Abstract
It is shown that short-range correlations between large prime numbers (~10^5 and larger) have a Poissonian nature. Correlation length ζ= 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.
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