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 Feb 2021

en.wikipedia.org en.wikipedia.org
 Feb 2014

empslocal.ex.ac.uk empslocal.ex.ac.uk

If the Riemann hypothesis is true, Im tn = 0 for all n, and the function f(u), constructed from the primes, has a discrete spectrum; that is, the support of its Fourier transform is discrete. If the Riemann hypothesis is false, this is not the case. The frequencies tn are reminiscent of the decomposition of a musical sound into its constituent harmonics. Therefore there is a sense in which we can give a oneline nontechnical statement of the Riemann hypothesis: "The primes have music in them."
The frequencies are reminiscent of the decomposition of a musical sound into its constituent harmonics; the primes have music in them.
