What is the smallest positive number that is prime and $10$ less than a perfect square?
The smallest perfect square is $1^2 = 1$, but $1 - 10 = -9$, which is not positive. The next perfect square is $2^2 = 4$, but $4 - 10 = -6$, which is also not positive. The next perfect square is $3^2 = 9$, but $9 - 10 = -1$, which is still not positive. The next perfect square is $4^2 = 16$, and $16 - 10 = 6$, which is positive, but not prime. The next perfect square is $5^2 = 25$, and $25 - 10 = 15$, which is positive, but also not prime. The next perfect square is $6^2 = 36$, and $36 - 10 = 26$, which is positive, but also not prime. The next perfect square is $7^2 = 49$, and $49 - 10 = 39$, which is positive, but also not prime. The next perfect square is $8^2 = 64$, and $64 - 10 = 54$, which is positive, but also not prime. The next perfect square is $9^2 = 81$, and $81 - 10 = 71$, which is positive, and finally prime! Therefore, the smallest positive number that is prime and $10$ less than a perfect square is $71$. 