Physicist Giovanni Santostasi says Bitcoin’s long-term price trajectory is not 
best understood as an S-curve, speculative bubble, or simple exponential 
trend, but as a power law similar to patterns found in cities, biology and 
other natural systems. Speaking with Nathalie Brunell on the May 12 episode of 
the Coin Stories podcast, the director of the Scientific Bitcoin Institute 
argued that Bitcoin’s historical data points to roughly $1 million per coin in 
about eight years and $10 million in roughly 20 years. Santostasi explained 
his Bitcoin Power Law thesis in detail. His core claim is that Bitcoin’s price 
has followed a nonlinear mathematical relationship with time since the 
network’s early trading history. In his formulation, Bitcoin’s price is 
proportional to time raised to a power of roughly 5.8 to 5.9, often rounded to 
six. That exponent, he said, is not just a curve-fitting artifact but a 
“fingerprint” of the system. “With bitcoin we found a similar relationship 
where the price is proportional to the time,” Santostasi said. “So the age of 
bitcoin, how many years, you can measure it in days, you can measure it in 
years. And then you take the power and that power is 5.8.” Bitcoin Is Growing 
Like A City He acknowledged that Bitcoin remains volatile in the short term, 
with wars, crises and liquidity shocks producing large deviations. But he 
argued those moves are oscillations around a deeper trajectory. Related 
Reading: Bitcoin Exits ‘Panic Zone,’ But Capital Inflows Remain Weak According 
to Santostasi, Bitcoin’s power law currently implies a central price level 
around $120,000, while the market has recently traded below that level. He 
said the lower statistical band, which he described as a kind of floor, is 
currently near $56,000 to $57,000. He also cited a correlation coefficient of 
0.97 for the power law fit, arguing that only around 3% of Bitcoin’s long-term 
price variation is not described by the model. A key part of Santostasi’s 
thesis is that Bitcoin behaves more like a networked organism than a corporate 
asset. He compared Bitcoin to cities, which he said grow through bottom-up 
interaction and tend to endure far longer than corporations. Cities, in his 
telling, follow power laws because their value emerges from networks of people 
freely interacting, building and exchanging information. “Bitcoin is like a 
city,” Santostasi said. “Bitcoin is like tooth and nails and thorns and 
shells, these natural forms. To me, if you can simplify this message — and 
because it’s not poetry, it’s science actually, it’s based on data — it is one 
of the most convincing orange-pilling arguments that you can make.” The 
physicist contrasted that with exponential growth, which he associated with 
systems that expand quickly but eventually hit resource limits. He cited 
corporations as an example, saying most die within 150 years, while cities 
such as Rome can persist for millennia. That distinction led to one of the 
more provocative implications of the discussion: corporations backed by 
Bitcoin, Santostasi suggested, could theoretically become more city-like in 
their durability. “This is one of the reasons why I want Saylor to start 
adopting this language of a power law,” he said, referring to Strategy 
executive chairman Michael Saylor. “He could say exactly that. We are turning 
corporations into cities.” Related Reading: Arthur Hayes Says The Bitcoin Bull 
Market Has Begun: $126,000 Is Next Santostasi also argued that Bitcoin’s 
address growth supports the thesis. He said Bitcoin addresses have grown as a 
power law with time cubed, while price reacts to address growth roughly 
according to a square relationship, similar to Metcalfe’s Law. Combining those 
two relationships, he said, produces the observed price relationship of time 
to the sixth power. “If you double the number of addresses, the price goes up 
to four,” Santostasi said. “If you triple it, it goes to nine. So it’s a power 
law with the square.” That framework also leads Santostasi to reject the 
common view that Bitcoin adoption should be modeled primarily as an S-curve, 
like refrigerators, televisions or other consumer technologies. Those 
products, he argued, are not networks in the same way Bitcoin is. Bitcoin’s 
social, monetary and technical layers make it closer to the internet or a city 
than to a household appliance. Still, Santostasi stopped short of presenting 
the forecast as certainty. Asked how confident he is that Bitcoin will reach 
roughly $1 million per coin in about eight years and $10 million in roughly 20 
years, he put the probability near 90%, while leaving room for failure 
conditions. He said continued capital inflows, larger institutional 
participation and new pools of capital are necessary for the path to remain 
intact. At press time, BTC traded at $80,963. Featured image created with 
DALL.E, chart from TradingView.com

Here’s When Bitcoin Could Reach $10 Million Under Power Law Model

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Cryptocurrency price in INR

Market Overview