Why are 1 and 0 not a prime or composite number?

Answer 1

Because the concept of prime or composite is defined for whole numbers which are greater than 1. 1 is not divisible by any number except for 1 and itself (also 1). From that perspective, it should be classed as a prime. However, if 1 were considered a prime than the fundamental theorem of arithmetic - the unique prime factorisation theorem - would fail, and with it much of the theory of multiplication and division would collapse.