The Goldberg-conjecture primes within a modular ring

J. Leyendekkers and A. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 6, 2000, Number 4, Pages 101—112
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Authors and affiliations

J. Leyendekkers
The University of Sydney, 2006, Australia

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


We examine here the class structure of odd primes within the modular ring ℤ4 in relation to Goldbach’s Conjecture. Such analyses, together with the identification of compatible right-end digits for the Goldberg ‘system’, permit a more efficient search for prime pairs. This is useful for the study of very large even numbers, the distribution of twin primes and other prime constellations, and the relative distribution of primes between the classes l4 and 34 .

AMS Classification

  • 11P32
  • 11A41
  • 11F03


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Related papers

  1. Leyendekkers, J. V., & Shannon, A. G. (2003). Some characteristics of primes within modular rings. Notes on Number Theory and Discrete Mathematics, 9(3), 49-58.

Cite this paper

Leyendekkers, J. & Shannon, A. (2000). The Goldberg-conjecture primes within a modular ring. Notes on Number Theory and Discrete Mathematics, 6(4), 101-112.

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