Expert: Josh - 2/25/2004

Question
Why can't negative numbers be prime or composite can i have some examples please?

Answer
Hi Silvana,

This is a philosophical question for the mathematicians, I think it is a matter of convention really.

The dilemma is that if the negative of a prime number is considered prime, for instance, if -7 was prime, then, we will no longer have a "unique" prime factor decomposition for numbers such as 98.

There are procedures for factorizing a number into a product of prime numbers, and 98=2*7*7,
if -7 was allowed to be a prime number,
then, 98=2(-7)(-7).

We much prefer a consistent way of doing things. There is no advantage in letting there be negative prime numbers. It doesn't make factorization any easier, for a start. The problem is still essentially the same, the flipping of signs is just a distraction.