15. When classmates asked Kolya about the number of the apartment his family received in the new building, Kolya, a math enthusiast, replied: “Our apartment number is a three-digit number that is a perfect cube. If you swap the hundreds and units digits, you get a prime number.” What is Kolya's apartment number?
15. Among three-digit numbers, only 5 are perfect cubes: $5^{3}=125$, $6^{3}=216$, $7^{3}=343$, $8^{3}=512$, $9^{3}=729$. Only the number 125 satisfies the condition, as only 521 is prime.