Cunningham ECM efforts

[charybdis]

Originally Posted by R.D. Silverman

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]

The polynomial for 2,2246M was indeed very good, but that's still only a ~10% advantage over what we might have expected beforehand.

What surprised me about 2,1109+ was not that GNFS seemed harder than expected but that SNFS seemed easier than expected. I had naively been comparing degree-6 GNFS polys with degree-6 SNFS polys using the msieve Murphy-E score, which uses values for the sieve region and factor base bound that are far too small for a job this size. It was not at all hard to find a GNFS poly that beat the msieve E-score of the SNFS poly. However, the SNFS poly sieved much faster. I then used CADO to produce Murphy-E scores with more realistic parameters and this correctly showed the SNFS poly as the clear winner.

Let's see how 2,1091+ goes with 35-bit large primes. 2,1109+ is 5 digits larger so maybe 60% more difficult?

[pinhodecarlos]

2,1091+ sieving has begun. Think I'll turn on my machine to at least make a small contribution to this effort.

[frmky]

2,2390L is done. Approximately 3.8 billion raw relations yielded 2.4 billion unique relations. These produced a 96.4M matrix, which took about 55 hours to solve on four nVidia A100's. The factors were found on the 18th (!) dependency after 58.5 hours. Of these, 11 dependencies failed because of the "bad" algebraic polynomial and 6 simply failed to find the factors.

[pinhodecarlos]

For 2,1091+ how high will we be going for the Q range, 5000M? We are very close to the 2000M, did turn on my laptop ( you might have noticed a mini tiny peak, sorry about the server shake) and each wu now takes longer to be processed.

[frmky]

Originally Posted by pinhodecarlos

For 2,1091+ how high will we be going for the Q range, 5000M?

Somewhere between 3B and 4B. Not sure where yet. Depends on how fast the sieving drops off.

[pinhodecarlos]

Originally Posted by frmky

Somewhere between 3B and 4B. Not sure where yet. Depends on how fast the sieving drops off.

Sorry, you mean yield per special Q range, right? TIA.

[frmky]

Exactly.

[R.D. Silverman]

Originally Posted by frmky

Somewhere between 3B and 4B. Not sure where yet. Depends on how fast the sieving drops off.

In general, if the yield per q drops off too rapidly, it usually means that the factor bases are too small.
[I'm not suggesting that this is the case here].

[frmky]

Originally Posted by R.D. Silverman

In general, if the yield per q drops off too rapidly, it usually means that the factor bases are too small.
[I'm not suggesting that this is the case here].

That most definitely is the case here. I make the factor bases smaller than optimal to keep memory use under 1GB/core. This is a hard limit for numerous contributors to the project.

[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.

The gang of 32 just became the gang of 31 again. Greg queued 2,1097+.......

[pinhodecarlos]

Greg, did you manage to get 2,1091+ into LA stage?