I just thought of something can someone tell me if this is correct. for p primes p >=5 we can only get remainders 1 or 5 when dividing by 6 because if we get 2 3 4 we see what happens
6k + 2 = 2(3k +1)
6k + 3 = 3(2k +1)
6k + 4 = 2(2k + 2) and none of these can be prime because they have factors...
If p >= 5 is prime, prove that p^2 + 2 is composite.
So i noticed if we divide any p >= 5 by 6 we only get remainders of 1 or 5.
6 | 5 , r = 5
6 | 7 , r = 1
6 | 11, r = 5
6 | 13, r = 1
6 | 17, r = 5 and so on
so for my proof i am saying for p >= 5, p = 6k + 1 or 6k = 5
so for the first ...