As adverbs the difference between primarily and predominately
is that primarily is (focus) of a primary or central nature, first and foremost while predominately is in a predominate manner; predominantly.
primarily
English
Adverb
(-)
(focus) Of a primary or central nature, first and foremost
predominately
English
Adverb
(
en adverb)
in a predominate manner; predominantly
Usage notes
This is the adverb form of the adjective predominate, considered dated or non-standard, with predominant preferred. Likewise, predominantly is now preferred to predominately although the latter is 100 years or so older.