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GF Divisors of Fm = 22m+1
GF Divisors k•2n+1 of Fermat numbers Fm = 22m+1.
There are 184 GFN divisors:
| m | k | n | Discoverer |
|---|---|---|---|
| 38 | 3 | 41 | 1903 James Cullen,Allan Cunningham,Alfred Edward Western |
| 207 | 3 | 209 | 1956 Raphael M. Robinson |
| 157167 | 3 | 157169 | 1995-06 Jeffrey Young |
| 213319 | 3 | 213321 | 1996-08-21 Jeffrey Young |
| 303088 | 3 | 303093 | 1998-01-13 Jeffrey Young |
| 382447 | 3 | 382449 | 1999-07-25 John Cosgrave |
| 2145351 | 3 | 2145353 | 2003-02-21 John Cosgrave |
| 2478782 | 3 | 2478785 | 2003-10-10 John Cosgrave |
| 5 | 5 | 7 | 1732 Leonhard Euler |
| 23 | 5 | 25 | 1878 Ivan Mikheevich Pervushin |
| 36 | 5 | 39 | 1886 Paul Seelhoff |
| 73 | 5 | 75 | 1906 James Caddall Morehead |
| 125 | 5 | 127 | 1956 Raphael M. Robinson |
| 1945 | 5 | 1947 | 1957 Raphael M. Robinson |
| 3310 | 5 | 3313 | 1979 A. Oliver L. Atkin,Neil W. Rickert |
| 23471 | 5 | 23473 | 1984-09-05 Wilfrid Keller |
| 125410 | 5 | 125413 | 1995-08 Jeffrey Young |
| 12 | 7 | 14 | 1877 Ivan Mikheevich Pervushin,Édouard Lucas |
| 117 | 7 | 120 | 1956 Raphael M. Robinson |
| 284 | 7 | 290 | 1956 Raphael M. Robinson |
| 316 | 7 | 320 | 1956 Raphael M. Robinson |
| 95328 | 7 | 95330 | 1994-08-23 Jeffrey Young |
| 2167797 | 7 | 2167800 | 2007-04-17 Curtis Cooper |
| 18233954 | 7 | 18233956 | 2020-10-05 Ryan Propper |
| 63 | 9 | 67 | 1956 Raphael M. Robinson |
| 9428 | 9 | 9431 | 1983-04-01 Wilfrid Keller |
| 461076 | 9 | 461081 | 2003-08-04 Takahiro Nohara |
| 2543548 | 9 | 2543551 | 2011 James Scott Brown |
| 18749 | 11 | 18759 | 1992-09-12 Harvey Dubner |
| 960897 | 11 | 960901 | 2005-02-23 Michael Richard Eaton |
| 18 | 13 | 20 | 1903 Alfred Edward Western |
| 114293 | 13 | 114296 | 1995-08 Jeffrey Young |
| 5523858 | 13 | 5523860 | 2020-01-22 James Scott Brown,PrimeGrid Fermat Divisor Search,(Srsieve/LLR/PFGW) |
| 226 | 15 | 229 | 1956 Raphael M. Robinson |
| 144 | 17 | 147 | 1956 Raphael M. Robinson |
| 744 | 17 | 747 | 1976 G. Matthew,Hugh C. Williams |
| 6537 | 17 | 6539 | 1979 Gordon V. Cormack,Hugh C. Williams |
| 6835 | 19 | 6838 | 1978-09-30 Wilfrid Keller |
| 9448 | 19 | 9450 | 1980-08-30 Wilfrid Keller |
| 23288 | 19 | 23290 | 1992-12-14 Harvey Dubner |
| 39 | 21 | 41 | 1956 Raphael M. Robinson |
| 268 | 21 | 276 | 1956 Raphael M. Robinson |
| 94798 | 21 | 94801 | 1995-03 Jeffrey Young |
| 2141872 | 25 | 2141884 | 2011-09-09 Grzegorz Granowski |
| 452 | 27 | 455 | 1956 Raphael M. Robinson |
| 672005 | 27 | 672007 | 2005-08-30 Curtis Cooper |
| 7963245 | 27 | 7963247 | 2021-01-16 Tom Greer,PrimeGrid Fermat Divisor Search,(Srsieve/LLR/PFGW) |
| 55 | 29 | 57 | 1956 Raphael M. Robinson |
| 228 | 29 | 231 | 1956 Raphael M. Robinson |
| 2023 | 29 | 2027 | 1979 A. Oliver L. Atkin,Neil W. Rickert |
| 4724 | 29 | 4727 | 1979 Gordon V. Cormack,Hugh C. Williams |
| 18757 | 33 | 18766 | 1993-08-20 Harvey Dubner |
| 9 | 37 | 16 | 1903 Alfred Edward Western |
| 11 | 39 | 13 | 1899 Allan Cunningham |
| 113547 | 39 | 113549 | 1999-05-11 John Renze |
| 2747497 | 57 | 2747499 | 2013-05-14 Marshall Bishop |
| 270091 | 63 | 270094 | 2002-02-05 Tadashi Taura |
| 58 | 95 | 61 | 1957 Raphael M. Robinson |
| 11 | 119 | 13 | 1899 Allan Cunningham |
| 556 | 127 | 558 | 1976 G. Matthew,Hugh C. Williams |
| 1494096 | 131 | 1494099 | 2012-02-07 Rob Derrera |
| 267 | 177 | 271 | 1957 Raphael M. Robinson,John L. Selfridge |
| 1747656 | 183 | 1747660 | 2013-03-10 Bart van Rooijen |
| 3329780 | 193 | 3329782 | 2014-07-25 Raymond Ottusch |
| 2662088 | 267 | 2662090 | 2015-02-13 Jay Parangalan |
| 81 | 271 | 84 | 1957 Raphael M. Robinson,John L. Selfridge |
| 12 | 397 | 16 | 1903 Alfred Edward Western |
| 250 | 403 | 252 | 1957 Raphael M. Robinson,John L. Selfridge |
| 77 | 425 | 79 | 1957 Raphael M. Robinson,John L. Selfridge |
| 15 | 579 | 21 | 1925 Maurice Kraitchik |
| 255 | 629 | 257 | 1979 Robert Baillie |
| 71 | 683 | 73 | 1977 D. E. Shippee |
| 62 | 697 | 64 | 1977 D. E. Shippee |
| 12 | 973 | 16 | 1903 Alfred Edward Western |
| 6 | 1071 | 8 | 1855 Thomas Clausen,Fortuné Landry |
| 91 | 1421 | 93 | 1977 D. E. Shippee |
| 32 | 1479 | 34 | 1963 Claude P. Wrathall |
| 16 | 1575 | 19 | 1953-08-14 John L. Selfridge |
| 150 | 1575 | 157 | 1956 Raphael M. Robinson |
| 38 | 2653 | 40 | 1963 Claude P. Wrathall |
| 147 | 3125 | 149 | 1979 Gary B. Gostin,Philip B. McLaughlin |
| 52 | 4119 | 54 | 1963 Claude P. Wrathall |
| 201 | 4845 | 204 | 1980-07-27 Gary B. Gostin,Philip B. McLaughlin |
| 150 | 5439 | 154 | 1980-05 Gary B. Gostin,Philip B. McLaughlin,Hiromi Suyama |
| 66 | 7551 | 69 | 1977 D. E. Shippee |
| 10 | 11131 | 12 | 1953-08-15 John L. Selfridge |
| 99 | 16233 | 104 | 1979-11 Gary B. Gostin,Philip B. McLaughlin,Hiromi Suyama |
| 215 | 32111 | 217 | 1980-12-02 Hiromi Suyama |
| 19 | 33629 | 21 | 1962-11-16 Hans Riesel |
| 42 | 43485 | 45 | 1963 Claude P. Wrathall |
| 134995 | 47893 | 134998 | 2020-05-22 Gary B. Gostin |
| 25 | 48413 | 29 | 1963 Claude P. Wrathall |
| 5 | 52347 | 7 | 1732 Leonhard Euler |
| 93 | 92341 | 96 | 1979 Robert Baillie |
| 30 | 127589 | 33 | 1963 Claude P. Wrathall |
| 27 | 141015 | 30 | 1963 Claude P. Wrathall |
| 26 | 143165 | 29 | 1963 Claude P. Wrathall |
| 30 | 149041 | 32 | 1963 Claude P. Wrathall |
| 205 | 232905 | 207 | 1984-01-01 Wilfrid Keller |
| 19 | 308385 | 21 | 1963 Claude P. Wrathall |
| 10 | 395937 | 14 | 1962 John Brillhart |
| 21 | 534689 | 23 | 1963 Claude P. Wrathall |
| 66643 | 749893 | 66648 | 2021-08-12 Erwin Doescher |
| 29 | 1120049 | 31 | 1980-10-17 Gary B. Gostin,Philip B. McLaughlin |
| 75 | 3447431 | 77 | 1982-04 Gary B. Gostin |
| 36 | 3759613 | 38 | 1981-01-02 Gary B. Gostin,Philip B. McLaughlin |
| 635 | 4258979 | 645 | 1991-07-12 Gary B. Gostin |
| 122 | 5234775 | 124 | 1986-05-21 Gary B. Gostin |
| 142 | 8152599 | 145 | 1986-05-22 Gary B. Gostin |
| 12 | 11613415 | 14 | 1974 John C. Hallyburton,John Brillhart |
| 64 | 17853639 | 67 | 1986-05-13 Gary B. Gostin |
| 52 | 21626655 | 54 | 1982 Wilfrid Keller |
| 259 | 36654265 | 262 | 1991-01-21 Gary B. Gostin |
| 256 | 36986355 | 258 | 1991-01-20 Gary B. Gostin |
| 146 | 37092477 | 148 | 1987-12-23 Gary B. Gostin |
| 13 | 41365885 | 16 | 1974 John C. Hallyburton,John Brillhart |
| 61 | 54985063 | 66 | 1986-05-17 Gary B. Gostin |
| 17 | 59251857 | 19 | 1978-05 Gary B. Gostin |
| 232 | 70899775 | 236 | 1991-11-24 Gary B. Gostin |
| 72 | 76432329 | 74 | 1986-05-31 Gary B. Gostin |
| 251 | 85801657 | 254 | 1991-11-30 Gary B. Gostin |
| 184 | 117012935 | 187 | 1990-12-17 Gary B. Gostin |
| 147 | 124567335 | 149 | 1990-12-01 Gary B. Gostin |
| 11075 | 171369935 | 11077 | 2020-06-29 Gary B. Gostin |
| 178 | 313047661 | 180 | 1991-06-18 Gary B. Gostin |
| 230 | 372236097 | 232 | 2000-04-13 Leonid N. Durman |
| 27 | 430816215 | 29 | 1985-02-21 Gary B. Gostin |
| 284 | 1061341513 | 286 | 2000-12-25 Leonid N. Durman |
| 37 | 1275438465 | 39 | 1991-04-29 Gary B. Gostin |
| 107 | 1289179925 | 111 | 1992-11-08 Gary B. Gostin |
| 25 | 1522849979 | 27 | 1985-08-07 Gary B. Gostin |
| 164 | 1835601567 | 167 | 1993-05-31 Gary B. Gostin |
| 116 | 3433149787 | 120 | 1999-08-08 Tadashi Taura |
| 943 | 4785972759 | 954 | 2012-03-28 Andriy Sen,(GMP-Fermat) |
| 77 | 5940341195 | 79 | 1998-04-08 Tadashi Taura |
| 25 | 16168301139 | 27 | 1987-12-16 Philip B. McLaughlin |
| 15 | 17753925353 | 17 | 1987-08-04 Gary B. Gostin |
| 172 | 20569603303 | 174 | 2001-05-11 Leonid N. Durman |
| 28 | 25709319373 | 36 | 1997-02-05 Tadashi Taura |
| 12 | 76668221077 | 14 | 1986-07-25 Robert Baillie |
| 133 | 88075576149 | 135 | 2001-07-24 Payam Samidoost |
| 88 | 119942751127 | 90 | 2001-03-13 Takahiro Nohara |
| 90 | 198922467387 | 92 | 2001-03-26 Peter Grobstich |
| 1379 | 205071338665 | 1382 | 2021-11-24 Gary B. Gostin |
| 43 | 212675402445 | 45 | 2000-12-23 Payam Samidoost |
| 6 | 262814145745 | 8 | 1855 Thomas Clausen,Fortuné Landry,Henri Le Lasseur |
| 94 | 482524552001 | 97 | 2001-04-18 Peter Grobstich |
| 8 | 604944512477 | 11 | 1980 Richard P. Brent,John M. Pollard |
| 83 | 1595863660157 | 87 | 2005-05-12 Vasily A. Danilov |
| 48 | 2139543641769 | 50 | 2001-05-28 Marko Bodschwinna |
| 166 | 2674670937447 | 171 | 2012-07-10 Roman Maznichenko |
| 96 | 3334131633063 | 101 | 2008-11-25 Martin Ptáček,(Fermat) |
| 459 | 5449229488169 | 465 | 2013-05-08 Ryan Propper,(GMP-Fermat) |
| 31 | 5463561471303 | 33 | 2001-04-12 Alexander Kruppa,Tony Forbes |
| 13 | 6872386635861 | 19 | 1991-05-09 Richard Crandall |
| 86 | 20018578522347 | 88 | 2012-06-07 Michael Dangler |
| 13 | 20323554055421 | 17 | 1991-01-05 Richard Crandall |
| 195 | 48595346636925 | 197 | 2014-06-26 Serge Batalov |
| 52 | 81909357657279 | 54 | 2010-03-15 Cedric Vonck |
| 42 | 111318179143061 | 45 | 2011-03-20 Roman Maznichenko |
| 7 | 116503103764643 | 9 | 1970-09-13 Michael A. Morrison,John Brillhart |
| 132 | 1075441212722595 | 135 | 2018-12-19 Peter Strasser |
| 65 | 1210895760431083 | 68 | 2013-01-29 Roman Maznichenko |
| 118 | 1527888802614951 | 120 | 2019-01-28 Peter Strasser |
| 39 | 2864929972774011 | 41 | 2012-12-07 Tapio Rajala |
| 103 | 7595155767819149 | 105 | 2020-12-31 Peter Strasser,FermatSearch,(mmff) |
| 18 | 9688698137266697 | 23 | 1999-04-16 Richard E. Crandall,Richard J. McIntosh,Claude Tardif |
| 11 | 10253207784531279 | 14 | 1988-05-17 Richard P. Brent |
| 11 | 434673084282938711 | 13 | 1988-05-13 Richard P. Brent |
| 7 | 11141971095088142685 | 9 | 1970-09-13 Michael A. Morrison,John Brillhart |
| 16 | 180227048850079840107 | 20 | 1996-12 Richard E. Crandall,Karl Dilcher |
| 13 | 609485665932753836099 | 19 | 1995-06-16 Richard P. Brent |
| 15 | 1287603889690528658928101555 | 17 | 1997-07-03 Richard E. Crandall,C. van Halewyn |
| 22 | 3853959202444067657533632211 | 24 | 2010-03-26 David Bessell |
| 19 | 8962167624028624126082526703 | 22 | 2009-07-18 David Bessell |
| 10 | 113764057256348108966419940016...51<37> | 12 | 1995-10-20 Richard P. Brent |
| 17 | 147839757915544940745524731796...11<44> | 19 | 2011-03-15 David Bessell,(Prime95) |
| 9 | 364043106721088096110224401181...97<46> | 11 | 1990-06-15 Arjen K. Lenstra,Mark S. Manasse |
| 14 | 178418099781912795759637441764...17<49> | 16 | 2010-02-03 Tapio Rajala,(Prime95) |
| 12 | 173532302104295945791330996991...99<50> | 15 | 2010-03-27 Michael Vang,(GMP-ECM) |
| 8 | 456355662672646375825993936521...15<59> | 11 | 1980 Richard P. Brent,John M. Pollard |
| 9 | 362128936829849024182024971631...07<96> | 11 | 1990-06-15 Arjen K. Lenstra,Mark S. Manasse |
| 10 | 159228362311386950350933555659...03<248> | 13 | 1995 Richard P. Brent |
| 11 | 211746151341732855749827845293...53<560> | 13 | 1988-06-20 Richard P. Brent,François Morain |
