Prime Checker
Test whether a given integer is prime, with trial-division proof.
About Prime Checker
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. This calculator uses trial division: it tests all potential factors from 2 up to √n. If none divide n evenly, n is prime. Trial division is efficient for numbers up to about 10¹⁵.
Formula
Trial division bound
Test divisors d from 2 to floor(√n). If none divide n, n is prime.
- n
- Number to test
- d
- Trial divisor
Worked example
With the default values below, Prime Checker returns Is Prime? of Yes. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Numberminimum 1
- 97
Results
- Is Prime?
- Yes
- Smallest Factor
- N/A (prime)
Step by step
- 1Trial division
- 2Conclusion= 97 is prime
Assumptions and limits
- The result is derived only from the single input listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Is 1 prime?
No. By convention, 1 is neither prime nor composite. The smallest prime is 2, which is also the only even prime.
Why only check up to the square root?
If n = a × b and both a and b are greater than √n, then a × b > n — a contradiction. So at least one factor of a composite number must be ≤ √n.