What’s mysql’s “BETWEEN” performance over..?

As I recall, there’s no difference. But see for yourself if:

explain plan for 
SELECT * FROM `table` WHERE `unix_date` BETWEEN 1291736700 AND 1291737300

and:

explain plan for
SELECT * FROM `table` WHERE `unix_date` >= 1291736700 AND `unix_date` <= 1291737300

produce the same plans.

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