Math & Everyday
Prime Number Checker
Check primality, factor a number, or list primes up to N.
🔒 Runs entirely in your browser — nothing here is ever uploaded
CalcoTools · Prime Number Checker · generated 8/23/2026, 1:06:27 PM
About the Prime Number Checker
Checks whether a number is prime, shows its prime factorization if it isn't, and can list every prime number up to a chosen limit.
How to use it
- To check one number: enter it in the Number field.
- To list primes: enter a limit in the Up to field.
- Read the result — primality, factors, or the prime list — in each section.
Formula
A number n is prime if it has no divisors other than 1 and itself, checked by testing divisibility up to √n. Factorization repeatedly divides out the smallest prime factor.
Worked example
97 is prime. 84 factors into 2 × 2 × 3 × 7.
Recommendations
- • Testing divisors only up to the square root of the number is enough to confirm primality — that's why even large numbers check quickly.
- • The prime list is capped at 10,000 to keep the browser responsive.
- • 1 is not considered prime by mathematical convention, even though it has no divisors other than itself.
Frequently asked questions
A prime number must have exactly two distinct positive divisors — 1 and itself. Since 1 only has one divisor, it's excluded by mathematical convention.