Correlations between large prime numbers

2011/01/13 by A. Bershadskii, Bershadskii, A.
Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Mathematics #FOS: Physical sciences #Number Theory (math.NT) #math.NT #nlin.CD

paper · pdf · doi:10.48550/arxiv.1101.2595

arxiv created 2011/01/13 · arxiv updated 2011/01/14

Abstract

It is shown that short-range correlations between large prime numbers (~10⁵ and larger) have a Poissonian nature. Correlation length ζ= 4.5 for the primes ~10⁵ and it is increasing logarithmically according to the prime number theorem. For moderate prime numbers (~10⁴) 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.

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