[ExI] Holy cow!

[Adrian Tymes]

On Mon, Apr 13, 2026 at 11:59 AM Jason Resch via extropy-chat
<extropy-chat at lists.extropy.org> wrote:
> On Mon, Apr 13, 2026, 9:58 AM Adrian Tymes via extropy-chat <extropy-chat at lists.extropy.org> wrote:
>> On Mon, Apr 13, 2026 at 9:47 AM John Clark <johnkclark at gmail.com> wrote:
>> >> Consider that this would only be run on a computer that actually
>> >> exists - which, by consequence of existing, has finite memory and thus
>> >> a maximum exact value that it can hold in memory.  So, for a given
>> >> computer, we can know if foo() will be called, since we only need to
>> >> calculate up to that maximum number.
>> >
>> > Only?
>>
>> Only, to see what will happen on that particular computer - even for a
>> supercomputer.
>
> A typical computer today has 1 GB of memory.
>
> For a computer with 1 GB of memory to count through the maximum number of distinct states it can represent it would need to iterate through 2^(number of bits of memory) or 2^(2^33), or 2^(8 billion and change).

Which, so long as we're talking hypotheticals, is still less than
infinity - so it would hypothetically be possible to know whether it
would find a Goodbach conjecture counterexample within that space.

> Modern encryption keys are only 256 bits long, because no super computer can ever hope to count to 2^256.

Only in practice.  This discussion keeps leaning toward theory.

John's claim that "there is no shortcut" for computing the Goldbach
conjecture at high numbers is false - again, in practice.  Ask your
favorite AI, "When proving the Goodbach conjecture works up to some
staggeringly high number, in practice are there optimizations one can
take to prove this in a plausible amount of time?", and it'll probably
tell you.

Or to go back to that quoted claim: you never said the count couldn't
be in increments of 2^255.