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The wp-config-sample.php for WordPress 2.5.1 most DEFINITELY has that constant (line 13). Maybe you upgraded and used an old wp-config.php. You would never see the new constants unless you updated a wp-config-sample.php with your old database details.

// Change SECRET_KEY to a unique phrase.  You won't have to remember it later,

// so make it long and complicated.  You can visit https://api.wordpress.org/secret-key/1.0/

// to get a secret key generated for you, or just make something up.

define('SECRET_KEY', 'put your unique phrase here'); // Change this to a unique phrase.