Small Gaps between Primes Exist
| dc.creator | Goldston, D. A. | |
| dc.creator | Motohashi, Y. | |
| dc.creator | Pintz, J. | |
| dc.creator | Yildirim, C. Y. | |
| dc.date | 2005-05-14 | |
| dc.date.accessioned | 2026-07-07T05:19:54Z | |
| dc.date.available | 2026-07-07T05:19:54Z | |
| dc.description | In the recent preprint [3], Goldston, Pintz, and Yıldırım established, among other things, $$ \liminf_{n\to\infty}{p_{n+1}-p_n\over\log p_n}=0,\leqno(0) $$ with $p_n$ the $n$th 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 Bombieri--Vinogradov prime number theorem would give rise infinitely often to bounded differences between consecutive primes. We include a short expository last section. Detailed discussions of quantitative results and a historical review will appear in the publication version of [3] and its continuations. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0505300 | |
| dc.identifier | http://arxiv.org/abs/math/0505300 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75193 | |
| dc.subject | Number Theory | |
| dc.subject | 11N05 (Primary); 11P32 (Secondary) | |
| dc.title | Small Gaps between Primes Exist | |
| dc.type | text |