Introduced in July 2013, Primecoin uses an entirely different method for mining coins. Proof-of-work is presented to the network in the form of prime numbers. Claiming to be the first cryptocurrency designed with scientific computing as its work, the miners compete for primecoins by searching for very large prime numbers.

There is no predefined limit to the number of primecoins, just the natural distribution based on the set of prime numbers. The scarcity of primecoins is set by the distribution of prime numbers within a given set. While each confirmed Bitcoin block contains a nonce and hash solution, each Primecoin block contains a prime number set as the proof-of-work.

Another significant difference between Primecoin and Bitcoin is the mechanism that governs the difficulty level. Rather than using an average block rate calculated after every 2,016 blocks, Primecoin adjusts the difficulty to search for prime number sets after each block with a target rate of one block a minute....