(from a Will Edgington's idea of a 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=600000000000000000 # Doublemersennes.org and George Woltman's mmff since 2012 September 1
M( M( 89 ) )U: k=70000000000000000 # Doublemersennes.org and George Woltman's mmff since 2012 September 1
M( M( 107 ) )U: k=300000000000000000 # Doublemersennes.org and George Woltman's mmff since 2012 September 1
M( M( 127 ) )U: k=1152921504606846976 # 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=250000000000 # Luigi Morelli, 2025 Oct. 27, dmdsieve, Stopped.
M( M( 607 ) )U: k=96096000000 # Tony Forbes, MFAC.
M( M( 607 ) )U: k=250000000000 # Luigi Morelli, 2025 Oct. 31, dmdsieve, Stopped.
M( M( 1279 ) )U: k=2001753600 # Reto Keiser, 2004 Feb 6, MFAC 2.29
M( M( 1279 ) )U: k=2500000000 # Luigi Morelli, 2025 Oct 21, dmdsieve, Stopped.
M( M( 1279 ) )U: k=80000000000 # Gary Gostin, 2025 Nov 3, dmfs.
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, 2025 Oct 22, dmdsieve, Stopped.
M( M( 2203 ) )U: k=20000000000 # Gary Gostin, 2025 Nov 3, dmfs.
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( 2281 ) )U: k=500000000 # Luigi Morelli, dmdsieve, 2025 Oct 16. Stopped.
M( M( 2281 ) )U: k=16000000000 # Gary Gostin, dmfs, 2025 Nov 3.
M( M( 3217 ) )U: k=7203992 # Tony Forbes, MFAC.
M( M( 3217 ) )U: k=100000000 # LaurV, 2013 Oct 3, PARI and pfgw.
M( M( 3217 ) )U: k=210000000 # Luigi Morelli, 2025 Oct 15, GMP-Double-Mersenne. Stopped.
M( M( 3217 ) )U: k=6400000000 # Gary Gostin, 2025 Nov 3, dmfs.
M( M( 4253 ) )U: k=4697044 # Tony Forbes, own program.
M( M( 4253 ) )U: k=18121640 # LaurV, 2013 Sep 6, PARI and pfgw.
M( M( 4253 ) )U: k=210000000 # Luigi Morelli, 2025 Oct 15, GMP-Double-Mersenne. Stopped.
M( M( 4253 ) )U: k=3200000000 # Gary Gostin, 2025 Nov 3, dmfs.
M( M( 4423 ) )U: k=5052299 # Tony Forbes, own program.
M( M( 4423 ) )U: k=17258708 # LaurV, 2013 Sep 6, PARI and pfgw.
M( M( 4423 ) )U: k=210000000 # Luigi Morelli, 2025 Oct 15, GMP-Double-Mersenne. Stopped.
M( M( 4423 ) )U: k=3000000000 # Gary Gostin, 2025 Nov 3, dmfs.
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.
M( M( 9689 ) )U: k=250000000 # Luigi Morelli, 2025 Oct 23, dmdsieve.
M( M( 9689 ) )U: k=1600000000 # Gary Gostin, 2025 Nov 3, dmfs.
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.
M( M( 9941 ) )U: k=250000000 # Luigi Morelli, 2025 Oct 23, dmdsieve.
M( M( 9941 ) )U: k=1600000000 # Gary Gostin, 2025 Nov 3, dmfs.
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-Double-Mersenne.
M( M( 11213 ) )U: k=200000000 # Dylan Delgado, 2019 Jun 29, dmdsieve. Stopped.
M( M( 11213 ) )U: k=210000000 # Luigi Morelli, 2025 Oct 15, dmdsieve. Stopped.
M( M( 11213 ) )U: k=250000000 # Mark Rodenkirch, 2025 Oct 20, dmdsieve. Doublecheck. Stopped.
M( M( 11213 ) )U: k=1024000000 # Gary Gostin, 2025 Nov 3, dmfs.
M( M( 19937 ) )U: k=356320 # Tony Forbes, own program.
M( M( 19937 ) )U: k=610068 # LaurV, 2013 Sep 6, PARI and pfgw.
M( M( 19937 ) )U: k=15000000 # Mark Rodenkirch, 2025 Oct 20, dmdsieve. Doublecheck. Stopped.
M( M( 19937 ) )U: k=384000000 # Gary Gostin, 2025 Nov 3, dmfs.
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( 21701 ) )U: k=12050000 # Luigi Morelli, 2025 Oct 14, dmdsieve and mprime. Stopped.
M( M( 21701 ) )U: k=288000000 # Gary Gostin, 2025 Nov 3, dmfs.
M( M( 23209 ) )U: k=566072 # Tony Forbes, own program.
M( M( 23209 ) )U: k=10000000 # Luigi Morelli, 2013 Nov 17, PARI and pfgw.
M( M( 23209 ) )U: k=12050000 # Luigi Morelli, 2025 Oct 14, GMP-Double-Mersenne. Stopped.
M( M( 23209 ) )U: k=256000000 # Gary Gostin, 2025 Nov 3, dmfs.
M( M( 44497 ) )U: k=1702545 # Tony Forbes, own program, Stopped.
M( M( 44497 ) )U: k=10100000 # Luigi Morelli, 2025 Oct 14, dmdsieve and mprime, Stopped.
M( M( 44497 ) )U: k=64000000 # Gary Gostin, 2025 Nov 3, dmfs.
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( 86243 ) )U: k=10010000 # Luigi Morelli, 2025 Oct 22, dmdsieve and mprime, Stopped.
M( M( 86243 ) )U: k=15000000 # Mark Rodenkirch, 2025 Oct 30, dmdsieve.
M( M( 86243 ) )U: k=16000000 # Gary Gostin, 2025 Nov 3, dmfs.
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( 110503 ) )U: k=10000000 # Luigi Morelli, 2024 Dec 13, dmdsieve and mprime, 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( 132049 ) )U: k=7500000 # Luigi Morelli, 2025 Jan 03, dmdsieve and mprime, 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( 216091 ) )U: k=5000000 # Luigi Morelli, 2025 Apr 09, dmdsieve and mprime, 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( 756839 ) )U: k=2502297 # Luigi Morelli, 2025 Oct 03, dmdsieve and mprime, Continuing.
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( 859433 ) )U: k=2100045 # Luigi Morelli, 2025 Jul 11, dmdsieve and mprime, Stopped.
M( M( 1257787 ) )U: k=2000083 # DoubleMersennes.org, sieved k= 2000084 to 1000T - Continuing.
M( M( 1398269 ) )U: k=1500007 # DoubleMersennes.org, sieved k= 1500008 to 700T - Continuing.
M( M( 2976221 ) )U: k=350459 # DoubleMersennes.org, sieved k= 350460 to 400T - Continuing.
M( M( 3021377 ) )U: k=311212 # DoubleMersennes.org, sieved k= 311213 to 365T - Continuing.
M( M( 6972593 ) )U: k=114119 # DoubleMersennes.org, sieved k= 114120 to 1600T - Continuing.
M( M( 13466917 ) )U: k=100535 # DoubleMersennes.org, sieved k= 100536 to 302T - Continuing.
M( M( 20996011 ) )U: k=1112 # DoubleMersennes.org, sieved k= 1113 to 300T - Continuing.
M( M( 24036583 ) )U: k=1079 # DoubleMersennes.org, sieved k= 1080 to 331T - Continuing.
M( M( 25964951 ) )U: k=779 # DoubleMersennes.org, sieved k= 780 to 331T - Continuing.
M( M( 30402457 ) )U: k=719 # DoubleMersennes.org, sieved k= 720 to 400T - Continuing.
M( M( 32582657 ) )U: k=715 # DoubleMersennes.org, sieved k= 716 to 500T - Continuing.
M( M( 37156667 ) )U: k=683 # DoubleMersennes.org, sieved k= 684 to 2100T - Continuing.
M( M( 42643801 ) )U: k=647 # DoubleMersennes.org, sieved k= 648 to 2500T - Continuing.
M( M( 43112609 ) )U: k=512 # DoubleMersennes.org, sieved k= 513 to 500T - Continuing.
M( M( 57885161 ) )U: k=484 # DoubleMersennes.org, sieved k= 485 to 750T - Continuing.
M( M( 74207281 ) )U: k=283 # DoubleMersennes.org, sieved k= 284 to 1600T - Continuing.
M( M( 77232917 ) )U: k=148 # DoubleMersennes.org, sieved k= 149 to 2400T - Continuing.
M( M( 82589933 ) )U: k=340 # DoubleMersennes.org, sieved k= 341 to 3600T - Continuing.
M( M( 136279841 ) )U: k=40 # DoubleMersennes.org, sieved k= 41 to 5000T - Continuing.
Legend:
George Woltman released a fast program, mmff to factor small double mersenne numbers.
Mark Rodenkirch also released a specific siever called dmdsieve (and dmdsievecl that uses OpenCL on GPUs) from his compilation of sievers (Mtsieve) help searching for higher Mersenne numbers up to MM136,279,841.
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