  Define $\psi_m$ to be the smallest strong pseudoprime to the first $m$ prime
bases. The exact value of $\psi_m$ is known for $1\le m \le 8$. Z. Zhang have
found a 19-decimal-digit number $Q_{11}=3825\,12305\,65464\,13051$ which is a
strong pseudoprime to the first 11 prime bases and he conjectured that
$$\psi_9=\psi_{10}=\psi_{11}=Q_{11}.$$ We prove the conjecture by algorithms.
