JESS: Sign this. [hands him a piece of paper]
LUKE: The registration?
JESS: I’m still a minor.
It’s now late October to early November, and Jess says he still hasn’t turned eighteen yet, which means his birthday must be either in November or December, making him a month or two younger than Rory.
Yet when Jess moved to Stars Hollow in September 2001, Luke said he was seventeen, meaning his birthday had already occurred by then. Either he has a movable birthday (like Rory), or Luke meant that he would turn seventeen within that calendar year. Parental figures love rounding their kids’ ages up on this show.
The Annotated Gilmore Girls 