As a fun little exercise I wrote an algorithm that will give a

minimum bound for pi(p(i)^2).

I wish I could turn at least part of it into some sort of proof.

(For example, for all i>12, can it be proved that there are at least

X many primes between p(i)^2 and p(i)?) But I'm not skilled at

proofs, so the paper only highlights an algorithm.

(Is there such a proof out there with that form, by the way? I tried

to ask about that earlier, but I think my email got drowned in a

flurry of other posts. Or maybe I asked the question poorly.)

It's probably nothing significant... just a little trinket. But I

wrote it up as I explored it if anyone wants some light reading:

http://homepage.mac.com/bricolage1/primes/PatternsPSquared.pdf
Hope everyone who's on holiday is having a pleasant and safe time.

Regards,

- Jeremy