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 Sd-extensions that the number of such primes is normally distributed withmean and variance log log X.
Lemke Oliver, Robert J., and Frank Thorne. "The Number of Ramified Primes in Number Fields of Small Degree." Proceedings of the American Mathematical Society 145, no. 8 (April 26, 2017): 3201-3210. doi:10.1090/proc/13467.