current_time(‘timestamp’) seems to be different from the real current time

The output of current_time('timestamp') should be

time() + ( get_option( 'gmt_offset' ) * HOUR_IN_SECONDS );

according to WP 3.5.2, so you should check your get_option( 'gmt_offset' ) settings.

Also current_time('timestamp', 1 ) should give you time().

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