New Estimates for the nth Prime Number
Department of Mathematics
In this paper we establish new upper and lower bounds for the nth prime
which improve several existing bounds of similar shape. As the
main tool, we use some explicit estimates recently obtained for the prime
counting function. A further main tool is the use of estimates concerning
the reciprocal of log pn.
As an application, we derive new estimates for
ϑ(pn), where ϑ(x)
is Chebyshev's ϑ-function.
Full version: pdf,
(Concerned with sequences
Received December 12 2017; revised versions received March 15 2018; February 18 2019;
February 25 2019; May 21 2019.
Published in Journal of Integer Sequences,
May 23 2019.
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