A problem about prime numbers and the random walk I
Henry P. McKean · Illinois Journal of Mathematics · 1961
Consider the set Q of 3-dimensional lattice points (11,12, l) with 11 >= 2 prime, 12 l 0. K.It and H. P. McKean, Jr. [1, p. 131] posed the prob- lem of computing the probability , that the standard 3-dimensionM random wlk hits Q n infinite number of times.Given string B of m 2) consecutive integers [2 -, 2 ), A. Selberg's sieve estimate [2, p. 290] provides the upper bound r(B) < c m/lg m to the number of primes in B, and this can be used to prove that