Erdős arcsine law
In number theory, the Erdős arcsine law, named after Paul Erdős, states that the prime divisors of a number have a distribution related to the arcsine distribution.
Specifically, say that the jth prime factor p of a given number n is "small" when.
Then, for any fixed parameter u, in the limit as x goes to infinity, the proportion of the integers n less than x that have fewer than small prime factors converges to
