Prime numbers

A prime number is defined as a number only dividable as whole numbers by itself and one.

The four smallest prime numbers are 2, 3, 5 and 7.

All other prime numbers are part of one of two number sets. The 5 set and the 7 set. But all the numbers in these two sets are not prime.

The 5 set are all numbers start with 5 and incremented by 6.
5 11 17 23 29 the next number is 35 and not prime.

35 divisable as whole numbers, 35 and 1. And 7 and 5.

The 7 set are all numbers start with 7 and incremented by 6.
7 13 19 the next number is 25 and not prime.

25 divisable as whole numbers, 25 and 1. And 5. Being 5 squared.

Prime pairs are two prime numbers with a difference of 2.
3 and 5
5 and 7
11 and 13
17 and 19
29 and 31