I imagine that to get the hardest white and softest yolk one would put an egg from the fridge into boiling water, but they are likely to crack. However, this formula is an approximation of a more general egg-boiling formula and is valid only for a standard weight range of between 60 and 70 grams. If the egg is placed straight into a pan of water at T water , it will be ready when the centre temperature of the yolk has risen to T yolk . If one makes some reasonable simplifying assumptions about the cooking process and the egg, then the cooling time t can be deduced from the solution to the heat-diffusion equation for a spherical object. The result is shells that are rather thinner than they were 20 years ago.
Fresh eggs require longer than older eggs.
As eggs age, proteins stiffen and the air bubble at the blunt end of the egg expands, lowering the egg's density and pushing the yolk closer to the pointed end. Fresh eggs tumble to a quick halt because the yolk wobbles in the liquid egg white in its position away from the spinning axis. With a little experience, both methods allow an estimate of the freshness of an egg. But I doubt that either has been described in an equation yielding cooking time. This means the temperature is higher than the coagulation point of the white, and lower than the coagulation point of the yolk.