On Legendre’s Conjecture

A. G. Shannon and J. V. Leyendekkers
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 2, Pages 117–125
Full paper (PDF, 197 Kb)

Details

Authors and affiliations

A. G. Shannon
Emeritus Professor, University of Technology Sydney, NSW 2007
Campion College, PO Box 3052, Toongabbie East, NSW 2146, Australia

J. V. Leyendekkers
Faculty of Science, The University of Sydney
NSW 2006, Australia

Abstract

This paper considers some aspects of Legendre’s conjecture as a conjecture and estimates the number of primes in some intervals in order to portray a compelling picture of some of the computational issues generated by the conjecture.

Keywords

• Conjectures
• Twin primes
• Sieves
• Almost-primes
• Chen primes
• Arithmetic functions
• Characteristic functions

AMS Classification

• 11A41
• 11-01

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