20160402, 18:56  #34 
(loop (#_fork))
Feb 2006
Cambridge, England
14466_{8} Posts 
10400 stage1 curves run on C190_149_91, 84% of them taken to stage 2, found a P55 but it turns out that it had already been submitted

20160403, 23:56  #35 
Jan 2005
Minsk, Belarus
2^{4}·5^{2} Posts 
C177_148_94 was suggested as GNFS, but its SNFS difficulty is not too high:
Difficulty 248: 4879681*(47^{24})^{6} + 29986576*(2^{6}*37^{15})^{6} = 58008018918812545143463727211454278525294078099759247887923759309261425 * C177 Difficulty 254: 1369*(47^{25})^{6} + 35344*(2^{6}*37^{16})^{6} = 175423268180778312831796670198430324228190852757122036482075886926082969832425 * C177 
20160407, 11:00  #36 
Jun 2012
2^{3}×13×37 Posts 
C177_148_94 is on the list of possible GNFS candidates because the best SNFS poly I could find using Yafu would take an estimated 247M coreseconds to sieve versus ~85M coreseconds using GNFS. If my estimates are off then perhaps GNFS is not the best path forward.
Can anybody provide a quick and dirty GNFS poly we can test with? Using an ECM rule of thumb of 0.31*GNFS gives ~t55, which this number has already survived. The 5000 curves @B1=26e7 listed in this thread may be unnecessary though certainly prudent (for peace of mind if nothing else). Best SNFS poly I found follows: Code:
n: 509324937687618809222445320276337252810119679947032399409215533120195327608346172383916906170272967333837017570484086026229163006167878198943819573285050609840596958297287281873 # 148^94+94^148, difficulty: 248.37, anorm: 3.92e+033, rnorm: 1.41e+055 # scaled difficulty: 251.97, suggest sieving rational side # size = 1.438e017, alpha = 0.000, combined = 7.015e014, rroots = 1 type: snfs size: 248 skew: 20.7443 c5: 1 c0: 3841451 Y1: 3096263264537031876137686856267255616967297523567 Y0: 159982589693655584703558945119488 rlim: 57000000 alim: 57000000 lpbr: 31 lpba: 31 mfbr: 62 mfba: 62 rlambda: 2.7 alambda: 2.7 
20160407, 20:40  #37 
Sep 2009
3D3_{16} Posts 
The sextic SNFS polynomial produced by snfspoly has hideous coefficients, yeah... but a quintic of that SNFS difficulty is no piece of cake either.

20160407, 20:54  #38  
"Ben"
Feb 2007
2^{2}×3×311 Posts 
Quote:


20160407, 21:56  #39  
Jun 2012
111100001000_{2} Posts 
Quote:
I have found a lot of scatter when plotting sieving times vs SNFS difficulty  hardly surprising  and this particular case is especially hideous as Lionel notes. It's just a case where the ugly SNFS poly can likely be beat by a decent GNFS poly. That said, of course we can use SNFS to factor this number. My list is hardly authoritative  it's just a set of candidates that are likely best solved via GNFS. 

20160407, 22:02  #40  
"Ben"
Feb 2007
111010010100_{2} Posts 
Quote:


20160407, 22:24  #41 
"Curtis"
Feb 2005
Riverside, CA
2·2,819 Posts 
I'll let a GPU run a few hours to get an "in the vicinity" poly for your comparison task this evening. We can estimate the improvement for a full polysearch using the estimatedgood poly score that msieve produces in case the test is inconclusive.

20160407, 22:27  #42 
Jun 2012
2^{3}·13·37 Posts 
Agreed. Before embarking on a big factoring job, one should definitely perform extensive test sieving. 1% difference in performance is negligible when it's a 1000 hour job, not so much when it's 200000 hours.
So back to an earlier question  does anyone have a quick and dirty GNFS poly so we can decide a path forward? ETA: thanks VBCurtis! Last fiddled with by swellman on 20160407 at 22:28 
20160408, 03:03  #43 
"Curtis"
Feb 2005
Riverside, CA
2×2,819 Posts 
2 GPUhr produced this:
Code:
N 509324937687618809222445320276337252810119679947032399409215533120195327608346172383916906170272967333837017570484086026229163006167878198943819573285050609840596958297287281873 SKEW 44744195.26 R0 15372279160491459270723477022022637 R1 42075573946251179 A0 28036751366398061170413492158368626575647616 A1 2446095126548667802453043510317136360 A2 132445682988042341783594025606 A3 4958312126359633450937 A4 102677914180448 A5 593340 skew 44744195.26, size 2.117e17, alpha 7.554, combined = 1.104e13 rroots = 3 
20160408, 16:33  #44 
Jun 2012
2^{3}·13·37 Posts 
I ran some test sieving using a Win64 box with an i53340M processor. Results follow, but GNFS is the clear winner.
poly siever lpbr/a a/r ETA (wks) yield a/rlim (M) spec_Q0 (M) spec_Q range gnfs 15e 31 a 55 1.70 120 40 4000 gnfs 14e 31 a 61 0.78 120 40 4000 gnfs 15e 31 a 56 1.58 150 50 4000 gnfs 14e 31 a 65 0.74 150 50 4000 snfs 15e 31 r 108 1.32 57 28.5 4000 snfs 14e 31 r 83 0.58 57 28.5 4000 snfs 14e 31 r 82 0.58 57 28.5 10000 gnfs 15e 31 a 49 1.68 150 50 10000 Do we need to run more ECM (5000 curves @B1=26e7) prior to starting GNFS? 
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