### Properties

- There is an infinite number of prime numbers.
- By definition, the numbers 0 and 1 are neither prime nor composite.
- A whole number greater than 1 that is not prime is a composite number and vice versa.
- All composite numbers can be expressed in a unique way in the form of a product of prime numbers.

### Example

- The number 13 is a prime number because it only divisible by 1 and 13.
- Here is a list of the 15 prime numbers less than 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
- The number 15 is not a prime number, because it has more than two divisors: div (15) = {1, 3, 5, 15}.
- The number 9 is not a prime number, because it has more than two divisors: div (9) = {1, 3, 9}.

### Historical Note

The first incontestable trace of the appearance of prime numbers dates back to Antiquity (around 300 B.C.), and is found in the *Elements* by Euclid (books VII to IX). Euclid gave the definition of prime numbers and proof of their infinity.