Easy as boiling eggs?

I've always thought it was easy to hard-boil eggs and I've been dubious about long complicated explanations. I always put them in cold water, bring them to a boil, and leave them for 12 minutes.

Yesterday I had a shock when I started peeling the eggs I had boiled according to this method earlier in the day -- they were still soft, though done enough to eat. I forgot that I'm up here on a mountain at 8000 feet where water boils at a much lower temperature -- in the 190s not at around 212 like at home. Seems as though I should let them spend longer with the water at a rolling boil, and also leave them longer after turning off the burner. I'll give it a try.

I wonder what else is different, and I wonder why I never noticed this during prior trips. I guess I didn't happen to boil any eggs.

UPDATE: on my second try, I left the eggs for 5 mins on a slow boil and then 20 mins on simmer and they were perfect for making egg salad. No greenish rim around the yolk, either.