I need information about the following conjecture:
Every primary number (except 1,2,3) is a multiple of 6 plus or minus 1.
For instance: 19 = 6*3 + 1.
Is this conjecture treated seriously by mathematicians?
does it have a name?
Is it proved to be true or false?

This is a nice little problem. I would assume it is treated seriously by mathematicians. I don't know whether it has a name or not. It isn't hard to prove.

Basic number theory.

Let's take 6k+1, has no immediate factors so it could be prime

p=0, 6k is divisible by 6.

p=2, 6k+2=2(3k+1), not prime

p=3, 6k+3=3(2k+1), not prime

p=4, 6k+4=2(3k+2), not prime

p=5, 6k+5 has no immediate factors so it could be a prime.

Therefore, the only ones for primes are 6k+1 and 6k+5.

Since 6k+5=6p-1 when p=k+1.

So, all primes are can be expressed as 6n\pm{1}