Prime factors  k · 2n + 1  of Fermat numbers  Fm
and complete factoring status

Compiled by Wilfrid Keller

 News Flash! 
 On April 18, 2009 Takahiro Nohara discovered another new factor
of a Fermat number: 71007 · 249490 + 1 divides F49488.
This is his fifth factor so far.

  The other most recently discovered factors 
Date  Divisibility Discoverer
Mar 31, 2009     659 · 2617815 + 1 divides F617813     Eric Embling (PG)
Mar 06, 2009     519 · 2567235 + 1 divides F567233     Senji Yamashita (PG)
Jan 10, 2009     177795 · 238969 + 1 divides F38967     Takahiro Nohara

*   *   *

Prime Fermat numbers

F0 = 3,   F1 = 5,   F2 = 17,   F3 = 257,   F4 = 65537

Completely factored Fermat numbers

m     k     n     Year     Discoverer
5 5 7 1732 L. Euler
52347 7 1732 L. Euler
6 1071 8 1855 T. Clausen; F. Landry 1880
262814145745 8 1855 T. Clausen; F. Landry & H. Le Lasseur 1880
7 116503103764643 9 1970 M. A. Morrison & J. Brillhart
11141971095088142685 9 1970 M. A. Morrison & J. Brillhart
8 604944512477 11 1980 R. P. Brent & J. M. Pollard
[59 digits] 11 1980 R. P. Brent & J. M. Pollard
9 37 16 1903 A. E. Western
[46 digits] 11 1990 A. K. Lenstra, M. S. Manasse & a larger team
[96 digits] 11 1990 A. K. Lenstra, M. S. Manasse & a larger team
10 11131 12 1953 J. L. Selfridge
395937 14 1962 J. Brillhart
[37 digits] 12 1995 R. P. Brent
[248 digits] 13 1995 R. P. Brent
11 39 13 1899 A. Cunningham
119 13 1899 A. Cunningham
10253207784531279 14 1988 R. P. Brent
434673084282938711 13 1988 R. P. Brent
[560 digits] 13 1988 R. P. Brent & F. Morain

46 digit  k = 3640431067210880961102244011816628378312190597
37 digit  k = 1137640572563481089664199400165229051

Complete factorizations in standard notation

 F5 = 641 · 6700417
 F6 = 274177 · 67280421310721
 F7 = 59649589127497217 · 5704689200685129054721
 F8 = 1238926361552897 · P62
 F9 = 2424833 · 7455602825647884208337395736200454918783366342657 · P99
F10 = 45592577 · 6487031809 · 4659775785220018543264560743076778192897 · P252
F11 = 319489 · 974849 · 167988556341760475137 · 3560841906445833920513 · P564

Factorizations known to be incomplete

m     k     n     Year     Discoverer
12 7 14 1877 I. M. Pervushin; E. Lucas
397 16 1903 A. E. Western
973 16 1903 A. E. Western
11613415 14 1974 J. C. Hallyburton & J. Brillhart
76668221077 14 1986 R. Baillie
13 41365885 16 1974 J. C. Hallyburton & J. Brillhart
20323554055421 17 1991 R. E. Crandall
6872386635861 19 1991 R. E. Crandall
609485665932753836099 19 1995 R. P. Brent
15 579 21 1925 M. Kraitchik
17753925353 17 1987 G. B. Gostin
1287603889690528658928101555 17 1997 R. E. Crandall & C. van Halewyn
16 1575 19 1953 J. L. Selfridge
180227048850079840107 20 1996 R. E. Crandall & K. Dilcher
17 59251857 19 1978 G. B. Gostin
18 13 20 1903 A. E. Western (Prime: P. Seelhoff 1886)
9688698137266697 23 1999 R. E. Crandall, R. J. McIntosh & C. Tardif
19 33629 21 1962 H. Riesel
308385 21 1963 C. P. Wrathall
21 534689 23 1963 C. P. Wrathall
23 5 25 1878 I. M. Pervushin

Incomplete factorizations in standard notation

F12 = 114689 · 26017793 · 63766529 · 190274191361 · 1256132134125569 · C1187
F13 = 2710954639361 · 2663848877152141313 · 3603109844542291969 ·
319546020820551643220672513 · C2391
F15 = 1214251009 · 2327042503868417 · 168768817029516972383024127016961 · C9808
F16 = 825753601 · 188981757975021318420037633 · C19694
F17 = 31065037602817 · C39444
F18 = 13631489 · 81274690703860512587777 · C78884
F19 = 70525124609 · 646730219521 · C157804
F21 = 4485296422913 · C631294
F23 = 167772161 · C2525215

Composite cofactors of Fermat numbers  Fm 

m     Digits     Year     Prover
12 1187 1986 R. Baillie
13 2391 1995 R. P. Brent
15 9808 1997 R. P. Brent
16 19694 1996 R. P. Brent
17 39444 1987 R. Baillie
18 78884 1999 R. E. Crandall
19 157804 1993 R. E. Crandall, J. Doenias, C. Norrie & J. Young
21 631294 1993 R. E. Crandall, J. Doenias, C. Norrie & J. Young
23 2525215 2000 E. W. Mayer, J. S. Papadopoulos & R. E. Crandall

Composite Fermat numbers  Fm  without known factor

m     Digits     Year     Prover
14 4933 1963 J. L. Selfridge & A. Hurwitz
20 315653 1987 D. A. Buell & J. Young
22 1262612 1993 R. E. Crandall, J. Doenias, C. Norrie & J. Young
24 5050446 1999 E. W. Mayer, J. S. Papadopoulos & R. E. Crandall

Prime factors  k · 2n + 1  of larger Fermat numbers  Fm

m     k     n     Year     Discoverer
25 48413 29 1963 C. P. Wrathall
1522849979 27  07 Aug 1985 G. B. Gostin
16168301139 27 16 Dec 1987 P. B. McLaughlin
26 143165 29 1963 C. P. Wrathall
27 141015 30 1963 C. P. Wrathall
430816215 29 21 Feb 1985 G. B. Gostin
28 25709319373 36 05 Feb 1997 T. Taura
29 1120049 31 17 Oct 1980 G. B. Gostin & P. B. McLaughlin
30 149041 32 1963 C. P. Wrathall
127589 33 1963 C. P. Wrathall
31 5463561471303 33 12 Apr 2001 A. Kruppa & T. Forbes
32 1479 34 1963 C. P. Wrathall
36 5 39 1886 P. Seelhoff
3759613 38 02 Jan 1981 G. B. Gostin & P. B. McLaughlin
37 1275438465 39 29 Apr 1991 G. B. Gostin
38 3 41 1903 J. Cullen & A. Cunningham; A. E. Western
2653 40 1963 C. P. Wrathall
39 21 41 1956 R. M. Robinson
42 43485 45 1963 C. P. Wrathall
43 212675402445 45 23 Dec 2000 P. Samidoost & Durman
48 2139543641769 50 28 May 2001 M. Bodschwinna & Durman
52 4119 54 1963 C. P. Wrathall
21626655 54 1982 W. Keller
55 29 57 1956 R. M. Robinson
58 95 61 1957 R. M. Robinson
61 54985063 66 17 May 1986 G. B. Gostin
62 697 64 1977 D. E. Shippee
63 9 67 1956 R. M. Robinson
64 17853639 67 13 May 1986 G. B. Gostin
66 7551 69 1977 D. E. Shippee
71 683 73 1977 D. E. Shippee
72 76432329 74 31 May 1986 G. B. Gostin
73 5 75 1906 J. C. Morehead
75 3447431 77 Apr 1982 G. B. Gostin
77 425 79 1957 R. M. Robinson & J. L. Selfridge
5940341195 79 08 Apr 1998 T. Taura
81 271 84 1957 R. M. Robinson & J. L. Selfridge
83 1595863660157 87 12 May 2005 V. A. Danilov & Durman
88 119942751127 90 13 Mar 2001 T. Nohara & Durman
90 198922467387 92 26 Mar 2001 P. Grobstich & Durman
91 1421 93 1977 D. E. Shippee
93 92341 96 1979 R. Baillie
94 482524552001 97 18 Apr 2001 P. Grobstich & Durman
96 3334131633063 101 25 Nov 2008 M. Ptáček & Durman
99 16233 104 Nov 1979 G. B. Gostin & P. B. McLaughlin;
H. Suyama
107 1289179925 111 08 Nov 1992 G. B. Gostin
116 3433149787 120 08 Aug 1999 T. Taura
117 7 120 1956 R. M. Robinson
122 5234775 124 21 May 1986 G. B. Gostin
125 5 127 1956 R. M. Robinson
133 88075576149 135 24 Jul 2001 P. Samidoost & Durman
142 8152599 145 22 May 1986 G. B. Gostin
144 17 147 1956 R. M. Robinson
146 37092477 148 23 Dec 1987 G. B. Gostin
147 3125 149 Dec 1979 G. B. Gostin & P. B. McLaughlin
124567335 149 01 Dec 1990 G. B. Gostin
150 1575 157 1956 R. M. Robinson
5439 154 May 1980 G. B. Gostin & P. B. McLaughlin;
H. Suyama
164 1835601567 167 31 May 1993 G. B. Gostin
172 20569603303 174 11 May 2001 L. N. Durman
178 313047661 180 18 Jun 1991 G. B. Gostin
184 117012935 187 17 Dec 1990 G. B. Gostin
201 4845 204 27 Jul 1980 G. B. Gostin & P. B. McLaughlin
205 232905 207 01 Jan 1984 W. Keller
207 3 209 1956 R. M. Robinson
215 32111 217 02 Dec 1980 H. Suyama
226 15 229 1956 R. M. Robinson
228 29 231 1956 R. M. Robinson
230 372236097 232 13 Apr 2000 L. N. Durman
232 70899775 236 24 Nov 1991 G. B. Gostin
250 403 252 1957 R. M. Robinson & J. L. Selfridge
251 85801657 254 30 Nov 1991 G. B. Gostin
255 629 257 1979 R. Baillie
256 36986355 258 20 Jan 1991 G. B. Gostin
259 36654265 262 21 Jan 1991 G. B. Gostin
267 177 271 1957 R. M. Robinson & J. L. Selfridge
268 21 276 1956 R. M. Robinson
275 22347 279 16 Jan 1984 W. Keller
284 7 290 1956 R. M. Robinson
1061341513 286 25 Dec 2000 L. N. Durman
286 78472588395 288 02 Nov 2002 V. A. Danilov & Durman
287 5915 289 26 Dec 1980 H. Suyama
297 72677552745 301 13 Feb 2003 V. A. Danilov & Durman
298 247 302 1979 R. Baillie
301 7183437 304 04 Nov 1990 G. B. Gostin
316 7 320 1956 R. M. Robinson
329 1211 333 12 Jan 1981 H. Suyama
334 27609 341 25 Jan 1984 W. Keller
338 27654487 342 22 Dec 1990 G. B. Gostin
343 4844391185 345 29 Aug 2001 V. A. Danilov & Durman
353 18908555 355 25 Dec 1990 G. B. Gostin
370 573230511 373 22 Aug 2000 L. N. Durman
375 733251 377 09 Jun 1986 G. B. Gostin
376 810373 378 09 Jun 1986 G. B. Gostin
380 321116871 385 26 Jun 2000 L. N. Durman
398 120845 401 18 Apr 1984 W. Keller
416 8619 418 1981 H. Suyama
38039 419 16 Feb 1984 W. Keller
417 118086729 421 13 Jun 1992 G. B. Gostin
431 5769285 434 30 Nov 1990 G. B. Gostin
452 27 455 1956 R. M. Robinson
468 27114089 471 25 Sep 1992 G. B. Gostin
480 5673968845 484 24 Nov 2001 V. A. Danilov & Durman
544 225 547 1979 R. Baillie
547 77377 550 05 Jun 1986 G. B. Gostin
556 127 558 1976 G. Matthew & H. C. Williams
569 6616590375 575 25 Feb 2003 S. Kuzmin & Durman
579 63856313 581 04 Oct 1999 T. Taura
600 6213186413 605 29 Sep 2005 A. Vuori & Durman
620 10084141 624 19 Jan 1992 G. B. Gostin
635 4258979 645 12 Jul 1991 G. B. Gostin
637 11969 643 08 Mar 1984 W. Keller
642 52943971 644 08 Aug 1999 T. Taura
667 491628159 669 12 Mar 2001 T. Taura
692 717 695 1979 A. O. L. Atkin & N. W. Rickert
723 554815 730 04 Jan 1991 G. B. Gostin
744 17 747 1976 G. Matthew & H. C. Williams
851 497531 859 18 Jan 1988 G. B. Gostin
885 16578999 887 12 Jul 1992 G. B. Gostin
906 57063 908 19 May 1986 G. B. Gostin
931 1985 933 22 Dec 1980 W. Keller
971 541664191 976 04 Apr 2002 D. Komin & Durman
1069 137883 1073 01 Sep 1992 G. B. Gostin
1082 82165 1084 08 Apr 1991 G. B. Gostin
1114 11618577 1116 22 Jan 2001 G. B. Gostin
1123 25835 1125 15 Jan 1987 G. B. Gostin
1160 2018719057 1162 15 May 2005 M. Pacher & Durman
1225 79707 1231 08 Jun 1991 G. B. Gostin
1229 29139 1233 07 Dec 1987 G. B. Gostin
1394 62705223 1396 06 Dec 2001 T. Taura
1451 13143 1454 30 Oct 1986 G. B. Gostin
1551 291 1553 1979 A. O. L. Atkin & N. W. Rickert
1598 10923781 1600 21 Dec 2000 T. Taura
1710 351276975 1719 09 Mar 2008 M. Pacher, Jobling, Woltman & Fougeron
1722 364182745 1724 19 Apr 2008 M. Pacher, Jobling, Woltman & Fougeron
1849 98855 1851 01 Sep 1992 G. B. Gostin
1945 5 1947 1957 R. M. Robinson
1990 150863 1993 30 Oct 1995 T. Taura
2023 29 2027 1979 A. O. L. Atkin & N. W. Rickert;
G. V. Cormack & H. C. Williams
2059 591909 2063 09 May 2000 R. Ballinger & Gallot
2089 431 2099 17 Aug 1983 H. Suyama
2456 85 2458 1979 A. O. L. Atkin & N. W. Rickert
3310 5 3313 1979 A. O. L. Atkin & N. W. Rickert;
G. V. Cormack & H. C. Williams
3506 501 3508 26 Jul 1986 G. B. Gostin
3723 13308899 3725 03 Jul 2002 J. Fougeron
4250 173373 4252 22 Dec 1999 C. F. Kerchner
4258 1435 4262 05 Aug 1993 G. B. Gostin
4332 2466157 4334 15 Oct 2002 J. Fougeron
4724 29 4727 1979 G. V. Cormack & H. C. Williams
5320 21341 5323 22 Apr 1998 T. Taura
5531 1503975 5533 11 Apr 2002 G. B. Gostin
5792 8872947 5794 03 Mar 2003 J. Fougeron
5957 421435 5960 16 Jan 2001 G. B. Gostin
6208 763 6210 05 Aug 1993 G. B. Gostin
6355 115185 6358 14 Nov 2000 C. F. Kerchner
6390 303 6393 06 Oct 1993 G. B. Gostin
6537 17 6539 1979 G. V. Cormack & H. C. Williams
6835 19 6838 30 Sep 1978 W. Keller
6909 6021 6912 12 Nov 1993 G. B. Gostin
7181 168329 7187 26 Dec 2000 G. B. Gostin
7309 145 7312 25 Oct 1992 H. Dubner
8239 7473 8242 25 Jun 1998 R. Prethaler & Gallot
8269 592131 8271 21 May 2003 G. B. Gostin
8298 1054057 8300 01 Nov 2003 C. Kitchen & Gallot
8555 645 8557 01 Nov 1993 H. Dubner
9322 8247 9324 16 Nov 1999 C. F. Kerchner
9428 9 9431 01 Apr 1983 W. Keller
9448 19 9450 30 Aug 1980 W. Keller
9549 1211 9551 15 Feb 1998 T. Taura
9691 260435 9693 12 Dec 2001 G. B. Gostin
11695 203355 11703 31 Dec 2001 G. B. Gostin
12185 81 12189 04 Sep 1993 H. Dubner
13250 351 13252 01 Oct 1996 T. Taura
13623 48265 13626 14 Dec 2000 G. B. Gostin
14252 1173 14254 07 Mar 1997 T. Taura
14276 157 14280 31 Aug 1996 T. Taura
14528 17217 14530 24 Dec 2000 G. B. Gostin
15161 55 15164 28 Aug 1993 H. Dubner
17906 135 17909 31 Aug 1996 T. Taura (Prime: J. Young 1993)
18749 11 18759 12 Sep 1992 H. Dubner
18757 33 18766 20 Aug 1993 H. Dubner
19211 13323 19220 18 May 2001 G. B. Gostin
22296 4777 22298 07 Mar 2001 G. B. Gostin
23069 681 23071 Jul 1997 T. Taura; Y. Gallot
(Prime: P. Demichel 1996)
23288 19 23290 14 Dec 1992 H. Dubner
23471 5 23473 05 Sep 1984 W. Keller
24651 99 24653 11 Sep 1996 T. Taura
25006 57 25010 18 Dec 1993 J. Young
28281 81 28285 18 Aug 1996 T. Taura
30256 121531 30260 16 May 2006 A. Vuori, Fougeron, Woltman & Gallot
35563 357 35567 27 Aug 2000 N. S. Melo & Gallot
38967 177795 38969 10 Jan 2009 T. Nohara, Fougeron & Penné
41894 4935 41897 15 Aug 2001 J. Fougeron
43665 2495 43667 21 Aug 2001 J. Fougeron
48624 28949 48627 03 May 2008 T. Nohara, Fougeron & Penné
49093 165 49095 19 Aug 1998 Y. Gallot
49488 71007 49490 18 Apr 2009 T. Nohara, Fougeron & Penné
50078 7619 50081 06 Mar 2002 G. Axelsson, Jobling, Woltman & Gallot
60079 5731 60084 14 Feb 2005 M. R. Eaton, Jobling, Woltman & Gallot
63679 169 63686 19 May 1998 H. Dubner & Gallot
79221 6089 79223 01 Aug 2008 P. Samidoost, Fougeron & Penné
83861 99 83863 12 Oct 1998 G. N. Gusev & Gallot
90057 189 90061 20 Sep 1999 D. Morenus & Gallot
91213 585 91215 30 Jul 2001 G. Axelsson, Jobling, Woltman & Gallot
94798 21 94801 Mar 1995 J. Young
95328 7 95330 23 Aug 1994 J. Young
104448 927 104451 30 Nov 2001 A. P. Oleynick & Gallot
113547 39 113549 11 May 1999 J. Renze & Gallot
114293 13 114296 Aug 1995 J. Young
125410 5 125413 Aug 1995 J. Young
142460 159 142462 14 Nov 2001 N. S. Melo & Gallot
146221 57 146223 11 Feb 2000 R. Lewis & Gallot
157167 3 157169 14 Jun 1995 J. Young
213319 3 213321 21 Aug 1996 J. Young
270091 63 270094 05 Feb 2002 T. Taura & Gallot
282717 51 282719 13 Nov 2002 K. Odermatt & Gallot
287384 211 287388 13 Dec 2004 J. Fougeron
303088 3 303093 13 Jan 1998 J. Young
338295 485 338297 21 Aug 2007 W. Keller, S. Murata, Penné & Fougeron
382447 3 382449 25 Jul 1999 J. B. Cosgrave & Gallot
410105 1207 410108 22 Nov 2005 J. Tajima, Jobling, Woltman & Gallot
461076 9 461081 04 Aug 2003 T. Nohara, Jobling, Woltman & Gallot
472097 89 472099 05 Oct 2004 P. Samidoost, Fougeron & Woltman
476624 651 476632 28 Dec 2008 E. Ueda, Reynolds, Penné & Fougeron
495728 243 495732 29 May 2007 R. Keiser, Jobling, Penné & Fougeron
567233 519 567235 06 Mar 2009 S. Yamashita, Reynolds, Penné & Fougeron
585042 151 585044 17 Mar 2007 P. Saridis, Jobling, Penné & Gallot
617813 659 617815 31 Mar 2009 E. Embling, Reynolds, Penné & Fougeron
672005 27 672007 30 Aug 2005 C. Cooper, Jobling, Woltman & Gallot
960897 11 960901 23 Feb 2005 M. R. Eaton, Jobling, Woltman & Gallot
2145351 3 2145353 21 Feb 2003 J. B. Cosgrave, Jobling, Woltman & Gallot
2167797 7 2167800 17 Apr 2007 C. Cooper, Jobling, Woltman & Gallot
2478782 3 2478785 10 Oct 2003 J. B. Cosgrave, Jobling, Woltman & Gallot

Full names of researchers

Pierre de Fermat (1601-1665), Leonhard Euler (1707-1783), Thomas Clausen (1801-1885), James Cullen (1867-1933), Allan J. C. Cunningham (1842-1928), Maurice Kraitchik (1882-1957), Fortuné Landry, H. Le Lasseur, Édouard Lucas (1842-1891), J. C. Morehead, Ivan M. Pervushin (Іван М. Первушин, 1827-1900), Paul Seelhoff (1829-1896), A. E. Western.

A. Oliver L. Atkin (1925-2008), Göran Axelsson, Robert Baillie, J. Ray Ballinger, Marko Bodschwinna, Richard P. Brent, John Brillhart, Duncan A. Buell, Gordon V. Cormack, Curtis Cooper, John B. Cosgrave, Richard E. Crandall, Vasily A. Danilov (Василий А. Данилов), Patrick Demichel, Karl Dilcher, J. Doenias, Harvey Dubner, Leonid N. Durman (Леонид Н. Дурман), Michael R. Eaton, Eric Embling, Tony Forbes, Jim Fougeron, Yves Gallot, Gary B. Gostin, Peter Grobstich, Gennady N. Gusev (Геннадий Н. Гусев), John C. Hallyburton Jr., Alexander Hurwitz, Paul Jobling, Reto Keiser, Wilfrid Keller, Charles F. Kerchner III, Craig Kitchen, Dmitry Komin (Дмитрий Комин), Alexander Kruppa, Sergey Kuzmin (Сергеий Кузмин), Arjen K. Lenstra, Rachel Lewis, Mark S. Manasse, G. Matthew, Ernst W. Mayer, Richard J. McIntosh, Michael A. Morrison, Philip P. McLaughlin Jr., Nestor S. de Araújo Melo, François Morain, Dan Morenus, Souichi Murata, C. Norrie, Takahiro Nohara, Kevin Odermatt, Anton P. Oleynick (Антон П. Олеиник), Maximilian Pacher, Jason S. Papadopoulos, Jean Penné, John M. Pollard, Robert Prethaler, Martin Ptáček, John Renze, Geoffrey Reynolds, N. W. Rickert, Hans Riesel, Raphael M. Robinson (1911-1995), Payam Samidoost, Pavlos Saridis, John L. Selfridge, D. E. Shippee, Hiromi Suyama, Jun Tajima, Tadashi Taura, Claude Tardif, Eric Ueda, C. van Halewyn, Asko Vuori, Hugh C. Williams, George F. Woltman, Claude P. Wrathall, Senji Yamashita, Jeffrey Young.

Names given without initials in the discoverer column refer to an indirect involvement of programmers whose software was essential for the discovery of the particular prime factor: Durman (Fermat), Fougeron (FermFact, PFGW), Gallot (Proth), Jobling (NewPGen), Penné (LLR), Reynolds (Srsieve), Woltman (PRP).
A semicolon indicates independent discovery by two individuals or teams.

Summary of factoring status for Fermat numbers  Fm 
as of April 18, 2009

Prime   m = 0, 1, 2, 3, 4
Completely factored m = 5, 6, 7, 8 (two factors each), 9 (3 factors),
       10 (4 factors), 11 (5 factors)
Five prime factors known m = 12*
Four prime factors known m = 13*
Three prime factors known m = 15*, 25
Two prime factors known m = 16*, 18*, 19*, 27, 30, 36, 38, 52, 77, 147, 150,
       284, 416
Only one prime factor known m = 17*, 21*, 23*, 26, 28, 29, 31, 32, 37, 39, 42, 43
       and 201 values of  m  with  43 < m < 2478782
Composite but no factor known   m = 14, 20, 22, 24
Character unknown   m = 33, 34, 35, 40, 41, 44, 45, 46, 47, 49, 50, . . .
* Cofactor composite

274 prime factors known
241 Fermat numbers known to be composite

Count of factors according to difference  n - m

n − m   = 2, 3, 4, 5, 6, 7, 8, 9,   10
Frequency 137,   66,   37,   10,   8,   5,   5,   3,   3

Search limits for  k · 2n + 1  as possible factors of some  Fm,  m < n − 2
All odd  k < Ln  tested

For more detailed information,
see http://www.fermatsearch.org/status.htm
and http://www.prothsearch.net/status.html

n Ln
14 -16 700000000000000  =7 · 1014
17 -25 500000000000000  =5 · 1014
26 -28 300000000000000  =3 · 1014
29 -34 150000000000000  =1.5 · 1014
  35 1000000000000000  = 1015
36 -38 400000000000000 =4 · 1014
39 -49 100000000000000 =1014
50 -51 80000000000000 =8 · 1013
52 -64 30000000000000 =3 · 1013
65 -71 10000000000000 =1013
72 -100 1000000000000 =1012
101 -200       100000000000 =1011
201 -220       40000000000 =4 · 1010
221 -500       10000000000 =1010
501 -809 1000000000 =109
810 -999 300000000 =3 · 108
1000 -1199 3400000000 =3.4 · 109
1200 -1999 90000000 =9 · 107
2000 -2014 33554432 =225
2015 -3999 32000000 =3.2 · 107
4000 -4062 16777216 =224
4063 -5999 16000000 =1.6 · 107
6000 -8158 2097152 =221
8159 -9000 1000000 =106
9001 -10000 500000 =5 · 105
10001 -16350 400000 =4 · 105
16351 -32734 50000 =5 · 104
32735 -35300 10000 =104
35301 -40000 100000 =105
40001 -55000 50000 =5 · 104
55001 -100000 10000 =104
100001 -170000 1200 
170001 -180000 2048 
180001 -600000 1200 

URL: http://www.prothsearch.net/fermat.html
Last modified: April 18, 2009.