When an egg is bad the bad egg will smell like sulphur.
That same goes for natural gas when it leaks if you've ever smelled a gas leak then the bad eggs will put off an odor similar to a natural gas leak.
You can also tell if eggs are bad or good by doing a floating egg test.
Fill a bowl with water and place the egg into the bowl and if the egg floats to the top the egg is bad and should be thrown out.
If the egg sinks to the bottom the egg is still good and fresh.
If the egg sinks to the bottom but the egg stands up on one end the egg is still good but not as fresh.