New bounds for the sum of the first n prime numbers

2016/06/22 by Christian Axler, Axler, Christian
Mathematics · #11A41 #11L20 #11N37 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1606.06874

openalex publication_date 2016/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Approximate formulas for some functions of prime numbers
• Estimates of Some Functions Over Primes without R.H.
• New estimates for the nth prime number

Related

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