4. If the product of three prime numbers is exactly 23 times their sum, then these three prime numbers are $\qquad$

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4. $23,13,3$ or $23,7,5$.

Let the three prime numbers be $p, q, r$.
Thus, $p q r=23(p+q+r)$.
From this, we know that one of $p, q, r$ must be 23.
Without loss of generality, let $p=23$, and $q \geqslant r$.
Then $23 q r=23(23+q+r)$
$$
\begin{array}{l}
\Rightarrow(q-1)(r-1)=24 \\
\Rightarrow(q-1, r-1) \\
\quad=(24,1),(12,2),(8,3),(6,4) .
\end{array}
$$

From this, we know the prime pairs $(q, r)=(13,3)$ or $(7,5)$.