I went in March 1971 (US Army - RA) and never had anything but my SS#.
I didn't realize they had switched over while I was still in. Maybe the Army switched over before the Navy did.
I enlisted in 1966. At the time, all Navy serial numbers were in the form: Bxx-xx-xx. At that time, Army enlistees got "RA" followed by some numbers; draftees got "US" followed by some numbers.