When and how Fermat numbers F_m were proven composite
 (on the occasion of a remarkable discovery) 

m	Year	Discoverer	Method
5	1732	Euler	Factorization
6	1855	Clausen	Factorization
7	1905	Morehead	Pépin test
8	1909	Morehead & Western	Pépin test
9	1903	Western	factor
10	1952	Robinson	Pépin test
11	1899	Cunningham	factors
12	1877	Pervushin / Lucas	factor
13	1961	Paxson	Pépin test
14	1961	Hurwitz & Selfridge	Pépin test
15	1925	Kraitchik	factor
16	1953	Selfridge	factor
17	1979	Gostin	factor
18	1903	Western	factor
19	1962	Riesel	factor
20	1987	Young & Buell	Pépin test
21	1963	Wrathall	factor
22	1993	Crandall & others	Pépin test
23	1878	Pervushin	factor
24	1999	Crandall & others	Pépin test
25	1963	Wrathall	factor
26	1963	Wrathall	factor
27	1963	Wrathall	factor
28	1997	Taura	factor
29	1980	Gostin & McLaughlin	factor
30	1963	Wrathall	factor
31	2001	Kruppa & Forbes	factor
32	1963	Wrathall	factor
33	----	u n k n o w n
34	----	u n k n o w n
35	----	u n k n o w n
36	1886	Seelhoff	factor
37	1991	Gostin	factor
38	1903	Cullen & Cunningham	factor
39	1956	Robinson	factor
40	2021	Morelli	factor
41	----	u n k n o w n
42	1963	Wrathall	factor
43	2000	Samidoost	factor
44	----	u n k n o w n
45	----	u n k n o w n
46	----	u n k n o w n
47	----	u n k n o w n
48	2001	Bodschwinna	factor
49	----	u n k n o w n
50	----	u n k n o w n