Cunningham ECM efforts

[VBCurtis]

Nice work!

Was the job run 34/35, or 35 on both sides? Looks like there's room for one more bit of LP on one side while staying comfortably within msieve's relations-count bound.

[frmky]

Originally Posted by VBCurtis

Was the job run 34/35, or 35 on both sides?

35 on both sides.

[swellman]

Congratulations on factoring that beast!

Looking ahead to the Gang of 31, 2,2222L is a GNFS 228 or a SNFS 334, very similar to 2,1109+, i.e. a GNFS 225 or SNFS 334. No idea how efficiently 2,2222L sieves as a SNFS but if it’s similar to 2,1109+ do we need to bother running ECM on it and instead just jump right to SNFS via NFS@Home or perhaps a team CADO effort?

Keep in mind that I currently have 2,2222L first in the Gang of 31 ECM list, and I plan to keep it there unless this matter is decided otherwise. But I ask the question.

Alternatively, should we add 2,1109+ to the Gang of 31 before attempting to sieve it by whatever method?

[swellman]

I got the following SNFS polynomial for 2,2222L, with a competitive escore.

n: 498182294243708816934953758200571293828380952324990796450108172678901306777660557394701463533080260632512879410875999929172206863194431411006233976375867957164259819114952920343808614673946286820544900427755366971820147029014473
skew: 1.22639
type: snfs
c6: 2
c5: 0
c4: 0
c3: -2
c2: 0
c1: 0
c0: 1
Y1: 1
Y0: -49039857307708443467467104868809893875799651909875269632
# cownoise score = 1.652e-16 (same skew recommended, no surprise)

[R.D. Silverman]

Originally Posted by swellman

Congratulations on factoring that beast!

Looking ahead to the Gang of 31, 2,2222L is a GNFS 228 or a SNFS 334,

I believe that Greg will agree with the following......

Too big for NFS@Home. He has said SNFS 330/GNFS 225 is the limit. This places even 2,1097+
and 2, 2194L or M out of reach.

Alternatively, should we add 2,1109+ to the Gang of 31 before attempting to sieve it by whatever method?

Yes. Add it to the Gang of 31 [will be 32]. Several efforts could not get a sufficiently good polynomial to do it by
GNFS (even though it is at the stated size limit) and is clearly too big via SNFS.

NFS@Home had to hit a ceiling sooner or later. C'est la vie.

[R.D. Silverman]

Originally Posted by R.D. Silverman

I believe that Greg will agree with the following......

Too big for NFS@Home. He has said SNFS 330/GNFS 225 is the limit. This places even 2,1097+
and 2, 2194L or M out of reach.




Yes. Add it to the Gang of 31 [will be 32]. Several efforts could not get a sufficiently good polynomial to do it by
GNFS (even though it is at the stated size limit) and is clearly too big via SNFS.

NFS@Home had to hit a ceiling sooner or later. C'est la vie.

I'm not sure why 2,2222L (or M) is even being proposed before several smaller numbers. (6 of them by my count)

[charybdis]

Originally Posted by frmky

2,1180+ is done. It was our first with 35-bit large primes, and everything went surprisingly smoothly.

Excellent work!

Originally Posted by R.D. Silverman

I believe that Greg will agree with the following......

Too big for NFS@Home. He has said SNFS 330/GNFS 225 is the limit. This places even 2,1097+
and 2, 2194L or M out of reach.

The work on 2,1109+ seems to suggest that SNFS-334 is easier than GNFS-225, so I don't see how "SNFS-330/GNFS-225" makes sense as a limit. If GNFS-225 is possible - which it probably is, given that there was room to spare with 2,2246M - then SNFS-335 should be too. Yes, sieving will take a while, and the memory limitations of the clients make it a harder lift than it should be, but I don't see why sieving up to Q=5G or so would be infeasible. 35-bit large primes will help.

[R.D. Silverman]

Originally Posted by charybdis

Excellent work!



The work on 2,1109+ seems to suggest that SNFS-334 is easier than GNFS-225

The work on 2,2246M C221 suggests that a C225 via GNFS should have been within reach.

However, a suitable polynomial for 2,1109+ could not be found. Perhaps it is just an outlier for GNFS.

Prior work suggests that a typical C225 would be easier than 2,1109+. Thus, I am not sure that
your conclusion that SNFS 334 is easier than GNFS 225 is justified. A single data point is bad
statistics. It is also possible that the polynomial search was unlucky.

OTOH, I am not sure that your conclusion is false either.

Greg is the one who suggested SNFS 330 as a limit.

Note that I would be quite happy to learn that SNFS 334 is doable.

Clearly, if SNFS 334 is possible, then the "gang of 32" will need adjustment.

[swellman]

Originally Posted by R.D. Silverman

I'm not sure why 2,2222L (or M) is even being proposed before several smaller numbers. (6 of them by my count)

Because if a SNFS 334 is feasible target, then those other 6 are also likely to be feasible on NFS@Home (or a local team sieve effort). Of course if it’s found a S-334 is beyond local reach then all bets are off.

Clearly, if SNFS 334 is possible, then the "gang of 32" will need adjustment.

Here’s hoping the Gang becomes 25!

[charybdis]

Originally Posted by R.D. Silverman

The work on 2,2246M C221 suggests that a C225 via GNFS should have been within reach.

However, a suitable polynomial for 2,1109+ could not be found. Perhaps it is just an outlier for GNFS.

The e-scores of the best polynomials were in line with what one would expect for a GNFS-225. As far as I know, the only reason they were not considered suitable is that they didn't outperform the SNFS poly. Had it been out of reach by SNFS, it might have been added to the NFS@Home queue by now.
(Caveat: I haven't actually test-sieved the best GNFS poly to see how feasible it is. A task for another day.)

[R.D. Silverman]

Originally Posted by charybdis

The e-scores of the best polynomials were in line with what one would expect for a GNFS-225. As far as I know, the only reason they were not considered suitable is that they didn't outperform the SNFS poly. Had it been out of reach by SNFS, it might have been added to the NFS@Home queue by now.
(Caveat: I haven't actually test-sieved the best GNFS poly to see how feasible it is. A task for another day.)

Interesting. Was 2,2246M unusually easy? 2,1109+ is 4 digits larger. It should therefore be slightly less than twice as hard. Would this not be less work than 1110 bits of SNFS? [1110 is divisible by 6, 1109 is not]

Of course small variations in e-score can make a significant difference.

I am just trying to adjust my expectations about relative difficulty, since my initial guess was that GNFS 225 was
doable.