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-   -   7- table (https://www.mersenneforum.org/showthread.php?t=3575)

wblipp 2007-08-13 17:14

[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.

fivemack 2007-12-10 09:11

Factorisation of 7^263-1
 
1 Attachment(s)
87808581809525792134370860453721419342992604246001922594107781828847401497090250623000616403314204187748641525231019439257581826238153281895147142837427201101541 = 330356473356706630143084182110481076968694111519479821312366757981 * 265799489010506998952247476548157401788003618449001603472530395754819736985343973809633195038761

Software used: gnfs-lasieve4I14e for sieving, msieve-1.30 for linalg (the merge phase did not fit in 4GB under msieve-1.28)

Polynomials used: x^6-7 and 7^44-x

Sieving limits: small primes to 40 million, large primes to 2^30

Sieved algebraic special-Q from 36.5e6 to 79e6 in 5600 CPU-hours, on six CPUs (three dual-core 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

R.D. Silverman 2007-12-10 14:48

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.

fivemack 2007-12-10 15:21

At present I'm doing, with a collaborator, a C156 GNFS on a non-Cunningham 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 mid-January. I don't yet have a plan for the stage after that; I'm vaguely contemplating wider collaborations to do a larger GNFS job.

akruppa 2007-12-12 13:24

I'll do 7,269- c224.

Alex

bdodson 2008-01-10 15:19

[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 non-sticky] 2-
discussion. -Bruce

akruppa 2008-01-14 13:16

7,269-:

[CODE]
Probable prime factor 1 has 82 digits:
4462060605403381961780411332028022754534242152003773412732171224503049883657394827
Probable prime factor 2 has 142 digits:
3720848769582826092237529016309237616548794511295400940058189854803271477562040904704041158521598520073343762354423669834498921937027750690971
[/CODE]

Alex

fivemack 2008-01-14 13:27

Congratulations! What are you sieving next?

akruppa 2008-01-14 13:31

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

fivemack 2008-02-25 08:52

7^387-1 C154 cofactor splits as
[code]
P70 4583142681916056752995023804494031799489400087334962946866717203441543
P84 457299108883653825883853223306465080566360541916826721338777118806091728304473122859
[/code]

Not quite sure how much CPU time I used, but it took two weeks real-time on maybe six cores; 100 hours for the linear algebra (95 hours of that on two cores for the matrix), using msieve-1.29 with default parameters because I'd just had a couple of failures with msieve-1.33. x^6+x^3+1, x-7^43; 30-bit 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 (154-digit 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 = 1.957443e-10, Murphy alpha = 1.935662, combined = 1.125911e-10
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 in-memory 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 in-memory 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 in-memory 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 in-memory 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 in-memory 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 in-memory 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 in-memory 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 in-memory 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 in-memory 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 in-memory 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 in-memory 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 2-way 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]

Raman 2008-06-23 19:11

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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