"The underlying mathematics behind why six confirmations is a fairly safe threshold is independent of block confirmation time, so the Primecoin transaction at six confirmations is no less secure"

I think this is wrong. 6 conformations in Bitcoin means that 1 hours worth of work has gone into sealing the transaction into the blockchain. To invalidate these 6 blocks you would need, for example, twice the compute power of the honest nodes for 2 hours. With primecoin you would only require this power for 12 minutes, which is 10 times less work.

Lowering the confirmation time only increases the granularity of the confidence in a certain transaction over time.

This is actually a common misconception, and you're wrong. If you read Satoshi's original paper, the probability of someone with substantially less than 50% of the total compute power decreases exponentially as the number of confirmations increases. The reason Bitcoin uses 6 confirmations is because this was judged to give the best balance between time taken to confirm and probability of a sub-50% attacker succeeding.

It has nothing to do with stopping attacks by someone with a majority of the total compute power - realistically, if requring someone to dedicate that amount of compute power for 12 minutes isn't enough to make an attack infeasable, making them dedicate it for 2 hours is unlikely to do the job either.

Edit: Also, requiring only one confirmation - which is what you'd have to do to make Bitcoin as fast as 6 confirmations in Primecoin - is especially risky because it allows any attacker capable of generating a block in a reasonable amount of time to double-spend with very high probability at the cost of one block's payout.

Yep. This is a mistake that a lot of Bitcoin-clones seem to make. Sure Litecoin "needs" less time to gain six confirmations, but you end up with a much lower ultimate difficulty. There's extensions on this with alt-coins, where people modify the client to have 10 second block targets and <10 confirmations, which ultimately makes the entire "currency" insecure and worthless.

Well, no, primes aren't very useful, though this might have lead to a bit of an arms race in probabilistic prime-finding algorithms - which would be good, I suppose.

I wonder if you could make a proof-of-work algorithm based on, say, protein folding?

That (or any other useful work beyond just finding primes) would be great, and it's mentioned in the article (as something that cryptocurrency "newbies" commonly suggest), but the concern with all of that is efficient verification.

Another issue is that the input to the calculation has to be, at least in part, the transactions which you're verifying. That's not a problem if you're just looking for hashes, and I imagine they have a similar process when looking for primes, though I'm curious about exactly how they do it.

cache: http://webcache.googleusercontent.com/search?q=cache:r6c_Ul6...

Claiming that finding prime numbers is useful seems like a stretch to me.

Not necessarily. See http://arstechnica.com/science/2013/02/ask-ars-why-spend-tim...

I'm still not convinced. I did read the whole article, but the subhead sums it up well:

> That new 17-million digit Mersenne prime number might matter. Someday.

(Emphasis mine, but that's not much of ringing endorsement of the usefulness of prime numbers.)

This could become a new Proof-Of-Work function for Bitcoin itself.

Dan Kaminsky assigned 0% probability that the current proof-of-work function will be used by the end of this year, due to problems with ASICs and the centralization of hashing power: http://bitcoinnews.io/dan-kaminsky-predicts-the-end-of-the-c...

I think his argument is on shaky ground. No matter what you change the proof-of-work function to, it will always be possible to develop specialized hardware that outperforms general purpose hardware.

I accept his argument that it's dangerous for vast amounts of mining power to be centralized to a small number of actors. I don't agree that changing the PoW function would solve this in the medium term. It might work in the short term, as developing specialized hardware would take time.

I suppose one solution would be to change the PoW function at set intervals, randomly selecting one function from a large pool. This would discourage the development of specialized hardware.

Zero probability? So will he pay out all his bitcoins to me if his prediction fails? That's the meaning of zero %.

I'm not quite sure myself, it might have been hyperbole. He doesn't seem to participate in this bet however: http://betsofbitco.in/item?id=1432

We all know that the proof of work algorithm won't ever change from double SHA256; the network wouldn't allow it. Start a fork with a few miners and the current one will outrun the new one in a matter of seconds. Higher difficulty is a good thing, that's the entire point.

Gavin Andreesen said there is a 99% chance (or something like that... may have been 99.9%) that the current proof-of-work will survive the year.

This more or less addresses all of the major complaints I have about Bitcoin; you know, minus the whole insane deflationary spiral which arguably is also its' main feature.

Pretty sure the "spiral" part is not lauded as a feature. Or accepted as an inevitable outcome, for that matter.

I'm not sure about the spiral, but the deflation aspect is definitely part of the plan.

Those most in love with BTC seem basically to just want to sit on something and get richer, because anything else is the government/other people/moochers stealing their money through inflation.

It depends on who you are listening to. There are certainly enthusiasts chanting BTC 10,000 (or more).

That's at least close to deserving the label spiral (the devaluing of the dollar over history has been something like a factor of 30 (depending on your dates), a factor of 100 is pretty impressive compared to that).

Does Primecoin cryptography depend on the difficulty of finding prime numbers and then try to find them?

PrimeCoin searches for prime chains. For example 6 is at the center of a bitwin prime chain of length 2.

6 - 1 = 5, prime 6 + 1 = 7, prime 6 * 2 - 1 = 11, prime 6 * 2 + 1 = 13, prime

The design paper is a light and interesting read:

http://ppcoin.org/static/primecoin-paper.pdf

Also:

http://en.wikipedia.org/wiki/Cunningham_chain