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Math Help - Find largest value d, with corresponding k for following theorem: And proof!

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    Find largest value d, with corresponding k for following theorem: And proof!

    Find the largest value of "d" and the corresponding value of k, for which this is true:

    "If all of p, p+2, p+6 and p+8 are prime, then p= k (mod d) except in one case"

    Also, what is the exceptional value of p that does not satisfy the theorem? And prove the theorem is true in all other cases.
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    Re: Find largest value d, with corresponding k, for following theorem and proof!

    Obviously p must be odd. I would say p\equiv1\mod{10} except when p=5, because if p\not\equiv1\mod{10} then one of p, p+2, p+6, p+8 would be divisible by 5. In the case p=5, it is okay for p to be divisible by 5 because 5 is prime.
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    Re: Find largest value d, with corresponding k for following theorem: And proof!

    Thanks Sylvia, any idea how you'd go about a proof of the theorem?
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