If 0 and 1 are not composite or prime numbers then what are they?

First, zero is not applied to the terms prime and composite because the definitions only apply to natural numbers (positive whole numbers, which does not include zero). One is not prime or composite because one is the unit that is used within the definition of prime of composite numbers, and many definitions of prime and composite even exclude one from the definition. If you want to categorize one within a discussion of prime and composite, it is common to simply call one the unit.