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.

arXiv commentv2: 11 pages

References in corpus (3)

• Estimates of Some Functions Over Primes without R.H.
• New estimates for the $n$th prime number
• Some new inequalities for primes