What is the definition of a prime number?

Prime numbers are only divisible by 1 and themselves.

A prime number is a number that can only be divided by itself and 1, so it only appears in the 1 times table and it’s own. For example, 5 is a prime number because it cannot be divided by another number and the outcome be an integer (whole number). 5/2=2.5. Whereas 12 is not a whole number because it can be divided by 2, 3, 4 and 6.

In Emyr's excellent response, the last sentence should have read "Whereas 12 is not a prime number"!

Hi Sebastian,

At GCSE level I think the best definition is (working in positive whole numbers)

A prime number is a whole number which has two different whole number factors Those are 1 and itself.

A lot of people are confused as to why 1 is not prime.



The answer has some university level maths involved but for now let’s say if I wanted to write 6 as a product of primes I can only do it as 2x3. And 3x2 counts as the same.

Sorry continued response

If I could say 1 is a prime then

6=3x2x1

6=3x2x1x1

6=3x2x1x1x1

and so on, would be ways to make prime factorisations of 6

I can’t write 6 uniquely as the product of primes

This actually causes annoying problems in higher maths, so saying a prime is a number only divisible by itself and 1 causes quite a lot of grief because most students assume that means 1 is prime. 1 is definitely not currently thought of as prime.

A number that can only be divided by one and itself, like 3.

A prime number is a number that is only divisible by 1 and itself, thus has two factors (1 and itself). This means 1 is not a prime number, since it only has one prime factor. The first and only even prime number is in fact 2: you can only divide 2 by itself (2) or by 1!

A prime number is a number that is only divisible by itself or 1 (For example 2, 5, 7, 11)

A prime number is only divisible by itself and 1 (only in these 2 circumstances there is no remainder).

For example 5 is a prime number as only divisible by 5 and 1.

Important to note prime numbers only have TWO factors so 1 is NOT a prime number.

2 is the only EVEN prime number.

A prime number is one that has only two factors.