the exponent of thabit primes of the second kind cannot congruent to 1 mod 3 (except 1 itself), the exponent of williams primes of the first kind cannot congruent to 4 mod 6, and the exponent of williams primes of the second kind cannot congruent to 1 mod 6 (except 1 itself), since the corresponding polynomial to "b" is a reducible polynomial. (if "n" ≡ 1 mod 3, then ("b"+1)·"b" + 1 is divisible by "b" + "b" + 1; if "n" ≡ 4 mod 6, then ("b"−1)·"b" − 1 is divisible by "b" − "b" + 1; and if "n" ≡ 1 mod 6, then ("b"−1)·"b" + 1 is divisible by "b" − "b" + 1) otherwise, the corresponding polynomial to "b" is an irreducible polynomial, so if bunyakovsky conjecture is true, then there are infinitely many bases "b" such that the corresponding number (for fixed exponent "n" satisfying the condition) is prime. (("b"+1)·"b" − 1 is irreducible for all nonnegative integer "n", so if bunyakovsky conjecture is true, then there are infinitely many bases "b" such that the corresponding number (for fixed exponent "n") is prime)