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

2010/11/07 by Nilotpal Sinha, Sinha, Nilotpal Kanti
Mathematics · #11A41 #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1011.1667

openalex publication_date 2010/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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