Note On Prime Gaps And Very Short Intervals
Number Theory
2010-09-01 v2
Abstract
Assuming the Riemann hypothesis, this article discusses a new elementary argument that seems to prove that the maximal prime gap of a finite sequence of primes p_1, p_2, ..., p_n <= x, satisfies max {p_(n+1) - p_n : p_n <= x} <= c1((logx)^2)/loglogx, c1 > 0 constant. Equivalently, it shows that the very short intervals (x, x + y] contain prime numbers for all y > c2((logx)^2)/loglogx, c2 > 0 constant, and sufficiently large x > 0.
Cite
@article{arxiv.1008.2381,
title = {Note On Prime Gaps And Very Short Intervals},
author = {N. A. Carella},
journal= {arXiv preprint arXiv:1008.2381},
year = {2010}
}
Comments
12 Pages, 1 Table, Improved