Riesel conjectures

Definition
For the original Riesel problem, it is finding and proving the smallest k such that k×bn-1 is not prime for all integers n ≥ 1 and GCD(k-1, b-1)=1.

Extended definiton
Finding and proving the smallest k such that (k×bn-1)/GCD(k-1, b-1) is not prime for all integers n ≥ 1.