Solve the Problem $2 ^ { 2 ^ { n } } + 1$

question 113

Essay

Solve the problem.
-Fermat conjectured that the formula $2 ^ { 2 ^ { n } } + 1$ would always produce a prime for any whole number $\mathrm { n }$ . The sixth Fermat number is $2 ^ { 2 ^ { 5 } } + 1$ . Evaluate this number. In seeking possible prime factors of this Fermat number, what is the largest potential prime factor that one would have to try?

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Definitions:

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