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

arXiv eprints
 Pub Date:
 January 2014
 DOI:
 10.48550/arXiv.1401.6959
 arXiv:
 arXiv:1401.6959
 Bibcode:
 2014arXiv1401.6959K
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Probability;
 Mathematics  Statistics Theory;
 Primary 11N05;
 secondary 60G70;
 62E20
 EPrint:
 12 pages, 2 figures, errata fixed