Sorry, I should have been clearer: what I said also applies to "serial number". If you are asking for the word-for-word meaning, then "under" is ok; in context however it would normally not be translated. A lot of Google hits for "under serial number xxxxx" seem to mean "με αύξοντα αριθμόν χχχχχ"
But how shall men meditate in that, which they cannot understand? How shall they understand that which is kept close in an unknown tongue?
THE TRANSLATORS TO THE READER
Preface to the King James Version 1611