Last Updated：2025/12/31
Sentence
It
is
not
hard
to
prove
that
the
only
way
that
the
number
1+2ᵉ
can
possibly
be
prime
is
when
e
is
a
power
of
2,
and
so
all
Fermat
primes
must
have
the
form
1+2
for
integers
a>0.
The
numbers
F_a=1+2
are
called
Fermat
numbers,
and
although
it
is
true
that
every
Fermat
prime
is
a
Fermat
number,
it
is
certainly
not
true
that
every
Fermat
number
is
prime.
Quizzes for review
It is not hard to prove that the only way that the number 1+2ᵉ can possibly be prime is when e is a power of 2, and so all Fermat primes must have the form 1+2 for integers a>0. The numbers F_a=1+2 are called Fermat numbers, and although it is true that every Fermat prime is a Fermat number, it is certainly not true that every Fermat number is prime.
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