Polynomial Request Thread - Page 29

YuL · 2013-10-27, 10:47

Didn't know where to ask my questions, strictly speaking I'm not requesting a polynomial, but I thought this is the place. I am working on the C145 cofactor of (10^217-6*10^108-1)/3, just wanted to know whether the following polynomial is OK

Code:

Wed Oct 23 22:40:07 2013  Msieve v. 1.51 (SVN 845)
Wed Oct 23 22:40:07 2013  random seeds: d7d00c10 b8601b40
Wed Oct 23 22:40:07 2013  factoring 1038857565233722974620749986771872310155473637361038529312939753315767829250305261136208190969374664663374293668205652462401937401450324574458129 (145 digits)
Wed Oct 23 22:40:10 2013  searching for 15-digit factors
Wed Oct 23 22:40:13 2013  commencing number field sieve (145-digit input)
Wed Oct 23 22:40:13 2013  commencing number field sieve polynomial selection
Wed Oct 23 22:40:13 2013  polynomial degree: 5
Wed Oct 23 22:40:13 2013  max stage 1 norm: 1.08e+022
Wed Oct 23 22:40:13 2013  max stage 2 norm: 1.77e+020
Wed Oct 23 22:40:13 2013  min E-value: 9.48e-012
Wed Oct 23 22:40:13 2013  poly select deadline: 331657
Wed Oct 23 22:40:13 2013  time limit set to 92.13 CPU-hours
Wed Oct 23 22:40:13 2013  expecting poly E from 1.17e-011 to > 1.35e-011
Wed Oct 23 22:40:13 2013  searching leading coefficients from 1 to 3000000
Wed Oct 23 22:40:14 2013  using GPU 0 (GeForce GTX 660)

... 

Sun Oct 27 10:52:24 2013  R0: -12360953197594707983004655009
Sun Oct 27 10:52:24 2013  R1: 4088891911315799
Sun Oct 27 10:52:24 2013  A0: -83774480776385476950466422782623344
Sun Oct 27 10:52:24 2013  A1: 95553101899647010050333365472
Sun Oct 27 10:52:24 2013  A2: 679770526324878378799096
Sun Oct 27 10:52:24 2013  A3: -175851899955834973
Sun Oct 27 10:52:24 2013  A4: -157977719430
Sun Oct 27 10:52:24 2013  A5: 3600
Sun Oct 27 10:52:24 2013  skew 2100532.04, size 5.911e-014, alpha -6.985, combined = 1.226e-011 rroots = 5

I ran phase 1 for about 1 GPU day (leading coeff was around 9000 when I stopped the search), then phase 2 for 2 CPU days, I then selected the 100 best hits from ms file as input for the -npr phase.
Is it the right way to do it for a composite of that size or should I have let the 3 phases run together (-np flag)?
How comes the more lines I input to -npr phase the slower each line gets processed?

firejuggler · 2013-10-27, 11:12

What I (we?) do is to combine -np1 and -nps phase, with a strict stage2 norm bond by a 10 to 20 factor. in your example, this will turn out in

Code:

msieve151_gpu -np1 -nps "stage2_norm=2e19"

This will reduce significantly the number of retained polynomial. A smaller norm has better potential. You may have fewer hit than normal, but they are better.
As for the npr stage, leave it as it is ie " msieve151_gpu -npr -v" (the v is for verbose, it give a bit of detail at the start of the stage, nothing much)
Instead of 20 000 hit passing the -npr stage, you will have only a few hundred.
As for your poly quality , the excepted score is 1.17e-011 to > 1.35e-011, (look at the start of your log file). Your score is the combined one, 1.226e-011.So it fall in the excepted range, so it is a good one.

fivemack · 2013-10-27, 11:13

That looks a decent polynomial for a C145; I've successfully sieved at that size with both slightly larger and slightly smaller E values. I don't see E-value having much of a correlation with sieving time at that sort of size - the effect is completely swamped by my desire to sieve a round number of millions of Q.

YuL · 2013-10-27, 11:54

OK, thanks for your replies.

And what about the leading coeff, for a number of that size, is it OK to let it explore the 1-10000 range or should I directly jump to greater values ?
I have 12 cores (with 2 hyperthreads each) and two GeForce GTX660, for what composite sizes is it worth splitting the coeff range and running two different poly searches?

lorgix · 2013-10-27, 12:28

I think you should start at a higher leading coefficient.

Splitting the range should be worthwhile even for small composites. The different runs would cover different polys.

firejuggler · 2013-10-27, 12:37

59^136+1
expecting poly E from 2.25e-012 to > 2.59e-012

Code:

R0: -887837726938190453909365324487
R1: 51405401215361483
A0: -1938938237106607295985277217218758528
A1: 751321357635665072528066289728
A2: 23530875884501281524204042
A3: -5587734391468382997
A4: -54467751848530
A5: 1224300
skew 769512.78, size 3.097e-015, alpha -7.006, combined = 2.163e-012 rroots = 5

Just a bit below it, but skew below 1M.

wombatman · 2013-10-27, 23:03

For 26^166+1:

Code:

expecting poly E from 2.20e-012 to > 2.53e-012
polynomial selection complete
R0: -1552555711706534179107974467322
R1: 18247246900717403
A0: -3450563282932049789973012144891832245
A1: 2967698980468546492153761480204
A2: 9091125809522678273087165
A3: -2983765064804576792
A4: 662896455728
A5: 104940
skew 2791926.48, size 3.288e-015, alpha -6.137, combined = 2.297e-012 rroots = 3

sashamkrt · 2013-10-28, 07:41

Code:

# norm 3.849185e-015 alpha -7.638710 e 2.217e-012 rroots 5
skew: 6977513.01
c0: 200014128932032035109930215162727570400
c1: 435935776855985900818236864190620
c2: -211762065047515199447925394
c3: -19952125135703740200
c4: 4017733344281
c5: 155100
Y0: -1342111053484085118596918736213
Y1: 76946354609549767

# norm 3.639234e-015 alpha -6.480925 e 2.172e-012 rroots 3
skew: 3428164.12
c0: 10973012853022727370877919321059781823
c1: -35214265595100672036261670394795
c2: -21238282564922885813939791
c3: 4664728558704624343
c4: 613767785100
c5: 131760
Y0: -1386609569505784167410822006690
Y1: 107637883974575333

firejuggler · 2013-10-28, 17:14

59^136+1

Code:

R0: -1557041023585869614990158630796
R1: 223730118804831109
A0: -5611452494496160121982308088837437315
A1: -8945246453775039439725422898084
A2: 8666689497882725965482357
A3: 788514654796889300
A4: -2281059720330
A5: 73800
skew 2811808.01, size 3.341e-015, alpha -6.334, combined = 2.311e-012 rroots = 3

sashamkrt · 2013-10-28, 19:57

Code:

# norm 3.867886e-015 alpha -7.650330 e 2.235e-012 rroots 3
skew: 3670054.48
c0: -13094197530954234530970080297535934085
c1: -106976176363993434015932320815706
c2: 60118151055104388778256559
c3: 32188186727827492426
c4: -2582652990730
c5: 168504
Y0: -1412256270614572171801468030782
Y1: 151670378897342719

# norm 3.726247e-015 alpha -8.511336 e 2.161e-012 rroots 3
skew: 8619284.10
c0: 2372966860980133119182477719908041669625
c1: -1100777831110322713315181722655390
c2: -208060936250711412311330748
c3: 11329908735396306390
c4: 7882784245859
c5: 180264
Y0: -1393328013547498761697815086126
Y1: 88800791108501449

sashamkrt · 2013-10-30, 12:18

Code:

# norm 4.292249e-015 alpha -7.532676 e 2.394e-012 rroots 5
skew: 5388935.60
c0: -34427316821248774173822300189444021615
c1: 261830522806233745904527729155009
c2: 13612409189360629251269684
c3: -29762818284115926464
c4: -516284889774
c5: 245700
Y0: -1224136698442901405932040941756
Y1: 49749519101050373

# norm 4.231168e-015 alpha -7.153548 e 2.357e-012 rroots 5
skew: 3601103.03
c0: -17830146319914240195682921247097658400
c1: 61824037258178751183982162646150
c2: -2889004352259852170329663
c3: -30059397937315986128
c4: -290475533274
c5: 245700
Y0: -1224136689298492049487072930999
Y1: 49749519101050373

# norm 4.172692e-015 alpha -7.451756 e 2.337e-012 rroots 5
skew: 5805930.14
c0: -299050938625636504723620215488265726175
c1: 372910114676448997875182230061340
c2: -33204557318633960312108875
c3: -30172884280488668912
c4: 121107593226
c5: 245700
Y0: -1224136672630960414581267515182
Y1: 49749519101050373

# norm 4.094435e-015 alpha -7.245866 e 2.321e-012 rroots 5
skew: 4492003.44
c0: 5204924716607310342525355310024593296
c1: 133373914868914117399952783311638
c2: 13354970109400287702820997
c3: -29768751659644927232
c4: -512743124274
c5: 245700
Y0: -1224136698299473542363712716397
Y1: 49749519101050373

2013-10-27, 11:12	#310
firejuggler Apr 2010 Over the rainbow 2³·5²·13 Posts	What I (we?) do is to combine -np1 and -nps phase, with a strict stage2 norm bond by a 10 to 20 factor. in your example, this will turn out in Code: msieve151_gpu -np1 -nps "stage2_norm=2e19" This will reduce significantly the number of retained polynomial. A smaller norm has better potential. You may have fewer hit than normal, but they are better. As for the npr stage, leave it as it is ie " msieve151_gpu -npr -v" (the v is for verbose, it give a bit of detail at the start of the stage, nothing much) Instead of 20 000 hit passing the -npr stage, you will have only a few hundred. As for your poly quality , the excepted score is 1.17e-011 to > 1.35e-011, (look at the start of your log file). Your score is the combined one, 1.226e-011.So it fall in the excepted range, so it is a good one. Last fiddled with by firejuggler on 2013-10-27 at 11:18

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

2013-10-27, 11:13	#311
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 1913₁₆ Posts	That looks a decent polynomial for a C145; I've successfully sieved at that size with both slightly larger and slightly smaller E values. I don't see E-value having much of a correlation with sieving time at that sort of size - the effect is completely swamped by my desire to sieve a round number of millions of Q.

2013-10-27, 11:54	#312
YuL Feb 2012 Paris, France 7·23 Posts	OK, thanks for your replies. And what about the leading coeff, for a number of that size, is it OK to let it explore the 1-10000 range or should I directly jump to greater values ? I have 12 cores (with 2 hyperthreads each) and two GeForce GTX660, for what composite sizes is it worth splitting the coeff range and running two different poly searches?

2013-10-27, 12:28	#313
lorgix Sep 2010 Scandinavia 3·5·41 Posts	I think you should start at a higher leading coefficient. Splitting the range should be worthwhile even for small composites. The different runs would cover different polys.