Status of M(M(p)) where M(p) is a Mersenne prime
$Id: MMP.status,v 1.90 2011/11/19 19:09:35 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 mersfmt.txt .
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.
The combination of the prior two restrictions limits k to
0, 5, 8, and 9 modulo 12.
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(also unpublished) 1994 discovery.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(19) and no P-1
save files for these exponents, but others, as noted, should.
Note also that the ECM "work" or "effort" is not listed here.
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 ) )C: 210206826754181103207028761697008013415622289
# k = 2^3 * 3^4 * 11 * 512237490733 * 3514316262671725281413641
# Phil Moore, Prime95 ECM, 2003 June 12
M( M( 13 ) )H: 2^55 # Charles F. Kerchner III, Prime95, stopped
M( M( 13 ) )H: k=2250524799600 # Jocelyn Larouche, MFAC, stopped, 2000 Feb 16
# More trial factoring should be pointless due to:
M( M( 13 ) )H # Reto Keiser, Prime95 ECM, stopped, 2002 Apr 26
# ... but ECM is partially random, so more ECM or P-1 is probably worthwhile.
M( M( 13 ) )o: 3e9 # Warut Roonguthai, Factor95, stopped (no P-1 save file)
M( M( 13 ) )c: 2410 # Phil Moore, w/Prime95, Maple, & PrimeForm, 2003 June 12
M( M( 17 ) )C: 231733529 # k = 884, Raphael Robinson (1957)
M( M( 17 ) )C: 64296354767 # k = 245273, Wilfrid Keller (1983?)
M( M( 17 ) )H: k=17608434819360 # Jocelyn Larouche, MFAC, stopped, 2000 Feb 16
M( M( 17 ) )H # Reto Keiser, Prime95 ECM, stopped, 2002 Apr 26
M( M( 17 ) )o: 200000000 4290000000 # Reto Keiser, Prime95 P-1, stopped, 2000 Nov 21, save file avail.
M( M( 17 ) )c: 39438 # Phil Moore, 2001 January, Chris Nash's Primeform
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 ) )C: 824271579602877114508714150039
# Phil Moore, Prime95 ECM 2000 Dec 6
# k = 3*11*199*39509*3029759717908279
M( M( 19 ) )C: 2106734551102073202633922471
# Phil Moore, Prime95 ECM 2003 Mar 20
# k = 3*5*113*112877*10501118807327
M( M( 19 ) )C: 65997004087015989956123720407169
# Phil Moore, Prime95 ECM 2011 Sep 30
# B1=3e6; cofactor composite
M( M( 19 ) )H: 2^60 # Warut Roonguthai, Prime95, stopped
M( M( 19 ) )H: k=4398054899728 # "
M( M( 19 ) )H # Reto Keiser, Prime95 ECM, stopped, 2002 Apr 26
M( M( 19 ) )o: 30000000 1500000000 # Reto Keiser, Prime95 P-1, stopped, 2000 Nov 21, save file avail.
M( M( 19 ) )c: 157749 # Phil Moore, 2003 Mar 20, Chris Nash's Primeform
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 ) )C: 242557615644693265201 # k = 56474845800, Reto Keiser 1999 Dec 6
M( M( 31 ) )C: 178021379228511215367151 # k = 41448832329225, Ernst Mayer 2005 June 20
M( M( 31 ) )H: k=5105100000000 # Reto Keiser, MFAC 2.29, 2004 Feb 6 continuing to 10T
M( M( 61 ) )U: k=9363198284 # Landon Curt Noll, own program, stopped
# Tony Forbes & others, continuing 2001 May 12
# http://www.ltkz.demon.co.uk/ar2/mm61prog.htm
M( M( 89 ) )U: k=6942936000000 # Tony Forbes, MFAC, continuing, 2001 May 12
M( M( 107 ) )U: k=4084080000000 # Tony Forbes, MFAC, continuing, 2001 May 12
M( M( 127 ) )U: k=3000000000000 # Landon Curt Noll, calc, continuing, 2003 Sep 01
M( M( 127 ) )U: k=500*102102000000 to 516*102102000000
# Tony Forbes, MFAC, continuing, 2001 May 12
M( M( 521 ) )U: k=156156000000 # Tony Forbes, MFAC, continuing, 2001 May 12
M( M( 607 ) )U: k=96096000000 # Tony Forbes, MFAC, continuing, 2001 May 12
M( M( 1279 ) )U: k=2001753600 # Reto Keiser, 2004 Feb 6, MFAC 2.29
M( M( 2203 ) )U: k=207243960 # Reto Keiser, 2004 Feb 6, MFAC 2.29
M( M( 2281 ) )U: k=8717474 # James Wanless, unknown program, stopped, 2004 Aug 9
M( M( 2281 ) )U: k=8717474 to 50000000 # Timothy Sorbera, GMP-Double-Mersenne, stopped, 2011 Jan 2
M( M( 3217 ) )U: k=7203992 # Tony Forbes, own program, stopped
M( M( 4253 ) )U: k=4697044 # Tony Forbes, own program, stopped
M( M( 4423 ) )U: k=5052299 # Tony Forbes, own program, stopped
M( M( 9689 ) )U: k=1302840 # Reto Keiser, 2004 Feb 6, MFAC 2.29
M( M( 9941 ) )U: k=1329452 # Tony Forbes, own program, stopped
M( M( 11213 ) )U: k=863503 # Tony Forbes, own program, stopped
M( M( 11213 ) )U: k=863503 to 1000000 # Timothy Sorbera, PFGW and GMP-Double-Mersenne, stopped 2011 Jan 2
M( M( 19937 ) )U: k=356320 # Tony Forbes, own program, stopped
M( M( 21701 ) )U: k=308792 # Tony Forbes, own program, stopped
M( M( 23209 ) )U: k=566072 # Tony Forbes, own program, stopped
M( M( 44497 ) )U: k=1702545 # Tony Forbes, own program, stopped
M( M( 86243 ) )U: k=546184 # Tony Forbes, own program, stopped, 2001 May 12
M( M( 110503 ) )U: k=645491 # Tony Forbes, own program, stopped, 2001 May 12
M( M( 132049 ) )U: k=244903 # Tony Forbes, own program, continuing, 2001 May 12
M( M( 216091 ) )U: k=123376 # Tony Forbes, own program, continuing, 2001 May 12
M( M( 756839 ) )U: k=11588 # Tony Forbes, own program, continuing, 2001 May 12
M( M( 859433 ) )U: k=10127 # Tony Forbes, own program, continuing, 2001 May 12
M( M( 1257787 ) )U: k=91 # Phil Moore, using Tony Forbes sieve and pfgw, 2005 Feb 28
Tony has already sieved the possible factors _much_ farther than this,
so contact him before doing work on this exponent.
M( M( 1398269 ) )U: k=67 # Phil Moore, using Tony Forbes sieve and pfgw, 2005 Feb 28
Tony has already sieved the possible factors _much_ farther than this,
so contact him or me before starting work on this exponent.
M( M( 2976221 ) )U: k=83 # Phil Moore, own program and Prime95, 2005 Feb 28
M( M( 3021377 ) )U: k=103 # Phil Moore, own program, Prime95, and pfgw, 2005 Feb 28
M( M( 6972593 ) )U: k=88 # Phil Moore, own program, Prime95, and pfgw, 2005 Feb 28
M( M( 13466917 ) )U: k=88 # Phil Moore, own program and Prime95, 2005 Feb 28
M( M( 20996011 ) )U: k=248 # Phil Moore, own program, Prime95, and pfgw, 2005 Mar 28
M( M( 24036583 ) )U: k=47,49-64,66,67 # Phil Moore, own program and Prime95, 2005 Feb 28
M( M( 25964951 ) )U: k=44 # Phil Moore, own program, 2005 Feb 28
M( M( 30402457 ) )U: k=40 # Phil Moore, own program, 2006 Jan 06
Phil Moore has also sent me (starting 2005 Mar 28) some of the 64 bit
residues from testing for later double-checking, mostly because he's
presently using an alpha release version of pfgw:
Testing Q=2*8*(2^1257787-1)+1
2^(2^p) mod Q is: 15014429868655832299
MMp+1 mod Q is: 7507214934327916142
Base-2 Fermat residue of Q is: 11111855935941879230
Testing Q=2*5*(2^1398269-1)+1
2^(2^p) mod Q is: 7142321001040845878
MMp+1 mod Q is: 12794532537375198747
Base-2 Fermat residue of Q is: 3649019670492788933
Testing Q=2*29*(2^1257787-1)+1
MMp+1 mod Q is: 9767415438985614067
Base-2 Fermat residue of Q is: 2174966271466088299
Testing Q=2*48*(2^1257787-1)+1
MMp+1 mod Q is: 16316628194680534952
Base-2 Fermat residue of Q is: 17198317548773192287
Testing Q=2*53*(2^1257787-1)+1
MMp+1 mod Q is: 8347901009962164874
Base-2 Fermat residue of Q is: 9034660674105456695
Testing Q=2*44*(2^1398269-1)+1
MMp+1 mod Q is: 14840952197919118511
Base-2 Fermat residue of Q is: 5417452879065340566
Testing Q=2*44*(2^3021377-1)+1
MMp+1 mod Q is: 793372301581782912
Base-2 Fermat residue of Q is: 3439490272329066447
Testing Q=2*60*(2^3021377-1)+1
MMp+1 mod Q is: 14809298235281584738
Base-2 Fermat residue of Q is: 11637403745852953264
Testing Q=2*5*(2^6972593-1)+1
MMp+1 mod Q is: 1201174313396732329
Base-2 Fermat residue of Q is: 5098661671882105020
Testing Q=2*8*(2^20996011-1)+1
2^(2^p) mod Q is: 18413704535061513081
MMp+1 mod Q is: 18430224304385532341
Base-2 Fermat residue of Q is: 697082499562303341
Landon Curt Noll
was using the calc
program to factor M( M( 127 ) ).
Rob Hooft has sent me a copy of his program, mmtrial, which uses
freeLIP; it is in the mers package, which is available here on my personal web pages .
Conrad Curry's mmfac program is available on his ftp site as mmfac.zip
His ecm3 for DOS, a port of the mers package's ecm3 v4.1, is also
there as
ecm3.zip .
Tony Forbes also includes large prime numbers that he finds while
sieving possible factors; the present list follows. I believe these
are in the "generalized repunits" class and there may be a list of
such elsewhere on the net.
11213:
117618*(2^11213-1) + 1 is prime
119400*(2^11213-1) + 1 is prime
122626*(2^11213-1) + 1 is prime
158682*(2^11213-1) + 1 is prime
194688*(2^11213-1) + 1 is prime
203970*(2^11213-1) + 1 is prime
240096*(2^11213-1) + 1 is prime
267760*(2^11213-1) + 1 is prime
281896*(2^11213-1) + 1 is prime
342978*(2^11213-1) + 1 is prime
345418*(2^11213-1) + 1 is prime
348786*(2^11213-1) + 1 is prime
350752*(2^11213-1) + 1 is prime
356080*(2^11213-1) + 1 is prime
361962*(2^11213-1) + 1 is prime
366616*(2^11213-1) + 1 is prime
381466*(2^11213-1) + 1 is prime
388882*(2^11213-1) + 1 is prime
389346*(2^11213-1) + 1 is prime
408528*(2^11213-1) + 1 is prime
413770*(2^11213-1) + 1 is prime
417130*(2^11213-1) + 1 is prime
423106*(2^11213-1) + 1 is prime
423682*(2^11213-1) + 1 is prime
465640*(2^11213-1) + 1 is prime
475186*(2^11213-1) + 1 is prime
490936*(2^11213-1) + 1 is prime
545928*(2^11213-1) + 1 is prime
634728*(2^11213-1) + 1 is prime
679192*(2^11213-1) + 1 is prime
680002*(2^11213-1) + 1 is prime
705162*(2^11213-1) + 1 is prime
707208*(2^11213-1) + 1 is prime
714960*(2^11213-1) + 1 is prime
728008*(2^11213-1) + 1 is prime
755320*(2^11213-1) + 1 is prime
763600*(2^11213-1) + 1 is prime
768768*(2^11213-1) + 1 is prime
790602*(2^11213-1) + 1 is prime
827128*(2^11213-1) + 1 is prime
836920*(2^11213-1) + 1 is prime
849642*(2^11213-1) + 1 is prime
880192*(2^11213-1) + 1 is prime
902626*(2^11213-1) + 1 is prime
905752*(2^11213-1) + 1 is prime
905992*(2^11213-1) + 1 is prime
916978*(2^11213-1) + 1 is prime
918730*(2^11213-1) + 1 is prime
920368*(2^11213-1) + 1 is prime
923562*(2^11213-1) + 1 is prime
923688*(2^11213-1) + 1 is prime
971992*(2^11213-1) + 1 is prime
982618*(2^11213-1) + 1 is prime
997162*(2^11213-1) + 1 is prime
1013778*(2^11213-1) + 1 is prime
1030720*(2^11213-1) + 1 is prime
1048960*(2^11213-1) + 1 is prime
1071888*(2^11213-1) + 1 is prime
1072512*(2^11213-1) + 1 is prime
1120458*(2^11213-1) + 1 is prime
1121058*(2^11213-1) + 1 is prime
1136818*(2^11213-1) + 1 is prime
1146688*(2^11213-1) + 1 is prime
1153810*(2^11213-1) + 1 is prime
1174306*(2^11213-1) + 1 is prime
1174320*(2^11213-1) + 1 is prime
1176538*(2^11213-1) + 1 is prime
1181746*(2^11213-1) + 1 is prime
1202410*(2^11213-1) + 1 is prime
1207578*(2^11213-1) + 1 is prime
1232248*(2^11213-1) + 1 is prime
1244320*(2^11213-1) + 1 is prime
1246722*(2^11213-1) + 1 is prime
1254072*(2^11213-1) + 1 is prime
1264248*(2^11213-1) + 1 is prime
1271488*(2^11213-1) + 1 is prime
1311450*(2^11213-1) + 1 is prime
1358890*(2^11213-1) + 1 is prime
1407192*(2^11213-1) + 1 is prime
1419282*(2^11213-1) + 1 is prime
1423512*(2^11213-1) + 1 is prime
1440480*(2^11213-1) + 1 is prime
1452328*(2^11213-1) + 1 is prime
1453648*(2^11213-1) + 1 is prime
1456818*(2^11213-1) + 1 is prime
1481248*(2^11213-1) + 1 is prime
1488792*(2^11213-1) + 1 is prime
1509208*(2^11213-1) + 1 is prime
1563162*(2^11213-1) + 1 is prime
1573666*(2^11213-1) + 1 is prime
1608306*(2^11213-1) + 1 is prime
1617888*(2^11213-1) + 1 is prime
1621408*(2^11213-1) + 1 is prime
1657746*(2^11213-1) + 1 is prime
1669050*(2^11213-1) + 1 is prime
1675818*(2^11213-1) + 1 is prime
1678072*(2^11213-1) + 1 is prime
1712968*(2^11213-1) + 1 is prime
19937: All from 2*k = 66898 tested for primality
71056*(2^19937-1) + 1 is prime
171162*(2^19937-1) + 1 is prime
192232*(2^19937-1) + 1 is prime
198378*(2^19937-1) + 1 is prime
230856*(2^19937-1) + 1 is prime
245248*(2^19937-1) + 1 is prime
257040*(2^19937-1) + 1 is prime
266250*(2^19937-1) + 1 is prime
297360*(2^19937-1) + 1 is prime
310488*(2^19937-1) + 1 is prime
352138*(2^19937-1) + 1 is prime
407872*(2^19937-1) + 1 is prime
424456*(2^19937-1) + 1 is prime
455698*(2^19937-1) + 1 is prime
467640*(2^19937-1) + 1 is prime
470928*(2^19937-1) + 1 is prime
543136*(2^19937-1) + 1 is prime
563058*(2^19937-1) + 1 is prime
565170*(2^19937-1) + 1 is prime
570928*(2^19937-1) + 1 is prime
604632*(2^19937-1) + 1 is prime
655410*(2^19937-1) + 1 is prime
687706*(2^19937-1) + 1 is prime
23 primes found
21701: All from 2*k = 50208 tested for primality
57586*(2^21701-1) + 1 is prime
73008*(2^21701-1) + 1 is prime
86248*(2^21701-1) + 1 is prime
165778*(2^21701-1) + 1 is prime
185730*(2^21701-1) + 1 is prime
211746*(2^21701-1) + 1 is prime
219618*(2^21701-1) + 1 is prime
230698*(2^21701-1) + 1 is prime
247426*(2^21701-1) + 1 is prime
274200*(2^21701-1) + 1 is prime
315090*(2^21701-1) + 1 is prime
336112*(2^21701-1) + 1 is prime
344082*(2^21701-1) + 1 is prime
353938*(2^21701-1) + 1 is prime
354666*(2^21701-1) + 1 is prime
364432*(2^21701-1) + 1 is prime
410136*(2^21701-1) + 1 is prime
428776*(2^21701-1) + 1 is prime
430818*(2^21701-1) + 1 is prime
463002*(2^21701-1) + 1 is prime
523656*(2^21701-1) + 1 is prime
533152*(2^21701-1) + 1 is prime
598336*(2^21701-1) + 1 is prime
23 primes found
23209: All from 2*k = 5460 tested for primality
20808*(2^23209-1) + 1 is prime
35178*(2^23209-1) + 1 is prime
37056*(2^23209-1) + 1 is prime
89026*(2^23209-1) + 1 is prime
103506*(2^23209-1) + 1 is prime
160378*(2^23209-1) + 1 is prime
164322*(2^23209-1) + 1 is prime
249336*(2^23209-1) + 1 is prime
253986*(2^23209-1) + 1 is prime
275346*(2^23209-1) + 1 is prime
279552*(2^23209-1) + 1 is prime
322290*(2^23209-1) + 1 is prime
397402*(2^23209-1) + 1 is prime
410746*(2^23209-1) + 1 is prime
422056*(2^23209-1) + 1 is prime
430440*(2^23209-1) + 1 is prime
431520*(2^23209-1) + 1 is prime
475402*(2^23209-1) + 1 is prime
484690*(2^23209-1) + 1 is prime
491578*(2^23209-1) + 1 is prime
572400*(2^23209-1) + 1 is prime
656842*(2^23209-1) + 1 is prime
665058*(2^23209-1) + 1 is prime
759280*(2^23209-1) + 1 is prime
828466*(2^23209-1) + 1 is prime
852880*(2^23209-1) + 1 is prime
872880*(2^23209-1) + 1 is prime
882480*(2^23209-1) + 1 is prime
926802*(2^23209-1) + 1 is prime
944976*(2^23209-1) + 1 is prime
993592*(2^23209-1) + 1 is prime
1007178*(2^23209-1) + 1 is prime
1020576*(2^23209-1) + 1 is prime
1024842*(2^23209-1) + 1 is prime
1028602*(2^23209-1) + 1 is prime
1035472*(2^23209-1) + 1 is prime
1047490*(2^23209-1) + 1 is prime
1058778*(2^23209-1) + 1 is prime
1100986*(2^23209-1) + 1 is prime
39 primes found
44497:
134008*(2^44497-1) + 1 is prime
137218*(2^44497-1) + 1 is prime
232360*(2^44497-1) + 1 is prime
319842*(2^44497-1) + 1 is prime
536272*(2^44497-1) + 1 is prime
566272*(2^44497-1) + 1 is prime
643482*(2^44497-1) + 1 is prime
678496*(2^44497-1) + 1 is prime
688200*(2^44497-1) + 1 is prime
707506*(2^44497-1) + 1 is prime
707850*(2^44497-1) + 1 is prime
857808*(2^44497-1) + 1 is prime
943936*(2^44497-1) + 1 is prime
952858*(2^44497-1) + 1 is prime
1092058*(2^44497-1) + 1 is prime
1106872*(2^44497-1) + 1 is prime
1265370*(2^44497-1) + 1 is prime
1305000*(2^44497-1) + 1 is prime
1355410*(2^44497-1) + 1 is prime
1415152*(2^44497-1) + 1 is prime
1664800*(2^44497-1) + 1 is prime
1668298*(2^44497-1) + 1 is prime
1824538*(2^44497-1) + 1 is prime
1873720*(2^44497-1) + 1 is prime
1881432*(2^44497-1) + 1 is prime
1898008*(2^44497-1) + 1 is prime
2042496*(2^44497-1) + 1 is prime
2049322*(2^44497-1) + 1 is prime
2088378*(2^44497-1) + 1 is prime
2182216*(2^44497-1) + 1 is prime
2204176*(2^44497-1) + 1 is prime
2246610*(2^44497-1) + 1 is prime
2260746*(2^44497-1) + 1 is prime
2398282*(2^44497-1) + 1 is prime
2594706*(2^44497-1) + 1 is prime
2598178*(2^44497-1) + 1 is prime
2635482*(2^44497-1) + 1 is prime
2654680*(2^44497-1) + 1 is prime
2812600*(2^44497-1) + 1 is prime
2817418*(2^44497-1) + 1 is prime
2869296*(2^44497-1) + 1 is prime
2883576*(2^44497-1) + 1 is prime
2995632*(2^44497-1) + 1 is prime
3006712*(2^44497-1) + 1 is prime
3071640*(2^44497-1) + 1 is prime
3214632*(2^44497-1) + 1 is prime
3292312*(2^44497-1) + 1 is prime
3314130*(2^44497-1) + 1 is prime
3335232*(2^44497-1) + 1 is prime
3403968*(2^44497-1) + 1 is prime
86243: (All from 2*k = 9954 tested for primality)
15418*(2^86243-1) + 1 is prime
58818*(2^86243-1) + 1 is prime
293866*(2^86243-1) + 1 is prime
577968*(2^86243-1) + 1 is prime
668818*(2^86243-1) + 1 is prime
676728*(2^86243-1) + 1 is prime
702850*(2^86243-1) + 1 is prime
110503: (All from 2*k = 11770 tested for primality)
1030360*(2^110503-1) + 1 is prime
1127296*(2^110503-1) + 1 is prime
132049: (All from 2*k = 2410 tested for primality)
30690*(2^132049-1) + 1 is prime
148536*(2^132049-1) + 1 is prime
185056*(2^132049-1) + 1 is prime
216091: (All from 2*k = 1914 tested for primality)
(none so far)
756839: (All tested)
(none so far)
859433: (All tested)
(none so far)
Tim Sorbera sent me more primes related to MM11213, 2011 Jan 2:
1730382*(2^11213-1)+1
1739916*(2^11213-1)+1
1746678*(2^11213-1)+1
1749226*(2^11213-1)+1
1751356*(2^11213-1)+1
1827616*(2^11213-1)+1
1854840*(2^11213-1)+1
1858722*(2^11213-1)+1
1885840*(2^11213-1)+1
1892338*(2^11213-1)+1
1895992*(2^11213-1)+1
1928482*(2^11213-1)+1
1954536*(2^11213-1)+1
1955706*(2^11213-1)+1
1969000*(2^11213-1)+1
1979848*(2^11213-1)+1
1981272*(2^11213-1)+1
1996512*(2^11213-1)+1
1998048*(2^11213-1)+1
Tony also reported the following twin primes:
8339328*(2^2281-1) +/- 1 are prime
15920058*(2^2281-1) +/- 1 are prime
3198240*(2^3217-1) +/- 1 are prime
4106592*(2^3217-1) +/- 1 are prime
2445810*(2^4253-1) +/- 1 are prime
6942546*(2^4423-1) +/- 1 are prime
7354704*(2^4423-1) +/- 1 are prime
7777200*(2^4423-1) +/- 1 are prime
Please send updates, corrections, questions, and new information to
wedgingt@acm.org (me) .
Thanks,
Will Edgington
Last updated: $Id: MMP.status,v 1.90 2011/11/19 19:09:35 wedgingt Exp $