Fermat number

Named after French lawyer and amateur mathematician Pierre de Fermat (1601–1665).

Fermat number (plural Fermat numbers)

1. (number theory) An integer which is one more than two raised to a power which is itself a power of two (i.e., is expressible in the form ${\displaystyle 2^{2^{n}}+1}$ for some ${\displaystyle n\geq 0}$); equivalently, a number that is one more than two raised to some power (is expressible as ${\displaystyle 2^{n}+1}$) and is prime.

   Hyponym: Fermat prime

The equivalence of the two definitions follows from the fact that, as can be demonstrated, for a number of the form ${\displaystyle 2^{n}+1}$ to be prime it is necessary (though not sufficient) that ${\displaystyle n=2^{k}}$ for some ${\displaystyle k}$.