Prime is a word not a fact of the universe, just like Planet is a word and not a fact of the universe. Those words, unlike most words, have definitions put in place by authorities. The authorities might change the definitions over time as a new definition's usefulness exceeds that of an old definition.
Practically:
It's more useful to think of primes and planets as not including their recent ex-members than it is to include them.
Prime is a word not a fact of the universe, just like Planet is a word and not a fact of the universe. Those words, unlike most words, have definitions put in place by authorities. The authorities might change the definitions over time as a new definition's usefulness exceeds that of an old definition.
Practically:
It's more useful to think of primes and planets as not including their recent ex-members than it is to include them.