# Definition:Fermat Number/Sequence

 $\displaystyle 2^{\paren {2^0} } + 1$ $=$ $\displaystyle 3$ $\displaystyle 2^{\paren {2^1} } + 1$ $=$ $\displaystyle 5$ $\displaystyle 2^{\paren {2^2} } + 1$ $=$ $\displaystyle 17$ $\displaystyle 2^{\paren {2^3} } + 1$ $=$ $\displaystyle 257$ $\displaystyle 2^{\paren {2^4} } + 1$ $=$ $\displaystyle 65 \, 537$ $\displaystyle 2^{\paren {2^5} } + 1$ $=$ $\displaystyle 4 \, 294 \, 967 \, 297$ $\displaystyle 2^{\paren {2^6} } + 1$ $=$ $\displaystyle 18 \, 446 \, 744 \, 073 \, 709 \, 551 \, 617$