An improved bound on the sum of prime numbers

We derive two asymptotic formulae, for the upper bound on the sum of the first n primes. Both the Supremum and the Estimate of the sum are superior to known bounds. The Estimate bound had been derived to promote the efficiency of estimation of the sum.

Content

Author and article information

Journal

Title: ScienceOpen Preprints

Publisher: ScienceOpen

Publication date (Electronic preprint): 9 July 2021

Affiliations

[1 ] N.A.

Author notes

[* ]Email: monicafeliksiak@ 123456yahoo.com .

Author information

Monica Feliksiak https://orcid.org/0000-0002-5786-4227

Article

DOI: 10.14293/S2199-1006.1.SOR-.PPD7MQS.v1

SO-VID: f2ef45bb-c734-4cb2-9527-b41c7eb264d2

License:

This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .

History

Date received : 9 July 2021

Data availability: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

ScienceOpen disciplines: Mathematics

Keywords: R. Mandl inequality; sum of primes Supremum; sum of primes Estimate.