Factorization of generalized Fermat numbers
for small indices  m

Overview extending material contained in the paper

Anders Björn and Hans Riesel, Factors of generalized Fermat numbers,
Math. Comp. 67 (1998), pp. 441-446 (reference BR98 in the Prime Pages).

Compiled by Wilfrid Keller


  a   b   m: factorization  [new factors in blue color]
--------------------------------------------------------------------------------

  3   1   0: 1,  1: 5,  2: 41,  3: 17.193,  4: 21523361,  5: 926510094425921 
          6: 1716841910146256242328924544641 
          7: 257.275201.138424618868737.3913786281514524929.P21 
          8: 12289.8972801.891206124520373602817.P90 
          9: 134382593.22320686081.12079910333441.100512627347897906177.
               18520354538401444499841570033918296309456534611568\
               2981302539679248192554448695865898272140289.P101 
         10: 59393.448524289.847036417.C466 
         11: 790529.524455937.C963 
         12: C1954 
         13: 8468256208273409.C3893 
         14: 7814629721992554719390301061121.C7786 
         15: 65537.786433.3041503300933451777.951901181416549122049.C15584 
         16: 33033842491392559808513.C31246 
         17: C62538 
         18: C125075 
         19: 13631489.72029899522572289.C250125 
         20: C500298 
         21: 155189249.114135647911937.9434973308190721.C1000558 
         22: 512349003254811590657.C2001171 

  3   2   0: 5,  1: 13,  2: 97,  3: 17.401,  4: 3041.14177
          5: 1153.1607133116929 
          6: 769.121899667073.36629538145348481 
          7: 257.P59 
          8: 72222721.343200070657.2226198380033.
               3376663028737.1839605176202823817996787333633.P48 
          9: 4043777.57987375533057.
               406297848379393.296909426637032277938768757025793.
               1440276254252769698681054259953238091664449537.
               2236335363090199099071989377913382509011409921.P87 
         10: 2330249132033.10176954088500686156890644481.C449 
         11: 625483777.C969 
         12: 286721.1810433.C1943 
         13: 14496395542529.100044919126633332737.C3876 
         14: 2752513.3684688527361.
               6391459250177.67501891551233.166638802232307548161.C7752 
         15: 65537.348061697.151597350913.C15610 
         16: 319291393.3937533953.C31251 
         17: 54498164737.C62527 
         18: C125075 
         19: 7340033.13631489.18682824622081.C250129 
         20: 23068673.C500291
         21: 2878894768129.C1000584
         22: 453236490241.U2001180

  4   3   0: 7,  1: 5.5,  2: 337,  3: 17.4241,  4: 4338014017 
          5: 11969.1541364950613953 
          6: 337153.1009281751473729386230842057136129 
          7: 257.P75 
          8: 75312448711023950033227312129.P126 
          9: 52996750337.59577991748609.218006702009297259268280227412993.
               171508794008544584341528042030314497.P217 
         10: 147457.50157582448776955667389571090866177.C577 
         11: 14012417.1332929273857.60839036773930407240919299371009.C1182 
         12: 48070657.53619326977.
               2398726908928001.1195961298147151709581729793.C2406 
         13: 2281538378663182337.C4914 
         14: 21626881.C9857 
         15: 65537.667540318343441154049.C19703 
         16: 58851329.89522177.192544769.3616871660126209.C39418 
         17: 270833286381569.C78899 
         18: 260571137.667131376201891841.C157801 
         19: 13631489.3379146503749633.C315631 
         20: 292533213069313.4318175780929537.C631276
         21: C1262612
         22: U2525223

  5   1   0: 3,  1: 13,  2: 313,  3: 17.11489,  4: 2593.29423041 
          5: 641.75068993.241931001601 
          6: 769.3666499598977.96132956782643741951225664001 
          7: 257.23653200983830003298459393.P62 
          8: 1655809.101199664791578113.4563566430220614493697.
               12025702000065183805751513732616276516181800961.P88 
          9: 19457.23606273.236554494714698753.C329 
         10: 222098200322834700098885633.2572682777891009859905092988929.C659 
         11: 1503233.18395137.C1418 
         12: 125960554963956072449.C2843 
         13: 163841.2405576034895487214392845762561.C5691 
         14: 1367005311397627489855671697409.
               28179909134980218971238166865805313.C11388 
         15: 65537.152297193534717953.C22882 
         16: 39714817.354004455607901970620743681.C45774 
         17: 786433.4643094529.47148957697.43547626242440987934721.C91567 
         18: 14155777.C183224 
         19: 7340033.6616514561.C366445  
         20: 729938285969318871041.C732903  
         21: 19988838858438475777.C1465827  
         22: C2931693  

  5   2   0: 7,  1: 29,  2: 641,  3: 17.22993,  4: 97.1573071713 
          5: 193.102593.1175885676400129 
          6: 274568286337.1974376186976624976974230015921793 
          7: 257.115201.152833.79280897.2076762034602227299841.P48 
          8: 211457.993793.215579097177089.1366655753051261778433.
               7723238627324814197474553017429398370918112560207155581196780033.P69
          9: 12289.351741334212115457.461568161099143936014461448593889281.P301 
         10: C716 
         11: 5189633.C1425 
         12: 5488091137.61555838924091904830922753.C2828 
         13: 1364951041.186678460417.
               5332422520860819457.761525838615040844430917633.C5660 
         14: 26411009.261352539744501761.C11428 
         15: 65537.479403950715043841.C22882 
         16: C45808 
         17: C91616 
         18: 93847553.C183223 
         19: 2569456412786689.C366447
         20: 230686721.29336604246017.1157236743208961.C732887
         21: 8303272796356609.3803417506207498241.19526763586854584321.C1465793
         22: 167772161.U2931685

  5   3   0: 1,  1: 17,  2: 353,  3: 198593,  4: 97.786757409 
          5: 143797249.80957968182017 
          6: 257.290320001.3632789233881076244813676034342529 
          7: 7681.36097.259841.21440257.26556161.P61 
          8: 4619081063385038596097.16371209198385476643841.
               197957021612106218195201608012801.P103 
          9: 63588063233.11124644958799710157378318337.C319 
         10: 1210484069369857.C701 
         11: 20365313.32786906591233.50495551940572069550706689.P1385
         12: 4595713.1876317058244609.5366989900281972080641.C2820 
         13: 29939081576449.682665592324097.C5698 
         14: 65537.1146881.138721591297.C11430 
         15: 5301131104313471072468993.C22879 
         16: 6049115799553.18711118251163649.C45779 
         17: 786433.206423995711489.C91596 
         18: 21495809.2062622392321.C183211 
         19: C366462
         20: 27786421925683658753.C732904
         21: 11813748335443969.C1465830
         22: 6593445889.159006038903750657.U2931666

  5   4   0: 3.3,  1: 41,  2: 881,  3: 17.26833,  4: 4801.32677121 
          5: 641.5953.59925889.101900353 
          6: 1699132282369.319046040234900998188151306914049 
          7: 257.1719885157889.P75 
          8: 176129.2514433.446202881.
               48825225762058599296189953.847709658141595165151863297.P107 
          9: 917443645870848075624428054384896646956033.P316 
         10: 18433.40961.C707 
         11: 1179649.24084841234259969.C1410 
         12: 275280174840979457.C2846 
         13: 14238056449.44476097568255394938881.C5694 
         14: 48463873.C11445 
         15: 65537.110555887501313.C22885 
         16: 1532362753.C45799 
         17: 83406094337.C91605 
         18: 241537908737.C183220 
         19: 29645211623772651521.C366443
         20: 635437057.970752786433.C732903 
         21: C1465847
         22: 136131471726346241.U2931676

  6   1   0: 7,  1: 37,  2: 1297,  3: 17.98801,  4: 353.1697.4709377 
          5: 2753.145601.19854979505843329 
          6: 4926056449.447183309836853377.28753787197056661026689 
          7: 257.763649.50307329.3191106049.2339340566463317436161.
               2983028405608735541756929.18247770097021321924017185281 
          8: 18433.
               69615986569139423375849495295909549956813828853888948633601.P137 
          9: 80897.3360769.12581314681802812884728041373153281.
               3513902440204553274892072241244613302018049.P311 
         10: 376037377.916326983681.C777 
         11: 96479889653761.27235071532927521153002936160735956993.C1543 
         12: 825168562105301526233089.
               95784065216473934511681790307842080769.C3126 
         13: 86958504245590708098930120015173020696577.C6334 
         14: 18220289247208144897.C12730 
         15: 65537.C25494 
         16: 124346659627466753.C50980  
         17: 1192970340246662212485121.C101970 
         18: 1877597356032001.C203973 
         19: 13631489.C407969  
         20: 26560667903774949377.522767209448794182647809.C815908  
         21: 52787303940097.C1631888  
         22: 58460259483649.U3263790  

  6   5   0: 11,  1: 61,  2: 17.113,  3: 2070241,  4: 2973697798081 
          5: 193.577.645313.9104321.12199937 
          6: 257.1189782673537.207149065298675818568214979118531969 
          7: 3329.8253953.3108109313.
               29759533890817.28232308132114188879656724422657.P35 
          8: 90409829824372737427553799930642893534048917392055\
               78878208413109886576129.P127 
          9: 12289.10193921.C388 
         10: 99204476929.2283789078576650720836691969.C759 
         11: 62328486893421172927344641.C1568 
         12: 270337.737281.80044033.9669640193.129182023681.
               6490246807553.20143267717121.11302668608681341206529.C3099 
         13: 147457.
               1032193.6198190227457.1001919462572033.2526067760332801.C6321 
         14: 65537.326728155137.2990305640449.C12721 
         15: C25499 
         16: 62517411841.C50987 
         17: 8588060000257.393969071333834753.C101964 
         18: 5767169.227226000818177.C203967 
         19: C407976
         20: 69206017.4483710977.67236790273.1445743739011073.C815908
         21: C1631902
         22: U3263803

  7   1   0: 1,  1: 5.5,  2: 1201,  3: 17.169553,  4: 353.47072139617 
          5: 7699649.134818753.531968664833 
          6: 35969.1110623386241.15266848196793556098085000332888634369 
          7: 257.769.197231873.6856531741041792239054980342217258517995521.P52 
          8: 28667393.126575155274810369.P192 
          9: 13313.943558259713.
               275102002206713516320479233.1338330888777063359811677099009.
               656929861401793262700329631944023570433.P321 
         10: 12289.C861 
         11: 114689.9379841.1914651123967377663990077882369.C1689 
         12: 11886593.C3455 
         13: 2506294041191316526935613358081.4069994522486575285342303223809.C6862 
         14: 163841.112909861743231211766808577.C13815 
         15: 65537.C27688 
         16: C55385 
         17: 64749569.10923258413057.C110748 
         18: C221538 
         19: 70254593.C443067  
         20: 2173458972673.C886137  
         21: 4643094529.19847446529.50194722165096449.C1772263  
         22: 20827885658921521643521.C3544576  

  7   2   0: 3.3,  1: 53,  2: 2417,  3: 17.339121,  4: 97.449.8513.89633 
          5: 876097.1260622595721616043201 
          6: 47047681.62177153.416970669270749472494126795751788515969 
          7: 257.7681.1321729.408733507831078753793.P76 
          8: 30465024299265331445226520335290499200584427333334\
               3329385830106948028759018183626185266072912178177.P118
          9: 5463041.13951408129.2741830231600129.739060412351362864129.C380 
         10: 4638721.26615375647350719465473.C837 
         11: 1454081.58212962131660801.C1708 
         12: 114689.113418241.13037142017.483047882753.176129918181377.C3413 
         13: 2572289.246742794241.C6906 
         14: 27688961.513137344513.C13827 
         15: 65537.93847553.970310308805345281.C27662 
         16: 374734849.C55376 
         17: 3731619841.C110760 
         18: 7340033.283980595201.704401721786369.C221505 
         19: 5095746196996097.C443060
         20: C886150
         21: 46127760015361.C1772286
         22: 352740261756929.U3544584

  7   3   0: 5,  1: 29,  2: 17.73,  3: 113.25537,  4: 97.171303987713 
          5: 257.4673.459809966454270232961 
          6: 271004161.2250446050597421823605463563798919148824618881 
          7: 316783338241.P97 
          8: P217 
          9: 366900449720765979347030017.P406
         10: 12289.4697681385326593.2384507113450252289.C827 
         11: 64616251393.P1720 
         12: 40961.2875393.353007075329.814674493441.P3427 
         13: 17758151063633921.C6907 
         14: 65537.65014938580002355838977.C13819 
         15: 980661698561.2105852723626180609.493227222978148958209.C27641 
         16: 8519681.216600543233.C55366 
         17: 10152212013505576961.C110750 
         18: C221538 
         19: 7340033.924844033.C443059
         20: 111564292097.14080951713793.337918417698817.20715615966724097.98196842679894017.C886078
         21: 11802771457.C1772289
         22: U3544598

  7   4   0: 11,  1: 5.13,  2: 2657,  3: 17.193.1777,  4: 563777.58954561 
          5: 577.648449.2951791308975956929 
          6: 400303811518337.3047086868869250345637754038506015544961 
          7: 257.4313052929.P97 
          8: 114689.22555340356609.114903327899216754311312897.
               14138620053270279171951987149801906201593040733468161.P120
          9: 653239127986454056836845736180737.C400 
         10: 1032193.13498294273.33255682049.
               42520314512068138939628780054389278721.C802 
         11: 1236217487684647157761.404378969345736811548673.C1687 
         12: 1376257.39006346293944328193.C3436 
         13: 46514177.C6916 
         14: 2654209.596082689.C13831 
         15: 65537.C27688 
         16: 786433.5767169.55443457.1874329601.5444730881.C55345 
         17: C110769 
         18: 21495809.36175873.C221523 
         19: 3704639142756353.C443060
         20: 69206017.C886142
         21: 469762049.U1772291
         22: U3544599

  7   5   0: 3,  1: 37,  2: 17.89,  3: 97.31729,  4: 16692759230113 
          5: 2689.3329.4018753.15350429395841 
          6: 257.6529.9345903233.6084515529914753.6391716288418607254529 
          7: 769.2694401.2948353.92904262589441.854060358502835716134913.P55 
          8: 24001679904969263617.16017375143929691692033.P175 
          9: 6398538377352193.7287383505100801.2934499029066948891165697.C377 
         10: 3642406657228301985793.C844 
         11: C1731 
         12: 4626737293361153.9707282524141535233.
               1491534218635400847361.4540148807705884889112577.C3381 
         13: 65537.147457.159445345895055361.PRP6896 
         14: 163841.92110849.C13833 
         15: 16580609.85196801.8035750542046605434748929.C27652 
         16: 1503264769.C55375 
         17: C110769 
         18: 93847553.C221530 
         19: 2649751553.180940618494640129.C443048
         20: C886150
         21: 4643094529.524803147806277633.U1772272
         22: 217734709249.U3544587

  7   6   0: 13,  1: 5.17,  2: 3697,  3: 353.21089,  4: 36054040477057 
          5: 257.4328351499431389288675841 
          6: 1441838081.45814876214017.18466054092468533735568034082561 
          7: 3329.7329793.1066005182572362964065225039667736303849504290049.P50 
          8: 380417.1721774081.5193296897.12492559873.
               353241473065946449901726315430570540777570849533085697.P129
          9: 15361.58580044801.1203048651390566401.P400 
         10: 184321.1198081.68115890177.C844 
         11: 102780827908570402817.C1711 
         12: 147457.17037904730796368084993.C3435 
         13: 23124019888129.4439899112691038216749057.C6886 
         14: 65537.C13842 
         15: 78053377.C27685 
         16: C55385 
         17: 97335115777.6332870557697.C110745 
         18: 292654940161.24100846698497.C221513 
         19: 574923735041.C443064
         20: 11262006145318913.C886134
         21: 6155904483329.U1772287
         22: U3544599

  8   1   0: 3,  1: 13,  2: 241,  3: 97.673,  4: 193.22253377 
          5: 18446744069414584321 
          6: 769.442499826945303593556473164314770689 
          7: 349621839326921795694385454593.P48 
          8: 212780015855109121.2220842644284984664160257.
               1796602923899342630768062019504577056782884736988571649.P59 
          9: 10259749374292951523157004642279801700591617.P266 
         10: 12289.P613 
         11: 2422022479873.C1221 
         12: 78996096857210881.C2450
         13: 39714817.152371201.261167435022337.26373221006868481.C4886  
         14: 241223912428645318657.C9844 
         15: 11560943617.C19719 
         16: 786433.6110791635217482322280449.C39426 
         17: C78914 
         18: C157827 
         19: 597688321.C315645 
         20: C631306
         21: 7348420609.C1262602
         22: 448203325441.U2525211

  8   3   0: 11,  1: 73,  2: 4177,  3: 17.113.8737,  4: 193.599009.2434721 
          5: 34032769.2327996364746758943233 
          6: 35201.13298174977.13409485752562918448342707397650793232918401 
          7: 257.7681.9473.479258428673.P94 
          8: 383489.1004033.16515073.6534275708989615146537473.
               13942462615017032634896842241.92843302626321539153235911142512129.
               251107214447979493327692397230353921.P90 
          9: 13313.C459 
         10: 12289.C921 
         11: 495617.164477961755961213173761.C1821 
         12: 40961.1376257.C3689 
         13: 2277377.2654209.13882908082177.104382952243201.C7359 
         14: 163841.557057.C14786 
         15: 65537.44722128814081.C29574 
         16: 786433.C59180 
         17: C118370 
         18: 254279681.C236732 
         19: 13631489.C473473
         20: C946959
         21: 57713916641281.U1893904
         22: 3112173569.U3787825

  8   5   0: 13,  1: 89,  2: 4721,  3: 17.1009873,  4: 641.29569.14858689 
          5: 769.1217.84656984224706453739457 
          6: 7681.9857.82908039533579409153578534393535276660420426832513 
          7: 257.7937.3665153.2183727850753.3173794245121.32285994877302017.P62 
          8: 206102775026177.25083346678208656976952833. 
               14571454116637488440882751359138387691414529.
               208539956790304503336536265315334996865376394753.P101
          9: 9296766367028101121.C444 
         10: 1511034252341249.207575244797401802753.C890 
         11: 634822004737.34542946567083160879583233.
               543769404430155025715281921.358274680681257643999452327937.C1756 
         12: C3700 
         13: 147457.9338881.C7386 
         14: 10780673.52896268289.C14779 
         15: 65537.27652318167041.49653576433729537.C29558 
         16: 39714817.C59178 
         17: 786433.C118364 
         18: 2718957569.C236731 
         19: 269672525070337.75733465459326977.C473448
         20: C946959
         21: 167772161.U1893909
         22: U3787834

  8   7   0: 3.5,  1: 113,  2: 73.89,  3: 17.1326001,  4: 314707907280257 
          5: 33857.1347511751681.1760802861761 
          6: 1153.257921.865537.186270593.130947618578460692408608101578574209 
          7: 257.769.5830814152999853879888129.
               519975935060346660783986052760977025136897.P44 
          8: 12289.758747195169711613006171529428481.P195 
          9: 22074740042753.P450 
         10: 7664901937153.C912 
         11: 40961.2383682777089.466462706254073857.16880619740893982825103361.C1790 
         12: 114689.147457.119451319074817.1548181405868033.
               612728554165518337.8487573545987482069822464001.C3614 
         13: C7399 
         14: 820248577.115003949057.C14777 
         15: 65537.2752513.800063489.C29573 
         16: 215482369.769614151681.11331301108744193.29192219369537537.C59133 
         17: C118370 
         18: 12475432961.C236730 
         19: C473480
         20: 459276289.C946950
         21: U1893917
         22: U3787834

  9   2   0: 11,  1: 5.17,  2: 6577,  3: 449.95873,  4: 1601.20353.56867009 
          5: 1248533862155521.2750172762126337 
          6: 257.32310529.480865793.2952701387950377265900522969510993211622913 
          7: 5968023592938492929.P104 
          8: 25601.51968170840252661043821997424311417238529.P200
          9: 8452097.38031361.5844992551524510215341809761853571073.C438
         10: 176129.1936768727567831041.C954
         11: 40961.163841.26419201.C1938 
         12: 144310273.69748787036161.1093509721838118950144270472281079809.C3851 
         13: 1179649.C7812 
         14: 65537.697434113.62872289281.C15610 
         15: 59637761.1634310644207190017.C31243 
         16: C62538 
         17: 13631489.7547650049.25335611523073.152639561531393.C125030 
         18: 1307710539694081.2913045162051502081.16222522580528005121.U250097 
         19: 1572864001.6493675978753.C500276
         20: C1000596
         21: U2001192
 
  9   5   0: 7,  1: 53,  2: 3593,  3: 17.1277569,  4: 673.970561.1418561 
          5: 1217.4807681.293429712112056751489 
          6: 15539860481.5584960066874701094401.67924026214760827303058881153 
          7: 257.P120 
          8: 138241.12436993.56920389769478657.
               45166441601694982196398891929107361097875536081400837121.P160 
          9: 5323777.1801924609.5418641379329.59210885004055553.C443 
         10: 480015303449013614593.65936398534194188141074433.C931 
         11: 249857.6156998954315777.
               59158520596982670708737.18192332841271809127182337.C1885 
         12: 436879361.106848251772929.82320461472480133121.C3866 
         13: C7817 
         14: C15635 
         15: 65537.309432680449.48763768671895553.C31236 
         16: C62537 
         17: 786433.C125069 
         18: C250149 
         19: C500298
         20: 113246209.C1000588
         21: 59357790209.1315346023710721.29944585666487648257.U2001146

  9   7   0: 1,  1: 5.13,  2: 4481,  3: 17.17.84449,  4: 449.2100504587329 
          5: 5547814913.309562260261976083457 
          6: 206697065730709487073032833.28520447921741769926385807851011457 
          7: 257.43025783215873.273660317560727167550544641.
               71217259250084391387664628924760289537.P42 
          8: 810112911187969.
               12945777297340100106727783150253516140318282917377.
               36742670326357555376571656645025024923996704002629\
                                                   49621820478448348161.P111
          9: C489 
         10: 12289.120833.49988808297023819471561188686917633.C933 
         11: 1130497.
               6111233.9392129.69620580353.556484746533493288108033.  
               1774649741699960521677406983356417.C1867
         12: 20717569.30515201.95819991859201.4059650585677299713.
               3358855350857433784321.1941684638727006370357249.C3816 
         13: 14909441.1052643852289.C7798 
         14: 11468801.206060473679873.C15613 
         15: 65537.620017711710209.C31249 
         16: 57358092992513.C62524 
         17: 2722103297.C125065 
         18: 236577235518619649.439690816402751489.C250114 
         19: 52630024713404417.C500281
         20: 136314881.C1000588
         21: 754974721.U2001183

  9   8   0: 17,  1: 5.29,  2: 10657,  3: 577.103681 
          4: 193.1217.16001.567937 
          5: 3512911982806776822251393039617 
          6: 257.17921.21750529.
               124683908353.10517420781313.89798052356669480217601 
          7: 39881729.3074033868289.4864864030721.
               2703501313826274642433.164559126078230038853821441.P42 
          8: 642049.3034501121.734178875393.21357964615681.
               15055361739759617.501670054818946049.749452768427489281.P153
          9: 83969.66795862216119302883329.P461
         10: 12289.53661697.144248833.392724481.
               3099058177.11297701889.358589595425505892629750180499457.C897 
         11: C1955 
         12: 6936330241.782379140939777.79321576354234369.
               2193721159492206593.3425196861372906494820353.C3825 
         13: 719388673.1963982849.8482920742233210881.C7781 
         14: 65537.11272193.8634233315131393.18662744441218007041.C15588 
         15: 394987710054401.C31255 
         16: 786433.13631489.169869313.146561302529.C62505 
         17: C125075 
         18: C250149 
         19: C500298
         20: 3230830969225217.140759451446542337.C1000564
         21: 4630511617.4635410563073.1126623348910981121.U2001152

 10   1   0: 11,  1: 101,  2: 73.137,  3: 17.5882353,  4: 353.449.641.1409.69857 
          5: 19841.976193.6187457.834427406578561 
          6: 1265011073.
               15343168188889137818369.515217525265213267447869906815873 
          7: 257.15361.453377.P116 
          8: 10753.8253953.9524994049.73171503617.P225 
          9: 1514497.302078977.3611707318387778163302401.C473 
         10: 1856104284667693057.315827195278624446663038977.
               1567629031101501414376301131777.C950 
         11: 106907803649.3835256936681473.9027276203313319937.
               969220351349023606432543884535631873.C1967 
         12: 458924033.728157653661622273.50628372428722965086209.C4047  
         13: 3635898263938497962802538435084289.C8159 
         14: C16385 
         15: 65537.5767169.C32757 
         16: 8257537.C65530 
         17: 175636481.C131064 
         18: 639631361.C262136 
         19: 70254593.212733001729.13462517317633.C524256  
         20: 167772161.C1048568  
         21: C2097153  

 10   3   0: 13,  1: 109,  2: 17.593,  3: 100006561,  4: 9697.1031246781793 
          5: 769.1518977.85609598896830600941057 
          6: 257.7800222337.4988384196692145582667808890329898418176842028878209 
          7: 5065729.35057921.3769618899016961.167631329932307201.P81 
          8: 121857976458483132859080942732289.
               15089588514599698695668660804347393.C190 
          9: 1508223300748289.P497 
         10: 8344768038913.22793716654787432449.C992 
         11: 81555457.C2041 
         12: 40961.417793.C4086 
         13: 36372481.51238993921.C8174 
         14: 65537.7340033.C16373 
         15: 11599873.C32761 
         16: 466960432496641.C65522 
         17: 8237774798849.C131060 
         18: 762997884417212417.C262127 
         19: C524289
         20: C1048577
         21: U2097153

 10   7   0: 17,  1: 149,  2: 12401,  3: 353.299617,  4: 7297.1374980530433 
          5: 193.1772609.7930832257.36856642754689 
          6: 257.143489.7354241.407083829648792831580161.P26 
          7: 721921.1340804755457.84899535812416513.P94 
          8: 16509953.1080958652444021761.
               120148693217563742209.12423510660058534720887676973057.
               5040112032155671654956190812913679429543006209.
               11858212028719574709162062173452152499699166067424483329.P79 
          9: 414721.3068929.78501624833.
               3282575483230082132993.420682501426231008472517416961.C438 
         10: 1057093826561.2717018247169.C1000 
         11: 40961.1382823743489.C2032 
         12: 153839173633.102917950198546433.C4068 
         13: 65537.19207659667457.457620801732197341888513.C8152 
         14: 119603201.6655761189273601.C16361 
         15: C32769 
         16: C65537 
         17: 7358575280129.C131060 
         18: 70254593.531628033.4513811423643566081.C262109 
         19: 7340033.270532609.3771727873.C524264
         20: 81788929.C1048569
         21: 3451912193.U2097143

 10   9   0: 19,  1: 181,  2: 16561,  3: 17.1249.6737,  4: 97.2689.45442946977 
          5: 9601.55861633561729.192855438828289 
          6: 4993.1010193993337978111110606210433.P31 
          7: 257.68117064829477739821224158209.
               387699394148722959933810366563329.P65 
          8: 969163624541432772600898040283470088671584128178624780738146\
               22690888264136641431180749381562485055138692996997842038273.P138
          9: C513 
         10: C1025 
         11: 86017.C2044 
         12: 1726169089.C4087 
         13: 147457.163841.266125313.
               33786710504822132883457.53601702381034645946369.C8128 
         14: 9444019010248704001.C16366 
         15: 65537.16788357121.61676791503716353.C32737 
         16: C65537 
         17: 8650753.6138005291009.C131053 
         18: C262145 
         19: 28915497623879681.C524272
         20: C1048577
         21: 138412033.U2097144

 11   1   0: 3,  1: 61,  2: 7321,  3: 17.6304673,  4: 51329.447600088289 
          5: 193.257.21283620033217629539178799361 
          6: 316955440822738177.P49
          7: 15361.111489577217.574341646346402207998363393.
               4018529583345312964042058778793458689.P55 
          8: 15190529.4696846849.19618834249745000485889.
               4393553986026616439660661873903822389581313. 
               290103547098489711747952055517085778590240759297.P138
          9: C533 
         10: 1760464897.42237203863381694192672035203997697.C1023 
         11: 1691123713.3351550775297.9244941807617.
               56310874893475841.6813914451182200255935098881.C2054 
         12: 72019615177179018262963851313153.C4234 
         13: C8531 
         14: 163841.18948781388906004481.C17038 
         15: 65537.146919221005803847681.2899194668990451548161.C34078 
         16: 149300051969.C68238 
         17: C136498 
         18: C272995 
         19: 70254593.6874464257.C545972  
         20: C1091980  
         21: 1224818179440641.105204008343306241.U2183927  

 11   2   0: 13,  1: 5.5.5,  2: 14657,  3: 17.241.52321,  4: 697409.65886344833 
          5: 257.558205057.14717669124989680991233 
          6: 98561.235009.749633772534063781633.P36 
          7: 1012394241086414163482790913.P107
          8: 26113.442483095553.126558143142913.
               15076789482504193.106169195466283249021578144211969.P189 
          9: 755184641.11598906596353.46923860630466803713.P492 
         10: 6186003052408544884518913.1368962556000192967204527917057.C1012 
         11: 12289.3433910273.C2120 
         12: 5557248001.689863229441.812697321840641.C4230 
         13: C8532 
         14: 23068673.8142833614849.83392072995005300737.C17022 
         15: 65537.33475421165715457.C34104 
         16: C68249 
         17: 10737426890753.C136485 
         18: 702218169745409.746593753201377281.C272963 
         19: C545990
         20: C1091980
         21: 17343447041.U2183949

 11   3   0: 7,  1: 5.13,  2: 17.433,  3: 107182721,  4: 68074913.337493857 
          5: 193.364417.15009975792943059177726401 
          6: 641.1409.P61
          7: 257.P131
          8: 3430486387626057217.1826300595737909153428993580626433.
             132980092956629419115138154564331009.
             11765487608073254883107740674172674049.
             2528915723723193785484317922176389632945401316320818347450982913.
                                                                          P79
          9: 638977.25563964417.512598923368254548816765595649.C487 
         10: 1103873.C1061 
         11: 29601789544989597697.C2113 
         12: 15974401.2877011484673.C4246 
         13: 167528251393.1428726602514433.C8505 
         14: 65537.119224041473.205302799223095297.C17029 
         15: 11599873.C34117 
         16: C68249 
         17: 14942209.68681729.208931389441.C136471 
         18: 5189902143747260417.C272976 
         19: C545990
         20: 23068673.C1091972
         21: 167772161.3179669295445573633.U2183932

 11   4   0: 3.5,  1: 137,  2: 14897,  3: 17.17.97.7649 
          4: 1249.59009.623450977 
          5: 257.1153.1217.54804376513.106831093776257 
          6: 3730817.117071733905921.P47 
          7: 769.41117958000584381628617252562440142071191512315649.P81 
          8: C267 
          9: 9259243847681.494822504836788698553799681.C494
         10: 79873.5402744833.C1052 
         11: 61441.164510312690692097.C2111 
         12: 55939588097.1985582891009.4686216896755179521.C4224 
         13: 6752501761.422147994891405770753.C8501 
         14: 203172118529.C17051 
         15: 65537.3735553.122355713.C34105 
         16: C68249 
         17: 786433.35691429889.C136481 
         18: 6940455862273.11005544366081.C272969 
         19: 7340033.C545983
         20: C1091980
         21: U2183959

 11   5   0: 1,  1: 73,  2: 17.449,  3: 1009.106417,  4: 25633.896303250721 
          5: 2113.18157889.27520769.999793963860481 
          6: 3602561.13347415255864961.P44 
          7: 257.41729.614332747131162113.4706098047201057281.P90 
          8: 295533569.1927097391948818162217774865409.
               3149420724925366252865464391502449775079211471303681.P177
          9: 1349150774273.256573963099185188409097620299462657.C486 
         10: 5538232159815682049.248946669669012143708161.C1024 
         11: 12289.114689.249857.1847297.295296972610267537409.C2092 
         12: 7726171236199853410639873.C4241 
         13: 65537.C8526 
         14: 163841.26017793.C17050 
         15: 5789581313.34734407681.76732628993.C34104 
         16: C68249 
         17: 28311553.371458049.74841587713.C136471 
         18: 1172832257.1953142437250072577.C272968 
         19: C545990
         20: C1091980
         21: 168453677575569409.U2183942

 11   6   0: 17,  1: 157,  2: 15937,  3: 97.2227201,  4: 673.1153.39521.1498433 
          5: 2839553.22259029358081.33404865330049 
          6: 641.10369.11777.97624432793901757313.P36 
          7: 257.769.103082490116881712897.15828696452514653336833.P86 
          8: 31641907624152571040257.
               64360977262646304179884033.340111216350166308645711361.
               514266110566464107971992726293486044583987201.P148 
          9: 83262895998743710670849.C511 
         10: 430081.26471431987201.4684480478416897.C1032 
         11: 12289.40961.447757520897.551379373403207527601655809.C2086 
         12: 5039112193.C4256 
         13: 379992997889.105427171065857.C8506 
         14: 65537.2045784391681.C17046 
         15: 131530753.C34117 
         16: 49152001.C68242 
         17: 932478713857.429606563479553.C136471 
         18: 7340033.26298792017921.C272975 
         19: 12217304457498591233.C545971
         20: 81788929.15154020353.U1091962
         21: U2183959

 11   7   0: 3.3,  1: 5.17,  2: 8521,  3: 337.326593,  4: 22991481397070881 
          5: 1055689389481464764733130779754561 
          6: 610344589666960166969722938113.P37
          7: 257.11335169.431662694135572123286273.27530486024537889210524417.
               406841061975985346299089788652443137.P39 
          8: 330030593.234274744366093313.C241 
          9: 380929.878593.5698627849217.P509 
         10: 6103085378777089.4596494272246243885057.P1029 
         11: 65537.14344193.55037953.3122454529.265064816641.C2092 
         12: 163841.88989697.5858451457.83351101441.261068120180497358849.C4211 
         13: 10076161.232980481.501891463999980552193.C8495 
         14: C17062 
         15: 130809857.94586208257.C34105 
         16: 1826719793153.1716394786817.C68224 
         17: 786433.111149057.1330012487681.2790662363676673.C136456 
         18: 70254593.C272987 
         19: C545990
         20: 264705673265153.10440269855981569.U1091949
         21: U2183959

 11   8   0: 19,  1: 5.37,  2: 41.457,  3: 17.13596241,  4: 577.80123405269121 
          5: 193.257.622337.685697.5727809.17415878657 
          6: 4457915690803004131256192897205630962697827851093882159977969339137 
          7: 364289.444929.166840051457.12819266670337.
               12164872949149300151297.51511555905802800113153.P53 
          8: C267 
          9: 414721.P528 
         10: 1325055031900819016122321290213038081.C1031
         11: 136883453953.1324783167946753.
               374880846012989441.262313029280641047059412246529.C2060 
         12: 7033077050262631997441.C4244 
         13: 1179649.49998364673.95773333241857.C8501 
         14: 2223931393.C17053 
         15: 65537.C34120 
         16: 5767169.C68242 
         17: C136498 
         18: C272995 
         19: 5788443683586049.C545974
         20: U1091980
         21: U2183959

 11   9   0: 5,  1: 101,  2: 10601,  3: 17.97.78049,  4: 577.41423526908513 
          5: 193.1153.4751765743690817372185811969 
          6: 257.13313.2947336985726430593.P42 
          7: 769.31489.P126 
          8: 10753.216801281.3596336641.22586282835294209.P229 
          9: 2772389308265902081.5072405903723340779521.C493 
         10: 249857.946177.7919617.532389889.3781690819133441.C1024 
         11: 86017.3179630593.80360951809.2703756857208833.C2092 
         12: 131817332737.C4255 
         13: 41680897.2893627393.4803145433089.5322087325286401.C8486 
         14: 177340417.C17054 
         15: 65537.C34120 
         16: 21495809.557553567662081.C68227 
         17: 138412033.C136489 
         18: 701843374081.C272983 
         19: 7340033.101711873.C545975
         20: 327952629761.1378545843931447297.U1091950
         21: U2183959

 11  10   0: 3.7,  1: 13.17,  2: 41.601,  3: 113.2781937 
          4: 97.3617.159469543489 
          5: 2211377674535255285545615254209921 
          6: 15361.137089.2518913.3736495361.P42 
          7: 257.41822241103109377.P115 
          8: 5625857.17937703937.528219678931883689217547596362241.
               25282569519796208600890399549770078689479423449601. 
               25542825926769107342676534435111073798194258061378032162105857.
                                                                         P107 
          9: 86017.1712129.12942337.59619252253697.803393263488001.
               406537098760697857.2682267731033540609.
               78042471415871133952241369573736125441.C413 
         10: 160935937.C1059 
         11: 526835713.623540580353.C2113 
         12: 114689.385067411888791553.7729849692725329921.C4225 
         13: 65537.1179649.C8521 
         14: 11599873.26017793.C17048 
         15: 60597906849595393.C34108 
         16: 5427537457051598849.8200129138474352641.C68212 
         17: 29884417.70254593.C136483 
         18: C272995 
         19: C545990
         20: 24641536001.U1091969
         21: 138412033.11339384750081.U2183938

 12   1   0: 13,  1: 5.29,  2: 89.233,  3: 17.97.260753 
          4: 153953.1200913648289
          5: 769.44450180997616192602560262634753 
          6: 36097.81281.69619841.73389730593973249.P35
          7: 257.P136 
          8: 8253953.295278642689.5763919006323142831065059613697.
               45227165404509537635482902446862065510716804453718\
               9917947981878284544891082485331470888529210881.P132  
          9: C553 
         10: 6528575489.24110712231602691105891902802257921.C1061 
         11: 1724417.4550657.159522817.6306638252521651010964783566849.C2159 
         12: 40961.11304961.77651969.
               838668475199050951255833586002275246081.C4382 
         13: 10201930296100387864577.C8819 
         14: 163841.76836942020609.
               2175819405561659393.9082188067711220471568498689.C17616 
         15: 65537.1036475984590405633.C35345 
         16: 402995281921.C70714 
         17: 112213463751061467824129.C141451 
         18: 5767169.21495809.147849217.4345302542670888961.C282860 
         19: 13631489.158334977.27286044673.C565777  
         20: C1131604  
         21: 1711276033.9570286043137.U2263185  

 12   5   0: 17,  1: 13.13,  2: 41.521,  3: 1873.229777,  4: 184884411482927041 
          5: 449.3385409.22487562743191278689965441 
          6: 257.769.13186177.2877166849.15068584506047617.P32 
          7: 16411393.
               6872107157734532479938449850741615750858665477881983812185440769.
                                                                            P68 
          8: 17921.24040731233566906982986746922580534217217.P232 
          9: 543347713.2939401905162823996417.C523 
         10: 50449130416826369.C1089 
         11: C2211 
         12: 51007836784158132807811073.C4395 
         13: C8841 
         14: 65537.163841.39213416603445231617.C17652 
         15: C35363 
         16: 1262092289.13126540984321.C70704 
         17: C141451 
         18: 11127488513.C282891 
         19: 74841915916289.C565788
         20: U1131604
         21: 4407082023387137.U2263192

 12   7   0: 19,  1: 193,  2: 17.1361,  3: 435746497,  4: 2693153.68662081889 
          5: 257.13572412993.9799630438110085329857 
          6: 1153.6189697.46380768089432146049.P40 
          7: 769.14081.2278525278365457409.P113 
          8: 10332091238401.3910528785528692737.
               3188843968634807002996825607382360356582161149953.C197 
          9: 6930764801.701651418113.
               200616805475329.8042225267272416257.89717569451504437249.P478 
         10: 92672980622986776346915373057.C1077 
         11: 244709213972791217546465281.C2184 
         12: 1673936897.C4412 
         13: 163841.C8836 
         14: 65537.5629403922433.C17664 
         15: 2752513.C35357 
         16: 786433.C70720 
         17: C141451 
         18: C282901 
         19: 201890725889.1784846059831297.17240995248734209.C565759
         20: U1131604
         21: U2263208

 12  11   0: 23,  1: 5.53,  2: 17.2081,  3: 113.5702129 
          4: 929.2689.262369.352193 
          5: 449.80831997464815383957493223207873 
          6: 641.441738113.P58
          7: 257.32257.183809.5162106428759041.58799431072030651395293934337.P82 
          8: 562574849.479464757891497596929.P247 
          9: 2378806273.C544 
         10: 6782977.12777473.P1092 
         11: 2540433409.C2201 
         12: C4421 
         13: 163841.818544641.2275674360140414977.C8809 
         14: 65537.537964019713.C17665 
         15: 67969155073.C35352 
         16: C70726 
         17: 786433.414576541697.99838658169274369.C141416 
         18: 142795746574337.C282887 
         19: C565802
         20: 1120902578177.U1131592
         21: 699274362881.U2263196


A total of  350  new prime factors in this range, contributed by Anonymous (1), Serge Batalov (6), Jon Becker (7), Jay Berg (11), Karsten Bonath (2), Richard Brent (1), Bruce Dodson (3), Leonid Durman (1), Jim Fougeron (87), Kenji Ibusuki (8), Yousuke Koide (1), Nestor de Araújo Melo (55), François Morain (1), Takahiro Nohara (4), Tapio Rajala (7), Alfred Reich (1), Geoffrey Reynolds (146), Robert Silverman (2), Tom Womack (6).


Last modified: January 15, 2018.