This is the number assigned to Alex, the protagonist of A Clockwork Orange, in Stanley Kubrick's film based on Anthony Burgess's novel.
In the novel, the number appears as 6655321. The six was dropped in the film, presumably to allow for faster reading. In the film it is pronounced very quickly: "Six double-five three two one!" again and again to remind the audience Alex is transforming from a boy to a little machine, a clockwork.