Excluding posts with accurate pagination in wp_query

Hi there,

Currently I have a wp_query that I am excluding some posts from using the post__not_in parameter. The code is as follows:

<?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 am excluding a post with the id of 3. Well what is happening is that say I have 5 posts. This means that I should see the first two posts, click next, see the following 2. Done.

But for whatever reason when I am on page two, viewing the last two posts, I also see a link to view the next page. Problem is since I excluded that post, nothing shows up on the last page. I suspect wp is attempting to show post 5 with the id 3 which I am trying to exclude.

Is it possible to somehow not have the next post link show up? I am currently using the following for pagination:

<?php next_posts_link(); ?>
<?php previous_posts_link(); ?>

Any help would be greatly appreciated. Open to all ideas.