 Fermat number

A Fermat number is $F_n=2^{2^n}+1$ for $n\ge 0$. Distinct Fermat numbers are coprime integers. Their prime divisors are constrained by the multiplicative order of $2$ modulo that prime; this remains useful whether or not the Fermat number itself is prime. The initial value $F_0=3$ must be distinguished when a statement restricts to positive indices.

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. Fermat numbers were named after Pierre de Fermat, a French mathematician, who studied these numbers in the 17th century.