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Difference between revisions of "Generalized Fermat number 2 1"
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[[Category:Generalized Fermat number 2 1| ]] | [[Category:Generalized Fermat number 2 1| ]] | ||
Latest revision as of 22:50, 10 September 2021
Factorizations and statistics of Fermat numbers Fm = 22m+1 and their factors k•2n+1.
Currently there are 189 factors known.
Count of factors according to difference n - m
| n-m | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Frequency | 100 | 49 | 18 | 8 | 5 | 2 | 2 | 1 | 2 | 1 | 1 |
Factorizations
There are 152 Fermat numbers:
| m | State | Factorization |
|---|---|---|
| 0 | PR | 3 |
| 1 | PR | 5 |
| 2 | PR | 17 |
| 3 | PR | 257 |
| 4 | PR | 65537 |
| 5 | FF | 641 * 6700417 |
| 6 | FF | 274177 * 67280421310721<14> |
| 7 | FF | 59649589127497217<17> * 5704689200685129054721<22> |
| 8 | FF | 1238926361552897<16> |
| 9 | FF | 2424833 |
| 10 | FF | 45592577 * 6487031809<10> |
| 11 | FF | 319489 * 974849 * 167988556341760475137<21> * 3560841906445833920513<22> |
| 12 | CF | 114689 * 26017793 * 63766529 * 190274191361<12> * 1256132134125569<16> * C<1133> |
| 13 | CF | 2710954639361<13> * 2663848877152141313<19> * 3603109844542291969<19> * 319546020820551643220672513<27> * C<2391> |
| 14 | CF | C<4880> |
| 15 | CF | 1214251009<10> * 2327042503868417<16> * 168768817029516972383024127016961<33> * C<9808> |
| 16 | CF | 825753601 * 188981757975021318420037633<27> * C<19694> |
| 17 | CF | 31065037602817<14> * C<39395> |
| 18 | CF | 13631489 * 81274690703860512587777<23> * C<78884> |
| 19 | CF | 70525124609<11> * 646730219521<12> * 37590055514133754286524446080499713<35> * C<157770> |
| 20 | CO | C<315653> |
| 21 | CF | 4485296422913<13> * C<631294> |
| 22 | CF | 64658705994591851009055774868504577<35> * C<1262577> |
| 23 | CF | 167772161 * C<2525215> |
| 24 | CO | C<5050446> |
| 25 | CF | 25991531462657<14> * 204393464266227713<18> * 2170072644496392193<19> * C<10100842> |
| 26 | CF | 76861124116481<14> * C<20201768> |
| 27 | CF | 151413703311361<15> * 231292694251438081<18> * C<40403531> |
| 28 | CF | 1766730974551267606529<22> * C<80807103> |
| 29 | CF | 2405286912458753<16> * C<161614233> |
| 30 | CF | 640126220763137<15> * 1095981164658689<16> * C<323228467> |
| 31 | UF | 46931635677864055013377<23> |
| 32 | UF | 25409026523137<14> |
| 33 | UN | |
| 36 | UF | 2748779069441<13> * 1033434552359452673<19> |
| 37 | UF | 701179711390136401921<21> |
| 38 | UF | 6597069766657<13> * 2917004348489729<16> |
| 39 | UF | 46179488366593<14> * 6300047635658008393597059073<28> |
| 40 | UF | 326895348124320718380574179329<30> |
| 42 | UF | 1529992420282859521<19> * 3916660235220715932328394753<28> |
| 43 | UF | 7482850493766970889994241<25> |
| 48 | UF | 2408911986953445595315961857<28> |
| 52 | UF | 74201307460556292097<20> * 389591181597081096683521<24> * 1475547810493913550438096961537<31> |
| 55 | UF | 4179340454199820289<19> |
| 58 | UF | 219055085875300925441<21> |
| 61 | UF | 4057181540151185357230047233<28> |
| 62 | UF | 12857380619375557476353<23> |
| 63 | UF | 1328165573307087716353<22> |
| 64 | UF | 2634732075339197803231444993<28> |
| 65 | UF | 357393347081793620781479724788482049<36> |
| 66 | UF | 4457323664018586376077313<25> |
| 71 | UF | 6450752615599935361908737<25> |
| 72 | UF | 1443765874709062348345951911937<31> |
| 73 | UF | 188894659314785808547841<24> |
| 75 | UF | 520961043404985083798310879233<30> |
| 77 | UF | 256896736668108699625062401<27> * 3590715923977960355577974656860161<34> |
| 81 | UF | 5241902353849032101525979137<28> |
| 83 | UF | 246947940268608417020015902258307792897<39> |
| 86 | UF | 6195449970597928748332522715641578258433<40> |
| 88 | UF | 148481934042154969241780501829489000449<39> |
| 90 | UF | 985016348367230226078056532654006730753<39> |
| 91 | UF | 14072902366596202965053244178433<32> |
| 93 | UF | 7316007754729683197725441917976577<34> |
| 94 | UF | 76459067246115642538831634131564386844673<41> |
| 96 | UF | 8453027931784477309850388309101819121893377<43> |
| 99 | UF | 329244355096077565991935730125897729<36> |
| 103 | UF | 308096120572890968848095925369777111595921440769<48> |
| 107 | UF | 3346902437331832346018436558958369334886401<43> |
| 116 | UF | 4563438810603420826872624280490561141381005313<46> |
| 117 | UF | 9304595970494411110326649421962412033<37> |
| 118 | UF | 2030912570882086247957711831528946513898296129355777<52> |
| 122 | UF | 111331351706159727817280425663664652445286401<45> |
| 125 | UF | 850705917302346158658436518579420528641<39> |
| 132 | UF | 46842071212744845599962218807393559947324348854918184961<56> |
| 133 | UF | 3836232386548105510567872577199319351015739156856833<52> |
| 142 | UF | 363618066009591119386121910507749518730588867002369<51> |
| 144 | UF | 3032901347000164747248857685080177164813336577<46> |
| 146 | UF | 13235038053749721162769301995307025251972223086886913<53> |
| 147 | UF | 2230074519853062314153571827264836150598041600001<49> * 88894220732640180500173831441107513117330143465963521<53> |
| 150 | UF | 287733134849521512021350451441018219494761719398401<51> * 124204803210043452689216278205372864748572142206977<51> |
| 160 | UF | 1014636747094880794614972066871046493126084253283324393917775873<64> |
| 164 | UF | 343390041044181900054983258125842173093877961821829176754177<60> |
| 166 | UF | 8005705634611551271269985633916919970948098093294822472135213057<64> |
| 172 | UF | 492544145925433733451855533863925475950550777193174123310743553<63> |
| 178 | UF | 479744144560996421795040836675707785358665797968769873751310337<63> |
| 184 | UF | 22953190542224652377639611826608942557783370967811443134226759681<65> |
| 195 | UF | 9761213910603494986281795830720869047027739722070601061612088452553113601<73> |
| 201 | UF | 124569837190956926160012901398286924947521176078042100592562667521<66> |
| 205 | UF | 47905779865361936656012887182939964920375512098173614759150973091841<68> |
| 207 | UF | 2468256835981809063232453773836025757474103798450369795022913537<64> |
| 215 | UF | 6763365995538079644113691573900682504384080816814065022974359599316993<70> |
| 226 | UF | 12940774400232307101440167241769422723345829322819474790929732919623681<71> |
| 228 | UF | 100075322028463174917803960003016869060541080096470605049856601245089793<72> |
| 230 | UF | 2569079122613327940664251164321869487190059887122386310274973217735004454387713<79> |
| 232 | UF | 7829316209512367114436352285045953475968909194037786694784768894390715704934401<79> |
| 250 | UF | 2916513247664901672231194184906326679054237738765821706743837897199311952805889<79> |
| 251 | UF | 2483788281013398950069551842716895472418469388169137840250018522273911908790580543489<85> * 4661686559697520141696768482149753369468062525063355663959099333948327408328477720621088769<91> |
| 255 | UF | 145666448260543773842852299140929388079413640709375829561637640681954717087039489<81> |
| 256 | UF | 17130909274892224204742287276924036176273326254751752815854448838235991288094780293121<86> |
| 259 | UF | 271633531123727085814230920372446328111957704606740840259311919391091836851300398530561<87> |
| 267 | UF | 671586706882722745220204604507349309522863301781696670432755461960519645471331844097<84> |
| 268 | UF | 2549752921046269405581793752705868564968158976255933121643003787782311874331836153857<85> |
| 284 | UF | 13925050619474025980350702948110983522812772222325736088332991353008465916350934514925569<89> * 131957449045304910698095744085372069143037300769353295703839631164445734977400288187812709138433<96> |
| 316 | UF | 14951909251446370576765151943186864802218931656496569389629291254755538080464483850160734608556033<98> |
| 452 | UF | P<139> |
| 459 | UF | P<153> |
| 556 | UF | P<171> |
| 635 | UF | P<201> |
| 744 | UF | P<227> |
| 943 | UF | P<297> |
| 1379 | UF | P<428> |
| 1945 | UF | P<587> |
| 2023 | UF | P<612> |
| 3310 | UF | P<999> |
| 4724 | UF | P<1425> |
| 6537 | UF | P<1970> |
| 6835 | UF | P<2060> |
| 9428 | UF | P<2840> |
| 9448 | UF | P<2847> |
| 11075 | UF | P<3343> |
| 18749 | UF | P<5649> |
| 18757 | UF | P<5651> |
| 23288 | UF | P<7013> |
| 23471 | UF | P<7067> |
| 66643 | UF | P<20069> |
| 94798 | UF | P<28540> |
| 95328 | UF | P<28699> |
| 113547 | UF | P<34184> |
| 114293 | UF | P<34408> |
| 125410 | UF | P<37754> |
| 134995 | UF | P<40644> |
| 157167 | UF | P<47314> |
| 213319 | UF | P<64217> |
| 270091 | UF | P<81309> |
| 303088 | UF | P<91241> |
| 382447 | UF | P<115130> |
| 461076 | UF | P<138801> |
| 672005 | UF | P<202296> |
| 960897 | UF | P<289262> |
| 1494096 | UF | P<449771> |
| 1747656 | UF | P<526101> |
| 2141872 | UF | P<644773> |
| 2145351 | UF | P<645817> |
| 2167797 | UF | P<652574> |
| 2478782 | UF | P<746190> |
| 2543548 | UF | P<765687> |
| 2662088 | UF | P<801372> |
| 2747497 | UF | P<827082> |
| 3329780 | UF | P<1002367> |
| 5523858 | UF | P<1662849> |
| 7963245 | UF | P<2397178> |
| 18233954 | UF | P<5488969> |
Generalized Fermat numbers
| Miscellaneous |
| Fermat numbers |
|
| Gen. Fermat primes |
| Gen. Fermat primes |
| Gen. Fermat primes categories |
| GF Divisors |
