Ultimate Prog Challenge 2023

Given the function `f` defined as:
f(0) = 2
f(N) = f(N-1) ** f(N-1)

calculate `f(5)`

If you want to hire me please see my web page. I would love to put my team of experts onto this problem!

f(5) = f(4) ** f(4)
f(4) = f(3) ** f(3)
f(3) = f(2) ** f(2)
f(2) = f(1) ** f(1)
f(1) = f(0) ** f(0)
f(0) = 2
f(1) = 2 ** 2 = 4
f(2) = 4 ** 4 = 256
f(3) = 256 ** 256 = (2 ** 8) ** 256 = 2 ** 2048
f(4) = (2 ** 2048) ** (2 ** 2048) = 2 ** (2048 * (2 ** 2048) = 2 ** ((2 ** 11)*(2 ** 2048)) = 2 ** (2 ** 2059)
f(5) = (2 ** (2 ** 2059)) ** (2 ** (2 ** 2059)) = 2 ** ((2 ** 2059)*(2 ** (2 ** 2059))) = 2 ** (2 ** (2059 + (2 ** 2059)))

scheme@(guile-user)> (expt 2 (expt 2 (+ 2059 (expt 2 2059))))
ERROR: Throw to key `numerical-overflow' with args `("integer-expt" "Numerical overflow" #f #f)'.

nigger

>>3

Your Scheme interpreter is broken.
Haskell doesn't have such errors.

>>5
but can you play jazz jackrabbit in haskell like the hackers of old?

7 constanza

Should the output be serial or parallel? I only have 30 bits.

>>7
can't standjah!

>>5
Ok, please compute in Haskell the number
2 ** (2 ** 66185228434044942951864067458396061614989522267577311297802947435570493724401440549267868490798926773634494383968047143923956857140205406402740536087446083831052036848232439995904404992798007514718326043410570379830870463780085260619444417205199197123751210704970352727833755425876102776028267313405809429548880554782040765277562828362884238325465448520348307574943345990309941642666926723379729598185834735054732500415409883868361423159913770812218772711901772249553153402287759789517121744336755350465901655205184917370974202405586941211065395540765567663193297173367254230313612244182941999500402388195450053080385547)

>>10
Computed. Learn about the lazy evaluation.

>>11
What's the answer?

>>12
True

>>13
It should be a very large integer.

>>14
Which is not zero, therefore logically true.

>>15
x takes log_2(x) bytes to store, so 2 ** (2 ** 66185228434044942951864067458396061614989522267577311297802947435570493724401440549267868490798926773634494383968047143923956857140205406402740536087446083831052036848232439995904404992798007514718326043410570379830870463780085260619444417205199197123751210704970352727833755425876102776028267313405809429548880554782040765277562828362884238325465448520348307574943345990309941642666926723379729598185834735054732500415409883868361423159913770812218772711901772249553153402287759789517121744336755350465901655205184917370974202405586941211065395540765567663193297173367254230313612244182941999500402388195450053080385547) would take 2 ** 66185228434044942951864067458396061614989522267577311297802947435570493724401440549267868490798926773634494383968047143923956857140205406402740536087446083831052036848232439995904404992798007514718326043410570379830870463780085260619444417205199197123751210704970352727833755425876102776028267313405809429548880554782040765277562828362884238325465448520348307574943345990309941642666926723379729598185834735054732500415409883868361423159913770812218772711901772249553153402287759789517121744336755350465901655205184917370974202405586941211065395540765567663193297173367254230313612244182941999500402388195450053080385547 bytes to store.
Do you understand the implications?

>>16
>Do you understand the implications?
You're going to put a log up my ass?

>>16
I meant bits, sorry.
>>17
No, but if the earth has around 10^50~~100*10^48~~100*2^160<2^167 atoms, and it takes more than one atom to build a flip flop of one bit, then the whole earth would not be enough to store the number required by the OP's challenge.

>>18
That's a lot of atoms. How many of them will go up my anus?

Due to the number being such large, it could have a lot of child porn hidden, which is a function of probability. Given that, any sufficiently large number is illegal.