twin prime numbers

eh?
isn't that too easy?

See for any prime > 2 all primes are odd So twin primes will always be consecutive odd numbers. The number between them will always be even and hence will be divisible by 2 . :)

To build up on this:

Prove that for any prime p we cannot find twin primes p_1, p_2 such that p_1+p_2=2p

let p_{1}=p_{2}+2
so, 2p₂+2=2p
or,p₂+1=p

therefore p₂ and p are consecutive primes..........
2 and 3 may be the sol.................
but 2*3≠2+4
or, 2*2≠3+5
so no sol.

also p = p₁+p₂2 would be a prime lying between p₁ and p₂ which is absurd as p₁ and p₂ are consecutive primes

Something interesting to build up ont he question

take this as part 2 of the question
see this first: http://mathworld.wolfram.com/PrimePairs.html

Pairs of primes separated by a single number are called prime pairs. Example: 17,19.

Here's the quetsion:

Prove that the number between prime pair is always divisible by 6 (assuming both numbers are greater than 6)

hint: first prove all primes are of the form 6k±1,easy

Sorry for the mistake.
It should be divisible by 6.
And Nasiko has just answered it