3. A four-digit number has the following properties:
1) the first and fourth digits are the same,
2) the second and third digits are the same,
3) the number is equal to the product of three consecutive prime numbers.

What is that number?
Solution. Let the four-digit number be $x=\overline{a b b a}$. Then

$$
x=1000 a+100 b+10 b+a=1001 a+110 b=11(91 a+10 b)
$$

According to this, $x$ is divisible by 11, so according to the condition $x=5 \cdot 7 \cdot 11$ or $x=7 \cdot 11 \cdot 13$ or $x=11 \cdot 13 \cdot 17$, that is, $x=385$ or $x=1001$ or $x=2431$. Clearly, only the number $x=1001$ satisfies the conditions.