# Thread: Show that p = 3 in two scenarios

1. ## Show that p = 3 in two scenarios

Part (i): Suppose p, p+2 and p+4 are prime numbers. Show that p=3
Part (ii); Suppose that p, p+4, and p+8 are prime numbers. Show that p=3.

I feel like this is a pretty straightforward question but I am beyond lost.

2. ## Re: Show that p = 3 in two scenarios

For part (i) consider whether for any value of p one of p, p+2, and p+4 must be divisible by 3. The only multiple of 3 that is prime is 3, so either p, p+2, or p+4 must equal 3.

Same argument for part (ii).

3. ## Re: Show that p = 3 in two scenarios

You also need to show that $p$ is not even.

4. ## Re: Show that p = 3 in two scenarios

Originally Posted by azollner95
Part (i): Suppose p, p+2 and p+4 are prime numbers. Show that p=3
Part (ii); Suppose that p, p+4, and p+8 are prime numbers. Show that p=3.
i) Is it possible to have another set(run) of three twin primes?

5. ## Re: Show that p = 3 in two scenarios

So for part i) I basically stated that because they are twin primes, thus p = 3.
Could I use this argument for part ii?