An equivalent problem to the Twin Prime Conjecture

TL;DR

This paper demonstrates that the Twin Prime Conjecture is equivalent to a potentially simpler problem involving the non-existence of infinite strings of natural numbers satisfying certain equations, using elementary arguments.

Contribution

It establishes an equivalence between the Twin Prime Conjecture and a new problem involving finite strings of natural numbers, offering a different approach to the conjecture.

Findings

Twin Prime Conjecture is equivalent to a problem about finite strings of natural numbers.

Elementary arguments are used to establish the equivalence.

Proving the conjecture reduces to showing no infinite string satisfies certain equations.

Abstract

In this short paper we will show, via elementary arguments, the equivalence of the Twin Prime Conjecture to a problem which might be simpler to prove. Some conclusions are drawn, and it is shown that proving the Twin Prime Conjecture is equivalent to proving that there cannot be an infinite string of consecutive natural numbers satisfying some specified equations.