Proof that Fermat Prime Numbers are Infinite

Fermat prime is a prime number that are a special case, given by the binomial number of the form: Fn = 22n + 1, for n ≥ 0 They are named after Pierre de Fermat, a Frenchman of the 17th Century, Pierre de Fermat, effectively invented modern number theory virtually single-handedly, despite being a small-town amateur mathematician. Throughout his life he devised a wide range of conjectures and theorems. He is also given credit for early developments that led to modern calculus, and for early progress in probability theory. The only known Fermat primes are: F0 = 3 F1 = 5 F2 = 17 F3 = 257 F4 = 65,537 It has been conjectured that there are only a finite number of Fermat primes, however, we will use the same technique the author used to prove that the Mersenne primes are infinite, to prove the Fermat primes are infinite.