An optical Eratosthenes' sieve for large prime numbers

TL;DR

This paper demonstrates an innovative optical method to sieve large prime numbers using linear optics and holography, enabling the identification of all primes below 22,201 through a novel experimental setup.

Contribution

It introduces the first experimental optical prime number sieve using a spatial light modulator and diffraction gratings, advancing prime number detection techniques.

Findings

Successfully sieved all primes below 22,201 using optical methods

Implemented diffraction gratings to encode prime distributions

Overcame resolution limitations with additional gratings and sequential recordings

Abstract

We report the first experimental demonstration of prime number sieve via linear optics. The prime numbers distribution is encoded in the intensity zeros of the far field produced by a spatial light modulator hologram, which comprises a set of diffraction gratings whose periods correspond to all prime numbers below 149. To overcome the limited far field illumination window and the discretization error introduced by the SLM finite spatial resolution, we rely on additional diffraction gratings and sequential recordings of the far field. This strategy allows us to optically sieve all prime numbers below $149^2=22201$.