There's more than one state that has the most prisons.
The states however with the most prisons which are 35 plus prisons in each state are Texas, Georgia, Florida, California, Ohio, Illinois, Virginia, North Carolina and New York.
The other states have fewer prisons which are, Kansas, Oklahoma, Missouri, Nebraska, Colorado, New Mexico, Arizona, Nevada, Wyoming, Montana, Washington, North Dakota, South Dakota and other states.
Texas and Florida seem to have the most prisoners in the USA.
Wikipedia has a map that shows the states with the most prisons.
https://en.wikipedia.org/wiki/Lists_of_United_States_state_prisons
Kansas has around 9,000 to 12,000 prisoners and others in jails.
It's estimated that Kansas has around 17,000 people incarcerated in their jails and prison systems.