I think a distinction must be made about what one means by "prime". allchopin refers to maturity of conception, but that is not to say that either Horowitz or Rubinstein were not known or accomplished for their feats before they were old men - far from it. They were well known all throughout their careers.
In terms of physical peak, I doubt few would contend the assertion that one's best years are from late teens to mid-life. This is simply a biological fact. Granted, many pianists still go on to play exceptionally well in their old age, but I suspect that compromises are made. In terms of physical conditioning, pianists are no different from sports people, I suspect.
Combine the physical with the spiritual, and I would say that one's overall prime is in late mid-life. This leads me to make another distinction, and that is there's a difference between "prime" and prominence. Perhaps it's a function of marketing, but there's probably an excess public focus on an artist's early years and final years. It might be a fair question to ask how many musicians themselves would assert that those were their finest moments.
tph