Although it seems like a fundamentally easy task, boiling an egg can result in yellow yolks acquiring a green/gray outer coating. These are not the most appetizing nor do they make the best looking deviled eggs.
The question is can it be avoided? The answer is yes. It is actually fairly easy to consistently have little or no green/gray color to the yolks.
When cooking hard boiled eggs, start with a non-reactive pot or pan (enamel or stainless-steel). I like to have a large enough pot or pan that I can place the eggs in just a single layer to cook (two layers at most). If the eggs are over crowded, they bump into each other and break more in my experience.
Place the eggs in the pot and cover with cold water. The water should be at least one or two inches higher than the eggs. Place on stove and bring to a boil. Once the water is boiling, turn off the burner and allow eggs to sit for 15 minutes. Test one egg to see if has reached the desired state. If not, allow the rest of the eggs to sit for a few more minutes. If they sit for too long, the yolks will start turning green/gray. Twenty minutes is usually the maximum.
Drain hot water from eggs and rinse with cold water to stop the cooking process.
It turns out the key to a great hard boiled egg is not boiling it long at all.