What problem does this service solve?

Primecoin uses prime number generation to improve Bitcoin's PoW protocol.Bitcoin Gold reduces the competitive advantage of professional miners and adds greater decentralization to the Bitcoin protocol.

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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.

Bitcoin Gold (BTG) is a cryptocurrency that began in 2017 as a hard fork of the Bitcoin blockchain. BTG was created to reduce the monopolizing power of dedicated ASIC mining operations within the original Bitcoin network. Bitcoin Gold mining can be done by anyone with a standard computer and provides greater decentralization to the system. The hard fork that created BTG was meant to combat the disproportionate influence and competitive advantage of professional miners.

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