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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## 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*) = ½*n*(*an* ± 1), *a* = 1, 3, 5 with *n* = 1, 2, …, 200, generated 615 primes of the modular ring Z_{6}. 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*h*2– 1 Using Modular Rings Z^{n}_{4}and Z_{6}.*Notes on Number Theory & Discrete Mathematics*. 7 (1): 21-28. - Leyendekkers, J.V., A.G. Shannon
*.*2001. The Analysis of Twin Primes within Z_{6}.*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.

## Related papers

## Cite this paper

APALeyendekkers, J. V., & Shannon, A. G. (2008). The identification of rows of primes in the modular ring Z_{6}. Notes on Number Theory and Discrete Mathematics, 14(4), 10-15.

Leyendekkers, JV, and AG Shannon. “The Identification of Rows of Primes in the Modular Ring Z_{6}.” Notes on Number Theory and Discrete Mathematics 14, no. 4(2008): 10-15.

Leyendekkers, JV, and AG Shannon. “The Identification of Rows of Primes in the Modular Ring Z_{6}.” Notes on Number Theory and Discrete Mathematics 14.4 (2008): 10-15. Print.