Polynomial Request Thread - Page 71

Max0526 · 2017-02-14, 12:25

@richs

Code:

Y0: -802491073375414832049437700665826
Y1: 17773467038463166224451
c0: 281450494700811560760839813890939051120
c1: -59185115778630761425559458207234
c2: -681290192857977360683711431
c3: -186171856825853336081
c4: 177529875832800
c5: 6874560
skew: 2210380.09649
# MurphyE=3.03338768e-13

Max0526 · 2017-02-15, 03:37

Code:

Y0: -691735415860028161291242601067023
Y1: 25898420289952162105307
c0: 577300829383670786734653724089000359155200
c1: -45090526843823845959056529260126600
c2: -6637850955461852556600436653
c3: 111155248878476001023
c4: 42917566535268
c5: 5418720
skew: 12640532.26887
# MurphyE=3.05653198e-13

Code:

Y0: -803751455843259212672712847254981
Y1: 864581296717236270923
c0: -285484927206354497927796006707577717312
c1: 190607726108324557464500216348560
c2: 846894054469728955224899163
c3: -492239302261749233215
c4: -217266315868896
c5: -17914680
skew: 2425436.95571
# MurphyE=2.99962291e-13

Code:

Y0: -654035970248107691085069922013531
Y1: 1350822226295549689231
c0: 36860592170702325669218218368535419684768
c1: -2543745023823771483378850007823916
c2: -4676662370246444072129246739
c3: 232336354977493976595
c4: 44096544672790
c5: 2391000
skew: 7854939.34557
# MurphyE=2.95052464e-13

Code:

Y0: -1028511587689284667445138373376675
Y1: 665535349247962788221
c0: 22533008545320724338946558961105602417284
c1: -13487962063174154176858318389486031
c2: -4221943086576449154161816835
c3: 691820990086461083128
c4: 50377334496579
c5: -1118880
skew: 9768597.42761
# MurphyE=2.88467876e-13

Code:

Y0: -1527241659984638577722022092845741
Y1: 98615006614726432337
c0: 1551797973527777343502001314371109831429620
c1: -179044194645784780867209554001496051
c2: -18577403418136911264177315420
c3: -1626286374330428138973
c4: 22941820816816
c5: 275520
skew: 37940978.94624
# MurphyE=2.88411600e-13

Code:

Y0: -653427900355868874360576643427098
Y1: 4616438473145694210583
c0: 111896729588287178704430215285391549856
c1: 774805738647581580011686968630366
c2: -807963142329967887562959403
c3: -437165908293276868141
c4: 87606193554720
c5: 19217280
skew: 2549136.20448
# MurphyE=2.87193336e-13

Code:

Y0: -689795874507435216678843558826287
Y1: 1908332137424347372291
c0: -7342030739720333539261812968871993657000
c1: -12820259708389481053006085563824986
c2: -4593074902761256051542240913
c3: 346593234042892118206
c4: -43368508076322
c5: 2748600
skew: 7056957.29227
# MurphyE=2.79971088e-13

Code:

Y0: -631953363466978811546908255857153
Y1: 2913589592814534639431
c0: 724178019260093763001501131570723466520
c1: -3266887919909219915449846919384122
c2: -7242003286559748550929114959
c3: -23123752658855491802
c4: 14084723240490
c5: 1419480
skew: 8721896.15958
# MurphyE=2.78661745e-13

Max0526 · 2017-02-15, 04:40

@richs
Msieve's pick

Code:

R0: -691759524440491874859424810300253
R1: 25898420289952162105307
A0: 613461853462764228314022286702260688380900
A1: -32561477763161255775397850413517360
A2: -6768839093161172980776241263
A3: -1694631477025393057
A4: 17696405231268
A5: 5418720
skew 12652731.84, size 1.103e-016, alpha -8.595, combined = 3.057e-013

richs · 2017-02-15, 16:28

Thanks very much, Max. I will trial sieve these polys and see how they perform.

richs · 2017-02-18, 16:31

This was the best poly that I found by CPU search:

Code:

# norm 1.433572e-016 alpha -8.545613 e 3.128e-013 rroots 5
n: 143078471890001396404975722954703592875148935188191068938072316014184174902812459038968421963880118593068060667758149846867638636307227896395788079777289956829055499772249
skew: 718798201.99
c0: -20927250992693086458259129496993713626586796400
c1: 23809337639420727499940642755002298868
c2: 325528092819547637374452732948
c3: -141143903779127307669
c4: -826446704440
c5: 84
Y0: -4428524236781113000924987068997327
Y1: 126683988140215801

I will now test sieve with the various polys. Max, if you can optimize this poly with CADO, that would be great!

Max0526 · 2017-02-21, 02:56

@richs
CADO can't optimize your last poly, sorry.

richs · 2017-02-21, 21:22

Thanks for trying, Max.

RichD · 2017-03-21, 03:35

I can't find anything better than the following poly for the remaining OPN composite. Any help is appreciated.

Code:

N: 48617051659411879901148500183191173740459719818818239572906825331510589697540739558361422095833883018398491446348980638157678408112092901699165057691650922870794961
#  12400411646533^17-1  (C164)
#  expecting poly E from 7.50e-13 to > 8.62e-13
R0: -39473793098609748035930791458335
R1: 261219411908353
A0: -79506750899122167078435904866945771228
A1: 198162089109303566012723859657744
A2: -89849179280019767242017511
A3: -22750770139482346637
A4: 3542486324931
A5: 507276
skew 4138471.73, size 5.151e-16, alpha -5.250, combined = 7.630e-13 rroots = 5

Max0526 · 2017-03-21, 19:31

@RichD
I'll do a CADO run for this number and a CADO optimization for your poly when I get home. Will let you know tomorrow.

Max0526 · 2017-03-22, 03:09

@RichD
Your poly can be optimized by CADO-NFS. Do sieving and pick the best one.

Code:

Y0: -39473793098845147737507887122756
Y1: 261219411908353
c0: -6830288066541248281806141898016863107
c1: 59132071551759142629528655523557
c2: -14794676992600995256675732
c3: -31400608615324626065
c4: 1256809733271
c5: 507276
skew: 3046940.43999
# lognorm 49.83, E 44.55, alpha -5.28 (proj -1.67), 5 real roots
# MurphyE=8.04313460e-13

OR:

Code:

Y0: -39473793098425407586702362013059
Y1: 261219411908353
c0: 36414268145373788770115624216770967668
c1: 42969519334008936189506779266008
c2: -125646566348823834900729739
c3: -10224912539480172989
c4: 5332389399891
c5: 507276
skew: 4174573.51659
# lognorm 50.86, E 44.97, alpha -5.88 (proj -1.67), 5 real roots
# MurphyE=8.65454021e-13

Max0526 · 2017-03-22, 04:20

@RichD
Just throwing stuff into the mix, it'll be so much better at the end of the run:

Code:

Y0: -81148938188395992589149600045435
Y1: 79052040992330600806697
c0: 18544266948722570756177786709532060268656
c1: -8028036987025083800172268123394832
c2: -228574636379475055640641343
c3: 95579261398293234945
c4: 1048094307910
c5: 26520
skew: 16552788.76419
# lognorm 52.13, E 44.68, alpha -7.45 (proj -1.95), 3 real roots
# MurphyE=7.84174299e-13

2017-02-21, 02:56	#776
Max0526 "Max" Jun 2016 Toronto 19·47 Posts	C171 poly @richs CADO can't optimize your last poly, sorry.

2017-02-21, 21:22	#777
richs "Rich" Aug 2002 Benicia, California 2³·3·5·11 Posts	Thanks for trying, Max. Last fiddled with by richs on 2017-02-21 at 21:23 Reason: typo

2017-03-21, 19:31	#779
Max0526 "Max" Jun 2016 Toronto 19·47 Posts	C164 @RichD I'll do a CADO run for this number and a CADO optimization for your poly when I get home. Will let you know tomorrow.

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

2017-02-15, 16:28	#774
richs "Rich" Aug 2002 Benicia, California 2³×3×5×11 Posts	Thanks very much, Max. I will trial sieve these polys and see how they perform.