Fermat number

== English == === Etymology === Named after French lawyer and amateur mathematician Pierre de Fermat (1601–1665). === Noun === Fermat number (plural Fermat numbers) (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 2 2 n + 1 {\displaystyle 2^{2^{n}}+1} for some n ≥ 0 {\displaystyle n\geq 0} ); equivalently, a number that is one more than two raised to some power (is expressible as 2 n + 1 {\displaystyle 2^{n}+1} ) and is prime. Hyponym: Fermat prime ==== Usage notes ==== The equivalence of the two definitions follows from the fact that, as can be demonstrated, for a number of the form 2 n + 1 {\displaystyle 2^{n}+1} to be prime it is necessary (though not sufficient) that n = 2 k {\displaystyle n=2^{k}} for some k {\displaystyle k} . ==== Translations ====