What is a prime number
A prime number is a natural number greater than 1 that is only divisible by 1 and itself. Numbers with other divisors are called composite. The number 1 is defined as neither prime nor composite.
How the test works
This tool tests divisors from 2 up to the square root of the given number — if none divides it evenly, the number is prime. This method (called trial division) is efficient for numbers up to the millions.
Examples
17 is prime (no divisors besides 1 and 17). 15 is composite: 15 = 3 × 5. 2 is the only even prime number — every other prime is odd.
Prime factorization
Every composite number can be written as a unique product of primes — the Fundamental Theorem of Arithmetic. For example, 60 = 2² × 3 × 5.
Frequently asked questions
Is the number 1 prime?
No — by definition, prime numbers must be greater than 1 and have exactly two distinct divisors: 1 and itself.
What is the only even prime number?
2. Every other even number is divisible by 2, so it can never be prime.
How does prime factorization work?
Every composite number can be broken down into a unique product of prime factors, like 60 = 2² × 3 × 5.
Up to what size does this tool work well?
It performs well up to numbers in the millions, thanks to testing divisors only up to the square root.