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13*2^800-1 factorization

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Jul 11th, 2017
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  1. Fri Jul 7 21:56:33 2017 Msieve v. 1.52 (SVN unknown)
  2. Fri Jul 7 21:56:33 2017 random seeds: 89ef5633 2d475396
  3. Fri Jul 7 21:56:33 2017 factoring 293279338268454023866245440870308237806520338071962741869336774244320823422643775297036986460002650705701592500634862028121070426777291354105093480717237604707298542950947863172273537595119 (189 digits)
  4. Fri Jul 7 21:56:34 2017 no P-1/P+1/ECM available, skipping
  5. Fri Jul 7 21:56:34 2017 commencing number field sieve (189-digit input)
  6. Fri Jul 7 21:56:34 2017 R0: -10889035741470030830827987437816582766592
  7. Fri Jul 7 21:56:34 2017 R1: 1
  8. Fri Jul 7 21:56:34 2017 A0: -1
  9. Fri Jul 7 21:56:34 2017 A1: 0
  10. Fri Jul 7 21:56:34 2017 A2: 0
  11. Fri Jul 7 21:56:34 2017 A3: 0
  12. Fri Jul 7 21:56:34 2017 A4: 0
  13. Fri Jul 7 21:56:34 2017 A5: 0
  14. Fri Jul 7 21:56:34 2017 A6: 52
  15. Fri Jul 7 21:56:34 2017 skew 1.00, size 5.933e-12, alpha 1.164, combined = 4.319e-13 rroots = 2
  16. Fri Jul 7 21:56:34 2017
  17. Fri Jul 7 21:56:34 2017 commencing relation filtering
  18. Fri Jul 7 21:56:34 2017 setting target matrix density to 128.0
  19. Fri Jul 7 21:56:34 2017 estimated available RAM is 15888.6 MB
  20. Fri Jul 7 21:56:34 2017 commencing duplicate removal, pass 1
  21. Fri Jul 7 22:22:15 2017 error -15 reading relation 283825034
  22. Fri Jul 7 22:25:58 2017 skipped 206 relations with b > 2^32
  23. Fri Jul 7 22:25:58 2017 found 21940010 hash collisions in 322206423 relations
  24. Fri Jul 7 22:26:11 2017 commencing duplicate removal, pass 2
  25. Fri Jul 7 22:27:55 2017 found 1 duplicates and 322206422 unique relations
  26. Fri Jul 7 22:27:55 2017 memory use: 1257.5 MB
  27. Fri Jul 7 22:27:55 2017 reading ideals above 119996416
  28. Fri Jul 7 22:27:55 2017 commencing singleton removal, initial pass
  29. Fri Jul 7 23:02:51 2017 memory use: 6024.0 MB
  30. Fri Jul 7 23:02:52 2017 reading all ideals from disk
  31. Fri Jul 7 23:03:12 2017 memory use: 5838.2 MB
  32. Fri Jul 7 23:03:30 2017 commencing in-memory singleton removal
  33. Fri Jul 7 23:03:42 2017 begin with 322206422 relations and 296876476 unique ideals
  34. Fri Jul 7 23:05:56 2017 reduce to 170449805 relations and 124239033 ideals in 17 passes
  35. Fri Jul 7 23:05:56 2017 max relations containing the same ideal: 52
  36. Fri Jul 7 23:06:06 2017 reading ideals above 720000
  37. Fri Jul 7 23:06:06 2017 commencing singleton removal, initial pass
  38. Fri Jul 7 23:30:46 2017 memory use: 3012.0 MB
  39. Fri Jul 7 23:30:46 2017 reading all ideals from disk
  40. Fri Jul 7 23:31:04 2017 memory use: 6612.3 MB
  41. Fri Jul 7 23:31:25 2017 keeping 137057647 ideals with weight <= 200, target excess is 864228
  42. Fri Jul 7 23:31:46 2017 commencing in-memory singleton removal
  43. Fri Jul 7 23:31:55 2017 begin with 170449805 relations and 137057647 unique ideals
  44. Fri Jul 7 23:32:40 2017 reduce to 170449693 relations and 137057535 ideals in 4 passes
  45. Fri Jul 7 23:32:40 2017 max relations containing the same ideal: 200
  46. Fri Jul 7 23:33:43 2017 removing 13854760 relations and 11854760 ideals in 2000000 cliques
  47. Fri Jul 7 23:33:47 2017 commencing in-memory singleton removal
  48. Fri Jul 7 23:33:56 2017 begin with 156594933 relations and 137057535 unique ideals
  49. Fri Jul 7 23:35:23 2017 reduce to 155797475 relations and 124392959 ideals in 9 passes
  50. Fri Jul 7 23:35:23 2017 max relations containing the same ideal: 195
  51. Fri Jul 7 23:36:19 2017 removing 10209419 relations and 8209419 ideals in 2000000 cliques
  52. Fri Jul 7 23:36:23 2017 commencing in-memory singleton removal
  53. Fri Jul 7 23:36:31 2017 begin with 145588056 relations and 124392959 unique ideals
  54. Fri Jul 7 23:37:41 2017 reduce to 145089165 relations and 115678024 ideals in 8 passes
  55. Fri Jul 7 23:37:41 2017 max relations containing the same ideal: 190
  56. Fri Jul 7 23:38:32 2017 removing 9058500 relations and 7058500 ideals in 2000000 cliques
  57. Fri Jul 7 23:38:36 2017 commencing in-memory singleton removal
  58. Fri Jul 7 23:38:43 2017 begin with 136030665 relations and 115678024 unique ideals
  59. Fri Jul 7 23:39:58 2017 reduce to 135603073 relations and 108186146 ideals in 8 passes
  60. Fri Jul 7 23:39:58 2017 max relations containing the same ideal: 183
  61. Fri Jul 7 23:40:50 2017 removing 8424323 relations and 6424323 ideals in 2000000 cliques
  62. Fri Jul 7 23:40:53 2017 commencing in-memory singleton removal
  63. Fri Jul 7 23:41:00 2017 begin with 127178750 relations and 108186146 unique ideals
  64. Fri Jul 7 23:42:03 2017 reduce to 126784570 relations and 101362281 ideals in 8 passes
  65. Fri Jul 7 23:42:03 2017 max relations containing the same ideal: 176
  66. Fri Jul 7 23:42:52 2017 removing 8012700 relations and 6012700 ideals in 2000000 cliques
  67. Fri Jul 7 23:42:55 2017 commencing in-memory singleton removal
  68. Fri Jul 7 23:43:01 2017 begin with 118771870 relations and 101362281 unique ideals
  69. Fri Jul 7 23:43:54 2017 reduce to 118396838 relations and 94969087 ideals in 7 passes
  70. Fri Jul 7 23:43:54 2017 max relations containing the same ideal: 166
  71. Fri Jul 7 23:44:36 2017 removing 7724746 relations and 5724746 ideals in 2000000 cliques
  72. Fri Jul 7 23:44:39 2017 commencing in-memory singleton removal
  73. Fri Jul 7 23:44:44 2017 begin with 110672092 relations and 94969087 unique ideals
  74. Fri Jul 7 23:45:40 2017 reduce to 110302909 relations and 88869614 ideals in 8 passes
  75. Fri Jul 7 23:45:40 2017 max relations containing the same ideal: 158
  76. Fri Jul 7 23:46:21 2017 removing 7509288 relations and 5509288 ideals in 2000000 cliques
  77. Fri Jul 7 23:46:24 2017 commencing in-memory singleton removal
  78. Fri Jul 7 23:46:29 2017 begin with 102793621 relations and 88869614 unique ideals
  79. Fri Jul 7 23:47:21 2017 reduce to 102425171 relations and 82986084 ideals in 7 passes
  80. Fri Jul 7 23:47:21 2017 max relations containing the same ideal: 150
  81. Fri Jul 7 23:47:59 2017 removing 7347857 relations and 5347857 ideals in 2000000 cliques
  82. Fri Jul 7 23:48:02 2017 commencing in-memory singleton removal
  83. Fri Jul 7 23:48:07 2017 begin with 95077314 relations and 82986084 unique ideals
  84. Fri Jul 7 23:48:55 2017 reduce to 94703092 relations and 77257711 ideals in 8 passes
  85. Fri Jul 7 23:48:55 2017 max relations containing the same ideal: 143
  86. Fri Jul 7 23:49:30 2017 removing 7229138 relations and 5229138 ideals in 2000000 cliques
  87. Fri Jul 7 23:49:33 2017 commencing in-memory singleton removal
  88. Fri Jul 7 23:49:37 2017 begin with 87473954 relations and 77257711 unique ideals
  89. Fri Jul 7 23:50:21 2017 reduce to 87089692 relations and 71637068 ideals in 8 passes
  90. Fri Jul 7 23:50:21 2017 max relations containing the same ideal: 138
  91. Fri Jul 7 23:50:54 2017 removing 7131491 relations and 5131491 ideals in 2000000 cliques
  92. Fri Jul 7 23:50:56 2017 commencing in-memory singleton removal
  93. Fri Jul 7 23:51:01 2017 begin with 79958201 relations and 71637068 unique ideals
  94. Fri Jul 7 23:51:37 2017 reduce to 79558422 relations and 66097728 ideals in 7 passes
  95. Fri Jul 7 23:51:37 2017 max relations containing the same ideal: 130
  96. Fri Jul 7 23:52:09 2017 removing 7057537 relations and 5057537 ideals in 2000000 cliques
  97. Fri Jul 7 23:52:11 2017 commencing in-memory singleton removal
  98. Fri Jul 7 23:52:15 2017 begin with 72500885 relations and 66097728 unique ideals
  99. Fri Jul 7 23:52:57 2017 reduce to 72078344 relations and 60608570 ideals in 8 passes
  100. Fri Jul 7 23:52:57 2017 max relations containing the same ideal: 121
  101. Fri Jul 7 23:53:23 2017 removing 7005678 relations and 5005678 ideals in 2000000 cliques
  102. Fri Jul 7 23:53:26 2017 commencing in-memory singleton removal
  103. Fri Jul 7 23:53:29 2017 begin with 65072666 relations and 60608570 unique ideals
  104. Fri Jul 7 23:54:02 2017 reduce to 64619675 relations and 55139090 ideals in 8 passes
  105. Fri Jul 7 23:54:02 2017 max relations containing the same ideal: 111
  106. Fri Jul 7 23:54:26 2017 removing 6970793 relations and 4970793 ideals in 2000000 cliques
  107. Fri Jul 7 23:54:28 2017 commencing in-memory singleton removal
  108. Fri Jul 7 23:54:31 2017 begin with 57648882 relations and 55139090 unique ideals
  109. Fri Jul 7 23:54:57 2017 reduce to 57156683 relations and 49663136 ideals in 8 passes
  110. Fri Jul 7 23:54:57 2017 max relations containing the same ideal: 102
  111. Fri Jul 7 23:55:18 2017 removing 6950096 relations and 4950096 ideals in 2000000 cliques
  112. Fri Jul 7 23:55:20 2017 commencing in-memory singleton removal
  113. Fri Jul 7 23:55:23 2017 begin with 50206587 relations and 49663136 unique ideals
  114. Fri Jul 7 23:55:45 2017 reduce to 49656136 relations and 44146374 ideals in 8 passes
  115. Fri Jul 7 23:55:45 2017 max relations containing the same ideal: 94
  116. Fri Jul 7 23:56:03 2017 removing 6943902 relations and 4943902 ideals in 2000000 cliques
  117. Fri Jul 7 23:56:06 2017 commencing in-memory singleton removal
  118. Fri Jul 7 23:56:08 2017 begin with 42712234 relations and 44146374 unique ideals
  119. Fri Jul 7 23:56:30 2017 reduce to 42087014 relations and 38555949 ideals in 8 passes
  120. Fri Jul 7 23:56:30 2017 max relations containing the same ideal: 86
  121. Fri Jul 7 23:56:44 2017 removing 6944121 relations and 4944121 ideals in 2000000 cliques
  122. Fri Jul 7 23:56:46 2017 commencing in-memory singleton removal
  123. Fri Jul 7 23:56:48 2017 begin with 35142893 relations and 38555949 unique ideals
  124. Fri Jul 7 23:57:04 2017 reduce to 34400058 relations and 32838842 ideals in 9 passes
  125. Fri Jul 7 23:57:04 2017 max relations containing the same ideal: 75
  126. Fri Jul 7 23:57:17 2017 removing 2521969 relations and 1963258 ideals in 558711 cliques
  127. Fri Jul 7 23:57:18 2017 commencing in-memory singleton removal
  128. Fri Jul 7 23:57:20 2017 begin with 31878089 relations and 32838842 unique ideals
  129. Fri Jul 7 23:57:34 2017 reduce to 31758729 relations and 30754471 ideals in 7 passes
  130. Fri Jul 7 23:57:34 2017 max relations containing the same ideal: 68
  131. Fri Jul 7 23:57:51 2017 relations with 0 large ideals: 33059
  132. Fri Jul 7 23:57:51 2017 relations with 1 large ideals: 20195
  133. Fri Jul 7 23:57:51 2017 relations with 2 large ideals: 261197
  134. Fri Jul 7 23:57:51 2017 relations with 3 large ideals: 1491462
  135. Fri Jul 7 23:57:51 2017 relations with 4 large ideals: 4481575
  136. Fri Jul 7 23:57:51 2017 relations with 5 large ideals: 7860618
  137. Fri Jul 7 23:57:51 2017 relations with 6 large ideals: 8447022
  138. Fri Jul 7 23:57:51 2017 relations with 7+ large ideals: 9163601
  139. Fri Jul 7 23:57:51 2017 commencing 2-way merge
  140. Fri Jul 7 23:58:05 2017 reduce to 19787720 relation sets and 18783462 unique ideals
  141. Fri Jul 7 23:58:05 2017 commencing full merge
  142. Sat Jul 8 00:04:38 2017 memory use: 2528.5 MB
  143. Sat Jul 8 00:04:40 2017 found 8823903 cycles, need 8789662
  144. Sat Jul 8 00:04:42 2017 weight of 8789662 cycles is about 1125879080 (128.09/cycle)
  145. Sat Jul 8 00:04:42 2017 distribution of cycle lengths:
  146. Sat Jul 8 00:04:42 2017 1 relations: 331735
  147. Sat Jul 8 00:04:42 2017 2 relations: 456586
  148. Sat Jul 8 00:04:42 2017 3 relations: 538068
  149. Sat Jul 8 00:04:42 2017 4 relations: 564237
  150. Sat Jul 8 00:04:42 2017 5 relations: 592668
  151. Sat Jul 8 00:04:42 2017 6 relations: 596453
  152. Sat Jul 8 00:04:42 2017 7 relations: 591516
  153. Sat Jul 8 00:04:42 2017 8 relations: 582631
  154. Sat Jul 8 00:04:42 2017 9 relations: 558619
  155. Sat Jul 8 00:04:42 2017 10+ relations: 3977149
  156. Sat Jul 8 00:04:42 2017 heaviest cycle: 28 relations
  157. Sat Jul 8 00:04:45 2017 commencing cycle optimization
  158. Sat Jul 8 00:05:02 2017 start with 84413755 relations
  159. Sat Jul 8 00:08:02 2017 pruned 3902185 relations
  160. Sat Jul 8 00:08:02 2017 memory use: 2177.9 MB
  161. Sat Jul 8 00:08:02 2017 distribution of cycle lengths:
  162. Sat Jul 8 00:08:02 2017 1 relations: 331735
  163. Sat Jul 8 00:08:02 2017 2 relations: 467067
  164. Sat Jul 8 00:08:02 2017 3 relations: 559373
  165. Sat Jul 8 00:08:02 2017 4 relations: 586624
  166. Sat Jul 8 00:08:02 2017 5 relations: 621554
  167. Sat Jul 8 00:08:02 2017 6 relations: 624978
  168. Sat Jul 8 00:08:02 2017 7 relations: 623970
  169. Sat Jul 8 00:08:02 2017 8 relations: 612959
  170. Sat Jul 8 00:08:02 2017 9 relations: 587540
  171. Sat Jul 8 00:08:02 2017 10+ relations: 3773862
  172. Sat Jul 8 00:08:02 2017 heaviest cycle: 28 relations
  173. Sat Jul 8 00:08:21 2017 RelProcTime: 7907
  174. Sat Jul 8 00:08:21 2017
  175. Sat Jul 8 00:08:21 2017 commencing linear algebra
  176. Sat Jul 8 00:08:22 2017 read 8789662 cycles
  177. Sat Jul 8 00:08:41 2017 cycles contain 31203777 unique relations
  178. Sat Jul 8 00:11:43 2017 read 31203777 relations
  179. Sat Jul 8 00:12:27 2017 using 20 quadratic characters above 4294917296
  180. Sat Jul 8 00:14:26 2017 building initial matrix
  181. Sat Jul 8 00:19:35 2017 memory use: 4000.0 MB
  182. Sat Jul 8 00:19:39 2017 read 8789662 cycles
  183. Sat Jul 8 00:19:40 2017 matrix is 8789485 x 8789662 (4359.3 MB) with weight 1253780767 (142.64/col)
  184. Sat Jul 8 00:19:40 2017 sparse part has weight 1046082505 (119.01/col)
  185. Sat Jul 8 00:21:06 2017 filtering completed in 2 passes
  186. Sat Jul 8 00:21:07 2017 matrix is 8789368 x 8789545 (4359.3 MB) with weight 1253776139 (142.64/col)
  187. Sat Jul 8 00:21:07 2017 sparse part has weight 1046080569 (119.01/col)
  188. Sat Jul 8 00:21:39 2017 matrix starts at (0, 0)
  189. Sat Jul 8 00:21:40 2017 matrix is 8789368 x 8789545 (4359.3 MB) with weight 1253776139 (142.64/col)
  190. Sat Jul 8 00:21:40 2017 sparse part has weight 1046080569 (119.01/col)
  191. Sat Jul 8 00:21:40 2017 saving the first 48 matrix rows for later
  192. Sat Jul 8 00:21:42 2017 matrix includes 64 packed rows
  193. Sat Jul 8 00:21:43 2017 matrix is 8789320 x 8789545 (4179.9 MB) with weight 1083461177 (123.27/col)
  194. Sat Jul 8 00:21:43 2017 sparse part has weight 1007841341 (114.66/col)
  195. Sat Jul 8 00:21:43 2017 using block size 8192 and superblock size 1474560 for processor cache size 15360 kB
  196. Sat Jul 8 00:22:15 2017 commencing Lanczos iteration (6 threads)
  197. Sat Jul 8 00:22:15 2017 memory use: 3551.1 MB
  198. Sat Jul 8 00:22:58 2017 linear algebra at 0.0%, ETA 64h22m
  199. Sat Jul 8 00:23:10 2017 checkpointing every 150000 dimensions
  200. Mon Jul 10 17:43:44 2017 lanczos halted after 138988 iterations (dim = 8789320)
  201. Mon Jul 10 17:43:54 2017 recovered 40 nontrivial dependencies
  202. Mon Jul 10 17:43:54 2017 BLanczosTime: 236133
  203. Mon Jul 10 17:43:54 2017
  204. Mon Jul 10 17:43:54 2017 commencing square root phase
  205. Mon Jul 10 17:43:54 2017 handling dependencies 1 to 64
  206. Mon Jul 10 17:43:54 2017 reading relations for dependency 1
  207. Mon Jul 10 17:43:55 2017 read 4394271 cycles
  208. Mon Jul 10 17:44:02 2017 cycles contain 15600868 unique relations
  209. Mon Jul 10 17:45:48 2017 read 15600868 relations
  210. Mon Jul 10 17:46:36 2017 multiplying 15600868 relations
  211. Mon Jul 10 17:55:27 2017 multiply complete, coefficients have about 466.80 million bits
  212. Mon Jul 10 17:55:28 2017 initial square root is modulo 237588067
  213. Mon Jul 10 18:05:08 2017 sqrtTime: 1274
  214. Mon Jul 10 18:05:08 2017 prp81 factor: 160495860510299089900884881150565381014314892318013981084372922252235562566936671
  215. Mon Jul 10 18:05:08 2017 prp109 factor: 1827332725815904515769354793594180789579187639474678166920356073397044898104863056938970852957550120922053489
  216. Mon Jul 10 18:05:08 2017 elapsed time 68:08:35
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