# Graham’s number – The Largest Number ever Used.

```...02425950695064738395657479136519351798334535362521
43003540126026771622672160419810652263169355188780
38814483140652526168785095552646051071172000997092
91249544378887496062882911725063001303622934916080
25459461494578871427832350829242102091825896753560
43086993801689249889268099510169055919951195027887
17830837018340236474548882222161573228010132974509
27344594504343300901096928025352751833289884461508
94042482650181938515625357963996189939679054966380
03222348723967018485186439059104575627262464195387.```

Graham’s number, named after Ronald Graham, is a large number that is an upper bound on the solution to a certain problem in Ramsey theory.

The number gained a degree of popular attention when Martin Gardner described it in the “Mathematical Games” section of Scientific American in November 1977, writing that “In an unpublished proof, Graham has recently established … a bound so vast that it holds the record for the largest number ever used in a serious mathematical proof.”

The 1980 Guinness Book of World Records repeated Gardner’s claim, adding to the popular interest in this number. Graham’s number is unimaginably larger than other well-known large numbers such as a googol, googolplex, and even larger than Skewes’ number and Moser’s number. Indeed, the observable universe is far too small to contain an ordinary digital representation of Graham’s number, assuming that each digit occupies at least one Planck volume. Even power towers of the form a^b^c……..  are useless for this purpose, although it can be easily described by recursive formulas using Knuth’s up-arrow notation or the equivalent, as was done by Graham. The last ten digits of Graham’s number are …2464195387.

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