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

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.