Development of the matrix of primes and proof of an infinite number of primes-twins

TL;DR

This paper introduces a matrix of prime numbers and uses it alongside classical theorems to prove there are infinitely many twin primes, contributing a new approach to prime number theory.

Contribution

It proposes a novel matrix framework for primes and provides a proof of the infinite twin primes using this structure and established theorems.

Findings

Proof of infinite twin primes

Introduction of prime matrix concept

New lemmas supporting prime density analysis

Abstract

This paper is devoted to the theory of prime numbers. In this paper we first introduce the notion of a matrix of prime numbers. Then, in order to investigate the density of prime numbers in separate rows of the matrix under consideration, we propose a number of lemmas and theorems that, together with the Dirichlet and Euler theorems, make it possible to prove the infinity of prime twins.