# Prime Decomposition of 6th Fermat Number

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## Contents

## 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

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $257$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $257$