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Approximation of pn by Hn

Alikhani, Akram and Hassani, Mehdi (2005) Approximation of pn by Hn. Research report collection, 8 (4).

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Abstract

In this paper we introduce some bounds including Hn = ∑n k=1, (1/k), for pn, nth prime number. Then we observe that the Prime Number Theorem is equivalent with pn ~ nHn, when n tends to infinity.

Item Type: Article
Uncontrolled Keywords: primes, harmonic series, ρ, η,
Subjects: Current > FOR Classification > 0101 Pure Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Depositing User: Research Group in Mathematical Inequalities and Applications
Date Deposited: 25 Sep 2012 23:04
Last Modified: 07 Aug 2020 02:17
URI: http://vuir.vu.edu.au/id/eprint/18117
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