WASHINGTON — The case that could transform privacy law in the digital era began with the armed robbery of a Radio Shack store in Detroit, a couple of weeks before Christmas in 2010. In the next three months, eight more stores in Michigan and Ohio were robbed at gunpoint.

The robbers took bags filled with smartphones. Their own phones would help send them to prison.

On Wednesday, the Supreme Court will consider whether prosecutors violated the Fourth Amendment, which bars unreasonable searches, by collecting vast amounts of data from cellphone companies showing the movements of the man they say organized most of the robberies.

Experts in privacy law said the case, Carpenter v. United States, No. 16-402, was a potential blockbuster.

“Carpenter could be the most important electronic privacy case of the 21st century,” said Jeffrey Rosen, the president of the National Constitution Center, a nonprofit group devoted to educating the public about the Constitution.