C :: Storing A 10 Digit Number

I wanted to find all the prime until a specified limit in C. I use the Sieve of Eratosthenes. But when I define the limit to anything more than a 7 digit number the program terminates.

Code:

#include<stdio.h>
#define limit 1000000000
int main(void)
{
unsigned long long int i,j;
int primes[limit] = {0};
//int count =0;
for(i=2;i<limit;i++)
}

[code]....

I believe that this might be because the size cannot be declared array cannot be more than the a 7 digit number. I think so. how to store a 10 digit number in C?And can't unsigned long long hold a 10 digit?