From Increase MySQL connection limit:-
MySQL’s default configuration sets the maximum simultaneous connections to 100. If you need to increase it, you can do it fairly easily:
For MySQL 3.x:
# vi /etc/my.cnf
set-variable = max_connections = 250
For MySQL 4.x and 5.x:
# vi /etc/my.cnf
max_connections = 250
Restart MySQL once you’ve made the changes and verify with:
echo "show variables like 'max_connections';" | mysql
EDIT:-(From comments)
The maximum concurrent connection can be maximum range: 4,294,967,295. Check MYSQL docs