- **ElevenSmooth**
(*https://www.mersenneforum.org/forumdisplay.php?f=31*)

- - **New factor**
(*https://www.mersenneforum.org/showthread.php?t=10065*)

New factorThe C149 of M1575 splits as 745832506848141808511611576240568244832258614550704416204357517716551 * 46988139879538892325015289211281843797083431443099045770269959929002737021425551
GNFS with polynomial [code] R0: -30104817950070729324593475027 R1: 5053580822033843 A0: 1582043507098494327107617309192676 A1: 39725247684687428138366842123 A2: -24684440038757266241210 A3: -2155369437080572429 A4: 88032011055 A5: 1417260 [/code] Small primes to 20M rational and to 25M algebraic; 29-bit large primes. Sieved 25M->48M getting 46404925 relations of which 41907595 unique. [code] Thu Mar 6 20:10:53 2008 matrix is 4158099 x 4158315 (1167.1 MB) with weight 3\ 09840159 (74.51/col) Thu Mar 6 20:10:53 2008 sparse part has weight 264370975 (63.58/col) [/code] Sieving took about 1300 CPU-hours on a collection of Core2/2400 and K8/2300 cores, filtering (with -nc 1000000,1000000) was about two hours, linear algebra step about two days with four threads on a quad-core (interrupted half-way through and resumed; run such jobs with nohup, otherwise a crash of the machine running the terminal window in which you started the job). 2.5hrs per square root. [code] Thu Mar 6 18:48:57 2008 Thu Mar 6 18:48:57 2008 Thu Mar 6 18:48:57 2008 Msieve v. 1.33 Thu Mar 6 18:48:57 2008 random seeds: c07ba91b 42e70207 Thu Mar 6 18:48:57 2008 factoring 35045282158487636123259014292004089245227471550191132494367732831303373727594575532334779423274207863833033604171200909745257231922557618156366994601 (149 digits) Thu Mar 6 18:48:59 2008 no P-1/P+1/ECM available, skipping Thu Mar 6 18:48:59 2008 commencing number field sieve (149-digit input) Thu Mar 6 18:48:59 2008 R0: -30104817950070729324593475027 Thu Mar 6 18:48:59 2008 R1: 5053580822033843 Thu Mar 6 18:48:59 2008 A0: 1582043507098494327107617309192676 Thu Mar 6 18:48:59 2008 A1: 39725247684687428138366842123 Thu Mar 6 18:48:59 2008 A2: -24684440038757266241210 Thu Mar 6 18:48:59 2008 A3: -2155369437080572429 Thu Mar 6 18:48:59 2008 A4: 88032011055 Thu Mar 6 18:48:59 2008 A5: 1417260 Thu Mar 6 18:48:59 2008 size score = 3.315952e-15, Murphy alpha = -5.040913, combined = 1.779734e-14 Thu Mar 6 18:55:02 2008 restarting with 46400759 relations Thu Mar 6 18:55:05 2008 added 4170 free relations Thu Mar 6 18:55:05 2008 Thu Mar 6 18:55:05 2008 commencing relation filtering Thu Mar 6 18:55:05 2008 commencing duplicate removal, pass 1 Thu Mar 6 18:58:37 2008 error -9 reading relation 22538101 Thu Mar 6 18:58:37 2008 error -11 reading relation 22538102 Thu Mar 6 18:58:56 2008 error -11 reading relation 24547549 Thu Mar 6 18:58:56 2008 error -1 reading relation 24547550 Thu Mar 6 19:02:20 2008 found 6731638 hash collisions in 46404925 relations Thu Mar 6 19:02:20 2008 commencing duplicate removal, pass 2 Thu Mar 6 19:03:13 2008 found 4497330 duplicates and 41907595 unique relations Thu Mar 6 19:03:13 2008 memory use: 153.2 MB Thu Mar 6 19:03:14 2008 ignoring smallest 78498 rational and 78116 algebraic ideals Thu Mar 6 19:03:14 2008 filtering rational ideals above 1000000 Thu Mar 6 19:03:14 2008 filtering algebraic ideals above 1000000 Thu Mar 6 19:03:14 2008 need 266243 more relations than ideals Thu Mar 6 19:03:14 2008 commencing singleton removal, pass 1 Thu Mar 6 19:10:39 2008 relations with 0 large ideals: 631 Thu Mar 6 19:10:39 2008 relations with 1 large ideals: 423 Thu Mar 6 19:10:39 2008 relations with 2 large ideals: 13230 Thu Mar 6 19:10:39 2008 relations with 3 large ideals: 166204 Thu Mar 6 19:10:39 2008 relations with 4 large ideals: 1103550 Thu Mar 6 19:10:39 2008 relations with 5 large ideals: 4198743 Thu Mar 6 19:10:39 2008 relations with 6 large ideals: 9348063 Thu Mar 6 19:10:39 2008 relations with 7+ large ideals: 27076751 Thu Mar 6 19:10:39 2008 41907595 relations and about 37255927 large ideals Thu Mar 6 19:10:39 2008 commencing singleton removal, pass 2 Thu Mar 6 19:18:07 2008 found 11128703 singletons Thu Mar 6 19:18:07 2008 current dataset: 30778892 relations and about 24784166 large ideals Thu Mar 6 19:18:07 2008 commencing singleton removal, pass 3 Thu Mar 6 19:23:43 2008 found 2308815 singletons Thu Mar 6 19:23:43 2008 current dataset: 28470077 relations and about 22401951 large ideals Thu Mar 6 19:23:43 2008 commencing singleton removal, pass 4 Thu Mar 6 19:28:59 2008 found 489745 singletons Thu Mar 6 19:28:59 2008 current dataset: 27980332 relations and about 21908511 large ideals Thu Mar 6 19:28:59 2008 commencing singleton removal, final pass Thu Mar 6 19:37:37 2008 memory use: 954.0 MB Thu Mar 6 19:37:47 2008 commencing in-memory singleton removal Thu Mar 6 19:37:54 2008 begin with 27980332 relations and 26968974 unique ideals Thu Mar 6 19:39:18 2008 reduce to 20216944 relations and 18771328 ideals in 16 passes Thu Mar 6 19:39:18 2008 max relations containing the same ideal: 219 Thu Mar 6 19:39:45 2008 removing 2967428 relations and 2567428 ideals in 400000 cliques Thu Mar 6 19:39:47 2008 commencing in-memory singleton removal Thu Mar 6 19:39:52 2008 begin with 17249516 relations and 18771328 unique ideals Thu Mar 6 19:40:29 2008 reduce to 16974741 relations and 15922385 ideals in 9 passes Thu Mar 6 19:40:29 2008 max relations containing the same ideal: 187 Thu Mar 6 19:40:50 2008 removing 2186299 relations and 1786299 ideals in 400000 cliques Thu Mar 6 19:40:51 2008 commencing in-memory singleton removal Thu Mar 6 19:40:55 2008 begin with 14788442 relations and 15922385 unique ideals Thu Mar 6 19:41:27 2008 reduce to 14602209 relations and 13945659 ideals in 9 passes Thu Mar 6 19:41:27 2008 max relations containing the same ideal: 171 Thu Mar 6 19:41:45 2008 removing 1893292 relations and 1502986 ideals in 390306 cliques Thu Mar 6 19:41:46 2008 commencing in-memory singleton removal Thu Mar 6 19:41:49 2008 begin with 12708917 relations and 13945659 unique ideals Thu Mar 6 19:42:14 2008 reduce to 12543518 relations and 12273387 ideals in 8 passes Thu Mar 6 19:42:14 2008 max relations containing the same ideal: 149 Thu Mar 6 19:42:30 2008 dataset has 72.5% excess relations Thu Mar 6 19:42:31 2008 ignoring smallest 71274 rational and 70844 algebraic ideals Thu Mar 6 19:42:31 2008 filtering rational ideals above 900000 Thu Mar 6 19:42:31 2008 filtering algebraic ideals above 900000 Thu Mar 6 19:42:31 2008 need 243117 more relations than ideals Thu Mar 6 19:42:31 2008 commencing singleton removal, final pass Thu Mar 6 19:45:51 2008 memory use: 426.3 MB Thu Mar 6 19:45:55 2008 commencing in-memory singleton removal Thu Mar 6 19:45:58 2008 begin with 12543518 relations and 12287883 unique ideals Thu Mar 6 19:46:01 2008 reduce to 12543518 relations and 12287883 ideals in 1 passes Thu Mar 6 19:46:01 2008 max relations containing the same ideal: 163 Thu Mar 6 19:46:18 2008 dataset has 63.2% excess relations Thu Mar 6 19:46:19 2008 ignoring smallest 63951 rational and 63631 algebraic ideals Thu Mar 6 19:46:19 2008 filtering rational ideals above 800000 Thu Mar 6 19:46:19 2008 filtering algebraic ideals above 800000 Thu Mar 6 19:46:19 2008 need 204508 more relations than ideals Thu Mar 6 19:46:19 2008 commencing singleton removal, final pass Thu Mar 6 19:49:37 2008 memory use: 432.2 MB Thu Mar 6 19:49:43 2008 commencing in-memory singleton removal Thu Mar 6 19:49:46 2008 begin with 12543518 relations and 12302419 unique ideals Thu Mar 6 19:49:49 2008 reduce to 12543518 relations and 12302419 ideals in 1 passes Thu Mar 6 19:49:49 2008 max relations containing the same ideal: 168 Thu Mar 6 19:50:04 2008 removing 146751 relations and 128456 ideals in 18295 cliques Thu Mar 6 19:50:05 2008 commencing in-memory singleton removal Thu Mar 6 19:50:08 2008 begin with 12396767 relations and 12302419 unique ideals Thu Mar 6 19:50:22 2008 reduce to 12395773 relations and 12172968 ideals in 5 passes Thu Mar 6 19:50:22 2008 max relations containing the same ideal: 166 Thu Mar 6 19:50:36 2008 removing 122071 relations and 103776 ideals in 18295 cliques Thu Mar 6 19:50:36 2008 commencing in-memory singleton removal Thu Mar 6 19:50:39 2008 begin with 12273702 relations and 12172968 unique ideals Thu Mar 6 19:50:57 2008 reduce to 12272927 relations and 12068415 ideals in 6 passes Thu Mar 6 19:50:57 2008 max relations containing the same ideal: 166 Thu Mar 6 19:51:01 2008 dataset has 30.6% excess relations Thu Mar 6 19:51:01 2008 ignoring smallest 56543 rational and 56210 algebraic ideals Thu Mar 6 19:51:01 2008 filtering rational ideals above 700000 Thu Mar 6 19:51:01 2008 filtering algebraic ideals above 700000 Thu Mar 6 19:51:01 2008 need 169143 more relations than ideals Thu Mar 6 19:51:01 2008 commencing singleton removal, final pass Thu Mar 6 19:54:19 2008 memory use: 429.1 MB Thu Mar 6 19:54:24 2008 commencing in-memory singleton removal Thu Mar 6 19:54:27 2008 begin with 12272927 relations and 12083244 unique ideals Thu Mar 6 19:54:30 2008 reduce to 12272927 relations and 12083244 ideals in 1 passes Thu Mar 6 19:54:30 2008 max relations containing the same ideal: 186 Thu Mar 6 19:54:45 2008 removing 66659 relations and 56389 ideals in 10270 cliques Thu Mar 6 19:54:45 2008 commencing in-memory singleton removal Thu Mar 6 19:54:49 2008 begin with 12206268 relations and 12083244 unique ideals Thu Mar 6 19:55:00 2008 reduce to 12206046 relations and 12026633 ideals in 4 passes Thu Mar 6 19:55:00 2008 max relations containing the same ideal: 186 Thu Mar 6 19:55:14 2008 removing 62981 relations and 52712 ideals in 10269 cliques Thu Mar 6 19:55:14 2008 commencing in-memory singleton removal Thu Mar 6 19:55:17 2008 begin with 12143065 relations and 12026633 unique ideals Thu Mar 6 19:55:29 2008 reduce to 12142833 relations and 11973687 ideals in 4 passes Thu Mar 6 19:55:29 2008 max relations containing the same ideal: 184 Thu Mar 6 19:55:33 2008 dataset has 8.0% excess relations Thu Mar 6 19:55:39 2008 relations with 0 large ideals: 470 Thu Mar 6 19:55:39 2008 relations with 1 large ideals: 137 Thu Mar 6 19:55:39 2008 relations with 2 large ideals: 4202 Thu Mar 6 19:55:39 2008 relations with 3 large ideals: 47149 Thu Mar 6 19:55:39 2008 relations with 4 large ideals: 288856 Thu Mar 6 19:55:39 2008 relations with 5 large ideals: 1057133 Thu Mar 6 19:55:39 2008 relations with 6 large ideals: 2391238 Thu Mar 6 19:55:39 2008 relations with 7+ large ideals: 8353648 Thu Mar 6 19:55:39 2008 commencing 2-way merge Thu Mar 6 19:55:58 2008 reduce to 7715679 relation sets and 7546532 unique ideals Thu Mar 6 19:55:58 2008 commencing full merge Thu Mar 6 19:59:15 2008 memory use: 923.6 MB Thu Mar 6 19:59:15 2008 found 4216899 cycles, need 4160732 Thu Mar 6 19:59:17 2008 weight of 4160732 cycles is about 270625461 (65.04/cycle) Thu Mar 6 19:59:17 2008 distribution of cycle lengths: Thu Mar 6 19:59:17 2008 1 relations: 592041 Thu Mar 6 19:59:17 2008 2 relations: 580481 Thu Mar 6 19:59:17 2008 3 relations: 549722 Thu Mar 6 19:59:17 2008 4 relations: 486665 Thu Mar 6 19:59:17 2008 5 relations: 421911 Thu Mar 6 19:59:17 2008 6 relations: 357647 Thu Mar 6 19:59:17 2008 7 relations: 298193 Thu Mar 6 19:59:17 2008 8 relations: 241011 Thu Mar 6 19:59:17 2008 9 relations: 189410 Thu Mar 6 19:59:17 2008 10+ relations: 443651 Thu Mar 6 19:59:17 2008 heaviest cycle: 17 relations Thu Mar 6 19:59:18 2008 commencing cycle optimization Thu Mar 6 19:59:25 2008 start with 20428107 relations Thu Mar 6 20:00:05 2008 pruned 128617 relations Thu Mar 6 20:00:05 2008 memory use: 706.6 MB Thu Mar 6 20:00:05 2008 distribution of cycle lengths: Thu Mar 6 20:00:05 2008 1 relations: 592041 Thu Mar 6 20:00:05 2008 2 relations: 581592 Thu Mar 6 20:00:05 2008 3 relations: 553367 Thu Mar 6 20:00:05 2008 4 relations: 489254 Thu Mar 6 20:00:05 2008 5 relations: 426001 Thu Mar 6 20:00:05 2008 6 relations: 359696 Thu Mar 6 20:00:05 2008 7 relations: 300095 Thu Mar 6 20:00:05 2008 8 relations: 240853 Thu Mar 6 20:00:05 2008 9 relations: 188975 Thu Mar 6 20:00:05 2008 10+ relations: 428858 Thu Mar 6 20:00:05 2008 heaviest cycle: 17 relations Thu Mar 6 20:00:17 2008 Thu Mar 6 20:00:17 2008 commencing linear algebra Thu Mar 6 20:00:19 2008 read 4160732 cycles Thu Mar 6 20:00:38 2008 cycles contain 11903155 unique relations Thu Mar 6 20:02:46 2008 read 11903155 relations Thu Mar 6 20:03:07 2008 using 32 quadratic characters above 536870564 Thu Mar 6 20:05:06 2008 building initial matrix Thu Mar 6 20:08:22 2008 memory use: 1580.3 MB Thu Mar 6 20:08:24 2008 read 4160732 cycles Thu Mar 6 20:08:41 2008 matrix is 4160564 x 4160732 (1201.9 MB) with weight 399461439 (96.01/col) Thu Mar 6 20:08:41 2008 sparse part has weight 265150709 (63.73/col) Thu Mar 6 20:09:27 2008 filtering completed in 2 passes Thu Mar 6 20:09:29 2008 matrix is 4158147 x 4158315 (1201.7 MB) with weight 399361579 (96.04/col) Thu Mar 6 20:09:29 2008 sparse part has weight 265129714 (63.76/col) Thu Mar 6 20:10:39 2008 read 4158315 cycles Thu Mar 6 20:10:51 2008 matrix is 4158147 x 4158315 (1201.7 MB) with weight 399361579 (96.04/col) Thu Mar 6 20:10:51 2008 sparse part has weight 265129714 (63.76/col) Thu Mar 6 20:10:51 2008 saving the first 48 matrix rows for later Thu Mar 6 20:10:53 2008 matrix is 4158099 x 4158315 (1167.1 MB) with weight 309840159 (74.51/col) Thu Mar 6 20:10:53 2008 sparse part has weight 264370975 (63.58/col) Thu Mar 6 20:10:53 2008 matrix includes 64 packed rows Thu Mar 6 20:10:53 2008 using block size 65536 for processor cache size 4096 kB Thu Mar 6 20:11:24 2008 commencing Lanczos iteration (4 threads) Thu Mar 6 20:11:24 2008 memory use: 1214.6 MB Sat Mar 8 01:54:51 2008 Sat Mar 8 01:54:51 2008 Sat Mar 8 01:54:51 2008 Msieve v. 1.33 Sat Mar 8 01:54:51 2008 random seeds: 2d3f5fd0 2ef5217c Sat Mar 8 01:54:51 2008 factoring 35045282158487636123259014292004089245227471550191132494367732831303373727594575532334779423274207863833033604171200909745257231922557618156366994601 (149 digits) Sat Mar 8 01:54:52 2008 no P-1/P+1/ECM available, skipping Sat Mar 8 01:54:52 2008 commencing number field sieve (149-digit input) Sat Mar 8 01:54:52 2008 R0: -30104817950070729324593475027 Sat Mar 8 01:54:52 2008 R1: 5053580822033843 Sat Mar 8 01:54:52 2008 A0: 1582043507098494327107617309192676 Sat Mar 8 01:54:52 2008 A1: 39725247684687428138366842123 Sat Mar 8 01:54:52 2008 A2: -24684440038757266241210 Sat Mar 8 01:54:52 2008 A3: -2155369437080572429 Sat Mar 8 01:54:52 2008 A4: 88032011055 Sat Mar 8 01:54:52 2008 A5: 1417260 Sat Mar 8 01:54:52 2008 size score = 3.315952e-15, Murphy alpha = -5.040913, combined = 1.779734e-14 Sat Mar 8 01:54:52 2008 Sat Mar 8 01:54:52 2008 commencing linear algebra Sat Mar 8 01:54:53 2008 read 4158315 cycles Sat Mar 8 01:54:56 2008 matrix is 4158147 x 4158315 (1201.7 MB) with weight 399361579 (96.04/col) Sat Mar 8 01:54:56 2008 sparse part has weight 265129714 (63.76/col) Sat Mar 8 01:54:56 2008 saving the first 48 matrix rows for later Sat Mar 8 01:54:58 2008 matrix is 4158099 x 4158315 (1167.1 MB) with weight 309840159 (74.51/col) Sat Mar 8 01:54:58 2008 sparse part has weight 264370975 (63.58/col) Sat Mar 8 01:54:58 2008 matrix includes 64 packed rows Sat Mar 8 01:54:58 2008 using block size 65536 for processor cache size 4096 kB Sat Mar 8 01:55:38 2008 Sat Mar 8 01:55:38 2008 Sat Mar 8 01:55:38 2008 Msieve v. 1.33 Sat Mar 8 01:55:38 2008 random seeds: 1e1aba23 9d91f5fa Sat Mar 8 01:55:38 2008 factoring 35045282158487636123259014292004089245227471550191132494367732831303373727594575532334779423274207863833033604171200909745257231922557618156366994601 (149 digits) Sat Mar 8 01:55:39 2008 no P-1/P+1/ECM available, skipping Sat Mar 8 01:55:39 2008 commencing number field sieve (149-digit input) Sat Mar 8 01:55:39 2008 R0: -30104817950070729324593475027 Sat Mar 8 01:55:39 2008 R1: 5053580822033843 Sat Mar 8 01:55:39 2008 A0: 1582043507098494327107617309192676 Sat Mar 8 01:55:39 2008 A1: 39725247684687428138366842123 Sat Mar 8 01:55:39 2008 A2: -24684440038757266241210 Sat Mar 8 01:55:39 2008 A3: -2155369437080572429 Sat Mar 8 01:55:39 2008 A4: 88032011055 Sat Mar 8 01:55:39 2008 A5: 1417260 Sat Mar 8 01:55:39 2008 size score = 3.315952e-15, Murphy alpha = -5.040913, combined = 1.779734e-14 Sat Mar 8 01:55:39 2008 Sat Mar 8 01:55:39 2008 commencing linear algebra Sat Mar 8 01:55:40 2008 read 4158315 cycles Sat Mar 8 01:55:43 2008 matrix is 4158147 x 4158315 (1201.7 MB) with weight 399361579 (96.04/col) Sat Mar 8 01:55:43 2008 sparse part has weight 265129714 (63.76/col) Sat Mar 8 01:55:43 2008 saving the first 48 matrix rows for later Sat Mar 8 01:55:45 2008 matrix is 4158099 x 4158315 (1167.1 MB) with weight 309840159 (74.51/col) Sat Mar 8 01:55:45 2008 sparse part has weight 264370975 (63.58/col) Sat Mar 8 01:55:45 2008 matrix includes 64 packed rows Sat Mar 8 01:55:45 2008 using block size 65536 for processor cache size 4096 kB Sat Mar 8 01:56:17 2008 commencing Lanczos iteration (4 threads) Sat Mar 8 01:56:17 2008 memory use: 1214.6 MB Sat Mar 8 01:56:18 2008 restarting at iteration 44294 (dim = 2800781) Sat Mar 8 15:08:46 2008 lanczos halted after 65762 iterations (dim = 4158097) Sat Mar 8 15:08:55 2008 recovered 44 nontrivial dependencies Sat Mar 8 15:08:56 2008 elapsed time 13:13:18 Sat Mar 8 15:08:56 2008 Sat Mar 8 15:08:56 2008 Sat Mar 8 15:08:56 2008 Msieve v. 1.33 Sat Mar 8 15:08:56 2008 random seeds: 3d43e06a a732b2b1 Sat Mar 8 15:08:56 2008 factoring 35045282158487636123259014292004089245227471550191132494367732831303373727594575532334779423274207863833033604171200909745257231922557618156366994601 (149 digits) Sat Mar 8 15:08:58 2008 no P-1/P+1/ECM available, skipping Sat Mar 8 15:08:58 2008 commencing number field sieve (149-digit input) Sat Mar 8 15:08:58 2008 R0: -30104817950070729324593475027 Sat Mar 8 15:08:58 2008 R1: 5053580822033843 Sat Mar 8 15:08:58 2008 A0: 1582043507098494327107617309192676 Sat Mar 8 15:08:58 2008 A1: 39725247684687428138366842123 Sat Mar 8 15:08:58 2008 A2: -24684440038757266241210 Sat Mar 8 15:08:58 2008 A3: -2155369437080572429 Sat Mar 8 15:08:58 2008 A4: 88032011055 Sat Mar 8 15:08:58 2008 A5: 1417260 Sat Mar 8 15:08:58 2008 size score = 3.315952e-15, Murphy alpha = -5.040913, combined = 1.779734e-14 Sat Mar 8 15:08:58 2008 Sat Mar 8 15:08:58 2008 commencing square root phase Sat Mar 8 15:08:58 2008 reading relations for dependency 1 Sat Mar 8 15:08:58 2008 read 2079326 cycles Sat Mar 8 15:09:06 2008 cycles contain 7226553 unique relations Sat Mar 8 15:15:09 2008 read 7226553 relations Sat Mar 8 15:16:16 2008 multiplying 10147628 relations Sat Mar 8 16:04:21 2008 multiply complete, coefficients have about 555.91 million bits Sat Mar 8 16:04:47 2008 initial square root is modulo 97171 Sat Mar 8 17:41:31 2008 reading relations for dependency 2 Sat Mar 8 17:41:36 2008 read 2078713 cycles Sat Mar 8 17:41:45 2008 cycles contain 7224575 unique relations Sat Mar 8 17:47:24 2008 read 7224575 relations Sat Mar 8 17:48:31 2008 multiplying 10148250 relations Sat Mar 8 18:36:29 2008 multiply complete, coefficients have about 555.95 million bits Sat Mar 8 18:36:54 2008 initial square root is modulo 97231 Sat Mar 8 20:13:15 2008 prp69 factor: 745832506848141808511611576240568244832258614550704416204357517716551 Sat Mar 8 20:13:15 2008 prp80 factor: 46988139879538892325015289211281843797083431443099045770269959929002737021425551 Sat Mar 8 20:13:15 2008 elapsed time 05:04:19 [/code] |

[QUOTE=fivemack;128220]The C149 of M1575 splits as 745832506848141808511611576240568244832258614550704416204357517716551 * 46988139879538892325015289211281843797083431443099045770269959929002737021425551
[code] Sat Mar 8 20:13:15 2008 prp69 factor: 745832506848141808511611576240568244832258614550704416204357517716551 Sat Mar 8 20:13:15 2008 prp80 factor: 46988139879538892325015289211281843797083431443099045770269959929002737021425551 [/code][/QUOTE] :tu: That explains why ECM was unable to factor it... |

Well, yes ... I'm not exactly sure of the statistics (I've done them, but I didn't know how to do the Bayesian prior ab-initio so used the distribution of second-largest factors among the partition numbers), but I suspect that the right amount of ECM to do on a number of this sort of size is a few hundred hours, then go to GNFS. With jasonp's software, GNFS really isn't scary on numbers up to 512 bits; a month on ten cores.
One curve at 43M on the C149 takes about 7.5 minutes on the same machine I did the sieving on, so the 3800 that were done took about a quarter as long as the whole GNFS sieving. I'm not sure there's much GNFS scope left in elevensmooth; M2376 is a relatively difficult SNFS number (and various people, including me, are sieving it as I type), the cofactors if ECM finds a 50-60-digit factor of 3360 would be trivial. If ECM finds a 50-60 digit factor of 3168 it would be tempting to do the hard-to-very-hard cofactor by GNFS, ditto for a 60+digit factor of 3080. |

Congratulations and Thank you!
The ElevenSmooth [URL="http://elevensmooth.com/ElevenFactors.html"]factors page[/URL] and [URL="http://elevensmooth.com/"]news page[/URL]factors page and news page have been updated. |

The C195 of 2^1188+1 splits as 277122598884572475987115421160411960915959497148103077473 * 788665950001479674650705813903186632356777925726120062399203449921568833081885177105857167806618988123915663929402035777496273563382522049
After sieving, it took two hours on one C2/2400 CPU to build a 7933391 x 7933638 matrix with weight 536309417, about 180 hours on four C2/2400 CPUs to find 49 dependencies, and about 2:45 per dependency for the square roots; success came on the second dependency. It's a P57 factor, so it would have been unusual luck for the ECM done so far to have found it. This marks the end of my involvement with ElevenSmooth, until computers grow a good deal faster. |

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