There has been a lot of discussion about peeling hard cooked eggs. (They are not boiled. LOL)
Some say they should be old eggs.
Some say make a pin prick through the shell at one end.
Add vinegar to the water.
Start with cold water.
Add here what you have heard.
Last week I wanted to make Deviled Eggs for a pot luck, so left a dozen eggs sit on the counter for more than a week. (These were very fresh eggs to start with, from my neighbor's chickens.) When I boiled, no, cooked them I added a couple of fresh eggs from the new dozen with pin pricks in one end. I had the pot full of eggs, so I could stand them on end with the pricked end up.
The pricked ones did not peel easier or even easy.
The old ones peeled better, but when eggs sit around like that you need to turn them over each day. That's what mama hen does when she lays her eggs one-a-day until she is ready to sit on them. That keeps the yolk in the center. My yolks were all way off center. Not nice for Deviled Eggs.
I ended up making potato salad with most of those eggs, which was very good. The last six I put into the fridge and am eating them for breakfast each day.