The biggest number with a name: history in the making!

[Jamie123]

According to this website http://www.googolplexian.com/ the largest number with a name is a "googolplexian".

 

To explain: a "googol" is 10^100, or 1 with 100 zeros: 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

 

(I may have missed the odd zero - or added 1 too many - but if you're planning to count them to make sure then you're as sad as I am! Having said that, anyone who thinks numbers of that size have no practical purpose needs to read up about RSA.)

 

A "googolplex" is 10^(1 googol), or 10^10^100 or 1 and a googol zeros. (And if you watched Carl Sagan's Cosmos back in the 1980s you'll know that is unwriteoutable. Sagan ran around Trinity College Cambridge with rolls and rolls of paper with zeros on, but eventually admitted that the paper needed couldn't be stuffed into the known universe.)

 

A "googolplexian" is 10^(1 googolplex), or 10^10^10^100 or 1 and a googolplex zeros. (Don't even think about it.)

 

OK.....so I'm now going to make history....

 

A "googolplexiantantiddlyupmumpum" is 10^(1 googolplexian), or 10^10^10^10^100 or 1 and a googolplexian zeros.

 

Time to re-write the maths books!

[Just_A_Guy]

Words fail me at an event of such magnitude...

[clwnuke]

Mathematicians and scientists need things to do. This might be one way to be entertained.

[Guest]

anyone who thinks numbers of that size have no practical purpose needs to read up about RSA.

 

I think you have underestimated just how big a number a googol is.  Astrophysicists say that a googol is greater than the number of elementary particles in the universe.  Think again whether it will be practical to have a number as big as a googolplexian.

[Vort]

Numbers have been defined that are so vastly much larger than a googol (or a googolplex) that it almost hurts just to contemplate it. One example is Graham's number, which is so unthinkably large that if you allowed every particle in the universe to represent a googolplex and then stacked them in a "power tower" (i.e. x^x), the resulting number still would be fantastically less than Graham's number. Donald Knuth developed a so-called "up-arrow" notation that allows Graham's number to be represented as 3↑↑↑↑3.

 

But, to give just one example, even Graham's number is tiny compared with the so-called "busy beaver" function, represented as Σ(64). So we can easily invent numbers that are vastly larger, such as Σ(100), or Σ(googol), or Σ(Graham's number), or Σ(Σ(64)).

 

And all of these are microscopically, unfathomably small compared with the vast majority of numbers, almost all of which are incalculably larger.

[Jamie123]

I think you have underestimated just how big a number a googol is.  Astrophysicists say that a googol is greater than the number of elementary particles in the universe.  Think again whether it will be practical to have a number as big as a googolplexian.

A googolplexian maybe but numbers much bigger than a googol are used in public key cryptographic algorithms like RSA. What's more these numbers need to be prime numbers - or at least very strong pseudoprimes.

[The Folk Prophet]

All your puny numbers pale in comparison to mine!

 

[Guest]

A googolplexian maybe but numbers much bigger than a googol are used in public key cryptographic algorithms like RSA. What's more these numbers need to be prime numbers - or at least very strong pseudoprimes.

 

Think about it.  Unless you're using an electronic mechanism that allows for a very large base numbering system, to even have a key that will calculate a number in the range of a googolplex would be impossible to fabricate.

 

A base two numbering electronic mechanism would not be able to be fabricated to even count upto a googolplex without the computer being tremendously huge.

 

Counting upto a googol in binary would take 300 to 400 digits.  To count to a googolplex in binary would take a secondary numbering system that counts up each digit... I'd have to spend some time thinking about how that would be done and what space it would take.

Edited November 11, 2015 by Guest

[Vort]

Think about it.  Unless you're using an electronic mechanism that allows for a very large base numbering system, to even have a key that will calculate a number in the range of a googolplex would be impossible to fabricate.

 

A base two numbering electronic mechanism would not be able to be fabricated to even count upto a googolplex without the computer being tremendously huge.

 

Counting upto a googol in binary would take 300 to 400 digits.  To count to a googolplex in binary would take a secondary numbering system that counts up each digit... I'd have to spend some time thinking about how that would be done and what space it would take.

 

10¹⁰⁰ = [2^(3.322)]⁽¹⁰⁰⁾ = 2^332.2

 

So we would need 333 places to allow a computer algorithm to count up past a googol. We are currently using 64-bit systems, with 128-bit systems on the horizon. The next logical step is 256 bits, and then 512 bits. So a system that considers addresses and numbers greater than 333 bits is not at all far-fetched, though it is outside today's architecture.

 

EDIT: Oh, wait. You said "googolplex". Yes, I agree, that would not be likely to happen in computer terms. But if computers had need to deal with such absurd numbers in a mathematical way, they would be represented and dealt with differently, not as actual numbers encoded in the RAM but something more along the line of strings of digits, where we apply operations the way we would do it on paper.

Edited November 11, 2015 by Vort

[Jamie123]

Think about it.  Unless you're using an electronic mechanism that allows for a very large base numbering system, to even have a key that will calculate a number in the range of a googolplex would be impossible to fabricate.

 

A base two numbering electronic mechanism would not be able to be fabricated to even count upto a googolplex without the computer being tremendously huge.

 

Counting upto a googol in binary would take 300 to 400 digits.  To count to a googolplex in binary would take a secondary numbering system that counts up each digit... I'd have to spend some time thinking about how that would be done and what space it would take.

 

I was actually talking about a googol, not a googolplex, far less a googolplexian.

 

(And less still a googolplexiantantiddlyumpumpum.)

[David13]

What?  Is that where the national debt is now?

dc

[Backroads]

I feel like I'm reading clones of my dad writing this thread...