7 table
[code]Size Base Index Mod Diff Ratio
320 7 379  320.2 1 274 7 383  323.6 0.846 299 7 389  328.7 0.909 220 7 395  267.0 0.823 /5q 214 7 419  354 0.60 /gnfs 305 7 421  355.7 0.855 221 7 425  287.3 0.767 /5q 315 7 431  364.2 0.863 342 7 433  365.9 0.933 341 7 439  370.9 0.917[/code] 
[code]
7,259 C175 = P69 * P106 P69 = 357708888729481429441295130414301389734167320382217282028474835603757 P106 = 4105565335483009892405469384537186162336640263688626513538197586407434630567675699756450562264314334763133 [/code] This was done using ggnfs. 
2300 curves at B1=11M on 7,263 7,281 7,387 7,361 7,373 7,389 7,391. Adds 0.50108 to p45 and 0.06662 to p50 for each.
Alex 
8394 curves at B1=44M on 7,379 c320. Adds 6.47185 to p45, 1.09425 to p50 and 0.16726 to p55.
Alex 
[QUOTE=akruppa]8394 curves at B1=44M on 7,379 c320. Adds 6.47185 to p45, 1.09425 to p50 and 0.16726 to p55.
Alex[/QUOTE] Hi, What criteria do you use to select your ECM candidates? 
Mostly base 3, where 3,487 just started the matrix job. I'll do others soon. Besides base 3, p,q with p,q prime and no/few known primitive factors are high on my list, too. Currently ECM is running on 11,239 c246.
Alex 
263 = 50 + 213, completes 7, 347
[QUOTE=garo;48284][CODE]Base Index Size 11M(45digits) 43M(50digits) 110M(55digits) 260M(60digits) Decimal
... 7 347 C263 0(0.267423) 0(0.0522979) 165(0.00921839) 0(0.00148122) 33026113620772114208766604063467661003723471054258542654638480163235395066667816968649454626706486286757449262870499223580340566358988528768748899525538521074418576135045990723823283809539231151245039475832681824086824878451971862643338135772425108809320687434713 ... [/CODE][/QUOTE] p50 = 89823582672830825295829211905814036272016809423171 nearing halfway through the last run on the last large incomplete range for testing to p50, 2100 curves/7830 left to go on the generic c251c299 list (not 2 or 2+ with n < 1200). The only other, smaller range left having been updated on the 2 discussion thread. I'm assuming this one's complete, but Paul notes that he has the 213digit cofactor listed as "prp213", with the comment [QUOTE]PS: note that I write 'prp213' and not 'p213', since one of the major computer algebra systems (which I am using) says (courtesy Richard Pinch): > ifactor(381707*293621*29363); (3290922560713061) > isprime(2432870015941); true > ifactor(2432870015941); (1213) (551461) (3637) [/QUOTE] bd (factor reported May 14th) 
New 7repunit pseudoprime
(7^352011)/6 is a base3 pseudoprime.
At 29749 digits it's much too big for ECPP (20562 digits took six K8/2400years, 15071 digits took two Xeon/2600years); 35200 looks splendidly composite, so I suppose I should start hunting cyclotomic factors. 
[QUOTE=fivemack;110607](7^352011)/6 is a base3 pseudoprime.
At 29749 digits it's much too big for ...[/QUOTE] Not to mention being a bit beyond the limit for the Cunningham Tables. bd 
[QUOTE=fivemack;110607](7^352011)/6 is a base3 pseudoprime.
At 29749 digits it's much too big for ECPP (20562 digits took six K8/2400years, 15071 digits took two Xeon/2600years); 35200 looks splendidly composite, so I suppose I should start hunting cyclotomic factors.[/QUOTE] Indeed. The cyclotomic factors will not help ECPP, but they can greatly help APRCL. 
[QUOTE=garo;48284][CODE]Base Index Size 11M(45digits) 43M(50digits) 110M(55digits) 260M(60digits) Decimal
... 7 317 C202 5215(1.40359) 0(0.203361) 165(0.00921839) 0(0.00148122) 4817387775478910748337470675295461658412305210077087712511098562369825581753381999542716517188369317201504120140218066670989302797199195269475798377529788582602272660294198048152636381680533617071470639 ... [/CODE][/QUOTE] This short table's now one shorter, after 7,317 c202 = p51*p151, with p51 = 399676211948778347375576150888294069325575626336229 The 3rd cure2 duo factor (from the B1 = 260M run; on the part of c190c209 above difficulty 250). PaulZ's c120355 file lists this as entering ecmnet files as a c249, with what looks like a p47 found by Philip McLaughlin 20.02.05. Bruce 
[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... 
Sieving was done rapidly on Core 2 Duos at my university (NIT, Trichy) which helped me to sieve rapidly at that time.
When vacation started on 29 Apr 2008, the sieving was 86% done on this number. After that for 20 days, I was without any resources, so sieving was suspended On 20 May 2008, we bought a new Core 2 Quad @ 2.4 GHz at home which helped to finish the sieving rapidly. Around June 9th the sieving was sufficient enough with about 78 million specialq sieved. Five days ago, the linear algebra was started on my Core 2 Duo laptop @ 1.7 GHz. Since there wasn't enough virtual memory available in normal mode, the post processing went in safe mode with the /3GB switch. Regarding square root, each dependency takes about two hours to solve it up, the first dependency failed. Cleverly simultaneously I picked up the 4th dependency on the other core of my laptop. The dependency was a good choice to give me away with the factors! I have chosen up with the fourth dependency in the square root stage because 2,1039 gave away the factors at the 4th dependency! Notice that 6,305 took 8 months to complete. But 7,295 which is twice as harder took only 6 months, eventhough I was idle for sometime between. Sieving was rushed through with those Core 2 Duos at my college. 10,312+ is halfway through sieved. It will take a couple of weeks if 30 million specialq suffice. 
[QUOTE=Raman;136494]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...[/QUOTE]Nice one! I'm glad it worked out in the end. Good luck with the next. Paul 
[quote=xilman;136497]
Nice one! I'm glad it worked out in the end. Good luck with the next. [/quote] What is the best polynomial that I can use so for 10,375 Since 3 and 5 both divide 375, So, the polynomial that I currently think so of, is x[sup]10[/sup]+x[sup]5[/sup]+1 divided by x[sup]2[/sup]+x+1 which is, [tex]x^8x^7+x^5x^4+x^3x+1[/tex] which has SNFS difficulty of 200 digits 
[QUOTE=Raman;136500]
[tex]x^8x^7+x^5x^4+x^3x+1[/tex] which has SNFS difficulty of 200 digits[/QUOTE] Yep, but make it degree 4. Not great, but the best you can do. [TEX]x^4x^34x^2+4x+1[/TEX] [TEX]10^{25}x(10^{50}+1)[/TEX] Greg 
[quote=frmky;136505]
Yep, but make it degree 4. Not great, but the best you can do. [tex]x^4x^34x^2+4x+1[/tex] [tex]10^{25}x(10^{50}+1)[/tex] [/quote] Sure? Is biquadratic (aka quartic) the best polynomial that I can use so for 10,375? No quintics or sextics are available for it, of course with difficulty 200? And eighth degree is not feasible? I think that it makes the algebraic coefficients too larger, right? [code] Similarly I think that for a multiple of 11, say 7,319 you will certainly not be using [tex]\sum_{i=0}^{10} x^i[/tex] and [tex]x7^{29}[/tex] You would be reducing it to degree 5, right? And for a multiple of 13, for example 6,299 [tex]\sum_{i=0}^{12} x^i[/tex] should be reduced to degree 6. Although both of these are reduced to degree 5 and 6, a multiple of 17 or higher cannot be reduced this way to degree 8 or higher and should be treated up as a prime exponent, right? For example, for 2,799 Dr. Kleinjung et al. would certainly not have used [tex]\sum_{i=0}^{16} x^i[/tex] and [tex]x2^{47}[/tex] or of course, the one reduced up to degree 8 for it. I think that they would only have used up so with [tex]2x^61[/tex] and [tex]x2^{133}[/tex] in the Bonn University. [/code]What about reducing the degree 14 for 10,375 (since it is a multiple of 15) this way up to degree 7 directly? [tex]\sum_{i=0}^{14} x^i[/tex] and [tex]x10^{25}[/tex] 
[QUOTE=Raman;136580]Sure? Is biquadratic (aka quartic) the best polynomial that I can use so
for 10,375? No quintics or sextics are available for it, of course with difficulty 200? And eighth degree is not feasible? I think that it makes the algebraic coefficients too larger, right? [/QUOTE] Correct, the algebraic sieve values grow too large too quickly, so the number of algebraic sieve values that are smooth enough drops too fast. The asymptotic estimates for NFS indicate that a degree7 polynomial is feasible only for inputs that have many hundreds, if not thousands, of digits. Most of the smallest cunningham numbers that are left have similar difficulty; if an available cunningham number is unusually small, it's probably because the NFS polynomials involved are unusually bad :) 
[QUOTE=jasonp;136586]Correct, the algebraic sieve values grow too large too quickly, so the number of algebraic sieve values that are smooth enough drops too fast. The asymptotic estimates for NFS indicate that a degree7 polynomial is feasible only for inputs that have many hundreds, if not thousands, of digits.
Most of the smallest cunningham numbers that are left have similar difficulty; if an available cunningham number is unusually small, it's probably because the NFS polynomials involved are unusually bad :)[/QUOTE] Actually, there are a fair number of composites left under 230 digits that do not require a quartic. 10,312+ Raman; in progress 2,2106L quartic; yech 10,378+ 7,384+ 5,341 reserved 2,1694M 3,517+ I will do shortly 7,393+ 2,1104+ in progress; LA 75% 10,259+ 10,339 2,1119+ 2,1128+ 2,1149 2,1161+ 2,1161 10,339+ 7,396+ 
I'm about to start 10,259+ if nobody else is interested in it.

I'm going after 10,339

[QUOTE=R.D. Silverman;136655]Actually, there are a fair number of composites left under 230 digits that
do not require a quartic. 10,312+ Raman; in progress 2,2106L quartic; yech 10,378+ 7,384+ 5,341 reserved 2,1694M 3,517+ I will do shortly 7,393+ 2,1104+ in progress; LA 75% 10,259+ 10,339 2,1119+ 2,1128+ 2,1149 2,1161+ 2,1161 10,339+ 7,396+[/QUOTE] And there are also lots of them that do require a quartic: 3,565, 580+ 6,335 6,370+ 5,370+, 400+, 410+ 430+ 7,335 320+, 340+ 2,860+, 865+, 925+..... etc. etc. etc. 7,320+, 340+ 3,580+ 
[quote=frmky;136505]Yep, but make it degree 4. Not great, but the best you can do.
[tex]x^4x^34x^2+4x+1[/tex] [tex]10^{25}x(10^{50}+1)[/tex] Greg [/quote] So, can you please explain to me up how you derived the 4th degree polynomial from the 8th degree one for [tex]10,375[/tex] [tex]x^8x^7+x^5x^4+x^3x+1[/tex] [tex]x10^{25}[/tex] I am starting to sieve for 10,375 now. 10,312+ is in Linear Algebra and will finish up within about 12 hours or so (Matrix has less than 20 million rows!) :exclaim: [SIZE=4]EMERGENCY[/SIZE] Also that I can't enter the value of [B]m[/B] in the GGNFS poly file too, because of the fact that [tex]\division_{10^{25}}^{(10^{50}+1)}[/tex] is again not an integer at all 
[QUOTE=Raman;138062]So, can you please explain to me up how you derived the 4th degree
polynomial from the 8th degree one for [tex]10,375[/tex] [tex]x^8x^7+x^5x^4+x^3x+1[/tex] [tex]x10^{25}[/tex][/quote] Substitute x = y + 1/y in the octic and see what you get ... [QUOTE=Raman;138062] I am starting to sieve for 10,375 now. 10,312+ is in Linear Algebra and will finish up within about 12 hours or so (Matrix has less than 20 million rows!) :exclaim: [SIZE=4]EMERGENCY[/SIZE] Also that I can't enter the value of [B]m[/B] in the GGNFS poly file too, because of the fact that [tex]\division_{10^{25}}^{(10^{50}+1)}[/tex] is again not an integer at all[/QUOTE]Solve the equation 10^25x = 1 (mod 10^50) in integers. The solution is the integer you want. Paul 
[QUOTE=xilman;138066]
Solve the equation 10^25x = 1 (mod 10^50) in integers. The solution is the integer you want. Paul[/QUOTE] Although it's certainly a good exercise, actually entering m in the GGNFS poly file causes it to use the rational poly xm. Enter the rational poly coefficients using Y1 and Y0, and the programs will calculate m. Greg 
[quote=xilman;138066]
Solve the equation 10[sup]25[/sup]x = 1 (mod 10[sup]50[/sup]) in integers. The solution is the integer you want. [/quote] Be careful! There exist no solution to this equation. Since 10[sup]25[/sup] is even, a multiple of it is always even, and on the right hand side, 1 (mod 10[sup]50[/sup]) is always odd. A solution is impossible to exist! [quote=xilman;138066] Substitute x = y + 1/y in the octic and see what you get ... [/quote] No hopes for degree 4. Substituting x = y + (1/y) in x[sup]8[/sup], so it gives up [tex]\sum_{z=0}^8 ^8C_z y^z (1/y)^{8z}[/tex] which is clearly being at degree 8. Other terms will have their appropriate degrees. So, when substituted, the whole algebraic polynomial will be of degree 8 only. And the linear polynomial becomes more cumbersome, in this form, with 10[sup]25[/sup](y+(1/y))  (10[sup]50[/sup]+1) 
Hi Raman.
The calculation of M should be modulo the number you're trying to factor  ie 10^25 N = (10^50+1) mod cofactor. But as xilman pointed out you just fill in the numerator and denominator in the Y0 and Y1 fields. The idea of substituting y+1/y is to take advantage of the symmetry of the octic; you write {octic} = x^4 * quartic(x+1/x) for some suitablychosen quartic, and the 10^50+1 and 10^25 are from (x + 1/x) written as (x^2+1)/x. 
[QUOTE=fivemack;138325]Hi Raman.
The calculation of M should be modulo the number you're trying to factor  ie 10^25 N = (10^50+1) mod cofactor. But as xilman pointed out you just fill in the numerator and denominator in the Y0 and Y1 fields. The idea of substituting y+1/y is to take advantage of the symmetry of the octic; you write {octic} = x^4 * quartic(x+1/x) for some suitablychosen quartic, and the 10^50+1 and 10^25 are from (x + 1/x) written as (x^2+1)/x.[/QUOTE] The reason this works is that *reversing* the coefficients of any polynomial results in a homomorphism of its splitting field, sending a root r of the polynomial to 1/r. Thus, if the coefficients of the polynomial are the same when reversed, we can replace the polynomial with one whose roots are r + 1/r and get an isomorphic field. 
[QUOTE=garo;48284][CODE]Base Index Size 11M(45digits) 43M(50digits) 110M(55digits) 260M(60digits) Decimal
7 271 C214 : 1570202...53660188716054727305891 ... 7 301 C189 : 7473377...279834566763898163532521 ... 7 393 C217 : 580546345...10110568816475625168427 [/CODE][/QUOTE] These three cofactors are no longer in the ECMNET input file, and the indices 271, 301 and 393 are not in the 7/08 appendix C. That leaves 18, with the NFSNET number 7,319 sieved. with the matrix running; and 7,313 a C/D number, also sieved, with matrix running. Bruce 
count/recount
[QUOTE=bdodson;142925] ... That leaves 18, with the NFSNET number 7,319
sieved. with the matrix running; and 7,313 a C/D number, also sieved, with matrix running. Bruce[/QUOTE] OK, the database is now closer to being current than the table in the first post. There should be 15, with [code] 7 277 C201 done 7 311 C225 first 7 313 C248 done 7 323 C241 second, &etc. [/code] If I'm reading the thread activity correctly, out of 18 tables (with four base2's and two each for 3, 5, 6, 7, 10, 11 and 12, so 4+2*7 = 18) this one is the one that's gone the longest without a new factor report? No reserved numbers, either; with 311 on the more wanted list. Bruce Off Topic PS: from the old pages on Sam's site, the cover letter for page 80 (from 1998) lists a bunch of the tables as having been extended [QUOTE] to insure that every table has at least five holes [/QUOTE] which explains which tables would be extended, but the trigger seems to have been an update 2.C. There was also an update 2.E, followed the the 3rd edition of the tables, Sept 2001. I don't see any update 3.*'s; so suppose that it's unclear whether dropping one of the table below five entries would trigger an update and extension, or we might have some more time to clear an entire table (most likely 3 perhaps). 
In the DB, someone has entered the (previously unknown) factor of 7,391:
p57 = 478566296656273815311438559010751123205277732759848440243 with a p187 cofactor. However, it can be found nowhere else  at least the forum and Sam's page don't mention it, and Google doesn't return any results for it. I expect the finder will come forward soon, but anyway, that's one "impossible" out of the way. :smile: 
[quote=10metreh;199499]In the DB, someone has entered the (previously unknown) factor of 7,391:
p57 = 478566296656273815311438559010751123205277732759848440243 with a p187 cofactor. However, it can be found nowhere else  at least the forum and Sam's page don't mention it, and Google doesn't return any results for it. I expect the finder will come forward soon, but anyway, that's one "impossible" out of the way. :smile:[/quote] Have you checked up the ECMNET page of Mr. Paul Zimmermann? 
[QUOTE=Raman;199502]Have you checked up the ECMNET page of Mr. Paul Zimmermann?[/QUOTE]Indeed, Paul mailed it out to the usual suspects yesterday evening.
Paul (the other one) 
LA Failure?
Did the LA for 7,311 fail?

[QUOTE=R.D. Silverman;203602]Did the LA for 7,311 fail?[/QUOTE]
Nope. Just delayed a bit. [CODE]prp66 factor: 300816696076140900609570360532034016686672572500196266141997289033 prp160 factor: 1756560862778457393639774753663646868150598408308118878219230555826805955171841738531624623756542243961880565002404773332396762823189273396255385704913755864589 [/CODE] 
1 Attachment(s)
NFS@Home has completed 7,311. Thanks again goes to Jeff Gilchrist for completing the linear algebra. The log is attached.
[CODE]prp66 factor: 300816696076140900609570360532034016686672572500196266141997289033 prp160 factor: 1756560862778457393639774753663646868150598408308118878219230555826805955171841738531624623756542243961880565002404773332396762823189273396255385704913755864589 [/CODE] 
7,335
1 Attachment(s)
big ecm miss :smile:
that case is or rather a classical split up? exactly one week is being left over to be due for 6,365 to be better rather 
1 Attachment(s)
NFS@Home has finished 7,323.
[CODE]prp92 factor: 32384164657733079891391121799890231790807215307992831784347992344927666001261536118647303847 prp150 factor: 100011917693440889990646365234918262541012912410693093181881147536745060244890241473886354837045585427711925587468654875546212644201041776410406437489 [/CODE] 
1 Attachment(s)
7,365 is done.
[CODE]prp97 factor: 1148894468667091286204692970416827261082319331812342797384451313174700604983148313611338121323891 prp125 factor: 55942721279166257780056698503293547824721169030993103136330677356165810182496283619262220938337482111161828773871354771730871 [/CODE] 
7,353 is done.
[PASTEBIN]ZbN6fjx2[/PASTEBIN] 
7,401 is done. P65 is the smallest I've seen in a while.
[PASTEBIN]2VEQB3bj[/PASTEBIN] 
7,373 is done.
[PASTEBIN]jJvG0Spx[/PASTEBIN] 
7,359 done by NFS@Home.

7,413 Done by usual suspect

6486 7, 367 c252 1514075552509869783989080300976998865425149737988637980846413561226082200895909501. p171 NFS@Home snfs

[QUOTE=garo;48284][code]Size Base Index Mod Diff Ratio
320 7 379  320.2 1 274 7 383  323.6 0.846 299 7 389  328.7 0.909 220 7 395  267.0 0.823 /5q 281 7 419  354 0.792 305 7 421  355.7 0.855 221 7 425  287.3 0.767 /5q 315 7 431  364.2 0.863 342 7 433  365.9 0.933 341 7 439  370.9 0.917 [/code][/QUOTE] 7,379 was already done in December 2021 
[QUOTE=sweety439;605408]7,379 was already done in December 2021[/QUOTE]
Stop necroposting. This is a 3year old thread. And [URL="https://mersenneforum.org/showthread.php?p=568480#post568480"]we already had discussed this[/URL]. Was it not spelled out enough? All results are maintained at [url]https://homes.cerias.purdue.edu/~ssw/cun/[/url] and NFS @ Home achievements and results at the NFS @ Home subfoum. 
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