It's OK if they smell "gassy"
If It doesn't take that long to make a hard-boiled egg. All you need is ten minutes, a stove, and a pot of water. But knowing how long hard-boiled eggs last? Well, that's a little more complicated. According to the eggy experts at the American Egg Board, you can keep a hard-boiled egg in its shell for up to a week in the refrigerator. A peeled hard-boiled egg, however, should be eaten the same day it's peeled for best quality. It seems counterintuitive, that hard-boiled eggs don't last as long as fresh eggs, since they're cooked, not raw—but there's science to explain that.
The US Department of Agriculture explains that, "When shell eggs are hard cooked, the protective coating is washed away, leaving bare the pores in the shell for bacteria to enter and contaminate it." That means they won't last nearly as long as a raw egg in the fridge. (For comparison, raw eggs can sit in your fridge for up to a month after purchase.) If you really want to make sure the hard-boiled, or hard-cooked, eggs that you're saving are safe, the USDA recommends letting the eggs quickly cool on your kitchen counter in a shallow container and then popping it in the fridge within two hours of cooking.
There's not much prep you have to do when you're ready to eat that hard-boiled egg that's been sitting in your fridge for less than a week—though the US Food and Drug Administration firmly reminds consumers that you should be quick about it. "Never leave cooked eggs or egg dishes out of the refrigerator for more than 2 hours or for more than 1 hour when temperatures are above 90° F." The reason? Bacteria can form and make you sick. That means if you're bringing a hard-cooked egg to work as part of your lunch, be sure to pop it in the office fridge as soon as you arrive in the morning.
There are other considerations to be made when you're storing hard-boiled eggs in the refrigerator, however. For one, hard-boiled eggs might stink up your fridge, even if you store them properly. The folks from the Canadian Egg Industry point out this "'gassy' odor in your refrigerator" from your hard-cooked eggs is totally normal. "The odor is caused by hydrogen sulphide, which forms when eggs are cooked. It's harmless and usually dissipates in a few hours."
You should also be sure to differentiate your hard-cooked eggs from the raw ones so you don't go to peel a hard-boiled egg and end up with a runny, raw mess. To do that, simply spin the egg. As the Los Angeles Times test kitchen director Noelle Carter writes, "A hard-boiled egg will spin smoothly; a raw egg won't. Because the yolk and white aren't set in a raw egg, motion can cause the center of gravity to shift easily, causing the egg to wobble rather than spin."
And no matter what, don't freeze your hard-cooked eggs. It's not recommended by the American Egg Board, the Canadian Egg Industry, or the USDA because, as the CEI explains, "Hard-cooked whole eggs and whites become tough and watery when frozen." Besides, by the time you're trying to make the most of frozen, gross egg whites, it's probably easier to just cook a whole new batch of hard-boiled eggs.