6. If $p$ is a prime number, and $p^{3}+3$ is also a prime number, then the last digit of $p^{33}+33$ is ( ).
(A) 5
(B) 7
(C) 9
(D) cannot be determined
6.A.

From $p^{3}+3$ being a prime number, we know that $p$ is even. Since $p$ is also a prime number, then $p=2$.
Thus, $p^{33}+33=2^{33}+33=\left(2^{4}\right)^{8} \times 2+33$.
Since the last digit of $\left(2^{4}\right)^{8}$ is 6, the last digit of $\left(2^{4}\right)^{8} \times 2$ is 2.
Therefore, the last digit of $p^{33}+33$ is 5.