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
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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

References

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Cite this paper

Leyendekkers, J. V., and Shannon, A. G. (2004). An extension of Euler’s prime-generating function. Notes on Number Theory and Discrete Mathematics, 10(4), 100-105.

 

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