Enumerate grid points on 2D plane with descending order of (x * y)

Question

Given N > 0 and M > 0, I want to enumerate all (x, y) pairs such that 1 <= x <= N and 1 <= y <= M in descending order of (x * y). An

Answer 1

This is effectively equivalent to enumerating the prime numbers; the numbers you want are all the numbers that aren't prime (except for all those that have x or y equal to 1).

I'm not sure there's a method of enumerating primes that's going to be quicker than what you're already proposing (at least in terms of algorithmic complexity).