What is Primecoin? The Prime Number Hunter

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Primecoin is a rather interesting digital currency.  It was developed by Sunny King, one of the same developers that created PPCoin and invented Proof-of-stake. Primecoin does not follow the same rules as the other currencies, and has a built in mathematical benefit.  Due to the way it is mined, Primecoin actually discovers previously unknown prime numbers.

Primecoin Discovering New Prime Numbers

Primecoin, like Bitcoin and many other digital currencies, uses a proof-of-work algorithm for mining.  However, rather than using the Hashcash method that is used by the other currencies, Primecoin instead uses an algorithm that searches for, and verifies, specific types of prime numbers.

Primecoin utilizes chains like this to discover advanced prime numbers

A simple example of a Cunningham / bi-twin chain, via primenumbers.net

These types of prime numbers, known as Cunningham chains (of the first and second kind), and bi-twin chains, were chosen for two main reasons:

  • There are likely many of these chains that are not unusably large, so it is worthwhile to search for primes that are possible to verify with consumer-grade processors.
  • Using a formula involving the length of the prime chains, and Fermat’s test, the developers were able to implement a difficulty formula that would increase at a mostly linear rate with increasing hashing power.
Primecoin utilizes Cunningham chains, a specific sequence of prime numbers

An advanced example of a Cunningham / bi-twin chain, via primenumbers.net

One of the big challenges in making this work effectively was finding a way to prevent the same proof-of-work from being used multiple times.  However, this was also solved by King by requiring that the origin of the prime, which is a number directly adjacent to the prime, be divisible by the block header.  As the block header changes for each block, and is influenced by previous blocks, this requirement guarantees that the solution for each block is unique.

Primecoin Made Secure by Prime Numbers

Prime numbers are very useful.  They are important in cryptography, and used in many keysecret encryption systems.  The larger the list of known primes grows, and as the value of the numbers increases, the security of encryption methods utilizing them improves.

Understanding prime numbers is also very important for high level mathematics, physics, and engineering.  All non-prime numbers can be constructed from two or more prime numbers, yet a prime number itself cannot be created from any other number.  Prime numbers are the building blocks of math.  The more we understand about primes, we more we understand about mathematics.  The more we understand about mathematics, the more we understand about the universe, and everything in it.

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