Re: How the requirements that Professor Sipser agreed to are exactly met

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
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