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 e-prints
- Pub Date:
- June 2016
- DOI:
- 10.48550/arXiv.1606.06874
- arXiv:
- arXiv:1606.06874
- Bibcode:
- 2016arXiv160606874A
- Keywords:
-
- Mathematics - Number Theory;
- 11L20;
- 11N37;
- 11A41
- E-Print:
- v2: 11 pages