  A recent construction by Amarra, Devillers and Praeger of block designs with
specific parameters depends on certain quadratic polynomials, with integer
coefficients, taking prime power values. The Bunyakovsky Conjecture, if true,
would imply that each of them takes infinitely many prime values, giving an
infinite family of block designs with the required parameters. We have found
large numbers of prime values of these polynomials, and the numbers found agree
very closely with the estimates for them provided by Li's recent modification
of the Bateman-Horn Conjecture. While this does not prove that these
polynomials take infinitely many prime values, it provides strong evidence for
this, and it also adds extra support for the validity of the Bunyakovsky and
Bateman-Horn Conjectures.
