This paper introduces a novel approach to estimating the sum of prime numbers by leveraging insights from partition theory, prime number gaps, and the angles of triangles. The methodology is applied to infinite sums and the nth sum, and several ways of defining the nth sum of a prime number are proposed. By using the Ramanujan infinite series of natural numbers, it is possible to derive an infinite series of prime numbers.

BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:

@booklet{EasyChair:11309,
author = {Budee U Zaman},
title = {New Prime Number Theory},
howpublished = {EasyChair Preprint 11309},
year = {EasyChair, 2023}}