number one vs former

number one and former both are nouns.

Word	Noun	Adjective	Verb	Adverb
number one	Yes	No	No	No
former	Yes	Yes	No	No

As nouns, former is a hyponym of number one; that is, former is a word with a more specific, narrower meaning than number one:

number one (noun)	former (noun)
a reference to yourself or myself etc.; `take care of number one' means to put your own interests first	the first of two or the first mentioned of two
the first element in a countable series
the first or highest in an ordering or series

number one (adjective)	former (adjective)
	referring to the first of two things or persons mentioned (or the earlier one or ones of several)
	belonging to the distant past
	belonging to some prior time
	(used especially of persons) of the immediate past