3,748+ c204 Smaller-but-Needed

[EdH]

Originally Posted by Plutie

I've been trying to run some polyselect with the individual sopt/ropt binaries. Is there a good way to sort out a certain amount of the highest scoring polynomials after the size optimization phase? I found a script from Dubslow from a few years ago, but it doesn't seem to work on the files I have. I have a feeling it's something to do with the fact that CADO doesn't output Murphy-E values from the sopt run, only the ropt run.

I think CADO-NFS uses the exp_E score with the lowest being the best.

[Gimarel]

I have a poly with a higher score, but I'm not sure that it sieves better because of the higher skew.

# norm 6.818228e-20 alpha -8.672366 e 2.910e-15 rroots 5
skew: 481915633.31
c0: -16767623414186593925342335649364464889222864703360
c1: 755475814165796441796091555811675522615312
c2: -1862355782954281845249626369142333
c3: -11089326275872160438115659
c4: 6063247064396140
c5: 11642400
Y0: -2468393961149314452796772519977513714557
Y1: 38282254249238850734383

I'll continue my search.

[Plutie]

Found this one! No spin done yet apart from EdH's script, which produced no better results.

n: 533439167600904850230361756102700151678687933392166847323827307497363839257031077774321424872955045754669625577486179222154434651598903112919949771321416511589029559325246084363632977829645558547714072241
Y0: -5364063517160195101439064344720425686774
Y1: 38191391760434248123003
c0: -515349887751874687116560925109512114626453230780
c1: 17974344725264404895365666536735938178777
c2: -101346622782727207541871449878174
c3: -1497180969353527609911507
c4: 1395152266302128
c5: 240240
skew: 428721961.354
# lognorm 62.56, E 54.79, alpha -7.77 (proj -2.37), 3 real roots
# MurphyE(Bf=1.000e+07,Bg=5.000e+06,area=1.000e+16)=3.496e-15

[swellman]

Originally Posted by Plutie

Found this one! No spin done yet apart from EdH's script, which produced no better results.

n: 533439167600904850230361756102700151678687933392166847323827307497363839257031077774321424872955045754669625577486179222154434651598903112919949771321416511589029559325246084363632977829645558547714072241
Y0: -5364063517160195101439064344720425686774
Y1: 38191391760434248123003
c0: -515349887751874687116560925109512114626453230780
c1: 17974344725264404895365666536735938178777
c2: -101346622782727207541871449878174
c3: -1497180969353527609911507
c4: 1395152266302128
c5: 240240
skew: 428721961.354
# lognorm 62.56, E 54.79, alpha -7.77 (proj -2.37), 3 real roots
# MurphyE(Bf=1.000e+07,Bg=5.000e+06,area=1.000e+16)=3.496e-15

[swellman]

These ultra high skews associated with high e-score polys may be reducible by half (or more) with Max’s script(s). He has managed this feat several times in the past.

Regardless, I’m in awe of the polys presented here. You guys are going to break the trend line!

[VBCurtis]

Plutie's poly makes the job more than 1 digit easier than the previous best. Bravo!

[charybdis]

Originally Posted by Plutie

Found this one! No spin done yet apart from EdH's script, which produced no better results.

# MurphyE(Bf=1.000e+07,Bg=5.000e+06,area=1.000e+16)=3.496e-15

Wow! This beats the polynomial used for RSA-200 in 2005! (3.464e-15)

[Max0526]

Originally Posted by Gimarel

I have a poly with a higher score, but I'm not sure that it sieves better because of the higher skew.

# norm 6.818228e-20 alpha -8.672366 e 2.910e-15 rroots 5
skew: 481915633.31
c0: -16767623414186593925342335649364464889222864703360
c1: 755475814165796441796091555811675522615312
c2: -1862355782954281845249626369142333
c3: -11089326275872160438115659
c4: 6063247064396140
c5: 11642400
Y0: -2468393961149314452796772519977513714557
Y1: 38282254249238850734383

I'll continue my search.

A bit higher here, with a lower skew:

Y0: -2468393961212256527378692570323255399071
Y1: 114846762747716552203149
c0: -667212226291265697384319795788252764666577494660
c1: 84612198807548503754244868832804518444888
c2: -602520047946604336765528388542069
c3: -11128887296718070048380139
c4: 17902612016700420
c5: 104781600
skew: 165972817.88
# size 5.647e-20, alpha -8.673, combined = 2.942e-15 rroots = 5

[swellman]

Originally Posted by Plutie

Found this one! No spin done yet apart from EdH's script, which produced no better results.

n: 533439167600904850230361756102700151678687933392166847323827307497363839257031077774321424872955045754669625577486179222154434651598903112919949771321416511589029559325246084363632977829645558547714072241
Y0: -5364063517160195101439064344720425686774
Y1: 38191391760434248123003
c0: -515349887751874687116560925109512114626453230780
c1: 17974344725264404895365666536735938178777
c2: -101346622782727207541871449878174
c3: -1497180969353527609911507
c4: 1395152266302128
c5: 240240
skew: 428721961.354
# lognorm 62.56, E 54.79, alpha -7.77 (proj -2.37), 3 real roots
# MurphyE(Bf=1.000e+07,Bg=5.000e+06,area=1.000e+16)=3.496e-15

Plutie -

I am curious, what parameters did you use in finding this poly?

One other note, when I first saw this posted it had another skew per CADO but then you edited it to match cownoise. Do you still have the old skew value? Most folks don’t bother changing the skew from the CADO result - it seems to have little effect on sieving efficiency with these big GNFS jobs. And I believe the old skew value was < 300e6 which is the upper limit on skew per an old rule of thumb.

One could extend this argument further by saying if the skew is too high just lower it until it’s not too high…

[Plutie]

Originally Posted by swellman

Plutie -

I am curious, what parameters did you use in finding this poly?

One other note, when I first saw this posted it had another skew per CADO but then you edited it to match cownoise. Do you still have the old skew value? Most folks don’t bother changing the skew from the CADO result - it seems to have little effect on sieving efficiency with these big GNFS jobs. And I believe the old skew value was < 300e6 which is the upper limit on skew per an old rule of thumb.

One could extend this argument further by saying if the skew is too high just lower it until it’s not too high…

Msieve-GPU stage1 w/ LC 120120 only, CADO sopt/ropt. I believe the old skew was around 210e6?

[Max0526]

Originally Posted by Plutie

Found this one! No spin done yet apart from EdH's script, which produced no better results.

n: 533439167600904850230361756102700151678687933392166847323827307497363839257031077774321424872955045754669625577486179222154434651598903112919949771321416511589029559325246084363632977829645558547714072241
Y0: -5364063517160195101439064344720425686774
Y1: 38191391760434248123003
c0: -515349887751874687116560925109512114626453230780
c1: 17974344725264404895365666536735938178777
c2: -101346622782727207541871449878174
c3: -1497180969353527609911507
c4: 1395152266302128
c5: 240240
skew: 428721961.354
# lognorm 62.56, E 54.79, alpha -7.77 (proj -2.37), 3 real roots
# MurphyE(Bf=1.000e+07,Bg=5.000e+06,area=1.000e+16)=3.496e-15

Scaled Plutie's poly with a lower skew. The only one so far with a 3-handle. EdH is welcome to try the CADO script on it.

Y0: -5364063515837856467699964219012314183783
Y1: 76382783520868496246006
c0: -18657659155224957284886697922211402602218993485
c1: 2902551913126853302500286670463847876254
c2: -246726843765655051378358372520499
c3: -2602155859693914100054886
c4: 5746970445994112
c5: 1921920
skew: 216595388.25
# size 6.032e-20, alpha -7.767, combined = 3.022e-15 rroots = 3