In medieval times who was most likely to search for the Philosophers' Stone?

It was generally European and middle eastern alchemists who searched for the stone. However, there were also a number of other people who sought after the stone, including magicians, noblemen, kings and quite obviously, philosophers.

One of the most notable noblemen to search for the Philosophers' Stone was Rudolf the second, Emperor of the Holy Roman Empire. He hired quite literally hundreds of alchemists and various occult practitioners from dozens of nations in order to attempt to secure the prize, including the famed John Dee and Edward Kelley.