Analog of the Skewes number for twin primes
| dc.creator | Wolf, Marek | |
| dc.date | 2007-07-06 | |
| dc.date | 2008-01-15 | |
| dc.date.accessioned | 2026-07-07T08:54:06Z | |
| dc.date.available | 2026-07-07T08:54:06Z | |
| dc.description | The results of the computer investigation of the sign changes of the difference between the number of twin primes $π_2(x)$ and the Hardy--Littlewood conjecture $c_2\Li_2(x)$ are reported. It turns out that $π_2(x) - c_2\Li_2(x)$ changes the sign at unexpectedly low values of $x$ and for $x<2^{42}$ there are over 90000 sign changes of this difference. It is conjectured that the number of sign changes of $π_2(x) - c_2\Li_2(x)$ for $x\in (1, T)$ is given by $\sqrt T/\log(T)$. | |
| dc.description | Changes: New Figure 1 and a few sentences of justification in favor of the conjecture (5) are made | |
| dc.identifier | https://arxiv.org/abs/0707.0980 | |
| dc.identifier | http://arxiv.org/abs/0707.0980 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145810 | |
| dc.subject | Number Theory | |
| dc.title | Analog of the Skewes number for twin primes | |
| dc.type | text |