Erdös-Kac Theorem
A deeper result than the Hardy-Ramanujan Theorem. Let 
be the number of Integers in 
such thatinequality
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.
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