Riesel bases always have a trivial factor of b1 rather than b+1. Technically k=1 IS considered in the Riesel base 2 conjecture because you cannot have a trivial factor of 1 since it is not considered prime. But k=1 has a prime at n=2 and hence is quickly eliminated.
For Sierp, k=1 always make Generalized Fermat #'s (GFNs). GFNs are forms that can reduce to b^n+1, hence k's where k=b^q and q>=0 are also not considered.
We do not consider GFNs in testing because n must be 2^q to make a prime, resulting in few possibilities of primes. Most mathematicians agree that the number of primes of such forms is finite.
See the project definition for more details about exclusions and inclusions of kvalues in the 'come join us' thread.
Gary
