Problem Solving (PS) | Re: 22! is divisible by x but not by x^2. If x is a prime number, what is

We can eliminate the prime numbers below 10 because they will have a double between 10-20 which will make the number 22! divisible by their squares.
To find the range we need to find the lowest and the highest number. Between 11 and 22 we have the lowest prime as 11 the square of which also being a square prime will not divide 22! The highest prime between 11 and 22 is 19, the square of which also will not divide 22!
Having got our lowest and highest number, we now have the range too, i.e. 19-11=8.