Thread: how to cleanup prime numbers program?

I got my prime numbers software to work. It first gets a max (so there is no annoying infinite loop), then enters for loop 'i' (which is the number to be tested). For loop 'j' is where is counts up to the current number/'i', checking is there is a '%'/remainder of 0 (after first ignoring every even number). The problem I had was how to both escape the counting/'j' loop, and be able to report a printf to console for the number being found as a prime number. Right now, I have an int 'isPrime' that will either be '1' or '0' (my quick emulation of bools). That entire sections seams like it is excessive, and would like to know how I can condense it- or make it 'smarter'. (yes my method for finding prime number may not be the best, but that is ok)

Code:

#include<stdio.h>

int main (){
    
    int max, remainder, i, j, isPrime;
    printf("Please provide a maximum number: ");
    scanf("%d", &max);
    printf("\nThank You!\n\n");
    for (i = 2; i <= max; i++){
        if ((i%2) != 0){
            for (j = 2; j < i; j++){
                remainder = i % j;
                //printf("J : %d | I: %d | R : %d \n",j,i,remainder); //Emergency Line for Reading Information
                if (remainder == 0){
                    isPrime = 0;
                    break;
                } else {
                    isPrime = 1;
                }
            }
            if (isPrime == 1){
                printf("%d \n", i);
            }
        }
    }
    printf("Done!");
    return 0;
}

Handle 2 separately.
Start your loops at 3 and increment by 2.
End your inner loop at the square root of i.
Do away with the flag and just test the loop variable to see why the loop terminated.

Putting this together:

Code:

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

int main(void) {
    int max, n, d;

    printf("Enter the maximum: ");
    scanf("%d", &max);

    if (max > 1) printf("2 ");
    
    for (n = 3; n <= max; n += 2) {
        int sq = (int)sqrt(n);
        for (d = 3; d <= sq; d += 2)
            if (n % d == 0)
                break;
        if (d > sq)
            printf("%d ", n);
    }

    printf("\n");
    return 0;
}