Function Repository Resource:

FermatPrime

Find the nth Fermat number that is also a prime number

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["FermatPrime"][n]

returns the n^th Fermat number that is prime.

Details and Options

A Fermat number is a number of the form 2^2ⁿ+1.

Find the 3rd Fermat prime:

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Find all known Fermat primes:

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There are only 5 known Fermat primes. Therefore, FermatPrime[n] will return unevaluated for n>5:

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