float test the eggs...
fill a glass with cold water and put the egg in it...make sure the water completely covers the egg....it should lay on its side...if it is standing straight up the egg is bad. you can tell when the egg is going bad as it starts to stand up. If it is slightly off the side and starting to stand you are good if it is halfway or completely upright, toss it.
eggs can stay on the counter for a week or two in cool weather...hot weather only a couple of days then refrigerate them to be safe. Just do not wash them...the bloom on the egg is what helps preserve it, once that is gone the egg starts going.