An example is Sierp base 311, all k's that between a multiple of 3 and a multiple of 13 have the covering set {3,13}, the first such k's are 14, 25, 53, 64, 92, 103, 131, 142, ..., however all such k's < 142 are also trivial (i.e. gcd(k+1,3111) is not 1), thus the conjectured k for Sierp base 311 is 142. (this conjecture is proven, all k's except 10, 46, and 76 have an easy prime)
