Fermat prime

plural Fermat primes

1. mathematicsA Fermat number that is prime.

   F₀ = 3, F₁ = 5, F₂ = 17, F₃ = 257, and F₄ = 65537. The next 28 Fermat numbers, F₅ through F₃₂, are known to be composite.

   2013, Dean Hathout, Wearing Gauss’s Jersey, Taylor & Francis (CRC Press), page xi, Believe it or not, so far only five Fermat primes are known

   2 more examples

   It is not hard to prove that the only way that the number 1#43;2ᵉ can possibly be prime is when e is a power of 2, and so all Fermat primes must have the form 1#43;2#123;2ᵃ#125; for integers a#92;ge 0. The numbers F#95;a#61;1#43;2#123;2ᵃ#125; 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.

   2001, I. Martin Isaacs, Geometry for College Students, American Mathematical Society, page 201

   Rather surprisingly, it turns out that Fermat primes play an important special role in this context, a phenomenon hitherto unobserved in the arithmetic theory of Hecke groups, and, as a byproduct of our investigation, several new characterizations of Fermat primes are obtained.

   2004, T. W. Müller, “12: Parity patterns in Hecke groups and Fermat primes”, in Thomas Wolfgang Müller, editor, Groups: Topological, Combinatorial and Arithmetic Aspects, Cambridge University Press, page 327