On the sum of the first n prime numbers
Journal de Théorie des Nombres de Bordeaux, Volume 31 (2019) no. 2, pp. 293-311.

In this paper we establish an asymptotic formula for the sum of the first n prime numbers, more precise than the one given by Massias and Robin in 1996. 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.

Dans cet article, nous établissons une formule asymptotique pour la somme des n premiers nombres premiers, plus précise que celle donnée par Massias et Robin en 1996. En outre, nous prouvons un certain nombre de résultats concernant l’inégalité de Mandl pour la somme des n premiers nombres premiers. Nous utilisons ces résultats pour établir de nouvelles estimations explicites de la somme des n premiers nombres premiers, qui améliorent les meilleures estimations actuellement connues.

Received:
Accepted:
Published online:
DOI: 10.5802/jtnb.1081
Classification: 11N05,  11A41
Keywords: Asymptotic expansion, Mandl’s inequality, Sum of prime numbers
Christian Axler 1

1 Institute of Mathematics Heinrich-Heine-University Düsseldorf Building 25.22, Room 02.42 Universitätsstraße 1 40225 Düsseldorf, Germany
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Christian Axler. On the sum of the first $n$ prime numbers. Journal de Théorie des Nombres de Bordeaux, Volume 31 (2019) no. 2, pp. 293-311. doi : 10.5802/jtnb.1081. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1081/

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