Sierpinski conjectures

Definition
For the original Sierpinski 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.