According to the American Egg Board, although "hard boiling" is how most people describe cooking any egg in its shell, the proper term is "hard cooking." To truly boil an egg will make it tough and dry. And the jury is still out on whether adding salt to the boiling water helps the cooking process or makes hard-boiled eggs easier to peel.
Hard-boiled eggs in the shell that have been properly cooled before storing will keep for up to one week in the refrigerator. Discard the eggs if the shells discolor, feel dry or slimy, or develop powdery spots of mold. Fresh eggs will keep for about three weeks in the fridge after you buy them.
Hard-boiled eggs brought outdoors should be kept at refrigerator temperature at all times with ice, an insulated bag or another cooling device.
Before hard boiling, keep eggs in their carton on a shelf inside the refrigerator to maintain even cooling. The carton keeps them from soaking up other foods' smells and taste.
Hard-boiled eggs may emit a sulfurous odor that comes from hydrogen sulfide created during cooking. It's smelly, but harmless.
Put the eggs in a saucepan filled with water an inch higher than the eggs. Cover the pan and bring the water to a boil. Immediately remove the pan from the heat and let them stand in the hot water, still covered, for 18 minutes if they're extra-large, 15 minutes if large or 12 minutes if medium. To stop the internal cooking, immerse the eggs in ice water until they cool.
Eggs cooked at about a week old are easiest to peel, but the yolks may be off-center because the whites slightly dry out. However, the drying creates space between the egg and shell for easier peeling. Crack the shell with gentle taps, then roll the egg to loosen the shell. Peel, starting at the large end. If the shell is still tight, hold the egg under running water while peeling.
To keep the yolks centered, store eggs with the small end up for 24 hours before hard boiling. Eggs with blood spots on the yolk aren't fertilized; those are accidental blood vessel ruptures. Such eggs are safe to eat. At altitudes above 10,000 feet, eggs can't be hard boiled. Only about one in every 20,000 eggs is contaminated with Salmonella bacteria, and proper handling reduces the risk of becoming ill from eggs.