A **Fermat number**, named after Pierre de Fermat, is a number of the form:

- \(F_{n} = 2^{2^{ \overset{n} {}}} + 1\)

It was originally conjectured that all Fermat numbers were prime, but this has been proven false; in fact, only the first five Fermat numbers (F_{0} to F_{4}) are known to be prime.

F_{334} is the first Fermat number that is larger than a googolplex. The largest Fermat number which is known to be composite, as of February 2015, is F_{3,329,782}.

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