twenty-one vs large integer

twenty-one and large integer both are nouns.

Word	Noun	Adjective	Verb	Adverb
twenty-one	Yes	Yes	No	No
large integer	Yes	No	No	No

As nouns, large integer is a hypernym of twenty-one; that is, large integer is a word with a broader meaning than twenty-one:

twenty-one (noun)	large integer (noun)
a gambling game using cards; the object is to hold cards having a higher count than those dealt to the banker up to but not exceeding 21	an integer equal to or greater than ten
the cardinal number that is the sum of twenty and one

twenty-one (adjective)	large integer (adjective)
being one more than twenty