On the asymptotic expansion of the sum of the first n primes

Abstract

An asymptotic formula for the sum of the first n primes is derived. This result improves the previous results of P. Dusart. Using this asymptotic expansion, we prove the conjectures of R. Mandl and G. Robin on the upper and the lower bound of the sum of the first n primes respectively.

arXiv comment5 pages, prime numbers, Mandl's inequality, Robin's conjecture

References in corpus (1)

• A Remark on the Mandl's Inequality

Cited by in corpus (2)

• On the sum of the first n prime numbers
• Curious conjectures on the distribution of primes among the sums of the first $2n$ primes