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Prime Number Calculator

Check whether a number is prime, or list all prime numbers up to a given limit.

About the Prime Number Calculator

A prime number is a whole number greater than 1 with no divisors other than 1 and itself — the building blocks of number theory. This calculator either checks whether a specific number is prime, or lists every prime number up to a limit you choose.

How It Works

To check a single number, the calculator tests divisibility by every whole number from 2 up to its square root — if none divide evenly, the number is prime. To list primes up to a limit, it applies that same primality test to every number in the range and collects the ones that pass.

A number n is prime if no integer from 2 to √n divides it evenly.

Example

Scenario: Checking whether 97 is prime.

Result: 97 is a prime number, since no whole number between 2 and its square root divides it evenly.

Assumptions & Limitations

  • Only tests whole numbers 2 or greater — 0, 1, and negative numbers are not considered prime by mathematical definition.
  • The 'list primes' mode caps results at a reasonable number of entries for readability.
  • Listing primes up to very large limits can take noticeably longer, since the check scales with the size of the range.

Frequently Asked Questions

Why isn't 1 a prime number?
By mathematical definition, a prime number must have exactly two distinct positive divisors (1 and itself) — since 1 only has one divisor (itself), it is specifically excluded from the definition of prime.
Why check divisibility only up to the square root?
If a number n has a divisor larger than its square root, it must also have a corresponding divisor smaller than the square root, so checking up to the square root is sufficient to catch every possible factor pair, making the test much faster.
Is 2 a prime number?
Yes — 2 is the smallest and only even prime number, since every other even number is divisible by 2 and therefore not prime.

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