Place eggs in a pot and cover with cold water, (enough to cover the eggs by about an inch). Bring to a boil and cook for 3 minutes. Remove from heat, cover and let sit 13 minutes.
Peel eggs under cold water and viola, perfect hard boiled eggs w/o the green circle.
UPDATED FACTS:
1) Add 1/2 tsp baking soda and eggs will peel easily w/o breaking the eggs.
2) Flip your eggs over the night before you boil them and the yolk will be centered when you boil it.
3) Older eggs peel easier.
