The arithmetic of 1/f noise in a phase locked loop

Frequency countings close to a phase locked zone in an electronic receiver show a 1/f power spectral density. The noise scaling versus the frequency deviation and the open loop gain is found from Adler´s model of the phase locked loop. This fully agrees with experiments performed at 5 MHz on a receiver with a Schottky diode mixer and a low pass filter. The 1/f amplitude and frequency noise due to the whole set of (sub)harmonics is explained from a nonlinear mapping, with a coupling coefficient related to the structure of prime numbers. The number theoretical approach of 1/f noise and the link to the generalized Riemann hypothesis is explained.