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Fermat number

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A Fermat number, named after Pierre de Fermat, is a number of the form:

\(F_{n} = 2^{2^{ \overset{n} {}}} + 1\)

It is a generalization of the Fermat prime, which are exactly primes that are one more than a power of two. If \(2^k + 1\) is prime, then \(k\) must be a power of two, so all Fermat primes are also of the form \(2^{2^n + 1}\). It was originally conjectured that all Fermat numbers were prime, but this has been proven false; in fact, only the first five Fermat numbers (F0 to F4) are known to be prime.

The first Fermat number known to be composite is F5, which is equal to 4,294,967,297. The prime factorizations of this number are 641 and 6,700,417.

F334 is the first Fermat number that is larger than a googolplex. The largest Fermat number which is known to be composite, as of October 2020, is F18,233,954.[1]

Known Fermat factors[]

Fermat factors in the form k • 2n + 1[2]

F# k n Factor Digits Date Discoverer
F0 PRIME
F1 PRIME
F2 PRIME
F3 PRIME
F4 PRIME
F5 5 7 641 3 1732 Leonhard Euler
cofactor 6700417 7
F6 1071 8 274177 6 1855 Thomas Clausen; Fortuné Landry 1880
cofactor 67280421310721 14
F7 116503103764643 9 59649589127497217 17 1970-09-13 Michael A. Morrison & John Brillhart
cofactor 5704689200685129054721 22
F8 604944512477 11 1238926361552897 16 1980 Richard Peirce Brent & John M. Pollard
cofactor 93461...80321 62
F9 37 16 2424833 7 1903 Alfred Edward Western
~3.640431067 * \(10^{45}\) 11 74556...42657 49 1990-06-15 Arjen Klaas Lenstra, Mark S. Manasse & a larger team
cofactor 74164...40737 99
F10 11131 12 45592577 8 1953-08-15 John Lewis Selfridge
395937 14 6487031809 10 1962 John Brillhart
~1.137640573 * \(10^{36}\) 12 46597...92897 40 1995-10-20 Richard Peirce Brent
cofactor ~1.304398744 * \(10^{215}\) 252
F11 39 13 319489 6 1899 Allan Joseph Champneys Cunningham
119 13 974849 6 1899 Allan Joseph Champneys Cunningham
10253207784531279 14 167988556341760475137 21 1988-05-17 Richard Peirce Brent
434673084282938711 13 3560841906445833920513 22 1988-05-13 Richard Peirce Brent
cofactor 17346...34177 564
F12[3] 7 14 114689 6 1877 Ivan Mikheevich Pervushin; Édouard Lucas
397 16 26017793 8 1903 Alfred Edward Western
973 16 63766529 8 1903 Alfred Edward Western
11613415 14 190274191361 12 1974 John C. Hallyburton Jr. & John Brillhart
76668221077 14 1256132134125569 16 1986-07-25 Robert Baillie
~1.735323021 * \(10^{49}\) 15 56863...18433 54 2010-03-27 Michael Vang, Paul Zimmermann & Alexander Kruppa
F13 41365885 16 2710954639361 13 1974 John C. Hallyburton Jr. & John Brillhart
20323554055421 17 2663848877152141313 19 1991-01-05 Richard E. Crandall
6872386635861 19 3603109844542291969 19 1991-05-09 Richard E. Crandall
609485665932753836099 19 319546020820551643220672513 27 1995-06-16 Richard Peirce Brent
F14 ~1.784180998 * \(10^{48}\) 16 11692...73313 54 2010-02-03 Tapio Rajala & George F. Woltman
F15 579 21 1214251009 10 1925 Maurice Borisovich Kraitchik
17753925353 17 2327042503868417 16 1987-08-04 Gary B. Gostin
~1.287603890 * \(10^{27}\) 17 16876...16961 33 1997-07-03 Richard E. Crandall & C. van Halewyn
F16 1575 19 825753601 9 1953-08-14 John Lewis Selfridge
180227048850079840107 20 188981757975021318420037633 27 1996-12 Richard E. Crandall & Karl Dilcher
F17 59251857 19 31065037602817 14 1978-05 Gary B. Gostin
~1.478397579 * \(10^{43}\) 19 77510...23169 49 2011-03-15 David Bessell & George F. Woltman
F18 13 20 13631489 8 1903 Alfred Edward Western (Prime: Paul Peter Heinrich Seelhoff 1886)
9688698137266697 23 81274690703860512587777 23 1999-04-16 Richard E. Crandall, Richard J. McIntosh & Claude Tardif
F19 33629 21 70525124609 11 1962-11-16 Hans Riesel
308385 21 646730219521 12 1963 Claude P. Wrathall
~8.962167624 * \(10^{24}\) 22 37590...99713 35 2009-07-18 David Bessell & George F. Woltman
F20 no known factors
F21 534689 23 4485296422913 13 1963 Claude P. Wrathall
F22 ~3.8539592024 * \(10^{27}\) 24 64658...04577 35 2010-03-26 David Bessell & George F. Woltman
F23 5 25 167772161 9 1878 Ivan Mikheevich Pervushin
F24 no known factors
F25 48413 29 25991531462657 14 1963 Claude P. Wrathall
1522849979 27 204393464266227713 18 1985-08-07 Gary B. Gostin
16168301139 27 2170072644496392193 19 1987-12-16 Philip B. McLaughlin Jr.
F26 143165 29 76861124116481 14 1963 Claude P. Wrathall
F27 141015 30 151413703311361 15 1963 Claude P. Wrathall
430816215 29 231292694251438081 18 1985-02-21 Gary B. Gostin
F28 25709319373 36 1766730974551267606529 22 1997-02-05 Tadashi Taura
F29 1120049 31 2405286912458753 16 1980-10-17 Gary B. Gostin & Philip B. McLaughlin Jr.
F30 149041 32 640126220763137 15 1963 Claude P. Wrathall
127589 33 1095981164658689 16 1963 Claude P. Wrathall
F31 5463561471303 33 46931635677864055013377 23 2001-04-12 Alexander Kruppa & Tony Forbes
F32 1479 34 25409026523137 14 1963 Claude P. Wrathall
F36 5 39 2748779069441 13 1886 Paul Peter Heinrich Seelhoff
3759613 38 1033434552359452673 19 1981-01-02 Gary B. Gostin & Philip B. McLaughlin Jr.
F37 1275438465 39 701179711390136401921 21 1991-04-29 Gary B. Gostin
F38 3 41 6597069766657 13 1903 James Cullen & Allan Joseph Champneys Cunningham; Alfred Edward Western
2653 40 2917004348489729 16 1963 Claude P. Wrathall
F39 21 41 46179488366593 14 1956 Raphael M. Robinson
2864929972774011 41 63000...59073 28 2012-12-07 Tapio Rajala & George F. Woltman
F40 74327396788321657 42 32689...79329 30 2021-03-01 Luigi Morelli & George F. Woltman
F42 43485 45 1529992420282859521 19 1963 Claude P. Wrathall
111318179143061 45 3916660235220715932328394753 28 2011-03-20 Roman Maznichenko & Mark Rodenkirch
F43 212675402445 45 7482850493766970889994241 25 2000-12-23 Payam Samidoost & Leonid N. Durman
F48 2139543641769 50 2408911986953445595315961857 28 2001-05-28 Marko Bodschwinna & Leonid N. Durman
F52 4119 54 74201307460556292097 20 1963 Claude P. Wrathall
21626655 54 389591181597081096683521 24 1982 Wilfrid Keller
81909357657279 54 14755...61537 31 2010-03-15 Cedric Vonck & Leonid N. Durman
F55 29 57 4179340454199820289 19 1956 Raphael M. Robinson
F58 95 61 219055085875300925441 21 1957 Raphael M. Robinson
F61 54985063 66 4057181540151185357230047233 28 1986-05-17 Gary B. Gostin
F62 697 64 12857380619375557476353 23 1977 David Edgar Shippee
F63 9 67 1328165573307087716353 22 1956 Raphael M. Robinson
F64 17853639 67 2634732075339197803231444993 28 1986-05-13 Gary B. Gostin
F65 1210895760431083 68 35739...82049 36 2013-01-29 Roman Maznichenko & George F. Woltman
F66 7551 69 4457323664018586376077313 25 1977 David Edgar Shippee
F71 683 73 6450752615599935361908737 25 1977 David Edgar Shippee
F72 76432329 74 14437...11937 31 1986-05-31 Gary B. Gostin
F73 5 75 188894659314785808547841 24 1906 James Caddall Morehead
F75 3447431 77 52096...79233 30 1982-04 Gary B. Gostin
F77 425 79 256896736668108699625062401 27 1957 Raphael M. Robinson & John Lewis Selfridge
5940341195 79 35907...60161 34 1998-04-08 Tadashi Taura
F81 271 84 5241902353849032101525979137 28 1957 Raphael M. Robinson & John Lewis Selfridge
F83 1595863660157 87 24694...92897 39 2005-05-12 Vasily A. Danilov & Leonid N. Durman
F86 20018578522347 88 61954...58433 40 2012-06-07 Michael Dangler & Mark Rodenkirch
F88 119942751127 90 14848...00449 39 2001-03-13 Takahiro Nohara & Leonid N. Durman
F90 198922467387 92 98501...30753 39 2001-03-26 Peter Grobstich & Leonid N. Durman
F91 1421 93 14072...78433 32 1977 David Edgar Shippee
F93 92341 96 73160...76577 34 1979 Robert Baillie
F94 482524552001 97 76459...44673 41 2001-04-18 Peter Grobstich & Leonid N. Durman
F96 3334131633063 101 84530...93377 43 2008-11-25 Martin Ptáček & Leonid N. Durman
F99 16233 104 32924...97729 36 1979-11 Gary B. Gostin & Philip B. McLaughlin Jr.; Hiromi Suyama
F103 7595155767819149 105 30809...40769 48 2020-12-31 Peter Strasser & George F. Woltman
F107 1289179925 111 33469...86401 43 1992-11-08 Gary B. Gostin
F116 3433149787 120 45634...05313 46 1999-08-08 Tadashi Taura
F117 7 120 93045...12033 37 1956 Raphael M. Robinson
F118 1527888802614951 120 20309...55777 52 2019-01-28 Peter Strasser & George F. Woltman
F122 5234775 124 11133...86401 45 1986-05-21 Gary B. Gostin
F125 5 127 85070...28641 39 1956 Raphael M. Robinson
F132 1075441212722595 135 46842...84961 56 2018-12-19 Peter Strasser & George F. Woltman
F133 88075576149 135 38362...56833 52 2001-07-24 Payam Samidoost & Leonid N. Durman
F142 8152599 145 36361...02369 51 1986-05-22 Gary B. Gostin
F144 17 147 30329...36577 46 1956 Raphael M. Robinson
F146 37092477 148 13235...86913 53 1987-2-23 Gary B. Gostin
F147 3125 149 22300...00001 49 1979-12 Gary B. Gostin & Philip B. McLaughlin Jr.
124567335 149 88894...63521 53 1990-12-01 Gary B. Gostin
F150 5439 154 12420...06977 51 1980-05 Gary B. Gostin & Philip B. McLaughlin Jr.; Hiromi Suyama
1575 157 28773...98401 51 1956 Raphael M. Robinson
F160 43390164659167 164 10146...75873 64 2023-07-27 Erwin Doescher
F164 1835601567 167 34339...54177 60 1993-05-31 Gary B. Gostin
F166 2674670937447 171 80057...13057 64 2012-07-10 Roman Maznichenko & Mark Rodenkirch
F172 20569603303 174 49254...43553 63 2001-05-11 Leonid N. Durman
F178 313047661 180 47974...10337 63 1991-06-18 Gary B. Gostin
F184 117012935 187 22953...59681 65 1990-12-17 Gary B. Gostin
F195 48595346636925 197 97612...13601 73 2014-06-26 Serge Batalov & George F. Woltman
F201 4845 204 12456...67521 66 1980-07-27 Gary B. Gostin & Philip B. McLaughlin Jr.
F205 232905 207 47905...91841 68 1984-01-01 Wilfrid Keller
F207 3 209 24682...13537 64 1956 Raphael M. Robinson
F215 32111 217 67633...16993 70 1980-12-02 Hiromi Suyama
F226 15 229 12940...23681 71 1956 Raphael M. Robinson
F228 29 231 10007...89793 72 1956 Raphael M. Robinson
F230 372236097 232 25690...87713 79 2000-04-13 Leonid N. Durman
F232 70899775 236 78293...34401 79 1991-11-24 Gary B. Gostin
F250 403 252 29165...05889 79 1957 Raphael M. Robinson & John Lewis Selfridge
F251 85801657 254 24837...43489 85 1991-11-30 Gary B. Gostin
322072887044529 253 46616...88769 91 2024-05-24 Gary B. Gostin
F255 629 257 14566...39489 81 1979 Robert Baillie
F256 36986355 258 17130...93121 86 1991-01-20 Gary B. Gostin
F259 36654265 262 27163...30561 87 1991-01-21 Gary B. Gostin
F267 177 271 67158...44097 84 1957 Raphael M. Robinson & John Lewis Selfridge
F268 21 276 25497...53857 85 1956 Raphael M. Robinson
F274 58130105122923 277 14115...61057 98 2018-04-05 Roman Maznichenko
F275 22347 279 21706...69537 89 1984-01-16 Wilfrid Keller
F284 7 290 13925...25569 89 1956 Raphael M. Robinson
1061341513 286 13195...38433 96 2000-12-25 Leonid N. Durman
F286 78472588395 288 39026...85121 98 2002-11-02 Vasily A. Danilov & Leonid N. Durman
F287 5915 289 58833...52481 91 1980-12-26 Hiromi Suyama
8662575142599 289 86161...05089 100 2016-11-28 Roman Maznichenko
21346190509623 290 42463...91553 101 2015-12-25 Roman Maznichenko
F297 72677552745 301 29609...94241 102 2003-02-13 Vasily A. Danilov & Leonid N. Durman
F298 247 302 20125...07489 94 1979 Robert Baillie
F299 272392805475 304 88779...37601 103 2010-11-20 Alexey V. Komkov
F301 7183437 304 23412...80993 99 1990-11-04 Gary B. Gostin
F316 7 320 14951...56033 98 1956 Raphael M. Robinson
F329 1211 333 21190...46913 104 1981-01-12 Hiromi Suyama
F334 27609 341 12367...19169 108 1984-01-25 Wilfrid Keller
F338 27654487 342 24775...47649 111 1990-12-22 Gary B. Gostin
F343 4844391185 345 34720...05921 114 2001-08-29 Vasily A. Danilov & Leonid N. Durman
F353 18908555 355 13877...66241 115 1990-12-25 Gary B. Gostin
F370 573230511 373 11028...13313 122 2000-08-22 Leonid N. Durman
F375 733251 377 22571...18273 120 1986-06-09 Gary B. Gostin
F376 810373 378 49891...46913 120 1986-06-09 Gary B. Gostin
F380 321116871 385 25305...85473 125 2000-06-26 Leonid N. Durman
F398 120845 401 62410...45441 126 1984-04-18 Wilfrid Keller
F416 8619 418 58343...43137 130 1981 Hiromi Suyama
38039 419 51498...79233 131 1984-02-16 Wilfrid Keller
F417 118086729 421 63948...67809 135 1992-06-13 Gary B. Gostin
303472680883 420 82170...44609 138 2013-01-30 Roman Maznichenko & Mark Rodenkirch
F425 44893411020831 427 15559...03969 143 2023-06-25 Gary B. Gostin
F431 5769285 434 25594...73441 138 1990-11-30 Gary B. Gostin
F452 27 455 25119...51137 139 1956 Raphael M. Robinson
F459 5449229488169 465 51913...34209 153 2013-05-08 Ryan Propper & Mark Rodenkirch
F468 27114089 471 16531...29473 150 1992-09-25 Gary B. Gostin
F480 5673968845 484 28340...67521 156 2001-11-24 Vasily A. Danilov & Leonid N. Durman
F517 84977118993 520 29167...43969 168 2010-01-25 Sergei Maiorov & Leonid N. Durman
F544 225 547 10365...48801 168 1979 Robert Baillie
F547 77377 550 28517...57249 171 1986-06-05 Gary B. Gostin
F556 127 558 11982...31489 171 1976 G. Matthew & Hugh Cowie Williams
F569 6616590375 575 81824...08001 183 2003-02-25 Sergey Kuzmin & Leonid N. Durman
F579 63856313 581 50539...58177 183 1999-10-04 Tadashi Taura
F600 6213186413 605 82501...81217 192 2005-09-29 Asko Vuori & Leonid N. Durman
F620 10084141 624 70203...87457 195 1992-01-19 Gary B. Gostin
F635 4258979 645 62180...50529 201 1991-07-12 Gary B. Gostin
F637 11969 643 43686...59553 198 1984-03-08 Wilfrid Keller
F642 52943971 644 38648...51937 202 1999-08-08 Tadashi Taura
F666 217924552867 668 26689...81153 213 2014-05-26 Roman Maznichenko
F667 491628159 669 12042...66209 211 2001-03-12 Tadashi Taura
F692 717 695 11785...51457 213 1979 Arthur Oliver Lonsdale Atkin & Neil W. Rickert
F723 554815 730 31336...02561 226 1991-01-04 Gary B. Gostin
F744 17 747 12585...12577 227 1976 G. Matthew & Hugh Cowie Williams
F851 497531 859 19124...12129 265 1988-01-18 Gary B. Gostin
F885 16578999 887 17106...17473 275 1992-07-12 Gary B. Gostin
F906 57063 908 12347...00129 279 1986-05-19 Gary B. Gostin
F931 1985 933 14412...45121 285 1980-12-22 Wilfrid Keller
F943 4785972759 954 72876...57857 297 2012-03-28 Andriy Sen & Mark Rodenkirch
F971 541664191 976 34594...22977 303 2002-04-04 Dmitry Komin & Leonid N. Durman
F1069 137883 1073 13953...51137 329 1992-09-01 Gary B. Gostin
F1082 82165 1084 17029...16641 332 1991-04-08 Gary B. Gostin
F1114 11618577 1116 10342...94273 344 2001-01-22 Gary B. Gostin
F1123 25835 1125 11774...70721 344 1987-01-15 Gary B. Gostin
F1132 10111717305 1136 94384...96481 352 2012-12-26 Serge Batalov & Mark Rodenkirch
F1160 2018719057 1162 12645...54529 360 2005-05-15 Maximilian Pacher & Leonid N. Durman
F1201 837747239 1203 11539...26913 372 2011-01-12 Maximilian Pacher, Paul Jobling, George F. Woltman & Jim Fougeron
F1225 79707 1231 29472...03137 376 1991-06-08 Gary B. Gostin
F1229 29139 1233 43098...52289 376 1987-12-07 Gary B. Gostin
F1296 58951871175 1299 64337...18401 402 2016-10-30 Gary B. Gostin
F1379 205071338665 1382 21645...60161 428 2021-11-24 Gary B. Gostin
F1394 62705223 1396 10843...48929 429 2001-12-06 Tadashi Taura
F1436 713828860473 1438 54291...52513 445 2023-04-21 Gary B. Gostin
F1451 13143 1454 65510...43713 442 1986-10-30 Gary B. Gostin
F1493 623619365837 1495 68353...39617 462 2023-02-09 Gary B. Gostin
F1551 291 1553 91934...08673 470 1979 Arthur Oliver Lonsdale Atkin & Neil W. Rickert
F1598 10923781 1600 48569...86657 489 2000-12-21 Tadashi Taura
F1680 26778342591 1683 11515...44129 518 2016-12-05 Gary B. Gostin
F1710 351276975 1719 10380...68801 527 2008-03-09 Maximilian Pacher, Paul Jobling, George F. Woltman & Jim Fougeron
F1722 364182745 1724 34437...77921 528 2008-04-19 Maximilian Pacher, Paul Jobling, George F. Woltman & Jim Fougeron
F1784 321941255325 1788 56157...23201 550 2023-05-31 Gary B. Gostin
F1849 98855 1851 15904...11041 563 1992-09-01 Gary B. Gostin
F1945 5 1947 63734...36641 587 1957 Raphael M. Robinson
F1990 150863 1993 13532...46497 606 1995-10-30 Tadashi Taura
F2023 29 2027 44688...54113 612 1979 Arthur Oliver Lonsdale Atkin & Neil W. Rickert; Gordon Villy Cormack & Hugh Cowie Williams
F2059 591909 2063 62681...77473 627 2000-05-09 J. Ray Ballinger & Yves Gallot
F2089 431 2099 31364...18529 635 1983-08-17 Hiromi Suyama
F2123 9659599821 2125 47173...08673 650 2016-12-16 Gary B. Gostin
F2144 19789270693 2148 81070...32609 657 2018-11-02 Gary B. Gostin
F2286 4004779405 2288 22866...11681 699 2015-11-25 Gary B. Gostin
F2420 103257279 2422 12840...02817 738 2010-11-07 Peter Strasser
F2456 85 2458 72635...58241 742 1979 Arthur Oliver Lonsdale Atkin & Neil W. Rickert
F2587 15249465809 2591 14189...14433 791 2019-12-09 Gary B. Gostin
F2606 238451805 2608 29082...42081 794 2012-03-11 Takahiro Nohara, Paul Jobling, George F. Woltman & Jim Fougeron
F3056 3370842847 3058 11952...35169 931 2017-01-28 Gary B. Gostin
F3310 5 3313 10264...20961 999 1979 Arthur Oliver Lonsdale Atkin & Neil W. Rickert; Gordon Villy Cormack & Hugh Cowie Williams
F3314 406860969 3322 42765...88577 1009 2013-01-18 Maximilian Pacher, Paul Jobling, George F. Woltman & Jim Fougeron
F3335 43714055 3337 15056...28961 1013 2011-07-05 Mykola Kamenyuk, Jim Fougeron & Jean Penné
F3345 6604326057 3347 23292...09697 1018 2018-12-13 Gary B. Gostin
F3506 501 3508 51649...88257 1059 1986-07-26 Gary B. Gostin
F3576 1132007355 3578 13777...81121 1087 2015-07-21 Takahiro Nohara & Jim Fougeron
F3703 262254673 3706 10861...43073 1125 2012-06-17 Takahiro Nohara, Paul Jobling, George F. Woltman & Jim Fougeron
F3723 13308899 3725 28898...26369 1129 2002-07-03 Jim Fougeron
F3730 1127899657 3732 31348...61473 1133 2015-08-17 Takahiro Nohara & Jim Fougeron
F3850 787703529 3854 11640...49537 1170 2015-08-13 Maximilian Pacher, Paul Jobling, George F. Woltman & Jim Fougeron
F4184 465917283 4189 48190...37697 1270 2014-12-27 Serge Batalov & Jim Fougeron
F4250 173373 4252 16539...59009 1286 1999-12-22 Charles F. Kerchner III
F4258 1435 4262 14018...22241 1287 1993-08-05 Gary B. Gostin
F4260 209161375 4262 20432...08001 1292 2014-03-14 Takahiro Nohara, Paul Jobling & Jim Fougeron
F4265 72179955 4269 90254...52961 1293 2012-08-03 Takahiro Nohara, Paul Jobling, George F. Woltman & Jim Fougeron
F4332 2466157 4334 11376...69889 1312 2002-10-15 Jim Fougeron
F4652 143918649 4654 14181...75617 1410 2012-10-09 Tapio Rajala, Paul Jobling & Jim Fougeron
F4724 29 4727 26989...58113 1425 1979 Gordon Villy Cormack & Hugh Cowie Williams
F5199 1488947679 5201 67590...12609 1575 2018-07-24 Mark Rodenkirch & Jim Fougeron
F5320 21341 5323 51508...47329 1607 1998-04-22 Tadashi Taura
F5531 1503975 5533 59731...03201 1672 2002-04-11 Gary B. Gostin
F5792 8872947 5794 13057...46049 1752 2003-03-03 Jim Fougeron
F5957 421435 5960 58010...70561 1800 2001-01-16 Gary B. Gostin
F6208 763 6210 19001...05313 1873 1993-08-05 Gary B. Gostin
F6355 115185 6358 10235...52641 1920 2000-11-14 Charles F. Kerchner III
F6390 303 6393 92513...66977 1927 1993-10-06 Gary B. Gostin
F6537 17 6539 46301...76097 1970 1979 Gordon Villy Cormack & Hugh Cowie Williams
F6835 19 6838 52706...39937 2060 1978-09-30 Wilfrid Keller
F6909 6021 6912 31549...46017 2085 1993-11-12 Gary B. Gostin
F7137 118807331 7139 13427...60929 2158 2016-02-21 Gary B. Gostin
F7181 168329 7187 53547...79713 2169 2000-12-26 Gary B. Gostin
F7220 1995420873 7222 21810...11393 2184 2024-12-07 Lélio Ribeiro de Paula, Mark Rodenkirch & Jim Fougeron
F7309 145 7312 19619...53921 2204 1992-10-25 Harvey Dubner
F8239 7473 8242 91773...04193 2485 1998-06-25 Robert Prethaler & Yves Gallot
F8269 592131 8271 39040...49089 2496 2003-05-21 Gary B. Gostin
F8298 1054057 8300 37310...14433 2505 2003-11-01 Craig Kitchen & Yves Gallot
F8555 645 8557 52872...37441 2579 1993-11-01 Harvey Dubner
F9322 8247 9324 52477...56353 2811 1999-11-16 Charles F. Kerchner III
F9428 9 9431 92924...20833 2840 1983-04-01 Wilfrid Keller
F9447 5505161 9449 14900...59233 2852 2012-11-09 Serge Batalov, Paul Jobling & Jim Fougeron
F9448 19 9450 10285...53857 2847 1980-08-30 Wilfrid Keller
F9549 1211 9551 16620...95329 2879 1998-02-15 Tadashi Taura
F9552 60567741 9555 13299...16289 2885 2016-04-04 Gary B. Gostin
F9691 260435 9693 19927...39521 2924 2001-12-12 Gary B. Gostin
F9747 44670651 9749 24629...58113 2943 2014-12-20 Takahiro Nohara & Jim Fougeron
F9863 332436749 9865 15227...16769 2979 2019-03-23 Gary B. Gostin
F11075 171369935 11077 55360...52321 3343 2020-06-29 Gary B. Gostin
F11695 203355 11703 18293...31841 3529 2001-12-31 Gary B. Gostin
F12185 81 12189 14558...83073 3672 1993-09-04 Harvey Dubner
F12825 1814649 12827 37200...33473 3868 2009-10-09 Takahiro Nohara, Jim Fougeron & Jean Penné
F13250 351 13252 62346...56097 3992 1996-10-01 Tadashi Taura
F13623 48265 13626 32987...80961 4107 2000-12-14 Gary B. Gostin
F14252 1173 14254 89300...91233 4294 1997-03-07 Tadashi Taura
F14276 157 14280 80211...93633 4301 1996-08-31 Tadashi Taura
F14528 17217 14530 15914...43809 4379 200012-24 Gary B. Gostin
F14587 24142479 14590 25728...31297 4400 2016-05-25 Adolf Nordin & Jim Fougeron
F15161 55 15164 36242...18881 4567 1993-08-28 Harvey Dubner
F17748 3860269 17750 73967...57857 5350 2012-11-21 Serge Batalov, Paul Jobling & Jim Fougeron
F17906 135 17909 18902...49121 5394 1996-08-31 Tadashi Taura (Prime: Jeffrey Young 1993)
F18345 15071297 18347 14978...08417 5531 2017-09-07 Gary B. Gostin
F18749 11 18759 11563...94369 5649 1992-09-12 Harvey Dubner
F18757 33 18766 44403...37313 5651 1993-08-20 Harvey Dubner
F18933 15175951 18936 30560...59937 5708 2017-09-13 Gary B. Gostin
F19211 13323 19220 83390...14049 5790 2001-05-18 Gary B. Gostin
F22296 4777 22298 11117...76289 6717 2001-03-07 Gary B. Gostin
F23069 681 23071 78736...03489 6948 1997-07 Tadashi Taura; Yves Gallot (Prime: Patrick Demichel 1996)
F23288 19 23290 18507...92257 7013 1992-12-14 Harvey Dubner
F23471 5 23473 59711...76961 7067 1984-09-05 Wilfrid Keller
F24651 99 24653 19414...86209 7424 1996-09-11 Tadashi Taura
F25006 57 25010 32814...58369 7531 1993-12-18 Jeffrey Young
F25599 14698299 25602 13715...01697 7715 2021-03-03 Gary B. Gostin
F28281 81 28285 34826...32193 8517 1996-08-18 Tadashi Taura
F30256 121531 30260 17879...92257 9115 2006-05-16 Asko Vuori, Jim Fougeron, George F. Woltman & Yves Gallot
F31880 10981209 31883 60256...90273 9605 2023-07-10 Serge Batalov
F35563 357 35567 19343...95297 10710 2000-08-27 Nestor S. de Araújo Melo & Yves Gallot
F37236 1844383 37238 10491...19553 11217 2017-12-19 Gary B. Gostin
F38795 1514535 38797 17418...07521 11686 2017-12-27 Gary B. Gostin
F38967 177795 38969 12241...95041 11737 2009-01-10 Takahiro Nohara, Jim Fougeron & Jean Penné
F41894 4935 41897 88514...76321 12616 2001-08-15 Jim Fougeron
F43665 2495 43667 29777...15361 13149 2001-08-21 Jim Fougeron
F45278 547653 45280 23807...80929 13637 2018-01-18 Gary B. Gostin
F48624 28949 48627 44384...39873 14643 2008-05-03 Takahiro Nohara, Jim Fougeron & Jean Penné
F49093 165 49095 19280...02721 14782 1998-08-19 Yves Gallot
F49488 71007 49490 66955...05569 14903 2009-04-18 Takahiro Nohara, Jim Fougeron & Jean Penné
F50078 7619 50081 58225...09889 15080 2002-03-06 Göran Axelsson, Paul Jobling, George F. Woltman & Yves Gallot
F60079 5731 60084 69902...14497 18091 2005-02-14 Michael R. Eaton, Paul Jobling, George F. Woltman & Yves Gallot
F63480 242445 63484 93941...25121 19116 2018-03-10 Gary B. Gostin
F63679 169 63686 42091...95617 19174 1998-05-19 Harvey Dubner & Yves Gallot
F66643 749893 66648 83589...47809 20069 2021-08-11 Erwin Doescher, Jean Penné & Jim Fougeron
F79221 6089 79223 19226...18113 23853 2008-08-01 Payam Samidoost, Jim Fougeron & Jean Penné
F83861 99 83863 18800...20993 25248 1998-10-12 Gennady N. Gusev & Yves Gallot
F90057 189 90061 21822...56929 27114 1999-09-20 Dan Morenus & Yves Gallot
F91213 585 91215 16527...29281 27462 2001-07-30 Göran Axelsson, Paul Jobling, George F. Woltman & Yves Gallot
F94798 21 94801 18485...29793 28540 1995-03 Jeffrey Young
F95328 7 95330 10828...76769 28699 1994-08-23 Jeffrey Young
F100518 79425 100520 27234...48801 30265 2014-10-22 Payam Samidoost, Jim Fougeron & Jean Penné
F104448 927 104451 70983...28897 31446 2001-11-30 Anton P. Oleynick & Yves Gallot
F106432 30967 106436 83084...11713 32045 2012-11-13 Serge Batalov, Paul Jobling & Jim Fougeron
F113547 39 113549 17621...11169 34184 1999-05-11 John Renze & Yves Gallot
F114293 13 114296 43483...30369 34408 1995-08 Jeffrey Young
F125410 5 125413 59404...80961 37754 1995-08 Jeffrey Young
F134995 47893 134998 13416...36193 40644 2020-05-22 Gary B. Gostin
F138557 7333 138560 38148...55009 41715 2011-03-12 D. D'huyvetters, Reynolds, Penné & Fougeron
F142460 159 142462 34406...20737 42888 2001-11-14 Nestor S. de Araújo Melo & Yves Gallot
F146221 57 146223 18404...62657 44020 2000-02-11 Rachel Lewis & Yves Gallot
F157167 3 157169 11495...31137 47314 1995-06-14 Jeffrey Young
F213319 3 213321 31392...99457 64217 1996-08-21 Jeffrey Young
F221670 3771 221676 50324...77857 66735 2011-07-01 Mark Doom, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F223380 56073 223382 26992...83393 67250 2024-07-04 Ryan Propper & Serge Batalov, Jim Fougeron
F226614 4479 226618 29291...78977 68223 2011-07-08 Peter Doggart, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F270091 63 270094 15667...17793 81309 2002-02-05 Tadashi Taura & Yves Gallot
F282717 51 282719 40449...34689 85109 2002-11-13 Kevin Odermatt & Yves Gallot
F287384 211 287388 54035...30817 86515 2004-12-13 Jim Fougeron
F303088 3 303093 36441...61377 91241 1998-01-13 Jeffrey Young
F338295 485 338297 16989...65921 101841 2007-08-21 Wilfrid Keller, S. Murata, Jean Penné & Jim Fougeron
F352279 7905 352281 11112...62561 106052 2012-05-31 James Boerner, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F382447 3 382449 12529...07937 115130 1999-07-25 John B. Cosgrave & Yves Gallot
F410105 1207 410108 77833...40993 123458 2005-11-22 Jun Tajima, Paul Jobling, George F. Woltman & Yves Gallot
F461076 9 461081 14644...91169 138801 2003-08-04 Takahiro Nohara, Paul Jobling, George F. Woltman & Yves Gallot
F472097 89 472099 81154...79233 142118 2004-10-05 Payam Samidoost, Jim Fougeron & George F. Woltman
F476624 651 476632 22002...65697 143484 2008-12-28 Eric Ueda, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F495728 243 495732 38673...68929 149233 2007-05-29 Reto Keiser, Paul Jobling, Jean Penné & Jim Fougeron
F567233 519 567235 29158...16993 170758 2009-03-06 Senji Yamashita, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F585042 151 585044 93704...06817 176118 2007-03-17 Pavlos Saridis, Paul Jobling, Jean Penné & Yves Gallot
F617813 659 617815 46308...50113 185984 2009-03-31 Eric Embling, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F672005 27 672007 49620...23457 202296 2005-08-30 Curtis Cooper, Paul Jobling, George F. Woltman & Yves Gallot
F699760 13243 699764 11908...06689 210655 2023-07-28 Ryan Propper & Serge Batalov, Geoffrey Reynolds, Jean Penné
F906108 1705 906110 33196...65921 272770 2012-06-13 Robert Boniecki, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F960897 11 960901 11621...14273 289262 2005-02-23 Michael R. Eaton, Paul Jobling, George F. Woltman & Yves Gallot
F1099061 2145 1099064 36524...16321 330855 2013-06-18 Sai Yik Tang, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F1246013 329 1246017 10216...02689 375092 2012-01-06 Bruce Dodson, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F1494096 131 1494099 54045...72129 449771 2012-02-07 Rob Derrera, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F1747656 183 1747660 22114...64609 526101 2013-03-10 Bart van Rooijen, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F2141872 25 2141884 53600...70401 644773 2011-09-09 Grzegorz Granowski, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F2145351 3 2145353 12061...10977 645817 2003-02-21 John B. Cosgrave, Paul Jobling, George F. Woltman & Yves Gallot
F2167797 7 2167800 46741...81633 652574 2007-04-17 Curtis Cooper, Paul Jobling, George F. Woltman & Yves Gallot
F2478782 3 2478785 13029...84897 746190 2003-10-10 John B. Cosgrave, Paul Jobling, George F. Woltman & Yves Gallot
F2543548 9 2543551 12610...87233 765687 2011-06-22 J. Scott Brown, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F2662088 267 2662090 23316...27809 801372 2015-02-13 Jay Parangalan, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F2747497 57 2747499 23330...17217 827082 2013-05-14 Marshall Bishop, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F3329780 193 3329782 35202...31873 1002367 2014-07-25 Raymond Ottusch, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F4192909 141 4192911 13470...00769 1262195 2023-07-17 J. Scott Brown, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F5523858 13 5523860 46322...34689 1662849 2020-01-22 J. Scott Brown, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F5798447 99 5798449 11829...41889 1745510 2025-01-14 Valter Cavecchia, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F7963245 27 7963247 43776...25857 2397178 2021-01-16 Tom Greer, Geoffrey Reynolds, Jean Penné & Jim Fougeron
F18233954[4] 7 18233956 34730...83553 5488969 2020-10-05 Ryan Propper, Geoffrey Reynolds, Jean Penné & Jim Fougeron

Sources[]

  1. ↑ Top 20 Fermat Divisors
  2. ↑ https://www.mersenne.ca/fermat.php
  3. ↑ https://64ordle.au/fermat/small/#sum
  4. ↑ http://www.fermatsearch.org/news.html

External links[]

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