Optical Eratosthenes' sieve for large prime numbers

Area of Science:

• Quantum optics
• Number theory
• Optical computing

Background:

• Prime number sieving is a fundamental problem in number theory.
• Previous methods for prime number sieving were primarily computational.
• Optical methods offer potential for parallel processing and speed.

Purpose of the Study:

• To experimentally demonstrate a prime number sieve using linear optics.
• To encode prime number distribution within optical far-field patterns.
• To extend the sieving range beyond initial limitations.

Main Methods:

• Utilizing a spatial light modulator (SLM) hologram with diffraction gratings corresponding to prime numbers below 149.
• Encoding prime number distribution in the intensity zeros of the far field.
• Employing additional diffraction gratings and sequential far-field recordings to overcome SLM limitations.

Main Results:

• Successful experimental demonstration of an optical prime number sieve.
• Optical sieving of prime numbers up to 149.
• Extension of the optical sieving range to 149^2 = 22201 through advanced techniques.

Conclusions:

• Linear optics can be effectively utilized for prime number sieving.
• The developed optical method overcomes limitations of SLM resolution and far-field window size.
• This work presents a novel approach to optical number theory computations.