Fermat Primes

Fermat primes  are Fermat numbers that are also prime numbers. A Fermat number has the following properties: F n  = 2 (2^n)  + 1.

All the Fermat primes
3

5

17

257

65537

Note that 65537 (F 5 ) is the largest known Fermat prime, being 2 16  + 1. The next Fermat number (F 6 ), 2 32  + 1 = 4294967297, is divisible by 641 and 6700471.

All the Fermat primes
Fermat primes are related to constructible polygons- regular polygons which one can construct using only a straightedge and circles. Polygons can be constructed if the number of sides' prime factors are either powers of two or powers of Fermat primes