The largest known prime I was refering too was what is known now - http://en.wikipedia.org/wiki/Largest_known_prime_number

So given that to know with all certaintity that only upto that value three times would be the only provable maximum value, until a new know prime is found and somebody invents a formular to drop in N and get the Nth prime out without waiting more than few seconds. Currently we can not do that at all, let alone that dream of many, maybe one day in our lifetimes.

I agree, it is a fine proof. I hope to appreciete it more over the following days. Lots to go over.