You prefer soft-boiled to hard-boiled eggs, but you hate waiting next to your eggs to check if they're cooked. Therefore, you want to determine how often do you need to check the eggs so that they're not overcooked.

Question

What time does it take in minutes for a soft-boiled egg to become a hard-boiled one?

Note: A soft boiled egg is when only the egg white is solid, whereas a hard boiled egg is when both the egg white and yolk are solid.

Details and assumptions
The egg can be modeled as a sphere of radius 2 cm and density 1000 kg/m3.
Egg white solidifies at 50¡ãC while yolk solidifies at 65¡ãC
The heat capacity of an egg is c=4200Jkg⋅K
The power transferred from the heater to the egg is P=20 W