Sum of two Primes, one of which is 2.

Dinarius

1. Am I right in thinking that, if you add any two primes excluding 2 (e.g. 7+11, 23+31, 1+47) you get an even number? i.e. a number divisible by two.

2. But, if you add any two primes, one of which is 2, (e.g. 2+11, 2+23, 2+31, 2+1, 2+47), you always get an uneven number?

If I’m correct, has the curious quirk been written about (I’m sure it has) and is there a name for this observation?

Thanks.

D.

Halfbaker

I wouldn't call it a quirk. Every prime number larger than 2 is uneven.

seamus

Well, it's one of the fundamental rules of maths.

If you think about it logically, the modulus/remainder of any odd number divided by 2, is 1

Therefore, every single odd number can be expressed in the form

(x * 2) + 1

Thus, adding two odd numbers gives you (x * 2) + 1 + (y * 2) +1 = 2 * (x + y + 1)

And since any number multiplied by two must be even, the sum of two odd numbers is always even.

The same rule holds true for 2 + (any odd number).

Adding them you get 2 + (x * 2) + 1. Since any attempt to divide this equation by 2 will give a non-integer result, it is not an even number.