# Small gaps between primes exist

@inproceedings{Goldston2005SmallGB, title={Small gaps between primes exist}, author={D. A. Goldston and Yoichi Motohashi and Janos Pintz and C. Y. Yildirim}, year={2005} }

In the recent preprint (3), Goldston, Pintz, and Yoldorom established, among other things, (0) liminf n→∞ pn+1 − pn log pn = 0, with pn the nth prime. In the present article, which is essentially self-contained, we shall develop a simplified account of the method used in (3). While (3) also includes quantitative versions of (0), we are concerned here solely with proving the qualitative (0), which still exhibits all the essentials of the method. We also show here that an improvement of the… Expand

#### 46 Citations

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