Fresh eggs are great- they're healthy, offer a cheap source of protein and taste great - but they absolutely suck for making pretty hard boiled eggs. Allow me to explain- as an egg "ages" oxygen permeates the shell, the more oxygen within the shell, the easier it is to peel the egg.
How to Properly Cook an Egg
First, How to Properly Hard Cook an Egg (notice I said, Hard Cook, rather than hard Boil- hard cooking is when you cook the egg throughout so that both the yolk and the white are firm. Hard Boiling an egg often overcooks the egg resulting in a green tinted yolk that is hard and dry). While it's safe to eat a "Hard Boiled" egg, they aren't quite as tasty and if you're using them in a recipe such as egg salad- you might find that you're using more mayo to make up for the overly dry yolks.
- Place eggs in saucepan large enough to hold them in a single layer.
- Add cold water to cover eggs by 1 inch, add 1/2 tsp salt to the water.
- Heat over high heat just to boiling.
- Remove from burner and Cover pan.
- Let eggs stand in the hot water, covered.
- 12 minutes for Medium eggs
- 15 minutes for Large eggs
- 18 minutes for Extra Large eggs
- Cool completely under cold running water or in a bowl of ice water.
- Peel and eat, or store unpeeled in the refrigerator for up to 1 week.
Eggs- The Good, The Bad, The Ugly!
How to tell if an egg is bad: Place eggs in a bowl of water, if the egg floats, the egg is bad. Eggs that have gone bad float due to the gases that have built up within the egg.
If the egg "stands" it will create perfect hard boiled eggs. This means that the egg has aged enough to allow just the right amount of oxygen into the shell, allowing for easy peeling.
If the egg immediately sinks to the bottom- it's too fresh and will not peel well, resulting in eggs that look like these:
Store bought eggs are often several weeks old by the time you purchase them. Most of the time these eggs are ready to be hard cooked.
See also: How to Tell the Age of Eggs