prime number puzzle:

Consider the prime set (11,13) (17,19) (29,31).....and so on.

which have one number between them.

prove that the number is divisible by 6.




 Proof:
          
For any given 3 consecutive numbers one of them is 

divisible by 3. 

each given prime set have an even number in between.

By definition primes are only divisible 1 and itself.

so, the missed number is divisible by 3. since it is also even it 

is divisible by 2.

The number divisible by 3 and 2 is also divisible by 6.