12+256 matrix job

[fivemack]

I have found 35 dependencies, but then the network card on the machine I found them on failed so it will be a little while before I can get the square root done

[bdodson]

Originally Posted by fivemack

I have found 35 dependencies, but then the network card on the machine I found them on failed so it will be a little while before I can get the square root done

Sorry to hear about the card; but glad to hear that
the matrix finished. I was wondering whether you're
impatient yet for gnfs data? Sieving for Serge's
2, 2086M is just about done, so I would switch to
our c163 if you wanted more data soon. -Bruce

[fivemack]

It turns out that unplugging the computer, plugging it in again, turning it on (at which point it fails to start booting), turning it off again and turning it on for a second time will sometimes make the network interface reappear.

Fri Jun 26 00:58:30 2009  memory use: 7421.1 MB
Tue Aug 11 19:38:36 2009  lanczos halted after 387759 iterations (dim = 24519655)
Tue Aug 11 19:39:17 2009  recovered 35 nontrivial dependencies
Tue Aug 11 19:39:18 2009  BLanczosTime: 4045839
Tue Aug 11 19:39:18 2009  elapsed time 1123:50:42
...
Sun Aug 16 20:34:00 2009  commencing square root phase
Sun Aug 16 20:34:00 2009  reading relations for dependency 1
Sun Aug 16 20:34:10 2009  read 12262248 cycles
Sun Aug 16 20:34:29 2009  cycles contain 38132421 unique relations

 6783 nfsslave  20   0 4513m 3.9g 1028 R   47 33.4   3:49.06 msieve             
 6783 nfsslave  20   0 5929m 5.7g 1028 R   55 48.6   7:31.56 msieve

The square roots are clearly not trivial jobs; I don't know whether it's more realistic to expect factors in 12 hours or in 36; I suspect that, as in the other 32-bit-each-side example, there are no quadratic characters in play and so a lot of the square roots will fail.

[fivemack]

Sun Aug 16 20:49:14 2009  multiplying 30857386 relations
Sun Aug 16 22:23:43 2009  multiply complete, coefficients have about 841.60 million bits
Sun Aug 16 22:23:52 2009  initial square root is modulo 35517907
Mon Aug 17 01:24:32 2009  sqrtTime: 17432
Mon Aug 17 01:24:32 2009  prp96 factor: 452271654045095376354829024468620655107168044537189917947981878284544891082485331470888529210881
Mon Aug 17 01:24:32 2009  prp132 factor: 293351100534073339320273736685554040546989773558978742766077630132017865996601983557083266543920963624936810354879103450020778081793
Mon Aug 17 01:24:32 2009  elapsed time 04:50:34

Full processing log attached; note that I did a lot of duplicate-counting runs and several matrix-making runs before deciding that I had a small enough matrix. There were over 675 million input relations for the final reasonable-sized matrix (and 433 million unique) even with substantial pre-uniquing at Dodson's end, I would say the duplication rate means that this was about as large a number as you'd want to use siever 15e on.

[Andi_HB]

Wow ! Over 400 Million unique relations are impressive.
Congratulation to this big job.

[jasonp]

Yup, this is the record now. A matrix of size 24M is about 36% the size of a matrix for SNFS1024.

Would it be possible to run dependency #1 through the latest SVN version of msieve? It would be nice to see if the GMP square root code can scale to a number this large.

[bdodson]

Originally Posted by Andi_HB

Wow ! Over 400 Million unique relations are impressive.
Congratulation to this big job.

Sam's just updated his "Champions" page

Special number field sieve by SNFS difficulty:
5501	c307	2,1039-	K.Aoki+J.Franke+T.Kleinjung+A.K.Lenstra+D.A.Osvik
5739	c228	12,256+	T.Womack+B.Dodson

But if I recall correctly, this is the third factorization with over
400 Million unique relations collected, the other two being
5,389+ C265 and 2,908+ C268 (there was also 5, 383+ C267,
but that was easier, by snfs difficulty), all Childers/Dodson.
There's a fourth one pending, which Greg is currently working on
5,398+ C274, the first number done with Greg's binary of Serge's
new 16e siever (the others are with 15e).

So far as I know, it's the 433 Million unique that's the largest
successful filtering. I'm not sure which of Greg's was the largest
(not counting relations found but not successfully through filtering).

-Bruce

[Batalov]

Congratulations!
The last Generalized Fermat! Huge difficulty number.
If only you could have sieved it again, now with 16e. ;-)

P.S. Do let Prof.Keller now.
http://www1.uni-hamburg.de/RRZ/W.Keller/GFN12.html

[frmky]

Originally Posted by jasonp

Yup, this is the record now. A matrix of size 24M is about 36% the size of a matrix for SNFS1024.

Would it be possible to run dependency #1 through the latest SVN version of msieve? It would be nice to see if the GMP square root code can scale to a number this large.

It's a bit more than 5,398+, which has 426561140 unique relations. These resulted in a 21354298 x 21354546 matrix, which is coming along, albeit slowly. The LA is 19.1% done.

2,908+ had 559633687 unique relations, but msieve couldn't make a matrix. I ended up using 488188552 unique relations to make a 20719167 x 20719414 matrix. I still have the original relations, so I should try it with the new filtering code.

[fivemack]

Originally Posted by jasonp

Yup, this is the record now. A matrix of size 24M is about 36% the size of a matrix for SNFS1024.

Would it be possible to run dependency #1 through the latest SVN version of msieve? It would be nice to see if the GMP square root code can scale to a number this large.

Mon Aug 17 20:34:10 2009  Msieve v. 1.43
Mon Aug 17 20:34:13 2009  commencing square root phase
Mon Aug 17 20:34:13 2009  reading relations for dependency 1
Mon Aug 17 20:34:24 2009  read 12262248 cycles
Mon Aug 17 20:34:53 2009  cycles contain 38132421 unique relations
Mon Aug 17 20:46:51 2009  read 38132421 relations
Mon Aug 17 20:52:09 2009  multiplying 30857386 relations
Mon Aug 17 23:58:44 2009  multiply complete, coefficients have about 841.60 million bits
Mon Aug 17 23:58:51 2009  initial square root is modulo 35517907
Tue Aug 18 05:51:37 2009  sqrtTime: 33444
Tue Aug 18 05:51:37 2009  prp96 factor: 452271654045095376354829024468620655107168044537189917947981878284544891082485331470888529210881
Tue Aug 18 05:51:37 2009  prp132 factor: 293351100534073339320273736685554040546989773558978742766077630132017865996601983557083266543920963624936810354879103450020778081793
Tue Aug 18 05:51:37 2009  elapsed time 09:17:27

so it works but is about a factor two slower than 1.42. Though I'd not trust these timings since I was running up to seven other jobs on the i7 at the time, so at times msieve will have had only half a core.

[10metreh]

Originally Posted by fivemack

Msieve v. 1.43

Why does the latest SVN call itself 1.43?