201101.2595v1 Correlations between large prime numbers

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