A number of the form $2^{2^n}+1.$ Pierre de Fermat noticed that the first few are all prime numbers and thought they might all be, but that turns out not to be true. Numbers of this form that are prime are called Fermat primes. You can read more about them on that page.

One of many types of number
MersennePrime (none) (none)
FermatPrime (none)

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FermatNumber
PierreDeFermat
TypesOfNumber
Euler
MersennePrime
RulerAndCompass
(none) AlgebraicGeometry
AlgebraicNumber
CategoryMetaTopic
ComplexNumber
CompositeNumber
CountingNumber
Divisor
FamousPeople
FermatsLastTheorem
FermatsLittleTheorem
ImaginaryNumber
Integer
IrrationalNumber
PerfectNumber
PrimePair
Quaternion
RationalNumber
RealNumber
SquareNumber
TranscendentalNumber
WholeNumber