A corollary: The sum of twin primes (with both larger than 3) is always divisible by 12

As we saw earlier, primes can only be expressed in the form of 6n+1 or 6n-1 (or 6k+5, whichever is more convenient depending on the context). A twin prime means two prime numbers that are only be separated by one integer, eg. 11 and 13. Hence the smaller number of a twin prime can only take the form of 6n-1 and the other will be 6n+1, in order to make both 'n' equal. Therefore, the sum of twin prime will be

S.O.T.P. = (6n-1) + (6n+1) = 12n

which means S.O.T.P. will ultimately be a multiple of 12 for all twin primes.

This ends the proof.