Copyright © 2009 R. A. Mollin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We completely classify all polynomials of type (x2+x−(Δ−1))/4 which are prime or 1 for a range of consecutive integers x≥0, called Rabinowitsch polynomials, where Δ≡1(mod⁡4) with Δ>1 square-free. This corrects, extends, and completes the results by Byeon and Stark (2002, 2003) via the use of an updated version of what Andrew Granville has dubbed the Rabinowitsch-Mollin-Williams Theorem—by Granville and Mollin (2000) and Mollin (1996). Furthermore, we verify conjectures of this author and pose more based on the new data.