Structural sequences for primes using right-end-digits

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 2, Pages 63–70
DOI: 10.7546/nntdm.2018.24.2.63-70
Full paper (PDF, 169 Kb)

Details

Authors and affiliations

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

A. G. Shannon
Warrane College, The University of New South Wales, NSW 2033, Australia

Abstract

Integers are expressed in the form nR where R represents the right-end-digits and nrepresents the digits to the left of R. n can be classified by the sequences {3t}, {3t + 1}, {3t+ 2}. When n = 3t + 2, no primes with R = 1 or 7 can be formed with these n; when n = 3tno primes can be formed with R = 3 or 9, but when n = 3t + 1, all REDs can form a prime within the constraints of imbedded sequences.

Keywords

• Prime numbers
• Composite numbers
• Right-end-digits
• Integer structure

2010 Mathematics Subject Classification

• 11B50

References

1. Leyendekkers, J. V. & Shannon, A.G. (2008) Analysis of Primes Using Right-End-Digits and Integer Structure. Notes on Number Theory & Discrete Mathematics, 14 (3), 1–10.
2. Shannon, A. G., & Leyendekkers, J. V. (2018) The Fibonacci Numbers and Integer Structure. New York: Nova Science Publishers, Chs. 2, 3, 6.