2^877-1 polynomial selection - Page 4

fivemack · 2009-06-06, 10:20

Quote:

Originally Posted by jasonp

Stage 1 of the poly selector cannot generate polynomials when the leading rational coefficient exceeds 2^64; you'll either have to use a larger leading algebraic coefficient or reduce the stage 1 norm. The 109!+1 job was very nearly at the limit of what the current code can handle.

Degree 6 might make this work :)

I'm trying with 1.42, but the 'rational coefficient too large' message is appearing when I try algebraic leading coefficients greater than 10^5, whilst from your message I would expect it to go away as the algebraic leading coefficient gets larger.

jasonp · 2009-06-06, 13:45

I was mistaken, it's actually more complicated than that. The maximum size of the leading rational poly coefficient depends on the minimum amount of skew, and the minimum skew increases as the leading algebraic coefficient goes down in size, so smaller A5 make it behave better. However, the minimum skew decreases as the stage 1 norm increases, since a bigger stage 1 norm allows larger poly coefficients. So there are two variables at work here.

frmky · 2009-06-07, 04:21

20-112 excluding 28, 47, 56 is done. Nothing better was found. I'm going to take a brief hiatus from this search.

Andi47 · 2009-06-07, 05:09

Quote:

Originally Posted by Andi47

No polynomial found, extending the search up to 6000.

done, not a single poly was found.

antiroach · 2009-06-08, 12:39

5-14 and 15-20 done, nothing better to report.

fivemack · 2009-06-11, 09:36

Here are the three from 400-500:

Code:

BEGIN POLY #skewness 465680.17 norm 8.35e+24 alpha -6.31 Murphy_E 8.81e-14
X5 40299860160
X4 235310542479263808
X3 -10166626421992966484146
X2 -42835392428744393030601577469
X1 6995897745216155501363510652321730
X0 -5127746137235669841841905105599430040
Y1 11931033499362022133
Y0 -2269587558640472874786564125501403

BEGIN POLY #skewness 623977.12 norm 4.37e+24 alpha -5.96 Murphy_E 8.94e-14
X5 41569206780
X4 59882073035976427
X3 -57887318793989696267254
X2 -20230067836366880725744598330
X1 7679773862519236732320648037307826
X0 1072443984015981718495646298701289292320
Y1 1376981466270636991
Y0 -2255554395062708894197055179304491

BEGIN POLY #skewness 513074.17 norm 4.91e+24 alpha -6.25 Murphy_E 9.21e-14
X5 41030450460
X4 136480592987988374
X3 -34294082605344992122939
X2 -35066803684635202530370114749
X1 3623833375018730887856549694002911
X0 -2901386802923525511376226880411147353
Y1 3738548270753899207
Y0 -2261446901996884615927450785999990

If anyone else has polys with >8.75e-14, please post them - there shouldn't be very many. I'll run trial sieving on several, though the yield differences tend to be subtle enough that the amount of sieving required for an absolutely conclusive six-sigmas-different answer is infeasible.

I'll be interested to see how the alpha=-3.75 E=9.23e-14 polynomial behaves

frmky · 2009-06-11, 17:01

Quote:

Originally Posted by fivemack

If anyone else has polys with >8.75e-14, please post them

Here are all that I have, including those that I posted earlier.

Code:

BEGIN POLY #skewness 1393083.78 norm 4.32e+24 alpha -5.89 Murphy_E 8.79e-14
X5 7988831280
X4 14580970602222246
X3 -43626745638692430955673
X2 -23453719860277233924190210954
X1 33555650001835538690751465264624684
X0 4905406813113028099117851393045009054672
Y1 1101532662216731173
Y0 -3136974603281296346860328593765169
M 77136085883276765998210435227835276382341446467614801510505079315310000373622605481250616753542469126513792$
END POLY

BEGIN POLY #skewness 780026.74 norm 3.65e+24 alpha -5.51 Murphy_E 8.81e-14
X5 13000516680
X4 -45296223506109810
X3 -18213959072444250473351
X2 21665281762134638674519711570
X1 3458718514427545774465599237423196
X0 -2615561694883948640813219594401494531080
Y1 9404071755074711761
Y0 -2845873102726668873357575048477587
M 1869109963635646999760847421932073297151167223249859566950252871258750150747885605924081797666005148450485446948783993485062485457815470180476054150189470552500729457736156947329
END POLY

BEGIN POLY #skewness 528296.15 norm 8.16e+24 alpha -6.07 Murphy_E 8.82e-14
X5 55467209700
X4 -164173983484368885
X3 11919491487886964116412
X2 39212532310490893146589374482
X1 2652616887900135951914093258058208
X0 -921528738083745230393483499488053381160
Y1 7359538803884504347
Y0 -2129121226236193682999914208403663
M 1844892432856715509368832408493309442065870891943336341626510101027334798171838922594575631172248835929692500688355280994571462283713107003145379679434560547223524199831022791643
END POLY

BEGIN POLY #skewness 1143982.06 norm 4.65e+24 alpha -5.82 Murphy_E 8.89e-14
X5 7988831280
X4 10375969369681446
X3 -48881279608136921884121
X2 -8799361963629732263869085764
X1 18158264694109471864216802516637286
X0 1669877081881186666743828463666352210208
Y1 1101532662216731173
Y0 -3136974603397256893277208317809225
M 771360858832767659982104352278352763823414464676148015105050793153100003736226054812506167535424691265137926467147986075799825879180827083569477342245548065867122060824750219250
END POLY

BEGIN POLY #skewness 816327.37 norm 5.05e+24 alpha -6.28 Murphy_E 8.92e-14
X5 32055918720
X4 29798457608433028
X3 -14991575404744201989244
X2 -33293542816855421501424946835
X1 1861911933976428628889004560330878
X0 5853519671908144161306021419056494976741
Y1 11279933095083334099
Y0 -2375888232626177991970686615196770
M 345124291056658873510246773954192676954118293214361587101272871924764284399735190560363622435955938656963581805856304157439725629671960934892083562575672644874302507782755750283
END POLY

BEGIN POLY #skewness 1309487.87 norm 3.78e+24 alpha -5.97 Murphy_E 8.94e-14
X5 7988831280
X4 14234934375329046
X3 -44126010008333484640865
X2 -22313390707844341396888367113
X1 33952149215622249513539262518829085
X0 2771979958202819495946282164505631248855
Y1 1101532662216731173
Y0 -3136974603290838924313112135916868
M 771360858832767659982104352278352763823414464676148015105050793153100003736226054812506167535424691265137926467147986075799825879180827083569477342245548065867122060824750122641
END POLY

BEGIN POLY #skewness 449294.72 norm 5.96e+24 alpha -5.74 Murphy_E 9.02e-14
X5 53280993600
X4 90761570626362492
X3 -35620195999940336867612
X2 -28527768291697396842138328615
X1 -3198053015272499345309922251089958
X0 -4554569779439147645579767084289032452
Y1 5102421388954328857
Y0 -2146313658094193048763594490802221
M 577217871174834044810358612956499157369864151158702100765868859978804229326438870528288741575943416039961958293850851850612756243192962960032087156758656134650502277954391515603
END POLY

BEGIN POLY #skewness 547461.22 norm 5.80e+24 alpha -6.05 Murphy_E 9.20e-14
X5 52101320040
X4 -44407918935106581
X3 -79015216368833586747403
X2 11164378525237099289579014018
X1 5527464674743398811310201276866547
X0 -673974942315034055091970689174411290421
Y1 1493967901901591351
Y0 -2155946141079123383394238690321070
M 1150037515776903529929513338174844080666513470844815234134299773706957463920508105588340991081428622325264919469255000550148116581269548623513203251071007991618198832709506873084
END POLY

fivemack · 2009-06-12, 23:15

One measly polynomial from the 1000-1260 range

BEGIN POLY #skewness 399354.08 norm 1.31e+25 alpha -6.75 Murphy_E 8.87e-14
X5 118218336600
X4 398813504004653258
X3 -72296606985522952769515
X2 -33233670867863958975378982480
X1 5075531829147750504995984232104640
X0 534552531565360239042526799477898421617
Y1 2169344085574070207
Y0 -1830082564238746573289030503773310

frmky · 2009-06-13, 06:18

I've got some more computer time to devote to this. I'll take 600-800.

fivemack · 2009-06-13, 17:01

How can I not imitate such an example? Taken 800-1000

frmky · 2009-06-14, 04:44

The range is still in progress, but here's an early result:

Code:

BEGIN POLY #skewness 519625.47 norm 9.53e+24 alpha -6.60 Murphy_E 9.32e-14
X5 64557142440
X4 167973044528239654
X3 -100111516133628328149175
X2 -31507635276309757652045157209
X1 7112018715529532370533366009722415
X0 628512337968260604360134830489290707475
Y1 9625907267817689563
Y0 -2065469526312388448258409994269014
M 64809919909302589430337323549770166569128750198434648834853370378821790630706924008987853190550511031140520182008906058746339373345894047269277137605044662697707893154615005941
END POLY

2009-06-12, 23:15	#41
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 7²×131 Posts	Not a terribly high yield from eight CPU-weeks One measly polynomial from the 1000-1260 range BEGIN POLY #skewness 399354.08 norm 1.31e+25 alpha -6.75 Murphy_E 8.87e-14 X5 118218336600 X4 398813504004653258 X3 -72296606985522952769515 X2 -33233670867863958975378982480 X1 5075531829147750504995984232104640 X0 534552531565360239042526799477898421617 Y1 2169344085574070207 Y0 -1830082564238746573289030503773310

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2009-06-06, 13:45	#35
jasonp Tribal Bullet Oct 2004 6725₈ Posts	I was mistaken, it's actually more complicated than that. The maximum size of the leading rational poly coefficient depends on the minimum amount of skew, and the minimum skew increases as the leading algebraic coefficient goes down in size, so smaller A5 make it behave better. However, the minimum skew decreases as the stage 1 norm increases, since a bigger stage 1 norm allows larger poly coefficients. So there are two variables at work here.

2009-06-07, 04:21	#36
frmky Jul 2003 So Cal 2×3⁴×13 Posts	20-112 excluding 28, 47, 56 is done. Nothing better was found. I'm going to take a brief hiatus from this search.

2009-06-08, 12:39	#38
antiroach Jun 2003 2²×61 Posts	5-14 and 15-20 done, nothing better to report.

2009-06-13, 06:18	#42
frmky Jul 2003 So Cal 2·3⁴·13 Posts	I've got some more computer time to devote to this. I'll take 600-800.

2009-06-13, 17:01	#43
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 14423₈ Posts	How can I not imitate such an example? Taken 800-1000