Fermat numbers are a special sequence of integers defined by the formula 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 their properties in the 17th century. Fermat numbers have unique characteristics, such as the fact that any two distinct Fermat numbers are coprime, meaning they share no common factors other than 1. Additionally, it is known that only the first five Fermat numbers are prime; the primality of larger Fermat numbers remains an open question in mathematics.