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 2008-01-11, 16:16 #1 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 645310 Posts Bernoulli and Euler numbers (Sam Wagstaff project) http://homes.cerias.purdue.edu/~ssw/...lli/index.html is the main page for this project; http://homes.cerias.purdue.edu/~ssw/bernoulli/bnum and http://homes.cerias.purdue.edu/~ssw/bernoulli/enum list the factors known. http://en.wikipedia.org/wiki/Euler_numbers and http://en.wikipedia.org/wiki/Bernoulli_number define the Euler and Bernoulli numbers; the N### being factorised here are the numerators of the Bernoulli numbers, obtained in gp as Code: numerator(bernfrac(###)) and the E### by Code: N=### default(seriesprecision, N+10) T=taylor(1/cosh(x),x) polcoeff(T,N) * prod(i=1,N,i) The numbers are not as far as I know SNFS-amenable, and they grow quite large quite quickly, so this is mostly an ECM project; Sam has done a fair amount of ECM over these and found at least one 50-digit factor. Though sievers (OK, sievers with incredible resources in the cases of the last four numbers) might be interested in Code: *N176 C138 561602126238949966093208044713565096735647776816214118967637030543319164290535687405179873997375297259308787285343674519616007041894252147 *N218 C141 304231555057698888502708670679920297446936633334755377559718454327465917469538949036477054533335898617528911439255596338155475711196193349907 N190 C152 15715496152776982489778142635341275866050684476125452035397458516486943107317760601061082109700169864160537677622973197179487906036510768485502942125239 N222 C160 1944507419702020239105947860297224309650538619435034558524428604333013765995502187641029511486447333003210637642920189364415139564903097189370535817294173277263 E122 C169 3818723881495031819672087511891226633108668231418417614458853563199270304677387223426769127666923474708712472353170702968802174836014233752821322232673203335351690972993 E120 C170 30614112198603477540294953453509600250642722488962340055423980380793433321880177726367467667922713955685560746809449855119053214908867791649739871010411068882989664254337 N202 C173 17207166720977090018555554232695219240449673152984728941390151653840542465501186304298189852428343402432734665195226293993239530334336681612897891942559122093290584231690241 N236 C174 138118725770091309803503176746772215425355788906411993609345186278517863537509783400599679746045473713900370128406411687517775462051181593984806553696358200115520161404684413 ECM work Code: E120 4590@11e6, 7000@43e6 (sean) GNFS results Code: N176 finished by fivemack, 14/2/2008 N218 finished by fivemack, 23/2/2008 Last fiddled with by fivemack on 2008-02-23 at 17:21
2008-01-13, 00:54   #2
bdodson

Jun 2005
lehigh.edu

210 Posts

Quote:
 Originally Posted by fivemack http://homes.cerias.purdue.edu/~ssw/...lli/index.html is the main page for this project; http://homes.cerias.purdue.edu/~ssw/bernoulli/bnum and http://homes.cerias.purdue.edu/~ssw/bernoulli/enum list the factors known.
Sam reports that he is updating the bernouli, euler and bell lists as soon
as he gets factors. He's also added a link with the remaining composites
(all three lists combined),

http://homes.cerias.purdue.edu/~ssw/bernoulli/composite

we had 82 when we started our current run (I had three factors from an
earlier run, 2004). Sam reports the current count as 76 (which includes
remaining composite cofactors, so we found more than six). I'm about
to finish a t45, then switch that cluster back to Cunninghams. -bruce

[the Bell numbers are perhaps snfs candidates?]

 2008-02-14, 18:31 #3 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 11001001101012 Posts N176 splits as Code: P60 161682280601750017807051565594123306297091203059258385807467 P79 3473492111496547587945366626225248021650210851846887340916568090835384897238041 Half a day to get the polynomials, four and a half days on about four CPUs to get 23725909 relations of which 21708585 unique, twelve hours on two CPUs to solve a 2063037 x 2063285 matrix with weight 145645111 (70.59/col), 70 minutes for the square root, factors from the first dependency.
 2008-02-23, 17:20 #4 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 144658 Posts N218 splits as Code: P66 529041127136621894810092661001283800527316908098655885710614302743 P75 575062201126629614470645738970165209255701496570272209233469241277154408549 This took about 48 CPU-hours polynomial search, almost exactly 600 CPU-hours to sieve, 48 CPU-hours on two cores to do the linear algebra, and a slightly frustrating 18 hours on one core to find the factors on the ninth dependency. Code: Thu Feb 21 18:15:08 2008 Msieve v. 1.33 Thu Feb 21 18:15:08 2008 random seeds: 1a29a284 f5aafdbe Thu Feb 21 18:15:08 2008 factoring 304231555057698888502708670679920297446936633334755377559718454327465917469538949036477054533335898617528911439255596338155475711196193349907 (141 digits) Thu Feb 21 18:15:09 2008 no P-1/P+1/ECM available, skipping Thu Feb 21 18:15:09 2008 commencing number field sieve (141-digit input) Thu Feb 21 18:15:09 2008 R0: -811108827276972422199078148 Thu Feb 21 18:15:09 2008 R1: 455195620287979 Thu Feb 21 18:15:09 2008 A0: 57184039631828920586603735624145 Thu Feb 21 18:15:09 2008 A1: -7783023214726791392303474410 Thu Feb 21 18:15:09 2008 A2: 28580437883961308732287 Thu Feb 21 18:15:09 2008 A3: 287657668694377976 Thu Feb 21 18:15:09 2008 A4: -154800049518 Thu Feb 21 18:15:09 2008 A5: 866580 Thu Feb 21 18:15:09 2008 size score = 1.504655e-14, Murphy alpha = -5.292384, combined = 8.781893e-14 Thu Feb 21 18:17:04 2008 restarting with 40737161 relations Thu Feb 21 18:17:08 2008 added 3741 free relations Thu Feb 21 18:17:08 2008 Thu Feb 21 18:17:08 2008 commencing relation filtering Thu Feb 21 18:17:08 2008 commencing duplicate removal, pass 1 Thu Feb 21 18:23:35 2008 found 5048404 hash collisions in 40740902 relations Thu Feb 21 18:23:35 2008 commencing duplicate removal, pass 2 Thu Feb 21 18:24:23 2008 found 3077851 duplicates and 37663051 unique relations Thu Feb 21 18:24:23 2008 memory use: 153.2 MB Thu Feb 21 18:24:24 2008 ignoring smallest 78498 rational and 78521 algebraic ideals Thu Feb 21 18:24:24 2008 filtering rational ideals above 1000000 Thu Feb 21 18:24:24 2008 filtering algebraic ideals above 1000000 Thu Feb 21 18:24:24 2008 need 266932 more relations than ideals Thu Feb 21 18:24:24 2008 commencing singleton removal, pass 1 Thu Feb 21 18:31:08 2008 relations with 0 large ideals: 645 Thu Feb 21 18:31:08 2008 relations with 1 large ideals: 927 Thu Feb 21 18:31:08 2008 relations with 2 large ideals: 26089 Thu Feb 21 18:31:08 2008 relations with 3 large ideals: 300411 Thu Feb 21 18:31:08 2008 relations with 4 large ideals: 1796078 Thu Feb 21 18:31:08 2008 relations with 5 large ideals: 5867662 Thu Feb 21 18:31:08 2008 relations with 6 large ideals: 10537022 Thu Feb 21 18:31:08 2008 relations with 7+ large ideals: 19134217 Thu Feb 21 18:31:08 2008 37663051 relations and about 35123001 large ideals Thu Feb 21 18:31:09 2008 commencing singleton removal, pass 2 Thu Feb 21 18:37:57 2008 found 11945747 singletons Thu Feb 21 18:37:57 2008 current dataset: 25717304 relations and about 21390814 large ideals Thu Feb 21 18:37:58 2008 commencing singleton removal, pass 3 Thu Feb 21 18:42:56 2008 found 2710394 singletons Thu Feb 21 18:42:56 2008 current dataset: 23006910 relations and about 18560255 large ideals Thu Feb 21 18:42:57 2008 commencing singleton removal, pass 4 Thu Feb 21 18:47:14 2008 found 669266 singletons Thu Feb 21 18:47:14 2008 current dataset: 22337644 relations and about 17882645 large ideals Thu Feb 21 18:47:15 2008 commencing singleton removal, pass 5 Thu Feb 21 18:51:26 2008 found 165033 singletons Thu Feb 21 18:51:26 2008 current dataset: 22172611 relations and about 17717079 large ideals Thu Feb 21 18:51:27 2008 commencing singleton removal, final pass Thu Feb 21 18:58:34 2008 memory use: 715.7 MB Thu Feb 21 18:59:10 2008 commencing in-memory singleton removal Thu Feb 21 18:59:17 2008 begin with 22172611 relations and 21691047 unique ideals Thu Feb 21 19:01:02 2008 reduce to 14595796 relations and 13630413 ideals in 23 passes Thu Feb 21 19:01:02 2008 max relations containing the same ideal: 176 Thu Feb 21 19:01:28 2008 removing 2771538 relations and 2422313 ideals in 349225 cliques Thu Feb 21 19:01:30 2008 commencing in-memory singleton removal Thu Feb 21 19:01:34 2008 begin with 11824258 relations and 13630413 unique ideals Thu Feb 21 19:02:15 2008 reduce to 11460968 relations and 10833677 ideals in 12 passes Thu Feb 21 19:02:15 2008 max relations containing the same ideal: 137 Thu Feb 21 19:02:33 2008 removing 2035086 relations and 1685861 ideals in 349225 cliques Thu Feb 21 19:02:35 2008 commencing in-memory singleton removal Thu Feb 21 19:02:37 2008 begin with 9425882 relations and 10833677 unique ideals Thu Feb 21 19:03:05 2008 reduce to 9162490 relations and 8876526 ideals in 10 passes Thu Feb 21 19:03:05 2008 max relations containing the same ideal: 114 Thu Feb 21 19:03:19 2008 removing 187553 relations and 168522 ideals in 19031 cliques Thu Feb 21 19:03:20 2008 commencing in-memory singleton removal Thu Feb 21 19:03:23 2008 begin with 8974937 relations and 8876526 unique ideals Thu Feb 21 19:03:38 2008 reduce to 8972392 relations and 8705456 ideals in 6 passes Thu Feb 21 19:03:38 2008 max relations containing the same ideal: 112 Thu Feb 21 19:03:42 2008 dataset has 70.0% excess relations Thu Feb 21 19:03:42 2008 ignoring smallest 71274 rational and 71232 algebraic ideals Thu Feb 21 19:03:42 2008 filtering rational ideals above 900000 Thu Feb 21 19:03:42 2008 filtering algebraic ideals above 900000 Thu Feb 21 19:03:42 2008 need 240242 more relations than ideals Thu Feb 21 19:03:42 2008 commencing singleton removal, final pass Thu Feb 21 19:06:13 2008 memory use: 288.0 MB Thu Feb 21 19:06:18 2008 commencing in-memory singleton removal Thu Feb 21 19:06:21 2008 begin with 8972392 relations and 8719969 unique ideals Thu Feb 21 19:06:23 2008 reduce to 8972392 relations and 8719969 ideals in 1 passes Thu Feb 21 19:06:24 2008 max relations containing the same ideal: 126 Thu Feb 21 19:06:39 2008 dataset has 60.8% excess relations Thu Feb 21 19:06:40 2008 ignoring smallest 63951 rational and 63944 algebraic ideals Thu Feb 21 19:06:40 2008 filtering rational ideals above 800000 Thu Feb 21 19:06:40 2008 filtering algebraic ideals above 800000 Thu Feb 21 19:06:40 2008 need 201938 more relations than ideals Thu Feb 21 19:06:40 2008 commencing singleton removal, final pass Thu Feb 21 19:09:15 2008 memory use: 292.4 MB Thu Feb 21 19:09:23 2008 commencing in-memory singleton removal Thu Feb 21 19:09:25 2008 begin with 8972392 relations and 8734580 unique ideals Thu Feb 21 19:09:28 2008 reduce to 8972392 relations and 8734580 ideals in 1 passes Thu Feb 21 19:09:28 2008 max relations containing the same ideal: 134 Thu Feb 21 19:09:43 2008 removing 144301 relations and 126364 ideals in 17937 cliques Thu Feb 21 19:09:43 2008 commencing in-memory singleton removal Thu Feb 21 19:09:46 2008 begin with 8828091 relations and 8734580 unique ideals Thu Feb 21 19:09:58 2008 reduce to 8826558 relations and 8606679 ideals in 5 passes Thu Feb 21 19:09:58 2008 max relations containing the same ideal: 132 Thu Feb 21 19:10:11 2008 removing 133397 relations and 115460 ideals in 17937 cliques Thu Feb 21 19:10:12 2008 commencing in-memory singleton removal Thu Feb 21 19:10:15 2008 begin with 8693161 relations and 8606679 unique ideals Thu Feb 21 19:10:29 2008 reduce to 8691658 relations and 8489713 ideals in 6 passes Thu Feb 21 19:10:29 2008 max relations containing the same ideal: 130 Thu Feb 21 19:10:33 2008 dataset has 28.6% excess relations Thu Feb 21 19:10:33 2008 ignoring smallest 56543 rational and 56481 algebraic ideals Thu Feb 21 19:10:33 2008 filtering rational ideals above 700000 Thu Feb 21 19:10:33 2008 filtering algebraic ideals above 700000 Thu Feb 21 19:10:33 2008 need 169580 more relations than ideals Thu Feb 21 19:10:33 2008 commencing singleton removal, final pass Thu Feb 21 19:12:56 2008 memory use: 287.8 MB Thu Feb 21 19:13:04 2008 commencing in-memory singleton removal Thu Feb 21 19:13:07 2008 begin with 8691658 relations and 8504584 unique ideals Thu Feb 21 19:13:10 2008 reduce to 8691658 relations and 8504584 ideals in 1 passes Thu Feb 21 19:13:10 2008 max relations containing the same ideal: 143 Thu Feb 21 19:13:25 2008 removing 66828 relations and 58081 ideals in 8747 cliques Thu Feb 21 19:13:25 2008 commencing in-memory singleton removal Thu Feb 21 19:13:28 2008 begin with 8624830 relations and 8504584 unique ideals Thu Feb 21 19:13:40 2008 reduce to 8624469 relations and 8446138 ideals in 5 passes Thu Feb 21 19:13:40 2008 max relations containing the same ideal: 143 Thu Feb 21 19:13:53 2008 removing 62131 relations and 53384 ideals in 8747 cliques Thu Feb 21 19:13:53 2008 commencing in-memory singleton removal Thu Feb 21 19:13:56 2008 begin with 8562338 relations and 8446138 unique ideals Thu Feb 21 19:14:08 2008 reduce to 8562020 relations and 8392436 ideals in 5 passes Thu Feb 21 19:14:08 2008 max relations containing the same ideal: 142 Thu Feb 21 19:14:12 2008 dataset has 8.0% excess relations Thu Feb 21 19:14:15 2008 relations with 0 large ideals: 476 Thu Feb 21 19:14:15 2008 relations with 1 large ideals: 332 Thu Feb 21 19:14:15 2008 relations with 2 large ideals: 7818 Thu Feb 21 19:14:15 2008 relations with 3 large ideals: 76541 Thu Feb 21 19:14:15 2008 relations with 4 large ideals: 393865 Thu Feb 21 19:14:15 2008 relations with 5 large ideals: 1185580 Thu Feb 21 19:14:15 2008 relations with 6 large ideals: 2151598 Thu Feb 21 19:14:15 2008 relations with 7+ large ideals: 4745810 Thu Feb 21 19:14:15 2008 commencing 2-way merge Thu Feb 21 19:14:34 2008 reduce to 5042656 relation sets and 4873072 unique ideals Thu Feb 21 19:14:34 2008 commencing full merge Thu Feb 21 19:17:07 2008 memory use: 591.0 MB Thu Feb 21 19:17:07 2008 found 2721571 cycles, need 2665272 Thu Feb 21 19:17:09 2008 weight of 2665272 cycles is about 173381650 (65.05/cycle) Thu Feb 21 19:17:09 2008 distribution of cycle lengths: Thu Feb 21 19:17:09 2008 1 relations: 407063 Thu Feb 21 19:17:09 2008 2 relations: 357605 Thu Feb 21 19:17:09 2008 3 relations: 341292 Thu Feb 21 19:17:09 2008 4 relations: 303387 Thu Feb 21 19:17:09 2008 5 relations: 258936 Thu Feb 21 19:17:09 2008 6 relations: 224016 Thu Feb 21 19:17:09 2008 7 relations: 187295 Thu Feb 21 19:17:09 2008 8 relations: 152413 Thu Feb 21 19:17:09 2008 9 relations: 122717 Thu Feb 21 19:17:09 2008 10+ relations: 310548 Thu Feb 21 19:17:09 2008 heaviest cycle: 16 relations Thu Feb 21 19:17:10 2008 commencing cycle optimization Thu Feb 21 19:17:15 2008 start with 13209822 relations Thu Feb 21 19:17:42 2008 pruned 67989 relations Thu Feb 21 19:17:43 2008 memory use: 477.3 MB Thu Feb 21 19:17:43 2008 distribution of cycle lengths: Thu Feb 21 19:17:43 2008 1 relations: 407063 Thu Feb 21 19:17:43 2008 2 relations: 358360 Thu Feb 21 19:17:43 2008 3 relations: 343421 Thu Feb 21 19:17:43 2008 4 relations: 304652 Thu Feb 21 19:17:43 2008 5 relations: 261024 Thu Feb 21 19:17:43 2008 6 relations: 224900 Thu Feb 21 19:17:43 2008 7 relations: 188093 Thu Feb 21 19:17:43 2008 8 relations: 152385 Thu Feb 21 19:17:43 2008 9 relations: 122611 Thu Feb 21 19:17:43 2008 10+ relations: 302763 Thu Feb 21 19:17:43 2008 heaviest cycle: 16 relations Thu Feb 21 19:17:53 2008 Thu Feb 21 19:17:53 2008 commencing linear algebra Thu Feb 21 19:17:56 2008 read 2665272 cycles Thu Feb 21 19:18:08 2008 cycles contain 8270613 unique relations Thu Feb 21 19:19:44 2008 read 8270613 relations Thu Feb 21 19:20:01 2008 using 32 quadratic characters above 536868594 Thu Feb 21 19:21:24 2008 building initial matrix Thu Feb 21 19:23:30 2008 memory use: 1101.8 MB Thu Feb 21 19:23:37 2008 read 2665272 cycles Thu Feb 21 19:23:44 2008 matrix is 2665100 x 2665272 (769.7 MB) with weight 255503864 (95.86/col) Thu Feb 21 19:23:44 2008 sparse part has weight 169800303 (63.71/col) Thu Feb 21 19:24:34 2008 filtering completed in 2 passes Thu Feb 21 19:24:35 2008 matrix is 2659205 x 2659377 (769.2 MB) with weight 255252074 (95.98/col) Thu Feb 21 19:24:35 2008 sparse part has weight 169740539 (63.83/col) Thu Feb 21 19:25:26 2008 read 2659377 cycles Thu Feb 21 19:25:35 2008 matrix is 2659205 x 2659377 (769.2 MB) with weight 255252074 (95.98/col) Thu Feb 21 19:25:35 2008 sparse part has weight 169740539 (63.83/col) Thu Feb 21 19:25:35 2008 saving the first 48 matrix rows for later Thu Feb 21 19:25:36 2008 matrix is 2659157 x 2659377 (743.7 MB) with weight 196294453 (73.81/col) Thu Feb 21 19:25:36 2008 sparse part has weight 168360661 (63.31/col) Thu Feb 21 19:25:36 2008 matrix includes 64 packed rows Thu Feb 21 19:25:36 2008 using block size 65536 for processor cache size 4096 kB Thu Feb 21 19:25:57 2008 commencing Lanczos iteration (2 threads) Thu Feb 21 19:25:57 2008 memory use: 728.0 MB Fri Feb 22 18:32:38 2008 lanczos halted after 42058 iterations (dim = 2659157) Fri Feb 22 18:32:44 2008 recovered 44 nontrivial dependencies Fri Feb 22 18:32:46 2008 Fri Feb 22 18:32:46 2008 commencing square root phase Fri Feb 22 18:32:46 2008 reading relations for dependency 64 Fri Feb 22 18:32:46 2008 read 0 cycles Fri Feb 22 18:32:46 2008 elapsed time 24:17:38 (I was out that evening) Sat Feb 23 00:01:25 2008 Sat Feb 23 00:01:25 2008 Sat Feb 23 00:01:25 2008 Msieve v. 1.33 Sat Feb 23 00:01:25 2008 random seeds: 47e8057e 95e77763 Sat Feb 23 00:01:25 2008 factoring 304231555057698888502708670679920297446936633334755377559718454327465917469538949036477054533335898617528911439255596338155475711196193349907 (141 digits) Sat Feb 23 00:01:26 2008 no P-1/P+1/ECM available, skipping Sat Feb 23 00:01:26 2008 commencing number field sieve (141-digit input) Sat Feb 23 00:01:26 2008 R0: -811108827276972422199078148 Sat Feb 23 00:01:26 2008 R1: 455195620287979 Sat Feb 23 00:01:26 2008 A0: 57184039631828920586603735624145 Sat Feb 23 00:01:26 2008 A1: -7783023214726791392303474410 Sat Feb 23 00:01:26 2008 A2: 28580437883961308732287 Sat Feb 23 00:01:26 2008 A3: 287657668694377976 Sat Feb 23 00:01:26 2008 A4: -154800049518 Sat Feb 23 00:01:26 2008 A5: 866580 Sat Feb 23 00:01:26 2008 size score = 1.504655e-14, Murphy alpha = -5.292384, combined = 8.781893e-14 Sat Feb 23 00:01:26 2008 Sat Feb 23 00:01:26 2008 commencing square root phase Sat Feb 23 00:01:26 2008 reading relations for dependency 1 Sat Feb 23 00:01:26 2008 read 1331041 cycles Sat Feb 23 00:01:31 2008 cycles contain 4945480 unique relations Sat Feb 23 00:03:50 2008 read 4945480 relations Sat Feb 23 00:04:35 2008 multiplying 6575590 relations Sat Feb 23 00:46:32 2008 multiply complete, coefficients have about 350.42 million bits Sat Feb 23 00:46:48 2008 initial square root is modulo 1939279 Sat Feb 23 01:45:23 2008 reading relations for dependency 2 Sat Feb 23 01:45:23 2008 read 1328665 cycles Sat Feb 23 01:45:28 2008 cycles contain 4938185 unique relations Sat Feb 23 01:46:28 2008 read 4938185 relations Sat Feb 23 01:47:13 2008 multiplying 6562068 relations Sat Feb 23 02:28:38 2008 multiply complete, coefficients have about 349.69 million bits Sat Feb 23 02:28:54 2008 initial square root is modulo 1881949 Sat Feb 23 03:26:18 2008 reading relations for dependency 3 Sat Feb 23 03:26:19 2008 read 1329478 cycles Sat Feb 23 03:26:24 2008 cycles contain 4941515 unique relations Sat Feb 23 03:27:51 2008 read 4941515 relations Sat Feb 23 03:28:35 2008 multiplying 6566668 relations Sat Feb 23 04:10:00 2008 multiply complete, coefficients have about 349.93 million bits Sat Feb 23 04:10:16 2008 initial square root is modulo 1901027 Sat Feb 23 05:07:37 2008 reading relations for dependency 4 Sat Feb 23 05:07:38 2008 read 1330019 cycles Sat Feb 23 05:07:43 2008 cycles contain 4944160 unique relations Sat Feb 23 05:08:43 2008 read 4944160 relations Sat Feb 23 05:09:28 2008 multiplying 6574662 relations Sat Feb 23 05:51:20 2008 multiply complete, coefficients have about 350.37 million bits Sat Feb 23 05:51:36 2008 initial square root is modulo 1935589 Sat Feb 23 06:49:58 2008 reading relations for dependency 5 Sat Feb 23 06:49:59 2008 read 1330461 cycles Sat Feb 23 06:50:04 2008 cycles contain 4946758 unique relations Sat Feb 23 06:51:08 2008 read 4946758 relations Sat Feb 23 06:51:53 2008 multiplying 6576428 relations Sat Feb 23 07:33:20 2008 multiply complete, coefficients have about 350.46 million bits Sat Feb 23 07:33:36 2008 initial square root is modulo 1942657 Sat Feb 23 08:31:02 2008 reading relations for dependency 6 Sat Feb 23 08:31:03 2008 read 1329134 cycles Sat Feb 23 08:31:08 2008 cycles contain 4942230 unique relations Sat Feb 23 08:32:08 2008 read 4942230 relations Sat Feb 23 08:32:53 2008 multiplying 6568714 relations Sat Feb 23 09:14:20 2008 multiply complete, coefficients have about 350.04 million bits Sat Feb 23 09:14:36 2008 initial square root is modulo 1909637 Sat Feb 23 10:12:20 2008 reading relations for dependency 7 Sat Feb 23 10:12:21 2008 read 1328681 cycles Sat Feb 23 10:12:26 2008 cycles contain 4939463 unique relations Sat Feb 23 10:14:17 2008 read 4939463 relations Sat Feb 23 10:15:02 2008 multiplying 6566370 relations (stopped job to replace CPU heatsink on NFS server) Sat Feb 23 11:14:16 2008 Sat Feb 23 11:14:16 2008 Sat Feb 23 11:14:16 2008 Msieve v. 1.33 Sat Feb 23 11:14:16 2008 random seeds: a0e0453c 17a5295d Sat Feb 23 11:14:16 2008 factoring 304231555057698888502708670679920297446936633334755377559718454327465917469538949036477054533335898617528911439255596338155475711196193349907 (141 digits) Sat Feb 23 11:14:17 2008 no P-1/P+1/ECM available, skipping Sat Feb 23 11:14:17 2008 commencing number field sieve (141-digit input) Sat Feb 23 11:14:17 2008 R0: -811108827276972422199078148 Sat Feb 23 11:14:17 2008 R1: 455195620287979 Sat Feb 23 11:14:17 2008 A0: 57184039631828920586603735624145 Sat Feb 23 11:14:17 2008 A1: -7783023214726791392303474410 Sat Feb 23 11:14:17 2008 A2: 28580437883961308732287 Sat Feb 23 11:14:17 2008 A3: 287657668694377976 Sat Feb 23 11:14:17 2008 A4: -154800049518 Sat Feb 23 11:14:17 2008 A5: 866580 Sat Feb 23 11:14:17 2008 size score = 1.504655e-14, Murphy alpha = -5.292384, combined = 8.781893e-14 Sat Feb 23 11:14:17 2008 Sat Feb 23 11:14:17 2008 commencing square root phase Sat Feb 23 11:14:17 2008 reading relations for dependency 7 Sat Feb 23 11:14:21 2008 read 1328681 cycles Sat Feb 23 11:14:26 2008 cycles contain 4939463 unique relations Sat Feb 23 11:18:15 2008 read 4939463 relations Sat Feb 23 11:19:00 2008 multiplying 6566370 relations Sat Feb 23 12:03:24 2008 multiply complete, coefficients have about 349.92 million bits Sat Feb 23 12:03:41 2008 initial square root is modulo 1899917 Sat Feb 23 13:11:52 2008 reading relations for dependency 8 Sat Feb 23 13:11:53 2008 read 1327644 cycles Sat Feb 23 13:11:58 2008 cycles contain 4938431 unique relations Sat Feb 23 13:13:25 2008 read 4938431 relations Sat Feb 23 13:14:15 2008 multiplying 6561678 relations Sat Feb 23 14:02:05 2008 multiply complete, coefficients have about 349.67 million bits Sat Feb 23 14:02:22 2008 initial square root is modulo 1880581 Sat Feb 23 15:12:01 2008 reading relations for dependency 9 Sat Feb 23 15:12:02 2008 read 1330553 cycles Sat Feb 23 15:12:09 2008 cycles contain 4944016 unique relations Sat Feb 23 15:13:25 2008 read 4944016 relations Sat Feb 23 15:14:16 2008 multiplying 6572596 relations Sat Feb 23 16:03:02 2008 multiply complete, coefficients have about 350.26 million bits Sat Feb 23 16:03:21 2008 initial square root is modulo 1926481 Sat Feb 23 17:14:02 2008 prp66 factor: 529041127136621894810092661001283800527316908098655885710614302743 Sat Feb 23 17:14:02 2008 prp75 factor: 575062201126629614470645738970165209255701496570272209233469241277154408549 Sat Feb 23 17:14:02 2008 elapsed time 05:59:46
2008-02-24, 00:39   #5
jasonp
Tribal Bullet

Oct 2004

5×709 Posts

Quote:
 Originally Posted by fivemack Thu Feb 21 18:24:24 2008 filtering rational ideals above 1000000 Thu Feb 21 18:24:24 2008 filtering algebraic ideals above 1000000
Ouch, 9 dependencies is pretty crazy. For the record, I'm working on changes to the filtering that will always choose a low bound and keep only the ideals that occur a few times. This will make the filtering work a bit more like the CWI suite, allowing it to hopefully produce better matrices without an explosion in memory use.

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¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣ … ⋯ ⋮ ⋰ ⋱
∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ
𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎𝜍 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔