Process of "Primoverization" of Numbers of the Form a^n-1

TL;DR

This paper introduces the concept of 'primover' numbers, proving Fermat numbers are primover to base 2 and presenting a method to find primover divisors of numbers like a^n-1.

Contribution

It defines primover numbers, proves Fermat numbers are primover to base 2, and proposes a simple process to find primover divisors of a^n-1.

Findings

Fermat numbers are primover to base 2.

A simple process to find primover divisors of a^n-1.

Primover numbers include primes and overpseudoprimes to a given base.

Abstract

We call an integer N>1 primover to base a if it either prime or overpseudoprime to base a. We prove, in particular, that every Fermat number is primover to base 2. We also indicate a simple process of receiving of primover divisors of numbers of the form a^n-1.