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Primecoin uses prime number generation to improve Bitcoin's PoW protocol.Ravencoin wants to create a blockchain that will improve the tracking of digital asset ownership.

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Primecoin is a cryptocurrency based on finding prime numbers. Identifying prime numbers plays a central role in cryptography. Primecoin's unique Proof-of-Work (PoW) consensus mechanism is able to increase transaction speeds and improve energy efficiency.
The network searches for special prime number chains known as Cunningham chains and bi-twin chains, which are of interest in mathematical research.

Ravencoin is a blockchain created by the owner of Overstock.com. It is a use case specific blockchain for the declaration of ownership of digital assets. Ravecoin is a fork of Bitcoin, and was originally funded by Medici Ventures, a blockchain investment fund owned by Overstock.com.
Ravencoin's name is inspired by the use of Ravens in sending messages, and its blockchain is designed to carry statements of truth about who owns what asset. The developers created a new consensus algorithm called x16r to solve the problems of centralized ASIC mining. The algorithm is unique in that it consists of 16 different hashing algorithms whose order are randomly changed.

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