Fermat number

English

Etymology

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Noun

1. Template:Lb 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 $2^{2^n}+1$ for some $n\ge 0$); equivalently, a number that is one more than two raised to some power (is expressible as $2^n+1$) and is prime.

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Usage notes

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