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Thread: Show that p = 3 in two scenarios

  1. #1
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    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.
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  2. #2
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    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).
    Last edited by ChipB; Mar 17th 2017 at 12:08 PM.
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  3. #3
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    Re: Show that p = 3 in two scenarios

    You also need to show that p is not even.
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    Re: Show that p = 3 in two scenarios

    Quote Originally Posted by azollner95 View Post
    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?
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  5. #5
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    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?
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