After longer-than-expected delay my program is now ready.
You can download 'MFAC' from
http://www.ltkz.demon.co.uk/AR2/MFAC225.ZIP
and e-mail me for a range.
MFAC searches for divisors of double-Mersenne numbers M_M_e =
2^(2^e-1) - 1 for not-too-large exponents e. (It can also look
for factors of Fermat numbers F_e = 2^2^e + 1.).
MFAC runs on any PC from a 486 upwards and on any system that
supports MSDOS. You can even run it entirely from a bootable
diskette. Memory usage is small and the files require less
than a megabyte of disk space. The program is easily stopped
and restarted.
I am volunteering to coordinate a search for factors of M_M_61.
Let d be a divisor of M_M_61. Then we know that
d = N*(2^61 - 1) + 1.
The parameters I intend to send out will set up MFAC to look
for divisors of M_M_61 with N's in ranges of 204,204,000,000
To give some idea about timing, an AMD K6/2/400 will do a
range in about 4 days.
According to Will Edgington, up to N=18,726,396,568 has been
done. (Note: My N = Will's 2*k.) However it may be that someone
is seriously continuing the search. Therefore I suggest, unless
you specifically want to do smaller N's, that I start handing
out ranges from, say, N = 10^13. One possibility is that we do
all divisors with N from 10^13 to 10^14 and mop up 0 to 10^13
later.
A word or two of warning. Unlike GIMPS, where we can be
confident of finding a new Mersenne prime within a reasonable
time, it may be the case that we are attempting the impossible.
All we can do is hope that (i) M_M_61 is composite, and
(ii) it has a factor small enough to be discoverable.
--
Tony
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