August 31, 2024Open Access

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

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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.

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Michael Th. Rassias (Sat,) studied this question.

synapsesocial.com/papers/68e5a2bab6db64358753ce26 https://doi.org/https://doi.org/10.48550/arxiv.2409.00394

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