The analysis of twin primes within Z₆

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 7, 2001, Number 4, Pages 115–124
Full paper (PDF, 490 Kb)

Details

Authors and affiliations

J. V. Leyendekkers
The University of Sydney
NSW 2006, Australia

A. G. Shannon
Warrane College, The University of New South Wales, 1465, &
KvB Institute of Technology, North Sydney, 2060, Australia

Abstract

The modular ring Z₆ defines integers via (6r_i + (i – 3)) where i is the Class and r, the row when tabulated in an array. Since only Classes 2₆ and 4₆ (; contain odd primes, this modular ring is ideally suited for the analysis of twin primes. In considering a series of integers, a simple method is used to calculate rows (F rows) that do not contain twin primes. This allows the distribution of other primes to be found. Then, in considering the corresponding array of rows, elimination of the F rows yields the rows which contain twin primes. The calculations are facilitated by the use of the right-end digit (RED) technique.

AMS Classification

• 11A41
• 11A51

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