[QUOTE=R. Gerbicz;207866]
[code]
48 c256
[/code]
[/QUOTE]

p-1: B1=1e9, B2=1e14, no factor.

Very exciting stuff

Will try to run a large number of curves at 43e6 while I'm on vacation (set off 16 jobs at 1e8 but this made the machine swap beyond the point of usability).

[QUOTE=fivemack;208070]Will try to run a large number of curves at 43e6 while I'm on vacation (set off 16 jobs at 1e8 but this made the machine swap beyond the point of usability).[/QUOTE]

Ask Bruce to take a whack at it.

2000 curves completed @ 3e6.

currently running 43e6

[QUOTE=R.D. Silverman;208071]Ask Bruce to take a whack at it.[/QUOTE]

I've spent the past 10-days-or-so "whack"ing on the current NFS@Home
reservation, with another 10-days-or-so left to go. I recently completed
p55-tests on the Cunninghams from c190-c209.99 (either 7t50 or 6t50,
depending on the difficulty); and am currently working toward t55's on
c210-c233, in between NFS@Home and Batalov+Dodson numbers. I'm also
making a lower priority run through c234-c289.487 plus the 2- and 2+
numbers (not including 2LMs) the rest of the way up, through C355; working
toward 3t50. Likely enough to keep our cpus busy the rest of 2010.

Almost all curves are with p60-optimal limits (B1=26e7=260e6, gmp-ecm
default B2); except for a few xp's with just 500Mb available for condor jobs,
running p55-limits.

Uhm. This is a c256 gnfs number, currently in testing for p50's? I'm having
some trouble seeing this as the first gnfs number above 768-bits
(232-digits). -Bruce

By definition, the single smallest factor is enough to continue the sequence.

But from the current status, it is going to take a leap of faith, if (e.g.) a p54 factor is found. This iteration may need a lot of subsequent ECM to minimize the probability that [I]that[/I] would be the smallest factor (and still not remove the doubt entirely). Tough!

(The same was or still is the case on the -1 analog of EM sequence, right? I don't see the p51 there, it was mentioned earlier in this thread. Sloane's A005265)

Remember that if we do find a factor with ECM and the cofactor is composite, we will still have to factor the cofactor to check that the ECM factor is indeed the smallest prime factor.

[QUOTE=Batalov;208181]By definition, the single smallest factor is enough to continue the sequence.

But from the current status, it is going to take a leap of faith, if (e.g.) a p54 factor is found. This iteration may need a lot of subsequent ECM to minimize the probability that [I]that[/I] would be the smallest factor (and still not remove the doubt entirely). Tough! ...[/QUOTE]

A p54 would go a long way towards making a composite cofactor nearer
to our current gnfs range; or perhaps better yet, leave a large prime
cofactor. I'd consider running a second t55, once the first one fails.
So somewhere past the effort of 4 t50's (with t55 = c. 5.7*t50?). Finding
a p53/p54 isn't among my objectives, unless it's from a Cunningham.
Once p53/p54 is unlikely, EM48 is as good as any other candidate for
finding a nice p60+ factor (which would get recorded, for a while at least
.... uhm, maybe p62+, Brent's list of p60+ is already past 10). -Bruce

10,000 curves done at 11M, so the smallest factor should be at least 45 digits. Just for fun, I'm running some curves at 260M... but even if there was a factor in the appropriate range, there's only about a [TEX]1-(1-1/52000)^{1000}\approx[/TEX]2% chance I'd find it with as few curves as I'm running.

p+/-1
 

Has any p+/-1 been done besides my p-1 with B1=1e9, B2=1e14?

For p-1 I have extended B1 to 1e10 (no factor with B2=1e13) and I'm currently extending it to B1=2e10 or even further (maybe 5e10).

As soon as my laptop will get free (currently running a GNFS-job, will be finished around Wednesday) I will do B2=1e15 for whatever B1 I will have reached by then. (B2=1e18 will be left to someone with a machine with 8 cores and 32+ GB RAM)