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.

© 1996-9

1999-05-25