Yup. 12 miles. 91.1 says that Part 91 broadly applies "within the United States, including the waters within 3 nautical miles of the U.S. coast," and then goes on to say that certain sections apply all the way out to 12 miles. 91.117 is in the list of those that go to 12 miles. However, keep in mind that if airspace which falls under 91.117(c) is beyond 12 miles (trying to think whether that's possible, but too sleepy...), then you're going to have to comply with 91.117(c) even though you're better than 12 miles out.
I'd also point out a distinction within 91.117 that is important...
(a) Unless otherwise authorized by the Administrator, no person may operate an aircraft below 10,000 feet MSL at an indicated airspeed of more than 250 knots (288 m.p.h.).
(b) Unless otherwise authorized or required by ATC, no person may operate an aircraft at or below 2,500 feet above the surface within 4 nautical miles of the primary airport of a Class C or Class D airspace area at an indicated airspeed of more than 200 knots (230 mph). This paragraph (b) does not apply to any operations within a Class B airspace area. Such operations shall comply with paragraph (a) of this section.
(c) No person may operate an aircraft in the airspace underlying a Class B airspace area designated for an airport or in a VFR corridor designated through such a Class B airspace area, at an indicated airspeed of more than 200 knots (230 mph).
(d) If the minimum safe airspeed for any particular operation is greater than the maximum speed prescribed in this section, the aircraft may be operated at that minimum speed.
There's a reason that (a) says "the Administrator" and (b) says "ATC."
I believe that your local FSDO will tell you that, although you MAY fly at the minimum safe airspeed for your operation even if it is more than 250k (ala (d)), and that ATC can certainly authorize different speeds under subparagraph (b), ATC is NOT empowered to OK speeds above 250k below 10,000 feet. If you want to ignore the 250 below 10 rule and your operation doesn't require you to fly faster than 250, you're going to need a waiver from your local FSDO. The controller can't approve it. That's because "the Administrator" means the actual FAA Administrator or someone he/she (and actually, I think the reg still calls the Administrator "he...") delegates. This one has been delgated to Flight Standards, not ATC.
So when the assigned speed is 280 (or 380 or whatever), that means beyond 12 miles or above 10,000, unless your operation requires it. Of course, as always, I strongly suggest you get verification from the FAA on something like this. And if I've somehow gotten this wrong, tell me.
Dave