[ExI] Holy cow!

[John Clark]

On Mon, Apr 13, 2026 at 12:14 PM Adrian Tymes via extropy-chat <
extropy-chat at lists.extropy.org> wrote:


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> *> John's claim that "there is no shortcut" for computing the
> Goldbachconjecture at high numbers is false - again, in practice.  Ask
> yourfavorite AI, "When proving the Goodbach conjecture works up to
> somestaggeringly high number, in practice are there optimizations one
> cantake to prove this in a plausible amount of time?", and it'll
> probablytell you.*


*I Took your advice and asked Gemini that very question and it did come up
with some very clever optimization techniques that would dramatically speed
things up, Gemini concluded with this:*

*"As of the latest major computations, the conjecture has been verified to
4 *10^18. To give you a sense of the efficiency: on a standard modern
processor, testing an interval of 10^12 (one trillion) integers near the
current limit takes roughly 45 to 50 minutes. Without these optimizations,
it would take centuries."*

*And that sounds great but even with these dramatic speed ups, to go
from 4*10^18 to 5*10^18 would take 34,722 days, or 95 years. And as you
proceed to deal with larger and larger numbers the slower your progress
will be.  *

*And if you were trying to calculate Busy Beaver numbers things would be
even worse because at some point BB grows faster been super exponential, in
fact it grows faster than ANY conceivable computable function. If there was
a computable function that grew faster than **Busy Beaver then you could
use it to solve the Halting Problem, but Alan Turing proved in 1936 that
was logically impossible. *

*  John K Clark*


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