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Old 2015-03-09, 07:01   #12
VBCurtis's Avatar
Feb 2005
Riverside, CA

4,219 Posts

Originally Posted by henryzz View Post
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?
I've done some more tests on large LP bounds for smaller numbers, and am pretty sure that sieving is fastest with bounds 1 or 2 bits bigger than traditional. However, when extrapolating this to large projects, optimizing for sieve time alone isn't ideal- filtering a 34 or 35 bit project will take MUCH longer than 33, and a matrix size 10 or 20 % bigger can eat up whatever sieve-time savings one can find.

At smaller sizes, those steps are so fast that optimizing for fastest sieve is generally best. Starting with Mr Womack's data above, 29LP can be used as small as 125 and be faster than any 28LP alternative. It was nearly 10% faster, so the 28/29 cutoff is likely even lower.

If anyone is willing to try this experiment on a GNFS 123 or 124, run 13e twice with 28 and 29LP and report timings. 28M rels or fewer for 29 bit!
I'm not going to run GNFS-140s twice, but I believe the 29/30 transition is around 143-144. I'm going to try my next GNFS141 with 13e/30 and see how that does. Perhaps 29/30 transition should happen before 13e/14e!

Other tests posted in the forum recently suggest 14e/32 is superior for GNFS-164 and up. I only have one sample point, but G156 with 31LP (133M raw rels) was almost as fast as G155 with 30 (80M raw rels). So, I think 30/31 cutoff is 154 or so.

So, perhaps a rule of thumb: every 10 digits, go up a bit of LP *or* a siever. That might make 15e/32 correct up to ~174, 15e/33 to ~184, and by then filtering and matrix time-effects need to be considered.

Additional data appreciated!
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