Prime Number Checker
Check whether any number up to 12 digits is prime. Composite numbers show the smallest factor and a factor pair, plus the nearest primes either side.
About the Prime Number Checker
A prime number has exactly two divisors: 1 and itself. This prime number checker tests any integer up to 12 digits instantly and gives a clear verdict. When the number is composite, it does not just say no — it shows the smallest prime factor and a full factor pair (91 = 7 × 13), so you can see exactly why the number fails.
The checker uses optimized trial division: after testing 2 and 3, it only tries candidates of the form 6k ± 1 up to the square root of the number, because every prime above 3 has that form. It also finds the nearest prime below and above your number, which is handy when you need a prime of a certain size for a hash table, cryptography exercise or math problem.
Students verifying homework, teachers building worksheets, and programmers picking bucket sizes all use quick primality checks. Everything runs client-side with no signup.
How to Use the Prime Number Checker
- 1Enter a whole number of 2 or more (up to 12 digits).
- 2Read the Prime / Not prime verdict instantly.
- 3For composite numbers, check the smallest factor and factor pair.
- 4Use the nearest-primes result to find a prime close to your number.
Frequently Asked Questions
Is 91 a prime number?
No. 91 looks prime but equals 7 × 13, so it is composite. It is one of the most common trick questions — the checker shows the smallest prime factor 7 and the pair 91 = 7 × 13 immediately.
How do I check if a number is prime by hand?
Test divisibility by every prime up to its square root. For 97: √97 ≈ 9.85, so test 2, 3, 5 and 7 — none divides 97, so it is prime. You never need to test beyond the square root, because factors come in pairs that straddle it.
Is 1 a prime number? Is 2?
1 is not prime — a prime needs exactly two distinct divisors, and 1 has only one. 2 is prime, and it is the only even prime: every other even number is divisible by 2 and therefore composite.
What is the largest number this checker handles?
Up to 12 digits (999,999,999,999). Trial division up to the square root means at most about a million tests, which finishes in milliseconds in your browser. Numbers beyond JavaScript's safe-integer range would need specialised big-number primality tests.
Why do the nearest primes matter?
Many applications need 'a prime near n' rather than n itself — hash-table sizes, modular-arithmetic exercises and RSA toy examples. If you enter 100, the checker reports 97 below and 101 above, saving you from testing candidates one by one.