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134^116+116^134

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May 25th, 2017
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  1. Mon May 22 09:00:35 2017 Msieve v. 1.53 (SVN unknown)
  2. Mon May 22 09:00:35 2017 random seeds: a6fe6ec7 b85f4f6b
  3. Mon May 22 09:00:35 2017 factoring 3114838196474848401017534969278136946153919548388919037455862029215826205663291191713338072012752224860495020719132978042251134209328679199490935084320168132879686971760719106955915811907681949463853146413963049 (211 digits)
  4. Mon May 22 09:00:37 2017 searching for 15-digit factors
  5. Mon May 22 09:00:38 2017 commencing number field sieve (211-digit input)
  6. Mon May 22 09:00:38 2017 R0: 3278278256307802865247951091628947592180469334016
  7. Mon May 22 09:00:38 2017 R1: -999356547346805156075552524294177648535563
  8. Mon May 22 09:00:38 2017 A0: 1943
  9. Mon May 22 09:00:38 2017 A1: 0
  10. Mon May 22 09:00:38 2017 A2: 0
  11. Mon May 22 09:00:38 2017 A3: 0
  12. Mon May 22 09:00:38 2017 A4: 0
  13. Mon May 22 09:00:38 2017 A5: 4
  14. Mon May 22 09:00:38 2017 skew 3.45, size 1.013e-16, alpha -0.719, combined = 2.264e-13 rroots = 1
  15. Mon May 22 09:00:38 2017
  16. Mon May 22 09:00:38 2017 commencing relation filtering
  17. Mon May 22 09:00:38 2017 setting target matrix density to 140.0
  18. Mon May 22 09:00:38 2017 estimated available RAM is 16003.1 MB
  19. Mon May 22 09:00:38 2017 commencing duplicate removal, pass 1
  20. Mon May 22 09:33:03 2017 error -1 reading relation 198088673
  21. Mon May 22 09:38:34 2017 skipped 71 relations with b > 2^32
  22. Mon May 22 09:38:34 2017 found 11687805 hash collisions in 232020609 relations
  23. Mon May 22 09:39:09 2017 added 731291 free relations
  24. Mon May 22 09:39:09 2017 commencing duplicate removal, pass 2
  25. Mon May 22 09:41:38 2017 found 0 duplicates and 232751900 unique relations
  26. Mon May 22 09:41:38 2017 memory use: 756.8 MB
  27. Mon May 22 09:41:38 2017 reading ideals above 219873280
  28. Mon May 22 09:41:38 2017 commencing singleton removal, initial pass
  29. Mon May 22 10:11:07 2017 memory use: 3012.0 MB
  30. Mon May 22 10:11:07 2017 reading all ideals from disk
  31. Mon May 22 10:11:35 2017 memory use: 3732.5 MB
  32. Mon May 22 10:11:47 2017 commencing in-memory singleton removal
  33. Mon May 22 10:11:59 2017 begin with 232751900 relations and 161516912 unique ideals
  34. Mon May 22 10:14:11 2017 reduce to 179374287 relations and 104388793 ideals in 11 passes
  35. Mon May 22 10:14:11 2017 max relations containing the same ideal: 43
  36. Mon May 22 10:14:24 2017 reading ideals above 720000
  37. Mon May 22 10:14:24 2017 commencing singleton removal, initial pass
  38. Mon May 22 10:44:46 2017 memory use: 3012.0 MB
  39. Mon May 22 10:44:46 2017 reading all ideals from disk
  40. Mon May 22 10:45:39 2017 memory use: 7109.2 MB
  41. Mon May 22 10:46:13 2017 keeping 127698751 ideals with weight <= 200, target excess is 920290
  42. Mon May 22 10:46:48 2017 commencing in-memory singleton removal
  43. Mon May 22 10:47:15 2017 begin with 179374287 relations and 127698751 unique ideals
  44. Mon May 22 10:50:14 2017 reduce to 179367072 relations and 127691534 ideals in 7 passes
  45. Mon May 22 10:50:14 2017 max relations containing the same ideal: 200
  46. Mon May 22 10:52:12 2017 removing 8794225 relations and 6794225 ideals in 2000000 cliques
  47. Mon May 22 10:52:17 2017 commencing in-memory singleton removal
  48. Mon May 22 10:52:41 2017 begin with 170572847 relations and 127691534 unique ideals
  49. Mon May 22 10:55:34 2017 reduce to 170239089 relations and 120558684 ideals in 7 passes
  50. Mon May 22 10:55:34 2017 max relations containing the same ideal: 200
  51. Mon May 22 10:57:27 2017 removing 6824825 relations and 4824825 ideals in 2000000 cliques
  52. Mon May 22 10:57:31 2017 commencing in-memory singleton removal
  53. Mon May 22 10:57:52 2017 begin with 163414264 relations and 120558684 unique ideals
  54. Mon May 22 11:00:00 2017 reduce to 163187140 relations and 115503848 ideals in 6 passes
  55. Mon May 22 11:00:00 2017 max relations containing the same ideal: 197
  56. Mon May 22 11:01:37 2017 removing 6271244 relations and 4271244 ideals in 2000000 cliques
  57. Mon May 22 11:01:41 2017 commencing in-memory singleton removal
  58. Mon May 22 11:02:01 2017 begin with 156915896 relations and 115503848 unique ideals
  59. Mon May 22 11:03:57 2017 reduce to 156721032 relations and 111035369 ideals in 6 passes
  60. Mon May 22 11:03:57 2017 max relations containing the same ideal: 192
  61. Mon May 22 11:05:30 2017 removing 5982671 relations and 3982671 ideals in 2000000 cliques
  62. Mon May 22 11:05:35 2017 commencing in-memory singleton removal
  63. Mon May 22 11:05:53 2017 begin with 150738361 relations and 111035369 unique ideals
  64. Mon May 22 11:07:43 2017 reduce to 150562045 relations and 106874152 ideals in 6 passes
  65. Mon May 22 11:07:43 2017 max relations containing the same ideal: 189
  66. Mon May 22 11:09:08 2017 removing 5795007 relations and 3795007 ideals in 2000000 cliques
  67. Mon May 22 11:09:12 2017 commencing in-memory singleton removal
  68. Mon May 22 11:09:23 2017 begin with 144767038 relations and 106874152 unique ideals
  69. Mon May 22 11:10:36 2017 reduce to 144600667 relations and 102910614 ideals in 6 passes
  70. Mon May 22 11:10:36 2017 max relations containing the same ideal: 184
  71. Mon May 22 11:11:36 2017 removing 5661306 relations and 3661306 ideals in 2000000 cliques
  72. Mon May 22 11:11:40 2017 commencing in-memory singleton removal
  73. Mon May 22 11:11:51 2017 begin with 138939361 relations and 102910614 unique ideals
  74. Mon May 22 11:12:48 2017 reduce to 138779066 relations and 99086870 ideals in 5 passes
  75. Mon May 22 11:12:48 2017 max relations containing the same ideal: 180
  76. Mon May 22 11:13:38 2017 removing 5562980 relations and 3562980 ideals in 2000000 cliques
  77. Mon May 22 11:13:41 2017 commencing in-memory singleton removal
  78. Mon May 22 11:13:50 2017 begin with 133216086 relations and 99086870 unique ideals
  79. Mon May 22 11:14:45 2017 reduce to 133059700 relations and 95365389 ideals in 6 passes
  80. Mon May 22 11:14:45 2017 max relations containing the same ideal: 177
  81. Mon May 22 11:15:33 2017 removing 5483413 relations and 3483413 ideals in 2000000 cliques
  82. Mon May 22 11:15:36 2017 commencing in-memory singleton removal
  83. Mon May 22 11:15:44 2017 begin with 127576287 relations and 95365389 unique ideals
  84. Mon May 22 11:16:45 2017 reduce to 127422255 relations and 91725717 ideals in 6 passes
  85. Mon May 22 11:16:45 2017 max relations containing the same ideal: 171
  86. Mon May 22 11:17:25 2017 removing 5420822 relations and 3420822 ideals in 2000000 cliques
  87. Mon May 22 11:17:28 2017 commencing in-memory singleton removal
  88. Mon May 22 11:17:35 2017 begin with 122001433 relations and 91725717 unique ideals
  89. Mon May 22 11:18:20 2017 reduce to 121848363 relations and 88149493 ideals in 6 passes
  90. Mon May 22 11:18:20 2017 max relations containing the same ideal: 167
  91. Mon May 22 11:18:57 2017 removing 5369593 relations and 3369593 ideals in 2000000 cliques
  92. Mon May 22 11:19:01 2017 commencing in-memory singleton removal
  93. Mon May 22 11:19:08 2017 begin with 116478770 relations and 88149493 unique ideals
  94. Mon May 22 11:19:51 2017 reduce to 116325865 relations and 84624557 ideals in 6 passes
  95. Mon May 22 11:19:51 2017 max relations containing the same ideal: 160
  96. Mon May 22 11:20:27 2017 removing 5326401 relations and 3326401 ideals in 2000000 cliques
  97. Mon May 22 11:20:30 2017 commencing in-memory singleton removal
  98. Mon May 22 11:20:36 2017 begin with 110999464 relations and 84624557 unique ideals
  99. Mon May 22 11:21:11 2017 reduce to 110843602 relations and 81139702 ideals in 5 passes
  100. Mon May 22 11:21:11 2017 max relations containing the same ideal: 156
  101. Mon May 22 11:21:45 2017 removing 5291834 relations and 3291834 ideals in 2000000 cliques
  102. Mon May 22 11:21:48 2017 commencing in-memory singleton removal
  103. Mon May 22 11:21:54 2017 begin with 105551768 relations and 81139702 unique ideals
  104. Mon May 22 11:22:26 2017 reduce to 105393372 relations and 77686770 ideals in 5 passes
  105. Mon May 22 11:22:26 2017 max relations containing the same ideal: 153
  106. Mon May 22 11:22:59 2017 removing 5266303 relations and 3266303 ideals in 2000000 cliques
  107. Mon May 22 11:23:01 2017 commencing in-memory singleton removal
  108. Mon May 22 11:23:07 2017 begin with 100127069 relations and 77686770 unique ideals
  109. Mon May 22 11:23:37 2017 reduce to 99965719 relations and 74256249 ideals in 5 passes
  110. Mon May 22 11:23:37 2017 max relations containing the same ideal: 149
  111. Mon May 22 11:24:09 2017 removing 5242408 relations and 3242408 ideals in 2000000 cliques
  112. Mon May 22 11:24:11 2017 commencing in-memory singleton removal
  113. Mon May 22 11:24:16 2017 begin with 94723311 relations and 74256249 unique ideals
  114. Mon May 22 11:24:45 2017 reduce to 94556857 relations and 70844221 ideals in 5 passes
  115. Mon May 22 11:24:45 2017 max relations containing the same ideal: 143
  116. Mon May 22 11:25:17 2017 removing 5226442 relations and 3226442 ideals in 2000000 cliques
  117. Mon May 22 11:25:20 2017 commencing in-memory singleton removal
  118. Mon May 22 11:25:25 2017 begin with 89330415 relations and 70844221 unique ideals
  119. Mon May 22 11:26:03 2017 reduce to 89156720 relations and 67440726 ideals in 6 passes
  120. Mon May 22 11:26:03 2017 max relations containing the same ideal: 141
  121. Mon May 22 11:26:36 2017 removing 5214460 relations and 3214460 ideals in 2000000 cliques
  122. Mon May 22 11:26:38 2017 commencing in-memory singleton removal
  123. Mon May 22 11:26:43 2017 begin with 83942260 relations and 67440726 unique ideals
  124. Mon May 22 11:27:13 2017 reduce to 83762846 relations and 64043203 ideals in 6 passes
  125. Mon May 22 11:27:13 2017 max relations containing the same ideal: 132
  126. Mon May 22 11:27:39 2017 removing 5208936 relations and 3208936 ideals in 2000000 cliques
  127. Mon May 22 11:27:41 2017 commencing in-memory singleton removal
  128. Mon May 22 11:27:45 2017 begin with 78553910 relations and 64043203 unique ideals
  129. Mon May 22 11:28:09 2017 reduce to 78364689 relations and 60640789 ideals in 5 passes
  130. Mon May 22 11:28:09 2017 max relations containing the same ideal: 125
  131. Mon May 22 11:28:33 2017 removing 5204328 relations and 3204328 ideals in 2000000 cliques
  132. Mon May 22 11:28:35 2017 commencing in-memory singleton removal
  133. Mon May 22 11:28:39 2017 begin with 73160361 relations and 60640789 unique ideals
  134. Mon May 22 11:29:05 2017 reduce to 72960042 relations and 57231605 ideals in 6 passes
  135. Mon May 22 11:29:05 2017 max relations containing the same ideal: 118
  136. Mon May 22 11:29:29 2017 removing 5209417 relations and 3209417 ideals in 2000000 cliques
  137. Mon May 22 11:29:31 2017 commencing in-memory singleton removal
  138. Mon May 22 11:29:34 2017 begin with 67750625 relations and 57231605 unique ideals
  139. Mon May 22 11:29:58 2017 reduce to 67536425 relations and 53802811 ideals in 6 passes
  140. Mon May 22 11:29:58 2017 max relations containing the same ideal: 115
  141. Mon May 22 11:30:20 2017 removing 5215914 relations and 3215914 ideals in 2000000 cliques
  142. Mon May 22 11:30:22 2017 commencing in-memory singleton removal
  143. Mon May 22 11:30:25 2017 begin with 62320511 relations and 53802811 unique ideals
  144. Mon May 22 11:30:47 2017 reduce to 62089152 relations and 50349584 ideals in 6 passes
  145. Mon May 22 11:30:47 2017 max relations containing the same ideal: 109
  146. Mon May 22 11:31:07 2017 removing 5231211 relations and 3231211 ideals in 2000000 cliques
  147. Mon May 22 11:31:09 2017 commencing in-memory singleton removal
  148. Mon May 22 11:31:13 2017 begin with 56857941 relations and 50349584 unique ideals
  149. Mon May 22 11:31:33 2017 reduce to 56605586 relations and 46858975 ideals in 6 passes
  150. Mon May 22 11:31:33 2017 max relations containing the same ideal: 103
  151. Mon May 22 11:31:50 2017 removing 5257276 relations and 3257276 ideals in 2000000 cliques
  152. Mon May 22 11:31:52 2017 commencing in-memory singleton removal
  153. Mon May 22 11:31:55 2017 begin with 51348310 relations and 46858975 unique ideals
  154. Mon May 22 11:32:16 2017 reduce to 51066688 relations and 43311753 ideals in 7 passes
  155. Mon May 22 11:32:16 2017 max relations containing the same ideal: 93
  156. Mon May 22 11:32:32 2017 removing 5292893 relations and 3292893 ideals in 2000000 cliques
  157. Mon May 22 11:32:34 2017 commencing in-memory singleton removal
  158. Mon May 22 11:32:36 2017 begin with 45773795 relations and 43311753 unique ideals
  159. Mon May 22 11:32:55 2017 reduce to 45449561 relations and 39684032 ideals in 7 passes
  160. Mon May 22 11:32:55 2017 max relations containing the same ideal: 87
  161. Mon May 22 11:33:09 2017 removing 5351799 relations and 3351799 ideals in 2000000 cliques
  162. Mon May 22 11:33:11 2017 commencing in-memory singleton removal
  163. Mon May 22 11:33:13 2017 begin with 40097762 relations and 39684032 unique ideals
  164. Mon May 22 11:33:31 2017 reduce to 39713237 relations and 35933581 ideals in 8 passes
  165. Mon May 22 11:33:31 2017 max relations containing the same ideal: 82
  166. Mon May 22 11:33:44 2017 removing 5443356 relations and 3443356 ideals in 2000000 cliques
  167. Mon May 22 11:33:46 2017 commencing in-memory singleton removal
  168. Mon May 22 11:33:48 2017 begin with 34269881 relations and 35933581 unique ideals
  169. Mon May 22 11:34:01 2017 reduce to 33782088 relations and 31982427 ideals in 7 passes
  170. Mon May 22 11:34:01 2017 max relations containing the same ideal: 74
  171. Mon May 22 11:34:12 2017 removing 2406387 relations and 1674263 ideals in 732124 cliques
  172. Mon May 22 11:34:13 2017 commencing in-memory singleton removal
  173. Mon May 22 11:34:15 2017 begin with 31375701 relations and 31982427 unique ideals
  174. Mon May 22 11:34:27 2017 reduce to 31229199 relations and 30158698 ideals in 7 passes
  175. Mon May 22 11:34:27 2017 max relations containing the same ideal: 67
  176. Mon May 22 11:34:42 2017 relations with 0 large ideals: 17602
  177. Mon May 22 11:34:42 2017 relations with 1 large ideals: 22025
  178. Mon May 22 11:34:42 2017 relations with 2 large ideals: 288829
  179. Mon May 22 11:34:42 2017 relations with 3 large ideals: 1568469
  180. Mon May 22 11:34:42 2017 relations with 4 large ideals: 4524105
  181. Mon May 22 11:34:42 2017 relations with 5 large ideals: 7726290
  182. Mon May 22 11:34:42 2017 relations with 6 large ideals: 8462674
  183. Mon May 22 11:34:42 2017 relations with 7+ large ideals: 8619205
  184. Mon May 22 11:34:42 2017 commencing 2-way merge
  185. Mon May 22 11:34:55 2017 reduce to 21887710 relation sets and 20817209 unique ideals
  186. Mon May 22 11:34:55 2017 commencing full merge
  187. Mon May 22 11:41:32 2017 memory use: 2561.1 MB
  188. Mon May 22 11:41:34 2017 found 9325699 cycles, need 9299409
  189. Mon May 22 11:41:36 2017 weight of 9299409 cycles is about 1302556238 (140.07/cycle)
  190. Mon May 22 11:41:36 2017 distribution of cycle lengths:
  191. Mon May 22 11:41:36 2017 1 relations: 189587
  192. Mon May 22 11:41:36 2017 2 relations: 376767
  193. Mon May 22 11:41:36 2017 3 relations: 505349
  194. Mon May 22 11:41:36 2017 4 relations: 574449
  195. Mon May 22 11:41:36 2017 5 relations: 628418
  196. Mon May 22 11:41:36 2017 6 relations: 654517
  197. Mon May 22 11:41:36 2017 7 relations: 671306
  198. Mon May 22 11:41:36 2017 8 relations: 658924
  199. Mon May 22 11:41:36 2017 9 relations: 636358
  200. Mon May 22 11:41:36 2017 10+ relations: 4403734
  201. Mon May 22 11:41:36 2017 heaviest cycle: 28 relations
  202. Mon May 22 11:41:37 2017 commencing cycle optimization
  203. Mon May 22 11:41:55 2017 start with 92646944 relations
  204. Mon May 22 11:45:11 2017 pruned 5708567 relations
  205. Mon May 22 11:45:11 2017 memory use: 2244.5 MB
  206. Mon May 22 11:45:11 2017 distribution of cycle lengths:
  207. Mon May 22 11:45:11 2017 1 relations: 189587
  208. Mon May 22 11:45:11 2017 2 relations: 388880
  209. Mon May 22 11:45:11 2017 3 relations: 530490
  210. Mon May 22 11:45:11 2017 4 relations: 606840
  211. Mon May 22 11:45:11 2017 5 relations: 671317
  212. Mon May 22 11:45:11 2017 6 relations: 700991
  213. Mon May 22 11:45:11 2017 7 relations: 723608
  214. Mon May 22 11:45:11 2017 8 relations: 709136
  215. Mon May 22 11:45:11 2017 9 relations: 685013
  216. Mon May 22 11:45:11 2017 10+ relations: 4093547
  217. Mon May 22 11:45:11 2017 heaviest cycle: 28 relations
  218. Mon May 22 11:45:24 2017 RelProcTime: 9886
  219. Mon May 22 11:45:24 2017
  220. Mon May 22 11:45:24 2017 commencing linear algebra
  221. Mon May 22 11:45:28 2017 read 9299409 cycles
  222. Mon May 22 11:45:48 2017 cycles contain 30770845 unique relations
  223. Mon May 22 11:48:58 2017 read 30770845 relations
  224. Mon May 22 11:49:44 2017 using 20 quadratic characters above 4294917295
  225. Mon May 22 11:51:45 2017 building initial matrix
  226. Mon May 22 11:57:55 2017 memory use: 3987.2 MB
  227. Mon May 22 11:57:59 2017 read 9299409 cycles
  228. Mon May 22 11:58:00 2017 matrix is 9299232 x 9299409 (4900.1 MB) with weight 1419645148 (152.66/col)
  229. Mon May 22 11:58:00 2017 sparse part has weight 1182245929 (127.13/col)
  230. Mon May 22 11:59:58 2017 filtering completed in 2 passes
  231. Mon May 22 12:00:00 2017 matrix is 9299179 x 9299356 (4900.1 MB) with weight 1419643356 (152.66/col)
  232. Mon May 22 12:00:00 2017 sparse part has weight 1182245505 (127.13/col)
  233. Mon May 22 12:00:43 2017 matrix starts at (0, 0)
  234. Mon May 22 12:00:44 2017 matrix is 9299179 x 9299356 (4900.1 MB) with weight 1419643356 (152.66/col)
  235. Mon May 22 12:00:44 2017 sparse part has weight 1182245505 (127.13/col)
  236. Mon May 22 12:00:44 2017 saving the first 48 matrix rows for later
  237. Mon May 22 12:00:46 2017 matrix includes 64 packed rows
  238. Mon May 22 12:00:47 2017 matrix is 9299131 x 9299356 (4706.7 MB) with weight 1233529176 (132.65/col)
  239. Mon May 22 12:00:47 2017 sparse part has weight 1140833351 (122.68/col)
  240. Mon May 22 12:00:47 2017 using block size 8192 and superblock size 589824 for processor cache size 6144 kB
  241. Mon May 22 12:01:30 2017 commencing Lanczos iteration (4 threads)
  242. Mon May 22 12:01:30 2017 memory use: 3986.8 MB
  243. Mon May 22 12:02:17 2017 linear algebra at 0.0%, ETA 78h34m
  244. Mon May 22 12:02:32 2017 checkpointing every 120000 dimensions
  245. Thu May 25 02:11:10 2017 lanczos halted after 147061 iterations (dim = 9299128)
  246. Thu May 25 02:11:28 2017 recovered 38 nontrivial dependencies
  247. Thu May 25 02:11:28 2017 BLanczosTime: 224764
  248. Thu May 25 02:11:28 2017
  249. Thu May 25 02:11:28 2017 commencing square root phase
  250. Thu May 25 02:11:28 2017 handling dependencies 1 to 64
  251. Thu May 25 02:11:28 2017 reading relations for dependency 1
  252. Thu May 25 02:11:29 2017 read 4647914 cycles
  253. Thu May 25 02:11:37 2017 cycles contain 15381850 unique relations
  254. Thu May 25 02:14:15 2017 read 15381850 relations
  255. Thu May 25 02:15:07 2017 multiplying 15381850 relations
  256. Thu May 25 02:22:15 2017 multiply complete, coefficients have about 435.46 million bits
  257. Thu May 25 02:22:16 2017 initial square root is modulo 65096351
  258. Thu May 25 02:30:31 2017 found factor: 109735561309304560221463133474329535600764091143693568715954505671461
  259. Thu May 25 02:30:31 2017 reading relations for dependency 2
  260. Thu May 25 02:30:32 2017 read 4644745 cycles
  261. Thu May 25 02:30:40 2017 cycles contain 15375380 unique relations
  262. Thu May 25 02:33:10 2017 read 15375380 relations
  263. Thu May 25 02:34:02 2017 multiplying 15375380 relations
  264. Thu May 25 02:41:11 2017 multiply complete, coefficients have about 435.28 million bits
  265. Thu May 25 02:41:13 2017 initial square root is modulo 64609981
  266. Thu May 25 02:49:28 2017 sqrtTime: 2280
  267. Thu May 25 02:49:28 2017 p69 factor: 109735561309304560221463133474329535600764091143693568715954505671461
  268. Thu May 25 02:49:28 2017 p71 factor: 67752105415300838924282204064992365878065752425147730800062519612265101
  269. Thu May 25 02:49:28 2017 p72 factor: 418953001977940720655803018952893507752913636124211978751654299380920009
  270. Thu May 25 02:49:28 2017 elapsed time 65:48:53
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