Fermat number

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English

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Etymology

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

Noun

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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 for some ); equivalently, a number that is one more than two raised to some power (is expressible as ) and is prime.
    Hyponym: Fermat prime

Usage notes

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The equivalence of the two definitions follows from the fact that, as can be demonstrated, for a number of the form to be prime it is necessary (though not sufficient) that for some .