Editing Roshan's Conjecture

When I was a young child, I noticed a pattern. Every number past 3 seemed to have a pair of primes 'around' it.

# <math> (4-1) < 4 < (4+1) </math>
# <math> (5-2) < 5 < (5+2) </math>
# <math> (6-1) < 6 < (6+1) </math>
# <math> (7-4) < 7 < (7+4) </math>
# <math> (11324-45) < 11324 < (11324+45) </math>

Notice how for every number you can think of, there's a prime below it and a prime above it equidistant from it.

Better stated, what I concluded was that:

<math>\forall n > 3 \in N, \exists k \ge 1 \in N</math> such that <math>n-k</math> and <math>n+k</math> are both prime. I couldn't find a single counter-example to this. I was terribly excited, of course, because I thought I'd discovered some fundamental property of the universe.

Of course this turns out to be almost entirely equivalent to the famous modern form of [[wikipedia:Goldbach's conjecture|Goldbach's conjecture]] with a little cajoling. So much for my foray into Mathematics!