A 2013 power-law model for Bitcoin’s price, first published on the Bitcointalk forum and left unadjusted for more than 13 years, has been extended to 2050 in recent analysis. The original formula continues to place current prices slightly below its long-term fair-value line of roughly $99,000, while outlining multi-year targets that reach several million dollars per coin.
On February 13, 2013, Bitcointalk user dacoinminster opened a thread titled “[GRAPH] This is not a bubble.” Bitcoin traded near $25 that week. The poster compiled available historical price points stretching back toward the genesis block of January 3, 2009, and asked Excel for a trendline. The software returned a power function rather than an exponential: Price = 4.41877086088824E-17 × (days since genesis block)^5.59806919936792.
The post argued that growth had always occurred on a logarithmic scale, that the 2011 spike stood out as a bubble, and that the price at the time appeared reasonable. The author added the explicit caveat that past performance does not guarantee anything.
Excel’s power-function fit produced a higher R-squared (0.7728) than a competing exponential fit (0.6990) on the data available then. The constants have never been refitted. Later analysis of the same unadjusted equation has shown it continuing to track the center of Bitcoin’s long-term log-log path through subsequent market cycles. The original forum post remains publicly accessible.
At 06:15 AM UTC on October 13, 2026, BTC was trading at $83,555 with a 24 hour trading volume near $32 billion, as per CoinGecko market data.
Current Positioning and Long-Term Projections
Recent posts by analyst Caffe’ Satoshi on X have applied the identical, unadjusted formula and extended the resulting curve forward to 2050. The model currently assigns a fair value near $99,000. Bitcoin has traded in the low-to-mid $80,000s in mid-October 2026, leaving it modestly below the line. Observations associated with the model note that periods spent below the curve have historically coincided with periods of accumulation.
The same extension produces the following central-path figures: approximately $251,000 in 2030, $830,000 in 2035, $2.2 million in 2040, $5.1 million in 2045, and $10.6 million in 2050. These values represent the middle of the long-term trajectory rather than projected cycle peaks or troughs. Cycle highs and lows have historically oscillated around the line, with the magnitude of overshoots appearing to moderate over time in the analysis presented.
The projections arrive against a backdrop of other institutional outlooks. Citigroup recently raised its 12-month Bitcoin target to $113,000 from $82,000, citing expected ETF inflows and a supportive macro backdrop.
Separately, Coinbase CEO Brian Armstrong has described $400,000 by 2030 as a reasonable long-term level. Bitcoin reached an all-time high near $126,000 in early October 2025 before declining to a cycle low near $58,000 in early July 2026, a drawdown of roughly 54% from the peak. Price has since recovered into the mid-$80,000 range.
The model remains a statistical description of historical price behavior rather than a fundamental valuation grounded in network effects, monetary theory, or adoption forecasts. Its continued alignment after more than 13 years of additional market data has drawn renewed attention among observers who track long-term Bitcoin price models.
The original poster’s caveat that past performance does not guarantee future results continues to apply, and the figures above should not be read as investment advice.
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