Is 1 a prime number?


Dr Dillion Mayhew, School of Mathematics and Statistics, answers:

A common definition of a prime number is that it can only be divided by 1 and the number itself. For example:

  • 13 is prime, because the only numbers that divide into 13 are 1 and 13 itself.
  • 6 is not prime, because it can be divided by 2 and 3 as well as 1 and 6.

Using this definition, 1 can be divided by 1 and the number itself, which is also 1, so 1 is a prime number.

However, modern mathematicians define a number as prime if it is divided by exactly two numbers. For example:

  • 13 is prime, because it can be divided by exactly two numbers, 1 and 13.
  • 6 is not prime, because it can be divided by four numbers, 1, 2, 3 and 6.

1 can only be divided by one number, 1 itself, so with this definition 1 is not a prime number.

It is important to remember that mathematical definitions develop and evolve. Throughout history, many mathematicians considered 1 to be a prime number although that is not now a commonly held view. So when debating if 1 is a prime number, I'm prepared to call it a draw.