Prime arithmetic progressions of arbitrary length
- 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.
>I haven't read this paper but it sights Goldston and Yildirim in its--- In email@example.com, Brian Schroeder <schroe79@m...>
>summary and I thought the news about that was that they made an
>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 lessa 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."
> Here is a preprint of a paper by Ben Green and Terence Tao whichproves
> that for every k >= 3 there exist infinitely many arithmeticsequences of
> primes of length k. I thought people might be interested in it.