After doing some research on eggs I have found no reason to believe that boiling leaches out any nutrional value from the shell of the egg. All the good stuff is inside the shell. Here's what I've found to answer your question and more:
- Calories: 1 large egg: 80 1 large egg white: 20 1 large egg yolk: 60
- Don't overcook eggs or the yolk may turn a greenish color as a result of the leaching out of iron sulfide
- While eggs contain cholesterol (in the yolk), they also contain lecithin which may provide enought good cholesterol to conteract the bad cholesterol
- 12.5% of the weight of the egg is protein and it is found in both the yolk and the albumen. Although protein is more concentrated around the yolk, there is in fact more protein in the albumen
- Eggs contain most of the recognized vitamins with the exception of vitamin C. The egg is a good source of all the B vitamins, plus the fat-soluble vitamin A. It also provides useful amounts of vitamin D, as well as some vitamin E
- Eggs contain most of the minerals that the human body requires for health
- Eggs contain only traces of carbohydrate and no dietary fiber
- 10.8% of the egg content is fat. The fat of an egg is found almost entirely in the yolk; there is less than 0.05% in the albumen. Approximately 11% of an egg’s fatty acids are polyunsaturated, 44% monounsaturated and only 29% saturated.
- If cooking a hard-cooked egg you should cover and submerge eggs and can start with simmering or cold water
- Stir while boiling to keep yolks centered (especially if for deviled eggs)
- It is possible to modify some aspects of the nutritional composition of eggs by feeding the hens special diets. Modified "designer" eggs containing increased amounts of omega-3 fatty acids and vitamin E are now on the market. Whether these modified eggs have special health benefits has not been established.
Hope this answered some of your questions.