Comments - Data Sampling: Techniques for Efficiently Finding a Random Row
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There is no hidden "row number". A UDF can't do better than use the PRIMARY KEY. For MyISAM, the location of a row is the byte offset into the .MYD; there is no list of these to probe. For InnoDB, one should provide a PK; if you don't there is an inaccessible 6-byte number that acts sort of like AUTO_INCREMENT; again, not practical.