Question 7
One may express a number in base-8. For example, 37 could be written as $(45)_8$ in base-8 because $(45)_8=4\times8+5=37$. On the other hand, $(49)_8$ does not exist because $4\times8+9=41$ should be expressed as $(51)_8$. Let $\overline{AB}$ be a two-digit prime number in base-10, where $A,B<8$. If the value of $(\overline{AB})_8$ is also a prime number in base-10, how many possible values of $(\overline{AB})_8$ can we obtain?