J. V. Leyendekkers and A. G. Shannon

Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132

Volume 14, 2008, Number 3, Pages 1–10

**Full paper (PDF, 86 Kb)**

## Details

### Authors and affiliations

J. V. Leyendekkers

*The University of Sydney, 2006 Australia*

A. G. Shannon

*Warrane College, University of New South Wales
Kensington, 1465 Australia*

### Abstract

Primes were separated according to the right-end-digits (REDs) and classes in the modular ring Z_{6}. The primes are given by *jR*, where *j* is the number of consecutive integers with RED = *R* (for *p* = 37, *R* = 7 and *j* = 3, and so on). The rows of *j*, in classes ̅2_{6}, ̅4_{6} ⊂ Z_{6}, that contain primes, are found to have the form ½*n*(*an* ± 1), *a* = 1, 3, 5. A total of 499 primes were generated for *n* = 1 to 80 for RED = 7. Similar results apply to REDs 1, 3 and 9. A scalar characteristic was detected in the row structure of *j*.

### Keywords

- Modular ring
- Triangular numbers
- Pentagonal numbers

### AMS Classification

- 11A41
- 11A07

### References

- Calinger, Ronald.
*Classics of Mathematics*. New Jersey: Prentice-Hall, 1995. - Leyendekkers, J.V., A.G. Shannon, J. Rybak.
*Pattern Recognition: Modular Rings and Integer Structure*. North Sydney: Raffles KvB Monograph No 9. 2007. - Leyendekkers, J.V., A.G. Shannon, C.K. Wong. Integer Structure Analysis of the Product of Adjacent Integers and Euler’s Extension of Fermat’s Last Theorem.
*Advanced Studies in Contemporary Mathematics*17,2 (2008): 221-229. - Sloane, N.J.A., Simon Plouffe.
*The Encyclopedia of Integer Sequences.*San Diego: Academic Press, 1995.

## Related papers

- Leyendekkers, J. V., & Shannon, A. G. (2009). The integer structure of the difference of two odd-powered odd integers.
*Notes on Number Theory and Discrete Mathematics*, 15(3), 14-20.

## Cite this paper

Leyendekkers, J. V., & Shannon, A. G. (2008). Analysis of primes using right-end-digits and integer structure. *Notes on Number Theory and Discrete Mathematics*, 14(3), 1-10.