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Primecoin is a cryptocurrency that uses a novel proof-of-work system based on finding prime number chains rather than solving arbitrary computational puzzles, making its mining process mathematically productive. The blockchain simultaneously serves as a record of transactions and a searchable database of prime numbers, combining cryptocurrency security with scientific contribution. This unique approach allows miners to contribute to mathematical research while earning XPM rewards, distinguishing it from other cryptocurrencies that use traditional proof-of-work mechanisms.