All researchers of Fermat numbers, who found at least one factor

N	Complete name and links to the biography or personal sites.	Years of life	Quantity of found divisors personally or in co-authorship	Year of the first mention	Country	Portrait
Manual calculations
1	Pierre Fermat	(1601-1665)	5 prime	1640	France
2	Leonhard Euler	(1707-1783)	2	1732	Switzerland/Russia
3	Thomas Clausen	(1801-1885)	2	1855	Denmark/Russia
4	Edouard Lucas	(1842-1891)	1	1877	France
5	Ivan Mikheevich Pervushin	(1829-1900)	2	1877	Russia
6	Fortune Landry	(1798-?)	2	1880	France
7	Paul Peter Heinrich Seelhoff	(1829-1896)	1	1886	Germany
8	Allan J.C. Cunningham		3	1899
9	A.E.Western		5	1903
10	James Cullen	(1867-1933)	1	1903	Ireland
11	J.C.Morehead		1	1906
12	Maurice Borisovich Kraitchik	(1882-1957)	1	1925	Belgium
Computer calculations
13	John L. Selfridge		6	1953	USA
14	Raphael M. Robinson	(1911-1994)	20	1956	USA
15	John Brillhart	(1930 - )	5	1962	USA
16	Hans Riesel	(1929 - )	1	1962	Sweden
17	Claude P. Wrathall		11	1963	USA
18	Michael A.Morrison		2	1970
19	John C. Hallyburton		2	1974
20	G. Matthew		2	1976
21	Hugh C. Williams		6	1976	Canada
22	D.E.Shippee		4	1977	USA
23	Gary B.Gostin	(1954 - )	65	1978	USA
24	Wilfrid Keller	(1937 - )	13	1978	Argentina/Germany
25	Robert J. Baillie		5	1979
26	Philip B. McLaughlin		7	1979	USA
27	Hiromi Suyama		7	1979	Japan
28	A.Oliver L.Atkin		5	1979
29	N.W.Rickert		5	1979
30	Gordon V. Cormack	(1956 - )	4	1979	Canada
31	Richard Peirce Brent	(1946 - )	8	1980	Australian
32	John M.Pollard		2	1980	England
33	Francois Morain		1	1988	France
34	Arjen K.Lenstra		2	1990
35	Mark S.Manasse		2	1990	USA
36	Richard E. Crandall	(1947 - )	5	1991	USA
37	Harvey Dubner		8	1992	USA
38	Jeffrey Young		8	1993	USA
39	Tadashi Taura	(1954 -)	18	1995	Japan
40	Karl Dilcher		1	1996	Germany/Canada
41	Chris Van Halewyn		1	1997
42	Patrick Demichel		1	1997	France
43	Yves Gallot	(1966 - )	26	1997	France
44	Robert Prethaler		1	1998
45	Gennady Nikolaevich Gusev	(1954 - )	1	1998	Russia
46	Richard McIntosh		1	1999
47	Claude Tardif		1	1999
48	Charles F. Kerchner III		3	1999
49	Dan Morenus		1	1999
50	John Renze		1	1999
51	John B. Cosgrave	(1946 - )	3	1999	Ireland
52	Rachel Lewis		1	2000	USA
53	Leonid Nikolaevich Durman	(1975 - )	20	2000	Russia
54	James Ray Ballinger	(1953 - )	1	2000	USA
55	Nestor Sergio de Araujo Melo	(1971 - )	2	2000	Brazil
56	Payam Samidoost	(1969 - )	3	2000	Iran
57	Takahiro Nohara	(1969 - )	2	2001	Japan
58	Peter Grobstich	(1942 - )	2	2001	Germany
59	Alexander Kruppa	(1974 - )	1	2001	Germany
60	Tony Forbes	(1944 - )	1	2001	England
61	Marko Bodschwinna	(1974 - )	1	2001	Germany
62	Göran Axelsson	(1966 - )	2	2001	Sweden
63	Paul Jobling	(1964 - )	10	2001	England
64	George Woltman	(1957 - )	15	2001	USA
65	Jim Fougeron	(1966 - )	10	2001	USA
66	Vasily Anatol'evich Danilov	(1957 - )	5	2001	Russia
67	Anton Petrovich Oleynik	(1972 - )	1	2001	Russia
68	Dmitry Komin	(1971 - )	1	2002	Russia
69	Kevin Odermatt		1	2002
70	Sergey Kuzmin		1	2003	Russia
71	Craig Kitchen		1	2003	USA
72	Asko Vuori		2	2005	Finland
73	Maximilian Pacher		1	2005	Austria
74	Michael Eaton		2	2005	-
75	Jun Tajima		1	2005	Japan
76	Curtis Cooper		2	2005	USA
77	Reto Keiser		1	2007	Switzerland
78	Jean Penné		2	2007	France
79	Pavlos Saridis		1	2007	Greece
80	Souichi Murata		1	2007	Japan

Before computer epoch

Factors found by year

16 factors found earlier (1732-1925)

1640 Dec 25
Fermat wrote to Mersenne:«If I can determine the basic reason why
3, 5, 7, 17, 257, 65 537, ...
are prime numbers, I feel that I would find very interesting results, for I have already found marvelous things [along these lines] which I will tell you about later.» Thus Fermat did not know, that F₅ was not prime
[Knuth, The Art Of Computer Programming, vol. 2, #4.5.4]
Neither of them ever resolved this problem, althogh they could have done it as follows: The number 3^{2^32} mod(2³²+1) can be computed by doing 32 operations of squaring modulo 2³²+1, and the answer is 3029026160, therefore (by Fermat's own theorem, which he discovered in the same year 1640!) the number F₅ is not prime. For further details, look at this interesting page.

1730
Goldbach called Euler's attention to Fermat's conjecture that F_m is always prime, and remarked that: - no F_m has a factor < 100 - no two F_m have a common factor

1732
Euler proved that every factor of F_m is of the form k.2^m+1+1, and noted that each factor of F₅ has the form 64k+1, k=10 giving the factor 641: F₅=2³²+1=641*6700417

1801
Gauss in his Disquisitions Arithmaticae, Proved that a regular n-gon can be constructed by ruler and compass iff n is a product of a power of 2 and distinct odd F_m primes.

1855 Jan 1
Thomas Clausen in a letter to Gauss provided the factorization F₆ = 274177 * 67280421310721 with both factors known to be primes, without proving, however, that the second factor is prime. BUT THIS FACT WAS NEVER PUBLISHED UNTIL 1964 by K.Biermann.

1877
T.Pepin: (basic idea from Lucas) F_m is prime (m>1) iff a^(Fm-1)/2 = -1 mod F_m where a is any non-residue of F_m like 3, 5 or 10

1877 Nov.
Pervouchin: 114689 = 7.2¹⁴ +1 divides F₁₂. Lucas announced the same result 2 months later.

1878 Jan 27.
Lucas: every factor of F_m is of the form k.2^m+2 +1. Click here for detail information.

1878 Feb.
Pervouchin: 167772161 = 5.2²⁵ +1 divides F₂₃

1878
Proth: Let N=k.2ⁿ+1, where k<2ⁿ is odd. Suppose that (a/N)=-1. Then N is prime iff a^(N-1)/2 = -1 mod N

1879
Lucas: had verified the compositeness of F₆ in 30 hours.

1880 July 7
Landry, when of age 82 and after several months labor found that F₆ = 274177 * 67280421310721 both factors being prime, the second with some doubt. See Landry's mail to Lucas.

1880
LeLasseur and Gerardin: each verified the primeness of the second factor of F₆

1886
Seelhoff: 2748779069441 = 5.2³⁹ +1 divides F₃₆

1896
Jacques Hadamard: found a very simple proof of the 1878 Lucas's theorem.

1899
Cunningham: found two factors of F₁₁ by trial division: 319489 = 39.2¹³ +1, 974849 = 119.2¹³ +1

1903
Western:
2424833 = 37.2¹⁶ +1 divides F₉
13631489 = 13.2²⁰ +1 divides F₁₈
26017793 = 397.2¹⁶ +1 divides F₁₂
63766529 = 973.2¹⁶ +1 divides F₁₂

1903
Cullen & Cunningham: 6597069766657 = 3.2⁴¹ +1 divides F₃₈ Western verified its primality

1903
Western & Cunningham: no more F_m have factors < 10^6

1905
Morehead & Western (independently) using Pepin's test with a=3 verified that F₇ is composite

1905
Morehead: 188894659314785808547841 = 5.2⁷⁵+1 divides F₇₃

1909
Morehead & Western (by a very long computation) verified that F₈ is composite. (Pepin test a=3)

1925
Kraitchik 1214251009 = 579.2²¹+1 divides F₁₅

Computer epoch

Beginnings from the famous computer SWAC

251 prime factors found since the advent of computers

267 prime factors currently known