Check if a number is prime, see its factors, and list all primes up to any number.
This tool determines whether a given number is prime (having no divisors other than 1 and itself) or composite (having additional factors). It's useful for math homework, understanding number theory, and applications in cryptography and computer science.
The calculator tests whether the number has any divisors other than 1 and itself, typically checking divisibility only up to the square root of the number for efficiency, since any factor larger than the square root would have a corresponding factor smaller than it.
Enter any whole number, and the checker instantly tells you whether it's prime or composite, often listing its factors if composite.
Example 1: 17 is prime, since its only divisors are 1 and 17.
Example 2: 18 is composite, since it's divisible by 1, 2, 3, 6, 9, and 18.
Is 1 a prime number? No, by mathematical convention, 1 is neither prime nor composite, since primes require exactly two distinct positive divisors, and 1 has only one.
Is 2 the only even prime number? Yes, 2 is the only even prime number — every other even number is divisible by 2 in addition to 1 and itself, making it composite by definition.
Why only check divisibility up to the square root? If a number n has a factor larger than its square root, it must also have a corresponding factor smaller than the square root, so checking beyond that point would only find duplicate factor pairs already discovered.
Why are prime numbers important in cryptography? Modern encryption methods, like RSA, rely on the fact that multiplying two large primes together is easy, but factoring that resulting large number back into its original primes is computationally very difficult — this asymmetry is the foundation of secure digital communication.
Are there infinitely many prime numbers? Yes, this was proven by the ancient Greek mathematician Euclid over 2,000 years ago — there is no largest prime number, and primes continue indefinitely.