basic

Euler Perfect Number Formula from Mersenne Exponent Calculator

N = 2^(p−1) × (2^p − 1); σ(N) = 2N if (2^p−1) prime.

Computes an even perfect number using Euler's theorem: N = 2^(p−1) × M_p where M_p = 2^p − 1 is the Mersenne number. Known perfect numbers: 6, 28, 496, 8128, 33550336.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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  1. Fill in the inputs above using the units you already have.
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  3. Hover any result row for the underlying formula and intermediate values.

Formula

M_p = 2^p − 1; N = 2^(p−1) × M_p; σ(N) = 2N (if M_p prime)

In depth

Computes an even perfect number using Euler's theorem: N = 2^(p−1) × M_p where M_p = 2^p − 1 is the Mersenne number. Known perfect numbers: 6, 28, 496, 8128, 33550336.