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Math Help - A problem on primes

  1. #1
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    Talking A problem on primes

    Hi
    I am unable to crack it anyone plz through some light.
    if p is a prime,p^2+2 is a prime prove that p^3 +2 is a prime.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: A problem on primes

    Quote Originally Posted by Learner248 View Post
    Hi
    I am unable to crack it anyone plz through some light.
    if p is a prime,p^2+2 is a prime prove that p^3 +2 is a prime.
    Hint:

    Any prime number bigger than 3 is congruent to 1 or 5 modulo 6.
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  3. #3
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    Re: A problem on primes

    Quote Originally Posted by Learner248 View Post
    Hi
    I am unable to crack it anyone plz through some light.
    if p is a prime,p^2+2 is a prime prove that p^3 +2 is a prime.
    If p is prime p=6k+1 or p=6k+5;
    1)p=6k+1 then 3|p^2+2>3 contradiction
    2)p=6k+5,3| p^2+2>3 so you have a problem with your problem
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  4. #4
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: A problem on primes

    Quote Originally Posted by TheodorMunteanu View Post
    If p is prime p=6k+1 or p=6k+5;
    1)p=6k+1 then 3|p^2+2>3 contradiction
    2)p=6k+5,3| p^2+2>3 so you have a problem with your problem

    Only p=3 satisfying the problem conditions.
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