Written by Alex Chen · Reviewed by Sarah Mitchell · August 1, 2026
Check if a number is prime, find its prime factors, or list all primes up to a limit.
Enter a number and click Check.
Set a limit and click Find Primes.
A prime is a whole number greater than one that has exactly two divisors: itself and one. Four is not prime because two divides it evenly, while seven is prime because nothing between two and its square root divides it. This page decides the question for any integer you enter and adds useful context around the answer.
Try 97 first. Its square root is just under ten, so the tool tests the primes two, three, five, and seven, finds no divisor, and declares 97 prime, with a divisor count of exactly two. Now try 91. Seven divides 91 evenly, giving 13, so the verdict flips to composite and the factorization pane reports 7 × 13. Two similar-looking numbers, two different answers, and the tool shows the reasoning for both.
If a number has a divisor larger than its square root, it must also have a smaller partner divisor, so checking everything up to the square root is sufficient. Testing 97 only requires trying divisors through nine rather than every number up to 96. The checker skips even numbers beyond two as well, which roughly halves the work for large inputs.
Zero has infinitely many divisors, so it cannot have exactly two. One has exactly one divisor, itself, which also fails the definition. The page explains this for any input below two, returning a clear verdict with the reasoning shown, so the edge cases do not come as a surprise.
When people needed every prime below a limit, the classic approach was a sieve: write out the integers, cross off multiples of two, then three, then five, and the survivors are prime. The checker answers one number at a time with trial division instead, which is simpler for a single query. Both methods rest on the same fact: no composite hides beyond the square root of the largest candidate.
Composite results expand into their prime factors, written out with multiplication signs, so 84 becomes 2 × 2 × 3 × 7 rather than a bare verdict. That breakdown doubles as a sanity check: multiply the factors back together and you should recover the original input exactly. Prime results skip the pane entirely because there is nothing to factor.
Alongside the verdict, the page lists the nearest prime below and above your number. For 91 those are 89 and 97, which brackets the composite nicely. The divisor count tells you how many whole numbers divide the input, with primes always scoring exactly two, squares scoring three, and highly composite numbers like 60 scoring twelve.
Primes thin out as numbers grow, but they never disappear entirely. Twin primes, pairs that differ by two like 11 and 13, appear throughout the list, and mathematicians still have not proved whether infinitely many exist. The nearest-prime readout on this page lets you explore those gaps yourself: pick any number and see how far the closest primes sit on either side. The largest known twin pairs run hundreds of thousands of digits long and were found by distributed computing projects.
Deciding whether a number is prime is comparatively fast, while pulling a large composite into its factors is hard, which is exactly the gap cryptography exploits. The checker returns both when available: the verdict arrives immediately, and the factorization pane fills in the factors for composites of practical size. For numbers with very large prime factors, the factorization may take longer than the verdict.
Some numbers masquerade as primes: they pass the simplest modular checks used by fast screening routines, yet turn out to be composite. The best-known group are the Carmichael numbers, which defeat the basic Fermat test for almost every base. This page sticks with exact trial division, so its verdict is always certain rather than very likely, at the cost of more work for huge inputs.
The trial-division method is exact but grows with the square root of the input, so a number with fifteen digits takes noticeably longer than a four-digit one. Answers are still returned in a fraction of a second for everyday values. If you need to test a candidate that is hundreds of digits long, the checker will do its best, but probabilistic tests are the standard tool for that scale.
The factorization and all related arithmetic run locally in the browser. Your input is not transmitted, logged, or stored, so you can check homework, contest entries, or the seed value of a private experiment without concern. Reloading the page clears the field and resets the output.