mersenneforum.org 29 to 30 bit large prime SNFS crossover
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 2014-05-16, 03:30 #1 VBCurtis     "Curtis" Feb 2005 Riverside, CA 4,211 Posts 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
 2014-05-16, 07:09 #2 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 2·52·127 Posts I do this fairly constantly for GNFS as I work through aliquot sequences. It looks as if 28-29 is at about C148, 29-30 is at about C153, and 30-31 at about C158. But it's a reasonably subtle effect and there's about 10% noise in my measurements simply from sometimes sieving a bit too far. Here are some high tide marks Code: CPU-hours size lp 284.9 C139 29 288.5 C140 29 334.9 C142 29 342.6 C142 29 359.6 C143 29 422.0 C144 29 452.9 C145 29 548.4 C146 29 713.8 C148 30 762.8 C148 29 768.4 C149 30 823.6 C149 29 899.3 C150 30 1038.9 C150 30 1100.6 C152 30 1206.6 C153 30 1341.4 C154 30 2500.2 C157 30 2520.5 C158 31 2538.7 C159 31 3012.6 C161 31 4495.7 C162 31 4906.0 C163 31 11246 C169 30(3a)/15 12619 C170 32 19261 C172 31/15 Last fiddled with by fivemack on 2014-05-16 at 07:09
 2014-05-16, 07:18 #3 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 635010 Posts For SNFS, my data's not as good; I haven't done as many numbers, and I haven't been so careful in noting which computer I used for the sieving. But: Code: diff lp time/hrs 204.1 29 441.3 208.3 29 767.3 214.9 30 920.7 216.3 30 1031.2 222.0 30 2459.8 (sieved both A and R) 227.7 30 3494.9 233.2 31r30a 5623.6 248.9 31 18034.3 250.4 31/3r 25997.8 (15e) 285.1 33/3r 166625.8 (16e) so I think I concur that 29/30 is somewhere around 210 and 30/31 somewhere around 230, and everything gets a bit more confusing as you consider using 3 large primes, different LP bounds on the two sides, and the larger-range sievers at the 250-digit level. Last fiddled with by fivemack on 2014-05-16 at 07:19
2014-05-16, 13:07   #4
henryzz
Just call me Henry

"David"
Sep 2007
Cambridge (GMT)

567710 Posts

Quote:
 Originally Posted by fivemack It looks as if 28-29 is at about C148, 29-30 is at about C153, and 30-31 at about C158. But it's a reasonably subtle effect and there's about 10% noise in my measurements simply from sometimes sieving a bit too far. Here are some high tide marks
Extrapolating from those numbers C163 31-32 and C168 32-33. Does this mean when we do a 180+ digit number our large prime bounds are much too small?

 2014-05-16, 15:17 #5 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 2×52×127 Posts I honestly don't know. I don't think the optimal large prime bound can possibly grow that fast - but it's quite possible that it does grow that fast if we assume use of the 14e siever, which obviously we're not using as the numbers get huge.
 2014-05-16, 16:40 #6 Gimarel   Apr 2010 8916 Posts I use 29 at 120 digits GNFS. It's faster then 28 even with the increased filtering time. Code: lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 alambda: 2.55 rlambda: 2.55 alim: 99500000 rlim: 1400000 I start sieving at 1000000 and aim for 18300000 raw relations. Thats enough to build a matrix at target_density 90. The resulting matrix has about 670000 dimensions.
2014-05-16, 22:04   #7
VBCurtis

"Curtis"
Feb 2005
Riverside, CA

4,211 Posts

Quote:
 Originally Posted by fivemack I do this fairly constantly for GNFS as I work through aliquot sequences. It looks as if 28-29 is at about C148, 29-30 is at about C153, and 30-31 at about C158.
Looks to me like your data indicates 29-30 at C148 and 30-31 at C158. There are no 28-bit projects listed in the data. That takes care of part of Henry's question!

Thank you for the data and confirmation.

 2014-05-18, 21:48 #8 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 2×52×127 Posts Thanks for suggesting this: I have spent most of the weekend running through various parameter choices on C115, C125, C133, C136 that I had lying around, and am now reckoning that it's worth using significantly larger large-prime bounds than I'd previously considered - if you're careful about limits, 28-bit LP seems worthwhile as small as C115.
 2014-05-19, 04:28 #9 VBCurtis     "Curtis" Feb 2005 Riverside, CA 4,211 Posts Does using larger LP bounds shift where the 13e to 14e crossover is? It should move a bit upward, right? I use the python script for my factoring, but am working on building a list of script edits to post here. Perhaps we can build a 2014 consensus for cutoffs for 28-29-30-31 LP bounds, and likewise the points to move to 13e-14e-15e sievers. I'll play with 13e vs 14e with these new LP bounds myself, but would appreciate if others post their findings also.
 2014-05-19, 22:20 #10 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 2×52×127 Posts Here, for a random C124 with Murphy score 1.77e-10, are some timings for different alim and different ranges. They're really not what I expected: I would have thought that sieving well beyond Q0 was a bad idea. Code: alim Q (with 28/12e) time rel uniq ideals matrix 2 2-7 101870.2275 11905078 10430364 14715990 fail 2-8 121324.1423 13759598 11864512 15749318 fail 2-9 140607.982 15538550 13213233 16632104 fail 2-10 159487.2929 17218204 14465025 17381742 fail 2-11 178047.7998 18849180 15663145 18044872 1051033 4 2-9 204011.4358 21658907 18547562 20149112 879637 2-8.5 189501.4654 20339028 17534519 19671448 975442 2-8 174845.7571 18978238 16478927 19137617 fail 3-9 177762.3 18430231 16338414 19131390 fail 6 3-9 216706.984 20554991 18272260 20173211 1018070 3-8.5 197834.5111 18989740 17003043 19563723 fail 8 3-8.5 220669.0495 19632466 17601209 19902924 1178651 3-8 198166.9867 17846588 too slow even if it worked Currently running similar sorts of things with lpbr=29 and with 13e to see how the numbers compare Last fiddled with by fivemack on 2014-05-19 at 22:27
 2014-05-23, 21:51 #11 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 2·52·127 Posts I can get the sieving time down to 166k seconds with 13e, 29-bit large primes, alim=4000000, sieve 1.5M-4M for 27.9M relations.

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