(1)n is not a prime number, so there must be a prime factor. Let p be the smallest prime factor of n, then N = PQ, and p is divisible by n, otherwise, p≤q, otherwise, Q.

(2) If 467 is not a prime number, it is known from (1) that there is a prime factor p≤√467=2 1.6 10 ... and the largest prime number less than √467 is 19, then P ≤/kloc-.

(3) Verify that 2, 3, 5, 7, 1 1, 13, 17, 19 can all be divisible by 467, so 467 is a prime number.