Prime Number Checker
Check primality, factorize, and find the next prime — runs entirely in your browser.
How prime checking and factorization work
A prime number is a positive integer greater than 1 that has no divisors other than 1 and itself. This tool uses trial division to test primality: it checks whether the input is divisible by any integer from 2 up to its square root. If none divides it evenly, the number is prime. The same method drives factorization — the tool finds each smallest divisor in turn, dividing it out until the remainder is itself prime. The next prime is found by incrementing from the input and testing each candidate.
All three operations (prime check, factorization, next prime) run instantly in your browser for typical inputs. No data is sent to any server. The tool handles integers up to the safe integer limit of JavaScript (2^53 − 1), though very large numbers may take a noticeable moment to factor because trial division is O(sqrt(n)).
FAQ
Is 1 a prime number? No. By definition, primes must be greater than 1. The number 1 has only one divisor (itself), which fails the two-divisor requirement.
What does the prime factorization show? It lists every prime factor with repetition, sorted ascending. For example, 12 factors as 2 × 2 × 3.
What is the next prime used for? It finds the smallest prime strictly greater than the input — useful when iterating through primes or finding the next candidate in cryptographic key generation exercises.
Can I check a prime factorization of a prime itself? Yes. A prime number factorizes to just itself, e.g. 7 → [7].