Note also that the modern "UTC epoch" is January 1, 1972. Before this date, UTC used a different second than TAI: [1]
> As an intermediate step at the end of 1971, there was a final irregular jump of exactly 0.107758 TAI seconds, making the total of all the small time steps and frequency shifts in UTC or TAI during 1958–1971 exactly ten seconds, so that 1 January 1972 00:00:00 UTC was 1 January 1972 00:00:10 TAI exactly, and a whole number of seconds thereafter. At the same time, the tick rate of UTC was changed to exactly match TAI. UTC also started to track UT1 rather than UT2.
So Unix times in the years 1970 and 1971 do not actually match UTC times from that period. [2]
[1] https://en.wikipedia.org/wiki/Coordinated_Universal_Time#His...