A Fermat Prime is a special type of prime number that can be expressed in the form 2^2^n + 1, where n is a non-negative integer. The first few Fermat primes are 3, 5, 17, 257, and 65537. These numbers are named after the French mathematician Pierre de Fermat, who studied them in the 17th century. Fermat primes are significant in number theory and have applications in fields like cryptography and computer science. However, it is still an open question whether there are infinitely many Fermat primes, as only a limited number have been discovered so far.