Prime Number Decomposition using the Talbot Effect

TL;DR

This paper introduces a novel optical method for prime number decomposition using the Talbot effect, leveraging its connection to Gauss sums to analyze prime and composite numbers through the intensity profile of the Talbot carpet.

Contribution

The paper presents a new optical algorithm for prime decomposition based on the Talbot effect and Gauss sums, experimentally verified and discussing its limitations.

Findings

Successfully decomposed prime numbers using optical Talbot effect

Demonstrated the connection between optical patterns and number theory

Discussed the limits and potential of the optical approach

Abstract

We report on prime number decomposition by use of the Talbot effect, a well-known phenomenon in classical near field optics whose description is closely related to Gauss sums. The latter are a mathematical tool from number theory used to analyze the properties of prime numbers as well as to decompose composite numbers into their prime factors. We employ the well-established connection between the Talbot effect and Gauss sums to implement prime number decompositions with a novel approach, making use of the longitudinal intensity profile of the Talbot carpet. The new algorithm is experimentally verified and the limits of the approach are discussed.