The number of ramified primes in number fields of small degree
  In this paper we investigate the distribution of the number of primes which ramify in number fields of degree d <= 5. In analogy with the classical Erdos-Kac theorem, we prove for S_d-extensions that the number of such primes is normally distributed with mean and variance log log X. 
Robert J. Lemke Oliver, Frank Thorne
math.NT