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25408Pie in the sky or a reasonable thought?

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  • Bob Gilson
    Nov 29, 2013
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      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