Re: A useless machine

From	Michael S <already5chosen@yahoo.com>
Newsgroups	comp.arch
Subject	Re: A useless machine
Date	2026-02-16 12:31 +0200
Organization	A noiseless patient Spider
Message-ID	<20260216123131.00003e22@yahoo.com> (permalink)
References	<10mpgtp$32h0n$1@dont-email.me> <10ms1rm$3s9f4$1@dont-email.me> <20260215153526.00005240@yahoo.com> <20260215183335.0000649e@yahoo.com> <10mt67k$996a$1@dont-email.me>

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On Sun, 15 Feb 2026 19:19:16 -0000 (UTC)
Thomas Koenig <tkoenig@netcologne.de> wrote:

> Michael S <already5chosen@yahoo.com> schrieb:
> 
> > "Unknown" is a correct theoretically answer, but I can provide a
> > very educated guess that on average it would take ~500 steps and
> > the worst case would not exceed 2000 steps.
> > So, bad news are that overall it will take more than a million
> > years on your machine. And good news are that it'll take less than
> > 2 million years.  
> 
> Not as bad, very many simplifications are possible.
> 
> For one, you can discount all even numbers as starting values.

O.k.

> You can go further: If you look at residues modulo 2^n of your
> starting numbers, there are only A076227(n) "interesting" remaiders
> that you need to look at.

Can not say that I understood.

> If you take n=39, only 3611535862 cases
> need to be looked at, so only 3611535862/2^39 of all cases need to
> be looked at, a reduction of a factor around 150.  You can also
> do some more reductions (only 2/3 of those numbers need checking
> if you can calculate the remainder by 3 fast).  There are different
> tradeoffs for different n, of course (a factor of 16 for n=10,
> for example).
> 

The estimate above was done for loop that finishes at 1.
For brute-force disproof  of Collatz conjecture it is unnecessary. We
can stop at n < n0. I think, you mentioned it in your original post,
but I didn't pay attention. 
Due to early exit mean number of iteration is cut from ~500 to 7 or at
worst 8. 

> The main key is parallelization.

And here is a problem.
If one want to finish in, say, 1 month, one would need ALOT of
parallelization. Even after all improvements we are talking about
several millions of testing nodes. At such scale I can think about two
main problems:
1. Dispatcher become a bottleneck
2. Some node will fail. It has to be detected and their jobs
re-allocated. Which further complicates a scheduler.

It does not sound particularly hard if somebody pays for engineering,
esp. if the whole work done in one dedicated data center.
Otherwise it does not sound easy.

The worst part is that that there is nothing special about 2**71.
Or about 2**80 for that matter. Tim Reintch already said that better
than I can. The machine is not merely useless, it is pointless.

Thread

A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-14 09:57 +0000
  Re: A useless machine MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-14 18:48 +0000
    Re: A useless machine David Brown <david.brown@hesbynett.no> - 2026-02-14 20:18 +0100
      Re: A useless machine MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-14 21:22 +0000
        Re: A useless machine Stephen Fuld <sfuld@alumni.cmu.edu.invalid> - 2026-02-14 13:30 -0800
        Re: A useless machine David Brown <david.brown@hesbynett.no> - 2026-02-15 12:50 +0100
          Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-21 13:48 -0600
            Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-21 21:40 +0100
              Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-21 15:17 -0600
                Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-22 04:50 -0600
              Re: A useless machine Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-03-12 21:01 -0700
            Re: A useless machine David Brown <david.brown@hesbynett.no> - 2026-02-22 14:43 +0100
              Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-22 12:38 -0600
                Re: A useless machine David Brown <david.brown@hesbynett.no> - 2026-02-23 10:51 +0100
                Re: A useless machine MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-26 01:27 +0000
                Re: A useless machine David Brown <david.brown@hesbynett.no> - 2026-02-26 09:21 +0100
                Re: A useless machine Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-03-12 21:11 -0700
      Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-15 14:58 +0100
      Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-21 12:27 -0600
        Re: A useless machine David Brown <david.brown@hesbynett.no> - 2026-02-22 15:14 +0100
      Re: A useless machine Stefan Monnier <monnier@iro.umontreal.ca> - 2026-02-22 11:41 -0500
        Re: A useless machine David Brown <david.brown@hesbynett.no> - 2026-02-23 10:53 +0100
          Re: A useless machine Stefan Monnier <monnier@iro.umontreal.ca> - 2026-02-23 10:52 -0500
  Re: A useless machine Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-02-14 21:19 -0800
  Re: A useless machine Robert Finch <robfi680@gmail.com> - 2026-02-15 03:58 -0500
    Re: A useless machine David Brown <david.brown@hesbynett.no> - 2026-02-15 13:14 +0100
      Re: A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-15 15:46 +0000
      Re: A useless machine Robert Finch <robfi680@gmail.com> - 2026-02-15 10:56 -0500
        Re: A useless machine MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-15 19:16 +0000
          Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-15 22:40 +0100
            Re: A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-26 19:31 +0000
        Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-18 18:22 +0200
          Re: A useless machine Robert Finch <robfi680@gmail.com> - 2026-02-18 22:56 -0500
            Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-19 12:10 +0200
              Re: A useless machine Robert Finch <robfi680@gmail.com> - 2026-02-21 01:56 -0500
                Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-21 19:23 +0200
                Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-21 20:36 +0200
                Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-22 10:46 +0200
                Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-22 12:45 +0100
                Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-22 16:35 +0200
                Re: A useless machine Robert Finch <robfi680@gmail.com> - 2026-02-22 19:12 -0500
                Re: A useless machine Robert Finch <robfi680@gmail.com> - 2026-02-22 19:47 -0500
                Re: A useless machine EricP <ThatWouldBeTelling@thevillage.com> - 2026-02-21 15:39 -0500
                Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-22 03:16 +0200
                Re: A useless machine EricP <ThatWouldBeTelling@thevillage.com> - 2026-02-22 14:48 -0500
                Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-22 23:25 +0200
            Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-19 11:51 +0100
              Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-19 23:12 +0200
                Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-20 15:11 +0100
            Re: A useless machine Stefan Monnier <monnier@iro.umontreal.ca> - 2026-02-19 15:27 -0500
              Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-20 11:41 +0200
              Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-22 18:41 -0600
                Re: A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-23 11:10 +0000
                Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-23 17:24 -0600
                Re: A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-24 06:44 +0000
                Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-24 01:38 -0600
                Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-24 03:16 -0600
                Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-24 04:52 -0600
                Re: A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-24 11:16 +0000
                Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-24 13:19 -0600
                Re: A useless machine Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-03-12 21:14 -0700
          Re: A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-20 08:01 +0000
    Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-15 15:35 +0200
      Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-15 18:33 +0200
        Re: A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-15 19:19 +0000
          Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-16 12:31 +0200
            Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-17 15:41 +0200
              Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-17 18:17 +0200
    Re: A useless machine anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-02-15 22:41 +0000
  Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-15 14:52 +0100
    Re: A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-15 16:45 +0000
      Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-15 18:01 +0100
        Re: A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-15 19:42 +0000
          Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-15 22:59 +0100
            Re: A useless machine Robert Finch <robfi680@gmail.com> - 2026-02-15 21:53 -0500
              Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-16 12:40 +0200
                Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-16 20:34 +0200
              Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-16 16:08 +0100
  Re: A useless machine Stephen Fuld <sfuld@alumni.cmu.edu.invalid> - 2026-02-16 07:50 -0800
    Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-16 18:31 +0200
    Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-18 21:56 +0100

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