1/f Noise in the Distribution of Prime Numbers

Marek Wolf

Physica A , 241:493-499 (1997).


Abstract

The Fourier Transform of the "signal" given by the number of primes contained in the successive intervals of equal length l=216 =65536 up to N=238 ~ 2.749 x 1011 was performed. It turns out that the power spectrum displays the 1/fbeta behaviour with the exponent beta ~ 1.64. This slope beta does not depend on the length of the sampled intervals, what suggests some kind of selfsimilarity in the distribution of primes.