Why do digits 1, 2 and 3 appear so frequently using C rand() function?

Question

What I am trying to do is to generate some random numbers (not necessarily single digit) like

29106
7438
5646
4487
9374
28671
92
13941
25226
10076

and then count the number of digits I get:

count[0] =       3  Percentage =  6.82
count[1] =       5  Percentage = 11.36
count[2] =       6  Percentage = 13.64
count[3] =       3  Percentage =  6.82
count[4] =       6  Percentage = 13.64
count[5] =       2  Percentage =  4.55
count[6] =       7  Percentage = 15.91
count[7] =       5  Percentage = 11.36
count[8] =       3  Percentage =  6.82
count[9] =       4  Percentage =  9.09

This is the code I am using:

#include <stdio.h>
#include <time.h>
#include <stdlib.h>

int main() {

    int i;
    srand(time(NULL));
    FILE* fp = fopen("random.txt", "w");    
    // for(i = 0; i < 10; i++)
    for(i = 0; i < 1000000; i++)
        fprintf(fp, "%d\n", rand());
    fclose(fp);

    int dummy;
    long count[10] = {0,0,0,0,0,0,0,0,0,0};
    fp = fopen("random.txt", "r");
    while(!feof(fp)) {
        fscanf(fp, "%1d", &dummy);
        count[dummy]++;                 
    }
    fclose(fp);

    long sum = 0;
    for(i = 0; i < 10; i++)
        sum += count[i];

    for(i = 0; i < 10; i++)
        printf("count[%d] = %7ld  Percentage = %5.2f\n",
            i, count[i], ((float)(100 * count[i])/sum));

}

If I generate a large number of random numbers (1000000), this is the result I get:

count[0] =  387432  Percentage =  8.31
count[1] =  728339  Percentage = 15.63
count[2] =  720880  Percentage = 15.47
count[3] =  475982  Percentage = 10.21
count[4] =  392678  Percentage =  8.43
count[5] =  392683  Percentage =  8.43
count[6] =  392456  Percentage =  8.42
count[7] =  391599  Percentage =  8.40
count[8] =  388795  Percentage =  8.34
count[9] =  389501  Percentage =  8.36

Notice that 1, 2 and 3 have too many hits. I have tried running this several times and each time I get very similar results.

I am trying to understand what could cause 1, 2 and 3 to appear much more frequently than any other digit.

---

Taking hint from what Matt Joiner and Pascal Cuoq pointed out,

I changed the code to use

for(i = 0; i < 1000000; i++)
    fprintf(fp, "%04d\n", rand() % 10000);
// pretty prints 0
// generates numbers in range 0000 to 9999

and this is what I get (similar results on multiple runs):

count[0] =  422947  Percentage = 10.57
count[1] =  423222  Percentage = 10.58
count[2] =  414699  Percentage = 10.37
count[3] =  391604  Percentage =  9.79
count[4] =  392640  Percentage =  9.82
count[5] =  392928  Percentage =  9.82
count[6] =  392737  Percentage =  9.82
count[7] =  392634  Percentage =  9.82
count[8] =  388238  Percentage =  9.71
count[9] =  388352  Percentage =  9.71

What can be the reason that 0, 1 and 2 are favored?

---

Thanks everyone. Using

int rand2(){
    int num = rand();
    return (num > 30000? rand2():num);     
}

    fprintf(fp, "%04d\n", rand2() % 10000);

I get

count[0] =  399629  Percentage =  9.99
count[1] =  399897  Percentage = 10.00
count[2] =  400162  Percentage = 10.00
count[3] =  400412  Percentage = 10.01
count[4] =  399863  Percentage = 10.00
count[5] =  400756  Percentage = 10.02
count[6] =  399980  Percentage = 10.00
count[7] =  400055  Percentage = 10.00
count[8] =  399143  Percentage =  9.98
count[9] =  400104  Percentage = 10.00

Answer 1

rand() generates a value from 0 to RAND_MAX. RAND_MAX is set to INT_MAX on most platforms, which may be 32767 or 2147483647.

For your example given above, it appears that RAND_MAX is 32767. This will place an unusually high frequency of 1, 2 and 3 for the most significant digit for the values from 10000 to 32767. You can observe that to a lesser degree, values up to 6 and 7 will also be slightly favored.