ZCoin is a privacy focused cryptocurrency built on Ethereum. The ZCoin protocol enables anonymous transactions with cryptography that utilizes Zero-Knowledge Proofs (ZKP). ZCoin increases privacy on their network by using a coin-mixer contract that wraps transactions in a serial number and destroying wrapped coins once they have been redeemed.
Zcoin was the first cryptocurrency to use a Merkle Tree Proof (MTP) as its proof of work algorithm. Merkle Tree Proofs are an innovative solution to achieving network consensus, and can increase transaction time while reducing the centralizing tendency of ASIC mining.

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.

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.