The identification of rows of primes in the modular ring Z₆

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 14, 2008, Number 4, Pages 10–15
Full paper (PDF, 2618 Kb)

Details

Authors and affiliations

J. V. Leyendekkers
The University of Sydney
2006, Australia

A. G. Shannon
Raffles College of Design and Commerce, North Sydney, NSW 2060, &
Warrane College, University of New South Wales, NSW 1464, Australia

Abstract

The simple function f(n) = ½n(an ± 1), a = 1, 3, 5 with n = 1, 2, …, 200, generated 615 primes of the modular ring Z₆. 194 of these were twin primes. Values of n which yielded primes for all f(n) were simply related to the number of primes in a given range.

Keywords

• Primes
• Composites
• Modular rings
• Right-end digits
• Integer structure

AMS Classification

• 11A41
• 11A07

References

1. Leyendekkers, J.V., A.G. Shannon. 2001. An Analysis of Twin Primes h2ⁿ – 1 Using Modular Rings Z₄ and Z₆. Notes on Number Theory & Discrete Mathematics. 7 (1): 21-28.
2. Leyendekkers, J.V., A.G. Shannon. 2001. The Analysis of Twin Primes within Z₆. Notes on Number Theory & Discrete Mathematics. 7 (4): 115-124.
3. Leyendekkers, J.V., A.G. Shannon, J. Rybak. 2007. Pattern Recognition: Modular Rings and Integer Structure. North Sydney: Raffles KvB Monograph No 9.
4. Leyendekkers, J.V., A.G. Shannon. 2009. Analysis of Primes Using Right-end-digits and Integer Structure.
5. Riesel, Hans. 1994. Prime Numbers and Computer Methods for Factorization. 2nd edition. Progress in Mathematics, Volume 126. Boston: Birkhäuser, 1994.