Prove there are no others.

I haven't read any of the posted comments yet, but I have a partial solution.

p=1 yields 3 and p=3 yields 17.

The only other p that yields any kind of prime number is in the form p=3+6n where n=0,1,2.... Of course this given p is divisible by 3. So there are no other prime numbers.

I can deduce that any other prime will not be even, and it will not be of the form p=3+6n. But I don't know why the odd prime numbers not of the form p=3 + 6n yields a number that is divisible by 3.

It's easy to follow that for p = 2n where n=0,1,2... that these p numbers are prime nor is the resulting function for they are both divisible by 2. I'm not sure how to go about prooving that there are no other primes.