Prime Number Decomposition using the Talbot Effect
arXiv:1803.01559 · doi:10.1364/OE.26.015009
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.
- 6 pages, 3 figures - 6 pages, 3 figures, added references in the introduction
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- Suppression of the Talbot effect in Fourier transform acousto-optic imaging
- Ghost factors in Gauss-sum factorization with transmon qubits
- Simple wave-optical superpositions as prime number sieves
- An optical Eratosthenes' sieve for large prime numbers
- Exact Self-Imaging with Arbitrary Revival Spacings