Paginate wp_query while utilizing post__not_in

I'm currently running a wp_query like this:

?php 
            $the_query = new WP_Query( array(
                'post_type' = 'photos',
                'posts_per_page' = '2',
                'post__not_in' = array(3),
                'paged' = $paged
                )
            );
        ?
        ?php while ( $the_query-have_posts() ) : $the_query-the_post(); ? 
         ?php the_title(); ?
        ?php endwhile; ?

I then have some pagination at the bottom as such:

?php next_posts_link(); ?
?php previous_posts_link(); ?

Say I have 11 posts that the query would return but one of them has the id of '3'. This means that I have 10 total posts and should return a number of 'next' links. For whatever reason at the end of those pages, there will be a 'next' link that links to a page that is blank.

I believe this empty page is the post I'm attempting to exclude with 'post__not_in'.

How can I exclude posts from my wp_query and still have accurate pagination?