Vol. 13, No. 2, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Editorial Login
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Author Index
Coming Soon
 
Other MSP Journals
Arithmetic functions of higher-order primes

Kyle Czarnecki and Andrew Giddings

Vol. 13 (2020), No. 2, 181–191
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.

Keywords
prime-indexed primes, abstract analytic number theory, Beurling zeta function
Mathematical Subject Classification 2010
Primary: 11A41, 11N37, 11N80
Milestones
Received: 29 August 2018
Revised: 25 July 2019
Accepted: 28 December 2019
Published: 30 March 2020

Communicated by Filip Saidak
Authors
Kyle Czarnecki
University of Wisconsin
Platteville, WI
United States
Andrew Giddings
University of Wisconsin
Platteville, WI
United States