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arXiv · 1608.01671

The $n$th+1 Prime Number Limit Formulas

Artur Kawalec
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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 $p_{n+1}$.

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Artur Kawalec. 2016-08-04. The $n$th+1 Prime Number Limit Formulas. https://arxiv.org/abs/1608.01671

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