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![#china Graham's number is a gigantic number that serves as an upper bound for solving a certain problem in Ramsey theory. It is a very large power of three, expressed using Knuth's up-arrow notation. It is named after Ronald Graham. It became known to the general public after Martin Gardner described it in his “Mathematical Games” column in Scientific American in November 1977, where he wrote: “In an unpublished proof, Graham recently established a bound so large that it holds the record as the largest number ever used in a serious mathematical proof.” In 1980, the Guinness Book of Records repeated Gardner’s statements, further increasing public interest in this number. Graham’s number is incomprehensibly larger than other well-known large numbers such as a googol, a googolplex, and even larger than Skewes’ number and Moser’s number. The entire observable universe is far too small to contain the ordinary decimal representation of Graham’s number (assuming each digit occupies at least a Planck volume). Even exponential towers of the form � are useless for this purpose, although the number can be expressed using recursive formulas, such as Knuth’s notation or equivalent methods, which is what Graham did. The last 500 digits of Graham’s number are [source not provided].](/video/cover/7665380144592194836.webp)
