Random sieves,II

A proof is presented that the random sieve, a stochastic analogue of the sieve of Eratosthenes, generates sequences of numbers approximating the density of primes. The expected number E_nh] of such numbers less than n satisfies

$\text{E}{}_{\mathrm{n}}\text{h]/π(n)→1}$

and the actual number h(n), on any trial, approximates π(n) in the sense of the weak law of large numbers. Some additional results are given.