29 to 30 bit large prime SNFS crossover
Conclusion: SNFS213 is a bit faster using 30bit 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 29bit large primes require more relations than ~200 difficulty projects; say, 46M raw relations instead of 4143M. I decided to try running a pair of samesize factorizations with 29 and 30 bit large primes, to compare sieve time.
5*2^7021: SNFS213 diffficulty, 29bit large primes, sextic poly Escore 4.47e12. factmsieve runs with 300k blocks of specialq, and needed 46.8M raw relations, 40.6M unique to build a density70 matrix of size 4.7M. Specialq from 8.9M to 29.3M were sieved.
13*2^7021: SNFS213 difficulty, 30bit large primes, sextic poly score 4.27e12. factmsieve built a matrix the first try with 76.5M raw relations, 69.2M unique to build a density70 matrix of size 5.3M. Specialq 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 specialq blocks, which took about 5% longer in wallclock time compared to the 30bit project. However, the 30bit 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 Escores, but the better Escore took the same time as a 29bit project as the lower one did with 30bit primes.
I already factored 13*2^7071 with 29bit primes; I'll do 13*2^7061 and 5*2^7061 as 30bit 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 20140516 at 03:33
