I have to show that every prime can be expressed in the form with an integer.

So I figure I need to show that is always an integer. If the numerator is divisible by 24 then it must be divisible by i.e. divisible by 2 at least three times. How can I show this is true?

My idea is to show that is always divisible by 8 and 3 but I don't know how to do it. I'm thinking something about the last digit of only taking certain values meaning that is divisible by 8 but am having difficulty deciding how to do it. Maybe I'm going about this the wrong way.

Any help is appreciated.