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.

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- Feb 4th 2008, 02:28 PMtttcomraderPorve 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. - Feb 4th 2008, 03:15 PMPlato
All twin primes except (3, 5) are of the form $\displaystyle 6n\pm1$.

Twin Primes -- from Wolfram MathWorld

Can you use that?