The theater that opened last is Blackfriars. Option 4 is correct.
The first theater opened was The Rose in 1587. Later on, The Swan opened in 1595 and the last one in opening its doors to the public was The Blackfriars in 1599 even thought it was buit in 1956 by Richard Burbage.
Blackfriars Theatre was the name given to two separate theatres located in the former Blackfriars Dominican priory in the City of London during the Renaissance. The second theatre dates from the purchase of the upper part of the priory and another building by Burbage in 1596, which included the Parliament Chamber on the upper floor that was converted into the playhouse