  In this paper we show that the natural density $\mathcal{D}[(U_m)]$ of Ulam
numbers $(U_m)$ satisfies $\mathcal{D}[(U_m)]=0$. That is, we show that for
$(U_m)\subset [1,k]$ then \begin{align}\lim \limits_{k\longrightarrow
\infty}\frac{\left |(U_m)\cap [1,k]\right |}{k}=0.\nonumber \end{align}
