I went through the trouble of:
1) Boiling three eggs, then opening the first immediately, cooling the second in tap water before opening and letting the third and last to cool naturally before cracking the shell. It is believed that cooling the egg immediately after boiling prevents the sticking of shell to egg white.
2) Slow cooking of eggs for 30 minutes. The reason might be the same as sticking of fish to frying pan. Fish proteins stick to pan when heated slowly.
Later, I found the fresh egg shells naturally sticks to white part when cooked. Allowing the commodity aged for two to three days loosen the forces between layers.
Then I found a post of Homesteading/Survivalism stating that adding 1/2 teaspoon baking soda to boiling water will make peeling off shells easier.
Time to try.
I bought four eggs. I never had any clue about its freshness. I boiled the first two eggs in 500ml water with one teaspoon baking soda for 15 minutes. Cooled in tap water and did a peeling test.
I boiled the second two eggs using the same parameters but with no addition of baking soda.
In the first batch, boiling water became white as a result of baking soda addition. The cooking vessel sides also became tinted with white. The eggs appeared cleaner than before. No notable changes observed on second batch except for the long irregular lines of cracks.
I thought the eggs with cracks were easier to peel. But I had to pry the shell slowly and carefully in order to prevent damaged to egg white surface. Eggs boiled with baking soda had no cracks. I tapped it gently against the wall to start the peeling process. It was significantly easier to peel. The shell appeared to be looser and weaker.