9^(9^9)

[Raman]

9^9[SUP]9[/SUP] = 9^387420489 is being the largest number that can be written with 3 digits.
The decimal representation contains 369693100 digits. I executed the program
from apfloat.org, along with some certain modifications, in order to print out
the entire 369693100 digit number.

Extract all the files from the attachment to the same folder.
For the linux users; run ./commands.bat; that will create out all the linux executables
as such. For some reason, I am not able to get a Windows executable at all

Then, running away with
./powers 9 387420489 > "9^9^9.txt"
prints out the entire decimal representation for the number, as such.
It will create to 74 temporary ap0000xx files meanwhile

If it looks too large enough for you rather at first,
you can try out starting off from with the values for
./powers 8 16777216 <base> > "8^8^8.txt"
for printing out the value for 8^8[SUP]8[/SUP] as such,
./powers 7 823543 <base> > "7^7^7.txt"
for printing out the value for 7^7[SUP]7[/SUP] as since,

furthermore x⁹ = 9^9[SUP]9[/SUP]
x = 9^9[SUP]8[/SUP]
./powers 9 43046721 > "9^9^8.txt"

Other popular options are being
./powers 2 65536 > "2^{2[SUP]2[SUP]2[SUP]2}[/SUP][/SUP][/SUP].txt"
./powers 3 6566 > "3^6566.txt"
./powering 3 2 10 209 for printing out Squares of 3 in base 10 till 3²⁰⁹ (100 digits)
./ladder 1 2 10 332 Keep on multiplying by 2 starting with 1 in base 10 for 332 times (100 digits)
./ladder 1 3 16 153 Keep on multiplying by 3 starting with 1 in base 16 for 153 times
./lucas 1 1 10 37 The value for the 37^th Fibonacci number
./lucas 1 3 10 78 The value for the 78^th Lucas number ~ 2*10¹⁶
./fibonacci 1 1 10 100 for listing out the first 100 Fibonacci numbers
./fibonacci 1 3 10 100 for listing out the first 100 Lucas numbers
./factorial 1 1 10 1000 for printing out the value for the number 1000 Factorial
./power 1 1 10 100 for listing out the first 100 Factorial numbers
./power 3628800 11 10 10
11! ... 20!

[Batalov]

What a way to solve problems! A poll of public opinion!

This is not math. This is numerology. Wrong forum.

GP> Mod(9,1000)^(9^9)

[Raman]

Originally Posted by Batalov

What a way to solve problems! A poll of public opinion!

This is not math. This is numerology. Wrong forum.

GP> Mod(9,1000)^(9^9)

My intention is being to get the decimal representation value for the entire 369693100 digit number, for that you need to run the commands
./commands.bat
./powers 9 387420489 > "9^9^9.txt"
from the attachment file

The poll is being a sideways extra for my own testing to the general public knowledge for the value computation for the number.
The poll is not being the main intention at all.
I wanted to test over on into how many people give away with the wrong thing, rather

I see that entire full decimal representation value are being extracted for the values for M43112609, M42643801, M37156667, etc. ...

[science_man_88]

Originally Posted by Raman

9^9[SUP]9[/SUP] = 9^387420489 is being the largest number that can be written with 3 digits.
The decimal representation contains 369693100 digits. I executed the program
from apfloat.org, along with some certain modifications, in order to print out
the entire 369693100 digit number.

Extract all the files from the attachment to the same folder.
For the linux users; run ./commands.bat; that will create out all the linux executables
as such. For some reason, I am not able to get a Windows executable at all

Then, running away with
./powers 9 387420489 > "9^9^9.txt"
prints out the entire decimal representation for the number, as such.
It will create to 74 temporary ap0000xx files meanwhile

If it looks too large enough for you rather at first,
you can try out starting off from with the values for
./powers 8 16777216 <base> > "8^8^8.txt"
for printing out the value for 8^8[SUP]8[/SUP] as such,
./powers 7 823543 <base> > "7^7^7.txt"
for printing out the value for 7^7[SUP]7[/SUP] as since,

furthermore x⁹ = 9^9[SUP]9[/SUP]
x = 9^9[SUP]8[/SUP]
./powers 9 43046721 > "9^9^8.txt"

Other popular options are being
./powers 2 65536 > "2^{2[SUP]2[SUP]2[SUP]2}[/SUP][/SUP][/SUP].txt"
./powering 3 2 10 209 for printing out Squares of 3 in base 10 till 3²⁰⁹ (100 digits)
./ladder 1 2 10 332 Keep on multiplying by 2 starting with 1 in base 10 for 332 times (100 digits)
./ladder 1 3 16 153 Keep on multiplying by 3 starting with 1 in base 16 for 153 times
./lucas 1 1 10 37 The value for the 37^th Fibonacci number
./lucas 1 3 10 78 The value for the 78^th Lucas number ~ 2*10¹⁶
./fibonacci 1 1 10 100 for listing out the first 100 Fibonacci numbers
./fibonacci 1 3 10 100 for listing out the first 100 Lucas numbers
./factorial 1 1 10 1000 for printing out the value for the number 1000 Factorial
./power 1 1 10 100 for listing out the first 100 Factorial numbers
./power 3628800 11 10 10
11! ... 20!

did you try running a pari script ? I can take a guess at it using the information I gained by that! doh I realized know thanks to Batalov's post I missed something.

[fivemack]

If you want to check that people have computed the whole number, ask for the md5sum of its decimal representation. But to say 'did you get it right' when asking several people to run the same program is a fairly perfect waste of time.

(I think asking for the last three digits of 6^6^6 is quite a reasonable early-stage-of-Olympiad sort of problem; 9^9^9 is just mindless weight-lifting)

It's possible to set very hard multi-choice problems (to be lazy, set a non-trivial question to a whole class and pick the most common answers given, adding the right one if your question turns out to have been too non-trivial); it's an interesting exercise to find questions where wrong methods give clearly distinct wrong answers.

[cheesehead]

Originally Posted by Batalov

What a way to solve problems! A poll of public opinion!

It's a multiple-choice test rather than a poll.

That the forum software offers only a way to post a "poll" and not a way to post a "multiple-choice test" is not the fault of the OP.

This is not math. This is numerology. Wrong forum.

It's a multiple-choice math test question.

Please look beyond the literal wording, to the practical meaning. Do not allow the limitations of the forum software (using "poll" multiple times) to determine the meaning for you.

[science_man_88]

Originally Posted by cheesehead

It's a multiple-choice test rather than a poll.

That the forum software offers only a way to post a "poll" and not a way to post a "multiple-choice test" is not the fault of the OP.

It's a multiple-choice math question.

Please look beyond the literal wording, to the practical meaning. Do not allow the limitations of the forum software (using "poll" multiple times) to determine the meaning for you.

I failed, of course that's because I forgot the simple method and tried a more complicated way but made a mistake on it ( admittedly I guessed on data I had collected leaning me towards taking the exponent mod 49)

[Batalov]

Originally Posted by cheesehead

It's a multiple-choice test rather than a poll.

That the forum software offers only a way to post a "poll" and not a way to post a "multiple-choice test" is not the fault of the OP.

It's a multiple-choice math test question.

Please look beyond the literal wording, to the practical meaning. Do not allow the limitations of the forum software (using "poll" multiple times) to determine the meaning for you.

Oh, I see. It's a multiple-choice math test question. Got that!

So what you are saying is that this belongs to "Puzzles" or "Homework help" forum? I agree!

[CRGreathouse]

Originally Posted by Batalov

So what you are saying is that this belongs to "Puzzles" or "Homework help" forum? I agree!

Puzzles, probably. Better fit than Math or Homework Help.

[LaurV]

... and what do you need the parenthesis for?
it should be the same 9^9^9 and you save two keypresses

Bitchy LaurV

[Batalov]

Originally Posted by Raman

9^9[SUP]9[/SUP] = 9^387420489 is being the largest number that can be written with 3 digits...

9!^9!^9! seems to be slightly larger.