
View Poll Results: Which number next?  
2^9471 : first hole  13  68.42%  
Fib(1373) : not a Mersenne number  4  21.05%  
2^9911 : interestingly large  2  10.53%  
Voters: 19. You may not vote on this poll 

Thread Tools 
20121217, 11:21  #1 
(loop (#_fork))
Feb 2006
Cambridge, England
13×491 Posts 
Now what (VII)
2^9291 is pretty close to completion.
So I should at least be doing the setup for the next job. But I'm not sure what the next job is. Hence this thread. 
20121217, 11:55  #2 
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
3×419 Posts 
..
Last fiddled with by Raman on 20121217 at 12:43 
20121217, 12:13  #3 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2×7^{2}×109 Posts 
My most wanted number is W(951), or 951*2^9511, 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 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 
20121217, 16:51  #4 
Jun 2003
2^{5}·5·31 Posts 
Have you tried using msieve to score them? It is a pretty good indication as to which is better.

20121217, 22:49  #5 
(loop (#_fork))
Feb 2006
Cambridge, England
13·491 Posts 
msieve says 4.748e15 for 951*2^9548 and 5.128e15 for 7608*2^9481 (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 CPUweek 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 CPUyears and getting that down to 75 would be worth it. Last fiddled with by fivemack on 20121218 at 00:12 
20121218, 01:28  #6  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
24672_{8} Posts 
Quote:


20121218, 03:50  #7 
Jun 2003
11540_{8} Posts 
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) 
20121218, 08:16  #8 
(loop (#_fork))
Feb 2006
Cambridge, England
13×491 Posts 
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 CPUyear 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. 
20121219, 19:23  #9 
(loop (#_fork))
Feb 2006
Cambridge, England
14357_{8} Posts 
After a little more tedious investigation (sixteen runs):
7608* 33bit large primes 3A2R Sieve with 16e on rational side Around 50 CPUyears Last fiddled with by fivemack on 20121219 at 19:23 
20121219, 22:34  #10 
"Ben"
Feb 2007
D6C_{16} Posts 
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....

20121220, 00:56  #11 
(loop (#_fork))
Feb 2006
Cambridge, England
13×491 Posts 
gmpecm reckons it would take six CPUyears 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 155/60); the SNFS takes 50 CPUyears; so a whole t60 is too much.
gmpecm reckons that a t55 would be about one CPUyear 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. 