Number-theoretic expressions obtained through analogy between prime factorization and optical interferometry

TL;DR

This paper explores an innovative analogy between prime factorization and optical interferometry to derive new analytic expressions for functions related to prime factors, advancing understanding in number theory and cryptography.

Contribution

It introduces a novel analogy-based approach to derive analytic expressions for prime factorization functions, a first in the field.

Findings

Derived analytic expressions for the number of distinct prime factors.

Established a new analogy between prime factorization and optical interferometry.

Potential implications for cryptography and number theory.

Abstract

Prime factorization is an outstanding problem in arithmetic, with important consequences in a variety of fields, most notably cryptography. Here we employ the intriguing analogy between prime factorization and optical interferometry in order to obtain, for the first time, analytic expressions for closely related functions, including the number of distinct prime factors.