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I have a mysql database in which i am using auto_increment(integer), can you tell me till what integer it can incremented. How we can increase the limit of auto_increment?

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The limit of an auto_increment column is the size of the column:

Use a large enough integer data type for the AUTO_INCREMENT column to hold the maximum sequence value you will need. When the column reaches the upper limit of the data type, the next attempt to generate a sequence number fails. For example, if you use TINYINT, the maximum permissible sequence number is 127. For TINYINT UNSIGNED, the maximum is 255.

The limits of the integer types are:

TINYINT            - 127
UNSIGNED TINYINT   - 255
SMALLINT           - 32767
UNSIGNED SMALLINT  - 65535
MEDIUMINT          - 8388607
UNSIGNED MEDIUMINT - 16777215
INT                - 2147483647
UNSIGNED INT       - 4294967295
BIGINT             - 9223372036854775807
UNSIGNED BIGINT    - 18446744073709551615