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Re: Prime arithmetic progressions of arbitrary length

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  • Adam
    ... proves ... sequences of
    Message 1 of 2 , Apr 15 7:28 AM
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      >I haven't read this paper but it sights Goldston and Yildirim in its
      >summary and I thought the news about that was that they made an
      >error, e.g.,
      >
      >http://www.sciencenews.org/articles/20030531/note17.asp
      >
      >which states in part that
      >
      >"Mathematicians Andrew Granville of the University of Montreal and
      >Kannan Soundararajan of the University of Michigan in Ann Arbor
      >discovered the error in Goldston and Yildirim's work after realizing,
      >to their surprise, that they could adapt the new result to prove in
      >just a few additional lines that there are infinitely many pairs of
      >primes differing by 12 or less—a finding almost as strong as the
      >elusive twin-primes conjecture.
      >
      >This result seemed too good to be true. Scrutinizing Goldston and
      >Yildirim's work line by line, Granville and Soundararajan found that
      >one term in a complicated expression wasn't as well behaved
      >mathematically as Goldston and Yildirim had thought, making the final
      >result fall through."
      >
      >Adam



      --- In primenumbers@yahoogroups.com, Brian Schroeder <schroe79@m...>
      wrote:
      > Here is a preprint of a paper by Ben Green and Terence Tao which
      proves
      > that for every k >= 3 there exist infinitely many arithmetic
      sequences of
      > primes of length k. I thought people might be interested in it.
      >
      > http://www.arxiv.org/abs/math.NT/0404188
      >
      > Brian
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