Current Effort

[R.D. Silverman]

7,277+ has (barely) finished sieving. I will do some
over-sieving to make the matrix more manageable.

Please reserve 6,335- for me. I will do it next.
My surgery is on Mar 2. I will switch projects toward
the end of next week...


Meanwhile, there is quite a gap between the first two
holes in the 2- table. It would be nice if someone did
M827. I don't have the resources. My upper limit is
about 780 bits.

It would also be nice if people were to work on the
2LM table. It is, as always, relatively neglected.

Bob

[fivemack]

2,1606M would take about 40M CPU-seconds, which isn't really worth the setup effort on a cluster or the admin effort for a distributed attack, while being a bit much for a single computer; it would fit my resources quite nicely, but what's not committed to linalg jobs will be doing a largish personal GNFS for the next couple of months.

2-827 would be a nice one for mersenneforum, but mersenneforum's factorisers are booked up until May; if nobody else has done it by then it might be an opportunity for calm relaxation after the big GNFS.

[R.D. Silverman]

Originally Posted by fivemack

2,1606M would take about 40M CPU-seconds, which isn't really worth the setup effort on a cluster or the admin effort for a distributed attack, while being a bit much for a single computer; it would fit my resources quite nicely, but what's not committed to linalg jobs will be doing a largish personal GNFS for the next couple of months.

2-827 would be a nice one for mersenneforum, but mersenneforum's factorisers are booked up until May; if nobody else has done it by then it might be an opportunity for calm relaxation after the big GNFS.

My resources are 2 full-time machines, one is a core-duo,
and ~15 machines half-time, several of which are core-duos.
Most of the latter have only 1G of DRAM. The DRAM limit
also limits my factor base size.

7,277+ is about 780 bits and took me 3 months to sieve.

[J.F.]

What would it take to do M827? I don't know anything about polynomial selection and such (and I'd like to keep it that way), so would anyone like to team up or something?

[fivemack]

M827 would require about 20000 CPU-hours for the sieving followed by a couple of weeks on a quad-core with 8G memory for the linear algebra; if you don't have such a box, I'll happily run the linear algebra if you do the sieving.

If you're interested, PM me, and I'll run a parameter-selection job and send you a .poly file.

[J.F.]

I should have figured... 20000hrs is quite a bit out of my league. Thanks for the estimate and offer.

[10metreh]

What would the poly be, anyway? Hmmm...

c5: 4
c0: -1
Y1: -1
Y0: 46768052394588893382517914646921056628989841375232

c6: 1
c0: -2
Y1: -1
Y0: 348449143727040986586495598010130648530944

are the two you think of first...

[fivemack]

Originally Posted by J.F.

I should have figured... 20000hrs is quite a bit out of my league. Thanks for the estimate and offer.

A 10MQ both-sides chunk for 10^263-1 was about 4000 CPU-hours, so M827 is not amazingly much larger than things you've done already, but it depends how much access you have to the cluster.

[Raman]

I have 90% completed sieving for 6,343-
and just started up so with 6,343+

I see that nobody is ready to take up with
11²²⁹-1? It has been standing in the Wanted Lists for already more than over 3 years.

Sat Jan 31 01:58:21 2009  
Sat Jan 31 01:58:21 2009  
Sat Jan 31 01:58:21 2009  Msieve v. 1.38
Sat Jan 31 01:58:21 2009  random seeds: 2dd3dbd0 b0e64db8
Sat Jan 31 01:58:21 2009  factoring 4353084279465471236993675231471658322855285085288018587696753593002074624697573400982036418055827897146317140063377813885557624999850231373576930085296121779853543537188567707144180933943323891018955967519960133495049773807349 (226 digits)
Sat Jan 31 01:58:24 2009  searching for 15-digit factors
Sat Jan 31 01:58:28 2009  commencing number field sieve (226-digit input)
Sat Jan 31 01:58:28 2009  R0: -134713546244127343440523266742756048896
Sat Jan 31 01:58:28 2009  R1:  1
Sat Jan 31 01:58:28 2009  A0:  1
Sat Jan 31 01:58:28 2009  A1:  1
Sat Jan 31 01:58:28 2009  A2:  1
Sat Jan 31 01:58:28 2009  A3:  1
Sat Jan 31 01:58:28 2009  A4:  1
Sat Jan 31 01:58:28 2009  A5:  1
Sat Jan 31 01:58:28 2009  A6:  1
Sat Jan 31 01:58:28 2009  size score = 5.844430e-011, Murphy alpha = 2.427706, combined = 2.920803e-011
Sat Jan 31 01:58:28 2009  
Sat Jan 31 01:58:28 2009  commencing relation filtering
Sat Jan 31 01:58:28 2009  commencing duplicate removal, pass 1
Sat Jan 31 02:14:47 2009  found 20341574 hash collisions in 64353153 relations
Sat Jan 31 02:15:17 2009  added 2438460 free relations
Sat Jan 31 02:15:17 2009  commencing duplicate removal, pass 2
Sat Jan 31 02:21:33 2009  found 26772164 duplicates and 40019449 unique relations
Sat Jan 31 02:21:33 2009  memory use: 270.4 MB
Sat Jan 31 02:21:33 2009  reading rational ideals above 39911424
Sat Jan 31 02:21:33 2009  reading algebraic ideals above 39911424
Sat Jan 31 02:21:33 2009  commencing singleton removal, pass 1
Sat Jan 31 02:32:28 2009  relations with 0 large ideals: 1258720
Sat Jan 31 02:32:28 2009  relations with 1 large ideals: 4986397
Sat Jan 31 02:32:28 2009  relations with 2 large ideals: 12037173
Sat Jan 31 02:32:28 2009  relations with 3 large ideals: 13662114
Sat Jan 31 02:32:28 2009  relations with 4 large ideals: 6026679
Sat Jan 31 02:32:28 2009  relations with 5 large ideals: 14566
Sat Jan 31 02:32:28 2009  relations with 6 large ideals: 9
Sat Jan 31 02:32:28 2009  relations with 7+ large ideals: 2033791
Sat Jan 31 02:32:28 2009  40019449 relations and about 34943193 large ideals
Sat Jan 31 02:32:28 2009  commencing singleton removal, pass 2
Sat Jan 31 02:42:02 2009  found 10094204 singletons
Sat Jan 31 02:42:02 2009  current dataset: 29925245 relations and about 23231312 large ideals
Sat Jan 31 02:42:02 2009  commencing singleton removal, pass 3
Sat Jan 31 02:50:46 2009  found 3491255 singletons
Sat Jan 31 02:50:46 2009  current dataset: 26433990 relations and about 19572969 large ideals
Sat Jan 31 02:50:46 2009  commencing singleton removal, pass 4
Sat Jan 31 02:58:54 2009  found 1032240 singletons
Sat Jan 31 02:58:54 2009  current dataset: 25401750 relations and about 18524222 large ideals
Sat Jan 31 02:58:54 2009  commencing singleton removal, pass 5
Sat Jan 31 03:07:23 2009  found 308750 singletons
Sat Jan 31 03:07:23 2009  current dataset: 25093000 relations and about 18213966 large ideals
Sat Jan 31 03:07:23 2009  commencing singleton removal, final pass
Sat Jan 31 03:17:32 2009  memory use: 476.8 MB
Sat Jan 31 03:17:33 2009  commencing in-memory singleton removal
Sat Jan 31 03:17:35 2009  begin with 25093000 relations and 22180790 unique ideals
Sat Jan 31 03:18:22 2009  reduce to 16003514 relations and 12549620 ideals in 26 passes
Sat Jan 31 03:18:22 2009  max relations containing the same ideal: 18
Sat Jan 31 03:18:26 2009  reading rational ideals above 720000
Sat Jan 31 03:18:26 2009  reading algebraic ideals above 720000
Sat Jan 31 03:18:26 2009  commencing singleton removal, final pass
Sat Jan 31 03:26:43 2009  keeping 16271467 ideals with weight <= 20, new excess is 1134373
Sat Jan 31 03:27:09 2009  memory use: 498.2 MB
Sat Jan 31 03:27:09 2009  commencing in-memory singleton removal
Sat Jan 31 03:27:12 2009  begin with 16003609 relations and 16271467 unique ideals
Sat Jan 31 03:27:52 2009  reduce to 15972366 relations and 16239731 ideals in 15 passes
Sat Jan 31 03:27:52 2009  max relations containing the same ideal: 20
Sat Jan 31 03:27:54 2009  filtering wants 1000000 more relations
Sat Jan 31 03:27:54 2009  elapsed time 01:29:33

[R.D. Silverman]

Originally Posted by R.D. Silverman

7,277+ has (barely) finished sieving. I will do some
over-sieving to make the matrix more manageable.

Please reserve 6,335- for me. I will do it next.
My surgery is on Mar 2. I will switch projects toward
the end of next week...

Bob

Status:

I am filtering the data for 2,277+ now.

Paul: I will send the data to you after I have done several filtering
passes. The matrix will be too big for me.

I have started sieving 6,335-. I hope to do 2,865+ after that.

[Raman]

I will rather, better start up with the Linear Algebra (post processing) for 6,343-, on this Sunday, when my Laptop becomes available as it is up so, thus, hence.

Post processing stages of steps, within the sequence are including Filtering, Linear Algebra, and then the Square Root to yield the ultimate factor, at once, after all, of course, for ever, every factoring attempt or try, indeed, really.

Resuming up for the 6,343+ case, since, within my Desktop computer... starting up yet, still, as usual.

found 25164005 hash collisions in 80687050 relations
added 1 free relations
commencing duplicate removal, pass 2
found 32276277 duplicates and 48410774 unique relations
memory use: 504.8 MB
reading rational ideals above 49872896
reading algebraic ideals above 49872896
commencing singleton removal, pass 1
relations with 0 large ideals: 1874920
relations with 1 large ideals: 7069231
relations with 2 large ideals: 14885574
relations with 3 large ideals: 15102575
relations with 4 large ideals: 6686766
relations with 5 large ideals: 801487
relations with 6 large ideals: 49276
relations with 7+ large ideals: 1940945
48410774 relations and about 36043797 large ideals
commencing singleton removal, pass 2
found 9154899 singletons
current dataset: 39255875 relations and about 25950160 large ideals
commencing singleton removal, pass 3
found 2273290 singletons
current dataset: 36982585 relations and about 23624999 large ideals
commencing singleton removal, pass 4
found 455260 singletons
current dataset: 36527325 relations and about 23167444 large ideals
commencing singleton removal, final pass
memory use: 620.1 MB
commencing in-memory singleton removal
begin with 36527325 relations and 28174352 unique ideals
reduce to 29890382 relations and 21264048 ideals in 15 passes
max relations containing the same ideal: 28
reading rational ideals above 720000
reading algebraic ideals above 720000
commencing singleton removal, final pass
keeping 25130109 ideals with weight <= 20, new excess is 2120356
memory use: 950.8 MB
commencing in-memory singleton removal
begin with 29890382 relations and 25130109 unique ideals
reduce to 29877824 relations and 25117550 ideals in 9 passes
max relations containing the same ideal: 20
removing 2947073 relations and 2547073 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 26930751 relations and 25117550 unique ideals
reduce to 26676726 relations and 22311691 ideals in 11 passes
max relations containing the same ideal: 20
removing 2179210 relations and 1779210 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 24497516 relations and 22311691 unique ideals
reduce to 24351101 relations and 20383765 ideals in 9 passes
max relations containing the same ideal: 20
removing 1939410 relations and 1539410 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 22411691 relations and 20383765 unique ideals
reduce to 22288165 relations and 18718834 ideals in 7 passes
max relations containing the same ideal: 20
removing 1810876 relations and 1410877 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 20477289 relations and 18718834 unique ideals
reduce to 20361103 relations and 17189870 ideals in 8 passes
max relations containing the same ideal: 20
removing 1734572 relations and 1334572 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 18626531 relations and 17189870 unique ideals
reduce to 18512575 relations and 15739400 ideals in 9 passes
max relations containing the same ideal: 20
removing 1372117 relations and 1058555 ideals in 313562 cliques
commencing in-memory singleton removal
begin with 17140458 relations and 15739400 unique ideals
reduce to 17061016 relations and 14600167 ideals in 8 passes
max relations containing the same ideal: 20
relations with 0 large ideals: 227581
relations with 1 large ideals: 834673
relations with 2 large ideals: 2668971
relations with 3 large ideals: 4655425
relations with 4 large ideals: 4664752
relations with 5 large ideals: 2658624
relations with 6 large ideals: 810498
relations with 7+ large ideals: 540492
commencing 2-way merge
failed to reallocate 245760000 bytes