(from Will Edgington's Double Mersenne Primes' page)
For the second factor of M(M(17)) and the first factor of M(M(31)) see also page 45 of Guy Haworth's 1987 report on Mersenne Numbers.
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( 13 ) )o: 2000000000000 20000000000000000
# Yaroslav Berezhko, own program (B1) and GMP-ECM (B2) stopped, 2020 Dec 21, save file avail.
M( M( 13 ) )o: 100000 268760436374430 # Jorge Coveiro, Prime95 P-1, 2022 Jan 24
M( M( 13 ) )o: 1000000000 268760436374430
# Jorge Coveiro, Prime95 P-1, 2022 Jan 24
M( M( 13 ) )o: 20000000000 268760436374430
# Jorge Coveiro, Prime95 P-1, 2022 Jan 29
M( M( 17 ) )C: 231733529 # k = 884, Raphael Robinson (1957)
M( M( 17 ) )C: 64296354767 # k = 245273, Wilfrid Keller (1981 Nov 27)
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 Aug 20
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 ) )C: 4565880376922810768406683467841114102689
# Phil Moore, Prime95 ECM 2023 Dec 06
# B1=11e6, B2=1.1e9 cofactor composite
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( 19 ) )o: 1000000000 2100000000 # Jorge Coveiro, gpuowl P-1, 2022 Jan 30
M( M( 19 ) )o: 1000000000 659751021930 # Jorge Coveiro, Prime95 P-1, 2023 Apr 11
M( M( 31 ) )C: 295257526626031 # k = 68745, Wilfrid Keller 1981 Nov 27
M( M( 31 ) )C: 87054709261955177 # k = 20269004, Tony Forbes - Wilfrid Keller 1994 Aug 20
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=1152921505143717888 # Doublemersennes.org and George Woltman's mmff since 2012 September 1
M( M( 61 ) )U: k=280000000000000000 # Doublemersennes.org and George Woltman's mmff since 2012 September 1
M( M( 89 ) )U: k=62000000000000000 # Doublemersennes.org and George Woltman's mmff since 2012 September 1
M( M( 107 ) )U: k=220000000000000000 # Doublemersennes.org and George Woltman's mmff since 2012 September 1
M( M( 127 ) )U: k=1105000000000000000 # Doublemersennes.org and George Woltman's mmff since 2012 September 1
M( M( 521 ) )U: k=156156000000 # Tony Forbes, MFAC.
M( M( 521 ) )U: k=200000000000 # Luigi Morelli, GMP-Double-Mersenne, Stopped.
M( M( 607 ) )U: k=96096000000 # Tony Forbes, MFAC.
M( M( 607 ) )U: k=200000000000 # Luigi Morelli, GMP-Double-Mersenne, Stopped.
M( M( 1279 ) )U: k=2001753600 # Reto Keiser, 2004 Feb 6, MFAC 2.29
M( M( 1279 ) )U: k=2500000000 # Luigi Morelli, 2019 Jun 16, dmdsieve and pfgw, Continuing.
M( M( 2203 ) )U: k=207243960 # Reto Keiser, 2004 Feb 6, MFAC 2.29
M( M( 2203 ) )U: k=341437005 # LaurV, 2013 Sep 6, PARI and pfgw.
M( M( 2203 ) )U: k=1000000000 # Luigi Morelli, 2015 Oct 22, GMP-Double-Mersenne, Stopped.
M( M( 2281 ) )U: k=8717474 # James Wanless, 2004 Aug 9, unknown program.
M( M( 2281 ) )U: k=50000000 # Timothy Sorbera, 2011 Jan 12, GMP-Double-Mersenne
M( M( 2281 ) )U: k=400000000 # LaurV, pfgw, 2013 Sep 24. Stopped.
M( M( 3217 ) )U: k=7203992 # Tony Forbes, own program.
M( M( 3217 ) )U: k=100000000 # LaurV, 2013 Oct 3, PARI and pfgw. Stopped.
M( M( 4253 ) )U: k=4697044 # Tony Forbes, own program.
M( M( 4253 ) )U: k=18121640 # LaurV, 2013 Sep 6, PARI and pfgw. Stopped.
M( M( 4423 ) )U: k=5052299 # Tony Forbes, own program.
M( M( 4423 ) )U: k=17258708 # LaurV, 2013 Sep 6, PARI and pfgw. Stopped.
M( M( 9689 ) )U: k=1302840 # Reto Keiser, 2004 Feb 6, MFAC 2.29
M( M( 9689 ) )U: k=3656009 # LaurV, 2013 Sep 6, PARI and pfgw. Stopped.
M( M( 9941 ) )U: k=1329452 # Tony Forbes, own program.
M( M( 9941 ) )U: k=3521045 # LaurV, 2013 Sep 6, PARI and pfgw.
M( M( 9941 ) )U: k=100000000 # Dylan Delgado, 2019 May 10, GMP-Double-Mersenne. Stopped.
M( M( 11213 ) )U: k=863503 # Tony Forbes, own program.
M( M( 11213 ) )U: k=1000000 # Timothy Sorbera, 2011 Jan 2, pfgw and GMP-Double-Mersenne
M( M( 11213 ) )U: k=100000000 # Dylan Delgado, 2019 Mar 29, gmp-doublemersennes.
M( M( 11213 ) )U: k=200000000 # Dylan Delgado, 2019 Jun 29, dmdsieve. Stopped.
M( M( 19937 ) )U: k=356320 # Tony Forbes, own program.
M( M( 19937 ) )U: k=610068 # LaurV, 2013 Sep 6, PARI and pfgw. Stopped.
M( M( 21701 ) )U: k=308792 # Tony Forbes, own program.
M( M( 21701 ) )U: k=501524 # LaurV, 2013 Sep 6, PARI and pfgw. Stopped.
M( M( 23209 ) )U: k=566072 # Tony Forbes, own program.
M( M( 23209 ) )U: k=10000000 # Luigi Morelli, 2013 Nov 17, PARI and pfgw. Stopped.
M( M( 44497 ) )U: k=1702545 # Tony Forbes, own program, Stopped.
M( M( 86243 ) )U: k=546184 # Tony Forbes, 2001 May 12, own program.
M( M( 86243 ) )U: k=1000000 # Timothy Sorbera, 2011 Jan 12, pfgw and GMP-Double-Mersenne. Stopped.
M( M( 110503 ) )U: k=645491 # Tony Forbes, 2001 May 12, own program.
M( M( 110503 ) )U: k=2000000 # Luigi Morelli, 2014 Feb 12, Pari and pfgw.
M( M( 110503 ) )U: k=8000000 # Dylan Delgado, 2019 Jan 5, dmdsieve and LLR, Stopped.
M( M( 132049 ) )U: k=244903 # Tony Forbes, own program.
M( M( 132049 ) )U: k=2000000 # Luigi Morelli, 2014 Feb 05, Pari and pfgw, Stopped.
M( M( 216091 ) )U: k=123376 # Tony Forbes, own program.
M( M( 216091 ) )U: k=1739793 # Serge Batalov, PARI and LLR.
M( M( 216091 ) )U: k=2000000 # Luigi Morelli, 2014 Jun 26, own program, Pari and pfgw. Stopped.
M( M( 756839 ) )U: k=11588 # Tony Forbes, own program.
M( M( 756839 ) )U: k=2000000 # Luigi Morelli, 2017 Jun 30, Pari, own siever, LLR and pfgw. Stopped.
M( M( 859433 ) )U: k=10127 # Tony Forbes, own program.
M( M( 859433 ) )U: k=2000000 # Luigi Morelli, Carlos Pinho and Oliver Kruse, PARI, own siever, LLR and mprime. Stopped.
M( M( 1257787 ) )U: k=1619096 # DoubleMersennes.org, sieved k= 1619097 to 220T - Continuing.
M( M( 1398269 ) )U: k=1453960 # DoubleMersennes.org, sieved k= 1453961 to 220T - Continuing.
M( M( 2976221 ) )U: k=350183 # DoubleMersennes.org, sieved k= 350184 to 240T - Continuing.
M( M( 3021377 ) )U: k=310888 # DoubleMersennes.org, sieved k= 310889 to 240T - Continuing.
M( M( 6972593 ) )U: k=113675 # DoubleMersennes.org, sieved k= 113676 to 260T - Continuing.
M( M( 13466917 ) )U: k=100535 # DoubleMersennes.org, sieved k= 100536 to 260T - Continuing.
M( M( 20996011 ) )U: k=1112 # DoubleMersennes.org, sieved k= 1113 to 280T - Continuing.
M( M( 24036583 ) )U: k=484 # DoubleMersennes.org, sieved k= 485 to 300T - Continuing.
M( M( 25964951 ) )U: k=44 # DoubleMersennes.org, sieved k= 45 to 330T - Continuing.
M( M( 30402457 ) )U: k=40 # DoubleMersennes.org, sieved k= 41 to 350T - Continuing.
M( M( 32582657 ) )U: k=59 # DoubleMersennes.org, sieved k= 60 to 370T - Continuing.
M( M( 37156667 ) )U: k=23 # DoubleMersennes.org, sieved k= 24 to 400T - Continuing.
M( M( 42643801 ) )U: k=32 # DoubleMersennes.org, sieved k= 33 to 450T - Continuing.
M( M( 43112609 ) )U: k=512 # DoubleMersennes.org, sieved k= 513 to 500T - Continuing.
M( M( 57885161 ) )U: k=248 # DoubleMersennes.org, sieved k= 249 to 750T - Continuing.
M( M( 74207281 ) )U: k=112 # DoubleMersennes.org, sieved k= 113 to 1000T - Continuing.
M( M( 77232917 ) )U: k=103 # DoubleMersennes.org, sieved k= 104 to 1030T - Continuing.
M( M( 82589933 ) )U: k=340 # DoubleMersennes.org, sieved k= 341 to 3000T - Continuing.
M( M( 136279841 ) )U: k=40 # DoubleMersennes.org, sieved k= 41 to 2600T - Continuing.
George Woltman released a fast program, mmff to factor small double mersenne numbers.
Mark Rodenkirch adapted his program (GMP_Fermat) to search for double Mersenne numbers up to MM86243.
Mark Rodenkirch also released a specific siever called dmdsieve from his compilation of sievers (Mtsieve) help searching for higher Mersenne numbers up to MM82589933.
Ernst W. Mayer developed a siever to attack small k ofthe largest double Mersenne numbers.
Landon Curt Noll was using the calc program to factor M( M( 127 ) ).
Rob Hooft developed a program, mmtrial, which uses freeLIP; it is in the mers package, which is available at this address on Will Edgington's 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 maintained a distributerd project to search for factors of 2261-1-1.
His website records his work.
Here is an interesting article written by I.J. Good, titled Conjectures concerning the Mersenne Numbers.
Please send updates, corrections, questions, and new information to me .
Thanks,
Luigi Morelli