  We study the spacing of the primes using methods from information theory. In
information theory, the equivalence of continuous and discrete representations
of information is established by Shannon sampling theory. Here, we use Shannon
sampling methods to construct continuous functions whose varying bandwidth
follows the distribution of the prime numbers. The Fourier transforms of these
signals spike at frequently occurring spacings between the primes. We find
prominent spikes, in particular, at the primorials. Previously, the primorials
have been conjectured to be the most frequent gaps between subsequent primes,
the so-called "jumping champions". Here, we find a foreshadowing of the
primorial's role as jumping champions in the sense that Fourier spikes for the
primorials arise much earlier on the number axis than where the primorials in
question are expected to reign as jumping champions.
