# Prime Decomposition of 6th Fermat Number

## Theorem

The prime decomposition of the $6$th Fermat number is given by:

 $\displaystyle 2^{\paren {2^6} } + 1$ $=$ $\displaystyle 18 \, 446 \, 744 \, 073 \, 709 \, 551 \, 617$ Sequence of Fermat Numbers $\displaystyle$ $=$ $\displaystyle 274 \, 177 \times 67 \, 280 \, 421 \, 310 \, 721$

## Historical Note

The prime decomposition of the $6$th Fermat number was determined by Fortuné Landry in $1880$.