Mersenne Primes and the Lucas–Lehmer Test

Manuel Eberl 🌐

January 17, 2020

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.


This article provides formal proofs of basic properties of Mersenne numbers, i. e. numbers of the form 2n - 1, and especially of Mersenne primes.

In particular, an efficient, verified, and executable version of the Lucas–Lehmer test is developed. This test decides primality for Mersenne numbers in time polynomial in n.

BSD License


Theories of Mersenne_Primes