Any more than 11-12 minutes and you get the green discoloration between the yolk and the egg-white.

I make boiled eggs for my wife, 8 at a time, every couple of days. It took a while, but my time has finally settled at 12 minutes at a slow simmer.

By the way, I slightly crack the 'blunt' end before putting the eggs into the boiling water. That allows expansion of the egg contents and the air-space without the egg exploding.

At 12 minutes, I take the eggs off the heat and soak them in the saucepan several times with cold water to cool them down quickly. I then let them cool down for about half-an-hour in cold water before peeling them.