The Distribution of Maximal Prime Gaps in Cramer's Probabilistic Model of Primes
- Alexei Kourbatov
AbstractIn 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.
This work is licensed under a Creative Commons Attribution 4.0 License.
- Aerospace Database
- BASE (Bielefeld Academic Search Engine)
- Elektronische Zeitschriftenbibliothek (EZB)
- Google Scholar
- Harvard Library
- Library and Archives Canada
- PKP Open Archives Harvester
- Standard Periodical Directory
- UC Riverside Library
- Wendy SmithEditorial Assistant