916864910615544580991786263169013953137748282195897806913<102>

(52·10¹⁸⁷-61)/9 = 5(7)₁₈₆1_<188> = 3 · C188
C188 = P45 · P143
P45 = 997793808332543677053158286151927821814822559_<45>
P143 = 19301842824064261453747979950422179754811960550020042043615918104333792084576947186435597860092240404685797062886895860454794938508264046395623_<143>

N=19259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259257 ( 188 digits) SNFS difficulty: 189 digits. Divisors found: r1=997793808332543677053158286151927821814822559 (pp45) r2=19301842824064261453747979950422179754811960550020042043615918104333792084576947186435597860092240404685797062886895860454794938508264046395623 (pp143) Version: Msieve v. 1.41 Total time: 282.71 hours. Scaled time: 562.03 units (timescale=1.988). Factorization parameters were as follows: n: 19259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259257 m: 20000000000000000000000000000000000000 deg: 5 c5: 325 c0: -122 skew: 0.82 type: snfs lss: 1 rlim: 9900000 alim: 9900000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 9900000/9900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4950000, 9550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1870949 x 1871196 Total sieving time: 276.07 hours. Total relation processing time: 0.35 hours. Matrix solve time: 5.54 hours. Time per square root: 0.76 hours. Prototype def-par.txt line would be: snfs,189.000,5,0,0,0,0,0,0,0,0,9900000,9900000,28,28,54,54,2.5,2.5,100000 total time: 282.71 hours. --------- CPU info (if available) ----------

(56·10¹⁸²-11)/9 = 6(2)₁₈₁1_<183> = 3² · 17 · C181
C181 = P64 · P118
P64 = 2554359733901468190141458804443443258365734902731179951456506049_<64>
P118 = 1592106176735574063902134000268509870312626111202742168378927583346294201956929891804436477420044365348350553606283093_<118>

N=4066811909949164851125635439360929557007988380537400145243282498184458968772694262890341321713870733478576615831517792302106027596223674655047204066811909949164851125635439360929557 ( 181 digits) SNFS difficulty: 183 digits. Divisors found: r1=2554359733901468190141458804443443258365734902731179951456506049 (pp64) r2=1592106176735574063902134000268509870312626111202742168378927583346294201956929891804436477420044365348350553606283093 (pp118) Version: Msieve v. 1.41 Total time: 150.33 hours. Scaled time: 296.00 units (timescale=1.969). Factorization parameters were as follows: n: 4066811909949164851125635439360929557007988380537400145243282498184458968772694262890341321713870733478576615831517792302106027596223674655047204066811909949164851125635439360929557 m: 2000000000000000000000000000000000000 deg: 5 c5: 175 c0: -11 skew: 0.58 type: snfs lss: 1 rlim: 8100000 alim: 8100000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 8100000/8100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [4050000, 6450001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1499532 x 1499780 Total sieving time: 146.32 hours. Total relation processing time: 0.29 hours. Matrix solve time: 3.54 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,183.000,5,0,0,0,0,0,0,0,0,8100000,8100000,28,28,53,53,2.5,2.5,100000 total time: 150.33 hours. --------- CPU info (if available) ----------

(2·10²⁰⁷+1)/3 = (6)₂₀₆7_<207> = 11870767 · C200
C200 = P32 · C169
P32 = 12351258440178597743332350167861_<32>
C169 = [4546935055405781507044615238355866287232446105157119558592794940265286537341198984719464906928858883530666741572376981390043297745552656048588332199211361207357791391441_<169>]

GMP-ECM 6.2.3 [powered by GMP 4.3.0] [ECM] Input number is 56160369980024598803654950574521988904901146376360235751124309546861349958824620739895464772130281612524840784649102005512084153169434347979929743938758689027142615693380778737099857714894637108677701 (200 digits) Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=572703295 Step 1 took 224907ms Step 2 took 55328ms ********** Factor found in step 2: 12351258440178597743332350167861 Found probable prime factor of 32 digits: 12351258440178597743332350167861 Composite cofactor 4546935055405781507044615238355866287232446105157119558592794940265286537341198984719464906928858883530666741572376981390043297745552656048588332199211361207357791391441 has 169 digits

By Dmitry Domanov / ECMNET, ggnfs/msieve 1.41, GMP-ECM 6.2.3 / Jun 19, 2009
(16·10¹⁷¹-61)/9 = 1(7)₁₇₀1_<172> = 7 · 11 · 6869 · 478273 · C160
C160 = P58 · P103
P58 = 1326288982702582673029121665373066080254716222864506558111_<58>
P103 = 5298820469813085006548338151874038728594716331197631203696580068921274591131231214539222639337102417189_<103>

N=7027767210432017693197162292111583596851847704497755291936070419810200093347522268321872666523258643695391096428782659743696661732069745996297465301960793769979 ( 160 digits) SNFS difficulty: 172 digits. Divisors found: r1=1326288982702582673029121665373066080254716222864506558111 (pp58) r2=5298820469813085006548338151874038728594716331197631203696580068921274591131231214539222639337102417189 (pp103) Version: Msieve v. 1.41 Total time: 43.23 hours. Scaled time: 85.93 units (timescale=1.988). Factorization parameters were as follows: n: 7027767210432017693197162292111583596851847704497755291936070419810200093347522268321872666523258643695391096428782659743696661732069745996297465301960793769979 m: 20000000000000000000000000000000000 deg: 5 c5: 5 c0: -61 skew: 1.65 type: snfs lss: 1 rlim: 5200000 alim: 5200000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5200000/5200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2600000, 4800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 870887 x 871135 Total sieving time: 41.66 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.04 hours. Time per square root: 0.37 hours. Prototype def-par.txt line would be: snfs,172.000,5,0,0,0,0,0,0,0,0,5200000,5200000,27,27,52,52,2.4,2.4,100000 total time: 43.23 hours. --------- CPU info (if available) ----------

(2·10²³²+1)/3 = (6)₂₃₁7_<232> = 491 · 54681433 · C222
C222 = P34 · C188
P34 = 7430349296958259255009925644985843_<34>
C188 = [33417821221541330852542188413689425137725811211108368838101480074258853205202674229068504165866529215131936272245109112256704331846203516632198560835389525811428095563532128787664936663923_<188>]

C222=P34*C188 C222=7430349296958259255009925644985843<34>*33417821221541330852542188413689425137725811211108368838101480074258853205202674229068504165866529215131936272245109112256704331846203516632198560835389525811428095563532128787664936663923<188>

Jun 19, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Jun 18, 2009
(58·10¹⁶²-31)/9 = 6(4)₁₆₁1_<163> = 3 · 47 · 641 · 2767 · 130829 · 494051 · 271311440270983020815509571_<27> · C118
C118 = P53 · P65
P53 = 24954118155618919079580333638817425652891937701291029_<53>
P65 = 58886134193713359403521657026257990804220556027035516543340997003_<65>

Number: n N=1469451550397554580732676837059180360646094335779406648161528362300117656219537283085352644318514476025995697119786087 ( 118 digits) Divisors found: Thu Jun 18 14:54:49 2009 prp53 factor: 24954118155618919079580333638817425652891937701291029 Thu Jun 18 14:54:49 2009 prp65 factor: 58886134193713359403521657026257990804220556027035516543340997003 Thu Jun 18 14:54:49 2009 elapsed time 00:47:19 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 26.24 hours. Scaled time: 69.80 units (timescale=2.660). Factorization parameters were as follows: n: 1469451550397554580732676837059180360646094335779406648161528362300117656219537283085352644318514476025995697119786087 Y0: -46893879102853055658803 Y1: 3141268982191 c0: -3760144619058917366194126238400 c1: 68800418075202982299435180 c2: 44964992749753915636 c3: -1417804088061757 c4: -118330278 c5: 6480 skew: 268641.15 type: gnfs name: KA_6_4_161_1 rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 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 [2250000, 3700000) Primes: RFBsize:315948, AFBsize:316236, largePrimes:14559686 encountered Relations: rels:13791475, finalFF:805925 Max relations in full relation-set: 28 Initial matrix: 632261 x 805925 with sparse part having weight 75126954. Pruned matrix : 490038 x 493263 with weight 46026915. Msieve: found 1187436 hash collisions in 14695534 relations Msieve: matrix is 563385 x 563633 (154.8 MB) Total sieving time: 25.17 hours. Total relation processing time: 0.67 hours. Matrix solve time: 0.41 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,28,28,56,56,2.4,2.4,60000 total time: 26.24 hours. --------- CPU info (if available) ----------

(13·10¹⁷¹-31)/9 = 1(4)₁₇₀1_<172> = 11 · 845599 · 14030443675276817_<17> · 256462931804549017510633552397_<30> · C119
C119 = P57 · P63
P57 = 116063407036321876724157657256907246256483937762664427391_<57>
P63 = 371836804863893294145143569503109186718694143977647172218587591_<63>

Number: n N=43156646434003437590709513779974321417811490608715284910791365906651077456606782151395693253101947622545235176793105081 ( 119 digits) Divisors found: Thu Jun 18 22:22:17 2009 prp57 factor: 116063407036321876724157657256907246256483937762664427391 Thu Jun 18 22:22:17 2009 prp63 factor: 371836804863893294145143569503109186718694143977647172218587591 Thu Jun 18 22:22:17 2009 elapsed time 00:45:54 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 33.10 hours. Scaled time: 88.40 units (timescale=2.671). Factorization parameters were as follows: n: 43156646434003437590709513779974321417811490608715284910791365906651077456606782151395693253101947622545235176793105081 Y0: -82873704940012508645811 Y1: 5558225810587 c0: 390332349543191292661504637720 c1: 11283470990773849387345742 c2: 27771274009983295117 c3: -848230578916907 c4: -1954794837 c5: 11040 skew: 148251.93 type: gnfs name: KA_1_4_170_1 rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 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 [2250000, 4100000) Primes: RFBsize:315948, AFBsize:315748, largePrimes:14766964 encountered Relations: rels:14062877, finalFF:788445 Max relations in full relation-set: 28 Initial matrix: 631777 x 788445 with sparse part having weight 79095519. Pruned matrix : 509527 x 512749 with weight 52748937. Msieve: found 1396489 hash collisions in 15182031 relations Msieve: matrix is 605319 x 605567 (165.1 MB) Total sieving time: 31.45 hours. Total relation processing time: 0.85 hours. Matrix solve time: 0.80 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,28,28,56,56,2.4,2.4,60000 total time: 33.10 hours. --------- CPU info (if available) ----------

By Robert Backstrom / GGNFS, Msieve / Jun 19, 2009
(14·10¹⁷¹-41)/9 = 1(5)₁₇₀1_<172> = 3 · 11 · 144264311 · C162
C162 = P58 · P104
P58 = 8422572196437277344165892625074975797910517101552896422569_<58>
P104 = 38794301624236914293793808123357843854869719962248434313381337905654704362886863912964954781426002751633_<104>

Number: n N=326747806240499343230759596100293564963118613154761041676746005032714834420399700505602789363046603661020070633672157059323827132394838374455190425704435922805177 ( 162 digits) SNFS difficulty: 172 digits. Divisors found: Fri Jun 19 11:40:48 2009 prp58 factor: 8422572196437277344165892625074975797910517101552896422569 Fri Jun 19 11:40:48 2009 prp104 factor: 38794301624236914293793808123357843854869719962248434313381337905654704362886863912964954781426002751633 Fri Jun 19 11:40:48 2009 elapsed time 01:16:46 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 55.33 hours. Scaled time: 143.58 units (timescale=2.595). Factorization parameters were as follows: name: KA_1_5_170_1 n: 326747806240499343230759596100293564963118613154761041676746005032714834420399700505602789363046603661020070633672157059323827132394838374455190425704435922805177 m: 10000000000000000000000000000000000 deg: 5 c5: 140 c0: -41 skew: 0.78 type: snfs lss: 1 rlim: 5200000 alim: 5200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 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 [2600000, 5682731) Primes: RFBsize:361407, AFBsize:361488, largePrimes:17700805 encountered Relations: rels:17570935, finalFF:657599 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2124084 hash collisions in 19715067 relations Msieve: matrix is 839295 x 839543 (222.4 MB) Total sieving time: 54.53 hours. Total relation processing time: 0.80 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,172,5,0,0,0,0,0,0,0,0,5200000,5200000,28,28,56,56,2.4,2.4,100000 total time: 55.33 hours. --------- CPU info (if available) ----------

Jun 19, 2009

By Jo Yeong Uk / GGNFS/Msieve v1.39, GMP-ECM 6.2.3, YAFU 1.10, Msieve 1.38 / Jun 18, 2009
(2·10¹⁸⁹+1)/3 = (6)₁₈₈7_<189> = 258925710247_<12> · 697907276489069_<15> · 103472810660886766470523_<24> · C140
C140 = P55 · P85
P55 = 4746350295580571237653643884883727173586562822307651507_<55>
P85 = 7511900121266661845814589063433511839761657945042526497565623384799661040038440081329_<85>

Number: 66667_189 N=35654109360945749376081662769339983989787406080664915477018647301233533367134903422592365407581183879146350856255226267556261179388069412803 ( 140 digits) SNFS difficulty: 190 digits. Divisors found: r1=4746350295580571237653643884883727173586562822307651507 r2=7511900121266661845814589063433511839761657945042526497565623384799661040038440081329 Version: Total time: 121.93 hours. Scaled time: 291.79 units (timescale=2.393). Factorization parameters were as follows: n: 35654109360945749376081662769339983989787406080664915477018647301233533367134903422592365407581183879146350856255226267556261179388069412803 m: 100000000000000000000000000000000000000 deg: 5 c5: 1 c0: 5 skew: 1.38 type: snfs lss: 1 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4500000, 7700001) Primes: rational ideals reading, algebraic ideals reading, Relations: 20417084 Max relations in full relation-set: Initial matrix: Pruned matrix : 1659788 x 1660036 Total sieving time: 112.16 hours. Total relation processing time: 3.42 hours. Matrix solve time: 6.18 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: snfs,190,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,54,54,2.5,2.5,100000 total time: 121.93 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672386) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672306) Calibrating delay using timer specific routine.. 5237.81 BogoMIPS (lpj=2618905)

(2·10²²⁹+1)/3 = (6)₂₂₈7_<229> = 7² · 23321 · 23767 · 322159063 · 78124519400027_<14> · 1738216785948389_<16> · 13256504103154300738627_<23> · C159
C159 = P34 · P37 · P41 · P49
P34 = 1237470824271985512472690448473327_<34>
P37 = 3750161593708449394591669208868139007_<37>
P41 = 18395753866925715147248317212109801384969_<41>
P49 = 4957901829527390747060609927610231043240041489103_<49>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 423253407774740648022246108235966296444851118790323740603674354528601384880202632965018613844937841027261734318817645520742415810378445164456463254205170583223 (159 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=704297402 Step 1 took 5585ms Step 2 took 4914ms ********** Factor found in step 2: 1237470824271985512472690448473327 Found probable prime factor of 34 digits: 1237470824271985512472690448473327 Composite cofactor 342031019619185111284341039676048075550210964995684373883223922629868991470538634305390046991088073329628622395980813626622649 has 126 digits GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 342031019619185111284341039676048075550210964995684373883223922629868991470538634305390046991088073329628622395980813626622649 (126 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4528562233 Step 1 took 4165ms Step 2 took 4103ms ********** Factor found in step 2: 3750161593708449394591669208868139007 Found probable prime factor of 37 digits: 3750161593708449394591669208868139007 Composite cofactor 91204341752366576110296493038317865627250705073055612416739775293441219621456530521492807 has 89 digits 06/18/09 22:22:38 v1.10 @ 조영욱-PC, starting SIQS on c89: 91204341752366576110296493038317865627250705073055612416739775293441219621456530521492807 06/18/09 22:22:38 v1.10 @ 조영욱-PC, random seeds: 1827674413, 2265870248 06/18/09 22:22:38 v1.10 @ 조영욱-PC, ==== sieve params ==== 06/18/09 22:22:38 v1.10 @ 조영욱-PC, n = 89 digits, 302 bits 06/18/09 22:22:38 v1.10 @ 조영욱-PC, factor base: 64055 primes (max prime = 1699001) 06/18/09 22:22:38 v1.10 @ 조영욱-PC, single large prime cutoff: 186890110 (110 * pmax) 06/18/09 22:22:38 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits 06/18/09 22:22:38 v1.10 @ 조영욱-PC, double large prime cutoff: 774203936799977 06/18/09 22:22:38 v1.10 @ 조영욱-PC, using 15 large prime slices of factor base 06/18/09 22:22:38 v1.10 @ 조영욱-PC, buckets hold 1024 elements 06/18/09 22:22:38 v1.10 @ 조영욱-PC, sieve interval: 9 blocks of size 65536 06/18/09 22:22:38 v1.10 @ 조영욱-PC, polynomial A has ~ 12 factors 06/18/09 22:22:38 v1.10 @ 조영욱-PC, using multiplier of 55 06/18/09 22:22:38 v1.10 @ 조영욱-PC, using small prime variation correction of 21 bits 06/18/09 22:22:38 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning 06/18/09 22:22:38 v1.10 @ 조영욱-PC, trial factoring cutoff at 101 bits 06/18/09 22:22:38 v1.10 @ 조영욱-PC, ==== sieving started ==== 06/18/09 23:09:51 v1.10 @ 조영욱-PC, sieve time = 1414.9750, relation time = 346.6610, poly_time = 1070.8390 06/18/09 23:09:51 v1.10 @ 조영욱-PC, 64149 relations found: 22732 full + 41417 from 529677 partial, using 563791 polys (276 A polys) 06/18/09 23:09:51 v1.10 @ 조영욱-PC, on average, sieving found 0.98 rels/poly and 194.96 rels/sec 06/18/09 23:09:51 v1.10 @ 조영욱-PC, trial division touched 12214549 sieve locations out of 665074925568 06/18/09 23:09:51 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ==== 06/18/09 23:09:52 v1.10 @ 조영욱-PC, begin with 552409 relations 06/18/09 23:09:52 v1.10 @ 조영욱-PC, reduce to 123820 relations in 8 passes 06/18/09 23:09:53 v1.10 @ 조영욱-PC, recovered 123820 relations 06/18/09 23:09:53 v1.10 @ 조영욱-PC, recovered 111157 polynomials 06/18/09 23:09:53 v1.10 @ 조영욱-PC, attempting to build 64149 cycles 06/18/09 23:09:53 v1.10 @ 조영욱-PC, found 64149 cycles in 4 passes 06/18/09 23:09:53 v1.10 @ 조영욱-PC, distribution of cycle lengths: 06/18/09 23:09:53 v1.10 @ 조영욱-PC, length 1 : 22732 06/18/09 23:09:53 v1.10 @ 조영욱-PC, length 2 : 19952 06/18/09 23:09:53 v1.10 @ 조영욱-PC, length 3 : 11344 06/18/09 23:09:53 v1.10 @ 조영욱-PC, length 4 : 5697 06/18/09 23:09:53 v1.10 @ 조영욱-PC, length 5 : 2597 06/18/09 23:09:53 v1.10 @ 조영욱-PC, length 6 : 1045 06/18/09 23:09:53 v1.10 @ 조영욱-PC, length 7 : 482 06/18/09 23:09:53 v1.10 @ 조영욱-PC, length 9+: 300 06/18/09 23:09:53 v1.10 @ 조영욱-PC, largest cycle: 16 relations 06/18/09 23:09:53 v1.10 @ 조영욱-PC, matrix is 64055 x 64149 (13.5 MB) with weight 3021778 (47.11/col) 06/18/09 23:09:53 v1.10 @ 조영욱-PC, sparse part has weight 3021778 (47.11/col) 06/18/09 23:09:54 v1.10 @ 조영욱-PC, filtering completed in 3 passes 06/18/09 23:09:54 v1.10 @ 조영욱-PC, matrix is 56373 x 56437 (12.1 MB) with weight 2721078 (48.21/col) 06/18/09 23:09:54 v1.10 @ 조영욱-PC, sparse part has weight 2721078 (48.21/col) 06/18/09 23:09:54 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later 06/18/09 23:09:54 v1.10 @ 조영욱-PC, matrix is 56325 x 56437 (8.0 MB) with weight 2068248 (36.65/col) 06/18/09 23:09:54 v1.10 @ 조영욱-PC, sparse part has weight 1535318 (27.20/col) 06/18/09 23:09:54 v1.10 @ 조영욱-PC, matrix includes 64 packed rows 06/18/09 23:09:54 v1.10 @ 조영욱-PC, using block size 22574 for processor cache size 4096 kB 06/18/09 23:09:54 v1.10 @ 조영욱-PC, commencing Lanczos iteration 06/18/09 23:09:54 v1.10 @ 조영욱-PC, memory use: 7.4 MB 06/18/09 23:10:06 v1.10 @ 조영욱-PC, lanczos halted after 892 iterations (dim = 56323) 06/18/09 23:10:06 v1.10 @ 조영욱-PC, recovered 18 nontrivial dependencies 06/18/09 23:10:06 v1.10 @ 조영욱-PC, prp49 = 4957901829527390747060609927610231043240041489103 06/18/09 23:10:07 v1.10 @ 조영욱-PC, prp41 = 18395753866925715147248317212109801384969 06/18/09 23:10:07 v1.10 @ 조영욱-PC, Lanczos elapsed time = 14.3360 seconds. 06/18/09 23:10:07 v1.10 @ 조영욱-PC, Sqrt elapsed time = 0.9360 seconds. 06/18/09 23:10:07 v1.10 @ 조영욱-PC, SIQS elapsed time = 2848.7480 seconds. 06/18/09 23:10:07 v1.10 @ 조영욱-PC, 06/18/09 23:10:07 v1.10 @ 조영욱-PC,

By Jo Yeong Uk / GMP-ECM 6.2.3, YAFU 1.10, Msieve 1.38 / Jun 19, 2009
(2·10²⁴⁵+1)/3 = (6)₂₄₄7_<245> = 23 · 153669121 · 869061193254415949_<18> · 38056099737006898261987_<23> · 39366916868321772201193201_<26> · C170
C170 = P42 · C129
P42 = 143367365426738090002045861251553483338881_<42>
C129 = [101050381168499134820535981759329661173475719716918113615492884413715003106991408503990025473220959006588553102747390264655274683_<129>]

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 14487326923495388617824015611778517505155899148341968548636740762719170987406338312232633735870766518958322657602899284502551991614008890281311729164701564107015028849723 (170 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3765053233 Step 1 took 4782ms Step 2 took 2800ms ********** Factor found in step 2: 143367365426738090002045861251553483338881 Found probable prime factor of 42 digits: 143367365426738090002045861251553483338881 Composite cofactor 101050381168499134820535981759329661173475719716918113615492884413715003106991408503990025473220959006588553102747390264655274683 has 129 digits

(2·10²¹³+1)/3 = (6)₂₁₂7_<213> = 642623 · 68623043 · 1464084467605343_<16> · 4409891276148706861866704821_<28> · 118009803355233384577031249267259421_<36> · C122
C122 = P34 · P42 · P47
P34 = 7115150503396792667994916837952063_<34>
P42 = 166507482518017499178086786863171180756723_<42>
P47 = 16747599071352727268207577662937259514746886269_<47>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 19841312675353812400480170290920785443960159561950228060042177768467208735513015756609844426709640725339681886570157222681 (122 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2561369874 Step 1 took 4197ms Step 2 took 4383ms ********** Factor found in step 2: 7115150503396792667994916837952063 Found probable prime factor of 34 digits: 7115150503396792667994916837952063 Composite cofactor 2788600559592030339441370842570956136373448758960749300573053163294910487916335438136487 has 88 digits 06/19/09 10:49:18 v1.10 @ 조영욱-PC, starting SIQS on c88: 2788600559592030339441370842570956136373448758960749300573053163294910487916335438136487 06/19/09 10:49:18 v1.10 @ 조영욱-PC, random seeds: 3105731754, 2216531008 06/19/09 10:49:18 v1.10 @ 조영욱-PC, ==== sieve params ==== 06/19/09 10:49:18 v1.10 @ 조영욱-PC, n = 88 digits, 294 bits 06/19/09 10:49:18 v1.10 @ 조영욱-PC, factor base: 61083 primes (max prime = 1621237) 06/19/09 10:49:18 v1.10 @ 조영욱-PC, single large prime cutoff: 178336070 (110 * pmax) 06/19/09 10:49:18 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits 06/19/09 10:49:18 v1.10 @ 조영욱-PC, double large prime cutoff: 711591161729305 06/19/09 10:49:18 v1.10 @ 조영욱-PC, using 15 large prime slices of factor base 06/19/09 10:49:18 v1.10 @ 조영욱-PC, buckets hold 1024 elements 06/19/09 10:49:18 v1.10 @ 조영욱-PC, sieve interval: 9 blocks of size 65536 06/19/09 10:49:18 v1.10 @ 조영욱-PC, polynomial A has ~ 11 factors 06/19/09 10:49:18 v1.10 @ 조영욱-PC, using multiplier of 7 06/19/09 10:49:18 v1.10 @ 조영욱-PC, using small prime variation correction of 21 bits 06/19/09 10:49:18 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning 06/19/09 10:49:18 v1.10 @ 조영욱-PC, trial factoring cutoff at 97 bits 06/19/09 10:49:18 v1.10 @ 조영욱-PC, ==== sieving started ==== 06/19/09 11:14:09 v1.10 @ 조영욱-PC, sieve time = 705.0230, relation time = 283.2280, poly_time = 502.4320 06/19/09 11:14:09 v1.10 @ 조영욱-PC, 61155 relations found: 22477 full + 38678 from 495499 partial, using 270969 polys (264 A polys) 06/19/09 11:14:09 v1.10 @ 조영욱-PC, on average, sieving found 1.91 rels/poly and 347.31 rels/sec 06/19/09 11:14:09 v1.10 @ 조영욱-PC, trial division touched 11124401 sieve locations out of 319648038912 06/19/09 11:14:09 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ==== 06/19/09 11:14:09 v1.10 @ 조영욱-PC, begin with 517976 relations 06/19/09 11:14:09 v1.10 @ 조영욱-PC, reduce to 116716 relations in 7 passes 06/19/09 11:14:10 v1.10 @ 조영욱-PC, failed to read relation 31420 06/19/09 11:14:10 v1.10 @ 조영욱-PC, failed to read relation 63878 06/19/09 11:14:10 v1.10 @ 조영욱-PC, recovered 116714 relations 06/19/09 11:14:10 v1.10 @ 조영욱-PC, recovered 95103 polynomials 06/19/09 11:14:10 v1.10 @ 조영욱-PC, attempting to build 61153 cycles 06/19/09 11:14:10 v1.10 @ 조영욱-PC, found 61153 cycles in 4 passes 06/19/09 11:14:10 v1.10 @ 조영욱-PC, distribution of cycle lengths: 06/19/09 11:14:10 v1.10 @ 조영욱-PC, length 1 : 22477 06/19/09 11:14:10 v1.10 @ 조영욱-PC, length 2 : 18718 06/19/09 11:14:10 v1.10 @ 조영욱-PC, length 3 : 10834 06/19/09 11:14:10 v1.10 @ 조영욱-PC, length 4 : 5187 06/19/09 11:14:10 v1.10 @ 조영욱-PC, length 5 : 2310 06/19/09 11:14:10 v1.10 @ 조영욱-PC, length 6 : 994 06/19/09 11:14:10 v1.10 @ 조영욱-PC, length 7 : 410 06/19/09 11:14:10 v1.10 @ 조영욱-PC, length 9+: 223 06/19/09 11:14:10 v1.10 @ 조영욱-PC, largest cycle: 13 relations 06/19/09 11:14:11 v1.10 @ 조영욱-PC, matrix is 61083 x 61153 (12.3 MB) with weight 2744311 (44.88/col) 06/19/09 11:14:11 v1.10 @ 조영욱-PC, sparse part has weight 2744311 (44.88/col) 06/19/09 11:14:11 v1.10 @ 조영욱-PC, filtering completed in 4 passes 06/19/09 11:14:11 v1.10 @ 조영욱-PC, matrix is 52042 x 52106 (10.8 MB) with weight 2412409 (46.30/col) 06/19/09 11:14:11 v1.10 @ 조영욱-PC, sparse part has weight 2412409 (46.30/col) 06/19/09 11:14:11 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later 06/19/09 11:14:11 v1.10 @ 조영욱-PC, matrix is 51994 x 52106 (7.5 MB) with weight 1883866 (36.15/col) 06/19/09 11:14:11 v1.10 @ 조영욱-PC, sparse part has weight 1455034 (27.92/col) 06/19/09 11:14:11 v1.10 @ 조영욱-PC, matrix includes 64 packed rows 06/19/09 11:14:11 v1.10 @ 조영욱-PC, using block size 20842 for processor cache size 4096 kB 06/19/09 11:14:11 v1.10 @ 조영욱-PC, commencing Lanczos iteration 06/19/09 11:14:11 v1.10 @ 조영욱-PC, memory use: 6.9 MB 06/19/09 11:14:21 v1.10 @ 조영욱-PC, lanczos halted after 824 iterations (dim = 51989) 06/19/09 11:14:21 v1.10 @ 조영욱-PC, recovered 14 nontrivial dependencies 06/19/09 11:14:22 v1.10 @ 조영욱-PC, prp42 = 166507482518017499178086786863171180756723 06/19/09 11:14:22 v1.10 @ 조영욱-PC, prp47 = 16747599071352727268207577662937259514746886269 06/19/09 11:14:22 v1.10 @ 조영욱-PC, Lanczos elapsed time = 12.3240 seconds. 06/19/09 11:14:22 v1.10 @ 조영욱-PC, Sqrt elapsed time = 0.5620 seconds. 06/19/09 11:14:22 v1.10 @ 조영욱-PC, SIQS elapsed time = 1504.2710 seconds. 06/19/09 11:14:22 v1.10 @ 조영욱-PC, 06/19/09 11:14:22 v1.10 @ 조영욱-PC,

Jun 18, 2009

By Serge Batalov / PFGW / Jun 17, 2009
(2·10⁵⁵⁵⁴⁴+1)/3 = (6)₅₅₅₄₃7_<55544> is PRP.

Jun 17, 2009 (6th)

By Andreas Tete / Msieve 1.42/GGNFS / Jun 17, 2009
(68·10¹⁷⁰+13)/9 = 7(5)₁₆₉7_<171> = 139 · 29473 · 290911573 · 32154519786569_<14> · 23839585429968260174265553579269018490660487_<44> · C99
C99 = P49 · P51
P49 = 3094951329199020842510313392944073185116931701059_<49>
P51 = 267221692159180547256882648639110381886247612020911_<51>

Tue Jun 16 22:04:28 2009 Msieve v. 1.42 Tue Jun 16 22:04:28 2009 random seeds: ea0da198 42de2300 Tue Jun 16 22:04:28 2009 factoring 827038131338867400594187976741748355884015349016991665314607084014181746469763768683616779908844749 (99 digits) Tue Jun 16 22:04:28 2009 searching for 15-digit factors Tue Jun 16 22:04:30 2009 commencing quadratic sieve (99-digit input) Tue Jun 16 22:04:30 2009 using multiplier of 5 Tue Jun 16 22:04:30 2009 using 32kb Intel Core sieve core Tue Jun 16 22:04:30 2009 sieve interval: 36 blocks of size 32768 Tue Jun 16 22:04:30 2009 processing polynomials in batches of 6 Tue Jun 16 22:04:30 2009 using a sieve bound of 2642771 (96471 primes) Tue Jun 16 22:04:30 2009 using large prime bound of 396415650 (28 bits) Tue Jun 16 22:04:30 2009 using double large prime bound of 2996893989271350 (43-52 bits) Tue Jun 16 22:04:30 2009 using trial factoring cutoff of 52 bits Tue Jun 16 22:04:30 2009 polynomial 'A' values have 13 factors Tue Jun 16 22:04:42 2009 restarting with 20829 full and 1327127 partial relations Tue Jun 16 22:45:30 2009 96657 relations (22826 full + 73831 combined from 1456926 partial), need 96567 Tue Jun 16 22:45:42 2009 begin with 1479752 relations Tue Jun 16 22:45:43 2009 reduce to 256034 relations in 11 passes Tue Jun 16 22:45:43 2009 attempting to read 256034 relations Tue Jun 16 22:45:47 2009 recovered 256034 relations Tue Jun 16 22:45:47 2009 recovered 247013 polynomials Tue Jun 16 22:45:47 2009 attempting to build 96657 cycles Tue Jun 16 22:45:47 2009 found 96655 cycles in 5 passes Tue Jun 16 22:45:47 2009 distribution of cycle lengths: Tue Jun 16 22:45:47 2009 length 1 : 22826 Tue Jun 16 22:45:47 2009 length 2 : 16496 Tue Jun 16 22:45:47 2009 length 3 : 16148 Tue Jun 16 22:45:47 2009 length 4 : 13213 Tue Jun 16 22:45:47 2009 length 5 : 10056 Tue Jun 16 22:45:47 2009 length 6 : 7061 Tue Jun 16 22:45:47 2009 length 7 : 4484 Tue Jun 16 22:45:47 2009 length 9+: 6371 Tue Jun 16 22:45:47 2009 largest cycle: 19 relations Tue Jun 16 22:45:47 2009 matrix is 96471 x 96655 (25.0 MB) with weight 6159330 (63.72/col) Tue Jun 16 22:45:47 2009 sparse part has weight 6159330 (63.72/col) Tue Jun 16 22:45:48 2009 filtering completed in 3 passes Tue Jun 16 22:45:48 2009 matrix is 92701 x 92765 (24.1 MB) with weight 5939028 (64.02/col) Tue Jun 16 22:45:48 2009 sparse part has weight 5939028 (64.02/col) Tue Jun 16 22:45:48 2009 saving the first 48 matrix rows for later Tue Jun 16 22:45:48 2009 matrix is 92653 x 92765 (13.4 MB) with weight 4416948 (47.61/col) Tue Jun 16 22:45:48 2009 sparse part has weight 2953275 (31.84/col) Tue Jun 16 22:45:48 2009 matrix includes 64 packed rows Tue Jun 16 22:45:48 2009 using block size 37106 for processor cache size 2048 kB Tue Jun 16 22:45:49 2009 commencing Lanczos iteration Tue Jun 16 22:45:49 2009 memory use: 14.2 MB Tue Jun 16 22:46:25 2009 lanczos halted after 1466 iterations (dim = 92652) Tue Jun 16 22:46:25 2009 recovered 17 nontrivial dependencies Tue Jun 16 22:46:26 2009 prp49 factor: 3094951329199020842510313392944073185116931701059 Tue Jun 16 22:46:26 2009 prp51 factor: 267221692159180547256882648639110381886247612020911 Tue Jun 16 22:46:26 2009 elapsed time 00:41:58 Tue Jun 16 22:46:26 2009 total time 07:44:45

(17·10¹⁷⁰+7)/3 = 5(6)₁₆₉9_<171> = 559631 · 104675792068314853_<18> · 322875512531802497_<18> · 162573751231188186196793586329_<30> · C102
C102 = P39 · P64
P39 = 102486391641802624865794677615608882159_<39>
P64 = 1798158246875135173916969236304899898630006002386192375498498449_<64>

Wed Jun 17 10:43:02 2009 Msieve v. 1.42 Wed Jun 17 10:43:02 2009 random seeds: 433ed298 64d9e482 Wed Jun 17 10:43:02 2009 factoring 184286750323182314380444905316628685751186302523555068558316595554862239297139529533915383571885271391 (102 digits) Wed Jun 17 10:43:03 2009 searching for 15-digit factors Wed Jun 17 10:43:04 2009 commencing number field sieve (102-digit input) Wed Jun 17 10:43:04 2009 R0: -48886729453583034047 Wed Jun 17 10:43:04 2009 R1: 27538271657 Wed Jun 17 10:43:04 2009 A0: 1655221487135049353428650 Wed Jun 17 10:43:04 2009 A1: 139986539947248807243 Wed Jun 17 10:43:04 2009 A2: -493487056659667 Wed Jun 17 10:43:04 2009 A3: -286852384879 Wed Jun 17 10:43:04 2009 A4: -12793664 Wed Jun 17 10:43:04 2009 A5: 660 Wed Jun 17 10:43:04 2009 skew 23388.86, size 1.238991e-009, alpha -4.826938, combined = 2.969698e-009 Wed Jun 17 10:43:04 2009 Wed Jun 17 10:43:04 2009 commencing relation filtering Wed Jun 17 10:43:04 2009 commencing duplicate removal, pass 1 Wed Jun 17 10:43:38 2009 found 226641 hash collisions in 3981204 relations Wed Jun 17 10:43:49 2009 added 30399 free relations Wed Jun 17 10:43:49 2009 commencing duplicate removal, pass 2 Wed Jun 17 10:43:54 2009 found 206333 duplicates and 3805269 unique relations Wed Jun 17 10:43:54 2009 memory use: 36.7 MB Wed Jun 17 10:43:54 2009 reading rational ideals above 2162688 Wed Jun 17 10:43:54 2009 reading algebraic ideals above 2162688 Wed Jun 17 10:43:54 2009 commencing singleton removal, pass 1 Wed Jun 17 10:44:30 2009 relations with 0 large ideals: 87613 Wed Jun 17 10:44:30 2009 relations with 1 large ideals: 607266 Wed Jun 17 10:44:30 2009 relations with 2 large ideals: 1422964 Wed Jun 17 10:44:30 2009 relations with 3 large ideals: 1293039 Wed Jun 17 10:44:30 2009 relations with 4 large ideals: 365325 Wed Jun 17 10:44:30 2009 relations with 5 large ideals: 0 Wed Jun 17 10:44:30 2009 relations with 6 large ideals: 29062 Wed Jun 17 10:44:30 2009 relations with 7+ large ideals: 0 Wed Jun 17 10:44:30 2009 3805269 relations and about 3828438 large ideals Wed Jun 17 10:44:30 2009 commencing singleton removal, pass 2 Wed Jun 17 10:45:06 2009 found 1847305 singletons Wed Jun 17 10:45:06 2009 current dataset: 1957964 relations and about 1579102 large ideals Wed Jun 17 10:45:06 2009 commencing singleton removal, pass 3 Wed Jun 17 10:45:31 2009 found 388897 singletons Wed Jun 17 10:45:31 2009 current dataset: 1569067 relations and about 1160524 large ideals Wed Jun 17 10:45:31 2009 commencing singleton removal, final pass Wed Jun 17 10:45:50 2009 memory use: 24.2 MB Wed Jun 17 10:45:50 2009 commencing in-memory singleton removal Wed Jun 17 10:45:50 2009 begin with 1569067 relations and 1190472 unique ideals Wed Jun 17 10:45:51 2009 reduce to 1319249 relations and 933729 ideals in 13 passes Wed Jun 17 10:45:51 2009 max relations containing the same ideal: 16 Wed Jun 17 10:45:51 2009 reading rational ideals above 100000 Wed Jun 17 10:45:51 2009 reading algebraic ideals above 100000 Wed Jun 17 10:45:51 2009 commencing singleton removal, final pass Wed Jun 17 10:46:09 2009 keeping 1233284 ideals with weight <= 25, new excess is 99584 Wed Jun 17 10:46:11 2009 memory use: 34.3 MB Wed Jun 17 10:46:11 2009 commencing in-memory singleton removal Wed Jun 17 10:46:11 2009 begin with 1332898 relations and 1233284 unique ideals Wed Jun 17 10:46:12 2009 reduce to 1310030 relations and 1144254 ideals in 12 passes Wed Jun 17 10:46:12 2009 max relations containing the same ideal: 25 Wed Jun 17 10:46:13 2009 removing 196021 relations and 170892 ideals in 25129 cliques Wed Jun 17 10:46:13 2009 commencing in-memory singleton removal Wed Jun 17 10:46:13 2009 begin with 1114009 relations and 1144254 unique ideals Wed Jun 17 10:46:14 2009 reduce to 1095209 relations and 954131 ideals in 9 passes Wed Jun 17 10:46:14 2009 max relations containing the same ideal: 25 Wed Jun 17 10:46:15 2009 removing 146412 relations and 121283 ideals in 25129 cliques Wed Jun 17 10:46:15 2009 commencing in-memory singleton removal Wed Jun 17 10:46:15 2009 begin with 948797 relations and 954131 unique ideals Wed Jun 17 10:46:15 2009 reduce to 934995 relations and 818721 ideals in 7 passes Wed Jun 17 10:46:15 2009 max relations containing the same ideal: 25 Wed Jun 17 10:46:16 2009 relations with 0 large ideals: 4286 Wed Jun 17 10:46:16 2009 relations with 1 large ideals: 38985 Wed Jun 17 10:46:16 2009 relations with 2 large ideals: 142845 Wed Jun 17 10:46:16 2009 relations with 3 large ideals: 264588 Wed Jun 17 10:46:16 2009 relations with 4 large ideals: 270213 Wed Jun 17 10:46:16 2009 relations with 5 large ideals: 154225 Wed Jun 17 10:46:16 2009 relations with 6 large ideals: 50521 Wed Jun 17 10:46:16 2009 relations with 7+ large ideals: 9332 Wed Jun 17 10:46:16 2009 commencing 2-way merge Wed Jun 17 10:46:16 2009 reduce to 557916 relation sets and 441642 unique ideals Wed Jun 17 10:46:16 2009 commencing full merge Wed Jun 17 10:46:24 2009 memory use: 36.4 MB Wed Jun 17 10:46:24 2009 found 262675 cycles, need 247842 Wed Jun 17 10:46:24 2009 weight of 247842 cycles is about 17409653 (70.24/cycle) Wed Jun 17 10:46:24 2009 distribution of cycle lengths: Wed Jun 17 10:46:24 2009 1 relations: 23301 Wed Jun 17 10:46:24 2009 2 relations: 24561 Wed Jun 17 10:46:24 2009 3 relations: 24959 Wed Jun 17 10:46:24 2009 4 relations: 23784 Wed Jun 17 10:46:24 2009 5 relations: 22348 Wed Jun 17 10:46:24 2009 6 relations: 19801 Wed Jun 17 10:46:24 2009 7 relations: 18209 Wed Jun 17 10:46:24 2009 8 relations: 16045 Wed Jun 17 10:46:24 2009 9 relations: 14195 Wed Jun 17 10:46:24 2009 10+ relations: 60639 Wed Jun 17 10:46:24 2009 heaviest cycle: 19 relations Wed Jun 17 10:46:24 2009 commencing cycle optimization Wed Jun 17 10:46:25 2009 start with 1626188 relations Wed Jun 17 10:46:29 2009 pruned 47838 relations Wed Jun 17 10:46:29 2009 memory use: 41.4 MB Wed Jun 17 10:46:29 2009 distribution of cycle lengths: Wed Jun 17 10:46:29 2009 1 relations: 23301 Wed Jun 17 10:46:29 2009 2 relations: 25154 Wed Jun 17 10:46:29 2009 3 relations: 26000 Wed Jun 17 10:46:29 2009 4 relations: 24495 Wed Jun 17 10:46:29 2009 5 relations: 23048 Wed Jun 17 10:46:29 2009 6 relations: 20446 Wed Jun 17 10:46:29 2009 7 relations: 18605 Wed Jun 17 10:46:29 2009 8 relations: 16292 Wed Jun 17 10:46:29 2009 9 relations: 14364 Wed Jun 17 10:46:29 2009 10+ relations: 56137 Wed Jun 17 10:46:29 2009 heaviest cycle: 19 relations Wed Jun 17 10:46:29 2009 RelProcTime: 193 Wed Jun 17 10:46:29 2009 Wed Jun 17 10:46:29 2009 commencing linear algebra Wed Jun 17 10:46:29 2009 read 247842 cycles Wed Jun 17 10:46:30 2009 cycles contain 843980 unique relations Wed Jun 17 10:46:43 2009 read 843980 relations Wed Jun 17 10:46:44 2009 using 20 quadratic characters above 67106562 Wed Jun 17 10:46:49 2009 building initial matrix Wed Jun 17 10:47:00 2009 memory use: 91.7 MB Wed Jun 17 10:47:01 2009 read 247842 cycles Wed Jun 17 10:47:01 2009 matrix is 247647 x 247842 (70.5 MB) with weight 23537024 (94.97/col) Wed Jun 17 10:47:01 2009 sparse part has weight 16510401 (66.62/col) Wed Jun 17 10:47:04 2009 filtering completed in 2 passes Wed Jun 17 10:47:04 2009 matrix is 246637 x 246832 (70.4 MB) with weight 23478090 (95.12/col) Wed Jun 17 10:47:04 2009 sparse part has weight 16482270 (66.78/col) Wed Jun 17 10:47:05 2009 read 246832 cycles Wed Jun 17 10:47:06 2009 matrix is 246637 x 246832 (70.4 MB) with weight 23478090 (95.12/col) Wed Jun 17 10:47:06 2009 sparse part has weight 16482270 (66.78/col) Wed Jun 17 10:47:06 2009 saving the first 48 matrix rows for later Wed Jun 17 10:47:06 2009 matrix is 246589 x 246832 (67.2 MB) with weight 18694202 (75.74/col) Wed Jun 17 10:47:06 2009 sparse part has weight 16146110 (65.41/col) Wed Jun 17 10:47:06 2009 matrix includes 64 packed rows Wed Jun 17 10:47:06 2009 using block size 65536 for processor cache size 3072 kB Wed Jun 17 10:47:08 2009 commencing Lanczos iteration Wed Jun 17 10:47:08 2009 memory use: 65.0 MB Wed Jun 17 10:55:12 2009 lanczos halted after 3903 iterations (dim = 246589) Wed Jun 17 10:55:13 2009 recovered 36 nontrivial dependencies Wed Jun 17 10:55:13 2009 BLanczosTime: 524 Wed Jun 17 10:55:13 2009 Wed Jun 17 10:55:13 2009 commencing square root phase Wed Jun 17 10:55:13 2009 reading relations for dependency 1 Wed Jun 17 10:55:13 2009 read 123117 cycles Wed Jun 17 10:55:14 2009 cycles contain 520801 unique relations Wed Jun 17 10:55:20 2009 read 520801 relations Wed Jun 17 10:55:22 2009 multiplying 420376 relations Wed Jun 17 10:56:05 2009 multiply complete, coefficients have about 15.35 million bits Wed Jun 17 10:56:06 2009 initial square root is modulo 656468557 Wed Jun 17 10:57:29 2009 reading relations for dependency 2 Wed Jun 17 10:57:30 2009 read 123574 cycles Wed Jun 17 10:57:30 2009 cycles contain 523003 unique relations Wed Jun 17 10:57:43 2009 read 523003 relations Wed Jun 17 10:57:45 2009 multiplying 421782 relations Wed Jun 17 10:58:28 2009 multiply complete, coefficients have about 15.40 million bits Wed Jun 17 10:58:29 2009 initial square root is modulo 703063901 Wed Jun 17 10:59:51 2009 sqrtTime: 278 Wed Jun 17 10:59:51 2009 prp39 factor: 102486391641802624865794677615608882159 Wed Jun 17 10:59:51 2009 prp64 factor: 1798158246875135173916969236304899898630006002386192375498498449 Wed Jun 17 10:59:51 2009 elapsed time 00:16:49 total time 4,5 hours

Jun 17, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / Jun 17, 2009
(58·10¹⁵²-31)/9 = 6(4)₁₅₁1_<153> = 43 · 59 · 1387660273_<10> · 6622312771_<10> · 2204947328723_<13> · C119
C119 = P50 · P69
P50 = 29094058807903755108349233484470242778633421481941_<50>
P69 = 430893200761032977032832794015273047754856060570037729587831660047397_<69>

Number: n N=12536432122867372519200253053164652442871301443065502726646145676657703651611969289789345370155994930176926330039557577 ( 119 digits) SNFS difficulty: 154 digits. Divisors found: Wed Jun 17 16:40:36 2009 prp50 factor: 29094058807903755108349233484470242778633421481941 Wed Jun 17 16:40:36 2009 prp69 factor: 430893200761032977032832794015273047754856060570037729587831660047397 Wed Jun 17 16:40:36 2009 elapsed time 00:30:16 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 15.52 hours. Scaled time: 41.27 units (timescale=2.660). Factorization parameters were as follows: name: KA_6_4_151_1 n: 12536432122867372519200253053164652442871301443065502726646145676657703651611969289789345370155994930176926330039557577 m: 2000000000000000000000000000000 deg: 5 c5: 725 c0: -124 skew: 0.70 type: snfs lss: 1 rlim: 2600000 alim: 2600000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 2600000/2600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1300000, 2305363) Primes: RFBsize:189880, AFBsize:190566, largePrimes:11573313 encountered Relations: rels:10680437, finalFF:303015 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 939344 hash collisions in 11511210 relations Msieve: matrix is 472487 x 472735 (126.7 MB) Total sieving time: 15.33 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,28,28,56,56,2.4,2.4,100000 total time: 15.52 hours. --------- CPU info (if available) ----------

Jun 17, 2009 (4th)

By Serge Batalov / GMP-ECM 6.2.3 / Jun 17, 2009
(2·10²¹³+1)/3 = (6)₂₁₂7_<213> = 642623 · 68623043 · 1464084467605343_<16> · 4409891276148706861866704821_<28> · C157
C157 = P36 · C122
P36 = 118009803355233384577031249267259421_<36>
C122 = [19841312675353812400480170290920785443960159561950228060042177768467208735513015756609844426709640725339681886570157222681_<122>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=2629839573 Step 1 took 3869ms Step 2 took 3416ms ********** Factor found in step 2: 118009803355233384577031249267259421 Found probable prime factor of 36 digits: 118009803355233384577031249267259421 Composite cofactor has 122 digits

Jun 17, 2009 (3rd)

Factorizations of 66...667 have been extended up to n=250. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Jun 17, 2009 (2nd)

By Andreas Tete / Msieve 1.42/GGNFS / Jun 17, 2009
2·10²⁰⁷-1 = 1(9)_207<208> = 59 · 3094811768747411_<16> · 617154916981980493532291_<24> · 1381098786990645604063367397059_<31> · C137
C137 = P47 · P91
P47 = 10018631606052288287701622273517610992315312691_<47>
P91 = 1282674318787362762030604322874622092382640612854027342323747789696130963429438316715523069_<91>

Tue Jun 16 08:41:15 2009 Msieve v. 1.42 Tue Jun 16 08:41:15 2009 random seeds: e7048544 5712ebb3 Tue Jun 16 08:41:15 2009 factoring 12850641470474661004875505196236329003404849262692486716060856559801450057354066892544499120803880203791248408541006698806056308358968679 (137 digits) Tue Jun 16 08:41:16 2009 searching for 15-digit factors Tue Jun 16 08:41:19 2009 commencing number field sieve (137-digit input) Tue Jun 16 08:41:19 2009 R0: -184938694941958480622306328 Tue Jun 16 08:41:19 2009 R1: 1210976711056969 Tue Jun 16 08:41:19 2009 A0: -389193885300554948797063324008702305 Tue Jun 16 08:41:19 2009 A1: 317170412277137560002579632698 Tue Jun 16 08:41:19 2009 A2: 342990442362395307028433 Tue Jun 16 08:41:19 2009 A3: -98772152073117598 Tue Jun 16 08:41:19 2009 A4: -12135218028 Tue Jun 16 08:41:19 2009 A5: 59400 Tue Jun 16 08:41:19 2009 skew 1751330.93, size 3.148758e-013, alpha -8.406469, combined = 3.071070e-011 Tue Jun 16 08:41:19 2009 Tue Jun 16 08:41:19 2009 commencing relation filtering Tue Jun 16 08:41:19 2009 commencing duplicate removal, pass 1 Tue Jun 16 08:42:58 2009 error -5 reading relation 7150400 Tue Jun 16 08:45:52 2009 found 4303051 hash collisions in 21013118 relations Tue Jun 16 08:46:53 2009 added 117519 free relations Tue Jun 16 08:46:53 2009 commencing duplicate removal, pass 2 Tue Jun 16 08:48:02 2009 found 4382890 duplicates and 16747746 unique relations Tue Jun 16 08:48:02 2009 memory use: 106.6 MB Tue Jun 16 08:48:02 2009 reading rational ideals above 15663104 Tue Jun 16 08:48:02 2009 reading algebraic ideals above 15663104 Tue Jun 16 08:48:02 2009 commencing singleton removal, pass 1 Tue Jun 16 08:51:52 2009 relations with 0 large ideals: 487570 Tue Jun 16 08:51:52 2009 relations with 1 large ideals: 2808823 Tue Jun 16 08:51:52 2009 relations with 2 large ideals: 5803004 Tue Jun 16 08:51:52 2009 relations with 3 large ideals: 5237520 Tue Jun 16 08:51:52 2009 relations with 4 large ideals: 2029946 Tue Jun 16 08:51:52 2009 relations with 5 large ideals: 271692 Tue Jun 16 08:51:52 2009 relations with 6 large ideals: 109191 Tue Jun 16 08:51:52 2009 relations with 7+ large ideals: 0 Tue Jun 16 08:51:52 2009 16747746 relations and about 15351641 large ideals Tue Jun 16 08:51:52 2009 commencing singleton removal, pass 2 Tue Jun 16 08:56:10 2009 found 6725926 singletons Tue Jun 16 08:56:10 2009 current dataset: 10021820 relations and about 7447053 large ideals Tue Jun 16 08:56:10 2009 commencing singleton removal, pass 3 Tue Jun 16 08:58:55 2009 found 1478173 singletons Tue Jun 16 08:58:55 2009 current dataset: 8543647 relations and about 5886766 large ideals Tue Jun 16 08:58:55 2009 commencing singleton removal, pass 4 Tue Jun 16 09:01:34 2009 found 397854 singletons Tue Jun 16 09:01:34 2009 current dataset: 8145793 relations and about 5481664 large ideals Tue Jun 16 09:01:34 2009 commencing singleton removal, final pass Tue Jun 16 09:04:43 2009 memory use: 133.2 MB Tue Jun 16 09:04:43 2009 commencing in-memory singleton removal Tue Jun 16 09:04:44 2009 begin with 8145793 relations and 6066424 unique ideals Tue Jun 16 09:04:53 2009 reduce to 6656410 relations and 4531042 ideals in 14 passes Tue Jun 16 09:04:53 2009 max relations containing the same ideal: 24 Tue Jun 16 09:04:55 2009 reading rational ideals above 720000 Tue Jun 16 09:04:55 2009 reading algebraic ideals above 720000 Tue Jun 16 09:04:55 2009 commencing singleton removal, final pass Tue Jun 16 09:07:42 2009 keeping 6066245 ideals with weight <= 20, new excess is 496511 Tue Jun 16 09:07:53 2009 memory use: 182.1 MB Tue Jun 16 09:07:53 2009 commencing in-memory singleton removal Tue Jun 16 09:07:54 2009 begin with 6660230 relations and 6066245 unique ideals Tue Jun 16 09:08:06 2009 reduce to 6551115 relations and 5938488 ideals in 12 passes Tue Jun 16 09:08:06 2009 max relations containing the same ideal: 20 Tue Jun 16 09:08:11 2009 removing 247011 relations and 228674 ideals in 18337 cliques Tue Jun 16 09:08:11 2009 commencing in-memory singleton removal Tue Jun 16 09:08:12 2009 begin with 6304104 relations and 5938488 unique ideals Tue Jun 16 09:08:20 2009 reduce to 6298481 relations and 5704165 ideals in 8 passes Tue Jun 16 09:08:20 2009 max relations containing the same ideal: 20 Tue Jun 16 09:08:25 2009 removing 179348 relations and 161011 ideals in 18337 cliques Tue Jun 16 09:08:25 2009 commencing in-memory singleton removal Tue Jun 16 09:08:26 2009 begin with 6119133 relations and 5704165 unique ideals Tue Jun 16 09:08:31 2009 reduce to 6115696 relations and 5539705 ideals in 6 passes Tue Jun 16 09:08:31 2009 max relations containing the same ideal: 20 Tue Jun 16 09:08:33 2009 relations with 0 large ideals: 8428 Tue Jun 16 09:08:33 2009 relations with 1 large ideals: 98147 Tue Jun 16 09:08:33 2009 relations with 2 large ideals: 511881 Tue Jun 16 09:08:33 2009 relations with 3 large ideals: 1359789 Tue Jun 16 09:08:33 2009 relations with 4 large ideals: 1976358 Tue Jun 16 09:08:33 2009 relations with 5 large ideals: 1508005 Tue Jun 16 09:08:33 2009 relations with 6 large ideals: 549511 Tue Jun 16 09:08:33 2009 relations with 7+ large ideals: 103577 Tue Jun 16 09:08:33 2009 commencing 2-way merge Tue Jun 16 09:08:40 2009 reduce to 3654554 relation sets and 3078563 unique ideals Tue Jun 16 09:08:40 2009 commencing full merge Tue Jun 16 09:09:49 2009 memory use: 277.3 MB Tue Jun 16 09:09:50 2009 found 1863902 cycles, need 1788763 Tue Jun 16 09:09:50 2009 weight of 1788763 cycles is about 125390665 (70.10/cycle) Tue Jun 16 09:09:50 2009 distribution of cycle lengths: Tue Jun 16 09:09:50 2009 1 relations: 214445 Tue Jun 16 09:09:50 2009 2 relations: 230761 Tue Jun 16 09:09:50 2009 3 relations: 226678 Tue Jun 16 09:09:50 2009 4 relations: 200070 Tue Jun 16 09:09:50 2009 5 relations: 173029 Tue Jun 16 09:09:50 2009 6 relations: 144276 Tue Jun 16 09:09:50 2009 7 relations: 120117 Tue Jun 16 09:09:50 2009 8 relations: 100783 Tue Jun 16 09:09:50 2009 9 relations: 82547 Tue Jun 16 09:09:50 2009 10+ relations: 296057 Tue Jun 16 09:09:50 2009 heaviest cycle: 19 relations Tue Jun 16 09:09:51 2009 commencing cycle optimization Tue Jun 16 09:09:55 2009 start with 9955039 relations Tue Jun 16 09:10:24 2009 pruned 243613 relations Tue Jun 16 09:10:24 2009 memory use: 266.1 MB Tue Jun 16 09:10:24 2009 distribution of cycle lengths: Tue Jun 16 09:10:24 2009 1 relations: 214445 Tue Jun 16 09:10:24 2009 2 relations: 236371 Tue Jun 16 09:10:24 2009 3 relations: 235532 Tue Jun 16 09:10:24 2009 4 relations: 204943 Tue Jun 16 09:10:24 2009 5 relations: 176486 Tue Jun 16 09:10:24 2009 6 relations: 145380 Tue Jun 16 09:10:24 2009 7 relations: 120359 Tue Jun 16 09:10:24 2009 8 relations: 99668 Tue Jun 16 09:10:24 2009 9 relations: 80917 Tue Jun 16 09:10:24 2009 10+ relations: 274662 Tue Jun 16 09:10:24 2009 heaviest cycle: 19 relations Tue Jun 16 09:10:27 2009 RelProcTime: 1388 Tue Jun 16 09:10:27 2009 Tue Jun 16 09:10:27 2009 commencing linear algebra Tue Jun 16 09:10:28 2009 read 1788763 cycles Tue Jun 16 09:10:33 2009 cycles contain 5592553 unique relations Tue Jun 16 09:12:10 2009 read 5592553 relations Tue Jun 16 09:12:22 2009 using 20 quadratic characters above 268435034 Tue Jun 16 09:13:00 2009 building initial matrix Tue Jun 16 09:14:39 2009 memory use: 666.8 MB Tue Jun 16 09:15:01 2009 read 1788763 cycles Tue Jun 16 09:15:04 2009 matrix is 1788464 x 1788763 (515.1 MB) with weight 170626373 (95.39/col) Tue Jun 16 09:15:04 2009 sparse part has weight 120728082 (67.49/col) Tue Jun 16 09:15:46 2009 filtering completed in 3 passes Tue Jun 16 09:15:47 2009 matrix is 1778355 x 1778555 (513.7 MB) with weight 170014583 (95.59/col) Tue Jun 16 09:15:47 2009 sparse part has weight 120432214 (67.71/col) Tue Jun 16 09:16:17 2009 read 1778555 cycles Tue Jun 16 09:16:20 2009 matrix is 1778355 x 1778555 (513.7 MB) with weight 170014583 (95.59/col) Tue Jun 16 09:16:20 2009 sparse part has weight 120432214 (67.71/col) Tue Jun 16 09:16:20 2009 saving the first 48 matrix rows for later Tue Jun 16 09:16:21 2009 matrix is 1778307 x 1778555 (491.3 MB) with weight 135611324 (76.25/col) Tue Jun 16 09:16:21 2009 sparse part has weight 118111865 (66.41/col) Tue Jun 16 09:16:21 2009 matrix includes 64 packed rows Tue Jun 16 09:16:21 2009 using block size 65536 for processor cache size 3072 kB Tue Jun 16 09:16:37 2009 commencing Lanczos iteration Tue Jun 16 09:16:37 2009 memory use: 489.2 MB Tue Jun 16 18:00:35 2009 lanczos halted after 28124 iterations (dim = 1778306) Tue Jun 16 18:00:41 2009 recovered 30 nontrivial dependencies Tue Jun 16 18:00:41 2009 BLanczosTime: 31814 Tue Jun 16 18:00:41 2009 Tue Jun 16 18:00:41 2009 commencing square root phase Tue Jun 16 18:00:41 2009 reading relations for dependency 1 Tue Jun 16 18:00:43 2009 read 889064 cycles Tue Jun 16 18:00:46 2009 cycles contain 3390342 unique relations Tue Jun 16 18:01:49 2009 read 3390342 relations Tue Jun 16 18:02:12 2009 multiplying 2790492 relations Tue Jun 16 18:10:35 2009 multiply complete, coefficients have about 135.95 million bits Tue Jun 16 18:10:41 2009 initial square root is modulo 75679 Tue Jun 16 18:24:12 2009 sqrtTime: 1411 Tue Jun 16 18:24:12 2009 prp47 factor: 10018631606052288287701622273517610992315312691 Tue Jun 16 18:24:12 2009 prp91 factor: 1282674318787362762030604322874622092382640612854027342323747789696130963429438316715523069 Tue Jun 16 18:24:12 2009 elapsed time 09:42:57 total time 358,5 hours

Jun 17, 2009

By Markus Tervooren / lasieve/msieve / Jun 17, 2009
(52·10²⁰⁴+11)/9 = 5(7)₂₀₃9_<205> = 7 · C204
C204 = P52 · P153
P52 = 3489796835931103361689260396347023065416395122343361_<52>
P153 = 236517156786464756205308903707715975525031761922301258980101045633547768238421296759011363918993807438685658380715328301003618543542563650318286959170677_<153>

Msieve v. 1.41 Mon Jun 15 11:30:04 2009 random seeds: 15203ffb 1cd35f9e factoring 825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825397 (204 digits) searching for 15-digit factors commencing number field sieve (204-digit input) R0: -100000000000000000000000000000000000000000 R1: 1 A0: 55 A1: 0 A2: 0 A3: 0 A4: 0 A5: 26 skew 1.16, size 2.311556e-14, alpha 1.167854, combined = 8.053847e-12 commencing relation filtering commencing duplicate removal, pass 1 error -11 reading relation 4747171 error -11 reading relation 36981095 error -11 reading relation 37269830 error -9 reading relation 37529624 error -15 reading relation 37808078 found 6615974 hash collisions in 41847181 relations added 36 free relations commencing duplicate removal, pass 2 found 5189566 duplicates and 36657651 unique relations memory use: 165.2 MB reading rational ideals above 27066368 reading algebraic ideals above 27066368 commencing singleton removal, pass 1 relations with 0 large ideals: 854492 relations with 1 large ideals: 4838519 relations with 2 large ideals: 11747822 relations with 3 large ideals: 12974157 relations with 4 large ideals: 5544950 relations with 5 large ideals: 51281 relations with 6 large ideals: 646430 relations with 7+ large ideals: 0 36657651 relations and about 31746105 large ideals commencing singleton removal, pass 2 found 11657926 singletons current dataset: 24999725 relations and about 18520428 large ideals commencing singleton removal, pass 3 found 2458512 singletons current dataset: 22541213 relations and about 15954383 large ideals commencing singleton removal, pass 4 found 610781 singletons current dataset: 21930432 relations and about 15335945 large ideals commencing singleton removal, pass 5 found 151119 singletons current dataset: 21779313 relations and about 15184347 large ideals commencing singleton removal, final pass memory use: 360.3 MB commencing in-memory singleton removal begin with 21779313 relations and 18395015 unique ideals reduce to 15354339 relations and 11633580 ideals in 18 passes max relations containing the same ideal: 46 reading rational ideals above 720000 reading algebraic ideals above 720000 commencing singleton removal, final pass keeping 13441317 ideals with weight <= 20, new excess is 1564387 memory use: 489.2 MB commencing in-memory singleton removal begin with 15354376 relations and 13441317 unique ideals reduce to 15313044 relations and 13399791 ideals in 13 passes max relations containing the same ideal: 20 removing 728555 relations and 679273 ideals in 49282 cliques commencing in-memory singleton removal begin with 14584489 relations and 13399791 unique ideals reduce to 14556496 relations and 12692371 ideals in 8 passes max relations containing the same ideal: 20 removing 524992 relations and 475710 ideals in 49282 cliques commencing in-memory singleton removal begin with 14031504 relations and 12692371 unique ideals reduce to 14016019 relations and 12201099 ideals in 8 passes max relations containing the same ideal: 20 relations with 0 large ideals: 121410 relations with 1 large ideals: 784824 relations with 2 large ideals: 2483536 relations with 3 large ideals: 4142115 relations with 4 large ideals: 3815762 relations with 5 large ideals: 1924327 relations with 6 large ideals: 648133 relations with 7+ large ideals: 95912 commencing 2-way merge reduce to 8245211 relation sets and 6430293 unique ideals ignored 2 oversize relation sets commencing full merge memory use: 604.6 MB found 4064935 cycles, need 3832493 weight of 3832493 cycles is about 268453437 (70.05/cycle) distribution of cycle lengths: 1 relations: 555724 2 relations: 487158 3 relations: 462672 4 relations: 405356 5 relations: 357807 6 relations: 296266 7 relations: 254182 8 relations: 213886 9 relations: 178724 10+ relations: 620718 heaviest cycle: 20 relations commencing cycle optimization start with 20801266 relations pruned 493110 relations memory use: 717.1 MB distribution of cycle lengths: 1 relations: 555724 2 relations: 498808 3 relations: 479788 4 relations: 414965 5 relations: 364985 6 relations: 299239 7 relations: 255275 8 relations: 212681 9 relations: 175573 10+ relations: 575455 heaviest cycle: 20 relations RelProcTime: 1843 commencing linear algebra read 3832493 cycles cycles contain 12267129 unique relations read 12267129 relations using 20 quadratic characters above 536870840 building initial matrix memory use: 1538.9 MB read 3832493 cycles matrix is 3830980 x 3832493 (1149.3 MB) with weight 338758144 (88.39/col) sparse part has weight 259136904 (67.62/col) filtering completed in 3 passes matrix is 3777859 x 3778059 (1139.2 MB) with weight 335479132 (88.80/col) sparse part has weight 257071186 (68.04/col) read 3778059 cycles matrix is 3777859 x 3778059 (1139.2 MB) with weight 335479132 (88.80/col) sparse part has weight 257071186 (68.04/col) saving the first 48 matrix rows for later matrix is 3777811 x 3778059 (1080.2 MB) with weight 265630651 (70.31/col) sparse part has weight 245398470 (64.95/col) matrix includes 64 packed rows using block size 65536 for processor cache size 4096 kB commencing Lanczos iteration (4 threads) memory use: 1135.5 MB linear algebra completed 3777680 of 3778059 dimensions (100.0%, ETA 0h 0m) lanczos halted after 59744 iterations (dim = 3777811) recovered 37 nontrivial dependencies BLanczosTime: 95960 commencing square root phase reading relations for dependency 1 read 1889489 cycles cycles contain 7358025 unique relations read 7358025 relations multiplying 6101724 relations multiply complete, coefficients have about 175.74 million bits initial square root is modulo 2028101 reading relations for dependency 2 read 1888830 cycles cycles contain 7354128 unique relations read 7354128 relations multiplying 6099464 relations multiply complete, coefficients have about 175.68 million bits initial square root is modulo 2017991 reading relations for dependency 3 read 1888847 cycles cycles contain 7355319 unique relations read 7355319 relations multiplying 6101654 relations multiply complete, coefficients have about 175.74 million bits initial square root is modulo 2027561 sqrtTime: 4290 prp52 factor: 3489796835931103361689260396347023065416395122343361 prp153 factor: 236517156786464756205308903707715975525031761922301258980101045633547768238421296759011363918993807438685658380715328301003618543542563650318286959170677 elapsed time 28:21:58 Sieving CPU time 551:45:01

Jun 16, 2009 (3rd)

By Wataru Sakai / Msieve, GMP-ECM 6.2.1 / Jun 16, 2009
(32·10¹⁹⁰+31)/9 = 3(5)₁₈₉9_<191> = 3 · 229 · C188
C188 = P86 · P102
P86 = 52311355555847030303143653332060151795995423261951000945838450963825453383089608706687_<86>
P102 = 989360933782077602757730767136340057134054664376326080972807007427391485597216486100369325941804525111_<102>

Number: 35559_190 N=51754811580139091056121623807213326863981885815946951318130357431667475335597606339964418567038654374898916383632540837781012453501536470968785379265728610706776645641274462235160925117257 ( 188 digits) SNFS difficulty: 191 digits. Divisors found: r1=52311355555847030303143653332060151795995423261951000945838450963825453383089608706687 r2=989360933782077602757730767136340057134054664376326080972807007427391485597216486100369325941804525111 Version: Total time: 386.28 hours. Scaled time: 721.57 units (timescale=1.868). Factorization parameters were as follows: n: 51754811580139091056121623807213326863981885815946951318130357431667475335597606339964418567038654374898916383632540837781012453501536470968785379265728610706776645641274462235160925117257 m: 200000000000000000000000000000000000000 deg: 5 c5: 1 c0: 31 skew: 1.99 type: snfs lss: 1 rlim: 10900000 alim: 10900000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 10900000/10900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [5450000, 9050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1769931 x 1770179 Total sieving time: 386.28 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,191,5,0,0,0,0,0,0,0,0,10900000,10900000,28,28,54,54,2.5,2.5,100000 total time: 386.28 hours. --------- CPU info (if available) ----------

(17·10¹⁷⁰+7)/3 = 5(6)₁₆₉9_<171> = 559631 · 104675792068314853_<18> · 322875512531802497_<18> · C131
C131 = P30 · C102
P30 = 162573751231188186196793586329_<30>
C102 = [184286750323182314380444905316628685751186302523555068558316595554862239297139529533915383571885271391_<102>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3231751289 Step 1 took 38311ms Step 2 took 14187ms ********** Factor found in step 2: 162573751231188186196793586329 Found probable prime factor of 30 digits: 162573751231188186196793586329 Composite cofactor 184286750323182314380444905316628685751186302523555068558316595554862239297139529533915383571885271391 has 102 digits

Jun 16, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Jun 16, 2009
(7·10²⁰⁷-43)/9 = (7)₂₀₆3_<207> = 29 · C206
C206 = P58 · P148
P58 = 3525612691841796717716571447742461396593977021280549090597_<58>
P148 = 7607166673102896895035924993239057602596719975676720837964603242247454297832536031682543083611128181134404747535699168691579388841629444804314983421_<148>

Number: n N=26819923371647509578544061302681992337164750957854406130268199233716475095785440613026819923371647509578544061302681992337164750957854406130268199233716475095785440613026819923371647509578544061302681992337 ( 206 digits) SNFS difficulty: 208 digits. Divisors found: Tue Jun 16 14:27:57 2009 prp58 factor: 3525612691841796717716571447742461396593977021280549090597 Tue Jun 16 14:27:57 2009 prp148 factor: 7607166673102896895035924993239057602596719975676720837964603242247454297832536031682543083611128181134404747535699168691579388841629444804314983421 Tue Jun 16 14:27:57 2009 elapsed time 34:01:05 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20050930-k8 Total time: 109.38 hours. Scaled time: 161.56 units (timescale=1.477). Factorization parameters were as follows: name: KA_7_206_3 n: 26819923371647509578544061302681992337164750957854406130268199233716475095785440613026819923371647509578544061302681992337164750957854406130268199233716475095785440613026819923371647509578544061302681992337 m: 200000000000000000000000000000000000000000 deg: 5 c5: 175 c0: -344 skew: 1.14 type: snfs lss: 1 rlim: 21000000 alim: 21000000 lpbr: 29 lpba: 29 mfbr: 57 mfba: 57 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 21000000/21000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 57/57 Sieved special-q in [10500000, 31534423) Primes: RFBsize:1329943, AFBsize:1329867, largePrimes:40241582 encountered Relations: rels:40602379, finalFF:1267324 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 7729398 hash collisions in 46531126 relations Msieve: matrix is 4107666 x 4107914 (1109.4 MB) Total sieving time: 108.14 hours. Total relation processing time: 1.24 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,208,5,0,0,0,0,0,0,0,0,21000000,21000000,29,29,57,57,2.6,2.6,100000 total time: 109.38 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3368968k/3407296k available (2748k kernel code, 36964k reserved, 1425k data, 416k init, 2489792k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830496) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830447) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Total of 4 processors activated (22643.71 BogoMIPS).

Jun 16, 2009

By Sinkiti Sibata / Msieve / Jun 16, 2009
(58·10¹⁶⁹-31)/9 = 6(4)₁₆₈1_<170> = 4759 · 990345030902428049_<18> · 1040962582350012886277401_<25> · C125
C125 = P44 · P81
P44 = 36034728933765103515768049208221872190779947_<44>
P81 = 364524626825221980305319507663534157249009284349617294059232336100323699966871333_<81>

Number: 64441_169 N=13135546117328753501423666515409815427710732848545414983081187338314684998812020480051106583513231610413546102918990665559351 ( 125 digits) SNFS difficulty: 171 digits. Divisors found: r1=36034728933765103515768049208221872190779947 (pp44) r2=364524626825221980305319507663534157249009284349617294059232336100323699966871333 (pp81) Version: Msieve-1.40 Total time: 93.24 hours. Scaled time: 193.10 units (timescale=2.071). Factorization parameters were as follows: name: 64441_169 n: 13135546117328753501423666515409815427710732848545414983081187338314684998812020480051106583513231610413546102918990665559351 m: 10000000000000000000000000000000000 deg: 5 c5: 29 c0: -155 skew: 1.40 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, 6000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 984133 x 984381 Total sieving time: 88.91 hours. Total relation processing time: 0.23 hours. Matrix solve time: 3.87 hours. Time per square root: 0.24 hours. Prototype def-par.txt line would be: snfs,171.000,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000 total time: 93.24 hours. --------- CPU info (if available) ----------

Jun 15, 2009 (4th)

By Sinkiti Sibata / Msieve / Jun 15, 2009
(58·10¹⁷¹-31)/9 = 6(4)₁₇₀1_<172> = 3 · 131 · 1072439 · C164
C164 = P45 · P120
P45 = 152397504383392681380161331359317911517374557_<45>
P120 = 100332695395700957993833618354525485896082262537839241810909027600644295331161884483270160049035739884288720424176670819_<120>

Number: 64441_171 N=15290452386363939446525848048541105999225523296178280103094019270493344440033228019525273934498184829930241610767876967583025349943732440179203332172996263714952183 ( 164 digits) SNFS difficulty: 173 digits. Divisors found: r1=152397504383392681380161331359317911517374557 (pp45) r2=100332695395700957993833618354525485896082262537839241810909027600644295331161884483270160049035739884288720424176670819 (pp120) Version: Msieve-1.40 Total time: 101.26 hours. Scaled time: 257.59 units (timescale=2.544). Factorization parameters were as follows: name: 64441_171 n: 15290452386363939446525848048541105999225523296178280103094019270493344440033228019525273934498184829930241610767876967583025349943732440179203332172996263714952183 m: 20000000000000000000000000000000000 deg: 5 c5: 145 c0: -248 skew: 1.11 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, 6950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1067207 x 1067455 Total sieving time: 101.26 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,173.000,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,52,52,2.4,2.4,100000 total time: 101.26 hours. --------- CPU info (if available) ----------

Jun 15, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Jun 15, 2009
(68·10¹⁷⁰+13)/9 = 7(5)₁₆₉7_<171> = 139 · 29473 · 290911573 · 32154519786569_<14> · C143
C143 = P44 · C99
P44 = 23839585429968260174265553579269018490660487_<44>
C99 = [827038131338867400594187976741748355884015349016991665314607084014181746469763768683616779908844749_<99>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1694953640 Step 1 took 42454ms Step 2 took 14836ms ********** Factor found in step 2: 23839585429968260174265553579269018490660487 Found probable prime factor of 44 digits: 23839585429968260174265553579269018490660487 Composite cofactor 827038131338867400594187976741748355884015349016991665314607084014181746469763768683616779908844749 has 99 digits

(58·10¹⁸⁹-31)/9 = 6(4)₁₈₈1_<190> = 3 · 1298969585567877829600303_<25> · 104526430293899563124851798413289_<33> · C134
C134 = P35 · P99
P35 = 27851355416234957710219931262472333_<35>
P99 = 568058146616729197426787256156526078124017948322299569993098655486669818175582047103675908213848777_<99>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=98376821 Step 1 took 38188ms Step 2 took 14478ms ********** Factor found in step 2: 27851355416234957710219931262472333 Found probable prime factor of 35 digits: 27851355416234957710219931262472333 Probable prime cofactor 568058146616729197426787256156526078124017948322299569993098655486669818175582047103675908213848777 has 99 digits

(32·10²⁰⁵+13)/9 = 3(5)₂₀₄7_<206> = 37 · 967379807683_<12> · 1184417920426891_<16> · 795593320256493401773149644687597_<33> · C145
C145 = P51 · P94
P51 = 523543438969426161642554706724547076253559125346249_<51>
P94 = 2013538358755604989175086781461802433222124306874954367100349986369529759283778641199459395229_<94>

Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=3446144840 Step 1 took 1563441ms Step 2 took 378657ms ********** Factor found in step 2: 523543438969426161642554706724547076253559125346249 Found probable prime factor of 51 digits: 523543438969426161642554706724547076253559125346249 Probable prime cofactor 2013538358755604989175086781461802433222124306874954367100349986369529759283778641199459395229 has 94 digits

(17·10¹⁶⁹+7)/3 = 5(6)₁₆₈9_<170> = 23 · 12541 · 14323 · 87332633531070045486751_<23> · C138
C138 = P37 · P101
P37 = 2324768203435506363366226453197815069_<37>
P101 = 67558104709023990501069888186016245427948179198146067231684361193242776832285202310303887339358758159_<101>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2047747038 Step 1 took 42655ms Step 2 took 14967ms ********** Factor found in step 2: 2324768203435506363366226453197815069 Found probable prime factor of 37 digits: 2324768203435506363366226453197815069 Probable prime cofactor 67558104709023990501069888186016245427948179198146067231684361193242776832285202310303887339358758159 has 101 digits

(52·10¹⁶⁹-61)/9 = 5(7)₁₆₈1_<170> = 3 · 89 · 278903 · 3279377 · 32360346197_<11> · 4451979143044721_<16> · C130
C130 = P47 · P83
P47 = 53078376861500775441655726585136757521797989163_<47>
P83 = 30940058238615665313403938893991266571394807926612012937315069117082296436341232033_<83>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=616297871 Step 1 took 38399ms Step 2 took 6654ms ********** Factor found in step 2: 53078376861500775441655726585136757521797989163 Found probable prime factor of 47 digits: 53078376861500775441655726585136757521797989163 Probable prime cofactor 30940058238615665313403938893991266571394807926612012937315069117082296436341232033 has 83 digits

Jun 15, 2009 (2nd)

By Robert Backstrom / GMP-ECM / Jun 15, 2009
(11·10¹⁷¹-17)/3 = 3(6)₁₇₀1_<172> = 7 · 83 · 89 · 37879493 · 83385999899891719865878511313987222461_<38> · C122
C122 = P43 · P79
P43 = 4418221078669137442616872879018688733164741_<43>
P79 = 5081132846877830440997852063020506750789351211654669138222845010685572422958853_<79>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 22449568247593753184083167533291975290884854540034547605076554357224725377782546501707146485392713868517979960233913402073 (122 digits) Using B1=7962000, B2=23420528050, polynomial Dickson(12), sigma=3300305035 Step 1 took 88764ms Step 2 took 30982ms ********** Factor found in step 2: 4418221078669137442616872879018688733164741 Found probable prime factor of 43 digits: 4418221078669137442616872879018688733164741 Probable prime cofactor 5081132846877830440997852063020506750789351211654669138222845010685572422958853 has 79 digits

Jun 15, 2009

By Andreas Tete / Msieve v. 1.42 / Jun 15, 2009
(16·10¹⁹⁹-7)/9 = 1(7)_199<200> = 264007 · 6353173 · 23291472982858333436228811919662999043691_<41> · 1502739138045835488243594532007091714625588183_<46> · C102
C102 = P42 · P60
P42 = 452241368214969009042683359968470074470559_<42>
P60 = 669607810762702090792985421889647833991658340054391761378041_<60>

Sun Jun 14 14:08:47 2009 Msieve v. 1.42 Sun Jun 14 14:08:47 2009 random seeds: c7bcd9dc 96bf054c Sun Jun 14 14:08:47 2009 factoring 302824352506754444443578645843911185284478634106196572443295670733987494299384968724155242087323594919 (102 digits) Sun Jun 14 14:08:48 2009 searching for 15-digit factors Sun Jun 14 14:08:49 2009 commencing quadratic sieve (102-digit input) Sun Jun 14 14:08:49 2009 using multiplier of 1 Sun Jun 14 14:08:49 2009 using 32kb Intel Core sieve core Sun Jun 14 14:08:49 2009 sieve interval: 36 blocks of size 32768 Sun Jun 14 14:08:49 2009 processing polynomials in batches of 6 Sun Jun 14 14:08:49 2009 using a sieve bound of 3198347 (114987 primes) Sun Jun 14 14:08:49 2009 using large prime bound of 479752050 (28 bits) Sun Jun 14 14:08:49 2009 using double large prime bound of 4225034777495250 (44-52 bits) Sun Jun 14 14:08:49 2009 using trial factoring cutoff of 52 bits Sun Jun 14 14:08:49 2009 polynomial 'A' values have 13 factors Sun Jun 14 14:08:59 2009 restarting with 17685 full and 1114340 partial relations Sun Jun 14 18:09:23 2009 115177 relations (27268 full + 87909 combined from 1713973 partial), need 115083 Sun Jun 14 18:09:39 2009 begin with 1741241 relations Sun Jun 14 18:09:40 2009 reduce to 304006 relations in 15 passes Sun Jun 14 18:09:40 2009 attempting to read 304006 relations Sun Jun 14 18:09:48 2009 recovered 304006 relations Sun Jun 14 18:09:48 2009 recovered 294904 polynomials Sun Jun 14 18:09:48 2009 attempting to build 115177 cycles Sun Jun 14 18:09:48 2009 found 115177 cycles in 6 passes Sun Jun 14 18:09:48 2009 distribution of cycle lengths: Sun Jun 14 18:09:48 2009 length 1 : 27268 Sun Jun 14 18:09:48 2009 length 2 : 19448 Sun Jun 14 18:09:48 2009 length 3 : 19360 Sun Jun 14 18:09:48 2009 length 4 : 15827 Sun Jun 14 18:09:49 2009 length 5 : 12078 Sun Jun 14 18:09:49 2009 length 6 : 8314 Sun Jun 14 18:09:49 2009 length 7 : 5356 Sun Jun 14 18:09:49 2009 length 9+: 7526 Sun Jun 14 18:09:49 2009 largest cycle: 20 relations Sun Jun 14 18:09:49 2009 matrix is 114987 x 115177 (32.8 MB) with weight 8128071 (70.57/col) Sun Jun 14 18:09:49 2009 sparse part has weight 8128071 (70.57/col) Sun Jun 14 18:09:50 2009 filtering completed in 3 passes Sun Jun 14 18:09:50 2009 matrix is 110432 x 110496 (31.6 MB) with weight 7844676 (71.00/col) Sun Jun 14 18:09:50 2009 sparse part has weight 7844676 (71.00/col) Sun Jun 14 18:09:50 2009 saving the first 48 matrix rows for later Sun Jun 14 18:09:50 2009 matrix is 110384 x 110496 (20.4 MB) with weight 6291124 (56.94/col) Sun Jun 14 18:09:50 2009 sparse part has weight 4671682 (42.28/col) Sun Jun 14 18:09:50 2009 matrix includes 64 packed rows Sun Jun 14 18:09:50 2009 using block size 44198 for processor cache size 2048 kB Sun Jun 14 18:09:51 2009 commencing Lanczos iteration Sun Jun 14 18:09:51 2009 memory use: 19.2 MB Sun Jun 14 18:10:58 2009 lanczos halted after 1747 iterations (dim = 110382) Sun Jun 14 18:10:58 2009 recovered 17 nontrivial dependencies Sun Jun 14 18:10:59 2009 prp42 factor: 452241368214969009042683359968470074470559 Sun Jun 14 18:10:59 2009 prp60 factor: 669607810762702090792985421889647833991658340054391761378041 Sun Jun 14 18:10:59 2009 elapsed time 04:02:12 total time 11:33:01

Jun 14, 2009 (2nd)

By Justin Card / ggnfs, msieve 1.41 / Jun 14, 2009
(56·10¹⁷³+61)/9 = 6(2)₁₇₂9_<174> = 37 · 1456321 · 223735397 · 47438213027_<11> · 6724817532511251616845931_<25> · C123
C123 = P58 · P66
P58 = 1076573811006174078255496603425369798195157247908414024513_<58>
P66 = 150279363077127682942036206681415950498349083088117034520490825661_<66>

Sieving with ggnfs over 2 days. post processing: Fri Jun 12 19:58:59 2009 Fri Jun 12 19:58:59 2009 Fri Jun 12 19:58:59 2009 Msieve v. 1.41 Fri Jun 12 19:58:59 2009 random seeds: d4231cb1 94d197db Fri Jun 12 19:58:59 2009 factoring 161786826623523873106331984288573086057036069356281984589662923023302881395583523319398596356535562638667735369803263428093 (123 digits) Fri Jun 12 19:59:01 2009 searching for 15-digit factors Fri Jun 12 19:59:01 2009 commencing number field sieve (123-digit input) Fri Jun 12 19:59:01 2009 R0: -403531707038578195679824 Fri Jun 12 19:59:01 2009 R1: 18400543438849 Fri Jun 12 19:59:01 2009 A0: 288596986503835432574359753965 Fri Jun 12 19:59:01 2009 A1: -7558628649210801901609443 Fri Jun 12 19:59:01 2009 A2: -90495200746547881266 Fri Jun 12 19:59:01 2009 A3: 367691967788437 Fri Jun 12 19:59:01 2009 A4: 2322968419 Fri Jun 12 19:59:01 2009 A5: 15120 Fri Jun 12 19:59:01 2009 skew 1.00, size 1.029077e-11, alpha -6.403071, combined = 5.274824e-12 Fri Jun 12 19:59:02 2009 generating factor base Fri Jun 12 19:59:07 2009 factor base complete: Fri Jun 12 19:59:07 2009 424490 rational roots (max prime = 6181811) Fri Jun 12 19:59:07 2009 425953 algebraic roots (max prime = 6181753) Fri Jun 12 19:59:07 2009 a range: [-28363636, 28363636] Fri Jun 12 19:59:07 2009 b range: [1, 4294967295] Fri Jun 12 19:59:07 2009 number of hash buckets: 95 Fri Jun 12 19:59:07 2009 sieve block size: 65536 Fri Jun 12 19:59:07 2009 Fri Jun 12 19:59:07 2009 maximum RFB prime: 6181811 Fri Jun 12 19:59:07 2009 RFB entries: 424490 Fri Jun 12 19:59:07 2009 medium RFB entries: 6542 Fri Jun 12 19:59:07 2009 resieved RFB entries: 6374 Fri Jun 12 19:59:07 2009 small RFB prime powers: 25 Fri Jun 12 19:59:07 2009 projective RFB roots: 5 Fri Jun 12 19:59:07 2009 RFB trial factoring cutoff: 59 or 88 bits Fri Jun 12 19:59:07 2009 single large prime RFB range: 23 - 27 bits Fri Jun 12 19:59:07 2009 double large prime RFB range: 46 - 52 bits Fri Jun 12 19:59:07 2009 triple large prime RFB range: 71 - 79 bits Fri Jun 12 19:59:07 2009 Fri Jun 12 19:59:07 2009 maximum AFB prime: 6181753 Fri Jun 12 19:59:07 2009 AFB entries: 425953 Fri Jun 12 19:59:07 2009 medium AFB entries: 6520 Fri Jun 12 19:59:07 2009 resieved AFB entries: 6275 Fri Jun 12 19:59:07 2009 small AFB prime powers: 131 Fri Jun 12 19:59:07 2009 projective AFB roots: 4 Fri Jun 12 19:59:07 2009 AFB trial factoring cutoff: 59 or 88 bits Fri Jun 12 19:59:07 2009 single large prime AFB range: 23 - 27 bits Fri Jun 12 19:59:07 2009 double large prime AFB range: 46 - 52 bits Fri Jun 12 19:59:07 2009 triple large prime AFB range: 71 - 79 bits Fri Jun 12 19:59:07 2009 Fri Jun 12 19:59:08 2009 multiplying 1639202 primes from 6181753 to 33554432 Fri Jun 12 19:59:40 2009 Fri Jun 12 19:59:40 2009 Fri Jun 12 19:59:40 2009 Msieve v. 1.41 Fri Jun 12 19:59:40 2009 random seeds: 2353b878 c382ae6b Fri Jun 12 19:59:40 2009 factoring 161786826623523873106331984288573086057036069356281984589662923023302881395583523319398596356535562638667735369803263428093 (123 digits) Fri Jun 12 19:59:42 2009 searching for 15-digit factors Fri Jun 12 19:59:43 2009 commencing number field sieve (123-digit input) Fri Jun 12 19:59:43 2009 R0: -403531707038578195679824 Fri Jun 12 19:59:43 2009 R1: 18400543438849 Fri Jun 12 19:59:43 2009 A0: 288596986503835432574359753965 Fri Jun 12 19:59:43 2009 A1: -7558628649210801901609443 Fri Jun 12 19:59:43 2009 A2: -90495200746547881266 Fri Jun 12 19:59:43 2009 A3: 367691967788437 Fri Jun 12 19:59:43 2009 A4: 2322968419 Fri Jun 12 19:59:43 2009 A5: 15120 Fri Jun 12 19:59:43 2009 skew 1.00, size 1.029077e-11, alpha -6.403071, combined = 5.274824e-12 Fri Jun 12 19:59:43 2009 Fri Jun 12 19:59:43 2009 commencing relation filtering Fri Jun 12 19:59:43 2009 commencing duplicate removal, pass 1 Fri Jun 12 19:59:43 2009 found 0 hash collisions in 0 relations Fri Jun 12 19:59:43 2009 reading rational ideals above 327680 Fri Jun 12 19:59:43 2009 reading algebraic ideals above 327680 Fri Jun 12 19:59:43 2009 commencing singleton removal, pass 1 Fri Jun 12 19:59:43 2009 relations with 0 large ideals: 0 Fri Jun 12 19:59:43 2009 relations with 1 large ideals: 0 Fri Jun 12 19:59:43 2009 relations with 2 large ideals: 0 Fri Jun 12 19:59:43 2009 relations with 3 large ideals: 0 Fri Jun 12 19:59:43 2009 relations with 4 large ideals: 0 Fri Jun 12 19:59:43 2009 relations with 5 large ideals: 0 Fri Jun 12 19:59:43 2009 relations with 6 large ideals: 0 Fri Jun 12 19:59:43 2009 relations with 7+ large ideals: 0 Fri Jun 12 19:59:43 2009 0 relations and about 0 large ideals Fri Jun 12 19:59:43 2009 commencing singleton removal, pass 2 Fri Jun 12 19:59:43 2009 found 0 singletons Fri Jun 12 19:59:43 2009 current dataset: 0 relations and about 0 large ideals Fri Jun 12 19:59:43 2009 commencing singleton removal, final pass Fri Jun 12 19:59:43 2009 memory use: 0.1 MB Fri Jun 12 19:59:43 2009 commencing in-memory singleton removal Fri Jun 12 19:59:43 2009 begin with 0 relations and 0 unique ideals Fri Jun 12 19:59:43 2009 reduce to 0 relations and 0 ideals in 1 passes Fri Jun 12 19:59:43 2009 max relations containing the same ideal: 0 Fri Jun 12 19:59:44 2009 reading rational ideals above 100000 Fri Jun 12 19:59:44 2009 reading algebraic ideals above 100000 Fri Jun 12 19:59:44 2009 commencing singleton removal, final pass Fri Jun 12 19:59:44 2009 keeping 0 ideals with weight <= 25, new excess is 19224 Fri Jun 12 20:00:21 2009 Fri Jun 12 20:00:21 2009 Fri Jun 12 20:00:21 2009 Msieve v. 1.41 Fri Jun 12 20:00:21 2009 random seeds: bf533eb4 9b4b30df Fri Jun 12 20:00:21 2009 factoring 161786826623523873106331984288573086057036069356281984589662923023302881395583523319398596356535562638667735369803263428093 (123 digits) Fri Jun 12 20:00:22 2009 searching for 15-digit factors Fri Jun 12 20:00:23 2009 commencing number field sieve (123-digit input) Fri Jun 12 20:00:23 2009 R0: -403531707038578195679824 Fri Jun 12 20:00:23 2009 R1: 18400543438849 Fri Jun 12 20:00:23 2009 A0: 288596986503835432574359753965 Fri Jun 12 20:00:23 2009 A1: -7558628649210801901609443 Fri Jun 12 20:00:23 2009 A2: -90495200746547881266 Fri Jun 12 20:00:23 2009 A3: 367691967788437 Fri Jun 12 20:00:23 2009 A4: 2322968419 Fri Jun 12 20:00:23 2009 A5: 15120 Fri Jun 12 20:00:23 2009 skew 1.00, size 1.029077e-11, alpha -6.403071, combined = 5.274824e-12 Fri Jun 12 20:00:23 2009 Fri Jun 12 20:00:23 2009 commencing relation filtering Fri Jun 12 20:00:23 2009 commencing duplicate removal, pass 1 Fri Jun 12 20:01:23 2009 found 245218 hash collisions in 4342759 relations Fri Jun 12 20:01:48 2009 added 32761 free relations Fri Jun 12 20:01:48 2009 commencing duplicate removal, pass 2 Fri Jun 12 20:01:52 2009 found 221724 duplicates and 4153796 unique relations Fri Jun 12 20:01:52 2009 memory use: 36.7 MB Fri Jun 12 20:01:52 2009 reading rational ideals above 7929856 Fri Jun 12 20:01:52 2009 reading algebraic ideals above 7929856 Fri Jun 12 20:01:52 2009 commencing singleton removal, pass 1 Fri Jun 12 20:02:51 2009 relations with 0 large ideals: 225807 Fri Jun 12 20:02:51 2009 relations with 1 large ideals: 904826 Fri Jun 12 20:02:51 2009 relations with 2 large ideals: 1503333 Fri Jun 12 20:02:51 2009 relations with 3 large ideals: 1135579 Fri Jun 12 20:02:51 2009 relations with 4 large ideals: 345538 Fri Jun 12 20:02:51 2009 relations with 5 large ideals: 10406 Fri Jun 12 20:02:51 2009 relations with 6 large ideals: 28307 Fri Jun 12 20:02:51 2009 relations with 7+ large ideals: 0 Fri Jun 12 20:02:51 2009 4153796 relations and about 4466316 large ideals Fri Jun 12 20:02:51 2009 commencing singleton removal, pass 2 Fri Jun 12 20:03:49 2009 found 2073269 singletons Fri Jun 12 20:03:49 2009 current dataset: 2080527 relations and about 1761280 large ideals Fri Jun 12 20:03:49 2009 commencing singleton removal, pass 3 Fri Jun 12 20:04:20 2009 found 669977 singletons Fri Jun 12 20:04:20 2009 current dataset: 1410550 relations and about 987820 large ideals Fri Jun 12 20:04:20 2009 commencing singleton removal, pass 4 Fri Jun 12 20:04:42 2009 found 251716 singletons Fri Jun 12 20:04:42 2009 current dataset: 1158834 relations and about 716140 large ideals Fri Jun 12 20:04:42 2009 commencing singleton removal, final pass Fri Jun 12 20:04:59 2009 memory use: 16.6 MB Fri Jun 12 20:04:59 2009 commencing in-memory singleton removal Fri Jun 12 20:04:59 2009 begin with 1158834 relations and 737995 unique ideals Fri Jun 12 20:05:01 2009 reduce to 901584 relations and 471390 ideals in 19 passes Fri Jun 12 20:05:01 2009 max relations containing the same ideal: 19 Fri Jun 12 20:05:01 2009 reading rational ideals above 720000 Fri Jun 12 20:05:01 2009 reading algebraic ideals above 720000 Fri Jun 12 20:05:01 2009 commencing singleton removal, final pass Fri Jun 12 20:05:18 2009 keeping 1394025 ideals with weight <= 20, new excess is 116433 Fri Jun 12 20:05:19 2009 memory use: 34.6 MB Fri Jun 12 20:05:19 2009 commencing in-memory singleton removal Fri Jun 12 20:05:19 2009 begin with 913236 relations and 1394025 unique ideals Fri Jun 12 20:05:19 2009 reduce to 525 relations and 19 ideals in 8 passes Fri Jun 12 20:05:19 2009 max relations containing the same ideal: 2 Fri Jun 12 20:05:19 2009 filtering wants 403668 more relations Fri Jun 12 20:05:19 2009 elapsed time 00:04:58 Fri Jun 12 22:19:23 2009 Fri Jun 12 22:19:23 2009 Fri Jun 12 22:19:23 2009 Msieve v. 1.41 Fri Jun 12 22:19:23 2009 random seeds: bfd03f0f 5f41b48a Fri Jun 12 22:19:23 2009 factoring 161786826623523873106331984288573086057036069356281984589662923023302881395583523319398596356535562638667735369803263428093 (123 digits) Fri Jun 12 22:19:25 2009 searching for 15-digit factors Fri Jun 12 22:19:26 2009 commencing number field sieve (123-digit input) Fri Jun 12 22:19:26 2009 R0: -403531707038578195679824 Fri Jun 12 22:19:26 2009 R1: 18400543438849 Fri Jun 12 22:19:26 2009 A0: 288596986503835432574359753965 Fri Jun 12 22:19:26 2009 A1: -7558628649210801901609443 Fri Jun 12 22:19:26 2009 A2: -90495200746547881266 Fri Jun 12 22:19:26 2009 A3: 367691967788437 Fri Jun 12 22:19:26 2009 A4: 2322968419 Fri Jun 12 22:19:26 2009 A5: 15120 Fri Jun 12 22:19:26 2009 skew 1.00, size 1.029077e-11, alpha -6.403071, combined = 5.274824e-12 Fri Jun 12 22:19:26 2009 Fri Jun 12 22:19:26 2009 commencing relation filtering Fri Jun 12 22:19:26 2009 commencing duplicate removal, pass 1 Fri Jun 12 22:20:40 2009 error -15 reading relation 4853261 Fri Jun 12 22:20:44 2009 found 332870 hash collisions in 5121689 relations Fri Jun 12 22:21:10 2009 added 32874 free relations Fri Jun 12 22:21:10 2009 commencing duplicate removal, pass 2 Fri Jun 12 22:21:15 2009 found 302652 duplicates and 4851911 unique relations Fri Jun 12 22:21:15 2009 memory use: 40.3 MB Fri Jun 12 22:21:15 2009 reading rational ideals above 8192000 Fri Jun 12 22:21:15 2009 reading algebraic ideals above 8192000 Fri Jun 12 22:21:15 2009 commencing singleton removal, pass 1 Fri Jun 12 22:22:24 2009 relations with 0 large ideals: 264315 Fri Jun 12 22:22:24 2009 relations with 1 large ideals: 1052504 Fri Jun 12 22:22:24 2009 relations with 2 large ideals: 1735144 Fri Jun 12 22:22:24 2009 relations with 3 large ideals: 1319991 Fri Jun 12 22:22:24 2009 relations with 4 large ideals: 424942 Fri Jun 12 22:22:24 2009 relations with 5 large ideals: 26723 Fri Jun 12 22:22:24 2009 relations with 6 large ideals: 28292 Fri Jun 12 22:22:24 2009 relations with 7+ large ideals: 0 Fri Jun 12 22:22:24 2009 4851911 relations and about 4759380 large ideals Fri Jun 12 22:22:24 2009 commencing singleton removal, pass 2 Fri Jun 12 22:23:33 2009 found 2063490 singletons Fri Jun 12 22:23:33 2009 current dataset: 2788421 relations and about 2200671 large ideals Fri Jun 12 22:23:33 2009 commencing singleton removal, pass 3 Fri Jun 12 22:24:15 2009 found 656390 singletons Fri Jun 12 22:24:15 2009 current dataset: 2132031 relations and about 1474736 large ideals Fri Jun 12 22:24:15 2009 commencing singleton removal, pass 4 Fri Jun 12 22:24:46 2009 found 242361 singletons Fri Jun 12 22:24:46 2009 current dataset: 1889670 relations and about 1220553 large ideals Fri Jun 12 22:24:46 2009 commencing singleton removal, final pass Fri Jun 12 22:25:15 2009 memory use: 26.0 MB Fri Jun 12 22:25:15 2009 commencing in-memory singleton removal Fri Jun 12 22:25:15 2009 begin with 1889670 relations and 1258949 unique ideals Fri Jun 12 22:25:18 2009 reduce to 1593421 relations and 955497 ideals in 16 passes Fri Jun 12 22:25:18 2009 max relations containing the same ideal: 27 Fri Jun 12 22:25:19 2009 reading rational ideals above 720000 Fri Jun 12 22:25:19 2009 reading algebraic ideals above 720000 Fri Jun 12 22:25:19 2009 commencing singleton removal, final pass Fri Jun 12 22:25:48 2009 keeping 1913424 ideals with weight <= 20, new excess is 125729 Fri Jun 12 22:25:49 2009 memory use: 64.8 MB Fri Jun 12 22:25:49 2009 commencing in-memory singleton removal Fri Jun 12 22:25:49 2009 begin with 1596892 relations and 1913424 unique ideals Fri Jun 12 22:26:08 2009 reduce to 1013701 relations and 1301558 ideals in 73 passes Fri Jun 12 22:26:08 2009 max relations containing the same ideal: 20 Fri Jun 12 22:26:08 2009 filtering wants 1000000 more relations Fri Jun 12 22:26:08 2009 elapsed time 00:06:45 Fri Jun 12 23:46:27 2009 Fri Jun 12 23:46:27 2009 Fri Jun 12 23:46:27 2009 Msieve v. 1.41 Fri Jun 12 23:46:27 2009 random seeds: deb8b6cc 2e1ca6cf Fri Jun 12 23:46:27 2009 factoring 161786826623523873106331984288573086057036069356281984589662923023302881395583523319398596356535562638667735369803263428093 (123 digits) Fri Jun 12 23:46:28 2009 searching for 15-digit factors Fri Jun 12 23:46:29 2009 commencing number field sieve (123-digit input) Fri Jun 12 23:46:29 2009 R0: -403531707038578195679824 Fri Jun 12 23:46:29 2009 R1: 18400543438849 Fri Jun 12 23:46:29 2009 A0: 288596986503835432574359753965 Fri Jun 12 23:46:29 2009 A1: -7558628649210801901609443 Fri Jun 12 23:46:29 2009 A2: -90495200746547881266 Fri Jun 12 23:46:29 2009 A3: 367691967788437 Fri Jun 12 23:46:29 2009 A4: 2322968419 Fri Jun 12 23:46:29 2009 A5: 15120 Fri Jun 12 23:46:29 2009 skew 1.00, size 1.029077e-11, alpha -6.403071, combined = 5.274824e-12 Fri Jun 12 23:46:29 2009 Fri Jun 12 23:46:29 2009 commencing relation filtering Fri Jun 12 23:46:29 2009 commencing duplicate removal, pass 1 Fri Jun 12 23:47:47 2009 error -15 reading relation 5041416 Fri Jun 12 23:47:53 2009 found 378687 hash collisions in 5493173 relations Fri Jun 12 23:48:20 2009 added 32906 free relations Fri Jun 12 23:48:20 2009 commencing duplicate removal, pass 2 Fri Jun 12 23:48:25 2009 found 345149 duplicates and 5180930 unique relations Fri Jun 12 23:48:25 2009 memory use: 40.3 MB Fri Jun 12 23:48:25 2009 reading rational ideals above 9109504 Fri Jun 12 23:48:25 2009 reading algebraic ideals above 9109504 Fri Jun 12 23:48:25 2009 commencing singleton removal, pass 1 Fri Jun 12 23:49:39 2009 relations with 0 large ideals: 345545 Fri Jun 12 23:49:39 2009 relations with 1 large ideals: 1266516 Fri Jun 12 23:49:39 2009 relations with 2 large ideals: 1888794 Fri Jun 12 23:49:39 2009 relations with 3 large ideals: 1282726 Fri Jun 12 23:49:39 2009 relations with 4 large ideals: 355464 Fri Jun 12 23:49:39 2009 relations with 5 large ideals: 13999 Fri Jun 12 23:49:39 2009 relations with 6 large ideals: 27886 Fri Jun 12 23:49:39 2009 relations with 7+ large ideals: 0 Fri Jun 12 23:49:39 2009 5180930 relations and about 4783311 large ideals Fri Jun 12 23:49:39 2009 commencing singleton removal, pass 2 Fri Jun 12 23:50:52 2009 found 2032546 singletons Fri Jun 12 23:50:52 2009 current dataset: 3148384 relations and about 2315356 large ideals Fri Jun 12 23:50:52 2009 commencing singleton removal, pass 3 Fri Jun 12 23:51:37 2009 found 618234 singletons Fri Jun 12 23:51:37 2009 current dataset: 2530150 relations and about 1643805 large ideals Fri Jun 12 23:51:37 2009 commencing singleton removal, pass 4 Fri Jun 12 23:52:14 2009 found 211011 singletons Fri Jun 12 23:52:14 2009 current dataset: 2319139 relations and about 1425302 large ideals Fri Jun 12 23:52:14 2009 commencing singleton removal, final pass Fri Jun 12 23:52:48 2009 memory use: 33.3 MB Fri Jun 12 23:52:48 2009 commencing in-memory singleton removal Fri Jun 12 23:52:48 2009 begin with 2319138 relations and 1470374 unique ideals Fri Jun 12 23:52:51 2009 reduce to 2065653 relations and 1212121 ideals in 14 passes Fri Jun 12 23:52:51 2009 max relations containing the same ideal: 32 Fri Jun 12 23:52:52 2009 reading rational ideals above 720000 Fri Jun 12 23:52:52 2009 reading algebraic ideals above 720000 Fri Jun 12 23:52:52 2009 commencing singleton removal, final pass Fri Jun 12 23:53:27 2009 keeping 2244398 ideals with weight <= 20, new excess is 151810 Fri Jun 12 23:53:29 2009 memory use: 66.1 MB Fri Jun 12 23:53:29 2009 commencing in-memory singleton removal Fri Jun 12 23:53:30 2009 begin with 2065846 relations and 2244398 unique ideals Fri Jun 12 23:53:40 2009 reduce to 1751486 relations and 1923897 ideals in 24 passes Fri Jun 12 23:53:40 2009 max relations containing the same ideal: 20 Fri Jun 12 23:53:40 2009 filtering wants 1000000 more relations Fri Jun 12 23:53:40 2009 elapsed time 00:07:13 Sat Jun 13 01:02:32 2009 Sat Jun 13 01:02:32 2009 Sat Jun 13 01:02:32 2009 Msieve v. 1.41 Sat Jun 13 01:02:32 2009 random seeds: 82748a4d d51598b3 Sat Jun 13 01:02:32 2009 factoring 161786826623523873106331984288573086057036069356281984589662923023302881395583523319398596356535562638667735369803263428093 (123 digits) Sat Jun 13 01:02:33 2009 searching for 15-digit factors Sat Jun 13 01:02:34 2009 commencing number field sieve (123-digit input) Sat Jun 13 01:02:34 2009 R0: -403531707038578195679824 Sat Jun 13 01:02:34 2009 R1: 18400543438849 Sat Jun 13 01:02:34 2009 A0: 288596986503835432574359753965 Sat Jun 13 01:02:34 2009 A1: -7558628649210801901609443 Sat Jun 13 01:02:34 2009 A2: -90495200746547881266 Sat Jun 13 01:02:34 2009 A3: 367691967788437 Sat Jun 13 01:02:34 2009 A4: 2322968419 Sat Jun 13 01:02:34 2009 A5: 15120 Sat Jun 13 01:02:34 2009 skew 1.00, size 1.029077e-11, alpha -6.403071, combined = 5.274824e-12 Sat Jun 13 01:02:34 2009 Sat Jun 13 01:02:34 2009 commencing relation filtering Sat Jun 13 01:02:34 2009 commencing duplicate removal, pass 1 Sat Jun 13 01:03:48 2009 error -15 reading relation 5182393 Sat Jun 13 01:03:55 2009 found 414465 hash collisions in 5772298 relations Sat Jun 13 01:04:22 2009 added 32928 free relations Sat Jun 13 01:04:22 2009 commencing duplicate removal, pass 2 Sat Jun 13 01:04:27 2009 found 378446 duplicates and 5426780 unique relations Sat Jun 13 01:04:27 2009 memory use: 40.3 MB Sat Jun 13 01:04:27 2009 reading rational ideals above 9240576 Sat Jun 13 01:04:27 2009 reading algebraic ideals above 9240576 Sat Jun 13 01:04:27 2009 commencing singleton removal, pass 1 Sat Jun 13 01:05:43 2009 relations with 0 large ideals: 377155 Sat Jun 13 01:05:43 2009 relations with 1 large ideals: 1362769 Sat Jun 13 01:05:43 2009 relations with 2 large ideals: 1994385 Sat Jun 13 01:05:43 2009 relations with 3 large ideals: 1314888 Sat Jun 13 01:05:43 2009 relations with 4 large ideals: 342912 Sat Jun 13 01:05:43 2009 relations with 5 large ideals: 6832 Sat Jun 13 01:05:43 2009 relations with 6 large ideals: 27839 Sat Jun 13 01:05:43 2009 relations with 7+ large ideals: 0 Sat Jun 13 01:05:43 2009 5426780 relations and about 4859513 large ideals Sat Jun 13 01:05:43 2009 commencing singleton removal, pass 2 Sat Jun 13 01:06:59 2009 found 2010559 singletons Sat Jun 13 01:06:59 2009 current dataset: 3416221 relations and about 2450810 large ideals Sat Jun 13 01:06:59 2009 commencing singleton removal, pass 3 Sat Jun 13 01:07:49 2009 found 597342 singletons Sat Jun 13 01:07:49 2009 current dataset: 2818879 relations and about 1808301 large ideals Sat Jun 13 01:07:49 2009 commencing singleton removal, pass 4 Sat Jun 13 01:08:29 2009 found 196450 singletons Sat Jun 13 01:08:29 2009 current dataset: 2622429 relations and about 1605872 large ideals Sat Jun 13 01:08:29 2009 commencing singleton removal, final pass Sat Jun 13 01:09:08 2009 memory use: 35.7 MB Sat Jun 13 01:09:08 2009 commencing in-memory singleton removal Sat Jun 13 01:09:08 2009 begin with 2622429 relations and 1656743 unique ideals Sat Jun 13 01:09:11 2009 reduce to 2379143 relations and 1409509 ideals in 13 passes Sat Jun 13 01:09:11 2009 max relations containing the same ideal: 34 Sat Jun 13 01:09:12 2009 reading rational ideals above 720000 Sat Jun 13 01:09:12 2009 reading algebraic ideals above 720000 Sat Jun 13 01:09:12 2009 commencing singleton removal, final pass Sat Jun 13 01:09:54 2009 keeping 2439301 ideals with weight <= 20, new excess is 178904 Sat Jun 13 01:09:56 2009 memory use: 89.9 MB Sat Jun 13 01:09:56 2009 commencing in-memory singleton removal Sat Jun 13 01:09:56 2009 begin with 2379242 relations and 2439301 unique ideals Sat Jun 13 01:10:04 2009 reduce to 2157977 relations and 2214963 ideals in 16 passes Sat Jun 13 01:10:04 2009 max relations containing the same ideal: 20 Sat Jun 13 01:10:05 2009 filtering wants 1000000 more relations Sat Jun 13 01:10:05 2009 elapsed time 00:07:33 Sat Jun 13 09:20:57 2009 Sat Jun 13 09:20:57 2009 Sat Jun 13 09:20:57 2009 Msieve v. 1.41 Sat Jun 13 09:20:57 2009 random seeds: d4f72b0d 5f6e8dac Sat Jun 13 09:20:57 2009 factoring 161786826623523873106331984288573086057036069356281984589662923023302881395583523319398596356535562638667735369803263428093 (123 digits) Sat Jun 13 09:20:59 2009 searching for 15-digit factors Sat Jun 13 09:21:00 2009 commencing number field sieve (123-digit input) Sat Jun 13 09:21:00 2009 R0: -403531707038578195679824 Sat Jun 13 09:21:00 2009 R1: 18400543438849 Sat Jun 13 09:21:00 2009 A0: 288596986503835432574359753965 Sat Jun 13 09:21:00 2009 A1: -7558628649210801901609443 Sat Jun 13 09:21:00 2009 A2: -90495200746547881266 Sat Jun 13 09:21:00 2009 A3: 367691967788437 Sat Jun 13 09:21:00 2009 A4: 2322968419 Sat Jun 13 09:21:00 2009 A5: 15120 Sat Jun 13 09:21:00 2009 skew 1.00, size 1.029077e-11, alpha -6.403071, combined = 5.274824e-12 Sat Jun 13 09:21:00 2009 Sat Jun 13 09:21:00 2009 commencing relation filtering Sat Jun 13 09:21:00 2009 commencing duplicate removal, pass 1 Sat Jun 13 09:22:35 2009 error -15 reading relation 6135277 Sat Jun 13 09:22:57 2009 found 693492 hash collisions in 7649825 relations Sat Jun 13 09:23:25 2009 added 32973 free relations Sat Jun 13 09:23:25 2009 commencing duplicate removal, pass 2 Sat Jun 13 09:23:32 2009 found 641368 duplicates and 7041430 unique relations Sat Jun 13 09:23:32 2009 memory use: 48.6 MB Sat Jun 13 09:23:32 2009 reading rational ideals above 9633792 Sat Jun 13 09:23:32 2009 reading algebraic ideals above 9633792 Sat Jun 13 09:23:32 2009 commencing singleton removal, pass 1 Sat Jun 13 09:25:14 2009 relations with 0 large ideals: 506739 Sat Jun 13 09:25:14 2009 relations with 1 large ideals: 1797606 Sat Jun 13 09:25:14 2009 relations with 2 large ideals: 2579855 Sat Jun 13 09:25:14 2009 relations with 3 large ideals: 1674934 Sat Jun 13 09:25:14 2009 relations with 4 large ideals: 440116 Sat Jun 13 09:25:14 2009 relations with 5 large ideals: 14500 Sat Jun 13 09:25:14 2009 relations with 6 large ideals: 27680 Sat Jun 13 09:25:14 2009 relations with 7+ large ideals: 0 Sat Jun 13 09:25:14 2009 7041430 relations and about 5295063 large ideals Sat Jun 13 09:25:14 2009 commencing singleton removal, pass 2 Sat Jun 13 09:27:01 2009 found 1790083 singletons Sat Jun 13 09:27:01 2009 current dataset: 5251347 relations and about 3286858 large ideals Sat Jun 13 09:27:01 2009 commencing singleton removal, pass 3 Sat Jun 13 09:28:24 2009 found 425197 singletons Sat Jun 13 09:28:24 2009 current dataset: 4826150 relations and about 2847189 large ideals Sat Jun 13 09:28:24 2009 commencing singleton removal, final pass Sat Jun 13 09:29:36 2009 memory use: 69.3 MB Sat Jun 13 09:29:37 2009 commencing in-memory singleton removal Sat Jun 13 09:29:37 2009 begin with 4826149 relations and 2931993 unique ideals Sat Jun 13 09:29:43 2009 reduce to 4568128 relations and 2670795 ideals in 11 passes Sat Jun 13 09:29:43 2009 max relations containing the same ideal: 42 Sat Jun 13 09:29:44 2009 reading rational ideals above 720000 Sat Jun 13 09:29:44 2009 reading algebraic ideals above 720000 Sat Jun 13 09:29:44 2009 commencing singleton removal, final pass Sat Jun 13 09:31:07 2009 keeping 3506550 ideals with weight <= 20, new excess is 444702 Sat Jun 13 09:31:12 2009 memory use: 127.2 MB Sat Jun 13 09:31:12 2009 commencing in-memory singleton removal Sat Jun 13 09:31:13 2009 begin with 4568195 relations and 3506550 unique ideals Sat Jun 13 09:31:21 2009 reduce to 4532733 relations and 3470763 ideals in 9 passes Sat Jun 13 09:31:21 2009 max relations containing the same ideal: 20 Sat Jun 13 09:31:26 2009 removing 1083262 relations and 810204 ideals in 273058 cliques Sat Jun 13 09:31:27 2009 commencing in-memory singleton removal Sat Jun 13 09:31:27 2009 begin with 3449471 relations and 3470763 unique ideals Sat Jun 13 09:31:32 2009 reduce to 3299683 relations and 2500727 ideals in 7 passes Sat Jun 13 09:31:32 2009 max relations containing the same ideal: 20 Sat Jun 13 09:31:36 2009 removing 833905 relations and 560847 ideals in 273058 cliques Sat Jun 13 09:31:36 2009 commencing in-memory singleton removal Sat Jun 13 09:31:37 2009 begin with 2465778 relations and 2500727 unique ideals Sat Jun 13 09:31:40 2009 reduce to 2332272 relations and 1795523 ideals in 8 passes Sat Jun 13 09:31:40 2009 max relations containing the same ideal: 19 Sat Jun 13 09:31:43 2009 removing 106458 relations and 85564 ideals in 20894 cliques Sat Jun 13 09:31:43 2009 commencing in-memory singleton removal Sat Jun 13 09:31:43 2009 begin with 2225814 relations and 1795523 unique ideals Sat Jun 13 09:31:45 2009 reduce to 2223285 relations and 1707413 ideals in 5 passes Sat Jun 13 09:31:45 2009 max relations containing the same ideal: 18 Sat Jun 13 09:31:46 2009 relations with 0 large ideals: 35555 Sat Jun 13 09:31:46 2009 relations with 1 large ideals: 212163 Sat Jun 13 09:31:46 2009 relations with 2 large ideals: 514722 Sat Jun 13 09:31:46 2009 relations with 3 large ideals: 659685 Sat Jun 13 09:31:46 2009 relations with 4 large ideals: 493889 Sat Jun 13 09:31:46 2009 relations with 5 large ideals: 226498 Sat Jun 13 09:31:46 2009 relations with 6 large ideals: 67432 Sat Jun 13 09:31:46 2009 relations with 7+ large ideals: 13341 Sat Jun 13 09:31:46 2009 commencing 2-way merge Sat Jun 13 09:31:49 2009 reduce to 1578507 relation sets and 1062635 unique ideals Sat Jun 13 09:31:49 2009 commencing full merge Sat Jun 13 09:32:19 2009 memory use: 104.7 MB Sat Jun 13 09:32:19 2009 found 793018 cycles, need 722835 Sat Jun 13 09:32:20 2009 weight of 722835 cycles is about 51025720 (70.59/cycle) Sat Jun 13 09:32:20 2009 distribution of cycle lengths: Sat Jun 13 09:32:20 2009 1 relations: 70009 Sat Jun 13 09:32:20 2009 2 relations: 75914 Sat Jun 13 09:32:20 2009 3 relations: 81835 Sat Jun 13 09:32:20 2009 4 relations: 78723 Sat Jun 13 09:32:20 2009 5 relations: 74097 Sat Jun 13 09:32:20 2009 6 relations: 67368 Sat Jun 13 09:32:20 2009 7 relations: 59972 Sat Jun 13 09:32:20 2009 8 relations: 52597 Sat Jun 13 09:32:20 2009 9 relations: 44793 Sat Jun 13 09:32:20 2009 10+ relations: 117527 Sat Jun 13 09:32:20 2009 heaviest cycle: 15 relations Sat Jun 13 09:32:20 2009 commencing cycle optimization Sat Jun 13 09:32:22 2009 start with 4135027 relations Sat Jun 13 09:32:36 2009 pruned 184148 relations Sat Jun 13 09:32:36 2009 memory use: 126.0 MB Sat Jun 13 09:32:36 2009 distribution of cycle lengths: Sat Jun 13 09:32:36 2009 1 relations: 70009 Sat Jun 13 09:32:36 2009 2 relations: 78957 Sat Jun 13 09:32:36 2009 3 relations: 87287 Sat Jun 13 09:32:36 2009 4 relations: 83219 Sat Jun 13 09:32:36 2009 5 relations: 78985 Sat Jun 13 09:32:36 2009 6 relations: 70517 Sat Jun 13 09:32:36 2009 7 relations: 62392 Sat Jun 13 09:32:36 2009 8 relations: 53131 Sat Jun 13 09:32:36 2009 9 relations: 43708 Sat Jun 13 09:32:36 2009 10+ relations: 94630 Sat Jun 13 09:32:36 2009 heaviest cycle: 15 relations Sat Jun 13 09:32:37 2009 RelProcTime: 578 Sat Jun 13 09:32:37 2009 elapsed time 00:11:40 Sat Jun 13 10:08:45 2009 Sat Jun 13 10:08:45 2009 Sat Jun 13 10:08:45 2009 Msieve v. 1.41 Sat Jun 13 10:08:45 2009 random seeds: b95777f6 913f57c4 Sat Jun 13 10:08:45 2009 factoring 161786826623523873106331984288573086057036069356281984589662923023302881395583523319398596356535562638667735369803263428093 (123 digits) Sat Jun 13 10:08:46 2009 searching for 15-digit factors Sat Jun 13 10:08:47 2009 commencing number field sieve (123-digit input) Sat Jun 13 10:08:47 2009 R0: -403531707038578195679824 Sat Jun 13 10:08:47 2009 R1: 18400543438849 Sat Jun 13 10:08:47 2009 A0: 288596986503835432574359753965 Sat Jun 13 10:08:47 2009 A1: -7558628649210801901609443 Sat Jun 13 10:08:47 2009 A2: -90495200746547881266 Sat Jun 13 10:08:47 2009 A3: 367691967788437 Sat Jun 13 10:08:47 2009 A4: 2322968419 Sat Jun 13 10:08:47 2009 A5: 15120 Sat Jun 13 10:08:47 2009 skew 1.00, size 1.029077e-11, alpha -6.403071, combined = 5.274824e-12 Sat Jun 13 10:08:47 2009 Sat Jun 13 10:08:47 2009 commencing linear algebra Sat Jun 13 10:08:48 2009 read 722835 cycles Sat Jun 13 10:08:50 2009 cycles contain 1990579 unique relations Sat Jun 13 10:09:22 2009 read 1990579 relations Sat Jun 13 10:09:27 2009 using 20 quadratic characters above 67108668 Sat Jun 13 10:09:48 2009 building initial matrix Sat Jun 13 10:10:31 2009 memory use: 267.2 MB Sat Jun 13 10:10:32 2009 read 722835 cycles Sat Jun 13 10:10:33 2009 matrix is 722618 x 722835 (213.2 MB) with weight 67963204 (94.02/col) Sat Jun 13 10:10:33 2009 sparse part has weight 47938517 (66.32/col) Sat Jun 13 10:11:07 2009 filtering completed in 3 passes Sat Jun 13 10:11:07 2009 matrix is 721430 x 721630 (213.0 MB) with weight 67890760 (94.08/col) Sat Jun 13 10:11:07 2009 sparse part has weight 47901032 (66.38/col) Sat Jun 13 10:11:15 2009 read 721630 cycles Sat Jun 13 10:11:16 2009 matrix is 721430 x 721630 (213.0 MB) with weight 67890760 (94.08/col) Sat Jun 13 10:11:16 2009 sparse part has weight 47901032 (66.38/col) Sat Jun 13 10:11:16 2009 saving the first 48 matrix rows for later Sat Jun 13 10:11:16 2009 matrix is 721382 x 721630 (205.5 MB) with weight 53354728 (73.94/col) Sat Jun 13 10:11:16 2009 sparse part has weight 46662784 (64.66/col) Sat Jun 13 10:11:16 2009 matrix includes 64 packed rows Sat Jun 13 10:11:16 2009 using block size 10922 for processor cache size 256 kB Sat Jun 13 10:11:22 2009 commencing Lanczos iteration Sat Jun 13 10:11:22 2009 memory use: 192.6 MB Sat Jun 13 12:59:06 2009 lanczos halted after 11408 iterations (dim = 721381) Sat Jun 13 12:59:08 2009 recovered 32 nontrivial dependencies Sat Jun 13 12:59:08 2009 BLanczosTime: 10221 Sat Jun 13 12:59:08 2009 elapsed time 02:50:23 Sat Jun 13 17:14:02 2009 Sat Jun 13 17:14:02 2009 Sat Jun 13 17:14:02 2009 Msieve v. 1.41 Sat Jun 13 17:14:02 2009 random seeds: 705341fb cc3403da Sat Jun 13 17:14:02 2009 factoring 161786826623523873106331984288573086057036069356281984589662923023302881395583523319398596356535562638667735369803263428093 (123 digits) Sat Jun 13 17:14:03 2009 searching for 15-digit factors Sat Jun 13 17:14:04 2009 commencing number field sieve (123-digit input) Sat Jun 13 17:14:04 2009 R0: -403531707038578195679824 Sat Jun 13 17:14:04 2009 R1: 18400543438849 Sat Jun 13 17:14:04 2009 A0: 288596986503835432574359753965 Sat Jun 13 17:14:04 2009 A1: -7558628649210801901609443 Sat Jun 13 17:14:04 2009 A2: -90495200746547881266 Sat Jun 13 17:14:04 2009 A3: 367691967788437 Sat Jun 13 17:14:04 2009 A4: 2322968419 Sat Jun 13 17:14:04 2009 A5: 15120 Sat Jun 13 17:14:04 2009 skew 1.00, size 1.029077e-11, alpha -6.403071, combined = 5.274824e-12 Sat Jun 13 17:14:04 2009 Sat Jun 13 17:14:04 2009 commencing square root phase Sat Jun 13 17:14:04 2009 reading relations for dependency 1 Sat Jun 13 17:14:05 2009 read 360628 cycles Sat Jun 13 17:14:05 2009 cycles contain 1248013 unique relations Sat Jun 13 17:14:23 2009 read 1248013 relations Sat Jun 13 17:14:33 2009 multiplying 994200 relations Sat Jun 13 17:18:41 2009 multiply complete, coefficients have about 44.73 million bits Sat Jun 13 17:18:43 2009 initial square root is modulo 2645257 Sat Jun 13 17:24:35 2009 reading relations for dependency 2 Sat Jun 13 17:24:35 2009 read 360316 cycles Sat Jun 13 17:24:36 2009 cycles contain 1248281 unique relations Sat Jun 13 17:24:54 2009 read 1248281 relations Sat Jun 13 17:25:03 2009 multiplying 995182 relations Sat Jun 13 17:29:11 2009 multiply complete, coefficients have about 44.78 million bits Sat Jun 13 17:29:13 2009 initial square root is modulo 2683463 Sat Jun 13 17:35:12 2009 sqrtTime: 1268 Sat Jun 13 17:35:12 2009 prp58 factor: 1076573811006174078255496603425369798195157247908414024513 Sat Jun 13 17:35:12 2009 prp66 factor: 150279363077127682942036206681415950498349083088117034520490825661 Sat Jun 13 17:35:12 2009 elapsed time 00:21:10

Jun 14, 2009

By Dmitry Domanov
3·10¹⁷⁰+1 = 3(0)₁₆₉1_<171> = 7 · 43 · 199 · 57529 · 1526651229058273_<16> · C146
C146 = P42 · P105
P42 = 261968755177133227477927295381326837835413_<42>
P105 = 217683509057887059702713392168572709659690627314116574373411276814837715368246493032016769217598949465919_<105>

C146=P42*P105 261968755177133227477927295381326837835413<42>*217683509057887059702713392168572709659690627314116574373411276814837715368246493032016769217598949465919<105>

Jun 13, 2009

By Dmitry Domanov / GMP-ECM 6.2.3/GGNFS/msieve 1.41 / Jun 13, 2009
(16·10¹⁹⁸-7)/9 = 1(7)_198<199> = 1549 · 838171 · 125956137380071_<15> · 419305834596410850871_<21> · C155
C155 = P43 · P51 · P62
P43 = 2304592382652143961731264096224704807494453_<43>
P51 = 970232895675790774671967182467598265874128054928869_<51>
P62 = 11595061808911655986014839901941482182826165063259278842132599_<62>

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=359511029 Step 1 took 596172ms ********** Factor found in step 1: 2304592382652143961731264096224704807494453 Found probable prime factor of 43 digits: 2304592382652143961731264096224704807494453 Composite cofactor 11249910394400128588769006741704920966079711840343348528218384849373111775151335952807607620202060052645211100531 has 113 digits Number: 113 N=11249910394400128588769006741704920966079711840343348528218384849373111775151335952807607620202060052645211100531 ( 113 digits) Divisors found: r1=970232895675790774671967182467598265874128054928869 (pp51) r2=11595061808911655986014839901941482182826165063259278842132599 (pp62) Version: Msieve v. 1.41 Total time: 22.41 hours. Scaled time: 43.85 units (timescale=1.957). Factorization parameters were as follows: name: 113 n: 11249910394400128588769006741704920966079711840343348528218384849373111775151335952807607620202060052645211100531 skew: 59745.59 # norm 3.15e+015 c5: 5160 c4: -1695445366 c3: -45700015886565 c2: 3212891314605306753 c1: 22427336187626592335133 c0: 681835847596764281493583285 # alpha -6.11 Y1: 71639820263 Y0: -4652649231129391287936 # Murphy_E 7.55e-010 # M 1907449802102492470588219400247055954751799605254586842573274650345131418013743453796202936420222481907727438553 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 2650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 364394 x 364642 Polynomial selection time: 2.11 hours. Total sieving time: 19.77 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.31 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 22.41 hours. --------- CPU info (if available) ----------

(16·10¹⁹⁰-7)/9 = 1(7)_190<191> = 6067 · 376882183 · C178
C178 = P58 · P59 · P62
P58 = 6945950415193564269695115861239077510702586733059382852791_<58>
P59 = 64441391317514719880046737523653294644667708778777048133109_<59>
P62 = 17370058629430105732971321653115633962410075240228083185104703_<62>

N=7774954774392157161927067104500558023545269774120869069685490738315009061192661033202790969577883277483294279822564047287532151045058863141496220336288440400519147292742336300957 ( 178 digits) SNFS difficulty: 191 digits. Divisors found: r1=6945950415193564269695115861239077510702586733059382852791 (pp58) r2=64441391317514719880046737523653294644667708778777048133109 (pp59) r3=17370058629430105732971321653115633962410075240228083185104703 (pp62) Version: Msieve v. 1.41 Total time: 237.40 hours. Scaled time: 467.44 units (timescale=1.969). Factorization parameters were as follows: n: 7774954774392157161927067104500558023545269774120869069685490738315009061192661033202790969577883277483294279822564047287532151045058863141496220336288440400519147292742336300957 m: 200000000000000000000000000000000000000 deg: 5 c5: 1 c0: -14 skew: 1.70 type: snfs lss: 1 rlim: 10900000 alim: 10900000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 10900000/10900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [5450000, 9050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1830662 x 1830910 Total sieving time: 230.22 hours. Total relation processing time: 0.35 hours. Matrix solve time: 6.34 hours. Time per square root: 0.49 hours. Prototype def-par.txt line would be: snfs,191.000,5,0,0,0,0,0,0,0,0,10900000,10900000,28,28,54,54,2.5,2.5,100000 total time: 237.40 hours. --------- CPU info (if available) ----------

(13·10¹⁸⁵-31)/9 = 1(4)₁₈₄1_<186> = 3² · 11 · 43² · 145650497 · 616424391175458370238527_<24> · C148
C148 = P29 · P120
P29 = 65179480030846277956271414089_<29>
P120 = 134842271464926635129442045399461515806781710308343035529982485877975632051921808466844841500311919558453436567204757101_<120>

C148=P29*P120 C148=65179480030846277956271414089<29>*134842271464926635129442045399461515806781710308343035529982485877975632051921808466844841500311919558453436567204757101<120>

(13·10¹⁸⁴-31)/9 = 1(4)₁₈₃1_<185> = 7 · 34283 · 55249 · C175
C175 = P28 · C147
P28 = 8073813069587996438988098243_<28>
C147 = [134933837651912564103374368384507680483444062389797150170691343744949834607546660900113391183180100724265992335560088217959448485874274082253775023_<147>]

C175=P28*C147 C175=8073813069587996438988098243<28>*134933837651912564103374368384507680483444062389797150170691343744949834607546660900113391183180100724265992335560088217959448485874274082253775023<147>

Jun 12, 2009 (4th)

By Justin Card / GGNFS, msieve / Jun 12, 2009
(65·10¹⁶⁶+43)/9 = 7(2)₁₆₅7_<167> = 12263 · 603213984515802900576681227024393_<33> · C130
C130 = P57 · P74
P57 = 450631373675458452337775455499947328084685648775502985779_<57>
P74 = 21666127415793961010964729859371091707932535791390299034807201472008220607_<74>

Sieving performed over 2.5 days manually Postprocessing log: Thu Jun 11 22:15:03 2009 Thu Jun 11 22:15:03 2009 Thu Jun 11 22:15:03 2009 Msieve v. 1.41 Thu Jun 11 22:15:03 2009 random seeds: 891788b7 6f9284bd Thu Jun 11 22:15:03 2009 factoring 9763436759606743427904739583306785308462946373464374213867612168717174093348236091973396634356359866256404708584327307961415747853 (130 digits) Thu Jun 11 22:15:04 2009 searching for 15-digit factors Thu Jun 11 22:15:05 2009 commencing number field sieve (130-digit input) Thu Jun 11 22:15:05 2009 R0: -1000000000000000000000000000000000 Thu Jun 11 22:15:05 2009 R1: 1 Thu Jun 11 22:15:05 2009 A0: 43 Thu Jun 11 22:15:05 2009 A1: 0 Thu Jun 11 22:15:05 2009 A2: 0 Thu Jun 11 22:15:05 2009 A3: 0 Thu Jun 11 22:15:05 2009 A4: 0 Thu Jun 11 22:15:05 2009 A5: 650 Thu Jun 11 22:15:05 2009 skew 1.00, size 9.555107e-12, alpha -0.317313, combined = 3.222005e-10 Thu Jun 11 22:15:05 2009 Thu Jun 11 22:15:05 2009 commencing relation filtering Thu Jun 11 22:15:05 2009 commencing duplicate removal, pass 1 Thu Jun 11 22:17:35 2009 found 2090217 hash collisions in 13684980 relations Thu Jun 11 22:18:13 2009 added 357929 free relations Thu Jun 11 22:18:13 2009 commencing duplicate removal, pass 2 Thu Jun 11 22:18:27 2009 found 2030428 duplicates and 12012481 unique relations Thu Jun 11 22:18:27 2009 memory use: 69.3 MB Thu Jun 11 22:18:27 2009 reading rational ideals above 6094848 Thu Jun 11 22:18:27 2009 reading algebraic ideals above 6094848 Thu Jun 11 22:18:27 2009 commencing singleton removal, pass 1 Thu Jun 11 22:20:57 2009 relations with 0 large ideals: 299061 Thu Jun 11 22:20:57 2009 relations with 1 large ideals: 1856276 Thu Jun 11 22:20:57 2009 relations with 2 large ideals: 4373394 Thu Jun 11 22:20:57 2009 relations with 3 large ideals: 4053181 Thu Jun 11 22:20:57 2009 relations with 4 large ideals: 1048259 Thu Jun 11 22:20:57 2009 relations with 5 large ideals: 39190 Thu Jun 11 22:20:57 2009 relations with 6 large ideals: 343119 Thu Jun 11 22:20:57 2009 relations with 7+ large ideals: 1 Thu Jun 11 22:20:57 2009 12012481 relations and about 9765690 large ideals Thu Jun 11 22:20:57 2009 commencing singleton removal, pass 2 Thu Jun 11 22:23:39 2009 found 3384675 singletons Thu Jun 11 22:23:39 2009 current dataset: 8627806 relations and about 5627344 large ideals Thu Jun 11 22:23:39 2009 commencing singleton removal, pass 3 Thu Jun 11 22:25:22 2009 found 877593 singletons Thu Jun 11 22:25:22 2009 current dataset: 7750213 relations and about 4725529 large ideals Thu Jun 11 22:25:22 2009 commencing singleton removal, pass 4 Thu Jun 11 22:26:57 2009 found 139102 singletons Thu Jun 11 22:26:57 2009 current dataset: 7611111 relations and about 4585593 large ideals Thu Jun 11 22:26:57 2009 commencing singleton removal, final pass Thu Jun 11 22:28:37 2009 memory use: 123.1 MB Thu Jun 11 22:28:37 2009 commencing in-memory singleton removal Thu Jun 11 22:28:38 2009 begin with 7611111 relations and 4846475 unique ideals Thu Jun 11 22:28:45 2009 reduce to 7238441 relations and 4470046 ideals in 8 passes Thu Jun 11 22:28:45 2009 max relations containing the same ideal: 31 Thu Jun 11 22:28:46 2009 reading rational ideals above 720000 Thu Jun 11 22:28:46 2009 reading algebraic ideals above 720000 Thu Jun 11 22:28:46 2009 commencing singleton removal, final pass Thu Jun 11 22:30:40 2009 keeping 4652011 ideals with weight <= 20, new excess is 661449 Thu Jun 11 22:30:45 2009 memory use: 177.4 MB Thu Jun 11 22:30:45 2009 commencing in-memory singleton removal Thu Jun 11 22:30:46 2009 begin with 7239473 relations and 4652011 unique ideals Thu Jun 11 22:30:50 2009 reduce to 7238347 relations and 4645988 ideals in 4 passes Thu Jun 11 22:30:50 2009 max relations containing the same ideal: 20 Thu Jun 11 22:30:55 2009 removing 1370225 relations and 970225 ideals in 400000 cliques Thu Jun 11 22:30:56 2009 commencing in-memory singleton removal Thu Jun 11 22:30:56 2009 begin with 5868122 relations and 4645988 unique ideals Thu Jun 11 22:31:02 2009 reduce to 5763246 relations and 3565026 ideals in 7 passes Thu Jun 11 22:31:02 2009 max relations containing the same ideal: 20 Thu Jun 11 22:31:06 2009 removing 1048359 relations and 648359 ideals in 400000 cliques Thu Jun 11 22:31:06 2009 commencing in-memory singleton removal Thu Jun 11 22:31:07 2009 begin with 4714887 relations and 3565026 unique ideals Thu Jun 11 22:31:10 2009 reduce to 4612574 relations and 2807796 ideals in 6 passes Thu Jun 11 22:31:10 2009 max relations containing the same ideal: 20 Thu Jun 11 22:31:13 2009 removing 958972 relations and 558972 ideals in 400000 cliques Thu Jun 11 22:31:14 2009 commencing in-memory singleton removal Thu Jun 11 22:31:14 2009 begin with 3653602 relations and 2807796 unique ideals Thu Jun 11 22:31:17 2009 reduce to 3546460 relations and 2133022 ideals in 6 passes Thu Jun 11 22:31:17 2009 max relations containing the same ideal: 19 Thu Jun 11 22:31:19 2009 removing 927820 relations and 527820 ideals in 400000 cliques Thu Jun 11 22:31:20 2009 commencing in-memory singleton removal Thu Jun 11 22:31:20 2009 begin with 2618640 relations and 2133022 unique ideals Thu Jun 11 22:31:22 2009 reduce to 2502532 relations and 1476617 ideals in 7 passes Thu Jun 11 22:31:22 2009 max relations containing the same ideal: 16 Thu Jun 11 22:31:24 2009 removing 617081 relations and 358447 ideals in 258634 cliques Thu Jun 11 22:31:24 2009 commencing in-memory singleton removal Thu Jun 11 22:31:24 2009 begin with 1885451 relations and 1476617 unique ideals Thu Jun 11 22:31:25 2009 reduce to 1796412 relations and 1019287 ideals in 7 passes Thu Jun 11 22:31:25 2009 max relations containing the same ideal: 14 Thu Jun 11 22:31:26 2009 removing 44809 relations and 34965 ideals in 9844 cliques Thu Jun 11 22:31:27 2009 commencing in-memory singleton removal Thu Jun 11 22:31:27 2009 begin with 1751603 relations and 1019287 unique ideals Thu Jun 11 22:31:27 2009 reduce to 1750837 relations and 983553 ideals in 4 passes Thu Jun 11 22:31:27 2009 max relations containing the same ideal: 14 Thu Jun 11 22:31:28 2009 relations with 0 large ideals: 174112 Thu Jun 11 22:31:28 2009 relations with 1 large ideals: 583484 Thu Jun 11 22:31:28 2009 relations with 2 large ideals: 636673 Thu Jun 11 22:31:28 2009 relations with 3 large ideals: 282529 Thu Jun 11 22:31:28 2009 relations with 4 large ideals: 64640 Thu Jun 11 22:31:28 2009 relations with 5 large ideals: 7757 Thu Jun 11 22:31:28 2009 relations with 6 large ideals: 1629 Thu Jun 11 22:31:28 2009 relations with 7+ large ideals: 13 Thu Jun 11 22:31:28 2009 commencing 2-way merge Thu Jun 11 22:31:29 2009 reduce to 1298618 relation sets and 531334 unique ideals Thu Jun 11 22:31:29 2009 commencing full merge Thu Jun 11 22:31:35 2009 memory use: 52.1 MB Thu Jun 11 22:31:35 2009 found 764728 cycles, need 661649 Thu Jun 11 22:31:35 2009 weight of 661649 cycles is about 32721827 (49.45/cycle) Thu Jun 11 22:31:35 2009 distribution of cycle lengths: Thu Jun 11 22:31:35 2009 1 relations: 174112 Thu Jun 11 22:31:35 2009 2 relations: 97968 Thu Jun 11 22:31:35 2009 3 relations: 80875 Thu Jun 11 22:31:35 2009 4 relations: 65935 Thu Jun 11 22:31:35 2009 5 relations: 56261 Thu Jun 11 22:31:35 2009 6 relations: 46805 Thu Jun 11 22:31:35 2009 7 relations: 40424 Thu Jun 11 22:31:35 2009 8 relations: 33366 Thu Jun 11 22:31:35 2009 9 relations: 27756 Thu Jun 11 22:31:35 2009 10+ relations: 38147 Thu Jun 11 22:31:35 2009 heaviest cycle: 14 relations Thu Jun 11 22:31:35 2009 matrix can improve, retrying Thu Jun 11 22:31:36 2009 reading rational ideals above 720000 Thu Jun 11 22:31:36 2009 reading algebraic ideals above 720000 Thu Jun 11 22:31:36 2009 commencing singleton removal, final pass Thu Jun 11 22:33:29 2009 keeping 4741281 ideals with weight <= 25, new excess is 572179 Thu Jun 11 22:33:34 2009 memory use: 177.4 MB Thu Jun 11 22:33:34 2009 commencing in-memory singleton removal Thu Jun 11 22:33:35 2009 begin with 7239473 relations and 4741281 unique ideals Thu Jun 11 22:33:40 2009 reduce to 7238347 relations and 4735258 ideals in 4 passes Thu Jun 11 22:33:40 2009 max relations containing the same ideal: 25 Thu Jun 11 22:33:45 2009 removing 1370225 relations and 970225 ideals in 400000 cliques Thu Jun 11 22:33:46 2009 commencing in-memory singleton removal Thu Jun 11 22:33:47 2009 begin with 5868122 relations and 4735258 unique ideals Thu Jun 11 22:33:52 2009 reduce to 5763246 relations and 3654296 ideals in 7 passes Thu Jun 11 22:33:52 2009 max relations containing the same ideal: 25 Thu Jun 11 22:33:57 2009 removing 1048359 relations and 648359 ideals in 400000 cliques Thu Jun 11 22:33:57 2009 commencing in-memory singleton removal Thu Jun 11 22:33:58 2009 begin with 4714887 relations and 3654296 unique ideals Thu Jun 11 22:34:02 2009 reduce to 4612548 relations and 2897043 ideals in 6 passes Thu Jun 11 22:34:02 2009 max relations containing the same ideal: 24 Thu Jun 11 22:34:05 2009 removing 958960 relations and 558960 ideals in 400000 cliques Thu Jun 11 22:34:05 2009 commencing in-memory singleton removal Thu Jun 11 22:34:06 2009 begin with 3653588 relations and 2897043 unique ideals Thu Jun 11 22:34:09 2009 reduce to 3546576 relations and 2222376 ideals in 6 passes Thu Jun 11 22:34:09 2009 max relations containing the same ideal: 23 Thu Jun 11 22:34:12 2009 removing 927863 relations and 527863 ideals in 400000 cliques Thu Jun 11 22:34:12 2009 commencing in-memory singleton removal Thu Jun 11 22:34:13 2009 begin with 2618713 relations and 2222376 unique ideals Thu Jun 11 22:34:15 2009 reduce to 2502567 relations and 1565849 ideals in 7 passes Thu Jun 11 22:34:15 2009 max relations containing the same ideal: 19 Thu Jun 11 22:34:17 2009 removing 645878 relations and 372888 ideals in 272990 cliques Thu Jun 11 22:34:17 2009 commencing in-memory singleton removal Thu Jun 11 22:34:18 2009 begin with 1856689 relations and 1565849 unique ideals Thu Jun 11 22:34:19 2009 reduce to 1761413 relations and 1086714 ideals in 7 passes Thu Jun 11 22:34:19 2009 max relations containing the same ideal: 17 Thu Jun 11 22:34:20 2009 removing 49978 relations and 39007 ideals in 10971 cliques Thu Jun 11 22:34:21 2009 commencing in-memory singleton removal Thu Jun 11 22:34:21 2009 begin with 1711435 relations and 1086714 unique ideals Thu Jun 11 22:34:22 2009 reduce to 1710437 relations and 1046700 ideals in 5 passes Thu Jun 11 22:34:22 2009 max relations containing the same ideal: 16 Thu Jun 11 22:34:22 2009 relations with 0 large ideals: 113635 Thu Jun 11 22:34:22 2009 relations with 1 large ideals: 443963 Thu Jun 11 22:34:22 2009 relations with 2 large ideals: 615026 Thu Jun 11 22:34:22 2009 relations with 3 large ideals: 381062 Thu Jun 11 22:34:22 2009 relations with 4 large ideals: 128224 Thu Jun 11 22:34:22 2009 relations with 5 large ideals: 24417 Thu Jun 11 22:34:22 2009 relations with 6 large ideals: 3945 Thu Jun 11 22:34:22 2009 relations with 7+ large ideals: 165 Thu Jun 11 22:34:22 2009 commencing 2-way merge Thu Jun 11 22:34:23 2009 reduce to 1266153 relation sets and 602416 unique ideals Thu Jun 11 22:34:23 2009 commencing full merge Thu Jun 11 22:34:38 2009 memory use: 58.1 MB Thu Jun 11 22:34:38 2009 found 666737 cycles, need 584616 Thu Jun 11 22:34:39 2009 weight of 584616 cycles is about 41139292 (70.37/cycle) Thu Jun 11 22:34:39 2009 distribution of cycle lengths: Thu Jun 11 22:34:39 2009 1 relations: 113778 Thu Jun 11 22:34:39 2009 2 relations: 61154 Thu Jun 11 22:34:39 2009 3 relations: 53353 Thu Jun 11 22:34:39 2009 4 relations: 47482 Thu Jun 11 22:34:39 2009 5 relations: 44643 Thu Jun 11 22:34:39 2009 6 relations: 40899 Thu Jun 11 22:34:39 2009 7 relations: 38087 Thu Jun 11 22:34:39 2009 8 relations: 34576 Thu Jun 11 22:34:39 2009 9 relations: 31157 Thu Jun 11 22:34:39 2009 10+ relations: 119487 Thu Jun 11 22:34:39 2009 heaviest cycle: 18 relations Thu Jun 11 22:34:39 2009 matrix can improve, retrying Thu Jun 11 22:34:40 2009 reading rational ideals above 720000 Thu Jun 11 22:34:40 2009 reading algebraic ideals above 720000 Thu Jun 11 22:34:40 2009 commencing singleton removal, final pass Thu Jun 11 22:37:12 2009 keeping 4838805 ideals with weight <= 30, new excess is 474655 Thu Jun 11 22:37:20 2009 memory use: 177.4 MB Thu Jun 11 22:37:20 2009 commencing in-memory singleton removal Thu Jun 11 22:37:22 2009 begin with 7239473 relations and 4838805 unique ideals Thu Jun 11 22:37:29 2009 reduce to 7238347 relations and 4832782 ideals in 4 passes Thu Jun 11 22:37:29 2009 max relations containing the same ideal: 30 Thu Jun 11 22:37:39 2009 removing 1370225 relations and 970225 ideals in 400000 cliques Thu Jun 11 22:37:40 2009 commencing in-memory singleton removal Thu Jun 11 22:37:42 2009 begin with 5868122 relations and 4832782 unique ideals Thu Jun 11 22:37:53 2009 reduce to 5763246 relations and 3751820 ideals in 7 passes Thu Jun 11 22:37:53 2009 max relations containing the same ideal: 30 Thu Jun 11 22:38:01 2009 removing 1048359 relations and 648359 ideals in 400000 cliques Thu Jun 11 22:38:02 2009 commencing in-memory singleton removal Thu Jun 11 22:38:03 2009 begin with 4714887 relations and 3751820 unique ideals Thu Jun 11 22:38:11 2009 reduce to 4612549 relations and 2994568 ideals in 6 passes Thu Jun 11 22:38:11 2009 max relations containing the same ideal: 28 Thu Jun 11 22:38:17 2009 removing 958958 relations and 558958 ideals in 400000 cliques Thu Jun 11 22:38:18 2009 commencing in-memory singleton removal Thu Jun 11 22:38:19 2009 begin with 3653591 relations and 2994568 unique ideals Thu Jun 11 22:38:25 2009 reduce to 3546538 relations and 2319864 ideals in 6 passes Thu Jun 11 22:38:25 2009 max relations containing the same ideal: 26 Thu Jun 11 22:38:30 2009 removing 927846 relations and 527846 ideals in 400000 cliques Thu Jun 11 22:38:31 2009 commencing in-memory singleton removal Thu Jun 11 22:38:31 2009 begin with 2618692 relations and 2319864 unique ideals Thu Jun 11 22:38:36 2009 reduce to 2502397 relations and 1663234 ideals in 7 passes Thu Jun 11 22:38:36 2009 max relations containing the same ideal: 21 Thu Jun 11 22:38:39 2009 removing 676969 relations and 388406 ideals in 288563 cliques Thu Jun 11 22:38:40 2009 commencing in-memory singleton removal Thu Jun 11 22:38:41 2009 begin with 1825428 relations and 1663234 unique ideals Thu Jun 11 22:38:44 2009 reduce to 1723810 relations and 1160990 ideals in 7 passes Thu Jun 11 22:38:44 2009 max relations containing the same ideal: 18 Thu Jun 11 22:38:46 2009 removing 55463 relations and 43243 ideals in 12220 cliques Thu Jun 11 22:38:47 2009 commencing in-memory singleton removal Thu Jun 11 22:38:47 2009 begin with 1668347 relations and 1160990 unique ideals Thu Jun 11 22:38:49 2009 reduce to 1667063 relations and 1116452 ideals in 5 passes Thu Jun 11 22:38:49 2009 max relations containing the same ideal: 18 Thu Jun 11 22:38:49 2009 relations with 0 large ideals: 65458 Thu Jun 11 22:38:49 2009 relations with 1 large ideals: 297828 Thu Jun 11 22:38:49 2009 relations with 2 large ideals: 530856 Thu Jun 11 22:38:49 2009 relations with 3 large ideals: 462549 Thu Jun 11 22:38:49 2009 relations with 4 large ideals: 229066 Thu Jun 11 22:38:49 2009 relations with 5 large ideals: 67346 Thu Jun 11 22:38:49 2009 relations with 6 large ideals: 12804 Thu Jun 11 22:38:49 2009 relations with 7+ large ideals: 1156 Thu Jun 11 22:38:49 2009 commencing 2-way merge Thu Jun 11 22:38:52 2009 reduce to 1233370 relation sets and 682759 unique ideals Thu Jun 11 22:38:52 2009 commencing full merge Thu Jun 11 22:39:14 2009 memory use: 65.7 MB Thu Jun 11 22:39:14 2009 found 634387 cycles, need 560959 Thu Jun 11 22:39:15 2009 weight of 560959 cycles is about 39428217 (70.29/cycle) Thu Jun 11 22:39:15 2009 distribution of cycle lengths: Thu Jun 11 22:39:15 2009 1 relations: 72319 Thu Jun 11 22:39:15 2009 2 relations: 52148 Thu Jun 11 22:39:15 2009 3 relations: 55635 Thu Jun 11 22:39:15 2009 4 relations: 54694 Thu Jun 11 22:39:15 2009 5 relations: 54247 Thu Jun 11 22:39:15 2009 6 relations: 49707 Thu Jun 11 22:39:15 2009 7 relations: 45747 Thu Jun 11 22:39:15 2009 8 relations: 40721 Thu Jun 11 22:39:15 2009 9 relations: 35481 Thu Jun 11 22:39:15 2009 10+ relations: 100260 Thu Jun 11 22:39:15 2009 heaviest cycle: 16 relations Thu Jun 11 22:39:15 2009 commencing cycle optimization Thu Jun 11 22:39:17 2009 start with 3244833 relations Thu Jun 11 22:39:31 2009 pruned 210947 relations Thu Jun 11 22:39:31 2009 memory use: 93.5 MB Thu Jun 11 22:39:31 2009 distribution of cycle lengths: Thu Jun 11 22:39:31 2009 1 relations: 72319 Thu Jun 11 22:39:31 2009 2 relations: 54853 Thu Jun 11 22:39:31 2009 3 relations: 60718 Thu Jun 11 22:39:31 2009 4 relations: 60060 Thu Jun 11 22:39:31 2009 5 relations: 60069 Thu Jun 11 22:39:31 2009 6 relations: 54268 Thu Jun 11 22:39:31 2009 7 relations: 49024 Thu Jun 11 22:39:31 2009 8 relations: 42072 Thu Jun 11 22:39:31 2009 9 relations: 35161 Thu Jun 11 22:39:31 2009 10+ relations: 72415 Thu Jun 11 22:39:31 2009 heaviest cycle: 16 relations Thu Jun 11 22:39:34 2009 RelProcTime: 1326 Thu Jun 11 22:39:34 2009 elapsed time 00:24:31 Thu Jun 11 22:39:45 2009 Thu Jun 11 22:39:45 2009 Thu Jun 11 22:39:45 2009 Msieve v. 1.41 Thu Jun 11 22:39:45 2009 random seeds: 2f7019d3 c696b041 Thu Jun 11 22:39:45 2009 factoring 9763436759606743427904739583306785308462946373464374213867612168717174093348236091973396634356359866256404708584327307961415747853 (130 digits) Thu Jun 11 22:39:47 2009 searching for 15-digit factors Thu Jun 11 22:39:48 2009 commencing number field sieve (130-digit input) Thu Jun 11 22:39:48 2009 R0: -1000000000000000000000000000000000 Thu Jun 11 22:39:48 2009 R1: 1 Thu Jun 11 22:39:48 2009 A0: 43 Thu Jun 11 22:39:48 2009 A1: 0 Thu Jun 11 22:39:48 2009 A2: 0 Thu Jun 11 22:39:48 2009 A3: 0 Thu Jun 11 22:39:48 2009 A4: 0 Thu Jun 11 22:39:48 2009 A5: 650 Thu Jun 11 22:39:48 2009 skew 1.00, size 9.555107e-12, alpha -0.317313, combined = 3.222005e-10 Thu Jun 11 22:39:48 2009 Thu Jun 11 22:39:48 2009 commencing linear algebra Thu Jun 11 22:39:48 2009 read 560959 cycles Thu Jun 11 22:39:51 2009 cycles contain 1460370 unique relations Thu Jun 11 22:40:18 2009 Thu Jun 11 22:40:18 2009 Thu Jun 11 22:40:18 2009 Msieve v. 1.41 Thu Jun 11 22:40:18 2009 random seeds: 896479b4 8c2297c6 Thu Jun 11 22:40:18 2009 factoring 9763436759606743427904739583306785308462946373464374213867612168717174093348236091973396634356359866256404708584327307961415747853 (130 digits) Thu Jun 11 22:40:19 2009 searching for 15-digit factors Thu Jun 11 22:40:20 2009 commencing number field sieve (130-digit input) Thu Jun 11 22:40:20 2009 R0: -1000000000000000000000000000000000 Thu Jun 11 22:40:20 2009 R1: 1 Thu Jun 11 22:40:20 2009 A0: 43 Thu Jun 11 22:40:20 2009 A1: 0 Thu Jun 11 22:40:20 2009 A2: 0 Thu Jun 11 22:40:20 2009 A3: 0 Thu Jun 11 22:40:20 2009 A4: 0 Thu Jun 11 22:40:20 2009 A5: 650 Thu Jun 11 22:40:20 2009 skew 1.00, size 9.555107e-12, alpha -0.317313, combined = 3.222005e-10 Thu Jun 11 22:40:20 2009 Thu Jun 11 22:40:20 2009 commencing linear algebra Thu Jun 11 22:40:20 2009 read 560959 cycles Thu Jun 11 22:40:21 2009 cycles contain 1460370 unique relations Thu Jun 11 22:40:43 2009 read 1460370 relations Thu Jun 11 22:40:46 2009 using 20 quadratic characters above 134210724 Thu Jun 11 22:41:00 2009 building initial matrix Thu Jun 11 22:41:26 2009 memory use: 185.1 MB Thu Jun 11 22:41:27 2009 read 560959 cycles Thu Jun 11 22:41:27 2009 matrix is 560744 x 560959 (161.1 MB) with weight 48786446 (86.97/col) Thu Jun 11 22:41:27 2009 sparse part has weight 36056943 (64.28/col) Thu Jun 11 22:41:43 2009 filtering completed in 2 passes Thu Jun 11 22:41:43 2009 matrix is 559754 x 559954 (160.9 MB) with weight 48736748 (87.04/col) Thu Jun 11 22:41:43 2009 sparse part has weight 36028515 (64.34/col) Thu Jun 11 22:41:47 2009 read 559954 cycles Thu Jun 11 22:41:48 2009 matrix is 559754 x 559954 (160.9 MB) with weight 48736748 (87.04/col) Thu Jun 11 22:41:48 2009 sparse part has weight 36028515 (64.34/col) Thu Jun 11 22:41:48 2009 saving the first 48 matrix rows for later Thu Jun 11 22:41:48 2009 matrix is 559706 x 559954 (153.0 MB) with weight 38273617 (68.35/col) Thu Jun 11 22:41:48 2009 sparse part has weight 34501380 (61.61/col) Thu Jun 11 22:41:48 2009 matrix includes 64 packed rows Thu Jun 11 22:41:48 2009 using block size 10922 for processor cache size 256 kB Thu Jun 11 22:41:52 2009 commencing Lanczos iteration (2 threads) Thu Jun 11 22:41:52 2009 memory use: 149.8 MB Thu Jun 11 23:37:37 2009 lanczos halted after 8855 iterations (dim = 559706) Thu Jun 11 23:37:38 2009 recovered 39 nontrivial dependencies Thu Jun 11 23:37:38 2009 BLanczosTime: 3438 Thu Jun 11 23:37:38 2009 elapsed time 00:57:20 Thu Jun 11 23:42:07 2009 Thu Jun 11 23:42:07 2009 Thu Jun 11 23:42:07 2009 Msieve v. 1.41 Thu Jun 11 23:42:07 2009 random seeds: f3d8e841 ee630f48 Thu Jun 11 23:42:07 2009 factoring 9763436759606743427904739583306785308462946373464374213867612168717174093348236091973396634356359866256404708584327307961415747853 (130 digits) Thu Jun 11 23:42:09 2009 searching for 15-digit factors Thu Jun 11 23:42:09 2009 commencing number field sieve (130-digit input) Thu Jun 11 23:42:09 2009 R0: -1000000000000000000000000000000000 Thu Jun 11 23:42:09 2009 R1: 1 Thu Jun 11 23:42:09 2009 A0: 43 Thu Jun 11 23:42:09 2009 A1: 0 Thu Jun 11 23:42:09 2009 A2: 0 Thu Jun 11 23:42:09 2009 A3: 0 Thu Jun 11 23:42:09 2009 A4: 0 Thu Jun 11 23:42:09 2009 A5: 650 Thu Jun 11 23:42:09 2009 skew 1.00, size 9.555107e-12, alpha -0.317313, combined = 3.222005e-10 Thu Jun 11 23:42:10 2009 Thu Jun 11 23:42:10 2009 commencing square root phase Thu Jun 11 23:42:10 2009 reading relations for dependency 1 Thu Jun 11 23:42:10 2009 read 279367 cycles Thu Jun 11 23:42:10 2009 cycles contain 921779 unique relations Thu Jun 11 23:42:27 2009 read 921779 relations Thu Jun 11 23:42:33 2009 multiplying 729442 relations Thu Jun 11 23:44:19 2009 multiply complete, coefficients have about 22.36 million bits Thu Jun 11 23:44:20 2009 initial square root is modulo 2636251 Thu Jun 11 23:47:12 2009 reading relations for dependency 2 Thu Jun 11 23:47:12 2009 read 279179 cycles Thu Jun 11 23:47:13 2009 cycles contain 921197 unique relations Thu Jun 11 23:47:29 2009 read 921197 relations Thu Jun 11 23:47:35 2009 multiplying 728430 relations Thu Jun 11 23:49:22 2009 multiply complete, coefficients have about 22.33 million bits Thu Jun 11 23:49:22 2009 initial square root is modulo 2586791 Thu Jun 11 23:52:15 2009 sqrtTime: 605 Thu Jun 11 23:52:15 2009 prp57 factor: 450631373675458452337775455499947328084685648775502985779 Thu Jun 11 23:52:15 2009 prp74 factor: 21666127415793961010964729859371091707932535791390299034807201472008220607 Thu Jun 11 23:52:15 2009 elapsed time 00:10:08

Jun 12, 2009 (3rd)

By Dmitry Domanov / ECM / Jun 12, 2009
(13·10¹⁷¹-31)/9 = 1(4)₁₇₀1_<172> = 11 · 845599 · 14030443675276817_<17> · C149
C149 = P30 · C119
P30 = 256462931804549017510633552397_<30>
C119 = [43156646434003437590709513779974321417811490608715284910791365906651077456606782151395693253101947622545235176793105081_<119>]

C149=P30*C119 C140=256462931804549017510633552397<30>*43156646434003437590709513779974321417811490608715284910791365906651077456606782151395693253101947622545235176793105081<119>

(19·10²⁰⁵+11)/3 = 6(3)₂₀₄7_<206> = 47 · 1049 · 28439 · 301073 · 226406454334346351603_<21> · 1677465659365970615668154819_<28> · C144
C144 = P33 · P111
P33 = 720739136192652754793757399275881_<33>
P111 = 548090560221826880156372241250752203241766441099323845908077403370902283241257961429117324365891642207569996921_<111>

C144=P33*P111 C144=720739136192652754793757399275881<33>*548090560221826880156372241250752203241766441099323845908077403370902283241257961429117324365891642207569996921<111>

(31·10¹⁷⁰-13)/9 = 3(4)₁₆₉3_<171> = 7² · 4629920455654758013498867_<25> · C145
C145 = P42 · P103
P42 = 232031625289267285997872846548274872654251_<42>
P103 = 6543383771920925262771313657337423017658900689973818172304650431186996923388887223462560916516787337371_<103>

C145=P42*P103 C145=232031625289267285997872846548274872654251<42>*6543383771920925262771313657337423017658900689973818172304650431186996923388887223462560916516787337371<103>

Jun 12, 2009 (2nd)

By Sinkiti Sibata / Msieve / Jun 12, 2009
(19·10¹⁶³+11)/3 = 6(3)₁₆₂7_<164> = 23 · 212240551 · 507368374445072909_<18> · C137
C137 = P50 · P87
P50 = 78154045810066885489839026558465998531596120691381_<50>
P87 = 327190953676735888663357517665468214766548405810117447443857596565381215359865497358761_<87>

Number: 63337_163 N=25571296782291088901074669831696584997219804892506777450351526895074193322549230921193042451835425230969964312171558082984763036717538941 ( 137 digits) SNFS difficulty: 165 digits. Divisors found: r1=78154045810066885489839026558465998531596120691381 (pp50) r2=327190953676735888663357517665468214766548405810117447443857596565381215359865497358761 (pp87) Version: Msieve-1.40 Total time: 52.38 hours. Scaled time: 109.58 units (timescale=2.092). Factorization parameters were as follows: name: 63337_163 n: 25571296782291088901074669831696584997219804892506777450351526895074193322549230921193042451835425230969964312171558082984763036717538941 m: 500000000000000000000000000000000 deg: 5 c5: 152 c0: 275 skew: 1.13 type: snfs lss: 1 rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2000000, 4000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 737427 x 737675 Total sieving time: 49.68 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.06 hours. Time per square root: 0.45 hours. Prototype def-par.txt line would be: snfs,165.000,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,51,51,2.4,2.4,100000 total time: 52.38 hours. --------- CPU info (if available) ----------

Jun 12, 2009

By Robert Backstrom / GMP-ECM / Jun 12, 2009
(58·10¹⁷³-31)/9 = 6(4)₁₇₂1_<174> = 7 · 43 · 10141 · 39563 · 48491 · 212579 · 154774691 · 34627365762419_<14> · 80771274582319_<14> · C118
C118 = P37 · P81
P37 = 3252686432044830575611644891450269629_<37>
P81 = 367662177813584306398113689094894372531220364516609385149063751165849999660842617_<81>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 1195889777350299605771289107018392405410588807124263934343162265572375663837663946874692414404316491260057477983979093 (118 digits) Using B1=4518000, B2=8562077170, polynomial Dickson(6), sigma=2004421685 Step 1 took 50653ms Step 2 took 14851ms ********** Factor found in step 2: 3252686432044830575611644891450269629 Found probable prime factor of 37 digits: 3252686432044830575611644891450269629 Probable prime cofactor 367662177813584306398113689094894372531220364516609385149063751165849999660842617 has 81 digits

Jun 11, 2009 (6th)

By Robert Backstrom / GGNFS / Jun 11, 2009
(58·10¹⁴⁷-31)/9 = 6(4)₁₄₆1_<148> = 3 · 19 · 4099 · 9319 · C139
C139 = P52 · P88
P52 = 1676223678292203960049128169722890860607910437181707_<52>
P88 = 1765758994698086055170520278368619003216331480155940049496103700209244596464918718463639_<88>

Number: n N=2959807037070370077701588675503483600950004631059528994363964170551323205253630464699789086748024196236570518498067476640101738676115451773 ( 139 digits) SNFS difficulty: 149 digits. Divisors found: r1=1676223678292203960049128169722890860607910437181707 (pp52) r2=1765758994698086055170520278368619003216331480155940049496103700209244596464918718463639 (pp88) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 12.28 hours. Scaled time: 32.52 units (timescale=2.649). Factorization parameters were as follows: name: KA_6_4_146_1 n: 2959807037070370077701588675503483600950004631059528994363964170551323205253630464699789086748024196236570518498067476640101738676115451773 m: 200000000000000000000000000000 deg: 5 c5: 725 c0: -124 skew: 0.70 type: snfs lss: 1 rlim: 2200000 alim: 2200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.3 alambda: 2.3 qintsize: 100000 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [1100000, 3200001) Primes: RFBsize:162662, AFBsize:163211, largePrimes:8173952 encountered Relations: rels:7706656, finalFF:392959 Max relations in full relation-set: 28 Initial matrix: 325940 x 392959 with sparse part having weight 44229416. Pruned matrix : 301299 x 302992 with weight 32110514. Total sieving time: 11.27 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.42 hours. Total square root time: 0.44 hours, sqrts: 5. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,2200000,2200000,28,28,56,56,2.3,2.3,100000 total time: 12.28 hours. --------- CPU info (if available) ----------

Jun 11, 2009 (5th)

By Dmitry Domanov / GGNFS/msieve 1.41 / Jun 11, 2009
(26·10²⁰³+1)/9 = 2(8)₂₀₂9_<204> = 61 · 9819918737_<10> · 37287396313_<11> · 100744959165252560987_<21> · 5394637429152624442511_<22> · C140
C140 = P49 · P92
P49 = 1591392095289804421962004160362504930638566818651_<49>
P92 = 14954375035445075432517592802281751545607225577975759746369031858970547474844079393319097347_<92>

N=23798274221406481862937388696721507629375257074001696626340245646231006728544866514463627094525111474872935700567490601892062846556764218897 ( 140 digits) Divisors found: r1=1591392095289804421962004160362504930638566818651 (pp49) r2=14954375035445075432517592802281751545607225577975759746369031858970547474844079393319097347 (pp92) Version: Msieve v. 1.41 Total time: 484.30 hours. Scaled time: 959.88 units (timescale=1.982). Factorization parameters were as follows: n: 23798274221406481862937388696721507629375257074001696626340245646231006728544866514463627094525111474872935700567490601892062846556764218897 Y0: -734848807318907386147773470 Y1: 3828307784904209 c0: -575676726393303313640246491759215387 c1: 241313731949091829399125074778 c2: 679634942601726569804696 c3: -345838423607777188 c4: -106656386559 c5: 111060 skew: 1624324.30 type: gnfs # size 1.397696e-013, alpha -7.351016, combined = 1.920798e-011 rlim: 12000000 alim: 12000000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.6 alambda: 2.6 Factor base limits: 12000000/12000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved algebraic special-q in [6000000, 13400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2138724 x 2138969 Total sieving time: 470.62 hours. Total relation processing time: 0.42 hours. Matrix solve time: 10.64 hours. Time per square root: 2.62 hours. Prototype def-par.txt line would be: gnfs,139,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,12000000,12000000,28,28,55,55,2.6,2.6,100000 total time: 484.30 hours. --------- CPU info (if available) ----------

(55·10¹⁷⁰+71)/9 = 6(1)₁₆₉9_<171> = 5867 · 1686669207321401057_<19> · C149
C149 = P41 · P109
P41 = 15417904565595260846145189831758985988853_<41>
P109 = 4005427012872325335566780151439560381843187368300758259621127417374298478093358344498755291601015884297338617_<109>

C149=P41*P109 C149=15417904565595260846145189831758985988853<41>*4005427012872325335566780151439560381843187368300758259621127417374298478093358344498755291601015884297338617<109>

Jun 11, 2009 (4th)

By Wataru Sakai / Msieve / Jun 11, 2009
8·10¹⁷⁰+9 = 8(0)₁₆₉9_<171> = 113 · 452926193 · 3182006963_<10> · 3558984497657_<13> · C139
C139 = P52 · P87
P52 = 3739349584888004768232061820906349177229967138340283_<52>
P87 = 369114253681640613419529242815258516418059888685901830643751071825955380199942725832817_<87>

Number: 80009_170 N=1380247231280688513519537236207908295619969438829829240186899926792486920831167751357193427318708350016115652627084598605877702542314467211 ( 139 digits) SNFS difficulty: 170 digits. Divisors found: r1=3739349584888004768232061820906349177229967138340283 r2=369114253681640613419529242815258516418059888685901830643751071825955380199942725832817 Version: Total time: 70.90 hours. Scaled time: 129.39 units (timescale=1.825). Factorization parameters were as follows: n: 1380247231280688513519537236207908295619969438829829240186899926792486920831167751357193427318708350016115652627084598605877702542314467211 m: 10000000000000000000000000000000000 deg: 5 c5: 8 c0: 9 skew: 1.02 type: snfs lss: 1 rlim: 4900000 alim: 4900000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4900000/4900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2450000, 4650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 617808 x 618056 Total sieving time: 70.90 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000 total time: 70.90 hours. --------- CPU info (if available) ----------

Jun 11, 2009 (3rd)

By matsui / GGNFS / Jun 11, 2009
(46·10²⁰²+17)/9 = 5(1)₂₀₁3_<203> = 1933 · C200
C200 = P41 · P76 · P84
P41 = 25095474208856818167520252174989158442949_<41>
P76 = 3297726093382206271419702874019435673426517286346071139459697077025086546391_<76>
P84 = 319501926354791297344734539988594417282060450051494131411273826097979565702137229279_<84>

N=26441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340461 ( 200 digits) SNFS difficulty: 204 digits. Divisors found: r1=25095474208856818167520252174989158442949 (pp41) r2=3297726093382206271419702874019435673426517286346071139459697077025086546391 (pp76) r3=319501926354791297344734539988594417282060450051494131411273826097979565702137229279 (pp84) Version: GGNFS-0.77.1-20060722-nocona Total time: 1246.67 hours. Scaled time: 2805.00 units (timescale=2.250). Factorization parameters were as follows: n: 26441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340461 m: 20000000000000000000000000000000000000000 deg: 5 c5: 575 c0: 68 skew: 0.65 type: snfs lss: 1 rlim: 17800000 alim: 17800000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 Factor base limits: 17800000/17800000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [8900000, 25100001) Primes: RFBsize:1139344, AFBsize:1139550, largePrimes:39498154 encountered Relations: rels:43640536, finalFF:2563810 Max relations in full relation-set: 32 Initial matrix: 2278961 x 2563810 with sparse part having weight 390927558. Pruned matrix : 2046135 x 2057593 with weight 354661269. Total sieving time: 1150.15 hours. Total relation processing time: 5.81 hours. Matrix solve time: 90.28 hours. Time per square root: 0.42 hours. Prototype def-par.txt line would be: snfs,204,5,0,0,0,0,0,0,0,0,17800000,17800000,29,29,56,56,2.6,2.6,100000 total time: 1246.67 hours.

Jun 11, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jun 11, 2009
(58·10¹⁵³-31)/9 = 6(4)₁₅₂1_<154> = 3 · 367 · 112967 · 2319381799539473_<16> · 165136459534555368901_<21> · C111
C111 = P50 · P61
P50 = 17078280205792035788335884856822731960474470615281_<50>
P61 = 7921131453941733646557818615716638624170555497980778464200671_<61>

Number: 64441_153 N=135279302517329798555025774871892764507712533727343188426012269005859259034731526227526481196165806601223053551 ( 111 digits) Divisors found: r1=17078280205792035788335884856822731960474470615281 r2=7921131453941733646557818615716638624170555497980778464200671 Version: Total time: 10.01 hours. Scaled time: 23.92 units (timescale=2.390). Factorization parameters were as follows: name: 64441_153 n: 135279302517329798555025774871892764507712533727343188426012269005859259034731526227526481196165806601223053551 skew: 23605.40 # norm 1.03e+15 c5: 22800 c4: 2606101498 c3: -45023322297711 c2: -1636176262836888459 c1: 13673763986598234398219 c0: -27225391059235964049208347 # alpha -5.58 Y1: 181355987777 Y0: -1427769303683968481770 # Murphy_E 9.32e-10 # M 81165317231035287838596792647390099905123823365903785899096838405611340060018680107531939427877027642720548542 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, 1800001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8141639 Max relations in full relation-set: Initial matrix: Pruned matrix : 387419 x 387667 Polynomial selection time: 0.76 hours. Total sieving time: 8.27 hours. Total relation processing time: 0.58 hours. Matrix solve time: 0.31 hours. Time per square root: 0.08 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: 10.01 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673795) Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672355) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672378) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672339)

2·10¹⁷¹-9 = 1(9)₁₇₀1_<172> = 11² · 541 · 77524813986331865479_<20> · 334794278410722364007416315208828631701999789_<45> · C103
C103 = P40 · P63
P40 = 5034377696798900669436721889289682064351_<40>
P63 = 233820618672097095012926459422107581471500507709899340258393951_<63>

Number: 19991_171 N=1177141307694526201464716642183051523982966901517506432181852284630204945543901005711357960481491140801 ( 103 digits) Divisors found: r1=5034377696798900669436721889289682064351 r2=233820618672097095012926459422107581471500507709899340258393951 Version: Total time: 3.55 hours. Scaled time: 8.41 units (timescale=2.373). Factorization parameters were as follows: name: 19991_171 n: 1177141307694526201464716642183051523982966901517506432181852284630204945543901005711357960481491140801 skew: 5404.07 # norm 2.21e+13 c5: 43680 c4: -5969942 c3: -1865578457695 c2: -7134246430272257 c1: 9256714106389184315 c0: 106135789530131846696475 # alpha -5.04 Y1: 78574733761 Y0: -30627336107087582486 # Murphy_E 2.77e-09 # M 912930077984427313258403547379730171018387886625134225735594264395813050211885657140230567293533718485 type: gnfs rlim: 1500000 alim: 1500000 lpbr: 26 lpba: 26 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 50/50 Sieved algebraic special-q in [750000, 1350001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4960858 Max relations in full relation-set: Initial matrix: Pruned matrix : 221323 x 221571 Polynomial selection time: 0.28 hours. Total sieving time: 2.84 hours. Total relation processing time: 0.29 hours. Matrix solve time: 0.10 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000 total time: 3.55 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673795) Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672355) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672378) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672339)

Jun 11, 2009

By Sinkiti Sibata / GGNFS / Jun 11, 2009
(58·10¹⁵⁹-31)/9 = 6(4)₁₅₈1_<160> = 3² · 199 · 1093443781_<10> · C148
C148 = P42 · P107
P42 = 209900031606919638060250968011950579085083_<42>
P107 = 15677648943826422381981429129925161545478792495477603112103677976852749787973098495048186703923564765299937_<107>

Number: 64441_159 N=3290739008831356339219803947719937682395452958069035022616313113583137251250683536978098961627564466067632336829533503848993054608278016739537539771 ( 148 digits) SNFS difficulty: 161 digits. Divisors found: r1=209900031606919638060250968011950579085083 (pp42) r2=15677648943826422381981429129925161545478792495477603112103677976852749787973098495048186703923564765299937 (pp107) Version: GGNFS-0.77.1-20060513-nocona Total time: 63.25 hours. Scaled time: 162.17 units (timescale=2.564). Factorization parameters were as follows: name: 64441_159 n: 3290739008831356339219803947719937682395452958069035022616313113583137251250683536978098961627564466067632336829533503848993054608278016739537539771 m: 100000000000000000000000000000000 deg: 5 c5: 29 c0: -155 skew: 1.40 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 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: 51/51 Sieved rational special-q in [1200000, 3700001) Primes: RFBsize:176302, AFBsize:176834, largePrimes:9998293 encountered Relations: rels:11718185, finalFF:504709 Max relations in full relation-set: 28 Initial matrix: 353201 x 504709 with sparse part having weight 72785254. Pruned matrix : 312059 x 313889 with weight 49222426. Total sieving time: 61.84 hours. Total relation processing time: 0.20 hours. Matrix solve time: 1.08 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,51,51,2.4,2.4,100000 total time: 63.25 hours. --------- CPU info (if available) ----------

Jun 10, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM 6.2.3 / Jun 10, 2009
(58·10¹⁴²-31)/9 = 6(4)₁₄₁1_<143> = 13 · 23 · 16921 · 9524591 · C130
C130 = P37 · P93
P37 = 1527327053387300561922655200517536151_<37>
P93 = 875608341824785328181448860447816700700338797768291942567678323978198356949700451593224781019_<93>

Number: 64441_142 N=1337340308640589620461913848808391038150893661277969899138772830138477829834862994727105090713233954169870052955561019646391117869 ( 130 digits) SNFS difficulty: 144 digits. Divisors found: r1=1527327053387300561922655200517536151 r2=875608341824785328181448860447816700700338797768291942567678323978198356949700451593224781019 Version: Total time: 5.36 hours. Scaled time: 12.80 units (timescale=2.390). Factorization parameters were as follows: n: 1337340308640589620461913848808391038150893661277969899138772830138477829834862994727105090713233954169870052955561019646391117869 m: 20000000000000000000000000000 deg: 5 c5: 725 c0: -124 skew: 0.70 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1200000, 2350001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4659016 Max relations in full relation-set: Initial matrix: Pruned matrix : 353852 x 354100 Total sieving time: 4.60 hours. Total relation processing time: 0.47 hours. Matrix solve time: 0.26 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,144,5,0,0,0,0,0,0,0,0,2400000,2400000,26,26,49,49,2.3,2.3,50000 total time: 5.36 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673795) Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672355) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672378) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672339)

(58·10¹⁵⁷-31)/9 = 6(4)₁₅₆1_<158> = 2648031729249449_<16> · 361382784217781834150297587_<27> · C116
C116 = P35 · P37 · P46
P35 = 37727530996966089900393367642062277_<35>
P37 = 1174640614178015563795193560615453921_<37>
P46 = 1519607549694666831724736274979975973591058671_<46>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 67343369134565438844901431185162974421508417199500632120324380433626581713504247852334181996419224033954426575162507 (116 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3241163861 Step 1 took 4758ms Step 2 took 4056ms ********** Factor found in step 2: 37727530996966089900393367642062277 Found probable prime factor of 35 digits: 37727530996966089900393367642062277 Composite cofactor 1784992745482892754448907629357284460115231211814851591365797111193768269607998991 has 82 digits Wed Jun 10 20:58:37 2009 Wed Jun 10 20:58:37 2009 Wed Jun 10 20:58:37 2009 Msieve v. 1.39 Wed Jun 10 20:58:37 2009 random seeds: 09b54ec4 e4f52600 Wed Jun 10 20:58:37 2009 factoring 1784992745482892754448907629357284460115231211814851591365797111193768269607998991 (82 digits) Wed Jun 10 20:58:38 2009 searching for 15-digit factors Wed Jun 10 20:58:39 2009 commencing quadratic sieve (82-digit input) Wed Jun 10 20:58:39 2009 using multiplier of 2 Wed Jun 10 20:58:39 2009 using VC8 32kb sieve core Wed Jun 10 20:58:39 2009 sieve interval: 12 blocks of size 32768 Wed Jun 10 20:58:39 2009 processing polynomials in batches of 17 Wed Jun 10 20:58:39 2009 using a sieve bound of 1334353 (51039 primes) Wed Jun 10 20:58:39 2009 using large prime bound of 126763535 (26 bits) Wed Jun 10 20:58:39 2009 using trial factoring cutoff of 27 bits Wed Jun 10 20:58:39 2009 polynomial 'A' values have 10 factors Wed Jun 10 21:12:23 2009 51267 relations (26158 full + 25109 combined from 276608 partial), need 51135 Wed Jun 10 21:12:26 2009 begin with 302766 relations Wed Jun 10 21:12:26 2009 reduce to 73151 relations in 2 passes Wed Jun 10 21:12:26 2009 attempting to read 73151 relations Wed Jun 10 21:12:26 2009 recovered 73151 relations Wed Jun 10 21:12:26 2009 recovered 63902 polynomials Wed Jun 10 21:12:26 2009 attempting to build 51267 cycles Wed Jun 10 21:12:26 2009 found 51267 cycles in 1 passes Wed Jun 10 21:12:26 2009 distribution of cycle lengths: Wed Jun 10 21:12:26 2009 length 1 : 26158 Wed Jun 10 21:12:26 2009 length 2 : 25109 Wed Jun 10 21:12:26 2009 largest cycle: 2 relations Wed Jun 10 21:12:26 2009 matrix is 51039 x 51267 (7.7 MB) with weight 1598396 (31.18/col) Wed Jun 10 21:12:26 2009 sparse part has weight 1598396 (31.18/col) Wed Jun 10 21:12:27 2009 filtering completed in 4 passes Wed Jun 10 21:12:27 2009 matrix is 36342 x 36406 (6.0 MB) with weight 1273006 (34.97/col) Wed Jun 10 21:12:27 2009 sparse part has weight 1273006 (34.97/col) Wed Jun 10 21:12:27 2009 saving the first 48 matrix rows for later Wed Jun 10 21:12:27 2009 matrix is 36294 x 36406 (4.5 MB) with weight 1009038 (27.72/col) Wed Jun 10 21:12:27 2009 sparse part has weight 825277 (22.67/col) Wed Jun 10 21:12:27 2009 matrix includes 64 packed rows Wed Jun 10 21:12:27 2009 using block size 14562 for processor cache size 4096 kB Wed Jun 10 21:12:27 2009 commencing Lanczos iteration Wed Jun 10 21:12:27 2009 memory use: 4.3 MB Wed Jun 10 21:12:31 2009 lanczos halted after 576 iterations (dim = 36292) Wed Jun 10 21:12:31 2009 recovered 17 nontrivial dependencies Wed Jun 10 21:12:31 2009 prp37 factor: 1174640614178015563795193560615453921 Wed Jun 10 21:12:31 2009 prp46 factor: 1519607549694666831724736274979975973591058671 Wed Jun 10 21:12:31 2009 elapsed time 00:13:54

(58·10¹⁹⁵-31)/9 = 6(4)₁₉₄1_<196> = 3³ · 121205741 · 843725777 · 3449383496233_<13> · 131039417139088721513_<21> · 43268274902688917839656473_<26> · C120
C120 = P34 · P86
P34 = 3808947365887241518949456612924387_<34>
P86 = 31331358494823262828693743658366323430037124627429151340540267581059886550031789827861_<86>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 119339495408525915193752433668177694063200767597864676491438032551608032555488259949937499272744109343579204370538946207 (120 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2513972108 Step 1 took 4243ms Step 2 took 4087ms ********** Factor found in step 2: 3808947365887241518949456612924387 Found probable prime factor of 34 digits: 3808947365887241518949456612924387 Probable prime cofactor 31331358494823262828693743658366323430037124627429151340540267581059886550031789827861 has 86 digits

Jun 10, 2009 (3rd)

By Sinkiti Sibata / Msieve / Jun 10, 2009
(58·10¹³⁹-31)/9 = 6(4)₁₃₈1_<140> = 107 · 80387 · C133
C133 = P62 · P72
P62 = 30526319028262238359498114223427853590308640702586934246165653_<62>
P72 = 245437798286995703352529829459865094652787031237088609961669260962599733_<72>

Number: 64441_139 N=7492312532103105949786185547559062061162821631251861694339200059483794392807555650992115878275808584900967323428573672574393851570649 ( 133 digits) SNFS difficulty: 141 digits. Divisors found: r1=30526319028262238359498114223427853590308640702586934246165653 (pp62) r2=245437798286995703352529829459865094652787031237088609961669260962599733 (pp72) Version: Msieve-1.40 Total time: 7.19 hours. Scaled time: 18.43 units (timescale=2.564). Factorization parameters were as follows: name: 64441_139 n: 7492312532103105949786185547559062061162821631251861694339200059483794392807555650992115878275808584900967323428573672574393851570649 m: 10000000000000000000000000000 deg: 5 c5: 29 c0: -155 skew: 1.40 type: snfs lss: 1 rlim: 1600000 alim: 1600000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [800000, 1800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 254885 x 255133 Total sieving time: 7.19 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,141.000,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000 total time: 7.19 hours. --------- CPU info (if available) ----------

(58·10¹³⁶-31)/9 = 6(4)₁₃₅1_<137> = 13 · 47939 · 4176817 · 5558906216847676501769_<22> · C103
C103 = P39 · P64
P39 = 633355274586104563509265411646604936091_<39>
P64 = 7031872289102237803989792955009556850261052778421728047172153941_<64>

Number: 64441_136 N=4453673404518767477016279696608870096235646732603416366253344277217826059089646595306167583295118784631 ( 103 digits) SNFS difficulty: 138 digits. Divisors found: r1=633355274586104563509265411646604936091 (pp39) r2=7031872289102237803989792955009556850261052778421728047172153941 (pp64) Version: Msieve-1.40 Total time: 6.33 hours. Scaled time: 13.23 units (timescale=2.092). Factorization parameters were as follows: name: 64441_136 n: 4453673404518767477016279696608870096235646732603416366253344277217826059089646595306167583295118784631 m: 2000000000000000000000000000 deg: 5 c5: 145 c0: -248 skew: 1.11 type: snfs lss: 1 rlim: 1430000 alim: 1430000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1430000/1430000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [715000, 1540001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 221217 x 221449 Total sieving time: 6.01 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.16 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,138.000,5,0,0,0,0,0,0,0,0,1430000,1430000,26,26,48,48,2.3,2.3,75000 total time: 6.33 hours. --------- CPU info (if available) ----------

Jun 10, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Jun 10, 2009
(58·10¹⁴³-31)/9 = 6(4)₁₄₂1_<144> = 7 · 26683 · C139
C139 = P48 · P92
P48 = 342602696066354823193997798573370772650604826459_<48>
P92 = 10070754559295277760249566975349829558487644575316533280632068011095277845540303297091747479_<92>

Number: n N=3450267663437097158942528653580634242478862649008434714689633551830456226513641347055880654051774240658549019677828282557885675975845746861 ( 139 digits) SNFS difficulty: 146 digits. Divisors found: r1=342602696066354823193997798573370772650604826459 (pp48) r2=10070754559295277760249566975349829558487644575316533280632068011095277845540303297091747479 (pp92) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 9.29 hours. Scaled time: 24.72 units (timescale=2.660). Factorization parameters were as follows: name: KA_6_4_142_1 n: 3450267663437097158942528653580634242478862649008434714689633551830456226513641347055880654051774240658549019677828282557885675975845746861 m: 50000000000000000000000000000 deg: 5 c5: 464 c0: -775 skew: 1.11 type: snfs lss: 1 rlim: 1920000 alim: 1920000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.3 alambda: 2.3 qintsize: 100000 Factor base limits: 1920000/1920000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [960000, 2560001) Primes: RFBsize:143414, AFBsize:143328, largePrimes:7362448 encountered Relations: rels:6792022, finalFF:324534 Max relations in full relation-set: 28 Initial matrix: 286809 x 324534 with sparse part having weight 33806415. Pruned matrix : 273676 x 275174 with weight 26500476. Total sieving time: 8.45 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.31 hours. Total square root time: 0.36 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1920000,1920000,28,28,56,56,2.3,2.3,100000 total time: 9.29 hours. --------- CPU info (if available) ----------

(64·10²¹¹-1)/9 = 7(1)_211<212> = 71 · 236879 · C205
C205 = P51 · P73 · P82
P51 = 643057363391772539930509437073292784585159499609363_<51>
P73 = 1745172861926735098113731730696839166480106417061262769272337987121179921_<73>
P82 = 3767596531307051231311670269449565300807368866581972286491213685667330975891607973_<82>

Number: n N=4228171113635725656993542677616599234274247410151050025665989637373613111151661914697823742490214806353627808142322565179091025263513992977047419355250018661759926941431327488296372808576073462781830975279 ( 205 digits) SNFS difficulty: 212 digits. Divisors found: Wed Jun 10 10:00:33 2009 prp51 factor: 643057363391772539930509437073292784585159499609363 Wed Jun 10 10:00:33 2009 prp73 factor: 1745172861926735098113731730696839166480106417061262769272337987121179921 Wed Jun 10 10:00:33 2009 prp82 factor: 3767596531307051231311670269449565300807368866581972286491213685667330975891607973 Wed Jun 10 10:00:33 2009 elapsed time 31:29:32 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20050930-k8 Total time: 113.30 hours. Scaled time: 173.69 units (timescale=1.533). Factorization parameters were as follows: name: KA_7_1_211 n: 4228171113635725656993542677616599234274247410151050025665989637373613111151661914697823742490214806353627808142322565179091025263513992977047419355250018661759926941431327488296372808576073462781830975279 m: 200000000000000000000000000000000000 deg: 6 c6: 10 c0: -1 skew: 0.68 type: snfs lss: 1 rlim: 25000000 alim: 25000000 lpbr: 29 lpba: 29 mfbr: 57 mfba: 57 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 25000000/25000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 57/57 Sieved special-q in [12500000, 33599990) Primes: RFBsize:1565927, AFBsize:1564806, largePrimes:38685477 encountered Relations: rels:38036155, finalFF:2004157 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 7242530 hash collisions in 46516704 relations Msieve: matrix is 4096749 x 4096997 (1112.1 MB) Total sieving time: 112.10 hours. Total relation processing time: 1.20 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,212,6,0,0,0,0,0,0,0,0,25000000,25000000,29,29,57,57,2.6,2.6,100000 total time: 113.30 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3368968k/3407296k available (2748k kernel code, 36964k reserved, 1425k data, 416k init, 2489792k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830496) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830447) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Total of 4 processors activated (22643.71 BogoMIPS).

(58·10¹⁶⁶-31)/9 = 6(4)₁₆₅1_<167> = 13 · 3673 · 29669 · 237791 · C153
C153 = P39 · P114
P39 = 278920477089003851435716097376075149113_<39>
P114 = 685871066084268679784539153202401450105862248666859370968796776773667518547705937015346850643694246601536809957367_<114>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 191303484973767908831484385073305410609307331952420749269253261812451372451202115512906550164548598382034855111281939724339195680624834936274137697865471 (153 digits) Using B1=2144000, B2=2854157680, polynomial Dickson(6), sigma=333789588 Step 1 took 32822ms Step 2 took 10920ms ********** Factor found in step 2: 278920477089003851435716097376075149113 Found probable prime factor of 39 digits: 278920477089003851435716097376075149113 Probable prime cofactor 685871066084268679784539153202401450105862248666859370968796776773667518547705937015346850643694246601536809957367 has 114 digits

(32·10¹⁶⁸-23)/9 = 3(5)₁₆₇3_<169> = 99787 · 35110973901895945362440267_<26> · C139
C139 = P59 · P80
P59 = 25148140795056499081497427625137336246538170970339484970739_<59>
P80 = 40353828462554322758429865388999567026694081322219443685122757666884960343307763_<80>

Number: n N=1014823759795874448307906099141215069716476101479601314893226854770980254415688256799200840659055310493204808095612598493667121316526546857 ( 139 digits) SNFS difficulty: 170 digits. Divisors found: Wed Jun 10 22:39:16 2009 prp59 factor: 25148140795056499081497427625137336246538170970339484970739 Wed Jun 10 22:39:16 2009 prp80 factor: 40353828462554322758429865388999567026694081322219443685122757666884960343307763 Wed Jun 10 22:39:16 2009 elapsed time 01:42:21 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 40.62 hours. Scaled time: 63.49 units (timescale=1.563). Factorization parameters were as follows: name: KA_3_5_167_3 n: 1014823759795874448307906099141215069716476101479601314893226854770980254415688256799200840659055310493204808095612598493667121316526546857 m: 4000000000000000000000000000000000 deg: 5 c5: 125 c0: -92 skew: 0.94 type: snfs lss: 1 rlim: 4800000 alim: 4800000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2400000, 4648807) Primes: RFBsize:335439, AFBsize:335677, largePrimes:16462283 encountered Relations: rels:15982118, finalFF:631639 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1679083 hash collisions in 17631665 relations Msieve: matrix is 762700 x 762948 (205.3 MB) Total sieving time: 40.05 hours. Total relation processing time: 0.57 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,4800000,4800000,28,28,56,56,2.4,2.4,100000 total time: 40.62 hours. --------- CPU info (if available) ----------

(46·10¹⁶⁸+53)/9 = 5(1)₁₆₇7_<169> = 11 · 2383919 · 404892423714526201213_<21> · C141
C141 = P57 · P85
P57 = 130013906438737421609827744440291958180593859853561963893_<57>
P85 = 3702556412970577933431326070205991960265739985195153009374566172308595834356085499657_<85>

Number: n N=481383823060103954194458622525066612872526569817422802914373422723167098834287235699476136882982546717677639945688012941180066526049097884701 ( 141 digits) SNFS difficulty: 171 digits. Divisors found: Wed Jun 10 23:32:14 2009 prp57 factor: 130013906438737421609827744440291958180593859853561963893 Wed Jun 10 23:32:14 2009 prp85 factor: 3702556412970577933431326070205991960265739985195153009374566172308595834356085499657 Wed Jun 10 23:32:14 2009 elapsed time 02:34:18 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 52.58 hours. Scaled time: 139.85 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_1_167_7 n: 481383823060103954194458622525066612872526569817422802914373422723167098834287235699476136882982546717677639945688012941180066526049097884701 m: 5000000000000000000000000000000000 deg: 5 c5: 368 c0: 1325 skew: 1.29 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2500000, 5496571) Primes: RFBsize:348513, AFBsize:348491, largePrimes:16732815 encountered Relations: rels:16217712, finalFF:697188 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1947970 hash collisions in 18297886 relations Msieve: matrix is 856679 x 856927 (229.3 MB) Total sieving time: 51.90 hours. Total relation processing time: 0.67 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000 total time: 52.58 hours. --------- CPU info (if available) ----------

Jun 10, 2009

By Dmitry Domanov / ggnfs/msieve 1.41 / Jun 10, 2009
(58·10¹⁶¹-31)/9 = 6(4)₁₆₀1_<162> = 7 · 67 · C160
C160 = P58 · P102
P58 = 4093134095623509822924789862483442313088777192093517929121_<58>
P102 = 335704117919347485954227762146677853991802972588438738421183653051486156771646723097088789614286700309_<102>

N=1374081971096896470030798389007344231224828239753612887941246150201374081971096896470030798389007344231224828239753612887941246150201374081971096896470030798389 ( 160 digits) SNFS difficulty: 163 digits. Divisors found: r1=4093134095623509822924789862483442313088777192093517929121 (pp58) r2=335704117919347485954227762146677853991802972588438738421183653051486156771646723097088789614286700309 (pp102) Version: Msieve v. 1.41 Total time: 34.54 hours. Scaled time: 68.66 units (timescale=1.988). Factorization parameters were as follows: n: 1374081971096896470030798389007344231224828239753612887941246150201374081971096896470030798389007344231224828239753612887941246150201374081971096896470030798389 m: 200000000000000000000000000000000 deg: 5 c5: 145 c0: -248 skew: 1.11 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, 3750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 703581 x 703829 Total sieving time: 33.57 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.76 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,163.000,5,0,0,0,0,0,0,0,0,3700000,3700000,27,27,51,51,2.4,2.4,100000 total time: 34.54 hours. --------- CPU info (if available) ----------

(58·10¹²¹-31)/9 = 6(4)₁₂₀1_<122> = 61 · C121
C121 = P51 · P70
P51 = 464920469417375193572200232662861103514882907303691_<51>
P70 = 2272359192297716094864344333471243185707117555901008894066572651550791_<70>

N=1056466302367941712204007285974499089253187613843351548269581056466302367941712204007285974499089253187613843351548269581 ( 121 digits) SNFS difficulty: 123 digits. Divisors found: r1=464920469417375193572200232662861103514882907303691 (pp51) r2=2272359192297716094864344333471243185707117555901008894066572651550791 (pp70) Version: Msieve v. 1.41 Total time: 2.40 hours. Scaled time: 4.75 units (timescale=1.982). Factorization parameters were as follows: n: 1056466302367941712204007285974499089253187613843351548269581056466302367941712204007285974499089253187613843351548269581 m: 2000000000000000000000000 deg: 5 c5: 145 c0: -248 skew: 1.11 type: snfs lss: 1 rlim: 810000 alim: 810000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 810000/810000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [405000, 955001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 89180 x 89409 Total sieving time: 2.31 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.02 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,123.000,5,0,0,0,0,0,0,0,0,810000,810000,25,25,46,46,2.2,2.2,50000 total time: 2.40 hours. --------- CPU info (if available) ----------

2·10¹⁷¹+9 = 2(0)₁₇₀9_<172> = 7² · 3181 · 55360013450292649181_<20> · C147
C147 = P36 · C111
P36 = 332698364302461530229511915253909389_<36>
C111 = [696664039882704701975721828063080480151348232344868154988400858011494357876797914528601178091872120507409021829_<111>]

C147=P36*C111 C147=332698364302461530229511915253909389<36>*6966640398827047019757218280630804801513482323448681549884008580114943578767979145286011780918721205 07409021829<111>

2·10¹⁷¹-9 = 1(9)₁₇₀1_<172> = 11² · 541 · 77524813986331865479_<20> · C147
C147 = P45 · C103
P45 = 334794278410722364007416315208828631701999789_<45>
C103 = [1177141307694526201464716642183051523982966901517506432181852284630204945543901005711357960481491140801_<103>]

C147=P45*C103 C147=334794278410722364007416315208828631701999789<45>*1177141307694526201464716642183051523982966901517506432181852284630204945543901005711357960481491140801<103>

(19·10¹⁷¹+11)/3 = 6(3)₁₇₀7_<172> = 17 · C171
C171 = P38 · P134
P38 = 25310355343227723063527451248702974397_<38>
P134 = 14719233078943155176128039350114423645313440687246188053637990114166597188559130734521853858080446251446814489501657905107267542908413_<134>

N=372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843137254901961 ( 171 digits) SNFS difficulty: 172 digits. Divisors found: r1=25310355343227723063527451248702974397 (pp38) r2=14719233078943155176128039350114423645313440687246188053637990114166597188559130734521853858080446251446814489501657905107267542908413 (pp134) Version: Msieve v. 1.41 Total time: 60.02 hours. Scaled time: 118.95 units (timescale=1.982). Factorization parameters were as follows: n: 372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843137254901961 m: 10000000000000000000000000000000000 deg: 5 c5: 190 c0: 11 skew: 0.57 type: snfs lss: 1 rlim: 5200000 alim: 5200000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5200000/5200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2600000, 5600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 968092 x 968339 Total sieving time: 58.28 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.44 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,172.000,5,0,0,0,0,0,0,0,0,5200000,5200000,27,27,52,52,2.4,2.4,100000 total time: 60.02 hours. --------- CPU info (if available) ----------

Jun 9, 2009 (6th)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Jun 9, 2009
(19·10¹⁶⁸-7)/3 = 6(3)₁₆₇1_<169> = 2194638858649_<13> · 40919237740408367_<17> · C140
C140 = P33 · P43 · P65
P33 = 241612742823526534650909688816909_<33>
P43 = 6233028353893749389383907598437941819707581_<43>
P65 = 46829854524857710207917680811999264463722603395805706199658829933_<65>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 70524781078454483013796349470455628281280408219714768823579374956912502233135840477646284348677885337018782934159342461747464081084903832357 (140 digits) Using B1=1046000, B2=1045563762, polynomial Dickson(6), sigma=4279458543 Step 1 took 14398ms Step 2 took 6069ms ********** Factor found in step 2: 241612742823526534650909688816909 Found probable prime factor of 33 digits: 241612742823526534650909688816909 Composite cofactor 291891811062157604903137230387297274730508932417381545453883499198383081542958422133134293492730462669822073 has 108 digits Number: n N=291891811062157604903137230387297274730508932417381545453883499198383081542958422133134293492730462669822073 ( 108 digits) Divisors found: r1=6233028353893749389383907598437941819707581 (pp43) r2=46829854524857710207917680811999264463722603395805706199658829933 (pp65) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 10.60 hours. Scaled time: 27.41 units (timescale=2.585). Factorization parameters were as follows: n: 291891811062157604903137230387297274730508932417381545453883499198383081542958422133134293492730462669822073 name: KA_6_3_167_1 Y0: -561705156206669121855 Y1: 197076323297 c0: 203638276723910946303732994 c1: 11325872543009262796133 c2: -569264334750724044 c3: -25179488545454 c4: 320512286 c5: 5220 skew: 30973.96 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [1250000, 2400001) Primes: RFBsize:183072, AFBsize:183947, largePrimes:15902600 encountered Relations: rels:14110942, finalFF:413269 Max relations in full relation-set: 28 Initial matrix: 367098 x 413269 with sparse part having weight 38019278. Pruned matrix : 336788 x 338687 with weight 28286917. Total sieving time: 9.14 hours. Total relation processing time: 0.52 hours. Matrix solve time: 0.52 hours. Total square root time: 0.42 hours, sqrts: 2. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,28,28,56,56,2.6,2.6,150000 total time: 10.60 hours. --------- CPU info (if available) ----------

(52·10¹⁶⁸+11)/9 = 5(7)₁₆₇9_<169> = 7 · 3631 · 18695220169_<11> · 4918399219037_<13> · C142
C142 = P65 · P78
P65 = 22052280975865092692525800150982807244061830250598730578589972079_<65>
P78 = 112105950947613006602391329605195305461345950480308802909553359992427651958801_<78>

Number: n N=2472191929363311566113899520147805286457413223560785065597047238434828374391621498727947661965678444475466010146628383966893721000200248317279 ( 142 digits) SNFS difficulty: 171 digits. Divisors found: Tue Jun 09 23:43:23 2009 prp65 factor: 22052280975865092692525800150982807244061830250598730578589972079 Tue Jun 09 23:43:23 2009 prp78 factor: 112105950947613006602391329605195305461345950480308802909553359992427651958801 Tue Jun 09 23:43:23 2009 elapsed time 01:16:52 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 47.54 hours. Scaled time: 125.47 units (timescale=2.639). Factorization parameters were as follows: name: KA_5_7_167_9 n: 2472191929363311566113899520147805286457413223560785065597047238434828374391621498727947661965678444475466010146628383966893721000200248317279 m: 10000000000000000000000000000000000 deg: 5 c5: 13 c0: 275 skew: 1.84 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2500000, 5174293) Primes: RFBsize:348513, AFBsize:348622, largePrimes:16908539 encountered Relations: rels:16337061, finalFF:749922 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1847517 hash collisions in 18248277 relations Msieve: matrix is 844859 x 845107 (224.0 MB) Total sieving time: 47.00 hours. Total relation processing time: 0.54 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000 total time: 47.54 hours. --------- CPU info (if available) ----------

Jun 9, 2009 (5th)

By Sinkiti Sibata / Msieve, GGNFS / Jun 9, 2009
(58·10¹²⁶-31)/9 = 6(4)₁₂₅1_<127> = 3 · 7411 · 17231 · 149711 · 151643837421842767195511_<24> · C90
C90 = P33 · P58
P33 = 230317917783472779280908801355139_<33>
P58 = 3217145707328322487608679926740369461372781503408846476493_<58>

Tue Jun 09 05:40:41 2009 Msieve v. 1.39 Tue Jun 09 05:40:41 2009 random seeds: dba3cd58 e3fe0ec0 Tue Jun 09 05:40:41 2009 factoring 740966300517896959122455501051949913568949425089984203468076083503353610890837643708247527 (90 digits) Tue Jun 09 05:40:42 2009 searching for 15-digit factors Tue Jun 09 05:40:44 2009 commencing quadratic sieve (90-digit input) Tue Jun 09 05:40:44 2009 using multiplier of 23 Tue Jun 09 05:40:44 2009 using 64kb Pentium 4 sieve core Tue Jun 09 05:40:44 2009 sieve interval: 18 blocks of size 65536 Tue Jun 09 05:40:44 2009 processing polynomials in batches of 6 Tue Jun 09 05:40:44 2009 using a sieve bound of 1611319 (61176 primes) Tue Jun 09 05:40:44 2009 using large prime bound of 135350796 (27 bits) Tue Jun 09 05:40:44 2009 using double large prime bound of 433141090259052 (42-49 bits) Tue Jun 09 05:40:44 2009 using trial factoring cutoff of 49 bits Tue Jun 09 05:40:44 2009 polynomial 'A' values have 12 factors Tue Jun 09 07:58:27 2009 61458 relations (16936 full + 44522 combined from 659490 partial), need 61272 Tue Jun 09 07:58:28 2009 begin with 676426 relations Tue Jun 09 07:58:28 2009 reduce to 148302 relations in 10 passes Tue Jun 09 07:58:28 2009 attempting to read 148302 relations Tue Jun 09 07:58:30 2009 recovered 148302 relations Tue Jun 09 07:58:30 2009 recovered 127865 polynomials Tue Jun 09 07:58:31 2009 attempting to build 61458 cycles Tue Jun 09 07:58:31 2009 found 61458 cycles in 5 passes Tue Jun 09 07:58:31 2009 distribution of cycle lengths: Tue Jun 09 07:58:31 2009 length 1 : 16936 Tue Jun 09 07:58:31 2009 length 2 : 11789 Tue Jun 09 07:58:31 2009 length 3 : 10877 Tue Jun 09 07:58:31 2009 length 4 : 8015 Tue Jun 09 07:58:31 2009 length 5 : 5699 Tue Jun 09 07:58:31 2009 length 6 : 3616 Tue Jun 09 07:58:31 2009 length 7 : 2045 Tue Jun 09 07:58:31 2009 length 9+: 2481 Tue Jun 09 07:58:31 2009 largest cycle: 17 relations Tue Jun 09 07:58:31 2009 matrix is 61176 x 61458 (14.8 MB) with weight 3643194 (59.28/col) Tue Jun 09 07:58:31 2009 sparse part has weight 3643194 (59.28/col) Tue Jun 09 07:58:33 2009 filtering completed in 3 passes Tue Jun 09 07:58:33 2009 matrix is 57138 x 57201 (13.9 MB) with weight 3410202 (59.62/col) Tue Jun 09 07:58:33 2009 sparse part has weight 3410202 (59.62/col) Tue Jun 09 07:58:33 2009 saving the first 48 matrix rows for later Tue Jun 09 07:58:33 2009 matrix is 57090 x 57201 (8.7 MB) with weight 2676739 (46.80/col) Tue Jun 09 07:58:33 2009 sparse part has weight 1950038 (34.09/col) Tue Jun 09 07:58:33 2009 matrix includes 64 packed rows Tue Jun 09 07:58:33 2009 using block size 21845 for processor cache size 512 kB Tue Jun 09 07:58:33 2009 commencing Lanczos iteration Tue Jun 09 07:58:33 2009 memory use: 8.6 MB Tue Jun 09 07:59:05 2009 lanczos halted after 905 iterations (dim = 57090) Tue Jun 09 07:59:05 2009 recovered 18 nontrivial dependencies Tue Jun 09 07:59:06 2009 prp33 factor: 230317917783472779280908801355139 Tue Jun 09 07:59:06 2009 prp58 factor: 3217145707328322487608679926740369461372781503408846476493 Tue Jun 09 07:59:06 2009 elapsed time 02:18:25

(58·10¹²⁴-31)/9 = 6(4)₁₂₃1_<125> = 13 · 35495845603181599_<17> · C108
C108 = P44 · P65
P44 = 10365682454341659712247078164498849241329819_<44>
P65 = 13473074299298846240802412667099780125728616836040931580302460697_<65>

Number: 64441_124 N=139657609870283601668911375940815747186350774436336032162631242504400623898265616657709917390014558261623843 ( 108 digits) SNFS difficulty: 126 digits. Divisors found: r1=10365682454341659712247078164498849241329819 (pp44) r2=13473074299298846240802412667099780125728616836040931580302460697 (pp65) Version: Msieve-1.40 Total time: 2.53 hours. Scaled time: 5.12 units (timescale=2.026). Factorization parameters were as follows: name: 64441_124 n: 139657609870283601668911375940815747186350774436336032162631242504400623898265616657709917390014558261623843 m: 10000000000000000000000000 deg: 5 c5: 29 c0: -155 skew: 1.40 type: snfs lss: 1 rlim: 900000 alim: 900000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 900000/900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [450000, 800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 118575 x 118811 Total sieving time: 2.43 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.05 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,126.000,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000 total time: 2.53 hours. --------- CPU info (if available) ----------

(58·10¹²⁷-31)/9 = 6(4)₁₂₆1_<128> = 125311 · 609769384018041241_<18> · C105
C105 = P37 · P69
P37 = 4563387659778388937693511871883853581_<37>
P69 = 184817592939026058870817741062463000395240787066825512930841487415611_<69>

Number: 64441_127 N=843394322927897026365377549418668488290321211203191730227702468445885249759060112943616393213835217652991 ( 105 digits) SNFS difficulty: 129 digits. Divisors found: r1=4563387659778388937693511871883853581 (pp37) r2=184817592939026058870817741062463000395240787066825512930841487415611 (pp69) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 5.20 hours. Scaled time: 2.46 units (timescale=0.473). Factorization parameters were as follows: name: 64441_127 n: 843394322927897026365377549418668488290321211203191730227702468445885249759060112943616393213835217652991 m: 20000000000000000000000000 deg: 5 c5: 725 c0: -124 skew: 0.70 type: snfs lss: 1 rlim: 1000000 alim: 1000000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [500000, 950001) Primes: RFBsize:78498, AFBsize:78647, largePrimes:2613755 encountered Relations: rels:2478315, finalFF:176856 Max relations in full relation-set: 28 Initial matrix: 157212 x 176856 with sparse part having weight 13708487. Pruned matrix : 151509 x 152359 with weight 9984418. Total sieving time: 4.70 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.34 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,129,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000 total time: 5.20 hours. --------- CPU info (if available) ----------

(58·10¹³²-31)/9 = 6(4)₁₃₁1_<133> = 3² · 1129 · 1621 · 16858112517613651_<17> · C110
C110 = P44 · P66
P44 = 34466753311020998457630093985809224389075193_<44>
P66 = 673374543227464904583619694013355768942795706554365875033955504127_<66>

Number: 64441_132 N=23209034267342478453008918977902204295017917623204003350478450858683155607960876824016810806416786769624821511 ( 110 digits) SNFS difficulty: 134 digits. Divisors found: r1=34466753311020998457630093985809224389075193 (pp44) r2=673374543227464904583619694013355768942795706554365875033955504127 (pp66) Version: Msieve-1.40 Total time: 4.57 hours. Scaled time: 9.65 units (timescale=2.112). Factorization parameters were as follows: name: 64441_132 n: 23209034267342478453008918977902204295017917623204003350478450858683155607960876824016810806416786769624821511 m: 200000000000000000000000000 deg: 5 c5: 725 c0: -124 skew: 0.70 type: snfs lss: 1 rlim: 1210000 alim: 1210000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1210000/1210000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [605000, 1205001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 205047 x 205295 Total sieving time: 4.22 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.14 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,134.000,5,0,0,0,0,0,0,0,0,1210000,1210000,26,26,47,47,2.3,2.3,75000 total time: 4.57 hours. --------- CPU info (if available) ----------

(19·10¹⁶²+11)/3 = 6(3)₁₆₁7_<163> = 29 · 29308250296927268355754842857_<29> · C133
C133 = P49 · P85
P49 = 1291194527858043387638211121856667727905724778137_<49>
P85 = 5771022661503775565834617477507816177513092462939509440235021835776577960538998268717_<85>

Number: 63337_162 N=7451512880678436435055571220951791531103776927461414651478143238821216572496591422500580442134129208413266665885995744128931932640229 ( 133 digits) SNFS difficulty: 164 digits. Divisors found: r1=1291194527858043387638211121856667727905724778137 (pp49) r2=5771022661503775565834617477507816177513092462939509440235021835776577960538998268717 (pp85) Version: Msieve-1.40 Total time: 44.28 hours. Scaled time: 113.54 units (timescale=2.564). Factorization parameters were as follows: name: 63337_162 n: 7451512880678436435055571220951791531103776927461414651478143238821216572496591422500580442134129208413266665885995744128931932640229 m: 200000000000000000000000000000000 deg: 5 c5: 475 c0: 88 skew: 0.71 type: snfs lss: 1 rlim: 3800000 alim: 3800000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3800000/3800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1900000, 3900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 718107 x 718355 Total sieving time: 44.28 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,164.000,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000 total time: 44.28 hours. --------- CPU info (if available) ----------

(58·10¹³⁴-31)/9 = 6(4)₁₃₃1_<135> = 197 · 1217 · 2011 · C127
C127 = P48 · P79
P48 = 271751257225613675644169237643916573741484702123_<48>
P79 = 4918640111763998771075163673454473204834564360412556035749135411931945947164253_<79>

Number: 64441_134 N=1336646634212199628172054116219545703948108311669051107140593065931122376318243861956011152390469522275355700445792232258809119 ( 127 digits) SNFS difficulty: 136 digits. Divisors found: r1=271751257225613675644169237643916573741484702123 (pp48) r2=4918640111763998771075163673454473204834564360412556035749135411931945947164253 (pp79) Version: Msieve-1.40 Total time: 5.11 hours. Scaled time: 10.66 units (timescale=2.085). Factorization parameters were as follows: name: 64441_134 n: 1336646634212199628172054116219545703948108311669051107140593065931122376318243861956011152390469522275355700445792232258809119 m: 1000000000000000000000000000 deg: 5 c5: 29 c0: -155 skew: 1.40 type: snfs lss: 1 rlim: 1320000 alim: 1320000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1320000/1320000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [660000, 1335001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 204143 x 204372 Total sieving time: 4.89 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.14 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,136.000,5,0,0,0,0,0,0,0,0,1320000,1320000,26,26,48,48,2.3,2.3,75000 total time: 5.11 hours. --------- CPU info (if available) ----------

Jun 9, 2009 (4th)

By Wataru Sakai / Msieve / Jun 9, 2009
8·10¹⁹⁷-3 = 7(9)₁₉₆7_<198> = 11 · 23873 · C193
C193 = P54 · P140
P54 = 140821602104944344191203976546352435011228207631215297_<54>
P140 = 21633212827108175193600382697413167083794938983381715227587944143322409584255496805513095712742862874312277348366992788638949071288208626967_<140>

Number: 79997_197 N=3046423688990605590949075220008910789290297521353526045018526064058674120249959063681679188737371621801731130261268911627056811993770063556014211566509141175081777435901341568832039237937114199 ( 193 digits) SNFS difficulty: 197 digits. Divisors found: r1=140821602104944344191203976546352435011228207631215297 r2=21633212827108175193600382697413167083794938983381715227587944143322409584255496805513095712742862874312277348366992788638949071288208626967 Version: Total time: 576.63 hours. Scaled time: 1145.20 units (timescale=1.986). Factorization parameters were as follows: n: 3046423688990605590949075220008910789290297521353526045018526064058674120249959063681679188737371621801731130261268911627056811993770063556014211566509141175081777435901341568832039237937114199 m: 2000000000000000000000000000000000000000 deg: 5 c5: 25 c0: -3 skew: 0.65 type: snfs lss: 1 rlim: 13900000 alim: 13900000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5Factor base limits: 13900000/13900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6950000, 12650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1981883 x 1982131 Total sieving time: 576.63 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,197,5,0,0,0,0,0,0,0,0,13900000,13900000,28,28,55,55,2.5,2.5,100000 total time: 576.63 hours. --------- CPU info (if available) ----------

(19·10²⁰⁵-7)/3 = 6(3)₂₀₄1_<206> = C206
C206 = P50 · P157
P50 = 14447627005804904645234614420982884085254814760187_<50>
P157 = 4383649529980713498048347690027570917080963555852230233404851224727836970133139701807922977479993415798243544960995282024391148278612096474108353621266360713_<157>

Number: 63331_205 N=63333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 ( 206 digits) SNFS difficulty: 206 digits. Divisors found: r1=14447627005804904645234614420982884085254814760187 r2=4383649529980713498048347690027570917080963555852230233404851224727836970133139701807922977479993415798243544960995282024391148278612096474108353621266360713 Version: Total time: 968.77 hours. Scaled time: 1886.19 units (timescale=1.947). Factorization parameters were as follows: n: 63333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 m: 100000000000000000000000000000000000000000 deg: 5 c5: 19 c0: -7 skew: 0.82 type: snfs lss: 1 rlim: 19200000 alim: 19200000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6Factor base limits: 19200000/19200000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [9600000, 18800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 3340362 x 3340609 Total sieving time: 968.77 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,206,5,0,0,0,0,0,0,0,0,19200000,19200000,29,29,56,56,2.6,2.6,100000 total time: 968.77 hours. --------- CPU info (if available) ----------

5·10¹⁸³-1 = 4(9)_183<184> = 23 · 11633 · C179
C179 = P78 · P101
P78 = 945200151001218657635011445058228730913844677283075507271374283027271720740913_<78>
P101 = 19770909942771694388069711525503787363511760112454424254375327438641837630246346547998813862502042297_<101>

Number: 49999_183 N=18687467063339300864482226350076057990947790954518442661244809556023157509184890061631266374893014251062382502550839254145814568001823896785381915764373465291767423259916504397161 ( 179 digits) SNFS difficulty: 184 digits. Divisors found: r1=945200151001218657635011445058228730913844677283075507271374283027271720740913 r2=19770909942771694388069711525503787363511760112454424254375327438641837630246346547998813862502042297 Version: Total time: 197.96 hours. Scaled time: 379.48 units (timescale=1.917). Factorization parameters were as follows: n: 18687467063339300864482226350076057990947790954518442661244809556023157509184890061631266374893014251062382502550839254145814568001823896785381915764373465291767423259916504397161 m: 5000000000000000000000000000000000000 deg: 5 c5: 8 c0: -5 skew: 0.91 type: snfs lss: 1 rlim: 8300000 alim: 8300000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 8300000/8300000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4150000, 6050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1592809 x 1593055 Total sieving time: 197.96 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,184,5,0,0,0,0,0,0,0,0,8300000,8300000,28,28,54,54,2.5,2.5,100000 total time: 197.96 hours. --------- CPU info (if available) ----------

Jun 9, 2009 (3rd)

By Serge Batalov / GMP-ECM 6.2.3, Msieve / Jun 9, 2009
(58·10¹⁷⁵-31)/9 = 6(4)₁₇₄1_<176> = 55714679 · 5235442620557_<13> · 6232928151786767_<16> · 232729247283047481153469816271_<30> · C111
C111 = P30 · P81
P30 = 454908773934063966445433989859_<30>
P81 = 334807400088451839410571141352346615537487208329487130708430760155293207884291769_<81>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3320324933 Step 1 took 5604ms Step 2 took 6120ms ********** Factor found in step 2: 454908773934063966445433989859 Found probable prime factor of 30 digits: 454908773934063966445433989859 Probable prime cofactor has 81 digits

(58·10¹⁷⁸-31)/9 = 6(4)₁₇₇1_<179> = 13 · 2985950646001_<13> · 103729544616818033_<18> · C149
C149 = P32 · P118
P32 = 15760309062369653259657044097511_<32>
P118 = 1015528943204105616882829519823718893580572556570303575730382698748439447747013081058056037752739634733914242599226139_<118>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1343471373 Step 1 took 8065ms Step 2 took 7684ms ********** Factor found in step 2: 15760309062369653259657044097511 Found probable prime factor of 32 digits: 15760309062369653259657044097511 Probable prime cofactor has 118 digits

(58·10¹⁶⁴-31)/9 = 6(4)₁₆₃1_<165> = 23² · 383 · 1106512672418801_<16> · C145
C145 = P34 · P112
P34 = 2153842407797207605842854513620151_<34>
P112 = 1334629507037536053292771611266454391010528184018975178657665649995918628661229565400499790650495782091540687313_<112>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3471677956 Step 1 took 9761ms Step 2 took 9648ms ********** Factor found in step 2: 2153842407797207605842854513620151 Found probable prime factor of 34 digits: 2153842407797207605842854513620151 Probable prime cofactor has 112 digits

(58·10¹¹⁰-31)/9 = 6(4)₁₀₉1_<111> = 43 · 89 · 709 · 63516017 · C97
C97 = P44 · P53
P44 = 64029904137894160699939453653382583511076709_<44>
P53 = 58400246311501793633262292351880538367399994103824779_<53>

SNFS difficulty: 111 digits. Divisors found: r1=64029904137894160699939453653382583511076709 (pp44) r2=58400246311501793633262292351880538367399994103824779 (pp53) Version: Msieve v. 1.42 Total time: 0.44 hours. Scaled time: 1.20 units (timescale=2.739). Factorization parameters were as follows: n: 3739362172954866891959870454158433811546691347795804580424247967542367672806713155626329363972311 m: 10000000000000000000000 deg: 5 c5: 58 c0: -31 skew: 0.88 type: snfs lss: 1 rlim: 510000 alim: 510000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 510000/510000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [255000, 405001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 49264 x 49504 Total sieving time: 0.41 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,111.000,5,0,0,0,0,0,0,0,0,510000,510000,25,25,44,44,2.2,2.2,50000 total time: 0.44 hours.

(58·10¹¹⁷-31)/9 = 6(4)₁₁₆1_<118> = 3 · 151 · C116
C116 = P57 · P59
P57 = 335590386834784504387239992197852758626517636211067047607_<57>
P59 = 42391401048926704326708187457225970435707174842995360025571_<59>

SNFS difficulty: 119 digits. Divisors found: r1=335590386834784504387239992197852758626517636211067047607 (pp57) r2=42391401048926704326708187457225970435707174842995360025571 (pp59) Version: Msieve v. 1.42 Total time: 0.87 hours. Scaled time: 2.38 units (timescale=2.736). Factorization parameters were as follows: n: 14226146676477802305616875153298994358597007603630120186411577140053961246014226146676477802305616875153298994358597 m: 200000000000000000000000 deg: 5 c5: 725 c0: -124 skew: 0.70 type: snfs lss: 1 rlim: 680000 alim: 680000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 680000/680000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [340000, 640001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 76358 x 76584 Total sieving time: 0.82 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,119.000,5,0,0,0,0,0,0,0,0,680000,680000,25,25,45,45,2.2,2.2,50000 total time: 0.87 hours.

Jun 9, 2009 (2nd)

By Dmitry Domanov / ECMNET/GMP-ECM 6.2.3 / Jun 9, 2009
(58·10²⁰⁴-31)/9 = 6(4)₂₀₃1_<205> = 3² · 227 · 4337 · 8581 · 522523 · 92090216387547454209696971_<26> · C163
C163 = P33 · C130
P33 = 225681106744058840576374317838111_<33>
C130 = [7805049924632190975500473119323412038681495890816226485855611592217951151934608322814868752014324502254708615145997800942003863817_<130>]

[2009-06-08 19:49:16 GMT] a: Factor found! / (probable) 225681106744058840576374317838111 B1: 3000000 sigma: 2193550413 (found in step 2) [2009-06-08 19:49:16 GMT] a: Co-factor: / (Composite) 7805049924632190975500473119323412038681495890816226485855611592217951151934608322814868752014324502254708615145997800942003863817

Jun 9, 2009

Factorizations of 644...441 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Jun 8, 2009 (4th)

By Sinkiti Sibata / GGNFS / Jun 8, 2009
(19·10¹⁶⁷+11)/3 = 6(3)₁₆₆7_<168> = 43 · 293 · 377329 · 453317541319_<12> · 59752351280420531883007677311069_<32> · C115
C115 = P33 · P83
P33 = 451635143998643094798214056395897_<33>
P83 = 10890074034432660056461130378390738916429422879842755660108083810782993459835053541_<83>

Number: 63337_167 N=4918340154696878584797715035296828294757600408247419664161466612691457251945246728276473762673861793707090487721277 ( 115 digits) Divisors found: r1=451635143998643094798214056395897 (pp33) r2=10890074034432660056461130378390738916429422879842755660108083810782993459835053541 (pp83) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 56.94 hours. Scaled time: 26.88 units (timescale=0.472). Factorization parameters were as follows: name: 63337_167 n: 4918340154696878584797715035296828294757600408247419664161466612691457251945246728276473762673861793707090487721277 skew: 41061.75 # norm 3.68e+15 c5: 19440 c4: 21217646 c3: -194470098863967 c2: 312840910399259543 c1: 91867653659978829575663 c0: 671399258331606106211358267 # alpha -5.86 Y1: 124570391 Y0: -12039943812266001523120 # Murphy_E 6.16e-10 # M 954209243953220357002622527516688316195460346728018691553675653695772336926992012472982582020705135658684704564758 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 2950001) Primes: RFBsize:250150, AFBsize:250374, largePrimes:7767187 encountered Relations: rels:7848397, finalFF:722910 Max relations in full relation-set: 28 Initial matrix: 500605 x 722910 with sparse part having weight 66809160. Pruned matrix : 337685 x 340252 with weight 39640429. Total sieving time: 50.55 hours. Total relation processing time: 0.60 hours. Matrix solve time: 5.44 hours. Time per square root: 0.34 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 56.94 hours. --------- CPU info (if available) ----------

Jun 8, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jun 8, 2009
(2·10¹⁸⁷+1)/3 = (6)₁₈₆7_<187> = 7³ · 509 · 6807883 · C175
C175 = P48 · P127
P48 = 832957047027425833335054553975046273267520991369_<48>
P127 = 6733830004153306475052063018140541113462683578069214987182885775529843283897925895868514070483631862407825839272911409226010683_<127>

Number: 66667_187 N=5608991155444216796145843881216219198330238812809990245289610633020319055475951327318681109826779298887702399873401084096868614468301634210121695696972944460387689897144795027 ( 175 digits) SNFS difficulty: 187 digits. Divisors found: r1=832957047027425833335054553975046273267520991369 r2=6733830004153306475052063018140541113462683578069214987182885775529843283897925895868514070483631862407825839272911409226010683 Version: Total time: 114.35 hours. Scaled time: 272.96 units (timescale=2.387). Factorization parameters were as follows: n: 5608991155444216796145843881216219198330238812809990245289610633020319055475951327318681109826779298887702399873401084096868614468301634210121695696972944460387689897144795027 m: 20000000000000000000000000000000000000 deg: 5 c5: 25 c0: 4 skew: 0.69 type: snfs lss: 1 rlim: 8400000 alim: 8400000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 8400000/8400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4200000, 7200001) Primes: rational ideals reading, algebraic ideals reading, Relations: 20006057 Max relations in full relation-set: Initial matrix: Pruned matrix : 1668637 x 1668883 Total sieving time: 103.50 hours. Total relation processing time: 3.18 hours. Matrix solve time: 6.64 hours. Time per square root: 1.03 hours. Prototype def-par.txt line would be: snfs,187,5,0,0,0,0,0,0,0,0,8400000,8400000,28,28,54,54,2.5,2.5,100000 total time: 114.35 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

Jun 8, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Jun 8, 2009
(19·10¹⁶⁵+11)/3 = 6(3)₁₆₄7_<166> = 13127 · 13229 · 1605041 · C152
C152 = P67 · P85
P67 = 2791700755882992873339918737978119310151779702113163525509754308843_<67>
P85 = 8139258648311733962685908037081497873764129440073504717377547968433533826435397148353_<85>

Number: n N=22722374520819054559718952394116308190104376321680853380543504496639755831541448161475981772137990356697581047755307729999750673967210420073896650785579 ( 152 digits) SNFS difficulty: 166 digits. Divisors found: Mon Jun 08 04:39:24 2009 prp67 factor: 2791700755882992873339918737978119310151779702113163525509754308843 Mon Jun 08 04:39:24 2009 prp85 factor: 8139258648311733962685908037081497873764129440073504717377547968433533826435397148353 Mon Jun 08 04:39:24 2009 elapsed time 01:42:10 (Msieve 1.39 - dependency 6) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 33.04 hours. Scaled time: 54.02 units (timescale=1.635). Factorization parameters were as follows: name: KA_6_3_164_7 n: 22722374520819054559718952394116308190104376321680853380543504496639755831541448161475981772137990356697581047755307729999750673967210420073896650785579 m: 1000000000000000000000000000000000 deg: 5 c5: 19 c0: 11 skew: 0.90 type: snfs lss: 1 rlim: 4200000 alim: 4200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4200000/4200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2100000, 4000907) Primes: RFBsize:296314, AFBsize:296017, largePrimes:15395159 encountered Relations: rels:14739602, finalFF:489099 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1463873 hash collisions in 15897279 relations Msieve: matrix is 737574 x 737822 (197.4 MB) Total sieving time: 32.56 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,166,5,0,0,0,0,0,0,0,0,4200000,4200000,28,28,56,56,2.4,2.4,100000 total time: 33.04 hours. --------- CPU info (if available) ----------

(56·10¹⁶⁹+61)/9 = 6(2)₁₆₈9_<170> = 3³ · 212332831 · C161
C161 = P39 · P39 · P42 · P42
P39 = 424274908169666727454295410341629377361_<39>
P39 = 744256981543256710605164151127424339141_<39>
P42 = 142246468831973644407334999953831883982951_<42>
P42 = 241631107074584670119388266251172464439467_<42>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 10853369863331184124031483771365186333201545340097971388628670188884701563828629413905976457174413200556159317183157365669906297429153018284425120160496591494417 (161 digits) Using B1=3094000, B2=5707048630, polynomial Dickson(6), sigma=3228879520 Step 1 took 52338ms Step 2 took 16848ms ********** Factor found in step 2: 424274908169666727454295410341629377361 Found probable prime factor of 39 digits: 424274908169666727454295410341629377361 Composite cofactor 25580984532299850721733509754897028278292393878345135113886787454119781358631871189418843479083638795833911078559833986497 has 122 digits Number: n N=25580984532299850721733509754897028278292393878345135113886787454119781358631871189418843479083638795833911078559833986497 ( 122 digits) SNFS difficulty: 171 digits. Divisors found: Mon Jun 08 05:04:28 2009 prp39 factor: 744256981543256710605164151127424339141 Mon Jun 08 05:04:28 2009 prp42 factor: 142246468831973644407334999953831883982951 Mon Jun 08 05:04:28 2009 prp42 factor: 241631107074584670119388266251172464439467 Mon Jun 08 05:04:28 2009 elapsed time 01:46:24 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 57.37 hours. Scaled time: 151.98 units (timescale=2.649). Factorization parameters were as follows: name: KA_6_2_168_9 # n: 10853369863331184124031483771365186333201545340097971388628670188884701563828629413905976457174413200556159317183157365669906297429153018284425120160496591494417 n: 25580984532299850721733509754897028278292393878345135113886787454119781358631871189418843479083638795833911078559833986497 m: 10000000000000000000000000000000000 deg: 5 c5: 28 c0: 305 skew: 1.61 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2500000, 5711327) Primes: RFBsize:348513, AFBsize:348667, largePrimes:17581904 encountered Relations: rels:17491753, finalFF:578623 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2140410 hash collisions in 19295644 relations Msieve: matrix is 855294 x 855542 (227.4 MB) Total sieving time: 56.51 hours. Total relation processing time: 0.86 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000 total time: 57.37 hours. --------- CPU info (if available) ----------

Jun 8, 2009

By Serge Batalov / PFGW / Jun 7, 2009
(23·10⁸¹²¹⁴+1)/3 = 7(6)₈₁₂₁₃7_<81215> is PRP.

Jun 7, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Jun 7, 2009
(89·10¹⁶⁸+1)/9 = 9(8)₁₆₇9_<169> = 31 · 15467 · 14156321914008218389_<20> · C145
C145 = P46 · P100
P46 = 1197741581225809551137206782460379046419207957_<46>
P100 = 1216371290130096965390512251725852109764456594341931436026498758415155508058087929946270416461522909_<100>

Number: n N=1456898472398100290050596745119217016354672758605044647270127522188882139954015967734324164186163472619789554745096128190882591606939001790586913 ( 145 digits) SNFS difficulty: 171 digits. Divisors found: Sun Jun 07 06:14:32 2009 prp46 factor: 1197741581225809551137206782460379046419207957 Sun Jun 07 06:14:32 2009 prp100 factor: 1216371290130096965390512251725852109764456594341931436026498758415155508058087929946270416461522909 Sun Jun 07 06:14:32 2009 elapsed time 01:18:27 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 37.15 hours. Scaled time: 96.40 units (timescale=2.595). Factorization parameters were as follows: name: KA_9_8_167_9 n: 1456898472398100290050596745119217016354672758605044647270127522188882139954015967734324164186163472619789554745096128190882591606939001790586913 m: 10000000000000000000000000000000000 deg: 5 c5: 89 c0: 100 skew: 1.02 type: snfs lss: 1 rlim: 5200000 alim: 5200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 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 [2600000, 4572629) Primes: RFBsize:361407, AFBsize:361067, largePrimes:16319409 encountered Relations: rels:15511318, finalFF:797908 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1476171 hash collisions in 17185281 relations Msieve: matrix is 795559 x 795807 (216.5 MB) Total sieving time: 36.66 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,171,5,0,0,0,0,0,0,0,0,5200000,5200000,28,28,56,56,2.4,2.4,100000 total time: 37.15 hours. --------- CPU info (if available) ----------

(56·10¹⁷¹-11)/9 = 6(2)₁₇₀1_<172> = 18289 · C168
C168 = P52 · P117
P52 = 1688756690963537752408473787951585430593702236955631_<52>
P117 = 201459835463477766709930841456375992587398927045022191791163930369390792616322549362470313523356697387941237086565619_<117>

Number: n N=340216645099361486260715305496321407524863153929806015759321024781137417148133972454602341419553951677085801422834612183401072897491509772115600755766975899295873050589 ( 168 digits) SNFS difficulty: 173 digits. Divisors found: Sun Jun 07 20:39:56 2009 prp52 factor: 1688756690963537752408473787951585430593702236955631 Sun Jun 07 20:39:56 2009 prp117 factor: 201459835463477766709930841456375992587398927045022191791163930369390792616322549362470313523356697387941237086565619 Sun Jun 07 20:39:56 2009 elapsed time 01:43:30 (Msieve 1.39 - dependency 4) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 62.43 hours. Scaled time: 166.07 units (timescale=2.660). Factorization parameters were as follows: name: KA_6_2_170_1 n: 340216645099361486260715305496321407524863153929806015759321024781137417148133972454602341419553951677085801422834612183401072897491509772115600755766975899295873050589 m: 20000000000000000000000000000000000 deg: 5 c5: 35 c0: -22 skew: 0.91 type: snfs lss: 1 rlim: 5400000 alim: 5400000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 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 [2700000, 6139019) Primes: RFBsize:374362, AFBsize:374788, largePrimes:18470689 encountered Relations: rels:18863544, finalFF:793404 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2353896 hash collisions in 20946880 relations Msieve: matrix is 847908 x 848156 (224.6 MB) Total sieving time: 61.47 hours. Total relation processing time: 0.97 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,173,5,0,0,0,0,0,0,0,0,5400000,5400000,28,28,56,56,2.4,2.4,100000 total time: 62.43 hours. --------- CPU info (if available) ----------

(19·10¹⁵⁸+11)/3 = 6(3)₁₅₇7_<159> = 7 · 13 · 109 · 139 · 12507541 · 14102089 · C139
C139 = P48 · P91
P48 = 890298629966988697335260273638928061736248977777_<48>
P91 = 2925220203141326850950535511175349840756501552381707616474921977213766925742775925795078409_<91>

Number: n N=2604319539208479662296566196626281659401273439107427083867761096506661355606572402680653377381481359641859195173125630014326233603813516793 ( 139 digits) SNFS difficulty: 160 digits. Divisors found: Sun Jun 07 20:45:45 2009 prp48 factor: 890298629966988697335260273638928061736248977777 Sun Jun 07 20:45:45 2009 prp91 factor: 2925220203141326850950535511175349840756501552381707616474921977213766925742775925795078409 Sun Jun 07 20:45:45 2009 elapsed time 01:45:45 (Msieve 1.39 - dependency 4) Version: GGNFS-0.77.1-20051202-athlon Total time: 24.03 hours. Scaled time: 43.80 units (timescale=1.823). Factorization parameters were as follows: name: KA_6_3_157_7 n: 2604319539208479662296566196626281659401273439107427083867761096506661355606572402680653377381481359641859195173125630014326233603813516793 m: 50000000000000000000000000000000 deg: 5 c5: 152 c0: 275 skew: 1.13 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1700000, 3000000) Primes: RFBsize:243539, AFBsize:243160, largePrimes:13719071 encountered Relations: rels:13002746, finalFF:619676 Max relations in full relation-set: 28 Initial matrix: 486766 x 619676 with sparse part having weight 94340976. Pruned matrix : 439537 x 442034 with weight 58453176. Msieve: found 1164952 hash collisions in 13921564 relations Msieve: matrix is 561281 x 561529 (150.0 MB) Total sieving time: 23.75 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,160,5,0,0,0,0,0,0,0,0,3400000,3400000,28,28,56,56,2.4,2.4,100000 total time: 24.03 hours. --------- CPU info (if available) ----------

Jun 7, 2009

By Sinkiti Sibata / Msieve / Jun 7, 2009
(19·10¹⁶⁰+11)/3 = 6(3)₁₅₉7_<161> = 71 · 78858923431_<11> · 2376673566823_<13> · 19232519182912433163629_<23> · C114
C114 = P49 · P65
P49 = 5145544189689853686084609914300609465992312536511_<49>
P65 = 48093471998115581878663595761747484801061854861862293238174882901_<65>

Number: 63337_160 N=247467085401915310220618172014915005673608575042370220062176194352664913172346163743395659359667859872701712098411 ( 114 digits) SNFS difficulty: 161 digits. Divisors found: r1=5145544189689853686084609914300609465992312536511 (pp49) r2=48093471998115581878663595761747484801061854861862293238174882901 (pp65) Version: Msieve-1.40 Total time: 29.14 hours. Scaled time: 75.04 units (timescale=2.575). Factorization parameters were as follows: name: 63337_160 n: 247467085401915310220618172014915005673608575042370220062176194352664913172346163743395659359667859872701712098411 m: 100000000000000000000000000000000 deg: 5 c5: 19 c0: 11 skew: 0.90 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1700000, 3000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 640283 x 640531 Total sieving time: 29.14 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,161.000,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 29.14 hours. --------- CPU info (if available) ----------

(19·10¹⁵⁵+11)/3 = 6(3)₁₅₄7_<156> = 17 · 2819 · 90377489523395579_<17> · C135
C135 = P47 · P88
P47 = 34157108083670710906043469808823415090877040147_<47>
P88 = 4281017286969461896442622204066901741881371785859940186877570995394406015230096372670563_<88>

Number: 63337_155 N=146227170179078662500471844618178651924786228401446376604148500459079741163926619676302325596862400065732441170848197134506827356092761 ( 135 digits) SNFS difficulty: 156 digits. Divisors found: r1=34157108083670710906043469808823415090877040147 (pp47) r2=4281017286969461896442622204066901741881371785859940186877570995394406015230096372670563 (pp88) Version: Msieve-1.40 Total time: 23.07 hours. Scaled time: 47.79 units (timescale=2.071). Factorization parameters were as follows: name: 63337_155 n: 146227170179078662500471844618178651924786228401446376604148500459079741163926619676302325596862400065732441170848197134506827356092761 m: 10000000000000000000000000000000 deg: 5 c5: 19 c0: 11 skew: 0.90 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, 2300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 513105 x 513353 Total sieving time: 21.77 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.94 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,156.000,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 23.07 hours. --------- CPU info (if available) ----------

Jun 6, 2009 (3rd)

By Sinkiti Sibata / Msieve / Jun 6, 2009
(19·10¹⁴¹+11)/3 = 6(3)₁₄₀7_<142> = 23 · 3424151153_<10> · 254758733191_<12> · C120
C120 = P46 · P74
P46 = 5050129058517986723316852587290974346406186227_<46>
P74 = 62505757846387088561289339012886665141712282005484871401793013435241437139_<74>

Number: 63337_141 N=315662144024728088954673401382175903113016566302661569618687283007998859457218463561321830356053124278841664279548084553 ( 120 digits) SNFS difficulty: 142 digits. Divisors found: r1=5050129058517986723316852587290974346406186227 (pp46) r2=62505757846387088561289339012886665141712282005484871401793013435241437139 (pp74) Version: Msieve-1.40 Total time: 6.59 hours. Scaled time: 13.82 units (timescale=2.098). Factorization parameters were as follows: name: 63337_141 n: 315662144024728088954673401382175903113016566302661569618687283007998859457218463561321830356053124278841664279548084553 m: 10000000000000000000000000000 deg: 5 c5: 190 c0: 11 skew: 0.57 type: snfs lss: 1 rlim: 1650000 alim: 1650000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1650000/1650000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [825000, 1625001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 277291 x 277539 Total sieving time: 6.17 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.26 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,142.000,5,0,0,0,0,0,0,0,0,1650000,1650000,26,26,48,48,2.3,2.3,100000 total time: 6.59 hours. --------- CPU info (if available) ----------

(19·10¹⁴⁵+11)/3 = 6(3)₁₄₄7_<146> = 133183 · 818689 · 1404005417_<10> · 121490964551680697_<18> · C109
C109 = P39 · P70
P39 = 512414144904096443350797214360954687769_<39>
P70 = 6645546857480804860225968131089235254175762793540245993870446512951071_<70>

Number: 63337_145 N=3405272210396131896853192046880242928373403317362054445048532704581653759643181140672663734035062647579150599 ( 109 digits) SNFS difficulty: 146 digits. Divisors found: r1=512414144904096443350797214360954687769 (pp39) r2=6645546857480804860225968131089235254175762793540245993870446512951071 (pp70) Version: Msieve-1.40 Total time: 9.27 hours. Scaled time: 23.67 units (timescale=2.554). Factorization parameters were as follows: name: 63337_145 n: 3405272210396131896853192046880242928373403317362054445048532704581653759643181140672663734035062647579150599 m: 100000000000000000000000000000 deg: 5 c5: 19 c0: 11 skew: 0.90 type: snfs lss: 1 rlim: 1920000 alim: 1920000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1920000/1920000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [960000, 2160001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 296008 x 296256 Total sieving time: 9.27 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,146.000,5,0,0,0,0,0,0,0,0,1920000,1920000,26,26,49,49,2.3,2.3,100000 total time: 9.27 hours. --------- CPU info (if available) ----------

(19·10¹⁴⁴+11)/3 = 6(3)₁₄₃7_<145> = 1439 · 58897 · 2161819295110817870598641_<25> · C113
C113 = P41 · P73
P41 = 16608864835497717889409845648017981835361_<41>
P73 = 2081225022557446636993986742266210526066920283027389665865883672099304039_<73>

Number: 63337_144 N=34566785091912320142172687249517564182023491309663939642348715633880788938470418987969605576911440066471980323079 ( 113 digits) SNFS difficulty: 146 digits. Divisors found: r1=16608864835497717889409845648017981835361 (pp41) r2=2081225022557446636993986742266210526066920283027389665865883672099304039 (pp73) Version: Msieve-1.40 Total time: 11.32 hours. Scaled time: 23.76 units (timescale=2.099). Factorization parameters were as follows: name: 63337_144 n: 34566785091912320142172687249517564182023491309663939642348715633880788938470418987969605576911440066471980323079 m: 100000000000000000000000000000 deg: 5 c5: 19 c0: 110 skew: 1.42 type: snfs lss: 1 rlim: 1920000 alim: 1920000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1920000/1920000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [960000, 2360001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 338620 x 338848 Total sieving time: 10.80 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.39 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,146.000,5,0,0,0,0,0,0,0,0,1920000,1920000,26,26,49,49,2.3,2.3,100000 total time: 11.32 hours. --------- CPU info (if available) ----------

Jun 6, 2009 (2nd)

By Jo Yeong Uk / GGNFS / Msieve v1.39 / Jun 6, 2009
(19·10¹⁶⁶+11)/3 = 6(3)₁₆₅7_<167> = 67 · 3911 · 14202604430369_<14> · 86380538071123_<14> · 8368840124326806116601083_<25> · C110
C110 = P49 · P61
P49 = 6262082223742718300440148144843541334567401119143_<49>
P61 = 3759255070882753743580420042857440550706597169458132984067267_<61>

Number: 63337_166 N=23540764353889564672128696226443881624693799593278057392043683758795636761529340169115771824957267483793392181 ( 110 digits) Divisors found: r1=6262082223742718300440148144843541334567401119143 r2=3759255070882753743580420042857440550706597169458132984067267 Version: Total time: 8.56 hours. Scaled time: 20.44 units (timescale=2.389). Factorization parameters were as follows: name: 63337_166 n: 23540764353889564672128696226443881624693799593278057392043683758795636761529340169115771824957267483793392181 skew: 29345.35 # norm 1.91e+15 c5: 40080 c4: 1978609108 c3: -130421089236824 c2: -1597893340708739207 c1: 37398680496777286640604 c0: 277920807332288752590379839 # alpha -6.54 Y1: 138689822447 Y0: -899037708825546047086 # Murphy_E 1.11e-09 # M 19367926142172829006431938429769541855506380602628362297909528725610931992982566228734831217917220084588038212 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, 1650001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7917419 Max relations in full relation-set: Initial matrix: Pruned matrix : 364689 x 364937 Polynomial selection time: 0.66 hours. Total sieving time: 7.02 hours. Total relation processing time: 0.46 hours. Matrix solve time: 0.28 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000 total time: 8.56 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

Jun 6, 2009

By Dmitry Domanov / GGNFS / Jun 6, 2009
(56·10¹⁷⁸+43)/9 = 6(2)₁₇₇7_<179> = 11 · C178
C178 = P59 · P120
P59 = 11344343380024260457115967605538423116332562634899263825067_<59>
P120 = 498624333474077167029242363855886817081848222640868644668813635343289283688929391503016030544074083603519829915383917771_<120>

[06/05 12:08:29] GGNFS-0.77.1-VC8(Sat 01/17/2009) : procrels [06/05 12:18:07] There were 328787/9999999 duplicates. [06/05 12:18:07] RelProcTime: 538.1 [06/05 12:19:22] GGNFS-0.77.1-VC8(Sat 01/17/2009) : procrels [06/05 12:32:10] There were 821816/9694483 duplicates. [06/05 12:32:10] RelProcTime: 702.5 [06/05 12:33:33] largePrimes: 17825819 , relations: 18543879 [06/05 12:33:50] GGNFS-0.77.1-VC8(Sat 01/17/2009) : matbuild [06/05 12:36:44] largePrimes: 17825819 , relations: 18543879 [06/05 12:47:26] reduceRelSets dropped relation-set weight from 38957706 to 29025895. [06/05 12:51:32] reduceRelSets dropped relation-set weight from 29025895 to 28948873. [06/05 12:51:32] After removing heavy rel-sets, weight is 26752953. [06/05 12:59:09] Heap stats for matbuild run. [06/05 12:59:09] Max heap usage: 0 MB [06/05 12:59:09] malloc/realloc errors: 0 [06/05 12:59:09] total malloc's : 991 [06/05 12:59:09] total realloc's: 569 [06/05 12:59:09] rels:18543879, initialFF:0, finalFF:1674782 [06/05 12:59:09] depinf file written. Run matprune. [06/05 13:03:14] GGNFS-0.77.1-VC8(Sat 01/17/2009) : matprune [06/05 13:03:25] Pruning matrix with wt=0.700 [06/05 13:03:25] Initial matrix is 992017 x 1674782 with sparse part having weight 266215805. [06/05 13:03:26] (total weight is 401811151) [06/05 13:56:36] Matrix pruned to 813338 x 818362 with weight 93403634. [06/05 13:56:40] Matrix is pruned. Run matsolve. [06/05 13:56:40] Heap stats for matprune run: [06/05 13:56:40] Max heap usage: 0 MB [06/05 13:56:40] malloc/realloc errors: 0 [06/05 13:56:40] total malloc's : 16 [06/05 13:56:40] total realloc's: 0 [06/05 13:56:55] GGNFS-0.77.1-VC8(Sat 01/17/2009) : matsolve (seed=2116475424) [06/05 22:37:42] BLanczosTime: 31246.1 [06/05 22:37:42] Heap stats for matsolve run: [06/05 22:37:42] Max heap usage: 0 MB [06/05 22:37:42] malloc/realloc errors: 0 [06/05 22:37:42] total malloc's : 14 [06/05 22:37:42] total realloc's: 0 [06/05 22:42:59] GGNFS-0.77.1-VC8(Sat 01/17/2009) : sqrt [06/05 22:43:01] bmultiplier=1 [06/05 23:07:38] From dependence 0, sqrt obtained: [06/05 23:07:38] r1=1 [06/05 23:07:38] r2=5656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565657 [06/05 23:07:38] sqrtTime: 1478.7 [06/05 23:12:12] GGNFS-0.77.1-VC8(Sat 01/17/2009) : sqrt [06/05 23:12:13] bmultiplier=1 [06/05 23:36:49] From dependence 1, sqrt obtained: [06/05 23:36:49] r1=498624333474077167029242363855886817081848222640868644668813635343289283688929391503016030544074083603519829915383917771 (pp120) [06/05 23:36:49] r2=11344343380024260457115967605538423116332562634899263825067 (pp59) [06/05 23:36:49] (pp=probable prime, c=composite) [06/05 23:36:49] sqrtTime: 1477.0

Jun 5, 2009 (5th)

By Sinkiti Sibata / Msieve, GGNFS / Jun 5, 2009
(19·10¹²⁷+11)/3 = 6(3)₁₂₆7_<128> = 3457 · 29392248791_<11> · C114
C114 = P41 · P73
P41 = 64869638554838628758245001081530634426441_<41>
P73 = 9608568122148198650049870148335148191834916510556873243141924230269946711_<73>

Number: 63337_127 N=623304341113298190003715456304851113044797613882178039296795487508371893944858702136693299304697768174591119385551 ( 114 digits) SNFS difficulty: 129 digits. Divisors found: r1=64869638554838628758245001081530634426441 (pp41) r2=9608568122148198650049870148335148191834916510556873243141924230269946711 (pp73) Version: Msieve-1.40 Total time: 3.08 hours. Scaled time: 5.95 units (timescale=1.934). Factorization parameters were as follows: name: 63337_127 n: 623304341113298190003715456304851113044797613882178039296795487508371893944858702136693299304697768174591119385551 m: 20000000000000000000000000 deg: 5 c5: 475 c0: 88 skew: 0.71 type: snfs lss: 1 rlim: 1000000 alim: 1000000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [500000, 900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 150689 x 150919 Total sieving time: 2.90 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.08 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,129.000,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000 total time: 3.08 hours. --------- CPU info (if available) ----------

(55·10¹⁹⁹+53)/9 = 6(1)₁₉₈7_<200> = 67 · 127 · 149 · 15271 · 32537 · 64951 · 3491419 · 76893119 · 2984002608911_<13> · 73272202678356361_<17> · C137
C137 = P49 · P88
P49 = 4646275918046474726914070102202746441538122559419_<49>
P88 = 5476355976757986022100975097151083556451371821389834131152133448924920125725709745151429_<88>

Number: 61117_199 N=25444660893460510317172439394273556297338846060840182666903667766609275787693643836357738825942267824554292636529889428645386199205259751 ( 137 digits) Divisors found: r1=4646275918046474726914070102202746441538122559419 (pp49) r2=5476355976757986022100975097151083556451371821389834131152133448924920125725709745151429 (pp88) Version: Msieve-1.40 Total time: 455.10 hours. Scaled time: 1153.23 units (timescale=2.534). Factorization parameters were as follows: name: 61117_199 # Murphy_E = 3.193184e-11, selected by Jeff Gilchrist n: 25444660893460510317172439394273556297338846060840182666903667766609275787693643836357738825942267824554292636529889428645386199205259751 Y0: -195340899491540177501362945 Y1: 1646830578424513 c0: -17264089700630042706198979052928 c1: 4053148267436222996637322534 c2: -5446174057260405430633 c3: -42244614185732804 c4: 45385993146 c5: 89460 skew: 431663.49 type: gnfs # selected mechanically rlim: 14600000 alim: 14600000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.6 alambda: 2.6 Factor base limits: 14600000/14600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved algebraic special-q in [7300000, 13000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2006714 x 2006962 Total sieving time: 455.10 hours. Total relation processing 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,136,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,14600000,14600000,28,28,55,55,2.6,2.6,100000 total time: 455.10 hours. --------- CPU info (if available) ----------

(19·10¹²¹+11)/3 = 6(3)₁₂₀7_<122> = 337972093300564182992672797_<27> · C96
C96 = P35 · P61
P35 = 62733293684483999236989225276611999_<35>
P61 = 2987125124779044111070216291606218084493743214162216434936179_<61>

Fri Jun 05 06:31:30 2009 Msieve v. 1.39 Fri Jun 05 06:31:30 2009 random seeds: 2323b060 822852cc Fri Jun 05 06:31:30 2009 factoring 187392197725064686109742995863136748941619341863639505659853720451164022359704784009624910611821 (96 digits) Fri Jun 05 06:31:31 2009 searching for 15-digit factors Fri Jun 05 06:31:33 2009 commencing quadratic sieve (96-digit input) Fri Jun 05 06:31:33 2009 using multiplier of 61 Fri Jun 05 06:31:33 2009 using 64kb Pentium 4 sieve core Fri Jun 05 06:31:33 2009 sieve interval: 18 blocks of size 65536 Fri Jun 05 06:31:33 2009 processing polynomials in batches of 6 Fri Jun 05 06:31:33 2009 using a sieve bound of 2231297 (82353 primes) Fri Jun 05 06:31:33 2009 using large prime bound of 334694550 (28 bits) Fri Jun 05 06:31:33 2009 using double large prime bound of 2209873982808450 (43-51 bits) Fri Jun 05 06:31:33 2009 using trial factoring cutoff of 51 bits Fri Jun 05 06:31:33 2009 polynomial 'A' values have 13 factors Fri Jun 05 13:06:47 2009 82566 relations (20793 full + 61773 combined from 1213021 partial), need 82449 Fri Jun 05 13:06:51 2009 begin with 1233814 relations Fri Jun 05 13:06:53 2009 reduce to 211552 relations in 11 passes Fri Jun 05 13:06:53 2009 attempting to read 211552 relations Fri Jun 05 13:06:56 2009 recovered 211552 relations Fri Jun 05 13:06:56 2009 recovered 195515 polynomials Fri Jun 05 13:06:56 2009 attempting to build 82566 cycles Fri Jun 05 13:06:57 2009 found 82566 cycles in 7 passes Fri Jun 05 13:06:57 2009 distribution of cycle lengths: Fri Jun 05 13:06:57 2009 length 1 : 20793 Fri Jun 05 13:06:57 2009 length 2 : 15102 Fri Jun 05 13:06:57 2009 length 3 : 14124 Fri Jun 05 13:06:57 2009 length 4 : 11079 Fri Jun 05 13:06:57 2009 length 5 : 8138 Fri Jun 05 13:06:57 2009 length 6 : 5400 Fri Jun 05 13:06:57 2009 length 7 : 3467 Fri Jun 05 13:06:57 2009 length 9+: 4463 Fri Jun 05 13:06:57 2009 largest cycle: 22 relations Fri Jun 05 13:06:57 2009 matrix is 82353 x 82566 (22.0 MB) with weight 5433208 (65.80/col) Fri Jun 05 13:06:57 2009 sparse part has weight 5433208 (65.80/col) Fri Jun 05 13:06:59 2009 filtering completed in 3 passes Fri Jun 05 13:06:59 2009 matrix is 77904 x 77968 (20.9 MB) with weight 5161906 (66.21/col) Fri Jun 05 13:06:59 2009 sparse part has weight 5161906 (66.21/col) Fri Jun 05 13:07:00 2009 saving the first 48 matrix rows for later Fri Jun 05 13:07:00 2009 matrix is 77856 x 77968 (13.2 MB) with weight 4086517 (52.41/col) Fri Jun 05 13:07:00 2009 sparse part has weight 2989211 (38.34/col) Fri Jun 05 13:07:00 2009 matrix includes 64 packed rows Fri Jun 05 13:07:00 2009 using block size 21845 for processor cache size 512 kB Fri Jun 05 13:07:01 2009 commencing Lanczos iteration Fri Jun 05 13:07:01 2009 memory use: 12.6 MB Fri Jun 05 13:08:06 2009 lanczos halted after 1233 iterations (dim = 77852) Fri Jun 05 13:08:06 2009 recovered 15 nontrivial dependencies Fri Jun 05 13:08:08 2009 prp35 factor: 62733293684483999236989225276611999 Fri Jun 05 13:08:08 2009 prp61 factor: 2987125124779044111070216291606218084493743214162216434936179 Fri Jun 05 13:08:08 2009 elapsed time 06:36:38

(19·10¹²⁹+11)/3 = 6(3)₁₂₈7_<130> = 62851 · 139720167823_<12> · 58002654641443_<14> · C101
C101 = P35 · P66
P35 = 17449273243471122496481234616760253_<35>
P66 = 712583630602248633508269573326866172600331656507196538198864101611_<66>

Number: 63337_129 N=12434066479203327235310154754897020409422523293225327204362332170782668264539997328386255596218067583 ( 101 digits) SNFS difficulty: 131 digits. Divisors found: r1=17449273243471122496481234616760253 (pp35) r2=712583630602248633508269573326866172600331656507196538198864101611 (pp66) Version: Msieve-1.40 Total time: 3.35 hours. Scaled time: 7.01 units (timescale=2.092). Factorization parameters were as follows: name: 63337_129 n: 12434066479203327235310154754897020409422523293225327204362332170782668264539997328386255596218067583 m: 100000000000000000000000000 deg: 5 c5: 19 c0: 110 skew: 1.42 type: snfs lss: 1 rlim: 1080000 alim: 1080000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1080000/1080000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [540000, 990001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 176273 x 176521 Total sieving time: 3.17 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.10 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,131.000,5,0,0,0,0,0,0,0,0,1080000,1080000,26,26,47,47,2.3,2.3,50000 total time: 3.35 hours. --------- CPU info (if available) ----------

(19·10¹³⁸+11)/3 = 6(3)₁₃₇7_<139> = 9539 · 1061453 · C129
C129 = P30 · P100
P30 = 205884879028525378989717723409_<30>
P100 = 3038115476624172547568021652027874523576378588114643432322765099118331016365199930349650938900052879_<100>

Number: 63337_138 N=625502037379458488816395300931864859727403089208807473972117605577143483778134905225062631923110042485477446199442955993596144511 ( 129 digits) SNFS difficulty: 140 digits. Divisors found: r1=205884879028525378989717723409 (pp30) r2=3038115476624172547568021652027874523576378588114643432322765099118331016365199930349650938900052879 (pp100) Version: GGNFS-0.77.1-20060513-nocona Total time: 9.07 hours. Scaled time: 23.25 units (timescale=2.564). Factorization parameters were as follows: name: 63337_138 n: 625502037379458488816395300931864859727403089208807473972117605577143483778134905225062631923110042485477446199442955993596144511 m: 5000000000000000000000000000 deg: 5 c5: 152 c0: 275 skew: 1.13 type: snfs lss: 1 rlim: 1550000 alim: 1550000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1550000/1550000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [775000, 1675001) Primes: RFBsize:117663, AFBsize:117528, largePrimes:3737414 encountered Relations: rels:3888763, finalFF:406792 Max relations in full relation-set: 28 Initial matrix: 235258 x 406792 with sparse part having weight 39309693. Pruned matrix : 190098 x 191338 with weight 15984031. Total sieving time: 8.74 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.19 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1550000,1550000,26,26,48,48,2.3,2.3,100000 total time: 9.07 hours. --------- CPU info (if available) ----------

(19·10¹³⁵+11)/3 = 6(3)₁₃₄7_<136> = 157 · 1193 · 7127 · 182309 · C122
C122 = P38 · P84
P38 = 65553528374184830411681549262167408477_<38>
P84 = 396991593279050907298492993278089931927123423048089785475114566024909213674236773267_<84>

Number: 63337_135 N=26024199674331107471002085266667364048678991074073173613246618562363142575922389775938957979867675799494856731304022784359 ( 122 digits) SNFS difficulty: 136 digits. Divisors found: r1=65553528374184830411681549262167408477 (pp38) r2=396991593279050907298492993278089931927123423048089785475114566024909213674236773267 (pp84) Version: Msieve-1.40 Total time: 4.12 hours. Scaled time: 8.62 units (timescale=2.092). Factorization parameters were as follows: name: 63337_135 n: 26024199674331107471002085266667364048678991074073173613246618562363142575922389775938957979867675799494856731304022784359 m: 1000000000000000000000000000 deg: 5 c5: 19 c0: 11 skew: 0.90 type: snfs lss: 1 rlim: 1310000 alim: 1310000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1310000/1310000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [655000, 1180001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 203473 x 203721 Total sieving time: 3.90 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.14 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,136.000,5,0,0,0,0,0,0,0,0,1310000,1310000,26,26,48,48,2.3,2.3,75000 total time: 4.12 hours. --------- CPU info (if available) ----------

(19·10¹⁴⁰+11)/3 = 6(3)₁₃₉7_<141> = 7 · 13 · 3407 · 171823361 · 221764604227301363_<18> · C110
C110 = P43 · P68
P43 = 1710045167050240022231811529388514487003039_<43>
P68 = 31349946151692462001498077827253531605274742451697616985120067166313_<68>

Number: 63337_140 N=53609823903986965507620058340145593869320117918452590610271899609036796485551947681698832409120418760549425207 ( 110 digits) SNFS difficulty: 141 digits. Divisors found: r1=1710045167050240022231811529388514487003039 (pp43) r2=31349946151692462001498077827253531605274742451697616985120067166313 (pp68) Version: Msieve-1.40 Total time: 5.90 hours. Scaled time: 15.13 units (timescale=2.564). Factorization parameters were as follows: name: 63337_140 n: 53609823903986965507620058340145593869320117918452590610271899609036796485551947681698832409120418760549425207 m: 10000000000000000000000000000 deg: 5 c5: 19 c0: 11 skew: 0.90 type: snfs lss: 1 rlim: 1580000 alim: 1580000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1580000/1580000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [790000, 1590001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 223122 x 223370 Total sieving time: 5.90 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,141.000,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000 total time: 5.90 hours. --------- CPU info (if available) ----------

Jun 5, 2009 (4th)

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Jun 5, 2009
(19·10¹⁴⁹+11)/3 = 6(3)₁₄₈7_<150> = 472669 · 2502376448875356964523_<22> · 108515729007503118966010501_<27> · C97
C97 = P33 · P65
P33 = 412263120561519252622656422088931_<33>
P65 = 11968932109377920243791744162779339493133905057285675419912761321_<65>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 4934349301201108471565949482849373763257646188675193487984795052436076161688151809042115239037851 (97 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3312505575 Step 1 took 3051ms Step 2 took 1822ms ********** Factor found in step 2: 412263120561519252622656422088931 Found probable prime factor of 33 digits: 412263120561519252622656422088931 Probable prime cofactor 11968932109377920243791744162779339493133905057285675419912761321 has 65 digits

(19·10¹⁰⁸+11)/3 = 6(3)₁₀₇7_<109> = 8161 · C105
C105 = P41 · P64
P41 = 91472206780727469444733176114899308261069_<41>
P64 = 8483983432303508769598845872763266181025177265418747924732236893_<64>

Number: 63337_108 N=776048686843932524608912306498386635624719192909365682310174406731201241677898950292039374259690397418617 ( 105 digits) SNFS difficulty: 111 digits. Divisors found: r1=91472206780727469444733176114899308261069 r2=8483983432303508769598845872763266181025177265418747924732236893 Version: Total time: 0.39 hours. Scaled time: 0.89 units (timescale=2.299). Factorization parameters were as follows: n: 776048686843932524608912306498386635624719192909365682310174406731201241677898950292039374259690397418617 m: 10000000000000000000000 deg: 5 c5: 19 c0: 1100 skew: 2.25 type: snfs lss: 1 rlim: 360000 alim: 360000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 360000/360000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [180000, 320001) Primes: rational ideals reading, algebraic ideals reading, Relations: 1030824 Max relations in full relation-set: Initial matrix: Pruned matrix : 46772 x 47014 Total sieving time: 0.34 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000 total time: 0.39 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(19·10¹¹⁶+11)/3 = 6(3)₁₁₅7_<117> = 7 · 13 · 31 · C114
C114 = P40 · P74
P40 = 2432404320102848256993656968416427973341_<40>
P74 = 92298255789188300181247940446582418073169321267278450482509633620109979017_<74>

Number: 63337_116 N=224506676119579345385796998700224506676119579345385796998700224506676119579345385796998700224506676119579345385797 ( 114 digits) SNFS difficulty: 117 digits. Divisors found: r1=2432404320102848256993656968416427973341 r2=92298255789188300181247940446582418073169321267278450482509633620109979017 Version: Total time: 0.50 hours. Scaled time: 1.20 units (timescale=2.385). Factorization parameters were as follows: n: 224506676119579345385796998700224506676119579345385796998700224506676119579345385796998700224506676119579345385797 m: 100000000000000000000000 deg: 5 c5: 190 c0: 11 skew: 0.57 type: snfs lss: 1 rlim: 500000 alim: 500000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [250000, 425001) Primes: rational ideals reading, algebraic ideals reading, Relations: 1180696 Max relations in full relation-set: Initial matrix: Pruned matrix : 61967 x 62215 Total sieving time: 0.45 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,117,5,0,0,0,0,0,0,0,0,500000,500000,25,25,45,45,2.2,2.2,25000 total time: 0.50 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

Jun 5, 2009 (3rd)

By Dmitry Domanov / ECMNET/GMP-ECM 6.2.3, ggnfs/msieve 1.41 / Jun 5, 2009
(19·10¹⁸¹+11)/3 = 6(3)₁₈₀7_<182> = C182
C182 = P32 · P151
P32 = 11159287224414433102572369164279_<32>
P151 = 5675392348963995343600513340549846572758077864937588438849066954047336838627831641100426017661512177938167043255580512712225275971080992889921645619503_<151>

[2009-06-05 02:29:53 GMT] a: Factor found! new2 / (probable) 11159287224414433102572369164279 B1: 11000000 sigma: 2433365336 (found in step 2) [2009-06-05 02:29:53 GMT] a: Co-factor: new2 / (Probable) 5675392348963995343600513340549846572758077864937588438849066954047336838627831641100426017661512177938167043255580512712225275971080992889921645619503

(19·10¹⁴⁸+11)/3 = 6(3)₁₄₇7_<149> = C149
C149 = P38 · P112
P38 = 14440446545037476137898408596542568433_<38>
P112 = 4385829284143440551081787553942088343816297920166421201719640736203533717033343955624721785579707213468219251689_<112>

Number: 149 N=63333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337 ( 149 digits) SNFS difficulty: 150 digits. Divisors found: r1=14440446545037476137898408596542568433 (pp38) r2=4385829284143440551081787553942088343816297920166421201719640736203533717033343955624721785579707213468219251689 (pp112) Version: Msieve v. 1.41 Total time: 12.22 hours. Scaled time: 24.23 units (timescale=1.982). Factorization parameters were as follows: n: 63333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337 m: 500000000000000000000000000000 deg: 5 c5: 152 c0: 275 skew: 1.13 type: snfs lss: 1 rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4Factor 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 : 386066 x 386314 Total sieving time: 11.85 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.24 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,150.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 12.22 hours. --------- CPU info (if available) ----------

Jun 5, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Jun 5, 2009
(19·10¹¹⁴+11)/3 = 6(3)₁₁₃7_<115> = 37380337049761321074077_<23> · C93
C93 = P40 · P54
P40 = 1256600447385245073338384160128201847119_<40>
P54 = 134831672979018180497816847883716523804858773842922499_<54>

Number: n N=169429540587135304979822222408703249896601171683279232545042066240429357482811986336963430381 ( 93 digits) SNFS difficulty: 116 digits. Divisors found: r1=1256600447385245073338384160128201847119 (pp40) r2=134831672979018180497816847883716523804858773842922499 (pp54) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.38 hours. Scaled time: 2.52 units (timescale=1.823). Factorization parameters were as follows: name: KA_6_3_113_7 n: 169429540587135304979822222408703249896601171683279232545042066240429357482811986336963430381 m: 100000000000000000000000 deg: 5 c5: 19 c0: 110 skew: 1.42 type: snfs lss: 1 rlim: 610000 alim: 610000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 10000 Factor base limits: 610000/610000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [305000, 425001) Primes: RFBsize:49861, AFBsize:50010, largePrimes:5545888 encountered Relations: rels:4848782, finalFF:124010 Max relations in full relation-set: 48 Initial matrix: 99936 x 124010 with sparse part having weight 16116609. Pruned matrix : 94670 x 95233 with weight 9564276. Total sieving time: 1.21 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.06 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,610000,610000,28,28,56,56,2.6,2.6,50000 total time: 1.38 hours. --------- CPU info (if available) ----------

(56·10¹⁶⁹+43)/9 = 6(2)₁₆₈7_<170> = 179 · 135743941 · C160
C160 = P74 · P87
P74 = 19333098532550373816686399052437320026075307008972428010009612629104605191_<74>
P87 = 132455674486371148046277269230562934350373310994141895370938879096275193417660466241323_<87>

Number: n N=2560778606040432031409473120026286862842617515944645726231703028047780271030618289067540422150066760117190517505152551127225133147724890763191178312489644507693 ( 160 digits) SNFS difficulty: 171 digits. Divisors found: Fri Jun 05 16:15:56 2009 prp74 factor: 19333098532550373816686399052437320026075307008972428010009612629104605191 Fri Jun 05 16:15:56 2009 prp87 factor: 132455674486371148046277269230562934350373310994141895370938879096275193417660466241323 Fri Jun 05 16:15:56 2009 elapsed time 01:29:54 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 43.15 hours. Scaled time: 112.46 units (timescale=2.606). Factorization parameters were as follows: name: KA_6_2_168_7 n: 2560778606040432031409473120026286862842617515944645726231703028047780271030618289067540422150066760117190517505152551127225133147724890763191178312489644507693 m: 10000000000000000000000000000000000 deg: 5 c5: 28 c0: 215 skew: 1.50 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2500000, 4900589) Primes: RFBsize:348513, AFBsize:347706, largePrimes:16552047 encountered Relations: rels:15738848, finalFF:690603 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1615751 hash collisions in 17010335 relations Msieve: matrix is 911803 x 912051 (244.8 MB) Total sieving time: 42.67 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,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000 total time: 43.15 hours. --------- CPU info (if available) ----------

Jun 5, 2009

By Serge Batalov / GMP-ECM 6.2.3, Msieve / Jun 5, 2009
(19·10¹⁵⁹+11)/3 = 6(3)₁₅₈7_<160> = 47 · 2777 · 55488371 · 83963507 · 12461087964323018107_<20> · 47012464426731479399_<20> · C101
C101 = P30 · P71
P30 = 279929909870966847008523066101_<30>
P71 = 63510828694745285306996073091706073394019137483384890813990419744277463_<71>

Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=3996634525 Step 1 took 4696ms Step 2 took 4261ms ********** Factor found in step 2: 279929909870966847008523066101 Found probable prime factor of 30 digits: 279929909870966847008523066101 Probable prime cofactor has 71 digits

(19·10¹⁷⁶+11)/3 = 6(3)₁₇₅7_<177> = 7 · 13 · 31 · 329711 · C168
C168 = P33 · P136
P33 = 380411345154635513542806482329393_<33>
P136 = 1789956030815979787160246186972967745910411150766357772414416278341751433525261220762485364988957571956424883773305352022454824614214139_<136>

Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=1431286068 Step 1 took 7581ms Step 2 took 6112ms ********** Factor found in step 2: 380411345154635513542806482329393 Found probable prime factor of 33 digits: 380411345154635513542806482329393 Probable prime cofactor has 136 digits

(19·10¹²³+11)/3 = 6(3)₁₂₂7_<124> = 17 · 2221 · C120
C120 = P31 · P89
P31 = 2123006000891924143214151384847_<31>
P89 = 79010287948575789367851766818808637179491229043894459004745091157379088266646782235367203_<89>

Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=1215604976 Step 1 took 5396ms Step 2 took 4761ms ********** Factor found in step 2: 2123006000891924143214151384847 Found probable prime factor of 31 digits: 2123006000891924143214151384847 Probable prime cofactor has 89 digits

(19·10¹¹⁹+11)/3 = 6(3)₁₁₈7_<120> = 23 · C119
C119 = P54 · P65
P54 = 886378704567425127996664373012529164481079650712500457_<54>
P65 = 31065989900441411912454637184703297301511811585122769130099098167_<65>

SNFS difficulty: 121 digits. Divisors found: r1=886378704567425127996664373012529164481079650712500457 (pp54) r2=31065989900441411912454637184703297301511811585122769130099098167 (pp65) Version: Msieve v. 1.41 Total time: 0.88 hours. Scaled time: 2.39 units (timescale=2.734). Factorization parameters were as follows: n: 27536231884057971014492753623188405797101449275362318840579710144927536231884057971014492753623188405797101449275362319 m: 1000000000000000000000000 deg: 5 c5: 19 c0: 110 skew: 1.42 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, 670001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 83360 x 83587 Total sieving time: 0.82 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,121.000,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000 total time: 0.88 hours.

Jun 4, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve / Jun 4, 2009
(56·10¹⁷³-11)/9 = 6(2)₁₇₂1_<174> = 3² · C173
C173 = P48 · P125
P48 = 738564409141079321357570371709279096815335359017_<48>
P125 = 93608359153858981426105610055260809112478522633363061217130806551642027574933883449218513789486636057611681994106049642990557_<125>

Number: n N=69135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469 ( 173 digits) SNFS difficulty: 176 digits. Divisors found: Thu Jun 04 06:39:25 2009 prp48 factor: 738564409141079321357570371709279096815335359017 Thu Jun 04 06:39:25 2009 prp125 factor: 93608359153858981426105610055260809112478522633363061217130806551642027574933883449218513789486636057611681994106049642990557 Thu Jun 04 06:39:25 2009 elapsed time 01:57:21 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 77.32 hours. Scaled time: 206.51 units (timescale=2.671). Factorization parameters were as follows: name: KA_6_2_172_1 n: 69135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469 m: 100000000000000000000000000000000000 deg: 5 c5: 14 c0: -275 skew: 1.81 type: snfs lss: 1 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 [3000000, 6930323) Primes: RFBsize:412849, AFBsize:413097, largePrimes:20590929 encountered Relations: rels:20331002, finalFF:783769 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2478742 hash collisions in 22397806 relations Msieve: matrix is 1058956 x 1059204 (283.3 MB) Total sieving time: 76.03 hours. Total relation processing time: 1.29 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,176,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,56,56,2.5,2.5,100000 total time: 77.32 hours. --------- CPU info (if available) ----------

Jun 4, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jun 4, 2009
(2·10¹⁸⁶+1)/3 = (6)₁₈₅7_<186> = 251 · 6985625296223599274700793_<25> · C159
C159 = P52 · P107
P52 = 4206917503932403168642670324369591892367492856212867_<52>
P107 = 90378626505701927771029832024922188717613437390639233047108160799437912965230133400154778880592650723086707_<107>

Number: 66667_186 N=380215425828206486972276085410708135299591961689712370600918694125902131065848858643968804230144200389046038423936391956686137469192075622992358872536490058969 ( 159 digits) SNFS difficulty: 186 digits. Divisors found: r1=4206917503932403168642670324369591892367492856212867 r2=90378626505701927771029832024922188717613437390639233047108160799437912965230133400154778880592650723086707 Version: Total time: 98.62 hours. Scaled time: 235.31 units (timescale=2.386). Factorization parameters were as follows: n: 380215425828206486972276085410708135299591961689712370600918694125902131065848858643968804230144200389046038423936391956686137469192075622992358872536490058969 m: 10000000000000000000000000000000000000 deg: 5 c5: 20 c0: 1 skew: 0.55 type: snfs lss: 1 rlim: 7800000 alim: 7800000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 7800000/7800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [3900000, 6500001) Primes: rational ideals reading, algebraic ideals reading, Relations: 19636934 Max relations in full relation-set: Initial matrix: Pruned matrix : 1626273 x 1626520 Total sieving time: 89.24 hours. Total relation processing time: 2.68 hours. Matrix solve time: 6.01 hours. Time per square root: 0.68 hours. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,7800000,7800000,28,28,54,54,2.5,2.5,100000 total time: 98.62 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

Jun 4, 2009

Factorizations of 633...337 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Jun 3, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jun 3, 2009
(56·10¹⁶⁴+61)/9 = 6(2)₁₆₃9_<165> = 37 · 107143243 · 827738769862247647289_<21> · C135
C135 = P67 · P68
P67 = 6359269268231973633385412363501308099138996129477289618088897243227_<67>
P68 = 29817998891046624165279119258269213521683566428481920044352290969873_<68>

Number: 62229_164 N=189620683988007866952443937748701417479265735985124731986169809683284375738554208691520381887964237839718019582607285916537475810300171 ( 135 digits) SNFS difficulty: 166 digits. Divisors found: r1=6359269268231973633385412363501308099138996129477289618088897243227 r2=29817998891046624165279119258269213521683566428481920044352290969873 Version: Total time: 25.86 hours. Scaled time: 61.83 units (timescale=2.391). Factorization parameters were as follows: n: 189620683988007866952443937748701417479265735985124731986169809683284375738554208691520381887964237839718019582607285916537475810300171 m: 1000000000000000000000000000000000 deg: 5 c5: 28 c0: 305 skew: 1.61 type: snfs lss: 1 rlim: 4800000 alim: 4800000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 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: 51/51 Sieved rational special-q in [2400000, 4500001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9806459 Max relations in full relation-set: Initial matrix: Pruned matrix : 818905 x 819153 Total sieving time: 23.34 hours. Total relation processing time: 1.00 hours. Matrix solve time: 1.43 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,51,51,2.4,2.4,100000 total time: 25.86 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

Jun 3, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Jun 3, 2009
(19·10¹⁶⁶-7)/3 = 6(3)₁₆₅1_<167> = 1251201797773_<13> · C155
C155 = P40 · P115
P40 = 5222677376389994113737654403622761109617_<40>
P115 = 9691963898668385579244490463221708208315417143422065550154610103602175046798755781909933417277472713444234030147791_<115>

Number: n N=50618000586363942762203374279640780451317566357735062091510191730164175208514686857624038716426133302249351141792345827911123123457306830339243153661406047 ( 155 digits) SNFS difficulty: 168 digits. Divisors found: Wed Jun 03 10:22:45 2009 prp40 factor: 5222677376389994113737654403622761109617 Wed Jun 03 10:22:45 2009 prp115 factor: 9691963898668385579244490463221708208315417143422065550154610103602175046798755781909933417277472713444234030147791 Wed Jun 03 10:22:45 2009 elapsed time 01:10:24 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 34.34 hours. Scaled time: 90.96 units (timescale=2.649). Factorization parameters were as follows: name: KA_6_3_165_1 n: 50618000586363942762203374279640780451317566357735062091510191730164175208514686857624038716426133302249351141792345827911123123457306830339243153661406047 m: 2000000000000000000000000000000000 deg: 5 c5: 95 c0: -112 skew: 1.03 type: snfs lss: 1 rlim: 4600000 alim: 4600000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 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 [2300000, 4218517) Primes: RFBsize:322441, AFBsize:321861, largePrimes:15963971 encountered Relations: rels:15425943, finalFF:635132 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1491550 hash collisions in 16716161 relations Msieve: matrix is 728875 x 729123 (196.3 MB) Total sieving time: 33.78 hours. Total relation processing time: 0.55 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,4600000,4600000,28,28,56,56,2.4,2.4,100000 total time: 34.34 hours. --------- CPU info (if available) ----------

(56·10¹⁶⁸+61)/9 = 6(2)₁₆₇9_<169> = 13 · 331 · C166
C166 = P53 · P113
P53 = 96209819631831239463458686211657549363576689560960517_<53>
P113 = 15029854316755953449386612574288835256536189192545473764862710443914088338103651872711772544550625231249480134879_<113>

Number: n N=1446019572907790430449040720944044206884086038164588013530611717922896170630309603119270792986805071397216412322152503421385596612182714901748134376533168073953572443 ( 166 digits) SNFS difficulty: 170 digits. Divisors found: Wed Jun 03 17:30:16 2009 prp53 factor: 96209819631831239463458686211657549363576689560960517 Wed Jun 03 17:30:16 2009 prp113 factor: 15029854316755953449386612574288835256536189192545473764862710443914088338103651872711772544550625231249480134879 Wed Jun 03 17:30:16 2009 elapsed time 01:53:45 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 63.55 hours. Scaled time: 167.40 units (timescale=2.634). Factorization parameters were as follows: name: KA_6_2_167_9 n: 1446019572907790430449040720944044206884086038164588013530611717922896170630309603119270792986805071397216412322152503421385596612182714901748134376533168073953572443 m: 4000000000000000000000000000000000 deg: 5 c5: 875 c0: 976 skew: 1.02 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2500000, 6236533) Primes: RFBsize:348513, AFBsize:348732, largePrimes:17394588 encountered Relations: rels:17199344, finalFF:648711 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2276774 hash collisions in 19262903 relations Msieve: matrix is 898230 x 898478 (237.4 MB) Total sieving time: 62.63 hours. Total relation processing time: 0.92 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000 total time: 63.55 hours. --------- CPU info (if available) ----------

Jun 3, 2009

By Dmitry Domanov / ECM / Jun 3, 2009
(16·10¹⁹⁹-7)/9 = 1(7)_199<200> = 264007 · 6353173 · 23291472982858333436228811919662999043691_<41> · C147
C147 = P46 · C102
P46 = 1502739138045835488243594532007091714625588183_<46>
C102 = [302824352506754444443578645843911185284478634106196572443295670733987494299384968724155242087323594919_<102>]

[2009-06-02 23:45:23 GMT] a: Factor found! test61 / (probable) 1502739138045835488243594532007091714625588183 B1: 11000000 sigma: 540716867 (found in step 2) [2009-06-02 23:45:23 GMT] a: Co-factor: test61 / (Composite) 302824352506754444443578645843911185284478634106196572443295670733987494299384968724155242087323594919

Jun 2, 2009 (2nd)

By Dmitry Domanov / ggnfs, msieve / Jun 2, 2009
(19·10¹⁶⁹-7)/3 = 6(3)₁₆₈1_<170> = C170
C170 = P42 · P129
P42 = 454291383041177479146316118799864631194049_<42>
P129 = 139411258275160216175498607426380186850484941194923576476093434398091509434652722681972425582202165365944458263133700328849433619_<129>

Sieving in [2400000;5700000] took about 20hours on Xeon E5310 @ 4 cores Mon Jun 01 23:57:37 2009 Msieve v. 1.41 Mon Jun 01 23:57:37 2009 random seeds: d61aa0a0 238188c0 Mon Jun 01 23:57:37 2009 factoring 63333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 (170 digits) Mon Jun 01 23:57:39 2009 searching for 15-digit factors Mon Jun 01 23:57:41 2009 commencing number field sieve (170-digit input) Mon Jun 01 23:57:41 2009 R0: -10000000000000000000000000000000000 Mon Jun 01 23:57:41 2009 R1: 1 Mon Jun 01 23:57:41 2009 A0: -70 Mon Jun 01 23:57:41 2009 A1: 0 Mon Jun 01 23:57:41 2009 A2: 0 Mon Jun 01 23:57:41 2009 A3: 0 Mon Jun 01 23:57:41 2009 A4: 0 Mon Jun 01 23:57:41 2009 A5: 19 Mon Jun 01 23:57:41 2009 skew 1.30, size 4.593843e-012, alpha 1.501780, combined = 2.087721e-010 Mon Jun 01 23:57:41 2009 Mon Jun 01 23:57:41 2009 commencing relation filtering Mon Jun 01 23:57:41 2009 commencing duplicate removal, pass 1 Mon Jun 01 23:59:18 2009 found 1777090 hash collisions in 12098448 relations Mon Jun 01 23:59:39 2009 added 2707 free relations Mon Jun 01 23:59:39 2009 commencing duplicate removal, pass 2 Tue Jun 02 00:00:03 2009 found 1797917 duplicates and 10303238 unique relations Tue Jun 02 00:00:03 2009 memory use: 69.3 MB Tue Jun 02 00:00:03 2009 reading rational ideals above 5701632 Tue Jun 02 00:00:03 2009 reading algebraic ideals above 5701632 Tue Jun 02 00:00:03 2009 commencing singleton removal, pass 1 Tue Jun 02 00:01:33 2009 relations with 0 large ideals: 174319 Tue Jun 02 00:01:33 2009 relations with 1 large ideals: 1092040 Tue Jun 02 00:01:33 2009 relations with 2 large ideals: 3004490 Tue Jun 02 00:01:33 2009 relations with 3 large ideals: 3791203 Tue Jun 02 00:01:33 2009 relations with 4 large ideals: 1864703 Tue Jun 02 00:01:33 2009 relations with 5 large ideals: 22017 Tue Jun 02 00:01:33 2009 relations with 6 large ideals: 354460 Tue Jun 02 00:01:33 2009 relations with 7+ large ideals: 6 Tue Jun 02 00:01:33 2009 10303238 relations and about 10061091 large ideals Tue Jun 02 00:01:33 2009 commencing singleton removal, pass 2 Tue Jun 02 00:03:06 2009 found 3638251 singletons Tue Jun 02 00:03:06 2009 current dataset: 6664987 relations and about 5540314 large ideals Tue Jun 02 00:03:06 2009 commencing singleton removal, pass 3 Tue Jun 02 00:04:14 2009 found 1113381 singletons Tue Jun 02 00:04:14 2009 current dataset: 5551606 relations and about 4351780 large ideals Tue Jun 02 00:04:14 2009 commencing singleton removal, pass 4 Tue Jun 02 00:05:12 2009 found 330238 singletons Tue Jun 02 00:05:12 2009 current dataset: 5221368 relations and about 4013429 large ideals Tue Jun 02 00:05:12 2009 commencing singleton removal, final pass Tue Jun 02 00:06:12 2009 memory use: 88.2 MB Tue Jun 02 00:06:12 2009 commencing in-memory singleton removal Tue Jun 02 00:06:12 2009 begin with 5221368 relations and 4249847 unique ideals Tue Jun 02 00:06:20 2009 reduce to 4512893 relations and 3525902 ideals in 14 passes Tue Jun 02 00:06:20 2009 max relations containing the same ideal: 17 Tue Jun 02 00:06:21 2009 reading rational ideals above 720000 Tue Jun 02 00:06:21 2009 reading algebraic ideals above 720000 Tue Jun 02 00:06:21 2009 commencing singleton removal, final pass Tue Jun 02 00:07:23 2009 keeping 3861899 ideals with weight <= 20, new excess is 468053 Tue Jun 02 00:07:29 2009 memory use: 128.6 MB Tue Jun 02 00:07:29 2009 commencing in-memory singleton removal Tue Jun 02 00:07:30 2009 begin with 4515600 relations and 3861899 unique ideals Tue Jun 02 00:07:34 2009 reduce to 4511494 relations and 3844466 ideals in 8 passes Tue Jun 02 00:07:34 2009 max relations containing the same ideal: 20 Tue Jun 02 00:07:38 2009 removing 543410 relations and 481367 ideals in 62043 cliques Tue Jun 02 00:07:38 2009 commencing in-memory singleton removal Tue Jun 02 00:07:39 2009 begin with 3968084 relations and 3844466 unique ideals Tue Jun 02 00:07:44 2009 reduce to 3918567 relations and 3312614 ideals in 10 passes Tue Jun 02 00:07:44 2009 max relations containing the same ideal: 20 Tue Jun 02 00:07:47 2009 removing 403681 relations and 341638 ideals in 62043 cliques Tue Jun 02 00:07:47 2009 commencing in-memory singleton removal Tue Jun 02 00:07:48 2009 begin with 3514886 relations and 3312614 unique ideals Tue Jun 02 00:07:51 2009 reduce to 3483225 relations and 2938714 ideals in 7 passes Tue Jun 02 00:07:51 2009 max relations containing the same ideal: 20 Tue Jun 02 00:07:54 2009 relations with 0 large ideals: 41806 Tue Jun 02 00:07:54 2009 relations with 1 large ideals: 262264 Tue Jun 02 00:07:54 2009 relations with 2 large ideals: 761751 Tue Jun 02 00:07:54 2009 relations with 3 large ideals: 1115630 Tue Jun 02 00:07:54 2009 relations with 4 large ideals: 857838 Tue Jun 02 00:07:54 2009 relations with 5 large ideals: 342096 Tue Jun 02 00:07:54 2009 relations with 6 large ideals: 93408 Tue Jun 02 00:07:54 2009 relations with 7+ large ideals: 8432 Tue Jun 02 00:07:54 2009 commencing 2-way merge Tue Jun 02 00:07:57 2009 reduce to 2116068 relation sets and 1571558 unique ideals Tue Jun 02 00:07:57 2009 ignored 1 oversize relation sets Tue Jun 02 00:07:57 2009 commencing full merge Tue Jun 02 00:08:27 2009 memory use: 117.7 MB Tue Jun 02 00:08:28 2009 found 1009501 cycles, need 937758 Tue Jun 02 00:08:28 2009 weight of 937758 cycles is about 65932017 (70.31/cycle) Tue Jun 02 00:08:28 2009 distribution of cycle lengths: Tue Jun 02 00:08:28 2009 1 relations: 117955 Tue Jun 02 00:08:28 2009 2 relations: 103087 Tue Jun 02 00:08:28 2009 3 relations: 101087 Tue Jun 02 00:08:28 2009 4 relations: 92485 Tue Jun 02 00:08:28 2009 5 relations: 84611 Tue Jun 02 00:08:28 2009 6 relations: 75708 Tue Jun 02 00:08:28 2009 7 relations: 66535 Tue Jun 02 00:08:28 2009 8 relations: 57923 Tue Jun 02 00:08:28 2009 9 relations: 50477 Tue Jun 02 00:08:28 2009 10+ relations: 187890 Tue Jun 02 00:08:28 2009 heaviest cycle: 18 relations Tue Jun 02 00:08:28 2009 commencing cycle optimization Tue Jun 02 00:08:30 2009 start with 5543854 relations Tue Jun 02 00:08:44 2009 pruned 157739 relations Tue Jun 02 00:08:44 2009 memory use: 145.8 MB Tue Jun 02 00:08:44 2009 distribution of cycle lengths: Tue Jun 02 00:08:44 2009 1 relations: 117955 Tue Jun 02 00:08:44 2009 2 relations: 105792 Tue Jun 02 00:08:44 2009 3 relations: 105257 Tue Jun 02 00:08:44 2009 4 relations: 95447 Tue Jun 02 00:08:44 2009 5 relations: 87378 Tue Jun 02 00:08:44 2009 6 relations: 77385 Tue Jun 02 00:08:44 2009 7 relations: 67623 Tue Jun 02 00:08:44 2009 8 relations: 58211 Tue Jun 02 00:08:44 2009 9 relations: 50641 Tue Jun 02 00:08:44 2009 10+ relations: 172069 Tue Jun 02 00:08:44 2009 heaviest cycle: 18 relations Tue Jun 02 00:08:47 2009 RelProcTime: 612 Tue Jun 02 00:08:47 2009 elapsed time 00:11:10 Tue Jun 02 00:18:36 2009 Tue Jun 02 00:18:36 2009 Tue Jun 02 00:18:36 2009 Msieve v. 1.41 Tue Jun 02 00:18:36 2009 random seeds: 08740858 38647e30 Tue Jun 02 00:18:36 2009 factoring 63333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 (170 digits) Tue Jun 02 00:18:37 2009 searching for 15-digit factors Tue Jun 02 00:18:40 2009 commencing number field sieve (170-digit input) Tue Jun 02 00:18:40 2009 R0: -10000000000000000000000000000000000 Tue Jun 02 00:18:40 2009 R1: 1 Tue Jun 02 00:18:40 2009 A0: -70 Tue Jun 02 00:18:40 2009 A1: 0 Tue Jun 02 00:18:40 2009 A2: 0 Tue Jun 02 00:18:40 2009 A3: 0 Tue Jun 02 00:18:40 2009 A4: 0 Tue Jun 02 00:18:40 2009 A5: 19 Tue Jun 02 00:18:40 2009 skew 1.30, size 4.593843e-012, alpha 1.501780, combined = 2.087721e-010 Tue Jun 02 00:18:40 2009 Tue Jun 02 00:18:40 2009 commencing linear algebra Tue Jun 02 00:18:40 2009 read 937758 cycles Tue Jun 02 00:18:42 2009 cycles contain 3063344 unique relations Tue Jun 02 00:19:16 2009 read 3063344 relations Tue Jun 02 00:19:21 2009 using 20 quadratic characters above 134217402 Tue Jun 02 00:19:37 2009 building initial matrix Tue Jun 02 00:20:17 2009 memory use: 335.2 MB Tue Jun 02 00:20:18 2009 read 937758 cycles Tue Jun 02 00:20:22 2009 matrix is 937406 x 937758 (265.7 MB) with weight 82805041 (88.30/col) Tue Jun 02 00:20:22 2009 sparse part has weight 63082269 (67.27/col) Tue Jun 02 00:20:44 2009 filtering completed in 3 passes Tue Jun 02 00:20:44 2009 matrix is 929761 x 929961 (264.4 MB) with weight 82352811 (88.56/col) Tue Jun 02 00:20:44 2009 sparse part has weight 62803128 (67.53/col) Tue Jun 02 00:20:49 2009 read 929961 cycles Tue Jun 02 00:23:59 2009 matrix is 929761 x 929961 (264.4 MB) with weight 82352811 (88.56/col) Tue Jun 02 00:23:59 2009 sparse part has weight 62803128 (67.53/col) Tue Jun 02 00:24:00 2009 saving the first 48 matrix rows for later Tue Jun 02 00:24:00 2009 matrix is 929713 x 929961 (249.3 MB) with weight 64976976 (69.87/col) Tue Jun 02 00:24:00 2009 sparse part has weight 59762482 (64.26/col) Tue Jun 02 00:24:00 2009 matrix includes 64 packed rows Tue Jun 02 00:24:00 2009 using block size 65536 for processor cache size 6144 kB Tue Jun 02 00:24:07 2009 commencing Lanczos iteration (4 threads) Tue Jun 02 00:24:07 2009 memory use: 272.7 MB Tue Jun 02 01:46:04 2009 lanczos halted after 14705 iterations (dim = 929711) Tue Jun 02 01:46:06 2009 recovered 35 nontrivial dependencies Tue Jun 02 01:46:06 2009 BLanczosTime: 5246 Tue Jun 02 01:46:06 2009 elapsed time 01:27:30 Tue Jun 02 11:13:35 2009 Tue Jun 02 11:13:35 2009 Tue Jun 02 11:13:35 2009 Msieve v. 1.41 Tue Jun 02 11:13:35 2009 random seeds: 81a95a80 200be138 Tue Jun 02 11:13:35 2009 factoring 63333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 (170 digits) Tue Jun 02 11:13:37 2009 searching for 15-digit factors Tue Jun 02 11:13:39 2009 commencing number field sieve (170-digit input) Tue Jun 02 11:13:39 2009 R0: -10000000000000000000000000000000000 Tue Jun 02 11:13:39 2009 R1: 1 Tue Jun 02 11:13:39 2009 A0: -70 Tue Jun 02 11:13:39 2009 A1: 0 Tue Jun 02 11:13:39 2009 A2: 0 Tue Jun 02 11:13:39 2009 A3: 0 Tue Jun 02 11:13:39 2009 A4: 0 Tue Jun 02 11:13:39 2009 A5: 19 Tue Jun 02 11:13:39 2009 skew 1.30, size 4.593843e-012, alpha 1.501780, combined = 2.087721e-010 Tue Jun 02 11:13:39 2009 Tue Jun 02 11:13:39 2009 commencing square root phase Tue Jun 02 11:13:39 2009 reading relations for dependency 1 Tue Jun 02 11:13:40 2009 read 465397 cycles Tue Jun 02 11:13:40 2009 cycles contain 1871002 unique relations Tue Jun 02 11:14:08 2009 read 1871002 relations Tue Jun 02 11:14:18 2009 multiplying 1528186 relations Tue Jun 02 11:16:21 2009 multiply complete, coefficients have about 40.14 million bits Tue Jun 02 11:16:22 2009 initial square root is modulo 579011 Tue Jun 02 11:20:27 2009 sqrtTime: 408 Tue Jun 02 11:20:27 2009 prp42 factor: 454291383041177479146316118799864631194049 Tue Jun 02 11:20:27 2009 prp129 factor: 139411258275160216175498607426380186850484941194923576476093434398091509434652722681972425582202165365944458263133700328849433619 Tue Jun 02 11:20:27 2009 elapsed time 00:06:52

Jun 2, 2009

By Robert Backstrom / GGNFS, Msieve / Jun 2, 2009
(19·10¹⁶³-7)/3 = 6(3)₁₆₂1_<164> = 1528115427195860226452144519734181_<34> · C131
C131 = P42 · P90
P42 = 375054753555520893395695609169760004067579_<42>
P90 = 110504893874187591596413409495017682935672393337348376387307423814825042765064498801134869_<90>

Number: n N=41445385738662417611442928814986924314473384202452265032125295618316543566091246353416032258371712530792430821849165330461369312151 ( 131 digits) SNFS difficulty: 165 digits. Divisors found: Tue Jun 02 12:58:47 2009 prp42 factor: 375054753555520893395695609169760004067579 Tue Jun 02 12:58:47 2009 prp90 factor: 110504893874187591596413409495017682935672393337348376387307423814825042765064498801134869 Tue Jun 02 12:58:47 2009 elapsed time 01:07:01 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 39.96 hours. Scaled time: 105.85 units (timescale=2.649). Factorization parameters were as follows: name: KA_6_3_162_1 n: 41445385738662417611442928814986924314473384202452265032125295618316543566091246353416032258371712530792430821849165330461369312151 m: 500000000000000000000000000000000 deg: 5 c5: 152 c0: -175 skew: 1.03 type: snfs lss: 1 rlim: 4000000 alim: 4000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 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 [2000000, 4425397) Primes: RFBsize:283146, AFBsize:283092, largePrimes:15709237 encountered Relations: rels:15287211, finalFF:613633 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1801663 hash collisions in 16935383 relations Msieve: matrix is 712265 x 712513 (188.5 MB) Total sieving time: 39.44 hours. Total relation processing time: 0.51 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,56,56,2.4,2.4,100000 total time: 39.96 hours. --------- CPU info (if available) ----------

(53·10²⁰³-17)/9 = 5(8)₂₀₂7_<204> = 13 · C203
C203 = P42 · P59 · P102
P42 = 987350730914620921690289987203621855954963_<42>
P59 = 92566848900864095239779213632802017565483126475597474270379_<59>
P102 = 495636265293798401196317143432651643488247579932991797044874163185512392872923768166698869239772113987_<102>

Number: n N=45299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299 ( 203 digits) SNFS difficulty: 206 digits. Divisors found: Tue Jun 2 14:05:48 2009 prp42 factor: 987350730914620921690289987203621855954963 Tue Jun 2 14:05:48 2009 prp59 factor: 92566848900864095239779213632802017565483126475597474270379 Tue Jun 2 14:05:48 2009 prp102 factor: 495636265293798401196317143432651643488247579932991797044874163185512392872923768166698869239772113987 Tue Jun 2 14:05:48 2009 elapsed time 19:30:16 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20050930-k8 Total time: 99.56 hours. Scaled time: 200.62 units (timescale=2.015). Factorization parameters were as follows: name: KA_5_8_202_7 n: 45299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299 m: 50000000000000000000000000000000000000000 deg: 5 c5: 424 c0: -425 skew: 1.00 type: snfs lss: 1 rlim: 19000000 alim: 19000000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 19000000/19000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved special-q in [9500000, 29099990) Primes: RFBsize:1211050, AFBsize:1212352, largePrimes:35419729 encountered Relations: rels:33177779, finalFF:834914 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 7395621 hash collisions in 44885691 relations Msieve: matrix is 3359630 x 3359878 (905.5 MB) Total sieving time: 98.57 hours. Total relation processing time: 0.99 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,206,5,0,0,0,0,0,0,0,0,19000000,19000000,29,29,56,56,2.6,2.6,100000 total time: 99.56 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3368968k/3407296k available (2748k kernel code, 36964k reserved, 1425k data, 416k init, 2489792k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830496) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830447) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Total of 4 processors activated (22643.71 BogoMIPS).

Jun 1, 2009 (4th)

By Dmitry Domanov / GGNFS/msieve / Jun 1, 2009
(16·10¹⁷⁸-7)/9 = 1(7)_178<179> = 19 · 67247 · 6779280532223_<13> · 17847077925229148671_<20> · C141
C141 = P63 · P78
P63 = 351285801553477998259072973907150185197704089795714956495320427_<63>
P78 = 327370570697273242447130450554318941139597272631318183807575568975566864956879_<78>

Number: 577 N=115000633332411167647364546083294741615775101260141430479997902227306590463854471282709871778389721057965754878001756662197647499816642867333 ( 141 digits) SNFS difficulty: 180 digits. Divisors found: r1=351285801553477998259072973907150185197704089795714956495320427 (pp63) r2=327370570697273242447130450554318941139597272631318183807575568975566864956879 (pp78) Version: Msieve v. 1.41 Total time: 106.90 hours. Scaled time: 211.87 units (timescale=1.982). Factorization parameters were as follows: n: 115000633332411167647364546083294741615775101260141430479997902227306590463854471282709871778389721057965754878001756662197647499816642867333 m: 400000000000000000000000000000000000 deg: 5 c5: 125 c0: -56 skew: 0.85 type: snfs lss: 1 rlim: 7000000 alim: 7000000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7000000/7000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3500000, 5300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1198873 x 1199121 Total sieving time: 104.20 hours. Total relation processing time: 0.29 hours. Matrix solve time: 1.98 hours. Time per square root: 0.43 hours. Prototype def-par.txt line would be: snfs,180.000,5,0,0,0,0,0,0,0,0,7000000,7000000,28,28,53,53,2.5,2.5,100000 total time: 106.90 hours. --------- CPU info (if available) ----------

(16·10¹⁸⁰-7)/9 = 1(7)_180<181> = 1038694808570917_<16> · C166
C166 = P60 · P107
P60 = 137718772401945611066139183172563078616174576033116838801957_<60>
P107 = 12427860489216359333700314673797681425104380541244459983868501418546968585363216500853083110304729687523033_<107>

Number: 677 N=1711549690157520228330742557808063317961315632644673179819320806670356053994984550359977522136522021367570978466533605186365590753577246918825184595149011146562975581 ( 166 digits) SNFS difficulty: 181 digits. Divisors found: r1=137718772401945611066139183172563078616174576033116838801957 (pp60) r2=12427860489216359333700314673797681425104380541244459983868501418546968585363216500853083110304729687523033 (pp107) Version: Msieve v. 1.41 Total time: 101.21 hours. Scaled time: 201.21 units (timescale=1.988). Factorization parameters were as follows: n: 1711549690157520228330742557808063317961315632644673179819320806670356053994984550359977522136522021367570978466533605186365590753577246918825184595149011146562975581 m: 2000000000000000000000000000000000000 deg: 5 c5: 1 c0: -14 skew: 1.70 type: snfs lss: 1 rlim: 7400000 alim: 7400000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3700000, 5400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1390191 x 1390439 Total sieving time: 98.04 hours. Total relation processing time: 0.27 hours. Matrix solve time: 2.77 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,181.000,5,0,0,0,0,0,0,0,0,7400000,7400000,28,28,53,53,2.5,2.5,100000 total time: 101.21 hours. --------- CPU info (if available) ----------

Jun 1, 2009 (3rd)

By Serge Batalov / GMP-ECM 6.2.3 / Jun 1, 2009
(7·10²²⁷-43)/9 = (7)₂₂₆3_<227> = 3559 · C224
C224 = P28 · C196
P28 = 8458505971912909206817868981_<28>
C196 = [2583651199824609680034453819884625327726724648528050962698862538834572380539968219106118313227233933547355672372029262918293850733930449356683602772128068063946794992912419603436233160706908852287_<196>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3642532168 Step 1 took 16621ms Step 2 took 13553ms ********** Factor found in step 2: 8458505971912909206817868981 Found probable prime factor of 28 digits: 8458505971912909206817868981 Composite cofactor has 196 digits

(7·10²¹⁵-43)/9 = (7)₂₁₄3_<215> = 2081 · 1504051683081685150327_<22> · 4344239786129705012158373_<25> · C166
C166 = P34 · C133
P34 = 3024223307536720085994159843093307_<34>
C133 = [1891442074356078127435530811303209306810261564412542247972987797125896592894268399142579972662858268228984818353299092343914997992589_<133>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=3496836667 Step 1 took 3564ms Step 2 took 3300ms ********** Factor found in step 2: 3024223307536720085994159843093307 Found probable prime factor of 34 digits: 3024223307536720085994159843093307 Composite cofactor has 133 digits

(7·10²⁴⁵-43)/9 = (7)₂₄₄3_<245> = 53² · C242
C242 = P30 · C213
P30 = 147803791508418175555074273469_<30>
C213 = [187334694537922847786332374691014861222601208364833920555120484053811064039560744117770151237267789426518709898544015747455022079756915518534598493789954675170924442769261275475794400002491732103243135770913504313_<213>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=624630945 Step 1 took 6221ms Step 2 took 4776ms ********** Factor found in step 2: 147803791508418175555074273469 Found probable prime factor of 30 digits: 147803791508418175555074273469 Composite cofactor has 213 digits

(7·10²³⁴-43)/9 = (7)₂₃₃3_<234> = 73 · C233
C233 = P32 · P201
P32 = 70162570395366838677237918643007_<32>
P201 = 151854329830089387276948123171475465368043900564395635574907640527902177725953130967084760080446859468423858471494840344280032942052563119440955147796605889957623924505089000655025798808544614240070843_<201>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=762880277 Step 1 took 18957ms Step 2 took 8053ms ********** Factor found in step 2: 70162570395366838677237918643007 Found probable prime factor of 32 digits: 70162570395366838677237918643007 Probable prime cofactor has 201 digits

Jun 1, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jun 1, 2009
(7·10²²¹-43)/9 = (7)₂₂₀3_<221> = 17 · 281 · 1933050226305217_<16> · 7065680627293703578348517_<25> · 21626847603702295660286951_<26> · 94971446179866949702602973_<26> · 17941218631370458475790313427_<29> · C98
C98 = P35 · P63
P35 = 83917164802182940110279805322856967_<35>
P63 = 385490904422208015412208301554642767311267505646360635649004263_<63>

Number: 77773_221 N=32349303756140982366638500632066141116319673464587062506666215628176801423560827981638307922250321 ( 98 digits) Divisors found: r1=83917164802182940110279805322856967 r2=385490904422208015412208301554642767311267505646360635649004263 Version: Total time: 2.25 hours. Scaled time: 5.38 units (timescale=2.390). Factorization parameters were as follows: name: 77773_221 n: 32349303756140982366638500632066141116319673464587062506666215628176801423560827981638307922250321 skew: 2071.43 # norm 3.18e+13 c5: 786480 c4: -909597786 c3: -6090742551109 c2: 5271076042794314 c1: 5464881154623239836 c0: -8918248740224616729200 # alpha -5.76 Y1: 861948791 Y0: -2102981693400790119 # Murphy_E 4.30e-09 # M 13704586428295265528822636952842921510667563363553767895424173946931554241498540878006403524405789 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, 950001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4218915 Max relations in full relation-set: Initial matrix: Pruned matrix : 163307 x 163555 Polynomial selection time: 0.13 hours. Total sieving time: 1.82 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.06 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: gnfs,97,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1000000,1000000,26,26,49,49,2.5,2.5,50000 total time: 2.25 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

Jun 1, 2009

By Robert Backstrom / GGNFS, Msieve / Jun 1, 2009
(56·10¹⁶²+43)/9 = 6(2)₁₆₁7_<163> = 11 · 47 · 10296567877_<11> · 123990940208683_<15> · C136
C136 = P50 · P87
P50 = 23983976853277442191852487114470582321131826167551_<50>
P87 = 393053201540223607796745824158765838141928859295078242639142682262167967738704645960991_<87>

Number: n N=9426978887847316499591259177339751369402284659743241181896586427524629168471443390568790396652331861718178838223408061486266734976003041 ( 136 digits) SNFS difficulty: 163 digits. Divisors found: Mon Jun 01 03:05:09 2009 prp50 factor: 23983976853277442191852487114470582321131826167551 Mon Jun 01 03:05:09 2009 prp87 factor: 393053201540223607796745824158765838141928859295078242639142682262167967738704645960991 Mon Jun 01 03:05:09 2009 elapsed time 00:56:26 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 24.18 hours. Scaled time: 63.81 units (timescale=2.639). Factorization parameters were as follows: name: KA_6_2_161_7 n: 9426978887847316499591259177339751369402284659743241181896586427524629168471443390568790396652331861718178838223408061486266734976003041 m: 20000000000000000000000000000000