What is $0$ in the concept of prime and composite integers? All numbers could be prime or composite except $1$. But what about $0$, is it prime or composite?
 A: Actually, prime and composite numbers are defined only on the set of natural numbers greater than $1$. Since, 0 is not a natural number it isn't even eligible for classification as prime or composite.
Hope that answers your question.
A: A number is prime when it can only be divided by $1$ and itself but we choose to exclude $1$ as a prime because the Fundamental Theorem of Arithmetic would fail to produce a unique decomposition if we included it. For example $6$ uniquely decomposes as $2 \cdot 3$ but if we allowed $1$ then it could be decomposed as $1 \cdot 2 \cdot 3$ or $1^2 \cdot 2 \cdot 3$ which would give two distinct decompositions breaking uniqueness. Since $0 = 0^2$ it would also break uniqueness of the decomposition so it is excluded as a prime. Since a composite number has more than one prime in its decomposition $0$ is also not composite.
A: It cannot even be classified in your traditional prime/composite classification because it does not have a unique decomposition that, say, 211311 has. This is why the traditional prime/composite numbers extend only to positive integers.
