20210823, 12:23  #3048 
Apr 2020
2·251 Posts 
The poly I posted yesterday was the best from my range, but not by that much. Here are the next best two, let's see if Gimarel can work his magic.
Code:
n: 5272066026958413205513021090082556639441277154855572268239336980532402881465013381219738819137405617219594641652778228990107677072837959240400905630530715435664638237254654768053674178165309345879869729405448588458952991 skew: 1907251.281 c0: 8236427797628293049599408725893247072637239772 c1: 19162528353248595305446715812300596109295 c2: 21091088260708627616667662646742165 c3: 12419116707177921879187220801 c4: 7785775652933998252593 c5: 948954265351506 c6: 43482600 Y0: 249636408603218968365364360310503950 Y1: 22334710996682366819620031 # cownoise: e 3.62425400e16 n: 5272066026958413205513021090082556639441277154855572268239336980532402881465013381219738819137405617219594641652778228990107677072837959240400905630530715435664638237254654768053674178165309345879869729405448588458952991 skew: 1760341.42 c0: 15354638866604858505124720786978674723100123170 c1: 61469554170413960080201338721573680907367 c2: 29684864243265761798289322803166219 c3: 74136878484020854315362790097 c4: 5081461673273545660609 c5: 1949330215164330 c6: 699388200 Y0: 246835163382771953077067062497572256 Y1: 11904096208130921118914953 # cownoise: e 3.47247226e16 
20210823, 12:36  #3049 
"Ed Hall"
Dec 2009
Adirondack Mtns
7662_{8} Posts 
Couldn't almost any found poly be good enough to produce factors, while what we search for is the best poly, of those found, that will produce relations the fastest overall? And throughout the search, we try to balance the poly search time against the sieve time, minimizing the total?
When I was using Msieve across my farm (and working with smaller composites), I put a short hard time on polynomial searching and then went with whatever showed up in that limited search. Many of those polynomials weren't really good, but I still got factors. 
20210823, 12:49  #3050  
Apr 2020
502_{10} Posts 
Quote:
Poly selection is possibly the part of GNFS with most room for improvement. For example, the best polys for this c220 might have degrees 3 and 4 rather than 1 and 6, but we don't have a good way to find such polys. 

20210823, 13:40  #3051 
Jun 2012
3,203 Posts 
My redo of 4041M with nq=6^7 and P=10M gave a best cownoise score of 2.898e16.
10th best cownoise was 2.586e16. Going to finish my search range of 4050M with P=10M and nq=6^6. 
20210823, 14:03  #3052  
Apr 2010
2^{3}×23 Posts 
Quote:


20210823, 17:13  #3053 
Apr 2020
2×251 Posts 

20210823, 17:32  #3054 
Aug 2020
79*6581e4;3*2539e3
2×3×67 Posts 
Is that point already reached? When I extrapolate from my few factorizations in the 160170 range a c220 should take about 1000 coreyears (veery roughly). So even shaving 1% of the sieving time should save a lot of time. Wouldn't a few more days do some good? Or is the probability to find something better too low?

20210823, 18:57  #3055  
Apr 2020
2·251 Posts 
Quote:
We must have spent at least 2 coreyears on polyselect so far, and I've just queued up another ~1.5 coreyears, or 1% of the estimated sieving time. As the current best poly doesn't look like an outlier to me, I reckon there's enough chance of beating it by a few percent to make the extra polyselect time worthwhile. 

20210823, 20:09  #3056  
Jun 2012
Boulder, CO
101001000_{2} Posts 
Quote:


20210823, 21:42  #3057  
"Curtis"
Feb 2005
Riverside, CA
3·1,667 Posts 
Quote:
If you end up with a matrix 80 million dimensions or smaller, I can do the matrixsolving (though it would take me 34 months for a 7080M matrix on a dual10core 128GB ram machine). As for sievetime estimates: the C207 team sieve we did in 2019 took about 125 threadyears (some were not hyperthreaded, so say 70 coreyears). C220 is more than two doublings bigger, so I estimate 250300 coreyears of sieve. Note that using 34/35LP, as we did on the C207, will require nearly 4e9 raw relations these are the largest LP settings that don't need the extra CADOcompile flag set to handle more than 2^32 raw relations. In hindsight, 33/34 would likely have been optimal for C207, so 34/35 should be fine for C220. We learned from other suboptimal sieve choices in that effort, and I am confident we could get the sieve time below 60 coreyears for C207 if we did it again. For instance we started Q far too small, leading to yucky duplicate rates. We also shifted to I=15 to save memory and because it looked faster, which exacerbated the duplicaterelations problems. I bring this stuff up since Ryan suggested we select the params... Last fiddled with by VBCurtis on 20210823 at 21:44 

20210823, 23:44  #3058  
Apr 2020
2×251 Posts 
Quote:
Quote:
Edit: the usual doubling rule probably doesn't hold up around the degree 5/6 boundary does it? The degree 6 curve intercepts the degree 5 curve, so once you switch to degree 6 the number of digits per doubling should go up... Last fiddled with by charybdis on 20210823 at 23:53 

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