On the relationship between the Collatz conjecture and Mersenne prime numbers

TL;DR

This paper explores the connection between the Collatz conjecture and Mersenne primes by developing a matrix-based approach to identify prime numbers, focusing on patterns, structures, and symmetries related to the Collatz algorithm.

Contribution

It introduces a novel matrix method derived from the Collatz algorithm to analyze prime numbers, especially Mersenne primes, providing a new perspective on their properties.

Findings

Identified specific matrix patterns associated with Mersenne primes

Discovered symmetries in matrices related to the Collatz algorithm

Proposed a necessary criterion for prime numbers based on matrix analysis

Abstract

The purpose of this study is to show how to get a necessary criterion for prime numbers with the help of special matrices. My special interest lies in the empirical research of these matrices and their patterns, structures and symmetries. The matrices in turn depend on an expansion of the Collatz algorithm 3n+1.