19. Find all prime numbers $p$ such that the numbers $p+4$ and $p+8$ are also prime.
19. It is not hard to notice that the number 3 satisfies the requirements of the problem. Let's show that the problem has no other solutions. Indeed, every prime number not equal to 3 has one of two forms: $3k+1$ or $3k+2$, where $k$ is a non-negative integer. But in the case $p=3k+1$, the number $p+8$ is divisible by 3, and in the case $p=3k+2$, the number $p+4$ is divisible by 3.