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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## 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* = *x*^{2} + *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* = 6*r* ± 1, with specific values of *r* being rejected, in an analogous manner to the *x* values.

### AMS Classification

- 11A41
- 11A07

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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.