MERSENNE
PRIMES
| MERSENNE
PRIMES |
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Mersenne
Primes are of the form 2^p – 1, where p is
itself prime. |
• Return
to Integer Lists menu2^p – 1: by pure brain-power 2^p – 1: by mechanical calculators [Soviet calculators page] 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: M23: 2^ 11 213-1 has 3 376 digits [proved 1963, Gillies] M24: 2^ 19 937-1 has 6 002 digits [proved 1971, Tuckerman] M25: 2^ 21 701-1 has 6 533 digits [proved 1978, Noll/Nickel] M26: 2^ 23 209-1 has 6 987 digits [proved 1979, Noll] M27: 2^ 44 497-1 has 13 395 digits [proved 1979, Nelson/Slowinski] M28: 2^ 86 243-1 has 25 962 digits [proved 1982, Slowinski] M29: 2^ 110 503-1 has 33 265 digits [proved 1991, Colquitt/Welsh] M30: 2^ 132 049-1 has 39 751 digits [proved 1983, Slowinski] M31: 2^ 216 091-1 has 65 050 digits [proved 1985, Slowinski] M32: 2^ 756 839-1 has 227 832 digits [proved 1992, Slowinski/Gage] M33: 2^ 859 433-1 has 258 716 digits [proved 1994, Slowinski/Gage] M34: 2^ 1 257 787-1 has 378 632 digits [proved 1996, Slowinski/Gage] M35: 2^ 1 398 269-1 has 420 921 digits [proved 1996, Armengaud et al] M36: 2^ 2 976 221-1 has 895 932 digits [proved 1997, Spence et al] M37: 2^ 3 021 377-1 has 909 526 digits [proved 1998, Clarkson et al] M38? 2^ 6 972 593-1 has 2 098 960 digits [proved 1999, Hajratwala et al] M39? 2^13 466 917-1 has 4 053 946 digits [5th Dec 2001, Michael Cameron, Canada] M40? 2^20 996 011-1 has 6 320 430 digits [17th Nov 2003, Michael Shafer, USA] • See all the digits of M44: click here! (9827 kb) ..The elusive 10,000,000 digit prime number is still up for grabs! ..There must be more out there! • Keep in touch with the latest developments: ..GIMPS - Great Internet Mersenne Prime Search for the complete listing, history, and links to related sites • Why do people look for prime numbers? ..Some answers • Return to Integer Lists menu |
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