What fixed wing, and motor, plane or jet, has the largest range between its minimum and its maximum airspeed by which it can safely fly for prolonged periods?
The radio-controlled model sailplane that recently exceeded 540 mph while dynamic soaring has to be a contender. Minimum speed in this flight (immediately after launch) may have been as low as 10 mph, which probably could have been sustained by staying on the front side of the ridge.
Link to You Tube video--
Though any plane capable of routine flight at 0 mph would automatically win I suppose-- e.g. pretty much any hang glider or sailplane given the right conditions.
Or did you mean airspeed? The radio-controlled sailplane in the video may well be one of the top contenders.
The highest range of speeds will basically match up with a list of highest top speeds... take ~200 knots off of the top speed of the SR-71, and you probably have your answer. Or if the question is for currently flying jets, unless your #1 and #2 have top speeds so close that the delta in their landing speeds is greater than the delta in their max speeds, #1 is still first, #2 is second, and so on.
As for ratio, if VTOL jets aren't ruled out by the "fixed wing and motor" constraint (and actually, the nozzles pivot, not the motor, in most cases), you have to deal with an infinite ratio for a min speed of zero.
The dynamic soaring answer is inventive (and that video is amazing), and nothing else is likely to touch a 54X ratio (!!!), but the "and motor" constraint probably rules that one out too.
Even with VTOL ruled out, lowest landing speed is probably going to trump everything else; the garden-variety STOL single-engine prop with a range of 30-150 gets a ratio of 5x without even trying; the number of jets that land at 100 and reach 500 knots indicated is awfully small.
Oh, and for one more complication, are we talking KIAS or KTAS at the high end? That can make a difference too!
The Space Shuttle (or "Space Transportation System (STS)") reportedly re-entered the atmosphere from low Earth orbit at about 17,500 mph, and touched down as low as 214 mph, for a ratio of 81.77.