In number theory, the Erdős–Kac theorem, named after Paul Erdős and Mark Kac, and also known as the fundamental theorem of probabilistic number theory, states that if ω is the number of distinct prime factors of n, then, loosely speaking, the probability distribution of ω − log ⁡ log ⁡ n log ⁡ log ⁡ n {\displaystyle {\frac {\omega -\log \log n}{\sqrt {\log \log n}}}} is the standard normal distribution. Wikipedia