About Prime Number Check
Prime Number Check tests whether an integer is prime — divisible only by one and itself — using trial division up to the square root of the number. That bound is sufficient because any factor larger than the square root must be paired with one smaller than it, so no composite number can slip through.
The input is floored to an integer, and the test reports negatives, zero and one as not prime, which matches the definition: a prime must have exactly two distinct positive divisors, and one has only one. Getting that boundary right matters, since one is the classic false positive in hand-written checks.
The work grows with the square root of the input. Numbers up to a few billion are answered in a moment; a fifteen-digit input means millions of remainder operations before a verdict, so the check is meant for ordinary integers rather than cryptographic-scale primes, which need probabilistic tests over numbers far beyond the exact range of floating-point arithmetic.
The answer is a verdict, and nothing is reported around it. There is no list of divisors, no smallest prime factor when the number turns out to be composite, and no nearest primes on either side — all of which are the immediate next questions once a number has been tested. A range cannot be checked in one pass either, so finding the primes in an interval means entering values one at a time. Because the input is floored before the test, a decimal is silently truncated into a different number rather than being rejected, and the precision boundary is not enforced: a value beyond the range the arithmetic can hold exactly will still receive a verdict that carries no indication it may be unreliable. There is also no record of what was tested before.
How to use Prime Number Check
- 1 Enter a whole number.
- 2 Click to test it.
- 3 Read whether the number is prime or not prime.
Frequently asked questions
Is one a prime number?
No. A prime has exactly two distinct positive divisors, and one has only itself. The tool reports one, zero and all negative numbers as not prime, following that definition strictly.
How large a number can it handle?
It handles any integer a double-precision number can represent exactly, though the time needed rises with the square root, so very large inputs take noticeably longer. It is not intended for primes hundreds of digits long, which require probabilistic methods.
Can a prime test ever be wrong?
Trial division up to the square root is deterministic and exact, so for inputs within the exact integer range the answer is a proof rather than a probability. That is a different guarantee from the fast probabilistic tests used in cryptography.
Why does it not tell me the factors?
Because a yes-or-no verdict computes much less than a full factorisation: the test stops at the first divisor found, while factorisation continues until the number is fully decomposed. The Prime Factorization tool does that longer job.
Free, online, and private
Free to use
Prime Number Check is completely free. There is no account to create, no login, and no hidden charge or usage limit.
Runs online in your browser
It is a free online tool that runs entirely in your browser. Nothing to download or install — open the page and start using it right away.
Your data stays private
All processing happens locally on your device. Your input is never uploaded, stored, or tracked, so it never leaves your browser.
How Prime Number Check behaves in detail
These are the specifics of this implementation — the exact ranges, defaults and fixed settings you are working with.
| Parameter | Value |
|---|---|
| Test used | trial division by every integer from 2 up to √n, abandoning the test at the first even division |
| Lower bound | anything under 2 — including 0, 1 and every negative value — is reported as not prime rather than rejected |
| Decimals | the input is floored first, so 97.9 is tested as 97 |
| Output | one sentence naming the number and giving the verdict |
| No input ceiling | the field declares no max, so the size of the test is set entirely by what is typed into it |
| Default | 97, reported as prime |
Compiled from the implementation of this tool and checked against it by itoolnet.
What Prime Number Check does not do
Knowing the edges of a tool saves more time than another list of its features. These are the cases where it will not do what you might expect.
- The cost grows with the square root of the input while the field caps nothing. A fifteen-digit entry makes the loop run tens of millions of times and blocks the tab while it does, and it is the large primes — the case you most want an answer for — that take longest.
- One number per call. There is no way to paste a span and get the primes inside it, and when the verdict is negative no factorisation follows, so you learn that 96 is not prime but nothing about what it is built from.
- Flooring rather than rejecting means a fractional entry is answered about a different number. Type 17.9 and the reply discusses 17 and calls it prime, which is a true statement about a value you did not ask about, delivered as though it were the answer.
Tested and documented by itoolnet, the team that builds and maintains this site.