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Oct 8th, 2026
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  1. Thu Oct 8 11:59:45 2026 Msieve v. 1.54 (SVN Unversioned directory)
  2. Thu Oct 8 11:59:45 2026 random seeds: 666fc141 04c898d8
  3. Thu Oct 8 11:59:45 2026 Using 4 OpenMP threads
  4. Thu Oct 8 11:59:45 2026 factoring 73261723771354169049718477974000336387364226413915212567830091019839277769292951888053027413926477354553470435319006118105765896696652707920078260774589164086067 (161 digits)
  5. Thu Oct 8 11:59:46 2026 no P-1/P+1/ECM available, skipping
  6. Thu Oct 8 11:59:46 2026 commencing number field sieve (161-digit input)
  7. Thu Oct 8 11:59:46 2026 R0: -20038363987050802130622285672416
  8. Thu Oct 8 11:59:46 2026 R1: 419093078612002505953
  9. Thu Oct 8 11:59:46 2026 A0: -8070333076948752698425231634806789800
  10. Thu Oct 8 11:59:46 2026 A1: 10826483199868005241529425564710
  11. Thu Oct 8 11:59:46 2026 A2: 8444665989941859494737597
  12. Thu Oct 8 11:59:46 2026 A3: -6175084847328862853
  13. Thu Oct 8 11:59:46 2026 A4: -1542306180992
  14. Thu Oct 8 11:59:46 2026 A5: 181440
  15. Thu Oct 8 11:59:46 2026 skew 2138827.79, size 1.697e-15, alpha -6.678, combined = 1.621e-12 rroots = 5
  16. Thu Oct 8 11:59:46 2026
  17. Thu Oct 8 11:59:46 2026 commencing relation filtering
  18. Thu Oct 8 11:59:46 2026 estimated available RAM is 31874.3 MB
  19. Thu Oct 8 11:59:46 2026 commencing duplicate removal, pass 1
  20. Thu Oct 8 12:01:51 2026 error -1 reading relation 14732780
  21. Thu Oct 8 12:01:53 2026 error -1 reading relation 14914923
  22. Thu Oct 8 12:02:01 2026 error -1 reading relation 15845933
  23. Thu Oct 8 12:02:01 2026 error -1 reading relation 15845934
  24. Thu Oct 8 12:02:06 2026 error -1 reading relation 16356145
  25. Thu Oct 8 12:02:09 2026 error -1 reading relation 16619956
  26. Thu Oct 8 12:02:17 2026 error -6 reading relation 17366175
  27. Thu Oct 8 12:02:53 2026 error -1 reading relation 21100118
  28. Thu Oct 8 12:03:09 2026 error -1 reading relation 22485035
  29. Thu Oct 8 12:03:40 2026 error -1 reading relation 25689505
  30. Thu Oct 8 12:04:05 2026 error -1 reading relation 28496687
  31. Thu Oct 8 12:05:55 2026 error -1 reading relation 39914271
  32. Thu Oct 8 12:06:32 2026 error -1 reading relation 43844089
  33. Thu Oct 8 12:06:42 2026 error -1 reading relation 44906559
  34. Thu Oct 8 12:07:28 2026 error -1 reading relation 49953645
  35. Thu Oct 8 12:10:18 2026 error -11 reading relation 68764529
  36. Thu Oct 8 12:10:35 2026 error -1 reading relation 70733519
  37. Thu Oct 8 12:10:43 2026 error -1 reading relation 71599397
  38. Thu Oct 8 12:10:47 2026 error -1 reading relation 72078284
  39. Thu Oct 8 12:11:23 2026 error -1 reading relation 76225011
  40. Thu Oct 8 12:11:44 2026 error -1 reading relation 78776337
  41. Thu Oct 8 12:12:26 2026 error -1 reading relation 83474396
  42. Thu Oct 8 12:13:43 2026 error -1 reading relation 91074638
  43. Thu Oct 8 12:14:30 2026 error -1 reading relation 95935028
  44. Thu Oct 8 12:14:30 2026 error -1 reading relation 95935029
  45. Thu Oct 8 12:14:37 2026 error -1 reading relation 96647930
  46. Thu Oct 8 12:14:37 2026 error -1 reading relation 96647931
  47. Thu Oct 8 12:14:45 2026 error -1 reading relation 97619389
  48. Thu Oct 8 12:15:01 2026 error -1 reading relation 99437358
  49. Thu Oct 8 12:15:01 2026 error -1 reading relation 99437359
  50. Thu Oct 8 12:15:25 2026 error -1 reading relation 102127886
  51. Thu Oct 8 12:15:36 2026 error -1 reading relation 103296406
  52. Thu Oct 8 12:15:52 2026 error -1 reading relation 104974495
  53. Thu Oct 8 12:16:19 2026 error -1 reading relation 107874900
  54. Thu Oct 8 12:16:19 2026 error -1 reading relation 107949186
  55. Thu Oct 8 12:16:19 2026 error -1 reading relation 107949187
  56. Thu Oct 8 12:16:41 2026 error -1 reading relation 110155437
  57. Thu Oct 8 12:16:41 2026 error -1 reading relation 110155438
  58. Thu Oct 8 12:17:52 2026 error -1 reading relation 117048841
  59. Thu Oct 8 12:17:52 2026 error -1 reading relation 117048842
  60. Thu Oct 8 12:18:08 2026 skipped 4 malformed relations
  61. Thu Oct 8 12:18:08 2026 found 3161142 hash collisions in 118710939 relations
  62. Thu Oct 8 12:18:08 2026 cached 118710983 relation coordinates for pass 2 (2067.4 MB)
  63. Thu Oct 8 12:18:42 2026 added 121933 free relations
  64. Thu Oct 8 12:18:42 2026 commencing duplicate removal, pass 2
  65. Thu Oct 8 12:19:07 2026 found 0 duplicates and 118832872 unique relations
  66. Thu Oct 8 12:19:07 2026 memory use: 488.0 MB
  67. Thu Oct 8 12:19:08 2026 reading ideals above 720000
  68. Thu Oct 8 12:19:08 2026 commencing singleton removal, initial pass
  69. Thu Oct 8 12:39:43 2026 LP64 contains 118832872 relations and 115584339 unique large ideals
  70. Thu Oct 8 12:39:43 2026 memory use: 4268.0 MB
  71. Thu Oct 8 12:39:44 2026 preparing 64-bit LP file for common filtering
  72. Thu Oct 8 12:39:44 2026 start with 118832872 relations and 115584339 ideals
  73. Thu Oct 8 12:40:52 2026 compacted LP dataset has 118832872 relations and 115584339 large ideals
  74. Thu Oct 8 12:40:52 2026 reading all ideals from disk
  75. Thu Oct 8 12:41:13 2026 memory use: 5320.5 MB
  76. Thu Oct 8 12:41:30 2026 keeping 115079420 ideals with weight <= 200, target excess is 621116
  77. Thu Oct 8 12:41:53 2026 commencing in-memory singleton removal
  78. Thu Oct 8 12:42:12 2026 begin with 118832872 relations and 115079420 unique ideals
  79. Thu Oct 8 12:42:12 2026 memory use: 894.0 MB
  80. Thu Oct 8 12:42:35 2026 reduce to 62269138 relations and 51341468 ideals in 4 passes
  81. Thu Oct 8 12:42:35 2026 max relations containing the same ideal: 135
  82. Thu Oct 8 12:43:32 2026 removing 9868547 relations and 7868547 ideals in 2000000 cliques
  83. Thu Oct 8 12:43:34 2026 commencing in-memory singleton removal
  84. Thu Oct 8 12:43:43 2026 begin with 52400591 relations and 51341468 unique ideals
  85. Thu Oct 8 12:43:43 2026 memory use: 407.7 MB
  86. Thu Oct 8 12:43:49 2026 reduce to 51240721 relations and 42267216 ideals in 2 passes
  87. Thu Oct 8 12:43:49 2026 max relations containing the same ideal: 119
  88. Thu Oct 8 12:44:34 2026 removing 7682187 relations and 5682187 ideals in 2000000 cliques
  89. Thu Oct 8 12:44:36 2026 commencing in-memory singleton removal
  90. Thu Oct 8 12:44:43 2026 begin with 43558534 relations and 42267216 unique ideals
  91. Thu Oct 8 12:44:43 2026 memory use: 338.5 MB
  92. Thu Oct 8 12:44:45 2026 reduce to 42700217 relations and 35694239 ideals in 1 passes
  93. Thu Oct 8 12:44:45 2026 max relations containing the same ideal: 105
  94. Thu Oct 8 12:45:24 2026 removing 7068881 relations and 5068881 ideals in 2000000 cliques
  95. Thu Oct 8 12:45:25 2026 commencing in-memory singleton removal
  96. Thu Oct 8 12:45:31 2026 begin with 35631336 relations and 35694239 unique ideals
  97. Thu Oct 8 12:45:31 2026 memory use: 288.3 MB
  98. Thu Oct 8 12:45:34 2026 reduce to 34802309 relations and 29760415 ideals in 2 passes
  99. Thu Oct 8 12:45:34 2026 max relations containing the same ideal: 92
  100. Thu Oct 8 12:46:05 2026 removing 6767289 relations and 4767289 ideals in 2000000 cliques
  101. Thu Oct 8 12:46:07 2026 commencing in-memory singleton removal
  102. Thu Oct 8 12:46:11 2026 begin with 28035020 relations and 29760415 unique ideals
  103. Thu Oct 8 12:46:11 2026 memory use: 243.1 MB
  104. Thu Oct 8 12:46:14 2026 reduce to 27152807 relations and 24064983 ideals in 2 passes
  105. Thu Oct 8 12:46:14 2026 max relations containing the same ideal: 77
  106. Thu Oct 8 12:46:38 2026 removing 6562013 relations and 4562013 ideals in 2000000 cliques
  107. Thu Oct 8 12:46:40 2026 commencing in-memory singleton removal
  108. Thu Oct 8 12:46:43 2026 begin with 20590794 relations and 24064983 unique ideals
  109. Thu Oct 8 12:46:43 2026 memory use: 199.6 MB
  110. Thu Oct 8 12:46:44 2026 reduce to 19578575 relations and 18423576 ideals in 2 passes
  111. Thu Oct 8 12:46:44 2026 max relations containing the same ideal: 65
  112. Thu Oct 8 12:47:03 2026 removing 1958272 relations and 1523768 ideals in 434504 cliques
  113. Thu Oct 8 12:47:05 2026 commencing in-memory singleton removal
  114. Thu Oct 8 12:47:07 2026 begin with 17620303 relations and 18423576 unique ideals
  115. Thu Oct 8 12:47:07 2026 memory use: 156.6 MB
  116. Thu Oct 8 12:47:08 2026 reduce to 17500915 relations and 16778054 ideals in 1 passes
  117. Thu Oct 8 12:47:08 2026 max relations containing the same ideal: 59
  118. Thu Oct 8 12:47:25 2026 relations with 0 large ideals: 2194
  119. Thu Oct 8 12:47:25 2026 relations with 1 large ideals: 14709
  120. Thu Oct 8 12:47:25 2026 relations with 2 large ideals: 192097
  121. Thu Oct 8 12:47:25 2026 relations with 3 large ideals: 1039911
  122. Thu Oct 8 12:47:25 2026 relations with 4 large ideals: 2918018
  123. Thu Oct 8 12:47:25 2026 relations with 5 large ideals: 4709170
  124. Thu Oct 8 12:47:25 2026 relations with 6 large ideals: 4619271
  125. Thu Oct 8 12:47:25 2026 relations with 7+ large ideals: 4005545
  126. Thu Oct 8 12:47:25 2026 commencing 2-way merge
  127. Thu Oct 8 12:47:46 2026 reduce to 10914306 relation sets and 10191445 unique ideals
  128. Thu Oct 8 12:47:46 2026 commencing full merge
  129. Thu Oct 8 12:54:13 2026 memory use: 1348.8 MB
  130. Thu Oct 8 12:54:13 2026 found 5534438 cycles, need 5435645
  131. Thu Oct 8 12:54:14 2026 weight of 5435645 cycles is about 489491277 (90.05/cycle)
  132. Thu Oct 8 12:54:14 2026 distribution of cycle lengths:
  133. Thu Oct 8 12:54:14 2026 1 relations: 349724
  134. Thu Oct 8 12:54:14 2026 2 relations: 482830
  135. Thu Oct 8 12:54:14 2026 3 relations: 533405
  136. Thu Oct 8 12:54:14 2026 4 relations: 536277
  137. Thu Oct 8 12:54:14 2026 5 relations: 532738
  138. Thu Oct 8 12:54:14 2026 6 relations: 502222
  139. Thu Oct 8 12:54:14 2026 7 relations: 469015
  140. Thu Oct 8 12:54:14 2026 8 relations: 420232
  141. Thu Oct 8 12:54:14 2026 9 relations: 364568
  142. Thu Oct 8 12:54:14 2026 10+ relations: 1244634
  143. Thu Oct 8 12:54:14 2026 heaviest cycle: 20 relations
  144. Thu Oct 8 12:54:15 2026 commencing cycle optimization
  145. Thu Oct 8 12:54:32 2026 start with 36007388 relations
  146. Thu Oct 8 12:56:24 2026 pruned 1205023 relations
  147. Thu Oct 8 12:56:24 2026 memory use: 1144.5 MB
  148. Thu Oct 8 12:56:24 2026 distribution of cycle lengths:
  149. Thu Oct 8 12:56:24 2026 1 relations: 349724
  150. Thu Oct 8 12:56:24 2026 2 relations: 495126
  151. Thu Oct 8 12:56:24 2026 3 relations: 555362
  152. Thu Oct 8 12:56:24 2026 4 relations: 556254
  153. Thu Oct 8 12:56:24 2026 5 relations: 554722
  154. Thu Oct 8 12:56:24 2026 6 relations: 520637
  155. Thu Oct 8 12:56:24 2026 7 relations: 485429
  156. Thu Oct 8 12:56:24 2026 8 relations: 429187
  157. Thu Oct 8 12:56:24 2026 9 relations: 368916
  158. Thu Oct 8 12:56:24 2026 10+ relations: 1120288
  159. Thu Oct 8 12:56:24 2026 heaviest cycle: 20 relations
  160. Thu Oct 8 12:56:27 2026 RelProcTime: 3401
  161. Thu Oct 8 12:56:27 2026
  162. Thu Oct 8 12:56:27 2026 commencing linear algebra
  163. Thu Oct 8 12:56:27 2026 using VBITS=256
  164. Thu Oct 8 12:56:28 2026 read 5435645 cycles
  165. Thu Oct 8 12:56:40 2026 cycles contain 17074255 unique relations
  166. Thu Oct 8 13:00:11 2026 read 17074255 relations
  167. Thu Oct 8 13:00:36 2026 using 20 quadratic characters above 4294917295
  168. Thu Oct 8 13:01:10 2026 building initial matrix
  169. Thu Oct 8 13:02:58 2026 memory use: 2369.1 MB
  170. Thu Oct 8 13:03:06 2026 read 5435645 cycles
  171. Thu Oct 8 13:03:06 2026 matrix is 5435468 x 5435645 (2001.7 MB) with weight 621538012 (114.34/col)
  172. Thu Oct 8 13:03:06 2026 sparse part has weight 464936761 (85.53/col)
  173. Thu Oct 8 13:03:57 2026 filtering completed in 2 passes
  174. Thu Oct 8 13:03:59 2026 matrix is 5434660 x 5434837 (2001.6 MB) with weight 621502078 (114.36/col)
  175. Thu Oct 8 13:03:59 2026 sparse part has weight 464924082 (85.55/col)
  176. Thu Oct 8 13:04:18 2026 matrix starts at (0, 0)
  177. Thu Oct 8 13:04:19 2026 matrix is 5434660 x 5434837 (2001.6 MB) with weight 621502078 (114.36/col)
  178. Thu Oct 8 13:04:19 2026 sparse part has weight 464924082 (85.55/col)
  179. Thu Oct 8 13:04:19 2026 saving the first 240 matrix rows for later
  180. Thu Oct 8 13:04:20 2026 matrix includes 256 packed rows
  181. Thu Oct 8 13:04:23 2026 matrix is 5434420 x 5434837 (1837.2 MB) with weight 422168496 (77.68/col)
  182. Thu Oct 8 13:04:23 2026 sparse part has weight 394649683 (72.61/col)
  183. Thu Oct 8 13:04:23 2026 using GPU 0 (NVIDIA GeForce RTX 3080)
  184. Thu Oct 8 13:04:23 2026 selected card has CUDA arch 8.6
  185. Thu Oct 8 13:04:25 2026 storing a single copy of the matrix (no transpose) on the GPU
  186. Thu Oct 8 13:04:25 2026 computed block_nnz 16000000 (L2 cache 5242880 bytes, average column weight 72.6)
  187. Thu Oct 8 13:04:25 2026 note: single_copy's L2-sized blocks are smaller than its row pointer floor; expect it to be slower than two copies, only saving GPU memory
  188. Thu Oct 8 13:04:25 2026 nonzeros per matrix block: 16000000
  189. Thu Oct 8 13:04:25 2026 SpMV kernel: auto (by nonzeros per row)
  190. Thu Oct 8 13:04:25 2026 GPU memory: 9069 MB free, 1161 MB for vectors, 7742 MB for sparse matrix blocks (2074 MB needed)
  191. Thu Oct 8 13:05:06 2026 commencing Lanczos iteration
  192. Thu Oct 8 13:05:13 2026 memory use: 3350.6 MB
  193. Thu Oct 8 13:05:41 2026 linear algebra at 0.6%, ETA 1h 1m
  194. Thu Oct 8 13:06:12 2026 checking every 80000 dimensions, checkpointing every 5360000 dimensions
  195. Thu Oct 8 14:06:42 2026 lanczos halted after 21293 iterations (dim = 5434420)
  196. Thu Oct 8 14:07:14 2026 recovered 31 nontrivial dependencies
  197. Thu Oct 8 14:07:15 2026 BLanczosTime: 4248
  198. Thu Oct 8 14:07:15 2026
  199. Thu Oct 8 14:07:15 2026 commencing square root phase
  200. Thu Oct 8 14:07:15 2026 handling dependencies 1 to 64
  201. Thu Oct 8 14:07:15 2026 reading relations for dependency 1
  202. Thu Oct 8 14:07:16 2026 read 2716512 cycles
  203. Thu Oct 8 14:07:22 2026 cycles contain 8535550 unique relations
  204. Thu Oct 8 14:11:30 2026 read 8535550 relations
  205. Thu Oct 8 14:12:42 2026 multiplying 8535550 relations
  206. Thu Oct 8 14:14:53 2026 multiply complete, coefficients have about 459.71 million bits
  207. Thu Oct 8 14:14:55 2026 initial square root is modulo 177290599
  208. Thu Oct 8 14:19:52 2026 sqrtTime: 757
  209. Thu Oct 8 14:19:52 2026 p80 factor: 54958088400832334985377224011514885575072921807927497768595590288990669923520053
  210. Thu Oct 8 14:19:52 2026 p82 factor: 1333047161994168400872416658691257277490194618998689135751397893242351852354468039
  211. Thu Oct 8 14:19:52 2026 elapsed time 02:20:07
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