1. Given that $\overline{A B C A}$ represents a four-digit number. If the two-digit number $\overline{A B}$ is a prime number, $\overline{B C}$ is a perfect square not equal to 1, and $\overline{C A}$ is the product of a prime number and a perfect square not equal to 1, then the number of four-digit numbers that satisfy these conditions is ( ).
(A) 0
(B) 1
(C) 2
(D) 10
-,1.C.
Since $\overline{A B}$ is a prime number, $B$ can only be $1,3,5, 7,9$. Also, since $\overline{B C}$ is a perfect square not equal to 1, $\overline{B C}$ can only be 16 or 36. Since $\overline{C A}$ is the product of a prime number and a perfect square not equal to 1, $A$ must be 3 or 8.
Therefore, the four-digit number $\overline{A B C A}$ is 3163 or 8368.