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Re: [PrimeNumbers] Zhang's gap

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  • Bob Gilson
    ... Bob ... [Non-text portions of this message have been removed]
    Message 1 of 4 , Jul 27, 2013
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      On 26 Jul 2013, at 19:56, Jose Angel Gonzalez <josechu2004@...> wrote:

      > Zhang's gap as been reduced from 70 million to 5414 in a couple of months.
      > Wow.
      >
      > So, there is an infinite quantity of pairs of consecutive primes whose
      > distance is a fixed number below 5414.
      >
      > Source:
      >
      > http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes
      >
      > That assumes of course that the underlying analytical maths holds up under scrutiny. Alas, the process has no hope of reaching gap 2 - for that, even more original thinking is required. But it's great to see the progress on this thorny problem, especially as the breakthrough was totally out of left field.
      >

      Bob
      >
      >


      [Non-text portions of this message have been removed]
    • Roahn Wynar
      Bob, What is known about the fundamental lower limit of this method? I had not heard anything about a known lower bound, which your post suggests is 2.
      Message 2 of 4 , Jul 27, 2013
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        Bob,

        What is known about the fundamental lower limit of this method? I had not heard anything about a known lower bound, which your post suggests is >2. Thanks!

        Roahn




        ----- Original Message -----
        From: Bob Gilson
        To: Jose Angel Gonzalez
        Cc: primenumbers@yahoogroups.com
        Sent: Saturday, July 27, 2013 2:55 AM
        Subject: Re: [PrimeNumbers] Zhang's gap





        On 26 Jul 2013, at 19:56, Jose Angel Gonzalez <josechu2004@...> wrote:

        > Zhang's gap as been reduced from 70 million to 5414 in a couple of months.
        > Wow.
        >
        > So, there is an infinite quantity of pairs of consecutive primes whose
        > distance is a fixed number below 5414.
        >
        > Source:
        >
        > http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes
        >
        > That assumes of course that the underlying analytical maths holds up under scrutiny. Alas, the process has no hope of reaching gap 2 - for that, even more original thinking is required. But it's great to see the progress on this thorny problem, especially as the breakthrough was totally out of left field.
        >

        Bob
        >
        >

        [Non-text portions of this message have been removed]








        [Non-text portions of this message have been removed]
      • djbroadhurst
        ... The potential obstacle at a limit of 16 appears to come from the (conditional!) Theorem B of the fine article by Janos Pintz that Warren kindly advertized:
        Message 3 of 4 , Jul 27, 2013
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          --- In primenumbers@yahoogroups.com,
          "Roahn Wynar" <rwynar@...> wrote:

          > What is known about the fundamental lower limit of this method?

          The potential obstacle at a limit of 16 appears to come
          from the (conditional!) Theorem B of the fine article
          by Janos Pintz that Warren kindly advertized:

          http://arxiv.org/abs/1305.6289

          David
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