# Prime number

A prime number is a natural number that is greater than 1 that has exactly two factors, 1 and itself. In other words, a prime number is a number that cannot be formed by multiplying two smaller natural numbers since it has to include itself.

Prime numbers are an important concept in number theory, a branch of pure mathematics having to do with the study of integers. This is because the fundamental theorem of arithmetic states that all integers greater than 1 are either prime, or can be represented as the product of prime numbers.

There is no known formula that easily distinguishes a prime number from a composite number. Finding the prime factorization of a prime number has no known, simple algorithm, so finding the prime factorization of a large number is very tedious. No matter how you determine the prime factorization of a number though, the factors are unique; each number has only one set of prime factors.

Refer here for a list of up to the first 10,000 prime numbers.

Examples

The following are the first five prime numbers:

2 = 1 × 2

3 = 1 × 3

5 = 1 × 5

7 = 1 × 7

11 = 1 × 11

The number 1 has only one factor (1 × 1 = 1), so it is not a prime number. It is also not a composite number.

The natural numbers greater than 1 that aren't prime numbers are called composite numbers. Composite numbers can be formed by multiplying two smaller natural numbers.

Examples

The following are the first 5 composite numbers:

4 = 2 × 2

6 = 2 × 3

8 = 2 × 4

9 = 3 × 3

10 = 2 × 5