Fermat (1601-1665) conjectured that every number of the form  is prime. So we call these
the Fermat numbers, and when a number of this form is prime, we call it a
Fermat prime. The only known Fermat primes are the first five Fermat
numbers: F0=3, F1=5, F2=17, F3=257,
and F4=65537. The next
couble dozen are all composite with
F31 being the first Fermat number with unknown status.
The Fermat's grow so fast that
for the larger ones we can not complete a probable-primality test such as Pepin's test. Instead we seek
small divisors (called Fermat divisors). Below you will find a couple projects to seek such divisors.
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