What problem does this service solve?

Primecoin uses prime number generation to improve Bitcoin's PoW protocol.EOS.io is a decentralized platform designed to allow build DApps easily, without servers. It is meant to be more scalable than other blockchain platforms and it can support more transactions per second, with far lower transaction fees. It was created by Dan Larimer, who is an extremely talented and influential developer that was also involved with BitShares and Steemit.

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Company Description

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.

EOS is a blockchain development platform created by Block.one. Its goal is to become an all purpose operating system for blokchain applications. EOS allows developers to make underlying blockchains and create decentralized application more easily. It was designed from the ground up, to be more scalable and faster than other blockchain platforms. This allows for greater throughput, with more transactions per second, and much lower transaction fees. EOS tokens serve as the native currency. The network has a Delegated Proof-of-Stake (dPoS) consensus mechanism. Transactions are verified by 21 block producers that are chosen through a voting process that is designed to encourage community participation.

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