Prime Number Checker
Test whether a number is prime and view its prime factorization.
Formula
How this is calculated
You enter a single whole number n. The tool first checks that the input is a finite integer within the safe range (up to 2^53 − 1); larger values are rejected because floating-point arithmetic can no longer represent them exactly. It then runs a primality test.
A number is prime when it is greater than 1 and divisible only by 1 and itself. Trial division checks candidate divisors, but only up to √n: if n had a factor larger than its square root, the paired co-factor would be smaller than the square root and would already have been found. The test discards multiples of 2 and 3 up front, then probes the remaining candidates in steps of 6 (the form 6k ± 1), which skips numbers that can never be prime and keeps the search fast.
If n is composite, the tool factorizes it by repeatedly dividing out the smallest prime factor, producing the prime factorization in exponent form (e.g. 360 = 2³ × 3² × 5). Edge cases: 0, 1, and negative numbers are neither prime nor composite, and 2 is the only even prime.
About this calculator
A prime number is a whole number greater than 1 whose only divisors are 1 and itself. Numbers with additional divisors are composite, and 0 and 1 are neither prime nor composite.
This checker uses trial division: it tests potential divisors only up to the square root of the number, which is sufficient because any larger factor must pair with a smaller one. For composite numbers it also returns the prime factorization, expressed in exponent form like 360 = 2³ × 3² × 5.
Frequently asked questions
No. A prime must have exactly two distinct divisors (1 and itself). The number 1 has only one divisor, so it is neither prime nor composite.
If a number n has a divisor larger than √n, the matching co-divisor must be smaller than √n, so checking up to the square root catches every factor.
2 is the smallest and the only even prime number. Every other even number is divisible by 2 and therefore composite.
Also known as
TG we-Calculate Editorial Team. (2026). Prime Number Checker [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/prime-number-checker
TG we-Calculate Editorial Team. "Prime Number Checker." TG we-Calculate. 2026. https://we-calculate.com/calculator/prime-number-checker.
TG we-Calculate Editorial Team, "Prime Number Checker," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/prime-number-checker
@misc{wecalculate_prime_number_checker, title = {Prime Number Checker}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/prime-number-checker}}, year = {2026}, note = {TG we-Calculate} }
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