Infinitude of Primes Using Formal Language Theory

TL;DR

This paper explores the properties of regular languages in formal language theory to provide a novel proof that there are infinitely many prime numbers, connecting formal language concepts with number theory.

Contribution

It introduces a new approach by applying formal language theory, specifically regular languages, to prove the infinitude of primes, which is a novel intersection of these fields.

Findings

Regular languages have properties useful for number theory proofs.

A formal language-based proof of the infinitude of primes is presented.

The approach bridges formal language theory and number theory.

Abstract

Formal languages are sets of strings of symbols described by a set of rules specific to them. In this note, we discuss a certain class of formal languages, called regular languages, and put forward some elementary results. The properties of these languages are then employed to prove that there are infinitely many prime numbers.