Last Updated：2025/12/05

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(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 2^2ⁿ+1 for some n>0); equivalently, a number that is one more than two raised to some power (is expressible as 2ⁿ+1) and is prime.

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Fermat number

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Source Word

Fermat number

Noun

(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^(2ⁿ)+1 for some n>0); equivalently, a number that is one more than two raised to some power (is expressible as 2ⁿ+1) and is prime.

Japanese Meaning

（数論）フェルマー数とは、2をあるべき乗（このべき乗自体が2のべき乗となっている）にした値に1を加えた整数、すなわち2^(2ⁿ)+1（n>0）の形で表される数であり、同値的に2のべき乗に1を加えた素数となる数を指します。