Our first list.

For our list of primes we need a list (naturally).  The best way to understand data structures is to implement them in a low level language.  Since I don't feel like inflicting ASM on everyone (although I do like assembler) we will use the next best thing.  C

Out list needs a data element (the found prime) and a pointer to the next element.
In C that looks like this.

struct prime_elem_s {
  uint64_t prime;
  struct prime_elem_s *next;
};

typedef struct prime_elem_s prime_elem_t;

We define a structure containing the current prime and a pointer to the next element.  Then we define a type prime_elem_t to refer to that structure.

In this case we want to add elements to the end of the list so we will also need a tail pointer.  We will create a list header which will keep a head and tail pointer as well as the number of elements in the list.

typedef struct {
  uint64_t length;
  prime_elem_t *head;
  prime_elem_t *tail;
} prime_list_t;

Now we can write a function which appends a new prime to the list.

void push_prime(prime_list_t *prime_list, uint64_t prime)
{
  prime_elem_t *elem = malloc(sizeof(prime_elem_t));

  elem->prime = prime;
  elem->next = NULL;

  if( prime_list->tail )
    {
      prime_list->tail->next = elem;
      prime_list->tail = elem;
    }
  else
    {
      prime_list->head = prime_list->tail = elem;
    }
  prime_list->length++;
}

Here we:

1. allocate a new element
2. initialize its fields
3. if this isn't the first element then append it to the list's tail then update the tail pointrewolf
4. otherwise set both the head and tail to the new element
5. increment the list's length