Prime Number Checker
Check if a number is prime, find prime factors, and generate a list of prime numbers up to N.
Is this number prime?
Prime Factorization
Primes up to N
About this calculator
Is this number prime? Type it in and the checker tells you at once, and a second box factorises any number into its prime factors. A third box generates all primes up to N using the Sieve of Eratosthenes.
The sieve is the classic algorithm for finding all the primes up to a limit, and it runs instantly in your browser for the sizes you are likely to use.
How to use it
- Type a number and press Check.
- To factorise, type a number and press Factorize.
- To list primes, enter N and press Generate.
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 | 97 is a prime number |
| 91 | 91 = 7 × 13 |
| Primes up to 30 | 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 |
| 84 | 2² × 3 × 7 |
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.