Landau’s Fourth problem

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 22, 2016, Number 4, Pages 73–77
Full paper (PDF, 150 Kb)


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, Australia
Campion College, PO Box 3052, Toongabbie East, NSW 2146, Australia


Primes of the form n2 + 1 show no deviations contrary to the natural integer structure within the modular ring Z4 and the sum of two squares. Hence primes of this form should occur to infinity with other primes. Trend characteristics of primes and composites were compared graphically.


  • Modular rings
  • Primes
  • Composites

AMS Classification

  • 11A07
  • 11A51
  • 11B37


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Cite this paper

Leyendekkers, J. V., & Shannon, A. G. (2016). Landau’s Fourth problem. Notes on Number Theory and Discrete Mathematics, 22(4), 73-77.

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