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Re: Busy day in number theory

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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 1 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 2 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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