How to Decompose $\mathbb{N}$ like this? 
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Partitioning an infinite set
Partition of N into infinite number of infinite disjoint sets? 

Is it possible to find a family of sets $X_{i}$, $i\in\mathbb{N}$, such that:


*

*$\forall i$, $X_i$ is infinite, 

*$X_i\cap X_j=\emptyset$ for $i\neq j$, 

*$\mathbb{N}=\bigcup_{i=1}^{\infty}X_i$
Maybe it is an easy question, but I'm curious about the answer and I couldnt figure out any solution.
Thanks

Let $p_n$ be the $n$-th prime number. That is $p_1=2; p_2=3; p_3=5; p_4=7$ and so on.
For $n>0$ let $X_n=\{(p_n)^k\mid k\in\mathbb N\setminus\{0\}\}$. 
For $X_0$ take all the rest of the numbers available, namely $k\in X_0$ if and only if $k$ can be divided by two distinct prime numbers, or if $k=1$.
