Rastislav's four-digit PIN code for his mobile phone is interesting:

- individual digits form prime numbers,
- the 1st and 2nd digits in this order form a prime number,
- the 2nd and 3rd digits in this order form a prime number,
- the 3rd and 4th digits in this order form a prime number.

Rastislav has forgotten his PIN code, but he remembers all the above properties and is trying to activate his powered-off mobile. Which numbers should he try?

(M. Petrová)
First, we note that all one-digit prime numbers are 2, 3, 5, and 7. Next, we find that all two-digit prime numbers that can be constructed from these digits are

$$
23,37,53,73 \text {. }
$$

When we express Rastislav's PIN as $A B C D$, from the problem statement we know that $A B, B C$, and $C D$ must be prime numbers. (Note, nowhere is it stated that $A, B, C$, and $D$ must be distinct digits!) We will substitute the digits $2,3,5,7$ for $A$ one by one and determine which digits can replace $B, C, D$ to meet the given requirements. Everything is summarized in the following table:

| $A$ | $B$ | $C$ | $D$ | PIN |
| :---: | :---: | :---: | :---: | :---: |
| 2 | 3 | 7 | 3 | 2373 |
| 3 | 7 | 3 | 7 | 3737 |
| 5 | 3 | 7 | 3 | 5373 |
| 7 | 3 | 7 | 3 | 7373 |

Rastislav should try the following four numbers: 2373, 3737, 5373, and 7373.