Status of M(M(p)) where M(p) is a Mersenne prime $Id: MMP.status,v 1.91 2020/06/27 17:42:09 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 within either mers.tar.gz or mers.zip in the mers project files . 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 The one with my name is from my pre-GIMPS (see www.mersenne.org) data and probably pre-dates W. Keller's (also unpublished) 1994 discovery.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 <rkeiser@stud.ee.ethz.ch> 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 project on Sourceforge.net. 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 1.91 2020/06/27 17:42:09 wedgingt Exp $