MathWorld Headline News

47th Known Mersenne Prime Apparently Discovered

By Eric W. Weisstein

June 7, 2009--Less than a year after the 45th and 46th known Mersenne primes were discovered, Great Internet Mersenne Prime Search (GIMPS) project organizer George Woltman is reporting in a June 7 email to the GIMPS mailing list that a new Mersenne number has been flagged as prime and reported to the project's server. If verified, this would be the 47th Mersenne prime discovered. A verification run on the number has been started, and more details will be made available when confirmation of the discovery has been completed. The prime was apparently discovered in April, but was not noticed due to a configuration problem with the server that prevented a notification email being sent to the search organizers.

[Postscript: The prime has now been officially verified and announced to be M42643801, which has 12837064 decimal digits, making it the 46th known Mersenne prime ranked by size, and hence only the second largest. It was found by Norwegian GIMPS participant Odd Magnar Strindmo.]

Mersenne numbers are numbers of the form Mn = 2n - 1, giving the first few as 1, 3, 7, 15, 31, 63, 127, .... Interestingly, the definition of these numbers therefore means that the nth Mersenne number is simply a string of n 1s when represented in binary. For example, M7 = 27 - 1 = 127 = 11111112 is a Mersenne number. In fact, since 127 is also prime, 127 is also a Mersenne prime.

The study of such numbers has a long and interesting history, and the search for Mersenne numbers that are prime has been a computationally challenging exercise requiring the world's fastest computers. Mersenne primes are intimately connected with so-called perfect numbers, which were extensively studied by the ancient Greeks, including by Euclid. A complete list of indices n of the previously known Mersenne primes is given in the table below (as well as by sequence A000043 in Neil Sloane's On-Line Encyclopedia of Integer Sequences). The last of these has a whopping 12,978,189 decimal digits. However, note that the region between the 39th and 40th known Mersenne primes has not been completely searched, so it is not known if M20,996,011 is actually the 40th Mersenne prime.

The following table summarizes all known Mersenne primes.

#pdigitsyeardiscoverer (reference)value
51341461Reguis (1536), Cataldi (1603)8191
61761588Cataldi (1603)131071
71961588Cataldi (1603)524287
831101750Euler (1772)2147483647
961191883Pervouchine (1883), Seelhoff (1886)2305843009213693951
1089271911Powers (1911)618970019642690137449562111
11107331913Powers (1914)162259276829213363391578010288127
12127391876Lucas (1876)170141183460469231731687303715884105727
13521157Jan. 30, 1952Robinson (1954)68647976601306097149...12574028291115057151
14607183Jan. 30, 1952Robinson (1954)53113799281676709868...70835393219031728127
151279386Jun. 25, 1952Robinson (1954)10407932194664399081...20710555703168729087
162203664Oct. 7, 1952Robinson (1954)14759799152141802350...50419497686697771007
172281687Oct. 9, 1952Robinson (1954)44608755718375842957...64133172418132836351
183217969Sep. 8, 1957Riesel25911708601320262777...46160677362909315071
1942531281Nov. 3, 1961Hurwitz19079700752443907380...76034687815350484991
2044231332Nov. 3, 1961Hurwitz28554254222827961390...10231057902608580607
2196892917May 11, 1963Gillies (1964)47822027880546120295...18992696826225754111
2299412993May 16, 1963Gillies (1964)34608828249085121524...19426224883789463551
23112133376Jun. 2, 1963Gillies (1964)28141120136973731333...67391476087696392191
24199376002Mar. 4, 1971Tuckerman (1971)43154247973881626480...36741539030968041471
25217016533Oct. 30, 1978Noll and Nickel (1980)44867916611904333479...57410828353511882751
26232096987Feb. 9, 1979Noll (Noll and Nickel 1980)40287411577898877818...36743355523779264511
274449713395Apr. 8, 1979Nelson and Slowinski85450982430363380319...44867686961011228671
288624325962Sep. 25, 1982Slowinski53692799550275632152...99857021709433438207
2911050333265Jan. 28, 1988Colquitt and Welsh (1991)52192831334175505976...69951621083465515007
3013204939751Sep. 20, 1983Slowinski51274027626932072381...52138578455730061311
3121609165050Sep. 6, 1985Slowinski74609310306466134368...91336204103815528447
32756839227832Feb. 19, 1992Slowinski and Gage17413590682008709732...02603793328544677887
33859433258716Jan. 10, 1994Slowinski and Gage12949812560420764966...02414267243500142591
341257787378632Sep. 3, 1996Slowinski and Gage41224577362142867472...31257188976089366527
351398269420921Nov. 12, 1996Joel Armengaud/GIMPS81471756441257307514...85532025868451315711
362976221895832Aug. 24, 1997Gordon Spence/GIMPS62334007624857864988...76506256743729201151
373021377909526Jan. 27, 1998Roland Clarkson/GIMPS12741168303009336743...25422631973024694271
3869725932098960Jun. 1, 1999Nayan Hajratwala/GIMPS43707574412708137883...35366526142924193791
39134669174053946Nov. 14, 2001Michael Cameron/GIMPS92494773800670132224...30073855470256259071
40209960116320430Nov. 17, 2003Michael Shafer/GIMPS12597689545033010502...94714065762855682047
41?240365837235733May 15, 2004Josh Findley/GIMPS29941042940415717208...67436921882733969407
42?259649517816230Feb. 18, 2005Martin Nowak/GIMPS12216463006127794810...98933257280577077247
43?304024579152052Dec. 15, 2005Curtis Cooper and Steven Boone/GIMPS31541647561884608093...11134297411652943871
44?325826579808358Sep. 4, 2006Curtis Cooper and Steven Boone/GIMPS12457502601536945540...11752880154053967871
45?3715666711185272Sep. 6, 2008Hans-Michael Elvenich/GIMPS20225440689097733553...21340265022308220927
46?4264380112837064Jun. 12, 2009Odd Magnar Strindmo/GIMPS16987351645274162247...84101954765562314751
47?4311260912978189Aug. 23, 2008Edson Smith/GIMPS31647026933025592314...80022181166697152511

The 13 largest known Mersenne primes (including the latest candidate) have all been discovered by GIMPS, which is a distributed computing project being undertaken by an international collaboration of volunteers. Thus far, GIMPS participants have tested and double-checked all exponents n below 18,000,949, while all exponents below 26,181,803 have been tested at least once. The candidate prime has yet to be verified by independent software running on different hardware. If confirmed, GIMPS will make an official press release that will reveal the number and the name of the lucky discoverer.


Caldwell, C. K. "The Largest Known Primes."

GIMPS: The Great Internet Mersenne Prime Search. "47th Known Mersenne Prime Found!"

GIMPS: The Great Internet Mersenne Prime Search Status.

Woltman, G. "New Mersenne Prime?" Message to The Great Internet Mersenne Prime Search List. Jun. 4, 2009.

Woltman, G. "New Mersenne Prime?" Message to The Great Internet Mersenne Prime Search List. Jun. 7, 2009.

Woltman, G. "It's Official - 47th Mersenne Prime Found" Message to The Great Internet Mersenne Prime Search List. Jun. 12, 2009.