J. V. Leyendekkers and A. G. Shannon

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 24, 2018, Number 1, Pages 10—15

DOI: 10.7546/nntdm.2018.24.1.10-15

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## Details

### Authors and affiliations

J. V. Leyendekkers

*Faculty of Science, The University of Sydney, NSW 2006, Australia*

A. G. Shannon

*Emeritus Professor, University of Technology Sydney, NSW 2007, and
Warrane College, The University of New South Wales, NSW 2033, Australia*

### Abstract

The modular ring *Z*_{6} has twin primes located in the same row. This enables the structural mechanisms underlying the formation of twin primes to be summarised by simple equations. The classification system provided by right-end-digits applies equally in all integer domains of any size, and can be used to demonstrate the formation of twin primes in such domains.

### Keywords

- Modular rings
- Twin primes

### 2010 Mathematics Subject Classification

- 11K31
- 11A41

### References

- Abramowitz, M., & Stegun, I. A. (1964) Handbook of Mathematical Functions. Washington, DC: National Bureau of Standards.
- Freiberg, T. (2015) A note on the theorem of Maynard and Tao. In Ayşe Alaca, Şaban Alaca, Kenneth S. Williams (eds). Advances in the Theory of Numbers (Volume 77, Fields Institute Communications). New York: Springer, 87–103.
- Leyendekkers, J. V., & Rybak, J. M. (1995) The generation and analysis of Pythagorean triples within a two-parameter grid. International Journal of Mathematical Education in Science and Technology, 26, 6, 787–793.
- Leyendekkers, J. V., & Rybak, J. M., Shannon, A. G. (1997) Analysis of Diophantine properties using modular rings with four and six classes. Notes on Number Theory and Discrete Mathematics, 3, 2, 61–74.
- Leyendekkers, J. V., & Shannon, A. G. (2001) The analysis of twin primes within Z6. Notes on Number Theory and Discrete Mathematics, 7, 4, 115–124.
- Ribenboim, P. (1989) The Book of Prime Number Records. 2nd edition. New York: Springer.
- Zhang, Y. (2014) Bounded gaps between primes. Annals of Mathematics. 179, 3, 1121–1174.

## Related papers

## Cite this paper

APALeyendekkers, J. V., & Shannon, A. G. (2018). An indicator characteristic for twin prime

formation independent of integer size. Notes on Number Theory and Discrete Mathematics, 24(1), 10-15, doi: 10.7546/nntdm.2018.24.1.10-15.

Leyendekkers, J. V. and A. G. Shannon. “An Indicator Characteristic for Twin Prime

Formation Independent of Integer Size.” Notes on Number Theory and Discrete Mathematics 24, no. 1 (2018): 10-15, doi: 10.7546/nntdm.2018.24.1.10-15.

Leyendekkers, J. V. and A. G. Shannon. “An Indicator Characteristic for Twin Prime

Formation Independent of Integer Size.” Notes on Number Theory and Discrete Mathematics 24.1 (2018): 10-15. Print, doi: 10.7546/nntdm.2018.24.1.10-15.