Dear Mr. Franklin,
Thank you for posting your request on History Hub!
Since you served in the Navy prior to 1971, we suggest submitting a GSA Standard Form 180 to NARA's National Personnel Records Center (NPRC), (Military Personnel Records), 1 Archives Drive, St. Louis, MO 63138-1002 in order to receive your service number. Please provide all of the information you have.
We hope this is helpful!