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arXiv · 1803.01559

Prime Number Decomposition using the Talbot Effect

Karl Pelka·Jasmin Graf·Thomas Mehringer·Joachim von Zanthier
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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.

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Karl Pelka, Jasmin Graf, Thomas Mehringer, Joachim von Zanthier. 2018-03-12. Prime Number Decomposition using the Talbot Effect. https://doi.org/10.1364/oe.26.015009

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