Opening one MySQL connection vs opening and closing a lot of connections?

[hbsxxsome1elsexx]

I have a > x20000 loop in php that checks if an entry exists in a MySQL database, I open & close the connection for every entry in the loop, but a friend told me that's crazy and I should open one connection, run the loop and then close it, but he didn't tell me why. Could someone explain me the benefits of reusing the same connection? is it CPU usage or what?