The "24" Mystery!

This is a neat trick!
If you square ANY prime number bigger then 3, then subtract 1, the answer always divides by 24!
E.g. 112 = 121 then 121 - 1 = 120 and yes 120 does divide by 24.
WHY?
If you understand algebra, then you'll know that all prime numbers can be written as (6n+1) or (6n-1).
(6n+1)2 = 36n+12n+1. So (6n+1)2 -1 = 36n+12n. This factorises to 12n(3n+1). Either n or (3n+1) must be even, therefore the whole expression must be divisible by 24.
(6n-1)2 = 36n-12n+1. So (6n-1)2 -1 = 36n-12n. This factorises to 12n(3n-1). Either n or (3n-1) must be even, therefore the whole expression must be divisible by 24.