**Volume 10** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4

**A Fermatian Staudt—Clausen Theorem**

*Original research paper. Pages 89—99*

A. Shannon

Full paper (PDF, 120 Kb) | Abstract

**An extension of Euler’s prime-generating function**

*Original research paper. Pages 100—105*

J. Leyendekkers and A. Shannon

Full paper (PDF, 90 Kb) | Abstract

*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.

**On two Smarandache’s problems**

*Original research paper. Pages 106—112*

Krassimir T. Atanassov and Mladen V. Vassilev-Missana

Full paper (PDF, 1893 Kb)