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arXiv · 0707.0980

Analog of the Skewes number for twin primes

Marek Wolf
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Abstract

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 $\sqrt T/\log(T)$.

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Marek Wolf. 2008-01-15. Analog of the Skewes number for twin primes. https://arxiv.org/abs/0707.0980

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