On a large radial engine, priming may be done without any dedicated line to a particular cylinder. It used to be standard practice in the winter time to flood the supercharger while cranking until fuel ran out of the drain, with a five gallon bucket below to catch the fuel. Apply spark, begin advancing the mixture and cracking the throttle; the priming was simply raw fuel dumped into the supercharger.
Fuel doesn't need to flow to every cylinder to prime, as the fuel source is the carburetor. This is true whether it's a small horizontally opposed engine, or a large radial. The point of priming is to get the engine to start picking up the load of the starter and to be self-sustaining. Every cylinder will come to life on its own; regardless of the engine, mixture and fuel and ignition is different in every cylinder. Not all will fire off at the same time.
Priming every cylinder can result in a fire. Typical primers in small engines in light piston singles are often plunger type primers that move a very small amount of fuel. That fuel is more useful and effective if directed to one or two cylinders, than spread among multiple cylinders. Priming all cylinders with such a small amount of fuel might result in multiple plungers of fuel being required, and less precise application of the fuel (and the possibility of overpriming.
It should also be noted that under certain circumstances, an unlocked primer can result in a rich fuel situation and spark plug fouling (by drawing fuel through the primer), whereas a failure in a primer line can result in a lean cylinder operation, or a fire. It makes sense to limit the number of primer lines to those necessary to assist engine start. Some cylinders during start operate more lean than others due to intake design, distance from carburetor, etc.
In engines that are fuel injected, each cylinder is primed, in some cases, using a boost pump and normal fuel flow, and in others through dedicated priming lines to one or two cylinders only.
In a previously reply, someone mentioned pumping the throttle, which on certain installations, invokes an acceleration pump. The acceleration pump adds additional fuel, usually as a spray, during throttle advancement, helping to reduce engine stumble, or a lean mixture. Some times this accelerator pump is called for as part of the starting procedure, but in many cases, it's used incorrectly as a means of "priming the engine." It's a good example of the need to know one's aircraft, systems, and procedures. What's true of one aircraft model or engine installation is not necessarily true of another, even when the same engines are used.