How can I display a specific number of post in a category via a url

showposts is an alias of posts_per_page, which is a private query var, meaning it can’t be set from the query string. You could register your own query var and map that to posts_per_page in a pre_get_posts action. This could go in your theme’s functions.php and would work for any main query.

// add a new query var to the list of known query vars
function wpd_custom_posts_queryvar( $vars ){
    $vars[] = 'wpd-num';
    return $vars;
}
add_filter( 'query_vars', 'wpd_custom_posts_queryvar' );

// hook pre_get_posts and set posts_per_page
// if it's the main query and our custom query var is set 
function wpd_custom_posts_number( $query ){
    if( $query->is_main_query() && $query->get( 'wpd-num' ) ){
        $query->set( 'posts_per_page', $query->get( 'wpd-num' ) );
    }
}
add_action( 'pre_get_posts', 'wpd_custom_posts_number' );