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[QUOTE=jasonp;116673]
It's up to you if you want to make the change and start over, or take a chance and just keep going.[/QUOTE] The relations are still being converted from CWI format; they should be done literally any minute. I'll make the change and recompile before starting the run. Thanks for looking into this so quickly! Greg |
[QUOTE=math_uu;116671]you have two GNFS line sieve program (GGNFS and MSIEVE),can you explain the difference? block sieve and bucket sort sieve?[/QUOTE]
Both line sievers internally use bucket sorting and sieve a block at a time, although the implementation details are very different. The line siever in msieve is much more sophisticated and includes a full resieving implementation for factoring promising relations. [QUOTE] EDIT: Msieve can be downloaded at [URL]http://www.boo.net/~jasonp/qs.html[/URL][/QUOTE] Um, that's my web page :) |
The postprocessing for the NFSNET factorization of the 221-digit Cunningham composite 6,284+ was completed by msieve. Block Lanczos on the matrix of size 4633402 x 4633645 with weight 306917353 took 4.5 days on a 2.4 GHz Opteron. The factors were found on the first dependency. The total postprocessing time was 4.9 days.
Greg [CODE]Fri Oct 19 02:12:43 2007 Msieve v. 1.28 Fri Oct 19 02:12:43 2007 random seeds: 8aff3a48 dbfa0fc2 Fri Oct 19 02:12:43 2007 factoring 81189990518323874680236482840546923572638822 5624215739246271488477157204296630159167017176300547812680769096672103530797725091062178738782565380956109871414308403695233 (168 digits) Fri Oct 19 02:12:43 2007 commencing number field sieve (168-digit input) Fri Oct 19 02:12:43 2007 R0: -3742042951225759540014535187298779136 Fri Oct 19 02:12:43 2007 R1: 1 Fri Oct 19 02:12:43 2007 A0: 1 Fri Oct 19 02:12:43 2007 A1: 0 Fri Oct 19 02:12:43 2007 A2: 0 Fri Oct 19 02:12:43 2007 A3: 0 Fri Oct 19 02:12:43 2007 A4: 0 Fri Oct 19 02:12:43 2007 A5: 0 Fri Oct 19 02:12:43 2007 A6: 36 Fri Oct 19 02:12:43 2007 size score = 9.133584e-11, Murphy alpha = 0.946753, combined = 6.968900e-11 Fri Oct 19 02:19:45 2007 restarting with 119312943 relations Fri Oct 19 02:19:45 2007 generating factor base Fri Oct 19 02:20:25 2007 factor base complete: Fri Oct 19 02:20:25 2007 3001134 rational roots (max prime = 49999991) Fri Oct 19 02:20:25 2007 2998210 algebraic roots (max prime = 49999897) Fri Oct 19 02:20:27 2007 added 249582 free relations Fri Oct 19 02:20:27 2007 Fri Oct 19 02:20:27 2007 commencing relation filtering Fri Oct 19 02:20:27 2007 commencing duplicate removal, pass 1 Fri Oct 19 02:20:42 2007 error -10 reading relation 658119 Fri Oct 19 02:20:48 2007 error -14 reading relation 1262261 Fri Oct 19 02:20:48 2007 error -14 reading relation 1276888 Fri Oct 19 02:20:48 2007 error -14 reading relation 1281127 Fri Oct 19 02:20:48 2007 error -14 reading relation 1282576 Fri Oct 19 02:20:48 2007 error -8 reading relation 1285610 Fri Oct 19 02:20:49 2007 error -14 reading relation 1301551 Fri Oct 19 02:20:49 2007 error -1 reading relation 1315424 Fri Oct 19 02:20:49 2007 error -14 reading relation 1315665 Fri Oct 19 02:20:54 2007 error -10 reading relation 1910606 Fri Oct 19 02:20:54 2007 error -4 reading relation 1921958 Fri Oct 19 02:20:54 2007 error -14 reading relation 1940451 Fri Oct 19 02:20:54 2007 error -4 reading relation 1946318 Fri Oct 19 02:23:05 2007 error -10 reading relation 16993845 Fri Oct 19 02:23:05 2007 error -14 reading relation 16997897 Fri Oct 19 02:23:05 2007 error -8 reading relation 17005652 Fri Oct 19 02:23:05 2007 error -4 reading relation 17017522 Fri Oct 19 02:23:06 2007 error -14 reading relation 17063967 Fri Oct 19 02:23:06 2007 error -10 reading relation 17067059 Fri Oct 19 02:23:06 2007 error -14 reading relation 17079074 Fri Oct 19 02:23:06 2007 error -14 reading relation 17095601 Fri Oct 19 02:24:23 2007 error -14 reading relation 26001087 Fri Oct 19 02:24:25 2007 error -14 reading relation 26167257 Fri Oct 19 02:24:56 2007 error -10 reading relation 29643314 Fri Oct 19 02:25:01 2007 error -14 reading relation 30313915 Fri Oct 19 02:25:01 2007 error -8 reading relation 30322556 Fri Oct 19 02:25:01 2007 error -4 reading relation 30336701 Fri Oct 19 02:25:01 2007 error -10 reading relation 30346501 Fri Oct 19 02:25:02 2007 error -10 reading relation 30354503 Fri Oct 19 02:25:02 2007 error -1 reading relation 30362707 Fri Oct 19 02:25:06 2007 error -10 reading relation 30832969 Fri Oct 19 02:25:06 2007 error -14 reading relation 30835180 Fri Oct 19 02:25:06 2007 error -8 reading relation 30842868 Fri Oct 19 02:25:06 2007 error -14 reading relation 30853519 Fri Oct 19 02:25:06 2007 error -4 reading relation 30860516 Fri Oct 19 02:25:06 2007 error -14 reading relation 30870977 Fri Oct 19 02:25:06 2007 error -4 reading relation 30876832 Fri Oct 19 02:25:06 2007 error -14 reading relation 30882651 Fri Oct 19 02:25:06 2007 error -4 reading relation 30886191 Fri Oct 19 02:25:06 2007 error -14 reading relation 30896259 Fri Oct 19 02:25:07 2007 error -10 reading relation 30903942 Fri Oct 19 02:25:07 2007 error -14 reading relation 30912311 Fri Oct 19 02:25:07 2007 error -14 reading relation 30917961 Fri Oct 19 02:25:07 2007 error -10 reading relation 30923061 Fri Oct 19 02:25:07 2007 error -10 reading relation 30929091 Fri Oct 19 02:25:07 2007 error -8 reading relation 30939672 Fri Oct 19 02:25:07 2007 error -14 reading relation 30943717 Fri Oct 19 02:25:07 2007 error -8 reading relation 30952226 Fri Oct 19 02:25:07 2007 error -8 reading relation 30952906 Fri Oct 19 02:25:07 2007 error -14 reading relation 30959275 Fri Oct 19 02:25:07 2007 error -14 reading relation 30971910 Fri Oct 19 02:25:07 2007 error -1 reading relation 30972350 Fri Oct 19 02:25:07 2007 error -10 reading relation 30972861 Fri Oct 19 02:25:07 2007 error -14 reading relation 30973303 Fri Oct 19 02:25:07 2007 error -14 reading relation 30974052 Fri Oct 19 02:25:07 2007 error -1 reading relation 30974697 Fri Oct 19 02:25:07 2007 error -8 reading relation 30986754 Fri Oct 19 02:25:07 2007 error -10 reading relation 30987128 Fri Oct 19 02:25:11 2007 error -10 reading relation 31405086 Fri Oct 19 02:25:11 2007 error -8 reading relation 31416524 Fri Oct 19 02:25:12 2007 error -4 reading relation 31433862 Fri Oct 19 02:25:12 2007 error -8 reading relation 31438932 Fri Oct 19 02:26:52 2007 error -8 reading relation 43180117 Fri Oct 19 02:26:57 2007 error -14 reading relation 43723609 Fri Oct 19 02:26:57 2007 error -10 reading relation 43729378 Fri Oct 19 02:26:57 2007 error -10 reading relation 43742389 Fri Oct 19 02:26:57 2007 error -8 reading relation 43747277 Fri Oct 19 02:26:57 2007 error -1 reading relation 43763836 Fri Oct 19 02:26:57 2007 error -8 reading relation 43767901 Fri Oct 19 02:26:57 2007 error -14 reading relation 43770410 Fri Oct 19 02:26:57 2007 error -14 reading relation 43775667 Fri Oct 19 02:27:10 2007 error -10 reading relation 45127585 Fri Oct 19 02:27:28 2007 error -10 reading relation 47283084 Fri Oct 19 02:28:03 2007 error -14 reading relation 51235074 Fri Oct 19 02:29:45 2007 error -10 reading relation 62386972 Fri Oct 19 02:30:18 2007 error -14 reading relation 66232080 Fri Oct 19 02:30:18 2007 error -10 reading relation 66240297 Fri Oct 19 02:30:22 2007 error -14 reading relation 66668070 Fri Oct 19 02:30:22 2007 error -14 reading relation 66688423 Fri Oct 19 02:30:22 2007 error -14 reading relation 66689605 Fri Oct 19 02:30:22 2007 error -10 reading relation 66691025 Fri Oct 19 02:30:22 2007 error -14 reading relation 66698150 Fri Oct 19 02:30:22 2007 error -10 reading relation 66706828 Fri Oct 19 02:30:22 2007 error -10 reading relation 66707030 Fri Oct 19 02:30:25 2007 error -10 reading relation 67102511 Fri Oct 19 02:30:25 2007 error -4 reading relation 67109198 Fri Oct 19 02:30:25 2007 error -14 reading relation 67118962 Fri Oct 19 02:32:17 2007 error -10 reading relation 80220171 Fri Oct 19 02:32:17 2007 error -10 reading relation 80220305 Fri Oct 19 02:32:17 2007 error -14 reading relation 80237143 Fri Oct 19 02:32:17 2007 error -8 reading relation 80244558 Fri Oct 19 02:32:35 2007 error -14 reading relation 82407802 Fri Oct 19 02:32:35 2007 error -4 reading relation 82412653 Fri Oct 19 02:32:36 2007 error -8 reading relation 82544482 Fri Oct 19 02:32:36 2007 error -10 reading relation 82546300 Fri Oct 19 02:32:53 2007 error -14 reading relation 84514750 Fri Oct 19 02:33:06 2007 error -8 reading relation 86036154 Fri Oct 19 02:33:12 2007 error -8 reading relation 86691369 Fri Oct 19 02:33:12 2007 error -10 reading relation 86699300 Fri Oct 19 02:33:12 2007 error -10 reading relation 86708346 Fri Oct 19 02:33:12 2007 error -14 reading relation 86715686 Fri Oct 19 02:33:12 2007 error -10 reading relation 86731136 Fri Oct 19 02:33:12 2007 error -14 reading relation 86738895 Fri Oct 19 02:33:17 2007 error -14 reading relation 87341656 Fri Oct 19 02:33:17 2007 error -4 reading relation 87350171 Fri Oct 19 02:33:17 2007 error -8 reading relation 87354413 Fri Oct 19 02:33:17 2007 error -10 reading relation 87360296 Fri Oct 19 02:33:58 2007 error -10 reading relation 92270914 Fri Oct 19 02:34:48 2007 error -14 reading relation 98197536 Fri Oct 19 02:35:17 2007 error -14 reading relation 101287113 Fri Oct 19 02:35:31 2007 error -10 reading relation 102992353 Fri Oct 19 02:35:43 2007 error -14 reading relation 104345965 Fri Oct 19 02:35:57 2007 error -14 reading relation 106102421 Fri Oct 19 02:36:20 2007 error -14 reading relation 109008248 Fri Oct 19 02:37:03 2007 error -10 reading relation 114012725 Fri Oct 19 02:37:30 2007 error -14 reading relation 117049007 Fri Oct 19 02:37:34 2007 error -14 reading relation 117507142 Fri Oct 19 02:37:45 2007 error -14 reading relation 118876655 Fri Oct 19 02:38:01 2007 found 43198404 hash collisions in 119562407 relations Fri Oct 19 02:38:01 2007 commencing duplicate removal, pass 2 Fri Oct 19 02:49:17 2007 found 29712620 duplicates and 89849787 unique relations Fri Oct 19 02:49:17 2007 memory use: 973.5 MB Fri Oct 19 02:49:48 2007 ignoring smallest 3004744 rational and 3001872 algebraic ideals Fri Oct 19 02:49:48 2007 filtering rational ideals above 50065061 Fri Oct 19 02:49:48 2007 filtering algebraic ideals above 50065061 Fri Oct 19 02:49:48 2007 need 10211247 more relations than ideals Fri Oct 19 02:49:48 2007 commencing singleton removal, pass 1 Fri Oct 19 03:05:38 2007 relations with 0 large ideals: 2078815 Fri Oct 19 03:05:38 2007 relations with 1 large ideals: 11449432 Fri Oct 19 03:05:38 2007 relations with 2 large ideals: 28624378 Fri Oct 19 03:05:38 2007 relations with 3 large ideals: 32959807 Fri Oct 19 03:05:38 2007 relations with 4 large ideals: 14737355 Fri Oct 19 03:05:38 2007 relations with 5 large ideals: 0 Fri Oct 19 03:05:38 2007 relations with 6 large ideals: 0 Fri Oct 19 03:05:38 2007 relations with 7+ large ideals: 0 Fri Oct 19 03:05:38 2007 89849787 relations and about 60209928 large ideals Fri Oct 19 03:05:38 2007 commencing singleton removal, pass 2 Fri Oct 19 03:32:03 2007 found 16135688 singletons Fri Oct 19 03:32:03 2007 current dataset: 73714099 relations and about 42861555 large ideals Fri Oct 19 03:32:03 2007 commencing singleton removal, pass 3 Fri Oct 19 03:49:56 2007 relations with 0 large ideals: 2078815 Fri Oct 19 03:49:56 2007 relations with 1 large ideals: 10562540 Fri Oct 19 03:49:56 2007 relations with 2 large ideals: 24378086 Fri Oct 19 03:49:56 2007 relations with 3 large ideals: 25936203 Fri Oct 19 03:49:56 2007 relations with 4 large ideals: 10758455 Fri Oct 19 03:49:56 2007 relations with 5 large ideals: 0 Fri Oct 19 03:49:56 2007 relations with 6 large ideals: 0 Fri Oct 19 03:49:56 2007 relations with 7+ large ideals: 0 Fri Oct 19 03:49:56 2007 73714099 relations and about 54144664 large ideals Fri Oct 19 03:49:56 2007 commencing singleton removal, pass 4 Fri Oct 19 04:05:52 2007 found 12815635 singletons Fri Oct 19 04:05:53 2007 current dataset: 60898464 relations and about 40397932 large ideals Fri Oct 19 04:05:54 2007 commencing singleton removal, pass 5 Fri Oct 19 04:20:54 2007 found 2759641 singletons Fri Oct 19 04:20:54 2007 current dataset: 58138823 relations and about 37586643 large ideals Fri Oct 19 04:20:54 2007 commencing singleton removal, pass 6 Fri Oct 19 04:36:09 2007 found 556145 singletons Fri Oct 19 04:36:09 2007 current dataset: 57582678 relations and about 37028287 large ideals Fri Oct 19 04:36:11 2007 commencing singleton removal, pass 7 Fri Oct 19 04:52:00 2007 found 106624 singletons Fri Oct 19 04:52:00 2007 current dataset: 57476054 relations and about 36921565 large ideals Fri Oct 19 04:52:00 2007 commencing singleton removal, final pass Fri Oct 19 05:05:39 2007 memory use: 2116.1 MB Fri Oct 19 05:05:40 2007 commencing in-memory singleton removal Fri Oct 19 05:05:46 2007 begin with 57476054 relations and 42552145 unique ideals Fri Oct 19 05:07:17 2007 reduce to 51073443 relations and 36002651 ideals in 14 passes Fri Oct 19 05:07:17 2007 max relations containing the same ideal: 26 Fri Oct 19 05:07:48 2007 removing 3128630 relations and 2728630 ideals in 400000 cliques Fri Oct 19 05:07:51 2007 commencing in-memory singleton removal Fri Oct 19 05:07:56 2007 begin with 47944813 relations and 36002651 unique ideals Fri Oct 19 05:08:48 2007 reduce to 47843202 relations and 33171506 ideals in 9 passes Fri Oct 19 05:08:48 2007 max relations containing the same ideal: 26 Fri Oct 19 05:09:16 2007 removing 2313771 relations and 1913771 ideals in 400000 cliques Fri Oct 19 05:09:18 2007 commencing in-memory singleton removal Fri Oct 19 05:09:23 2007 begin with 45529431 relations and 33171506 unique ideals Fri Oct 19 05:10:01 2007 reduce to 45465867 relations and 31193636 ideals in 7 passes Fri Oct 19 05:10:01 2007 max relations containing the same ideal: 25 Fri Oct 19 05:10:27 2007 removing 2050098 relations and 1650098 ideals in 400000 cliques Fri Oct 19 05:10:29 2007 commencing in-memory singleton removal Fri Oct 19 05:10:33 2007 begin with 43415769 relations and 31193636 unique ideals Fri Oct 19 05:11:03 2007 reduce to 43363147 relations and 29490505 ideals in 6 passes Fri Oct 19 05:11:03 2007 max relations containing the same ideal: 23 Fri Oct 19 05:11:28 2007 removing 1899904 relations and 1499904 ideals in 400000 cliques Fri Oct 19 05:11:30 2007 commencing in-memory singleton removal Fri Oct 19 05:11:34 2007 begin with 41463243 relations and 29490505 unique ideals Fri Oct 19 05:12:02 2007 reduce to 41414733 relations and 27941734 ideals in 6 passes Fri Oct 19 05:12:02 2007 max relations containing the same ideal: 22 Fri Oct 19 05:12:25 2007 removing 1794665 relations and 1394665 ideals in 400000 cliques Fri Oct 19 05:12:27 2007 commencing in-memory singleton removal Fri Oct 19 05:12:31 2007 begin with 39620068 relations and 27941734 unique ideals Fri Oct 19 05:13:06 2007 reduce to 39574542 relations and 26501167 ideals in 8 passes Fri Oct 19 05:13:06 2007 max relations containing the same ideal: 22 Fri Oct 19 05:13:28 2007 removing 1721437 relations and 1321437 ideals in 400000 cliques Fri Oct 19 05:13:30 2007 commencing in-memory singleton removal Fri Oct 19 05:13:33 2007 begin with 37853105 relations and 26501167 unique ideals Fri Oct 19 05:13:58 2007 reduce to 37808705 relations and 25134991 ideals in 6 passes Fri Oct 19 05:13:58 2007 max relations containing the same ideal: 21 Fri Oct 19 05:14:19 2007 removing 1659026 relations and 1259026 ideals in 400000 cliques Fri Oct 19 05:14:20 2007 commencing in-memory singleton removal Fri Oct 19 05:14:24 2007 begin with 36149679 relations and 25134991 unique ideals Fri Oct 19 05:14:44 2007 reduce to 36106332 relations and 23832256 ideals in 5 passes Fri Oct 19 05:14:44 2007 max relations containing the same ideal: 21 Fri Oct 19 05:15:03 2007 removing 1609637 relations and 1209637 ideals in 400000 cliques Fri Oct 19 05:15:05 2007 commencing in-memory singleton removal Fri Oct 19 05:15:08 2007 begin with 34496695 relations and 23832256 unique ideals Fri Oct 19 05:15:30 2007 reduce to 34453060 relations and 22578573 ideals in 6 passes Fri Oct 19 05:15:30 2007 max relations containing the same ideal: 21 Fri Oct 19 05:15:48 2007 removing 1583785 relations and 1183785 ideals in 400000 cliques Fri Oct 19 05:15:50 2007 commencing in-memory singleton removal Fri Oct 19 05:15:53 2007 begin with 32869275 relations and 22578573 unique ideals Fri Oct 19 05:16:14 2007 reduce to 32827146 relations and 21352242 ideals in 6 passes Fri Oct 19 05:16:14 2007 max relations containing the same ideal: 21 Fri Oct 19 05:16:31 2007 removing 1533063 relations and 1133063 ideals in 400000 cliques Fri Oct 19 05:16:32 2007 commencing in-memory singleton removal Fri Oct 19 05:16:35 2007 begin with 31294083 relations and 21352242 unique ideals Fri Oct 19 05:16:55 2007 reduce to 31247302 relations and 20171959 ideals in 6 passes Fri Oct 19 05:16:55 2007 max relations containing the same ideal: 21 Fri Oct 19 05:17:11 2007 removing 1512220 relations and 1112220 ideals in 400000 cliques Fri Oct 19 05:17:12 2007 commencing in-memory singleton removal Fri Oct 19 05:17:15 2007 begin with 29735082 relations and 20171959 unique ideals Fri Oct 19 05:17:33 2007 reduce to 29690138 relations and 19014311 ideals in 6 passes Fri Oct 19 05:17:33 2007 max relations containing the same ideal: 20 Fri Oct 19 05:17:48 2007 removing 1484774 relations and 1084774 ideals in 400000 cliques Fri Oct 19 05:17:50 2007 commencing in-memory singleton removal Fri Oct 19 05:17:52 2007 begin with 28205364 relations and 19014311 unique ideals Fri Oct 19 05:18:15 2007 reduce to 28160687 relations and 17884358 ideals in 8 passes Fri Oct 19 05:18:15 2007 max relations containing the same ideal: 19 Fri Oct 19 05:18:29 2007 removing 321326 relations and 256245 ideals in 65081 cliques Fri Oct 19 05:18:30 2007 commencing in-memory singleton removal Fri Oct 19 05:18:33 2007 begin with 27839361 relations and 17884358 unique ideals Fri Oct 19 05:18:43 2007 reduce to 27837635 relations and 17626384 ideals in 4 passes Fri Oct 19 05:18:43 2007 max relations containing the same ideal: 18 Fri Oct 19 05:18:48 2007 dataset has 70.0% excess relations Fri Oct 19 05:19:15 2007 ignoring smallest 2721527 rational and 2719088 algebraic ideals Fri Oct 19 05:19:15 2007 filtering rational ideals above 45058554 Fri Oct 19 05:19:15 2007 filtering algebraic ideals above 45058554 Fri Oct 19 05:19:15 2007 need 9190125 more relations than ideals Fri Oct 19 05:19:15 2007 commencing singleton removal, final pass Fri Oct 19 05:28:28 2007 memory use: 835.6 MB Fri Oct 19 05:28:28 2007 commencing in-memory singleton removal Fri Oct 19 05:28:31 2007 begin with 27837635 relations and 18191764 unique ideals Fri Oct 19 05:28:44 2007 reduce to 27831435 relations and 18185560 ideals in 5 passes Fri Oct 19 05:28:44 2007 max relations containing the same ideal: 30 Fri Oct 19 05:28:58 2007 removing 848808 relations and 620933 ideals in 227875 cliques Fri Oct 19 05:28:59 2007 commencing in-memory singleton removal Fri Oct 19 05:29:01 2007 begin with 26982627 relations and 18185560 unique ideals Fri Oct 19 05:29:17 2007 reduce to 26965091 relations and 17546938 ideals in 6 passes Fri Oct 19 05:29:17 2007 max relations containing the same ideal: 30 Fri Oct 19 05:29:30 2007 removing 843787 relations and 615912 ideals in 227875 cliques Fri Oct 19 05:29:31 2007 commencing in-memory singleton removal Fri Oct 19 05:29:33 2007 begin with 26121304 relations and 17546938 unique ideals Fri Oct 19 05:29:48 2007 reduce to 26104027 relations and 16913610 ideals in 6 passes Fri Oct 19 05:29:48 2007 max relations containing the same ideal: 29 Fri Oct 19 05:30:01 2007 removing 2216 relations and 1925 ideals in 291 cliques Fri Oct 19 05:30:02 2007 commencing in-memory singleton removal Fri Oct 19 05:30:04 2007 begin with 26101811 relations and 16913610 unique ideals Fri Oct 19 05:30:06 2007 reduce to 26101811 relations and 16911685 ideals in 1 passes Fri Oct 19 05:30:06 2007 max relations containing the same ideal: 29 Fri Oct 19 05:30:10 2007 dataset has 53.0% excess relations Fri Oct 19 05:30:34 2007 ignoring smallest 2436604 rational and 2434330 algebraic ideals Fri Oct 19 05:30:34 2007 filtering rational ideals above 40052048 Fri Oct 19 05:30:34 2007 filtering algebraic ideals above 40052048 Fri Oct 19 05:30:34 2007 need 7352100 more relations than ideals Fri Oct 19 05:30:34 2007 commencing singleton removal, final pass Fri Oct 19 05:39:36 2007 memory use: 666.1 MB Fri Oct 19 05:39:36 2007 commencing in-memory singleton removal Fri Oct 19 05:39:38 2007 begin with 26101811 relations and 17480953 unique ideals Fri Oct 19 05:39:52 2007 reduce to 26097519 relations and 17476660 ideals in 5 passes Fri Oct 19 05:39:52 2007 max relations containing the same ideal: 30 Fri Oct 19 05:40:05 2007 removing 1375896 relations and 975896 ideals in 400000 cliques Fri Oct 19 05:40:07 2007 commencing in-memory singleton removal Fri Oct 19 05:40:09 2007 begin with 24721623 relations and 17476660 unique ideals Fri Oct 19 05:40:24 2007 reduce to 24672862 relations and 16451406 ideals in 6 passes Fri Oct 19 05:40:24 2007 max relations containing the same ideal: 27 Fri Oct 19 05:40:37 2007 removing 1427703 relations and 1027703 ideals in 400000 cliques Fri Oct 19 05:40:38 2007 commencing in-memory singleton removal Fri Oct 19 05:40:40 2007 begin with 23245159 relations and 16451406 unique ideals Fri Oct 19 05:40:54 2007 reduce to 23191473 relations and 15369252 ideals in 6 passes Fri Oct 19 05:40:54 2007 max relations containing the same ideal: 27 Fri Oct 19 05:41:06 2007 removing 1422951 relations and 1022951 ideals in 400000 cliques Fri Oct 19 05:41:07 2007 commencing in-memory singleton removal Fri Oct 19 05:41:09 2007 begin with 21768522 relations and 15369252 unique ideals Fri Oct 19 05:41:22 2007 reduce to 21712626 relations and 14289504 ideals in 6 passes Fri Oct 19 05:41:22 2007 max relations containing the same ideal: 27 Fri Oct 19 05:41:33 2007 removing 336188 relations and 265167 ideals in 71021 cliques Fri Oct 19 05:41:34 2007 commencing in-memory singleton removal Fri Oct 19 05:41:35 2007 begin with 21376438 relations and 14289504 unique ideals Fri Oct 19 05:41:46 2007 reduce to 21373935 relations and 14021828 ideals in 5 passes Fri Oct 19 05:41:46 2007 max relations containing the same ideal: 27 Fri Oct 19 05:41:49 2007 dataset has 22.4% excess relations Fri Oct 19 05:42:10 2007 ignoring smallest 2149354 rational and 2146304 algebraic ideals Fri Oct 19 05:42:10 2007 filtering rational ideals above 35045542 Fri Oct 19 05:42:10 2007 filtering algebraic ideals above 35045542 Fri Oct 19 05:42:10 2007 need 6487145 more relations than ideals Fri Oct 19 05:42:10 2007 commencing singleton removal, final pass Fri Oct 19 05:50:27 2007 memory use: 666.1 MB Fri Oct 19 05:50:27 2007 commencing in-memory singleton removal Fri Oct 19 05:50:29 2007 begin with 21373935 relations and 14596497 unique ideals Fri Oct 19 05:50:40 2007 reduce to 21367537 relations and 14590092 ideals in 5 passes Fri Oct 19 05:50:40 2007 max relations containing the same ideal: 28 Fri Oct 19 05:50:51 2007 removing 558925 relations and 413775 ideals in 145150 cliques Fri Oct 19 05:50:51 2007 commencing in-memory singleton removal Fri Oct 19 05:50:53 2007 begin with 20808612 relations and 14590092 unique ideals Fri Oct 19 05:51:04 2007 reduce to 20800196 relations and 14167860 ideals in 5 passes Fri Oct 19 05:51:04 2007 max relations containing the same ideal: 28 Fri Oct 19 05:51:14 2007 removing 536767 relations and 391617 ideals in 145150 cliques Fri Oct 19 05:51:15 2007 commencing in-memory singleton removal Fri Oct 19 05:51:17 2007 begin with 20263429 relations and 14167860 unique ideals Fri Oct 19 05:51:27 2007 reduce to 20254303 relations and 13767042 ideals in 5 passes Fri Oct 19 05:51:27 2007 max relations containing the same ideal: 28 Fri Oct 19 05:51:37 2007 removing 876 relations and 761 ideals in 115 cliques Fri Oct 19 05:51:38 2007 commencing in-memory singleton removal Fri Oct 19 05:51:39 2007 begin with 20253427 relations and 13767042 unique ideals Fri Oct 19 05:51:42 2007 reduce to 20253427 relations and 13766281 ideals in 1 passes Fri Oct 19 05:51:42 2007 max relations containing the same ideal: 28 Fri Oct 19 05:51:44 2007 dataset has 8.0% excess relations Fri Oct 19 05:51:46 2007 relations with 0 large ideals: 979181 Fri Oct 19 05:51:46 2007 relations with 1 large ideals: 3836006 Fri Oct 19 05:51:46 2007 relations with 2 large ideals: 6881487 Fri Oct 19 05:51:46 2007 relations with 3 large ideals: 5778223 Fri Oct 19 05:51:46 2007 relations with 4 large ideals: 2323969 Fri Oct 19 05:51:46 2007 relations with 5 large ideals: 381753 Fri Oct 19 05:51:46 2007 relations with 6 large ideals: 11793 Fri Oct 19 05:51:46 2007 relations with 7+ large ideals: 61015 Fri Oct 19 05:51:46 2007 commencing 2-way merge Fri Oct 19 05:52:00 2007 merged 6164730 relations Fri Oct 19 05:52:05 2007 reduce to 14088697 relation sets and 7601551 unique ideals Fri Oct 19 05:52:05 2007 commencing full merge Fri Oct 19 06:47:44 2007 found 7121167 cycles, need 4957358 Fri Oct 19 06:47:55 2007 weight of 4957358 cycles is about 294377133 (59.38/cycle) Fri Oct 19 06:47:56 2007 distribution of cycle lengths: Fri Oct 19 06:47:56 2007 1 relations: 1031297 Fri Oct 19 06:47:56 2007 2 relations: 580079 Fri Oct 19 06:47:56 2007 3 relations: 559518 Fri Oct 19 06:47:56 2007 4 relations: 536419 Fri Oct 19 06:47:56 2007 5 relations: 518040 Fri Oct 19 06:47:56 2007 6 relations: 489362 Fri Oct 19 06:47:56 2007 7 relations: 451358 Fri Oct 19 06:47:56 2007 8 relations: 397669 Fri Oct 19 06:47:56 2007 9 relations: 309324 Fri Oct 19 06:47:56 2007 10+ relations: 84292 Fri Oct 19 06:47:56 2007 heaviest cycle: 12 relations Fri Oct 19 06:47:56 2007 matrix not dense enough, retrying Fri Oct 19 06:47:57 2007 dataset has 8.0% excess relations Fri Oct 19 06:48:18 2007 ignoring smallest 1860152 rational and 1857190 algebraic ideals Fri Oct 19 06:48:18 2007 filtering rational ideals above 30039036 Fri Oct 19 06:48:18 2007 filtering algebraic ideals above 30039036 Fri Oct 19 06:48:18 2007 need 6487145 more relations than ideals Fri Oct 19 06:48:18 2007 commencing singleton removal, final pass Fri Oct 19 06:56:38 2007 memory use: 666.1 MB Fri Oct 19 06:56:38 2007 commencing in-memory singleton removal Fri Oct 19 06:56:40 2007 begin with 20253427 relations and 14344250 unique ideals Fri Oct 19 06:56:51 2007 reduce to 20249251 relations and 14340071 ideals in 5 passes Fri Oct 19 06:56:51 2007 max relations containing the same ideal: 30 Fri Oct 19 06:56:53 2007 dataset has -1.6% excess relations Fri Oct 19 06:56:55 2007 relations with 0 large ideals: 705105 Fri Oct 19 06:56:55 2007 relations with 1 large ideals: 2982110 Fri Oct 19 06:56:55 2007 relations with 2 large ideals: 6229552 Fri Oct 19 06:56:55 2007 relations with 3 large ideals: 6327338 Fri Oct 19 06:56:55 2007 relations with 4 large ideals: 3196626 Fri Oct 19 06:56:55 2007 relations with 5 large ideals: 693432 Fri Oct 19 06:56:55 2007 relations with 6 large ideals: 28651 Fri Oct 19 06:56:55 2007 relations with 7+ large ideals: 86437 Fri Oct 19 06:56:55 2007 commencing 2-way merge Fri Oct 19 06:57:08 2007 merged 6173757 relations Fri Oct 19 06:57:14 2007 reduce to 14075494 relation sets and 8166314 unique ideals Fri Oct 19 06:57:14 2007 commencing full merge Fri Oct 19 07:58:06 2007 found 6874574 cycles, need 4720514 Fri Oct 19 07:58:14 2007 weight of 4720514 cycles is about 307006353 (65.04/cycle) Fri Oct 19 07:58:15 2007 distribution of cycle lengths: Fri Oct 19 07:58:15 2007 1 relations: 794936 Fri Oct 19 07:58:15 2007 2 relations: 505942 Fri Oct 19 07:58:15 2007 3 relations: 512052 Fri Oct 19 07:58:15 2007 4 relations: 504411 Fri Oct 19 07:58:15 2007 5 relations: 497213 Fri Oct 19 07:58:15 2007 6 relations: 477742 Fri Oct 19 07:58:15 2007 7 relations: 450656 Fri Oct 19 07:58:15 2007 8 relations: 406825 Fri Oct 19 07:58:15 2007 9 relations: 346048 Fri Oct 19 07:58:15 2007 10+ relations: 224689 Fri Oct 19 07:58:15 2007 heaviest cycle: 12 relations Fri Oct 19 07:58:15 2007 commencing cycle optimization Fri Oct 19 08:19:49 2007 start with 22493571 relations Fri Oct 19 08:22:54 2007 pruned 571146 relations Fri Oct 19 08:22:56 2007 distribution of cycle lengths: Fri Oct 19 08:22:56 2007 1 relations: 794936 Fri Oct 19 08:22:56 2007 2 relations: 519884 Fri Oct 19 08:22:56 2007 3 relations: 533284 Fri Oct 19 08:22:56 2007 4 relations: 523837 Fri Oct 19 08:22:56 2007 5 relations: 522233 Fri Oct 19 08:22:56 2007 6 relations: 498835 Fri Oct 19 08:22:56 2007 7 relations: 464210 Fri Oct 19 08:22:56 2007 8 relations: 398485 Fri Oct 19 08:22:57 2007 9 relations: 303503 Fri Oct 19 08:22:57 2007 10+ relations: 161307 Fri Oct 19 08:22:57 2007 heaviest cycle: 12 relations Fri Oct 19 08:23:00 2007 Fri Oct 19 08:23:02 2007 commencing linear algebra Fri Oct 19 08:23:14 2007 factor base loaded: Fri Oct 19 08:23:14 2007 3001134 rational ideals (max prime = 49999991) Fri Oct 19 08:23:14 2007 2998210 algebraic ideals (max prime = 49999897) Fri Oct 19 08:23:15 2007 read 4720514 cycles Fri Oct 19 08:23:37 2007 cycles contain 13074004 unique relations Fri Oct 19 08:30:57 2007 read 13074004 relations Fri Oct 19 08:31:23 2007 using 32 quadratic characters above 1073740014 Fri Oct 19 08:40:55 2007 matrix is 4711626 x 4720514 with weight 409475570 (avg 86.74/col) Fri Oct 19 08:43:55 2007 filtering completed in 3 passes Fri Oct 19 08:43:57 2007 matrix is 4633450 x 4633645 with weight 403470863 (avg 87.07/col) Fri Oct 19 08:44:38 2007 saving the first 48 matrix rows for later Fri Oct 19 08:44:43 2007 matrix is 4633402 x 4633645 with weight 306917353 (avg 66.24/col) Fri Oct 19 08:44:44 2007 matrix includes 64 packed rows Fri Oct 19 08:44:44 2007 using block size 43690 for processor cache size 1024 kB Fri Oct 19 09:14:02 2007 commencing Lanczos iteration Tue Oct 23 21:47:16 2007 lanczos halted after 73269 iterations Tue Oct 23 21:47:40 2007 recovered 45 nontrivial dependencies Tue Oct 23 21:47:40 2007 Tue Oct 23 21:47:40 2007 commencing square root phase Tue Oct 23 21:47:40 2007 reading relations for dependency 1 Tue Oct 23 21:47:48 2007 read 2316875 cycles Tue Oct 23 21:47:57 2007 cycles contain 7751853 unique relations Tue Oct 23 21:55:02 2007 read 7751853 relations Tue Oct 23 21:56:11 2007 multiplying 10836684 relations Tue Oct 23 22:46:29 2007 multiply complete, coefficients have about 309.68 million bits Tue Oct 23 22:46:38 2007 initial square root is modulo 360391 Tue Oct 23 23:47:33 2007 prp69 factor: 555910000634197662765503723258626898712572755963073679357601281305609 Tue Oct 23 23:47:33 2007 prp100 factor: 1460488036295444672135442151657591624390265714559822646725589656189905643142544558329783709325745337 Tue Oct 23 23:47:33 2007 elapsed time 117:34:50 [/CODE] |
[QUOTE=jasonp;117235]Now available. Highlights include:
[/QUOTE] Two questions: 1.) I have got the sieving of a NFS factorization of a c114 almost ready (7.11M of 7.17M relations found) with 1.28. Can I switch to 1.29? 2.) Do you still plan to improve polynomial selection and / or implement a lattice siever - so that c120 factorizations become feasable (I mean: my c114 is almost out of range of the msieve sieving process)? |
[QUOTE=jasonp;117235]People are starting to throw NFSNET-size jobs at the NFS postprocessing[/QUOTE]
I guess that you could say that :) We (the NFSNet "people") are "throwing" actual NFSNet work at the post-processing. Thanks for the new additions. With our runs taking so long, the checkpointing feature is really needed. We have access to some powerful hardware, but not continuously for the week that even it will require to complete the task. By utilizing checkpoints, we can complete the calculation by using the more powerful machine on a part time basis rather than having to rely on a slower machine that can be dedicated on a continuous basis. |
@andi47: yes, the new version can perform all the same postprocessing that the previous version can do. Note that a C114 is easily within the capabilities of GGNFS to do all by itself. I still want to get to the polynomial selection and add lattice sieving, however right now the best use of my time is to forge ahead on the things that msieve already does well.
@wacky: Even non-NFSNET work is starting to get into the really big sizes (e.g. Tom's recent 205+ digit SNFS and 151 digit GNFS run). I'm especially interested in how well the linear algebra scales, since the threading implementation is fairly lackluster right now. |
I know that Wacky is preparing a lattice-sieving version of the NFSnet client, which ought to be able to do fantastic things; with the current line-sieve, the last time I looked (towards the end of 2,772+) I was getting 1/3 as many relations per second as all of NFSnet, with the same parameters, using four current-generation cores and gnfs-lasieve4I14e.
I'm currently doing 7,263- on six cores; 2 - 2.5 million relations per core per week, and I suspect I'll need around 80 million, which means it ought to be over by Christmas. I find myself tempted to buy a Q6600-based sieving machine most weeks - under £300 now - though have not yet succumbed. |
[QUOTE=fivemack;117340]I know that Wacky is preparing a lattice-sieving version of the NFSnet client, which ought to be able to do fantastic things; with the current line-sieve, the last time I looked (towards the end of 2,772+) I was getting 1/3 as many relations per second as all of NFSnet, with the same parameters, using four current-generation cores and gnfs-lasieve4I14e.
[/QUOTE] This timing confirms the recent experience with 6,284+, which finished way quick due to Greg's lattice siever contributions. Richard's fairly stingy with the nfsnet line-siever performance info (not to mention, selective about who hears what), but I gather that Lehigh's 2nd to U Gent; perhaps both around 30% each. My office pc counts as current, 1 P4 @ 3.1Ghz, then 15 dual cpu Macs, each cpu a bit slower than the 18 xeons, 32-bit 2.8Ghz. That's 30 cpus that were just installed last year; not sure whether that qualifies Macs as "current" or not. The 18 xeons/linux are due for replacement later this year, but were regarded as near top-of-the-line among 32-bit machines at the time, and (as mentioned) still sieve quicker per cpu than the new macs. Surely an apples-to-oranges comparison (so-to-speak), but the old CWI line-siever binaries (pre-RSA512, 1999?) sound way-out-of-line with current performance. Ah, Tom's 1/3 of the total nfsnet rate sounds like a four cores -to- fourty cpus comparison, for the same 1/3 rate. If anyone's qualified to offer Richard assistance, the potential returns would seem to be worth having. I'd be half willing to consider switching the xeons independently/earlier, except that "1 click" computing isn't the appropriate unix format, for multiple cpus (not that I'd know; I'd be happy to be wrong here --- at a minimum, I'm looking for comand-line remote login job submission). -Bruce |
[QUOTE=bdodson;117347]This timing confirms the recent experience with 6,284+, which finished way quick due to Greg's lattice siever contributions.
[/QUOTE] [QUOTE] Ah, Tom's 1/3 of the total nfsnet rate sounds like a four cores -to- fourty cpus comparison, for the same 1/3 rate.[/QUOTE] Those numbers are deceptive. You also need to assign a "quality factor" to the relations. Because of the nature of the lattice sieving algorithm, a significant number of those relations are not unique. And the percentage of unique relations decreases significantly when you generate a lot of relations by lattice sieving. On the other hand, line sieving decreases (due only to the scarcity of smooth values in larger norms) at a much slower rate. Assuming that you have enough memory, on equivalent cpu's, I would estimate that the lattice siever is about half of an order of magnitude faster. [QUOTE] Richard's fairly stingy with the nfsnet line-siever performance info (not to mention, selective about who hears what), but I gather that Lehigh's 2nd to U Gent; perhaps both around 30% each.[/QUOTE] Stinginess is primarily due to a lack of time to analyze the data. I have spent quite some effort, at various times, arranging to provide the data to various individuals who promised to set up something to convert it into useful data. But I have yet to see any results from any of those efforts. You are reasonably correct on the breakdown of line sieving effort. But we are now more like 18-16-6. And Greg's lattice sieving gets an effective rate of 60. [QUOTE]If anyone's qualified to offer Richard assistance, the potential returns would seem to be worth having. I'd be half willing to consider switching the xeons independently/earlier, except that "1 click" computing isn't the appropriate unix format, for multiple cpus (not that I'd know; I'd be happy to be wrong here --- at a minimum, I'm looking for comand-line remote login job submission). -Bruce[/QUOTE] |
[QUOTE=Wacky;117357]Those numbers are deceptive. You also need to assign a "quality factor" to the relations.
Because of the nature of the lattice sieving algorithm, a significant number of those relations are not unique. And the percentage of unique relations decreases significantly when you generate a lot of relations by lattice sieving. On the other hand, line sieving decreases (due only to the scarcity of smooth values in larger norms) at a much slower rate. Assuming that you have enough memory, on equivalent cpu's, I would estimate that the lattice siever is about half of an order of magnitude faster. [/QUOTE] The cabal did an extended, very careul comparison of line sieving and lattice sieving during the factorization of RSA512=RSA155 (1999). During three years following, 2002-2005, I did a fairly robust collection of small Cunninghams, some with line sieving only; some with lattice sieving only; and several with both sievers (CWI's and Arjen's). The rate of non-duplicate relations from lattice sieving holds up better for large q's than the rate for line sieving over the edges of the most productive central region. Consider that snfs1024 was entirely done by lattice sieving; and for the gnfs record RSA200, there were, from lattice sieving "26e8 relations. Together with 5e7" relations from line sieving. Lattice sieving is certainly the method of choice, at least, if someone else is doing the coding. [QUOTE] Stinginess is primarily due to a lack of time to analyze the data. I have spent quite some effort, at various times, arranging to provide the data to various individuals who promised to set up something to convert it into useful data. But I have yet to see any results from any of those efforts. You are reasonably correct on the breakdown of line sieving effort. But we are now more like 18-16-6. And Greg's lattice sieving gets an effective rate of 60.[/QUOTE] Sorry for the inappropriate snippiness on my part. As in our exchange of emails this afternoon, I'm not sure I understand these stats. But it's hard to see how to read them in a way that --- so far as I can tell --- doesn't give larger performance on lattice sieving from a much smaller number of cpus. In any case, we're certainly fortunate to have Greg's assistance; both on the sieving and the most recent (new) matrix. -Bruce |
Hi all,
As Richard posted in the NFSNet Discussion subforum, msieve 1.28 was used to complete the postprocessing of the NFSNet factorization of 5,323-. This one was a bit different in that a total of 87.9M relations were collected, but the CWI tools were used to initially filter the data, removing singletons and cliques to the point that there were 3.4M excess for ideals > 10M. The resultant 26M relations were fed to msieve to complete the filtering. A 6.4M x 6.4M matrix was constructed, and Block Lanczos running 4 threads on two 3GHz dual-core Core 2's (Xeon 5160's) took just over 4.5 days to complete and used about 3.6 GB of memory. Each square root took just over 2 hours to complete, and used about 3.2 GB of memory. The number split into three factors, the last of which was found on the 5th square root run. The complete log file is below. Overnight, I am running the matrix with a single thread to approximate how long it would take to complete. Greg [CODE]Thu Oct 25 10:41:19 2007 Thu Oct 25 10:41:19 2007 Thu Oct 25 10:41:19 2007 Msieve v. 1.28 Thu Oct 25 10:41:19 2007 random seeds: 4265581e ba30d595 Thu Oct 25 10:41:19 2007 factoring 495309299124357139316279379940432633769493573230593965141385458876013160503811123466253271109889608198235361530837001245349315590288899267199852659483378563331118780577737692994689114371 (186 digits) Thu Oct 25 10:41:20 2007 commencing number field sieve (186-digit input) Thu Oct 25 10:41:20 2007 R0: -55511151231257827021181583404541015625 Thu Oct 25 10:41:20 2007 R1: 1 Thu Oct 25 10:41:20 2007 A0: -5 Thu Oct 25 10:41:20 2007 A1: 0 Thu Oct 25 10:41:20 2007 A2: 0 Thu Oct 25 10:41:20 2007 A3: 0 Thu Oct 25 10:41:20 2007 A4: 0 Thu Oct 25 10:41:20 2007 A5: 0 Thu Oct 25 10:41:20 2007 A6: 1 Thu Oct 25 10:41:20 2007 size score = 7.018421e-11, Murphy alpha = 2.362581, combined = 3.573391e-11 Thu Oct 25 10:41:27 2007 restarting with 25995285 relations Thu Oct 25 10:41:27 2007 Thu Oct 25 10:41:27 2007 commencing relation filtering Thu Oct 25 10:41:27 2007 commencing duplicate removal, pass 1 Thu Oct 25 10:41:35 2007 error -10 reading relation 1339021 Thu Oct 25 10:41:55 2007 error -14 reading relation 5065990 Thu Oct 25 10:41:59 2007 error -14 reading relation 5671356 Thu Oct 25 10:42:32 2007 error -14 reading relation 11547334 Thu Oct 25 10:42:38 2007 error -10 reading relation 12709371 Thu Oct 25 10:42:41 2007 error -14 reading relation 13088512 Thu Oct 25 10:43:27 2007 error -14 reading relation 21297285 Thu Oct 25 10:43:28 2007 error -14 reading relation 21471403 Thu Oct 25 10:43:49 2007 error -10 reading relation 25107001 Thu Oct 25 10:43:58 2007 found 1219332 hash collisions in 25995276 relations Thu Oct 25 10:43:58 2007 commencing duplicate removal, pass 2 Thu Oct 25 10:44:14 2007 found 0 duplicates and 25995276 unique relations Thu Oct 25 10:44:14 2007 memory use: 65.3 MB Thu Oct 25 10:44:21 2007 ignoring smallest 1867878 rational and 1867082 algebraic ideals Thu Oct 25 10:44:21 2007 filtering rational ideals above 30171854 Thu Oct 25 10:44:21 2007 filtering algebraic ideals above 30171854 Thu Oct 25 10:44:21 2007 need 6349432 more relations than ideals Thu Oct 25 10:44:21 2007 commencing singleton removal, pass 1 Thu Oct 25 10:47:06 2007 relations with 0 large ideals: 590714 Thu Oct 25 10:47:06 2007 relations with 1 large ideals: 2692762 Thu Oct 25 10:47:06 2007 relations with 2 large ideals: 6707628 Thu Oct 25 10:47:06 2007 relations with 3 large ideals: 8359916 Thu Oct 25 10:47:06 2007 relations with 4 large ideals: 5438989 Thu Oct 25 10:47:06 2007 relations with 5 large ideals: 1765277 Thu Oct 25 10:47:06 2007 relations with 6 large ideals: 311819 Thu Oct 25 10:47:06 2007 relations with 7+ large ideals: 128171 Thu Oct 25 10:47:06 2007 25995276 relations and about 18877016 large ideals Thu Oct 25 10:47:06 2007 commencing singleton removal, pass 2 Thu Oct 25 10:49:51 2007 found 102513 singletons Thu Oct 25 10:49:51 2007 current dataset: 25892763 relations and about 18774376 large ideals Thu Oct 25 10:49:51 2007 commencing singleton removal, pass 3 Thu Oct 25 10:52:36 2007 found 10267 singletons Thu Oct 25 10:52:36 2007 current dataset: 25882496 relations and about 18764109 large ideals Thu Oct 25 10:52:36 2007 commencing singleton removal, final pass Thu Oct 25 10:56:11 2007 memory use: 835.6 MB Thu Oct 25 10:56:11 2007 commencing in-memory singleton removal Thu Oct 25 10:56:14 2007 begin with 25882496 relations and 20208771 unique ideals Thu Oct 25 10:56:33 2007 reduce to 25859196 relations and 20185467 ideals in 6 passes Thu Oct 25 10:56:33 2007 max relations containing the same ideal: 30 Thu Oct 25 10:56:36 2007 dataset has 51.9% excess relations Thu Oct 25 10:56:42 2007 ignoring smallest 1692152 rational and 1690686 algebraic ideals Thu Oct 25 10:56:42 2007 filtering rational ideals above 27154668 Thu Oct 25 10:56:42 2007 filtering algebraic ideals above 27154668 Thu Oct 25 10:56:42 2007 need 5106356 more relations than ideals Thu Oct 25 10:56:42 2007 commencing singleton removal, final pass Thu Oct 25 11:00:22 2007 memory use: 1069.9 MB Thu Oct 25 11:00:22 2007 commencing in-memory singleton removal Thu Oct 25 11:00:25 2007 begin with 25882496 relations and 20560594 unique ideals Thu Oct 25 11:00:44 2007 reduce to 25859194 relations and 20537288 ideals in 6 passes Thu Oct 25 11:00:44 2007 max relations containing the same ideal: 30 Thu Oct 25 11:01:00 2007 removing 470953 relations and 363178 ideals in 107775 cliques Thu Oct 25 11:01:01 2007 commencing in-memory singleton removal Thu Oct 25 11:01:04 2007 begin with 25388241 relations and 20537288 unique ideals Thu Oct 25 11:01:20 2007 reduce to 25382411 relations and 20168265 ideals in 5 passes Thu Oct 25 11:01:20 2007 max relations containing the same ideal: 29 Thu Oct 25 11:01:35 2007 removing 445612 relations and 337837 ideals in 107775 cliques Thu Oct 25 11:01:36 2007 commencing in-memory singleton removal Thu Oct 25 11:01:39 2007 begin with 24936799 relations and 20168265 unique ideals Thu Oct 25 11:01:54 2007 reduce to 24931148 relations and 19824763 ideals in 5 passes Thu Oct 25 11:01:54 2007 max relations containing the same ideal: 29 Thu Oct 25 11:01:58 2007 dataset has 36.7% excess relations Thu Oct 25 11:02:03 2007 ignoring smallest 1515188 rational and 1513510 algebraic ideals Thu Oct 25 11:02:03 2007 filtering rational ideals above 24137483 Thu Oct 25 11:02:03 2007 filtering algebraic ideals above 24137483 Thu Oct 25 11:02:03 2007 need 4085108 more relations than ideals Thu Oct 25 11:02:03 2007 commencing singleton removal, final pass Thu Oct 25 11:05:37 2007 memory use: 835.6 MB Thu Oct 25 11:05:37 2007 commencing in-memory singleton removal Thu Oct 25 11:05:40 2007 begin with 24931148 relations and 20178784 unique ideals Thu Oct 25 11:05:47 2007 reduce to 24931142 relations and 20178778 ideals in 2 passes Thu Oct 25 11:05:47 2007 max relations containing the same ideal: 30 Thu Oct 25 11:06:03 2007 removing 1204837 relations and 871209 ideals in 333628 cliques Thu Oct 25 11:06:05 2007 commencing in-memory singleton removal Thu Oct 25 11:06:08 2007 begin with 23726305 relations and 20178778 unique ideals Thu Oct 25 11:06:26 2007 reduce to 23680039 relations and 19260805 ideals in 6 passes Thu Oct 25 11:06:26 2007 max relations containing the same ideal: 28 Thu Oct 25 11:06:42 2007 removing 1299694 relations and 966066 ideals in 333628 cliques Thu Oct 25 11:06:43 2007 commencing in-memory singleton removal Thu Oct 25 11:06:46 2007 begin with 22380345 relations and 19260805 unique ideals Thu Oct 25 11:07:03 2007 reduce to 22327540 relations and 18241320 ideals in 6 passes Thu Oct 25 11:07:03 2007 max relations containing the same ideal: 28 Thu Oct 25 11:07:18 2007 removing 9110 relations and 7999 ideals in 1111 cliques Thu Oct 25 11:07:19 2007 commencing in-memory singleton removal Thu Oct 25 11:07:21 2007 begin with 22318430 relations and 18241320 unique ideals Thu Oct 25 11:07:24 2007 reduce to 22318430 relations and 18233321 ideals in 1 passes Thu Oct 25 11:07:24 2007 max relations containing the same ideal: 28 Thu Oct 25 11:07:28 2007 dataset has 9.4% excess relations Thu Oct 25 11:07:34 2007 relations with 0 large ideals: 396784 Thu Oct 25 11:07:34 2007 relations with 1 large ideals: 1827779 Thu Oct 25 11:07:34 2007 relations with 2 large ideals: 4974818 Thu Oct 25 11:07:34 2007 relations with 3 large ideals: 6912296 Thu Oct 25 11:07:34 2007 relations with 4 large ideals: 5255996 Thu Oct 25 11:07:34 2007 relations with 5 large ideals: 2209041 Thu Oct 25 11:07:34 2007 relations with 6 large ideals: 536129 Thu Oct 25 11:07:34 2007 relations with 7+ large ideals: 205587 Thu Oct 25 11:07:34 2007 commencing 2-way merge Thu Oct 25 11:07:50 2007 merged 7258995 relations Thu Oct 25 11:07:57 2007 reduce to 15059435 relation sets and 10974326 unique ideals Thu Oct 25 11:07:57 2007 commencing full merge Thu Oct 25 12:17:45 2007 found 7523803 cycles, need 6468526 Thu Oct 25 12:17:55 2007 weight of 6468526 cycles is about 420455872 (65.00/cycle) Thu Oct 25 12:17:55 2007 distribution of cycle lengths: Thu Oct 25 12:17:55 2007 1 relations: 837042 Thu Oct 25 12:17:55 2007 2 relations: 728368 Thu Oct 25 12:17:55 2007 3 relations: 777764 Thu Oct 25 12:17:55 2007 4 relations: 783769 Thu Oct 25 12:17:55 2007 5 relations: 755799 Thu Oct 25 12:17:55 2007 6 relations: 697123 Thu Oct 25 12:17:55 2007 7 relations: 615816 Thu Oct 25 12:17:55 2007 8 relations: 520486 Thu Oct 25 12:17:55 2007 9 relations: 421989 Thu Oct 25 12:17:55 2007 10+ relations: 330370 Thu Oct 25 12:17:55 2007 heaviest cycle: 13 relations Thu Oct 25 12:17:55 2007 commencing cycle optimization Thu Oct 25 12:57:44 2007 start with 31342602 relations Thu Oct 25 13:01:18 2007 pruned 433781 relations Thu Oct 25 13:01:21 2007 distribution of cycle lengths: Thu Oct 25 13:01:22 2007 1 relations: 837042 Thu Oct 25 13:01:22 2007 2 relations: 737029 Thu Oct 25 13:01:22 2007 3 relations: 795388 Thu Oct 25 13:01:22 2007 4 relations: 797691 Thu Oct 25 13:01:22 2007 5 relations: 775218 Thu Oct 25 13:01:22 2007 6 relations: 709824 Thu Oct 25 13:01:22 2007 7 relations: 625549 Thu Oct 25 13:01:22 2007 8 relations: 517646 Thu Oct 25 13:01:23 2007 9 relations: 398946 Thu Oct 25 13:01:23 2007 10+ relations: 274193 Thu Oct 25 13:01:23 2007 heaviest cycle: 13 relations Thu Oct 25 13:01:27 2007 Thu Oct 25 13:01:32 2007 commencing linear algebra Thu Oct 25 13:01:34 2007 factor base loaded: Thu Oct 25 13:01:34 2007 3001134 rational ideals (max prime = 49999991) Thu Oct 25 13:01:34 2007 3000510 algebraic ideals (max prime = 49999991) Thu Oct 25 13:01:36 2007 read 6468526 cycles Thu Oct 25 13:02:30 2007 cycles contain 18638978 unique relations Thu Oct 25 13:04:27 2007 read 18638978 relations Thu Oct 25 13:05:05 2007 using 32 quadratic characters above 999999740 Thu Oct 25 13:17:37 2007 matrix is 6466478 x 6468526 with weight 565096294 (avg 87.36/col) Thu Oct 25 13:20:29 2007 filtering completed in 3 passes Thu Oct 25 13:20:31 2007 matrix is 6406167 x 6406367 with weight 561759395 (avg 87.69/col) Thu Oct 25 13:22:14 2007 saving the first 48 matrix rows for later Thu Oct 25 13:22:21 2007 matrix is 6406119 x 6406367 with weight 426057561 (avg 66.51/col) Thu Oct 25 13:22:22 2007 matrix includes 64 packed rows Thu Oct 25 13:22:22 2007 using block size 65536 for processor cache size 4096 kB Thu Oct 25 14:33:54 2007 commencing Lanczos iteration (4 threads) Tue Oct 30 03:36:20 2007 lanczos halted after 101303 iterations Tue Oct 30 03:36:41 2007 recovered 47 nontrivial dependencies Tue Oct 30 03:36:41 2007 Tue Oct 30 03:36:41 2007 commencing square root phase Tue Oct 30 03:36:41 2007 reading relations for dependency 1 Tue Oct 30 03:36:45 2007 read 3202131 cycles Tue Oct 30 03:37:07 2007 cycles contain 11239050 unique relations Tue Oct 30 03:41:19 2007 read 11239050 relations Tue Oct 30 03:43:19 2007 multiplying 15391648 relations Tue Oct 30 04:28:23 2007 multiply complete, coefficients have about 366.90 million bits Tue Oct 30 04:28:30 2007 initial square root is modulo 3831937 Tue Oct 30 05:38:11 2007 reading relations for dependency 2 Tue Oct 30 05:38:19 2007 read 3203299 cycles Tue Oct 30 05:38:41 2007 cycles contain 11241741 unique relations Tue Oct 30 05:39:59 2007 read 11241741 relations Tue Oct 30 05:41:51 2007 multiplying 15398790 relations Tue Oct 30 06:26:44 2007 multiply complete, coefficients have about 367.06 million bits Tue Oct 30 06:26:51 2007 initial square root is modulo 3857263 Tue Oct 30 07:36:27 2007 reading relations for dependency 3 Tue Oct 30 07:36:35 2007 read 3203002 cycles Tue Oct 30 07:36:57 2007 cycles contain 11242189 unique relations Tue Oct 30 07:38:15 2007 read 11242189 relations Tue Oct 30 07:40:08 2007 multiplying 15396746 relations Tue Oct 30 08:25:01 2007 multiply complete, coefficients have about 367.02 million bits Tue Oct 30 08:25:08 2007 initial square root is modulo 3850813 Tue Oct 30 09:34:50 2007 reading relations for dependency 4 Tue Oct 30 09:34:58 2007 read 3202098 cycles Tue Oct 30 09:35:20 2007 cycles contain 11236931 unique relations Tue Oct 30 09:36:37 2007 read 11236931 relations Tue Oct 30 09:38:30 2007 multiplying 15387990 relations Tue Oct 30 10:23:22 2007 multiply complete, coefficients have about 366.81 million bits Tue Oct 30 10:23:29 2007 initial square root is modulo 3817753 Tue Oct 30 11:33:15 2007 reading relations for dependency 5 Tue Oct 30 11:33:23 2007 read 3201984 cycles Tue Oct 30 11:33:45 2007 cycles contain 11240415 unique relations Tue Oct 30 11:35:02 2007 read 11240415 relations Tue Oct 30 11:36:55 2007 multiplying 15394840 relations Tue Oct 30 12:21:55 2007 multiply complete, coefficients have about 366.97 million bits Tue Oct 30 12:22:02 2007 initial square root is modulo 3843577 Tue Oct 30 13:32:07 2007 prp54 factor: 824025642333621472612253607491152025643258690550015151 Tue Oct 30 13:32:07 2007 prp61 factor: 4520075300365525822415973296109200878340148487916084028121991 Tue Oct 30 13:32:07 2007 prp72 factor: 132981150324062454692451481044833258173562011479994362058454095433879531 Tue Oct 30 13:32:07 2007 elapsed time 122:50:48 [/CODE] |
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