The 40th century is a one-hundred year period of time that spans the years 3900-3999. Since this takes place soooooo far in the future, obviously all references to 40th century in media relate to the science fiction genre.
The most prominent film franchise to deal with the 40th century is the Planet of the Apes film series. Although the first two films in the series, Planet of the Apes and Beneath the Planet of the Apes use the 40th century as their central setting, there is some discrepency as to which year each film takes place.
In Planet of the Apes, the character of George Taylor tells his fellow astronauts Dodge and Landon that the time-meter on their ship's instrument panel establishes them as having landed in the year 3978. However, in Beneath the Planet of the Apes, which takes place only a short time later (days or weeks), the character of John Brent tells the dying Donovan Maddox that they have passed through a Hasslein Curve and landed in the year 3955.