Question

Find the number of all prime numbers p such that
p^2- 6 and p^2+ 6 are both prime numbers.

Answer 1

Answer:

Let the two odd prime numbers p

1

and p

2

be 7 and 5 respectively.

Then, p

1

2

=7

2

=49

and, p

2

2

=5

2

=25

So, p

1

2

−p

1

2

=49−25=24 which is an even number.

Take another examples with p

1

and p

2

be 17 and 13.

Then, p

1

2

=17

2

=289

and, p

2

2

=13

2

=169

So, p

1

2

−p

1

2

=289−169=120 which is an even number.

In general the square of odd prime number is odd.

Hence, the difference of square of two prime numbers is even.

So, A is the correct option.