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.

Diamond (DMD) is a Proof-of-Stake coin focused on scarcity. Their marketing materials emphasize the limited circulation of the coin, and the benefits of the network's incentivized cloud mining system, which rewards users for contributing their computing resources.