Erdös-Kac Theorem

A deeper result than the Hardy-Ramanujan Theorem. Let be the number of Integers in such that inequality

holds, where is the number of different Prime factors of . Then

The theorem is discussed in Kac (1959).

References

Kac, M. Statistical Independence in Probability, Analysis and Number Theory. New York: Wiley, 1959.

Riesel, H. The Erdös-Kac Theorem.'' Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser, pp. 158-159, 1994.