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. 
