Small gaps between primes or almost primes
| dc.creator | Goldston, D. A. | |
| dc.creator | Graham, S. W. | |
| dc.creator | Pintz, J. | |
| dc.creator | Yilidirm, C. Y. | |
| dc.date | 2005-06-03 | |
| dc.date.accessioned | 2026-07-07T05:20:30Z | |
| dc.date.available | 2026-07-07T05:20:30Z | |
| dc.description | Let $p_n$ denote the $n^{th}$ prime. Goldston, Pintz, and Yildirim recently proved that $ \liminf_{n\to \infty} \frac{(p_{n+1}-p_n)}{\log p_n} =0.$ We give an alternative proof of this result. We also prove some corresponding results for numbers with two prime factors. Let $q_n$ denote the $n^{th}$ number that is a product of exactly two distinct primes. We prove that $\liminf_{n\to \infty} (q_{n+1}-q_n) \le 26.$ If an appropriate generalization of the Elliott-Halberstam Conjecture is true, then the above bound can be improved to 6. | |
| dc.description | 49 pages | |
| dc.identifier | https://arxiv.org/abs/math/0506067 | |
| dc.identifier | http://arxiv.org/abs/math/0506067 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75399 | |
| dc.subject | Number Theory | |
| dc.subject | 11N25 (primary) 11N05, 11N36 (secondary) | |
| dc.title | Small gaps between primes or almost primes | |
| dc.type | text |