Definition:Fermat Prime/Sequence

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Sequence of Fermat Primes

The sequence of Fermat primes begins:

\(\displaystyle 2^{\paren {2^0} } + 1\) \(=\) \(\displaystyle 3\)
\(\displaystyle 2^{\paren {2^1} } + 1\) \(=\) \(\displaystyle 5\)
\(\displaystyle 2^{\paren {2^2} } + 1\) \(=\) \(\displaystyle 17\)
\(\displaystyle 2^{\paren {2^3} } + 1\) \(=\) \(\displaystyle 257\)
\(\displaystyle 2^{\paren {2^4} } + 1\) \(=\) \(\displaystyle 65 \, 537\)

This sequence is A019434 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


No other Fermat primes are known.


Sources