  We introduce a stochastic algorithm that acts as a prime number generator.
The dynamics of such algorithm gives rise to a continuous phase transition
which separates a phase where the algorithm is able to reduce a whole set of
integers into primes and a phase where the system reaches a frozen state with
low prime density. We present both numerical simulations and an analytical
approach in terms of an annealed approximation, by means of which the data are
collapsed. A critical slowing down phenomenon is also outlined.
