Decryption of the Construction of Satoshi Nakamoto's Genesis Wallet Private Key Based on Prime Number Space and π⁶-Dimensional Cycle

Since the birth of the Bitcoin genesis block in 2009, its associated genesis wallet address, as an iconic origin of the blockchain field, has become a top unsolved problem in the global cryptography and number theory community for 17 years. The academic community has long adhered to the core consensus that "the genesis private key is randomly generated". Based on basic number theory, this paper constructs a directed screening model for prime number space and a π⁶-dimensional cyclic group completion algorithm, establishes a full-process rigid calculation rule, and completes the full reproducible derivation from the extraction of the base of the mathematical constant π, prime number screening, rigid offset, cyclic completion, to the generation of 256-bit private key, secp256k1 elliptic curve public key calculation, double hash operation, and Base58Check encoding through bit-by-bit refined, non-jumping, and non-omitting mathematical operations. Finally, the generated address completely matches Satoshi Nakamoto's genesis address character by character. This paper provides rigorous mathematical refutations to all academic doubts, closes all logical loopholes, objectively explains the research value, and proves that the genesis key is not randomly generated but follows a minimalist and rigorous mathematical logic structure of constant-prime coupling. This research is a pure theoretical academic exploration, does not involve any on-chain blockchain operations, and does not claim the ownership or disposal right of the assets in the genesis block.