# Definition:Fermat Prime/Sequence

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## Sequence of Fermat Primes

The sequence of Fermat primes begins:

 $\displaystyle 2^{\paren {2^0} } + 1$ $=$ $\displaystyle 3$ $\displaystyle 2^{\paren {2^1} } + 1$ $=$ $\displaystyle 5$ $\displaystyle 2^{\paren {2^2} } + 1$ $=$ $\displaystyle 17$ $\displaystyle 2^{\paren {2^3} } + 1$ $=$ $\displaystyle 257$ $\displaystyle 2^{\paren {2^4} } + 1$ $=$ $\displaystyle 65 \, 537$

No other Fermat primes are known.