Definition:Fermat Prime/Sequence
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Sequence of Fermat Primes
The sequence of Fermat primes begins:
| \(\ds 2^{\paren {2^0} } + 1\) | \(=\) | \(\ds 3\) | ||||||||||||
| \(\ds 2^{\paren {2^1} } + 1\) | \(=\) | \(\ds 5\) | ||||||||||||
| \(\ds 2^{\paren {2^2} } + 1\) | \(=\) | \(\ds 17\) | ||||||||||||
| \(\ds 2^{\paren {2^3} } + 1\) | \(=\) | \(\ds 257\) | ||||||||||||
| \(\ds 2^{\paren {2^4} } + 1\) | \(=\) | \(\ds 65 \, 537\) |
No other Fermat primes are known.
This sequence is A019434 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Sources
- 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{IV}$: The Prince of Amateurs
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $257$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $257$
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $7$: Patterns in Numbers: Gauss