361. A prime number is divided by 21 with a remainder. Find all values of the remainder that are composite numbers.
$\triangle$ Let's denote a prime number by $p$, the quotient by $q$, and the remainder by $r$. Then

$$
p=21 q+r \quad(0<r<21)
$$

Since $p$ is a prime number, from all composite values of $r$ less than 21, we need to select those that are coprime with 3 and 7, otherwise the sum $21 q+r$ would be divisible by 3 or 7. The suitable values are

$$
r=4,8,10,16,20
$$

We also need to check that for each of these values of $r$, there exists a prime number $p$ that gives exactly this remainder when divided by 21; for example, for $r=4$, we can take $p=67$, where the number 67 is obtained as $21 \cdot 3+4$.

Answer: $4,8,10,16,20$.