Industry estimates suggest the company mines just over 5 percent of all Bitcoins, although no one would say how much was being mined here.

But competitors in Georgia reckon it was a fortune. Vakhtang Gogokhia, the chief executive of Golden Fleece, a small cryptomining start-up, said he was pulling in around 10 Bitcoins a month using one megawatt of energy, enough to light 1,000 homes. Bitfury says it constantly consumes at least 45 megawatts of energy, though Mr. Gogokhia suspected it was more.

Critics say the government, by subsidizing operations like Bitfury, is ripping off taxpayers by forcing them to foot the bill for well-connected companies.

Zurab Tchiaberashvili, a lawmaker from European Georgia, the largest opposition party in Parliament, said the government’s generosity toward Bitfury had deprived Georgians of millions in tax revenue.

“It’s a huge conflict of interest,” he said.

Mr. Urumashvili brushed off such concerns. “Bitfury has given our country many things, including a path to the future,” he said. “When you have a ticket to get onto the world map,” he added, “you should use it.”

Still, as Bitcoin prices highlight the uncertain nature of cryptocurrencies, the government isn’t putting all of its eggs in one basket.

“Georgia is interesting for cryptocurrency miners,” said Mr. Kobulia, the economy minister. “But would it be a major source of our economic growth? Maybe not.”