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
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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.

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Cite this paper

APA

Leyendekkers, J. V., & Shannon, A. G. (2008). The identification of rows of primes in the modular ring Z6. Notes on Number Theory and Discrete Mathematics, 14(4), 10-15.

Chicago

Leyendekkers, JV, and AG Shannon. “The Identification of Rows of Primes in the Modular Ring Z6.” Notes on Number Theory and Discrete Mathematics 14, no. 4(2008): 10-15.

MLA

Leyendekkers, JV, and AG Shannon. “The Identification of Rows of Primes in the Modular Ring Z6.” Notes on Number Theory and Discrete Mathematics 14.4 (2008): 10-15. Print.

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