On the differences between consecutive prime numbers, I
Number Theory
2012-06-29 v2
Abstract
We show by an inclusion-exclusion argument that the prime -tuple conjecture of Hardy and Littlewood provides an asymptotic formula for the number of consecutive prime numbers which are a specified distance apart. This refines one aspect of a theorem of Gallagher that the prime -tuple conjecture implies that the prime numbers are distributed in a Poisson distribution around their average spacing.
Cite
@article{arxiv.1111.3380,
title = {On the differences between consecutive prime numbers, I},
author = {D. A. Goldston and A. H. Ledoan},
journal= {arXiv preprint arXiv:1111.3380},
year = {2012}
}
Comments
6 pages