Peaks and gaps: Spectral analysis of the intervals between prime numbers

George G. Szpiro

Physica A: Statistical Mechanics and its Applications, 2007, vol. 384, issue 2, 291-296

Abstract: Prime numbers seem to be distributed somewhat randomly throughout the sequence of natural numbers. It is known, however, that gaps between consecutive primes exhibit a preponderance towards 6 and its multiples, and recently it was shown that the gaps between the gaps also exhibit a peculiar pattern. In this paper higher-order gaps are analyzed using Fourier decomposition. The resulting power spectra reveal additional patterns in the prime number sequence.

Keywords: Prime numbers; Gaps; Fourier analysis; Power spectrum; Experimental mathematics (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:384:y:2007:i:2:p:291-296

DOI: 10.1016/j.physa.2007.05.038

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