Bitcoiin is a cryptocurrency that was created to address some of the issues that have plagued the original Bitcoin ecosystem. It's Proof-of-Work (PoW) consensus mechanism is designed to decrease transactions times and fees, as well as make mining rewards easier to earn.

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.