# Porve the sum of twin primes is divisible by 12

• February 4th 2008, 02:28 PM
Porve the sum of twin primes is divisible by 12
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.
• February 4th 2008, 03:15 PM
Plato
All twin primes except (3, 5) are of the form $6n\pm1$.
Twin Primes -- from Wolfram MathWorld
Can you use that?