Comparing the Growth of the Prime Numbers to the Natural Numbers

Authors

Michael A. Brilleslyper, U.S. Air Force AcademyFollow
Nathan Wakefield, University of Nebraska-LincolnFollow
A. J. Wallerstein, Air Force Institute of TechnologyFollow
Bradley Warner, U.S. Air Force AcademyFollow

Document Type

Article

Date of this Version

2016

Citation

Preprint of article published in Fibonacci Quarterly 54 (2016), no. 1, 65–71.

Comments

US govt

Abstract

We define a new method of measuring the rate of divergence for an increasing positive sequence of integers. We introduce the growth function for such a sequence and its associated growth limit. We use these tools to study the divergence rate for the natural numbers, polynomial and exponential-type sequences, and the prime numbers. We conclude with a number of open questions concerning general properties and characterizations of growth functions and the set of possible growth limits.