Correlations between large prime numbers

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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