there is no theoretical limit to the number of black holes that can exist. As for how many are known to exist at a time, there is no exact number either, as black holes are difficult to detect and some may not emit any detectable radiation.

The number of black holes that can exist at any given time is difficult to determine because they are not directly observable. However, it is believed that black holes are formed from the collapse of very massive stars or the merging of two smaller black holes. Based on these processes, it is estimated that there could be a very large number of black holes in the universe.

To date, astronomers have identified thousands of black holes in our galaxy and others through indirect means, such as observing their effects on nearby stars or the radiation they emit. However, it is likely that there are many more black holes that remain undiscovered, particularly smaller ones that are harder to detect.

It's also worth noting that there are different types of black holes, such as stellar black holes and supermassive black holes, which can have vastly different masses and properties. The number of each type of black hole is also difficult to determine with certainty, but current estimates suggest that there are likely millions of stellar black holes in the Milky Way alone, as well as numerous supermassive black holes in the centers of galaxies.
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