An extension of Euler’s prime-generating function

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 10, 2004, Number 4, Pages 100–105
Full paper (PDF, 90 Kb)

Details

Authors and affiliations

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

A. G. Shannon
Warrane College, Kensington, NSW 1465,
& KvB Institute of Technology, North Sydney, NSW 2060, Australia

Abstract

Using integer structure, six simple functions are obtained to give values for x that result in composite N in Euler’s prime generating function N = x² + x + p; the remaining values for x yield primes. In 0 ≤ x ≤ 500, with p = 41, there are 314 values for x which generate primes, the formation of which follows an orderly pattern based on integer structure. All primes can be generated from N = 6r ± 1, with specific values of r being rejected, in an analogous manner to the x values.

AMS Classification

• 11A41
• 11A07

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