Storing many elements in std::vector c++

For one of my applications I need to generate vector of size 2^35 (the size of my RAM is 96 GB, so this vector can easily fit into RAM).

int main ()
{
  int i;

  /* initialize random seed: */
  srand (time(NULL));

  vector<int> vec;
  do {
     i = rand() % 10 + 1;
     vec.push_back(i);
  } while ((vec.size()*sizeof(int))<pow(2,35));

  return 0;
}

However, I notice that my do while loop executes infinitely. One of the possible reasons is range of vec.size() is long unsigned int, which is very less than the number of elements inserted i.e. pow(2,35), due to which I think it goes in an infinite loop. I may be wrong. Please correct me if I am wrong. But can someone please tell how can I insert greater than pow(2,35) numbers in vec.

gcc version:4.8.2