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

Kourbatov, Alexei
May 2014
International Journal of Statistics & Probability;May2014, Vol. 3 Issue 2, p18
Academic Journal
In the framework of Cramér'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 Cramér'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 Cramér's model.


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