# 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…

## 26 Citations

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