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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Graham's number canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T8657097 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Graham's number Context triple: [Ronald L. Graham, knownFor, Graham's number]
-
A.
Conway chained arrow notation
Conway chained arrow notation is a mathematical system of hyper-operator-style notation introduced by John Horton Conway to concisely represent extremely large numbers.
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B.
Numberwang
Numberwang is a surreal, fast-paced parody of television quiz shows from the British comedy duo Mitchell and Webb, known for its nonsensical rules and absurd humor.
-
C.
Ackermann function
The Ackermann function is a classic example of a computable function that grows faster than any primitive recursive function, often used in theoretical computer science to illustrate extreme computational complexity.
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D.
Feferman–Schütte ordinal
The Feferman–Schütte ordinal is a large countable ordinal that marks the proof-theoretic strength of predicative arithmetic and analysis, serving as a key boundary in ordinal analysis and foundations of mathematics.
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E.
Knuth’s up-arrow notation
Knuth’s up-arrow notation is a mathematical notation introduced by Donald Knuth to concisely represent very large integers using iterated exponentiation and its higher-order generalizations.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Graham's number Target entity description: 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.
-
A.
Conway chained arrow notation
Conway chained arrow notation is a mathematical system of hyper-operator-style notation introduced by John Horton Conway to concisely represent extremely large numbers.
-
B.
Numberwang
Numberwang is a surreal, fast-paced parody of television quiz shows from the British comedy duo Mitchell and Webb, known for its nonsensical rules and absurd humor.
-
C.
Ackermann function
The Ackermann function is a classic example of a computable function that grows faster than any primitive recursive function, often used in theoretical computer science to illustrate extreme computational complexity.
-
D.
Feferman–Schütte ordinal
The Feferman–Schütte ordinal is a large countable ordinal that marks the proof-theoretic strength of predicative arithmetic and analysis, serving as a key boundary in ordinal analysis and foundations of mathematics.
-
E.
Knuth’s up-arrow notation
Knuth’s up-arrow notation is a mathematical notation introduced by Donald Knuth to concisely represent very large integers using iterated exponentiation and its higher-order generalizations.
- F. None of above. chosen
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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Graham's number Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.