20210925, 18:39  #78 
"Ed Hall"
Dec 2009
Adirondack Mtns
2×2,251 Posts 

20210926, 14:59  #79  
"Max"
Jun 2016
Toronto
1110100000_{2} Posts 
Quote:
Code:
Y0: 10728127031432018094778041711124528492914 Y1: 38191391760434248123003 c0: 469306450383673786154179958923768036883220558848 c1: 16764898040765810552874639420851915901168 c2: 518184119670233545764543818527130 c3: 1282718100125517456876339 c4: 720287485214464 c5: 60060 skew: 925525618.81 # size 6.010e20, alpha 7.767, combined = 3.022e15 rroots = 3 

20210926, 15:09  #80 
"Max"
Jun 2016
Toronto
1110100000_{2} Posts 
The last one before I fire up my CADO.
Code:
Y0: 2682031757909474203063733054205920498761 Y1: 38191391760434248123003 c0: 35908619240718506542028162576570459628200092008 c1: 5559845291855259938458828146982323985017 c2: 497314341623175258490396369880660 c3: 5192928362539057069336396 c4: 11498698480023424 c5: 3843840 skew: 215953735.30 # size 6.029e20, alpha 7.765, combined = 2.981e15 rroots = 3 
20210926, 18:01  #81 
"Ed Hall"
Dec 2009
Adirondack Mtns
2·2,251 Posts 
For some reason, my machine I turned loose is still churning. It hasn't found anything better, but I'm wondering why it's still trying. I might have to try the latest ones on a different machine. . .

20210927, 15:00  #82 
"Ed Hall"
Dec 2009
Adirondack Mtns
2×2,251 Posts 
I tried the last two Max posted, but didn't get anything to be excited about:
Code:
Y0: 2682031753193739554089051909692707821633 Y1: 38191391760434248123003 c0: 2558958882078862036416567911929050848051646810840 c1: 14288895390205752696754550185547792236194 c2: 1296679606343231125776054513987683 c3: 1072389920449047317227700 c4: 13871815645642624 c5: 3843840 skew: 225516970.018 # lognorm 63.80, E 55.60, alpha 8.20 (proj 2.75), 5 real roots # MurphyE(Bf=1.000e+07,Bg=5.000e+06,area=1.000e+16)=3.094e15 Code:
316412275.01640 3.10650558e15 
20210927, 20:59  #83 
Jun 2012
13·269 Posts 
Lot of high escoring candidates!
How critical is the skew wrt sieving efficiency for these bigger GNFS jobs? Cownoise (and presumably msieve) doesn’t use an input value for skew in the score calculation, what’s to stop someone from using the highest scoring poly and cutting the skew in half or a third? Sieving efficiency could suffer but would the high escore carry the day? I noted that with Plutie’s record poly, the skew was ~210M per CADO but cownoise said 489.7M. What would be the effect(s) be if we ignore this suggestion from cownoise? Or set skew to say 290M? Most of us seem to use the output value for skew, often > 1e8, to two decimals places of precision. Is this strictly necessary? Just random musings. I know skew has been discussed before, likely numerous times but looking at the list of polys in this thread the proper method of selecting the “best one” is not obvious to me. 
20210927, 21:53  #84 
"Curtis"
Feb 2005
Riverside, CA
149D_{16} Posts 
cownoise is testing a bunch of skew values to see which one results in the highest escore.
If you use a nonoptimal skew, the poly will generally sieve less efficiently. But, this "efficiency" is not very sensitive; you might testsieve that Plutie poly with the CADO skew and the cownoise skew, and see the effect for yourself. 8+ sigfigs is definitely not important for skew. 
20210927, 22:08  #85 
Apr 2020
17×41 Posts 
The 3.496e15 poly scores so highly that it ought to beat all the others as long as the skew selected is vaguely sensible. Cownoise chooses the skew that produces the best MurphyE score as calculated by msieve with its default parameters. I'm not sure what CADO does, but in practice the difference in performance is going to be pretty small.

20210927, 22:40  #86  
Jun 2012
13×269 Posts 
Quote:
I’ve heard the rule of thumb never use a skew > 3e8. (Not sure if this is still true.) At least one of the high scoring polys in this thread had a skew exceeding this limit  dropping the skew to a lower value may help. Or not. Or do we filter out such polys from the list of finalists? Bottom line: how important is skew in a GNFS 204 job? [/babble] 

20210927, 23:01  #87 
Apr 2020
17·41 Posts 
I'd say testsieve each poly with whatever skew it came with (ideally these would be consistent i.e. all cownoise or all CADO, but this won't matter) and only try different skews if it's very close between the top two.
I see absolutely no mathematical reason to avoid skew > 3e8. For very large degree 5 jobs like this, a large skew is to be expected. Did the GGNFS sievers have trouble with huge skews perhaps? Extremely small skews (<< 1), sometimes seen with SNFS, pose a bigger problem, because on very large jobs they will produce lots of relations with b > 2^32 which msieve filtering can't deal with. 
20210927, 23:15  #88  
Jun 2012
110110101001_{2} Posts 
Quote:
Quote:
Last fiddled with by swellman on 20210927 at 23:16 

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