# Primecoin

**Primecoin** (sign: **Ψ**; code: **XPM**) is a peer-to-peer open-source cryptocurrency that implements a unique scientific computing proof-of-work system.^{[1]} 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.^{[2]}

Primecoin has been described 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. ^{[3]}

## Contents

## Review

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

**The differences in the system of confirmation**: the confirmation System of the Bitcoin based on the hash created by SHA-256. At the same time, when searching for hashes, all the computing power of the system is aimed only at maintaining its own economy, while in Primecoin useful calculations are made when the system is running. Primecoin’s confirmation system is based on finding long Cunningham chains.**Higher generation rate**: the purpose of the Bitcoin Protocol is to keep the generation rate at the value of 1 unit in 10 minutes. In Primecoin, the generation rate is maintained at 1 block per minute.**High speed of transaction confirmation**: since the rate of generating blocks at Primecoin is on average higher than that of Bitcoin by 10 times, the rate of transaction confirmation is higher by about 10 times.**Smooth difficulty change**: bitcoin mining Difficulty changes every 2016 blocks (approximately every 2 weeks), in Primecoin It changes every block (every minute).-
**Block reward**: the reward for a block of Bitcoin decreases as the number of coins issued increases. In Preimmune award for the unit depends on the complexity of the search block and is equal to 999/сложность2. **No premine**: Primecoin was launched without pre-generating units on July 7, 2013**There is no limit of the emission**: the Emission of Bitcoins is controlled by Protocol and limited was 21000000 BTC. In Primecoin, the final volume of coins is not fixed, but is regulated by Moore’s law through the advantages of mining equipment and improvement of the algorithm. According to the author, this approach is a more realistic simulation of the shortage of gold.

The innovative prime proof-of-work in Primecoin not only provides security and minting to the network, but also generates a special form of prime number chains of interest to mathematical research. Thus primecoin network is energy-multiuse, compared to bitcoin network. Primecoin is designed to sustain a prosperous mining market and high level of security, while maintaining good scarcity property like gold. Primecoin also processes payment transactions 10x faster than bitcoin network.

Primecoin features self-adjusting block reward: The number of Primecoins released per block is not fixed but is always equal to 999 divided by the square of the difficulty.

### Primecoin mining

The following programs are used for mining Primecoin:

- The original client Primecoin-Qt
- Amazon Prime launcher 0.2
- jhPrimeminer 7.1
- Primecoin High Performance 11 (a modified version of the original client)

### Wallet

XPM cryptocurrency has official wallet available on website: http://primecoin.io It supports Windows, Linux and MacOS (OS X) operating systems. You can easily download and install the Primecoin wallet.

### Primecoin price

The price of Primecoin (XPM) cryptocurrency is available online. In January 2018, the Primecoin price had risen significantly from $0.5 to $3.54. By the way, It’s important to have a secure wallet for Primecoin storage before buying it.

On May 28, 2018, market capitalization of Primecoin achieved 48,23 millions of US dollars.

## 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.^{[4]}

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

### Scientific value behind Primecoin

Primecoin network searches for special prime number chains known as Cunningham chains and bi-twin chains. The distribution of these prime chains are not well-understood currently as even for its simplest case twin primes their infinite existence is not proven. The distribution of primes has been one of the most important discoveries in arithmetic, and the study of prime chains traces its lineage to the work of Riemann and prime number theorem, with connections to the deeper nature of the seemingly random pattern of prime distribution. Prime distribution is not just an abstract interest of mathematicians. Riemann’s study revealed connections between Riemann zeta function and prime distribution, whereas later on Riemann zeta function has been shown to be highly relevant in other scientific disciplines such as physics, thus the study of prime distribution is an important part of the foundation of modern sciences.

## See Also on BitcoinWiki

## External links

- Primecoin website
- Primecoin on Twitter
- GitHub – Primecoin
- Primecoin BitcoinTalk
- Cryptsy – Trading Primecoin
- PrimeCoin (XLB) – BTC – PrimeCoin (XPM) – Overview,
- Primecoin price and market state on Coin360