The $n$th+1 Prime Number Limit Formulas

Abstract

A new derivation of Golomb's limit formula for generating the $n$th$+1$ prime number is presented. The limit formula is derived by extracting $p_{n+1}$ from Euler's prime product representation of the Riemann zeta function $\zeta(s)$ in the limit as $s$ approaches infinity. Also, new variations of these limit formulas are explored, such as the logarithm and a half-prime formulas for the $p_{n+1}$.