Detection and Discrimination of the Periodicity of Prime Numbers by Discrete Fourier Transform – Symphony of Primes

## Keywords

Von Mangoldt function
discrete fourier transform
prime numbers.

## How to Cite

L. Csoka. (2015). Detection and Discrimination of the Periodicity of Prime Numbers by Discrete Fourier Transform – Symphony of Primes. Journal of Advances in Applied &Amp; Computational Mathematics, 2(1), 01–04. https://doi.org/10.15377/2409-5761.2014.02.01.1

## Abstract

A novel representation of a quasi-periodic modified von Mangoldt function L(n) on prime numbers and its decomposition into Fourier series has been investigated. We focus on some particular quantities characterizing the modified von Mangoldt function. The results indicate that prime number progression can be decomposed into periodic sequences. The main approach is to decompose it into sin or cosine function. Basically, it is applied to extract hidden periodicities in seemingly quasi periodic prime function. Numerical evidences were provided to confirm the periodic distribution of primes.

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