proof Problem

[Sillysidley]

Prove that every prime number can be expressed as 6n+1or 6n-1. (How do you get a plus minus sign?)

[Sillysidley]

Hint: Consider all numbers mod 6.

[Sillysidley]

I guess I better start posting solutions to these:

Consider them all (mod 6)
If the number is:
0 (mod 6) it's divisible by 6, so not prime
1 (mod 6) prime.
2 (mod 6) Even, not prime
3 (mod 6) Divisible by 3
4 (mod 6) even, not prime
5 (mod 6) prime (note that this is also -1(mod 6))

So all primes are of the form 6n+1 and 6n-1 (Just because a number is in one of those forms doesn't mean it's prime)