Proof of the Twin Prime Conjecture (Together with the Proof of Polignac's Conjecture for Cousin Primes)

TL;DR

This paper claims to prove the twin prime conjecture and Polignac's conjecture for cousin primes by transforming the problem into a generative space and using a two-stage sieve process to demonstrate their infinitude.

Contribution

It introduces a novel two-stage sieve method that purportedly proves the infinitude of twin primes and cousin primes, addressing longstanding conjectures.

Findings

Proof of infinite twin primes

Proof of infinite cousin primes

Introduction of a new two-stage sieve method

Abstract

In this paper proof of the twin prime conjecture is going to be presented. Originally very difficult problem (in observational space) has been transformed into a simpler one (in generative space) that can be solved. It will be shown that twin primes could be obtained through two stage sieve process, and that will be used to show that exist infinite number of twin primes. The same approach is used to prove the Polignac's conjecture for cousin primes.