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Dec 15th, 2025
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  1. Fri Dec 12 00:03:21 2025
  2. Fri Dec 12 00:03:21 2025
  3. Fri Dec 12 00:03:21 2025 Msieve v. 1.54 (SVN Unversioned directory)
  4. Fri Dec 12 00:03:21 2025 random seeds: 4d3a45d0 8e0cf68c
  5. Fri Dec 12 00:03:21 2025 MPI process 0 of 1
  6. Fri Dec 12 00:03:21 2025 Using 32 OpenMP threads
  7. Fri Dec 12 00:03:21 2025 factoring 2369970599987002723447289682490372745199295423002957612089378714202031301535096430991518038038340277237276931832170242731309183009046309094220496841041299738814393619 (166 digits)
  8. Fri Dec 12 00:03:22 2025 searching for 15-digit factors
  9. Fri Dec 12 00:03:22 2025 commencing number field sieve (166-digit input)
  10. Fri Dec 12 00:03:22 2025 reversing signs of algebraic polynomial
  11. Fri Dec 12 00:03:22 2025 R0: -81117984972550717548330144834884
  12. Fri Dec 12 00:03:22 2025 R1: 10546681968983587060650379
  13. Fri Dec 12 00:03:22 2025 A0: 746351550463354332454893147593930085570
  14. Fri Dec 12 00:03:22 2025 A1: 1141804362388938171598440247914772
  15. Fri Dec 12 00:03:22 2025 A2: -798227995816160146133452113
  16. Fri Dec 12 00:03:22 2025 A3: -151467124992559405513
  17. Fri Dec 12 00:03:22 2025 A4: 55850712986142
  18. Fri Dec 12 00:03:22 2025 A5: 8845200
  19. Fri Dec 12 00:03:22 2025 skew 3295773.47, size 4.481e-16, alpha -7.942, combined = 7.139e-13 rroots = 5
  20. Fri Dec 12 00:03:22 2025
  21. Fri Dec 12 00:03:22 2025 commencing relation filtering
  22. Fri Dec 12 00:03:22 2025 setting target matrix density to 130.0
  23. Fri Dec 12 00:03:22 2025 reversing signs of algebraic polynomial
  24. Fri Dec 12 00:03:22 2025 estimated available RAM is 257736.5 MB
  25. Fri Dec 12 00:03:22 2025 commencing duplicate removal, pass 1
  26. Fri Dec 12 00:10:52 2025 skipped 109 malformed relations
  27. Fri Dec 12 00:10:52 2025 found 51805627 hash collisions in 282039525 relations
  28. Fri Dec 12 00:11:15 2025 added 122296 free relations
  29. Fri Dec 12 00:11:15 2025 commencing duplicate removal, pass 2
  30. Fri Dec 12 00:17:00 2025 found 48089635 duplicates and 234072186 unique relations
  31. Fri Dec 12 00:17:00 2025 memory use: 1449.5 MB
  32. Fri Dec 12 00:17:00 2025 reading ideals above 720000
  33. Fri Dec 12 00:17:00 2025 commencing singleton removal, initial pass
  34. Fri Dec 12 00:32:54 2025 memory use: 6024.0 MB
  35. Fri Dec 12 00:32:54 2025 reading all ideals from disk
  36. Fri Dec 12 00:32:58 2025 memory use: 10723.1 MB
  37. Fri Dec 12 00:33:24 2025 keeping 225531356 ideals with weight <= 200, target excess is 1135740
  38. Fri Dec 12 00:33:56 2025 commencing in-memory singleton removal
  39. Fri Dec 12 00:34:00 2025 begin with 234072186 relations and 225531356 unique ideals
  40. Fri Dec 12 00:34:19 2025 reduce to 126145017 relations and 103999425 ideals in 15 passes
  41. Fri Dec 12 00:34:19 2025 max relations containing the same ideal: 142
  42. Fri Dec 12 00:35:14 2025 removing 12077236 relations and 10077236 ideals in 2000000 cliques
  43. Fri Dec 12 00:35:19 2025 commencing in-memory singleton removal
  44. Fri Dec 12 00:35:21 2025 begin with 114067781 relations and 103999425 unique ideals
  45. Fri Dec 12 00:35:29 2025 reduce to 113183423 relations and 93019742 ideals in 9 passes
  46. Fri Dec 12 00:35:29 2025 max relations containing the same ideal: 134
  47. Fri Dec 12 00:36:16 2025 removing 9191463 relations and 7191463 ideals in 2000000 cliques
  48. Fri Dec 12 00:36:20 2025 commencing in-memory singleton removal
  49. Fri Dec 12 00:36:22 2025 begin with 103991960 relations and 93019742 unique ideals
  50. Fri Dec 12 00:36:28 2025 reduce to 103390172 relations and 85215621 ideals in 9 passes
  51. Fri Dec 12 00:36:28 2025 max relations containing the same ideal: 125
  52. Fri Dec 12 00:37:10 2025 removing 8334336 relations and 6334336 ideals in 2000000 cliques
  53. Fri Dec 12 00:37:14 2025 commencing in-memory singleton removal
  54. Fri Dec 12 00:37:16 2025 begin with 95055836 relations and 85215621 unique ideals
  55. Fri Dec 12 00:37:23 2025 reduce to 94512464 relations and 78327819 ideals in 10 passes
  56. Fri Dec 12 00:37:23 2025 max relations containing the same ideal: 116
  57. Fri Dec 12 00:38:03 2025 removing 7895521 relations and 5895521 ideals in 2000000 cliques
  58. Fri Dec 12 00:38:06 2025 commencing in-memory singleton removal
  59. Fri Dec 12 00:38:08 2025 begin with 86616943 relations and 78327819 unique ideals
  60. Fri Dec 12 00:38:14 2025 reduce to 86086404 relations and 71891422 ideals in 9 passes
  61. Fri Dec 12 00:38:14 2025 max relations containing the same ideal: 108
  62. Fri Dec 12 00:38:51 2025 removing 7648755 relations and 5648755 ideals in 2000000 cliques
  63. Fri Dec 12 00:38:55 2025 commencing in-memory singleton removal
  64. Fri Dec 12 00:38:56 2025 begin with 78437649 relations and 71891422 unique ideals
  65. Fri Dec 12 00:39:01 2025 reduce to 77898382 relations and 65692047 ideals in 8 passes
  66. Fri Dec 12 00:39:01 2025 max relations containing the same ideal: 100
  67. Fri Dec 12 00:39:35 2025 removing 7499071 relations and 5499071 ideals in 2000000 cliques
  68. Fri Dec 12 00:39:38 2025 commencing in-memory singleton removal
  69. Fri Dec 12 00:39:39 2025 begin with 70399311 relations and 65692047 unique ideals
  70. Fri Dec 12 00:39:43 2025 reduce to 69830292 relations and 59611020 ideals in 8 passes
  71. Fri Dec 12 00:39:43 2025 max relations containing the same ideal: 94
  72. Fri Dec 12 00:40:15 2025 removing 7423103 relations and 5423103 ideals in 2000000 cliques
  73. Fri Dec 12 00:40:18 2025 commencing in-memory singleton removal
  74. Fri Dec 12 00:40:19 2025 begin with 62407189 relations and 59611020 unique ideals
  75. Fri Dec 12 00:40:22 2025 reduce to 61784136 relations and 53549218 ideals in 8 passes
  76. Fri Dec 12 00:40:22 2025 max relations containing the same ideal: 85
  77. Fri Dec 12 00:40:50 2025 removing 7409471 relations and 5409471 ideals in 2000000 cliques
  78. Fri Dec 12 00:40:53 2025 commencing in-memory singleton removal
  79. Fri Dec 12 00:40:53 2025 begin with 54374665 relations and 53549218 unique ideals
  80. Fri Dec 12 00:40:56 2025 reduce to 53675168 relations and 47420327 ideals in 8 passes
  81. Fri Dec 12 00:40:56 2025 max relations containing the same ideal: 78
  82. Fri Dec 12 00:41:20 2025 removing 7440823 relations and 5440823 ideals in 2000000 cliques
  83. Fri Dec 12 00:41:22 2025 commencing in-memory singleton removal
  84. Fri Dec 12 00:41:23 2025 begin with 46234345 relations and 47420327 unique ideals
  85. Fri Dec 12 00:41:25 2025 reduce to 45410288 relations and 41128650 ideals in 9 passes
  86. Fri Dec 12 00:41:25 2025 max relations containing the same ideal: 71
  87. Fri Dec 12 00:41:46 2025 removing 7536233 relations and 5536233 ideals in 2000000 cliques
  88. Fri Dec 12 00:41:49 2025 commencing in-memory singleton removal
  89. Fri Dec 12 00:41:49 2025 begin with 37874055 relations and 41128650 unique ideals
  90. Fri Dec 12 00:41:51 2025 reduce to 36851805 relations and 34531246 ideals in 10 passes
  91. Fri Dec 12 00:41:51 2025 max relations containing the same ideal: 60
  92. Fri Dec 12 00:42:08 2025 removing 4559534 relations and 3556434 ideals in 1003100 cliques
  93. Fri Dec 12 00:42:10 2025 commencing in-memory singleton removal
  94. Fri Dec 12 00:42:10 2025 begin with 32292271 relations and 34531246 unique ideals
  95. Fri Dec 12 00:42:12 2025 reduce to 31848991 relations and 30521076 ideals in 10 passes
  96. Fri Dec 12 00:42:12 2025 max relations containing the same ideal: 56
  97. Fri Dec 12 00:42:27 2025 removing 98540 relations and 88084 ideals in 10456 cliques
  98. Fri Dec 12 00:42:28 2025 commencing in-memory singleton removal
  99. Fri Dec 12 00:42:28 2025 begin with 31750451 relations and 30521076 unique ideals
  100. Fri Dec 12 00:42:29 2025 reduce to 31750264 relations and 30432805 ideals in 5 passes
  101. Fri Dec 12 00:42:29 2025 max relations containing the same ideal: 56
  102. Fri Dec 12 00:42:32 2025 relations with 0 large ideals: 4023
  103. Fri Dec 12 00:42:32 2025 relations with 1 large ideals: 41365
  104. Fri Dec 12 00:42:32 2025 relations with 2 large ideals: 495649
  105. Fri Dec 12 00:42:32 2025 relations with 3 large ideals: 2415982
  106. Fri Dec 12 00:42:32 2025 relations with 4 large ideals: 6152200
  107. Fri Dec 12 00:42:32 2025 relations with 5 large ideals: 9009486
  108. Fri Dec 12 00:42:32 2025 relations with 6 large ideals: 7930649
  109. Fri Dec 12 00:42:32 2025 relations with 7+ large ideals: 5700910
  110. Fri Dec 12 00:42:32 2025 commencing 2-way merge
  111. Fri Dec 12 00:42:54 2025 reduce to 18871209 relation sets and 17553750 unique ideals
  112. Fri Dec 12 00:42:54 2025 commencing full merge
  113. Fri Dec 12 00:49:11 2025 memory use: 2126.8 MB
  114. Fri Dec 12 00:49:12 2025 found 8030485 cycles, need 8003950
  115. Fri Dec 12 00:49:14 2025 weight of 8003950 cycles is about 1041260162 (130.09/cycle)
  116. Fri Dec 12 00:49:14 2025 distribution of cycle lengths:
  117. Fri Dec 12 00:49:14 2025 1 relations: 488617
  118. Fri Dec 12 00:49:14 2025 2 relations: 505725
  119. Fri Dec 12 00:49:14 2025 3 relations: 514136
  120. Fri Dec 12 00:49:14 2025 4 relations: 506472
  121. Fri Dec 12 00:49:14 2025 5 relations: 506140
  122. Fri Dec 12 00:49:14 2025 6 relations: 499999
  123. Fri Dec 12 00:49:14 2025 7 relations: 490452
  124. Fri Dec 12 00:49:14 2025 8 relations: 478044
  125. Fri Dec 12 00:49:14 2025 9 relations: 457569
  126. Fri Dec 12 00:49:14 2025 10+ relations: 3556796
  127. Fri Dec 12 00:49:14 2025 heaviest cycle: 28 relations
  128. Fri Dec 12 00:49:17 2025 commencing cycle optimization
  129. Fri Dec 12 00:49:33 2025 start with 76141824 relations
  130. Fri Dec 12 00:52:20 2025 pruned 3228620 relations
  131. Fri Dec 12 00:52:20 2025 memory use: 2057.5 MB
  132. Fri Dec 12 00:52:20 2025 distribution of cycle lengths:
  133. Fri Dec 12 00:52:20 2025 1 relations: 488617
  134. Fri Dec 12 00:52:20 2025 2 relations: 517905
  135. Fri Dec 12 00:52:20 2025 3 relations: 533876
  136. Fri Dec 12 00:52:20 2025 4 relations: 525246
  137. Fri Dec 12 00:52:20 2025 5 relations: 528523
  138. Fri Dec 12 00:52:20 2025 6 relations: 520895
  139. Fri Dec 12 00:52:20 2025 7 relations: 513234
  140. Fri Dec 12 00:52:20 2025 8 relations: 499131
  141. Fri Dec 12 00:52:20 2025 9 relations: 478911
  142. Fri Dec 12 00:52:20 2025 10+ relations: 3397612
  143. Fri Dec 12 00:52:20 2025 heaviest cycle: 28 relations
  144. Fri Dec 12 00:52:33 2025 RelProcTime: 2951
  145. Fri Dec 12 00:52:33 2025
  146. Fri Dec 12 00:52:33 2025 commencing linear algebra
  147. Fri Dec 12 00:52:33 2025 using VBITS=256
  148. Fri Dec 12 00:52:33 2025 stopping after matrix build
  149. Fri Dec 12 00:52:33 2025 initialized process (0,0) of 1 x 1 grid
  150. Fri Dec 12 00:52:33 2025 reversing signs of algebraic polynomial
  151. Fri Dec 12 00:52:34 2025 read 8003950 cycles
  152. Fri Dec 12 00:52:48 2025 cycles contain 30832460 unique relations
  153. Fri Dec 12 00:56:49 2025 read 30832460 relations
  154. Fri Dec 12 00:56:53 2025 using 20 quadratic characters above 4294917295
  155. Fri Dec 12 00:56:57 2025 building initial matrix
  156. Fri Dec 12 01:02:52 2025 memory use: 4221.8 MB
  157. Fri Dec 12 01:02:58 2025 read 8003950 cycles
  158. Fri Dec 12 01:03:00 2025 matrix is 8003773 x 8003950 (4048.8 MB) with weight 1242770506 (155.27/col)
  159. Fri Dec 12 01:03:00 2025 sparse part has weight 965311468 (120.60/col)
  160. Fri Dec 12 01:05:01 2025 filtering completed in 2 passes
  161. Fri Dec 12 01:05:03 2025 matrix is 8003422 x 8003598 (4048.7 MB) with weight 1242752623 (155.27/col)
  162. Fri Dec 12 01:05:03 2025 sparse part has weight 965306689 (120.61/col)
  163. Fri Dec 12 01:05:50 2025 BLanczosTime: 797
  164. Fri Dec 12 01:05:50 2025 elapsed time 01:02:29
  165. Sat Dec 13 10:16:14 2025
  166. Sat Dec 13 10:16:14 2025
  167. Sat Dec 13 10:16:14 2025 Msieve v. 1.54 (SVN Unversioned directory)
  168. Sat Dec 13 10:16:14 2025 random seeds: 60f72059 09f98296
  169. Sat Dec 13 10:16:14 2025 MPI process 0 of 1
  170. Sat Dec 13 10:16:14 2025 Using 64 OpenMP threads
  171. Sat Dec 13 10:16:14 2025 factoring 2369970599987002723447289682490372745199295423002957612089378714202031301535096430991518038038340277237276931832170242731309183009046309094220496841041299738814393619 (166 digits)
  172. Sat Dec 13 10:16:15 2025 searching for 15-digit factors
  173. Sat Dec 13 10:16:15 2025 commencing number field sieve (166-digit input)
  174. Sat Dec 13 10:16:15 2025 reversing signs of algebraic polynomial
  175. Sat Dec 13 10:16:15 2025 R0: -81117984972550717548330144834884
  176. Sat Dec 13 10:16:15 2025 R1: 10546681968983587060650379
  177. Sat Dec 13 10:16:15 2025 A0: 746351550463354332454893147593930085570
  178. Sat Dec 13 10:16:15 2025 A1: 1141804362388938171598440247914772
  179. Sat Dec 13 10:16:15 2025 A2: -798227995816160146133452113
  180. Sat Dec 13 10:16:15 2025 A3: -151467124992559405513
  181. Sat Dec 13 10:16:15 2025 A4: 55850712986142
  182. Sat Dec 13 10:16:15 2025 A5: 8845200
  183. Sat Dec 13 10:16:15 2025 skew 3295773.47, size 4.481e-16, alpha -7.942, combined = 7.139e-13 rroots = 5
  184. Sat Dec 13 10:16:15 2025
  185. Sat Dec 13 10:16:15 2025 commencing linear algebra
  186. Sat Dec 13 10:16:15 2025 using VBITS=256
  187. Sat Dec 13 10:16:15 2025 skipping matrix build
  188. Sat Dec 13 10:16:15 2025 initialized process (0,0) of 1 x 1 grid
  189. Sat Dec 13 10:16:20 2025 matrix starts at (0, 0)
  190. Sat Dec 13 10:16:21 2025 matrix is 8003422 x 8003598 (4048.7 MB) with weight 1242752623 (155.27/col)
  191. Sat Dec 13 10:16:21 2025 sparse part has weight 965306689 (120.61/col)
  192. Sat Dec 13 10:16:21 2025 saving the first 240 matrix rows for later
  193. Sat Dec 13 10:16:24 2025 matrix includes 256 packed rows
  194. Sat Dec 13 10:16:26 2025 matrix is 8003182 x 8003598 (3633.3 MB) with weight 883102179 (110.34/col)
  195. Sat Dec 13 10:16:26 2025 sparse part has weight 824387771 (103.00/col)
  196. Sat Dec 13 10:16:26 2025 using block size 8192 and superblock size 1032192 for processor cache size 43008 kB
  197. Sat Dec 13 10:16:44 2025 commencing Lanczos iteration (64 threads)
  198. Sat Dec 13 10:16:44 2025 memory use: 5125.6 MB
  199. Sat Dec 13 10:17:51 2025 linear algebra at 0.4%, ETA 4h46m
  200. Sat Dec 13 10:19:26 2025 checking every 20000 dimensions, checkpointing every 1720000 dimensions
  201. Sat Dec 13 14:48:58 2025 lanczos halted after 31358 iterations (dim = 8003180)
  202. Sat Dec 13 14:49:36 2025 recovered 29 nontrivial dependencies
  203. Sat Dec 13 14:49:36 2025 BLanczosTime: 16401
  204. Sat Dec 13 14:49:36 2025
  205. Sat Dec 13 14:49:36 2025 commencing square root phase
  206. Sat Dec 13 14:49:36 2025 reversing signs of algebraic polynomial
  207. Sat Dec 13 14:49:36 2025 handling dependencies 1 to 64
  208. Sat Dec 13 14:49:36 2025 reading relations for dependency 1
  209. Sat Dec 13 14:49:37 2025 read 4000198 cycles
  210. Sat Dec 13 14:49:44 2025 cycles contain 15410522 unique relations
  211. Sat Dec 13 14:55:08 2025 read 15410522 relations
  212. Sat Dec 13 14:57:19 2025 multiplying 15410522 relations
  213. Sat Dec 13 15:00:25 2025 multiply complete, coefficients have about 903.61 million bits
  214. Sat Dec 13 15:00:29 2025 initial square root is modulo 127868779
  215. Sat Dec 13 15:11:25 2025 GCD is 1, no factor found
  216. Sat Dec 13 15:11:25 2025 reading relations for dependency 2
  217. Sat Dec 13 15:11:27 2025 read 4001601 cycles
  218. Sat Dec 13 15:11:44 2025 cycles contain 15414120 unique relations
  219. Sat Dec 13 15:17:55 2025 read 15414120 relations
  220. Sat Dec 13 15:20:13 2025 multiplying 15414120 relations
  221. Sat Dec 13 15:23:13 2025 multiply complete, coefficients have about 903.82 million bits
  222. Sat Dec 13 15:23:17 2025 initial square root is modulo 128420689
  223. Sat Dec 13 15:34:15 2025 GCD is 1, no factor found
  224. Sat Dec 13 15:34:15 2025 reading relations for dependency 3
  225. Sat Dec 13 15:34:17 2025 read 4002625 cycles
  226. Sat Dec 13 15:34:33 2025 cycles contain 15418252 unique relations
  227. Sat Dec 13 15:40:46 2025 read 15418252 relations
  228. Sat Dec 13 15:42:51 2025 multiplying 15418252 relations
  229. Sat Dec 13 15:45:48 2025 multiply complete, coefficients have about 904.06 million bits
  230. Sat Dec 13 15:45:53 2025 initial square root is modulo 129062933
  231. Sat Dec 13 15:56:49 2025 GCD is 1, no factor found
  232. Sat Dec 13 15:56:49 2025 reading relations for dependency 4
  233. Sat Dec 13 15:56:51 2025 read 4002540 cycles
  234. Sat Dec 13 15:57:07 2025 cycles contain 15424448 unique relations
  235. Sat Dec 13 16:03:19 2025 read 15424448 relations
  236. Sat Dec 13 16:05:31 2025 multiplying 15424448 relations
  237. Sat Dec 13 16:08:30 2025 multiply complete, coefficients have about 904.43 million bits
  238. Sat Dec 13 16:08:35 2025 initial square root is modulo 130043807
  239. Sat Dec 13 16:19:29 2025 GCD is N, no factor found
  240. Sat Dec 13 16:19:29 2025 reading relations for dependency 5
  241. Sat Dec 13 16:19:30 2025 read 4001392 cycles
  242. Sat Dec 13 16:19:47 2025 cycles contain 15418006 unique relations
  243. Sat Dec 13 16:25:59 2025 read 15418006 relations
  244. Sat Dec 13 16:28:15 2025 multiplying 15418006 relations
  245. Sat Dec 13 16:31:13 2025 multiply complete, coefficients have about 904.05 million bits
  246. Sat Dec 13 16:31:18 2025 initial square root is modulo 129030313
  247. Sat Dec 13 16:42:08 2025 sqrtTime: 6752
  248. Sat Dec 13 16:42:08 2025 p71 factor: 53051104400196104341925057873136665758162510221880283904968564647289183
  249. Sat Dec 13 16:42:08 2025 p95 factor: 44673350852583609651993532308944510236177554161896021265321622622767432827610800691712169561293
  250. Sat Dec 13 16:42:08 2025 elapsed time 06:25:54
  251.  
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