The list of known factors of iterated Mersenne numbers recently
forwarded to these lists include all factors known to me, but the
search limits have been significantly improved, some well before
Nov. 1996 I believe.
The MMPstats.txt file that I maintain is about to be updated to the
following. If you do not have web access, feel free to email me; I
can arrange to have it emailed to you automatically when it changes as
part of the script that updates my web pages.
Note the implication that I try to keep track of who is working on
which exponents; this is simply to avoid duplication of effort.
Will
http://www.garlic.com/~wedgingt/MMPstats.txt
mersfmt.txt
mersenne.html
Status of M(M(p)) where M(p) is a Mersenne prime
$Id: MMP.status,v 1.49 1999/09/23 23:00:18 wedgingt Exp $
A factor will always be of the form 2*k*m + 1 where m = M(p) = 2^p - 1
is a Mersenne prime.
'U: k=61' is short-hand that trial factors <= 2*k*m + 1 have been checked.
The format is otherwise based on my usual Mersenne format, described
in <A HREF="http://www.garlic.com/~wedgingt/mersfmt.txt"> mersfmt.txt </A>.
Note that, since m == 1 (mod 3), factors of M(m) cannot have k == 1 (mod 3)
since 2*k*m + 1 == 0 (mod 3) in that case.
Chris Nash pointed out on the Mersenne list (1999 Sep 22) that, for
odd Mersenne exponents, k must be 0 or 1 mod 4, since,
otherwise, 2 is not a quadratic residue of the supposed
factor.
Credit for first find of each factor (C: line) is given to the best of
my knowledge. The one with my name is from my pre-GIMPS (see
www.mersenne.org) data and probably pre-dates W. Keller's
(also unpublished) 1994 discovery.
Note that I have no P-1 factoring info for M(p) > M(17) and no P-1
save files.
M( M( 2 ) )P
M( M( 3 ) )P
M( M( 5 ) )P
M( M( 7 ) )P
M( M( 13 ) )C: 338193759479 # k = 20644229, Wilfrid Keller (1976)
M( M( 13 ) )H: 2^55 # Charles F. Kerchner III, Prime95, stopped
M( M( 13 ) )H: k=2199291723780 # "
M( M( 13 ) )o: 3e9 # Warut Roonguthai, Factor95, stopped (no P-1 save
file)
M( M( 17 ) )C: 231733529 # k = 884, Raphael Robinson (1957)
M( M( 17 ) )C: 64296354767 # k = 245273, Wilfrid Keller (1983?)
M( M( 17 ) )H: 2^60 # Charles F. Kerchner III, Prime95, stopped
M( M( 17 ) )H: k=17592320263168 # "
M( M( 17 ) )o: 3961649 # (unknown, no P-1 save file)
M( M( 19 ) )C: 62914441 # k = 60, Raphael Robinson (1957)
M( M( 19 ) )C: 5746991873407 # k = 5480769, Will Edgington (Wilfrid Keller 1994)
M( M( 19 ) )H: 2^60 # Warut Roonguthai, Prime95, stopped
M( M( 19 ) )H: k=4398054899728 # "
M( M( 31 ) )C: 295257526626031 # k = 68745, Warut Roonguthai (Guy Haworth 1983)
M( M( 31 ) )C: 87054709261955177 # k = 20269004, Tony Forbes (Wilfrid Keller
1994)
M( M( 31 ) )H: 1984697089407967495
M( M( 31 ) )H: k=462098301
M( M( 61 ) )U: k=9363198284 # Landon Curt Noll, own program, stopped
# Sturle Sunde, continuing 1999 Sep 22
M( M( 89 ) )U: k=13516351613 # Landon Curt Noll, own program, stopped
M( M( 107 ) )U: k=2016797660 # Landon Curt Noll, own program, stopped
M( M( 127 ) )U: k=1250000000000 # Landon Curt Noll, own program, continuing
M( M( 521 ) )U: k=20000000 # Rob Hooft, mmtrial, stopped
M( M( 607 ) )U: k=6170000 # Samuli Larvala, own program, stopped
M( M( 1279 ) )U: k=17758437 # Conrad Curry, mmfac (see below), stopped
M( M( 2203 ) )U: k=11356378 # Conrad Curry, mmfac, stopped
M( M( 2281 ) )U: k=3026696 # Rob Hooft, mmtrial, stopped
M( M( 3217 ) )U: k=304345 # Eric Prestemon, mmtrial, stopped
M( M( 4253 ) )U: k=580000 # Conrad Curry, mmfac, stopped
M( M( 4423 ) )U: k=880000 # Conrad Curry, mmfac, stopped
M( M( 9689 ) )U: k=69034 # Conrad Curry, mmfac, stopped
M( M( 9941 ) )U: k=14000 # Conrad Curry, mmfac, stopped
M( M( 11213 ) )U: k=2573 # Eric Prestemon, mmtrial, stopped
M( M( 19937 ) )U: k=1501 # Conrad Curry, mmfac, stopped
M( M( 21701 ) )U: k=7123 # Conrad Curry, mmfac, stopped
M( M( 23209 ) )U: k=2731 # Conrad Curry, mmfac, stopped
M( M( 44497 ) )U: k=30169 # Chris Nash, by sieving possible factors,
1999 Sep 21
M( M( 86243 ) )U: k=271 # Conrad Curry, mmfac, stopped
M( M( 110503 ) )U: k=7 # Will Edgington, mmtrial, stopped
M( M( 132049 ) )U: k=40 # Will Edgington, mmtrial, stopped
M( M( 216091 ) )U: k=19 # Charles F. Kerchner III, own program
M( M( 756839 ) )U: k=23 # Charles F. Kerchner III, own program
M( M( 859433 ) )U: k=32 # Charles F. Kerchner III, own program
M( M( 1257787 ) )U: k=7 # Charles F. Kerchner III, own program
M( M( 1398269 ) )U: k=4 # Charles F. Kerchner III, own program
M( M( 2976221 ) )U: k=55 # Eric Prestemon, mmtrial, stopped
M( M( 3021377 ) )U: k=43 # Charles F. Kerchner III, own program
M( M( 6972593 ) )U: k=4 # Will Edgington, mmtrial, stopped
Rob Hooft has sent me a copy of his program, mmtrial, which uses
freeLIP; it is in the mers package, which is available <a
href="http://www.garlic.com/~wedgingt/mers.tar.gz"> here </a> on <a
href="http://www.garlic.com/~wedgingt/"> my personal web pages </a>.
Conrad Curry's mmfac program is available on <a
href="ftp://ftp.netdoor.com/users/acurry/"> his ftp site </a> as <a
href="ftp://ftp.netdoor.com/users/acurry/mmfac.zip"> mmfac.zip </a>
His ecm3 for DOS, a port of the mers package's ecm3 v4.1, is also
there as <a href="ftp://ftp.netdoor.com/users/acurry/ecm3.zip">
ecm3.zip </a>.
Please send updates, corrections, questions, and new information to
<a href="mailto:[EMAIL PROTECTED]"> [EMAIL PROTECTED] (me) </a>.
Thanks,
Will Edgington
Last updated: $Id: MMP.status,v 1.49 1999/09/23 23:00:18 wedgingt Exp $
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