J. V. Leyendekkers and A. G. Shannon

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 11, 2005, Number 1, Pages 23—28

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## Details

### Authors and affiliations

J. V. Leyendekkers

*The University of Sydney, 2006 Australia*

A. G. Shannon

*Warrane College, Kensington, NSW 1465,
& KvB Institute of Technology, North Sydney, NSW 2060, Australia *

### Abstract

Prime grids are set up in the Modular Ring Z_{6} for the Classes 2_{6} and 4_{6}. The regular formation of composites intrudes into the grid in a predictable manner, which indicates that the primes form in a structured rather than a haphazard manner when viewed in this way.

### AMS Classification

- 11A41
- 11A07

### References

- John H Conway & Richard K Guy, The Book of Numbers. New York: Copernicus,

1996. - Ottavio M. D’Antona, The Would-Be Method of Targeted Rings. In Bruce E. Sagan & Richard P. Stanley (eds), Mathematical Essays in Honour of Gian-Carlo Rota. Boston: Birkhäuser, 1998, pp.157-172.
- J.V. Leyendekkers, J.M. Rybak & A.G. Shannon, Integer Class Properties Associated with an Integer Matrix. Notes on Number Theory & Discrete Mathematics. 1 (2) (1995): 53-59.
- J.V. Leyendekkers, J.M. Rybak & A.G. Shannon, Analysis of Diophantine Properties Using Modular Rings with Four and Six Classes. Notes on Number Theory & Discrete Mathematics. 3 (2) (1997): 61-74.
- J.V. Leyendekkers, J.M. Rybak & A.G. Shannon, The Characteristics of Primes and Other Integers within the Modular Ring Z
_{4}and in Class 1_{4}. Notes on Number Theory & Discrete Mathematics. 4 (1) (1998): 1-17. - J.V. Leyendekkers & A.G. Shannon, The Analysis of Twin Primes within Z
_{6}. Notes on Number Theory & Discrete Mathematics. 7(4) (2001): 115-124. - J.V. Leyendekkers & A.G. Shannon, Fermat’s Theorem on Binary Powers, Notes on Number Theory & Discrete Mathematics. In press.
- Neal H. McCoy, The Theory of Numbers. New York: Macmillan, 1965, Ch.2..

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## Cite this paper

APALeyendekkers, J. V., and Shannon, A. G. (2005). Prime grids in the modular ring Z_{6}. Notes on Number Theory and Discrete Mathematics, 11(1), 23-28.

Leyendekkers, JV, and AG Shannon. “Prime Grids in the Modular Ring Z_{6}.” Notes on Number Theory and Discrete Mathematics 11, no. 1 (2005): 23-28.

Leyendekkers, JV, and AG Shannon. “Prime Grids in the Modular Ring Z_{6}.” Notes on Number Theory and Discrete Mathematics 11.1 (2005): 23-28. Print.