Question

Why does all possible pair of prime numbers that add to a prime must contain the number 2?

Answer 1

Shown below

Explanation:

All primes are odd a apart from the first prime, 2, as due to all larger numbers that are even are devisable by 2, hence must be odd

When we add two primes that don't contain 2, we are adding an odd to an odd, what we know is even, hence this can never by prime

But when we add an odd to the number 2, we also get an odd number, hence this could be a prime

`=>` hence we must add a prime to 2, to get a chance of getting a prime

For example:

`3+5 = 8 " this is even, hence not prime"`

`2+3 = 5 " this is prime "`