it is a conjecture that for every integer "b" ≥ 2, there are infinitely many thabit primes of the first kind base "b", infinitely many williams primes of the first kind base "b", and infinitely many williams primes of the second kind base "b"; also, for every integer "b" ≥ 2 that is not congruent to 1 modulo 3, there are infinitely many thabit primes of the second kind base "b". (if the base "b" is congruent to 1 modulo 3, then all thabit numbers of the second kind base "b" are divisible by 3 (and greater than 3, since "b" ≥ 2), so there are no thabit primes of the second kind base "b".)