A conjecture on the prime factorization of $n!+1$

TL;DR

This paper proposes a conjecture about the prime factorization of factorial plus one numbers, explores its implications, and compares it with empirical data and known results related to the $abc$ conjecture.

Contribution

It introduces a new conjecture on the prime factors of $n!+1$ and analyzes its potential implications and connections to existing mathematical theories.

Findings

Empirical evidence supports the conjecture for small n.

Connections to the $abc$ conjecture suggest deep number theoretic implications.

Potential impact on understanding prime distributions in factorial-related numbers.

Abstract

In this paper, we state a conjecture on the prime factorization of numbers of the form $n!+1$, explore its implications, and compare it with empirical evidence and established results based on the $abc$ conjecture.