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2020 Arithmetic functions of higher-order primes
Kyle Czarnecki, Andrew Giddings
Involve 13(2): 181-191 (2020). DOI: 10.2140/involve.2020.13.181

Abstract

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 2={3,5,11,17,31,}. More generally, the application of the SoE k-times will yield the set k of k-th order primes. In this paper, we give an upper bound for the n-th k-order prime as well as some results relating to number-theoretic functions over k.

Citation

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Kyle Czarnecki. Andrew Giddings. "Arithmetic functions of higher-order primes." Involve 13 (2) 181 - 191, 2020. https://doi.org/10.2140/involve.2020.13.181

Information

Received: 29 August 2018; Revised: 25 July 2019; Accepted: 28 December 2019; Published: 2020
First available in Project Euclid: 25 June 2020

zbMATH: 1434.11015
MathSciNet: MR4080489
Digital Object Identifier: 10.2140/involve.2020.13.181

Subjects:
Primary: 11A41, 11N37, 11N80

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.13 • No. 2 • 2020
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