Primes in Tuples I
| dc.creator | Goldston, D. A. | |
| dc.creator | Pintz, J. | |
| dc.creator | Yildirim, C. Y. | |
| dc.date | 2005-08-10 | |
| dc.date.accessioned | 2026-07-07T05:22:18Z | |
| dc.date.available | 2026-07-07T05:22:18Z | |
| dc.description | 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 arbitrarily small multiple of the average spacing, that is, \[ \liminf_{n\to \infty} \frac{p_{n+1}-p_n}{\log p_n} =0 .\] This last result will be considerably improved in a later paper. | |
| dc.description | 36 pages | |
| dc.identifier | https://arxiv.org/abs/math/0508185 | |
| dc.identifier | http://arxiv.org/abs/math/0508185 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76005 | |
| dc.subject | Number Theory | |
| dc.subject | 11N05 | |
| dc.title | Primes in Tuples I | |
| dc.type | text |