Riecoin Crypto Currency Mines Primes For Riemann

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 Riecoin Crypto Currency Mines Primes For Riemann
Written by Mike James
Wednesday, 05 March 2014

What a waste of effort bitcoin mining is -all that computer time just to validate transactions! Riecoin is a new crypto currency that uses a search for prime constellations as its proof of work.

Bitcoin, being open source is fairly easy to fork to create new crypto currencies. The big problem is not in the engineering, but in getting anyone to take them seriously enough for them to have a value.

Riecoin increases its chance of success by making the proof of work algorithm do something useful - well useful if you care about the Riemann hypothesis or the Hardy-Littlewood k-tuple conjectures.

A proof of work algorithm makes use of the unpredictable time it takes to complete a task to ensure that distributed processing agents don't all try to validate a block at exactly the same time so generating a race hazard i.e. multiple validations being accepted in different parts of the network.

Imagine that you want to give out a prize in a classroom. If you ask all of the students to simply put up their hands if they want the prize you will have far too many candidates, as they all more or less put their hands up at the same time. If, however, you give them a very difficult sum to do before they can put up their hands you spread out the hand raising, perhaps enough to just get one hand in the air and you can verify that they haven't cheated by checking that the answer is correct.

This is the proof of work algorithm and in the case of Bitcoin it takes the form of finding a hash code on some data in the block with a particular value. As this task has become so important, special computers have been built to solve the problem. The result is that the time to solve the proof of work would have decreased over time but bitcoin has a mechanism that allow it to adjust the difficulty of the problem so that it takes about the same time.

Riecoin is essentially bitcoin with a proof of work based on prime numbers. You might think that the task could be based on finding a prime of a given size, but there is a difficulty.

The time to find a prime p goes like log(p)4 and the time to verify that p is a prime goes like log(p)3. This doesn't make for a good proof of work because the time to check the prime is almost the same as the time to find it.

The proof of work used by Riecoin is to find n primes that are close in some specified sense. This problem takes time of the order log(p)(n+3) but checking it only takes log(p)3. This allows the proof of work to be checked and the difficulty of the task versus the checking can be adjusted by modifying n.

At the moment, Riecoin has n=6 and close means p, p+4,p+6,p+10, p+12 and p+16 must be prime.

The exact algorithm still makes use of the block hash, but to generate a value b that sets the smallest p that starts the constellation of primes that is  p>b. Changing the size of b changes the difficulty of the problem. In addition there is an upper limit to the size of p that depends on the block so that same solutions cannot be reused with different blocks. That is, each block sets a range that the constellation must be in.

This is clever and the values found could help with work on the Riemann hypothesis which is, of course, one of the Millennium Prize problems and worth \$1 million. Less ambitiously the constellations can be used to verify the Hardy-Littlewood k-tuple conjecture - for k=6 at the moment.

You can find all the software you need to get started at the Reicoin website. It was launched on February 11th 2014 so don't expect it to have a well-established (or any) value just yet - it takes time.

For a quick introduction to the many other aspects of launching a new crypto currency see the following video:

The real value of Riecoin is that it demonstrates that it is possible for proof of work to be useful work. I can see no reason why the proof of work algorithm in bitcoin couldn't be varied to allow different tasks to be used to verify a block - as long as they all took an equal time to solve on average.

With a bit of creative thinking the change could be made without upsetting the current bitcoin infrastructure and it might even provide a way to fund bitcoin mining after the last bitcoin has been mined - yes there is a last bitcoin. If it was possible to buy all that processing power for a relatively small amount of money then mining might continue and there would be no need to add "bank" charges to bitcoin.

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Last Updated ( Wednesday, 05 March 2014 )

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