Thanks for the criticism and for the mathematical links.
And in return, thanks for your refreshingly mature response.
I consider Primecoin, Gapcoin, and Riecoin to be interesting and worthwhile projects that we can learn from ... My purpose in posting is not to discourage people from using these coins nor is it to be anything other than constructive. I currently want more people to mine Gapcoin.
Oh good, thanks for clarifying that.
I realize that these coins are in a sense better than just pure hashing, but I am also pointing that these coins may be improved by making the miners work on several prime related problems simultaneously (but this is risky since a complicated algorithm could have bugs that present a security weakness).
That's an
interesting suggestion. Although bereft of the mathematical coherence of your particular suggestion, the approach of multi-algo PoW has been adopted by a number of altcoins (
Myriadcoin is perhaps the most well-known and there are other less well-known examples such as
Unitus) and it's possible that the engineering solutions to a multi-algo (and multi-difficulty) PoW approach might be adaptable to an approach that integrated the different prime search approaches of Gapcoin, Riecoin, Primecoin and their derivatives (e.g. Datacoin which uses Primecoin's PoW algo).
Your concerns about securing the public ledger are indeed valid - Jonnie Frey, original developer of Gapcoin articulated his concerns about the then-extant implementation of Primecoin ...
Gapcoin follows Riecoin’s way and uses enough Miller-Rabin tests with random bases to avoid composite numbers being accepted as Proof of Work, like Primecoin mistakenly could.
Not being an able, or even capable, mathematician, I'm not in a position to verify that his criticism of Primecoin is accurate, nor does Jonnie Frey provide any detail, so we're obliged to take that statement on trust. fwiw, Sunny King provided an accessible description of his approach in the still-available
Primecoin white paperIn practice, the main issues seemed to revolve around pool mining as Jonnie Frey observed ...
In Primecoin, which is searching for long prime chains, you can easily modify your miner to search for smaller chains. In fact, it is mostly about a simple one-line-editing. As an example, just turn a 10 into a 7 in xolominer and you will get scads of 7-chains, but your chance to find a block has diminished.
To avoid this, pools supply better payment for shares with longer chain-lengths.
In Riecoin, it is even worse. Riecoin searches for prime tuples of length 6. Pools do accept tuples with less primes, but a 6-tuple only can occur in certain places. (Look at this post for a detailed explanation.) 4-tuples, by comparison, are more frequent. There are places, where a 4-tuple can occur, but no 6-tuple, which Riecoin truly needs. So pools have to check every submitted share whether the miner really searches for 6-tuples or not. Those facts are what make it so hard to create a Prime- or Riecoin pool.
I haven't researched these issues in detail because they apparently haven't presented significant impairement to the coins. Riecoin is currently in the process of migrating from a minimum of 6-tuples to a minimum of 7-tuples - details on the difference between versions are well-described on the
Riecoin web site. BTW, the Riecoin Discord server is quite active and contains useful up-to-date information -
https://discord.gg/2sJEayCI want mining algorithms to be optimal at not just establishing consensus but also at solving important computational problems without compromising security. I want mathematicians and cryptographers to continue to research scientific mining algorithms, and this research starts by highlighting the positive aspects and potential pitfalls of Gapcoin and related cryptocurrencies.
As I understand it, Primecoin's contribution to number theory is very slight (this from Sunny King's white paper):
“Primecoin is the first cryptocurrency on the market with non-hashcash proof-of-work, generating additional potential scientific value from the mining work. This research is meant to pave the way for other proof-of-work types with diverse scientific computing values to emerge.”Riecoin is less slight in that it offers an indirect contribution (according to
Newscientist) by attempting to prove the null hypothesis:
“Riecoin ... might find an example of a constellation that doesn’t fit with Riemann and so offer clues as to how to disprove it”As for Gapcoin, Jonnie Frey provides the following rationale:
“Researches about prime gaps could not only lead to new breakthroughs in the bounded gap, it may also help proving the Twin Prime Conjecture and maybe even the millennium problem, the Riemann hypothesis. Who knows?”Unfortunately, I'm obliged to confess that I don't get
why the prime gap search effort is being undertaken nor how it is a potential contribution to helping prove either the Twin Prime Conjecture or the Reimann Hypothesis. I do get that “many questions and conjectures remain unanswered” but I haven't yet encountered a straightforward explanation of the purpose of calculating record prime gaps and merits, there's not even an agreed null hyopthesis to prove. What's the point of the continual record-seeking? I can conjecture that the results
might inform a statistical analysis that
might in turn feed into an advance in number theory but that doesn't seem to be the way that number theorists are tackling the issue of formal characterisation (Terry Tao describes what I assume is a fairly typical approach in
“Long Gaps between Primes: What's New”).
Edit: but see postscriptMy lack of understanding has consequences. Setting higher shift values for the Gapcoin miner results in the calculation of fewer gaps but larger prime numbers as opposed to lower shift values resulting in more gaps between smaller primes. My naive view suggests that as merit is the key factor, more gaps with (potentially) greater merit are the most obvious target. More confusingly, I can't readily discern any size effect in the various conjectures - it's not as if anyone's saying “the
really interesting results will start to appear when we start to use
really big primes” - because the principle of calculating a gap's merit is explicitly designed to factor out the effect of prime digit size.
Aaanyway, back to your suggestion ...
-By 'useful', I clearly meant useful in other ways than simply establishing consensus. I decided to trade a thorough explanation of what I meant by 'useful' in exchange for brevity.
Not at all unreasonable, there's a
lot of room for discussion there and again, thanks for clarifying.
Leaving aside the fact that from my diminished perspective (as I describe above) "usefulness" is rather opaque, am I correct in understanding that your suggestion implies the potential construction of a mapping between the pairs of primes produced by Gapcoin and both Primecoin's chains and Riecoin's prime constellations? I hope you'll forgive my ignorance but I can't even begin to hallucinate any common numerical ground between them, you'll need to provide some concrete math to connect them up.
The main thing that you should have taken away from my post is that Gapcoin will do a decent job at advancing understanding when the market cap and mining reward for Gapcoin are low. However, if the market cap for Gapcoin were hundreds of billions of dollars and the mining reward as a result was very high, then Gapcoin will not longer do a good job at advancing understanding since the principle of diminishing returns applies to scientific cryptocurrency mining algorithms as well
https://en.wikipedia.org/wiki/Diminishing_returns.
It's not been demonstrated that the principle of diminishing returns applies to - let's be specific here - PoW algos based on prime number calculation. In this you are at odds with Jonny Frey who maintained that more mining = higher difficulty = more records: “if the difficulty reaches 35.4245, every block will be a new world record”.
It is not fair for a single type of computational problem in mathematics to be highlighted at the expense of all the other areas of mathematics, and if Gapcoin becomes really popular, then Gapcoin will do just that.
That's a pretty big (and in the current context, rather unlikely) “if”. Gapcoin has had quite a long trajectory and successive halvings have brought down the per-block reward to just 2.73 GAP, that's going to be a challenging place from which to start attracting large numbers of new miners.
Cheers
Graham
Edit: Aha, Tom Nicely's list of prime gaps is credited in Kourbatov's 2018 paper “On the
nth Record Gap Between Primes in an Arithmetic Progression” published in the International Mathematical Forum (
http://www.m-hikari.com/imf/imf-2018/1-4-2018/p/kourbatovIMF1-4-2018.pdf) which
does include statistical analysis ... “We will attempt to answer these questions using heuristics and statistical analysis of numerical results.” So there is some support for viewing the list of prime gaps as a usable dataset which is usefully extended.
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