// Number
Prime Number Checker online
Check if any number is prime and find its prime factorization
by
CHUNKY
MUNSTER
MUNSTER
Enter any positive integer and this tool reports whether it is prime, and if not, returns its full prime factorization. Internally it uses 6k±1 trial division: after eliminating 2 and 3, only divisors of those two forms up to √n are tested, which is roughly three times faster than naive trial division while remaining deterministic.
Trial division is exact for everything up to JavaScript's safe-integer ceiling of 2^53 − 1 (about 9 × 10^15). For larger numbers you would need BigInt arithmetic and a probabilistic primality test such as Miller-Rabin — out of scope for this single-page tool. The verdict updates on every keystroke and the factor list is shown in non-decreasing order with multiplicities collapsed.
No. By the modern definition a prime is an integer greater than 1 with exactly two distinct positive divisors: 1 and itself. The number 1 has only one divisor, so it sits outside both "prime" and "composite".
It uses 6k±1 trial division: after ruling out 2 and 3, it only tests divisors of the form 6k−1 and 6k+1 up to the square root. That skips two-thirds of the candidates of plain trial division while remaining deterministic.
Up to 2^53 − 1 (about 9 × 10^15), the JavaScript safe-integer limit. Above that, integer arithmetic loses precision in the browser and you would need a BigInt-based or Miller-Rabin probabilistic test instead.
Trial division is exact for numbers in range, so any composite is fully decomposed. Common surprises: numbers ending in 1, 3, 7, or 9 can still be products of larger primes — for example 91 = 7 × 13.
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