Have you double checked the number, looking at the butt of the gun? According to the info below, 1971 or 1972. By the way, that would place this gun in the pre-1980 S&W forum!
INFO ON MODEL 36 SERIALS:
Early J frame serial numbers
For models 36, 37, 38, 49, 50 and pre model number versions.
1950 = start at 1
1952 = 7369 - 21342
1953 = 28916
1955 = 55050 - 75000
1957 = 117770 - 125000
1962 = starts at 295000
1969 = ends at 786544
J serial Prefix serial numbers.
For models 36, 37, 38, 49, 50.
1969-1970 = J1 - J99999
1971-1972 = 1J1 - 999J99
1973-1974 = J100000 - J250000
1975-1976 = J250001 - J370000
1976-1977 = J370001 - J610000
1977-1978 = J610001 - J670000
1979-1980 = J670001 - J760000
1981 = J760001 - J915400
1982 = J915401 - 1J18600
1983 = 1J18601 - 1JXXXX
1955 - 4 screw side plate ends
1957 - stamping of model number at 125000
1966 - flat latch ends
1968 - diamond grips end
1975 - heavy barrel standard
1982 - end pinned barrel
