  In the present work we use maximum entropy methods to derive several theorems
in probabilistic number theory, including a version of the Hardy-Ramanujan
Theorem. We also provide a theoretical argument explaining the experimental
observations of Yang-Hui He about the learnability of primes, and posit that
the Erd\H{o}s-Kac law would very unlikely be discovered by current machine
learning techniques. Numerical experiments that we perform corroborate our
theoretical findings.
