SAN JUAN, P.R. — They call what they are building Puertopia. But then someone told them, apparently in all seriousness, that it translates to “eternal boy playground” in Latin. So they are changing the name: They will call it Sol.

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.