Fermat prime

It is not hard to prove that the only way that the number 1+2ᵉ can possibly be prime is when e is a power of 2, and so all Fermat primes must have the form 1+2 for integers a>0. The numbers F_a=1+2 are called Fermat numbers, and although it is true that every Fermat prime is a Fermat number, it is certainly not true that every Fermat number is prime.