An indicator characteristic for twin prime formation independent of integer size

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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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 Z6 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

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  4. 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.
  5. 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.
  6. Ribenboim, P. (1989) The Book of Prime Number Records. 2nd edition. New York: Springer.
  7. Zhang, Y. (2014) Bounded gaps between primes. Annals of Mathematics. 179, 3, 1121–1174.

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Cite this paper

APA

Leyendekkers, 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.

Chicago

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.

MLA

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.

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