My Brilliance or lack thereof

This morning I woke up with a funny idea in my head, the idea that primes are neatly ordered. At first I thought I was being brilliant, it was a wonderful idea. Every positive integer > 3, has atleast one pair of primes equidistant from it. For primes, the pair of equidistant primes are the prime itself. For every other number, you can see a pair like this. Now, this seemed really smart until I decided to think of the two primes as n + a and n – a (n being the positive integer in question and a being the distance away). Adding the two leads to 2n, an even number. Now basically, what I’ve said is that every even number is the sum of two primes. Hello Goldbach! :(

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