Improving the estimates for a sequence involving prime numbers

Christian Axler
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 1, Pages 8–13
DOI: 10.7546/nntdm.2019.25.1.8-13
Full paper (PDF, 146 Kb)

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Authors and affiliations

Christian Axler
Department of Mathematics, University of Düsseldorf
40225 Düsseldorf, Germany

Abstract

Based on new explicit estimates for the prime counting function, we improve the currently known estimates for the particular sequence C_n = np_n − ∑_{k ≤ n} p_k, n ≥ 1, involving the prime numbers.

Keywords

• Prime counting function
• Prime numbers
• Sum of primes

2010 Mathematics Subject Classification

• 11N05
• 11A41

References

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