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A Pattern for Odd Prime Numbers

1 points by zeepickler ↗ HN
Noticed 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.
then,

2n + 1 is an odd prime.

2 comments

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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...