About Is It Prime? Prime Number Checker
This prime number checker tells you whether a whole number is prime, and if it is not, it shows the factors that prove it. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The page opens on 1000001, which looks like it might be prime but is not: 101 × 9901. The smallest factor, 101, is the proof. In contrast, 7919 is prime: its only divisors are 1 and itself.
The test is exact for every number below 3.3 × 10²⁴, which covers all the 24-digit numbers this calculator accepts, so there is no chance of a wrong answer. The factorization is not needed for the verdict, so a large prime is confirmed quickly.
How to use Is It Prime? Prime Number Checker
- Choose Factorization, Factor tree, Is it prime or Divisors.
- Type a whole number of 2 or more. Up to 24 digits are accepted.
- Read the prime factorization in exponent form at the top.
- Look at the factor tree, the list of divisors and their count and sum underneath.
- Open the steps to see the repeated division that produced each prime.
Features
- Prime factorization in exponent form and as a plain product.
- Factor tree drawn as a scalable diagram, with the primes filled in.
- Is-it-prime check with the smallest factor when the number is composite.
- Every divisor listed, plus the count and the sum of divisors.
- Numbers of up to 24 digits using exact big-integer arithmetic.
- Trial division for small numbers and Pollard rho for large ones.
- Repeated-division steps in KaTeX.
What makes a number prime
A prime has exactly two divisors, 1 and itself. By hand you only need to test primes up to the square root.
n is prime if no prime p with p² ≤ n divides nWorked examples
1000001 gives not prime: 101 × 9901
Divisible by 101.
7919 gives prime
7919 is the 1000th prime.
Privacy: how it works
- Everything is calculated by code running in your browser tab. The number you enter is not sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- To test a number by hand, try dividing by primes up to its square root. If none divides it, it is prime.
- 1 is not prime and not composite. 2 is the only even prime.
- A number with an odd count of divisors is a perfect square.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Numbers are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Numbers are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
How do I check if a number is prime?
Try dividing it by every prime up to its square root. If none divides it exactly, it is prime. The calculator does this, and uses a faster exact test for large numbers.
Is 1 prime?
No. 1 has only one divisor. The smallest prime is 2, and it is the only even one.
Is there a quick test for small primes?
Check divisibility by 2, 3, 5 and 7 first. Any number below 121 with no factor among them is prime.
More Prime Factorization Calculator pages
- Prime Factorization CalculatorEnter a whole number to get its prime factors in exponent form, a factor tree and every divisor.
- Factor Tree CalculatorEnter a number to see its factor tree drawn, with the primes filled in.
- Factors of a Number CalculatorEnter a number to list all its factors, how many there are, and what they add up to.