A Proof There Exists Infinitely Many Primes with a Gap of Exactly 2

TL;DR

This paper claims to prove the existence of infinitely many twin primes by constructing an unbounded function related to prime pairs and demonstrating the infinite nature of such pairs through mathematical mappings.

Contribution

It introduces a novel function and methodology aiming to establish the infinitude of twin primes, a longstanding open problem in number theory.

Findings

The constructed function is unbounded.

There are infinitely many integers mapping twin prime pairs to larger ones.

The approach suggests an infinite sequence of twin primes exists.

Abstract

This document seeks to prove there are infinitely many primes whose difference is 2, referred to as twin prime pairs. This proof's methodology involves constructing a function that approximates the number of positive integers, less than a known twin prime pair, which can be mapped to a twin prime pair greater than the known one by multiplication. This function is shown to be unbounded and less than the true count of integers it seeks to approximate for the majority of twin prime pairs. Additionally, it is shown there must be infinitely many integers that map a twin prime pair to one larger than itself without the use of the previously mentioned approximation.