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Old 2014-05-16, 03:30   #1
VBCurtis's Avatar
Feb 2005
Riverside, CA

107116 Posts
Default 29 to 30 bit large prime SNFS crossover

Conclusion: SNFS-213 is a bit faster using 30-bit large primes than 29. The default factmsieve cutoff at 225 is too high.

As my SNFS tasks creep over 210 digit difficulty, I find that 29-bit large primes require more relations than ~200 difficulty projects; say, 46M raw relations instead of 41-43M. I decided to try running a pair of same-size factorizations with 29 and 30 bit large primes, to compare sieve time.

5*2^702-1: SNFS-213 diffficulty, 29-bit large primes, sextic poly E-score 4.47e-12. factmsieve runs with 300k blocks of special-q, and needed 46.8M raw relations, 40.6M unique to build a density-70 matrix of size 4.7M. Special-q from 8.9M to 29.3M were sieved.

13*2^702-1: SNFS-213 difficulty, 30-bit large primes, sextic poly score 4.27e-12. factmsieve built a matrix the first try with 76.5M raw relations, 69.2M unique to build a density-70 matrix of size 5.3M. Special-q from 8.9M to 27.5M were sieved. I'll edit my factmsieve to try building a matrix with fewer relations next time, which might save more time.

Despite a poly score 5% higher, the first project had to sieve almost 10% more special-q blocks, which took about 5% longer in wall-clock time compared to the 30-bit project. However, the 30-bit project had a matrix 15% larger, making up that 5% savings in sieve time to solve the matrix.

I don't know how to account for the different E-scores, but the better E-score took the same time as a 29-bit project as the lower one did with 30-bit primes.

I already factored 13*2^707-1 with 29-bit primes; I'll do 13*2^706-1 and 5*2^706-1 as 30-bit projects to see if my results here are a fluke.

Has anyone else compared 29 to 30 bits at SNFS difficulties under 220? Has someone done this for GNFS?

Last fiddled with by VBCurtis on 2014-05-16 at 03:33
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