@Charles: unfortunately your trick is not correct and won't work for solving Goldbach's conjecture, sorry for extending this off-topic here, but I try to explain why: you want to prove for a particular n>1 there are two primes p1 and p2 so that 2n=p1+p2. By Chen's result we know there is an r (r<c where c is an upperbound) so that there are prime numbers p1 and p2 that 2n=p1+p2^r. So here you suppose there could be an integer m so that p1^r+p2^r=m^r  BUT STOP, WHY?! Since p1 and p2 and r are fixed from the previous equation for 2n and not arbitrary, you will not certainly be able to deduce the existence of an m such that p1^r+p2^1=m^r for general (but fixed for each n) p1, p2 and r, other than when r=1, but that is exactly what you want to prove then after by the help of this trick Wink

What if we know something about the factorization of n and also about p1 and p2. I actually don't rely upon the chen result to prove 2n = p1 + p2^r rather a different method that tells me a lot more about (n,p1,p2), which in term is useful in discussing m.  The key is the relationship of (n,p1,p2,m) and this is why the problem is so interesting to me. It's expressing a relationship between a particular factorization, a Diophantine equation and prime distributions.

Another way to look at my approach is to start with a process from an arbitrary n to generate several special sets of the form (n,p1,p2,r) and then use the process to show m must exist by a reductio ad absurdum argument. This is a specific m in relation to a specific p1 and p2, but the process generates these sets for all n. Then show not a triple inferring r = 1.

I'd go into more specific details, but this isn't the forum and honestly these things are best discussed in person or over skype with a wacom tablet.

what if you could find a way to represent for n>1: 2n = p1 + p2^r where p1 and p2 are prime and r is a natural number and then show there exists m as an integer such that p1^r + p2^r = m^r. By fermat's last theorem r <= 2 and then show (p1,p2,m) are not a Pythagorean triple thus r =1 implying 2n = p1 + p2 for all n>1.

Tao and Chen's work allow for representing 2n in terms of the sum of a prime and a prime to an unknown power and wile's work allows for someone to discover that magic m which is an integer (all inspired by the Hardy-Littlewood Circle Method and semistable elliptic curves). The triple component should be trivial. That's the best corpus I can provide in this format. The devil is in actually demonstrating these things to be true which requires a mastery of concepts that are beyond my abilities at the moment.


Most of the code I've worked on falls into two categories: data analysis with python and R alongside a CAS like Sage and functional programming for FHE research using Haskell. I'm familiar with some web development concepts with JS, PHP and bots for scraping and also I've done a lot of work with neural networks, but I'm not a C++ developer.

Dan is an expert with modern C++ at the Bjarne Stroustrup level and also has become very skilled at developing p2p systems over the past few years. Outside of helping with the cryptanalysis and vetting the logic of ideas, I can't be much help in writing the core software of Keyhotee and the BitShares protocol.

This said, we are an open source company and I've been investing a lot of time into getting more developers and professionals to come help us make this a reality. We are not dealing with easy problems and we can't possibly have all the solutions. Instead we are aiming for getting a foundation of innovation, iteration and collaboration setup to eventually grow to a solution that works for everyone.

Here is my biggest problem in this project:



I'd have 15 devs if we were doing this in python.

 
  

We have thoroughly addressed your concerns beyond the point of good taste. You are slandering our company and have used a legal term in reference to BitShares. I am asking you to cease this campaign against our company. We have not accepted any community money. We are running all tests on company resources. We are not premining. Every line of code is open sourced. Invictus does not profit from the use of the BitShares protocol anymore than the developers of Bitcoin profit from it.  

I have no idea why you have decided to engage in this hostile pointless criticism, but it accomplishes nothing  other than destroying your own credibility. We have posted an example research paper discussing the economics our system is based upon:

http://www.brookings.edu/~/media/research/files/papers/2012/6/13%20prediction%20markets%20wolfers/13%20prediction%20markets%20wolfers.pdf

We are going to test every assumption we make with a public testnet prior to releasing BitShares into the wild. I just don't understand how we can be anymore open or transparent in this process? We are being called a ponzi scheme for spending our own money on an experiment?

Have you addressed the communication and ID system we are also building as open sourced projects? We have solved decentralized email and built a better web of trust and we are giving it away for free. But no, all of this is just some elaborate ponzi scheme where we don't take anyone's money, but somehow you lose it? Mr. Jackie Chan has an answer:



Meanwhile, I don't see you addressing the real scams in the market:



You're just pissed off because I went into your thread and corrected your whitepaper for an idea you're trying to raise 300k of community money for. It's amazing that you're this petty, but there is no other explanation.

Goldbach is actually one of the hardest problems to resolve in number theory in my opinion. It has some of the deepest connections possible in prime distribution and explaining how factorization changes with addition, which is why Hardy and Littlewood spent so much time analyzing it.

I actually came up with a corpus using Wiles work alongside some insights from Tao to resolve the Goldbach conjecture in a fairly creative way, but it's beyond my current mathematical ability to explore. I would need about ten years and access to some great minds. 

Thank you for your kind words. I just hope to make enough to retire and solve the Goldbach conjecture. Sadly, I think changing the world's money system is probably an easier problem.

What do you think of Hungerford's Algebra?

Lol, considering he's dead one would expect such. The book I was referring to was Survey on Diophantine Geometry which came out in 1997. Have you ever read Nathanson's books on additive number theory?

Also if you're up for the challenge:

http://www.stanford.edu/~zvika/localpapers/IdealHom.pdf

Analytic and Additive Number Theory out of CU Boulder and then moved into cryptography first studying public key cryptosystems and eventually fully homomorphic encryption. I've done some Galois theory and spent a great deal of time dealing with integer factorization.

I really admire the algebra in some of the fermat stuff dealing with semistable elliptic curves. I have this book written by Serge Lang that looks like a roadmap to hell. What was your specialty?

 

This is what makes our company so innovative. We've found ways of doing completely open source software and still making money. Once the model becomes known, we hope that it will spread across the Bitcoin and OS communities helping hundreds of small projects grow.

More in reference to events like these:

http://www.wired.com/techbiz/it/magazine/17-03/wp_quant?currentPage=all

Again it is difficult to understand what he is attacking, but the genesis appears to revolve around the ROI of holding onto a BitAsset. The dividends are like interest on a bond and as long as volatility of the derivative is low, over time most positions will result in a positive return.

We are making some economic assumptions based upon this paper alongside other works:

http://www.brookings.edu/~/media/research/files/papers/2012/6/13%20prediction%20markets%20wolfers/13%20prediction%20markets%20wolfers.pdf


It is an exercise in mechanism design and some theory explained in the paper above. This said, we are making economic assumptions in some cases about the nature of the market pegs and thus are launching a TestNet first to test our ideas. Bounties can create market incentives to break the system if possible. Again, we are not premining nor accepting anyone's money other than our VC partners. The TestNet does not contain real money. So we are basically being attacked for running an experiment with our own money.


First let's agree this could be better stated Second, I agree about scams in this market, which is why from day one we started this process with principles:

(1) Don't premine BitShares
(2) Test everything in the open domain
(3) Build the communication and reputation system first in the event we need to adopt a better exchange model

Our goal is to build a prediction market that serves as a decentralized p2p exchange for all cryptocurrencies and an effective way to facilitate fiat to CC transactions. Should the BitShares standard fail, the infrastructure we have built can adopt a different implementation. This is why I take such enormous umbrage to these allegations. They are both misguided and fundamentally dishonest. Our company is trying to build several extremely complex products and we are doing it off of our own money and time in the open domain.

First stop propagating the meme:



Second, we shouldn't wait until C3. Please shoot me a pm and I'll send you my skypeID and we can discuss this at length. BitShares has yet to be released as a product. The TestNet has yet to be released. The whitepaper update has yet to be released. And yet we are a ponzi scheme because we propose sharing the inflation produced from coinbase transactions with BitShares holders?

Maybe I'm missing his point, but dividends do not come from thin air. They are produced from the mining and transaction process and serve as an incentive to save in the system. In order to preserve a sum zero system, someone has to receive the Bitshares dividends from the units held in collateral for a BitAsset. We made a design decision to pay these to the BitAsset holder.

There is still volatility that could result in a BitAsset holder losing money similar to a T-Bill holder losing money. So again, either he doesn't understand our system or he is spreading FUD to promote his own product.

Also we don't have a premine, we have invested a massive amount of time in building several derivative technologies like our ID and anonymous communication system and we are planning on releasing a TestNet with fake BitShares to test our economic assumptions first. So where is the fucking Ponzi? Wouldn't it be discovered with the TestNet? How does my company value from a bad product? Everything we do is open sourced. Every idea we generate, we vet in the open domain.

This has got to stop. You are moving into the domain of slander and have attacked the work of many passionate people trying to build something innovative and cool while also trying to raise 300k for your own idea, Cunicula.

 

A sum zero system with no premine and fully collateralized positions to serve as a prediction market is in no way a ponzi scheme. I'm not going to argue with an idiot. We addressed your concerns in our thread. This is a thread about your product. Please do not slander ours in it. 

You know I just realized that I have still not received my miner that I ordered in April. Lol, Josh you're a funny man.

This isn't a disagreement it is a factually incorrect statement that you are broadcasting in your whitepaper right in the abstract:


Either you have bastardized the word trust to mean something beyond common notion or you have no understanding how Mastercoin and BitShares work. In any event, you are misrepresenting our brands and I have every right to post a disclaimer in your thread stating such. BitShares does not rely upon trust relationships.


When mathematics are used to justify arbitrary design decisions or override the will of the market, then I tend to discount the system. You can use any level of abstraction you desire with any level of complex relationships, but unless the system is actually tested with real users and predictive models are verified, the math is worth less than the ink on the paper. Ask David Li about this Cunicula.

Just as you discounted us for our lack of economists (and we do actually have one), I'll discount you for your lack of developers. They are the lifeblood of these ideas and the drivers of their implementation. I'll leave your thread now.

It's ok, he's got a lot of pretty math to make everything better . BitShares and Mastercoin do not require trust relationships, but I suppose people can write whatever they like in their whitepapers.

Everybody's a critic  . Goodluck and I hope some good ideas come from this proposal.

my company is actually building bitshares and we have yet to release a launch date nor how to mine them.

and how exactly will you be offering bitshares?

Gollum pm me. I think we might be able to work together.

Greyhawk, I just watched the documentary on you:

http://www.youtube.com/watch?v=EYX7ACuTBTY

Wow, Tom I don't know how you went through that.