C - Print all prime numbers from 1 to 100 using arrays - c

Question

OK so I got this challenge where I have to print all the primes from 1 to 100... However there is an error in my code that I am unable to find. Here is how I thought the problem should be done:
For any number from 3 to 100 check if there is any other number in the primes array that divides it. If there is the number is not prime. If there is not the number is prime and should be added to the array. Pretty simple, right ?
However it is not working.
Here is my code :
#include <stdio.h>
int main() {
int Primes[50] = {0};
int i, j, k;
Primes[0] = 2;
Primes[1] = 3;
for (i = 3; i < 101; i++) {
for (j = 2; j < 100; j++) {
if (i % Primes[j] != 0 && Primes[j] != 0) {
Primes[j] = i;
}
}
}
printf("Primes array : \n");
for (k = 0; k < 51; k++) {
printf("%d ", Primes[k]);
}
return 0;
}

Answer 1

instead of assuming the magic number as 25... that is k!=25, we can
replace it with i<=100.
#include <stdio.h>
#include <stdlib.h>
int main(void){
int Primes[50] = {0};
int i,j,k = 0;
Primes[0]=2;
Primes[1]=3;
for(i=0; i<=100; i++) {
for(j = 2; j<=i; j++) {
if(i % j == 0 ){
if(i == j)
Primes[k++]=i;
break;
}
}
}
printf("Primes array : \n");
for(int index = 0;index < k; index++) {
printf("%d\n", Primes[index]);
}
return 0;
}

Answer 2

When you do this:
if(i % Primes[j] != 0 && Primes[j] !=0)
{
Primes[j]=i;
}
You're saying "if the current number is not divisible by the given prime number, replace the given prime number with the current number". This is not what you want.
You need to check if the current number is not divisible by any prime number. So you need to loop though the list of primes to make sure your number isn't divisible by any of them, and if so add the number to the end of the list. You can do that as follows:
int num_primes = 0;
for (i=2;i<101;i++)
{
int is_prime = 1;
for(j=0; j<num_primes && is_prime; j++)
{
if(i % Primes[j] == 0)
{
is_prime = 0;
}
}
if (is_prime) {
Primes[num_primes++] = i;
}
}
In the above code, we use num_primes to count the number of primes we have so far, and is_prime to see if we found a prime that divides the current number. As you divide each number by a prime, if the remainder is 0 you know the number is not prime and set is_prime to 0. This also causes the inner loop to exit right away. Then if is_prime is still set at the end of the inner loop, you have a prime and you add it to the end of the list.
You also have an off-by-one error in the printing loop:
for(k=0;k<51;k++)
Since Primes has size 50, the largest valid index is 49. So change it to:
for(k=0;k<50;k++)

Answer 3

There are lot of issues in the algorithm you used. Use this simple version with issues addressed in the code.
int main(void){
int Primes[50] = {0};
int i,j,k = 0 /* use for prime count purpose */;
Primes[0]=2;
Primes[1]=3;
for(i=4 /* 3 is already stored */; k != 48; i++) { /* rotate loop until prime count doesn't reaches 48 */
for(j = 2; j<=i; j++) { /* i is the number you want to check whether its prime or not. SO rotate loop from 2 to "i" */
if(i % j == 0){ /* use i%j not i % Primes[j] as you want to check whether i is prime or not */
if(i == j) /* if its a prime numbur j reaches upto i */
Primes[k++]=i; /* store it */
break; /* comes out of inner loop */
}
}
}
printf("Primes array : \n");
for(int index = 0;index < k; index++) { /* rotate k times not some random 51 times */
printf("%d ", Primes[index]);
}
return 0;
}

Answer 4

The code above doesn't actually give what we want, but beautiful code nonetheless. Here is the edited code that gives the prime numbers from 1 to 100
int main(void){
int Primes[50] = {0};
int i,j,k = 0 /* use for prime count purpose */;
Primes[0]=2;
Primes[1]=3;
for(i=0 /* 3 is already stored */; k != 25; i++) { /* rotate loop until prime count doesn't reaches 48 */
for(j = 2; j<=i; j++) { /* i is the number you want to check whether its prime or not. SO rotate loop from 2 to "i" */
if(i % j == 0){ /* use i%j not i % Primes[j] as you want to check whether i is prime or not */
if(i == j) /* if its a prime numbur j reaches upto i */
Primes[k++]=i; /* store it */
break; /* comes out of inner loop */
}
}
}
printf("Primes array : \n");
for(int index = 0;index < k; index++) { /* rotate k times not some random 51 times */
printf("%d\n", Primes[index]);
}
return 0;
}