You can easily turn every statement into a program. If the program stops, or “halts”, then the statement is true, and if it never stops, or “loops”, the statement is false.

Like, for example, the following program corresponds to the statement: “There’s at least one even number that cannot be expressed as the sum of two primes” (this is the negation of the so-called “Goldbach Conjecture”):

So, if we can figure out if any program will halt or not halt, we can prove everything! Can we do that, though?

I believe the halting program/problem is inapplicable for a solution to the Goldbach problem. The solution to the Goldbach problem depends on the distribution of all odd primes less any given positive even integer.

Relevant Reference Link: https://energytheoryorg.wordpress.com/2021/01/10/what-could-be-an-indirect-proof-of-the-goldbachs-conjecture/?theme_preview=true&iframe=true&frame-nonce=d4f884a623

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Simon replies: I just used it as an example…it was not meant to be something the halting problem is applicable to

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Oops! I stand corrected. Thanks for the reply!

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