Let 
be the number of distinct prime factors
of 
.
If 
tends steadily to infinity with 
, then
 |
for almost all numbers 
. "almost all"
means here the frequency of those integers 
in the interval 
for which
 |
approaches 0 as 
.
Hardy-Ramanujan Theorem
See also
Distinct Prime Factors, Erdős-Kac TheoremExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Hardy-Ramanujan Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Hardy-RamanujanTheorem.html