Prime grids in the modular ring Z6

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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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 Z6 for the Classes 26 and 46. 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

  1. John H Conway & Richard K Guy, The Book of Numbers. New York: Copernicus,
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  2. 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.
  3. 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.
  4. 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.
  5. J.V. Leyendekkers, J.M. Rybak & A.G. Shannon, The Characteristics of Primes and Other Integers within the Modular Ring Z4 and in Class 14. Notes on Number Theory & Discrete Mathematics. 4 (1) (1998): 1-17.
  6. J.V. Leyendekkers & A.G. Shannon, The Analysis of Twin Primes within Z6. Notes on Number Theory & Discrete Mathematics. 7(4) (2001): 115-124.
  7. J.V. Leyendekkers & A.G. Shannon, Fermat’s Theorem on Binary Powers, Notes on Number Theory & Discrete Mathematics. In press.
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Cite this paper

APA

Leyendekkers, J. V., and Shannon, A. G. (2005). Prime grids in the modular ring Z6. Notes on Number Theory and Discrete Mathematics, 11(1), 23-28.

Chicago

Leyendekkers, JV, and AG Shannon. “Prime Grids in the Modular Ring Z6.” Notes on Number Theory and Discrete Mathematics 11, no. 1 (2005): 23-28.

MLA

Leyendekkers, JV, and AG Shannon. “Prime Grids in the Modular Ring Z6.” Notes on Number Theory and Discrete Mathematics 11.1 (2005): 23-28. Print.

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