Prime Decomposition of 6th Fermat Number
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Theorem
The prime decomposition of the $6$th Fermat number is given by:
| \(\ds 2^{\paren {2^6} } + 1\) | \(=\) | \(\ds 18 \, 446 \, 744 \, 073 \, 709 \, 551 \, 617\) | Sequence of Fermat Numbers | |||||||||||
| \(\ds \) | \(=\) | \(\ds 274 \, 177 \times 67 \, 280 \, 421 \, 310 \, 721\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {3^2 \times 7 \times 17 \times 2^8 + 1} \times \paren {5 \times 47 \times 373 \times 2 \, 998 \, 279 \times 2^8 + 1}\) |
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): $257$