\(P = 12\left( {{5^2} + 1} \right)\left( {{5^4} + 1} \right)\left( {{5^8} + 1} \right)\)\(\left( {{5^{16}} + 1} \right)\)
\( =\displaystyle{1 \over 2}\left( {{5^2} - 1} \right)\left( {{5^2} + 1} \right)\left( {{5^4} + 1} \right)\left( {{5^8} + 1} \right)\)\(\left( {{5^{16}} + 1} \right)\)
\( =\displaystyle {1 \over 2}\left( {{5^4} - 1} \right)\left( {{5^4} + 1} \right)\left( {{5^8} + 1} \right)\)\(\left( {{5^{16}} + 1} \right) \)
\( = \displaystyle{1 \over 2}\left( {{5^8} - 1} \right)\left( {{5^8} + 1} \right)\left( {{5^{16}} + 1} \right) \)
\(= \displaystyle{1 \over 2}\left( {{5^{16}} - 1} \right)\left( {{5^{16}} + 1} \right)\)\( = \displaystyle{1 \over 2}\left( {{5^{32}} - 1} \right) \)
