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Primecoin is an innovative cryptocurrency, a form of digital currency secured by cryptography and issued through a decentralized mining market. Derived from Satoshi Nakamoto's Bitcoin, Primecoin introduces an unique form of Proof-of-Work based on prime numbers. The innovative prime Proof-of-Work in Primecoin not only provides security and minting to the network, but also generates a special form of prime number chains of interest to mathematical research. Thus primecoin network is energy-multiuse, compared to bitcoin. Primecoin network searches for special prime number chains known as Cunningham chains and bi-twin chains. The distribution of these prime chains are not well-understood currently as even for its simplest case twin primes their infinite existence is not proven.