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The largest number representable in 64 bits

https://tromp.github.io/blog/2026/01/28/largest-number-revised
19•tromp•1h ago

Comments

masfuerte•52m ago
> The largest number (currently known to be) representable in 64 bits is w218

In my representation the bit pattern 00000000_00000000_00000000_00000000_00000000_00000000_00000000_00000001 stands for the number w218+1.

I win!

tromp•34m ago
> Precisely because the Turing machine model is so ancient and fixed, whatever emergent behavior we find in the Busy Beaver game, there can be no suspicion that we “cheated” by changing the model until we got the results we wanted.

Sorry; no winning for cheaters:-(

cortesoft•49m ago
This feels like the computer science version of this article: https://www.scottaaronson.com/writings/bignumbers.html
Sharlin•47m ago
FWIW, w218 equals

627,421,742,590,461,754

or

0x08B5_0CC0_2B76_073A

in case someone would like to memorize it or something.

tromp•21m ago
Following BLC8's bytewise encoding convention of [1], w218's binary encoding 0100 0101 1010 1000 0110 0110 0000 0001 0101 1011 1011 0000 0011 1001 1101 0 gets padded with 3 arbitrary least significant bits, say 000, and becomes 45A8_6601_5BB0_39C0 in hexadecimal.

[1] https://www.ioccc.org/2012/tromp/

heyitsdaad•41m ago
bits == entropy.

Everything else is word play.

IshKebab•38m ago
Once you allow any format the question is completely meaningless. You can just define 0 to mean any number you want.
tromp•31m ago
The post addresses this very issue:

> Precisely because the Turing machine model is so ancient and fixed, whatever emergent behavior we find in the Busy Beaver game, there can be no suspicion that we “cheated” by changing the model until we got the results we wanted.”

kstrauser•36m ago
What's the biggest up-arrow notation number you can spell with 64 bits?

https://mathworld.wolfram.com/KnuthUp-ArrowNotation.html

gegtik•20m ago
I can do you one better. I can represent the largest number with a single binary bit.
aimor•10m ago
I can do it in half a bit
bmacho•17m ago
Can you give a formulation of the problem you are trying to answer?
tromp•11m ago
To find the largest number that is computable by a program of at most 64 bits in a non-cheating language; i.e. one that's not geared toward producing large numbers.

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