Let $p_1,p_2\in\mathbb{Z}$ be distinct prime numbers. Show that $|\cdot|_{p_1}\not\sim|\cdot|_{p_2}$

Question

Let $p_1,p_2\in\mathbb{Z}$ be distinct prime numbers. Show that $|\cdot|_{p_1}\not\sim|\cdot|_{p_2}$ by finding a sequence in $\mathbb{Q}$ that is Cauchy with respect to $|\cdot|_{p_1}$ but not Cauchy with respect to $|\cdot|_{p_2}$.

I am having trouble finding such a Cauchy sequence. Can anyone help me with this problem. Thanks