Overview
Prime numbers are the building blocks of the integers: every number greater than 1 has a unique prime factorization. This calculator tests primality, shows the factorization, and lists primes up to a chosen limit.
Formula
A number n is prime if it is greater than 1 and is not divisible by any integer from 2 to √n.
How it works
Enter the number
It can be positive or negative; negative numbers are not prime.
Test divisibility
Potential divisors up to the square root are checked.
Read the result
Primality, factorization and the prime list are shown.
Worked examples
Example 1: 97
97 is prime because it is not divisible by any number up to √97 ≈ 9.8.
Example 2: 60
60 = 2^2 × 3 × 5, so it is not prime.
Frequently asked questions
Is 1 a prime number?
No. Prime numbers are greater than 1, and 1 is neither prime nor composite.
Is 2 a prime number?
Yes, and it is the only even prime number.
Is every odd number prime?
No. Numbers such as 9, 15 and 21 are odd but composite.
This calculator is for educational and informational purposes only and is not a substitute for professional advice.