The Distribution of Maximal Prime Gaps in Cramer's Probabilistic Model of Primes
- Alexei Kourbatov
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.- Full Text: PDF
- DOI:10.5539/ijsp.v3n2p18
This work is licensed under a Creative Commons Attribution 4.0 License.
Journal Metrics
- h-index (December 2021): 20
- i10-index (December 2021): 51
- h5-index (December 2021): N/A
- h5-median(December 2021): N/A
( The data was calculated based on Google Scholar Citations. Click Here to Learn More. )
Index
- ACNP
- Aerospace Database
- BASE (Bielefeld Academic Search Engine)
- CNKI Scholar
- COPAC
- DTU Library
- Elektronische Zeitschriftenbibliothek (EZB)
- EuroPub Database
- Excellence in Research for Australia (ERA)
- Google Scholar
- Harvard Library
- Infotrieve
- JournalTOCs
- LOCKSS
- MIAR
- Mir@bel
- PKP Open Archives Harvester
- Publons
- ResearchGate
- SHERPA/RoMEO
- Standard Periodical Directory
- Technische Informationsbibliothek (TIB)
- UCR Library
- WorldCat
Contact
- Wendy SmithEditorial Assistant
- ijsp@ccsenet.org