A Prime-Representing Constant

TL;DR

This paper introduces a constant and recursive relation that generates the sequence of prime numbers, proving its irrationality and exploring similar sequences.

Contribution

It presents a novel constant and recursive method to generate all primes, a significant advancement in prime number theory.

Findings

Defines a constant generating all primes via a recursive relation

Proves the constant is irrational

Explores other sequences generated by similar methods

Abstract

We present a constant and a recursive relation to define a sequence $f_n$ such that the floor of $f_n$ is the $n$th prime. Therefore, this constant generates the complete sequence of primes. We also show this constant is irrational and consider other sequences that can be generated using the same method.