Fermat number

Etymology
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Noun

 * 1)  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.

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 $$k$$.