8.1. Find any four different natural numbers that have the following property: if the product of any two of them is added to the product of the other two numbers, the result is a prime number.
Solution. For example, the numbers 1, 2, 3, and 5 will work. Indeed, the values of all three expressions $1 \cdot 2 + 3 \cdot 5 = 17$, $1 \cdot 3 + 2 \cdot 5 = 13$, and $1 \cdot 5 + 2 \cdot 3 = 11$ are prime numbers.

Remark. There are other examples, such as $(1,2,3,13)$, $(2,5,11,17)$, or $(4,5,7,11)$. It is not hard to see that in any such example, there must be exactly one even number.

Comment. A correct example without verifying that the given set of numbers works - 4 points.

Any incorrect example - 0 points.