On the random nature of (prime) number distribution
Number Theory
2007-05-23 v1
Abstract
Let pi(x) denote the number of primes smaller or equal to x. We compare sqrt{pi}(x) with sqrt{R}(x) and sqrt{li}(x), where R(x) and li(x) are the Riemann function and the logarithmic integral, respectively. We show a regularity in the distribution of the natural numbers in terms of a phase related to sqrt{pi}-sqrt{R} and indicate how li(x) can cross pi(x) for the first time.
Cite
@article{arxiv.math/0412288,
title = {On the random nature of (prime) number distribution},
author = {Erika Alvarez and Jean Pestieau},
journal= {arXiv preprint arXiv:math/0412288},
year = {2007}
}