Prime Number Checker

Deterministic primality testing with Miller-Rabin.

A prime number is an integer greater than 1 divisible only by 1 and itself. This tool uses deterministic Miller-Rabin with 12 fixed witnesses, guaranteeing correct results for any positive integer up to 10²⁴. For composite numbers, the full prime factorization is computed via optimized trial division.

Enter the number to check its primality.

1. Enter the positive integer you want to check.
2. The tool shows whether it is prime, composite, one, or zero.
3. For composite numbers, see the full prime factorization and whether it is a perfect square or cube.

Sources and references for this tool

These references help contextualize formulas, standards, APIs and limitations used on this page. They do not replace professional validation when a result has legal, financial, medical or operational impact.

• The Prime PagesUniversity of Tennessee at Martin — Canonical reference on prime numbers, distribution, tests and records.
• Miller-Rabin Primality TestWikipedia — Description of the Miller-Rabin probabilistic primality test.
• BigIntMDN Web Docs — API used for primality testing of large integers without overflow.

Frequently asked questions

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