Prime Number Checker
Enter any number and find out if it's prime or composite. You also get its full list of factors, the prime factorization, and the nearest primes on either side. Works up to a million.
How to use
- Type in any whole number up to 1,000,000.
- The result tells you immediately whether it's prime or composite.
- Scroll down to see all factors, the prime factorization, and which primes are closest to it.
Related tools:
A prime number has exactly two factors: 1 and itself. 2 is the only even prime. 1 is not prime (by convention - it has only one factor). Composite numbers have more than two factors. Checking primality for small numbers is easy enough by hand; for large numbers, even efficient algorithms take serious computation.
Prime factorisation breaks any composite number into a product of primes. 360 = 2^3 x 3^2 x 5. This is unique for every number (Fundamental Theorem of Arithmetic). Knowing the prime factors helps with GCD, LCM, and simplifying fractions. The tool also shows nearby primes, which is useful when you need a prime close to a specific number for cryptographic purposes.
Frequently Asked Questions
Is 1 a prime number?
No. By modern mathematical convention, 1 is neither prime nor composite. The definition of prime requires exactly two distinct divisors (1 and itself). Since 1 has only one divisor (itself), it does not qualify.
What is the largest known prime number?
As of 2024, the largest known prime has over 41 million digits. These Mersenne primes (of the form 2^p - 1) are found by the GIMPS (Great Internet Mersenne Prime Search) project using distributed computing across thousands of machines.
Why do prime numbers matter in everyday life?
RSA encryption, used in HTTPS and secure banking, relies on the fact that multiplying two large primes is easy but factoring the result is computationally infeasible. Every time you see a padlock in your browser, prime numbers are doing the security work behind the scenes.