Satoshi, the smallest unit of Bitcoin, is finite and cannot be divided further. This is a key feature of Bitcoin’s design, as it limits the total supply of the cryptocurrency and helps to prevent inflation
Bitcoin’s remarkable growth has spurred inquiries into its mathematical foundations. This study explores the finite nature of Bitcoin’s unit of account, the satoshi. Using a novel mathematical theorem, we demonstrate that the maximum number of satoshis is subject to natural logarithmic constraints. This finiteness, inherent to Bitcoin’s design, has significant implications for the cryptocurrency’s long-term price dynamics and the viability of proposed monetary use cases. Our analysis quantifies the scarcity of satoshis, revealing the extent to which the supply is constrained and highlighting the potential role of satoshis as a store of value.