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

Alexei Kourbatov

Type: Article

Publication Date: 2014-03-20

Citations: 6

DOI: https://doi.org/10.5539/ijsp.v3n2p18

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

Locations

International Journal of Statistics and Probability - View - PDF
arXiv (Cornell University) - View - PDF
DataCite API - View

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Works Cited by This (18)

Action	Title	Year	Authors
+	None	1999	Pavle Mladenović
+	Some heuristics on the gaps between consecutive primes	2011	Marek Wolf
+ PDF Chat	First occurrence prime gaps	1989	Jeff Young Aaron Potler
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+ PDF Chat	Cramér vs. Cramér. On Cramér's probabilistic model for primes	2007	J. Pintz
+ PDF Chat	Record Values and Maxima	1973	Sidney I. Resnick
+	The Longest Run of Heads	1990	Mark F. Schilling
+	Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅10¹⁸	2013	Tomás Oliveira e Silva Siegfried Herzog Silvio Pardi
+ PDF Chat	Some problems of ‘Partitio numerorum’; III: On the expression of a number as a sum of primes	1923	G. H. Hardy J. E. Littlewood
+	The rate of convergence in law of the maximum of an exponential sample	1979	William J. Hall Jon A. Wellner