Proving two graphs are isomorphic I need to prove that the following two countable undirected graphs $G_1$ and $G_2$ are isomorphic:
Set of vertices of $G_1$ is $\mathbb{N}$ and there is an edge between $i$ and $j$ if and only if the $j$ th bit of the binary representation of $i$ is $1$ or the $i$ th bit of the binary representation of $j$ is $1$. In the other graph $G_2$, the set of vertices is $\mathbb{N}_+ := \lbrace n\in\mathbb{N} : n>0\rbrace$ and there is an edge between $n$ and $m$, for $n>m$, if and only if $n$ is divisible by $p_m$, the $m$ th prime.
Any hints or ideas would be appreciated. 

HINT: These are both the Rado graph, which is the unique countable graph with the following extension property: if $U$ and $V$ are disjoint finite sets of vertices of the graph, there is a vertex $x$ connected to each vertex in $U$ and to no vertex in $V$. The link actually demonstrates this for $G_1$, and the same article proves uniqueness. Thus, you need only prove that $G_2$ has the extension property.
