A quick sketch of the proof is as follows: if k is integer, any integer number can be written as either 3k, 3k+1 or 3k-1, as any integer divided by 3 must have remainder 0, 1 or 2. However, if you could write a prime as 3k, it would be divisible by 3, so it's either 3 or not a prime; hence, any prime p>3 is of the form 3k+1 or 3k-1