Prime Number Checker
Enter a whole number — find out instantly if it's prime, and see its prime factorization.
Type a whole number above — you'll instantly see if it's prime and its prime factorization.
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How do I know if a number is prime?
A prime number is a whole number greater than 1 whose only divisors are 1 and itself — 7 is prime, but 9 = 3 × 3 is not. This prime number checker first tries dividing by small primes, then runs a Miller–Rabin primality test, so it decides in a split second even for large numbers. Just type a number and it tells you "Prime" or "Not prime" instantly.
What is prime factorization and how do I read exponent form?
Prime factorization breaks a number into the prime numbers that multiply to make it. This prime factorization calculator writes repeated factors as exponents: 360 = 2³ × 3² × 5 means 2 × 2 × 2 × 3 × 3 × 5. The small raised number (the exponent) is how many times that prime appears, so 2³ is "three twos multiplied together."
How large a number can it check?
The tool uses JavaScript BigInt, so it isn't limited to ordinary integers. Below roughly 3.3 × 10²⁴ the Miller–Rabin test is deterministic — the answer is exact. Above that it switches to a strong probabilistic test and labels the result "probable prime." Factorization of huge numbers with two large prime factors can be slow; if it hits the time limit it tells you rather than freezing.
Are 0 and 1 prime? Is 2 prime?
No — 0 and 1 are not prime, because a prime must be greater than 1 and have exactly two divisors. 1 has only one divisor (itself), and 0 is divisible by everything. 2 is the smallest prime and the only even prime; every other even number is divisible by 2. This checker handles all of these edge cases explicitly instead of erroring out.
Is my number sent to a server?
No. Every calculation — the primality test and the prime factorization — runs entirely in your browser with local JavaScript. Nothing you type is uploaded, logged or stored on a server, and there are no ads or sign-up. Your last input is saved only in your own browser (localStorage) so it's still there when you come back.