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25125infinitely popular prime gap sizes

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  • WarrenS
    May 30, 2013
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      > If there are infinitely many consecutive pairs of primes with some gap < 70
      > millions, why not all the other number bigger than 70 millions?

      --I suspect Zhang's proof could easily be modified to show that there are an infinite set of
      integers K>0, such that, for each K in the set, there are an infinite set of primes P
      with P+K simultaneously prime.

      Zhang's present proof creates a set S of integers within [2, 70000000]
      and proves that are an infinity of N such that N+S contains at least two primes.

      Instead create a finite set T of integers with all gaps between set members >70000000
      then prove there are an infinity of N such that N+T contains at least two primes...

      then continue on, each set having min-gaps > the previous set's max-element.

      This might be a good project for anybody trying to understand the Zhang proof.
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