Talk:Friedlander–Iwaniec theorem

Sieves
I am glad that the title of the article has been corrected. The article still seems to make a false claims about


 * the method used by F-Iw;
 * about the sieve theory in general.

I forgot the name of the mathematician, who went back to the original Brun's sieve. I think that F-Iw used his improved Brun's sieve, and developed it further.

I am aware of sieves created or started by Eratosthenes, Brun, Linnik, Selberg, ... but not of any initiated by Bombieri. From what I remember, Bombieri was one of the early pioneers, who continued the work by Linnik and Selberg.

I'll leave the necessary changes to the article to a specialist. -- Wlod (talk) 08:08, 5 January 2009 (UTC)

Importance
I think that the article should mention why this is important and not just a curios. To wit: the sequence is 'thin' (of natural density 0), and previous results showing the infinitude of primes in sequences have generally been 'thick', and the sieve used in the proof is parity-sensitive (where sieve theory usually has trouble distinguishing numbers with an even and an odd number of prime factors).

Is anyone up to the task?

CRGreathouse (t | c) 15:34, 16 October 2008 (UTC)