Erdős-Kac Theorem
المؤلف:
Kac, M
المصدر:
Statistical Independence in Probability, Analysis and Number Theory. New York: Wiley, 1959.
الجزء والصفحة:
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12-9-2020
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Erdős-Kac Theorem
A deeper result than the Hardy-Ramanujan theorem. Let 
be the number of integers in ![[n,x]](https://mathworld.wolfram.com/images/equations/Erdos-KacTheorem/Inline2.gif)
such that inequality
 |
(1)
|
holds, where 
is the number of distinct prime factors of 
. Then
where 
is a Landau symbol.
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 Erdős-Kac Theorem." Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser, pp. 158-159, 1994.
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