Expected gaps between prime numbers
Number Theory
2007-06-07 v1
Abstract
We study the gaps between consecutive prime numbers directly through Eratosthenes sieve. Using elementary methods, we identify a recursive relation for these gaps and for specific sequences of consecutive gaps, known as constellations. Using this recursion we can estimate the numbers of a gap or of a constellation that occur between a prime and its square. This recursion also has explicit implications for open questions about gaps between prime numbers, including three questions posed by Erd\"os and Tur\'an.
Cite
@article{arxiv.0706.0889,
title = {Expected gaps between prime numbers},
author = {Fred B. Holt},
journal= {arXiv preprint arXiv:0706.0889},
year = {2007}
}