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
All factorizations for m ≤ 8 completed in December 2022 !
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.
48453474888340457194894615152904765441.C7749
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
23: C4002383
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: 625483777.4910460769317099419184178986913042832453633.C926
12: 286721.1810433.C1943
13: 14496395542529.100044919126633332737.
1417886011057772761662821415960281089.C3840
14: 2752513.3684688527361.
6391459250177.67501891551233.166638802232307548161.C7752
15: 65537.348061697.151597350913.C15610
16: 319291393.3937533953.C31251
17: 54498164737.7954711857785277738431807489.C62499
18: 9835454533111783841333249.C125050
19: 7340033.13631489.18682824622081.C250129
20: 23068673.C500291
21: 2878894768129.C1000584
22: 453236490241.C2001180
23: 106216554497.277196316868609.C4002358
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: 14012417.1332929273857.13263651112295971469683628978177.
60839036773930407240919299371009.C1151
12: 48070657.53619326977.2398726908928001.
1195961298147151709581729793.
14529598066721471235210958841856001.C2387
13: 2281538378663182337.C4914
14: 21626881.15648604597172168603136527650455553.C9823
15: 65537.667540318343441154049.C19703
16: 58851329.89522177.192544769.
3616871660126209.22779349324501296574365697.C39392
17: 270833286381569.C78899
18: 260571137.667131376201891841.24810655860900495361.C157781
19: 13631489.3379146503749633.C315631
20: 292533213069313.4318175780929537.C631276
21: C1262612
22: C2525223
23: C5050446
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
23: 167772161.21937552097281.
2149328346352189441.2981400801699641172164609.C5863321
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: 1431459829606245207173905329679749121.C680
11: 5189633.C1425
12: 5488091137.61555838924091904830922753.C2828
13: 1364951041.186678460417.
5332422520860819457.761525838615040844430917633.C5660
14: 26411009.261352539744501761.9692662769315032894013441.C11403
15: 65537.479403950715043841.C22882
16: C45808
17: 1558147628346203114569729.C91592
18: 93847553.435447138843502307096657921.C183197
19: 2569456412786689.118064119380221624907202561.C366421
20: 230686721.29336604246017.1157236743208961.C732887
21: 8303272796356609.3803417506207498241.19526763586854584321.C1465793
22: 167772161.C2931685
23: U5863386
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: 65537.1146881.138721591297.6855108994346305312629881567473008641.C11393
15: 5301131104313471072468993.22302252883961311533465601.C22854
16: 6049115799553.18711118251163649.
19756988904344312703985577633120257.C45745
17: 786433.206423995711489.15076883889159538475009.C91573
18: 21495809.2062622392321.C183211
19: C366462
20: 27786421925683658753.C732904
21: 11813748335443969.C1465830
22: 6593445889.159006038903750657.C2931666
23: U5863386
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.
25675326136436675613600873198698497.C5659
14: 48463873.C11445
15: 65537.110555887501313.C22885
16: 1532362753.1246078933012280343607118921729.C45769
17: 83406094337.C91605
18: 241537908737.5506783089232565501953.C183198
19: 29645211623772651521.10243367459550892672592904193.C366415
20: 635437057.970752786433.C732903
21: 112230917497920946177.C1465827
22: 136131471726346241.C2931676
23: 167772161.24254472795631648769.U5863358
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: 58460259483649.177693281801366380592910542307329.C3263757
23: 40711978221569.7643646112561102849.C6527574
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: 5767169.227226000818177.72387072722435309569.C203947
19: C407976
20: 69206017.4483710977.67236790273.1445743739011073.C815908
21: 6449030029918152425473.C1631880
22: C3263803
23: 45862650642433.24495259585474100985857.U6527570
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: 65537.39066490326833002281506416331355062273.C27650
16: C55385
17: 64749569.10923258413057.C110748
18: C221538
19: 70254593.C443067
20: 2173458972673.13759070826189484276195975495681.C886106
21: 4643094529.19847446529.50194722165096449.C1772263
22: 20827885658921521643521.C3544576
23: U7089196
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: 2572289.246742794241.4106514459456739122082617911930494451713.C6866
14: 27688961.513137344513.C13827
15: 65537.93847553.970310308805345281.C27662
16: 374734849.C55376
17: 3731619841.126760506575345559486632558593.C110731
18: 7340033.283980595201.704401721786369.C221505
19: 5095746196996097.20147955856158228481.892720079946668572673.C443019
20: C886150
21: 46127760015361.C1772286
22: 352740261756929.C3544584
23: U7089197
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: 65537.65014938580002355838977.551260302115060356579329.C13795
15: 980661698561.2105852723626180609.493227222978148958209.C27641
16: 8519681.216600543233.2637785822596297523201.C55345
17: 10152212013505576961.C110750
18: C221538
19: 7340033.924844033.23904038241309818881.C443040
20: 111564292097.14080951713793.337918417698817.
20715615966724097.98196842679894017.C886078
21: 11802771457.C1772289
22: C3544598
23: 23017283387393.U7089183
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: 46514177.1332289971186494227277339108199546881.C6880
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.C1772291
22: C3544599
23: 4630511617.U7089187
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.P6896
14: 163841.92110849.C13833
15: 16580609.85196801.
8035750542046605434748929.10989129828586818215626014721.C27624
16: 1503264769.C55375
17: 340619827281298677301249.C110745
18: 93847553.C221530
19: 2649751553.180940618494640129.C443048
20: C886150
21: 4643094529.524803147806277633.C1772272
22: 217734709249.C3544587
23: 836520260927489.U7089181
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: 78053377.11092947697699719872513.64019110185456246072180932609.C27634
16: C55385
17: 97335115777.6332870557697.C110745
18: 292654940161.24100846698497.C221513
19: 574923735041.C443064
20: 11262006145318913.C886134
21: 6155904483329.C1772287
22: C3544599
23: 2323912851457.120693272262737921.U7089167
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: 7348420609.33079231742188321838827831297.C1262573
22: 448203325441.439186092349406236901377.C2525188
23: 1107296257.U5050437
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: 13313.298263335624322679638103183355877967873.C420
10: 12289.C921
11: 495617.164477961755961213173761.C1821
12: 40961.1376257.C3689
13: 2277377.2654209.13882908082177.
104382952243201.209413269255934384591034761217.C7329
14: 163841.557057.1331501301099328134243450881.C14759
15: 65537.44722128814081.C29574
16: 786433.C59180
17: C118370
18: 254279681.C236732
19: 13631489.C473473
20: C946959
21: 57713916641281.C1893904
22: 3112173569.C3787825
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
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543769404430155025715281921.358274680681257643999452327937.C1756
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8 7 0: 3.5, 1: 113, 2: 73.89, 3: 17.1326001, 4: 314707907280257
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519975935060346660783986052760977025136897.P44
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612728554165518337.8487573545987482069822464001.
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9 2 0: 11, 1: 5.17, 2: 6577, 3: 449.95873, 4: 1601.20353.56867009
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152639561531393.393636107833237952312578670593.C125001
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9 5 0: 7, 1: 53, 2: 3593, 3: 17.1277569, 4: 673.970561.1418561
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59158520596982670708737.18192332841271809127182337.C1885
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9 7 0: 1, 1: 5.13, 2: 4481, 3: 17.17.84449, 4: 449.2100504587329
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71217259250084391387664628924760289537.P42
8: 810112911187969.
12945777297340100106727783150253516140318282917377.
36742670326357555376571656645025024923996704002629\
49621820478448348161.P111
9: C489
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105532821253699171569756514884725806882817.C1826
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9 8 0: 17, 1: 5.29, 2: 10657, 3: 577.103681
4: 193.1217.16001.567937
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124683908353.10517420781313.89798052356669480217601
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2703501313826274642433.164559126078230038853821441.P42
8: 642049.3034501121.734178875393.21357964615681.
15055361739759617.501670054818946049.749452768427489281.P153
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2193721159492206593.3425196861372906494820353.C3825
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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
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1567629031101501414376301131777.C950
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969220351349023606432543884535631873.C1967
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10 3 0: 13, 1: 109, 2: 17.593, 3: 100006561, 4: 9697.1031246781793
5: 769.1518977.85609598896830600941057
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8: 121857976458483132859080942732289.
15089588514599698695668660804347393.
69915057472258961071772151436847568511903450783505\
23038272199088575097873138175154689.P105
9: 1508223300748289.P497
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10 7 0: 17, 1: 149, 2: 12401, 3: 353.299617, 4: 7297.1374980530433
5: 193.1772609.7930832257.36856642754689
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120148693217563742209.12423510660058534720887676973057.
5040112032155671654956190812913679429543006209.
11858212028719574709162062173452152499699166067424483329.P79
9: 414721.3068929.78501624833.
3282575483230082132993.420682501426231008472517416961.C438
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10 9 0: 19, 1: 181, 2: 16561, 3: 17.1249.6737, 4: 97.2689.45442946977
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11 1 0: 3, 1: 61, 2: 7321, 3: 17.6304673, 4: 51329.447600088289
5: 193.257.21283620033217629539178799361
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11 2 0: 13, 1: 5.5.5, 2: 14657, 3: 17.241.52321, 4: 697409.65886344833
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11 3 0: 7, 1: 5.13, 2: 17.433, 3: 107182721, 4: 68074913.337493857
5: 193.364417.15009975792943059177726401
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11765487608073254883107740674172674049.
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P79
9: 638977.25563964417.512598923368254548816765595649.
124417592218683875532181715340890466359297.
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11 4 0: 3.5, 1: 137, 2: 14897, 3: 17.17.97.7649
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358905207969814529.P199
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11 5 0: 1, 1: 73, 2: 17.449, 3: 1009.106417, 4: 25633.896303250721
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