Research prime's number

Is (n) the odd numbers.
If the couple it's made up of two numbers
addition =(n) to no admit common's divisor,
then(n) is prime number.

example:
(n) = 23
The couple (2,21), (3,20), (4,19), (5,18),
(6,17), (7,16),(8,15), (9,14), (10,13), (11,12);
no admit common's divisor then (n)=23 is prime number.

(n) = 15
The couple (2,13),(3,12),(4,11),(5,10),(6,9),(7,8);
admit (3,12),(6,9) divisor 3; and (5,10) divisor 5.
Then 15 = 3*5

Who explain it ?

Good bye
Vincenzo Librandi
vincenzo.librandweoz@xxxxxxxx
.