Primecoin (sign: Ψ; code: XPM) is a peer-to-peer open source cryptocurrency that implements a unique scientific computing proof-of-work system. Primecoin's proof-of-work system searches for chains of prime numbers. Primecoin was created by a person or group of people who use the pseudonym Sunny King. This entity is also related with the cryptocurrency Peercoin. The Primecoin source code is copyrighted by a person or group called “Primecoin Developers”, and distributed under a conditional MIT/X11 software license.

Primecoin has been described[by whom?] as the main cause of spot shortages of dedicated servers because at the time it was only possible to mine the currency with CPUs. For the same reason, Primecoin used to be the target of malware writers.

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When comparing Primecoin with today's most widely spread cryptocurrency called bitcoin some notable differences are:

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Scarcity is governed by the nature of prime number distribution

Almost all cryptocurrencies in existence define their scarcity properties merely by set of predefined values in source code, whereas scarcity of Primecoin is based purely on a relationship of a simple function and mathematical property of natural occurrence of prime chains in the set of whole numbers that are.

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No predefined ultimate number of coins

Instead of having hard-set ultimate number of coins in its code like many other alternative cryptocurrencies, number of Primecoins released per block is always equal to 999 divided by the square of the difficulty. There has been some attempts at approximating this number. The number of Primecoins that will be mined will be determined by the progress of its adaptation by the mining community, improvements that will be done to the mining algorithms and ultimately by Moore's law.

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Difficulty adjustment is more frequent

Primecoin protocol adjusts its difficulty slightly after every block. The difficulty change that occurs each block is targeted at achieving target of one new block created once per minute. As comparison the bitcoin protocol adjusts its difficulty every 2016 blocks, or approximately every two weeks.

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Faster transaction confirmations

Since Primecoin blocks are generated 8 to 10 times as fast as bitcoin blocks on average, Primecoin transactions are confirmed approximately 8 to 10 times as fast.

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Proof-of-work system

Primecoin uses the finding of prime chains composed of Cunningham chains and bi-twin chains for proof-of-work, which can lead to useful byproducts.

The system is designed so that the work is efficiently verifiable by all nodes on the Primecoin network. To meet this requirement, the size of the prime numbers in the system cannot be too large. The Primecoin proof-of-work system has the following characteristics:

Primecoin's work takes the form of prime number chains. Finding the prime number chains becomes exponentially harder as the chain length is increased. Verification of the reasonably sized prime number chains can be performed efficiently by all network nodes.

Mersenne primes are precluded due to their extremely large size.

Three types of prime number chains are accepted as proof-of-work:

Cunningham chain of the first kind

Cunningham chain of the second kind.

Bi-twin chain.

Other cryptocurrencies including bitcoin commonly use a Hashcash type of proof-of-work based on SHA-256 hash calculations, which are of no value beyond its own economy.

List of largest known Cunningham chains of given length includes several results generated by Primecoin miners.

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