1. Prime and Composite Numbers
Prime numbers are numbers that have exactly two factors: 1 and the number itself. For example, 2, 3, 5, 7 are prime numbers as they can only be divided by 1 and the number itself. Composite numbers, on the other hand, have more than two factors. For example, 4, 6, 8, 9 are composite numbers as they have factors other than 1 and the number itself.

2. Why is 1 neither Prime nor Composite?
- Factors of 1: The only factor of 1 is 1 itself. Since prime numbers have exactly 2 factors and composite numbers have more than 2 factors, 1 does not fit into either category.
- Definition of Prime and Composite Numbers: By definition, prime numbers should have exactly 2 factors, and composite numbers should have more than 2 factors. Since 1 does not meet these criteria, it is neither prime nor composite.

3. Special Status of 1
1 is a special number in mathematics known as a unit. A unit is a number that is associated with a ring, which is a mathematical structure. In the case of the set of integers, 1 acts as the multiplicative identity, meaning that any integer multiplied by 1 is equal to the integer itself.
Therefore, while 1 is not considered a prime or composite number, it does have a special status in mathematics as a unit or multiplicative identity in certain mathematical structures.