Spacing between consecutive primes

It is a folklore belief that the local spacings between consecutive primes follow the laws of random numbers (as in Problem 1). That is, if P_n is the n^th prime, then the distribution of $\Delta _n = \frac{P_{n+1} - P_n}{\log P_n},\ n=1,2,\dots$ will converge to

. There is, as far as we know, no serious experimentation confirming this conjecture.

DAVID SCHMIDT'S INVESTIGATIONS