I need help the sum of two prime numbers is an even number?

Question

I need to show the conjecture is false by finding one counterexample?

Answer 1

Well, the only way to get an odd number when you're summing two numbers is if you sum an odd and an even number together.

There is only one even prime number: 2

It is divisible only by itself and 1, all other even numbers are also divisible by 2, and therefore not prime.

So, add 2 and some other prime (say...13), and you get an odd number, in this case (2+13=15).

Wee!

Answer 2

Anything involving the prime number '2' will result in an odd number.

For example:

2 + 3 = 5

2 + 5 = 7

2 + 11 = 13

etc.

All the others will be a sum of two *odd* numbers which *will* result in a even sum.  (e.g. 3 + 5 = 8, 5 + 11 = 16, etc.)

Answer:

Any sum including 2 and a different prime number.

Answer 3

All prime numbers are odd...except 2.  Any odd number + any other odd number = an even number.  But any even number + any odd number is an odd number.

So...2 + any other prime = an odd number.  2+3, 2+5, 2+7, 2+11, etc.

Answer 4

2 and 3 = 5