Beal's conjecture prize

[retina]

Originally Posted by chalsall

... do an exhaustive search ...

Extensive?

I can't imagine even a dedicated Quantum Holographic Blockchain 1nm ASIC AGI that could do an exhaustive search over the integers!
_{I hope I used enough trendy buzzwords to make it sound like a futuristic super computer.}

[chalsall]

Originally Posted by retina

Extensive?

I can't imagine even a dedicated Quantum Holographic Blockchain 1nm ASIC AGI that could do an exhaustive search over the integers!
_{I hope I used enough trendy buzzwords to make it sound like a futuristic super computer.}

Cute.

[rebirther]

There were 2 BOINC Projects in the past Beal@home, BealF@home, nobody knows why they are gone, they had already a working app.

[storm5510]

Originally Posted by chalsall

Yeah...

In at least one case it has been well documented that if you're going to do an exhaustive search, it is best to use C. If not hand-crafted assembly, tuned to each processor...

I thought about C++ as a console program. No need for the GUI baggage. I recognize it when I see it, but little more.

Yafu can do this, to a point. I tried a few things in the form of a^x + b^y. It is capable of quite large exponentiation. Implementation could be a problem with the comparison. e.g. to c^z

[kriesel]

Originally Posted by storm5510

Implementation could be a problem with the comparison. e.g. to c^z

Compute a^x+b^y-c^z and compare to zero.

[bsquared]

Originally Posted by storm5510

I thought about C++ as a console program. No need for the GUI baggage. I recognize it when I see it, but little more.

Yafu can do this, to a point. I tried a few things in the form of a^x + b^y. It is capable of quite large exponentiation. Implementation could be a problem with the comparison. e.g. to c^z

I am not recommending yafu for this problem, quite the opposite in fact, but it does have the operator "eq" for comparison:

>> eq(137998080^3+940896^4,1359072^4)

ans = 1

>> eq(60000000000000000000^3+70000000000000000000^3,82376613842809255677^3)

ans = 0

[Batalov]

Originally Posted by storm5510

Implementation could be a problem with the comparison. e.g. to c^z

In most implementations, you don't know c or z. And why would scan over those? Wasteful.

It is simpler than that, you sum a^x + b^y, then run any implementation of ispower() on the result and ispower() will return 1 or 2 (which is of no use) ... or >2 and only then you have the solution.

With the disclaimer that this is just an answer to "your" approach. The real approach is that there are tons of theoretical results on restrictions on what triples are even eligible to start search. Those should be used and that will be 99% of the code. Checking a double for loop with ispower() inside is <1% of the "code".

[Batalov]

Originally Posted by rebirther

There were 2 BOINC Projects in the past Beal@home, BealF@home, nobody knows why they are gone, they had already a working app.

For all you know, they could have been simply mining for bitcoins (for the owner of course, not for the unsuspecting participants) and pretending to do the relevant work.
There were quite a few of such fake "BLABLA@Home" projects. Beware.

[chalsall]

Originally Posted by storm5510

I thought about C++ as a console program. No need for the GUI baggage. I recognize it when I see it, but little more.

Please trust me on this...

A beginner should not start with C++. It can actually be implemented using only macros, and confuses the beginner.

Either start with C, and enjoy "all the power, and all the safety features, of a chain saw.

Or start with something that holds your hand while you make mistakes. Like Python. Or Rust. Or Go. Or Perl...

Originally Posted by storm5510

Yafu can do this, to a point.

That's an independant code path (wrapped into an executable). Not a language.

[storm5510]

Originally Posted by chalsall

Please trust me on this...

A beginner should not start with C++. It can actually be implemented using only macros, and confuses the beginner.

Either start with C, and enjoy "all the power, and all the safety features, of a chain saw.

Or start with something that holds your hand while you make mistakes. Like Python. Or Rust. Or Go. Or Perl...

I had a Borland C variant back in the early '90's. It was console only. There were not that many GUI programs for Windows 3.x. I managed to write a few things with it. I sold the package to a trade school mate later on.

I don't recognize the names Rust and Go. Three years ago, and with some help from a member here, I managed to teach myself enough Perl to be dangerous. I didn't stick with it though.

Originally Posted by kriesel

Compute a^x + b^y - c^z and compare to zero.

An excellent idea and one I might not have though of.

What I am using now, I won't mention the name because I don't want to be scoffed at. It has hundreds of libraries which only requires an "include" type statement at the top. One library is called "BigInt." I managed to get it to display something around 2¹¹⁵⁰, more or less. It would not go much beyond that.

[xilman]

Originally Posted by storm5510

What I am using now, I won't mention the name because I don't want to be scoffed at. It has hundreds of libraries which only requires an "include" type statement at the top. One library is called "BigInt." I managed to get it to display something around 2¹¹⁵⁰, more or less. It would not go much beyond that.

Here is how I include a library into many of my number theory programs.

use bigint lib=>'GMP';


And here is how I test for primality of fairly small numbers (up to 1200 digits say)

# Primality testing function.
# Initial sanity check to see whether Pari/gp is installed and working correctly.
my $sc1 = `echo "isprime(1074884750872101952308847649628260864479,2)" | /usr/bin/gp -f -q`; # Known prime.
my $sc2 = `echo "isprime(1074884750872101952308847649628260864481,2)" | /usr/bin/gp -f -q`; # Known composite.
($sc1 != 1 or $sc2 != 0) and die "Failed gp sanity check\n";
sub is_prime($)
{
return `echo "isprime($_[0],2)" | /usr/bin/gp -f -q -s 104857600` == 1;
}


Scoff at me if you like.

The take home message is that it is largely irrelevant what the fancy bits is written in as long as all the computationally intensive work is done with a highly optimized library.