# Definition:Fermat Prime/Sequence

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