this variable $\Omega(n)$, the number of prime factors of $n$ counting multiplicity, has for large $n$ a normal distribution with mean $1+\log(\log n)$ and standard deviation $[\log(\log n)]^{1/2}$; see, for example, <A HREF="https://books.google.nl/books/about/Prime_Numbers_and_Computer_Methods_for_F.html?id=5cIN7kemQgYC&redir_esc=y">Prime Numbers and Computer Methods for Factorization</A>, page 167.