Correlations between large prime numbers
Number Theory
2011-01-14 v1 Chaotic Dynamics
Abstract
It is shown that short-range correlations between large prime numbers (~10^5 and larger) have a Poissonian nature. Correlation length \zeta = 4.5 for the primes ~10^5 and it is increasing logarithmically according to the prime number theorem. For moderate prime numbers (~10^4) the Poissonian distribution is not applicable while the correlation length surprisingly continues to follow to the logarithmical law. A chaotic (deterministic) hypothesis has been suggested to explain the moderate prime numbers apparent randomness.
Keywords
Cite
@article{arxiv.1101.2595,
title = {Correlations between large prime numbers},
author = {A. Bershadskii},
journal= {arXiv preprint arXiv:1101.2595},
year = {2011}
}