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arXiv · 1401.6959

The distribution of maximal prime gaps in Cramer's probabilistic model of primes

Alexei Kourbatov
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Abstract

In the framework of Cramer's probabilistic model of primes, we explore the exact and asymptotic distributions of maximal prime gaps. We show that the Gumbel extreme value distribution exp(-exp(-x)) is the limit law for maximal gaps between Cramer's random primes. The result can be derived from a general theorem about intervals between discrete random events occurring with slowly varying probability monotonically decreasing to zero. A straightforward generalization extends the Gumbel limit law to maximal gaps between prime constellations in Cramer's model.

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BibTeXRIS

Alexei Kourbatov. 2014-01-27. The distribution of maximal prime gaps in Cramer's probabilistic model of primes. https://doi.org/10.5539/ijsp.v3n2p18

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