On the relationship between the Collatz conjecture and Mersenne prime numbers

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.

v2: Additional Info: It turns out that m_C and n_c (Rows and Columns of the Collatzmatrix...) are linked by the following equation : (2^n_C)-1) mod m_C = 0!