MERSENNE PRIMES


Mersenne Primes are of the form 2^p – 1, where p is itself prime.

The search was on when it was noticed that most of the early primes worked, but 2^11-1 was not prime.
The great Mersenne Prime race has been in progress now for over 600 years and shows no sign of ending.
Some of the more reasonably sized numbers are given in this list together with the date of discovery.

Who was Mersenne? .. History of Prime discoveries
JavaScript Applet - finds factors of all positive integers up to 2^53-1 = 9007199254740991
. Online Big Number Calculator!

Return to Integer Lists menu
2^p – 1: by pure brain-power

M1: 2^ 2-1 = 3
M2: 2^ 3-1
= 7
M3: 2^ 5-1 = 31
M4: 2^ 7-1 = 127 --- 2^11-1 = 2047 = 23 x 89
M5: 2^13-1 = 8191 .. .. .. .. .. .. .. [proved 1456]
M6: 2^17-1
= 131071 .. .. .. .. .. .. .. [proved 1588, Cataldi]
M7: 2^19-1 = 524287 .. .. .. .. .. .. .. [proved 1588, Cataldi]
--- 2^23-1 = 8388607 = 47 x 178481
--- 2^29-1 = 536870911 = 233 x 1103 x 2089

M8: 2^31-1
= 2147483647 .. .. .. .. .. .. .. [proved 1772, Euler]
--- 2^37-1 = 137438953471 = 223 x 616318177
--- 2^41-1 = 2199023255551 = 13367 x 164511353
--- 2^43-1 = 8796093022207 = 431 x 9719 x 2099863
--- 2^47-1 = 140737488355327 = 2351 x 4513 x 13264529
--- 2^53-1 = 9007199254740991 = 6361 x 69431 x 20394401
--- 2^59-1 = 576460752303423487 = 179951 x 3203431780337

2^p – 1: by mechanical calculators [Soviet calculators page]

M 9: 2^ 61-1 [proved 1883, Pervushin] = 2.306 x 10^18 (4 s.f.) = 2305843009213693951 M10: 2^ 89-1 [proved 1911, Powers] = 6.190 x 10^26 (4 s.f.) = 618970019642690137449562111 M11: 2^107-1 [proved 1914, Powers] = 1.623 x 10^32 (4 s.f.) = 162259276829213363391578010288127 M12: 2^127-1 [proved 1914, Lucas] = 1.701 x 10^38 (4 s.f.) = 170141183460469231731687303715884105727

2^p – 1: by electronic calculators


M13: 2^521-1 [proved 1952, Robinson] = 6.865 x 10^156 (4 s.f.) 
   = 68647976601306097149819007990813932172694353001433054093944634591855431 
   8339765605212255964066145455497729631139148085803712198799971664381257402 
   8291115057151 
   --- 
M14: 2^607-1 [proved 1952, Robinson] = 5.311 x 10^182 (4 s.f.) 
   = 53113799281676709868958820655246862732959311772703192319944413820040355 
   9860852242739162502265229285668889329486246501015346579337652707239409519 
   978766587351943831270835393219031728127 
   --- 
M15: 2^1279-1 [proved 1952, Robinson] = 1.041 x 10^385 (4 s.f.) 
   = 10407932194664399081925240327364085538615262247266704805319112350403608 
   0596733602980122394417323241848424216139542810077913835662483234649081399 
   0660567732076292412950938922034577318334966158355047295942054768981121169 
   3677147548478866962501384438260291732348885311160828538416585028255604666 
   2248318909188018470682222031405210266984354887329580288780508697361869007 
   14720710555703168729087 
   --- 
M16: 2^2203-1 [proved 1952, Robinson] = 1.476 x 10^663 (4 s.f.) 
   = 14759799152141802350848986227373817363120661453331697751477712164785702 
   9787807894937740733704938928938274850753149648047728126483876025919181446 
   3365330269540496961201113430156902396093989090226259326935025281409614983 
   4993882228314485986018343185362309237726413902094902318364468996082107954 
   8296376309423663094541083279376990539998245718632294472963641889062337217 
   1723742105636440368218459649632948538696905872650486914434637457507280441 
   8236768135178520993486608471725794084223166780976702240119902801704748944 
   8742692474210882353680848507250224051945258754287534997655857267022963396 
   2575212637477897785501552646522609988869914013540483809865681250419497686 
   697771007 
   ---  
M17: 2^2281-1 [proved 1952, Robinson] = 4.461 x 10^686 (4 s.f.) 
   = 44608755718375842957115170640210180988620863241285990111199121996340468 
   5792820473369112545269003989026153245931124316702395758705693679364790903 
   4974611470710652541933539381249782263079473124107988748690400702793284288 
   1031175484410809487825249486676096958699812898264587759602897917153696250 
   3068429617331702184750324583009171832104916050157628886606372145501702225 
   9251252240768296054271735739648129952505694124807207384768552936816667128 
   4483119087762060678666386219024011857073683190188647922581041471407893538 
   6562497968178729127629594924411960961386713946279899275006954917139758796 
   0612238033935373810346664944029510520590479686932553886479304409251041868 
   17009640171764133172418132836351 
   ---  
M18: 2^3217-1 [proved 1957, Riesel] = 2.591 x 10^968 (4 s.f.) 
   = 25911708601320262777624676792244153094181888755312542730397492316187401 
   9266586362086201209516800483406550695241733194177441689509238807017410377 
   7095975120423130666240829163535179523111861548622656045476911275958487756 
   1056875793119101771140882625215384903583040118507211642474746182303147139 
   8340229288074545677907941037288235820705892351068433882986888616658650280 
   9276920803396058693087905004095037098759021190183719916209940025689351131 
   3654882973911265679730324198651725011641270350970542777347797234982167644 
   3446668383119322540099648994051790241624056519054483690809616061625743042 
   3617218633394158524264312087372665919620617535357488928945996291951830826 
   2186085340093793283942026186658614250325145077309627423537682293864940712 
   7700846077124211823080804139298087057504713825264571448379371125032081826 
   1265666490842516994539518877896136502484057393785945994443352311882801236 
   6040626246860921215034993758478229223714433962885848593821573882123239368 
   7046160677362909315071 
   ---  
M19: 2^4253-1 [proved 1961, Hurwitz] = 1.908 x 10^1280 (4 s.f.) 
   = 19079700752443907380746804296952917366935699474994017739474188267352897 
   9787005053706368049835514900244303495954950709725762186311224148828811920 
   2169045422069607446661693642211952895384368453902501686639328388051920551 
   3715439091266652753300730929268753909225704336251785736662469997540237546 
   2954490293259233303137330643531556539739921926201438606439020075174723029 
   0568382725050515719675946083500634044959776606562690208239608255670123441 
   8990892795664601199805798854863010763738099351982658238978188813570540865 
   3045219655801758081251164080554609057468028203308718724654081055323215860 
   1896113912960304711084431467456719677663089258585472715073115637651710083 
   1824864711009761489031356285654178415488174314603390960273794738505535596 
   0331855614540900081456378659068370317267696980001187750995491090350108417 
   0509179915621679722810701613059725180448720483313063837150948549384157385 
   4989460607072258473797817668642213435452698944302835364403718737538539783 
   8259511833166416134323695660367676897722287918773420968982326089026150031 
   5154241654621113375274311548906663273749214462768335645197767976338755035 
   4866509391455648203148224888312702377703966770797655985733335701372734207 
   9099064400455741830654320379350833236245819348824064783585692924881021978 
   332974949906122664421376034687815350484991 
   ---  
M20: 2^4423-1 [proved 1961, Hurwitz] = 2.855 x 10^1331 (4 s.f.) 
   = 28554254222827961390156356610216400832616423864470288919924745660228440 
   0390600653875954571505539843239754513915896150297878399377056071435169747 
   2211079887911982009884775313392142827720160590099045866862549890848157354 
   2248040902234429758835252600438389063261612407631738741688114859248618836 
   1873904175783145696016919574390765598280188599035578448591077683677175520 
   4340742877265780062667596159707595213278285556627816783856915818444364448 
   1251156242813674249045936321281018027609608811140100337757036354572512092 
   4073646921576797146199387619296560302680261790118132925012323046444438622 
   3088779246093737730124816816724244936744744885377701557830068808526481615 
   1306714481479028836666406225727466527578712737464923109637500117090189078 
   6263324619578795731425693805073056119677580338084333381987500902968831935 
   9130952698213111413223933564901784887289822881562826008138312961436638459 
   4543114404375382154287127774560644785856415921332844358020642271469491309 
   1762716447041689678070096773590429808909616750452927258000843500344831628 
   2970899027286499819943876472345742762637296948483047509171741861811306885 
   1879274862261229334136892805663438446664632657247616727566083910565052897 
   5713899320211121495795311427946254553305387067821067601768750977866100460 
   0146021384084480212250536890547937420030957220967329547507217181155318713 
   10231057902608580607 
   ---  
M21: 2^9689-1 [proved 1963, Gillies] = 4.782 x 10^2916 (4 s.f.) 
   = 47822027880546120295283929866000590974149717240223650085133451099183789 
   5094266297027892768611270789458682472098152425631930658505267683408748083 
   4429433264797425893247623688331021633208954847354805799943341309825989013 
   7438061871095810431486808137783215304967156015632826244140403981432076220 
   3627219040859079053720347525610556407157926386787524098557335652265610854 
   2128577321057879052328865035355873615679363655889925711574420153832091752 
   4228430469188114274006621355593035168537039768126863857503762277879495805 
   8208183126172570100349820651232987267723348951095346937568303703837399969 
   6771585788905639115522613405495707184524158219208223766442059014593330657 
   0097221539623768534237704861385780897756213011678112991664073617466066978 
   0818675796691467124607371290420058840892318638773788767529288695379706698 
   0967406053530122853539036965490224784924649007954898678503314655546475504 
   5016861873548669643745526141206407829496224520277889621386026659331476876 
   9632208950427879162465151931232783175655377937719452467339581928148666857 
   6384019590720179413349582970319393884388810494546040342087536563628332152 
   0731816143007217693714262385175405208452146653133011835519625918495589384 
   9902534878037671647707393063443684008446825593744345169031599934913766463 
   8968972614199015304906547819056227171224947070739716300953775743441307920 
   5018635322344665456456957743318850449782501486634673721303920998948521451 
   9099823287877248665051301081676990289251871925006694721570653621624869624 
   0569256865554296221552211560427778662545936998801070186162601476474293459 
   8301836512733634627326758830607014103592548291497743392971736807656109595 
   9991130918978823835013163567266143596921823997719693387439540399662367558 
   0528211207136396370858056051160781770985452576988032333812939272752101944 
   6295274903138355519851970959288852364153017892186751410145412030961912709 
   3436903952209828031766894206132557234964363840305648734929088422378629288 
   7472231219032385281034091824306618947740727265524284893304474861454942076 
   7990417394471658382816714104358312067905019145273262873703399747072060168 
   8256282740427017032260672798034347932642573009183981307771932245539476396 
   0606588214326603156141490740557698055166263044447583756711516490181193442 
   2368594241518437953893357654321299440548553451558592734245618251468137147 
   2060628778102124092370802149229834963517952727030296297015692768651163505 
   0080407282674252362644695710769768866137302789313609674382719017385508484 
   6633734761208435679830650595580729351106375442408073506670829872337797688 
   7493898358452309563899612061631863439196711208646438464947096323007272920 
   0912586147267999762496709852769503535733924416202657720741248683592202828 
   9833111408339233024339177979769903114258436193509367544838111944088127633 
   8808420445180491245438388418080094527562666805762895476338464130510775377 
   3247082495804533355717481965025070819730466422826105697510564289798951182 
   192885976352229053898948737614642139910911535864505818992696826225754111 
   ---  
M22: 2^9941-1 [proved 1963, Gillies] = 3.461 x 10^2992 (4 s.f.) 
   = 34608828249085121524296039576741331672262866890023854779048928344500622 
   0809834114464364375544153707533664486747635050186414707093323739706083766 
   9040422926578964799370976035846955231904548491005030414980981854028350715 
   9683562232941968059762281334544739720849260904855192770626054911793590389 
   0607959811638387214329942787636330953774381948448664711249676857988881722 
   1203300082146968446495614699719412692128433620646331385953757720046244202 
   9064681326087558257488470489384243989270236884978643063093004422939603370 
   0105465953863020090730439444822025590974067005973305707995078329631309387 
   3988508019841625863519452291304256293667985958749572103117374779641889506 
   0701941717506001937152430032363631934265798516236047451209089864707430780 
   3622983070381934454864937566479918042587755749738339033157350828910293923 
   5935275861718501994255483467186107454877243988072960624491194006668011282 
   3824095816458261761861746604034802056466823143718255492784779380991749580 
   2552633233265364577438941508489539699028185300578708762293298033382857354 
   1922825902216960266553221083478960205168654601146673798130605624748005507 
   1718250333737502267307344178512950738594330684340802698228963986562732597 
   1753720872956490728302897497713583308679515087108592167432185229188116706 
   3744849649854909443054127744407940798953985746945277213216658088575436047 
   7408842913327292948696897496141614919739845432835894324473601387609643750 
   5146992150326837445270717186840918321709483693962800611845937461435890688 
   1119025310187359531915610731919607115059848807002708870584274960520306319 
   4191166922106176157609367241948160625989032127984748081075324382632093913 
   7964446657006013912783603230022674342951943256072806612601193787194051514 
   9755518754925213426439464596385396491330969777653332940182215800318288927 
   8072368602128982710306618115118964131893657845400296860012420391376964670 
   1839835949541124845655973124607377987770920717067108245037074572201550158 
   9959176624495776800680248297667392039299541016422477644567122214980365792 
   7708412925555542817045572430846389988129960519227313987291200902060882060 
   7337620758922994736664058974270358117868798756943150786544200556034696253 
   0939965395593231046643003914646580545296501404001942389755267553476824862 
   4631951431493188170905972588780111850281190559073677771187432814088678674 
   2863021082751492584771012964518336519797173751709005056736459646963553313 
   6981929600026738958328929912673834572698032599895599750117666420104288854 
   6085699446442834195232948787488410595750197438786353119204210855804692460 
   5825338329677719469114599019213249849688100211899682849413315731640563047 
   2548086892182344253819959038385241278684083347961141997010179297835565365 
   0755329138298654246225346827207503606740745956958127383748717825918527473 
   1649705820951813129055192427102805730231455547936284990105092960558497123 
   7797898492183999703741589767415483070862914548472453672457262245013147999 
   2681684310464449439022250504859250834761894788889552527898400988196200014 
   8685756402331365091456281271913548582750839078914699790194262248837894635 
   51  

 2^p – 1: Remaining values of p discovered to date:
Mersenne 2^p - 1 Digits Date Researcher
M23:
M24:
M25:
M26:
M27:
M28:
M29:
M30:
M31:
M32:
M33:
M34:
M35:
M36:
M37:
M38:
M39:
M40:
M41:
M42:
M43:
M44:
M45:
M46:
M47:
2^ 11,213 - 1
2^ 19,937 - 1
2^ 21,701 - 1
2^ 23,209 - 1
2^ 44,497 - 1
2^ 86,243 - 1
2^ 110,503 - 1
2^ 132,049 - 1
2^ 216,091 - 1
2^ 756,839 - 1
2^ 859,433 - 1
2^ 1,257,787 - 1
2^ 1,398,269 - 1
2^ 2,976,221 - 1
2^ 3,021,377 - 1
2^ 6,972,593 - 1
2^13,466,917 - 1
2^20,996,011 - 1
2^24,036,583 - 1
2^25,964,951 - 1
2^30,402,457 - 1
2^32,582,657 - 1
2^37,156,667 - 1
2^43,112,609 - 1
2^42,643,801 - 1
3,376 digits
6,002 digits
6,533 digits
6,987 digits
13,395 digits
25,962 digits
33,265 digits
39,751 digits
65,050 digits
227,832 digits
258,716 digits
378,632 digits
420,921 digits
895,932 digits
909,526 digits
2,098,960 digits
4,053,946 digits
6,320,430 digits
7,235,733 digits
7,816,230 digits
9,152,052 digits
9,808,358 digits
11,185,272 digits
12,978,189 digits
12,837,064 digits
1963
1971
1978
1979
1979
1982
1991
1983
1985
1992
1994
1996
1996
1997
1998
1999
5 Dec 2001
17 Nov 2003
15 May 2004
18 Feb 2005
15 Dec 2005
4 Sept 2006
6 Sep 2008
23 Aug 2008
12 April 2009
Gillies
Tuckerman
Noll/Nickel
Noll
Nelson/Slowinski
Slowinski
Colquitt/Welsh
Slowinski
Slowinski
Slowinski/Gage
Slowinski/Gage
Slowinski/Gage
Armengaud et al
Spence et al
Clarkson et al
Hajratwala et al
Michael Cameron, Canada
Michael Shafer, USA
Josh Findley, USA
Martin Nowak, Germany
Dr Cooper/Dr Boone, USA
Dr Cooper/Dr Boone, USA
Hans-Michael Elvenich, Ger
Edsom Smith, UCLA, USA
Magnar Strindmo, Norway

M48:

2^57,885,161 - 1

17,425,170 digits

5 Feb 2013

Curtis Cooper, Missouri


See all the digits of M43: click here! (9 Mb)
See all the digits of M47: click here! (16.5 Mb)

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