1 year ago

What's 2 to the tetration of 5?

(If don't know what tetration is read Wikipedia about it)

But you just have to know that "^^" is notation for tetration.

(What a rhyme though)


Well we all know (or don't) that 2^^4 is 65536 or 2^16.

Next tetration of 2 is 2^^5 which is 2^65536 which is big.

But smol for me.

So I calculated its exact value.

However.....

It would be stupid to calculate it by doing multiplication in base 10 cuz base 10 is stupidly stupid in expressing large numbers.

So I used Base 32 which allowed me with ease calculate multiplication by just multiplying 2 digits by itself & remember about 0s.

First I converted 65536 to the Base 10 by doing wacky ass diving by 32.

Final number I got was

2000 in base 32 which is great.

Cuz 32^3 * 2 equals 2^16.

So now instead multiplying by 2 65536 times.

I multiplied 65536 by itself to get 2^32 by simple exponentiation rules.

Next I multiplied 2^32 by 2^32 which is basically (2^32)^2

By that we're going to get 2^64

I repeated entire process until I got 2^2^2^2^2 or 2^2^16 or 2^65536 or 2^2000 in base 32

After an hour of counting different powers of 2 i reached to my goal 2^2000 in base 32

Which is 2 * 10^12 in base 32 if you want to calculate exact value in base 10 well count 32^12 * 2 I guess.

How unsatisfying I know.

It's just 2000000000000 in base 32 but just imagine how big this number is in our number base.

So next number which I'm gonna calculate is.....

2 to the tetration of 10!

Which is basically 2*10^12 ^ 2*10^12 which should give us 10th tetration of 2.

I hope you liked this article if not well.... there's no dislike button so...... I just wastes your time I guess.

Have a gr8 day anyway!



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