What problem does this service solve?

Gulden allows users to make P2P payments. It has gained some adoption in the Netherlands, but it does not appear to have any significant advantages to other coins.Primecoin uses prime number generation to improve Bitcoin's PoW protocol.

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Gulden is a Dutch cryptocurrency based on a native blockchain with a Proof-of-Work (PoW) consensus mechanism. Gulden has gained traction in the Netherlands, where it can be used to make P2P payments, as well as send funds to an IBAN account. Gulden's marketing efforts emphasize the network's security and faster transaction times. Gulden's PoW² consensus combines aspects of PoS with PoW, and allows witnesses to add transactions to blocks after they have been mined. The network is powered by the NLG coin.

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.

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