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Graham's number is an immense number that arose as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is much larger than many other large numbers such as Skewes's number and Moser's number , both of which are in turn much larger than a googolplex .
Sagan gave an example that if the entire volume of the observable universe is filled with fine dust particles roughly 1.5 micrometers in size (0.0015 millimeters), then the number of different combinations in which the particles could be arranged and numbered would be about one googolplex. [8] [9]
googolplex = = Skewes's numbers: the first is approximately , the second ; Graham's number, larger than what can be represented even using power towers . However, it can be represented using layers of Knuth's up-arrow notation.
This is the minimum number of characters needed to encode a 32 bit number into 5 printable characters in a process similar to MIME-64 encoding, since 85 5 is only slightly bigger than 2 32. Such method is 6.7% more efficient than MIME-64 which encodes a 24 bit number into 4 printable characters.
At the same time that he suggested "googol" he gave a name for a still larger number: "googolplex". A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out. It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired.
(See googolplex for a comparable number) Now let's examine Graham's number, or since we can't look at the number itself, let's look at the tower of powers that appears in that article. That tower has 3^(3^...^3) layers, where the number of 3's in the ellipses is equal to 3^(3^3), which equals about 7.6 x 10^12.
Graham's number, one of the largest numbers ever used in serious mathematical proof, is an upper bound for a problem related to Ramsey theory. Another large example is the Boolean Pythagorean triples problem. [3]
Graham's number has 64 of the up arrows, so it's much more than what a brain can comprehend without just thinking of infinity. 98.223.56.77 02:14, 22 September 2008 (UTC) Graham's number has many, many, many more than 64 up arrows. g 1 has 4 up arrows. g 2 has g 1 up arrows.