[dromedariusCase]

I originally also thought about doing this (sort of) by hand, but once you realize that the possibility space is too large, programming it really helps you see what kinda pairs you are actually eliminating.

You can actually WLOG away all pairs where the second element is larger than the first.

Also, the most common kind of pair I eliminated was actually due to the size constraint (ie, 98 * 99) or pairs of (1, prime) which I didn't actually realize would be a thing until I coded it up.