Polynomial Request Thread - Page 39

wombatman · 2014-03-28, 18:57

Small improvement:

Code:

polynomial selection complete
R0: -313426207408478690741807350442
R1: 4985154433895227
A0: 64274525925439519677314518508387370465
A1: 50955331804223207969796444100169
A2: -16775534299649772885367939
A3: -14160958980613019665
A4: 335875177338
A5: 1093680
skew 2722245.55, size 5.610e-015, alpha -7.448, combined = 3.081e-012 rroots = 3

RichD · 2014-04-10, 04:09

Aliquot sequence 3408 is ready for GNFS and a poly.

The current term is here.

The C166 composite is:

Code:

1123367150134848120647467256535952482658686476885324744360520386356344637194859571636314844955603685901980138488599119535795850301781912277982445337403841501308675373

A nice poly is requested.

chris2be8 · 2014-04-12, 15:43

Since no one else seems interested I'll have a go. I'll let you know when I've got something.

Chris

sashamkrt · 2014-04-15, 04:33

Code:

N:  1123367150134848120647467256535952482658686476885324744360520386356344637194859571636314844955603685901980138488599119535795850301781912277982445337403841501308675373

# norm 4.740739e-016 alpha -6.805832 e 6.493e-013 rroots 3
skew: 4440977.86
c0: -177048535144577104002100358070738707625
c1: 365723560219633695438695599995825
c2: 495640540820121872411293295
c3: -111509067703870473337
c4: 7960709240186
c5: 1321320
Y0: -61080521272901563946054800533482
Y1: 875338835798211529

# norm 4.462039e-016 alpha -7.435898 e 6.237e-013 rroots 3
skew: 9112731.34
c0: -23808740138726624289321423454604296645443
c1: -1466967236654254780631224580887119
c2: 967665755570684778379380281
c3: -130649495154318981865
c4: -382514849014
c5: 1321320
Y0: -61080522378333716799855808469480
Y1: 875338835798211529

# norm 4.491349e-016 alpha -7.834517 e 6.233e-013 rroots 5
skew: 10120852.14
c0: -2487662169925619011414083785466603069415
c1: 17900717407620781734682035008680428
c2: 1738977030042289153018461673
c3: -780255315421125543468
c4: -15384833651358
c5: 1312740
Y0: -61160160247186338969070336749222
Y1: 864634448508699529

# norm 4.496146e-016 alpha -7.259351 e 6.231e-013 rroots 5
skew: 8596150.68
c0: 15831684823536804655058985745100802791721
c1: 10704450769273425265783975355355078
c2: 192151769714510808550440602
c3: -425569331212241159887
c4: 5995995318156
c5: 1447380
Y0: -59977426957982371068013390847954
Y1: 5137117526847881

chris2be8 · 2014-04-15, 04:47

My best result is:

Code:

n: 1123367150134848120647467256535952482658686476885324744360520386356344637194859571636314844955603685901980138488599119535795850301781912277982445337403841501308675373

# norm 5.501656e-16 alpha -7.179471 e 7.119e-13 rroots 5
skew: 36195688.86
c0: 75577562337689364028481050776760905394833
c1: 3224013476052476246459675851031357
c2: -1644146666659802871764747813
c3: -9297976523287591189
c4: 1376786174160
c5: 1692
Y0: -231432459847718112775382371692070
Y1: 2775839702823571

Chris

debrouxl · 2014-04-15, 09:23

My best one is below sashamkrt's polys.

chris2be8 · 2014-04-15, 15:32

And my second best result is:

Code:

# norm 5.386430e-16 alpha -7.124421 e 7.002e-13 rroots 5 skew: 39711911.18
c0: 313768005569780256947621801516554049147768
c1: 5242099641663080151981840862637332
c2: -1623782187706610058329399198
c3: -12691336302789308989
c4: 1371563435460
c5: 1692
Y0: -231432459849431763536721989131065
Y1: 2775839702823571

I should have posted that earlier, but sleep got in the way. Sorry.

Chris

VBCurtis · 2014-04-15, 23:03

If RichD does some test-sieving, I am curious to hear what yield is for Chris' polys vs sashamkrt's. I still don't have a firm grasp of the effect of skew on the sieving phase, but Chris' skews are very high due to his tiny A1 choice.

Or, for the NFS experts: what effect will sieving with a poly skew of 30-40M for this C166 have? Is that effect outweighed by the Murphy score running 10% higher than Sasahmkrt's polys, the best of which has skew 4M?

Is it valid that if the yield of the high-skew poly is good enough to produce enough relations before poly performance drops off, we don't care what skew is?

jasonp · 2014-04-16, 00:31

The Murphy score assumes a sieving region of fixed area, and factor bases of fixed (small) size. I don't think there's a set answer to your question, the sieving rate could be higher or lower than the Murphy score would indicate. Lattice sieving doesn't care very much that the sieving region is very wide and thin, and we don't have many samples of (good) polynomials with very large skew to compare with.

schickel · 2014-04-18, 05:01

I've got a c154 from aliquot sequence 611156:i7547 that needs a poly:

Code:

1233834109316954251065406210584382514482486785123839242711421920174697279622119210044011032460138316615713715099127735270405764948375711542820719611655437

Something nice would be appreciated.

sashamkrt · 2014-04-25, 04:27

Code:

611156:i7547

n: 1233834109316954251065406210584382514482486785123839242711421920174697279622119210044011032460138316615713715099127735270405764948375711542820719611655437
# norm 8.191801e-015 alpha -7.444448 e 3.477e-012 rroots 5
skew: 1837012.21
c0: 9524788629911251806899820614452358175
c1: 19825309048338991034711681062715
c2: -12548193435218537869063512
c3: -16897387341480048942
c4: 5214672777134
c5: 1375980
Y0: -245770001251625498938715399762
Y1: 43639219601327273

2014-04-10, 04:09	#420
RichD Sep 2008 Kansas 3376₁₀ Posts	C166 @ AS3408:i1399 Aliquot sequence 3408 is ready for GNFS and a poly. The current term is here. The C166 composite is: Code: 1123367150134848120647467256535952482658686476885324744360520386356344637194859571636314844955603685901980138488599119535795850301781912277982445337403841501308675373 A nice poly is requested.

2014-04-16, 00:31	#427
jasonp Tribal Bullet Oct 2004 3,541 Posts	The Murphy score assumes a sieving region of fixed area, and factor bases of fixed (small) size. I don't think there's a set answer to your question, the sieving rate could be higher or lower than the Murphy score would indicate. Lattice sieving doesn't care very much that the sieving region is very wide and thin, and we don't have many samples of (good) polynomials with very large skew to compare with. Last fiddled with by jasonp on 2014-04-16 at 00:32

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2014-04-12, 15:43	#421
chris2be8 Sep 2009 2·1,039 Posts	Since no one else seems interested I'll have a go. I'll let you know when I've got something. Chris

2014-04-15, 09:23	#424
debrouxl Sep 2009 977 Posts	My best one is below sashamkrt's polys.

2014-04-15, 23:03	#426
VBCurtis "Curtis" Feb 2005 Riverside, CA 4,861 Posts	If RichD does some test-sieving, I am curious to hear what yield is for Chris' polys vs sashamkrt's. I still don't have a firm grasp of the effect of skew on the sieving phase, but Chris' skews are very high due to his tiny A1 choice. Or, for the NFS experts: what effect will sieving with a poly skew of 30-40M for this C166 have? Is that effect outweighed by the Murphy score running 10% higher than Sasahmkrt's polys, the best of which has skew 4M? Is it valid that if the yield of the high-skew poly is good enough to produce enough relations before poly performance drops off, we don't care what skew is?

2014-04-18, 05:01	#428
schickel "Frank <^>" Dec 2004 CDP Janesville 2122₁₀ Posts	I've got a c154 from aliquot sequence 611156:i7547 that needs a poly: Code: 1233834109316954251065406210584382514482486785123839242711421920174697279622119210044011032460138316615713715099127735270405764948375711542820719611655437 Something nice would be appreciated.