Analysis of primes using right-end-digits and integer structure

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)

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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 Z₆. 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 ̅2₆, ̅4₆ ⊂ Z₆, that contain primes, are found to have the form ½n(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

1. Calinger, Ronald. Classics of Mathematics. New Jersey: Prentice-Hall, 1995.
2. Leyendekkers, J.V., A.G. Shannon, J. Rybak. Pattern Recognition: Modular Rings and Integer Structure. North Sydney: Raffles KvB Monograph No 9. 2007.
3. 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.
4. Sloane, N.J.A., Simon Plouffe. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.