[QUOTE=bdodson;112351]This short table's now one shorter, after 7,317 c202 = p51*p151, with
p51 = 399676211948778347375576150888294069325575626336229 [/QUOTE] Just a nitpick. It's p51*p152, not p151. 
Factorisation of 7^2631
1 Attachment(s)
87808581809525792134370860453721419342992604246001922594107781828847401497090250623000616403314204187748641525231019439257581826238153281895147142837427201101541 = 330356473356706630143084182110481076968694111519479821312366757981 * 265799489010506998952247476548157401788003618449001603472530395754819736985343973809633195038761
Software used: gnfslasieve4I14e for sieving, msieve1.30 for linalg (the merge phase did not fit in 4GB under msieve1.28) Polynomials used: x^67 and 7^44x Sieving limits: small primes to 40 million, large primes to 2^30 Sieved algebraic specialQ from 36.5e6 to 79e6 in 5600 CPUhours, on six CPUs (three dualcore machines) of average 2.3GHz Found 90729983 relations and 45934 free relations, from which 82107167 unique relations Constructed a 7163141 x 7163388 matrix of weight 478901308 in 173 minutes Solved in 176 hours (two CPUs), using 2.5G memory Square root took five hours; solution found on the first dependency msieve log attached 
7,263
Nice.
What do you intend to do next? I am about 85% sieved with 6,299 and will do 2,776+ next, which will take a while with my resources. I get about 140 hrs/day with my collection of machines. 
At present I'm doing, with a collaborator, a C156 GNFS on a nonCunningham number; I expect this to take about as much CPU time as 7,263, but thanks to the collaboration there will be more CPUs working on it, and it might be finished by midJanuary. I don't yet have a plan for the stage after that; I'm vaguely contemplating wider collaborations to do a larger GNFS job.

I'll do 7,269 c224.
Alex 
[QUOTE=garo;48284][CODE]Base Index Size 11M(45digits) 43M(50digits) 110M(55digits) 260M(60digits) Decimal
7 269 C224 0(0.267423) 0(0.0522979) 165(0.00921839) 0(0.00148122) 1660265... 7 271 C214 0(0.267423) 0(0.0522979) 165(0.00921839) 0(0.00148122) 157020... 7 277 C201 0(0.290133) 30(0.0561584) 165(0.00980315) 0(0.00148122) 274499... 7 281 C165 0(2.63512) 2160(0.477957) 0(0.0754361) 300(0.0068697) 185248827501208343062750485931112817975629927609513170657610022785421928683373794979982241274691966304649468484472255815588739520597115203376303263535408573237014157 ...[/CODE][/QUOTE] Looks like a 4th hole, pending Alex's breaking of the 1st hole. 7,281 c165 done with p53 = 41601158252896546668861917466611604127922008421733517 found during the 5th t50, before 4.5*t50, but not exactly late for a p53. 2nd of two factors this morning, the other in the [still nonsticky] 2 discussion. Bruce 
7,269:
[CODE] Probable prime factor 1 has 82 digits: 4462060605403381961780411332028022754534242152003773412732171224503049883657394827 Probable prime factor 2 has 142 digits: 3720848769582826092237529016309237616548794511295400940058189854803271477562040904704041158521598520073343762354423669834498921937027750690971 [/CODE] Alex 
Congratulations! What are you sieving next?

I'm not sieving anything at the moment, I'll run P+/1 stage 2 on a bunch of residues we accumulated for a while. The matrix for 3,533 is at 80%. When I do NFS again, it'll probably be one or both of the c160 from the 3 table.
Alex 
7^3871 C154 cofactor splits as
[code] P70 4583142681916056752995023804494031799489400087334962946866717203441543 P84 457299108883653825883853223306465080566360541916826721338777118806091728304473122859 [/code] Not quite sure how much CPU time I used, but it took two weeks realtime on maybe six cores; 100 hours for the linear algebra (95 hours of that on two cores for the matrix), using msieve1.29 with default parameters because I'd just had a couple of failures with msieve1.33. x^6+x^3+1, x7^43; 30bit large primes, small primes <25e6 on both sides. [code] Wed Feb 20 21:58:34 2008 Msieve v. 1.29 Wed Feb 20 21:58:34 2008 random seeds: 81975669 db274a81 Wed Feb 20 21:58:34 2008 factoring 2095867064326852049468708025219963891883437656350890684735312307910868519605941526543012489340565259400896935298036531088556378430157620037769819463531437 (154 digits) Wed Feb 20 21:58:34 2008 commencing number field sieve (154digit input) Wed Feb 20 21:58:35 2008 R0: 2183814375991796599109312252753832343 Wed Feb 20 21:58:35 2008 R1: 1 Wed Feb 20 21:58:35 2008 A0: 1 Wed Feb 20 21:58:35 2008 A1: 0 Wed Feb 20 21:58:35 2008 A2: 0 Wed Feb 20 21:58:35 2008 A3: 1 Wed Feb 20 21:58:35 2008 A4: 0 Wed Feb 20 21:58:35 2008 A5: 0 Wed Feb 20 21:58:35 2008 A6: 1 Wed Feb 20 21:58:35 2008 size score = 1.957443e10, Murphy alpha = 1.935662, combined = 1.125911e10 Wed Feb 20 22:09:03 2008 restarting with 86633601 relations Wed Feb 20 22:09:03 2008 Wed Feb 20 22:09:03 2008 commencing relation filtering Wed Feb 20 22:09:03 2008 commencing duplicate removal, pass 1 Wed Feb 20 22:09:17 2008 error 10 reading relation 1722289 Wed Feb 20 22:14:11 2008 error 10 reading relation 37387593 Wed Feb 20 22:15:08 2008 error 10 reading relation 44262255 Wed Feb 20 22:18:31 2008 error 10 reading relation 68351484 Wed Feb 20 22:21:32 2008 found 18462022 hash collisions in 86633597 relations Wed Feb 20 22:21:32 2008 commencing duplicate removal, pass 2 Wed Feb 20 22:30:05 2008 found 7991052 duplicates and 78642545 unique relations Wed Feb 20 22:30:05 2008 memory use: 504.8 MB Wed Feb 20 22:30:28 2008 ignoring smallest 3249249 rational and 3248797 algebraic ideals Wed Feb 20 22:30:28 2008 filtering ideals above 54412471 Wed Feb 20 22:30:28 2008 need 11046678 more relations than ideals Wed Feb 20 22:30:28 2008 commencing singleton removal, pass 1 Wed Feb 20 22:42:48 2008 relations with 0 large ideals: 2150491 Wed Feb 20 22:42:48 2008 relations with 1 large ideals: 11700615 Wed Feb 20 22:42:48 2008 relations with 2 large ideals: 26144693 Wed Feb 20 22:42:48 2008 relations with 3 large ideals: 27165833 Wed Feb 20 22:42:48 2008 relations with 4 large ideals: 11291370 Wed Feb 20 22:42:48 2008 relations with 5 large ideals: 189543 Wed Feb 20 22:42:48 2008 relations with 6 large ideals: 0 Wed Feb 20 22:42:48 2008 relations with 7+ large ideals: 0 Wed Feb 20 22:42:48 2008 78642545 relations and about 57801182 large ideals Wed Feb 20 22:42:48 2008 commencing singleton removal, pass 2 Wed Feb 20 22:54:41 2008 found 17689591 singletons Wed Feb 20 22:54:41 2008 current dataset: 60952954 relations and about 38361402 large ideals Wed Feb 20 22:54:47 2008 commencing singleton removal, pass 3 Wed Feb 20 23:04:39 2008 relations with 0 large ideals: 2150491 Wed Feb 20 23:04:39 2008 relations with 1 large ideals: 10507928 Wed Feb 20 23:04:39 2008 relations with 2 large ideals: 21103317 Wed Feb 20 23:04:39 2008 relations with 3 large ideals: 19705929 Wed Feb 20 23:04:39 2008 relations with 4 large ideals: 7370522 Wed Feb 20 23:04:39 2008 relations with 5 large ideals: 114767 Wed Feb 20 23:04:39 2008 relations with 6 large ideals: 0 Wed Feb 20 23:04:39 2008 relations with 7+ large ideals: 0 Wed Feb 20 23:04:39 2008 60952954 relations and about 48513054 large ideals Wed Feb 20 23:04:39 2008 commencing singleton removal, pass 4 Wed Feb 20 23:14:26 2008 found 13709829 singletons Wed Feb 20 23:14:26 2008 current dataset: 47243125 relations and about 33452791 large ideals Wed Feb 20 23:14:30 2008 commencing singleton removal, pass 5 Wed Feb 20 23:22:40 2008 found 3591646 singletons Wed Feb 20 23:22:40 2008 current dataset: 43651479 relations and about 29746456 large ideals Wed Feb 20 23:22:45 2008 commencing singleton removal, pass 6 Wed Feb 20 23:30:58 2008 found 946498 singletons Wed Feb 20 23:30:58 2008 current dataset: 42704981 relations and about 28791073 large ideals Wed Feb 20 23:31:02 2008 commencing singleton removal, pass 7 Wed Feb 20 23:39:15 2008 found 247491 singletons Wed Feb 20 23:39:15 2008 current dataset: 42457490 relations and about 28542982 large ideals Wed Feb 20 23:39:19 2008 commencing singleton removal, final pass Wed Feb 20 23:48:14 2008 memory use: 1315.2 MB Wed Feb 20 23:48:14 2008 commencing inmemory singleton removal Wed Feb 20 23:48:19 2008 begin with 42457490 relations and 32642470 unique ideals Wed Feb 20 23:49:32 2008 reduce to 35506412 relations and 25489736 ideals in 17 passes Wed Feb 20 23:49:32 2008 max relations containing the same ideal: 44 Wed Feb 20 23:49:36 2008 dataset has 54.1% excess relations Wed Feb 20 23:49:50 2008 ignoring smallest 2942925 rational and 2942497 algebraic ideals Wed Feb 20 23:49:50 2008 filtering ideals above 48971223 Wed Feb 20 23:49:50 2008 need 9015008 more relations than ideals Wed Feb 20 23:49:50 2008 commencing singleton removal, final pass Wed Feb 20 23:59:34 2008 memory use: 1307.2 MB Wed Feb 20 23:59:34 2008 commencing inmemory singleton removal Wed Feb 20 23:59:39 2008 begin with 42457490 relations and 33254381 unique ideals Thu Feb 21 00:00:55 2008 reduce to 35486599 relations and 26081020 ideals in 17 passes Thu Feb 21 00:00:55 2008 max relations containing the same ideal: 47 Thu Feb 21 00:01:20 2008 removing 2175672 relations and 1980387 ideals in 195285 cliques Thu Feb 21 00:01:22 2008 commencing inmemory singleton removal Thu Feb 21 00:01:26 2008 begin with 33310927 relations and 26081020 unique ideals Thu Feb 21 00:02:02 2008 reduce to 33228356 relations and 24017486 ideals in 9 passes Thu Feb 21 00:02:02 2008 max relations containing the same ideal: 45 Thu Feb 21 00:02:25 2008 removing 1572631 relations and 1377346 ideals in 195285 cliques Thu Feb 21 00:02:26 2008 commencing inmemory singleton removal Thu Feb 21 00:02:30 2008 begin with 31655725 relations and 24017486 unique ideals Thu Feb 21 00:03:00 2008 reduce to 31609120 relations and 22593236 ideals in 8 passes Thu Feb 21 00:03:00 2008 max relations containing the same ideal: 44 Thu Feb 21 00:03:22 2008 removing 12223 relations and 11348 ideals in 875 cliques Thu Feb 21 00:03:22 2008 commencing inmemory singleton removal Thu Feb 21 00:03:26 2008 begin with 31596897 relations and 22593236 unique ideals Thu Feb 21 00:03:33 2008 reduce to 31596896 relations and 22581887 ideals in 2 passes Thu Feb 21 00:03:33 2008 max relations containing the same ideal: 44 Thu Feb 21 00:03:43 2008 dataset has 38.7% excess relations Thu Feb 21 00:03:55 2008 ignoring smallest 2634707 rational and 2634397 algebraic ideals Thu Feb 21 00:03:55 2008 filtering ideals above 43529976 Thu Feb 21 00:03:55 2008 need 7212007 more relations than ideals Thu Feb 21 00:03:55 2008 commencing singleton removal, final pass Thu Feb 21 00:11:51 2008 memory use: 1069.9 MB Thu Feb 21 00:11:51 2008 commencing inmemory singleton removal Thu Feb 21 00:11:54 2008 begin with 31596896 relations and 23196884 unique ideals Thu Feb 21 00:12:20 2008 reduce to 31581170 relations and 23181158 ideals in 7 passes Thu Feb 21 00:12:20 2008 max relations containing the same ideal: 45 Thu Feb 21 00:12:43 2008 removing 2552970 relations and 2152970 ideals in 400000 cliques Thu Feb 21 00:12:45 2008 commencing inmemory singleton removal Thu Feb 21 00:12:48 2008 begin with 29028200 relations and 23181158 unique ideals Thu Feb 21 00:13:15 2008 reduce to 28892502 relations and 20890951 ideals in 8 passes Thu Feb 21 00:13:15 2008 max relations containing the same ideal: 43 Thu Feb 21 00:13:35 2008 removing 2301750 relations and 1901750 ideals in 400000 cliques Thu Feb 21 00:13:37 2008 commencing inmemory singleton removal Thu Feb 21 00:13:40 2008 begin with 26590752 relations and 20890951 unique ideals Thu Feb 21 00:14:01 2008 reduce to 26472647 relations and 18869598 ideals in 7 passes Thu Feb 21 00:14:01 2008 max relations containing the same ideal: 42 Thu Feb 21 00:14:19 2008 removing 2080170 relations and 1689129 ideals in 391041 cliques Thu Feb 21 00:14:21 2008 commencing inmemory singleton removal Thu Feb 21 00:14:24 2008 begin with 24392477 relations and 18869598 unique ideals Thu Feb 21 00:14:43 2008 reduce to 24287430 relations and 17074041 ideals in 7 passes Thu Feb 21 00:14:43 2008 max relations containing the same ideal: 40 Thu Feb 21 00:14:59 2008 removing 15591 relations and 14210 ideals in 1381 cliques Thu Feb 21 00:15:00 2008 commencing inmemory singleton removal Thu Feb 21 00:15:03 2008 begin with 24271839 relations and 17074041 unique ideals Thu Feb 21 00:15:08 2008 reduce to 24271837 relations and 17059829 ideals in 2 passes Thu Feb 21 00:15:08 2008 max relations containing the same ideal: 40 Thu Feb 21 00:15:15 2008 dataset has 11.0% excess relations Thu Feb 21 00:15:26 2008 ignoring smallest 2324114 rational and 2324293 algebraic ideals Thu Feb 21 00:15:26 2008 filtering ideals above 38088729 Thu Feb 21 00:15:26 2008 need 7017889 more relations than ideals Thu Feb 21 00:15:26 2008 commencing singleton removal, final pass Thu Feb 21 00:22:52 2008 memory use: 835.6 MB Thu Feb 21 00:22:52 2008 commencing inmemory singleton removal Thu Feb 21 00:22:54 2008 begin with 24271837 relations and 17678440 unique ideals Thu Feb 21 00:23:14 2008 reduce to 24251083 relations and 17657685 ideals in 7 passes Thu Feb 21 00:23:14 2008 max relations containing the same ideal: 40 Thu Feb 21 00:23:16 2008 dataset has 1.5% excess relations Thu Feb 21 00:23:19 2008 relations with 0 large ideals: 696101 Thu Feb 21 00:23:19 2008 relations with 1 large ideals: 3279608 Thu Feb 21 00:23:19 2008 relations with 2 large ideals: 7156515 Thu Feb 21 00:23:19 2008 relations with 3 large ideals: 7840821 Thu Feb 21 00:23:19 2008 relations with 4 large ideals: 4313963 Thu Feb 21 00:23:19 2008 relations with 5 large ideals: 964075 Thu Feb 21 00:23:19 2008 relations with 6 large ideals: 0 Thu Feb 21 00:23:19 2008 relations with 7+ large ideals: 0 Thu Feb 21 00:23:19 2008 commencing 2way merge Thu Feb 21 00:23:44 2008 reduce to 15318012 relation sets and 8724614 unique ideals Thu Feb 21 00:23:44 2008 commencing full merge Thu Feb 21 00:28:56 2008 found 7372243 cycles, need 5562814 Thu Feb 21 00:29:03 2008 weight of 5562814 cycles is about 361703750 (65.02/cycle) Thu Feb 21 00:29:03 2008 distribution of cycle lengths: Thu Feb 21 00:29:03 2008 1 relations: 1064006 Thu Feb 21 00:29:03 2008 2 relations: 712935 Thu Feb 21 00:29:03 2008 3 relations: 615306 Thu Feb 21 00:29:03 2008 4 relations: 540088 Thu Feb 21 00:29:03 2008 5 relations: 489752 Thu Feb 21 00:29:03 2008 6 relations: 444477 Thu Feb 21 00:29:03 2008 7 relations: 405935 Thu Feb 21 00:29:03 2008 8 relations: 368677 Thu Feb 21 00:29:03 2008 9 relations: 330499 Thu Feb 21 00:29:03 2008 10+ relations: 591139 Thu Feb 21 00:29:03 2008 heaviest cycle: 13 relations Thu Feb 21 00:29:04 2008 commencing cycle optimization Thu Feb 21 00:29:15 2008 start with 26668809 relations Thu Feb 21 00:30:17 2008 pruned 674553 relations Thu Feb 21 00:30:19 2008 distribution of cycle lengths: Thu Feb 21 00:30:19 2008 1 relations: 1064006 Thu Feb 21 00:30:19 2008 2 relations: 730569 Thu Feb 21 00:30:19 2008 3 relations: 638531 Thu Feb 21 00:30:19 2008 4 relations: 554043 Thu Feb 21 00:30:19 2008 5 relations: 507268 Thu Feb 21 00:30:19 2008 6 relations: 458475 Thu Feb 21 00:30:19 2008 7 relations: 418951 Thu Feb 21 00:30:19 2008 8 relations: 373663 Thu Feb 21 00:30:19 2008 9 relations: 325551 Thu Feb 21 00:30:19 2008 10+ relations: 491757 Thu Feb 21 00:30:19 2008 heaviest cycle: 13 relations Thu Feb 21 00:30:26 2008 Thu Feb 21 00:30:26 2008 commencing linear algebra Thu Feb 21 00:30:35 2008 read 5562814 cycles Thu Feb 21 00:31:09 2008 cycles contain 15512158 unique relations Thu Feb 21 00:38:17 2008 read 15512158 relations Thu Feb 21 00:38:49 2008 using 32 quadratic characters above 1073741312 Thu Feb 21 00:47:45 2008 read 5562814 cycles Thu Feb 21 00:50:44 2008 filtering completed in 3 passes Thu Feb 21 00:50:46 2008 matrix is 5409318 x 5409509 with weight 467914660 (avg 86.50/col) Thu Feb 21 00:52:34 2008 read 5409509 cycles Thu Feb 21 00:52:48 2008 matrix is 5409318 x 5409509 with weight 467914660 (avg 86.50/col) Thu Feb 21 00:52:48 2008 saving the first 48 matrix rows for later Thu Feb 21 00:52:51 2008 matrix is 5409270 x 5409509 with weight 356348373 (avg 65.87/col) Thu Feb 21 00:52:51 2008 matrix includes 64 packed rows Thu Feb 21 00:52:51 2008 using block size 65536 for processor cache size 4096 kB Thu Feb 21 00:53:25 2008 commencing Lanczos iteration (2 threads) Mon Feb 25 00:02:25 2008 lanczos halted after 85543 iterations (dim = 5409234) Mon Feb 25 00:02:39 2008 recovered 35 nontrivial dependencies Mon Feb 25 00:02:41 2008 Mon Feb 25 00:02:41 2008 commencing square root phase Mon Feb 25 00:02:41 2008 reading relations for dependency 1 Mon Feb 25 00:02:49 2008 read 2702718 cycles Mon Feb 25 00:03:01 2008 cycles contain 8998845 unique relations Mon Feb 25 00:11:58 2008 read 8998845 relations Mon Feb 25 00:13:24 2008 multiplying 12692472 relations Mon Feb 25 00:51:21 2008 multiply complete, coefficients have about 308.42 million bits Mon Feb 25 00:51:29 2008 initial square root is modulo 342047 Mon Feb 25 01:35:00 2008 prp70 factor: 4583142681916056752995023804494031799489400087334962946866717203441543 Mon Feb 25 01:35:00 2008 prp84 factor: 457299108883653825883853223306465080566360541916826721338777118806091728304473122859 Mon Feb 25 01:35:00 2008 elapsed time 99:36:26 [/code] 
Not an ECM miss, certainly worth by SNFS
7,295
[CODE] Tue Jun 24 00:30:50 2008 prp81 factor: 204239004182680605398190478754212368873366912490836010105265524712426411236134031 Tue Jun 24 00:30:51 2008 prp111 factor: 393263672474017252292660491631044385409360056708958704520879019006886885032467377758314801669636946200575798561 [/CODE] One minute... Let me mail Prof. Sam Wagstaff before posting further information about it... 
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