# Small Gaps Between Primes I

@article{Goldston2005SmallGB, title={Small Gaps Between Primes I}, author={D. A. Goldston and Cem Yalçın Yıldırım}, journal={arXiv: Number Theory}, year={2005} }

We use short divisor sums to approximate prime tuples and moments for primes in short intervals. By connecting these results to classical moment problems we are able to prove that a positive proportion of consecutive primes are within a quarter of the average spacing between primes.

## 21 Citations

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A famous theorem of Szemeredi asserts that all subsets of the integers with positive
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