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The first 600 PRIME NUMBERS (up to 4409)	POWERS OF 2 (up to 2^222)		MERSENNE PRIMES (up to 2^82,589,933 – 1)		PYTHAGOREAN TRIPLES (up to 2100)
			Who was Mersenne? (1588-1648) Prime Factorization Calculator History of Prime discoveries - Why?		Encyclopaedia of Integer Sequences
	MERSENNE PRIMES: 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* 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 M48 M49 M50 M51 *Provisional ranking, not all candidates between M45 and M49 have been eliminated.	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 2^57,885,161 – 1 2^74,207,281 – 1 2^77,232,917 – 1 2^82,589,933 – 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 17,425,170 digits 22,338,618 digits 23,249,425 digits 24,862,048 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 5 Feb 2013 7 Jan 2016 26 Dec 2017 21 Dec 2018	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 Curtis Cooper, Missouri Curtis Cooper, Missouri GIMPS GIMPS