Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: Richard Heathfield <rjh@cpax.org.uk>
Newsgroups: comp.theory
Subject: Re: How the requirements that Professor Sipser agreed to are exactly
 met
Date: Tue, 13 May 2025 06:11:05 +0100
Organization: Fix this later
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On 13/05/2025 03:01, olcott wrote:
> If the Goldbach conjecture is true (and there is
> no short-cut)

We don't know that. Fermat's Last Theorem had a short cut, but it 
took 358 years to find it. At that rate, we won't find Goldbach's 
short cut (if it has one) for another 75 years.

> this requires testing against every
> element of the set of natural numbers an infinite
> computation.

Only if it's true. So if it's true, the testing program will 
never halt. But if it's false, the tester will eventually find 
the counter-example, print it, and stop.

So a program that can tell whether another program will halt can 
tell us whether Goldbach's conjecture is true.

It would be the short cut that you say doesn't exist.

-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
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