12. Write an arithmetic sequence consisting of three prime numbers with a common difference of 8. The sequence is $\qquad$
12.3,11,19.

Let the first prime be $p=3k, 3k+1,3k+2$ $\left(k \in \mathbf{Z}_{+}\right)$ and discuss each case.
(1) If $p=3k$, then the sequence is $3k, 3k+8,3k+16$. Since $p$ is a prime, $k=1$. Therefore, the sequence is $3,11,19$.
(2) If $p=3k+1$, then the sequence is $3k+1,3k+9$, $3k+17$. But $3k+9$ is not a prime, which does not meet the requirement.
(3) If $p=3k+2$, then the sequence is $3k+2,3k+10$, $3k+18$. But $3k+18$ is not a prime, which does not meet the requirement.
Thus, the sequence that meets the requirement can only be $3,11,19$.