Studying Mathematics Thread

[robvalue]

Prime numbers are natural numbers p so that:

p>1; If a natural number n>0 divides exactly into p, then n=1 or n=p

Another way of saying this is that each p has exactly two factors among the natural numbers.

So why isn't 1 allowed to be a prime number? It's because we then wouldn't have unique factorization into primes for natural numbers. For example:

12 = 2 * 2 * 3 = 2^2 * 3

is a unique factorization. But if we allow 1 to be prime, we have

12 = 1 * 2^2 * 3 = 1^2 * 2^2 * 3 = 1^3 * 2^2 * 3 =...