In the first chapter of Fullmetal Alchemist, Ed and Al come across Father Cornello at the city of Reole.
The Elric brothers Edward and Alphonse discover, soon after arriving in Reole, that Cornello's 'miracles' are nothing more than alchemy augmented by a Philosopher's Stone that the priest has in his possession.
One of the biggest rules of Alchemy is Equivalent Exchange, and Ed sees Cornello obviously breaking those rules, something that should have been impossible in Alchemy without the philosopher's stone.
Ed and Al have been searching for the Philosophers Stone as a way of returning their bodies back to how it was. Even if it wasn't a complete Philosopher's stone, the fact Cornello was able to bypass equivalent exchange should have been incredibly significant in itself and pursuing this lead would likely have lead them a step closer to their goal.
And it was later revealed that a Homunculus was behind the incident.
However, Ed, upon realising the stone was not a true philosopher's stone, left the town. Why is this? Did he, for some reason, think of it as unimportant, and if so, why?