Consider the even number sequence 12, 18, 30, 42, 48, 60, 72, 78, 90, 102, 108, 120 . . .

It does not take a genius to produce a simple arithmetic function, f(x), which breaks the sequence into those even numbers to which twin primes are attracted, and those even numbers which do not attract twin primes.

Applying f(x) we get

12, 18, 30, 42, 60, 72, 102, 108 . . .

and

48, 78, 90, 120 . . .

So to prove the Twin Prime Conjecture all (?) we now need is a proof that the sequence

12, 18, 30, 42, 60, 72, 102, 108 . . .

has a bounded gap of any size whatsoever.

Does anyone know why it would not be possible to use Tom Yitang's techniques, or the subsequent Polymath project reasonings, to do this? A simple explanation would be welcomed as Kloostermania and Deligne is a little beyond my comprehension.

Bob