If you buy eggs in the store from a refrigerator then you should never leave those eggs out of the refrigerator for longer than a few hours unless they're in a cool room.
Eggs that have never been refrigerated can be safely left out of the refrigerator for as long as 4 to 5 weeks.
Eggs that have gone bad will have a rotten smell to them which will make you most likely gag when smelling it.