Power spectrum of the difference between the prime-number counting function and Riemann's function: 1/f2?

Gamba et al. [Phys. Lett. A 145 (1990) 106] numerically estimated the power spectrum of the difference between the prime-number counting function π(x) and its approximate given by Riemann's function R(x), but did not determine the functional dependence of the spectrum on the frequency. Our numerical estimates, based on samples of the difference function R(x)−π(x) at integer x up to x=109, strongly suggest that the difference function has a 1/f2 power spectrum.