So that would mean that for some colors Adobe RGB blue primary will be less than (normalized) 1, but the ProPhoto RGB blue primary is a little more than 1. If a color processing is such that it clips at 1, then it will clip it here.
Joofa
Let me elaborate a little here. The above mentioned applies to standard white points of D50 for ProPhoto RGB and D65 for Adobe RGB, and I think this corresponds to the first image in tho_mas' message above where profiles are shown. However, if the direction of primaries are kept the same, but the white points are changed, which means that the magnitude of unit stimulus changes, then the following situation emerges:
Fraction of unit stimulus blue ProPhoto RGB primary needed to match unit stimulus blue Adobe RGB primary:
(1) Adobe RGB white point=D65, PropPhoto RGB white point=D50, Fraction needed=1.2
(2) Adobe RGB white point=D65, PropPhoto RGB white point=D65, Fraction needed=0.91
(3) Adobe RGB white point=D50, PropPhoto RGB white point=D50, Fraction needed=0.88
(4) Adobe RGB white point=D50, PropPhoto RGB white point=D65, Fraction needed=0.67
So, except (1) other modes offer a scenario where no clipping needs to happen. However, (1) is the standard mode of specification of white points for both Adobe and ProPhoto RGB, and this does seem to clip. I think either (2) or (3) correspond to the second image shown by tho_mas in the above message.
Sincerely,
Joofa