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.

Sphere is a smart contract platform and peer-to-peer payment network. The network has a hybrid PoW and PoS consensus mechanism and is powered by the native SPHR token, which can be swapped for an ERC20 token over the Ubiq smart contract platform.

Sharechain is developing a Proof-of-Work cryptocurrency platform. Their network is currently fueled by the Ethereum-based SSS token. Their marketing materials are unclear and do not offer any information about its advantages.