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.

Qtum has been described as a hybrid between Ethereum and Bitcoin. Qtum is a smart contracts platform that places a strong focus on value transfers as well as decentralized apps. Qtum enables users to create smart contracts on the platform and conduct cryptocurrency transactions.
Qtum has a Proof-of-Stake (PoS) consensus algorithm. Several decentralized apps are already using the platform.

QChi is an Ethereum-based token with no clear benefits. Their marketing materials do not provide any specific information about their roadmap or what advantages it offers compared to other cryptocurrencies.