Mersenne Prime/Current Status
== Currently known Mersenne Primes == The list of all known Mersenne primes is as follows:  {{Begin-Mersenne-Primes}} {{Mersenne-Prime |  1 | 2 | 3 | 1 | Known to {{AuthorRef|Euclid}} | }} {{Mersenne-Prime |  2 | 3 | 7 | 1 | Known to {{AuthorRef|Euclid}} | }} {{Mersenne-Prime |  3 | 5 | 31 | 2 | Known to {{AuthorRef|Euclid}} | }} {{Mersenne-Prime |  4 | 7 | 127 | 3 | Known to {{AuthorRef|Euclid}} | }} {{Mersenne-Prime |  5 | 13 | 8191 | 4 | 1456 | }} {{Mersenne-Prime |  6 | 17 | 131 \, 071 | 6 | 1588 | {{AuthorRef|Pietro Antonio Cataldi}} }} {{Mersenne-Prime |  7 | 19 | 524 \, 287 | 6 | 1588 | {{AuthorRef|Pietro Antonio Cataldi}} }} {{Mersenne-Prime |  8 | 31 | 2 \, 147 \, 483 \, 647 | 10 | 1772 | {{AuthorRef|Leonhard Paul Euler|}} }} {{Mersenne-Prime |  9 | 61 | 2 \cdotp 305 \times 10^{18} | 19 | 1883 | {{AuthorRef|Ivan Mikheevich Pervushin}} }} {{Mersenne-Prime | 10 | 89 | 6 \cdotp 189 \times 10^{26} | 27 | 1911 | {{AuthorRef|R.E. Powers}} }} {{Mersenne-Prime | 11 | 107 | 1 \cdotp 622 \times 10^{32} | 33 | 1914 | {{AuthorRef|R.E. Powers}} }} {{Mersenne-Prime | 12 | 127 | 1 \cdotp 701 \times 10^{38} | 39 | 1876 | {{AuthorRef|François Édouard Anatole Lucas}} }} {{Mersenne-Prime | 13 | 521 | 6 \cdotp 865 \times 10^{156} | 157 | 30 Jan 1952 | {{AuthorRef|Raphael Mitchel Robinson}} }} {{Mersenne-Prime | 14 | 607 | 5 \cdotp 311 \times 10^{182} | 183 | 30 Jan 1952 | {{AuthorRef|Raphael Mitchel Robinson}} }} {{Mersenne-Prime | 15 | 1279 | 1 \cdotp 041 \times 10^{385} | 386 | 25 Jun 1952 | {{AuthorRef|Raphael Mitchel Robinson}} }} {{Mersenne-Prime | 16 | 2203 | 1 \cdotp 476 \times 10^{663} | 664 | 7 Oct 1952 | {{AuthorRef|Raphael Mitchel Robinson}} }} {{Mersenne-Prime | 17 | 2281 | 4 \cdotp 461 \times 10^{686} | 687 | 9 Oct 1952 | {{AuthorRef|Raphael Mitchel Robinson}} }} {{Mersenne-Prime | 18 | 3217 | 2 \cdotp 591 \times 10^{968} | 969 | 8 Sept 1957 | {{AuthorRef|Hans Ivar Riesel}} }} {{Mersenne-Prime | 19 | 4253 | 1 \cdotp 908 \times 10^{1280} | 1281 | 3 Nov 1961 | {{AuthorRef|Alexander Hurwitz}} }} {{Mersenne-Prime | 20 | 4423 | 2 \cdotp 855 \times 10^{1331} | 1332 | 3 Nov 1961 | {{AuthorRef|Alexander Hurwitz}} }} {{Mersenne-Prime | 21 | 9689 | 4 \cdotp 782 \times 10^{2916} | 2917 | 11 May 1963 | {{AuthorRef|Donald Bruce Gillies}} }} {{Mersenne-Prime | 22 | 9941 | 3 \cdotp 461 \times 10^{2992} | 2993 | 16 May 1963 | {{AuthorRef|Donald Bruce Gillies}} }} {{Mersenne-Prime | 23 | 11 \, 213 | 2 \cdotp 814 \times 10^{3375} | 3376 | 2 Jun 1963 | {{AuthorRef|Donald Bruce Gillies}} }} {{Mersenne-Prime | 24 | 19 \, 937 | 4 \cdotp 315 \times 10^{6001} | 6002 | 4 Mar 1971 | {{AuthorRef|Bryant Tuckerman}} }} {{Mersenne-Prime | 25 | 21 \, 701 | 4 \cdotp 487 \times 10^{6532} | 6533 | 30 Oct 1978 | {{AuthorRef|Landon Curt Noll}} and {{AuthorRef|Ariel Nickel}} }} {{Mersenne-Prime | 26 | 23 \, 209 | 4 \cdotp 029 \times 10^{6986} | 6987 | 9 Feb 1979 | {{AuthorRef|Landon Curt Noll}} }} {{Mersenne-Prime | 27 | 44 \, 497 | 8 \cdotp 545 \times 10^{13 \, 394} | 13 \, 395 | 8 Apr 1979 | {{AuthorRef|Harry Lewis Nelson}} and {{AuthorRef|David Slowinski}} }} {{Mersenne-Prime | 28 | 86 \, 243 | 5 \cdotp 369 \times 10^{25 \, 961} | 25 \, 962 | 25 Sept 1982 | {{AuthorRef|David Slowinski}} }} {{Mersenne-Prime | 29 | 110 \, 503 | 5 \cdotp 219 \times 10^{33 \, 264} | 33 \, 265 | 28 Jan 1988 | {{AuthorRef|Walt Colquitt}} and {{AuthorRef|Luke Welsh}} }} {{Mersenne-Prime | 30 | 132 \, 049 | 5 \cdotp 127 \times 10^{39 \, 750} | 39 \, 751 | 19 Sept 1983 | {{AuthorRef|David Slowinski}} }} {{Mersenne-Prime | 31 | 216 \, 091 | 7 \cdotp 461 \times 10^{65 \, 049} | 65 \, 050 | 1 Sept 1985 | {{AuthorRef|David Slowinski}} }} {{Mersenne-Prime | 32 | 756 \, 839 | 1 \cdotp 741 \times 10^{227 \, 831} | 227 \, 832 | 19 Feb 1992 | {{AuthorRef|David Slowinski}} and {{AuthorRef|Paul Gage}} }} {{Mersenne-Prime | 33 | 859 \, 433 | 1 \cdotp 295 \times 10^{258 \, 715} | 258 \, 716 | 4 Jan 1994 | {{AuthorRef|David Slowinski}} and {{AuthorRef|Paul Gage}} }} {{Mersenne-Prime | 34 | 1 \, 257 \, 787 | 4 \cdotp 122 \times 10^{378 \, 631} | 378 \, 632 | 3 Sept 1996 | {{AuthorRef|David Slowinski}} and {{AuthorRef|Paul Gage}} }} {{Mersenne-Prime | 35 | 1 \, 398 \, 269 | 8 \cdotp 147 \times 10^{420 \, 920} | 420 \, 921 | 13 Nov 1996 | GIMPS / {{AuthorRef|Joel Armengaud}} }} {{Mersenne-Prime | 36 | 2 \, 976 \, 221 | 6 \cdotp 233 \times 10^{895 \, 931} | 895 \, 932 | 24 Aug 1997 | GIMPS / {{AuthorRef|Gordon Spence}} }} {{Mersenne-Prime | 37 | 3 \, 021 \, 377 | 1 \cdotp 274 \times 10^{909 \, 525} | 909 \, 526 | 27 Jan 1998 | GIMPS / {{AuthorRef|Roland Clarkson}} }} {{Mersenne-Prime | 38 | 6 \, 972 \, 593 | 4 \cdotp 371 \times 10^{2 \, 098 \, 959} | 2 \, 098 \, 960 | 1 Jun 1999 | GIMPS / {{AuthorRef|Nayan Hajratwala}} }} {{Mersenne-Prime | 39 | 13 \, 466 \, 917 | 9 \cdotp 249 \times 10^{4 \, 053 \, 945} | 4 \, 053 \, 946 | 14 Nov 2001 | GIMPS / {{AuthorRef|Michael Cameron}} }} {{Mersenne-Prime | 40 | 20 \, 996 \, 011 | 1 \cdotp 260 \times 10^{6 \, 320 \, 429} | 6 \, 320 \, 430 | 17 Nov 2003 | GIMPS / {{AuthorRef|Michael Shafer}} }} {{Mersenne-Prime | 41 | 24 \, 036 \, 583 | 2 \cdotp 994 \times 10^{7 \, 235 \, 732} | 7 \, 235 \, 733 | 15 May 2004 | GIMPS / {{AuthorRef|Josh Findley}} }} {{Mersenne-Prime | 42 | 25 \, 964 \, 951 | 1 \cdotp 222 \times 10^{7 \, 816 \, 229} | 7 \, 816 \, 230 | 18 Feb 2005 | GIMPS / {{AuthorRef|Martin Nowak}} }} {{Mersenne-Prime | 43 | 30 \, 402 \, 457 | 3 \cdotp 154 \times 10^{9 \, 152 \, 051} | 9 \, 152 \, 052 | 15 Dec 2005 | GIMPS / {{AuthorRef|Curtis Cooper}} and {{AuthorRef|Steven Boone}} }} {{Mersenne-Prime | 44 | 32 \, 582 \, 657 | 1 \cdotp 246 \times 10^{9 \, 808 \, 358} | 9 \, 808 \, 358 | 4 Sept 2006 | GIMPS / {{AuthorRef|Curtis Cooper}} and {{AuthorRef|Steven Boone}} }} {{Mersenne-Prime | 45 | 37 \, 156 \, 667 | 2 \cdotp 023 \times 10^{11 \, 185 \, 271} | 11 \, 185 \, 272 | 6 Sept 2008 | GIMPS / {{AuthorRef|Hans-Michael Elvenich}} }} {{Mersenne-Prime | 46 | 42 \, 643 \, 801 | 1 \cdotp 699 \times 10^{12 \, 837 \, 063} | 12 \, 837 \, 064 | 12 Apr 2009 | GIMPS / {{AuthorRef|Odd Magnar Strindmo}} }} {{Mersenne-Prime | 47 | 43 \, 112 \, 609 | 3 \cdotp 165 \times 10^{12 \, 978 \, 188} | 12 \, 978 \, 189 | 23 Aug 2008 | GIMPS / {{AuthorRef|Edson Smith}} }} {{Mersenne-Prime |  | 57 \, 885 \, 161 | 5 \cdotp 818 \times 10^{17 \, 425 \, 169} | 17 \, 425 \, 170 | 25 Jan 2013 | GIMPS / {{AuthorRef|Curtis Cooper}} }} {{Mersenne-Prime |  | 74 \, 207 \, 281 | 3 \cdotp 003 \times 10^{22 \, 338 \, 617} | 22 \, 338 \, 618 | 07 Jan 2016 | GIMPS / {{AuthorRef|Curtis Cooper}} }} {{Mersenne-Prime |  | 77 \, 232 \, 917 | 4 \cdotp 673 \times 10^{23 \, 249 \, 424} | 23 \, 249 \, 425 | 26 Dec 2017 | GIMPS / {{AuthorRef|Jon Pace}} }} {{Mersenne-Prime |  | 82 \, 589 \, 933 | 1 \cdotp 488 \times 10^{24 \, 862 \, 047} | 24 \, 862 \, 048 | 07 Dec 2018 | GIMPS / {{AuthorRef|Patrick Laroche}} }} {{End-Mersenne-Primes}} Note that the index numbers of Mersenne primes after no. $47$ are uncertain, as there may still be undiscovered Mersenne primes between the $47$th and $51$st. Not all numbers in that range have been explored yet.  == Also see == {{OEIS|A000668}} {{OEIS|A000043|order = index}} == Sources == * {{BookReference|Curious and Interesting Numbers|1986|David Wells|prev = Barlow's Prediction|next = Do Mersenne Primes Go On For Ever?}}: $28$ * {{BookReference|Calculus Gems|1992|George F. Simmons|prev = Definition:Mersenne Prime/Historical Note|next = Mathematician:David Slowinski}}: Chapter $\text {B}.2$: More about Numbers: Irrationals, Perfect Numbers and Mersenne Primes * {{BookReference|Curious and Interesting Numbers|1997|David Wells|ed = 2nd|edpage = Second Edition|prev = Barlow's Prediction|next = Do Mersenne Primes Go On For Ever?}}: $28$ * {{BookReference|The Penguin Dictionary of Mathematics|1998|David Nelson|ed = 2nd|edpage = Second Edition|prev = Definition:Mersenne Prime/Historical Note|next = Theorem of Even Perfect Numbers|entry = Mersenne numbers}} * {{BookReference|The Penguin Dictionary of Mathematics|2008|David Nelson|ed = 4th|edpage = Fourth Edition|prev = Definition:Mersenne Prime/Historical Note|next = Theorem of Even Perfect Numbers|entry = Mersenne numbers}} * {{BookReference|Taming the Infinite|2008|Ian Stewart|prev = Definition:Mersenne Prime/Historical Note|next = Mathematician:Diophantus of Alexandria}}: Chapter $7$: Patterns in Numbers: Euclid * {{BookReference|The Concise Oxford Dictionary of Mathematics|2014|Christopher Clapham|author2 = James Nicholson|ed = 5th|edpage = Fifth Edition|prev = Definition:Mersenne Prime|next = 1,257,787/Historical Note|entry = Mersenne prime}}