On the sum of the first n prime numbers

TL;DR

This paper derives a general asymptotic formula for the sum of the first n prime numbers, improving upon previous estimates and providing a more accurate mathematical understanding of prime sums.

Contribution

It introduces a new, more precise asymptotic formula for summing the first n primes, extending prior work by Massias and Robin.

Findings

New asymptotic formula for prime sums

Improved accuracy over previous estimates

Generalization of Massias and Robin's formula

Abstract

In this paper we establish a general asymptotic formula for the sum of the first n prime numbers, which leads to a generalization of the most accurate asymptotic formula given by Massias and Robin in 1996.