The Rabinowitsch-Mollin-Williams Theorem Revisited

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) viathe use of an updated version of what Andrew Granville has dubbedthe Rabinowitsch-Mollin-Williams Theorem—by Granville and Mollin (2000) and Mollin (1996). Furthermore, we verify conjectures of this author and pose more basedon the new data