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On the sum of the first n prime numbers

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arxiv 1409.1777 v1 pith:UYTUZCFK submitted 2014-09-05 math.NT

Christian Axler This is my paper · ORCID
classification math.NT
keywords asymptoticfirstformulanumbersprimeaccurateestablishgeneral
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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 in 1996.

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  1. On the arithmetic average of the first $n$ primes

    math.NT 2025-05 conditional novelty 5.0 of 10

    For the averaged-prime sequence, analogues of the Cramer, Andrica, Legendre, Oppermann, Brocard, Firoozbakht, Fourges, Nicholson, and Farhadian conjectures are proved from known explicit estimates.

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