New bounds for the sum of the first n prime numbers
classification
🧮 math.NT
keywords
firstnumbersprimeasymptoticestimatesformularesultsaccurate
read the original 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. Further we prove a series of results concerning Mandl's inequality on the sum of the first $n$ prime numbers. We use these results to find new explicit estimates for the sum of the first $n$ prime numbers, which improve the currently best known estimates.
This paper has not been read by Pith yet.
Forward citations
Cited by 1 Pith paper
-
The Landau function and the Riemann Hypothesis
The inequality log g(n) < li^{-1}(n) for all n > 0 is equivalent to the Riemann hypothesis.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.