Ubuntu has moved from Upstart to Systemd in version 15.04 and no longer respects the limits in /etc/security/limits.conf for system services. These limits now apply only to user sessions.
The limits for the MySQL service are defined in the Systemd configuration file, which you should copy from its default location into /etc/systemd and then edit the copy.
sudo cp /lib/systemd/system/mysql.service /etc/systemd/system/
sudo vim /etc/systemd/system/mysql.service # or your editor of choice
Add the following lines to the bottom of the file:
LimitNOFILE=infinity
LimitMEMLOCK=infinity
You could also set a numeric limit, eg LimitNOFILE=4510.
Now reload the Systemd configuration with:
sudo systemctl daemon-reload
Restart MySQL and it should now obey the max_connections directive.
I also had problems stopping MySQL cleanly after upgrading to 15.04. If this affects you (you’ll know because it will take 300 seconds to time out when you do service mysql stop or service mysql restart) then adding the following line to the same /etc/systemd/system/mysql.service file fixed it for me:
ExecStop=/usr/bin/mysqladmin --defaults-file=/etc/mysql/debian.cnf shutdown
This latter problem seems to have been fixed by 16.04 and this line is no longer required, so before you do a distribution upgrade you’ll want to stop MySQL and remove the ExecStop line from the config file.