# Sequences sharing some primitive prime divisors

Let $q=p^\alpha$ and $q'=p'^\alpha$. Moreover, define $r_i$ and $u_i$ as primitive prime divisor of $q^i-1$ and $q'^i-1$, respectively. Let $\{r_1\}=\{u_1\}$, $\{r_2\}=\{u_2\}$, $\{r_3\}=\{u_3\}$, $\{r_6\}=\{u_6\}$ and $\{r_4,p\}=\{u_4,p'\}$. Now I want to know if it is possible that $p\neq p'$?