Prime Number Checker & Generator

Check primes or generate a whole list of them

A prime number is a whole number greater than 1 with exactly two divisors: 1 and itself. This tool works two ways — check any single number instantly and see its factorization if it's composite, or generate every prime number within a range you choose, complete with a count and running sum.

How to use the prime number tool

• In "Check a Number" mode, type any whole number — you'll instantly see whether it's prime, its prime factorization if it's composite, and the nearest prime numbers below and above it.
• In "Generate a Range" mode, enter a "From" and "To" value to list every prime number in that range, along with the total count found and their sum.
• For very large result sets, use "Copy List" to grab every prime as a comma-separated list without scrolling through hundreds of badges.

Real-world uses

Students use it to verify primality homework and explore factorization by hand. It's also a common reference for programming practice — testing your own prime-checking function's output against a known-correct source is a quick sanity check. Cryptography enthusiasts and puzzle solvers use the range generator to explore prime distributions or find specific primes for an exercise.

Frequently asked questions

Is 1 a prime number?

No — by definition, a prime number must have exactly two distinct positive divisors (1 and itself). Since 1 only has one divisor, it's classified as neither prime nor composite.

How does the tool check primality so fast?

It uses trial division up to the square root of the number — if no divisor is found up to that point, no larger one exists either, which makes checking even fairly large numbers quick in the browser.

Is 2 the only even prime number?

Yes — every other even number is divisible by 2 (in addition to 1 and itself), which disqualifies it from being prime, so 2 is the sole even number on the entire list of primes.

Is there a limit to how large a range I can generate?

Ranges are capped at 200,000 numbers per search to keep the tool fast and responsive directly in your browser without freezing the page.

What's prime factorization used for?

Breaking a composite number down into the primes that multiply together to form it is the basis for simplifying fractions, finding GCD/LCM, and a huge amount of number theory and cryptography — this tool shows that breakdown automatically for any composite number you check.