## Fermat Numbers

\[F_n\]

is a number of the form \[2^{2^n}+1\]

where \[n\]

is non negative.The first five Fermat numbers are>br />

\[F_0=3, \; F_1=5, \; F_2=17, \; F_3=257, \; F_4=65537\]

The first 5 are all prime numbers but

\[F_6=274177 \times 67280521310721\]

is composite.\[F_7 =59649589127497217 \times 5704689200685129054721\]

was not written as prime factors until 1970, \[F_8\]

not until 1980, and \[F_9\]

not until 1990.