Twin Primes

It is known that every twin prime pair is of the form (6n-1) & (6n+1)
.. WHY?

Because every prime is of the form (6n-1) or (6n+1).

Proof: (6n+K) is not prime for K = 2,3,4; is prime for K = 1 or 5.

(6n +5) = [6*(n+1) -1]

There are many (6n+1), (6n+5) pairs of primes

Why aren't such prime pairs also called "twin primes"?

Regards

Bill J.

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