A Proof There Exists Infinitely Many Primes with a Gap of Exactly 2
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.
Cite
@article{arxiv.1709.09950,
title = {A Proof There Exists Infinitely Many Primes with a Gap of Exactly 2},
author = {Kevin B. Espinet},
journal= {arXiv preprint arXiv:1709.09950},
year = {2017}
}
Comments
15 pages, 3 figures This proof assumes the concepts of probability can be applied to a particular map from the natural numbers to the direct product of finitely many groups of prime order. This assumption is not validated. This baseless assumption can be seen in equation (27)