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.