As shown by Milne in the early days of quantum mechanics, the non-relativistic binding energy of a heavy neutral atom with nuclear charge Ze is proportional to Z(7/3) in the large Z limit. Correction terms of order Z(2) and Z(5/3) to Milne's limiting large Z result were first calculated by Scott. Here, the question as to the power of Z at which correlation energy first appears in such a binding energy formula is addressed. It is shown that a recent approximation proposed by one of us (AN) supports an earlier extrapolation from large dimensionality D to D = 3 by Herschbach and co-workers, that correlation energy enters the large Z binding energy formula for the first time at o(Z(4/3)). (c) 2005 Elsevier B.V. All rights reserved.