Fermat number
= Fermat number
{c}
{title2=$F_n=2^{2^n}+1$}
{wiki}
A Fermat number is $F_n=2^{2^n}+1$ for $n\geq0$. 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.