20220107, 13:39  #1 
Dec 2021
17 Posts 
SNFS Performance
Does the performance of SNFS vary wildly? I saw a C155 number (a factor of a larger C205 number) factor with SNFS in a little over 2 hours. Now I have a C160 running (a factor of a larger C213 number) that is estimated to run like 35 hours. The stated scaled difficulty is definitely different (167 for the former vs 218 for the latter). I am just surprised that there can be such a longer runtime for just 5 additional digits. Is this an effect of polynomial selection? Is it possible YAFU (version 2.07) made a poor choice for the latter number, or is this par for the course with SNFS?
Thanks!  Kevin 
20220107, 13:57  #2  
"Ben"
Feb 2007
3,617 Posts 
Quote:
[edit] If you like, post the target number and what yafu picked and we can help figure out if it was the best choice. Last fiddled with by bsquared on 20220107 at 13:59 

20220107, 14:18  #3 
Dec 2021
17 Posts 
I am running the factor command on the C214:
Code:
9204214625221874710952946935076263878608726889174004840754589809679987461484965033357036848408384671559545992781188531318866340573729054722277805831939611797303471658749775441007571889786142040525120939985881393299 Code:
01/07/22 02:23:41, nfs: commencing nfs on c160: 1094978880991933841557716588685966958370702537417059147514661217327507272995782570163478397553503222964719677999983911694855297094453016882804532233693251575823 01/07/22 02:23:41, nfs: input divides 43^131  42^131 01/07/22 02:23:41, nfs: using supplied cofactor: 1094978880991933841557716588685966958370702537417059147514661217327507272995782570163478397553503222964719677999983911694855297094453016882804532233693251575823 01/07/22 02:23:41, nfs: commencing snfs on c160: 1094978880991933841557716588685966958370702537417059147514661217327507272995782570163478397553503222964719677999983911694855297094453016882804532233693251575823 01/07/22 02:23:41, gen: best 3 polynomials: n: 1094978880991933841557716588685966958370702537417059147514661217327507272995782570163478397553503222964719677999983911694855297094453016882804532233693251575823 # 43^13142^131, difficulty: 213.98, anorm: 8.04e+28, rnorm: 7.89e+48 # scaled difficulty: 217.98, suggest sieving rational side # size = 6.194e15, alpha = 0.995, combined = 3.414e12, rroots = 1 type: snfs size: 213 skew: 0.9953 c5: 43 c0: 42 Y1: 1601332619247764283850260201342556799238144 Y0: 2952431600795587633717359131697109546569049 n: 1094978880991933841557716588685966958370702537417059147514661217327507272995782570163478397553503222964719677999983911694855297094453016882804532233693251575823 # 43^13142^131, difficulty: 218.86, anorm: 3.54e+35, rnorm: 2.01e+42 # scaled difficulty: 220.21, suggest sieving rational side # size = 6.444e11, alpha = 0.798, combined = 2.431e12, rroots = 2 type: snfs size: 218 skew: 1.0039 c6: 42 c0: 43 Y1: 514617308132852400700537649353457664 Y0: 863586854220408743801513785592407849 n: 1094978880991933841557716588685966958370702537417059147514661217327507272995782570163478397553503222964719677999983911694855297094453016882804532233693251575823 # 43^13142^131, difficulty: 233.50, anorm: 3.01e+33, rnorm: 3.35e+50 # scaled difficulty: 236.91, suggest sieving rational side # size = 8.786e17, alpha = 1.236, combined = 2.748e13, rroots = 1 type: snfs size: 233 skew: 1.0190 c5: 3111696 c0: 3418801 Y1: 67255970008406099921710928456387385568002048 Y0: 126954558834210268249846442662975710502469107 01/07/22 02:23:46, test: fb generation took 3.9993 seconds 01/07/22 02:23:46, test: commencing test sieving of polynomial 0 on the rational side over range 2780000027801000 skew: 1.1247 c5: 43 c0: 42 Y1: 1601332619247764283850260201342556799238144 Y0: 2952431600795587633717359131697109546569049 rlim: 27800000 alim: 27800000 mfbr: 58 mfba: 58 lpbr: 29 lpba: 29 rlambda: 2.60 alambda: 2.60 01/07/22 02:23:46, test: estimated total sieving time = 11574 days 1h 46m 39s (with 40 threads) 01/07/22 02:23:52, test: fb generation took 6.5770 seconds 01/07/22 02:23:52, test: commencing test sieving of polynomial 1 on the rational side over range 2920000029201000 skew: 1.0742 c6: 42 c0: 43 Y1: 514617308132852400700537649353457664 Y0: 863586854220408743801513785592407849 rlim: 29200000 alim: 29200000 mfbr: 58 mfba: 58 lpbr: 29 lpba: 29 rlambda: 2.60 alambda: 2.60 01/07/22 02:23:53, test: estimated total sieving time = 11574 days 1h 46m 39s (with 40 threads) 01/07/22 02:23:59, test: fb generation took 6.2644 seconds 01/07/22 02:23:59, test: commencing test sieving of polynomial 2 on the rational side over range 4360000043601000 skew: 1.1311 c5: 3111696 c0: 3418801 Y1: 67255970008406099921710928456387385568002048 Y0: 126954558834210268249846442662975710502469107 rlim: 43600000 alim: 43600000 mfbr: 60 mfba: 60 lpbr: 30 lpba: 30 rlambda: 2.60 alambda: 2.60 01/07/22 02:23:59, test: estimated total sieving time = 11574 days 1h 46m 39s (with 40 threads) 01/07/22 02:23:59, gen: selected polynomial: n: 1094978880991933841557716588685966958370702537417059147514661217327507272995782570163478397553503222964719677999983911694855297094453016882804532233693251575823 # 43^13142^131, difficulty: 213.98, anorm: 8.04e+28, rnorm: 7.89e+48 # scaled difficulty: 217.98, suggest sieving rational side # size = 6.194e15, alpha = 0.995, combined = 3.414e12, rroots = 1 type: snfs size: 213 skew: 1.1247 c5: 43 c0: 42 Y1: 1601332619247764283850260201342556799238144 Y0: 2952431600795587633717359131697109546569049 01/07/22 02:23:59, nfs: commencing lattice sieving with 40 threads 
20220107, 14:56  #4 
"Ben"
Feb 2007
3617_{10} Posts 
The estimated total sieving time looks like it isn't being printed correctly, but other than that it all looks fine and the best poly was chosen. Note that this number isn't 5 digits larger, it is 10 digits larger than your previous one. Unless there are algebraic factors that can be pulled out, SNFS difficulty is proportional to the full input size, not the cofactor size. That's why it is sometimes better to run GNFS on SNFSable numbers.

20220107, 15:13  #5 
Dec 2021
17 Posts 
Thanks for the explanation. I did not realize the SNFS time was based on the original number and not the smaller factor. It's just so much easier when ECM finds all the factors :)
And, yes, I have noticed in the runs that I have done that the estimated total sieving times consistently do not print correctly for some reason. I just wait for the first sieving round to complete to get an estimate of the time. Last fiddled with by nivek000 on 20220107 at 15:22 
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