  Within the setting of rare event modelling, the method of level sets allows
us to define an equivalence relation over rare events with distinct rates of
entropy production. This method allows us to clarify the relation between the
empirical density of primes and their source distribution which then allows us
to address Cram\'er's conjecture, an open problem in probabilistic number
theory. As a natural consequence, this analysis places strong epistemic limits
on the application of machine learning to analyse the distribution of primes.
