Chosen Pokémon
There is one egg and one Pokémon shown on the Index page. While they are on the Index Page, they will gain twice the experience as usual if they are interacted with. They are replaced every five minutes at maximum with other random Pokémon or eggs whose owner has interacted with the previous chosen Pokémon. If an egg hatches in less than five minutes, it will be replaced with another one.
If you click the egg sprite or Pokemon sprite, its summary will open up.
Non-interactable Egg
When this occurs, then it would mean that the User who had their egg chosen to be put on Index page had moved their egg into Egg Storage.