1) "Next time you have a hard-boiled egg, smell it. You will probably catch a faint whiff of hydrogen sulphide. When an egg is boiled, proteins which contain sulphur in the white of the egg break down and a gas called hydrogen sulphide is formed. If the egg is fresh then there will only be a very faint whiff of hydrogen sulphide. Old, rotten eggs have a much stronger dose of it. This is because when eggs start to go bad, bacteria in the egg break down the sulphur-containing proteins much more than when you simply boil the egg. And that’s why hydrogen sulphide is often called "rotten-egg-gas". Even though our sense of smell is poor compared with many animals, we can easily detect just one part per billion of hydrogen sulphide. Want to do a freshness test on your eggs? Get an egg, and place it in a bowl of water. If the egg sinks, it’s fresh. If the egg floats, it might be rotten. This happens because every egg has an air space that gets larger as the bacteria in the egg produce more hydrogen sulphide gas. What if your eggs aren’t rotten? Well you can make them rotten. Take some eggs and get a sharp needle. Make a small hole in the top of each egg. Next, let the eggs sit in a warm place for about a week. Now you've got some rotten eggs that will only smell when you break them." Source and further information: http://www.abc.net.au/spark/smelly/whats/e.htm 2) Hard boiled eggs will brobably start to smell just after you boil them, if you don't use fresh eggs or cook them too long: "I find that if you overboil eggs, you can also smell a bad sulfurous pong. Which is a really bad idea!" Source: http://wokkingmum.blogspot.com/2007/07/getting-hard-boiled-egg-perfect.html Further information: http://answers.yahoo.com/question/index?qid=1006021409626 http://www.chowhound.com/topics/460804 3) Here some general information about egg safety: "How long do eggs last? Keep eggs refrigerated to promote quality and safety. Raw eggs can be kept in the refrigerator for 4-5 weeks after purchase. Refrigerated hard-boiled eggs should be eaten within 7 days. Why do hard-cooked eggs spoil faster than raw? A hen puts a protective coating (called the bloom) on the egg as she lays it. The bloom keeps contaminants from entering pores in the shell (eggshells have up to 17,000 pores). Processing plants wash the eggs and coat them with mineral oil to replace the bloom. This protective coating is removed when you wash or boil the egg." "What’s the difference between spoilage and food borne illness (FBI)? Spoilage is when foods “go bad.” You can see, smell or taste spoilage. Spoilage is usually caused by molds or bacteria. FBIs are caused by different molds and bacteria (as well as virsues, parasites and chemicals). You usually cannot tell by sight, smell, or taste if the food will cause a FBI, but you can prevent illness if you handle, store and prepare the foods safely." Source and further information: http://www.bfhd.wa.gov/forms/brochures/BFHD-E-0022a.pdf Further information: http://en.wikibooks.org/wiki/Cookbook:Egg

The short answer is when it spoils. In hot weather, that is real soon (one day), in cold weather, it takes longer.