@marttcc88: Graham’s number is a gigantic number that serves as an upper bound for solving a certain problem in Ramsey theory. It is an extremely large power tower, written using Knuth’s notation. 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described it in his “Mathematical Games” column in Scientific American in November 1977, where it was said: “In an unpublished paper, Graham has recently established a bound so large that it holds the record for the largest number ever used in a serious mathematical proof.” In 1980, the Guinness Book of World Records repeated Gardner’s claims, further fueling public interest in this number. Graham’s number is unimaginably larger than other well-known large numbers, such as the googol, googolplex, and even larger than Skewes’ number and Moser’s number. The entire observable universe is far too small to contain the ordinary decimal notation of Graham’s number (it is assumed that each digit would occupy at least a Planck volume). Even power towers of the form A B C ◎ ◎ ◎ {\displaystyle a ^{b ^{c ^{\cdot ^{\cdot ^{\cdot}}}}}} are useless for this purpose (in the same sense), although this number can be written using recursive formulas such as Knuth’s notation or equivalent, which was done by Graham. The last 500 digits of Graham’s number are …024259506950647383956574791365193517983345353362521 43003540126026771622672160419810652263169355188780 38814483140652526168785095552646051071172000997092 91249544378887496062882911725063001303622931916080 25459461494578871427832350829242102091825896753560 43086993801689249889268099510169055919951195027887 17830837018340236474548882222161573228010132974509 27344594504343300901096928025352751833289884461508 94042482650181938515625357963996189939679054966380 03222348723967018485186439059104575627262464195387. In modern mathematical proofs, numbers even larger than Graham’s number are sometimes encountered, for example in work on Friedman’s finite form of Kruskal’s theorem — the so-called TREE (3).

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Sunday 14 June 2026 02:50:13 GMT