A computation worthy of the name

[fivemack]

I think the maximum memory usage was somewhere between 9G and 10G; the matrix step was only just slightly over 8G.

I'm prepared to pull together another collaboration if there's a worthy target; M1061 is still a bit big, and I'd like to do a GNFS next.

Bos+Kleinjung have reserved 2^1175-1 which is GNFS of size 191.18, and long enough ago that they'll have an answer before we finish anything started now.

I have done 12 GPU-days of polsel on 2^1087-1 G192 size 191.00 (largest c5 reported was 62280, next-largest 59160, which given batching and blocking means I think that I've covered 0-60k), which might be a worthy target but will take a long time to sieve, and I think it would be overly gentlemanly to devote a lot of work to coming in as champion #2 by a nose.

2,2158M is of size 192.08 so would come in as #1, and it's got difficulty ratio 0.591 so is definitely easier by GNFS.

The other barely-possible GNFS would be 10^361-1 G198 (difficulty ratio 0.546), but I think jumping twenty digits ahead is optimistic. In which case 7,347+ G188 (log_10=187.43) might have some attraction.

Mon Dec  7 21:21:22 2009  factoring 100096568736088864791994195928139854117344123936564020830393153238248477781159483464892503078830652760009350458723758038760904327995304237928726896241501080385607237591889720058086626805203239 (192 digits)
Mon Dec  7 21:21:24 2009  no P-1/P+1/ECM available, skipping
Mon Dec  7 21:21:24 2009  commencing number field sieve (192-digit input)
Mon Dec  7 21:21:24 2009  commencing number field sieve polynomial selection
Mon Dec  7 21:21:24 2009  time limit set to 300.00 hours
Mon Dec  7 21:21:24 2009  searching leading coefficients from 1 to 118276837
Mon Dec  7 21:21:24 2009  using GPU 0 (GeForce GTX 275)
Sat Dec 19 19:19:59 2009  polynomial selection complete
Sat Dec 19 19:19:59 2009  R0: -21385126687916130901706513759515709828
Sat Dec 19 19:19:59 2009  R1:  179496927628782375091
Sat Dec 19 19:19:59 2009  A0: -12954373848960452244580925282302356820845400197555
Sat Dec 19 19:19:59 2009  A1: -184270751161275426584727762083224211169868
Sat Dec 19 19:19:59 2009  A2:  92816182311240496124571684306219
Sat Dec 19 19:19:59 2009  A3:  2417010961388667719846028
Sat Dec 19 19:19:59 2009  A4: -177566867392724
Sat Dec 19 19:19:59 2009  A5:  22380
Sat Dec 19 19:19:59 2009  skew 954073035.17, size 4.142128e-19, alpha -7.157560, combined = 9.252598e-15

[fivemack]

Originally Posted by bsquared

Congrats! Nice job to everyone involved!

Some scribbles on this napkin I have handy say that even if we were clairvoyant and used 69 digit optimal ECM parameters (~1.94e9 B1), we would have needed ~ 4 Gigaseconds to do ECM to t69 (and this on a top of the line workstation). 125 CPU years and still less than 1 chance in 3 of finding the factor... kinda puts things in perspective

The real factorisation was 220k CPU-hours sieving, so about 25 CPU-years; SNFS very much the right way to go for this one

[Raman]

Great job! BINGO!
Please apologize me. I didn't understand why you were asking apology for. I thought that I didn't accuse, insult or scold anyone, but you were talking about speed of publication, right?

My intention was to ask out of curiosity, why not report the factors of RSA768 on December 12 itself. I know that it will obviously take some time to publish the paper. I didn't hurry for the factors. I didn't intentionally criticize anyone at all.

Just got frustrated as soon as the square root phase got crashed. Already four numbers are in post processing load. Heavy pressure to relieve once I have the four factors simultaneously. That's why. Please apologize me and don't ignore me. I won't go violent and will behave myself then. I understand that the Factoring Forum has more attention than the Cunningham Tables Forum only. However, it is true that only a few people could possibly help me out on that matter, anyway.

Why does the square root crash for me on the Intel Xeon 8 core processor? It has 8 GB of RAM, for your information. Will the msieve binary compiled on that compute cluster itself work out properly? Or should I make use of an older version of msieve, such as 1.38?

[J.F.]

Great job all!

Raman, are you perhaps posting in the wrong thread?

Keep 'm coming, Fivemack. I'd slightly prefer 2- candidates, but you're the boss :).

[jrk]

Originally Posted by fivemack

2,2158M is of size 192.08 so would come in as #1,

The current #1 GNFS is the RSA768 (size 231.09), isn't it?

Or are you referring to the #1 GNFS for Cunningham numbers only?

[Raman]

Originally Posted by J.F.

Keep 'm coming, Fivemack. I'd slightly prefer 2- candidates, but you're the boss :).

In my opinion only,
M1087 is a good GNFS candidate.
I will prove that I will be able to crack off M935 with my resources... Already started up the sieving for this number, going on very rapidly!

[10metreh]

So this is a second-place champion for SNFS difficulty and for size, right?

Well, it won't stay in second place for difficulty for long - 2,1127- (Kleinjung) will beat it with difficulty 291.

[fivemack]

Originally Posted by jrk

The current #1 GNFS is the RSA768 (size 231.09), isn't it?

Or are you referring to the #1 GNFS for Cunningham numbers only?

Yes; I think the top general-GNFS at the moment are RSA768, RSA200, RSA640, whilst the 2-1087 cofactor is 635 bits.

[10metreh]

Originally Posted by fivemack

Bos+Kleinjung have reserved 2^1175-1 which is GNFS of size 191.18, and long enough ago that they'll have an answer before we finish anything started now.

To me, the fact that Thorsten has reserved 2,1127- suggests that 2,1175- is in the linear algebra phase.

Anyway, roughly what size GNFS was M941 equivalent to?

[fivemack]

Originally Posted by 10metreh

To me, the fact that Thorsten has reserved 2,1127- suggests that 2,1175- is in the linear algebra phase.

Anyway, roughly what size GNFS was M941 equivalent to?

Matrix size was about 25 million, versus about 17 million for 180-digit GNFS at Murphy about 7e-14; it looks as if the matrix size scales with the -0.4 power of the Murphy score, so that would be a Murphy around 3e-14. Murphy score goes down by 1/e when you add 7.5 more digits, so we're talking a GNFS size somewhere around 188.

[bdodson]

Originally Posted by 10metreh

To me, the fact that Thorsten has reserved 2,1127- suggests that 2,1175- is in the linear algebra phase.

Anyway, roughly what size GNFS was M941 equivalent to?

You're mixing Bos+Kleinjung with Kleinjung here. As I've observed over
on the 2- thread (in reply to your post there), reserving M1127 seems to
me to be more along the line of Thorsten having just finished M959 and M973,
and reserved M1043 --- all four with exponent divisible by 7. That's almost
a clean sweep, the remaining exception being M1183. -Bruce

PS --- Alternatively, under an assumption that Thorsten was supplying
sieving, but not running the matrix (?), it would have been his reservation
of M959 that would have marked the switch. So the c192 gnfs would be
somewhat further along.