9. What is the lowest prime number that is thirteen more than a cube?
Solution
229

We consider the cube numbers in sequence until we find one that is thirteen less than a prime. $1+13=14,8+13=21,27+13=40,64+13=77,125+13=138$, none of which are prime. $216+13=229$, which is prime, and therefore 229 is the answer.