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**sulley****Member**- Registered: 2012-11-26
- Posts: 4

Hello all,

I was hoping you would be so kind as to help me with a problem that I'm having. I would like to calculate 141^(162^164), but the result is rather large and exceeds the capabilities of any software I have yet encountered.

I've tried using BC (see en.wikipedia.org/wiki/Bc_programming_language), you probably know that it's a very capable arbitrary precision calculator, but it can't manage it, it tells me that the 'exponent is too large in raise'.

Does anyone have any ideas? Do I have any chance of producing an actual result?

It's might be worth telling you that I know C, so can write some code to help, but the issue I have is that the types available in C aren't big enough, so I wouldn't even know where to start.

Thanks,

Rob

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,032

Hi sulley;

Welcome to the forum!

The front part 16870151161094535473499554809767331400820946875159,,, called the mantissa is the first 50 digits of the number if you need more let me know.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**sulley****Member**- Registered: 2012-11-26
- Posts: 4

Wow, impressive! Thank you very much. Can you share how you did it please?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,032

There are a couple of ways of tackling tower problems as these are called.

There are math programs that can handle this large a number directly.

Both Maxima using the BFloat class and Derive 6.1 are capable of getting this answer and I used Derive 6.1 to check.

There is a math way but it is a bit complicated if you have never seen it before.

Are you interested?

If you think that number is massive then think again:

that's massive^massive. 10 or more years ago I went after the front digit of that number. I was a mere lad of only 82 years of age so I figured I would bring it to its knees before I died...

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,883

You never told which digit was actually the first one...

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,032

For the tower problem? I do not know which one it is.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**sulley****Member**- Registered: 2012-11-26
- Posts: 4

bobbym wrote:

There is a math way but it is a bit complicated if you have never seen it before.

Are you interested?

Yes it would interest me, but realistically I will have very little use for the knowledge, so I won't take any more of your time.

bobbym wrote:

that's massive^massive. 10 or more years ago I went after the front digit of that number. I was a mere lad of only 82 years of age so I figured I would bring it to its knees before I died...

Doesn't that make you 92? Or am I missing something.

Thanks again for you help,

Rob

*Last edited by sulley (2012-11-28 02:37:10)*

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,269

Or am I missing something.

Yes! bobbym regularly lies about his age.

As far as I know only three people know for sure, and two of those are doubtful.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,883

Well, he has given us some info about his age. He was born on the 3rd of July and on Sunday...

*Last edited by anonimnystefy (2012-11-28 04:10:48)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,269

Is that reliable information though?

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,883

I think so.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,032

Hi sulley and all;

I was not born in July. Records of my birth have been destroyed. Hospital burned down and so did the rectory.

Yes it would interest me, but realistically I will have very little use for the knowledge, so I won't take any more of your time.

Then it will die with me. It does appear I am 92 but no one believes that so sometimes I am younger.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**sulley****Member**- Registered: 2012-11-26
- Posts: 4

I'm back again! Is that 92 in hex?

I have an even bigger challenge for you, would you be so kind as to calculate 141!^(162!^164!) for me please? to as large an accuracy as you dare! (ridiculous, I know!)

Thanks,

Rob

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,032

Hi;

That is 92 in decimal. Your question boils down to this:

which means it is larger than my current limit of 9^(9^(9^5)). As a matter of fact

it is larger than 9^(9^(9^(9))) which I have struggled with for more than 10 years.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,883

Hi bobbym

Is there a way to get the front digits of a number other than the one you showed me in the big Oh thread?

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,032

Hi;

That is the only one that I use consistently. Of course there are other methods but they are all experimental.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,883

Do you know any?

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,032

This suggests another method but in this case it fails. As a matter of fact it fails for

9^(9^(9^9))) too! His number is just too large.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,883

I meant-do you have another method for evaluating those kinds of numbers in general, for example, less than 9^9^9^5?

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,032

Hi;

For 9^9^9^5 ( I leave out the bracketing from now on ) is a major undertaking and I used a

recurrence.

And you missed my point, post #18 does suggest another way.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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