Sum of bigomega

Arithmetic function $\mathrm{\Omega }(n)$ is the total number of prime factors of $n$, counting prime factors with multiplicity. For example, $\mathrm{\Omega }(3)=1$, $\mathrm{\Omega }(6)=2$, $\mathrm{\Omega }(72)=5$. Let $S(n)={\sum }_{x=1}^n\mathrm{\Omega }(x)$. You are given $S(10)=15$, $S(1000)=2877$.

Find $S({10}^{13})$.

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Thanks to baihacker for the idea.