Let p and p +2 be prime numbers and let Δ= |p!, ( p +1)!, ( p +2)!; ( p +1)!, ( p +2)!, ( p +3)!; ( p +2)!, ( p +3)!, ( p +4)!| Then the sum of the…

Let p and $\displaystyle \mathrm{p}+2$ be prime numbers and let $$\Delta=\left|\begin{array}{ccc} \mathrm{p}! & (\mathrm{p}+1)! & (\mathrm{p}+2)! \\ (\mathrm{p}+1)! & (\mathrm{p}+2)! & (\mathrm{p}+3)! \\ (\mathrm{p}+2)! & (\mathrm{p}+3)! & (\mathrm{p}+4)! \end{array}\right| $$ Then the sum of the maximum values of $\displaystyle \alpha$ and $\displaystyle \beta$, such that $\displaystyle \mathrm{p}^\alpha$ and $\displaystyle (\mathrm{p}+2)^\beta$ divide $\displaystyle \Delta$, is \_\_\_\_.