Studies of entropy measures concerning the gaps of prime numbers

TL;DR

This paper investigates the entropy of prime gaps using Shannon entropy, comparing it with artificially generated number sets to understand the complexity and distribution of prime gaps.

Contribution

It introduces an entropy-based framework for analyzing prime gaps and compares their entropy measures with those of synthetic number sets.

Findings

Prime gaps exhibit specific entropy characteristics.

Artificial sets show different entropy profiles from prime gaps.

Entropy measures can distinguish between natural prime distributions and artificial data.

Abstract

The Shannon entropy is used as a basis for applying different lemmas and conjectures concerning the set of gaps between prime numbers G_p , thus estimating several measures of it. The same procedures are applied to artificially created number sets, to compare the size of their entropy against G_p .