Discrete Reanalysis of a New Model of the Distribution of Twin Primes
| dc.creator | Kelly, P. F. | |
| dc.creator | Pilling, Terry | |
| dc.date | 2001-06-26 | |
| dc.date.accessioned | 2026-07-07T04:42:19Z | |
| dc.date.available | 2026-07-07T04:42:19Z | |
| dc.description | Recently we have introduced a novel characterisation of the distribution of twin primes that consists of three essential elements. These are: that the twins are most naturally viewed as a subsequence of the primes themselves, that the likelihood of a particular prime in sequence being the first element of a twin is akin to a fixed-probability random event, and that this probability varies with $π_{1}$, the count of primes up to this number, in a simple way. Our initial studies made use of two unproven assumptions: that it was consistent to model this fundamentally discrete system with a continuous probability density, and that the fact that an upper-bound cut-off for prime separations exists could be consistently ignored in the continuous analysis. The success of the model served as a posteriori justification for these assumptions. Here we perform the analysis using a discrete formalism -- not passing to integrals -- and explicitly include a self-consistently defined cut-off. In addition, we reformulate the model so as to minimise the input data needed. | |
| dc.description | 8 pages, 3 figures, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0106223 | |
| dc.identifier | http://arxiv.org/abs/math/0106223 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61734 | |
| dc.subject | Number Theory | |
| dc.subject | 11N05 | |
| dc.title | Discrete Reanalysis of a New Model of the Distribution of Twin Primes | |
| dc.type | text |