Yes, I agree there's probably a better way for the Mersenne and Fermat. And even the Germain we probably don't need to scan every shard for just the first page of them. Good points! And good idea to invert the lookup.

Thank you for the comment on interestingness. I thought so to, but I didn't realize it in same way you did in your observation that it gets more selective over time - I like that, in a sense that's kind of natural as the environment is more competitive over time. Thank you for the interesting idea!

edit: Your ideas are implemented!