220px-Pierre de Fermat

A portrait of Pierre de Fermat painted in the 17th century.

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 (F0 to F4) are known to be prime.

F334 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 F3,329,782.

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