3. As soon as Dima named the number 17 - the sum of four prime numbers, Andrey immediately found their product, even though Dima did not name the addends. How did Andrey reason? What is the product he found?
3. Since $17: 4=4$ (remainder 1), the prime numbers should be sought among numbers close to four. These are $2, 3, 5$ and 7. Indeed, they satisfy the condition $2+3+5+7=17$, and then the desired product $2 \cdot 3 \cdot 5 \cdot 7=210$.