1/ƒ noise in the distribution of prime numbers

The Fourier transform of the “signal” given by the number of primes contained in the successive intervals of equal length l = 216 = 65 536 up to N = 238 ≈ 2.749 × 1011 was performed. It turns out that the power spectrum displays the 1/ƒβ behaviour with the exponent β ≈ 1.64. This slope β does not depend on the length of the sampled intervals, which suggests some kind of self-similarity in the distribution of primes