Distributed Beal Conjecture Problem

[Joshua2]

I'm trying to find a counterexample to the beal conjecture from my honors project. I wrote a c# application that is several hundred times faster than Norvig's and several times faster than Dan's.

Would anyone be interested in looking at the math in my code and seeing if there is any easy improvements or possibly contributing some cpu cycles to this project?

I am only planning on running for 1 month until the end of my quarter, so its not that long. I would be interested in timings from different CPU's as well.

[Harvey563]

I would be happy to
put a core or two on the problem.

[Joshua2]

An addition; I am working on an Honor's project. Now I am just using my quad core. My program can run any number of threads efficiently, but needs 64-bit, and uses about 1 gig of ram.

All that you would have to do is run my program with the range you reserved, and zip the small txt file outputted and attach it or email it.

There has not been much computer search done on this, but two people have written programs before me, a NASA research scientist and a Google engineer, and my program hundreds of times faster than the first guy's who wrote it about ten years ago, and about 4x as fast as the second guy's who wrote it a couple summers ago.

I created a website for it.
Thanks!

[Joshua2]

http://jjoshua2.googlepages.com/BealConjecture.exe
There is the file; run it like bealconjecture.exe 4 10000-20000 to run 4 threads searching from 10k to 20k which would be a good range. I have only tested it with 4 threads so far, so it wouldn't hurt to run with it equal to 4 even with fewer cores.
I'm running 1-10k currently, and its half done after a couple hours. We need to go to 1 million, however, it gets much faster towards the end of the search. For example the last 10k only takes ~3 minutes.

[T.Rex]

Don't you have a C code that can be compiled/executed on Linux ?
Tony

[R.D. Silverman]

Originally Posted by Joshua2

I'm trying to find a counterexample to the beal conjecture from my honors project. I wrote a c# application that is several hundred times faster than Norvig's and several times faster than Dan's.

<snip>

If I were your faculty advisor I would counsel against such a computation.
It is almost surely a waste of time. The so-called Beal Conjecture is
almost certainly true. I say so-called because Beal has no right to claim
this conjecture as his own. It had been put forth by a number of other
people prior to his announcing a prize for it. Certainly we should call it
the Beal Prize, but he has no proper claim on the conjecture itself.

BTW, I have FIRST HAND experience of other people putting forth
the conjecture before Beal. In particular it was posed during a lecture
by John Tate at the Arcata conference in 1985. John gave a superb
lecture outlining the (new) work by Frey & Serre that implied TS --> FLT.
Ribet proved the Serre conjectures shortly thereafter and that paved the
way for Wiles' proof.


Several members of the audience raised their hands at the end of the
Tate lecture and asked if the same methods could be applied to the
case of *unequal* exponents. This is such a natural extension of
FLT, and so obvious to many people that it really does not deserve to have
any one's name attached to it.

[retina]

I realise this may be just hot air from the late mfgoode but any chance he was correct? Did anyone here see the paper?

[R.D. Silverman]

Originally Posted by retina

I realise this may be just hot air from the late mfgoode but any chance he was correct? Did anyone here see the paper?

No. There was ZERO chance that he was correct.

[Joshua2]

Originally Posted by T.Rex

Don't you have a C code that can be compiled/executed on Linux ?
Tony

I bet it could be run on wine. I have c# code, which I believe is not compilable on linux. I plan to rewrite my program into java as practice to learn java. I think linux can run that, at least macs can.

[Joshua2]

Originally Posted by R.D. Silverman

If I were your faculty advisor I would counsel against such a computation.
It is almost surely a waste of time. The so-called Beal Conjecture is
almost certainly true. I say so-called because Beal has no right to claim
this conjecture as his own. It had been put forth by a number of other
people prior to his announcing a prize for it. Certainly we should call it
the Beal Prize, but he has no proper claim on the conjecture itself.

What should I call it, because I have to call it something. I guess "An Extension of FLT"? What would you advise me to spend some time writing a program on? I figure it wouldn't be too bad to verify Beal Conjecture on small exponents where a solution is most likely to exist (which may or not have coprime bases) with bases up to something reasonable like 1 million. They have only been checked exp to 7 and bases to 250k, so it wouldn't take too much cpu time. If that doesn't work I plan on going to another project myself.

Any ideas? I was writing a program to find prime numbers using a sieve, but that is not really any use. I wrote a program to try and find a counterexample to the fortunate conjecture, but that took a lot of cpu time.

[CRGreathouse]

Originally Posted by Joshua2

I bet it could be run on wine. I have c# code, which I believe is not compilable on linux. I plan to rewrite my program into java as practice to learn java. I think linux can run that, at least macs can.

Mono *may* suffice for your needs:
http://mono-project.com/Main_Page