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    primes

    suppose p and p square + 8 are prime. show that P cube +4 is also prime
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: primes

    Quote Originally Posted by claudio411 View Post
    suppose p and p square + 8 are prime. show that P cube +4 is also prime
    Rewriting the question using LaTeX: Suppose p and p^2+8 are prime, show that p^3+4 is also prime.

    All primes p other than 3 are of the form 3k\pm 1.

    p^2+8=(3k\pm 1)^2+8

    =9k^2\pm 6k+9, which is divisible by 3.

    So, 3 is the only prime p such that p^2+8 is also prime. Then, p^3+4=31 is also prime.
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