Hi, I wrote a code to check all the primes between 2 and 1002, but I for each nth number tested, I go from 2 to n-1. By running the program, I got 168 numbers, which is correct according to a website. However, I've read it that I only need to check until the square root of n, but I tried making that change in the inner for loop by choosing j < sqr(i), and it just finds the number 2 as a prime. Why is this happening? Thanks in advance!

Code:

#include <stdio.h>
#include <math.h>
void primeFinder(void);
int main(void)
{
printf("Prime numbers from 1 to 1000:\n\n");
primeFinder();
return 0;
}
void primeFinder(void)
{
int i;
int j;
int k;
int n_primes = 0;
//i is the number to be tested:
for ( i = 2 ; i <= 1000 ; i++ )
{
//i must be divided by j, that goes from 2 to i - 1 [(i - 2) divisions]:
for ( j = 2, k = 0 ; j < i ; j++ )
{
//i is not prime, whatever is the value of j:
if ( i % j == 0 )
{
//If remainder is 0, there is no need to test that i anymore:
break;
}
else
{
k++;
}
} //End of inner for
//i is prime:
if ( k == i - 2 )
{
printf("%d\t", i);
n_primes++;
}
} //End of outer for
printf("\n\nIt was found %d prime(s) in the inverval considered.\n", n_primes);
}