Let $(u,v)\neq(0,0)$. Show the existence of a constant $C$ (depending on $(u,v)$) such that for all $d>0$,
$$|L_{\mathrm{prim}}(u,v,d)| \leq C\, 2^{|\mathcal{P}(d)|}.$$
Deduce that, for all $\varepsilon>0$, we have
$$|L_{\mathrm{prim}}(u,v,d)| = \underset{d\rightarrow+\infty}{o}\left(d^\varepsilon\right).$$