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1/ƒ noise in the distribution of prime numbers

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  • Wolf, Marek

Abstract

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.

Suggested Citation

  • Wolf, Marek, 1997. "1/ƒ noise in the distribution of prime numbers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 241(3), pages 493-499.
    • Handle: RePEc:eee:phsmap:v:241:y:1997:i:3:p:493-499
    DOI: 10.1016/S0378-4371(97)00251-3
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