Now what (VII)
 

2^929-1 is pretty close to completion.

So I should at least be doing the set-up for the next job.

But I'm not sure what the next job is. Hence this thread.

.[QUOTE=Raman;305930]
2,2042 L/M SNFS 308
[COLOR=Red][B]13,269- [COLOR=Black]SNFS 300[/COLOR][/B][/COLOR]
2,991- SNFS 299
2,947- SNFS 286
[STRIKE]2,929- SNFS 280[/STRIKE]
L1279 SNFS 268
L1277 SNFS 267
[/QUOTE].

My most wanted number is W(951), or 951*2^951-1, with no known factors and hence the composite is C290 as is the SNFS difficulty.

It has been run to t55 or so with ECM. Specifically, the ecmnet server records
[code]W_951_C290 N 18101159423518357666828255177479109538365804182759476871194099689081082431482170358290624858698812024459501904953261022348573575276969028199796222497643229300730947446598839553529533129630939491374047682419407574822021491459083058737118733981076145112889022659672203022021130838051387342847
W_951_C290 P 1345898799,0,0,active,nolocalcontrol,recurse
W_951_C290 B 2000 522:0 3:0 1:0
W_951_C290 B 50000 300:0 3:0 1:0
W_951_C290 B 250000 610:0 3:0 1:0
W_951_C290 B 1000000 900:0 3:0 1:0
W_951_C290 B 3000000 2437:0 3:0 1:0
W_951_C290 B 11000000 4238:0 3:0 1:0
W_951_C290 B 43000000 7660:0 3:0 1:0
W_951_C290 B 110000000 17924:0 14:0 1:0
W_951_C290 B 260000000 0:0 3:0 1:0
[/code] for the work done to date.

As 951 == 3 mod 6, there are two obvious sextics, one which factors a C291 with a low skew polynomial and the other with higher skew on the C290. It's not at all obvious to me which is likely to be the better in practice.

Paul

[QUOTE=xilman;321891]As 951 == 3 mod 6, there are two obvious sextics, one which factors a C291 with a low skew polynomial and the other with higher skew on the C290. It's not at all obvious to me which is likely to be the better in practice[/QUOTE]

Have you tried using msieve to score them? It is a pretty good indication as to which is better.

msieve says 4.748e-15 for 951*2^954-8 and 5.128e-15 for 7608*2^948-1 (they obviously have the same alpha, and the first has a slightly smaller size score). There's only a factor two in skew between them, which I'd really not expect to make a large difference; with identical sieving parameters I'm seeing very similar yield (7608* is slightly higher) but have not sieved statistically significantly far.

I suspect it would take about one CPU-week on each polynomial to get statistical significance, which is an amount of effort I'm not really willing to put in - though definitely worth doing, since the full sieving would take around 80 CPU-years and getting that down to 75 would be worth it.

[QUOTE=fivemack;321930]msieve says 4.748e-15 for 951*2^954-8 and 5.128e-15 for 7608*2^948-1 (they obviously have the same alpha, and the first has a slightly smaller size score). There's only a factor two in skew between them, which I'd really not expect to make a large difference; with identical sieving parameters I'm seeing very similar yield (7608* is slightly higher) but have not sieved statistically significantly far.

I suspect it would take about one CPU-week on each polynomial to get statistical significance, which is an amount of effort I'm not really willing to put in - though definitely worth doing, since the full sieving would take around 80 CPU-years and getting that down to 75 would be worth it.[/QUOTE]I can put in the effort easily enough if there's a reasonable chance of the factorization being completed. I could almost do the full sieving myself (28 cores in my study alone) but it's just a bit too much and I'd be unable to perform the LA anyway.

5.128/4.748=1.08

So the second is about 8% better. I'd just take these at their face value and go with that. (BTW, multiplying the skews by about 1.4 gives slightly better scores)

I will be happy to do the linear algebra for W951. It'll be comparable to the largest thing I've done so far, and I'd expect a runtime between six and twelve weeks.

I am also willing to throw in two dozen cores for a season to help with the sieving.

The 80 CPU-year figure came from grotesquely wrong parameters; I've got the estimate down to 40 years with only minor changes (this is a 3RLP 2ALP job), the question is whether this is an LP32 or an LP33 job. I'm now somewhat confident that 7608* is the way to go.

After a little more tedious investigation (sixteen runs):

7608*
33-bit large primes
3A2R
Sieve with 16e on rational side

Around 50 CPU-years

How much more ECM work is necessary for W951? Any? I'm forgetful of the rules of thumb for these things, but t55 seems inadequate for a SNFS 290....

gmp-ecm reckons it would take six CPU-years for a t60 (using b1=260e6). The probability of the t60 being useful is about 8% (the probability of a factor between 55 and 60 digits is about 1-55/60); the SNFS takes 50 CPU-years; so a whole t60 is too much.

gmp-ecm reckons that a t55 would be about one CPU-year but probably less chance of being useful. If there were the chance of doing another t55 before starting SNFS then it might be reasonable, but more than that would I think be excessive.