Question 186
Let $p_1, p_2, p_3$ and $p_4$ be four different prime numbers satisfying the equations
$$
2p_1 + 3p_2 + 5p_3 + 7p_4 = 162,
$$
$$
11p_1 + 7p_2 + 5p_3 + 4p_4 = 162.
$$
Find all possible values of the product $p_1p_2p_3p_4$.
$$
2p_1 + 3p_2 + 5p_3 + 7p_4 = 162,
$$
$$
11p_1 + 7p_2 + 5p_3 + 4p_4 = 162.
$$
Find all possible values of the product $p_1p_2p_3p_4$.