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Busy day in number theory

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  • djbroadhurst
    https://plus.google.com/114134834346472219368/posts/
    Message 1 of 3 , May 13, 2013
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    • WarrenS
      Wow! Allegedly Yitang Zhang proved there are infinitely many pairs of primes that are less than 70 million units apart:
      Message 2 of 3 , May 14, 2013
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        Wow!
        Allegedly Yitang Zhang proved there are infinitely many pairs of primes that are less than 70 million units apart:

        http://www.nature.com/news/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989

        And Harald A. Helfgott gives a long proof every odd number N>5 is the sum of three primes (this was already long known to be true except for a computable finite set of
        possible exceptions):

        http://arxiv.org/abs/1305.2897

        (plus additional papers).

        The Zhang result is to be published in Annals of Maths and would seem an absolutely fantastic breakthrough.
      • djbroadhurst
        ... That was my reaction. ... This is indeed cleaning up on previous breakthroughs, but very welcome, nonetheless. ... Happily, David
        Message 3 of 3 , May 14, 2013
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          --- In primenumbers@yahoogroups.com,
          "WarrenS" <warren.wds@...> wrote:

          > Wow!
          > Allegedly Yitang Zhang proved there are infinitely many
          > pairs of primes that are less than 70 million units apart:
          >
          > http://www.nature.com/news/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989
          >
          > The Zhang result is to be published in Annals of Maths and
          > would seem an absolutely fantastic breakthrough.

          That was my reaction.

          > And Harald A. Helfgott gives a long proof every odd number N > 5
          > is the sum of three primes (this was already long known to be true
          > except for a computable finite set of possible exceptions):
          >
          > http://arxiv.org/abs/1305.2897

          This is indeed cleaning up on previous breakthroughs,
          but very welcome, nonetheless.

          As Terence Tao had said, and I had here echoed:

          > Busy day in number theory

          Happily,

          David
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