How long does it take for PR-10,000 to work, and for the water to be safe to swim in again afterward?
The short answer is you can swim as soon as the water is clear enough to see the main drain.
PR-10,000 is NSF/ANSI Standard 50 Certified, meaning when used as directed, it is nontoxic and nonhazardous. The reason for waiting after PR-10,000 is not for health reasons, but for visibility/safety reasons. Cloudy (or turbid) water can obstruct your view of the entire pool, especially the bottom. Severe turbidity is a drowning hazard.
So this question is simply a matter of water clarity so you can see everything going on. If the water is too cloudy to see the bottom, someone (or something like a snake or snapping turtle) could be down there. Do not swim in murky water.
How to clear the water faster after using PR-10,000
Since PR-10,000 clouds the water when phosphates are present, one of the common questions we get is how to clear the water faster. There are essentially two answers: improve filtration, and accelerate the dropout of the dust.
Improving filtration can include adding something like Fiber Clear to your sand filter. Cartridges and DE filters tend to be able to capture PR-10,000 dust in one pass.
Accelerating the dropout of dust is most easily accomplished by removing oils and organics from the water with CV-600 or CV-700 enzymes. Oils and organics float, while dust wants to fall. If the sticky oils and organics adhere to the dust (which they often do), dust can stay suspended in the water much longer because it cannot fall as easily (if at all). Using enzymes accelerates the dropout of dust, and will clear the water faster.