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fivemack 2008-03-09 01:42

New factor
 
The 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]

rogue 2008-03-09 02:24

[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...

fivemack 2008-03-09 03:30

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.

wblipp 2008-03-09 05:01

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.

fivemack 2008-05-07 19:28

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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