What is a prime number?

An integer greater than 1 that has no positive divisors other than 1 and itself. The first few primes are 2, 3, 5, 7, 11, and 13.

No. 1 has only one divisor — itself — while a prime must have exactly two distinct divisors, 1 and the number. 1 is neither prime nor composite.

Yes. 2 is divisible only by 1 and 2, which makes it prime — and it is the only even prime, because every other even number is divisible by 2.

How does the checker know a number is prime?

It tries to divide the number by every candidate from 2 up to its square root. If nothing divides evenly, no factor exists, so the number is prime. Checking only to the square root is sufficient and keeps it fast.

What is the difference between prime and composite?

A prime has exactly two divisors (1 and itself); a composite number greater than 1 has at least one more. For example 7 is prime, while 9 is composite because 3 divides it.

Sumivo · Mathematics

Prime Number Checker

Test whether a whole number is prime — divisible only by 1 and itself — using trial division, and see the smallest factor when it is not.

01 / inputs

Whole number

integer

02 / result

IS IT PRIME?

Yes — prime

Prime?: Yes
Smallest factor: —
Cofactor: —

Calculation trace

no divisor found from 2 to √97
97
Result

Maintained by Jack Shi

How it works

A prime number is an integer greater than 1 whose only divisors are 1 and itself. The tool uses trial division: it checks whether the number is divisible by 2, then by each odd number 3, 5, 7, … up to its square root. If any of these divides evenly, the number is composite and that divisor is its smallest factor; if none does, the number is prime. Testing only up to the square root is enough, because any factor larger than √n must pair with a factor smaller than √n.

Assumptions & limits

A prime is an integer greater than 1; 1, 0, and negative numbers are reported as not prime.
For a composite number the tool reports the smallest prime factor and its cofactor.
Inputs are capped at 1,000,000,000,000 so the check stays fast in the browser.

Verified runs

Synthetic examples executed at build revision 9e21499 on 2026-11-01 UTC. Cards round decimal results to 6 significant figures; matching uses full precision and the tolerance below. Matches cover the displayed fields, not every possible input or clinical or engineering validation.

Inputs: Integer: 97 integer
Result: Prime: true boolean (expected Prime: true boolean) ✓
Inputs: Integer: 1 integer
Result: Prime: false boolean (expected Prime: false boolean) ✓
Inputs: Integer: 91 integer
Result: Prime: false boolean; Smallest factor: 7 (expected Prime: false boolean; Smallest factor: 7) ✓

How these runs were checked

Method: prime-checker@1.0.0. Expectations come from the listed test fixtures or hand arithmetic; they are not copied from these executions. Omitted optional inputs use the method defaults. Run dates record execution, not expert review or fresh measurements.

Download all verified runs (JSON) — full inputs, returned values, expectations, timestamps and buildRevision.

normal: 2026-11-01T06:44:58.881Z. Absolute tolerance: 1e-10. Text and booleans match exactly. Full-precision result: Prime: true boolean. Expected: Prime: true boolean. Expectation: packages/calculator-core/tests/prime-checker.test.ts
boundary: 2026-11-01T06:44:58.881Z. Absolute tolerance: 1e-10. Text and booleans match exactly. Full-precision result: Prime: false boolean. Expected: Prime: false boolean. Expectation: packages/calculator-core/tests/prime-checker.test.ts
sensitivity: 2026-11-01T06:44:58.881Z. Absolute tolerance: 1e-10. Text and booleans match exactly. Full-precision result: Prime: false boolean; Smallest factor: 7. Expected: Prime: false boolean; Smallest factor: 7. Expectation: packages/calculator-core/tests/prime-checker.test.ts

Reproduce from the source checkout with pnpm --filter @sumivo/web gen:verified-runs. A rebuild changes execution times; the revision identifies its Git starting point, including any uncommitted changes made for that build.

FAQ

What is a prime number?: An integer greater than 1 that has no positive divisors other than 1 and itself. The first few primes are 2, 3, 5, 7, 11, and 13.
Is 1 a prime number?: No. 1 has only one divisor — itself — while a prime must have exactly two distinct divisors, 1 and the number. 1 is neither prime nor composite.
Is 2 a prime number?: Yes. 2 is divisible only by 1 and 2, which makes it prime — and it is the only even prime, because every other even number is divisible by 2.
How does the checker know a number is prime?: It tries to divide the number by every candidate from 2 up to its square root. If nothing divides evenly, no factor exists, so the number is prime. Checking only to the square root is sufficient and keeps it fast.
What is the difference between prime and composite?: A prime has exactly two divisors (1 and itself); a composite number greater than 1 has at least one more. For example 7 is prime, while 9 is composite because 3 divides it.

Related calculators

SOURCES

OpenStax, Rice University
Prealgebra 2e ↗
Prime numbers and divisibility
Accessed 2026-09-02