arXiv:1311.4600math.NT
Small gaps between primes
Abstract
We introduce a refinement of the GPY sieve method for studying prime $k$-tuples and small gaps between primes. This refinement avoids previous limitations of the method, and allows us to show that for each $k$, the prime $k$-tuples conjecture holds for a positive proportion of admissible $k$-tuples. In particular, $\liminf_{n}(p_{n+m}-p_n)<\infty$ for any integer $m$. We also show that $\liminf(p_{n+1}-p_n)\le 600$, and, if we assume the Elliott-Halberstam conjecture, that $\liminf_n(p_{n+1}-p_n)\le 12$ and $\liminf_n (p_{n+2}-p_n)\le 600$.
I knew about the Wiki http://michaelnielsen.org/polymath1/index.php?title=Bounded_... However, I did not know about the solo paper http://arxiv.org/abs/1311.4600 In their celebrated paper [5], Goldston, Pintz and Yıldırım introduced a new method for counting tuples of primes…
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Okay it appears that you and several others have not read the preprint paper. The article's wording is a bit confusing but if you think carefully you'd realize that a later work can not be independent of an earlier well known result. The article does have a link to Maynard's…
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