Let N := 2*3*5*...*p denote the product of all prime numbers that are smaller than k +2, and note that none of the k numbers N + 2, N + 3, ... , N + k, N + k + 1 is prime, since for 2 <= i <= k + 1 we know that i has a prime factor that is smaller than k +2, and this factor also divides N, and hence also N + i. With this recipe, we find, for example, for k = 10 that none of the ten numbers 2312,2313,2314.. . .,2321 is prime.