How prime number checker works
A prime number is a whole number greater than 1 that has exactly two divisors: 1 and itself. The first primes are 2, 3, 5, 7, 11, 13. Numbers with more than two divisors are called composite.
This checker tests whether a given integer is prime by trial division. It first handles 2 (the only even prime) separately, then checks odd divisors from 3 up to the square root of the number. If any divisor is found, the number is composite and the smallest factor is returned.
Numbers less than 2 are not prime. The checker only accepts integers; decimal numbers are rejected. For very large numbers, the trial division approach is efficient up to about 16 digits.
Frequently asked questions
What is a prime number?
A prime number is a whole number greater than 1 that is only divisible by 1 and itself. Examples include 2, 3, 5, 7, and 11. Numbers with additional divisors are composite.
Is 1 a prime number?
No. By definition, a prime number has exactly two distinct divisors: 1 and itself. Since 1 has only one divisor (itself), it is not considered prime.
What is the smallest prime number?
2 is the smallest prime number, and the only even prime. All other even numbers are divisible by 2 and therefore composite.
How does the checker work?
It uses trial division: it tests divisors from 2 up to the square root of the number. If any divisor is found, the number is composite. The square root bound works because if a number has a factor larger than its root, it must also have one smaller.
