Pseudo Random test of prime numbers
Number Theory
2011-02-19 v1 Statistics Theory
Statistics Theory
Abstract
The prime numbers look like a randomly chosen sequence of natural numbers, but there is still no strict theory to determine 'Randomness'. In these years, cryptography has developed a battery of statistical tests for randomness. In this paper, we just apply these methods to study the distribution of primes. Here the binary sequence constructed by second difference of primes is used as samples. We find this sequence can't reach all the 'random standard' of FIPS 140-1/2, but still show obvious random feature. The interesting self-similarity is also observed in this sequence. These results add the evidence that prime numbers is a chaos system.
Cite
@article{arxiv.math/0603450,
title = {Pseudo Random test of prime numbers},
author = {Wang Liang and Huang Yan},
journal= {arXiv preprint arXiv:math/0603450},
year = {2011}
}
Comments
6 pages, 3 figures