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 half-way through the last run on the last large incomplete range for
testing to p50, 2100 curves/7830 left to go on the generic c251-c299 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 213-digit 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 7-repunit pseudoprime
 

(7^35201-1)/6 is a base-3 pseudoprime.

At 29749 digits it's much too big for ECPP (20562 digits took six K8/2400-years, 15071 digits took two Xeon/2600-years); 35200 looks splendidly composite, so I suppose I should start hunting cyclotomic factors.

[QUOTE=fivemack;110607](7^35201-1)/6 is a base-3 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](7^35201-1)/6 is a base-3 pseudoprime.

At 29749 digits it's much too big for ECPP (20562 digits took six K8/2400-years, 15071 digits took two Xeon/2600-years); 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
APR-CL.

[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
c190-c209 above difficulty 250). PaulZ's c120-355 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 7^263-1
 

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

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 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.

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 non-sticky] 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

7^387-1 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]

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 special-q 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 half-way through sieved. It will take a couple of weeks if 30 million special-q 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^8-x^7+x^5-x^4+x^3-x+1[/tex]

which has SNFS difficulty of 200 digits

[QUOTE=Raman;136500]
[tex]x^8-x^7+x^5-x^4+x^3-x+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^4-x^3-4x^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^4-x^3-4x^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]x-7^{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]x-2^{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^6-1[/tex] and [tex]x-2^{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]x-10^{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 degree-7 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 degree-7 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^4-x^3-4x^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^8-x^7+x^5-x^4+x^3-x+1[/tex]
[tex]x-10^{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^8-x^7+x^5-x^4+x^3-x+1[/tex]
[tex]x-10^{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 x-m. 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)^{8-z}[/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 suitably-chosen 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 suitably-chosen 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 base-2'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]

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-
 

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

NFS@Home has finished 7,323-.

[CODE]prp92 factor: 32384164657733079891391121799890231790807215307992831784347992344927666001261536118647303847
prp150 factor: 100011917693440889990646365234918262541012912410693093181881147536745060244890241473886354837045585427711925587468654875546212644201041776410406437489
[/CODE]

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 3-year 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.