A spokesperson for the Bureau of Prisons said the agency would comply with all presidential orders. The Justice Department and DHS did not immediately respond to requests for comment.

Speaking to reporters Sunday, Trump called the potential reopening “just an idea I’ve had,” and he repeated his previous criticism of judges he said were seeking trials for “every single person that’s in our country illegally.”

Details on the administration’s potential plans for Alcatraz remain unclear. Rep. Nancy Pelosi (D-California), the former House speaker, dismissed the proposal Sunday as “not a serious one.”

Built on a small island in the San Francisco Bay, Alcatraz opened in 1934 as a “maximum-security, minimum-privilege” facility dedicated to holding the “most incorrigible inmates,” according to the Bureau of Prisons. It housed several infamous criminals, including gangsters Al Capone and George “Machine Gun” Kelly, but mostly held inmates who refused to conform to the rules of other federal penitentiaries as well as those who were considered dangerous or an escape risk.

Prisoners had only four rights: food, clothing, shelter and medical care. Everything beyond that — family visits, correspondence, access to books or recreational activities — was treated as a privilege to be earned, the Prisons Bureau website says. Alcatraz held less than 1 percent of the federal prison population of the time, with an average of about 260 to 275 inmates.

There were more than a dozen escape attempts from Alcatraz during the 29 years it was in operation. Several inmates were recaptured, some were shot and killed, and others drowned. The unknown fate of three prisoners who attempted to escape in the early 1960s — Frank Morris, Clarence Anglin and John Anglin — transfixed the nation and inspired the hit 1979 film starring Clint Eastwood, “Escape from Alcatraz.” The mystery of their whereabouts is one of the many stories that have spurred tourists to visit the island over the past five decades.

The facility was shut down in March 1963 because of steep operational costs, which were nearly three times more than any other federal prison, according to the Prisons Bureau.

One reason it was so expensive to operate was its offshore location. All supplies — including water — had to be transported by boat. To this day, Alcatraz has no electrical or water lines from the mainland, and fuel for electric generators has to be ferried to the island, according to the National Park Service.

John Martini, an Alcatraz historian, said there are too many unknowns to determine whether Trump’s plan for reopening the prison is practical. In particular, it’s unclear whether Trump wants to restore and expand the current cellblocks on the island or build a new facility.

One estimate suggested that the island needed $5 million in repairs in 1962, which would be equivalent to about $53 million today, without taking into account modern infrastructure needs, Martini wrote in an email.

Following the prison’s closure, the island was effectively abandoned. In 1969, a group of Native Americans — many of them student activists — started inhabiting the island and symbolically claiming it as land for all tribes in the United States. The federal government took measures to push them out over the next year and a half, including by shutting off electricity and cutting off water supplies.

Some activists eventually left, and law enforcement officers forcibly removed the last occupants in 1971. Alcatraz became a national park in 1973. It is visited by more than 1.2 million people annually, according to the National Park Service.