Prime numbers: periodicity, chaos, noise

TL;DR

This paper investigates the periodicity in prime numbers by analyzing logarithmic gaps, revealing a hidden period of approximately 8, and validates this for smaller primes using a novel twin prime killing method.

Contribution

It introduces a method to detect periodic components in prime sequences obscured by noise and identifies a specific period in prime gaps.

Findings

Recovered a period of 8±1 in prime number sequence

Validated the periodicity for the first 2000 primes using twin prime killing

Suggests a hidden structured pattern in prime distribution

Abstract

Logarithmic gaps have been used in order to find a periodic component of the sequence of prime numbers, hidden by a random noise (stochastic or chaotic). The recovered period for the sequence of the first 10000 prime numbers is equal to 8\pm1 (subject to the prime number theorem). For small and moderate values of the prime numbers (first 2000 prime numbers) this result has been directly checked using the twin prime killing method.