Detection and discrimination of the periodicity of prime numbers by discrete Fourier transform

TL;DR

This paper introduces a Fourier-based method to detect and analyze the periodicity in prime numbers, revealing hidden regularities in their distribution through numerical evidence.

Contribution

It presents a novel Fourier series decomposition of a modified von Mangoldt function to uncover periodicities in prime number sequences.

Findings

Prime number progression can be decomposed into periodic sequences.

Fourier analysis reveals hidden periodicities in prime distributions.

Numerical evidence supports the periodic nature of primes.

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.