>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 lessÂ—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