The US has by far the largest number of prisons (4575); as well as the most prison inmates (2.2 million)---unless you count North Korea, which IS a prison of 25 million inhabitants. 

Saudi Arabia is currently executing more people as a function of its penal system than any other sovereign country. Other entities such as Boko … Read more

Which country executes the most would be hard to say, for sure ... Since many countries ruled by tyrants or corrupt governments execute thousands of people a year - but most of them are listed as "missing" since the government doesn't actually admit to killing them.