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.

Litecoin is a crytptocurrency that was created to serve as the “silver” to bitcoin’s "gold." It is based on the core Bitcoin protocol, but was designed with several key features that provide it with advantages over Bitcoin.
Litecoin has significantly reduced transaction times by limiting the target block processing time to 2.5 minutes. It also has a total coin supply that is 4 times larger, and utilizes a different hashing algorithm called Scrypt, that requires a smaller workload and less computation power than Bitcoin's SHA-256 algorithm. This enables much faster transactions at a much lower cost to users. These features make Litecoin easier to use and to mine. Since its creation, Litecoin has gained a large market cap and widespread adoption among cryptocurrency users in need of a coin for everyday transactions.