[hondaracer600]

Originally Posted by Reincarnate

[spoiler]

Again, it's collision testing. What I did, after creating my list of viable pq^a candidates, was a lazy "greedy" approach of just arranging my list of prime composites by the value they add (pq^a-p-q^b), and then, for a given q, take the composite that contributed the most value.

Obviously, this results in a few p-collisions.
So, it would appear you're still not sure what to do in the event of p-collisions?
Well, I'll tell you.
Alright. This is where my "manual" work came in. When I had a p-collision between two composites, I looked at their q values. For a shared p, one composite will have a bigger q than the other. You want to modify the one with a lower q.
You're wondering how to modify it, aren't you?
Quite literally, I looked at the value that the composite prime contributed for that composite of lower q, and I hardcoded it into an if-statement. If the value a composite is about to add to my list equals that, then don't add it. It'll find the next-best pq^a naturally. If you're dealing with the smallest prime p above sqrt(200k), then just remove the worse of the duplicates in terms of value added. I did this like 10 times or so and eventually my list was optimized without any p-collisions.

That's why I did it manually -- it was easier to just kick out the conflicting primes instead of coding and testing a collision subroutine.

That's what I do. Not correctly apparently. FUUUUU. thanks again.