Question

Find a counterexample for the statement.
If p is prime, then p^2 + 4 is prime.

Answer 1

do you know any prime numbers?
can you name the first few?

Answer 2

2,3, 73,79

Answer 3

you skipped a few
but anyways if p=2 then p^2+4=?

Answer 4

64

Answer 5

2^2 is 4
4+4=64? how do you get that?

Answer 6

8

Answer 7

yes 4+4 is 8 not 64

Answer 8

and is 8 a prime number?

Answer 9

no, (sorry...for some reason I have to keep refreshing my browser)

Answer 10

So we have shown the following is false:
if p is prime, then p^2+4 is prime.
We have shown this is false by choosing the counterexample where p=2.

Answer 11

all we had to do is find an example that satisfied the if part and not the then part
that is called a counterexample

Answer 12

Thank you! 1st time taking a course like this.

Answer 13

np