Beal's conjecture prize - Page 4

LaurV · 2022-10-20, 05:20

Quote:

Originally Posted by rebirther

From the translation:

Thanks.

So, as I said, the progress is slow (even when you know the theory, as I assume those guys do - a lot of computing power, and a dust particle of progress, compared with limits reached by other, unrelated, computational projects). This is HARD.

chalsall · 2022-10-20, 05:24

Quote:

Originally Posted by LaurV

This is HARD.

Compared to what?

storm5510 · 2022-10-20, 14:14

Quote:

Originally Posted by LaurV

Thanks.

So, as I said, the progress is slow (even when you know the theory, as I assume those guys do - a lot of computing power, and a dust particle of progress, compared with limits reached by other, unrelated, computational projects). This is HARD.

Things which are difficult make them worth the trying.

Something I have not seen, or missed, is clearly defined bounds for A,B,C,x,y, and z. The absolute floor value is 3. The ceiling could be anything, with exceptions, as long as it is positive.

kruoli · 2022-10-20, 19:32

Quote:

Originally Posted by chalsall

Compared to what?

Since "hard" is not a comparative, I would assume it is meant as "high" on an arbitrary personal scale and is not meant to be compared to something in specific.

a1call · 2022-10-20, 21:23

My posit is that the theorem is more likely to be false than true, since there is no reason for it to be true or someone would have proved and collected $1M (which AFAIK is the highest mathematical prize) by now. The problem is that, to find a counter-example is astronomically HARD.
In statistics the probability of any given non-zero, low-probability-occurrence can be made very high if you increase the trials enough and for a theoretical infinite trials, guaranteed/certain.
But, then again what do I know.

ETA: it’s a bit like theorizing that there are no purple cars in the world.
Google says there are about 1M(thousands) cars in the world. I bet you have never seen a purple one. Well, Google is all knowing all wise (after Wikipedia of course).

R. Gerbicz · 2022-10-20, 22:43

Quote:

Originally Posted by storm5510

This is most definitely over my head. Not a language I recognize.

"finding a way to parallelize the program, and re-coding in a faster compiled language (such as C++ or Go or Julia). Then I could invest thousands (or millions) of CPU hours searching for counterexamples.
But Witold Jarnicki and David Konerding already did that: they wrote a C++ program that, in parallel across thousands of machines, searched for A,B up to 200,000 and x,y up to 5,000, but found no counterexamples. So I don't think it is worthwhile to continue on that path."

Even this is a painfully slow program.

storm5510 · 2022-10-21, 22:48

Quote:

Originally Posted by R. Gerbicz

...But Witold Jarnicki and David Konerding already did that: they wrote a C++ program that, in parallel across thousands of machines, searched for A,B up to 200,000 and x,y up to 5,000, but found no counterexamples. So I don't think it is worthwhile to continue on that path.

If they did this in an incremental fashion, it is a wonder they ever got done. GIMPS work is much more preferable.

chalsall · 2022-10-22, 00:03

Quote:

Originally Posted by storm5510

GIMPS work is much more preferable.

Channeling my inner 1 year old... 9-)

"Why?

storm5510 · 2022-10-23, 13:56

Quote:

Originally Posted by chalsall

Channeling my inner 1 year old... 9-)

"Why?

Because there is generally always a resolution. Factor or no factor.

How many iterations have been thrown at Beal? Over a trillion, more, and no counterexample. Despite being a somewhat interesting problem, it is not something I want to mess with.

R. Gerbicz · 2022-10-23, 15:20

Quote:

Originally Posted by storm5510

How many iterations have been thrown at Beal? Over a trillion, more, and no counterexample. Despite being a somewhat interesting problem, it is not something I want to mess with.

The online checker, from the same Google director: http://norvig.com/bealcheck.html

Today passed his tests.. Do you think that it is worth 1 million bucks?
The first few digits of C is shown, it is a quite large number.
(I have really entered A,X,B,Y,C,Z; there was no dirty site hacking).

paulunderwood · 2022-10-23, 15:53

Quote:

Originally Posted by R. Gerbicz

The online checker, from the same Google director: http://norvig.com/bealcheck.html

Today passed his tests.. Do you think that it is worth 1 million bucks?
The first few digits of C is shown, it is a quite large number.
(I have really entered A,X,B,Y,C,Z; there was no dirty site hacking).

Have you confirmed it with Pari/GP? Maybe his (JS?) code suffers from a flaw.

2022-10-20, 21:23	#38
a1call "Rashid Naimi" Oct 2015 Remote to Here/There 2³×293 Posts	My posit is that the theorem is more likely to be false than true, since there is no reason for it to be true or someone would have proved and collected $1M (which AFAIK is the highest mathematical prize) by now. The problem is that, to find a counter-example is astronomically HARD. In statistics the probability of any given non-zero, low-probability-occurrence can be made very high if you increase the trials enough and for a theoretical infinite trials, guaranteed/certain. But, then again what do I know. ETA: it’s a bit like theorizing that there are no purple cars in the world. Google says there are about 1M(thousands) cars in the world. I bet you have never seen a purple one. Well, Google is all knowing all wise (after Wikipedia of course). Last fiddled with by a1call on 2022-10-20 at 21:50

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