From the film Forbidden Planet (link to scene)
Push The Button wrote:
I read somewhere that 1701 was part of the registration number of MJ's airplane.
I think that's an urban myth. Jefferies has explained that he chose the number because it read more clearly on camera than other numbers.
Navigator: "Ship on course sir. We'll reach De-'C' point at 1701
(Should put to rest any claims they were not influenced consciously or sub-consciously by the film when GR was creating/producing 'Star Trek'.