Primes in tuples I

@article{Goldston2009PrimesIT,
  title={Primes in tuples I},
  author={D. A. Goldston and Janos Pintz and C. Y. Yildirim},
  journal={Annals of Mathematics},
  year={2009},
  volume={170},
  pages={819-862}
}
We introduce a method for showing that there exist prime numbers which are very close together. The method depends on the level of distribution of primes in arithmetic progressions. Assuming the Elliott-Halberstam conjecture, we prove that there are infinitely often primes differing by 16 or less. Even a much weaker conjecture implies that there are infinitely often primes a bounded distance apart. Unconditionally, we prove that there exist consecutive primes which are closer than any… 
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