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Oct 4th, 2026
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  1. Sun Oct 4 01:02:48 2026 Msieve v. 1.54 (SVN Unversioned directory)
  2. Sun Oct 4 01:02:48 2026 random seeds: b1e80497 33e40a8b
  3. Sun Oct 4 01:02:48 2026 MPI process 0 of 1
  4. Sun Oct 4 01:02:48 2026 Using 32 OpenMP threads
  5. Sun Oct 4 01:02:48 2026 factoring 421814618398504170990582307700655284784979405558045128010606614278951696180228641742271716282976499851448889702496873412969556199963700243785509599565108884480909 (162 digits)
  6. Sun Oct 4 01:02:49 2026 searching for 15-digit factors
  7. Sun Oct 4 01:02:49 2026 commencing number field sieve (162-digit input)
  8. Sun Oct 4 01:02:49 2026 reversing signs of algebraic polynomial
  9. Sun Oct 4 01:02:49 2026 R0: -26073825497210578233148446970413
  10. Sun Oct 4 01:02:49 2026 R1: 682961051061263148606431
  11. Sun Oct 4 01:02:49 2026 A0: 87416985617647698717508234272269045200
  12. Sun Oct 4 01:02:49 2026 A1: 164899950892804591754363270391710
  13. Sun Oct 4 01:02:49 2026 A2: -31079408667570524195552671
  14. Sun Oct 4 01:02:49 2026 A3: -29788408006482232271
  15. Sun Oct 4 01:02:49 2026 A4: 4241955214812
  16. Sun Oct 4 01:02:49 2026 A5: 399840
  17. Sun Oct 4 01:02:49 2026 skew 3989671.65, size 1.044e-15, alpha -6.994, combined = 1.194e-12 rroots = 5
  18. Sun Oct 4 01:02:49 2026
  19. Sun Oct 4 01:02:49 2026 commencing relation filtering
  20. Sun Oct 4 01:02:49 2026 setting target matrix density to 120.0
  21. Sun Oct 4 01:02:49 2026 reversing signs of algebraic polynomial
  22. Sun Oct 4 01:02:49 2026 estimated available RAM is 128712.6 MB
  23. Sun Oct 4 01:02:49 2026 commencing duplicate removal, pass 1
  24. Sun Oct 4 01:03:25 2026 error -1 reading relation 16181740
  25. Sun Oct 4 01:03:45 2026 error -1 reading relation 24693331
  26. Sun Oct 4 01:05:02 2026 error -1 reading relation 58326128
  27. Sun Oct 4 01:05:19 2026 error -1 reading relation 66110435
  28. Sun Oct 4 01:05:22 2026 error -1 reading relation 67160853
  29. Sun Oct 4 01:05:59 2026 error -1 reading relation 83372678
  30. Sun Oct 4 01:06:02 2026 error -1 reading relation 84674229
  31. Sun Oct 4 01:07:00 2026 error -1 reading relation 109417948
  32. Sun Oct 4 01:07:21 2026 error -1 reading relation 118554318
  33. Sun Oct 4 01:07:25 2026 skipped 1 relations with composite factors
  34. Sun Oct 4 01:07:25 2026 skipped 56 malformed relations
  35. Sun Oct 4 01:07:25 2026 found 19628248 hash collisions in 120624061 relations
  36. Sun Oct 4 01:08:05 2026 commencing duplicate removal, pass 2
  37. Sun Oct 4 01:11:52 2026 found 17320458 duplicates and 103303603 unique relations
  38. Sun Oct 4 01:11:52 2026 memory use: 660.8 MB
  39. Sun Oct 4 01:11:52 2026 reading ideals above 720000
  40. Sun Oct 4 01:11:52 2026 commencing singleton removal, initial pass
  41. Sun Oct 4 01:21:27 2026 memory use: 3012.0 MB
  42. Sun Oct 4 01:21:28 2026 reading all ideals from disk
  43. Sun Oct 4 01:21:31 2026 memory use: 4623.9 MB
  44. Sun Oct 4 01:21:44 2026 keeping 108799083 ideals with weight <= 200, target excess is 553937
  45. Sun Oct 4 01:22:03 2026 commencing in-memory singleton removal
  46. Sun Oct 4 01:22:04 2026 begin with 103303603 relations and 108799083 unique ideals
  47. Sun Oct 4 01:22:12 2026 reduce to 43066539 relations and 39311044 ideals in 20 passes
  48. Sun Oct 4 01:22:12 2026 max relations containing the same ideal: 118
  49. Sun Oct 4 01:22:36 2026 removing 3782648 relations and 3382648 ideals in 400000 cliques
  50. Sun Oct 4 01:22:39 2026 commencing in-memory singleton removal
  51. Sun Oct 4 01:22:39 2026 begin with 39283891 relations and 39311044 unique ideals
  52. Sun Oct 4 01:22:42 2026 reduce to 39034879 relations and 35676241 ideals in 10 passes
  53. Sun Oct 4 01:22:42 2026 max relations containing the same ideal: 107
  54. Sun Oct 4 01:23:01 2026 removing 2786807 relations and 2386807 ideals in 400000 cliques
  55. Sun Oct 4 01:23:03 2026 commencing in-memory singleton removal
  56. Sun Oct 4 01:23:04 2026 begin with 36248072 relations and 35676241 unique ideals
  57. Sun Oct 4 01:23:06 2026 reduce to 36093722 relations and 33133409 ideals in 9 passes
  58. Sun Oct 4 01:23:06 2026 max relations containing the same ideal: 104
  59. Sun Oct 4 01:23:26 2026 removing 2470885 relations and 2070885 ideals in 400000 cliques
  60. Sun Oct 4 01:23:27 2026 commencing in-memory singleton removal
  61. Sun Oct 4 01:23:28 2026 begin with 33622837 relations and 33133409 unique ideals
  62. Sun Oct 4 01:23:30 2026 reduce to 33491884 relations and 30930192 ideals in 8 passes
  63. Sun Oct 4 01:23:30 2026 max relations containing the same ideal: 97
  64. Sun Oct 4 01:23:49 2026 removing 2303671 relations and 1903671 ideals in 400000 cliques
  65. Sun Oct 4 01:23:51 2026 commencing in-memory singleton removal
  66. Sun Oct 4 01:23:51 2026 begin with 31188213 relations and 30930192 unique ideals
  67. Sun Oct 4 01:23:53 2026 reduce to 31067267 relations and 28904282 ideals in 8 passes
  68. Sun Oct 4 01:23:53 2026 max relations containing the same ideal: 93
  69. Sun Oct 4 01:24:09 2026 removing 2193413 relations and 1793413 ideals in 400000 cliques
  70. Sun Oct 4 01:24:11 2026 commencing in-memory singleton removal
  71. Sun Oct 4 01:24:11 2026 begin with 28873854 relations and 28904282 unique ideals
  72. Sun Oct 4 01:24:13 2026 reduce to 28756353 relations and 26991954 ideals in 9 passes
  73. Sun Oct 4 01:24:13 2026 max relations containing the same ideal: 89
  74. Sun Oct 4 01:24:29 2026 removing 2116511 relations and 1716511 ideals in 400000 cliques
  75. Sun Oct 4 01:24:30 2026 commencing in-memory singleton removal
  76. Sun Oct 4 01:24:30 2026 begin with 26639842 relations and 26991954 unique ideals
  77. Sun Oct 4 01:24:32 2026 reduce to 26522572 relations and 25156755 ideals in 8 passes
  78. Sun Oct 4 01:24:32 2026 max relations containing the same ideal: 84
  79. Sun Oct 4 01:24:46 2026 removing 2060094 relations and 1660094 ideals in 400000 cliques
  80. Sun Oct 4 01:24:48 2026 commencing in-memory singleton removal
  81. Sun Oct 4 01:24:48 2026 begin with 24462478 relations and 25156755 unique ideals
  82. Sun Oct 4 01:24:49 2026 reduce to 24343844 relations and 23376519 ideals in 8 passes
  83. Sun Oct 4 01:24:49 2026 max relations containing the same ideal: 80
  84. Sun Oct 4 01:25:03 2026 removing 1701202 relations and 1376444 ideals in 324758 cliques
  85. Sun Oct 4 01:25:04 2026 commencing in-memory singleton removal
  86. Sun Oct 4 01:25:04 2026 begin with 22642642 relations and 23376519 unique ideals
  87. Sun Oct 4 01:25:06 2026 reduce to 22556884 relations and 21913381 ideals in 8 passes
  88. Sun Oct 4 01:25:06 2026 max relations containing the same ideal: 75
  89. Sun Oct 4 01:25:23 2026 relations with 0 large ideals: 1878
  90. Sun Oct 4 01:25:23 2026 relations with 1 large ideals: 10635
  91. Sun Oct 4 01:25:23 2026 relations with 2 large ideals: 147913
  92. Sun Oct 4 01:25:23 2026 relations with 3 large ideals: 905495
  93. Sun Oct 4 01:25:23 2026 relations with 4 large ideals: 2950420
  94. Sun Oct 4 01:25:23 2026 relations with 5 large ideals: 5542566
  95. Sun Oct 4 01:25:23 2026 relations with 6 large ideals: 6306730
  96. Sun Oct 4 01:25:23 2026 relations with 7+ large ideals: 6691247
  97. Sun Oct 4 01:25:23 2026 commencing 2-way merge
  98. Sun Oct 4 01:25:45 2026 reduce to 13407194 relation sets and 12763691 unique ideals
  99. Sun Oct 4 01:25:45 2026 commencing full merge
  100. Sun Oct 4 01:33:13 2026 memory use: 1612.3 MB
  101. Sun Oct 4 01:33:15 2026 found 5953635 cycles, need 5931891
  102. Sun Oct 4 01:33:17 2026 weight of 5931891 cycles is about 712406008 (120.10/cycle)
  103. Sun Oct 4 01:33:17 2026 distribution of cycle lengths:
  104. Sun Oct 4 01:33:17 2026 1 relations: 336299
  105. Sun Oct 4 01:33:17 2026 2 relations: 419988
  106. Sun Oct 4 01:33:17 2026 3 relations: 451188
  107. Sun Oct 4 01:33:17 2026 4 relations: 440312
  108. Sun Oct 4 01:33:17 2026 5 relations: 432125
  109. Sun Oct 4 01:33:17 2026 6 relations: 406875
  110. Sun Oct 4 01:33:17 2026 7 relations: 389169
  111. Sun Oct 4 01:33:17 2026 8 relations: 361091
  112. Sun Oct 4 01:33:17 2026 9 relations: 339632
  113. Sun Oct 4 01:33:17 2026 10+ relations: 2355212
  114. Sun Oct 4 01:33:17 2026 heaviest cycle: 28 relations
  115. Sun Oct 4 01:33:20 2026 commencing cycle optimization
  116. Sun Oct 4 01:33:40 2026 start with 52620666 relations
  117. Sun Oct 4 01:36:34 2026 pruned 1987097 relations
  118. Sun Oct 4 01:36:35 2026 memory use: 1460.7 MB
  119. Sun Oct 4 01:36:35 2026 distribution of cycle lengths:
  120. Sun Oct 4 01:36:35 2026 1 relations: 336299
  121. Sun Oct 4 01:36:35 2026 2 relations: 430628
  122. Sun Oct 4 01:36:35 2026 3 relations: 469261
  123. Sun Oct 4 01:36:35 2026 4 relations: 455846
  124. Sun Oct 4 01:36:35 2026 5 relations: 449206
  125. Sun Oct 4 01:36:35 2026 6 relations: 421772
  126. Sun Oct 4 01:36:35 2026 7 relations: 403028
  127. Sun Oct 4 01:36:35 2026 8 relations: 372734
  128. Sun Oct 4 01:36:35 2026 9 relations: 349477
  129. Sun Oct 4 01:36:35 2026 10+ relations: 2243640
  130. Sun Oct 4 01:36:35 2026 heaviest cycle: 28 relations
  131. Sun Oct 4 01:36:48 2026 RelProcTime: 2039
  132. Sun Oct 4 01:36:48 2026
  133. Sun Oct 4 01:36:48 2026 commencing linear algebra
  134. Sun Oct 4 01:36:48 2026 using VBITS=256
  135. Sun Oct 4 01:36:48 2026 stopping after matrix build
  136. Sun Oct 4 01:36:48 2026 initialized process (0,0) of 1 x 1 grid
  137. Sun Oct 4 01:36:48 2026 reversing signs of algebraic polynomial
  138. Sun Oct 4 01:36:49 2026 read 5931891 cycles
  139. Sun Oct 4 01:37:08 2026 cycles contain 22084398 unique relations
  140. Sun Oct 4 01:39:57 2026 read 22084398 relations
  141. Sun Oct 4 01:40:00 2026 using 20 quadratic characters above 4294917295
  142. Sun Oct 4 01:40:03 2026 building initial matrix
  143. Sun Oct 4 01:47:15 2026 memory use: 3017.5 MB
  144. Sun Oct 4 01:47:20 2026 read 5931891 cycles
  145. Sun Oct 4 01:47:21 2026 matrix is 5931714 x 5931891 (2819.5 MB) with weight 858164903 (144.67/col)
  146. Sun Oct 4 01:47:21 2026 sparse part has weight 667931104 (112.60/col)
  147. Sun Oct 4 01:49:06 2026 filtering completed in 2 passes
  148. Sun Oct 4 01:49:08 2026 matrix is 5931424 x 5931600 (2819.5 MB) with weight 858151082 (144.67/col)
  149. Sun Oct 4 01:49:08 2026 sparse part has weight 667927402 (112.60/col)
  150. Sun Oct 4 01:49:45 2026 BLanczosTime: 777
  151. Sun Oct 4 01:49:45 2026 elapsed time 00:46:57
  152. Sun Oct 4 01:59:29 2026
  153. Sun Oct 4 01:59:29 2026
  154. Sun Oct 4 01:59:29 2026 Msieve v. 1.54 (SVN Unversioned directory)
  155. Sun Oct 4 01:59:29 2026 random seeds: acfeff82 8cd07e95
  156. Sun Oct 4 01:59:29 2026 MPI process 0 of 1
  157. Sun Oct 4 01:59:29 2026 Using 64 OpenMP threads
  158. Sun Oct 4 01:59:29 2026 factoring 421814618398504170990582307700655284784979405558045128010606614278951696180228641742271716282976499851448889702496873412969556199963700243785509599565108884480909 (162 digits)
  159. Sun Oct 4 01:59:30 2026 searching for 15-digit factors
  160. Sun Oct 4 01:59:30 2026 commencing number field sieve (162-digit input)
  161. Sun Oct 4 01:59:30 2026 reversing signs of algebraic polynomial
  162. Sun Oct 4 01:59:30 2026 R0: -26073825497210578233148446970413
  163. Sun Oct 4 01:59:30 2026 R1: 682961051061263148606431
  164. Sun Oct 4 01:59:30 2026 A0: 87416985617647698717508234272269045200
  165. Sun Oct 4 01:59:30 2026 A1: 164899950892804591754363270391710
  166. Sun Oct 4 01:59:30 2026 A2: -31079408667570524195552671
  167. Sun Oct 4 01:59:30 2026 A3: -29788408006482232271
  168. Sun Oct 4 01:59:30 2026 A4: 4241955214812
  169. Sun Oct 4 01:59:30 2026 A5: 399840
  170. Sun Oct 4 01:59:30 2026 skew 3989671.65, size 1.044e-15, alpha -6.994, combined = 1.194e-12 rroots = 5
  171. Sun Oct 4 01:59:30 2026
  172. Sun Oct 4 01:59:30 2026 commencing linear algebra
  173. Sun Oct 4 01:59:30 2026 using VBITS=256
  174. Sun Oct 4 01:59:30 2026 skipping matrix build
  175. Sun Oct 4 01:59:30 2026 initialized process (0,0) of 1 x 1 grid
  176. Sun Oct 4 01:59:35 2026 matrix starts at (0, 0)
  177. Sun Oct 4 01:59:37 2026 matrix is 5931424 x 5931600 (2819.5 MB) with weight 858151082 (144.67/col)
  178. Sun Oct 4 01:59:37 2026 sparse part has weight 667927402 (112.60/col)
  179. Sun Oct 4 01:59:37 2026 saving the first 240 matrix rows for later
  180. Sun Oct 4 01:59:39 2026 matrix includes 256 packed rows
  181. Sun Oct 4 01:59:40 2026 matrix is 5931184 x 5931600 (2531.6 MB) with weight 607630188 (102.44/col)
  182. Sun Oct 4 01:59:40 2026 sparse part has weight 568745090 (95.88/col)
  183. Sun Oct 4 01:59:40 2026 using block size 8192 and superblock size 1032192 for processor cache size 43008 kB
  184. Sun Oct 4 01:59:53 2026 commencing Lanczos iteration (64 threads)
  185. Sun Oct 4 01:59:53 2026 memory use: 3649.3 MB
  186. Sun Oct 4 02:00:39 2026 linear algebra at 0.5%, ETA 2h24m
  187. Sun Oct 4 02:01:45 2026 checking every 40000 dimensions, checkpointing every 2520000 dimensions
  188. Sun Oct 4 04:21:28 2026 lanczos halted after 23240 iterations (dim = 5931184)
  189. Sun Oct 4 04:21:47 2026 recovered 29 nontrivial dependencies
  190. Sun Oct 4 04:21:47 2026 BLanczosTime: 8537
  191. Sun Oct 4 04:21:47 2026
  192. Sun Oct 4 04:21:47 2026 commencing square root phase
  193. Sun Oct 4 04:21:47 2026 reversing signs of algebraic polynomial
  194. Sun Oct 4 04:21:47 2026 handling dependencies 1 to 64
  195. Sun Oct 4 04:21:47 2026 reading relations for dependency 1
  196. Sun Oct 4 04:21:48 2026 read 2965185 cycles
  197. Sun Oct 4 04:21:52 2026 cycles contain 11040106 unique relations
  198. Sun Oct 4 04:23:33 2026 read 11040106 relations
  199. Sun Oct 4 04:24:47 2026 multiplying 11040106 relations
  200. Sun Oct 4 04:27:07 2026 multiply complete, coefficients have about 607.24 million bits
  201. Sun Oct 4 04:27:09 2026 initial square root is modulo 280499
  202. Sun Oct 4 04:34:16 2026 GCD is 1, no factor found
  203. Sun Oct 4 04:34:16 2026 reading relations for dependency 2
  204. Sun Oct 4 04:34:18 2026 read 2964320 cycles
  205. Sun Oct 4 04:34:28 2026 cycles contain 11039576 unique relations
  206. Sun Oct 4 04:37:11 2026 read 11039576 relations
  207. Sun Oct 4 04:38:27 2026 multiplying 11039576 relations
  208. Sun Oct 4 04:40:35 2026 multiply complete, coefficients have about 607.21 million bits
  209. Sun Oct 4 04:40:37 2026 initial square root is modulo 280499
  210. Sun Oct 4 04:47:39 2026 GCD is N, no factor found
  211. Sun Oct 4 04:47:39 2026 reading relations for dependency 3
  212. Sun Oct 4 04:47:40 2026 read 2965408 cycles
  213. Sun Oct 4 04:47:46 2026 cycles contain 11040608 unique relations
  214. Sun Oct 4 04:50:30 2026 read 11040608 relations
  215. Sun Oct 4 04:51:41 2026 multiplying 11040608 relations
  216. Sun Oct 4 04:53:51 2026 multiply complete, coefficients have about 607.27 million bits
  217. Sun Oct 4 04:53:54 2026 initial square root is modulo 280673
  218. Sun Oct 4 05:01:06 2026 GCD is N, no factor found
  219. Sun Oct 4 05:01:06 2026 reading relations for dependency 4
  220. Sun Oct 4 05:01:07 2026 read 2965107 cycles
  221. Sun Oct 4 05:01:17 2026 cycles contain 11041640 unique relations
  222. Sun Oct 4 05:04:01 2026 read 11041640 relations
  223. Sun Oct 4 05:05:23 2026 multiplying 11041640 relations
  224. Sun Oct 4 05:07:31 2026 multiply complete, coefficients have about 607.32 million bits
  225. Sun Oct 4 05:07:33 2026 initial square root is modulo 280967
  226. Sun Oct 4 05:14:40 2026 GCD is 1, no factor found
  227. Sun Oct 4 05:14:40 2026 reading relations for dependency 5
  228. Sun Oct 4 05:14:41 2026 read 2964877 cycles
  229. Sun Oct 4 05:14:51 2026 cycles contain 11043812 unique relations
  230. Sun Oct 4 05:17:35 2026 read 11043812 relations
  231. Sun Oct 4 05:18:50 2026 multiplying 11043812 relations
  232. Sun Oct 4 05:20:58 2026 multiply complete, coefficients have about 607.45 million bits
  233. Sun Oct 4 05:21:01 2026 initial square root is modulo 281717
  234. Sun Oct 4 05:28:02 2026 sqrtTime: 3975
  235. Sun Oct 4 05:28:02 2026 p74 factor: 20680062564748918928909534400864055699481754606204939408212388551508160363
  236. Sun Oct 4 05:28:02 2026 p89 factor: 20397163551986841518650046195760604568932274927576496250893367100509366493530620968423143
  237. Sun Oct 4 05:28:02 2026 elapsed time 03:28:33
  238.  
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