An intensity-expansion method to treat non-stationary time series: an application to the distance between prime numbers

TL;DR

This paper introduces an intensity-expansion method to transform non-stationary prime number distance data into stationary, revealing Gaussian properties and enhancing the understanding of their fractal characteristics.

Contribution

The paper presents a novel intensity-expansion technique to analyze non-stationary prime gap data, uncovering Gaussian behavior in a transformed stationary sequence.

Findings

Distance distribution is non-stationary exponential

Transformation increases Gaussian randomness range

Method reveals fractal properties of prime gaps

Abstract

We study the fractal properties of the distances between consecutive primes. The distance sequence is found to be well described by a non-stationary exponential probability distribution. We propose an intensity-expansion method to treat this non-stationarity and we find that the statistics underlying the distance between consecutive primes is Gaussian and that, by transforming the distance sequence into a stationary one, the range of Gaussian randomness of the sequence increases.