Sieve of Eratosthenes wrong output

Question

I was trying to find out the sum of all prime up to 2 million.

So I wrote the following code for it:

#include <math.h>
#include <stdlib.h>
#define limit 2000000
int main(void)
{
    unsigned int *sieve, i, j;
    unsigned long long int sum = 0;
    sieve = malloc(sizeof(int)*limit);
    for(i=2;i<=limit;i++)
        sieve[i] = 1;
    for(i=2;i<=limit;i++)
    {
        if(sieve[i])
        {
            for(j=i;j*i<=limit;j++)
                sieve[j*i] = 0;
        }
    }

    for(i=2;i<=limit;i++)
{
        if(sieve[i])
            sum += i;
    }
    printf("The sum is %llu\n",sum);
    return 0;
}

The answer should be 142913828922, but I am getting 142889228620.

Can you tell me what is going wrong? I can't figure it out.

Answer 1

unsigned int *sieve, i, j;
for(j=i;j*i<=limit;j++)

The calculation j*i overflows for i > 65535. In this case, that spuriously produces some pseudo-composites.

Stop sieving when i reaches the square root of the limit.