Approximation of pn by Hn

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


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
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords primes, harmonic series, ρ, η,
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