## What is a prime number?

A prime number is a natural number greater than 1 that is not a product of two

smaller natural numbers.

A prime number is a whole number greater than 1 whose only factors are 1 and

itself. A factor is a whole number that can be divided evenly into another

number.

For example, 5 is a prime number because the only ways of writing it as a

product, 1 × 5 or 5 × 1, involve 5 itself.

The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

Numbers that have more than two factors are called composite numbers. The

number 1 is neither prime nor composite.

A natural number greater than 1 that is not prime is called a composite

number. For example, 4 is a composite because it is a product (2 x 2) in which

both numbers are smaller than 4.

The property of being prime is called primality.

There are infinitely many primes, as demonstrated by Euclid around 300 BC. No

known simple formula separates prime numbers from composite numbers. However,

the distribution of primes within the natural numbers in the large can be

statistically modeled. The first result in that direction is the prime number

theorem, proven at the end of the 19th century, which says that the

probability of a randomly chosen large number being prime is inversely

proportional to its number of digits, that is, to its logarithm.