importance vs primacy

importance and primacy both are nouns.

Word	Noun	Adjective	Verb	Adverb
importance	Yes	No	No	No
primacy	Yes	No	No	No

As nouns, primacy is a hyponym of importance; that is, primacy is a word with a more specific, narrower meaning than importance:

Other hyponyms of importance include accent, emphasis.

importance (noun)	primacy (noun)
the quality of being important and worthy of note	the state of being first in importance
a prominent status