Fermat Numbers

A Fermat number  
  is a number of the form  
  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,  
  not until 1980, and  
  not until 1990.

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