Hi I wrote a paper involving prime numbers and I believe that I ended up deriving a formula for the set of prime numbers.
What I am proposing is that the next prime number exists within 2 formulas simultaneously with only a random probably of it occurring in either formula on any given calculation. It also states that the next prime number can't be calculated directly since the Pn+2 term is needed to generate the next prime number.
However with this formula you can still calculate approximations for the next prime number.