The "24" Mystery!

A Murderous Math fan called OBAID pointed out that 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, (and you've read The Phantom X ) 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 factories 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 factories to 12n(3n-1). Either n or 

(3n-1) must be even, therefore the whole expression must be divisible by 24.