It would take much longer than the age of the universe to write down Graham’s number.
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Graham’s number is an enormous number that was first described in a 1971 paper by mathematician Ronald Graham. The number is so large that it is practically impossible to comprehend its size. Its exact value is not known, but it is a number that is much larger than any number that could be practical in any area of science or engineering.
To give an idea of how large Graham’s number is, the number of atoms in the observable universe is estimated to be around 10^80. Graham’s number is much, much larger than this. As mathematician Martin Gardner explained it, “We don’t really know how big Graham’s number is, but we do know that the number of digits in that number, expressed in decimal notation, is itself a number so large that it would be impossible to write it down, even if you used all the particles in the observable universe to do the writing.”
So how long would it take to write down Graham’s number? It’s difficult to say exactly, but it would take much longer than the age of the universe. Professor Graham himself once commented on this, stating: “It’s not that it’s impossible to write down Graham’s number, it’s that the physical universe isn’t big enough to contain the pieces of paper you would need to write it down.”
To better visualize the size of Graham’s number, we can compare it to other well-known giant numbers:
| Number | Number of Digits |
|---|---|
| Graham’s number | Unknown |
| Skewes’ number | ~43 |
| Googolplex | 10^100 |
| TREE(3) | Unknown |
| Rayo’s number | Unknown |
As seen in this table, Graham’s number is much larger than Skewes’ number, which was the previous record holder for the largest number ever used in a computational proof.
In conclusion, it is safe to say that it is impossible to write down Graham’s number – it is just too large to comprehend. As Martin Gardner once wrote, “Graham’s number is simply too mind-bogglingly large to be of any use whatsoever, except perhaps as an example of the human mind’s ability to conceive of unimaginable abstractions.”
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How big is Graham’s number? Mathematicians explain that it’s a 3 four arrows 3 notation representing the number of arrows between two 3s in which each additional arrow means a larger number. The number’s size is so big that it remains beyond comprehension of mere mortals. Although the last 500 digits are predictable, the lack of information in-between thirteen dimensions and Graham’s number creates “a small gap in our knowledge.” Nevertheless, it’s known as the biggest number ever used in a constructive proof and has a bit of glamour as other mathematicians have since surpassed its size.
More answers to your inquiry
No one knows. It is a number so large no one knows how large it really is and no one is capable of imagining what it means. But it is safe to say it would take longer than until the end of the universe and the paper required to write it would take more mass than exists in the universe.
Infinite
Graham’s number is the largest finite number ever defined and the number of digits in it is estimated to exceed the number of atoms in the observable universe by a factor of 10. Therefore, it is impossible to accurately calculate the amount of time it would take to write out Graham’s number, as it would be infinite.
Graham’s number is the largest finite number ever defined and the number of digits in it is estimated to exceed the number of atoms in the observable universe by a factor of 10. Therefore, it is impossible to accurately calculate the amount of time it would take to write out Graham’s number, as it would be infinite.
No one knows. It is a number so large no one knows how large it really is and no one is capable of imagining what it means. But it is safe to say it would take longer than until the end of the universe and the paper required to write it would take more mass than exists in the universe.
Furthermore, people are interested
Also, Is it possible to write Graham’s number? Graham’s Number is so huge that it cannot be written down – the universe is simply not big enough. In fact, even specifying this number defies what’s possible using common mathematical notation. Instead, special notation has had to be developed.
Hereof, How many 3s are in Graham’s number? Response to this: 7.6 trillion 3s
So it’s a power tower that has 3 3 3 occurrences of in it, or about 7.6 trillion 3s. And there you have it. We just broke our brain.
Regarding this, Why does Graham’s number end in a 7? Graham’s number is bigger than the googolplex. It’s so big, the Universe does not contain enough stuff on which to write its digits: it’s literally too big to write. But this number is finite, it’s also an whole number, and despite it being so mind-bogglingly huge we know it is divisible by 3 and ends in a 7.
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Accordingly, How many digits of Graham’s number do we know? The answer is: So called Graham’s number it’s a three for arrows three that’s a big number. But what it represents is the number of arrows. Between. These two threes. Remember each additional arrow put you into a
Correspondingly, How big is Graham’s number?
Graham’s number is much larger than any other number you can imagine. It is so large that the observable universe is far too small to contain an ordinary digital representation of Graham’s number, assuming that each digit occupies one Planck volume which equals to about 4.2217\times 10^ {-105}\text { m}^ {3} 4.2217× 10−105 m3.
Beside this, Why is Graham’s number a power tower?
Response to this: Graham’s number is a "power tower" of the form 3↑↑ n (with a very large value of n ), so its rightmost decimal digits must satisfy certain properties common to all such towers. One of these properties is that all such towers of height greater than d (say), have the same sequence of d rightmost decimal digits.
Keeping this in consideration, What does Graham’s notation mean? Answer: As someone mentioned, here is what Graham’s notation means: (I’m using ^ to mean up-arrow. For exponentiation, ^ and up-arrow mean the same thing.) g (n) is defined as 3^^^…^^^3where the number of ^’s written is equal to g (n-1) That g (n) function increases _very_ rapidly, as n increases. Graham’s number is g (64). 2.
Moreover, What is Ronald Graham’s number? The response is: Nobody knows what the first digit of Graham’s number is, but the last digit is 7, in case it ever comes up in dinner conversation. Why would anyone need a number like this you ask? Mathematician Ronald Graham came up with it when talking to another mathematician named Martin Gardner.
Also Know, How big is Graham’s number?
Answer will be: Graham’s number is much larger than any other number you can imagine. It is so large that the observable universe is far too small to contain an ordinary digital representation of Graham’s number, assuming that each digit occupies one Planck volume which equals to about 4.2217\imes 10^ {-105}\ext { m}^ {3} 4.2217× 10−105 m3.
Keeping this in consideration, Why is Graham’s number a power tower? The answer is: Graham’s number is a "power tower" of the form 3↑↑ n (with a very large value of n ), so its rightmost decimal digits must satisfy certain properties common to all such towers. One of these properties is that all such towers of height greater than d (say), have the same sequence of d rightmost decimal digits.
What does Graham’s notation mean?
Answer: As someone mentioned, here is what Graham’s notation means: (I’m using ^ to mean up-arrow. For exponentiation, ^ and up-arrow mean the same thing.) g (n) is defined as 3^^^…^^^3where the number of ^’s written is equal to g (n-1) That g (n) function increases _very_ rapidly, as n increases. Graham’s number is g (64). 2.
Is Graham’s number a recursive number?
As a response to this: As there is a recursive formula to define it, it is much smaller than typical busy beaver numbers. Though too large to be computed in full, the sequence of digits of Graham’s number can be computed explicitly via simple algorithms; the last 13 digits are7262464195387.