Why is zero not a prime number?

Answer 1

Zero is neither prime nor composite.

Any number can multiply into zero, including zero itself (so it's not prime--it has infinite factors).

In fact, a zero product requires at least one zero factor (so it's not composite, either--no two numbers--or one used twice--other than zero can form a product of zero).

Indeed, zero's unique properties are what cause it to mess up divisions. They're why you can't divide by zero.

Zero is...a zero (or perhaps to use a more technical term, a zero-divisor), a unique and fundamentally important member of the integers. Its importance becomes more significant when one begins to study more fundamental mathematics like Modern Algebra.