20210531, 21:43  #12 
"Curtis"
Feb 2005
Riverside, CA
11612_{8} Posts 
Does CADO compute skew automagically, or does Bur need to supply it?
If you need it, I suggest you use myfactors.mooo.com, "calculators" link at the top of the page. Enter your poly, and the site's script will spit out the skew that yields the highest score for that poly. That's also how I got score numbers for my previous post. 
20210601, 02:15  #13  
Apr 2020
2·251 Posts 
Quote:
The skew controls the shape of the (a,b)rectangle in lattice sieving, so that skew is a typical value of a/b. For the polynomials we're considering, where the algebraic norm is c5*a^5 + c0*b^5, choosing skew = (c0/c5)^(1/5) makes the two terms comparable and the norm as small as possible. If some of the other coefficients are nonzero, the calculations aren't as simple. 

20210601, 08:09  #14 
Aug 2020
79*6581e4;3*2539e3
13×31 Posts 
Ok, so for number in my example I'd use skew = (4/1281979)^1/5 = 0.07922017839 (how many digits to use?), all else in the .poly file would be the selfconstructed values I posted earlier? I just omit c4 and so on because it's zero or do I need to specify them?
Then I edit the params.c120 file. "the algebraic and rational side parameters swapped (lim0 and lim1 etc)"  the 0 denotes algebraic and the 1 rational parameters? So if it says tasks.sieve.ncurves0 = 17 and tasks.sieve.ncurves1 = 20, I change that to tasks.sieve.ncurves0 = 20 and tasks.sieve.ncurves1 = 17? And the calculation of rels_wanted, you wrote lpba and lpbr, for algebraic and rational, I guess. In the params it's 0 and 1, which is which? Last fiddled with by bur on 20210601 at 08:12 
20210601, 09:28  #15 
Aug 2020
79*6581e4;3*2539e3
110010011_{2} Posts 
And yet one more question, which number do I feed to CADO? The numbers usually have a lot of known small factors, do I divide by them? It won't have the x^5 form anymore though, but it seems in EdH's guide he just uses the unknown cofactor for CADO, also it was mentioned in this thread that divisors of these numbers also can be factored with SNFS.
Last fiddled with by bur on 20210601 at 10:20 
20210601, 10:28  #16  
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
2·3^{2}·7·47 Posts 
Quote:


20210601, 10:38  #17  
Apr 2020
2·251 Posts 
Quote:
Quote:
Good luck! 

20210601, 11:01  #18 
Aug 2020
79*6581e4;3*2539e3
13×31 Posts 
I calculated rels_wanted and got 44.8e6 whereas Curtis' params.c120 file has rels_wanted 31.5e6. So I'll use the lower original value?
The skew from mooo.com gives 0.10906 instead 0.07 with the formula, should I go with the website's calculator? I have the following files now, does it look ok? n = (2^523*1281979+1)/740978807478081 c120.poly Code:
n: 47507574309657478521751799345139218804140387137236190452560952011171490037478086338262231226836394024672540061211068254774576452771166352879924377793 skew: 0.10906 c5: 1281979 c0: 4 Y1: 1 Y0: 40564819207303340847894502572032 Code:
tasks.lim0 = 4500000 tasks.lim1 = 2500000 tasks.lpb0 = 29 tasks.lpb1 = 29 tasks.sieve.mfb0 = 54 tasks.sieve.mfb1 = 54 tasks.sieve.lambda0 = 1.81 tasks.sieve.lambda1 = 1.81 tasks.sieve.ncurves0 = 20 tasks.sieve.ncurves1 = 17 tasks.I = 13 tasks.qmin = 60000 tasks.sieve.qrange = 2000 tasks.sieve.rels_wanted = 31500000 tasks.sieve.sqside = 0 Last fiddled with by bur on 20210601 at 11:44 
20210601, 13:17  #19  
Apr 2020
2×251 Posts 
Quote:
Go with what the website says  the formula is really only a guideline whereas the Murphy E score gives a better idea of how a polynomial will actually perform. Everything else looks good! 

20210601, 15:10  #20 
"Ben"
Feb 2007
6772_{8} Posts 
At the risk of increasing confusion, I ran this through yafu's poly select and it slightly prefers the other degree 5:
Code:
./yafu "snfs(2^523*1281979+1,475075743096574785217517993451392188041403871372361904525609520111714037478086338262231226836394024672540061211068254774576452771166352879924377793)" v ... gen: ======================================================== gen: selected polynomial: gen: ======================================================== n: 47507574309657478521751799345139218804140387137236190452560952011171490037478086338262231226836394024672540061211068254774576452771166352879924377793 # 1281979*2^523+1, difficulty: 163.55, anorm: 1.34e+39, rnorm: 1.18e+39 # scaled difficulty: 163.56, suggest sieving algebraic side # size = 4.795e12, alpha = 0.784, combined = 2.207e10, rroots = 1 type: snfs size: 163 skew: 0.0396 c5: 10255832 c0: 1 Y1: 1 Y0: 20282409603651670423947251286016 m: 20282409603651670423947251286016 
20210601, 15:55  #21 
Aug 2020
79*6581e4;3*2539e3
193_{16} Posts 
The factorization completed successfully!
Code:
Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire factorization: 68366.4/6925.44 14074467019842618596383447874291304186513827826802503924128815906893967308840587655218071 3375443932809663909086793903695124177071577045470998628634983 It went back to sieving a couple of times due to me setting the rels_wanted too low as charybdis mentioned. Very nice, I'll do this for another number and then compile an howto. Thanks again for the great help everybody! bsquared, are you using an older yafu version to circumvent the bug that was mentioned? Last fiddled with by bur on 20210601 at 15:57 
20210601, 16:06  #22 
"Ben"
Feb 2007
6772_{8} Posts 
Cool, good job working through this.
No, I fixed the bug. The latest git version should work (if you use precompiled windows binary, you will have to wait a bit until I can rebuild that). 
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