Wordpress short links don't automatically redirect to the post permalink, like some (me) might think they should. If you switch your permalink structure to something more SEO friendly, existing posts should automatically redirect to the proper format. However, future posts will not. If you want all "short links" (mywordpresssite.com/?p=123456) t…

wp_redirect_short_links.php

<?php

add_action('init', 'redirect_short_links');

function redirect_short_links()
{
    $id = $_GET['p'];

    // do not redirect post previews
    if (! $id || !preg_match('/^\d+$/', $id) || !empty($_GET['preview'])) {
        return;
    }

    $permalink = get_the_permalink($id);

    if ($permalink) {
        header('HTTP/1.1 301 Moved Permanently');
        header("Location: {$permalink}");
        exit();
    }
}