local subdirectory multisite problem

Hello,
I am trying to setup a multisite on localhost.

I have followed the creation process as described in WP documentation, and added the recommended code to the wp-config file and .htaccess file.
I tried to add new site “test” and thought it was successful.

The dashboard shows the network setup:
Main site URL is : localhost/wp
Second site URL is : localhost/wp/test

The main site works well, and the dashboard shows the menu for the network and the two sites, but when I try to access to the dashboard for the second site, I get “error 404”.

Here is my wp-config and .htaccess:

define ( 'WP_ALLOW_MULTISITE' , true );
define( 'MULTISITE', true );
define( 'SUBDOMAIN_INSTALL', false );
define( 'DOMAIN_CURRENT_SITE', 'localhost' );
define( 'PATH_CURRENT_SITE', '/wp/' );
define( 'SITE_ID_CURRENT_SITE', 1 );
define( 'BLOG_ID_CURRENT_SITE', 1 );

RewriteEngine On
RewriteRule .* - [E=HTTP_AUTHORIZATION:%{HTTP:Authorization}]
RewriteBase /wp/
RewriteRule ^index\.php$ - [L]

# add a trailing slash to /wp-admin
RewriteRule ^([_0-9a-zA-Z-]+/)?wp-admin$ $1wp-admin/ [R=301,L]

RewriteCond %{REQUEST_FILENAME} -f [OR]
RewriteCond %{REQUEST_FILENAME} -d
RewriteRule ^ - [L]
RewriteRule ^([_0-9a-zA-Z-]+/)?(wp-(content|admin|includes).*) $2 [L]
RewriteRule ^([_0-9a-zA-Z-]+/)?(.*\.php)$ $2 [L]
RewriteRule . index.php [L]

Thanks for your help!