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
- 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.
- Leyendekkers, J.V., A.G. Shannon. 2001. The Analysis of Twin Primes within Z6. Notes on Number Theory & Discrete Mathematics. 7 (4): 115-124.
- Leyendekkers, J.V., A.G. Shannon, J. Rybak. 2007. Pattern Recognition: Modular Rings and Integer Structure. North Sydney: Raffles KvB Monograph No 9.
- Leyendekkers, J.V., A.G. Shannon. 2009. Analysis of Primes Using Right-end-digits and Integer Structure.
- 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
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.