Originally posted by iamatiger
Equally, no primes are divisible by 3 either.
And now by induction I will expand this proof.
A prime P will not be divisible by any n where n != 1 or p.
Already it has been shown for n=2 and n=3. Therefore all I have to show is that if the nth case is true then the n+1th case is true.
So if no A exists such that n*A = p then then no B must exist such that (n+1)*B = P. Utilizing the properties of primes we can show that no B exists that divides P except P and 1.
Therefore the n+1th case is true.
Therefore by induction we have shown that a prime number is only divisible by 1 and itself.
(Seriously what's going on in this thread?)