True, but it's fairly easy to filter out the non-primitives.

If m and n are both even, skip (a, b, and c will all be divisible by two).

If m and n are both odd, skip (a, b, and c will all be divisible by two).

If m and n have a divisor in common (e.g., GCD{12,3} != 1) skip (a, b, and c will have that factor in common).

The first case can be wrapped up in third case (actually, it can be wrapped up in the second case too), but I find that it makes things clearer to separate them out.