What is the largest integer ever used in a mathematical proof?
Googolplex
Googol
Graham's number
Centillion
Graham's number is an enormous number that arises as an upper bound on the answer of a problem in the mathematical field of Ramsey theory.  The number was published in the 1980 Guinness Book of World Records, adding to its popular interest.
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Answers by country
Googolplex
Googol
Graham's number
Centillion
answers
 Australia
Australia25
 Pakistan
Pakistan12
 Ghana
Ghana12
 Republic of Ireland
Republic of Ireland14
 the United States
the United States109
 Greece
Greece22
 India
India79
 Austria
Austria75
 the United Kingdom
the United Kingdom73
 Spain
Spain10
 Germany
Germany497
 the Netherlands
the Netherlands20
 Canada
Canada14
 Poland
Poland6366
 Switzerland
Switzerland53
 France
France13
 Estonia
Estonia10