The largest number representable in 64 bits • Hacker News Board

Re: The largest number representable in 64 bits

#11

Post by tromp » Mon, Feb 02, 2026, 8:09 PM UTC

Sharlin wrote: post #4

(Edit: oops, incorrect numbers)

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/

Re: The largest number representable in 64 bits

#12

Post by gegtik » Mon, Feb 02, 2026, 8:10 PM UTC

I can do you one better. I can represent the largest number with a single binary bit.

Re: The largest number representable in 64 bits

#13

Post by bmacho » Mon, Feb 02, 2026, 8:13 PM UTC

Can you give a formulation of the problem you are trying to answer?

Re: The largest number representable in 64 bits

#14

Post by tromp » Mon, Feb 02, 2026, 8:19 PM UTC

bmacho wrote: post #13

Can you give a formulation of the problem you are trying to answer?

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.

Re: The largest number representable in 64 bits

#15

Post by aimor » Mon, Feb 02, 2026, 8:20 PM UTC

gegtik wrote: post #12

I can do you one better. I can represent the largest number with a single binary bit.

I can do it in half a bit

Re: The largest number representable in 64 bits

#16

Post by [deleted] » Mon, Feb 02, 2026, 8:22 PM UTC

tromp wrote: post #14

bmacho wrote: post #13

Can you give a formulation of the problem you are trying to answer?

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.

[deleted]

Re: The largest number representable in 64 bits

#17

Post by dmitrygr » Mon, Feb 02, 2026, 8:29 PM UTC

Given time, this will output a bigger number, and it is only 48 bits:

   B0 39      mov al,'9'     //load character '9' to AL
   CD 29      int 29h        //print to screen
   EB FA      jmp short -6   //go again

Re: The largest number representable in 64 bits

#18

Post by bmacho » Mon, Feb 02, 2026, 8:30 PM UTC

tromp wrote: post #14

bmacho wrote: post #13

Can you give a formulation of the problem you are trying to answer?

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.

Do you have a mathematical formulation, or?

Ultimately you seem to pick a random definition of computing and size and then work with that?

Re: The largest number representable in 64 bits

#19

Post by shhsshs » Mon, Feb 02, 2026, 8:37 PM UTC

kstrauser wrote: post #8

What's the biggest up-arrow notation number you can spell with 64 bits? https://mathworld.wolfram.com/KnuthUp-ArrowNotation.html

`9↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑9` seems like a reasonable guess (barring encoding cheats/trickery like @masfuerte commented!)

Edit: I've misread the above comment and my number is is 64 bytes (significantly more than 64 bits. The largest 64 bit number through my approach would be `9↑↑↑↑↑↑9`, which is significantly smaller.

Re: The largest number representable in 64 bits

#20

Post by dooglius » Mon, Feb 02, 2026, 8:40 PM UTC

I'm going to agree with the downvoted people and say that this sort of approach is largely meaningless if you allow arbitrary mappings. IMO the most reasonable mathematical formulation given the structure of the integers (in the sense of e.g. Peano) is that to truly represent an integer you have to represent zero and each other representable number has a representable predecessor, i.e. to say you can represent 5 you need 0,1,2,3,4, and 5 to be representable. By a straightforward counting argument, 2^64-1 is then the largest representable number, in other words the obvious thing is right.