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Abstract
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The sieve of Eratosthenes (SoE) is a well-known method of extracting the set of prime numbers
from the set positive
integers
. Applying
the SoE again to the index of the prime numbers will result in the set of prime-indexed primes
. More generally, the
application of the SoE
-times
will yield the set
of
-th
order primes. In this paper, we give an upper bound for the
-th
-order
prime as well as some results relating to number-theoretic functions over
.
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Keywords
prime-indexed primes, abstract analytic number theory,
Beurling zeta function
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Mathematical Subject Classification 2010
Primary: 11A41, 11N37, 11N80
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Milestones
Received: 29 August 2018
Revised: 25 July 2019
Accepted: 28 December 2019
Published: 30 March 2020
Communicated by Filip Saidak
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