Conjecture: the set of prime numbers is supernatural

TL;DR

This paper introduces a novel formal conjecture claiming the set of prime numbers is supernatural, supported by a Fermat-like function that yields more primes than Fermat's function, challenging existing mathematical understanding.

Contribution

It proposes the first formal conjecture that primes form a supernatural set and introduces a new Fermat-like function related to prime distribution.

Findings

A formal conjecture that primes are supernatural

A Fermat-like function generating more primes

Challenging existing prime distribution theories

Abstract

Prime numbers are fascinating by the way they appear in the set of natural numbers. Despite several results enlighting us about their repartition, the set of prime numbers is often informally qualified as misterious. In the present paper, we introduce a formalism allowing to state a formal conjecture: the set of prime numbers is supernatural. Our conjecture has no analog in the existing literature. This conjecture is expected to be a hard challenge for any kind of intelligence. We also find a Fermat-like function giving more prime numbers than Fermat's function.