New conjecture related to a conjecture of McIntosh

TL;DR

This paper proposes a new conjecture involving products of two primes that could partially resolve McIntosh's conjecture, and explores a polynomial expression related to binomial coefficients for prime numbers.

Contribution

It introduces a novel conjecture on prime products linked to McIntosh's conjecture and expresses a binomial coefficient in terms of a polynomial in prime p.

Findings

A new conjecture relating prime products to McIntosh's conjecture

Expression of inom{2p-1}{p-1}-1s a polynomial in prime p

Discussion on potential applications of the polynomial form

Abstract

We introduce a new conjecture on products of two distinct primes that would provide a partial answer to a conjecture of McIntosh. Also, $\binom{2p-1}{p-1}-1$ is written in terms of a polynomial in prime $p$ over the integers and we discuss one way this form may be useful.