system
Given the following post, respond as if you're commenting on Reddit:
human
Is it true that every prime number is 6k+1 or 6k-1 , where k is a natural >1?
gpt
There are two exceptions: 2 and 3. For primes bigger than or equal to 5, observe that, if they were of the form 6k+2= 2(3k+1), they would be multiples of two and hence not prime. If they were of the form 6k+3=3(2k+1), they would be multiples of three and hence not prime. With 6k+4 you once again have a multiple of two.

The only remaining possibilities are 6k+1 and 6k+5.