Prime Number Checker
Check if a number is prime and find prime numbers in any range.
About this calculator
Three tools in one: test whether a number is prime, list every prime in a range, and factorise a number into primes. Switch between the tabs for the task you need.
Use it for maths homework, puzzles, coding exercises or checking numbers such as 91, which looks prime but equals 7 × 13.
How to use it
- Choose a tab: Check Number, Primes in Range or Factorize.
- Enter the number or the range.
- Press the button and read the answer.
Method
A prime is a whole number above 1 with exactly two divisors, 1 and itself. To test n, try dividing by every prime up to √n: if none divides it, n is prime. Factorising repeatedly divides by the smallest prime factor. A sieve lists all primes up to N by crossing off multiples of each prime.
Worked example
Examples
| 97 | Prime |
| 91 | Not prime: 7 × 13 |
| Primes from 1 to 100 | 25 primes, from 2 to 97 |
| 360 | 2³ × 3² × 5 |
Tips and common mistakes
- 2 is the only even prime.
- To test a number, you only need to check primes up to its square root.
- 1 is not prime, and 0 is not either.
- A quick check: if the digits add to a multiple of 3, the number is divisible by 3.
- Large primes secure internet encryption (RSA).
Frequently asked questions
What is a prime number?
A number greater than 1 whose only divisors are 1 and itself.
Is 1 a prime number?
No.
What is the smallest prime?
2.
How many primes are below 100?
25.
What is prime factorisation?
Writing a number as a product of primes, such as 360 = 2³ × 3² × 5.
Are there infinitely many primes?
Yes, proved by Euclid over 2,000 years ago.