Can you list any functions F(n) = the nth prime number that will gve an answer independently of the determination of all lower primes?First, the function is just that: f(n) = the nth prime number, if n is a positive integer, and undefined otherwise.
But there are probably a good half dozen or dozen closed form versions of that formula, based on things like Wilson's Theorem. None of them are particularly interesting.
Also, can you give a function P(n) which gives a 1 or 0 depending upon whether n is prime or not that in effect does not depend upon the calculation or n! or of all primes less than the square root of 'n'?
If yes to either question, please cite relevant descriptive material.