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.

TrumpCoin is a cryptocurrency that was created to support Donald Trump. Their marketing materials do not provide specific details about what they hope to achieve, or why they need a blockchain-based digital currency. TrumpCoin has a hybrid Proof-of-Work (PoW) and Proof-of-Stake (PoS) consensus mechanism.