How many are? That should be the question, and Wikipedia has the answer - 19.1% of federal inmates are "housed" in private prisons. That's one in five, and growing.

"Stock prices for CCA and GEO Group surged following Donald Trump's victory in the 2016 elections.[39][40] On February 23, the DOJ under Attorney General Jeff Sessions overturned the ban on using private prisons. "     https://en.wikipedia.org/wiki/Private_prison