📂Number Theory

Prime and Composite Numbers

Definition ¹

1. A prime number is a natural number $p \ge 2$ that has only $1$ and $p$ as its divisors.
2. A natural number $m \ge 2$ that is not a prime number is called a composite number.

Explanation

According to the definition, $2$ is naturally a prime number.

The scope of numbers dealt with in Number Theory is quite broad, extending to rational numbers, but the actual subject of interest could justifiably be called ‘prime number theory’ due to the concentrated focus. The reason being, composite numbers can be expressed as the product of other prime numbers, and if some properties are identified for prime numbers, generalizing those properties tends to be relatively straightforward, which explains why many theorems in number theory require prime numbers as a condition.