Question

Find a counterexample for the statement.
If p is prime, then
p2 + 4
is prime.

Answer 1

If p is prime , then p could be 2.

p² + 4 could also be prime? p = 2

2² + 4 = 4 + 4 = 8, 8 is not prime.

Therefore p = 2 is a counter example. In the sense that p = 2, does not support the statement that p² + 4 which is 8 in this case is a prime.

So p = 2 is a counter example.

Answer 2

if p is prime, then p^2 + 4 is prime.

so we have to prove this wrong...
let p = 2 (a prime number)
2^2 + 4 = 4 + = 8 (not a prime number)....so we just proved it false