Search for: [Abstract = "The results of computer investigation of the sign changes of the difference between the number of twin primes π2 \(x\) and the Hardy\-Littlewood conjecture C2Li2 \(x\) are reported. It turns out that d2 \(x\) = π2 \(x\) − C2Li2 \(x\) changes the sign at unexpectedly low values of x and for x < 2 48 = 2.81... × 10 14 there are 477118 sign changes of this difference. It is conjectured that the number of sign changes of d2 \(x\) for x ∈\(1, T \) is given by T \/ log\(T\). The running logarithmic densities of the sets for which d2 \(x\) > 0 and d2 \(x\) < 0 are plotted for x up to 2 48."]
