Dozens of entrepreneurs, made newly wealthy by blockchain and cryptocurrencies, are heading en masse to Puerto Rico this winter. They are selling their homes and cars in California and establishing residency on the Caribbean island in hopes of avoiding what they see as onerous state and federal taxes on their growing fortunes, some of which now reach into the billions of dollars.

And these men — because they are almost exclusively men — have a plan for what to do with the wealth: They want to build a crypto utopia, a new city where the money is virtual and the contracts are all public, to show the rest of the world what a crypto future could look like. Blockchain, a digital ledger that forms the basis of virtual currencies, has the potential to reinvent society — and the Puertopians want to prove it.

For more than a year, the entrepreneurs had been searching for the best location. After Hurricane Maria decimated Puerto Rico’s infrastructure in September and the price of cryptocurrencies began to soar, they saw an opportunity and felt a sense of urgency.

So this crypto community flocked here to create its paradise. Now the investors are spending their days hunting for property where they could have their own airports and docks. They are taking over hotels and a museum in the capital’s historic section, called Old San Juan. They say they are close to getting the local government to allow them to have the first cryptocurrency bank.

“What’s happened here is a perfect storm,” said Halsey Minor, the founder of the news site CNET, who is moving his new blockchain company — called Videocoin — from the Cayman Islands to Puerto Rico this winter. Referring to Hurricane Maria and the investment interest that has followed, he added, “While it was really bad for the people of Puerto Rico, in the long term it’s a godsend if people look past that.”

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All across San Juan, many locals are trying to figure out what to do with the crypto arrivals.

Some are open to the new wave as a welcome infusion of investment and ideas.

“We’re open for crypto business,” said Erika Medina-Vecchini, the chief business development officer for the Department of Economic Development and Commerce, in an interview at her office. She said her office was starting an ad campaign aimed at the new crypto expat boom, with the tagline “Paradise Performs.”

Others worry about the island’s being used for an experiment and talk about “crypto colonialism.” At a house party in San Juan, Richard Lopez, 32, who runs a pizza restaurant, Estella, in the town of Arecibo, said: “I think it’s great. Lure them in with taxes, and they’ll spend money.”

Andria Satz, 33, who grew up in Old San Juan and works for the Conservation Trust of Puerto Rico, disagreed.

“We’re the tax playground for the rich,” she said. “We’re the test case for anyone who wants to experiment. Outsiders get tax exemptions, and locals can’t get permits.”

Mr. Lopez said the territory needed something to jump-start the economy. “We have to find a new way,” he said.

“Sure then, Bitcoin, why not,” Ms. Satz said, throwing up her hands.

Mr. Lopez said he and a childhood friend, Rafael Perez, 31, were trying to set up a Bitcoin mine in their hometown. But electricity has been inconsistent, and mining even a single Bitcoin takes a lot of power, he said.