What problem does this service solve?

Primecoin uses prime number generation to improve Bitcoin's PoW protocol.Crown is a European focused cryptocurrency.

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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.

Crown is a cryptocurrency and development platform with a Proof-of-Work (PoW) consensus mechanism, and an emphasis on community governance. It combines some of the technical capabilities of Bitcoin and Dash. It is currently merge mined with Bitcoin, but is developing a new consensus model called Crown Atomic.

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