The below information is with respect to RDS MySQL:
-- The default value of 'max_connections' in RDS MySQL is specific to a particular DB instance type. This is because, this parameter depends on the RAM available for a DB instance.
Max_connections (default value) = ‘DBInstanceClassMemory (in bytes)/12582880’.
-- However, the allowed values for this parameter is 1-100000
-- Hence, you can consider modifying the parameter 'max_connections' in the parameter group associated with your DB instance. But, it is recommended to increase this value if the DB instance has sufficient resources (CPU , Memory) to serve increased connections. This is because, each connection requires resources, if the connections are increased to a value higher than what could be handled by the DB instance type, the connections may not get required resources resulting in performance issues.
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