Finding the Nth prime number in C language

cnumber-theoryproject

The code runs just fine but instead of using "for loop" to iterate upto 200000 , I think there can be a better alternative and I am having trouble finding it. I need help to optimise this solution.The time taken by this solution currently is 56ms.

#include <stdio.h>
#include <math.h>
#include <stdbool.h>

int isPrime(long long int number)
{
    int i;
    for (i=2; i*i<=number; i++) {
        if (number % i == 0) return 0;
    }
    return 1;
}
int returnNPrime(int N)
{
    int counter = 0;
    int i ;
    if(N == 1) return 2;
    for(i=3;i<200000;i+=2)
    {
        if(isPrime(i))
        {
            counter++;
            if(counter == (N-1))
             return i;
        }
    }
    return 0;
}
   int main(int argc, char *argv[]) 
   {
       printf("%d",returnNPrime(10001));
       return 0;
   }

Best Answer

Don't put an arbitrary stop condition. You know that the list of primes is infinite and that the loop will eventually stop. Write it like this:

int returnNPrime (int N)
{
    int counter = 0;
    int i;
    if (N == 1) return 2;
    for (i = 3; ; i += 2)
    {
        if (isPrime(i))
        {
            counter++;
            if (counter == (N - 1))
                return i;
        }
    }
}

That being said, this solution is inefficient because you don't store previously found primes.

Try something like this:

#include <stdio.h>
#include <stdbool.h>

#define N 10001

int primes[N] = { 2, 3 };

int main ()
{
    for (int n = 2; n < N; n++) {
        for (int x = primes[n - 1] + 2; ; x += 2) {
            bool prime = true;
            for (int i = 0; i < n; i++) {
                int p = primes[i];
                if (p * p > x) {
                    break;
                }
                if (x % p == 0) {
                    prime = false;
                    break;
                }
            }
            if (prime) {
                primes[n] = x;
                break;
            }
        }
    }

    printf ("%d\n", primes[N - 1]);
}
Related Topic