  In the framework of Cramer's probabilistic model of primes, we explore the
exact and asymptotic distributions of maximal prime gaps. We show that the
Gumbel extreme value distribution exp(-exp(-x)) is the limit law for maximal
gaps between Cramer's random primes. The result can be derived from a general
theorem about intervals between discrete random events occurring with slowly
varying probability monotonically decreasing to zero. A straightforward
generalization extends the Gumbel limit law to maximal gaps between prime
constellations in Cramer's model.
