One of the problems that Bitcoin miners often point out is that solving the complex and random algorithms that generate digital coins is a difficult process that spends a lot of energy and doesn’t have any other practical benefit. Well, someone has created an alternative that might solve this problem: it’s the new form of digital currency called Primecoin.
Although it’s still in the beginning of its evolutionary process, Primecoin might have the answer to this problem. And that is why people call it the first proof-of-work based cryptocurrency. The mining process of this coin could contribute to develop computing projects that need an extra hand. We are talking about projects like this one from Stanford University, which aims to discover a cure to some diseases, or the project SETI.
However, there’s another way to use Primecoins’ mining “waste”: tracking down long chains of prime numbers (well, Primecoin doesn’t have this name by chance…).
The best way to give you an example of this could be done is by using part of the article published by Bitcoin Magazine.
There are three specific types of chains that are of interest: Cunningham chains of the first kind, Cunningham chains of the second kind, and “bi-twin” chains. The rule behind a Cunningham chain of the first kind is that each prime in the chain must be one less than twice the previous. The first Cunningham chain of length 5, for example, consists of the following six primes:
1531, 3061, 6121, 12241, 24481
In Cunningham chains of the second kind, each prime must be one more than twice the previous. Here, the first length-5 chain appears much sooner:
2, 5, 11, 23, 47
Finally, bi-twin chains are chains of pairs of twin primes, or primes that are 2 units apart from each other, with the average of each pair being twice the average of the previous pair. Each bi-twin chain must obviously have even length; the first chain six primes long is:
211049, 211051, 422099, 422101, 844199, 844201
Searching for prime numbers using this process could be very beneficial: it “leads us to useful byproducts in other areas of number theory, provides an incentive for computational hardware development and leads to insights in the underlying workings of prime numbers themselves”, you can also read in Bitcoin Magazine.
Primecoin only needs to redefine the difficulty of the proof of work, so it can become a viable cryptocurrency. Let’s wait to see what happens.
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