Fermat Primes

Fermat primes are a type of number that satisfies the properties of BOTH Fermat numbers and prime numbers. Just in case you haven't know yet, Fermat number has general form F_n = 2^{2^n} + 1.
==All the Fermat primes==
3.png|link=3
5.png|link=5
17.png|link=17
257.png|link=257
65537.png|link=65,537
Note that 65,537 (F_4) is the largest known Fermat prime, being 2^{16} + 1. However, The next Fermat number (F_5 = 2^{32} + 1 = 4,294,967,297) is divisible by 641 and 6,700,471.
==Applications in Mathematics==
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
Category:Types of Primes