Math & Number Tools Checker

Prime Number Checker: Is This Number Prime?

Check whether a number is prime, composite, or neither, with divisibility logic, examples, and explanations for math homework and number theory.

Analyze a number

See whether it is prime, why, its factors, and nearby primes in one place.

Explore primes in a range

Choose two endpoints to see every prime, a count, a visual distribution and the largest gap.

Advanced prime checks

Mersenne prime check

A number of the form 2^p − 1 is not necessarily prime. This test verifies the number itself.

Large-number prime test

Exact deterministic Miller–Rabin test for unsigned 64-bit integers.

What makes a number prime

A prime number is a whole number greater than 1 with exactly two positive factors: 1 and itself.

  • 2 is the only even prime number.
  • 1 is not prime and not composite.
  • A composite number has more than two positive factors.

How prime checking works

A practical prime test checks divisibility only up to the square root of the number.

  • If a factor exists above the square root, a paired factor exists below it.
  • Even numbers greater than 2 are not prime.
  • Numbers ending in 5 are not prime unless the number is 5.

Prime checker examples

Use examples to understand the result, not just the final yes or no.

  • 17 is prime because only 1 and 17 divide it evenly.
  • 21 is composite because 3 x 7 = 21.
  • 97 is prime because no integer from 2 to sqrt(97) divides it.

Prime Number Checker FAQ

What is a prime number?

A prime number is a whole number greater than 1 with exactly two positive factors: 1 and itself.

Is 1 a prime number?

No. 1 is not prime and not composite.

Is 2 prime?

Yes. 2 is prime and it is the only even prime number.

How do I check if a number is prime?

Test whether it has any divisors from 2 up to the square root of the number.

What is a composite number?

A composite number is a whole number greater than 1 with more than two positive factors.

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Focused prime number pages

Use this direct-answer page when the question is simply whether a number is prime or composite.