Capturing all prime numbers and only prime numbers greater than 3

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Please advice whether below is correct, anything new or useful?

where n, a and b are integers ≥ 1

For $6n - 1$ all numbers will be prime numbers except where $n= 6ab + b - a$

For $6n + 1$ all will be prime numbers except where $n= 6ab ±(b + a)$

I believe the above 2 will capture all the primes above 3.

This is my first post so forgive me if I have made any errors or you feel I am wasting your time.