A Fermat number is a specific type of integer that can be expressed in the form F_n = 2^2^n + 1 , where n is a non-negative integer. The first few Fermat numbers are 3, 5, 17, 257, and 65537. They were named after the French mathematician Pierre de Fermat, who studied them in the 17th century. Fermat numbers have unique properties, particularly in number theory. For example, any two distinct Fermat numbers are coprime, meaning they share no common factors other than 1. Additionally, it is still an open question whether there are infinitely many Fermat primes, which are Fermat numbers that are also prime.