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## Main Question or Discussion Point

How can a novice simply generate a large number > 10

^{10}in a few steps?- Thread starter Loren Booda
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How can a novice simply generate a large number > 10^{10} in a few steps?

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Not sure of what you really want, though.

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There are simple means of generating a series which, by the third step say, creates a huge number, on the order of greater than 10

Not sure of what you really want, though.

I recall one of the best such algorithms was created by a Turing-like machine. Within three steps it easily reached over 10

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9^9^9 has 369'693'100 decimal digits

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f(x) = 10How can a novice simply generate a large number > 10^{10}in a few steps?

That's how you would do it mathematically. You have a function that outputs a number that's literally greater than 10

Can you explain what you mean by "generate?" For example if you are using a computer, you would perhaps first install a bignum package -- specialized software to handle arbitrary-sized numbers. Then you could just write a loop to count up to your large number by 1; or you could just take your large number and store it in memory.

It's not clear to me what else you might be asking.

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As I indicated, f(x) = 10I recall one of the best such algorithms was created by a Turing-like machine. Within three steps it easily reached over 10^{100}.

But perhaps you are thinking of the Busy Beaver function. or the Ackermann function.

http://en.wikipedia.org/wiki/Busy_beaver

http://en.wikipedia.org/wiki/Ackermann_function

Those are functions used in computer science that grow very quickly. Ah you must be talking about functions that GROW very quickly, not just functions that output large numbers. Got it!

You see, f(x) = 10

Check out the Wiki links above, I think that's what you're talking about.

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You got it! Noncomputable growth. Busy beaver.

Thanks SteveL27.

Thanks SteveL27.

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number of tiers is something I was thinking of recently.

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What is the most "efficient" algorithm for generating a largest possible (computable) number?

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jedishrfu

Mentor

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Deveno

Science Advisor

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oh my goodness TREE(3) is huge!

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-Take an arbitrary number N and express it in base-2 hereditary notation (that all coefficients are less than or equal to 2, eg 35= 2

-Then take all 2's and replace them with 3's and subtract 1 from the result, expressing this in base-3 hereditary notation

-Then take all Ns and replace them with N+1s and subtract 1, expressing them in base-N+1 hereditary notation (3 to 4, 4 to 5, 5 to 6...)

Eventually you'll reach one but you'll hit enormous numbers on the way.

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