A Formalisation of Lehmer’s Primality Criterion

Abstract

In 1927, Lehmer presented criterions for primality, based on the converse of Fermat’s litte theorem [2]. This work formalizes the second criterion from Lehmer’s paper, a necessary and sufficient condition for primality. As a side product we formalize some properties of Euler’s ϕ-function, the notion of the order of an element of a group, and the cyclicity o