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	PUISSANCE de 2
Débutants Puissance	Nombres de Fermat et Mersenne		Glossaire Puissance
INDEX Puissance Décomposition Puissance de 2	FERMAT (biographie)	MERSENNE (biographie)
	Nombres de Fermat	Nombres de Mersenne
	Valeurs et facteurs	Valeurs et facteurs
	Diviseurs	Mersenne – Records
		Mersenne composés
		Carol et Kynea
		Williams
	Sommaire de cette page >>> Table des facteurs jusqu'à 200

NOMBRES de MERSENNE

M_n = 2ⁿ – 1

Table de ces nombres pour n de 2 à 200

Premiers ou composés

n est l'indice, coloré si n est premier.

M est la valeur du nombre de Mersenne.

La colonne "facteurs" est en jaune si le nombre de Mersenne est premier.

Le chapeau ^ signifie puissance.

Voir Factorisation des nombres de Mersenne / Table des puissances de 2

TABLE des nombres de Mersenne avec leurs facteurs

n	M = 2^n – 1	Facteurs	Commentaires
1	1	1
2	3	3
3	7	7
4	15	3×5	2^4 – 1 = (2^2 – 1) (2^2 + 1) >>>
5	31	31
6	63	3^2×7	2^6 – 1 = (2^3 – 1) (2^3 + 1)
7	127	127
8	255	3×5×17	2^8 – 1 = (2^4 – 1) (2^4 + 1)
9	511	7×73	2^9 – 1 divisible par 2^3 – 1 = 7 >>>
10	1023	3×11×31	2^10 – 1 divisible par 2^5 – 1 = 31 >>>
11	2047	23×89
12	4095	3^2×5×7×13
13	8191	8191	Curiosités
14	16383	3×43×127
15	32767	7×31×151
16	65535	3×5×17×257
17	131071	131071
18	262143	3^3×7×19×73
19	524287	524287
20	1048575	3×5^2×11×31×41
21	2097151	7^2×127×337
22	4194303	3×23×89×683
23	8388607	47×178481
24	16777215	3^2×5×7×13×17×241
25	33554431	31×601×1801
26	67108863	3×2731×8191
27	134217727	7×73×262657
28	268435455	3×5×29×43×113×127
29	536870911	233×1103×2089
30	1073741823	3^2×7×11×31×151×331
31	2147483647	2147483647	Voir Calcul Frénicle et Fermat
32	4294967295	3×5×17×257×65537
33	8589934591	7×23×89×599479
34	17179869183	3×131071×43691
35	34359738367	31×71×127×122921
36	68719476735	3^3×5×7×13×19×37×73×109
37	137438953471	223×616318177
38	274877906943	3×524287×174763
39	549755813887	7×79×121369×8191
40	1099511627775	3×5^2×11×17×31×41×61681
41	2199023255551	164511353×13367
42	4398046511103	3^2×7^2×43×127×337×5419
43	8796093022207	431×2099863×9719
44	17592186044415	3×5×23×89×397×683×2113
45	35184372088831	7×31×73×151×631×23311
46	70368744177663	3×47×2796203×178481
47	140737488355327	13264529×2351×4513
48	281474976710655	3^2×5×7×13×17×97×241×257×673
49	562949953421311	127×4432676798593

50	1125899906842623	3×11×31×251×601×4051×1801
51	2251799813685247	7×103×11119×2143×131071
52	4503599627370495	3×5×53×157×1613×2731×8191
53	9007199254740991	69431×20394401×6361
54	18014398509481983	3^4×7×19×73×262657×87211
55	36028797018963967	23×31×89×881×201961×3191
56	72057594037927935	3×5×17×29×43×113×127×15790321
57	144115188075855871	7×1212847×32377×524287
58	288230376151711743	3×59×233×1103×3033169×2089
59	576460752303423487	3203431780337×179951
60	1152921504606846975	3^2×5^2×7×11×13×31×41×61×151×331×1321
61	2305843009213693951	2305843009213693951 >>>
62	4611686018427387903	3×2147483647×715827883
63	9223372036854775807	7^2×73×127×337×649657×92737
64	18446744073709551615	3×5×17×257×641×6700417×65537
65	36893488147419103231	31×145295143558111×8191
66	73786976294838206463	3^2×7×23×67×89×683×599479×20857
67	147573952589676412927	761838257287×193707721 >>>
68	295147905179352825855	3×5×137×953×26317×131071×43691
69	590295810358705651711	7×47×10052678938039×178481
70	1180591620717411303423	3×11×31×43×71×127×281×86171×122921
71	2361183241434822606847	48544121×228479×212885833
72	4722366482869645213695	3^3×5×7×13×17×19×37×73×109×241×433×38737
73	9444732965739290427391	439×9361973132609×2298041
74	18889465931478580854783	3×223×25781083×616318177×1777
75	37778931862957161709567	7×31×151×601×10567201×100801×1801
76	75557863725914323419135	3×5×229×457×525313×524287×174763
77	151115727451828646838271	23×89×127×581283643249112959
78	302231454903657293676543	3^2×7×79×22366891×121369×2731×8191
79	604462909807314587353087	202029703×1113491139767×2687
80	1208925819614629174706175	3×5^2×11×17×31×41×257×4278255361×61681
81	2417851639229258349412351	7×73×97685839×71119×2593×262657
82	4835703278458516698824703	3×83×164511353×8831418697×13367
83	9671406556917033397649407	167×57912614113275649087721
84	19342813113834066795298815	3^2×5×7^2×13×29×43×113×127×337×1429×14449×5419
85	38685626227668133590597631	31×9520972806333758431×131071
86	77371252455336267181195263	3×431×2932031007403×2099863×9719
87	154742504910672534362390527	7×233×1103×9857737155463×4177×2089
88	309485009821345068724781055	3×5×17×23×89×353×397×683×2931542417×2113
89	618970019642690137449562111	618970019642690137449562111
90	1237940039285380274899124223	3^3×7×11×19×31×73×151×331×631×18837001×23311
91	2475880078570760549798248447	127×911×23140471537×112901153×8191
92	4951760157141521099596496895	3×5×47×277×1013×1657×30269×2796203×178481
93	9903520314283042199192993791	7×658812288653553079×2147483647
94	19807040628566084398385987583	3×283×165768537521×13264529×2351×4513
95	39614081257132168796771975167	31×191×30327152671×420778751×524287
96	79228162514264337593543950335	3^2×5×7×13×17×97×193×241×257×673×22253377×65537
97	158456325028528675187087900671	13842607235828485645766393×11447
98	316912650057057350374175801343	3×43×127×4363953127297×4432676798593
99	633825300114114700748351602687	7×23×73×89×199×33057806959×153649×599479

100	1267650600228229401496703205375	3×5^3×11×31×41×101×251×601×268501×8101×4051×1801
101	2535301200456458802993406410751	7432339208719×341117531003194129
102	5070602400912917605986812821503	3^2×7×103×307×11119×2143×6529×2857×131071×43691
103	10141204801825835211973625643007	3976656429941438590393×2550183799
104	20282409603651670423947251286015	3×5×17×53×157×1613×308761441×858001×2731×8191
105	40564819207303340847894502572031	7^2×31×71×127×151×337×152041×29191×106681×122921
106	81129638414606681695789005144063	3×107×28059810762433×69431×20394401×6361
107	162259276829213363391578010288127	162259276829213363391578010288127
108	324518553658426726783156020576255	3^4×5×7×13×19×37×73×109×246241×279073×262657×87211
109	649037107316853453566312041152511	745988807×870035986098720987332873
110	1298074214633706907132624082305023	3×11^2×23×31×89×683×881×48912491×201961×3191×2971
111	2596148429267413814265248164610047	7×223×319020217×26295457×321679×616318177
112	5192296858534827628530496329220095	3×5×17×29×43×113×127×257×54410972897×5153×15790321
113	10384593717069655257060992658440191	1066818132868207×23279×65993×1868569×3391
114	20769187434139310514121985316880383	3^2×7×571×160465489×1212847×32377×524287×174763
115	41538374868278621028243970633760767	31×47×2646507710984041×4036961×14951×178481
116	83076749736557242056487941267521535	3×5×59×233×1103×107367629×536903681×3033169×2089
117	166153499473114484112975882535043071	7×73×79×937×7830118297×86113×6553×121369×8191
118	332306998946228968225951765070086143	3×1824726041×3203431780337×179951×37171×2833
119	664613997892457936451903530140172287	127×239×62983048367×131105292137×20231×131071
120	1329227995784915872903807060280344575	3^2×5^2×7×11×13×17×31×41×61×151×241×331×1321×4562284561×61681
121	2658455991569831745807614120560689151	23×89×727×1786393878363164227858270210279
122	5316911983139663491615228241121378303	3×768614336404564651×2305843009213693951
123	10633823966279326983230456482242756607	7×177722253954175633×3887047×164511353×13367
124	21267647932558653966460912964485513215	3×5×384773×49477×5581×8681×2147483647×715827883
125	42535295865117307932921825928971026431	31×601×4710883168879506001×269089806001×1801
126	85070591730234615865843651857942052863	3^3×7^2×19×43×73×127×337×77158673929×649657×92737×5419
127	170141183460469231731687303715884105727	170141183460469231731687303715884105727 Le plus grand connu sans ordinateur >>>
128	340282366920938463463374607431768211455	3×5×17×257×641×67280421310721×274177×6700417×65537
129	680564733841876926926749214863536422911	7×431×11053036065049294753459639×2099863×9719
130	1361129467683753853853498429727072845823	3×11×31×131×145295143558111×409891×7623851×2731×8191
131	2722258935367507707706996859454145691647	263×10350794431055162386718619237468234569
132	5444517870735015415413993718908291383295	3^2×5×7×13×23×67×89×397×683×4327489×312709×599479×20857×2113
133	10889035741470030830827987437816582766591	127×163537220852725398851434325720959×524287
134	21778071482940061661655974875633165533183	3×6713103182899×761838257287×193707721×7327657
135	43556142965880123323311949751266331066367	7×31×73×151×271×631×49971617830801×348031×262657×23311
136	87112285931760246646623899502532662132735	3×5×17^2×137×953×2879347902817×354689×26317×131071×43691
137	174224571863520493293247799005065324265471	32032215596496435569×5439042183600204290159
138	348449143727040986586495598010130648530943	3^2×7×47×139×168749965921×10052678938039×2796203×178481
139	696898287454081973172991196020261297061887	123876132205208335762278423601×5625767248687
140	1393796574908163946345982392040522594123775	3×5^2×11×29×31×41×43×71×113×127×281×47392381×7416361×86171×122921
141	2787593149816327892691964784081045188247551	7×646675035253258729×4375578271×13264529×2351×4513
142	5575186299632655785383929568162090376495103	3×13952598148481×48544121×56409643×228479×212885833
143	11150372599265311570767859136324180752990207	23×89×158822951431×5782172113400990737×724153×8191
144	22300745198530623141535718272648361505980415	3^3×5×7×13×17×19×37×73×97×109×241×257×433×577×673×487824887233×38737
145	44601490397061246283071436545296723011960831	31×233×1103×2679895157783862814690027494144991×2089
146	89202980794122492566142873090593446023921663	3×439×9361973132609×1795918038741070627×2298041×1753
147	178405961588244985132285746181186892047843327	7^3×127×337×2741672362528725535068727×4432676798593
148	356811923176489970264571492362373784095686655	3×5×149×223×593×184481113×231769777×25781083×616318177×1777
149	713623846352979940529142984724747568191373311	86656268566282183151×8235109336690846723986161

150	1427247692705959881058285969449495136382746623	3^2×7×11×31×151×251×331×601×1133836730401×10567201×100801×4051×1801
151	2854495385411919762116571938898990272765493247	7289088383388253664437433×2332951×165799×55871×18121
152	5708990770823839524233143877797980545530986495	3×5×17×229×457×1217×24517014940753×148961×525313×524287×174763
153	11417981541647679048466287755595961091061972991	7×73×103×919×75582488424179347083438319×11119×2143×131071
154	22835963083295358096932575511191922182123945983	3×23×43×89×127×617×683×581283643249112959×35532364099×78233
155	45671926166590716193865151022383844364247891967	31^2×311×18158209813151×4649919401×73471×11471×2147483647
156	91343852333181432387730302044767688728495783935	3^2×5×7×13^2×53×79×157×313×1249×1613×21841×3121×22366891×121369×2731×8191
157	182687704666362864775460604089535377456991567871	60726444167×1654058017289×2134387368610417×852133201
158	365375409332725729550921208179070754913983135743	3×202029703×1113491139767×201487636602438195784363×2687
159	730750818665451459101842416358141509827966271487	7×229890275929×540701761×13960201×6679×69431×20394401×6361
160	1461501637330902918203684832716283019655932542975	3×5^2×11×17×31×41×257×44479210368001×414721×65537×4278255361×61681
161	2923003274661805836407369665432566039311865085951	47×127×1289×45076044553×14808607715315782481×3188767×178481
162	5846006549323611672814739330865132078623730171903	3^5×7×19×73×163×97685839×272010961×71119×135433×2593×262657×87211
163	11692013098647223345629478661730264157247460343807	110211473×36230454570129675721×27669118297×150287×704161
164	23384026197294446691258957323460528314494920687615	3×5×83×12112549×181549×43249589×10169×164511353×8831418697×13367
165	46768052394588893382517914646921056628989841375231	7×23×31×89×151×881×2048568835297380486760231×201961×3191×599479
166	93536104789177786765035829293842113257979682750463	3×167×499×1163×13455809771×57912614113275649087721×2657×155377
167	187072209578355573530071658587684226515959365500927	79638304766856507377778616296087448490695649×2349023
168	374144419156711147060143317175368453031918731001855	3^2×5×7^2×13×17×29×43×113×127×241×337×1429×88959882481×3361×15790321×14449×5419
169	748288838313422294120286634350736906063837462003711	3340762283952395329506327023033×6740339310641×4057×8191
170	1496577676626844588240573268701473812127674924007423	3×11×31×9520972806333758431×26831423036065352611×131071×43691
171	2993155353253689176481146537402947624255349848014847	7×73×3042645634792541312037847×93507247×1212847×32377×524287
172	5986310706507378352962293074805895248510699696029695	3×5×173×431×1759217765581×101653×500177×2932031007403×2099863×9719
173	11972621413014756705924586149611790497021399392059391	70084436712553223×155285743288572277679887×1505447×730753
174	23945242826029513411849172299223580994042798784118783	3^2×7×59×233×1103×9857737155463×96076791871613611×4177×3033169×2089
175	47890485652059026823698344598447161988085597568237567	31×71×127×601×535347624791488552837151×60816001×39551×1801×122921
176	95780971304118053647396689196894323976171195136475135	3×5×17×23×89×257×353×397×683×43872038849×119782433×229153×2931542417×2113
177	191561942608236107294793378393788647952342390272950271	7×9213624084535989031×27989941729×184081×3203431780337×179951
178	383123885216472214589586756787577295904684780545900543	3×179×18584774046020617×618970019642690137449562111×62020897
179	766247770432944429179173513575154591809369561091801087	359×1433×1489459109360039866456940197095433721664951999121
180	1532495540865888858358347027150309183618739122183602175	3^3×5^2×7×11×13×19×31×37×41×61×73×109×151×181×331×631×1321×29247661×54001×18837001×23311
181	3064991081731777716716694054300618367237478244367204351	7923871097285295625344647665764672671×7648337×1164193×43441
182	6129982163463555433433388108601236734474956488734408703	3×43×127×911×25829691707×1210483×23140471537×112901153×224771×2731×8191
183	12259964326927110866866776217202473468949912977468817407	7×367×37201708625305146303973352041×55633×2305843009213693951
184	24519928653854221733733552434404946937899825954937634815	3×5×17×47×277×1013×1657×291280009243618888211558641×30269×2796203×178481
185	49039857307708443467467104868809893875799651909875269631	31×223×1587855697992791×7248808599285760001152755641×616318177
186	98079714615416886934934209737619787751599303819750539263	3^2×7×529510939×658812288653553079×2903110321×2147483647×715827883
187	196159429230833773869868419475239575503198607639501078527	23×89×1032670816743843860998850056278950666491537×707983×131071
188	392318858461667547739736838950479151006397215279002157055	3×5×283×7484047069×140737471578113×3761×165768537521×13264529×2351×4513
189	784637716923335095479473677900958302012794430558004314111	7^2×73×127×337×207617485544258392970753527×1560007×262657×649657×92737
190	1569275433846670190958947355801916604025588861116008628223	3×11×31×191×30327152671×3011347479614249131×420778751×2281×524287×174763
191	3138550867693340381917894711603833208051177722232017256447	383×39940132241×87274497124602996457×332584516519201×7068569257
192	6277101735386680763835789423207666416102355444464034512895	3^2×5×7×13×17×97×193×241×257×641×673×18446744069414584321×6700417×22253377×65537
193	12554203470773361527671578846415332832204710888928069025791	61654440233248340616559×14732265321145317331353282383×13821503
194	25108406941546723055343157692830665664409421777856138051583	3×971×1553×1100876018364883721×13842607235828485645766393×11447×31817
195	50216813883093446110686315385661331328818843555712276103167	7×31×79×151×134304196845099262572814573351×145295143558111×121369×8191
196	100433627766186892221372630771322662657637687111424552206335	3×5×29×43×113×127×197×19707683773×4981857697937×4363953127297×4432676798593
197	200867255532373784442745261542645325315275374222849104412671	26828803997912886929710867041891989490486893845712448833×7487
198	401734511064747568885490523085290650630550748445698208825343	3^3×7×19×23×67×73×89×199×683×33057806959×242099935645987×5347×153649×599479×20857
199	803469022129495137770981046170581301261101496891396417650687	164504919713×4884164093883941177660049098586324302977543600799
200	1606938044258990275541962092341162602522202993782792835301375	3×5^3×11×17×31×41×101×251×401×601×3173389601×2787601×340801×268501×8101×4051×1801×61681

Factorisation de M₃₅₉

2^359 – 1

719 855857 778165529 65877330027880703 370906580744492785430299503112990447 100361196281293745682520861860411315001

Factorisation de M₄₁₉

2^419 – 1

839 903780021613921 5800422716722833271214743 10287968884341772230096159036619433593 29919490848598531825060153417921002916701815927

Factorisation de M₄₃₁

2^431 – 1

863 3449 36238481 76859369 558062249 4642152737 142850312799017452169 1807482391092819529831423005040763105191863029850140579776353298087457

Factorisation de M₃₅₉

2^491 – 1

983 110097436327057 6976447052525718623 19970905118623195851890562673 3717542676439779473786876643915388439 14797326616665978116353515926860025681383

Source GIMPS – Table de toutes les factorisations connues

Suite: Mersenne – Table des nombres de Mersenne premiers et records

Suite et Retour	Mersenne – Nombres Mersenne premier – Test de primalité Mersenne composés – Démonstrations Mersenne – Table des nombres et records Fermat
Voir	Carrés Magiques Géométrie – Index Humour – Index Jeux – Index Nombres magiques Rubriques débutants Tables de nombres – Index Théorie des nombres Tous les types de premiers
Sites	Table la plus complete des factorisations des nombres de Mersenne Sequence of Composite Mersenne Numbers – Proof Wiki OEIS 000043 – Mersenne exponents: primes p such that 2^p - 1 is prime. Then 2^p - 1 is called a Mersenne prime OEIS A135980 - Numbers n such that the Mersenne number 2^Prime[n]-1 is composite
Cette page	http://villemin.gerard.free.fr/Wwwgvmm/Decompos/Mersenn1.htm