No, you don't. Just type in your registration number on the section on the N-400 where that information is asked. If you feel so worried about it, then on the day of the interview bring the printout of your SS registration, which you can print from the SSR site.
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.