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Advances in Mathematical Physics
Volume 2011 (2011), Article ID 519178, 8 pages
http://dx.doi.org/10.1155/2011/519178
Research Article

Hidden Periodicity and Chaos in the Sequence of Prime Numbers

Physics Department, ICAR, P.O. Box 31155, Jerusalem 91000, Israel

Received 3 March 2011; Revised 2 May 2011; Accepted 3 May 2011

Academic Editor: Giorgio Kaniadakis

Copyright © 2011 A. Bershadskii. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Logarithmic gaps have been used in order to find a periodic component of the sequence of prime numbers, hidden by a random noise (stochastic or chaotic). It is shown that multiplicative nature of the noise is the main reason for the successful application of the logarithmic gaps transforming the multiplicative noise into an additive one. A relation of this phenomenon to spontaneous neuron activity and to chaotic brain computations has been discussed.