On twin primes associated with the Hawkins random sieve

We establish an asymptotic formula for the number of k-difference twin primes associated with the Hawkins random sieve, which is a probabilistic model of the Eratosthenes sieve. The formula for k=1 was obtained by M.C. Wunderlich [A probabilistic setting for prime number theory, Acta Arith. 26 (1974) 59–81]. We here extend this to k⩾2 and generalize it to all l-tuples of Hawkins primes.