The behaviour of a certain additive function in large intervals between consecutive primes

TL;DR

This paper studies how a specific additive function behaves over large intervals between consecutive primes, combining probabilistic number theory and prime gap analysis.

Contribution

It introduces a novel analysis of an additive function within large prime gaps using probabilistic models and prime gap results.

Findings

Characterizes the behavior of the additive function in large prime gaps

Utilizes the Erdős-Kac theorem and Kubilius model for analysis

Provides new insights into number distribution in prime gaps

Abstract

We investigate the behaviour of a certain additive function depending on prime divisors of specific integers lying in large gaps between consecutive primes. The result is obtained by a combination of results and ideas related to large gaps between primes and the Erd\"os-Kac theorem, especially the Kubilius model from Probabilistic Number Theory.