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It's fun but not very interesting. A real research paper would explain the method they used to find this examples. Even only a few lines if the method is alread

It's fun but not very interesting. A real research paper would explain the method they used to find this examples. Even only a few lines if the method is already known.

dahart 7y ago
“A direct search on the CDC 6600 yielded” That’s probably enough description of methodology for many people here to reproduce the results, right? :)
- mikeash 7y ago
  I wouldn’t even know where to start looking for a working CDC 6600.
  - jfk13 7y ago
    Someone's probably written an emulator in JavaScript, so you can just run it in your browser. :)
    - pinewurst 7y ago
      http://members.iinet.net.au/~tom-hunter/ http://members.iinet.net.au/~tom-hunter/ There's a C one. Truly though, it wouldn't be hard to just write a brute force checker for this in some reasonably efficient compiled language.
  - dahart 7y ago
    I wouldn’t either. But I guess I don’t consider a CDC 6600 specifically to be critical to the methodology. I just meant that a lot of people around here could certainly write a computer program for direct search of the sum of four fourth power integers. It seems like this might even be one of the problems on Project Euler...?
    - mikeash 7y ago
      I was just pretending to misunderstand as a joke. You did make me curious, though. The numbers are fairly small. I implemented the dumbest possible brute force search for all combinations of numbers 1-255. On my laptop, it found 133^5 + 110^5 + 84^5 + 27^5 = 144^5 in about 50 minutes. I'd guess that this laptop is something like 100,000 times faster than the CDC 6600, so that dumb search would have taken about a decade. However, you can get at least a couple orders of magnitude improvement with some simple improvements.
      - pinewurst 7y ago
        I took it down to under 5 mins on my old Macbook by memoizing exponentiation and aborting calculation/addition/comparison of later terms if the earlier sum exceeded the result.
        triska 7y ago
        Very nice! For comparison, here is a Prolog program that uses CLP(ℤ), constraint logic programming over integers, to search for solutions: solution(Options, Vs) :- A^5 + B^5 + C^5 + D^5 #= E^5, Vs = [A,B,C,D,E], A #>= B, B #>= C, C #>= D, length(_, Exp), Upper #= 2^Exp, portray_clause(Upper), Vs ins 1..Upper, labeling(Options, Vs). The speed of this program depends a lot on the Prolog implementation, and also on the options that are used to specify the search strategy. With this program, one can find a solution within one minute even with rather slow Prolog systems on (current) commodity machines: ?- time(solution([bisect], Vs)). 1. 2. 4. 8. 16. 32. 64. 128. 256. % 609,346,692 inferences, 57.855 CPU in 58.197 seconds (99% CPU, 10532282 Lips) Vs = [133, 110, 84, 27, 144] .
alimw 7y ago
This was a real research paper. The result would have been extremely interesting to any mathematician tempted to work on the conjecture. You can check it by tapping those numbers into a calculator—the search itself need never be performed again.

It's fun but not very interesting. A real research paper would explain the method they used to find this examples. Even only a few lines if the method is already known.

dahart 7y ago

“A direct search on the CDC 6600 yielded” That’s probably enough description of methodology for many people here to reproduce the results, right? :)

mikeash 7y ago
I wouldn’t even know where to start looking for a working CDC 6600.
- jfk13 7y ago
  Someone's probably written an emulator in JavaScript, so you can just run it in your browser. :)
  - pinewurst 7y ago
    http://members.iinet.net.au/~tom-hunter/ http://members.iinet.net.au/~tom-hunter/ There's a C one. Truly though, it wouldn't be hard to just write a brute force checker for this in some reasonably efficient compiled language.
- dahart 7y ago
  I wouldn’t either. But I guess I don’t consider a CDC 6600 specifically to be critical to the methodology. I just meant that a lot of people around here could certainly write a computer program for direct search of the sum of four fourth power integers. It seems like this might even be one of the problems on Project Euler...?
  - mikeash 7y ago
    I was just pretending to misunderstand as a joke. You did make me curious, though. The numbers are fairly small. I implemented the dumbest possible brute force search for all combinations of numbers 1-255. On my laptop, it found 133^5 + 110^5 + 84^5 + 27^5 = 144^5 in about 50 minutes. I'd guess that this laptop is something like 100,000 times faster than the CDC 6600, so that dumb search would have taken about a decade. However, you can get at least a couple orders of magnitude improvement with some simple improvements.
    - pinewurst 7y ago
      I took it down to under 5 mins on my old Macbook by memoizing exponentiation and aborting calculation/addition/comparison of later terms if the earlier sum exceeded the result.
      - triska 7y ago
        Very nice! For comparison, here is a Prolog program that uses CLP(ℤ), constraint logic programming over integers, to search for solutions: solution(Options, Vs) :- A^5 + B^5 + C^5 + D^5 #= E^5, Vs = [A,B,C,D,E], A #>= B, B #>= C, C #>= D, length(_, Exp), Upper #= 2^Exp, portray_clause(Upper), Vs ins 1..Upper, labeling(Options, Vs). The speed of this program depends a lot on the Prolog implementation, and also on the options that are used to specify the search strategy. With this program, one can find a solution within one minute even with rather slow Prolog systems on (current) commodity machines: ?- time(solution([bisect], Vs)). 1. 2. 4. 8. 16. 32. 64. 128. 256. % 609,346,692 inferences, 57.855 CPU in 58.197 seconds (99% CPU, 10532282 Lips) Vs = [133, 110, 84, 27, 144] .

alimw 7y ago

This was a real research paper. The result would have been extremely interesting to any mathematician tempted to work on the conjecture. You can check it by tapping those numbers into a calculator—the search itself need never be performed again.