When Khan remerges and prepares to unleash his wrath in Star Trek II: The Wrath of Khan, he reminds Chekov of his origin in the episode “Space Seed,” saying, “the Enterprise picked up the Botany Bay, lost in space from the year 1996.” And as established in “Space Seed,” according to Spock, “In 1993, a group of these young supermen [Khan and his people] did seize power simultaneously in over forty nations.”
