Analog of the Skewes number for twin primes

dc.creatorWolf, Marek
dc.date2007-07-06
dc.date2008-01-15
dc.date.accessioned2026-07-07T08:54:06Z
dc.date.available2026-07-07T08:54:06Z
dc.descriptionThe 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.descriptionChanges: New Figure 1 and a few sentences of justification in favor of the conjecture (5) are made
dc.identifierhttps://arxiv.org/abs/0707.0980
dc.identifierhttp://arxiv.org/abs/0707.0980
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145810
dc.subjectNumber Theory
dc.titleAnalog of the Skewes number for twin primes
dc.typetext

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