What problem does this service solve?

Primecoin uses prime number generation to improve Bitcoin's PoW protocol.ZClassic is a fork of ZCash. The key differences are that ZClassic doesn't charge miners a fee and there are no limitations to create artificial scarcity in the coin supply.

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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.

ZClassic is a privacy focused crytpocurrency that is a fork of ZCash. ZClassic enables a high degree of privacy and anonymity of transactions.The key differences between ZClassic and ZCash are the elimination of the 20% mining fee that are allocated as a "founders' reward" and the removal of ZCash's block limit, that was intended to create scarcity.

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