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Prime arithmetic progressions of arbitrary length

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  • Brian Schroeder
    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
    Message 1 of 2 , Apr 14, 2004
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      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
    • Adam
      ... proves ... sequences of
      Message 2 of 2 , Apr 15, 2004
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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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