I think something that would be a limiting factor is block validation.
The work to solve a block must be difficult but easy to verify. With SHA256 and scrypt, you can simply check the result. With primecoin, you run probable primality tests. With arbitrary digits of Pi, it takes almost as long to verify as it does to generate.
See this post: http://stackoverflow.com/a/14283481/477563
Topic: [Idea] Next logical step foward after Primecoin... PiCoin (Read 624 times)
Pi is an irrational number and can be written as generalised continued fraction as --
(from thread https://bitcointalksearch.org/topic/pi-coin-271568 )
Recursive function implementing 1st continued fraction for n iterations
Here 8 iterations produce first 3 correct digits of pi.
It can be seen that as the number of iterations are gradually increased,computational complexity increases exponentially.Block reward could be adjusted accordingly.
Verification of n th digit can be directly found using Bailey–Borwein–Plouffe formula. The formula can directly calculate the value of any given digit of pi without the need to calculate the preceding digits.
Attempt and result of obtaining 10 Trillion digits of pi
Other current problems from Experimental Maths could also be used for p2p alt coins.
(from thread https://bitcointalksearch.org/topic/pi-coin-271568 )
Recursive function implementing 1st continued fraction for n iterations
Quote
float rec(float x,int n){
float ret;
if(x>=n)
ret=1;
else
ret=(1+2*x)+((x+1)*(x+1)/rec(x+1));
return(ret);
}
int main(){
float x;
x=4/(1+(1/rec(1,8))); //here n=8
printf("\npi=%f",x);
return(0);
}
float ret;
if(x>=n)
ret=1;
else
ret=(1+2*x)+((x+1)*(x+1)/rec(x+1));
return(ret);
}
int main(){
float x;
x=4/(1+(1/rec(1,8))); //here n=8
printf("\npi=%f",x);
return(0);
}
Here 8 iterations produce first 3 correct digits of pi.
It can be seen that as the number of iterations are gradually increased,computational complexity increases exponentially.Block reward could be adjusted accordingly.
Verification of n th digit can be directly found using Bailey–Borwein–Plouffe formula. The formula can directly calculate the value of any given digit of pi without the need to calculate the preceding digits.
Attempt and result of obtaining 10 Trillion digits of pi
Other current problems from Experimental Maths could also be used for p2p alt coins.
Besides, cake is better than pi
Pi is a transcendental number, that means it is not a root of a polynomial with integer coefficients (in general algebraic coefficients).
The Decimal representation of a transcendental number is not periodic and there is not a general pattern of repetition..
Still it can be calculated using continued fractions or convergent analytic series, the problem is that different with prime numbers the sequence of digits are not independent and once one get in the loop of calculation, things become straight forward (so not good for block hashing and solving competition)
PS: and as I mentioned elsewhere primecoin does not do a shit on helping computations related to prime number theory investigations. The mass admires the kind of things that mostly have not any clue about!
The Decimal representation of a transcendental number is not periodic and there is not a general pattern of repetition..
Still it can be calculated using continued fractions or convergent analytic series, the problem is that different with prime numbers the sequence of digits are not independent and once one get in the loop of calculation, things become straight forward (so not good for block hashing and solving competition)
PS: and as I mentioned elsewhere primecoin does not do a shit on helping computations related to prime number theory investigations. The mass admires the kind of things that mostly have not any clue about!
To solve a block you have to find the right Pi Chain, since pi continues on forever (or so we think) it should work much the same way as Primecoin.
Here is the current world record holder for calculating Pi to the most places to the right of the decimal point.
http://www.engadget.com/2013/03/15/researcher-breaks-pi-record-with-nvidia/
Does this Idea have merit or am I completely nuts?
Btw, please don't steal my idea as your own, if you want to take on this project please include me that's all I ask.
Here is the current world record holder for calculating Pi to the most places to the right of the decimal point.
http://www.engadget.com/2013/03/15/researcher-breaks-pi-record-with-nvidia/
Does this Idea have merit or am I completely nuts?
Btw, please don't steal my idea as your own, if you want to take on this project please include me that's all I ask.
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