Hi,
out of curiosity I looked in primecointalk and found this information:
I like the idea to use mining for scientific issues. Can you explain to me, what the records mean?
My hypothesis is -- no, I don't have a hypothesis. Looking on
http://users.cybercity.dk/~dsl522332/math/simultprime.htm#history I found out there are several records for prime numbers, but primecoin is far away from the records with 17425170 digits. But there are several categories regarding to k. Is k the number of primes?
thanks
Simultaneous primes refers to a cluster of primes that are somehow connected to each other. 'k' is the number of primes in the cluster. Longer primes (in terms of how many digits you would need to write it down) are harder to find and are considered better. The first category where k=1 is equivalent to the largest known prime which is a Mersenne prime with a whopping 17425170 digits.
Primecoin is trying to find Cunningham chains. The primes in a Cunningham chain of the first kind follow the pattern:
n - 1
2n - 1
4n - 1
8n - 1
...
2^i * n - 1
As you can see all the primes are connected to 'n' which is called the origin. A Cunningham chain of the second kind looks like this:
n + 1
2n + 1
4n + 1
8n + 1
...
2^i * n + 1
Just to be once in this forum a smart ass
For Cunningham 1 either:
p2 = 2*p1 -1
p3 = 2*p2 -1
p4 = 2*p3 -1
German Wikipedia:
http://de.wikipedia.org/wiki/Cunningham-Ketteor:
p2 = 2*p1 +1
p3 = 4*p1 +3
p4 = 8*p1 +7
English Wikipedia:
http://en.wikipedia.org/wiki/Cunningham_chainIt is both the same.
p1=11
p2 = 2*11+1 = 2*11+1 = 23
p3 = 4*11 +3 = 2*23+1 = 47
p4 = 8*11 +7 = 2*47+1 = 95
-> 95 is no prime, so the chain is the length 3.
To get the decimal you take the Fermat Test(look up on Wikipedia): 2^94 mod 95 = 54
So you take (95-54)/(95) = 0.43
-> So the Chain has the length 3.43. The current difficulty to reach is 9.94something.
Primecoin is looking for chains that are at least 9 primes long (so k >= 9). The current mining algorithm is producing numbers that are about 300-bits long which is about 90 digits. The origin is always a multiple of the block header hash which is 256 bits long. This hash is then multiplied by a few small prime numbers and a multiplier produced by our sieve algorithm. The miner can occasionally try using big multipliers which may result in a new record if the numbers are primes.
Ah interesting. Sorry I'm not very good in c++ neither can I just simply change the code, compile and then find out. So in the miner you just multiply the block header (which is different to the showed hash in the explorer which is very confusing) which different primes? So the CSieveOfEratosthenes tries just to find this multipliers?
Sorry, I don't want to disturb u all the time. Are there somewhere more informations to the code?