Joe asked in Science & MathematicsMathematics · 9 months ago

# What is the largest number we have had a use for?

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• Dixon
Lv 7
9 months ago

For a while the largest number with reason to exist (other than making up big numbers) was Skewes number

10^10^10^34

and there was a whole bunch of variation on it over time

https://en.wikipedia.org/wiki/Skewes%27s_number

It doesn't look so crazy big at first glance but in fact even the number of digits in it, as a number itself, is beyond comprehension.

• 9 months ago

The number is in the horizon.

• Pope
Lv 7
9 months ago

That number changes every time I think about it, so there can be no answer that will hold up for long. I honestly remember working this out when I was a small child, having progressed no further than long division and simple fractions. Still, I have seen no valid refutation of my conclusion.

The number of people who live or have lived is finite. So is the number of breaths they have taken, and the number of numbers they have ever thought about. Therefore, at any given instance, there must be a greatest number ever used. I am thinking about that number now. I have no real sense of its magnitude, and in fact I do not even have a name for it, but none of that matters. The number must exist. I now add one to it. Having done so, I have formed the greatest number conceived in all human history.

It must be a number we have use for? I use it every time I tell this story.

• david
Lv 7
9 months ago

Depends on who "we" are. There is a story of a tribe that was discovered and their biggest number was "3" .. everything greater than 3 was just called "many". === So I say the biggest number needed just might be 3.

=== The story came from a book titled "ONE, TWO, THREE ... INFINITY" by George Gamow.

• 9 months ago

A googol is pretty useful, since it gives us a scale for reference. For instance, there are roughly 10^80 elementary particles in our universe. If we wanted a googol particles, we'd need a hundred billion billion universes all comparable to our own.

After that, I would say that most greater numbers serve no practical purpose, though it is still good to know them. For instance, Graham's Number serves as the upper bound to a solution to a particular problem in maths, with the lower bound being 6 or something. As one mathematician said, "There's room for improvement."

Factorials, while being exceedingly large (69! is just under a googol), are necessary for determining permutations and combinations.

There are exceptionally large prime numbers that have been found, on the order of millions of digits in length. They have some use in computer cryptography, and barring some advance in prime number theory and/or quantum computing, the ones we use right now are doing an exceptional job. For instance, RSA cryptography makes extensive use of near-primes, which are numbers that have 2 factors other than 1 and itself. The numbers used in the cryptography are massive, which makes finding their factors extremely difficult and time consuming. If we figured out algorithms to generate factors for near primes, then RSA cryptography would be rendered useless. Want to destroy the global economy, expose every classified secret on every database and expose everyone's personal information? Figure out the keys that are used in the cryptography or figure out an algorithm that can generate the keys for you and you'll be the most powerful person in the world (until someone kills you).

• TomV
Lv 7
9 months ago

I would propose the number representing the total number of subatomic particles in the observable universe.