Prime Decomposition of 6th Fermat Number

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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
\(\displaystyle \) \(=\) \(\displaystyle 274 \, 177 \times 67 \, 280 \, 421 \, 310 \, 721\)


Proof


Also see


Historical Note

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


Sources