A Pattern for Odd Prime Numbers

For 2n + 1, if n equals:

2xy + x + y

then,

2n + 1 is an odd composite.

For 2n + 1, if n equals:

  6
  (7 + 6x) + 1
  (7 + 6x) + 2
  5, 5+6, 5+6+7, 5+6+7+8, etc.

2n + 1 is an odd prime.

As I said 2xy + x + y creates odd composites (numbers that are odd and not prime).

I'm not saying this is prime. I was saying that the other patterns below are prime. However, since I posted this, I found a flaw with the 7 +6n +1 and 7+ 6n + 2 pattern. However, the 5,5+6,5+6+7, etc pattern holds up for up to the numbers I checked. I still have further investigation to do...