How much ECM has been done on 12^512+1 ?

[fivemack]

I suppose someone here would know if serious ECM work had been done on 12^512+1 already.

t45 (5000@1e7) would take about a week on the whole i7 using the Debian-distributed gmp-ecm (and obviously I should build an optimised svn gmp-ecm against optimised svn mpir before doing this seriously; does mpir have i7-optimised inner loops yet?); t50 (11000@3e7) would take about two months, which is a lot longer than I'd want to spend on an almost-sure failure.

Are there gmp-ecm parameters I can use to tell it to use more memory than default for stage 2, and do they help much?

[R.D. Silverman]

Originally Posted by fivemack

I suppose someone here would know if serious ECM work had been done on 12^512+1 already.

t45 (5000@1e7) would take about a week on the whole i7 using the Debian-distributed gmp-ecm (and obviously I should build an optimised svn gmp-ecm against optimised svn mpir before doing this seriously; does mpir have i7-optimised inner loops yet?); t50 (11000@3e7) would take about two months, which is a lot longer than I'd want to spend on an almost-sure failure.

Are there gmp-ecm parameters I can use to tell it to use more memory than default for stage 2, and do they help much?

Allow me to repeat a philosophy that I have espoused before.

My mother taught me: finish what you start before doing something new.

12^512+1 is well beyond current limits. Let's finish (or come close to
finishing) existing tables before extending them. 12^512+1 is large
enough to have no hope of finishing without a LOT of luck, and it
would (even if we got lucky) just represent an isolated factorization.

It seems to me to be a waste of computer time that would be better
spent doing numbers that we know we can do.

[MatWur-S530113]

Hello,

a cunningham number with one of the original bases (12 here) already should have a lot of work done on it. I think t50 is the lowest I would try. But I don't have serious information about the work done on it.
With the -maxmem option you can set the maximum of space gmp-ecm will use, the default value depends on B2, simply enlarge it to use more RAM . And surely a larger B2 is better, but 'much' is relative... I always use the default B2 gmp-ecm is calculating.

[Batalov]

I am not sure, but for GFNs, it seems to me, the special sieving may have reached farther than where ECM (which pokes randomly) can reach be chance. The factors must be of the (k*2¹⁰+1) form, while ECM goes all over the place. ask geoff (R.), maybe?

[bdodson]

Originally Posted by MatWur-S530113

Hello,

a cunningham number with one of the original bases (12 here) already should have a lot of work done on it. ...

This is beyond the current Cunningham limit,

 Table 12+             Factorizations of 12^n+1, n<=300
                               L,M for n=6k-3<=597

At one snapshot, each of the 16 tables were limited by a round n
so that b^n c.= 2^1200. Then for some b's most of the numbers
on that table were complete, and there was an extension. Many of the
largest Cunninghams are from these extensions, as for example,
base-10 (10- and 10+) were extended to n <=400. Other frequent
bases among the largest Cunningham's are base-7's, which also goes
to n <= 400. L/M's have a similar but different bound.

I've mentioned before, the initial ECMNET Cunningham.in was named
c120-c355, as c355 was the largest c. 1998 (or maybe 2000, I'm
not sure). Numbers are listed by number of digits on an early appendix C,
but the ordering was fixed, and kept in that order even as numbers
were completed, or partial factors found. Scrolling down to c355, numbers
from an extension are added --- it goes c355 then c142 and ... Looks
like the base-12 limit 300 was one of those table extensions ... base-3,
base-6, base-5. Not base-2, and I don't see any base 11's either(?).

If one follows posts over on the Cunningham Tables threads, some of
us are interested in triggering another such extension; as for example
the 3-table is down to just five numbers (barely enough to fill the
"first five holes" page).

Anyway, and in particular, generic base-12's above 12^300 will have
hardly any substantial ecm. 12^512+1 being a exception; but I'm
with Bob here, and only run ecm on the current table (c. 600 numbers,
as of the July 2009 update). -Bruce

[fivemack]

Originally Posted by R.D. Silverman

Allow me to repeat a philosophy that I have espoused before.

My mother taught me: finish what you start before doing something new.

I have just finished 12^(2^8)+1 and thought it might be worth poking at 12^(2^9)+1; this would be a first gap in a table of generalised Fermat numbers rather than a random point somewhere beyond the end of the Cunningham tables.