Prime Number Decomposition using the Talbot Effect
Optics
2018-07-04 v2
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.
Cite
@article{arxiv.1803.01559,
title = {Prime Number Decomposition using the Talbot Effect},
author = {Karl Pelka and Jasmin Graf and Thomas Mehringer and Joachim von Zanthier},
journal= {arXiv preprint arXiv:1803.01559},
year = {2018}
}
Comments
- 6 pages, 3 figures - 6 pages, 3 figures, added references in the introduction