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From FMNWiki
A Fermat number is a number of the form 
. The first few Fermat numbers are:
| n | number |
|---|---|
| 0 | 3 |
| 1 | 5 |
| 2 | 17 |
| 3 | 257 |
| 4 | 65537 |
| 5 | 4294967297 |
It was once thought that all Fermat numbers were also prime, but Euler found that F5 was divisible by 641. He also proved that every factor of Fn must be of the form 
. The k of the two factors of F5 are 10 and 104694. Note that both of these k are divisible by 2; Lucas proved that for n > 1, factors must be of the form 
.
Generalized Fermat Number
Generalized Fermat numbers are of the form 
. It is common to write generalized Fermat numbers (when b = 1) as Fn(a). For instance,
