Statement :
is a prime.
The statement is False.
\Proof :
\Let
be the statement
is a prime.
is the statement that
is a prime,
is true since
.
which is a prime number.
\Assume
is true where
is a positive integer and we have to prove that
must be true.
show that
is a prime number.
Substitute differerent values :
\For
:
is a prime number.
For
:
is a prime number.
For
:
which is not a prime number.
Therefore,
is not a prime for all integer values of
.
The expression
is not a prime number.