ToolBirch

Prime Number Checker

Primality test with full prime factorisation.Math & Statistics

Prime Number Checker

Check primality by trial division up to √n, with the full prime factorisation for composites.

About this tool

Trial division up to the square root decides primality, and composites come back with their complete prime factorisation — 360 becomes 2 × 2 × 2 × 3 × 3 × 5.

How to use the Prime Number Checker tool

  1. Enter an integer. Up to 2^53 in magnitude.
  2. Read the verdict. Prime or not, with the reason.
  3. Use the factorisation. Composites are fully factored for you.

Supported formats

Input

  • Plain text or file input

Output

  • Converted or analysed output

Inputs are validated before anything is processed. Invalid values and unsupported files are rejected with a clear error instead of failing silently.

Frequently asked questions

How does the test work?

Trial division by every candidate up to the square root — exact, if not the fastest known method.

Why is 1 not prime?

By definition: primes have exactly two divisors.

What about huge numbers?

2^53 is the integer-precision ceiling; beyond that, specialist tools apply.

Privacy

Everything you enter stays in this browser tab. There is no upload endpoint for tool inputs, no account, and no server-side copy of your text or files. Results are produced locally and disappear when you close the page.

No account is required and no file is ever uploaded. See the privacy policy for details about analytics and the limited data this site stores.

Known limitations

  • No probabilistic tests; results are deterministic but size-capped.

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