They are the 6-foot-5in twins whose quarrel with Mark Zuckerberg inspired a movie

Even in the early morning, the giant Pacha club in Ibiza was getting up. The lasers glittered over the sweaty crowd, choosing Naomi Campbell, Kate Moss and Paris Hilton as celebrities, while the music resounded.

Sinking on the dancefloor, dodging to avoid the half-naked acrobats swaying from the ceiling, a giant figure of a man – a well-educated and educated half-millionaire at Harvard. Then, as if it was not strange enough, the giant was joined at the bar by a doppelganger, a second athlete with a square jaw. Both appeared to be out of the pages of a Ralph Lauren catalog – two Great Gatsby characters transported into the heart-rending chaos of an Ibiza nightclub. Tyler Winklevoss and his identical twin brother, Cameron, were already famous for their long battle with Facebook billionaire Mark Zuckerberg and his dramatization in The Social Network, the Hollywood film about the site's creation. And that is the moment they were getting ready from that they were recognized. A muscular guy with wild eyes and a strong Brooklyn accent approached them. He seemed to know their wealth and their story and said that he had a great idea. The twins were not interested – until the stranger in Brooklyn accent said something that hit him hard: "Facebook is no longer the revolution. Facebook is the establishment. '

"So, what's the idea?" Asked Cameron. "Another social network?"

The guy pulled out a dollar bill from the pocket of his shirt.

"The oldest social network in the world," he smiled.

Tyler and Cameron Winklevoss still had only 31 years, but they had money to invest. A lot. It was only a year since Zuckerberg paid them $ 65 million following one of the most famous legal battles on the planet. They have always been an unlikely match. Zuckerberg was nerdy and socially awkward; The Winklevoss brothers were two elite East Coast celebrities who, already with a "house-sized brain," would become members of the 2008 US Olympic Rowing Team in Beijing. .

Two years later, they competed for Oxford in the boat race. Still, it's Zuckerberg who was making a real name. Originally obscure and disputed, it was transforming Facebook into one of the most powerful companies in the world, with 2.3 billion users.

The problem though was this: the Winklevosses believed that the idea of ​​such a network belonged to them and that Zuckerberg had indeed stolen them. In 2011, after years of quarrels – which included Zuckerberg's strange threat of "spitting in the ear" – they came to a settlement. Zuckerberg could certainly afford it, his fortune being estimated at $ 15 billion.

For the twins, it was a new start. It was a chance to emerge from the poison battles of the last four years and, as author Ben Mezrich explains in a fascinating new book about the brothers, she opened up the prospect of a revenge in its most beautiful known form – success.

Yet, as Mezrich reveals, Zuckerberg cast a drop shadow on something the twins would discover for themselves as they begin to explore the strange world of the tech boom. On one occasion, for example, they traveled to Silicon Valley, California, to meet a technical assistant looking for investors. It turned out that their appointment was in a burger bar with a young man with red hair and nervous, called Jake. It was the kind of place where whizkids and technology geeks came to eat and chat between Facebook's headquarters and Google, Apple and PayPal nearby.

Yet by the time they sat down, Jake had already become cold. No one in Silicon Valley looking for a seed capital would dare to take investment funds "from the two guys that Zuckerberg hates more than anyone in the world," he explained. "You should be happy that this place serves you even a burger." The Winklevoss twins knew then that they needed something quite separate from the gigantic guilds of the valley, something quite brilliant. This would be the beginning of their bet with the dark new world of cryptocurrency – and their ascent to a new level of fame and fortune based on such a powerful invention that it could even overshadow Zuckerberg's billions.

Google was born in a garage. PayPal was first launched in a pancake restaurant in Silicon Valley. And the Bitcoin investment revolution started in a nightclub in Ibiza at 3am in July 2012.

The muscular guy with the big idea was a man named David Avar. When they were all three at the Blue Marlin Beach Club – where a lounge chair costs £ 350 for an afternoon – he was sober. And while the twins were listening, everything was starting to make sense. With Facebook, you can create friendship links with anyone in the world. With Skype, you can talk to anyone in the world. But try to move money, and the banks would do it at a snail's pace and shrink themselves.

Money was always controlled by institutions formed centuries before the Internet. Bankers, governments, bureaucrats: all had a say in what you did with your money – your money, not theirs.

Avar explained that it was time for money to become a cryptocurrency without human authority and without a seat. It would be a currency of numerical data and pure mathematics, a currency that evolves at the speed of electricity. The implications were staggering.

Tyler and Cameron were cautious, replying that Bitcoin was just a gamble and that little enriched playing. "True," Azar said with a smile. "But you become rich if you own the casino."

Even today, the entire Bitcoin business looks like a crazy bet. But for the Winklevoss twins, widely read in economics, Bitcoin looked like something else. Originally created in 2009 by someone who calls himself (or themselves) Satoshi Nakamoto, Bitcoin is a digital currency that allows people to send or receive money from people around the world. money on the Internet. No identity is revealed or required, only encrypted "addresses". It is also "decentralized", which means in a sense that there is no human being in charge. It is rather governed by the laws of mathematics and processed via computers.

The Winklevosses did some research. Each figure of establishment they spoke to rejected Bitcoin as a scam, a Ponzi scheme. But what about the money, did they answer? No longer being tied to gold, any government can print as much as it wants. Was not it a ponzi scheme? On the other hand, the total number of Bitcoins had been fixed forever at 21 million by its dark creator. It would never change.

Then the brothers started meeting strangers, including 22-year-old Charlie Shrem, who smokes and makes the pot smoking. Genius of technology, he always lived in the basement of his mother in New York and believed in Bitcoin with passion.

They met an obese recluse called Mark Karpeles, who managed the Bitcoin exchange himself – who implemented the transactions. They met passionate libertarians who saw Bitcoin as a way to regain power in the state.

Cryptocurrency was also becoming a favorite of criminals, mainly on the so-called Dark Web. Cryptocurrency was the Wild West. But for Tyler and Cameron, the arguments were compelling. It was a good calculation. After all, no one escaped the money simply because criminals liked to use it. Same thing for Bitcoin.

Shortly after, they invested $ 800,000 in BitInstant, an electronic money buying and selling platform, and started buying massive amounts of Bitcoins. They started learning about cybersecurity. They were working on "cold" computers bought new and never connected to the Internet. The twins used them to set up accounts and store data. They bought a 16-sided die to generate random numbers for passwords.

On one occasion, Cameron took a load to a laptop to make sure they did not leave fingerprints. Soon, the Winklevosses would put $ 11 million into the virtual currency, which then brought in about one percent of all existing Bitcoins.

Bitcoin was considered a scam all over the world, but its value was growing. And then, in 2013, something happened to radically change the way the world saw cryptocurrency. When the European Union bailed out the Cypriot economy, it did so on the condition that the government imposes a huge tax on all bank holdings of more than € 100,000 (£ 88,150). The EU called it a tax, but for others, it seemed like a staggering robbery of private bank accounts – many of which were held by Russians – and on a colossal scale. It was just as the Bitcoin libertarians had warned: we could not trust governments and banks.

The price of a single Bitcoin unit has gone from 80 to 260 dollars in a few weeks.

Then, in April 2013, the New York Times published a title that shook the heart of the brothers: "Never mind Facebook: the rule of Winklevoss Twins in Digital Money." It was a dream come true for the brothers – full. Among the most skilled American leaders, they share an interest in the great dark haired beauties, with models Amanda Salvato, Natalia Beber and supermodel Irina Shayk appearing on their arms. They own separate luxury apartments in Manhattan, but regularly stay together, and share the property of a contemporary 18 million pound manor house located in Hollywood Hills.

Bitcoin became even respectable. Richard Branson has invested in another Bitcoin processing platform called BitPay. "One million dollars is not cool," said Tyler Winklevoss now. "You know what's cool? A billion dollars … in Bitcoin."

The brothers still have a long way to go to match their enemy Zuckerberg, estimated at nearly $ 69 billion. Even so, their 1% stake in all Bitcoins amounts to approximately £ 1,323 million, making it the world's first known Bitcoin billionaire. They also set up a cryptocurrency trading company called Gemini, valued at around one billion.

Passionately believing in the future of cryptocurrency, Tyler and Cameron claim that Bitcoin is, in fact, "gold 2.0", another form of investment that is immune to crises and economic crises. Just yesterday, this amazing story was perhaps the strangest: it was revealed that the Winklevoss twins had been approached by a major personality from Silicon Valley to collaborate on launching a new cryptocurrency, a digital coin that will be linked to the value of the US dollar. The figure in question is Mark Zuckerberg. For more than a year, a secret Facebook unit is working on the project, aimed at creating a usable currency on Facebook, WhatsApp, Instagram and beyond. Apparently called GlobalCoin, it should be launched next year.

The first commercial transaction involving Bitcoin took place on May 22, 2010, when a computer programmer in Florida called Laszlo Hanyecz paid 10,000 Bitcoins for two pizzas because he liked to have some spare pizza for nibbling the next day.

Ten thousand Bitcoins were worth about $ 30, so $ 15 per pizza with home delivery was about right.

A young student accepted the offer and the pizzas were duly delivered. If Hanyecz had retained these Bitcoins, today they would be around £ 62,800,000.

Even Zuckerberg, the eighth richest man in the world, has noticed. But this time is the Winklevoss advantage.

• Bit Milliardaires Bitcoin by Ben Mezrich is published by Little, Brown for £ 20.