

A Pattern for Odd Prime Numbers - zeepickler

Noticed a pattern for odd prime numbers:<p>For 2n + 1, if n equals:<p>2xy + x + y<p>then,<p>2n + 1 is an odd composite.<p>For 2n + 1, if n equals:<p><pre><code>  6
  (7 + 6x) + 1
  (7 + 6x) + 2
  5, 5+6, 5+6+7, 5+6+7+8, etc.
</code></pre>
then,<p>2n + 1 is an odd prime.
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wiener90
Counter example

    
    
      x = 3
      y = 5
      2*(2*3*5+3+5)+1
      2*38+1
      77

~~~
zeepickler
Yes, this an example of an odd composite.

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...

