p₁, p₂, p₃, p₄ and p₅ are five distinct prime numbers, arranged in strictly ascending order of magnitude, that satisfy this equation:

 p1*p2*p3*p4*p5
------------------ = px*py*pz
p12+p22+p32+p42+p52

where each of p_x, p_y, and p_z is a distinct
prime number ε {p₁, p₂, p₃, p₄, p₅}

Determine the minimum value of p_x*p_y*p_z.
What is the next minimum value of p_x*p_y*p_z?

Posted by K Sengupta on 2022-04-16 10:43:06