Eratosthenes prime numbers - c

Question

I have created a program to search for prime numbers. It works without problems until the entered number is smaller than 52, when it is bigger output prints out some blank (0) numbers and I don't know why. Also other numbers have blank output.
My code is:
#include <stdio.h> //Prime numbers
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include <unistd.h>
int c[100], n, a[50], d, e, b = 1;
void sort() {
for (int i = 1; i < n; i++) {
if (c[i] > 1) {
a[b] = c[i];
printf("%d %d %d\n", a[1], b, i);
b++;
e = 2;
d = 0;
while (d <= n) {
d = c[i] * e;
c[d - 1] = 0;
e++;
}
}
}
}
int main() {
printf("Enter number as an limit:\n");
scanf("%d", &n);
for (int i = 0; i < n; i++) {
c[i] = i + 1;
}
sort();
printf("Prime numbers between 1 and %d are:\n", n);
for (int i = 1; i < b; i++) {
printf("%d ", a[i]);
}
return 0;
}
Here is output for 25:
Enter number as an limit:
25
2 1 1
2 2 2
2 3 4
2 4 6
2 5 10
2 6 12
2 7 16
2 8 18
2 9 22
Prime numbers between 1 and 25 are:
2 3 5 7 11 13 17 19 23
But for 83 is:
Enter number as an limit:
83
2 1 1
2 2 2
2 3 4
2 4 6
2 5 10
2 6 12
2 7 16
2 8 18
2 9 22
2 10 28
2 11 30
2 12 36
2 13 40
2 14 42
2 15 46
2 16 52
0 17 58
0 18 60
0 19 66
0 20 70
0 21 72
0 22 78
0 23 82
Prime numbers between 1 and 83 are:
0 3 5 7 11 0 17 19 23 29 31 37 0 43 47 53 0 61 67 71 73 79 83
Blank spots always spots after 17th prime number. And always the blank numbers are the same. Can you help me please what is the problem?

Answer 1

The loop setting entries in c for multiples of c[i] runs too far: you should compute the next d before comparing against n:
for (d = c[i] * 2; d <= n; d += c[i]) {
c[d - 1] = 0;
}
As a matter of fact you could start at d = c[i] * c[i] because all lower multiples have already been seen during the previous iterations of the outer loop.
Also note that it is confusing to store i + 1 into c[i]: the code would be simpler with an array of booleans holding 1 for prime numbers and 0 for composite.
Here is a modified version:
#include <stdio.h>
int main() {
unsigned char c[101];
int a[50];
int n, b = 0;
printf("Enter number as a limit:\n");
if (scanf("%d", &n) != 1 || n < 0 || n > 100) {
printf("invalid input\n");
return 1;
}
for (int i = 0; i < n; i++) {
c[i] = 1;
}
for (int i = 2; i < n; i++) {
if (c[i] != 0) {
a[b] = i;
//printf("%d %d %d\n", a[0], b, i);
b++;
for (int d = i * i; d <= n; d += i) {
c[d] = 0;
}
}
}
printf("Prime numbers between 1 and %d are:\n", n);
for (int i = 0; i < b; i++) {
printf("%d ", a[i]);
}
printf("\n");
return 0;
}
Output:
chqrlie$ ./sieve4780
Enter number as a limit:
25
Prime numbers between 1 and 25 are:
2 3 5 7 11 13 17 19 23
chqrlie$ ./sieve4780
Enter number as a limit:
83
Prime numbers between 1 and 83 are:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79

Answer 2

Your problem seems to be caused by the fact that you have declared an array with size 50, but in fact it goes further than that: imagine you want to use Eratosthenes' procedure to find the first 10,000 prime numbers. Does this mean that you need to declare an array of size 10,000 first (or even bigger), risking to blow up your memory?
No: best thing to do is to work with collections where you don't need to set the maximum size at declaration time, like a linked list, a vector, ..., like that you can make your list grow as much as you like during runtime.