Statistical Mechanical Formulation and Simulation of Prime Factorization of Integers

TL;DR

This paper introduces a statistical mechanical approach to prime factorization, using replica exchange Monte Carlo simulation, revealing insights into the problem's computational complexity despite apparent hardness.

Contribution

It presents a novel formulation of prime factorization as a statistical mechanical problem and applies Monte Carlo simulation to analyze its complexity.

Findings

Observed behaviors suggest exponential hardness in prime factorization.

The formulation offers new perspectives on the problem's computational complexity.

Simulation results provide insights into the statistical mechanics of factorization.

Abstract

We propose a new formulation of the problem of prime factorization of integers. With replica exchange Monte Carlo simulation, the behavior which is seemed to indicate exponential computational hardness is observed. But this formulation is expected to give a new insight into the computational complexity of this problem from a statistical mechanical point of view.