  This paper deals with a quantitative analysis of the content of official
political speeches. We study a set of about one thousand talks pronounced by
the US Presidents, ranging from Washington to Trump. In particular, we search
for the relevance of the rare words, i.e. those said only once in each speech
-- the so-called hapaxes. We implement a rank-size procedure of Zipf-Mandelbrot
type for discussing the hapaxes' frequencies regularity over the overall set of
speeches. Starting from the obtained rank-size law, we define and detect the
core of the hapaxes set by means of a procedure based on an Hirsch index
variant. We discuss the resulting list of words in the light of the overall US
Presidents' speeches. We further show that this core of hapaxes itself can be
well fitted through a Zipf-Mandelbrot law and that contains elements producing
deviations at the low ranks between scatter plots and fitted curve -- the
so-called king and vice-roy effect. Some socio-political insights are derived
from the obtained findings about the US Presidents messages.
