Polynomial Request Thread - Page 208

wombatman · 2022-10-11, 04:05

This is the best Degree 5 I had found:

Code:

# norm 1.947865e-020 alpha -7.882661 e 1.297e-015 rroots 5
skew: 771127364.56
c0: 165792391853474935561243616954647727516748946250496
c1: 2160239644350504494844955872920952825447896
c2: -21514458180493538566295548810659238
c3: -5887571126475837688637761
c4: 35919796435243602
c5: 5588280
Y0: -17068243492239505219994785346910834818341
Y1: 1873940548553722757

And the best degree 6:

Code:

skew 62700718.06, size 3.776e-015, alpha -10.235, combined = 1.263e-015 rroots = 6
n: 8095101662371927421703337019465587498085337648622133688278589711654019359923503887978141510461468343349838217540569173400647791769725685803537804186347867144149599002247585690859122186539724272741806859085719
skew: 62700718.06
Y0: -11353290441397119072312837579451455
Y1: 721472725254353419
c0: -7268878955932321043506178633175304342255310769376
c1: 11016155344762659492616649313015306910692260
c2: -233336062956902148240614789416199020
c3: -16367152013593221654947383405
c4: 233435941623797381261
c5: 2509253035955
c6: 3780
type: gnfs

firejuggler · 2022-10-12, 11:59

not a very good one but still

Code:

n: 8095101662371927421703337019465587498085337648622133688278589711654019359923503887978141510461468343349838217540569173400647791769725685803537804186347867144149599002247585690859122186539724272741806859085719
Y0: -3403035680093388686833052287513969
Y1: 3387782731570550984386367
c0: 26671744634200730491114742724185978306229840
c1: 229806710474402321328281592960115464372
c2: -1923365191633819120479542675367052
c3: -2978744796039860751794086779
c4: 10570382236601192508751
c5: 5226163385407128
c6: 1589728140
skew: 423278.297
# lognorm 60.61, E 50.14, alpha -10.47 (proj -2.62), 4 real roots
# MurphyE(Bf=1.000e+07,Bg=5.000e+06,area=1.000e+16)=1.257e-15

swellman · 2022-10-12, 13:40

CADO gave me a decent result, with score in last line from msieve:

Code:

n: 8095101662371927421703337019465587498085337648622133688278589711654019359923503887978141510461468343349838217540569173400647791769725685803537804186347867144149599002247585690859122186539724272741806859085719
skew: 879285.978
c0: -29119675796009739247349641483732604108447480
c1: 153433556948946440300396859126168065434
c2: 1413527054900522228585250362796089
c3: -872394574204602910742548386
c4: -1779675141032363072121
c5: 236585480106920
c6: -35666400
Y0: -4569655408887966364776554798126199
Y1: 2030536897444999236071783
# MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=1.476e+17) = 7.638e-09
skew 879285.98, size 3.733e-015, alpha -9.373, combined = 1.302e-015 rroots = 4

This result was from a search with ad < 1M but I will extend my search.

EdH · 2022-10-12, 21:13

Here's a spin of the last few:

Code:

Y0: -4569663782822131427953404358159291
Y1: 2030536897444999236071783
c0: 172275861275645666881354279206694170815441664
c1: -247353348597909878912090467534088316630
c2: -1424091643452499771217672520176605
c3: 842996766064271980197749170
c4: 1784562632510298258521
c5: -237468009508520
c6: 35666400
skew: 990769.676
# lognorm 59.66, E 49.82, alpha -9.84 (proj -2.19), 4 real roots
# MurphyE(Bf=1.000e+07,Bg=5.000e+06,area=1.000e+16)=1.439e-15

Best poly cownoise values: 1200532.09405      1.43841539e-15

swellman · 2022-10-13, 18:50

CADO produced this polynomial after searching 1-5M, maybe it can be spun.

Code:

n: 8095101662371927421703337019465587498085337648622133688278589711654019359923503887978141510461468343349838217540569173400647791769725685803537804186347867144149599002247585690859122186539724272741806859085719
skew: 480748.255
c0: -9617905202845852348059028779643989643959360
c1: -53521093480122955249104112481375520152
c2: 283139919291185257484412116696878
c3: 553323331103078337169725405
c4: -1751032649544826107351
c5: -573790319238696
c6: -266222880
Y0: -3454248193118572247295050349639697
Y1: 3843233555815688649179317
# MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=1.476e+17) = 7.819e-09
# cownoise   536862.79178    1.36194536e-15

firejuggler · 2022-10-13, 19:46

just got

Code:

 n: 8095101662371927421703337019465587498085337648622133688278589711654019359923503887978141510461468343349838217540569173400647791769725685803537804186347867144149599002247585690859122186539724272741806859085719
 Y0: -3251845526958442597299007829060353
Y1: 4433147107782156207490271
c0: 1156490704088259791888670763769641485394560
c1: -24293638133264715793634182746925819052
c2: 107799207730902855966179958526300
c3: -309614932966239418647378447
c4: -1857220828178442110715
c5: 144786624394360
c6: -1780178400
skew: 329731.284
# lognorm 59.24, E 49.65, alpha -9.59 (proj -2.82), 2 real roots
# MurphyE(Bf=1.000e+07,Bg=5.000e+06,area=1.000e+16)=1.360e-15

 Best poly cownoise values: 365976.72477      1.36183534e-15

from searching 6-7M

EdH · 2022-10-14, 16:12

Nothing better came from a spin of the last two.

swellman · 2022-10-16, 11:02

CADO got a big one!

Code:

n: 8095101662371927421703337019465587498085337648622133688278589711654019359923503887978141510461468343349838217540569173400647791769725685803537804186347867144149599002247585690859122186539724272741806859085719
skew: 140138.379
c0: 25913254528907171652995260756449843374970
c1: -1290547516892777857501992555209822939
c2: 6199518954766254144637219981714
c3: 264525951419727864944487871
c4: 67907082683742692904
c5: -4745861603713440
c6: 4669896000
Y0: -2803680302662889860338703572179527
Y1: 1891192000626364510493327
# MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=1.476e+17) = 9.383e-09
# skew 140138.38, size 5.715e-015, alpha -8.931, combined = 1.856e-015 rroots = 6
# 
# cownoise suggests skew 164898.488 which msieve scores as
# skew 164898.49, size 5.715e-015, alpha -8.931, combined = 1.858e-015 rroots = 6

While there is no existing record deg 6 for a GNFS 208, this escore feels close to where such a record would be. This ends my deg 6 searching on this composite.

That said, I believe a very good deg 5 poly would be a better choice to sieve a C208 (all past jobs on record used a deg 5). So I will start searching for such using CADO.

firejuggler · 2022-10-16, 11:25

really, really nice. I guess i'll stop once my rootopt is done and I'll look at a 5th degree poly too.

EdH · 2022-10-16, 14:21

And, my script attempts still can't get near e-15. The original degree 5 that wombatman posted was "1.297e-015."

swellman · 2022-10-16, 14:30

Quote:

Originally Posted by EdH

And, my script attempts still can't get near e-15. The original degree 5 that wombatman posted was "1.297e-015."

Ed - can my best deg 6 poly be spun up?

And yes I won’t bother reporting anything below 1.3e-15. Seems like we should able to find a couple of good polys (> 1.4e-15) with a few individual machine-weeks between us all but who knows what results we’ll get.

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
GIMPS wiki account request thread	ixfd64	mersennewiki	169	2018-09-21 05:43
Polynomial Discriminant is n^k for an n-1 degree polynomial	carpetpool	Miscellaneous Math	14	2017-02-18 19:46
Lost Prime Raider password request thread	cheesehead	Forum Feedback	6	2009-07-28 13:02
Polynomial	R.D. Silverman	NFSNET Discussion	13	2005-09-16 20:07
Deutscher Thread (german thread)	TauCeti	NFSNET Discussion	0	2003-12-11 22:12

2022-10-14, 16:12	#2284
EdH "Ed Hall" Dec 2009 Adirondack Mtns 2³×677 Posts	Nothing better came from a spin of the last two.

2022-10-16, 11:25	#2286
firejuggler "Vincent" Apr 2010 Over the rainbow 2²·7·103 Posts	really, really nice. I guess i'll stop once my rootopt is done and I'll look at a 5th degree poly too.

2022-10-16, 14:21	#2287
EdH "Ed Hall" Dec 2009 Adirondack Mtns 12450₈ Posts	And, my script attempts still can't get near e-15. The original degree 5 that wombatman posted was "1.297e-015."