Analog of the Skewes number for twin primes

The results of the computer investigation of the sign changes of the difference between the number of twin primes ${\pi }_2(x)$ and the Hardy–Littlewood conjecture $c_2{\text{Li}}_2(x)$ are reported. It turns out that ${\pi }_2(x)-c_2{\text{Li}}_2(x)$ 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 ${\pi }_2(x)-c_2{\text{Li}}_2(x)$ for $x\in (1,T)$ is given by $\sqrt{T}\mathrm{/}\log (T)$.