Why you don't search (b-1)*b^n+1? In

http://oeis.org/A087139, someone is searching it for prime b, just as in

http://oeis.org/A122396, someone is searching (b-1)*b^n-1 for prime b.

According to

http://oeis.org/A087139, the b=251 case for (b-1)*b^n+1 is searched to n=73000, no prime was found. However, there is also no known prime for bases b=122, 123, 180, 202, ..., why you don't search (b-1)*b^n+1 for b=122? I searched (b-1)*b^n+1 for all bases 2<=b<=500, but only tested n<=1024. (except of the primes (88-1)*88^3022+1 and (158-1)*158^1620+1)

Besides, you said "k=2 and k=4 @ base=3 tested ...", are you searching all of the four families? (3-1)*3^n-1, (3-1)*3^n+1, (3+1)*3^n-1, and (3+1)*3^n+1?