New bounds for the sum of the first $n$ prime numbers
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.
 Publication:

arXiv eprints
 Pub Date:
 June 2016
 arXiv:
 arXiv:1606.06874
 Bibcode:
 2016arXiv160606874A
 Keywords:

 Mathematics  Number Theory;
 11L20;
 11N37;
 11A41
 EPrint:
 v2: 11 pages