What is the ceiling to prohibited space P-47 (or any other P-zone)? On the Dallas-Fort Worth sectional, notice one of the few permanently Prohibited airspace zones west of the Mississippi; P-47, around the PanTex nuclear plant in Amarillo, just northwest of Husband Intl (AMA) and within the outer cylinder of its Class C space.

Now, that zone is directly in the path of AMA's longer runway, 4/22, and Victor routes including V12-280 extend directly away from the PNH VORTAC at AMA right over the top of it.

That leads me to think that either P-47 has a ceiling above which airliners are allowed to operate, or else AMA Approach and Fort Worth Center via Amarillo RCO have a dickens of a time routing incoming traffic when the winds indicate use of runway 4/22. The outer Charlie cylinder begins at 4800 feet, but the chart also clearly states that P-47 is excluded from AMA's class C space where they overlap. That leads me to think that this P-space extends to Jupiter, and all flight traffic including AMA arrivals/departures (it's not a big town, but it's not exactly BFE either in part because of Pantex) have to maneuver specifically to avoid P-47.

So, to confirm, is there any altitude at which you can overfly P-47, or in more general terms any P-zone? 

It seems kind of silly for many P-zones, including this one, to extend all the way to space, as beyond a certain altitude if nothing else it becomes impractical to dive straight down into the facility under protection. But, if that's the law...
Special Use Airspace is defined by boundaries in all three dimensions1. The horizontal boundaries are depicted on the chart as you describe. The vertical boundaries are in the sidebar of the chart:



You can see here that P-47 exists from the surface (because there's nothing before the "TO") up to 4800 MSL. KAMA is at at 3607 MSL, so P-47 ends 1200' above the airport surface. At a little more than 5 NM away from the airport (measuring on the sectional), that's about 240 ft/NM climb: well within the performance capabilities of almost every powered aircraft. Overflights on the victor airway obviously have no problem at all.

This is used for allowing traffic where it might otherwise not be possible: Consider P-40 and R-4009, above Camp David in Maryland. When the President is not in residence, R-4009 lies exactly on top of P-40. P-40, from the surface to 5,000, is a no-fly zone. R-4009, from 5,000 to 12,500, can be transited with ATC permission.

(1)There's always an exception: see R-2933, over Cape Canaveral: 5,000 to UNLIMITED.