About prime number checker
A prime number has exactly two factors: 1 and itself. 2, 3, 5, 7 and 11 are prime; 1 is not prime.
How primality is tested
You only need to test divisors up to the square root of the number. To check 97, trying 2, 3, 5 and 7 is enough, and none divide it, so 97 is prime.
Prime factors
A number that is not prime can be written as a product of primes in exactly one way. 360 = 2³ × 3² × 5.
A worked example
The number 91 looks prime but is 7 × 13. The number 97 has no divisor among 2, 3, 5 and 7, which are all the primes up to its square root, so 97 is prime. The number 360 factors as 2³ × 3² × 5.
Why primes matter
Large primes secure much of the internet, since encryption methods such as RSA rely on the fact that multiplying two big primes is easy but factoring the product is very hard.
