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What Is a Prime Number? (Mathematics Glossary)

What Is a Prime Number?

A prime number is a number that can be divided by only itself and 1.

For example,
  • 2 is a prime number. It can only be divided exactly by 1 and 2 itself.

  • 3 is a prime number. It can only be divided exactly by 1 and 3 itself.

  • 4 is not a prime number. It can be divided exactly by 1, 2 and 4.

Dictionary Definition

The Oxford English Dictionary defines a prime number as "a number that cannot be divided by any whole number (without a remainder) other than itself and one."

The Prime Numbers

The prime numbers are:

In a number square, the prime numbers are shaded below:

These are just the prime numbers under 100. There are infinitely many prime numbers, they go on forever.
Interactive Test

Here's a second test on prime numbers.
Here's a third test on prime numbers.
Here's a dynamic test on prime numbers.

Prime Numbers Are Natural Numbers Greater Than 1

Prime numbers are natural numbers (the counting numbers: 1, 2, 3...) greater than 1.

1 is not a prime number, even though it can only be divided by 1 and itself. Some times in history is has been considered a prime number, but now it is not.


Numbers that divide exactly into another number are called factors.

For example, the factors of 4 are 1, 2 and 4 because they all divide exactly into 4.

Prime numbers only have two factors, 1 and the prime number itself.

The only factors of 2 are 1 and 2. The only factors of 3 are 1 and 3. The only factors of 5 are 1 and 5.

Prime Factors and the Fundamental Theorem of Arithmetic

Any whole number that is not prime (called a composite number) can be found by multiplying prime numbers together.

Any non-prime number is a product of prime factors.

For example, 12 = 2 × 2 × 3. 12 can be broken down into prime factors:

The fundamental theorem of arithmetic states that all natural numbers are either prime numbers or a product of prime numbers.