Graham's number
E748745
Graham's number is an extraordinarily large number that arose in a problem in Ramsey theory and became famous as one of the largest numbers ever used in a serious mathematical proof.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
integer
ⓘ
large number ⓘ natural number ⓘ number used in a mathematical proof ⓘ |
| appearedIn |
Guinness Book of World Records
NERFINISHED
ⓘ
Martin Gardner's Scientific American column NERFINISHED ⓘ |
| aroseIn | problem in Ramsey theory about edges of an n-dimensional hypercube ⓘ |
| category | large countable number ⓘ |
| comparedTo | other large named numbers in popular mathematics ⓘ |
| constructionStep |
g_1 = 3 ↑↑↑↑ 3 in Knuth up-arrow notation
ⓘ
g_{n+1} = 3 ↑^{g_n} 3 for n ≥ 1 ⓘ |
| context | extreme example in discussions of large numbers ⓘ |
| definedAs | g_{64} where g_1 = 3 ↑↑↑↑ 3 and g_{n+1} = 3 ↑^{g_n} 3 ⓘ |
| definedUsing | Knuth up-arrow notation NERFINISHED ⓘ |
| famousFor |
appearance in popular mathematics literature
ⓘ
being extraordinarily large ⓘ being one of the largest numbers ever used in a serious mathematical proof ⓘ |
| field |
Ramsey theory
NERFINISHED
ⓘ
combinatorics ⓘ |
| greaterThan |
Ackermann(4,2)
ⓘ
any power tower of 10 of fixed finite height ⓘ googol ⓘ googolplex NERFINISHED ⓘ |
| growthRate | far beyond primitive recursive functions of low rank ⓘ |
| hasBaseRepresentation | defined via iterated exponentials of 3 ⓘ |
| hasKnownProperty |
last digit is 7
ⓘ
last few hundred digits are known via modular arithmetic ⓘ last three digits are 387 ⓘ last two digits are 87 ⓘ |
| influenced | later constructions of even larger explicit numbers in logic and combinatorics ⓘ |
| isNot |
infinite
ⓘ
tight bound for the underlying Ramsey problem ⓘ transfinite number ⓘ |
| lessThan | some later large numbers defined in fast-growing hierarchies ⓘ |
| muchLargerThan | best known lower bound for the corresponding Ramsey number ⓘ |
| namedAfter | Ronald Graham NERFINISHED ⓘ |
| notationForm | g_{64} in a recursive sequence g_1, g_2, ..., g_{64} ⓘ |
| popularizedBy | Martin Gardner NERFINISHED ⓘ |
| property |
finite
ⓘ
integer with known last digits ⓘ well-defined ⓘ |
| relatedTo | Ramsey number problem for edge-colorings of a hypercube ⓘ |
| roleInProof | upper bound on a specific Ramsey number ⓘ |
| tooLargeTo |
be computed explicitly by any physical device in the observable universe
ⓘ
be represented by a power tower of 10 of any fixed finite height ⓘ be written in conventional decimal notation ⓘ |
| usedIn | upper bound in a Ramsey-theoretic problem ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.