C prime number bug

Question

I want to find if a number is a prime number or not using the square root method. My number is working fine for different numbers when I test it but I know there is a bug that I can not find. Any help will be highly appreciated.

#include <math.h>

int is_prime(int n)
{
    int i,root;

    if(n == 2){
        return 1;
    }
    if(n % 2 == 0){
        return 0;
    }

    root = sqrt(n);

    for(i = 3; i <= root; i = i + 2){
        if(n % i == 0){
            return 0;
        }
    }

    return 1;
}

int main()
{
    int n,m;

    while (1){
        printf("Please enter a number(enter 0 to exit):");
        scanf("%d", &n);
        if(n == 0){
            break;
        }
        if(1 == is_prime(n)){
            printf("%d is a prime number.\n", n);
        }
        else{
            printf("%d is not a prime number.\n", n);
        }
    }

    return 0;
} 

Answer 1

there is a bug that I can not find

Beware the subtleties of floating point math

root = sqrt(n); can result in a root that is one less than expected due to imprecision/rounding. Example: Consider sqrt(49) may return 6.999999999999999... making root = 6 . The loop stops before testing with 7 and returns prime(49) incorrectly as true.

Instead iterate until the quotient is too large. This becomes true when i is about the square root of n .

// for(i = 3; i <= root; i = i + 2){
for(i = 3; i <= n/i; i = i + 2){

Avoid the below as i*i may overflow for primes near INT_MAX .

for(i = 3; i*i <= n; i = i + 2){  // Potential overflow

n/i is often a "freebie" when near n%i as good compilers emit common efficient code.

Alternatively, round up the square root calculation, if one is compelled to use sqrt() . With other types like long long n , this may be insufficient. Best to use integer math for an integer problem.

root = ceil(sqrt(n));

Corner bug :

Code returns true for is_prime(1) . @Weather Vane Suggest returning in the end:

// return 1;
return n >= 2;

Code dies with is_prime(negative_odd) as sqrt(negative_odd) is attempted. Suggest sqrt() -less solution.

Other problems may exist.