I have a problem,
As with CUDA can be implemented algorithm testing Beal’s Conjecture?
The problem is described here: (it’s very simple)
http://en.wikipedia.org/wiki/Beal%27s_conjecture
I know that probably no one will help me with a very efficient solution. But how to solve this, even trivial in CUDA?
“I have a problem,”
such honesty
“(it’s very simple)”
but of course, that is why:
“For a proof or counterexample published in a refereed journal, Beal initially offered a prize of US $5,000 in 1997, raising it to $50,000 over ten years,[6] but has since raised it to US $1,000,000”
i think we should put forward a cuda team to tackle this
You should design a crypto currency that uses finding such a counterexample as its “proof of work” function. Then you could harness the power of a thousand cores, and you’d have the chance to profit a bit even if no such counterexample is ever found ;)
the billionaire offers $1m to solve the problem, so that he can take his remaining $999m and flush it through the solution…
“You should design a crypto currency”
…to compete with countless other crypto currencies…
honestly, is something like bitcoin mining still profitable? seems you have to be a bitcoin magnate these days to turn a profit
having finding a counterexample as ‘proof of work’ is not a bad idea, nonetheless
well, Rysiu; perhaps fate smiled upon you
i spent a few minutes on your problem, and may have the prelude to some pseudo code
a) introduce and utilize a cap or ceiling (argue 100) on the prime numbers, and the exponents/ powers, to consider (see below); this should make an initial implementation easier, and would always be easy to revise/ remove
b) for the chosen ceiling, find all prime numbers smaller than the ceiling
c) for the demarcated set of prime numbers, find all multiples of the prime numbers that are smaller than the ceiling
d) for the set of prime number multiples, find all possible combinations thereof
e) for the chosen ceiling, find all exponent combinations
f) for each prime number combination, apply each exponent combination, and evaluate A^x + B^y == C^z
now, this is very rudimentary, and others are welcome to comment
but clearly, this is an ‘advanced’ problem
i anticipate a 3 tier nested algorithm to simultaneously allow parallelism and reduce memory footprint, and the first draft code may easily be in the region of 2-5k lines of code, conditional on your use of libraries