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  1. Tue Sep 29 15:32:43 2026 Msieve v. 1.54 (SVN Unversioned directory)
  2. Tue Sep 29 15:32:43 2026 random seeds: a1fce954 02181626
  3. Tue Sep 29 15:32:43 2026 factoring 8409377095351680425669847941224110112689963986607947093516371609456054188717729355135344083513411136680829385238249747035151726612162512214375145303517672157965265807 (166 digits)
  4. Tue Sep 29 15:32:44 2026 no P-1/P+1/ECM available, skipping
  5. Tue Sep 29 15:32:44 2026 commencing number field sieve (166-digit input)
  6. Tue Sep 29 15:32:44 2026 R0: -223379688902700319518751259220128
  7. Tue Sep 29 15:32:44 2026 R1: 492681800667047261089
  8. Tue Sep 29 15:32:44 2026 A0: -2512526146458159383221016966186844525585
  9. Tue Sep 29 15:32:44 2026 A1: -2321073858762466386763648956669722
  10. Tue Sep 29 15:32:44 2026 A2: -202145512968532068750773861
  11. Tue Sep 29 15:32:44 2026 A3: 10525238678600662648
  12. Tue Sep 29 15:32:44 2026 A4: -100609976388
  13. Tue Sep 29 15:32:44 2026 A5: 15120
  14. Tue Sep 29 15:32:44 2026 skew 16238595.67, size 5.251e-16, alpha -7.181, combined = 7.989e-13 rroots = 3
  15. Tue Sep 29 15:32:44 2026
  16. Tue Sep 29 15:32:44 2026 commencing relation filtering
  17. Tue Sep 29 15:32:44 2026 estimated available RAM is 31871.6 MB
  18. Tue Sep 29 15:32:44 2026 commencing duplicate removal, pass 1
  19. Tue Sep 29 15:33:00 2026 error -1 reading relation 1588847
  20. Tue Sep 29 15:33:44 2026 error -1 reading relation 5972612
  21. Tue Sep 29 15:33:53 2026 error -1 reading relation 6919565
  22. Tue Sep 29 15:33:53 2026 error -1 reading relation 6919566
  23. Tue Sep 29 15:34:19 2026 error -1 reading relation 9490317
  24. Tue Sep 29 15:34:33 2026 error -11 reading relation 10858343
  25. Tue Sep 29 15:35:36 2026 error -1 reading relation 17305450
  26. Tue Sep 29 15:36:55 2026 error -1 reading relation 25078555
  27. Tue Sep 29 15:36:55 2026 error -1 reading relation 25078556
  28. Tue Sep 29 15:37:21 2026 error -1 reading relation 27581197
  29. Tue Sep 29 15:37:58 2026 error -1 reading relation 31021323
  30. Tue Sep 29 15:38:50 2026 error -1 reading relation 35928227
  31. Tue Sep 29 15:39:28 2026 error -1 reading relation 39480475
  32. Tue Sep 29 15:41:25 2026 error -1 reading relation 50947647
  33. Tue Sep 29 15:41:51 2026 error -1 reading relation 53317061
  34. Tue Sep 29 15:42:11 2026 error -1 reading relation 55206667
  35. Tue Sep 29 15:42:33 2026 error -1 reading relation 57385371
  36. Tue Sep 29 15:42:36 2026 error -11 reading relation 57621090
  37. Tue Sep 29 15:43:19 2026 error -1 reading relation 61639592
  38. Tue Sep 29 15:43:41 2026 error -1 reading relation 63676655
  39. Tue Sep 29 15:43:55 2026 error -1 reading relation 65106614
  40. Tue Sep 29 15:44:13 2026 error -1 reading relation 66909018
  41. Tue Sep 29 15:45:08 2026 error -1 reading relation 72400059
  42. Tue Sep 29 15:45:23 2026 error -1 reading relation 73910003
  43. Tue Sep 29 15:45:23 2026 error -6 reading relation 73910004
  44. Tue Sep 29 15:47:06 2026 error -1 reading relation 83845830
  45. Tue Sep 29 15:47:30 2026 error -1 reading relation 86135931
  46. Tue Sep 29 15:47:39 2026 error -15 reading relation 87024293
  47. Tue Sep 29 15:47:40 2026 error -1 reading relation 87093273
  48. Tue Sep 29 15:47:46 2026 error -1 reading relation 87706761
  49. Tue Sep 29 15:47:46 2026 error -1 reading relation 87706762
  50. Tue Sep 29 15:48:10 2026 error -1 reading relation 89641882
  51. Tue Sep 29 15:48:12 2026 error -1 reading relation 89832612
  52. Tue Sep 29 15:48:34 2026 error -1 reading relation 91783699
  53. Tue Sep 29 15:48:34 2026 error -1 reading relation 91783700
  54. Tue Sep 29 15:49:11 2026 error -1 reading relation 95274425
  55. Tue Sep 29 15:49:33 2026 error -1 reading relation 97344754
  56. Tue Sep 29 15:50:22 2026 error -1 reading relation 101709529
  57. Tue Sep 29 15:51:38 2026 skipped 4 malformed relations
  58. Tue Sep 29 15:51:38 2026 found 5127419 hash collisions in 108443538 relations
  59. Tue Sep 29 15:52:13 2026 added 122145 free relations
  60. Tue Sep 29 15:52:13 2026 commencing duplicate removal, pass 2
  61. Tue Sep 29 15:53:31 2026 found 0 duplicates and 108565682 unique relations
  62. Tue Sep 29 15:53:31 2026 memory use: 394.4 MB
  63. Tue Sep 29 15:53:31 2026 reading ideals above 720000
  64. Tue Sep 29 15:53:31 2026 commencing singleton removal, initial pass
  65. Tue Sep 29 16:16:11 2026 memory use: 3012.0 MB
  66. Tue Sep 29 16:16:12 2026 reading all ideals from disk
  67. Tue Sep 29 16:17:17 2026 memory use: 4945.9 MB
  68. Tue Sep 29 16:17:55 2026 keeping 112994592 ideals with weight <= 200, target excess is 561724
  69. Tue Sep 29 16:18:17 2026 commencing in-memory singleton removal
  70. Tue Sep 29 16:18:43 2026 begin with 108565682 relations and 112994592 unique ideals
  71. Tue Sep 29 16:21:06 2026 reduce to 49288898 relations and 45320853 ideals in 17 passes
  72. Tue Sep 29 16:21:06 2026 max relations containing the same ideal: 124
  73. Tue Sep 29 16:22:06 2026 removing 3730089 relations and 3330089 ideals in 400000 cliques
  74. Tue Sep 29 16:22:09 2026 commencing in-memory singleton removal
  75. Tue Sep 29 16:22:18 2026 begin with 45558809 relations and 45320853 unique ideals
  76. Tue Sep 29 16:23:11 2026 reduce to 45351939 relations and 41781624 ideals in 9 passes
  77. Tue Sep 29 16:23:11 2026 max relations containing the same ideal: 117
  78. Tue Sep 29 16:24:04 2026 removing 2761986 relations and 2361986 ideals in 400000 cliques
  79. Tue Sep 29 16:24:06 2026 commencing in-memory singleton removal
  80. Tue Sep 29 16:24:15 2026 begin with 42589953 relations and 41781624 unique ideals
  81. Tue Sep 29 16:24:58 2026 reduce to 42463095 relations and 39291659 ideals in 8 passes
  82. Tue Sep 29 16:24:58 2026 max relations containing the same ideal: 111
  83. Tue Sep 29 16:25:46 2026 removing 2453016 relations and 2053016 ideals in 400000 cliques
  84. Tue Sep 29 16:25:48 2026 commencing in-memory singleton removal
  85. Tue Sep 29 16:25:56 2026 begin with 40010079 relations and 39291659 unique ideals
  86. Tue Sep 29 16:26:42 2026 reduce to 39901676 relations and 37129219 ideals in 9 passes
  87. Tue Sep 29 16:26:42 2026 max relations containing the same ideal: 108
  88. Tue Sep 29 16:27:28 2026 removing 2285834 relations and 1885834 ideals in 400000 cliques
  89. Tue Sep 29 16:27:30 2026 commencing in-memory singleton removal
  90. Tue Sep 29 16:27:37 2026 begin with 37615842 relations and 37129219 unique ideals
  91. Tue Sep 29 16:28:10 2026 reduce to 37516305 relations and 35142930 ideals in 7 passes
  92. Tue Sep 29 16:28:10 2026 max relations containing the same ideal: 104
  93. Tue Sep 29 16:28:53 2026 removing 2176469 relations and 1776469 ideals in 400000 cliques
  94. Tue Sep 29 16:28:55 2026 commencing in-memory singleton removal
  95. Tue Sep 29 16:29:02 2026 begin with 35339836 relations and 35142930 unique ideals
  96. Tue Sep 29 16:29:38 2026 reduce to 35244141 relations and 33269877 ideals in 8 passes
  97. Tue Sep 29 16:29:38 2026 max relations containing the same ideal: 101
  98. Tue Sep 29 16:30:18 2026 removing 2099951 relations and 1699951 ideals in 400000 cliques
  99. Tue Sep 29 16:30:20 2026 commencing in-memory singleton removal
  100. Tue Sep 29 16:30:26 2026 begin with 33144190 relations and 33269877 unique ideals
  101. Tue Sep 29 16:31:00 2026 reduce to 33048421 relations and 31473250 ideals in 8 passes
  102. Tue Sep 29 16:31:00 2026 max relations containing the same ideal: 94
  103. Tue Sep 29 16:31:36 2026 removing 2040241 relations and 1640241 ideals in 400000 cliques
  104. Tue Sep 29 16:31:38 2026 commencing in-memory singleton removal
  105. Tue Sep 29 16:31:43 2026 begin with 31008180 relations and 31473250 unique ideals
  106. Tue Sep 29 16:32:10 2026 reduce to 30914335 relations and 29738141 ideals in 7 passes
  107. Tue Sep 29 16:32:10 2026 max relations containing the same ideal: 90
  108. Tue Sep 29 16:32:45 2026 removing 1997374 relations and 1597374 ideals in 400000 cliques
  109. Tue Sep 29 16:32:46 2026 commencing in-memory singleton removal
  110. Tue Sep 29 16:32:52 2026 begin with 28916961 relations and 29738141 unique ideals
  111. Tue Sep 29 16:33:19 2026 reduce to 28821452 relations and 28044181 ideals in 8 passes
  112. Tue Sep 29 16:33:19 2026 max relations containing the same ideal: 86
  113. Tue Sep 29 16:33:52 2026 removing 760553 relations and 634882 ideals in 125671 cliques
  114. Tue Sep 29 16:33:53 2026 commencing in-memory singleton removal
  115. Tue Sep 29 16:33:58 2026 begin with 28060899 relations and 28044181 unique ideals
  116. Tue Sep 29 16:34:18 2026 reduce to 28047795 relations and 27396152 ideals in 6 passes
  117. Tue Sep 29 16:34:18 2026 max relations containing the same ideal: 84
  118. Tue Sep 29 16:34:27 2026 relations with 0 large ideals: 2046
  119. Tue Sep 29 16:34:27 2026 relations with 1 large ideals: 7776
  120. Tue Sep 29 16:34:27 2026 relations with 2 large ideals: 117855
  121. Tue Sep 29 16:34:27 2026 relations with 3 large ideals: 787909
  122. Tue Sep 29 16:34:27 2026 relations with 4 large ideals: 2830420
  123. Tue Sep 29 16:34:27 2026 relations with 5 large ideals: 5996387
  124. Tue Sep 29 16:34:27 2026 relations with 6 large ideals: 7832877
  125. Tue Sep 29 16:34:27 2026 relations with 7+ large ideals: 10472525
  126. Tue Sep 29 16:34:27 2026 commencing 2-way merge
  127. Tue Sep 29 16:35:16 2026 reduce to 17157749 relation sets and 16506106 unique ideals
  128. Tue Sep 29 16:35:16 2026 commencing full merge
  129. Tue Sep 29 16:46:44 2026 memory use: 2064.9 MB
  130. Tue Sep 29 16:46:46 2026 found 8513614 cycles, need 8428306
  131. Tue Sep 29 16:46:52 2026 weight of 8428306 cycles is about 758682048 (90.02/cycle)
  132. Tue Sep 29 16:46:52 2026 distribution of cycle lengths:
  133. Tue Sep 29 16:46:52 2026 1 relations: 801021
  134. Tue Sep 29 16:46:52 2026 2 relations: 843578
  135. Tue Sep 29 16:46:52 2026 3 relations: 850808
  136. Tue Sep 29 16:46:52 2026 4 relations: 785540
  137. Tue Sep 29 16:46:52 2026 5 relations: 738658
  138. Tue Sep 29 16:46:52 2026 6 relations: 676852
  139. Tue Sep 29 16:46:52 2026 7 relations: 610767
  140. Tue Sep 29 16:46:52 2026 8 relations: 543858
  141. Tue Sep 29 16:46:52 2026 9 relations: 486574
  142. Tue Sep 29 16:46:52 2026 10+ relations: 2090650
  143. Tue Sep 29 16:46:52 2026 heaviest cycle: 23 relations
  144. Tue Sep 29 16:46:55 2026 commencing cycle optimization
  145. Tue Sep 29 16:47:28 2026 start with 56025345 relations
  146. Tue Sep 29 16:50:36 2026 pruned 1658486 relations
  147. Tue Sep 29 16:50:39 2026 memory use: 1727.0 MB
  148. Tue Sep 29 16:50:39 2026 distribution of cycle lengths:
  149. Tue Sep 29 16:50:39 2026 1 relations: 801021
  150. Tue Sep 29 16:50:39 2026 2 relations: 863915
  151. Tue Sep 29 16:50:39 2026 3 relations: 882907
  152. Tue Sep 29 16:50:39 2026 4 relations: 809193
  153. Tue Sep 29 16:50:39 2026 5 relations: 762672
  154. Tue Sep 29 16:50:39 2026 6 relations: 692110
  155. Tue Sep 29 16:50:39 2026 7 relations: 623773
  156. Tue Sep 29 16:50:39 2026 8 relations: 552021
  157. Tue Sep 29 16:50:39 2026 9 relations: 490780
  158. Tue Sep 29 16:50:39 2026 10+ relations: 1949914
  159. Tue Sep 29 16:50:39 2026 heaviest cycle: 23 relations
  160. Tue Sep 29 16:51:07 2026 RelProcTime: 4703
  161. Tue Sep 29 16:51:07 2026
  162. Tue Sep 29 16:51:07 2026 commencing linear algebra
  163. Tue Sep 29 16:51:07 2026 using VBITS=256
  164. Tue Sep 29 16:51:08 2026 read 8428306 cycles
  165. Tue Sep 29 16:51:29 2026 cycles contain 27645934 unique relations
  166. Tue Sep 29 16:56:32 2026 read 27645934 relations
  167. Tue Sep 29 16:58:39 2026 using 20 quadratic characters above 4294917295
  168. Tue Sep 29 17:01:43 2026 building initial matrix
  169. Tue Sep 29 17:10:42 2026 memory use: 3731.4 MB
  170. Tue Sep 29 17:11:06 2026 read 8428306 cycles
  171. Tue Sep 29 17:11:07 2026 matrix is 8428129 x 8428306 (3144.8 MB) with weight 970421382 (115.14/col)
  172. Tue Sep 29 17:11:07 2026 sparse part has weight 723246516 (85.81/col)
  173. Tue Sep 29 17:13:37 2026 filtering completed in 2 passes
  174. Tue Sep 29 17:13:41 2026 matrix is 8426419 x 8426596 (3144.6 MB) with weight 970352242 (115.15/col)
  175. Tue Sep 29 17:13:41 2026 sparse part has weight 723229125 (85.83/col)
  176. Tue Sep 29 17:14:11 2026 matrix starts at (0, 0)
  177. Tue Sep 29 17:14:13 2026 matrix is 8426419 x 8426596 (3144.6 MB) with weight 970352242 (115.15/col)
  178. Tue Sep 29 17:14:13 2026 sparse part has weight 723229125 (85.83/col)
  179. Tue Sep 29 17:14:13 2026 saving the first 240 matrix rows for later
  180. Tue Sep 29 17:14:15 2026 matrix includes 256 packed rows
  181. Tue Sep 29 17:14:19 2026 matrix is 8426179 x 8426596 (2876.9 MB) with weight 660811881 (78.42/col)
  182. Tue Sep 29 17:14:19 2026 sparse part has weight 619327470 (73.50/col)
  183. Tue Sep 29 17:14:20 2026 using GPU 0 (NVIDIA GeForce RTX 3080)
  184. Tue Sep 29 17:14:20 2026 selected card has CUDA arch 8.6
  185. Tue Sep 29 17:16:24 2026 commencing Lanczos iteration
  186. Tue Sep 29 17:16:26 2026 memory use: 7103.8 MB
  187. Tue Sep 29 17:16:59 2026 linear algebra at 0.4%, ETA 2h26m
  188. Tue Sep 29 17:17:48 2026 checking every 50000 dimensions, checkpointing every 3450000 dimensions
  189. Tue Sep 29 19:45:25 2026 lanczos halted after 33015 iterations (dim = 8426177)
  190. Tue Sep 29 19:46:34 2026 recovered 28 nontrivial dependencies
  191. Tue Sep 29 19:46:34 2026 BLanczosTime: 10527
  192. Tue Sep 29 19:46:34 2026
  193. Tue Sep 29 19:46:34 2026 commencing square root phase
  194. Tue Sep 29 19:46:34 2026 handling dependencies 1 to 64
  195. Tue Sep 29 19:46:34 2026 reading relations for dependency 1
  196. Tue Sep 29 19:46:38 2026 read 4212723 cycles
  197. Tue Sep 29 19:46:49 2026 cycles contain 13825406 unique relations
  198. Tue Sep 29 19:51:03 2026 read 13825406 relations
  199. Tue Sep 29 19:53:59 2026 multiplying 13825406 relations
  200. Tue Sep 29 20:12:56 2026 multiply complete, coefficients have about 708.01 million bits
  201. Tue Sep 29 20:13:03 2026 initial square root is modulo 2248849
  202. Tue Sep 29 20:31:47 2026 GCD is 1, no factor found
  203. Tue Sep 29 20:31:47 2026 reading relations for dependency 2
  204. Tue Sep 29 20:31:52 2026 read 4213155 cycles
  205. Tue Sep 29 20:32:03 2026 cycles contain 13820002 unique relations
  206. Tue Sep 29 20:36:04 2026 read 13820002 relations
  207. Tue Sep 29 20:39:22 2026 multiplying 13820002 relations
  208. Tue Sep 29 20:58:51 2026 multiply complete, coefficients have about 707.74 million bits
  209. Tue Sep 29 20:58:56 2026 initial square root is modulo 2236217
  210. Tue Sep 29 21:17:41 2026 GCD is N, no factor found
  211. Tue Sep 29 21:17:41 2026 reading relations for dependency 3
  212. Tue Sep 29 21:17:47 2026 read 4213322 cycles
  213. Tue Sep 29 21:17:58 2026 cycles contain 13821744 unique relations
  214. Tue Sep 29 21:21:55 2026 read 13821744 relations
  215. Tue Sep 29 21:25:38 2026 multiplying 13821744 relations
  216. Tue Sep 29 21:45:07 2026 multiply complete, coefficients have about 707.83 million bits
  217. Tue Sep 29 21:45:14 2026 initial square root is modulo 2240191
  218. Tue Sep 29 22:04:02 2026 GCD is N, no factor found
  219. Tue Sep 29 22:04:02 2026 reading relations for dependency 4
  220. Tue Sep 29 22:04:07 2026 read 4214732 cycles
  221. Tue Sep 29 22:04:18 2026 cycles contain 13828418 unique relations
  222. Tue Sep 29 22:08:03 2026 read 13828418 relations
  223. Tue Sep 29 22:09:57 2026 multiplying 13828418 relations
  224. Tue Sep 29 22:29:38 2026 multiply complete, coefficients have about 708.16 million bits
  225. Tue Sep 29 22:29:44 2026 initial square root is modulo 2255573
  226. Tue Sep 29 22:48:23 2026 GCD is N, no factor found
  227. Tue Sep 29 22:48:23 2026 reading relations for dependency 5
  228. Tue Sep 29 22:48:28 2026 read 4213895 cycles
  229. Tue Sep 29 22:48:40 2026 cycles contain 13824116 unique relations
  230. Tue Sep 29 22:52:04 2026 read 13824116 relations
  231. Tue Sep 29 22:54:17 2026 multiplying 13824116 relations
  232. Tue Sep 29 23:14:02 2026 multiply complete, coefficients have about 707.95 million bits
  233. Tue Sep 29 23:14:08 2026 initial square root is modulo 2245723
  234. Tue Sep 29 23:32:46 2026 GCD is 1, no factor found
  235. Tue Sep 29 23:32:46 2026 reading relations for dependency 6
  236. Tue Sep 29 23:32:50 2026 read 4212549 cycles
  237. Tue Sep 29 23:33:01 2026 cycles contain 13820506 unique relations
  238. Tue Sep 29 23:36:42 2026 read 13820506 relations
  239. Tue Sep 29 23:39:46 2026 multiplying 13820506 relations
  240. Tue Sep 29 23:59:27 2026 multiply complete, coefficients have about 707.76 million bits
  241. Tue Sep 29 23:59:32 2026 initial square root is modulo 2237189
  242. Wed Sep 30 00:18:19 2026 sqrtTime: 16305
  243. Wed Sep 30 00:18:19 2026 p60 factor: 757705082319056809737073371068618811665668045644371645454511
  244. Wed Sep 30 00:18:19 2026 p107 factor: 11098483158663351549417325796842845021738805022513734256743389309575177560957125904992531569744714279899937
  245. Wed Sep 30 00:18:19 2026 elapsed time 08:45:36
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