THEOREM 2 . Let k, 1, n be integers such that k >_ 3, 1 >_ 2 and n + k >_ p (k) , where p(k) is the least prime satisfying p (k) >_ k. Then there is a prime p >_ k for which a p # 0 (mod 1), where ap is the power of p dividing (n + 1) . . . (n + k) .