Are there any more Fermat Primes?
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Open Question
Are there any more Fermat primes than the $5$ that are known about?
Sequence
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.
Sources
- 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{IV}$: The Prince of Amateurs