All natural numbers are either prime numbers or composite numbers, right?

Wrong. Let's start with natural numbers. Natural numbers are ordered, starting from 0: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 16, 12. ...

Natural numbers include 0, and people tend to ignore the number 0, because we don't start counting from 0, but all start from 1, so we don't care about this 0. However, in mathematics, it is useful, just like this topic: all natural numbers are either prime numbers or composite numbers.

First of all, it affirms the mistake of this statement. The analysis is as follows:

0 is neither a prime number nor a composite number, and 1 is neither a prime number nor a composite number.