Graham’s number is a very large number, much larger than the number of atoms in the observable universe.
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Graham’s number is a mathematical concept that was first described by mathematician Ronald Graham in 1971. It is an extremely large number, and its exact value is difficult to express using traditional mathematical notation. In fact, the number is so large that it is practically impossible to comprehend its sheer magnitude.
To give you an idea of just how big Graham’s number is, consider this: the number of atoms in the observable universe is estimated to be around 10^80. Graham’s number, on the other hand, is so large that it cannot be expressed using exponential notation, which is typically used to represent very large numbers. If every single atom in the known universe were used to write out Graham’s number, there would not be enough space in the universe to contain it.
Here are some interesting facts about Graham’s number:
- The number was first defined as part of a proof in a paper written by mathematicians Ronald Graham, Bruce Rothschild, and Joel Spencer in 1971.
- At the time it was first described, Graham’s number was the largest number ever used in a mathematical proof.
- The number is so large that if you were to write it out using standard notation (i.e., writing out each digit), the number of digits would far exceed the number of particles in the observable universe.
- In a 1999 episode of the television show “The Simpsons,” the character Professor Frink claims to have discovered a new number that is “bigger than the biggest number anyone has ever written down.” He then proceeds to write Graham’s number on a chalkboard.
- The number is typically calculated using a process called Graham’s number of Graham’s number. Essentially, this involves repeating the process of raising numbers to increasingly large powers, until you arrive at a number so large that you cannot represent it using traditional mathematical notation.
In summary, Graham’s number is an incredibly vast concept that is virtually impossible to comprehend using our everyday understanding of numbers. As physicist Michio Kaku once put it, “Graham’s number is so mind-bogglingly large that it’s impossible to visualize, let alone actually compute.”
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Answer: about 9 × 10 184 . That’s bigger than a googol, but a lot smaller than a googolplex, and so just two applications of a log would cut it to size.
Graham’s number is a number so large that the observable universe is far too small to contain an ordinary digital representation of it. It is bigger than the number of atoms in the observable Universe, which is thought to be between 10^78 and 10^82. It is also bigger than the 48th Mersenne prime, 2^57,885,161 -1, the biggest prime number we know, which has an impressive 17,425,170 digits.
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 4.2217times 10^ {-105}text { m}^ {3} 4.2217× 10−105 m3.
Graham’s number is bigger the number of atoms in the observable Universe, which is thought to be between 10 78 and 10 82. It’s bigger than the 48th Mersenne prime, 2 57,885,161 -1, the biggest prime number we know, which has an impressive 17,425,170 digits.
The word ‘Big’ is entirely inadequate to even begin to describe the enormity of Graham’s number….!
People like to ask: “How many digits in Graham’s number?”
See: How many digits are there in Graham’s Number? Is it possible to know how many digits that number has? [ https://www.quora.com/How-many-digits-are-there-in-Grahams-Number-Is-it-possible-to-know-how-many-digits-that-number-has ]
That question also doesn’t even begin to get how BIG Graham’s number is, because the answer (how many digits?) is itself a number so incredibly vast as to have no meaning.
In fact, you could probably spend all eternity asking “How many digits in the number that states how many digits are in the number that states how many digits are in the number… etc… that states how many digits are in Graham’s number” before you got to a number that made any kind of sense!
Just consider the first term in Graham’s Number, g1.
The first term is [math]3\uparrow \uparrow \uparrow \uparrow3[/math].
(See: Knuth’…
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.
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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.
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| Number of digits (d) | 3↑x | 3↑3↑x |
|---|---|---|
| 1 | 4 (1,3,9,7) | 2 (3,7) |
| 2 | 20 (01,03,…,87,…,67) | 4 (03,27,83,87) |
| 3 | 100 (001,003,…,387,…,667) | 20 (003,027,…387,…,587) |
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