For boiling eggs- the *oldest* fresh eggs I've boiled have been about 10 days old.
I asked a group of old ladies how to do this, and I got ALL of the tried & true. This is what I do.
Take the oldest eggs I have out of the fridge. I put them in a pot, run cold tap water on them til they are covered. I put a lid on the pot (I always forget to salt them- I have done that once and couldn't tell that it made a difference.)
Put the pot on, bring to a boil & set my timer for 18 minutes. When the timer goes off, I turn the burner off, set the timer for another 12 minutes. When the timer beeps again, I dump all contents into the sink. I put the eggs back in the pot, run cold tap water on the eggs- while the pot is filling, I get a frozen 20 oz bottle out of my freezer and sit it in the middle of the pot. Then I get an egg, roll it with some preasure to crack the rest of the shell as fine as I can, allover, then put it back in the water, and complete with rest of eggs. Then I take one and working under the water and starting at the large end with the air pocket, I start peelingfrom there, so I get thru the membrane without scraping chunks of the white out too. I try to keep it one long piece of shell & membrane and it peels much easier. If you 'lose your end' on the egg and have to start over, that's where you run into problems. Keeping the egg submerged under the cold water is the key. I've tried without and get a big mess. Keeping it underwater it is perfectly smooth with no problems at all. Just use a big enough pot that you can work in it.