International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 819068, 14 pages
doi:10.1155/2009/819068

The Rabinowitsch-Mollin-Williams theorem revisited

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.