# Prime Number

## Prime Number

Whole number that is greater than 1 and that has exactly two distinct divisors, which are 1 and itself.

Whole number greater than 1 that has exactly two distinct whole divisors.

### 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.