Question

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.

What is the 10 001st prime number?

My solution:

public class Prime_Number {

    public static boolean isPrime(long n) {
        if ((n > 2 && n % 2 == 0) || (n > 3 && n % 3 == 0) || (n > 5 && n % 5 == 0) || n == 0 || n == 1) {
            return false;
        }
        return true;
    }

    public static void main(String[] args) {
        int count = 0;
        int prime = 0;
        while (prime <= 10001) {
            if (isPrime(count) == true) {
                prime++;
                if (prime == 10001) {
                    System.out.println(count + " is a prime number" + "(" + prime + ")");
                }
            }
            count++;
        }
    }
}

But it does not give a correct answer. Please help me to upgrade my code. For instance, program defines a 91 as a prime number, but it is not a prime number. How to improve it?

Answer 1

You need to test the number against every prime less than its square root to ensure it is prime.

You’re only testing against 2,3 and 5.

Because storing all the primes is not always space-feasable, a common technique is to test for 2, and then test all odd numbers starting at 3. This requires a loop.

consider:

boolean isPrime(long n) {
    if (n < 2) return false;
    if (n == 2) return true;
    if (n % 2 == 0) return false;
    if (n < 9) return true;
    if (n % 3 == 0) return false;
    long max = (long)(Math.sqrt(n + 0.0)) + 1;
    for (int i = 5; i <= max; i += 6) {
        if (n % i == 0) return false;
        if (n % (i + 2) == 0) return false;
    }
    return true;
}