Show that the sum of twin primes is divisible by 12, for all primes > 3.
Proof.
Let p = 4k+1, then p+p+2 = 8k+4, so it is divisible by 4.
Now, how do I get it to be divisible by 3?
Thanks.
All twin primes except (3, 5) are of the form $\displaystyle 6n\pm1$.
Twin Primes -- from Wolfram MathWorld
Can you use that?