Hi,
thank You for answering, but i still do not understand what GHash means if in comes to primecoin (while i understand quite ok with bitcoin).
"using a*x#-1 form of a number you guarantee, that number is not divisable by any number lower or equal x"
7*8-1 = 55 it is divisible by 5
I’ve never heard of the term GHash used in reference to Primecoin? Where are you getting that from?
Is there a way to test if a particular chain has already been used in a block before?
The chances of the origin of a chain being able to divide two different block header hashes is probably pretty small. I would imagine the chances of it occurring and the computation required to test if any of the other chains found could be used would probably be less efficient than just trying to find new chains. I could be wrong though, someone should try to figure it out exactly.
As for testing it should be pretty easy. Just check all of the blocks to see if any of them have the same origin and chain type as the one you are checking for.
is that test something which can be done with the client debug window with some command ?
also is there any way of submitting new chain without actually mining…basically directly via the debug window…?
Hi,
i found it here:
https://coinplorer.com/Charts/Difficulty/XPM
Is there anyone that could explain Me how this algorith works
It gets a base hash as input (let call it N) and desired chain length k (difficulty), then It tests specific kinds of numbers for primarity
i Guess they are AN-1 and AN+1 then (if it is pseudoprime) it checks if next k-1 numbers (2P+/-1) are prime as well.
if yes A is a proof of worl
My Question are:
Thank you in adwance for answer.
I’d like to add some comments to my previous post. a*n#+/-1 form is not dividable by any of numbers configuring n# till ‘a’ is a product of that numbers.
As for an algorithm for finding Cunningham chains, the case is that there is no such an algorithm (nowdays), but the algorithm of findig other elements in a chain once you’ve found a prime is quiet easy: just p2=2p1-1, p3=2p2-1 for 1CC and + for 2cc. case pn is not a prime (proubable prime is enough for primecoin) so you’ve got a chain n-1 length.
[quote=“imbocoffee, post:13, topic:1422”]I’d like to add some comments to my previous post. a*n#+/-1 form is not dividable by any of numbers configuring n# till ‘a’ is a product of that numbers.
As for an algorithm for finding Cunningham chains, the case is that there is no such an algorithm (nowdays), but the algorithm of findig other elements in a chain once you’ve found a prime is quiet easy: just p2=2p1-1, p3=2p2-1 for 1CC and + for 2cc. case pn is not a prime (proubable prime is enough for primecoin) so you’ve got a chain n-1 length.[/quote]
Not to nitpick, but that is still an algorithm that finds Cunningham chains.
Hi,
i found it here:
https://coinplorer.com/Charts/Difficulty/XPM[/quote]
If I had to guess, that website uses the GHash label for all of the coins, reguardless if it is relevant. I think the value that it is displaying as GHash has something to do with the normalized speed the blocks are found vs. 1 block every 60 seconds. Although that still looks a little off, maybe it is the speed vs. the total average speed.
Ok, here’s my attempt to answer many of the questions in this thread. Let’s take our latest 13-chain from yesterday as an example:
{
"time" : "2014-01-20 11:57:59 UTC",
"epoch" : 1390219079,
"height" : 368051,
"ismine" : false,
"mineraddress" : "AeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta",
"primedigit" : 107,
"primechain" : "1CC0d.c48332",
"primeorigin" : "12512390300891276190682243916246636610000954402441740274147501230375694290702478259358177371388272647651840",
"primorialform" : "106680560818292299253267832484567360951928953599522278361651385665522443588804123392*61#"
}
This is a Cunningham chain of the first kind (1CC). Other possible types are the second kind (2CC) and BiTwin (TWN).
The numbers of a 1CC chain look like this:
origin * 2^i - 1
Here ‘i’ starts from zero. So the first prime in the chain is origin - 1, the second prime is origin * 2 - 1, and then origin * 4 - 1, etc.
In Primecoin mining the origin is composed like this:
origin = headerHash * primorial * candidateMultiplier
The header hash is an intermediate hash calculated from the block header (it is NOT the final block hash). It’s a 256-bit number that is required to be greater than 2^255.
The primorial p# is defined as the product of all primes up until ‘p’, which means that 61# = 2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 * 23 * 29 * 31 * 37 * 41 * 43 * 47 * 53 * 59 * 61 = 117288381359406970983270.
The candidate multiplier is a number produced by sieve. It’s typically less than 1 million. The sieve uses an efficient algorithm to filter out a large number of prime factors. The sieve rejects all candidates x for which headerHash * primorial * x * 2^i - 1 is divisible by one of the first 8000 prime numbers.
Side note: The “extended” sieve algorithm considers multipliers of the form 2^j * x. So we are multiplying all the candidate numbers by powers of 2. It turns out that these new candidates can be checked efficiently because we are shifting the origin so that the second prime becomes the first prime and the third prime becomes the second prime etc.
I think many people are still wondering what “1CC0d.c48332” means. I already explained that 1CC is a Cunningham chain of the first kind. ‘0d’ is the length of the chain in hexadecimal (that is 13). ‘c48332’ is the 24-bit representation of the fractional length. We can convert it into the usual decimal notation:
0xc48332 / 0xffffff = 0.7676
So our example chain would meet a difficulty of 13.7676.
Ghashes are not applicable to Primecoin. I’m guessing some websites are trying to interpret the Primecoin difficulty like it would be Bitcoin/Litecoin difficulty, which doesn’t produce any sensible results. My Primecoin charts show the average prime chain rate for the network:
http://xpm.muuttuja.org/charts/
Right now it’s about 1.94 chains/min. So the total ‘chainsperday’ of the whole network would be about 2793 chains/day.
@mikaelh - excellent stuff and thanks a lot for the explanation…
please could you also elaborate on the significance of primorialform - as in why is it needed when primeorigin is already listed ?
also could you point anywhere to a resource which explains the algorithm (sieve, header hash etc) in a bit more detail…
again thanks a lot for your explanation
cheers,
It’s mainly a matter of convenience of not having to write down so many digits. If you look at the Wikipedia page for Cunningham chain, you can see records like 1249097877×6599# − 1. And that primorial there expands to about 2800 digits.
Well, the header hash can be defined like this:
blockHeaderHash = HASH(nVersion, hashPrevBlock, hashMerkleRoot, nTime, nBits, nNonce)
This is what Bitcoin would normally call the block hash. However, in Primecoin we calculate a second hash after we find a prime chain. This is used as the final hash for the block:
blockHash = HASH(nVersion, hashPrevBlock, hashMerkleRoot, nTime, nBits, nNonce, bnPrimeChainMultiplier)
The intermediate header hash makes sure that the prime chain is tied to the block’s content. The second hashing makes sure that the block hash depends on the prime chain solution.
The sieve isn’t easy to explain because it requires understanding modular arithmetic. So that will have to wait for another day.
@mikaelh thanks again for your wonderful support…
could I please ask you -
many thanks for your replies
Cheers,
You need more than any Cunningham chain to submit. The origin of the Cunningham Chain has to be divisible by the previous block header hash, which changes every minute, approximately. But yes, if you happened to find a Cunningham Chain that just happen to have an origin divisible by the last block header hash then you could probably use submitblock in the Primecoin wallet.
Yup, you can’t simply submit any chain to the client. In practice you need to submit a full block containing at least one transaction. Also, there’s no point in checking if a chain has been used already because every chain should be unique with a very high probability (since the header hash is essentially random).
@okzx @mikaelh - thanks guys for your continued support. apologies to be a bit of pain but I still have some queries -
Please could you clarify on how does does one mine(which i guess is equivalent to finding new chains) when the origin is dependent on a variable which keeps changing by the minute ? Does it mean that one has to find these chains within the period of 1 minute before the hash changes again…which would seem like a very little time to find such a chain ?
Also how does one include a transaction into the block or where do I get one if hypothetically I manage to find a chain which satisfies the criteria mentioned above.
cheers,
op
Short answer. Yes. But that is by design. We want to have block times of one minute. That means that the difficulty level will be set so that using the combined computing power of the network that on average only one Cunningham chain that meets the requirements to be submitted as a block is found.
I believe the transactions are stored in the block data as well as included in the hash for that block.
Well, you need to design your algorithm so that you get fast results. The reference client finds a bunch chain candidates and tests in less than one second.
If you’re using the getwork protocol, the daemon picks the transactions and makes the block. If you’re using getblocktemplate, you need to construct your own block (see libblkmaker).
@mikaelh @okzx thanks a ton…i’ll assimilate all this complexity before coming back w/ more 
cheers,
op
Block 354639 - http://primecoin.21stcenturymoneytalk.org/index.php?block_hash=f9909f15443fca320f2b38559e641855017cc9a9c9625f34d705082c14f7fe96
PrimeOrigin - 910349017770326773100803360454591087592649950817412857064426552616187722846458158311925176557280
Previous Block Hash - 998ec5856d6e0133360510414598a1941d2d03d929234112614346f84007a296 = [69456121357665805563614502505635608822143681338101999189895725832307621733014] (decimal equivalent)
I have checked that primeorigin is not actually divisible by the previous block hash.
@mikaelh @okzx Please can either of you confirm if this is the block hash which you had mentioned…
You need to use the “block header hash”.
In Primecoin mining the origin is composed like this: origin = headerHash * primorial * candidateMultiplierThe header hash is an intermediate hash calculated from the block header (it is NOT the final block hash). It’s a 256-bit number that is required to be greater than 2^255.
What he is referring to is commonly called the “block header hash”. Which is documented:
Well, the header hash can be defined like this: blockHeaderHash = HASH(nVersion, hashPrevBlock, hashMerkleRoot, nTime, nBits, nNonce)