# The Distribution of Maximal Prime Gaps in Cramer's Probabilistic Model of Primes

@article{Kourbatov2014TheDO, title={The Distribution of Maximal Prime Gaps in Cramer's Probabilistic Model of Primes}, author={Alexei Kourbatov}, journal={International Journal of Statistics and Probability}, year={2014}, volume={3}, pages={18} }

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…

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